Finite Group Databasebeta

← #6817585

Subgroups — #6817585

Order 512.

1384 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42972C211yesmaximal, characteristic, complemented
2#42486C211yesmaximal, characteristic
3#33216C211yesmaximal, characteristic, complemented
4#32584C211yesmaximal, characteristic, complemented
5#32581C211yesmaximal, characteristic, complemented
6#32347C211yesmaximal, characteristic, complemented
7#32342C211yesmaximal, characteristic, complemented
8#31887C211yesmaximal, characteristic, complemented
9#31882C211yesmaximal, characteristic, complemented
10#30959C211yesmaximal, characteristic, complemented
11#30950C211yesmaximal, characteristic, complemented
12#29979C211yesmaximal, characteristic, complemented
13#29962C211yesmaximal, characteristic
14#28966C211yesmaximal, characteristic, complemented
15#28960C211yesmaximal, characteristic, complemented
16#28957C211yesmaximal, characteristic, complemented
17#28952C211yesmaximal, characteristic, complemented
18#28787C211yesmaximal, characteristic, complemented
19#28783C211yesmaximal, characteristic, complemented
20#27830C211yesmaximal, characteristic, complemented
21#27829C211yesmaximal, characteristic, complemented
22#26003C211yesmaximal, characteristic, complemented
23#25995C211yesmaximal, characteristic, complemented
24#25952C211yesmaximal, characteristic
25#25950C211yesmaximal, characteristic
26#25473C211yesmaximal, characteristic, complemented
27#25469C211yesmaximal, characteristic, complemented
28#22584C211yesmaximal, characteristic
29#22584C211yesmaximal, characteristic
30#21602C211yesmaximal, characteristic, complemented
31#21091C211yesmaximal, characteristic
32C2×#499C2211yescharacteristic, complemented
33C2×#478C2211yescharacteristic
34C2×#474C2211yescharacteristic
35C2×C8×Q8C2211yescharacteristic, complemented
36C2×#418C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C2×#405C2211yescharacteristic
39#2845—21no—
40#2842—21no—
41#2790—21no—
42#2780—21no—
43#2768—21no—
44#2748—21no—
45#2732—21no—
46#2729—21no—
47#2704—21no—
48#2692—21no—
49#2660—21no—
50#2647—21no—
51#2629C2211yescharacteristic
52#2629C2211yescharacteristic
53#2626—21no—
54#2626—21no—
55#2612—21no—
56#2584C2211yescharacteristic, complemented
57#2580C2211yescharacteristic
58#2566C2211yescharacteristic
59#2552C2211yescharacteristic, complemented
60#2550C2211yescharacteristic, complemented
61#2546C2211yescharacteristic, complemented
62#2542C2211yescharacteristic
63#2538C2211yescharacteristic
64#2508C2211yescharacteristic, complemented
65#2507C2211yescharacteristic, complemented
66#2507C2211yescharacteristic, complemented
67#2506C2211yescharacteristic, complemented
68#2454C2211yescharacteristic
69#2454C2211yescharacteristic
70#2454C2211yescharacteristic
71#2452C2211yescharacteristic
72#2442C2211yescharacteristic
73#2441C2211yescharacteristic
74#2440C2211yescharacteristic
75#2439C2211yescharacteristic
76#2437—21no—
77#2396C2211yescharacteristic
78#2346C2211yescharacteristic
79#2346C2211yescharacteristic
80D4×C22⋊C4C2211yescharacteristic
81D4×C22⋊C4C2211yescharacteristic
82#2317C2211yescharacteristic
83#2309C2211yescharacteristic
84#2101C2211yescharacteristic, complemented
85#2100C2211yescharacteristic, complemented
86#2099C2211yescharacteristic, complemented
87#2099C2211yescharacteristic, complemented
88#2094C2211yescharacteristic
89#2093C2211yescharacteristic
90#2093C2211yescharacteristic
91#2092C2211yescharacteristic
92#2088C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2087C2211yescharacteristic, complemented
96#2087C2211yescharacteristic, complemented
97#2086C2211yescharacteristic, complemented
98#2086C2211yescharacteristic, complemented
99#2086C2211yescharacteristic, complemented
100#2085C2211yescharacteristic, complemented
101#2085C2211yescharacteristic, complemented
102#2084C2211yescharacteristic, complemented
103#2083C2211yescharacteristic, complemented
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2059C2211yescharacteristic, complemented
113#2059C2211yescharacteristic, complemented
114#2059C2211yescharacteristic, complemented
115#2059C2211yescharacteristic, complemented
116#2059C2211yescharacteristic, complemented
