Finite Group Databasebeta

← #6586136

Subgroups — #6586136

Order 512.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35815C211yesmaximal, characteristic
2#35786C211yesmaximal, characteristic
3#33219C211yesmaximal, characteristic
4#33157C211yesmaximal, characteristic
5#32964C211yesmaximal, characteristic
6#28956C211yesmaximal, characteristic, complemented
7#28953C211yesmaximal, characteristic, complemented
8#28785C211yesmaximal, characteristic
9#28783C211yesmaximal, characteristic
10#27818C211yesmaximal, characteristic, complemented
11#27305C211yesmaximal, characteristic, complemented
12#27295C211yesmaximal, characteristic, complemented
13#27012C211yesmaximal, characteristic, complemented
14#27000C211yesmaximal, characteristic, complemented
15#26054C211yesmaximal, characteristic, complemented
16#26003C211yesmaximal, characteristic
17#25991C211yesmaximal, characteristic
18#25965C211yesmaximal, characteristic
19#25955C211yesmaximal, characteristic
20#25848C211yesmaximal, characteristic, complemented
21#25480C211yesmaximal, characteristic, complemented
22#25463C211yesmaximal, characteristic, complemented
23#25074C211yesmaximal, characteristic, complemented
24#22973C211yesmaximal, characteristic, complemented
25#22970C211yesmaximal, characteristic, complemented
26#22964C211yesmaximal, characteristic, complemented
27#22585C211yesmaximal, characteristic
28#22581C211yesmaximal, characteristic
29#22527C211yesmaximal, characteristic, complemented
30#21604C211yesmaximal, characteristic
31#20417C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×#475C2211yescharacteristic
38C2×#475C2211yescharacteristic
39C2×#446C2211yescharacteristic
40C2×#419C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C2×#405C2211yescharacteristic
43#2666—21no—
44#2629—21no—
45#2629C2211yescharacteristic
46#2628C2211yescharacteristic
47#2605—21no—
48#2589—21no—
49#2582—21no—
50#2582C2211yescharacteristic
51#2574—21no—
52#2570—21no—
53#2567C2211yescharacteristic
54#2565—21no—
55#2565C2211yescharacteristic
56#2550C2211yescharacteristic
57#2508C2211yescharacteristic
58#2507C2211yescharacteristic
59#2465—21no—
60#2453—21no—
61#2453C2211yescharacteristic
62#2451—21no—
63#2451C2211yescharacteristic
64#2442C2211yescharacteristic
65#2441—21no—
66#2441C2211yescharacteristic
67#2440C2211yescharacteristic
68#2439—21no—
69#2439C2211yescharacteristic
70#2423—21no—
71#2399—21no—
72#2396—21no—
73#2396C2211yescharacteristic
74#2370C2211yescharacteristic
75#2365C2211yescharacteristic
76#2365C2211yescharacteristic
77#2355C2211yescharacteristic
78#2351C2211yescharacteristic
79Q8×C4⋊C4C2211yescharacteristic
80Q8×C4⋊C4C2211yescharacteristic
81#2347C2211yescharacteristic
82#2346C2211yescharacteristic
83Q8×C22⋊C4C2211yescharacteristic
84Q8×C22⋊C4C2211yescharacteristic
85#2274C2211yescharacteristic
86#2101C2211yescharacteristic
87#2099C2211yescharacteristic
88#2097C2211yescharacteristic
89#2096C2211yescharacteristic
90#2088C2211yescharacteristic
91#2087C2211yescharacteristic
92#2086C2211yescharacteristic
93#2086C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2084C2211yescharacteristic
97#2083C2211yescharacteristic
98#2068C2211yescharacteristic
99#2066C2211yescharacteristic
100#2066C2211yescharacteristic
101#2066C2211yescharacteristic
102#2059C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2058C2211yescharacteristic
106#2058C2211yescharacteristic
107#2058C2211yescharacteristic
108#2026C2211yescharacteristic
109#2024C2211yescharacteristic
110#1993C2211yescharacteristic
111#1992C2211yescharacteristic
112#1991C2211yescharacteristic
113#1991C2211yescharacteristic
114#1990C2211yescharacteristic
115#1990C2211yescharacteristic
116#1989C2211yescharacteristic
