Finite Group Databasebeta

← #6783006

Subgroups — #6783006

Order 512.

1708 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#36386C211yesmaximal, characteristic
2#36304C211yesmaximal, characteristic, complemented
3#33053C211yesmaximal, characteristic, complemented
4#32445C211yesmaximal, characteristic, complemented
5#32185C211yesmaximal, characteristic, complemented
6#32073C211yesmaximal, characteristic, complemented
7#31959C211yesmaximal, characteristic, complemented
8#31537C211yesmaximal, characteristic, complemented
9#31007C211yesmaximal, characteristic, complemented
10#30897C211yesmaximal, characteristic, complemented
11#30540C211yesmaximal, characteristic, complemented
12#30347C211yesmaximal, characteristic, complemented
13#30323C211yesmaximal, characteristic, complemented
14#29563C211yesmaximal, characteristic, complemented
15#29502C211yesmaximal, characteristic, complemented
16#29110C211yesmaximal, characteristic, complemented
17#28313C211yesmaximal, characteristic, complemented
18#24657C211yesmaximal, characteristic, complemented
19#24577C211yesmaximal, characteristic, complemented
20#24529C211yesmaximal, characteristic, complemented
21#24511C211yesmaximal, characteristic, complemented
22#24477C211yesmaximal, characteristic, complemented
23#24357C211yesmaximal, characteristic, complemented
24#24094C211yesmaximal, characteristic, complemented
25#24038C211yesmaximal, characteristic
26#23967C211yesmaximal, characteristic, complemented
27#23852C211yesmaximal, characteristic
28#22156C211yesmaximal, characteristic, complemented
29#22048C211yesmaximal, characteristic, complemented
30C2×#1973C211yesmaximal, characteristic, complemented
31#21107C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#546C2211yescharacteristic
35C2×#491C2211yescharacteristic, complemented
36C2×#483C2211yescharacteristic
37C2×#483C2211yescharacteristic
38C2×#464C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#451C2211yescharacteristic
43C2×#451C2211yescharacteristic
44C2×#432C2211yescharacteristic, complemented
45C22×#107C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#97C2211yescharacteristic
49#2863C2211yescharacteristic, complemented
50#2861C2211yescharacteristic
51#2857C2211yescharacteristic
52#2855C2211yescharacteristic, complemented
53#2851C2211yescharacteristic
54#2850C2211yescharacteristic
55#2588—21no—
56#2566C2211yescharacteristic
57#2559—21no—
58#2559—21no—
59#2558—21no—
60#2558—21no—
61#2545C2211yescharacteristic
62#2534—21no—
63#2534—21no—
64#2527—21no—
65#2523—21no—
66#2520—21no—
67#2514C2211yescharacteristic, complemented
68#2503C2211yescharacteristic
69#2500C2211yescharacteristic
70#2493—21no—
71#2489C2211yescharacteristic, complemented
72#2486C2211yescharacteristic
73#2453C2211yescharacteristic, complemented
74#2435C2211yescharacteristic
75#2432C2211yescharacteristic
76#2421C2211yescharacteristic, complemented
77#2419—21no—
78#2409C2211yescharacteristic
79#2359—21no—
80#2344C2211yescharacteristic
81#2343—21no—
82#2342—21no—
83#2342—21no—
84Q8×C22⋊C4C2211yescharacteristic
85C4×#124C2211yescharacteristic
86C4×C22⋊Q8C2211yescharacteristic, complemented
87#2297C2211yescharacteristic
88#2295C2211yescharacteristic, complemented
89C2×#391C2211yescharacteristic
90C2×#390C2211yescharacteristic
91C42×D4C2211yescharacteristic
92#2096C2211yescharacteristic, complemented
93#2096C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2074C2211yescharacteristic, complemented
97#2074C2211yescharacteristic, complemented
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2068C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic
104#2059C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2056C2211yescharacteristic, complemented
107#2056C2211yescharacteristic, complemented
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2036C2211yescharacteristic, complemented
115#2036C2211yescharacteristic, complemented
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2026C2211yescharacteristic, complemented
119#2026C2211yescharacteristic, complemented
120#2025C2211yescharacteristic
121#2025C2211yescharacteristic
122#2016C2211yescharacteristic, complemented
123#2016C2211yescharacteristic, complemented
124#2015C2211yescharacteristic
125#2015C2211yescharacteristic
126#2015C2211yescharacteristic
127#2015C2211yescharacteristic
128#2001C2211yescharacteristic, complemented
129#2001C2211yescharacteristic, complemented
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#1992C2211yescharacteristic, complemented
133#1983C2211yescharacteristic