117#2058C2211yescharacteristic, complemented
118#2057C2211yescharacteristic, complemented
119#2057C2211yescharacteristic, complemented
120#2025C2211yescharacteristic
121#2025C2211yescharacteristic
122#2025C2211yescharacteristic
123#2023C2211yescharacteristic
124#1993C2211yescharacteristic, complemented
125#1992C2211yescharacteristic, complemented
126#1992C2211yescharacteristic, complemented
127#1992C2211yescharacteristic, complemented
128#1991C2211yescharacteristic, complemented
129#1990C2211yescharacteristic, complemented
130#1989C2211yescharacteristic, complemented
131#1987C2211yescharacteristic, complemented
132#1985C2211yescharacteristic, complemented
133#1949C2211yescharacteristic, complemented
134#1947C2211yescharacteristic, complemented
135#1944C2211yescharacteristic, complemented
136#1943C2211yescharacteristic, complemented
137#1943C2211yescharacteristic, complemented
138#1943C2211yescharacteristic, complemented
139#1942C2211yescharacteristic, complemented
140#1942C2211yescharacteristic, complemented
141#1942C2211yescharacteristic, complemented
142#1941C2211yescharacteristic, complemented
143#1940C2211yescharacteristic, complemented
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1921C2211yescharacteristic, complemented
161#1921C2211yescharacteristic, complemented
162#1920C2211yescharacteristic, complemented
163#1918C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1864C2211yescharacteristic
167#1864C2211yescharacteristic
168#1864C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1853C2211yescharacteristic
177#1852C2211yescharacteristic
178#1850C2211yescharacteristic
179#1850C2211yescharacteristic
180#1845C2211yescharacteristic, complemented
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1808C2211yescharacteristic
186#1808C2211yescharacteristic
187#1804C2211yescharacteristic
188#1802C2211yescharacteristic
189#1798C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1771C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194#1770C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1736C2211yescharacteristic
202#1735C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125—21no—
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C22⋊C4—21no—
229C22×C22⋊C4—21no—
230#499—42no—
231#478—42no—
232#474—42no—
233C8×Q8—42no—
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256#418Q818yescomplemented
257C2×#102—42no—
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276#405—42no—
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285#400—21no—
286#400—21no—
287#400—21no—
288#400D411yescharacteristic
289#399—21no—
290#399—21no—
291#399—21no—
292#399—21no—
293#399—21no—
294#399—21no—
295#399—21no—
296#399D411yescharacteristic
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398D411yescharacteristic
316#398D411yescharacteristic
317#396—21no—
318#396—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#396—21no—
331#396D411yescharacteristic
332#396D411yescharacteristic
333#395—21no—
334#395—21no—
335#395—21no—
336#395D411yescharacteristic
337#393—21no—
338#393—21no—
339#393—21no—
340#393D411yescharacteristic
341#391—21no—
342#391—21no—
343#391—21no—
344#390—21no—
345#390—21no—
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
382#388—21no—
383#388—21no—
384#388—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#386—21no—
394#386—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#384—21no—
408#384—21no—
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#382—21no—
414#382—21no—
415#382—21no—
416#382—21no—
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#380—21no—
420#380—21no—
421#380—21no—
422#380—21no—
423#380—21no—
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#379—21no—
429#379—21no—
430#379—21no—
431#379—21no—
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441#376—21no—
442#376—21no—
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#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485C25—21no—
486C22×Q8—21no—
487C22×Q8—21no—
488C22×Q8C2×D411yescharacteristic
489C22×D4—21no—
490C22×D4—22no—
491C22×D4—41no—
492C22×D4—41no—
493C22×D4—41no—
494C22×D4—41no—
495C22×D4C2×Q814yes—
496C22×D4C2411yescharacteristic
