Finite Group Databasebeta

← #7125965

Subgroups — #7125965

Order 512.

1400 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44902C211yesmaximal, characteristic, complemented
2#42968C211yesmaximal, characteristic
3#32194C211yesmaximal, characteristic, complemented
4#32152C211yesmaximal, characteristic, complemented
5#32136C211yesmaximal, characteristic, complemented
6#31890C211yesmaximal, characteristic, complemented
7#31739C211yesmaximal, characteristic, complemented
8#31693C211yesmaximal, characteristic, complemented
9#31470C211yesmaximal, characteristic, complemented
10#31437C211yesmaximal, characteristic, complemented
11#28944C211yesmaximal, characteristic, complemented
12#28789C211yesmaximal, characteristic, complemented
13#28778C211yesmaximal, characteristic, complemented
14#28079C211yesmaximal, characteristic, complemented
15#27874C211yesmaximal, characteristic, complemented
16#27709C211yesmaximal, characteristic, complemented
17#27662C211yesmaximal, characteristic, complemented
18#27339C211yesmaximal, characteristic, complemented
19#27006C211yesmaximal, characteristic, complemented
20#26456C211yesmaximal, characteristic, complemented
21#26003C211yesmaximal, characteristic, complemented
22#26003C211yesmaximal, characteristic, complemented
23#24960C211yesmaximal, characteristic, complemented
24#24612C211yesmaximal, characteristic, complemented
25#24576C211yesmaximal, characteristic, complemented
26#24105C211yesmaximal, characteristic
27#23555C211yesmaximal, characteristic, complemented
28#22909C211yesmaximal, characteristic, complemented
29#22624C211yesmaximal, characteristic, complemented
30#22489C211yesmaximal, characteristic
31#21843C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C2×#480C2211yescharacteristic
35C2×C8×D4C2211yescharacteristic
36C2×#433C2211yescharacteristic
37C2×#428C2211yescharacteristic
38C22×#107C2211yescharacteristic
39#2820—21no—
40#2773—21no—
41#2765—21no—
42#2761—21no—
43#2721—21no—
44#2674—21no—
45#2674—21no—
46#2672—21no—
47#2672—21no—
48#2658—21no—
49#2628—21no—
50#2624C2211yescharacteristic
51#2611—21no—
52#2611—21no—
53#2570—21no—
54#2552C2211yescharacteristic
55#2551C2211yescharacteristic
56#2551C2211yescharacteristic
57#2528—21no—
58#2508C2211yescharacteristic
59#2507C2211yescharacteristic
60#2501C2211yescharacteristic
61#2496C2211yescharacteristic
62#2494C2211yescharacteristic
63#2491C2211yescharacteristic
64#2491C2211yescharacteristic
65#2487C2211yescharacteristic
66#2487C2211yescharacteristic
67#2479—21no—
68#2454C2211yescharacteristic
69#2454C2211yescharacteristic
70#2441C2211yescharacteristic
71#2441C2211yescharacteristic
72#2441C2211yescharacteristic
73#2441C2211yescharacteristic
74#2395C2211yescharacteristic
75#2370C2211yescharacteristic
76#2354C2211yescharacteristic
77#2346C2211yescharacteristic
78#2346C2211yescharacteristic
79#2344C2211yescharacteristic
80#2317C2211yescharacteristic
81#2314C2211yescharacteristic
82#2101C2211yescharacteristic
83#2100C2211yescharacteristic
84#2100C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2092C2211yescharacteristic
88#2087C2211yescharacteristic
89#2087C2211yescharacteristic
90#2087C2211yescharacteristic
91#2087C2211yescharacteristic
92#2086C2211yescharacteristic
93#2086C2211yescharacteristic
94#2083C2211yescharacteristic
95#2083C2211yescharacteristic
96#2083C2211yescharacteristic
97#2083C2211yescharacteristic
98#2077C2211yescharacteristic
99#2076C2211yescharacteristic
100#2076C2211yescharacteristic
101#2075C2211yescharacteristic
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2065C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2057C2211yescharacteristic
114#2057C2211yescharacteristic
115#2057C2211yescharacteristic
116#2057C2211yescharacteristic
117#2057C2211yescharacteristic
118#2057C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2025C2211yescharacteristic
122#1993C2211yescharacteristic
123#1992C2211yescharacteristic
124#1992C2211yescharacteristic
125#1991C2211yescharacteristic
126#1990C2211yescharacteristic
127#1990C2211yescharacteristic
128#1989C2211yescharacteristic
129#1989C2211yescharacteristic
130#1989C2211yescharacteristic
131#1988C2211yescharacteristic
132#1987C2211yescharacteristic
133#1987C2211yescharacteristic
134#1947C2211yescharacteristic
135#1947C2211yescharacteristic
136#1947C2211yescharacteristic
137#1944C2211yescharacteristic
138#1944C2211yescharacteristic
139#1942C2211yescharacteristic
140#1942C2211yescharacteristic
141#1942C2211yescharacteristic
142#1941C2211yescharacteristic