117#1989C2211yescharacteristic
118#1989C2211yescharacteristic
119#1987C2211yescharacteristic
120#1985C2211yescharacteristic
121#1949C2211yescharacteristic
122#1948C2211yescharacteristic
123#1948C2211yescharacteristic
124#1947C2211yescharacteristic
125#1944C2211yescharacteristic
126#1944C2211yescharacteristic
127#1944C2211yescharacteristic
128#1943C2211yescharacteristic
129#1942C2211yescharacteristic
130#1941C2211yescharacteristic
131#1941C2211yescharacteristic
132#1941C2211yescharacteristic
133#1940C2211yescharacteristic
134#1935C2211yescharacteristic
135#1935C2211yescharacteristic
136#1933C2211yescharacteristic
137#1933C2211yescharacteristic
138#1928C2211yescharacteristic
139#1928C2211yescharacteristic
140#1927C2211yescharacteristic
141#1927C2211yescharacteristic
142#1921C2211yescharacteristic
143#1920C2211yescharacteristic
144#1920C2211yescharacteristic
145#1920C2211yescharacteristic
146#1920C2211yescharacteristic
147#1919C2211yescharacteristic
148#1919C2211yescharacteristic
149#1919C2211yescharacteristic
150#1916C2211yescharacteristic
151#1916C2211yescharacteristic
152#1865C2211yescharacteristic
153#1865C2211yescharacteristic
154#1865C2211yescharacteristic
155#1865C2211yescharacteristic
156#1865C2211yescharacteristic
157#1865C2211yescharacteristic
158#1865C2211yescharacteristic
159#1863C2211yescharacteristic
160#1863C2211yescharacteristic
161#1863C2211yescharacteristic
162#1863C2211yescharacteristic
163#1863C2211yescharacteristic
164#1854C2211yescharacteristic
165#1854C2211yescharacteristic
166#1853C2211yescharacteristic
167#1853C2211yescharacteristic
168#1850C2211yescharacteristic
169#1850C2211yescharacteristic
170#1847C2211yescharacteristic
171#1825C2211yescharacteristic
172#1825C2211yescharacteristic
173#1809C2211yescharacteristic
174#1809C2211yescharacteristic
175#1808C2211yescharacteristic
176#1807C2211yescharacteristic
177#1805C2211yescharacteristic
178#1805C2211yescharacteristic
179#1805C2211yescharacteristic
180#1803C2211yescharacteristic
181#1798C2211yescharacteristic
182#1787C2211yescharacteristic
183#1787C2211yescharacteristic
184#1770C2211yescharacteristic
185#1770C2211yescharacteristic
186C8×C4⋊C4C2211yescharacteristic
187#1763C2211yescharacteristic
188#1763C2211yescharacteristic
189#1763C2211yescharacteristic
190#1763C2211yescharacteristic
191#1763C2211yescharacteristic
192#1763C2211yescharacteristic
193C4×#103C2211yescharacteristic
194C4×#103C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1736C2211yescharacteristic
202#1735C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206#557—24no—
207#557—42no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#125—21no—
213C2×#125—21no—
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×C22⋊Q8—21no—
218#519—24no—
219#519—42no—
220C2×C4×Q8—21no—
221C2×C4×Q8—21no—
222C2×C4×Q8—21no—
223C2×C4×Q8—21no—
224C2×C4×Q8—21no—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×#117—21no—
235C2×#117—21no—
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240#501—42no—
241#479—24no—
242#477—42no—
243#475—24no—
244#475—24no—
245#446—42no—
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268#419Q818yescomplemented
269C2×#103—24no—
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288#405—42no—
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400D411yescharacteristic
302#399—21no—
303#399—21no—
304#399D411yescharacteristic
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#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398D411yescharacteristic
320#398D411yescharacteristic
321#396—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#396D411yescharacteristic
326#396D411yescharacteristic
327#395—21no—
