Finite Group Databasebeta

← #72318725

Subgroups — #72318725

Order 2048.

At least 15331 conjugacy classes of subgroups; only the 4028 normal subgroups are shown.

The subgroup lattice has 1337 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72318648C211yesmaximal, characteristic, complemented
2#72318607C211yesmaximal, characteristic, complemented
3#72318595C211yesmaximal, characteristic, complemented
4#72318579C214yesmaximal, complemented
5#72318565C214yesmaximal, complemented
6#72318545C212yesmaximal, complemented
7#72318529C214yesmaximal, complemented
8#72318522C212yesmaximal, complemented
9#72318511C214yesmaximal, complemented
10#72318494C211yesmaximal, characteristic, complemented
11#72318436C211yesmaximal, characteristic, complemented
12#72317958C214yesmaximal, complemented
13#72317807C214yesmaximal, complemented
14#72317442C212yesmaximal, complemented
15#72311883C211yesmaximal, characteristic, complemented
16#72311286C214yesmaximal, complemented
17#72311262C212yesmaximal, complemented
18#72306390C212yesmaximal, complemented
19#72263498C214yesmaximal, complemented
20#72263493C214yesmaximal, complemented
21#72256384C212yesmaximal, complemented
22#72240649C212yesmaximal, complemented
23#72236771C214yesmaximal, complemented
24#72236680C211yesmaximal, characteristic, complemented
25#72213210C212yesmaximal, complemented
26#10586066C2211yescharacteristic, complemented
27#8934366C2211yescharacteristic
28#8934366C2211yescharacteristic, complemented
29#8926850C2211yescharacteristic
30#8926850C2211yescharacteristic, complemented
31#8904629C2212yes—
32#8904629C2212yescomplemented
33#8751738C2212yescomplemented
34#8181078C2212yescomplemented
35#8126631C2212yescomplemented
36#8126631C2212yescomplemented
37#7842457C2212yescomplemented
38#7837030C2212yescomplemented
39#7781053C2212yescomplemented
40#7743474C2212yescomplemented
41#7737955C2212yescomplemented
42#7715213C2211yescharacteristic, complemented
43#7708257C2211yescharacteristic, complemented
44#7631286C2212yes—
45#7630502C2211yescharacteristic
46#6629266C2212yescomplemented
47#6629262C2212yescomplemented
48#6629177C2211yescharacteristic, complemented
49#6629176C2211yescharacteristic, complemented
50#6628900C2212yescomplemented
51#6628896C2212yescomplemented
52#6628873C2211yescharacteristic, complemented
53#6628872C2211yescharacteristic, complemented
54#6470246C2214yescomplemented
55#6470244C2214yescomplemented
56#6470241C2214yescomplemented
57#6470237C2214yescomplemented
58#6470234C2214yescomplemented
59#6470233C2214yescomplemented
60#6470230C2214yescomplemented
61#6470225C2214yescomplemented
62#6470048C2214yescomplemented
63#6470048C2214yescomplemented
64#6470032C2214yescomplemented
65#6470032C2214yescomplemented
66#6440464C2214yescomplemented
67#6440353C2212yescomplemented
68#6437995C2214yescomplemented
69C2×#24404C2214yescomplemented
70#6437970C2212yescomplemented
71#6437969C2212yescomplemented
72#6437632C2214yescomplemented
73#6437451C2212yescomplemented
74#6370704C2211yescharacteristic, complemented
75C2×#20585C2212yescomplemented
76#512153C2218yescomplemented
77#512149C2218yescomplemented
78#512125C2214yescomplemented
79#512121C2214yescomplemented
80#511787C2214yescomplemented
81#511774C2214yescomplemented
82#508142C2218yescomplemented
83#508093C2218yescomplemented
84#508090C2218yescomplemented
85#508068C2218yescomplemented
86#502729C2218yescomplemented
87#502723C2218yescomplemented
88#502719C2218yescomplemented
89#502717C2218yescomplemented
90#502711C2218yescomplemented
91#502709C2218yescomplemented
92#502709C2218yescomplemented
93#502703C2218yescomplemented
94#502687C2218yescomplemented
95#502687C2218yescomplemented
96#502685C2218yescomplemented
97#502685C2218yescomplemented
98#501184C2218yescomplemented
99#501176C2218yescomplemented
100#501175C2218yescomplemented
101#501173C2218yescomplemented
102#501164C2218yescomplemented
103#501158C2218yescomplemented
104#501156C2218yescomplemented
105#501156C2218yescomplemented
106#501104C2218yescomplemented
107#501100C2218yescomplemented
108#501099C2214yescomplemented
109#501097C2214yescomplemented
110#501097C2214yescomplemented
111#501097C2214yescomplemented
112#500425C2214yescomplemented
113#500419C2214yescomplemented
114#500415C2214yescomplemented
115#500413C2214yescomplemented
116#500407C2214yescomplemented
117#500405C2214yescomplemented
118#500405C2214yescomplemented
119#500399C2214yescomplemented
120#500368C2214yescomplemented
121#500368C2214yescomplemented
122#500358C2214yescomplemented
123#500358C2214yescomplemented
124#500244C2214yescomplemented
125#500234C2214yescomplemented
126#500230C2214yescomplemented
127#500228C2214yescomplemented
128#500226C2214yescomplemented
129#500222C2214yescomplemented
130#500218C2214yescomplemented
131#500218C2214yescomplemented
132#500192C2214yescomplemented
133#500181C2214yescomplemented
134#500180C2212yescomplemented
135#500179C2212yescomplemented
136#500179C2212yescomplemented
137#500179C2212yescomplemented
138#500077C2214yescomplemented
139#500071C2214yescomplemented
140#500067C2214yescomplemented
141#500065C2214yescomplemented
142#500059C2214yescomplemented
143#500057C2214yescomplemented
144#500057C2214yescomplemented
145#500051C2214yescomplemented
146#500020C2214yescomplemented
147#500020C2214yescomplemented
148#500010C2214yescomplemented
149#500010C2214yescomplemented
150#499840C2214yescomplemented
151#499836C2214yescomplemented
152#499833C2212yescomplemented
153#499831C2212yescomplemented
154#499831C2212yescomplemented
155#499831C2212yescomplemented
156#499812C2214yescomplemented
157#499809C2214yescomplemented
158#499807C2214yescomplemented
159#499804C2214yescomplemented
160#499795C2214yescomplemented
161#499789C2214yescomplemented
162#499787C2214yescomplemented
163#499787C2214yescomplemented
164#496246C2212yescomplemented
165#496246C2212yescomplemented
166#496244C2214yescomplemented
167#496240C2212yescomplemented
168#496240C2212yescomplemented
169#496239C2214yescomplemented
170#496235C2214yescomplemented
171#496231C2214yescomplemented
172#496230C2214yescomplemented
173#496225C2214yescomplemented
174#496205C2212yescomplemented