143#1940C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1923C2211yescharacteristic
153#1923C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1921C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1920C2211yescharacteristic
160#1920C2211yescharacteristic
161#1919C2211yescharacteristic
162#1919C2211yescharacteristic
163#1918C2211yescharacteristic
164#1917C2211yescharacteristic
165#1916C2211yescharacteristic
166#1895C2211yescharacteristic
167#1893C2211yescharacteristic
168#1893C2211yescharacteristic
169#1875C2211yescharacteristic
170#1875C2211yescharacteristic
171#1870C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1850C2211yescharacteristic
179#1850C2211yescharacteristic
180#1834C2211yescharacteristic
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic
183#1825C2211yescharacteristic
184#1825C2211yescharacteristic
185#1824C2211yescharacteristic
186#1824C2211yescharacteristic
187#1823C2211yescharacteristic
188#1809C2211yescharacteristic
189#1808C2211yescharacteristic
190#1808C2211yescharacteristic
191#1808C2211yescharacteristic
192#1802C2211yescharacteristic
193#1776C2211yescharacteristic
194C4×#107C2211yescharacteristic
195C8×C4⋊C4C2211yescharacteristic
196C4×#102C2211yescharacteristic
197#1753C2211yescharacteristic
198#1752C2211yescharacteristic
199#1736C2211yescharacteristic
200#1735C2211yescharacteristic
201#1735C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206#555—24no—
207#555—42no—
208#544—24no—
209#544—42no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8—21no—
212C2×C4⋊Q8—21no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#125—21no—
218C2×#125—21no—
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#124—21no—
223C2×#124—21no—
224C2×#124—21no—
225C2×#124—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×#121—21no—
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×#117—21no—
236C2×#117—21no—
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244#480—42no—
245C8×D4—42no—
246#433—42no—
247#428—24no—
248C2×#107—42no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288#401—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400D411yescharacteristic
294#399—21no—
295#399—21no—
296#399—21no—
297#399—21no—
298#399—21no—
299#399—21no—
300#399—21no—
301#399—21no—
302#399—21no—
303#399—21no—
304#399—21no—
305#399D411yescharacteristic
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398D411yescharacteristic
312#397—21no—
313#397—21no—
314#397—21no—
315#397D411yescharacteristic
316#397D411yescharacteristic
317#397D411yescharacteristic
318#396—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#395—21no—
325#395—21no—
326#395—21no—
327#395—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394D411yescharacteristic
333#394D411yescharacteristic
334#393—21no—
335#393—21no—
336#390—21no—
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#386—21no—
392#386—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#384—21no—
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#382—21no—
406#382—21no—
407#382—21no—
408#382—21no—
409#382C2311yescharacteristic
410#381—21no—
411#380—21no—
412#380—21no—
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C22⋊C4C2311yescharacteristic
433C4×C22⋊C4C2311yescharacteristic
434C4×C22⋊C4C2311yescharacteristic
435#376—21no—
436#376—21no—
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
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#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C2×D411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4C2411yescharacteristic
498C23×C4C2411yescharacteristic
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—41no—
502C22×C8—22no—
503C22×C8—22no—
504C22×C8—22no—
505C22×C8—41no—
506C22×C8—41no—
507C22×C8—41no—
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C4⋊Q8—22no—
517C4⋊Q8—22no—
518C4⋊Q8—22no—
519C4⋊Q8—41no—
520C4⋊Q8—41no—
521C4⋊Q8—41no—
522C4⋊Q8—44no—
523C4⋊Q8—82no—
524C4⋊Q8—82no—
525#126—82no—
526#125—22no—
527#125—22no—
528#125—22no—
529#125—41no—
530#125—41no—
531#125—41no—
532#125—44no—
533#125—82no—
534#124—44no—
535#124—44no—
536#124—82no—
537#124—82no—
538#123—82no—
539#123—82no—
540C22⋊Q8—44no—
541C22⋊Q8—44no—
542#121—22no—
543#121—22no—
544#121—22no—
545#121—44no—
546#121—41no—
547C4×D4—22no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—41no—
551#117—22no—
552#117—22no—
553#117—22no—
554#117—22no—
555#117—22no—
556#117—22no—
557#117—44no—
558#117—41no—
559#117—41no—
560#117—41no—
561#117—82no—
562#117#4114yes—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675#107—22no—
676#107—22no—
677#107—22no—
678#107—41no—
679#107—41no—
