Finite Group Databasebeta

← #6728840

Subgroups — #6728840

Order 512.

1213 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42455C211yesmaximal, characteristic
2#35818C211yesmaximal, characteristic
3#33157C211yesmaximal, characteristic
4#32498C211yesmaximal, characteristic, complemented
5#32477C211yesmaximal, characteristic, complemented
6#32392C211yesmaximal, characteristic, complemented
7#32376C211yesmaximal, characteristic, complemented
8#32296C211yesmaximal, characteristic
9#32296C211yesmaximal, characteristic
10#32280C211yesmaximal, characteristic
11#32280C211yesmaximal, characteristic
12#29934C211yesmaximal, characteristic
13#29856C211yesmaximal, characteristic
14#28837C211yesmaximal, characteristic, complemented
15#28652C211yesmaximal, characteristic, complemented
16#27380C211yesmaximal, characteristic, complemented
17#27366C211yesmaximal, characteristic, complemented
18#27120C211yesmaximal, characteristic
19#27103C211yesmaximal, characteristic
20#27060C211yesmaximal, characteristic
21#27043C211yesmaximal, characteristic
22#26528C211yesmaximal, characteristic, complemented
23#26517C211yesmaximal, characteristic, complemented
24#26320C211yesmaximal, characteristic, complemented
25#26285C211yesmaximal, characteristic, complemented
26#26104C211yesmaximal, characteristic, complemented
27#26088C211yesmaximal, characteristic, complemented
28#23233C211yesmaximal, characteristic, complemented
29#22729C211yesmaximal, characteristic, complemented
30#22109C211yesmaximal, characteristic
31#21369C211yesmaximal, characteristic
32C2×#491C2211yescharacteristic
33C2×#446C2211yescharacteristic
34C2×#433C2211yescharacteristic
35#2839—21no—
36#2802—21no—
37#2725—21no—
38#2725—21no—
39#2719—21no—
40#2664—21no—
41#2655—21no—
42#2637—21no—
43#2629C2211yescharacteristic
44#2621C2211yescharacteristic
45#2584C2211yescharacteristic
46#2575—21no—
47#2573—21no—
48#2570C2211yescharacteristic
49#2568C2211yescharacteristic
50#2552C2211yescharacteristic
51#2552C2211yescharacteristic
52#2552C2211yescharacteristic
53#2527—21no—
54#2524—21no—
55#2520—21no—
56#2515—21no—
57#2514C2211yescharacteristic
58#2511C2211yescharacteristic
59#2509C2211yescharacteristic
60#2508C2211yescharacteristic
61#2503C2211yescharacteristic
62#2502C2211yescharacteristic
63#2497C2211yescharacteristic
64#2497C2211yescharacteristic
65#2496C2211yescharacteristic
66#2496C2211yescharacteristic
67#2462—21no—
68#2402—21no—
69#2396C2211yescharacteristic
70#2370C2211yescharacteristic
71#2365C2211yescharacteristic
72#2362C2211yescharacteristic
73#2362C2211yescharacteristic
74#2356C2211yescharacteristic
75#2355C2211yescharacteristic
76#2355C2211yescharacteristic
77Q8×C4⋊C4C2211yescharacteristic
78#2314C2211yescharacteristic
79#2274C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2100C2211yescharacteristic
83#2100C2211yescharacteristic
84#2096C2211yescharacteristic
85#2096C2211yescharacteristic
86#2096C2211yescharacteristic
87#2096C2211yescharacteristic
88#2096C2211yescharacteristic
89#2095C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2084C2211yescharacteristic
95#2084C2211yescharacteristic
96#2084C2211yescharacteristic
97#2083C2211yescharacteristic
98#2074C2211yescharacteristic
99#2074C2211yescharacteristic
100#2072C2211yescharacteristic
101#2072C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2068C2211yescharacteristic
106#2066C2211yescharacteristic
107#2066C2211yescharacteristic
108#2066C2211yescharacteristic
109#2066C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#1991C2211yescharacteristic
121#1989C2211yescharacteristic
122#1989C2211yescharacteristic
123#1984C2211yescharacteristic
124#1981C2211yescharacteristic
125#1981C2211yescharacteristic
126#1956C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1948C2211yescharacteristic
134#1948C2211yescharacteristic
135#1948C2211yescharacteristic
136#1948C2211yescharacteristic
137#1948C2211yescharacteristic
138#1948C2211yescharacteristic
139#1948C2211yescharacteristic
140#1947C2211yescharacteristic
141#1944C2211yescharacteristic
142#1942C2211yescharacteristic
143#1940C2211yescharacteristic
144#1939C2211yescharacteristic
145#1939C2211yescharacteristic
146#1935C2211yescharacteristic
147#1935C2211yescharacteristic
148#1935C2211yescharacteristic
149#1933C2211yescharacteristic
150#1933C2211yescharacteristic
151#1933C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1927C2211yescharacteristic