175#496205C2212yescomplemented
176#496203C2211yescharacteristic, complemented
177#496203C2211yescharacteristic, complemented
178#496203C2212yescomplemented
179#496200C2214yescomplemented
180#496200C2214yescomplemented
181#494713C2214yescomplemented
182#494713C2214yescomplemented
183#494695C2214yescomplemented
184C2×#13086C2214yescomplemented
185#494685C2214yescomplemented
186#494682C2214yescomplemented
187#493885C2212yescomplemented
188#493858C2214yescomplemented
189#493424C2214yescomplemented
190#493371C2212yescomplemented
191C2×H(7,𝔽2)C2311yescharacteristic
192C23×H(5,𝔽2)C2311yescharacteristic
193#62852C2312yes—
194#62842C2314yes—
195#62811C2312yes—
196C2×#3484D412yescomplemented
197C2×#3484C2312yes—
198C2×#3484C2314yes—
199C2×#3549C2311yescharacteristic, complemented
200C2×#3481C2311yescharacteristic, complemented
201C22×D42D412yescomplemented
202C2×#3449D411yescharacteristic, complemented
203C2×#3449C2311yescharacteristic
204C22×#535D411yescharacteristic, complemented
205#62652C2311yescharacteristic
206C2×#3026C2314yes—
207C22×B(4,𝔽2)C2314yes—
208C2×#3022C2312yes—
209C2×#3021C2312yes—
210C2×#2888C2312yes—
211C23×#99C2314yes—
212#60045C2312yes—
213#60045C2312yes—
214#59370C2312yes—
215#59370C2312yescomplemented
216#59006C2312yes—
217#59006C2312yescomplemented
218#58990C2312yes—
219#58990C2312yes—
220#58990C2312yescomplemented
221#58990C2312yescomplemented
222#52165C2312yescomplemented
223#52054C2311yescharacteristic
224#52054C2311yescharacteristic, complemented
225#52004C2311yescharacteristic
226#52004C2311yescharacteristic
227#52004C2311yescharacteristic
228#52004C2311yescharacteristic, complemented
229#52004C2311yescharacteristic, complemented
230#52004C2311yescharacteristic, complemented
231#51993C2312yescomplemented
232#51993C2312yescomplemented
233#51940C2312yescomplemented
234#51940C2312yescomplemented
235#51902C2312yescomplemented
236#51895C2312yescomplemented
237#51749C2312yes—
238#51530C2312yes—
239#50856C2312yes—
240#50856C2312yescomplemented
241#50635C2312yes—
242#50635C2312yescomplemented
243#48997C2312yes—
244#48997C2312yescomplemented
245#48113C2312yes—
246#48113C2312yescomplemented
247#48088C2312yes—
248#48088C2312yes—
249#48088C2312yescomplemented
250#48088C2312yescomplemented
251#47848C2312yes—
252#47848C2312yescomplemented
253#47827C2312yes—
254#47827C2312yescomplemented
255#46271C2312yes—
256#46271C2312yes—
257#45727C2312yes—
258#45727C2312yescomplemented
259#45568C2312yes—
260#45568C2312yescomplemented
261#45537C2312yes—
262#45537C2312yescomplemented
263#45439C2312yes—
264#45439C2312yescomplemented
265#37426C2312yescomplemented
266#37273C2312yescomplemented
267#37269C2312yescomplemented
268#35616D411yescharacteristic, complemented
269#35616D411yescharacteristic, complemented
270#35616C2311yescharacteristic
271#35616C2311yescharacteristic
272#35527D411yescharacteristic, complemented
273#35527D412yescomplemented
274#35527D411yescharacteristic, complemented
275#35527C2311yescharacteristic
276#35527C2312yes—
277#35527C2311yescharacteristic
278#35513D412yescomplemented
279#35513D412yescomplemented
280#35513C2312yes—
281#35513C2312yes—
282#35512D412yescomplemented
283#35512C2312yes—
284#35347D412yescomplemented
285#35347D412yescomplemented
286#35347C2312yes—
287#35347C2312yes—
288#35346D412yescomplemented
289#35346D412yescomplemented
290#35346C2312yes—
291#35346C2312yes—
292#35250D412yescomplemented
293#35250C2312yes—
294#35222C2312yes—
295#35222C2312yes—
296#35149D412yescomplemented
297#35149D412yescomplemented
298#34980D412yescomplemented
299#34980D412yescomplemented
300#34980C2312yes—
301#34980C2312yes—
302#34736D412yescomplemented
303#34736C2312yes—
304C2×#2403D412yescomplemented
305C2×#2403D412yescomplemented
306C2×#2403C2312yes—
307C2×#2403C2312yes—
308#34411C2312yescomplemented
309#34369C2311yescharacteristic, complemented
310#34360C2312yescomplemented
311#34346C2311yescharacteristic, complemented
312#34256D412yescomplemented
313#34256C2312yes—
314#34171D412yescomplemented
315#34044D411yescharacteristic, complemented
316#34044C2311yescharacteristic
317C2×#2309D411yescharacteristic, complemented
318C2×#2199C2318yescomplemented
319C2×#2198C2314yescomplemented
320C2×#2197C2318yescomplemented
321C2×#2196C2314yescomplemented
322C2×#2196C2314yescomplemented
323C2×#2196C2314yescomplemented
324C2×#2127C2314yescomplemented
325C2×#2127C2314yescomplemented
326C2×#2121C2318yescomplemented
327C22×AΣL(1,𝔽16)C2318yescomplemented
328#33023C2314yes—
329#33022C2314yes—
330#33021C2314yes—
331#33021C2314yes—
332#33021C2314yes—
333#33020C2314yes—
334#33020C2314yes—
335#33020C2314yes—
336#32993C2314yes—
337#32993C2314yes—
338#32990C2314yes—
339#32990C2314yes—
340#32901C2314yes—
341#32900C2314yes—
342#32899C2314yes—
343#32899C2314yes—
344#32899C2314yes—
345#32898C2314yes—
346#32898C2314yes—
347#32898C2314yes—
348#32891C2314yes—
349#32891C2314yes—
350#32888C2314yes—
351#32888C2314yes—
352#24413C2318yes—
353#24413C2318yes—
354#24412C2318yes—
355#24412C2318yes—
356#24405C2318yes—
357#24405C2318yes—
358#24404C2318yes—
359#24404C2318yes—
360#24404C2318yes—
361#24404C2318yes—
362#24404C2318yes—
363#24404C2318yes—
364#24059C2318yes—
365#24058C2318yes—
366#24057C2318yes—
367#24056C2318yes—
368#24025C2318yes—
369#24022C2318yes—
370#23912C2314yes—
371#23912C2314yes—
372#23908C2314yes—
373#23908C2314yes—
374#23904C2318yes—
375#23903C2318yes—
376#23902C2318yes—
377#23900C2318yes—
378#20960C2314yes—
379C2×#1889C2314yes—
380#20956C2312yes—
381#20955C2312yes—
382#20889C2314yes—
383C2×#1867C2314yes—
384#20855C2312yes—
385#20855C2312yes—
386#20615C2312yes—
387#20615C2312yes—
388#20609C2314yes—
389C2×#1790C2314yes—
390#20592C2311yescharacteristic
391#20592C2311yescharacteristic
392#20592C2314yes—
393#20591C2312yes—
394C2×#1783C2314yes—
395#20585C2314yes—
396#20585C2312yes—
397#20585C2314yes—
398#20585C2312yes—
399#20585C2314yes—
400C2×#1782C2314yes—
401C2×#1781C2314yes—
402#13463C2318yescomplemented
403#13463C2318yescomplemented
404#13462C2318yescomplemented
405#13462C2318yescomplemented
406#13425C2318yescomplemented
407#13424C2318yescomplemented
408#13424C2318yescomplemented
