Finite Group Databasebeta

← #7271412

Subgroups — #7271412

Order 512.

1472 conjugacy classes of subgroups.

The subgroup lattice has 1355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42976C211yesmaximal, characteristic, complemented
2#42467C211yesmaximal, characteristic, complemented
3#32765C211yesmaximal, characteristic, complemented
4#32681C211yesmaximal, characteristic, complemented
5#32675C211yesmaximal, characteristic, complemented
6#32457C211yesmaximal, characteristic, complemented
7#32452C211yesmaximal, characteristic, complemented
8#32193C211yesmaximal, characteristic, complemented
9#32188C211yesmaximal, characteristic, complemented
10#31008C211yesmaximal, characteristic, complemented
11#31000C211yesmaximal, characteristic, complemented
12#30830C211yesmaximal, characteristic, complemented
13#30825C211yesmaximal, characteristic, complemented
14#30539C211yesmaximal, characteristic, complemented
15#30535C211yesmaximal, characteristic, complemented
16#28425C211yesmaximal, characteristic, complemented
17#28422C211yesmaximal, characteristic, complemented
18#28319C211yesmaximal, characteristic, complemented
19#28021C211yesmaximal, characteristic, complemented
20#28021C211yesmaximal, characteristic, complemented
21#27898C211yesmaximal, characteristic, complemented
22#27591C211yesmaximal, characteristic, complemented
23#26812C211yesmaximal, characteristic, complemented
24#26811C211yesmaximal, characteristic, complemented
25#26602C211yesmaximal, characteristic, complemented
26#26601C211yesmaximal, characteristic, complemented
27#26568C211yesmaximal, characteristic, complemented
28#26564C211yesmaximal, characteristic, complemented
29#26332C211yesmaximal, characteristic, complemented
30#26331C211yesmaximal, characteristic, complemented
31#22326C211yesmaximal, characteristic, complemented
32C2×#490C2211yescharacteristic
33C2×#489C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#479C2211yescharacteristic, complemented
37C2×#474C2211yescharacteristic, complemented
38C2×#463C2211yescharacteristic
39C2×#459C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#442C2211yescharacteristic, complemented
43C2×#440C2211yescharacteristic, complemented
44#2830—21no—
45#2829—21no—
46#2751—21no—
47#2715—21no—
48#2712—21no—
49#2705—21no—
50#2697—21no—
51#2685—21no—
52#2685—21no—
53#2684—21no—
54#2662—21no—
55#2662—21no—
56#2648—21no—
57#2630—21no—
58#2620C2211yescharacteristic
59#2619C2211yescharacteristic
60#2592C2211yescharacteristic
61#2566C2211yescharacteristic, complemented
62#2563C2211yescharacteristic, complemented
63#2554—21no—
64#2550C2211yescharacteristic, complemented
65#2548C2211yescharacteristic
66#2548C2211yescharacteristic
67#2548C2211yescharacteristic, complemented
68#2544C2211yescharacteristic
69#2512C2211yescharacteristic
70#2512C2211yescharacteristic
71#2512C2211yescharacteristic, complemented
72#2512C2211yescharacteristic, complemented
73#2491C2211yescharacteristic
74#2490C2211yescharacteristic
75#2468—21no—
76#2448C2211yescharacteristic
77#2445C2211yescharacteristic
78#2435C2211yescharacteristic
79#2433C2211yescharacteristic
80#2422C2211yescharacteristic
81#2420C2211yescharacteristic
82#2396C2211yescharacteristic
83#2366C2211yescharacteristic, complemented
84#2363C2211yescharacteristic
85#2362C2211yescharacteristic
86#2355C2211yescharacteristic, complemented
87#2314C2211yescharacteristic
88#2309C2211yescharacteristic
89#2097C2211yescharacteristic, complemented
90#2093C2211yescharacteristic, complemented
91#2092C2211yescharacteristic
92#2092C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2074C2211yescharacteristic, complemented
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic, complemented
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic, complemented
102#2071C2211yescharacteristic, complemented
