Finite Group Databasebeta

← #6627172

Subgroups — #6627172

Order 512.

1282 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39681C211yesmaximal, characteristic
2#39673C211yesmaximal, characteristic
3#33292C211yesmaximal, characteristic
4#33262C211yesmaximal, characteristic
5#33257C211yesmaximal, characteristic
6#29217C211yesmaximal, characteristic
7#29202C211yesmaximal, characteristic
8#29196C211yesmaximal, characteristic
9#29187C211yesmaximal, characteristic
10#29182C211yesmaximal, characteristic
11#28962C211yesmaximal, characteristic
12#28961C211yesmaximal, characteristic
13#28956C211yesmaximal, characteristic
14#28953C211yesmaximal, characteristic
15#28948C211yesmaximal, characteristic
16#28948C211yesmaximal, characteristic
17#28947C211yesmaximal, characteristic
18#28945C211yesmaximal, characteristic
19#28526C211yesmaximal, characteristic
20#25488C211yesmaximal, characteristic
21#25487C211yesmaximal, characteristic
22#25474C211yesmaximal, characteristic
23#25471C211yesmaximal, characteristic
24#22980C211yesmaximal, characteristic
25#22977C211yesmaximal, characteristic
26#22967C211yesmaximal, characteristic
27#22964C211yesmaximal, characteristic
28#21645C211yesmaximal, characteristic
29#21645C211yesmaximal, characteristic
30C4×#487C211yesmaximal, characteristic
31#20516C211yesmaximal, characteristic
32C2×#487C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#477C2211yescharacteristic
36C2×#475C2211yescharacteristic
37C2×#446C2211yescharacteristic
38C2×C8×Q8C2211yescharacteristic
39#2864C2211yescharacteristic
40#2864C2211yescharacteristic
41#2806—21no—
42#2799—21no—
43#2792—21no—
44#2791—21no—
45#2791—21no—
46#2774—21no—
47#2774—21no—
48#2755—21no—
49#2660C2211yescharacteristic
50#2660C2211yescharacteristic
51#2647C2211yescharacteristic
52#2647C2211yescharacteristic
53#2590—21no—
54#2588—21no—
55#2586—21no—
56#2585—21no—
57#2584C2211yescharacteristic
58#2582C2211yescharacteristic
59#2581—21no—
60#2581C2211yescharacteristic
61#2567C2211yescharacteristic
62#2565—21no—
63#2520—21no—
64#2508C2211yescharacteristic
65#2508C2211yescharacteristic
66#2507C2211yescharacteristic
67#2506C2211yescharacteristic
68#2462—21no—
69#2453C2211yescharacteristic
70#2453C2211yescharacteristic
71#2451C2211yescharacteristic
72#2451C2211yescharacteristic
73#2370C2211yescharacteristic
74#2365C2211yescharacteristic
75#2351C2211yescharacteristic
76Q8×C4⋊C4C2211yescharacteristic
77#2331C2211yescharacteristic
78#2331C2211yescharacteristic
79#2327C2211yescharacteristic
80#2327C2211yescharacteristic
81C4×C4⋊Q8C2211yescharacteristic
82C4×C4⋊Q8C2211yescharacteristic
83#2295C2211yescharacteristic
84#2097C2211yescharacteristic
85#2097C2211yescharacteristic
86#2096C2211yescharacteristic
87#2095C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2087C2211yescharacteristic
93#2087C2211yescharacteristic
94#2087C2211yescharacteristic
95#2086C2211yescharacteristic
96#2068C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2066C2211yescharacteristic
101#2066C2211yescharacteristic
102#2066C2211yescharacteristic
103#2066C2211yescharacteristic
104#2059C2211yescharacteristic
105#2059C2211yescharacteristic
106#2058C2211yescharacteristic
107#2057C2211yescharacteristic
108#1993C2211yescharacteristic
109#1993C2211yescharacteristic
110#1993C2211yescharacteristic
111#1993C2211yescharacteristic
112#1992C2211yescharacteristic
