Finite Group Databasebeta

← #72341541

Subgroups — #72341541

Order 2048.

At least 14523 conjugacy classes of subgroups; only the 988 normal subgroups are shown.

The subgroup lattice has 616 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72341536C214yesmaximal, complemented
2#72341533C214yesmaximal, complemented
3#72341495C211yesmaximal, characteristic, complemented
4#72341473C211yesmaximal, characteristic, complemented
5#72341466C211yesmaximal, characteristic, complemented
6#72341320C211yesmaximal, characteristic, complemented
7#72341312C211yesmaximal, characteristic, complemented
8#72318598C214yesmaximal, complemented
9#72311295C211yesmaximal, characteristic, complemented
10#72306419C211yesmaximal, characteristic, complemented
11#72306417C211yesmaximal, characteristic, complemented
12#72306415C211yesmaximal, characteristic, complemented
13#72303095C211yesmaximal, characteristic, complemented
14#72284823C211yesmaximal, characteristic, complemented
15#72262266C214yesmaximal, complemented
16#72236975C211yesmaximal, characteristic, complemented
17#72234146C211yesmaximal, characteristic, complemented
18#72233917C211yesmaximal, characteristic, complemented
19#72210439C211yesmaximal, characteristic, complemented
20C2×#60389C2211yescharacteristic, complemented
21C2×#60388C2211yescharacteristic, complemented
22#8968143C2212yescomplemented
23#8934366C2211yescharacteristic
24#8926849C2211yescharacteristic
25#8823789C2212yescomplemented
26#8818039C2212yescomplemented
27#8360950C2212yescomplemented
28#7743195C2211yescharacteristic
29#7742598C2211yescharacteristic
30#7737411C2211yescharacteristic
31#7737041C2211yescharacteristic
32#7674604C2211yescharacteristic
33#6628901C2211yescharacteristic, complemented
34#6628897C2211yescharacteristic, complemented
35#6628896C2211yescharacteristic, complemented
36#6628896C2211yescharacteristic, complemented
37#6628896C2211yescharacteristic, complemented
38#499852C2214yescomplemented
39#499849C2214yescomplemented
40#499848C2214yescomplemented
41#499843C2214yescomplemented
42#499839C2214yescomplemented
43#499838C2214yescomplemented
44#499835C2214yescomplemented
45#499832C2214yescomplemented
46#494682C2211yescharacteristic, complemented
47#494682C2211yescharacteristic, complemented
48#494682C2211yescharacteristic, complemented
49#494682C2211yescharacteristic, complemented
50#494682C2211yescharacteristic, complemented
51#494682C2211yescharacteristic, complemented
52#494681C2211yescharacteristic, complemented
53#494681C2211yescharacteristic, complemented
54#493433C2211yescharacteristic, complemented
55#493433C2211yescharacteristic, complemented
56#493430C2211yescharacteristic, complemented
57#493430C2211yescharacteristic, complemented
58#449492C2212yescomplemented
59#417813C2212yescomplemented
60#417568C2212yescomplemented
61#417566C2212yescomplemented
62#374009C2211yescharacteristic, complemented
63#359606C2211yescharacteristic, complemented
64#359605C2211yescharacteristic, complemented
65#251844C2214yescomplemented
66#251828C2214yescomplemented
67#245255C2214yescomplemented
68#245233C2214yescomplemented
69#213860C2211yescharacteristic, complemented
70#213860C2211yescharacteristic, complemented
71#213855C2211yescharacteristic, complemented