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic, complemented
106#2065C2211yescharacteristic, complemented
107#2059C2211yescharacteristic, complemented
108#2058C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic, complemented
113#2042C2211yescharacteristic
114#2041C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2025C2211yescharacteristic
120#2023C2211yescharacteristic
121#2014C2211yescharacteristic, complemented
122#2012C2211yescharacteristic
123#2012C2211yescharacteristic
124#2012C2211yescharacteristic
125#2012C2211yescharacteristic, complemented
126#2012C2211yescharacteristic, complemented
127#2011C2211yescharacteristic
128#2011C2211yescharacteristic
129#2011C2211yescharacteristic
130#2011C2211yescharacteristic
131#2011C2211yescharacteristic
132#2011C2211yescharacteristic, complemented
133#2000C2211yescharacteristic
134#2000C2211yescharacteristic
135#1999C2211yescharacteristic
136#1999C2211yescharacteristic
137#1985C2211yescharacteristic, complemented
138#1985C2211yescharacteristic, complemented
139#1983C2211yescharacteristic
140#1982C2211yescharacteristic
141#1973C2211yescharacteristic, complemented
142#1972C2211yescharacteristic
143#1972C2211yescharacteristic
144#1972C2211yescharacteristic
145#1972C2211yescharacteristic
146#1972C2211yescharacteristic
147#1972C2211yescharacteristic
148#1972C2211yescharacteristic, complemented
149#1970C2211yescharacteristic
150#1970C2211yescharacteristic
151#1961C2211yescharacteristic
152#1959C2211yescharacteristic
153#1959C2211yescharacteristic, complemented
154#1958C2211yescharacteristic, complemented
155#1949C2211yescharacteristic, complemented
156#1948C2211yescharacteristic, complemented
157#1944C2211yescharacteristic, complemented
158#1944C2211yescharacteristic, complemented
159#1927C2211yescharacteristic, complemented
160#1927C2211yescharacteristic, complemented
161#1927C2211yescharacteristic, complemented
162#1926C2211yescharacteristic
163#1926C2211yescharacteristic
164#1926C2211yescharacteristic
165#1926C2211yescharacteristic
166#1926C2211yescharacteristic, complemented
167#1926C2211yescharacteristic, complemented
168#1926C2211yescharacteristic, complemented
169#1926C2211yescharacteristic, complemented
170#1926C2211yescharacteristic, complemented
171#1926C2211yescharacteristic, complemented
172#1925C2211yescharacteristic
173#1925C2211yescharacteristic
174#1925C2211yescharacteristic, complemented
175#1924C2211yescharacteristic
176#1924C2211yescharacteristic
177#1924C2211yescharacteristic
178#1924C2211yescharacteristic
179#1917C2211yescharacteristic, complemented
180#1917C2211yescharacteristic, complemented
181#1917C2211yescharacteristic, complemented
182#1917C2211yescharacteristic, complemented
183#1880C2211yescharacteristic, complemented
184#1879C2211yescharacteristic
185#1879C2211yescharacteristic
186#1879C2211yescharacteristic, complemented
187#1865C2211yescharacteristic, complemented
188#1864C2211yescharacteristic, complemented
189#1864C2211yescharacteristic, complemented
190#1862C2211yescharacteristic, complemented
191#1854C2211yescharacteristic
192#1854C2211yescharacteristic
193#1844C2211yescharacteristic, complemented
194#1836C2211yescharacteristic, complemented
195#1818C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1776C2211yescharacteristic, complemented
199#1776C2211yescharacteristic, complemented
200#1771C2211yescharacteristic, complemented
201#1771C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#126—21no—
217C2×#126—21no—
218C2×#126—21no—
219C2×#126—21no—
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×#123—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#120—21no—
234C2×#120—21no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243#490—42no—
244#489—42no—
245#482—42no—
246#482—42no—
247#479—42no—
248#474—42no—
249#463—42no—
250#459—42no—
251#447—42no—
252#447—42no—
253#442—42no—