113#1992C2211yescharacteristic
114#1991C2211yescharacteristic
115#1991C2211yescharacteristic
116#1990C2211yescharacteristic
117#1990C2211yescharacteristic
118#1990C2211yescharacteristic
119#1960C2211yescharacteristic
120#1960C2211yescharacteristic
121#1956C2211yescharacteristic
122#1949C2211yescharacteristic
123#1949C2211yescharacteristic
124#1948C2211yescharacteristic
125#1947C2211yescharacteristic
126#1944C2211yescharacteristic
127#1944C2211yescharacteristic
128#1943C2211yescharacteristic
129#1943C2211yescharacteristic
130#1942C2211yescharacteristic
131#1942C2211yescharacteristic
132#1942C2211yescharacteristic
133#1942C2211yescharacteristic
134#1942C2211yescharacteristic
135#1942C2211yescharacteristic
136#1941C2211yescharacteristic
137#1941C2211yescharacteristic
138#1941C2211yescharacteristic
139#1941C2211yescharacteristic
140#1941C2211yescharacteristic
141#1941C2211yescharacteristic
142#1935C2211yescharacteristic
143#1935C2211yescharacteristic
144#1935C2211yescharacteristic
145#1935C2211yescharacteristic
146#1933C2211yescharacteristic
147#1933C2211yescharacteristic
148#1933C2211yescharacteristic
149#1933C2211yescharacteristic
150#1933C2211yescharacteristic
151#1933C2211yescharacteristic
152#1933C2211yescharacteristic
153#1933C2211yescharacteristic
154#1921C2211yescharacteristic
155#1920C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1919C2211yescharacteristic
159#1918C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1865C2211yescharacteristic
163#1865C2211yescharacteristic
164#1865C2211yescharacteristic
165#1865C2211yescharacteristic
166#1863C2211yescharacteristic
167#1863C2211yescharacteristic
168#1863C2211yescharacteristic
169#1863C2211yescharacteristic
170#1847C2211yescharacteristic
171#1847C2211yescharacteristic
172#1846C2211yescharacteristic
173#1846C2211yescharacteristic
174#1836C2211yescharacteristic
175#1836C2211yescharacteristic
176#1835C2211yescharacteristic
177#1835C2211yescharacteristic
178#1834C2211yescharacteristic
179#1771C2211yescharacteristic
180#1771C2211yescharacteristic
181#1770C2211yescharacteristic
182C8×C4⋊C4C2211yescharacteristic
183C8×C4⋊C4C2211yescharacteristic
184C8×C4⋊C4C2211yescharacteristic
185#1768C2211yescharacteristic
186#1768C2211yescharacteristic
187#1767C2211yescharacteristic
188#1763C2211yescharacteristic
189#1763C2211yescharacteristic
190#1763C2211yescharacteristic
191#1763C2211yescharacteristic
192C4×#103C2211yescharacteristic
193C4×#103C2211yescharacteristic
194C4×#103C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200#1726C2211yescharacteristic
201#1726C2211yescharacteristic
202C42×C8C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#125—21no—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×C4×Q8—21no—
211C2×C4×Q8—21no—
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219#487Q818yescomplemented
220#479—24no—
221#479—24no—
222#477—24no—
223#475—24no—
224#446—24no—
225C8×Q8—24no—
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#97C2311yescharacteristic
265C2×#97C2311yescharacteristic
266C2×#97C2311yescharacteristic
267C2×#97C2311yescharacteristic
268C2×#97C2311yescharacteristic
269C2×#97C2311yescharacteristic
270C2×C4×C8C2311yescharacteristic
271C2×C4×C8C2311yescharacteristic
272C2×C4×C8C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
274C2×C4×C8C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
