Finite Group Databasebeta

← #6653548

Subgroups — #6653548

Order 512.

1580 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37385C211yesmaximal, characteristic, complemented
2#35240C211yesmaximal, characteristic
3#32959C211yesmaximal, characteristic
4#32905C211yesmaximal, characteristic
5#32448C211yesmaximal, characteristic, complemented
6#32428C211yesmaximal, characteristic, complemented
7#32187C211yesmaximal, characteristic, complemented
8#32171C211yesmaximal, characteristic, complemented
9#32074C211yesmaximal, characteristic, complemented
10#32052C211yesmaximal, characteristic, complemented
11#31956C211yesmaximal, characteristic, complemented
12#31936C211yesmaximal, characteristic, complemented
13#31540C211yesmaximal, characteristic, complemented
14#31520C211yesmaximal, characteristic, complemented
15#31012C211yesmaximal, characteristic
16#30996C211yesmaximal, characteristic
17#30901C211yesmaximal, characteristic, complemented
18#30885C211yesmaximal, characteristic, complemented
19#30543C211yesmaximal, characteristic
20#30531C211yesmaximal, characteristic
21#29695C211yesmaximal, characteristic, complemented
22#29664C211yesmaximal, characteristic, complemented
23#29151C211yesmaximal, characteristic, complemented
24#28730C211yesmaximal, characteristic, complemented
25#28390C211yesmaximal, characteristic, complemented
26#28390C211yesmaximal, characteristic, complemented
27#28293C211yesmaximal, characteristic, complemented
28#28258C211yesmaximal, characteristic, complemented
29#28215C211yesmaximal, characteristic, complemented
30#28168C211yesmaximal, characteristic, complemented
31#21928C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#488C2211yescharacteristic
36C2×#479C2211yescharacteristic, complemented
37C2×#479C2211yescharacteristic, complemented
38C2×#478C2211yescharacteristic
39C2×#478C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#464C2211yescharacteristic
42C2×#462C2211yescharacteristic, complemented
43C2×#462C2211yescharacteristic, complemented
44C2×#461C2211yescharacteristic
45C2×#461C2211yescharacteristic
46C2×#450C2211yescharacteristic
47C2×#450C2211yescharacteristic
48#2857C2211yescharacteristic
49#2851C2211yescharacteristic
50#2848—21no—
51#2848—21no—
52#2774—21no—
53#2767—21no—
54#2766—21no—
55#2758—21no—
56#2747—21no—
57#2745—21no—
58#2742—21no—
59#2738—21no—
60#2660C2211yescharacteristic, complemented
61#2642C2211yescharacteristic, complemented
62#2633—21no—
63#2633—21no—
64#2547C2211yescharacteristic
65#2547C2211yescharacteristic
66#2542C2211yescharacteristic
67#2542C2211yescharacteristic
68#2536—21no—
69#2536—21no—
70#2514C2211yescharacteristic, complemented
71#2511C2211yescharacteristic, complemented
72#2502C2211yescharacteristic
73#2502C2211yescharacteristic
74#2492C2211yescharacteristic
75#2489C2211yescharacteristic
76#2482—21no—
77#2482—21no—
78#2453C2211yescharacteristic, complemented
79#2451C2211yescharacteristic, complemented
80#2435C2211yescharacteristic
81#2435C2211yescharacteristic
82#2423C2211yescharacteristic
83#2421C2211yescharacteristic
84#2330C2211yescharacteristic, complemented
85#2327C2211yescharacteristic, complemented
86#2326C2211yescharacteristic
87#2326C2211yescharacteristic
88#2326C2211yescharacteristic
89#2326C2211yescharacteristic
90#2283C2211yescharacteristic
91#2096C2211yescharacteristic, complemented
92#2096C2211yescharacteristic, complemented
93#2095C2211yescharacteristic, complemented
94#2095C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2074C2211yescharacteristic, complemented
98#2073C2211yescharacteristic
99#2072C2211yescharacteristic, complemented
100#2072C2211yescharacteristic, complemented
101#2072C2211yescharacteristic, complemented
102#2071C2211yescharacteristic
103#2068C2211yescharacteristic, complemented
104#2067C2211yescharacteristic
105#2066C2211yescharacteristic, complemented
106#2065C2211yescharacteristic
107#2058C2211yescharacteristic, complemented
108#2057C2211yescharacteristic, complemented
109#2056C2211yescharacteristic, complemented
110#2056C2211yescharacteristic, complemented
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2043C2211yescharacteristic, complemented
114#2043C2211yescharacteristic, complemented