497C22×D4C2411yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C2411yescharacteristic
504C2×M16—41no—
505C2×M16—41no—
506C2×M16C2×Q814yes—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C4⋊Q8—41no—
519C4⋊Q8—41no—
520C4⋊Q8—41no—
521C4⋊Q8—41no—
522C4⋊Q8—82no—
523#125—41no—
524#125—41no—
525#125—41no—
526#125—41no—
527#125—41no—
528#125—41no—
529#125—41no—
530#125—41no—
531#125—82no—
532C22⋊Q8—82no—
533C22⋊Q8—82no—
534C22⋊Q8—82no—
535C22⋊Q8—82no—
536C22⋊Q8—82no—
537C4×Q8—41no—
538C4×Q8—41no—
539C4×D4—41no—
540C4×D4—41no—
541C4×D4—41no—
542C4×D4—41no—
543C4×D4—41no—
544C4×D4—41no—
545C4×D4—41no—
546C4×D4—41no—
547#117—22no—
548#117—41no—
549#117—41no—
550#117—41no—
551#117—41no—
552#117C2×Q814yes—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
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—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
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—82no—
646C2×C22⋊C4—82no—
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665#107—22no—
666#107—22no—
667#107—41no—
668#107—41no—
669#107—41no—
670#107—41no—
671#107—41no—
672#107—41no—
673#107—41no—
674#107—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679#106—41no—
680#106—41no—
681C4⋊C8—22no—
682C4⋊C8—22no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686C4⋊C8—41no—
687#102—22no—
688#102—22no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102C2×Q814yes—
700#102C2×Q814yes—
701#102C2×Q814yes—
702#102C2×Q814yes—
703C22⋊C8—22no—
704C22⋊C8—22no—
705#97—41no—
706#97—41no—
707#97—41no—
708#97—41no—
709C4×C8—22no—
710C4×C8—22no—
711C4×C8—41no—
712C4×C8—41no—
713#95—21no—
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#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755C24—21no—
756C24—21no—
757C24—24no—
758C24—81no—
759C24—81no—
760C24—81no—
761C24—81no—
762C24—81no—
763C24—81no—
764C24C22×D411yescharacteristic
765C2×Q8—22no—
766C2×Q8—41no—
767C2×Q8—41no—
768C2×Q8—42no—
769C2×Q8—42no—
770C2×Q8—81no—
771C2×Q8—81no—
772C2×Q8—81no—
773C2×Q8—81no—
774C2×D4—24no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—82no—
788C2×D4—82no—
789C2×D4—81no—
790C2×D4—81no—
791C2×D4C22×Q812yes—
792C2×D4C22×Q812yes—
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—21no—
810C22×C4—21no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4—81no—
819C22×C4—81no—
820C22×C4—81no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4—81no—
824C22×C4—81no—
825C22×C4—81no—
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×Q812yes—
840C22×C42−1+412yes—
841C22×C4C2511yescharacteristic
842M16—44no—
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—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—44no—
865C2×C8C22×Q812yes—
866C2×C8C22×Q812yes—
867C2×C8H(5,𝔽2)12yes—
868C4⋊C4—22no—
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—21no—
894C4⋊C4—21no—
895C4⋊C4—41no—
896C4⋊C4—41no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—41no—
900C4⋊C4—41no—
901C4⋊C4—41no—
902C4⋊C4—41no—
903C4⋊C4—41no—
904C4⋊C4—41no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—81no—
908C4⋊C4—81no—
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⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4C22×Q812yes—
945C4⋊C4C22×Q812yes—
946C22⋊C4—24no—
947C22⋊C4—22no—
948C22⋊C4—41no—
949C22⋊C4—41no—
950C22⋊C4—41no—
951C22⋊C4—41no—
952C22⋊C4—41no—
953C22⋊C4—42no—
954C22⋊C4—42no—
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—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C42—24no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—42no—
992C42—42no—
993C42—81no—
994C42—81no—
995C42—81no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—22no—
1003C23—22no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—84no—
1017C23—84no—
1018C23—84no—
1019C23—162no—
1020C23—162no—
1021C23—162no—
1022C23—162no—
1023C23D4×Q812yes—
1024C23C23×D411yescharacteristic
1025Q8—44no—
1026Q8—162no—
1027Q8—162no—
1028D4—22no—
1029D4—22no—
1030D4—22no—
1031D4—22no—
1032D4—41no—
1033D4—41no—
1034D4—41no—
1035D4—41no—
1036D4—84no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
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—21no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