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#395—21no—
311#395—21no—
312#395—21no—
313#395—21no—
314#395—21no—
315#395—21no—
316#395—21no—
317#395—21no—
318#395—21no—
319#395—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391D411yescharacteristic
331#391D411yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#389—21no—
339#389—21no—
340#389—21no—
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#389—21no—
351#389—21no—
352#389D411yescharacteristic
353#389D411yescharacteristic
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#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#387—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#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—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#387D411yescharacteristic
411#387D411yescharacteristic
412#387D411yescharacteristic
413#387D411yescharacteristic
414#384—21no—
415#384—21no—
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#382—21no—
421#382—21no—
422#382—21no—
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444#376C2311yescharacteristic
445#376C2311yescharacteristic
446C43C2311yescharacteristic
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#340C2311yescharacteristic
478#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8—21no—
488C22×Q8C2×D411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C4⋊Q8—22no—
500C4⋊Q8—22no—
501C4⋊Q8—22no—
502C4⋊Q8—22no—
503C4⋊Q8—41no—
504C4⋊Q8—41no—
505C4⋊Q8C2×Q814yes—
506C4⋊Q8C2×Q814yes—
507#125—22no—
508#125—22no—
509#125—41no—
510#125—41no—
511#125—82no—
512C4×Q8—22no—
513C4×Q8—22no—
514C4×Q8—22no—
515C4×Q8—22no—
516C4×Q8—22no—
517C4×Q8—22no—
518C4×Q8—41no—
519C4×Q8—41no—
520C4×Q8—41no—
521C4×Q8—41no—
522C4×Q8—41no—
523C4×Q8—41no—
524C4×Q8—41no—
525C4×Q8—41no—
526C4×Q8—82no—
527C4×Q8—82no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C42—21no—
597C2×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42C2×D411yescharacteristic
609C2×C42C2×D411yescharacteristic
610C2×C42C2×D411yescharacteristic
611C2×C42C2×D411yescharacteristic
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617C2×C42C2411yescharacteristic
618C2×C42C2411yescharacteristic
619#107—22no—
620#107—22no—
621#107—22no—
622#107—22no—
623#107—41no—
624#107—41no—
625#107—41no—
626#107—41no—
627#106—22no—
628#106—22no—
629#106—22no—
630#106—22no—
631#106—41no—
632#106—41no—
633#106—41no—
634#106—41no—
635C4⋊C8—22no—
636C4⋊C8—22no—
637C4⋊C8—22no—
638C4⋊C8—22no—
639C4⋊C8#4114yes—
640C4⋊C8#4114yes—
641#103—22no—
642#103—22no—
643#103—22no—
644#103—22no—
645#103—22no—
646#103—22no—
647#103—22no—
648#103—22no—
649#103—41no—
650#103—41no—
651#103—41no—
652#103—41no—
653#103C2×Q814yes—
654#103C2×Q814yes—
655#103C2×Q814yes—
656#103C2×Q814yes—
657#97—22no—
658#97—22no—
659#97—22no—
660#97—22no—
661#97—41no—
662#97—41no—
663C4×C8—22no—
664C4×C8—22no—
665C4×C8—22no—
666C4×C8—22no—
667C4×C8—22no—
668C4×C8—41no—
669C4×C8—41no—
670C4×C8—41no—
671C4×C8—41no—
672C4×C8C2×Q814yes—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
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#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739C2×Q8—22no—
740C2×Q8—24no—
741C2×Q8—22no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—41no—
753C2×Q8—42no—
754C2×Q8—81no—
755C2×Q8—81no—
756C2×Q8—81no—
757C2×Q8—81no—
758C2×Q8—81no—
759C2×Q8—81no—
760C2×Q8—81no—