328#395—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#395D411yescharacteristic
334#393—21no—
335#393—21no—
336#393D411yescharacteristic
337#391—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
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#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#385—21no—
402#385—21no—
403#384—21no—
404#384—21no—
405#384—21no—
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#383—21no—
410#382—21no—
411#382—21no—
412#382—21no—
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#380—21no—
417#380—21no—
418#380—21no—
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4C2311yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
448#376—21no—
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#340C2311yescharacteristic
480#340C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—22no—
496C22×Q8—22no—
497C22×Q8—22no—
498C22×Q8—41no—
499C22×Q8—41no—
500C22×Q8C2×D411yescharacteristic
501C22×Q8C2×Q814yes—
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C2411yescharacteristic
507C2×M16—41no—
508C2×M16—41no—
509C2×M16C2×Q814yes—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—41no—
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C4⋊Q8—22no—
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8—22no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8—44no—
528#125—22no—
529#125—22no—
530#125—22no—
531#125—22no—
532#125—41no—
533#125—41no—
534#125—44no—
535#125—44no—
536C22⋊Q8—82no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×Q8—41no—
554C4×Q8—44no—
555C4×Q8—44no—
556C4×Q8—44no—
557C4×Q8—82no—
558C4×Q8—82no—
559C4×Q8#4114yes—
560#117—22no—
561#117—22no—
562#117—22no—
563#117—22no—
564#117—44no—
565#117—44no—
566#117—41no—
567#117C2×Q814yes—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—22no—
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⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671#107—22no—
672#107—41no—
673#107—41no—
674#107—41no—
675#107—41no—
676#107—41no—
677#106—22no—
678#106—22no—
679#106—22no—
680#106—22no—
681#106—22no—
682#106—41no—
683#106—41no—
684#106—41no—
685#106—41no—
686#106—41no—
687C4⋊C8—22no—
688C4⋊C8—22no—
689C4⋊C8—22no—
690C4⋊C8—22no—
691C4⋊C8—41no—
692C4⋊C8—41no—
693#103—22no—
694#103—22no—
695#103—22no—
696#103—22no—
697#103—22no—
698#103—22no—
699#103—22no—
700#103—41no—
701#103—41no—
702#103—41no—
703#103—41no—
704#103C2×Q814yes—
705#103C2×Q814yes—
706#103C2×Q814yes—
707#103C2×Q814yes—
708#103#4114yes—
709C22⋊C8—22no—
710C22⋊C8—22no—
711#97—22no—
712#97—41no—
713#97—41no—
714#97—41no—
715C4×C8—22no—
716C4×C8—41no—
717C4×C8—41no—
718C4×C8—41no—
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#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771C24C22×D411yescharacteristic
772C2×Q8—22no—
773C2×Q8—24no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—28no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—41no—
784C2×Q8—41no—
785C2×Q8—42no—
786C2×Q8—42no—
787C2×Q8—42no—
788C2×Q8—42no—
789C2×Q8—44no—
790C2×Q8—44no—
791C2×Q8—44no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8—42no—
795C2×Q8—81no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×Q8—81no—
799C2×Q8C22×Q812yes—
800C2×Q8C22×Q812yes—
801C2×Q8C2×#4112yes—
802C2×Q8C2×#4112yes—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—24no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—81no—
828C22×C4—81no—
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×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×Q812yes—
843C22×C42−1+412yes—
844C22×C4C2511yescharacteristic
845M16—44no—
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—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—44no—
868C2×C8C22×Q812yes—
869C2×C8C22×Q812yes—
