Finite Group Databasebeta

← #6873994

Subgroups — #6873994

Order 512.

1693 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38041C211yesmaximal, characteristic, complemented
2#35522C211yesmaximal, characteristic, complemented
3#32962C211yesmaximal, characteristic, complemented
4#32465C211yesmaximal, characteristic, complemented
5#32463C211yesmaximal, characteristic, complemented
6#31801C211yesmaximal, characteristic, complemented
7#31786C211yesmaximal, characteristic, complemented
8#31681C211yesmaximal, characteristic, complemented
9#31680C211yesmaximal, characteristic, complemented
10#31036C211yesmaximal, characteristic, complemented
11#31016C211yesmaximal, characteristic, complemented
12#30023C211yesmaximal, characteristic, complemented
13#30007C211yesmaximal, characteristic, complemented
14#29476C211yesmaximal, characteristic, complemented
15#29468C211yesmaximal, characteristic, complemented
16#29247C211yesmaximal, characteristic, complemented
17#29234C211yesmaximal, characteristic, complemented
18#28276C211yesmaximal, characteristic, complemented
19#28191C211yesmaximal, characteristic, complemented
20#27887C211yesmaximal, characteristic, complemented
21#27636C211yesmaximal, characteristic, complemented
22#25481C211yesmaximal, characteristic, complemented
23#25477C211yesmaximal, characteristic, complemented
24#25027C211yesmaximal, characteristic, complemented
25#24974C211yesmaximal, characteristic, complemented
26#24128C211yesmaximal, characteristic, complemented
27#24116C211yesmaximal, characteristic, complemented
28#22533C211yesmaximal, characteristic, complemented
29#22090C211yesmaximal, characteristic, complemented
30#22081C211yesmaximal, characteristic, complemented
31#21458C211yesmaximal, characteristic, complemented
32C2×#547C2211yescharacteristic, complemented
33C2×#529C2211yescharacteristic
34C2×#518C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#480C2211yescharacteristic
37C2×#476C2211yescharacteristic
38C2×#474C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#446C2211yescharacteristic, complemented
41C2×#446C2211yescharacteristic, complemented
42C2×#442C2211yescharacteristic
43C2×C4×D8C2211yescharacteristic
44#2854C2211yescharacteristic, complemented
45#2723—21no—
46#2720—21no—
47#2718—21no—
48#2710—21no—
49#2628C2211yescharacteristic
50#2624C2211yescharacteristic, complemented
51#2580C2211yescharacteristic
52#2580C2211yescharacteristic, complemented
53#2567C2211yescharacteristic, complemented
54#2538C2211yescharacteristic
55#2537C2211yescharacteristic
56#2535C2211yescharacteristic
57#2501—21no—
58#2488—21no—
59#2487C2211yescharacteristic
60#2486C2211yescharacteristic
61#2485C2211yescharacteristic
62#2485C2211yescharacteristic
63#2480—21no—
64#2472—21no—
65#2467—21no—
66#2463—21no—
67#2460—21no—
68#2456—21no—
69#2430—21no—
70#2424—21no—
71#2418—21no—
72#2416C2211yescharacteristic
73#2414C2211yescharacteristic
74#2408C2211yescharacteristic
75#2408C2211yescharacteristic
76#2406—21no—
77#2352C2211yescharacteristic, complemented
78#2324C2211yescharacteristic
79#2324C2211yescharacteristic
80#2324C2211yescharacteristic
81#2317C2211yescharacteristic, complemented
82#2314C2211yescharacteristic
83C4×#121C2211yescharacteristic
84C4×#121C2211yescharacteristic
85C2×#389C2211yescharacteristic, complemented
86#2088C2211yescharacteristic, complemented
87#2088C2211yescharacteristic, complemented
88#2087C2211yescharacteristic, complemented
89#2086C2211yescharacteristic, complemented
90#2086C2211yescharacteristic, complemented
91#2086C2211yescharacteristic, complemented
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic, complemented
96#2077C2211yescharacteristic, complemented
97#2076C2211yescharacteristic
98#2076C2211yescharacteristic
99#2076C2211yescharacteristic, complemented
100#2076C2211yescharacteristic, complemented
101#2075C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic, complemented
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic, complemented
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic, complemented
115#2034C2211yescharacteristic, complemented
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic, complemented
121#2033C2211yescharacteristic, complemented
122#1999C2211yescharacteristic
123#1999C2211yescharacteristic
124#1999C2211yescharacteristic
125#1999C2211yescharacteristic
126#1993C2211yescharacteristic, complemented
127#1990C2211yescharacteristic, complemented
128#1972C2211yescharacteristic
129#1970C2211yescharacteristic