680#107—41no—
681#107—41no—
682#107—41no—
683#107—41no—
684#107—41no—
685#107—41no—
686#107—41no—
687#106—22no—
688#106—22no—
689#106—22no—
690#106—22no—
691C4⋊C8—22no—
692C4⋊C8—41no—
693C4⋊C8—41no—
694C4⋊C8—41no—
695C4⋊C8—41no—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704C22⋊C8—22no—
705C22⋊C8—22no—
706C22⋊C8—22no—
707C22⋊C8—41no—
708C22⋊C8—41no—
709#97—41no—
710#97—41no—
711C4×C8—22no—
712C4×C8—41no—
713C4×C8—41no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757C24—21no—
758C24C22×D411yescharacteristic
759C24C22×D411yescharacteristic
760C2×Q8—42no—
761C2×Q8—42no—
762C2×Q8—42no—
763C2×Q8—81no—
764C2×Q8—81no—
765C2×Q8—81no—
766C2×Q8—81no—
767C2×Q8—81no—
768C2×Q8—81no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—41no—
778C2×D4—42no—
779C2×D4—42no—
780C2×D4—81no—
781C2×D4—81no—
782C2×D4—81no—
783C2×D4—81no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C2×#4112yes—
831C22×C4H(5,𝔽2)12yes—
832C22×C4C2511yescharacteristic
833M16—44no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—44no—
857C2×C8—82no—
858C2×C82−1+412yes—
859C2×C82−1+412yes—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—41no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4C2×#4112yes—
932C4⋊C4C2×#4112yes—
933C4⋊C42−1+412yes—
934C22⋊C4—24no—
935C22⋊C4—22no—
936C22⋊C4—22no—
937C22⋊C4—22no—
938C22⋊C4—22no—
939C22⋊C4—22no—
940C22⋊C4—22no—
941C22⋊C4—41no—
942C22⋊C4—41no—
943C22⋊C4—41no—
944C22⋊C4—41no—
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—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C42—24no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—42no—
979C42—42no—
980C42—42no—
981C42—42no—
982C42—42no—
983C42—42no—
984C42—42no—
985C42—81no—
986C42—81no—
987C42—81no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23#54612yes—
1009C23C23×D411yescharacteristic
1010Q8—162no—
1011Q8—162no—
1012Q8—162no—
1013D4—44no—
1014D4—41no—
1015D4—41no—
1016D4—41no—
1017D4—41no—
1018D4—162no—
1019D4—162no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—84no—
1107C2×C4—84no—
1108C2×C4—162no—
1109C2×C4#54612yes—
1110C2×C4#57612yes—
1111C2×C4#57812yes—
1112C2×C4C22×#4111yescharacteristic
1113C2×C4C2×H(5,𝔽2)11yescharacteristic
1114C2×C4C2×2−1+411yescharacteristic
1115C2×C4C2×2−1+411yescharacteristic
1116C2×C4C2×2−1+411yescharacteristic
1117C2×C4#58511yescharacteristic
1118C8—22no—
1119C8—22no—
1120C8—41no—
1121C8—41no—
1122C8—41no—
1123C8—41no—
1124C8—41no—
1125C8—41no—
1126C22—22no—
1127C22—22no—
1128C22—22no—
1129C22—41no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22—41no—
1134C22—41no—
1135C22—41no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22C2×#54611yescharacteristic
1148C22#348911yescharacteristic
1149C22#349911yescharacteristic
1150C22C2×#57611yescharacteristic
1151C22C2×#57811yescharacteristic
1152C22#358411yescharacteristic
1153C22#358511yescharacteristic
1154C4—22no—
1155C4—22no—
1156C4—22no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—42no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—42no—
1166C4—41no—
1167C4—41no—
1168C4—42no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4#349511yescharacteristic
1182C4#350911yescharacteristic
1183C4#353511yescharacteristic
1184C4#354411yescharacteristic
1185C2—42no—
1186C2—81no—
1187C2—161no—
1188C2#4476111yescharacteristic
1189C2#6117311yescharacteristic
1190C2#6120511yescharacteristic
1191C2#6218111yescharacteristic
1192C2#6222211yescharacteristic
1193C2#6248711yescharacteristic
1194C2#6251811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#555C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #44902C2semidirect
3. #32194C2semidirect
4. #32152C2semidirect
5. #32136C2semidirect
6. #31890C2semidirect
7. #31739C2semidirect
8. #31693C2semidirect
9. #31470C2semidirect
10. #31437C2semidirect
11. #28944C2semidirect
12. #28789C2semidirect
13. #28778C2semidirect
14. #28079C2semidirect
15. #27874C2semidirect
16. #27709C2semidirect
17. #27662C2semidirect
18. #27339C2semidirect
19. #27006C2semidirect
20. #26456C2semidirect
21. #26003C2semidirect
22. #26003C2semidirect
23. #24960C2semidirect
24. #24612C2semidirect
25. #24576C2semidirect
27. #23555C2semidirect
28. #22909C2semidirect
29. #22624C2semidirect
31. #21843C2semidirect

Maximal subgroups

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

subgroupindex
#449022
#429682
#321942
#321522
#321362
#318902
#317392
#316932
#314702
#314372
#289442
#287892
#287782
#280792
#278742
#277092
#276622
#273392
#270062
#264562
#260032
#249602
#246122
#245762
#241052
#235552
#229092
#226242
#224892
#218432