409#13424C2318yescomplemented
410#13423C2318yescomplemented
411#13422C2318yescomplemented
412#13422C2318yescomplemented
413#13422C2318yescomplemented
414#13420C2318yescomplemented
415#13420C2318yescomplemented
416#13419C2318yescomplemented
417#13419C2318yescomplemented
418#13377C2318yescomplemented
419#13377C2318yescomplemented
420#13376C2318yescomplemented
421#13376C2318yescomplemented
422#13349C2318yescomplemented
423#13348C2318yescomplemented
424#13348C2318yescomplemented
425#13348C2318yescomplemented
426#13347C2318yescomplemented
427#13346C2318yescomplemented
428#13346C2318yescomplemented
429#13346C2318yescomplemented
430#13344C2318yescomplemented
431#13344C2318yescomplemented
432#13343C2318yescomplemented
433#13343C2318yescomplemented
434#13090C2314yes—
435#13090C2314yes—
436#13090C2314yes—
437#13090C2314yes—
438#13090C2318yescomplemented
439#13090C2318yescomplemented
440#13088C2314yes—
441#13088C2314yes—
442#13088C2314yes—
443#13088C2314yes—
444#13088C2318yescomplemented
445#13088C2318yescomplemented
446#13086C2314yes—
447#13086C2314yes—
448#13086C2314yes—
449#13086C2314yes—
450#13086C2314yes—
451#13086C2314yes—
452#13086C2318yescomplemented
453#13086C2318yescomplemented
454#13086C2318yescomplemented
455#13084C2314yes—
456#13084C2314yes—
457#13084C2318yescomplemented
458#13083C2314yes—
459#13083C2314yes—
460#13083C2314yes—
461#13083C2314yes—
462#13083C2314yes—
463#13083C2314yes—
464#13082C2318yescomplemented
465#13082C2318yescomplemented
466#13082C2318yescomplemented
467#13081C2314yes—
468#13081C2314yes—
469#13080C2318yescomplemented
470#13050C2318yescomplemented
471#13049C2314yescomplemented
472#13049C2314yescomplemented
473#13049C2314yescomplemented
474#13049C2314yescomplemented
475#13048C2318yescomplemented
476#13044C2318yescomplemented
477#13044C2318yescomplemented
478#13043C2318yescomplemented
479#13043C2318yescomplemented
480#13041C2318yescomplemented
481#13041C2318yescomplemented
482#13041C2318yescomplemented
483#13041C2318yescomplemented
484#12967C2318yescomplemented
485#12966C2314yescomplemented
486#12966C2314yescomplemented
487#12966C2314yescomplemented
488#12966C2314yescomplemented
489#12965C2318yescomplemented
490#12961C2318yescomplemented
491#12961C2318yescomplemented
492#12960C2318yescomplemented
493#12960C2318yescomplemented
494#12958C2318yescomplemented
495#12958C2318yescomplemented
496#12958C2318yescomplemented
497#12958C2318yescomplemented
498#12859C2318yescomplemented
499#12857C2312yes—
500#12857C2314yes—
501#12857C2312yes—
502#12855C2318yescomplemented
503#12854C2314yes—
504#12854C2314yes—
505#12853C2318yescomplemented
506#12852C2314yes—
507#12852C2314yes—
508#12763C2318yescomplemented
509#12761C2318yescomplemented
510#12760C2314yescomplemented
511#12759C2314yescomplemented
512#12759C2314yescomplemented
513#12759C2314yescomplemented
514#12698C2314yes—
515#12697C2312yes—
516#12697C2312yes—
517#12695C2314yescomplemented
518#12695C2314yescomplemented
519#12691C2318yescomplemented
520#12690C2314yes—
521#12690C2314yes—
522#12689C2318yescomplemented
523#12687C2314yes—
524#12687C2314yes—
525#12582C2318yescomplemented
526#12574C2318yescomplemented
527C2×#1390C2318yescomplemented
528C2×#585C2412yes—
529C22×H(5,𝔽2)C2×D411yescharacteristic
530C22×H(5,𝔽2)C2×D411yescharacteristic
531C22×H(5,𝔽2)C2×D412yes—
532C22×H(5,𝔽2)C2×D412yes—
533C22×H(5,𝔽2)C2×D412yes—
534C22×H(5,𝔽2)C2×D412yes—
535C22×H(5,𝔽2)C2×D412yes—
536C22×H(5,𝔽2)C2414yes—
537C22×H(5,𝔽2)C2411yescharacteristic
538C22×H(5,𝔽2)C2411yescharacteristic
539C22×H(5,𝔽2)C2412yes—
540C23×#41C2×D412yes—
541C23×#41C2×D412yes—
542C23×#41C2×D411yescharacteristic
543C23×#41C2×D411yescharacteristic, complemented
544C23×#41C2411yescharacteristic
545C24×D4C2×D412yes—
546C24×D4C2×D412yes—
547C24×D4C2×D412yes—
548C24×D4C2×D412yes—
549C24×D4C2×D411yescharacteristic
550C24×D4C2×D412yescomplemented
551C24×D4C2×D412yescomplemented
552C24×D4C2412yes—
553C2×H(3,𝔽4)C2412yes—
554#3485C2414yes—
555#3484C2414yes—
556#3484C2418yes—
557C2×#559C2411yescharacteristic
558C2×#551C2412yes—
559C2×D42C2411yescharacteristic
560C2×D42C2411yescharacteristic
561C2×D42C2411yescharacteristic
562C2×#537C2×D412yescomplemented
563C2×#537C2×D412yescomplemented
564C2×#536C2×D411yescharacteristic
565C2×#536C2×D411yescharacteristic, complemented
566C2×#536C2×D411yescharacteristic, complemented
567C2×#536C2×D411yescharacteristic, complemented
568C2×#536C2×D411yescharacteristic, complemented
569C2×#536C2411yescharacteristic
570C2×#535C2×D411yescharacteristic
571C2×#535C2×D412yes—
572C2×#535C2×D412yescomplemented
573C2×#535C2×D412yescomplemented
574C2×#535C2×D412yescomplemented
575C2×#535C2×D412yescomplemented
576C2×#535C2×D411yescharacteristic, complemented
577C2×#535C2×D411yescharacteristic, complemented
578C2×#535C2×D412yescomplemented
579C2×#535C2×D412yescomplemented
580C2×#535C2411yescharacteristic
581C2×#535C2411yescharacteristic
582C2×#535C2411yescharacteristic
583C2×#535C2412yes—
584C2×#534C2×D412yes—
585C2×#534C2×D412yes—
586C2×#534C2×D412yescomplemented
587C2×#534C2×D412yescomplemented
588C2×#534C2×D412yescomplemented
589C2×#534C2×D412yescomplemented
590C2×#534C2412yes—
591C2×#534C2412yes—
592C2×#532C2×D411yescharacteristic, complemented
593C2×#532C2×D411yescharacteristic, complemented
594C2×#532C2411yescharacteristic
595C2×#532C2411yescharacteristic
596C22×#127C2×D412yes—
597C22×#127C2×D411yescharacteristic
598C22×#127C2×D411yescharacteristic, complemented
599C22×#124C2×D411yescharacteristic
600C22×#124C2×D411yescharacteristic, complemented
601C2×#525C2×D412yes—
602C2×#525C2×D412yescomplemented
603C2×#525C2×D412yescomplemented
604C2×#525C2×D412yescomplemented
605C2×#525C2×D412yescomplemented
606C2×#525C2412yes—
607C22×#121C2×D412yes—
608C22×#121C2×D412yes—
609C22×#121C2×D412yescomplemented
610C22×#121C2×D412yescomplemented
611C22×#120C2×D412yes—
612C22×#120C2×D412yes—
613C22×#120C2×D412yes—
614C22×#120C2×D412yes—
615C22×#120C2×D412yescomplemented
616C22×#120C2×D412yescomplemented
617C22×#120C2×D412yescomplemented
618C22×#120C2×D412yescomplemented
619C22×#120C2×D412yescomplemented
620C22×#120C2×D412yescomplemented
621C22×#120C2412yes—