130#1955C2211yescharacteristic
131#1955C2211yescharacteristic
132#1955C2211yescharacteristic
133#1955C2211yescharacteristic, complemented
134#1954C2211yescharacteristic
135#1954C2211yescharacteristic, complemented
136#1949C2211yescharacteristic, complemented
137#1947C2211yescharacteristic, complemented
138#1944C2211yescharacteristic, complemented
139#1943C2211yescharacteristic, complemented
140#1943C2211yescharacteristic, complemented
141#1943C2211yescharacteristic, complemented
142#1942C2211yescharacteristic, complemented
143#1941C2211yescharacteristic, complemented
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic, complemented
150#1936C2211yescharacteristic, complemented
151#1934C2211yescharacteristic
152#1926C2211yescharacteristic, complemented
153#1925C2211yescharacteristic, complemented
154#1921C2211yescharacteristic, complemented
155#1921C2211yescharacteristic, complemented
156#1920C2211yescharacteristic, complemented
157#1919C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1875C2211yescharacteristic
163#1875C2211yescharacteristic
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic
166#1874C2211yescharacteristic
167#1874C2211yescharacteristic
168#1874C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic, complemented
179#1853C2211yescharacteristic, complemented
180#1853C2211yescharacteristic, complemented
181#1852C2211yescharacteristic, complemented
182#1852C2211yescharacteristic, complemented
183#1852C2211yescharacteristic, complemented
184#1847C2211yescharacteristic, complemented
185#1835C2211yescharacteristic, complemented
186#1825C2211yescharacteristic, complemented
187#1823C2211yescharacteristic, complemented
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic, complemented
191#1802C2211yescharacteristic, complemented
192#1798C2211yescharacteristic
193#1798C2211yescharacteristic, complemented
194#1797C2211yescharacteristic, complemented
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1762C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic, complemented
202#1749C2211yescharacteristic, complemented
203C22×#41—21no—
204C23×D4C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207#547—42no—
208#547—42no—
209C2×C4⋊Q8C2311yescharacteristic
210#529—42no—
211#529—42no—
212C2×#126D411yescharacteristic
213C2×#126D411yescharacteristic
214C2×#125D411yescharacteristic
215C2×#124D411yescharacteristic
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×#123D411yescharacteristic
221C2×#123D411yescharacteristic
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8D411yescharacteristic
225C2×#121—21no—
226C2×#121—21no—
227C2×#121D411yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237#518—42no—
238#518—42no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C22×C4⋊C4—21no—
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C22⋊C4—21no—
261C22×C22⋊C4—21no—
262C22×C42C2311yescharacteristic
263#482—24no—
264#480—24no—
265#476—42no—
266#474—42no—
267#447—24no—
268#446—42no—
269#446—42no—
270#442—42no—
271C4×D8—42no—
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330#400—21no—
331#400—21no—
332#399—21no—
333#399—21no—
334#399—21no—
335#399—21no—
336#399—21no—
337#398—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#395—21no—
347#395—21no—
348#395—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#393—21no—
360#393—21no—
361#393—21no—
362#392—21no—
363#392—21no—
364#392—21no—
365#392—21no—
366#391—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390—21no—
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#389—21no—
379#389—21no—
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
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#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#386—21no—
412#386—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#385—21no—
423#385—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#384—21no—
433#384—21no—
434#384C2311yescharacteristic
435#382—21no—
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#381—21no—
439#380—21no—
440#380—21no—
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#379—21no—
453#379—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C2×#95—21no—
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
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#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—44no—
495C2×#41—82no—
496C2×#41—82no—
497C22×Q8—21no—
498C22×Q8C2×D411yescharacteristic
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C2×D411yescharacteristic