870C2×C8C2×#4112yes—
871C4⋊C4—24no—
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—22no—
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—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—41no—
904C4⋊C4—41no—
905C4⋊C4—41no—
906C4⋊C4—41no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
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⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4C22×Q812yes—
947C4⋊C4C22×Q812yes—
948C4⋊C4C2×#4112yes—
949C4⋊C4C2×#4112yes—
950C22⋊C4—24no—
951C22⋊C4—22no—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—41no—
957C22⋊C4—42no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C42—24no—
963C42—24no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—42no—
975C42—42no—
976C42—42no—
977C42—42no—
978C42—42no—
979C42—42no—
980C42—42no—
981C42—42no—
982C42—42no—
983C42—42no—
984C42—81no—
985C42—81no—
986C42—81no—
987C42—81no—
988C42—81no—
989C42—81no—
990C42C2×#4112yes—
991C42H(5,𝔽2)12yes—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23D4×Q812yes—
999C23C23×D411yescharacteristic
1000Q8—22no—
1001Q8—22no—
1002Q8—22no—
1003Q8—22no—
1004Q8—22no—
1005Q8—48no—
1006Q8—41no—
1007Q8—41no—
1008Q8—82no—
1009Q8—84no—
1010Q8—84no—
1011Q8—84no—
1012Q8#53314yes—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—21no—
1029C2×C4—21no—
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—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—48no—
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—162no—
1102C2×C4#54612yes—
1103C2×C4#54612yes—
1104C2×C4D4×Q812yes—
1105C2×C4#57712yes—
1106C2×C4C23×Q811yescharacteristic
1107C2×C4C22×#4111yescharacteristic
1108C2×C4C22×#4111yescharacteristic
1109C2×C4C2×H(5,𝔽2)11yescharacteristic
1110C2×C4C2×2−1+411yescharacteristic
1111C2×C4#58511yescharacteristic
1112C8—22no—
1113C8—22no—
1114C8—22no—
1115C8—41no—
1116C8—41no—
1117C8—41no—
1118C8—41no—
1119C8—41no—
1120C22—22no—
1121C22—22no—
1122C22—22no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22C2×#54611yescharacteristic
1128C22C2×D4×Q811yescharacteristic
1129C22D4×#4111yescharacteristic
1130C22C2×#57711yescharacteristic
1131C22#358411yescharacteristic
1132C22#358611yescharacteristic
1133C22#358611yescharacteristic
1134C4—22no—
1135C4—22no—
1136C4—24no—
1137C4—22no—
1138C4—22no—
1139C4—41no—
1140C4—41no—
1141C4—41no—
1142C4—42no—
1143C4—41no—
1144C4—42no—
1145C4—41no—
1146C4—41no—
1147C4—42no—
1148C4—42no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—42no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4C2×#53311yescharacteristic
1164C4#349511yescharacteristic
1165C4#350111yescharacteristic
1166C4#352011yescharacteristic
1167C2—42no—
1168C2#3613011yescharacteristic
1169C2#6118111yescharacteristic
1170C2#6121311yescharacteristic
1171C2#6138311yescharacteristic
1172C2#6138611yescharacteristic
1173C2#6152011yescharacteristic
1174C2#6153311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
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
6. #28956C2semidirect
7. #28953C2semidirect
10. #27818C2semidirect
11. #27305C2semidirect
12. #27295C2semidirect
13. #27012C2semidirect
14. #27000C2semidirect
15. #26054C2semidirect
20. #25848C2semidirect
21. #25480C2semidirect
22. #25463C2semidirect
23. #25074C2semidirect
24. #22973C2semidirect
25. #22970C2semidirect
26. #22964C2semidirect
29. #22527C2semidirect
268. #419Q8semidirect

Maximal subgroups

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

subgroupindex
#358152
#357862
#332192
#331572
#329642
#289562
#289532
#287852
#287832
#278182
#273052
#272952
#270122
#270002
#260542
#260032
#259912
#259652
#259552
#258482
#254802
#254632
#250742
#229732
#229702
#229642
#225852
#225812
#225272
#216042
#204172