156#1927C2211yescharacteristic
157#1927C2211yescharacteristic
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic
160#1923C2211yescharacteristic
161#1923C2211yescharacteristic
162#1920C2211yescharacteristic
163#1920C2211yescharacteristic
164#1920C2211yescharacteristic
165#1920C2211yescharacteristic
166#1920C2211yescharacteristic
167#1919C2211yescharacteristic
168#1919C2211yescharacteristic
169#1919C2211yescharacteristic
170#1918C2211yescharacteristic
171#1918C2211yescharacteristic
172#1917C2211yescharacteristic
173#1916C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic
182#1853C2211yescharacteristic
183#1853C2211yescharacteristic
184#1847C2211yescharacteristic
185#1847C2211yescharacteristic
186#1847C2211yescharacteristic
187#1844C2211yescharacteristic
188#1844C2211yescharacteristic
189#1825C2211yescharacteristic
190#1825C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1798C2211yescharacteristic
194#1776C2211yescharacteristic
195#1776C2211yescharacteristic
196#1776C2211yescharacteristic
197C4×#107C2211yescharacteristic
198C4×#106C2211yescharacteristic
199C4×#106C2211yescharacteristic
200#1771C2211yescharacteristic
201#1763C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×#126—21no—
205C2×#126—21no—
206C2×#125—21no—
207C2×#125—21no—
208C2×#125—21no—
209C2×#125C2311yescharacteristic
210C2×C22⋊Q8C2311yescharacteristic
211C2×C22⋊Q8C2311yescharacteristic
212C2×C4×Q8—21no—
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×#117C2311yescharacteristic
217C2×#117C2311yescharacteristic
218C22×C4⋊C4C2311yescharacteristic
219#491—24no—
220#446—24no—
221#433—24no—
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#106C2311yescharacteristic
229C2×#106C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
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×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×C22⋊C8C2311yescharacteristic
267C2×C22⋊C8C2311yescharacteristic
268C2×C22⋊C8C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×#97C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
274C2×C4×C8C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276#401—21no—
277#400—21no—
278#400—21no—
279#400—21no—
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#400—21no—
291#400—21no—
292#400D411yescharacteristic
293#399D411yescharacteristic
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#398D411yescharacteristic
310#398D411yescharacteristic
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#396—21no—
319#396D411yescharacteristic
320#396D411yescharacteristic
321#395—21no—
322#395D411yescharacteristic
323#393D411yescharacteristic
324#391—21no—
325#391—21no—
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
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#385—21no—
391#385—21no—
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#384C2311yescharacteristic
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#383—21no—
401#383—21no—
402#382—21no—
403#382—21no—
404#382—21no—
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#381—21no—
410#381—21no—
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8C2×D411yescharacteristic
482C22×Q8C2411yescharacteristic
483C22×Q8C2411yescharacteristic
484C23×C4—21no—
485C23×C4C2411yescharacteristic
486C22×C8C2411yescharacteristic
487C22×C8C2411yescharacteristic
488C22×C8C2411yescharacteristic
489C22×C8C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C4⋊Q8—22no—
495C4⋊Q8—22no—
496#126—82no—
497#126—82no—
498#125—22no—
499#125—22no—
500#125—82no—
501#125—82no—
502#125—82no—
503C22⋊Q8—41no—
504C22⋊Q8—41no—
505C22⋊Q8—41no—
506C22⋊Q8—41no—
507C4×Q8—22no—
508C4×Q8—22no—
509C4×Q8—22no—
510C4×Q8—22no—
511C4×Q8—41no—
512C4×Q8—41no—
513C4×Q8—82no—
514#117—22no—
515#117—22no—
516#117—22no—
517#117—41no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
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—41no—
556C2×C4⋊C4—41no—
557C2×C4⋊C4C2×D411yescharacteristic
558C2×C4⋊C4C2×D411yescharacteristic
559C2×C4⋊C4C2×D411yescharacteristic
560C2×C4⋊C4C2×D411yescharacteristic
561C2×C4⋊C4C2×D411yescharacteristic
562C2×C4⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4C2×D411yescharacteristic
590C2×C22⋊C4C2×D411yescharacteristic
591C2×C22⋊C4C2×D411yescharacteristic
592C2×C22⋊C4C2×D411yescharacteristic
593C2×C22⋊C4C2×D411yescharacteristic
594C2×C22⋊C4C2×D411yescharacteristic
595C2×C42—21no—
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×C42—21no—