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2026C2211yescharacteristic, complemented
122#2025C2211yescharacteristic
123#2024C2211yescharacteristic, complemented
124#2024C2211yescharacteristic, complemented
125#2024C2211yescharacteristic, complemented
126#2023C2211yescharacteristic
127#2016C2211yescharacteristic, complemented
128#2016C2211yescharacteristic, complemented
129#2015C2211yescharacteristic
130#2015C2211yescharacteristic
131#2015C2211yescharacteristic
132#2015C2211yescharacteristic
133#2015C2211yescharacteristic
134#2015C2211yescharacteristic
135#2001C2211yescharacteristic
136#2001C2211yescharacteristic
137#2001C2211yescharacteristic
138#2001C2211yescharacteristic
139#1992C2211yescharacteristic, complemented
140#1990C2211yescharacteristic, complemented
141#1983C2211yescharacteristic
142#1983C2211yescharacteristic
143#1973C2211yescharacteristic
144#1973C2211yescharacteristic
145#1971C2211yescharacteristic, complemented
146#1971C2211yescharacteristic, complemented
147#1969C2211yescharacteristic, complemented
148#1969C2211yescharacteristic, complemented
149#1968C2211yescharacteristic
150#1968C2211yescharacteristic
151#1959C2211yescharacteristic
152#1958C2211yescharacteristic
153#1948C2211yescharacteristic, complemented
154#1947C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1926C2211yescharacteristic
158#1925C2211yescharacteristic
159#1924C2211yescharacteristic
160#1924C2211yescharacteristic
161#1923C2211yescharacteristic
162#1923C2211yescharacteristic
163#1917C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1878C2211yescharacteristic, complemented
170#1878C2211yescharacteristic, complemented
171#1877C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1872C2211yescharacteristic
176#1872C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1853C2211yescharacteristic
182#1852C2211yescharacteristic
183#1843C2211yescharacteristic, complemented
184#1836C2211yescharacteristic, complemented
185#1834C2211yescharacteristic, complemented
186#1832C2211yescharacteristic, complemented
187#1805C2211yescharacteristic, complemented
188#1805C2211yescharacteristic, complemented
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1803C2211yescharacteristic, complemented
192#1803C2211yescharacteristic, complemented
193#1803C2211yescharacteristic, complemented
194#1803C2211yescharacteristic, complemented
195#1802C2211yescharacteristic
196#1802C2211yescharacteristic
197#1797C2211yescharacteristic
198#1797C2211yescharacteristic
199#1786C2211yescharacteristic
200#1786C2211yescharacteristic
201#1768C2211yescharacteristic, complemented
202#1768C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C24×C4—21no—
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213#533—42no—
214#533—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#125—21no—
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C4×Q8—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4—42no—
243C2×C4×D4—42no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117—21no—
249C22×C4⋊C4C2311yescharacteristic
250C22×C22⋊C4—21no—
251C22×C42C2311yescharacteristic
252#489—42no—
253#488—42no—
254#479—42no—
255#479—42no—
256#478—42no—
257#478—42no—
258#464—42no—
259#464—42no—
260#462—42no—
261#462—42no—
262#461—42no—
263#461—42no—
264#450—42no—
265#450—42no—
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#401—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#399—21no—
335#399—21no—
336#399—21no—
337#399—21no—
338#399—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#395—21no—
355#395—21no—
356#395—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#393—21no—
362#391—21no—
363#391—21no—
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#383—21no—
437#383D411yescharacteristic
438#383D411yescharacteristic
439#382—21no—
440#382D411yescharacteristic
441#382D411yescharacteristic
442#382C2311yescharacteristic
443#382C2311yescharacteristic
444#381D411yescharacteristic
445#381D411yescharacteristic
446#380—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380—21no—
451#380—21no—
452#380D411yescharacteristic
453#380D411yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#379—21no—
457#379—21no—
458#379—21no—