254#440—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313#400D411yescharacteristic
314#399—21no—
315#399D411yescharacteristic
316#398—21no—
317#398D411yescharacteristic
318#398D411yescharacteristic
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#396—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396D411yescharacteristic
337#396D411yescharacteristic
338#395—21no—
339#395D411yescharacteristic
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#393—21no—
361#393—21no—
362#393—21no—
363#393—21no—
364#393D411yescharacteristic
365#392—21no—
366#392—21no—
367#392—21no—
368#392—21no—
369#391—21no—
370#391—21no—
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#390—21no—
374#390—21no—
375#390—21no—
376#390—21no—
377#390—21no—
378#390—21no—
379#390—21no—
380#390—21no—
381#390—21no—
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#389—21no—
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#381—21no—
442#380—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#379—21no—
447#379—21no—
448#379—21no—
449#379—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C22⋊C4—21no—
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×Q8—21no—
492C22×Q8C2×D411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2411yescharacteristic
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×D8—22no—
526C2×D8—22no—
527C2×D8—41no—
528C2×D8—41no—
529C2×D8—41no—
530C2×D8—41no—
531C2×D8—41no—
532C2×D8—41no—
533C2×D8—41no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8—41no—
542C2×D8—41no—
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553#127—41no—
554#127—41no—
555#127—41no—
556#127—41no—
557#127—41no—
558#127—41no—
559#126—82no—
560#126—82no—
561#126—82no—
562#126—82no—
563#125—41no—
564#125—41no—
565#124—41no—
566#124—41no—
567#124—41no—
568#124—41no—
569#124—41no—
570#124—41no—
571#124—82no—
572#124—82no—
573#124—82no—
574#123—82no—
575#123—82no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578#121—41no—
579#121—41no—
580#121—41no—
581#121—41no—
582#121—41no—
583#121—41no—
584#120—82no—
585#120—82no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—82no—
597#117—41no—
598#117—41no—
599#117—41no—
600#117—41no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709#107—22no—
710#107—22no—
711#107—41no—
712#107—41no—
713#106—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718#106—41no—
719#106—41no—
720#106—41no—
721C4⋊C8—22no—
722C4⋊C8—22no—
723C4⋊C8—41no—
724C4⋊C8—41no—
725#103—22no—
726#103—22no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757C22⋊C8—22no—
758C22⋊C8—22no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761#97—22no—
762#97—22no—
763#97—41no—
764#97—41no—
765#97—41no—
766C4×C8—41no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—42no—
805C24—81no—
806C24—81no—
807C24—81no—
808C24—81no—
809C24—81no—
810C24—81no—
811C24C22×D411yescharacteristic
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—41no—
819C2×Q8—41no—
820C2×Q8—41no—
821C2×Q8—81no—
822C2×Q8—81no—
823C2×Q8—81no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—82no—
877C2×D4—82no—
878C2×D4—82no—
879C2×D4—82no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—42no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C2511yescharacteristic
928SD16—44no—
929SD16—82no—
930D8—44no—
931D8—82no—
932D8—82no—
933D8—82no—
934D8—82no—
935D8—82no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8H(5,𝔽2)12yes—
959C2×C8H(5,𝔽2)12yes—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—42no—
1077C42—42no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—84no—
1127C23—162no—
1128C23—162no—
1129C23—162no—
1130C23—162no—
1131C23—162no—
1132C23—162no—
1133C23C23×D411yescharacteristic
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—82no—
1139Q8—162no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—41no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—84no—