72#213854C2211yescharacteristic, complemented
73#213854C2211yescharacteristic, complemented
74#213854C2211yescharacteristic, complemented
75#134011C2212yescomplemented
76#133905C2212yescomplemented
77#133904C2212yescomplemented
78#133835C2212yescomplemented
79#133433C2214yescomplemented
80#133429C2214yescomplemented
81#133360C2214yescomplemented
82#133359C2214yescomplemented
83#133358C2214yescomplemented
84#133356C2214yescomplemented
85#133336C2214yescomplemented
86#133335C2214yescomplemented
87#133334C2214yescomplemented
88#133332C2214yescomplemented
89#133311C2214yescomplemented
90#133308C2214yescomplemented
91C2×H(7,𝔽2)C2311yescharacteristic
92C2×#3500D411yescharacteristic, complemented
93C2×#3500C2311yescharacteristic
94C2×#3498D411yescharacteristic, complemented
95C2×#3498C2311yescharacteristic
96C22×#551D411yescharacteristic, complemented
97C22×D42D411yescharacteristic, complemented
98C22×H(3,𝔽4)D411yescharacteristic, complemented
99C22×#560D411yescharacteristic, complemented
100C2×#3019C2312yes—
101C2×#3019C2312yescomplemented
102C22×#455C2312yescomplemented
103C22×#453C2312yes—
104C2×#2888C2311yescharacteristic
105C2×#2888C2311yescharacteristic
106#59184D412yescomplemented
107#59162C2312yes—
108#59126C2312yes—
109#59041D412yescomplemented
110#52013D412yescomplemented
111#52012C2312yes—
112#52004D412yescomplemented
113#52004C2312yes—
114#51902C2312yes—
115#51895C2312yes—
116#51749D412yescomplemented
117#51530D412yescomplemented
118#46389C2312yes—
119#46386D412yescomplemented
120#46384D412yescomplemented
121#46384D412yescomplemented
122#46384D412yescomplemented
123#46384C2312yes—
124#46324C2312yes—
125#46276D412yescomplemented
126#46225D412yescomplemented
127#45977C2312yes—
128#37232C2312yes—
129#36955D411yescharacteristic, complemented
130#36955D411yescharacteristic, complemented
131#36721D412yescomplemented
132#36714D412yescomplemented
133#36702D411yescharacteristic, complemented
134#36702D411yescharacteristic, complemented
135#36702D411yescharacteristic, complemented
136#36702D411yescharacteristic, complemented
137#36702D411yescharacteristic, complemented
138#36702D411yescharacteristic, complemented
139#35676D411yescharacteristic, complemented
140#35616D411yescharacteristic, complemented
141#35527C2311yescharacteristic
142#35527C2312yes—
143#35527C2311yescharacteristic
144#35527C2312yescomplemented
145#35446C2311yescharacteristic
146#35346D412yescomplemented
147#35346D412yescomplemented
148#35346C2311yescharacteristic
149#35346C2311yescharacteristic
150#35346C2311yescharacteristic
151#35327D411yescharacteristic, complemented
152#35327C2311yescharacteristic
153#35272D411yescharacteristic, complemented
154#35272C2311yescharacteristic
155C2×#2657C2311yescharacteristic
156#34366D411yescharacteristic, complemented
157#34366D411yescharacteristic, complemented
158#34364D411yescharacteristic, complemented
159#34364D411yescharacteristic, complemented
160#34070D411yescharacteristic, complemented
161#34070D411yescharacteristic, complemented
162#32900C2314yescomplemented
163#32898C2314yes—
164#32898C2314yes—
165#32898C2314yescomplemented
166#20586C2311yescharacteristic
167#20586C2312yescomplemented
168#20585C2311yescharacteristic
169#20585C2311yescharacteristic
170#20585C2311yescharacteristic
171#20585C2311yescharacteristic