459#379—21no—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466#376C2311yescharacteristic
467#376C2311yescharacteristic
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#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—44no—
518C23×C4—82no—
519C23×C4—82no—
520C23×C4C2×D411yescharacteristic
521C23×C4C2×D411yescharacteristic
522C23×C4C2411yescharacteristic
523C2×Q16—41no—
524C2×Q16—41no—
525C2×Q16—41no—
526C2×Q16—41no—
527C2×Q16—41no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×Q16—41no—
531C2×Q16—41no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×Q16—41no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C4⋊Q8—22no—
556C4⋊Q8—22no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563#125—22no—
564#125—22no—
565#125—41no—
566#125—41no—
567#125—44no—
568#124—22no—
569#124—22no—
570#124—22no—
571#124—22no—
572#124—41no—
573#124—41no—
574#124—41no—
575#124—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—44no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—82no—
586C22⋊Q8—82no—
587C22⋊Q8—82no—
588C22⋊Q8—82no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—44no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×Q8—41no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—44no—
607C4×D4—44no—
608#117—44no—
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⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
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—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
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×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—44no—
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C42—22no—
692C2×C42—22no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42C2×D411yescharacteristic
700C2×C42C2×D411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707#107—41no—
708#107—41no—
709#107—41no—
710#107—41no—
711#106—41no—
712#106—41no—
713#106—41no—
714#106—41no—
715C4⋊C8—22no—
716C4⋊C8—22no—
717C4⋊C8—22no—
718C4⋊C8—22no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721C4⋊C8—41no—
722C4⋊C8—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755C22⋊C8—41no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758C22⋊C8—41no—
759#97—41no—
760#97—41no—
761C4×C8—41no—
762C4×C8—41no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
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#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#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815C24—21no—
816C24—21no—
817C24—42no—
818C24—42no—
819C24—42no—
820C24—42no—
821C24—42no—
822C24—81no—
823C24—81no—
824C24C22×D411yescharacteristic
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
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—21no—
849C2×Q8—42no—
850C2×Q8—42no—
851C2×Q8—42no—
852C2×Q8—81no—
853C2×Q8—81no—
854C2×Q8—81no—
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—21no—
864C2×D4—21no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4H(5,𝔽2)12yes—
873C2×D42−1+412yes—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
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—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—41no—
899C22×C4—41no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—816no—
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×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C2511yescharacteristic
930Q16—82no—
931Q16—82no—
932Q16—82no—
933Q16—82no—
934SD16—82no—
935SD16—82no—
936SD16—82no—
937SD16—82no—
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×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C4⋊C4—22no—
963C4⋊C4—22no—
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—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C22⋊C4—22no—
1022C22⋊C4—22no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
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—
1051C42—22no—
1052C42—22no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—42no—
1064C42—42no—
1065C42—81no—
1066C42—81no—
1067C42—81no—
1068C42—81no—
1069C42H(5,𝔽2)12yes—
1070C42H(5,𝔽2)12yes—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—22no—
1078C23—22no—
1079C23—48no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—84no—