134#1983C2211yescharacteristic
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic
138#1973C2211yescharacteristic
139#1973C2211yescharacteristic
140#1973C2211yescharacteristic
141#1973C2211yescharacteristic
142#1973C2211yescharacteristic
143#1971C2211yescharacteristic, complemented
144#1971C2211yescharacteristic, complemented
145#1971C2211yescharacteristic, complemented
146#1971C2211yescharacteristic, complemented
147#1960C2211yescharacteristic, complemented
148#1949C2211yescharacteristic, complemented
149#1949C2211yescharacteristic, complemented
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic
152#1936C2211yescharacteristic
153#1936C2211yescharacteristic
154#1935C2211yescharacteristic, complemented
155#1935C2211yescharacteristic, complemented
156#1935C2211yescharacteristic, complemented
157#1935C2211yescharacteristic, complemented
158#1928C2211yescharacteristic, complemented
159#1928C2211yescharacteristic, complemented
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1924C2211yescharacteristic, complemented
163#1924C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1892C2211yescharacteristic
167#1892C2211yescharacteristic
168#1892C2211yescharacteristic
169#1892C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1873C2211yescharacteristic, complemented
179#1873C2211yescharacteristic, complemented
180#1869C2211yescharacteristic
181#1869C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1863C2211yescharacteristic, complemented
185#1863C2211yescharacteristic, complemented
186#1854C2211yescharacteristic, complemented
187#1854C2211yescharacteristic, complemented
188#1850C2211yescharacteristic
189#1850C2211yescharacteristic
190#1836C2211yescharacteristic, complemented
191#1823C2211yescharacteristic
192#1823C2211yescharacteristic
193#1805C2211yescharacteristic, complemented
194#1805C2211yescharacteristic, complemented
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1767C2211yescharacteristic, complemented
200#1749C2211yescharacteristic
201#1749C2211yescharacteristic, complemented
202#1745C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×SD16—24no—
211C22×SD16—42no—
212C22×SD16—42no—
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#552—42no—
220#552—42no—
221#546—42no—
222#546—42no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×#126—21no—
225C2×#125—21no—
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#123—21no—
232C2×#123—21no—
233C2×#123—21no—
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×#121—21no—
240C2×#121C2311yescharacteristic
241C2×#120—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4D411yescharacteristic
246C2×C4×D4D411yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117—21no—
250C2×#117—21no—
251C2×#117C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257C22×C42C2311yescharacteristic
258C22×C42C2311yescharacteristic
259#491—42no—
260#483—42no—
261#483—42no—
262#464—24no—
263#464—42no—
264#452—24no—
265#452—42no—
266#451—42no—
267#451—42no—
268#432—42no—
269C2×#107—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×#103—42no—
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×#103C2311yescharacteristic
303C2×#102—42no—
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×#97—42no—
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329#401—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#398—21no—
337#398—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#395—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#393—21no—
353#391—21no—
354#391—21no—
355#391—21no—
356#391—21no—
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#390—21no—
370#390—21no—
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#389—21no—
378#389—21no—
379#389—21no—
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#388—21no—
387#388—21no—
388#388—21no—
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#387—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#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—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#384C2311yescharacteristic
430#383—21no—
431#383—21no—
432#382—21no—
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#381—21no—
437#381—21no—
438#381—21no—
439#381—21no—
440#381—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#379—21no—
449#379—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4D411yescharacteristic
453C4×C4⋊C4D411yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
464C4×C22⋊C4D411yescharacteristic
465C4×C22⋊C4D411yescharacteristic
466C4×C22⋊C4D411yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