761C2×Q8C22×Q812yes—
762C2×Q8C22×Q812yes—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4C22×D411yescharacteristic
780C22×C4C22×D411yescharacteristic
781C22×C4C22×D411yescharacteristic
782C22×C4C22×D411yescharacteristic
783C22×C4C22×D411yescharacteristic
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D411yescharacteristic
788C22×C4C22×D411yescharacteristic
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C2511yescharacteristic
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8C22×Q812yes—
813C2×C8C22×Q812yes—
814C2×C8C2×#4112yes—
815C2×C8C2×#4112yes—
816C2×C8C2×#4112yes—
817C2×C8C2×#4112yes—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—22no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—41no—
854C4⋊C4—41no—
855C4⋊C4—41no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—42no—
860C4⋊C4—42no—
861C4⋊C4—42no—
862C4⋊C4—42no—
863C4⋊C4—42no—
864C4⋊C4—42no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4C22×Q812yes—
899C4⋊C4C22×Q812yes—
900C42—22no—
901C42—22no—
902C42—21no—
903C42—21no—
904C42—21no—
905C42—21no—
906C42—21no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42—21no—
912C42—41no—
913C42—41no—
914C42—42no—
915C42—42no—
916C42—42no—
917C42—42no—
918C42—81no—
919C42—81no—
920C42—81no—
921C42—81no—
922C42—81no—
923C42—81no—
924C42—81no—
925C42—81no—
926C42C22×Q812yes—
927C42C2×#4112yes—
928C42C2×#4112yes—
929C422−1+412yes—
930C23C23×D411yescharacteristic
931Q8—22no—
932Q8—22no—
933Q8—22no—
934Q8—22no—
935Q8—44no—
936Q8—41no—
937Q8—41no—
938Q8—41no—
939Q8—41no—
940Q8—84no—
941Q8—84no—
942Q8—162no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4#53212yes—
1028C2×C4#53212yes—
1029C2×C4D4×Q812yes—
1030C2×C4D4×Q812yes—
1031C2×C4#57712yes—
1032C2×C4#57812yes—
1033C2×C4C23×Q811yescharacteristic
1034C2×C4C22×#4111yescharacteristic
1035C2×C4C22×#4111yescharacteristic
1036C2×C4C2×2−1+411yescharacteristic
1037C2×C4#58511yescharacteristic
1038C2×C4#58511yescharacteristic
1039C8—22no—
1040C8—22no—
1041C8—22no—
1042C8—22no—
1043C8—22no—
1044C8—22no—
1045C8—41no—
1046C8—41no—
1047C22C2×#53211yescharacteristic
1048C22C2×D4×Q811yescharacteristic
1049C22#350011yescharacteristic
1050C22C2×#57711yescharacteristic
1051C22C2×#57811yescharacteristic
1052C22#358411yescharacteristic
1053C22#358411yescharacteristic
1054C4—22no—
1055C4—22no—
1056C4—22no—
1057C4—22no—
1058C4—22no—
1059C4—22no—
1060C4—41no—
1061C4—41no—
1062C4—41no—
1063C4—41no—
1064C4—41no—
1065C4—41no—
1066C4—41no—
1067C4—41no—
1068C4—42no—
1069C4—42no—
1070C4—42no—
1071C4—42no—
1072C4—81no—
1073C4—81no—
1074C4—81no—
1075C4—81no—
1076C4—81no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4Q8×#4111yescharacteristic
1085C4Q8×#4111yescharacteristic
1086C4#351511yescharacteristic
1087C4#351511yescharacteristic
1088C2#3656211yescharacteristic
1089C2#6069411yescharacteristic
1090C2#6070811yescharacteristic
1091C2#6137111yescharacteristic
1092C2#6137211yescharacteristic
1093C2#6255111yescharacteristic
1094C2#6255511yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
219. #487Q8semidirect

Maximal subgroups

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

subgroupindex
#396812
#396732
#332922
#332622
#332572
#292172
#292022
#291962
#291872
#291822
#289622
#289612
#289562
#289532
#289482
#289472
#289452
#285262
#254882
#254872
#254742
#254712
#229802
#229772
#229672
#229642
#216452
C4×#4872
#205162