172#13082C2314yes—
173#13082C2314yes—
174#13082C2314yes—
175#13082C2314yes—
176#13082C2314yescomplemented
177#13082C2314yescomplemented
178#13080C2314yescomplemented
179#13080C2314yescomplemented
180#12696C2312yes—
181#12696C2312yes—
182#12696C2312yescomplemented
183#12696C2312yescomplemented
184#12694C2312yescomplemented
185#12694C2312yescomplemented
186#12693C2312yes—
187#12693C2312yes—
188#11167C2312yescomplemented
189#10989C2312yes—
190#10989C2312yescomplemented
191#10981C2312yescomplemented
192#10977C2312yescomplemented
193#10975C2312yes—
194#9501C2314yescomplemented
195#9497C2314yes—
196#9497C2314yes—
197#9497C2314yescomplemented
198#8748C2312yescomplemented
199#8748C2312yescomplemented
200#8546C2312yescomplemented
201#8546C2312yescomplemented
202C22×2−1+4C2×D411yescharacteristic
203C22×H(5,𝔽2)C2×D411yescharacteristic
204C22×H(5,𝔽2)C2×D411yescharacteristic, complemented
205C22×H(5,𝔽2)C2×D412yescomplemented
206C22×H(5,𝔽2)C2412yes—
207C22×H(5,𝔽2)C2411yescharacteristic
208C2×H(3,𝔽4)C2×D412yescomplemented
209C2×H(3,𝔽4)C2×D412yescomplemented
210C2×#560C2×D412yescomplemented
211C2×#560C2×D412yescomplemented
212C2×#551C2×D412yescomplemented
213C2×#551C2×D412yescomplemented
214C2×D42C2×D412yescomplemented
215C2×D42C2×D412yescomplemented
216C2×#536C2×D411yescharacteristic
217C2×#536C2×D411yescharacteristic
218C2×#536C2×D411yescharacteristic
219C2×#536C2×D411yescharacteristic, complemented
220C2×#535C2×D411yescharacteristic
221C2×#535C2×D411yescharacteristic
222C2×#535C2×D411yescharacteristic
223C2×#535C2×D411yescharacteristic
224C2×#535C2×D411yescharacteristic
225C2×#535C2×D411yescharacteristic
226C2×#535C2×D411yescharacteristic
227C2×#535C2×D411yescharacteristic
228C2×#535C2×D411yescharacteristic
229C2×#535C2×D411yescharacteristic, complemented
230C2×#535C2411yescharacteristic
231C2×#535C2411yescharacteristic
232C2×#534C2×D412yescomplemented
233C2×#532C2×D411yescharacteristic
234C2×#532C2×D411yescharacteristic
235C2×#532C2×D411yescharacteristic
236C2×#532C2×D411yescharacteristic
237C2×#532C2×D411yescharacteristic
238C2×#532C2×D411yescharacteristic
239C22×#127C2×D411yescharacteristic
240C22×#127C2×D411yescharacteristic
241C22×#127C2×D411yescharacteristic, complemented
242C22×#127C2411yescharacteristic
243C22×#127C2411yescharacteristic
244C22×#124C2×D411yescharacteristic
245C22×#124C2×D411yescharacteristic
246C22×#124C2×D411yescharacteristic, complemented
247C22×#124C2×D411yescharacteristic, complemented
248C22×#124C2411yescharacteristic
249C22×#123C2×D411yescharacteristic
250C22×#123C2×D411yescharacteristic
251C22×#123C2×D411yescharacteristic
252C22×#120C2×D411yescharacteristic
253C22×#120C2×D411yescharacteristic
254C22×#120C2×D411yescharacteristic
255C22×#120C2×D411yescharacteristic
256C22×#120C2×D411yescharacteristic
257C22×#120C2×D411yescharacteristic
258C22×#120C2×D411yescharacteristic
259C22×#120C2×D411yescharacteristic
260C22×#120C2×D411yescharacteristic
261C2×C4×#41C2×D411yescharacteristic
262C2×C4×#41C2×D411yescharacteristic
263C2×C4×#41C2×D411yescharacteristic, complemented
264C2×C4×#41C2×D411yescharacteristic, complemented
265C22×#100C2412yes—
266C22×#100C2412yes—
267#2842C2×D412yescomplemented
268#2842C2×D412yescomplemented
269#2717C2×D412yescomplemented