469#376—21no—
470C2×#95—21no—
471C2×#95—21no—
472C43C2311yescharacteristic
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#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8—22no—
508C22×Q8—22no—
509C22×Q8—22no—
510C22×Q8—41no—
511C22×Q8—41no—
512C22×Q8—41no—
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×D411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4C2×D411yescharacteristic
535C23×C4C2×D411yescharacteristic
536C23×C4C2×D411yescharacteristic
537C23×C4C2×D411yescharacteristic
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C2×Q16—22no—
541C2×Q16—22no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×Q16—41no—
545C2×Q16—41no—
546C2×Q16—41no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×SD16—416no—
564C2×SD16#4114yes—
565C22×C8—22no—
566C22×C8—22no—
567C22×C8—22no—
568C22×C8—22no—
569C22×C8—41no—
570C22×C8—41no—
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C4⋊Q8—41no—
580C4⋊Q8—41no—
581#126—44no—
582#125—41no—
583#125—41no—
584#125—41no—
585#125—41no—
586#125—44no—
587#124—22no—
588#124—41no—
589#124—41no—
590#124—41no—
591#124—41no—
592#124—41no—
593#123—44no—
594#123—44no—
595#123—44no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606#121—44no—
607#121—41no—
608#121—41no—
609#120—44no—
610C4×Q8—22no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×D4—22no—
617C4×D4—22no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—42no—
621C4×D4—42no—
622#117—44no—
623#117—44no—
624#117—41no—
625#117—41no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—22no—
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—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
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—44no—
698C2×C22⋊C4—44no—
699C2×C22⋊C4—44no—
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—41no—
713C2×C42—41no—
714C2×C42—41no—
715C2×C42—41no—
716C2×C42C2×D411yescharacteristic
717C2×C42C2×D411yescharacteristic
718C2×C42C2×D411yescharacteristic
719C2×C42C2×D411yescharacteristic
720C2×C42C2×D411yescharacteristic
721C2×C42C2×D411yescharacteristic
722C2×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#107—41no—
730#107—41no—
731#107—41no—
732#107—41no—
733#106—41no—
734#106—41no—
735#106—41no—
736#106—41no—
737C4⋊C8—22no—
738C4⋊C8—22no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—41no—
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#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#102—22no—
762#102—22no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773C22⋊C8—22no—
774C22⋊C8—22no—
775C22⋊C8—22no—
776C22⋊C8—22no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779#97—22no—
780#97—22no—
781#97—41no—
782#97—41no—
783#97—41no—
784#97—41no—
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—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833C24—21no—
834C24—21no—
835C24—42no—
836C24—42no—
837C24—42no—
838C24—42no—
839C24—81no—
840C24—81no—
841C24—81no—
842C24C22×D411yescharacteristic
843C24C22×D411yescharacteristic
844#41—82no—
845#41—82no—
846#41—82no—
847#41—82no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—42no—
872C2×Q8—44no—
873C2×Q8—44no—
874C2×Q8—42no—
875C2×Q8—81no—
876C2×Q8—82no—
877C2×Q8—82no—
878C2×Q8C2×#4112yes—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—82no—
901C2×D4—82no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4C2×#4112yes—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—41no—
936C22×C4—41no—
937C22×C4—41no—
938C22×C4—41no—
939C22×C4—41no—
940C22×C4—41no—
941C22×C4—41no—
942C22×C4—41no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4H(5,𝔽2)12yes—
971C22×C4H(5,𝔽2)12yes—
972C22×C4C2511yescharacteristic
973Q16—82no—
974Q16—82no—
975Q16—82no—
976Q16—82no—
977SD16—44no—
978SD16—44no—
979SD16—44no—
980SD16—44no—
981C2×C8—28no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—44no—
1005C2×C8C2×#4112yes—
1006C2×C8H(5,𝔽2)12yes—
1007C4⋊C4—22no—
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—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—41no—
1029C4⋊C4—41no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—41no—
1101C42—41no—
1102C42—41no—
1103C42—41no—
1104C42—41no—
1105C42—41no—
1106C42—41no—
1107C42—41no—
1108C42—42no—
1109C42—42no—
1110C42—42no—
1111C42—42no—
1112C42—42no—
1113C42—81no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—22no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
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—84no—
1140C23—84no—
1141C23—84no—
1142C23—84no—
1143C23—162no—
1144C23—162no—
1145C23—162no—