514C22×D4C2×D411yescharacteristic
515C22×D4C2×D411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8—41no—
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C4⋊Q8—22no—
547C4⋊Q8—22no—
548#126—42no—
549#126—42no—
550#125—42no—
551#124—42no—
552#123—42no—
553#123—44no—
554#123—44no—
555#123—42no—
556#123—82no—
557#123—82no—
558C22⋊Q8—42no—
559C22⋊Q8—44no—
560C22⋊Q8—82no—
561#121—22no—
562#121—22no—
563#121—22no—
564#121—22no—
565#121—22no—
566#121—42no—
567#121—41no—
568#121—41no—
569#121—41no—
570#121—41no—
571#121—41no—
572#121—41no—
573#121—41no—
574#121—41no—
575#121—41no—
576#121—82no—
577#121—82no—
578#120—82no—
579#120—82no—
580C4×Q8—22no—
581C4×Q8—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—44no—
599C4×D4—44no—
600C4×D4—82no—
601C4×D4—82no—
602#117—22no—
603#117—22no—
604#117—22no—
605#117—41no—
606#117—41no—
607#117—41no—
608#117—41no—
609#117—41no—
610C2×C4⋊C4—22no—
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—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—82no—
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊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—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×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42—41no—
717C2×C42C2×D411yescharacteristic
718C2×C42C2×D411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723#107—22no—
724#107—22no—
725#107—22no—
726#107—41no—
727#107—41no—
728#107—41no—
729#107—41no—
730#107—41no—
731#106—22no—
732#106—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—
741C4⋊C8—41no—
742C4⋊C8—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—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102#4114yescomplemented
763C22⋊C8—22no—
764C22⋊C8—22no—
765C22⋊C8—22no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775#97—22no—
776#97—41no—
777#97—41no—
778#97—41no—
779C4×C8—22no—
780C4×C8—41no—
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#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—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—42no—
816C24—42no—
817C24—42no—
818C24—81no—
819C24—81no—
820C24—81no—
821C24—81no—
822C24C22×D411yescharacteristic
823C24C22×D411yescharacteristic
824C24C22×D411yescharacteristic
825#41—816no—
826C2×Q8—22no—
827C2×Q8—41no—
828C2×Q8—41no—
829C2×Q8—42no—
830C2×Q8—81no—
831C2×Q8—81no—
832C2×D4—22no—
833C2×D4—22no—
834C2×D4—22no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—41no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—41no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—41no—
859C2×D4—41no—
860C2×D4—42no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
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—42no—
874C2×D4—42no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4C2×#4112yes—
886C2×D42−1+412yes—
887C22×C4—21no—
888C22×C4—22no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—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—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—41no—
920C22×C4—41no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—41no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C2511yescharacteristic
960D8—44no—
961D8—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—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8C2×#4112yes—
986C4⋊C4—22no—
987C4⋊C4—22no—
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—21no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—81no—
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⋊C4C2×#4112yes—
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—41no—
1050C22⋊C4—41no—
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—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
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—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—41no—
1097C42—41no—
1098C42—42no—
1099C42—42no—
1100C42—81no—
1101C42—81no—
1102C42—81no—
1103C42H(5,𝔽2)12yes—
1104C42H(5,𝔽2)12yes—
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—22no—
1121C23—21no—
1122C23—22no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—48no—
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—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—162no—
1148C23—162no—
1149C23—162no—
1150C23—162no—
1151C23—162no—
1152C23—162no—
1153C23#57612yes—
1154C23C23×D411yescharacteristic
1155Q8—82no—
1156Q8—84no—
1157D4—22no—
1158D4—22no—
1159D4—22no—
1160D4—22no—
1161D4—44no—
1162D4—48no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—82no—