622C22×#120C2412yes—
623#3428C2412yes—
624C2×#518C2×D412yescomplemented
625C2×#518C2×D412yescomplemented
626C2×#518C2414yes—
627C22×C4×D4C2×D412yescomplemented
628C22×C4×D4C2×D412yescomplemented
629C22×#117C2×D411yescharacteristic, complemented
630C22×#117C2×D411yescharacteristic, complemented
631C22×#117C2×D411yescharacteristic, complemented
632C2×#458C2418yes—
633C2×B(4,𝔽2)C2418yes—
634C2×B(4,𝔽2)C2418yes—
635C2×B(4,𝔽2)C2418yes—
636C2×#455C2414yes—
637C2×#455C2414yes—
638C2×#453C2414yes—
639C2×#453C2414yes—
640C2×#413C2412yes—
641C2×#413C2412yes—
642C22×#100C2418yes—
643C22×#99C2418yes—
644C22×#99C2414yes—
645C22×#99C2414yes—
646C22×#99C2418yes—
647#2804C2412yes—
648#2804C2412yes—
649#2748C2412yes—
650#2748C2412yes—
651#2717C2412yes—
652#2709C2412yes—
653#2697C2412yes—
654#2697C2412yes—
655#2684C2412yes—
656#2684C2412yes—
657#2684C2412yes—
658#2679C2412yes—
659#2679C2412yes—
660#2669C2412yes—
661#2669C2412yes—
662#2669C2412yes—
663#2435C2×D412yescomplemented
664#2435C2×D412yescomplemented
665#2435C2×D412yescomplemented
666#2435C2×D412yescomplemented
667#2435C2412yes—
668#2435C2412yes—
669#2435C2412yes—
670#2435C2412yes—
671#2433C2×D412yescomplemented
672#2433C2×D412yescomplemented
673#2433C2×D412yescomplemented
674#2433C2×D412yescomplemented
675#2433C2412yes—
676#2433C2412yes—
677#2433C2412yes—
678#2433C2412yes—
679#2432C2×D412yes—
680#2432C2×D412yes—
681#2432C2×D412yescomplemented
682#2432C2×D412yescomplemented
683#2432C2×D412yescomplemented
684#2432C2×D412yescomplemented
685#2432C2×D412yescomplemented
686#2432C2×D412yescomplemented
687#2431C2×D412yes—
688#2431C2×D412yes—
689#2431C2×D412yescomplemented
690#2431C2×D412yescomplemented
691#2431C2×D412yescomplemented
692#2431C2×D412yescomplemented
693#2431C2×D412yescomplemented
694#2431C2×D412yescomplemented
695#2406C2×D412yes—
696#2406C2×D412yescomplemented
697#2406C2×D412yescomplemented
698#2406C2412yes—
699#2405C2×D412yes—
700#2405C2×D412yes—
701#2405C2×D412yes—
702#2405C2×D412yes—
703#2405C2×D412yes—
704#2405C2×D412yescomplemented
705#2405C2×D412yescomplemented
706#2405C2×D412yescomplemented
707#2405C2×D412yescomplemented
708#2405C2412yes—
709#2405C2412yes—
710#2405C2412yes—
711#2404C2×D412yes—
712#2404C2×D412yes—
713#2404C2×D412yes—
714#2404C2×D412yescomplemented
715#2404C2×D412yescomplemented
716#2404C2×D412yescomplemented
717#2404C2×D412yescomplemented
718#2404C2×D412yescomplemented
719#2404C2×D412yescomplemented
720#2404C2412yes—
721#2404C2412yes—
722#2404C2412yes—
723#2403C2×D412yes—
724#2403C2×D412yes—
725#2403C2×D412yes—
726#2403C2×D412yes—
727#2403C2×D412yes—
728#2403C2×D412yes—
729#2403C2×D412yes—
730#2403C2×D412yes—
731#2403C2×D412yes—
732#2403C2×D412yes—
733#2403C2×D412yes—
734#2403C2×D412yes—
735#2403C2×D412yes—
736#2403C2×D412yes—
737#2403C2×D412yes—
738#2403C2×D412yescomplemented
739#2403C2×D412yescomplemented
740#2403C2×D412yescomplemented
741#2403C2×D412yescomplemented
742#2403C2×D412yescomplemented
743#2403C2×D412yescomplemented
744#2403C2×D412yescomplemented
745#2403C2×D412yescomplemented
746#2403C2×D412yescomplemented
747#2403C2×D412yescomplemented
748#2403C2×D412yescomplemented
749#2403C2×D412yescomplemented
750#2403C2412yes—
751#2403C2412yes—
752#2403C2412yes—
753#2403C2412yes—
754#2403C2412yes—
755#2403C2412yes—
756#2403C2412yes—
757#2403C2412yes—
758#2403C2412yes—
759#2380C2411yescharacteristic
760#2380C2411yescharacteristic
761#2380C2411yescharacteristic
762#2380C2411yescharacteristic
763#2379C2412yes—
764#2376C2412yes—
765#2376C2412yes—
766#2375C2412yes—
767#2375C2412yes—
768#2372C2412yes—
769#2358C2412yes—
770#2358C2412yes—
771#2358C2412yes—
772#2358C2412yes—
773#2311C2×D412yes—
774#2311C2×D412yescomplemented
775#2311C2×D412yescomplemented
776#2311C2×D412yescomplemented
777#2311C2412yes—
778#2311C2412yes—
779#2310C2×D412yescomplemented
780#2309C2×D411yescharacteristic
781#2309C2×D411yescharacteristic
782#2309C2×D412yes—
783#2309C2×D412yes—
784#2309C2×D411yescharacteristic, complemented
785#2309C2×D411yescharacteristic, complemented
786#2309C2×D412yescomplemented
787#2309C2×D412yescomplemented
788#2309C2412yes—
789#2308C2×D412yes—
790#2308C2×D412yes—
791#2308C2×D412yes—
792#2308C2×D412yes—
793#2308C2×D412yescomplemented
794#2308C2×D412yescomplemented
795#2308C2×D412yescomplemented
796#2308C2×D412yescomplemented
797#2308C2×D412yescomplemented
798#2308C2×D412yescomplemented
799#2308C2412yes—
800#2308C2412yes—
801#2297C2×D412yes—
802#2297C2×D411yescharacteristic
803#2297C2×D411yescharacteristic
804#2297C2×D411yescharacteristic, complemented
805#2297C2×D411yescharacteristic, complemented
806#2297C2×D412yescomplemented
807#2297C2×D412yescomplemented
808#2297C2×D412yescomplemented
809#2297C2×D412yescomplemented
810#2297C2×D411yescharacteristic, complemented
811#2297C2×D411yescharacteristic, complemented
812#2297C2411yescharacteristic
813#2297C2411yescharacteristic
814#2297C2412yes—
815C2×#390C2×D412yescomplemented
816C2×#390C2×D412yescomplemented
817C2×#386C2×D412yes—
818C2×#386C2×D412yes—
819C2×#386C2×D412yescomplemented
820C2×#386C2×D412yescomplemented
821C2×#386C2×D412yescomplemented
822C2×#386C2×D412yescomplemented
823C2×#386C2412yes—
824C2×#386C2412yes—
825#2280C2×D412yescomplemented
826#2280C2×D412yescomplemented
827#2280C2×D412yescomplemented
828#2280C2×D412yescomplemented
829C2×#379C2×D412yes—
830C2×#379C2×D412yes—
831C2×#379C2×D412yescomplemented
832C2×#379C2×D412yescomplemented
833C2×#354C2418yes—
834C2×#354C2418yes—
835C2×#353C2414yes—
836C2×#353C2414yes—
837C2×#353C2414yes—
838C2×#353C2414yes—
839C2×#352C2418yes—
840C2×#352C2418yes—
841C2×AΣL(1,𝔽16)C2418yes—
842C2×AΣL(1,𝔽16)C2418yes—
843C2×AΣL(1,𝔽16)C2418yes—
844C2×AΣL(1,𝔽16)C2418yes—
845C2×AΣL(1,𝔽16)C2418yes—
846C2×AΣL(1,𝔽16)C2418yes—
847#1890C2418yes—
848#1889C2418yes—
849#1889C2418yes—
850#1889C2418yes—
851#1887C2414yes—
852#1887C2414yes—
853#1885C2414yes—
854#1885C2414yes—
855#1867C2418yes—
856#1867C2418yes—
857#1867C2418yes—
858#1867C2418yes—
859#1856C2418yes—
860#1856C2418yes—
861#1792C2418yes—
862#1792C2418yes—
863#1790C2418yes—
864#1790C2418yes—
865#1790C2418yes—
866#1790C2418yes—
867#1785C2414yes—
868#1783C2414yes—
869#1783C2414yes—