270#2717C2×D412yescomplemented
271#2709C2×D412yescomplemented
272#2709C2×D412yescomplemented
273#2684C2×D412yescomplemented
274#2684C2×D412yescomplemented
275#2684C2×D412yescomplemented
276#2684C2×D412yescomplemented
277#2684C2×D412yescomplemented
278#2684C2×D412yescomplemented
279#2669C2×D412yescomplemented
280#2669C2×D412yescomplemented
281#2669C2×D412yescomplemented
282#2669C2×D412yescomplemented
283#2669C2×D412yescomplemented
284#2669C2×D412yescomplemented
285#2406C2×D412yes—
286#2406C2×D412yes—
287#2405C2×D412yes—
288#2405C2×D412yescomplemented
289#2405C2×D412yescomplemented
290#2405C2412yes—
291#2404C2×D412yes—
292#2404C2×D412yes—
293#2404C2×D412yes—
294#2404C2×D412yes—
295#2404C2×D412yes—
296#2404C2×D412yes—
297#2403C2×D412yes—
298#2403C2×D412yes—
299#2403C2×D412yes—
300#2403C2×D412yes—
301#2403C2×D412yes—
302#2403C2×D412yes—
303#2403C2×D412yes—
304#2403C2×D412yescomplemented
305#2403C2×D412yescomplemented
306#2403C2×D412yescomplemented
307#2403C2×D412yescomplemented
308#2403C2412yes—
309#2403C2412yes—
310#2403C2412yes—
311#2380C2×D412yescomplemented
312#2380C2×D412yescomplemented
313#2379C2×D412yescomplemented
314#2379C2×D412yescomplemented
315#2372C2×D412yescomplemented
316#2372C2×D412yescomplemented
317#2366C2×D412yescomplemented
318#2366C2×D412yescomplemented
319#2312C2×D412yescomplemented
320#2310C2×D411yescharacteristic, complemented
321#2309C2×D412yescomplemented
322#2309C2×D412yescomplemented
323#2309C2×D411yescharacteristic, complemented
324#2309C2×D411yescharacteristic, complemented
325#2309C2412yes—
326#2309C2411yescharacteristic
327#2308C2×D411yescharacteristic
328#2308C2×D411yescharacteristic
329#2308C2×D411yescharacteristic
330#2308C2×D411yescharacteristic
331#2308C2×D411yescharacteristic
332#2308C2×D411yescharacteristic
333#2308C2×D411yescharacteristic
334#2308C2×D411yescharacteristic
335#2308C2×D411yescharacteristic
336#2308C2×D411yescharacteristic
337#2308C2×D411yescharacteristic
338#2308C2×D411yescharacteristic
339#2308C2×D412yescomplemented
340#2308C2×D412yescomplemented
341#2308C2×D412yescomplemented
342#2297C2×D411yescharacteristic
343#2297C2×D411yescharacteristic
344#2297C2×D411yescharacteristic, complemented
345#2297C2×D411yescharacteristic, complemented
346#2285C2×D411yescharacteristic, complemented
347#2285C2×D411yescharacteristic, complemented
348C2×#376C2×D411yescharacteristic, complemented
349#1781C2412yes—
350#1781C2412yes—
351#1781C2412yes—
352#1781C2412yes—
353C26#12011yescharacteristic
354C26#12011yescharacteristic
355C26#12011yescharacteristic
356C22×#41#12011yescharacteristic
357C22×#41#12011yescharacteristic
358C22×#41#12011yescharacteristic
359C22×#41#12011yescharacteristic
360C22×#41C22×D411yescharacteristic
361C22×#41C22×D411yescharacteristic
362C22×#41C22×D411yescharacteristic
363C22×#41C22×D411yescharacteristic
364C22×#41C22×D411yescharacteristic
365C22×#41C22×D411yescharacteristic
366C22×#41C22×D411yescharacteristic
367C22×#41C22×D411yescharacteristic
368C23×Q8#12011yescharacteristic
369C23×Q8#12011yescharacteristic
370C23×Q8C22×D411yescharacteristic
371C23×D4#12011yescharacteristic
372C23×D4#12011yescharacteristic
373C23×D4C22×D411yescharacteristic
374C23×D4C22×D411yescharacteristic
375C23×D4C22×D411yescharacteristic
376C23×D4C22×D411yescharacteristic