1146C23#53512yes—
1147C23#57512yes—
1148C23#57512yes—
1149C23C23×D411yescharacteristic
1150Q8—22no—
1151Q8—22no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—84no—
1167D4—22no—
1168D4—22no—
1169D4—44no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—84no—
1177D4—84no—
1178D4—162no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
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—22no—
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—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
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—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—82no—
1265C2×C4—82no—
1266C2×C4—82no—
1267C2×C4—82no—
1268C2×C4—84no—
1269C2×C4—84no—
1270C2×C4—84no—
1271C2×C4—84no—
1272C2×C4—162no—
1273C2×C4#53512yes—
1274C2×C4C22×#4111yescharacteristic
1275C2×C4C2×H(5,𝔽2)11yescharacteristic
1276C2×C4C2×H(5,𝔽2)11yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4#58511yescharacteristic
1279C2×C4#58511yescharacteristic
1280C8—22no—
1281C8—22no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—41no—
1295C22—41no—
1296C22—42no—
1297C22—42no—
1298C22—41no—
1299C22—42no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—168no—
1316C22#321914yes—
1317C22C2×#53511yescharacteristic
1318C22D4×#4111yescharacteristic
1319C22#349611yescharacteristic
1320C22C2×#57511yescharacteristic
1321C22C2×#57511yescharacteristic
1322C22#358611yescharacteristic
1323C22#358611yescharacteristic
1324C4—22no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—42no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
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—81no—
1350C4#349011yescharacteristic
1351C4#351311yescharacteristic
1352C4#354211yescharacteristic
1353C4#354511yescharacteristic
1354C2—24no—
1355C2—81no—
1356C2—82no—
1357C2—161no—
1358C2#3842011yescharacteristic
1359C2C2×#321911yescharacteristic
1360C2#6082611yescharacteristic
1361C2#6145511yescharacteristic
1362C2#6145511yescharacteristic
1363C2#6229711yescharacteristic
1364C2#6229711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36304C2semidirect
3. #33053C2semidirect
4. #32445C2semidirect
5. #32185C2semidirect
6. #32073C2semidirect
7. #31959C2semidirect
8. #31537C2semidirect
9. #31007C2semidirect
10. #30897C2semidirect
11. #30540C2semidirect
12. #30347C2semidirect
13. #30323C2semidirect
14. #29563C2semidirect
15. #29502C2semidirect
16. #29110C2semidirect
17. #28313C2semidirect
18. #24657C2semidirect
19. #24577C2semidirect
20. #24529C2semidirect
21. #24511C2semidirect
22. #24477C2semidirect
23. #24357C2semidirect
24. #24094C2semidirect
26. #23967C2semidirect
28. #22156C2semidirect
29. #22048C2semidirect
30. C2×#1973C2semidirect
31. #21107C2semidirect
35. C2×#491C22semidirect
44. C2×#432C22semidirect
49. #2863C22semidirect
52. #2855C22semidirect
67. #2514C22semidirect
71. #2489C22semidirect
73. #2453C22semidirect
76. #2421C22semidirect
86. C4×C22⋊Q8C22semidirect
88. #2295C22semidirect
92. #2096C22semidirect
93. #2096C22semidirect
94. #2085C22semidirect
95. #2085C22semidirect
96. #2074C22semidirect
97. #2074C22semidirect
100. #2068C22semidirect
101. #2068C22semidirect
104. #2059C22semidirect
105. #2059C22semidirect
106. #2056C22semidirect
107. #2056C22semidirect
114. #2036C22semidirect
115. #2036C22semidirect
118. #2026C22semidirect
119. #2026C22semidirect
122. #2016C22semidirect
123. #2016C22semidirect
128. #2001C22semidirect
129. #2001C22semidirect
132. #1992C22semidirect
143. #1971C22semidirect
144. #1971C22semidirect
145. #1971C22semidirect
146. #1971C22semidirect
147. #1960C22semidirect
148. #1949C22semidirect
149. #1949C22semidirect
154. #1935C22semidirect
155. #1935C22semidirect
156. #1935C22semidirect
157. #1935C22semidirect
158. #1928C22semidirect
159. #1928C22semidirect
162. #1924C22semidirect
163. #1924C22semidirect
164. #1917C22semidirect
165. #1917C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
178. #1873C22semidirect
179. #1873C22semidirect
184. #1863C22semidirect
185. #1863C22semidirect
186. #1854C22semidirect
187. #1854C22semidirect
190. #1836C22semidirect
193. #1805C22semidirect
194. #1805C22semidirect
199. #1767C22semidirect
201. #1749C22semidirect
202. #1745C22semidirect

Maximal subgroups

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

subgroupindex
#363862
#363042
#330532
#324452
#321852
#320732
#319592
#315372
#310072
#308972
#305402
#303472
#303232
#295632
#295022
#291102
#283132
#246572
#245772
#245292
#245112
#244772
#243572
#240942
#240382
#239672
#238522
#221562
#220482
C2×#19732
#211072