870#1783C2414yes—
871#1782C2414yes—
872#1782C2414yes—
873#1782C2418yes—
874#1781C2418yes—
875#1781C2414yes—
876#1781C2414yes—
877#1393C2418yes—
878#1393C2418yes—
879#1393C2418yes—
880#1393C2418yes—
881#1390C2418yes—
882#1390C2418yes—
883#1390C2418yes—
884#1390C2418yes—
885#1390C2418yes—
886#1390C2418yes—
887#1390C2418yes—
888#1390C2418yes—
889C26#12011yescharacteristic
890C26#12011yescharacteristic
891C26C22×D412yes—
892C26C22×D412yes—
893C26C22×D412yes—
894C26C22×D412yes—
895C2×H(5,𝔽2)C2514yes—
896C22×#41#12012yes—
897C22×#41#12011yescharacteristic
898C22×#41#12011yescharacteristic
899C22×#41#12012yes—
900C22×#41#12012yes—
901C22×#41#12012yes—
902C22×#41#12012yes—
903C22×#41#12012yes—
904C22×#41#12012yes—
905C22×#41#12012yes—
906C22×#41#12012yes—
907C22×#41C22×D411yescharacteristic
908C22×#41C22×D411yescharacteristic
909C22×#41C22×D411yescharacteristic
910C22×#41C22×D411yescharacteristic
911C22×#41C22×D412yes—
912C22×#41C22×D412yes—
913C22×#41C22×D411yescharacteristic
914C22×#41C22×D412yes—
915C22×#41C22×D412yes—
916C22×#41C22×D411yescharacteristic
917C22×#41C22×D412yes—
918C22×#41C22×D412yes—
919C22×#41C22×D412yes—
920C22×#41C22×D412yes—
921C22×#41C22×D412yes—
922C22×#41C22×D412yes—
923C22×#41C22×D411yescharacteristic
924C22×#41C22×D411yescharacteristic
925C22×#41C22×D412yes—
926C22×#41C2511yescharacteristic
927C22×#41C2511yescharacteristic
928C23×Q8#12011yescharacteristic
929C23×Q8C22×D411yescharacteristic
930C23×Q8C22×D411yescharacteristic
931C23×D4#12012yes—
932C23×D4#12012yes—
933C23×D4#12012yes—
934C23×D4#12011yescharacteristic
935C23×D4#12012yes—
936C23×D4#12012yes—
937C23×D4#12012yes—
938C23×D4#12012yes—
939C23×D4#12012yes—
940C23×D4#12012yes—
941C23×D4#12011yescharacteristic
942C23×D4#12012yes—
943C23×D4#12012yes—
944C23×D4#12012yes—
945C23×D4#12012yes—
946C23×D4#12012yes—
947C23×D4#12012yes—
948C23×D4#12012yes—
949C23×D4#12012yes—
950C23×D4#12011yescharacteristic
951C23×D4C22×D412yes—
952C23×D4C22×D412yes—
953C23×D4C22×D412yes—
954C23×D4C22×D412yes—
955C23×D4C22×D412yes—
956C23×D4C22×D412yes—
957C23×D4C22×D412yes—
958C23×D4C22×D412yes—
959C23×D4C22×D412yes—
960C23×D4C22×D412yes—
961C23×D4C22×D412yes—
962C23×D4C22×D412yes—
963C23×D4C22×D412yes—
964C23×D4C22×D412yes—
965C23×D4C22×D412yes—
966C23×D4C22×D412yes—
967C23×D4C22×D412yes—
968C23×D4C22×D411yescharacteristic
969C23×D4C22×D412yes—
970C23×D4C22×D412yes—
971C23×D4C22×D412yes—
972C23×D4C22×D412yes—
973C23×D4C22×D412yes—
974C23×D4C22×D412yes—
975C23×D4C22×D412yes—
976C23×D4C22×D412yes—
977C23×D4C22×D412yes—
978C23×D4C22×D412yes—
979C23×D4C22×D412yes—
980C23×D4C22×D412yes—
981C23×D4C22×D412yes—
982C23×D4C22×D412yes—
983C23×D4C22×D411yescharacteristic
984C23×D4C22×D412yes—
985C23×D4C22×D411yescharacteristic
986C23×D4C22×D412yes—
987C23×D4C22×D412yes—
988C23×D4C22×D412yes—
989C23×D4C2512yes—
990C23×D4C2512yes—
991C23×D4C2511yescharacteristic
992C24×C4#12012yes—
993C24×C4#12012yes—
994C24×C4C22×D411yescharacteristic
995C24×C4C22×D412yes—
996C24×C4C22×D412yes—
997C24×C4C22×D412yes—
998C24×C4C22×D412yes—
999C24×C4C22×D412yes—
1000C2×C4⋊Q8C22×D411yescharacteristic
1001C2×C4⋊Q8C22×D411yescharacteristic
1002C2×C4⋊Q8C22×D411yescharacteristic
1003C2×C4⋊Q8C22×D411yescharacteristic
1004C2×#127C22×D411yescharacteristic
1005C2×#127C22×D412yes—
1006C2×#127C22×D412yes—
1007C2×#127C22×D411yescharacteristic
1008C2×#127C22×D412yes—
1009C2×#127C22×D412yes—
1010C2×#127C2511yescharacteristic
1011C2×#127C2511yescharacteristic
1012C2×#124C22×D411yescharacteristic
1013C2×#124C22×D411yescharacteristic
1014C2×#124C22×D411yescharacteristic
1015C2×#124C22×D411yescharacteristic
1016C2×#124C22×D411yescharacteristic
1017C2×#124C22×D411yescharacteristic
1018C2×#124C22×D412yes—
1019C2×#124C22×D412yes—
1020C2×#124C22×D412yes—
1021C2×#124C22×D412yes—
1022C2×#124C2511yescharacteristic
1023C2×#124C2511yescharacteristic
1024C2×#123C22×D412yes—
1025C2×#123C22×D412yes—
1026C2×#123C22×D412yes—
1027C2×#123C22×D412yes—
1028C2×#123C22×D412yes—
1029C2×#123C22×D412yes—
1030C2×#123C22×D412yes—
1031C2×#123C2512yes—
1032C2×C22⋊Q8C22×D412yes—
1033C2×C22⋊Q8C22×D412yes—
1034C2×C22⋊Q8C22×D412yes—
1035C2×C22⋊Q8C22×D412yes—
1036C2×#121C22×D412yes—
1037C2×#121C22×D412yes—
1038C2×#121C22×D412yes—
1039C2×#121C22×D412yes—
1040C2×#120C22×D412yes—
1041C2×#120C22×D412yes—
1042C2×#120C22×D412yes—
1043C2×#120C22×D412yes—
1044C2×#120C22×D412yes—
1045C2×#120C22×D412yes—
1046C2×#120C22×D412yes—
1047C2×#120C22×D412yes—
1048C2×#120C22×D412yes—
1049C2×#120C22×D412yes—
1050C2×#120C22×D412yes—
1051C2×#120C22×D412yes—
1052C2×#120C22×D412yes—
1053C2×#120C22×D412yes—
1054C2×#120C22×D412yes—
1055C2×#120C22×D412yes—
1056C2×#120C22×D412yes—
1057C2×#120C22×D412yes—
1058C2×#120C22×D412yes—
1059C2×#120C22×D412yes—
1060C2×#120C22×D412yes—
1061C2×#120C2512yes—
1062C2×#120C2512yes—
1063C2×#120C2512yes—
1064#518C2514yes—
1065C2×#117C22×D411yescharacteristic
1066C2×#117C22×D411yescharacteristic
1067C2×#117C22×D412yes—
1068C2×#117C22×D412yes—
1069C2×#117C22×D412yes—
1070C2×#117C22×D412yes—
1071C2×#117C22×D412yes—
1072C2×#117C22×D411yescharacteristic
1073C2×#117C22×D411yescharacteristic
1074C2×#117C22×D411yescharacteristic
1075C2×#117C22×D411yescharacteristic
1076C2×#117C22×D412yes—
1077C2×#117C22×D412yes—
1078C22×C4⋊C4C22×D412yes—
1079C22×C4⋊C4C22×D412yes—
1080C22×C4⋊C4C22×D412yes—
1081C22×C22⋊C4C22×D412yes—
1082C22×C22⋊C4C22×D412yes—
1083C22×C22⋊C4C22×D412yes—
1084C22×C22⋊C4C22×D412yes—
1085C22×C22⋊C4C22×D412yes—
1086C22×C22⋊C4C22×D412yes—
1087C22×C22⋊C4C22×D412yes—
1088C22×C22⋊C4C22×D412yes—
1089C22×C22⋊C4C22×D412yes—
1090C22×C22⋊C4C22×D412yes—
1091C22×C22⋊C4C22×D412yes—
1092C22×C22⋊C4C22×D412yes—
1093C22×C22⋊C4C22×D412yes—
1094C22×C22⋊C4C22×D412yes—
1095C22×C22⋊C4C22×D412yes—
1096C22×C22⋊C4C22×D412yes—
1097C22×C42C22×D412yes—
1098C22×C42C22×D411yescharacteristic
1099C22×C42C22×D411yescharacteristic
1100C22×C42C22×D411yescharacteristic
1101C22×C42C22×D411yescharacteristic
1102C2×#100C2514yes—
1103C2×#100C2514yes—
1104C2×#99C2518yes—
1105C2×#99C2518yes—
1106#391C22×D412yes—
1107#391C22×D412yes—
1108#391C22×D412yes—
1109#391C22×D412yes—
1110#390C22×D412yes—
1111#390C22×D412yes—
1112#390C22×D412yes—