377C23×D4C22×D412yes—
378C23×D4C22×D412yes—
379C23×D4C22×D412yes—
380C23×D4C22×D412yes—
381C23×D4C22×D412yes—
382C23×D4C22×D411yescharacteristic
383C23×D4C22×D411yescharacteristic
384C23×D4C22×D411yescharacteristic
385C23×D4C22×D411yescharacteristic
386C23×D4C22×D411yescharacteristic
387C23×D4C22×D411yescharacteristic
388C23×D4C2511yescharacteristic
389C24×C4#12011yescharacteristic
390C2×C4⋊Q8#12011yescharacteristic
391C2×C4⋊Q8#12011yescharacteristic
392C2×C4⋊Q8#12011yescharacteristic
393C2×C4⋊Q8#12011yescharacteristic
394C2×#127#12011yescharacteristic
395C2×#127#12011yescharacteristic
396C2×#127#12011yescharacteristic
397C2×#127#12011yescharacteristic
398C2×#127C22×D411yescharacteristic
399C2×#127C22×D411yescharacteristic
400C2×#127C22×D411yescharacteristic
401C2×#127C22×D411yescharacteristic
402C2×#127C22×D411yescharacteristic
403C2×#127C22×D411yescharacteristic
404C2×#127C22×D411yescharacteristic
405C2×#127C22×D411yescharacteristic
406C2×#124#12011yescharacteristic
407C2×#124#12011yescharacteristic
408C2×#124#12011yescharacteristic
409C2×#124#12011yescharacteristic
410C2×#124#12011yescharacteristic
411C2×#124#12011yescharacteristic
412C2×#124#12011yescharacteristic
413C2×#124#12011yescharacteristic
414C2×#124C22×D411yescharacteristic
415C2×#124C22×D411yescharacteristic
416C2×#124C22×D411yescharacteristic
417C2×#124C22×D411yescharacteristic
418C2×#124C22×D411yescharacteristic
419C2×#124C22×D411yescharacteristic
420C2×#124C22×D411yescharacteristic
421C2×#124C22×D411yescharacteristic
422C2×#123#12012yes—
423C2×#123#12012yes—
424C2×#123C22×D412yes—
425C2×#123C22×D412yes—
426C2×#120#12012yes—
427C2×#120#12012yes—
428C2×#120#12012yes—
429C2×#120#12012yes—
430C2×#120#12012yes—
431C2×#120#12012yes—
432C2×#120#12012yes—
433C2×#120#12012yes—
434C2×#120#12012yes—
435C2×#120#12012yes—
436C2×#120C22×D412yes—
437C2×#120C22×D412yes—
438C2×#120C22×D412yes—
439C2×#120C22×D412yes—
440C2×#120C22×D412yes—
441C2×#120C22×D412yes—
442C2×#117#12011yescharacteristic
443C2×#117#12011yescharacteristic
444C2×#117#12011yescharacteristic
445C2×#117#12011yescharacteristic
446C2×#117C22×D411yescharacteristic
447C2×#117C22×D411yescharacteristic
448C2×#117C22×D411yescharacteristic
449C2×#117C22×D411yescharacteristic
450C22×C4⋊C4#12012yes—
451C22×C22⋊C4#12012yes—
452C22×C22⋊C4#12012yes—
453C22×C22⋊C4#12011yescharacteristic
454C22×C22⋊C4#12011yescharacteristic
455C22×C22⋊C4#12011yescharacteristic
456C22×C22⋊C4#12011yescharacteristic
457C22×C22⋊C4#12012yes—
458C22×C22⋊C4#12011yescharacteristic
459C22×C22⋊C4#12011yescharacteristic
460C22×C22⋊C4#12011yescharacteristic
461C22×C22⋊C4#12011yescharacteristic
462C22×C22⋊C4#12011yescharacteristic
463C22×C22⋊C4#12011yescharacteristic
464C22×C22⋊C4#12011yescharacteristic
465C22×C22⋊C4#12011yescharacteristic
466C22×C22⋊C4C22×D412yes—
467C22×C42#12011yescharacteristic
468C22×C42#12011yescharacteristic
469C22×C42#12011yescharacteristic
470C22×C42#12011yescharacteristic
471C22×C42C22×D411yescharacteristic
472C22×C42C22×D411yescharacteristic
473C22×C42C22×D411yescharacteristic
474#386#12012yes—
475#386#12012yes—
476#386#12012yes—
477#386#12012yes—
478#386#12012yes—
479#386#12012yes—
480#386#12012yes—
481#386#12012yes—
482#386#12012yes—
483#386#12012yes—
484#386#12012yes—
485#386#12012yes—