1093C23—84no—
1094C23—84no—
1095C23—84no—
1096C23—84no—
1097C23—84no—
1098C23#57812yes—
1099C23C23×D411yescharacteristic
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—41no—
1115Q8—41no—
1116Q8—84no—
1117Q8—162no—
1118D4—22no—
1119D4—22no—
1120D4—22no—
1121D4—22no—
1122D4—48no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—44no—
1164C2×C4—44no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—84no—
1212C2×C4—84no—
1213C2×C4—84no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4#53512yes—
1217C2×C4#53512yes—
1218C2×C4#57712yes—
1219C2×C4C2×H(5,𝔽2)11yescharacteristic
1220C2×C4C2×H(5,𝔽2)11yescharacteristic
1221C2×C4C2×H(5,𝔽2)11yescharacteristic
1222C2×C4C2×2−1+411yescharacteristic
1223C2×C4#58511yescharacteristic
1224C2×C4#58511yescharacteristic
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C8—41no—
1229C8—41no—
1230C8—41no—
1231C8—41no—
1232C8—41no—
1233C22—22no—
1234C22—22no—
1235C22—22no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—816no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22C2×#53511yescharacteristic
1256C22#348811yescharacteristic
1257C22#348911yescharacteristic
1258C22C2×#57711yescharacteristic
1259C22C2×#57811yescharacteristic
1260C22#358511yescharacteristic
1261C22#358611yescharacteristic
1262C4—22no—
1263C4—22no—
1264C4—22no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4#353611yescharacteristic
1290C4#354011yescharacteristic
1291C4#354111yescharacteristic
1292C4#354211yescharacteristic
1293C2—42no—
1294C2—82no—
1295C2—82no—
1296C2#3727111yescharacteristic
1297C2#6081211yescharacteristic
1298C2#6081411yescharacteristic
1299C2#6205411yescharacteristic
1300C2#6207611yescharacteristic
1301C2#6216511yescharacteristic
1302C2#6218911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37385C2semidirect
5. #32448C2semidirect
6. #32428C2semidirect
7. #32187C2semidirect
8. #32171C2semidirect
9. #32074C2semidirect
10. #32052C2semidirect
11. #31956C2semidirect
12. #31936C2semidirect
13. #31540C2semidirect
14. #31520C2semidirect
17. #30901C2semidirect
18. #30885C2semidirect
21. #29695C2semidirect
22. #29664C2semidirect
23. #29151C2semidirect
24. #28730C2semidirect
25. #28390C2semidirect
26. #28390C2semidirect
27. #28293C2semidirect
28. #28258C2semidirect
29. #28215C2semidirect
30. #28168C2semidirect
31. #21928C2semidirect
36. C2×#479C22semidirect
37. C2×#479C22semidirect
42. C2×#462C22semidirect
43. C2×#462C22semidirect
60. #2660C22semidirect
61. #2642C22semidirect
70. #2514C22semidirect
71. #2511C22semidirect
78. #2453C22semidirect
79. #2451C22semidirect
84. #2330C22semidirect
85. #2327C22semidirect
91. #2096C22semidirect
92. #2096C22semidirect
93. #2095C22semidirect
94. #2095C22semidirect
95. #2084C22semidirect
96. #2083C22semidirect
97. #2074C22semidirect
99. #2072C22semidirect
100. #2072C22semidirect
101. #2072C22semidirect
103. #2068C22semidirect
105. #2066C22semidirect
107. #2058C22semidirect
108. #2057C22semidirect
109. #2056C22semidirect
110. #2056C22semidirect
113. #2043C22semidirect
114. #2043C22semidirect
121. #2026C22semidirect
123. #2024C22semidirect
124. #2024C22semidirect
125. #2024C22semidirect
127. #2016C22semidirect
128. #2016C22semidirect
139. #1992C22semidirect
140. #1990C22semidirect
145. #1971C22semidirect
146. #1971C22semidirect
147. #1969C22semidirect
148. #1969C22semidirect
153. #1948C22semidirect
154. #1947C22semidirect
155. #1928C22semidirect
156. #1927C22semidirect
163. #1917C22semidirect
164. #1917C22semidirect
165. #1916C22semidirect
166. #1916C22semidirect
169. #1878C22semidirect
170. #1878C22semidirect
183. #1843C22semidirect
184. #1836C22semidirect
185. #1834C22semidirect
186. #1832C22semidirect
187. #1805C22semidirect
188. #1805C22semidirect
191. #1803C22semidirect
192. #1803C22semidirect
193. #1803C22semidirect
194. #1803C22semidirect
201. #1768C22semidirect
202. #1768C22semidirect

Maximal subgroups

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

subgroupindex
#373852
#352402
#329592
#329052
#324482
#324282
#321872
#321712
#320742
#320522
#319562
#319362
#315402
#315202
#310122
#309962
#309012
#308852
#305432
#305312
#296952
#296642
#291512
#287302
#283902
#282932
#282582
#282152
#281682
#219282