1113#390C22×D412yes—
1114#390C22×D412yes—
1115#390C22×D412yes—
1116#390C22×D412yes—
1117#390C22×D412yes—
1118#390C22×D412yes—
1119#390C22×D412yes—
1120#390C2512yes—
1121#390C2512yes—
1122#386C22×D412yes—
1123#386C22×D412yes—
1124#386C22×D412yes—
1125#386C22×D412yes—
1126#386C22×D412yes—
1127#386C22×D412yes—
1128#386C22×D412yes—
1129#386C22×D412yes—
1130#386C22×D412yes—
1131#386C22×D412yes—
1132#386C22×D412yes—
1133#386C22×D412yes—
1134#386C22×D412yes—
1135#386C22×D412yes—
1136#386C22×D412yes—
1137#386C22×D412yes—
1138#386C22×D412yes—
1139#386C22×D412yes—
1140#386C22×D412yes—
1141#386C22×D412yes—
1142#386C22×D412yes—
1143#386C22×D412yes—
1144#386C22×D412yes—
1145#386C22×D412yes—
1146#386C22×D412yes—
1147#386C22×D412yes—
1148#386C22×D412yes—
1149#386C22×D412yes—
1150#386C2512yes—
1151#386C2512yes—
1152#386C2512yes—
1153#386C2512yes—
1154#381C22×D412yes—
1155#381C22×D412yes—
1156#381C22×D412yes—
1157#381C22×D412yes—
1158#379C22×D412yes—
1159#379C22×D412yes—
1160#379C22×D412yes—
1161#379C22×D412yes—
1162#379C22×D412yes—
1163#379C22×D412yes—
1164#379C22×D412yes—
1165#379C22×D412yes—
1166#379C22×D412yes—
1167#379C22×D412yes—
1168#379C22×D412yes—
1169#379C22×D412yes—
1170C4×C22⋊C4C22×D412yes—
1171C4×C22⋊C4C22×D412yes—
1172C4×C22⋊C4C22×D412yes—
1173C4×C22⋊C4C22×D412yes—
1174C4×C22⋊C4C22×D412yes—
1175C4×C22⋊C4C22×D412yes—
1176C4×C22⋊C4C22×D412yes—
1177C4×C22⋊C4C22×D412yes—
1178C25C2×#12011yescharacteristic
1179C25C2×#12012yes—
1180C25C2×#12012yes—
1181C25C2×#12012yes—
1182C25C2×#12011yescharacteristic
1183C25C2×#12012yes—
1184C25C2×#12011yescharacteristic
1185C25C2×#12012yes—
1186C25C2×#12012yes—
1187C25C2×#12012yes—
1188C25C2×#12011yescharacteristic
1189C25C2×#12012yes—
1190C25C2×#12012yes—
1191C25C2×#12011yescharacteristic
1192C25C23×D412yes—
1193C25C23×D412yes—
1194C25C23×D412yes—
1195C25C23×D412yes—
1196C25C23×D412yes—
1197C25C23×D412yes—
1198C25C23×D412yes—
1199C25C23×D412yes—
1200C22×Q8C2×#12011yescharacteristic
1201C22×Q8C2×#12012yes—
1202C22×Q8C2×#12011yescharacteristic
1203C22×Q8C2×#12012yes—
1204C22×Q8C23×D411yescharacteristic
1205C22×Q8C23×D411yescharacteristic
1206C22×Q8C23×D411yescharacteristic
1207C22×Q8C23×D411yescharacteristic
1208C22×D4B(4,𝔽2)18yes—
1209C22×D4C2×#12012yes—
1210C22×D4C2×#12012yes—
1211C22×D4C2×#12012yes—
1212C22×D4C2×#12012yes—
1213C22×D4C2×#12012yes—
1214C22×D4C2×#12012yes—
1215C22×D4C2×#12012yes—
1216C22×D4C2×#12012yes—
1217C22×D4C2×#12012yes—
1218C22×D4C2×#12012yes—
1219C22×D4C2×#12012yes—
1220C22×D4C2×#12012yes—
1221C22×D4C2×#12012yes—
1222C22×D4C2×#12012yes—
1223C22×D4C2×#12012yes—
1224C22×D4C2×#12012yes—
1225C22×D4C2×#12012yes—
1226C22×D4C2×#12012yes—
1227C22×D4C2×#12012yes—
1228C22×D4C2×#12012yes—
1229C22×D4C2×#12012yes—
1230C22×D4C2×#12012yes—
1231C22×D4C2×#12012yes—
1232C22×D4C2×#12012yes—
1233C22×D4C2×#12012yes—
1234C22×D4C2×#12011yescharacteristic
1235C22×D4C2×#12011yescharacteristic
1236C22×D4C23×D412yes—
1237C22×D4C23×D411yescharacteristic
1238C22×D4C23×D411yescharacteristic
1239C22×D4C23×D412yes—
1240C22×D4C23×D411yescharacteristic
1241C22×D4C23×D412yes—
1242C22×D4C23×D412yes—
1243C22×D4C23×D412yes—
1244C22×D4C23×D412yes—
1245C22×D4C23×D412yes—
1246C22×D4C23×D412yes—
1247C22×D4C23×D412yes—
1248C22×D4C2611yescharacteristic
1249C23×C4C2×#12011yescharacteristic
1250C23×C4C2×#12012yes—
1251C23×C4C2×#12012yes—
1252C23×C4C2×#12012yes—
1253C23×C4C2×#12012yes—
1254C23×C4C2×#12011yescharacteristic
1255C23×C4C2×#12012yes—
1256C23×C4C2×#12012yes—
1257C23×C4C2×#12012yes—
1258C23×C4C2×#12012yes—
1259C23×C4C2×#12012yes—
1260C23×C4C2×#12012yes—
1261C23×C4C2×#12012yes—
1262C23×C4C2×#12012yes—
1263C23×C4C2×#12012yes—
1264C23×C4C2×#12012yes—
1265C23×C4C2×#12011yescharacteristic
1266C23×C4C23×D411yescharacteristic
1267C23×C4C23×D412yes—
1268C23×C4C23×D412yes—
1269C23×C4C23×D411yescharacteristic
1270C23×C4C23×D411yescharacteristic
1271C23×C4C23×D412yes—
1272C23×C4C23×D412yes—
1273C23×C4C23×D412yes—
1274C23×C4C23×D412yes—
1275C23×C4C23×D412yes—
1276C23×C4C23×D412yes—
1277C23×C4C23×D412yes—
1278C2×C4⋊C4C23×D412yes—
1279C2×C4⋊C4C23×D412yes—
1280C2×C22⋊C4C23×D412yes—
1281C2×C22⋊C4C23×D412yes—
1282C2×C22⋊C4C23×D412yes—
1283C2×C22⋊C4C23×D412yes—
1284C2×C22⋊C4C23×D412yes—
1285C2×C22⋊C4C23×D412yes—
1286C2×C22⋊C4C23×D412yes—
1287C2×C22⋊C4C23×D412yes—
1288C2×C42C23×D411yescharacteristic
1289C2×C42C23×D411yescharacteristic
1290C2×C42C23×D411yescharacteristic
1291C2×C42C23×D411yescharacteristic
1292C2×C42C23×D412yes—
1293C2×C42C23×D412yes—
1294C24C2×B(4,𝔽2)14yes—
1295C24C2×B(4,𝔽2)14yes—
1296C24#302614yes—
1297C24C22×#12012yes—
1298C24C22×#12012yes—
1299C24C22×#12012yes—
1300C24C22×#12012yes—
1301C24C22×#12011yescharacteristic
1302C24C22×#12011yescharacteristic
1303C24C22×#12012yes—
1304C24C22×#12012yes—
1305C24C22×#12012yes—
1306C24C22×#12011yescharacteristic
1307C24C24×D412yes—
1308C2×D4C2×B(4,𝔽2)14yes—
1309C2×D4C2×B(4,𝔽2)18yes—
1310C2×D4C2×B(4,𝔽2)14yes—
1311C2×D4H(7,𝔽2)14yes—
1312C22×C4C2×B(4,𝔽2)14yes—
1313C22×C4C22×#12012yes—
1314C22×C4C22×#12012yes—
1315C22×C4C22×#12012yes—
1316C22×C4C22×#12012yes—
1317C22×C4C22×#12011yescharacteristic
1318C22×C4C22×#12011yescharacteristic
1319C22×C4C22×#12011yescharacteristic
1320C22×C4C24×D411yescharacteristic
1321C23C22×B(4,𝔽2)12yes—
1322C23C22×B(4,𝔽2)14yes—
1323C23C22×B(4,𝔽2)14yes—
1324C23C2×#302614yes—
1325C23C2×#302612yes—
1326C23C23×#12011yescharacteristic
1327C23#6284214yes—
1328C2×C4C22×B(4,𝔽2)12yes—
1329C2×C4C22×B(4,𝔽2)12yes—
1330C2×C4#6284212yes—
1331C22#763044211yescharacteristic
1332C22C23×B(4,𝔽2)11yescharacteristic
1333C22C22×#302611yescharacteristic
1334C2#7223484012yes—
1335C2#7223648311yescharacteristic
subgroupG/H
center, socleC22C23×B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C26
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23×D4 ◁ C23×H(5,𝔽2) ◁ G
LECSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #72318648C2semidirect
2. #72318607C2semidirect
3. #72318595C2semidirect
4. #72318579C2semidirect
5. #72318565C2semidirect
6. #72318545C2semidirect
7. #72318529C2semidirect
8. #72318522C2semidirect
9. #72318511C2semidirect
10. #72318494C2semidirect
11. #72318436C2semidirect
12. #72317958C2semidirect