486#386C22×D412yes—
487#386C22×D412yes—
488#386C22×D412yes—
489#386C22×D412yes—
490#386C22×D412yes—
491#386C22×D412yes—
492#386C22×D412yes—
493#386C22×D412yes—
494#381#12012yes—
495#381#12012yes—
496#381#12012yes—
497#381#12012yes—
498#379C22×D412yes—
499#379C22×D412yes—
500#379C22×D412yes—
501#379C22×D412yes—
502#379C22×D412yes—
503#379C22×D412yes—
504C25C2×#12011yescharacteristic
505C25C2×#12011yescharacteristic
506C25C2×#12011yescharacteristic
507C25C2×#12011yescharacteristic
508C25C2×#12012yes—
509C25C2×#12012yes—
510C25C2×#12012yes—
511C25C2×#12012yes—
512C25C23×D411yescharacteristic
513C25C23×D411yescharacteristic
514C22×Q8C2×#12011yescharacteristic
515C22×Q8C2×#12011yescharacteristic
516C22×Q8C2×#12011yescharacteristic
517C22×Q8C2×#12011yescharacteristic
518C22×Q8C2×#12011yescharacteristic
519C22×Q8C2×#12011yescharacteristic
520C22×D4C2×#12011yescharacteristic
521C22×D4C2×#12011yescharacteristic
522C22×D4C2×#12011yescharacteristic
523C22×D4C2×#12011yescharacteristic
524C22×D4C2×#12011yescharacteristic
525C22×D4C2×#12011yescharacteristic
526C22×D4C2×#12011yescharacteristic
527C22×D4C2×#12011yescharacteristic
528C22×D4C2×#12011yescharacteristic
529C22×D4C2×#12011yescharacteristic
530C22×D4C2×#12011yescharacteristic
531C22×D4C2×#12011yescharacteristic
532C22×D4C2×#12011yescharacteristic
533C22×D4C2×#12011yescharacteristic
534C22×D4C2×#12011yescharacteristic
535C22×D4C2×#12011yescharacteristic
536C22×D4C2×#12011yescharacteristic
537C22×D4C2×#12011yescharacteristic
538C22×D4C23×D411yescharacteristic
539C22×D4C23×D411yescharacteristic
540C22×D4C23×D411yescharacteristic
541C22×D4C23×D411yescharacteristic
542C23×C4C2×#12011yescharacteristic
543C23×C4C2×#12011yescharacteristic
544C23×C4C2×#12011yescharacteristic
545C23×C4C2×#12011yescharacteristic
546C23×C4C2×#12012yes—
547C23×C4C2×#12012yes—
548C23×C4C2×#12012yes—
549C23×C4C2×#12012yes—
550C23×C4C2×#12012yes—
551C23×C4C2×#12012yes—
552C23×C4C2×#12011yescharacteristic
553C23×C4C2×#12011yescharacteristic
554C23×C4C2×#12011yescharacteristic
555C23×C4C2×#12011yescharacteristic
556C23×C4C23×D411yescharacteristic
557#127B(4,𝔽2)14yescomplemented
558#124B(4,𝔽2)14yescomplemented
559C2×C22⋊C4C2×#12012yes—
560C2×C22⋊C4C2×#12012yes—
561C2×C22⋊C4C2×#12012yes—
562C2×C22⋊C4C2×#12012yes—
563C2×C22⋊C4C2×#12012yes—
564C2×C22⋊C4C2×#12012yes—
565C2×C22⋊C4C2×#12012yes—
566C2×C22⋊C4C2×#12012yes—
567C2×C22⋊C4C2×#12012yes—
568C2×C22⋊C4C2×#12012yes—
569C2×C42C2×#12011yescharacteristic
570C2×C42C2×#12011yescharacteristic
571C2×C42C2×#12011yescharacteristic
572C2×C42C2×#12011yescharacteristic
573C2×C42C2×#12011yescharacteristic
574C2×C42C2×#12011yescharacteristic
575C2×C42C2×#12011yescharacteristic
576C2×C42C2×#12011yescharacteristic
577C24#284611yescharacteristic
578C24#284611yescharacteristic
579C24#284611yescharacteristic
580C24#284611yescharacteristic
581C24C22×#12011yescharacteristic
582C24C22×#12011yescharacteristic
583C24C22×#12011yescharacteristic
584C24C22×#12011yescharacteristic
585C24C22×#12011yescharacteristic
586C2×Q8C2×B(4,𝔽2)12yes—
587C2×D4C2×B(4,𝔽2)12yes—
588C2×D4C2×B(4,𝔽2)12yes—
589C2×D4C2×B(4,𝔽2)12yes—
590C2×D4#302612yes—
591C2×D4#302612yes—
592C22×C4#284611yescharacteristic
593C22×C4#284611yescharacteristic
594C22×C4#284611yescharacteristic
