Finite Group Databasebeta

← #6476595

Subgroups — #6476595

Order 512.

1667 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35260C211yesmaximal, characteristic, complemented
2#34635C211yesmaximal, characteristic, complemented
3#33142C211yesmaximal, characteristic, complemented
4#33140C211yesmaximal, characteristic, complemented
5#33139C211yesmaximal, characteristic, complemented
6#33137C211yesmaximal, characteristic, complemented
7#30374C211yesmaximal, characteristic, complemented
8#30368C211yesmaximal, characteristic, complemented
9#30332C211yesmaximal, characteristic, complemented
10#30330C211yesmaximal, characteristic, complemented
11#29475C211yesmaximal, characteristic, complemented
12#29472C211yesmaximal, characteristic, complemented
13#29471C211yesmaximal, characteristic, complemented
14#29468C211yesmaximal, characteristic, complemented
15#29339C211yesmaximal, characteristic, complemented
16#29299C211yesmaximal, characteristic, complemented
17#29113C211yesmaximal, characteristic, complemented
18#28309C211yesmaximal, characteristic, complemented
19#27874C211yesmaximal, characteristic, complemented
20#27873C211yesmaximal, characteristic, complemented
21#25514C211yesmaximal, characteristic, complemented
22#25513C211yesmaximal, characteristic, complemented
23#24561C211yesmaximal, characteristic, complemented
24#24555C211yesmaximal, characteristic, complemented
25#24388C211yesmaximal, characteristic
26#24383C211yesmaximal, characteristic, complemented
27#22083C211yesmaximal, characteristic, complemented
28#22080C211yesmaximal, characteristic, complemented
29#22051C211yesmaximal, characteristic, complemented
30#22042C211yesmaximal, characteristic, complemented
31#20379C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C2×#485C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#467C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#449C2211yescharacteristic
43C2×#407C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic
45C2×#405C2211yescharacteristic
46C2×#405C2211yescharacteristic
47#2857C2211yescharacteristic
48#2850C2211yescharacteristic
49#2848C2211yescharacteristic
50#2847C2211yescharacteristic
51#2628C2211yescharacteristic
52#2625C2211yescharacteristic
53#2625C2211yescharacteristic
54#2625C2211yescharacteristic
55#2625C2211yescharacteristic
56#2625C2211yescharacteristic
57#2624C2211yescharacteristic
58#2624C2211yescharacteristic
59#2624C2211yescharacteristic
60#2624C2211yescharacteristic
61#2624C2211yescharacteristic
62#2623—21no—
63#2623—21no—
64#2622—21no—
65#2622—21no—
66#2620C2211yescharacteristic
67#2481—21no—
68#2479—21no—
69#2477—21no—
70#2474—21no—
71#2472—21no—
72#2470—21no—
73#2449—21no—
74#2418—21no—
75#2395—21no—
76#2395—21no—
77#2395—21no—
78#2395—21no—
79#2324C2211yescharacteristic
80#2323C2211yescharacteristic
81#2314C2211yescharacteristic
82C4×C22⋊Q8C2211yescharacteristic
83C4×#121C2211yescharacteristic
84#2297C2211yescharacteristic
85#2297C2211yescharacteristic
86#2296C2211yescharacteristic
87#2296C2211yescharacteristic
88#2280C2211yescharacteristic
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2092C2211yescharacteristic, complemented
93#2084C2211yescharacteristic, complemented
94#2083C2211yescharacteristic, complemented
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2076C2211yescharacteristic
98#2076C2211yescharacteristic
99#2072C2211yescharacteristic, complemented
100#2071C2211yescharacteristic, complemented
101#2058C2211yescharacteristic, complemented
102#2057C2211yescharacteristic, complemented
103#2042C2211yescharacteristic, complemented
104#2042C2211yescharacteristic, complemented
105#2036C2211yescharacteristic
106#2035C2211yescharacteristic
107#2035C2211yescharacteristic
108#2035C2211yescharacteristic
109#2034C2211yescharacteristic
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2024C2211yescharacteristic, complemented
114#2023C2211yescharacteristic, complemented
115#2015C2211yescharacteristic, complemented
116#2012C2211yescharacteristic, complemented
117#2001C2211yescharacteristic
118#2000C2211yescharacteristic
119#2000C2211yescharacteristic
120#1999C2211yescharacteristic
121#1973C2211yescharacteristic, complemented