1161D4—84no—
1162D4—162no—
1163D4—162no—
1164D4—162no—
1165D4—162no—
1166D4—162no—
1167D4—162no—
1168D4—162no—
1169D4—162no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—162no—
1247C2×C4—162no—
1248C2×C4—162no—
1249C2×C4C2×H(5,𝔽2)11yescharacteristic
1250C2×C4C2×H(5,𝔽2)11yescharacteristic
1251C2×C4#58511yescharacteristic
1252C2×C4#58511yescharacteristic
1253C2×C4#58511yescharacteristic
1254C2×C4#58511yescharacteristic
1255C8—22no—
1256C8—22no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—168no—
1306C22#348511yescharacteristic
1307C22#348711yescharacteristic
1308C22#349811yescharacteristic
1309C22#358511yescharacteristic
1310C22#358511yescharacteristic
1311C22#358511yescharacteristic
1312C22#358511yescharacteristic
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4#354011yescharacteristic
1338C4#354011yescharacteristic
1339C4#356011yescharacteristic
1340C4#356011yescharacteristic
1341C2—81no—
1342C2—161no—
1343C2—161no—
1344C2—161no—
1345C2—161no—
1346C2—161no—
1347C2#4721211yescharacteristic
1348C2#6178311yescharacteristic
1349C2#6179511yescharacteristic
1350C2#6194211yescharacteristic
1351C2#6194511yescharacteristic
1352C2#6244311yescharacteristic
1353C2#6244311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42976C2semidirect
2. #42467C2semidirect
3. #32765C2semidirect
4. #32681C2semidirect
5. #32675C2semidirect
6. #32457C2semidirect
7. #32452C2semidirect
8. #32193C2semidirect
9. #32188C2semidirect
10. #31008C2semidirect
11. #31000C2semidirect
12. #30830C2semidirect
13. #30825C2semidirect
14. #30539C2semidirect
15. #30535C2semidirect
16. #28425C2semidirect
17. #28422C2semidirect
18. #28319C2semidirect
19. #28021C2semidirect
20. #28021C2semidirect
21. #27898C2semidirect
22. #27591C2semidirect
23. #26812C2semidirect
24. #26811C2semidirect
25. #26602C2semidirect
26. #26601C2semidirect
27. #26568C2semidirect
28. #26564C2semidirect
29. #26332C2semidirect
30. #26331C2semidirect
31. #22326C2semidirect
36. C2×#479C22semidirect
37. C2×#474C22semidirect
42. C2×#442C22semidirect
43. C2×#440C22semidirect
61. #2566C22semidirect
62. #2563C22semidirect
64. #2550C22semidirect
67. #2548C22semidirect
71. #2512C22semidirect
72. #2512C22semidirect
83. #2366C22semidirect
86. #2355C22semidirect
89. #2097C22semidirect
90. #2093C22semidirect
95. #2074C22semidirect
97. #2073C22semidirect
101. #2071C22semidirect
102. #2071C22semidirect
105. #2065C22semidirect
106. #2065C22semidirect
107. #2059C22semidirect
108. #2058C22semidirect
109. #2055C22semidirect
112. #2054C22semidirect
121. #2014C22semidirect
125. #2012C22semidirect
126. #2012C22semidirect
132. #2011C22semidirect
137. #1985C22semidirect
138. #1985C22semidirect
141. #1973C22semidirect
148. #1972C22semidirect
153. #1959C22semidirect
154. #1958C22semidirect
155. #1949C22semidirect
156. #1948C22semidirect
157. #1944C22semidirect
158. #1944C22semidirect
159. #1927C22semidirect
160. #1927C22semidirect
161. #1927C22semidirect
166. #1926C22semidirect
167. #1926C22semidirect
168. #1926C22semidirect
169. #1926C22semidirect
170. #1926C22semidirect
171. #1926C22semidirect
174. #1925C22semidirect
179. #1917C22semidirect
180. #1917C22semidirect
181. #1917C22semidirect
182. #1917C22semidirect
183. #1880C22semidirect
186. #1879C22semidirect
187. #1865C22semidirect
188. #1864C22semidirect
189. #1864C22semidirect
190. #1862C22semidirect
193. #1844C22semidirect
194. #1836C22semidirect
198. #1776C22semidirect
199. #1776C22semidirect
200. #1771C22semidirect
201. #1771C22semidirect

Maximal subgroups

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

subgroupindex
#429762
#424672
#327652
#326812
#326752
#324572
#324522
#321932
#321882
#310082
#310002
#308302
#308252
#305392
#305352
#284252
#284222
#283192
#280212
#278982
#275912
#268122
#268112
#266022
#266012
#265682
#265642
#263322
#263312
#223262