595C22×C4#284611yescharacteristic
596C22×C4C22×#12011yescharacteristic
597C22×C4C22×#12011yescharacteristic
598C42C2×B(4,𝔽2)12yes—
599C42C2×B(4,𝔽2)12yes—
600C23#3289812yes—
601C23#3289812yes—
602C23#3289812yes—
603C23#3289812yes—
604C23C2×#284611yescharacteristic
605C23#6039912yes—
606C2×C4C22×B(4,𝔽2)11yescharacteristic
607C2×C4C22×B(4,𝔽2)11yescharacteristic
608C2×C4C2×#302611yescharacteristic
609C2×C4C2×#302611yescharacteristic
610C22C2×#3289811yescharacteristic
611C22C2×#3289811yescharacteristic
612C22#662889611yescharacteristic
613C2#7221632311yescharacteristic
614C2#7223320612yes—
subgroupG/H
center, socleC22#6628896
commutator, Frattini, cosocleC23×D4C25
LCSG ▷ C23×D4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C24 ◁ #35527 ◁ G
LECSG ▷ C23×D4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #72341536C2semidirect
2. #72341533C2semidirect
3. #72341495C2semidirect
4. #72341473C2semidirect
5. #72341466C2semidirect
6. #72341320C2semidirect
7. #72341312C2semidirect
8. #72318598C2semidirect
9. #72311295C2semidirect
10. #72306419C2semidirect
11. #72306417C2semidirect
12. #72306415C2semidirect
13. #72303095C2semidirect
14. #72284823C2semidirect
15. #72262266C2semidirect
16. #72236975C2semidirect
17. #72234146C2semidirect
18. #72233917C2semidirect
19. #72210439C2semidirect
20. C2×#60389C22semidirect
21. C2×#60388C22semidirect
22. #8968143C22semidirect
25. #8823789C22semidirect
26. #8818039C22semidirect
27. #8360950C22semidirect
33. #6628901C22semidirect
34. #6628897C22semidirect
35. #6628896C22semidirect
36. #6628896C22semidirect
37. #6628896C22semidirect
38. #499852C22semidirect
39. #499849C22semidirect
40. #499848C22semidirect
41. #499843C22semidirect
42. #499839C22semidirect
43. #499838C22semidirect
44. #499835C22semidirect
45. #499832C22semidirect
46. #494682C22semidirect
47. #494682C22semidirect
48. #494682C22semidirect
49. #494682C22semidirect
50. #494682C22semidirect
51. #494682C22semidirect
52. #494681C22semidirect
53. #494681C22semidirect
54. #493433C22semidirect
55. #493433C22semidirect
56. #493430C22semidirect
57. #493430C22semidirect
58. #449492C22semidirect
59. #417813C22semidirect
60. #417568C22semidirect
61. #417566C22semidirect
62. #374009C22semidirect
63. #359606C22semidirect
64. #359605C22semidirect
65. #251844C22semidirect
66. #251828C22semidirect
67. #245255C22semidirect
68. #245233C22semidirect
69. #213860C22semidirect
70. #213860C22semidirect
71. #213855C22semidirect
72. #213854C22semidirect
73. #213854C22semidirect
74. #213854C22semidirect
75. #134011C22semidirect
76. #133905C22semidirect
77. #133904C22semidirect
78. #133835C22semidirect
79. #133433C22semidirect
80. #133429C22semidirect
81. #133360C22semidirect
82. #133359C22semidirect
83. #133358C22semidirect
84. #133356C22semidirect
85. #133336C22semidirect
86. #133335C22semidirect
87. #133334C22semidirect
88. #133332C22semidirect
89. #133311C22semidirect
90. #133308C22semidirect
92. C2×#3500D4semidirect
94. C2×#3498D4semidirect
96. C22×#551D4semidirect
97. C22×D42D4semidirect
98. C22×H(3,𝔽4)D4semidirect
99. C22×#560D4semidirect
101. C2×#3019C23semidirect
102. C22×#455C23semidirect
106. #59184D4semidirect
109. #59041D4semidirect
110. #52013D4semidirect
112. #52004D4semidirect
116. #51749D4semidirect
117. #51530D4semidirect