122#1972C2211yescharacteristic, complemented
123#1970C2211yescharacteristic, complemented
124#1969C2211yescharacteristic, complemented
125#1969C2211yescharacteristic, complemented
126#1968C2211yescharacteristic, complemented
127#1968C2211yescharacteristic, complemented
128#1968C2211yescharacteristic, complemented
129#1944C2211yescharacteristic, complemented
130#1943C2211yescharacteristic, complemented
131#1942C2211yescharacteristic, complemented
132#1942C2211yescharacteristic, complemented
133#1942C2211yescharacteristic, complemented
134#1941C2211yescharacteristic, complemented
135#1941C2211yescharacteristic, complemented
136#1941C2211yescharacteristic, complemented
137#1936C2211yescharacteristic, complemented
138#1936C2211yescharacteristic, complemented
139#1936C2211yescharacteristic, complemented
140#1936C2211yescharacteristic, complemented
141#1936C2211yescharacteristic, complemented
142#1935C2211yescharacteristic, complemented
143#1935C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1935C2211yescharacteristic, complemented
147#1935C2211yescharacteristic, complemented
148#1935C2211yescharacteristic, complemented
149#1934C2211yescharacteristic, complemented
150#1934C2211yescharacteristic, complemented
151#1934C2211yescharacteristic, complemented
152#1933C2211yescharacteristic, complemented
153#1927C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1925C2211yescharacteristic, complemented
156#1925C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1921C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1919C2211yescharacteristic, complemented
161#1895C2211yescharacteristic
162#1894C2211yescharacteristic
163#1894C2211yescharacteristic
164#1894C2211yescharacteristic
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic
167#1893C2211yescharacteristic
168#1892C2211yescharacteristic
169#1880C2211yescharacteristic, complemented
170#1879C2211yescharacteristic, complemented
171#1878C2211yescharacteristic, complemented
172#1877C2211yescharacteristic, complemented
173#1875C2211yescharacteristic
174#1875C2211yescharacteristic
175#1873C2211yescharacteristic
176#1873C2211yescharacteristic
177#1865C2211yescharacteristic, complemented
178#1864C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic, complemented
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1825C2211yescharacteristic
186#1825C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1808C2211yescharacteristic
190#1807C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1750C2211yescharacteristic
194#1750C2211yescharacteristic
195#1750C2211yescharacteristic
196#1750C2211yescharacteristic
197#1749C2211yescharacteristic
198#1749C2211yescharacteristic
199C4×C22⋊C8C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1729C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#542—42no—
214#542—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219#525—42no—
220#525—42no—
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×#117—42no—
243C2×#117—42no—
244C2×#117D411yescharacteristic
245C2×#117D411yescharacteristic
246C2×#117D411yescharacteristic
247C2×#117D411yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C22×C4⋊C4D411yescharacteristic
256C22×C4⋊C4D411yescharacteristic
257C22×C22⋊C4D411yescharacteristic
258C22×C22⋊C4D411yescharacteristic
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261#485—24no—
262#482—24no—
263#469—42no—
264#468—42no—
265#467—42no—
266#465—42no—
267#452—24no—
268#449—24no—
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305#407—24no—
306C2×C22⋊C8—24no—
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315#405—42no—
316#405—42no—
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#399—21no—
332#399—21no—
333#399—21no—
334#399—21no—
335#399—21no—
336#399—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#397—21no—
357#396—21no—
358#396—21no—
359#395—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#393—21no—
373#391—21no—
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#390—21no—
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#389—21no—
388#389—21no—
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#384C2311yescharacteristic