1172D4—82no—
1173D4—84no—
1174D4—84no—
1175D4—84no—
1176D4—84no—
1177D4—162no—
1178D4—162no—
1179D4—162no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—22no—
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—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—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—84no—
1263C2×C4—82no—
1264C2×C4—82no—
1265C2×C4—84no—
1266C2×C4—84no—
1267C2×C4—84no—
1268C2×C4—162no—
1269C2×C4—162no—
1270C2×C4—162no—
1271C2×C4—162no—
1272C2×C4#53412yes—
1273C2×C4#53412yes—
1274C2×C4C22×#4111yescharacteristic
1275C2×C4C2×H(5,𝔽2)11yescharacteristic
1276C2×C4C2×H(5,𝔽2)11yescharacteristic
1277C2×C4C2×2−1+411yescharacteristic
1278C2×C4#58511yescharacteristic
1279C2×C4#58511yescharacteristic
1280C8—22no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—42no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—42no—
1301C22—42no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—42no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—42no—
1314C22—42no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—168no—
1331C22C2×#53411yescharacteristic
1332C22D4×#4111yescharacteristic
1333C22#348911yescharacteristic
1334C22C2×#57611yescharacteristic
1335C22#358511yescharacteristic
1336C22#358511yescharacteristic
1337C22#358611yescharacteristic
1338C4—22no—
1339C4—22no—
1340C4—42no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4#350611yescharacteristic
1363C4#352011yescharacteristic
1364C4#353911yescharacteristic
1365C4#354111yescharacteristic
1366C2—42no—
1367C2—81no—
1368C2—81no—
1369C2—82no—
1370C2—82no—
1371C2—161no—
1372C2#3988411yescharacteristic
1373C2#6075611yescharacteristic
1374C2#6077211yescharacteristic
1375C2#6151811yescharacteristic
1376C2#6151911yescharacteristic
1377C2#6215511yescharacteristic
1378C2#6223511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38041C2semidirect
2. #35522C2semidirect
3. #32962C2semidirect
4. #32465C2semidirect
5. #32463C2semidirect
6. #31801C2semidirect
7. #31786C2semidirect
8. #31681C2semidirect
9. #31680C2semidirect
10. #31036C2semidirect
11. #31016C2semidirect
12. #30023C2semidirect
13. #30007C2semidirect
14. #29476C2semidirect
15. #29468C2semidirect
16. #29247C2semidirect
17. #29234C2semidirect
18. #28276C2semidirect
19. #28191C2semidirect
20. #27887C2semidirect
21. #27636C2semidirect
22. #25481C2semidirect
23. #25477C2semidirect
24. #25027C2semidirect
25. #24974C2semidirect
26. #24128C2semidirect
27. #24116C2semidirect
28. #22533C2semidirect
29. #22090C2semidirect
30. #22081C2semidirect
31. #21458C2semidirect
32. C2×#547C22semidirect
40. C2×#446C22semidirect
41. C2×#446C22semidirect
44. #2854C22semidirect
50. #2624C22semidirect
52. #2580C22semidirect
53. #2567C22semidirect
77. #2352C22semidirect
81. #2317C22semidirect
85. C2×#389C22semidirect
86. #2088C22semidirect
87. #2088C22semidirect
88. #2087C22semidirect
89. #2086C22semidirect
90. #2086C22semidirect
91. #2086C22semidirect
95. #2077C22semidirect
96. #2077C22semidirect
99. #2076C22semidirect
100. #2076C22semidirect
106. #2067C22semidirect
109. #2065C22semidirect
114. #2034C22semidirect
115. #2034C22semidirect
120. #2033C22semidirect
121. #2033C22semidirect
126. #1993C22semidirect
127. #1990C22semidirect
133. #1955C22semidirect
135. #1954C22semidirect
136. #1949C22semidirect
137. #1947C22semidirect
138. #1944C22semidirect
139. #1943C22semidirect
140. #1943C22semidirect
141. #1943C22semidirect
142. #1942C22semidirect
143. #1941C22semidirect
149. #1936C22semidirect
150. #1936C22semidirect
152. #1926C22semidirect
153. #1925C22semidirect
154. #1921C22semidirect
155. #1921C22semidirect
156. #1920C22semidirect
157. #1919C22semidirect
158. #1918C22semidirect
159. #1918C22semidirect
178. #1854C22semidirect
179. #1853C22semidirect
180. #1853C22semidirect
181. #1852C22semidirect
182. #1852C22semidirect
183. #1852C22semidirect
184. #1847C22semidirect
185. #1835C22semidirect
186. #1825C22semidirect
187. #1823C22semidirect
190. #1804C22semidirect
191. #1802C22semidirect
193. #1798C22semidirect
194. #1797C22semidirect
201. #1750C22semidirect
202. #1749C22semidirect
762. #102#41semidirect

Maximal subgroups

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

subgroupindex
#380412
#355222
#329622
#324652
#324632
#318012
#317862
#316812
#316802
#310362
#310162
#300232
#300072
#294762
#294682
#292472
#292342
#282762
#281912
#278872
#276362
#254812
#254772
#250272
#249742
#241282
#241162
#225332
#220902
#220812
#214582