119. #46386D4semidirect
120. #46384D4semidirect
121. #46384D4semidirect
122. #46384D4semidirect
125. #46276D4semidirect
126. #46225D4semidirect
129. #36955D4semidirect
130. #36955D4semidirect
131. #36721D4semidirect
132. #36714D4semidirect
133. #36702D4semidirect
134. #36702D4semidirect
135. #36702D4semidirect
136. #36702D4semidirect
137. #36702D4semidirect
138. #36702D4semidirect
139. #35676D4semidirect
140. #35616D4semidirect
144. #35527C23semidirect
146. #35346D4semidirect
147. #35346D4semidirect
151. #35327D4semidirect
153. #35272D4semidirect
156. #34366D4semidirect
157. #34366D4semidirect
158. #34364D4semidirect
159. #34364D4semidirect
160. #34070D4semidirect
161. #34070D4semidirect
162. #32900C23semidirect
165. #32898C23semidirect
167. #20586C23semidirect
176. #13082C23semidirect
177. #13082C23semidirect
178. #13080C23semidirect
179. #13080C23semidirect
182. #12696C23semidirect
183. #12696C23semidirect
184. #12694C23semidirect
185. #12694C23semidirect
188. #11167C23semidirect
190. #10989C23semidirect
191. #10981C23semidirect
192. #10977C23semidirect
194. #9501C23semidirect
197. #9497C23semidirect
198. #8748C23semidirect
199. #8748C23semidirect
200. #8546C23semidirect
201. #8546C23semidirect
204. C22×H(5,𝔽2)C2×D4semidirect
205. C22×H(5,𝔽2)C2×D4semidirect
208. C2×H(3,𝔽4)C2×D4semidirect
209. C2×H(3,𝔽4)C2×D4semidirect
210. C2×#560C2×D4semidirect
211. C2×#560C2×D4semidirect
212. C2×#551C2×D4semidirect
213. C2×#551C2×D4semidirect
214. C2×D42C2×D4semidirect
215. C2×D42C2×D4semidirect
219. C2×#536C2×D4semidirect
229. C2×#535C2×D4semidirect
232. C2×#534C2×D4semidirect
241. C22×#127C2×D4semidirect
246. C22×#124C2×D4semidirect
247. C22×#124C2×D4semidirect
263. C2×C4×#41C2×D4semidirect
264. C2×C4×#41C2×D4semidirect
267. #2842C2×D4semidirect
268. #2842C2×D4semidirect
269. #2717C2×D4semidirect
270. #2717C2×D4semidirect
271. #2709C2×D4semidirect
272. #2709C2×D4semidirect
273. #2684C2×D4semidirect
274. #2684C2×D4semidirect
275. #2684C2×D4semidirect
276. #2684C2×D4semidirect
277. #2684C2×D4semidirect
278. #2684C2×D4semidirect
279. #2669C2×D4semidirect
280. #2669C2×D4semidirect
281. #2669C2×D4semidirect
282. #2669C2×D4semidirect
283. #2669C2×D4semidirect
284. #2669C2×D4semidirect
288. #2405C2×D4semidirect
289. #2405C2×D4semidirect
304. #2403C2×D4semidirect
305. #2403C2×D4semidirect
306. #2403C2×D4semidirect
307. #2403C2×D4semidirect
311. #2380C2×D4semidirect
312. #2380C2×D4semidirect
313. #2379C2×D4semidirect
314. #2379C2×D4semidirect
315. #2372C2×D4semidirect
316. #2372C2×D4semidirect
317. #2366C2×D4semidirect
318. #2366C2×D4semidirect
319. #2312C2×D4semidirect
320. #2310C2×D4semidirect
321. #2309C2×D4semidirect
322. #2309C2×D4semidirect
323. #2309C2×D4semidirect
324. #2309C2×D4semidirect
339. #2308C2×D4semidirect
340. #2308C2×D4semidirect
341. #2308C2×D4semidirect
344. #2297C2×D4semidirect
345. #2297C2×D4semidirect
346. #2285C2×D4semidirect
347. #2285C2×D4semidirect
348. C2×#376C2×D4semidirect
557. #127B(4,𝔽2)semidirect
558. #124B(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
#723415362
#723415332
#723414952
#723414732
#723414662
#723413202
#723413122
#723185982
#723112952
#723064192
#723064172
#723064152
#723030952
#722848232
#722622662
#722369752
#722341462
#722339172
#722104392