13. #72317807C2semidirect
14. #72317442C2semidirect
15. #72311883C2semidirect
16. #72311286C2semidirect
17. #72311262C2semidirect
18. #72306390C2semidirect
19. #72263498C2semidirect
20. #72263493C2semidirect
21. #72256384C2semidirect
22. #72240649C2semidirect
23. #72236771C2semidirect
24. #72236680C2semidirect
25. #72213210C2semidirect
26. #10586066C22semidirect
28. #8934366C22semidirect
30. #8926850C22semidirect
32. #8904629C22semidirect
33. #8751738C22semidirect
34. #8181078C22semidirect
35. #8126631C22semidirect
36. #8126631C22semidirect
37. #7842457C22semidirect
38. #7837030C22semidirect
39. #7781053C22semidirect
40. #7743474C22semidirect
41. #7737955C22semidirect
42. #7715213C22semidirect
43. #7708257C22semidirect
46. #6629266C22semidirect
47. #6629262C22semidirect
48. #6629177C22semidirect
49. #6629176C22semidirect
50. #6628900C22semidirect
51. #6628896C22semidirect
52. #6628873C22semidirect
53. #6628872C22semidirect
54. #6470246C22semidirect
55. #6470244C22semidirect
56. #6470241C22semidirect
57. #6470237C22semidirect
58. #6470234C22semidirect
59. #6470233C22semidirect
60. #6470230C22semidirect
61. #6470225C22semidirect
62. #6470048C22semidirect
63. #6470048C22semidirect
64. #6470032C22semidirect
65. #6470032C22semidirect
66. #6440464C22semidirect
67. #6440353C22semidirect
68. #6437995C22semidirect
69. C2×#24404C22semidirect
70. #6437970C22semidirect
71. #6437969C22semidirect
72. #6437632C22semidirect
73. #6437451C22semidirect
74. #6370704C22semidirect
75. C2×#20585C22semidirect
76. #512153C22semidirect
77. #512149C22semidirect
78. #512125C22semidirect
79. #512121C22semidirect
80. #511787C22semidirect
81. #511774C22semidirect
82. #508142C22semidirect
83. #508093C22semidirect
84. #508090C22semidirect
85. #508068C22semidirect
86. #502729C22semidirect
87. #502723C22semidirect
88. #502719C22semidirect
89. #502717C22semidirect
90. #502711C22semidirect
91. #502709C22semidirect
92. #502709C22semidirect
93. #502703C22semidirect
94. #502687C22semidirect
95. #502687C22semidirect
96. #502685C22semidirect
97. #502685C22semidirect
98. #501184C22semidirect
99. #501176C22semidirect
100. #501175C22semidirect
101. #501173C22semidirect
102. #501164C22semidirect
103. #501158C22semidirect
104. #501156C22semidirect
105. #501156C22semidirect
106. #501104C22semidirect
107. #501100C22semidirect
108. #501099C22semidirect
109. #501097C22semidirect
110. #501097C22semidirect
111. #501097C22semidirect
112. #500425C22semidirect
113. #500419C22semidirect
114. #500415C22semidirect
115. #500413C22semidirect
116. #500407C22semidirect
117. #500405C22semidirect
118. #500405C22semidirect
119. #500399C22semidirect
120. #500368C22semidirect
121. #500368C22semidirect
122. #500358C22semidirect
123. #500358C22semidirect
124. #500244C22semidirect
125. #500234C22semidirect
126. #500230C22semidirect
127. #500228C22semidirect
128. #500226C22semidirect
129. #500222C22semidirect
130. #500218C22semidirect
131. #500218C22semidirect
132. #500192C22semidirect
133. #500181C22semidirect
134. #500180C22semidirect
135. #500179C22semidirect
136. #500179C22semidirect
137. #500179C22semidirect
138. #500077C22semidirect
139. #500071C22semidirect
140. #500067C22semidirect
141. #500065C22semidirect
142. #500059C22semidirect
143. #500057C22semidirect
144. #500057C22semidirect
145. #500051C22semidirect
146. #500020C22semidirect
147. #500020C22semidirect
148. #500010C22semidirect
149. #500010C22semidirect
150. #499840C22semidirect
151. #499836C22semidirect
152. #499833C22semidirect
153. #499831C22semidirect
154. #499831C22semidirect
155. #499831C22semidirect
156. #499812C22semidirect
157. #499809C22semidirect
158. #499807C22semidirect
159. #499804C22semidirect
160. #499795C22semidirect
161. #499789C22semidirect
162. #499787C22semidirect
163. #499787C22semidirect
164. #496246C22semidirect
165. #496246C22semidirect
166. #496244C22semidirect
167. #496240C22semidirect
168. #496240C22semidirect
169. #496239C22semidirect
170. #496235C22semidirect
171. #496231C22semidirect
172. #496230C22semidirect
173. #496225C22semidirect
174. #496205C22semidirect
175. #496205C22semidirect
176. #496203C22semidirect
177. #496203C22semidirect
178. #496203C22semidirect
179. #496200C22semidirect
180. #496200C22semidirect
181. #494713C22semidirect
182. #494713C22semidirect
183. #494695C22semidirect
184. C2×#13086C22semidirect
185. #494685C22semidirect
186. #494682C22semidirect
187. #493885C22semidirect
188. #493858C22semidirect
189. #493424C22semidirect
190. #493371C22semidirect
196. C2×#3484D4semidirect
199. C2×#3549C23semidirect
200. C2×#3481C23semidirect
201. C22×D42D4semidirect
202. C2×#3449D4semidirect
204. C22×#535D4semidirect
215. #59370C23semidirect
217. #59006C23semidirect
220. #58990C23semidirect
221. #58990C23semidirect
222. #52165C23semidirect
224. #52054C23semidirect
228. #52004C23semidirect
229. #52004C23semidirect
230. #52004C23semidirect
231. #51993C23semidirect
232. #51993C23semidirect
233. #51940C23semidirect
234. #51940C23semidirect
235. #51902C23semidirect
236. #51895C23semidirect
240. #50856C23semidirect
242. #50635C23semidirect
244. #48997C23semidirect
246. #48113C23semidirect
249. #48088C23semidirect
250. #48088C23semidirect
252. #47848C23semidirect
254. #47827C23semidirect
258. #45727C23semidirect
260. #45568C23semidirect
262. #45537C23semidirect
264. #45439C23semidirect
265. #37426C23semidirect
266. #37273C23semidirect
267. #37269C23semidirect
268. #35616D4semidirect
269. #35616D4semidirect
272. #35527D4semidirect
273. #35527D4semidirect
274. #35527D4semidirect
278. #35513D4semidirect
279. #35513D4semidirect
282. #35512D4semidirect
284. #35347D4semidirect
285. #35347D4semidirect
288. #35346D4semidirect
289. #35346D4semidirect
292. #35250D4semidirect
296. #35149D4semidirect
297. #35149D4semidirect
298. #34980D4semidirect
299. #34980D4semidirect
302. #34736D4semidirect
304. C2×#2403D4semidirect
305. C2×#2403D4semidirect
308. #34411C23semidirect
309. #34369C23semidirect
310. #34360C23semidirect
311. #34346C23semidirect
312. #34256D4semidirect
314. #34171D4semidirect
315. #34044D4semidirect
317. C2×#2309D4semidirect