434#382C2311yescharacteristic
435#381—21no—
436#380—21no—
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#379—21no—
448#379—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
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#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25C2×D411yescharacteristic
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—22no—
515C23×C4—22no—
516C23×C4—22no—
517C23×C4—22no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4C2×D411yescharacteristic
523C23×C4C2×D411yescharacteristic
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C2×Q16—22no—
533C2×Q16—41no—
534C2×Q16—41no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×D8—22no—
542C2×D8—41no—
543C2×D8—41no—
544C2×M16—22no—
545C2×M16—22no—
546C2×M16—22no—
547C2×M16—22no—
548C2×M16—41no—
549C2×M16—41no—
550C22×C8—22no—
551C22×C8—22no—
552C22×C8—22no—
553C22×C8—22no—
554C22×C8—41no—
555C22×C8—41no—
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566#126—44no—
567#124—41no—
568#124—41no—
569#124—44no—
570#123—44no—
571#123—44no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—44no—
583C22⋊Q8—82no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—41no—
591#121—41no—
592#121—41no—
593#121—41no—
594#120—44no—
595#120—82no—
596C4×Q8—41no—
597C4×Q8—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—44no—
601C4×D4—44no—
602C4×D4—82no—
603#117—22no—
604#117—22no—
605#117—22no—
606#117—22no—
607#117—22no—
608#117—22no—
609#117—41no—
610#117—41no—
611#117—41no—
612#117—41no—
613#117—42no—
614#117—42no—
615#117—42no—
616#117—42no—
617#117—41no—
618#117—41no—
619#117—41no—
620#117—41no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—42no—
643C2×C4⋊C4—42no—
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—42no—
703C2×C22⋊C4—42no—
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—41no—
719C2×C42—41no—
720C2×C42—41no—
721C2×C42—41no—
722C2×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730#107—22no—
731#107—22no—
732#107—41no—
733#107—41no—
734#107—41no—
735#107—41no—
736#106—22no—
737#106—22no—
738#106—41no—
739#106—41no—
740#106—41no—
741#106—41no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766C22⋊C8—22no—
767C22⋊C8—22no—
768C22⋊C8—22no—
769C22⋊C8—22no—
770C22⋊C8—22no—
771C22⋊C8—22no—
772C22⋊C8#4114yes—
773C22⋊C8#4114yes—
774#97—41no—
775#97—41no—
776#97—41no—
777#97—41no—
778C4×C8—41no—
779C4×C8—41no—
780C4×C8—41no—
781C4×C8—41no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820C24—22no—
821C24—22no—
822C24—21no—
823C24—21no—
824C24—41no—
825C24—41no—
826C24—41no—
827C24—41no—
828C24—41no—
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
831C24C22×D411yescharacteristic
832#41—82no—
833#41—82no—
834#41—82no—
835#41—82no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—42no—
849C2×Q8—81no—
850C2×Q8—81no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
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—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—44no—
919C22×C4—44no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—41no—
923C22×C4—41no—
924C22×C4—41no—
925C22×C4—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—41no—
932C22×C4—41no—
933C22×C4—41no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C2×#4112yes—
952C22×C4C2×#4112yes—
953C22×C4H(5,𝔽2)12yes—
954C22×C4H(5,𝔽2)12yes—
955C22×C4C2511yescharacteristic
956Q16—82no—
957SD16—82no—
958SD16—82no—
959D8—82no—
960M16—44no—
961M16—44no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—44no—
983C2×C8—44no—
984C2×C8C2×#4112yes—
985C2×C8C2×#4112yes—
986C2×C8C2×#4112yes—
987C2×C8C2×#4112yes—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—41no—
1096C42—41no—
1097C42—41no—
1098C42—41no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—42no—
1103C42—81no—
1104C42—81no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—44no—
1125C23—44no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—82no—
1141C23—82no—
1142C23—82no—
1143C23—82no—
1144C23—82no—
1145C23#53212yes—
1146C23#53412yes—
1147C23C23×D411yescharacteristic
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—162no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—84no—
1166D4—84no—
1167D4—84no—