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—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—162no—
1121C2×C4—162no—
1122C2×C4—162no—
1123C2×C4—162no—
1124C2×C4—162no—
1125C2×C4D4×Q812yes—
1126C2×C4#57612yes—
1127C2×C4C23×Q811yescharacteristic
1128C2×C4C2×H(5,𝔽2)11yescharacteristic
1129C2×C4C2×2−1+411yescharacteristic
1130C2×C4#58511yescharacteristic
1131C2×C4#58511yescharacteristic
1132C2×C4#58511yescharacteristic
1133C8—22no—
1134C8—22no—
1135C8—22no—
1136C8—41no—
1137C8—41no—
1138C8—41no—
1139C8—41no—
1140C8—41no—
1141C22—22no—
1142C22—22no—
1143C22—22no—
1144C22—41no—
1145C22—41no—
1146C22—41no—
1147C22—41no—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—81no—
1155C22—81no—
1156C22—81no—
1157C22—81no—
1158C22—81no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—168no—
1163C22C2×D4×Q811yescharacteristic
1164C22#349611yescharacteristic
1165C22#350011yescharacteristic
1166C22C2×#57611yescharacteristic
1167C22#358411yescharacteristic
1168C22#358511yescharacteristic
1169C22#358611yescharacteristic
1170C4—22no—
1171C4—22no—
1172C4—41no—
1173C4—41no—
1174C4—41no—
1175C4—41no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—41no—
1180C4—41no—
1181C4—41no—
1182C4—41no—
1183C4—42no—
1184C4—42no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4#345811yescharacteristic
1198C4#350111yescharacteristic
1199C4#353511yescharacteristic
1200C4#356411yescharacteristic
1201C2—42no—
1202C2—82no—
1203C2—82no—
1204C2#3936411yescharacteristic
1205C2#6138111yescharacteristic
1206C2#6138511yescharacteristic
1207C2#6226611yescharacteristic
1208C2#6233311yescharacteristic
1209C2#6261011yescharacteristic
1210C2#6261211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42972C2semidirect
3. #33216C2semidirect
4. #32584C2semidirect
5. #32581C2semidirect
6. #32347C2semidirect
7. #32342C2semidirect
8. #31887C2semidirect
9. #31882C2semidirect
10. #30959C2semidirect
11. #30950C2semidirect
12. #29979C2semidirect
14. #28966C2semidirect
15. #28960C2semidirect
16. #28957C2semidirect
17. #28952C2semidirect
18. #28787C2semidirect
19. #28783C2semidirect
20. #27830C2semidirect
21. #27829C2semidirect
22. #26003C2semidirect
23. #25995C2semidirect
26. #25473C2semidirect
27. #25469C2semidirect
30. #21602C2semidirect
32. C2×#499C22semidirect
35. C2×C8×Q8C22semidirect
56. #2584C22semidirect
59. #2552C22semidirect
60. #2550C22semidirect
61. #2546C22semidirect
64. #2508C22semidirect
65. #2507C22semidirect
66. #2507C22semidirect
67. #2506C22semidirect
84. #2101C22semidirect
85. #2100C22semidirect
86. #2099C22semidirect
87. #2099C22semidirect
92. #2088C22semidirect
93. #2088C22semidirect
94. #2088C22semidirect
95. #2087C22semidirect
96. #2087C22semidirect
97. #2086C22semidirect
98. #2086C22semidirect
99. #2086C22semidirect
100. #2085C22semidirect
101. #2085C22semidirect
102. #2084C22semidirect
103. #2083C22semidirect
112. #2059C22semidirect
113. #2059C22semidirect
114. #2059C22semidirect
115. #2059C22semidirect
116. #2059C22semidirect
117. #2058C22semidirect
118. #2057C22semidirect
119. #2057C22semidirect
124. #1993C22semidirect
125. #1992C22semidirect
126. #1992C22semidirect
127. #1992C22semidirect
128. #1991C22semidirect
129. #1990C22semidirect
130. #1989C22semidirect
131. #1987C22semidirect
132. #1985C22semidirect
133. #1949C22semidirect
134. #1947C22semidirect
135. #1944C22semidirect
136. #1943C22semidirect
137. #1943C22semidirect
138. #1943C22semidirect
139. #1942C22semidirect
140. #1942C22semidirect
141. #1942C22semidirect
142. #1941C22semidirect
143. #1940C22semidirect
160. #1921C22semidirect
161. #1921C22semidirect
162. #1920C22semidirect
163. #1918C22semidirect
164. #1916C22semidirect
165. #1916C22semidirect
180. #1845C22semidirect
192. #1771C22semidirect
193. #1771C22semidirect
194. #1770C22semidirect
256. #418Q8semidirect

Maximal subgroups

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

subgroupindex
#429722
#424862
#332162
#325842
#325812
#323472
#323422
#318872
#318822
#309592
#309502
#299792
#299622
#289662
#289602
#289572
#289522
#287872
#287832
#278302
#278292
#260032
#259952
#259522
#259502
#254732
#254692
#225842
#216022
#210912