318. C2×#2199C23semidirect
319. C2×#2198C23semidirect
320. C2×#2197C23semidirect
321. C2×#2196C23semidirect
322. C2×#2196C23semidirect
323. C2×#2196C23semidirect
324. C2×#2127C23semidirect
325. C2×#2127C23semidirect
326. C2×#2121C23semidirect
327. C22×AΣL(1,𝔽16)C23semidirect
402. #13463C23semidirect
403. #13463C23semidirect
404. #13462C23semidirect
405. #13462C23semidirect
406. #13425C23semidirect
407. #13424C23semidirect
408. #13424C23semidirect
409. #13424C23semidirect
410. #13423C23semidirect
411. #13422C23semidirect
412. #13422C23semidirect
413. #13422C23semidirect
414. #13420C23semidirect
415. #13420C23semidirect
416. #13419C23semidirect
417. #13419C23semidirect
418. #13377C23semidirect
419. #13377C23semidirect
420. #13376C23semidirect
421. #13376C23semidirect
422. #13349C23semidirect
423. #13348C23semidirect
424. #13348C23semidirect
425. #13348C23semidirect
426. #13347C23semidirect
427. #13346C23semidirect
428. #13346C23semidirect
429. #13346C23semidirect
430. #13344C23semidirect
431. #13344C23semidirect
432. #13343C23semidirect
433. #13343C23semidirect
438. #13090C23semidirect
439. #13090C23semidirect
444. #13088C23semidirect
445. #13088C23semidirect
452. #13086C23semidirect
453. #13086C23semidirect
454. #13086C23semidirect
457. #13084C23semidirect
464. #13082C23semidirect
465. #13082C23semidirect
466. #13082C23semidirect
469. #13080C23semidirect
470. #13050C23semidirect
471. #13049C23semidirect
472. #13049C23semidirect
473. #13049C23semidirect
474. #13049C23semidirect
475. #13048C23semidirect
476. #13044C23semidirect
477. #13044C23semidirect
478. #13043C23semidirect
479. #13043C23semidirect
480. #13041C23semidirect
481. #13041C23semidirect
482. #13041C23semidirect
483. #13041C23semidirect
484. #12967C23semidirect
485. #12966C23semidirect
486. #12966C23semidirect
487. #12966C23semidirect
488. #12966C23semidirect
489. #12965C23semidirect
490. #12961C23semidirect
491. #12961C23semidirect
492. #12960C23semidirect
493. #12960C23semidirect
494. #12958C23semidirect
495. #12958C23semidirect
496. #12958C23semidirect
497. #12958C23semidirect
498. #12859C23semidirect
502. #12855C23semidirect
505. #12853C23semidirect
508. #12763C23semidirect
509. #12761C23semidirect
510. #12760C23semidirect
511. #12759C23semidirect
512. #12759C23semidirect
513. #12759C23semidirect
517. #12695C23semidirect
518. #12695C23semidirect
519. #12691C23semidirect
522. #12689C23semidirect
525. #12582C23semidirect
526. #12574C23semidirect
527. C2×#1390C23semidirect
543. C23×#41C2×D4semidirect
550. C24×D4C2×D4semidirect
551. C24×D4C2×D4semidirect
562. C2×#537C2×D4semidirect
563. C2×#537C2×D4semidirect
565. C2×#536C2×D4semidirect
566. C2×#536C2×D4semidirect
567. C2×#536C2×D4semidirect
568. C2×#536C2×D4semidirect
572. C2×#535C2×D4semidirect
573. C2×#535C2×D4semidirect
574. C2×#535C2×D4semidirect
575. C2×#535C2×D4semidirect
576. C2×#535C2×D4semidirect
577. C2×#535C2×D4semidirect
578. C2×#535C2×D4semidirect
579. C2×#535C2×D4semidirect
586. C2×#534C2×D4semidirect
587. C2×#534C2×D4semidirect
588. C2×#534C2×D4semidirect
589. C2×#534C2×D4semidirect
592. C2×#532C2×D4semidirect
593. C2×#532C2×D4semidirect
598. C22×#127C2×D4semidirect
600. C22×#124C2×D4semidirect
602. C2×#525C2×D4semidirect
603. C2×#525C2×D4semidirect
604. C2×#525C2×D4semidirect
605. C2×#525C2×D4semidirect
609. C22×#121C2×D4semidirect
610. C22×#121C2×D4semidirect
615. C22×#120C2×D4semidirect
616. C22×#120C2×D4semidirect
617. C22×#120C2×D4semidirect
618. C22×#120C2×D4semidirect
619. C22×#120C2×D4semidirect
620. C22×#120C2×D4semidirect
624. C2×#518C2×D4semidirect
625. C2×#518C2×D4semidirect
627. C22×C4×D4C2×D4semidirect
628. C22×C4×D4C2×D4semidirect
629. C22×#117C2×D4semidirect
630. C22×#117C2×D4semidirect
631. C22×#117C2×D4semidirect
663. #2435C2×D4semidirect
664. #2435C2×D4semidirect
665. #2435C2×D4semidirect
666. #2435C2×D4semidirect
671. #2433C2×D4semidirect
672. #2433C2×D4semidirect
673. #2433C2×D4semidirect
674. #2433C2×D4semidirect
681. #2432C2×D4semidirect
682. #2432C2×D4semidirect
683. #2432C2×D4semidirect
684. #2432C2×D4semidirect
685. #2432C2×D4semidirect
686. #2432C2×D4semidirect
689. #2431C2×D4semidirect
690. #2431C2×D4semidirect
691. #2431C2×D4semidirect
692. #2431C2×D4semidirect
693. #2431C2×D4semidirect
694. #2431C2×D4semidirect
696. #2406C2×D4semidirect
697. #2406C2×D4semidirect
704. #2405C2×D4semidirect
705. #2405C2×D4semidirect
706. #2405C2×D4semidirect
707. #2405C2×D4semidirect
714. #2404C2×D4semidirect
715. #2404C2×D4semidirect
716. #2404C2×D4semidirect
717. #2404C2×D4semidirect
718. #2404C2×D4semidirect
719. #2404C2×D4semidirect
738. #2403C2×D4semidirect
739. #2403C2×D4semidirect
740. #2403C2×D4semidirect
741. #2403C2×D4semidirect
742. #2403C2×D4semidirect
743. #2403C2×D4semidirect
744. #2403C2×D4semidirect
745. #2403C2×D4semidirect
746. #2403C2×D4semidirect
747. #2403C2×D4semidirect
748. #2403C2×D4semidirect
749. #2403C2×D4semidirect
774. #2311C2×D4semidirect
775. #2311C2×D4semidirect
776. #2311C2×D4semidirect
779. #2310C2×D4semidirect
784. #2309C2×D4semidirect
785. #2309C2×D4semidirect
786. #2309C2×D4semidirect
787. #2309C2×D4semidirect
793. #2308C2×D4semidirect
794. #2308C2×D4semidirect
795. #2308C2×D4semidirect
796. #2308C2×D4semidirect
797. #2308C2×D4semidirect
798. #2308C2×D4semidirect
804. #2297C2×D4semidirect
805. #2297C2×D4semidirect
806. #2297C2×D4semidirect
807. #2297C2×D4semidirect
808. #2297C2×D4semidirect
809. #2297C2×D4semidirect
810. #2297C2×D4semidirect
811. #2297C2×D4semidirect
815. C2×#390C2×D4semidirect
816. C2×#390C2×D4semidirect
819. C2×#386C2×D4semidirect
820. C2×#386C2×D4semidirect
821. C2×#386C2×D4semidirect
822. C2×#386C2×D4semidirect
825. #2280C2×D4semidirect
826. #2280C2×D4semidirect
827. #2280C2×D4semidirect
828. #2280C2×D4semidirect
831. C2×#379C2×D4semidirect
832. C2×#379C2×D4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#723186482
#723186072
#723185952
#723185792
#723185652
#723185452
#723185292
#723185222
#723185112
#723184942
#723184362
#723179582
#723178072
#723174422
#723118832
#723112862
#723112622
#723063902
#722634982
#722634932
#722563842
#722406492
#722367712
#722366802
#722132102