1168D4—84no—
1169D4—162no—
1170D4—162no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
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—21no—
1210C2×C4—44no—
1211C2×C4—44no—
1212C2×C4—44no—
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—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—84no—
1260C2×C4—82no—
1261C2×C4—82no—
1262C2×C4—82no—
1263C2×C4—82no—
1264C2×C4—162no—
1265C2×C4#53212yes—
1266C2×C4#53412yes—
1267C2×C4C22×#4111yescharacteristic
1268C2×C4C22×#4111yescharacteristic
1269C2×C4C2×H(5,𝔽2)11yescharacteristic
1270C2×C4C2×H(5,𝔽2)11yescharacteristic
1271C2×C4#58511yescharacteristic
1272C2×C4#58511yescharacteristic
1273C8—22no—
1274C8—22no—
1275C8—22no—
1276C8—22no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—88no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22C2×#53211yescharacteristic
1318C22C2×#53411yescharacteristic
1319C22#344911yescharacteristic
1320C22#358411yescharacteristic
1321C22#358411yescharacteristic
1322C22#358511yescharacteristic
1323C22#358611yescharacteristic
1324C4—22no—
1325C4—22no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4#351311yescharacteristic
1350C4#351311yescharacteristic
1351C4#351311yescharacteristic
1352C4#351311yescharacteristic
1353C2—42no—
1354C2—42no—
1355C2—81no—
1356C2—161no—
1357C2—161no—
1358C2#3506411yescharacteristic
1359C2#6068211yescharacteristic
1360C2#6070311yescharacteristic
1361C2#6076111yescharacteristic
1362C2#6076711yescharacteristic
1363C2#6098511yescharacteristic
1364C2#6098711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24388C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35260C2semidirect
2. #34635C2semidirect
3. #33142C2semidirect
4. #33140C2semidirect
5. #33139C2semidirect
6. #33137C2semidirect
7. #30374C2semidirect
8. #30368C2semidirect
9. #30332C2semidirect
10. #30330C2semidirect
11. #29475C2semidirect
12. #29472C2semidirect
13. #29471C2semidirect
14. #29468C2semidirect
15. #29339C2semidirect
16. #29299C2semidirect
17. #29113C2semidirect
18. #28309C2semidirect
19. #27874C2semidirect
20. #27873C2semidirect
21. #25514C2semidirect
22. #25513C2semidirect
23. #24561C2semidirect
24. #24555C2semidirect
26. #24383C2semidirect
27. #22083C2semidirect
28. #22080C2semidirect
29. #22051C2semidirect
30. #22042C2semidirect
31. #20379C2semidirect
89. #2101C22semidirect
90. #2101C22semidirect
91. #2097C22semidirect
92. #2092C22semidirect
93. #2084C22semidirect
94. #2083C22semidirect
99. #2072C22semidirect
100. #2071C22semidirect
101. #2058C22semidirect
102. #2057C22semidirect
103. #2042C22semidirect
104. #2042C22semidirect
113. #2024C22semidirect
114. #2023C22semidirect
115. #2015C22semidirect
116. #2012C22semidirect
121. #1973C22semidirect
122. #1972C22semidirect
123. #1970C22semidirect
124. #1969C22semidirect
125. #1969C22semidirect
126. #1968C22semidirect
127. #1968C22semidirect
128. #1968C22semidirect
129. #1944C22semidirect
130. #1943C22semidirect
131. #1942C22semidirect
132. #1942C22semidirect
133. #1942C22semidirect
134. #1941C22semidirect
135. #1941C22semidirect
136. #1941C22semidirect
137. #1936C22semidirect
138. #1936C22semidirect
139. #1936C22semidirect
140. #1936C22semidirect
141. #1936C22semidirect
142. #1935C22semidirect
143. #1935C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
146. #1935C22semidirect
147. #1935C22semidirect
148. #1935C22semidirect
149. #1934C22semidirect
150. #1934C22semidirect
151. #1934C22semidirect
152. #1933C22semidirect
153. #1927C22semidirect
154. #1927C22semidirect
155. #1925C22semidirect
156. #1925C22semidirect
157. #1921C22semidirect
158. #1921C22semidirect
159. #1919C22semidirect
160. #1919C22semidirect
169. #1880C22semidirect
170. #1879C22semidirect
171. #1878C22semidirect
172. #1877C22semidirect
177. #1865C22semidirect
178. #1864C22semidirect
179. #1863C22semidirect
180. #1862C22semidirect

Maximal subgroups

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

subgroupindex
#352602
#346352
#331422
#331402
#331392
#331372
#303742
#303682
#303322
#303302
#294752
#294722
#294712
#294682
#293392
#292992
#291132
#283092
#278742
#278732
#255142
#255132
#245612
#245552
#243882
#243832
#220832
#220802
#220512
#220422
#203792