609C2×C42—21no—
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615C2×C42C2411yescharacteristic
616#107—22no—
617#107—41no—
618#107—41no—
619#107—41no—
620#107—41no—
621#107—41no—
622#106—22no—
623#106—41no—
624#106—41no—
625#106—41no—
626#106—41no—
627#106—41no—
628#106—41no—
629#106—41no—
630#106—41no—
631#106—41no—
632#106—41no—
633#106—41no—
634#106—41no—
635#106—41no—
636C4⋊C8—22no—
637C4⋊C8—22no—
638C4⋊C8—22no—
639C4⋊C8—22no—
640C4⋊C8—22no—
641C4⋊C8—22no—
642C4⋊C8—41no—
643C4⋊C8—41no—
644#103—22no—
645#103—22no—
646#103—22no—
647#103—22no—
648#103—41no—
649#103—41no—
650#103—41no—
651#103—41no—
652#103—41no—
653#103—41no—
654#103—41no—
655#103—41no—
656#103—41no—
657#103—41no—
658#103—41no—
659#103—41no—
660C22⋊C8—22no—
661C22⋊C8—22no—
662C22⋊C8—41no—
663C22⋊C8—41no—
664#97—22no—
665#97—41no—
666#97#4114yes—
667C4×C8—22no—
668C4×C8—22no—
669C4×C8—41no—
670#95—21no—
671#95—21no—
672#95—21no—
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#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732C24C22×D411yescharacteristic
733C2×Q8—22no—
734C2×Q8—22no—
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—41no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—42no—
771C22×C4—81no—
772C22×C4—81no—
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D411yescharacteristic
775C22×C4C22×D411yescharacteristic
776C22×C4C22×D411yescharacteristic
777C22×C4C22×D411yescharacteristic
778C22×C4C22×D411yescharacteristic
779C22×C4C22×D411yescharacteristic
780C22×C4C22×D411yescharacteristic
781C22×C4C22×D411yescharacteristic
782C22×C4C22×D411yescharacteristic
783C22×C4C22×D411yescharacteristic
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C2511yescharacteristic
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
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×C8C2×#4112yes—
810C2×C8C2×#4112yes—
811C4⋊C4—22no—
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
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—41no—
847C4⋊C4—41no—
848C4⋊C4—41no—
849C4⋊C4—42no—
850C4⋊C4—42no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
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⋊C42−1+412yes—
887C22⋊C4—22no—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—41no—
892C22⋊C4—41no—
893C22⋊C4—42no—
894C22⋊C4—42no—
895C22⋊C4—42no—
896C22⋊C4—81no—
897C22⋊C4—81no—
898C22⋊C4—81no—
899C22⋊C4—81no—
900C42—21no—
901C42—21no—
902C42—21no—
903C42—21no—
904C42—21no—
905C42—21no—
906C42—21no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—42no—
911C42—42no—
912C42—42no—
913C42—42no—
914C42—42no—
915C42—42no—
916C42—81no—
917C42—81no—
918C42—81no—
919C42—81no—
920C42—81no—
921C42—81no—
922C42—81no—
923C42—81no—
924C42—81no—
925C42C2×#4112yes—
926C422−1+412yes—
927C23—21no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23C23×D411yescharacteristic
935Q8—44no—
936Q8—41no—
937Q8—41no—
938Q8—41no—
939Q8—41no—
940Q8—41no—
941Q8—41no—
942Q8—41no—
943Q8—41no—
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—21no—
968C2×C4—21no—
969C2×C4—21no—
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—41no—
981C2×C4—41no—
982C2×C4—41no—
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—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—162no—
1032C2×C4#54712yes—
1033C2×C4#54712yes—
1034C2×C4#57712yes—
1035C2×C4#57712yes—
1036C2×C4C22×#4111yescharacteristic
1037C2×C4C2×2−1+411yescharacteristic
1038C2×C4C2×2−1+411yescharacteristic
1039C2×C4#58511yescharacteristic
1040C2×C4#58511yescharacteristic
1041C2×C4#58511yescharacteristic
1042C8—22no—
1043C8—22no—
1044C8—41no—
1045C8—41no—
1046C8—41no—
1047C8—41no—
1048C8—41no—
1049C8—41no—
1050C22—41no—
1051C22—41no—
1052C22—41no—
1053C22—41no—
1054C22—41no—
1055C22—41no—
1056C22—41no—
1057C22C2×#54711yescharacteristic
1058C22#348711yescharacteristic
1059C22#348911yescharacteristic
1060C22C2×#57711yescharacteristic
1061C22C2×#57711yescharacteristic
1062C22#358611yescharacteristic
1063C22#358611yescharacteristic
1064C4—22no—
1065C4—22no—
1066C4—22no—
1067C4—22no—
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—41no—
1072C4—41no—
1073C4—41no—
1074C4—41no—
1075C4—41no—
1076C4—41no—
1077C4—42no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4—81no—
1086C4—81no—
1087C4—81no—
1088C4—81no—
1089C4—81no—
1090C4—81no—
1091C4—81no—
1092C4—81no—
1093C4#346111yescharacteristic
1094C4#351211yescharacteristic
1095C4#355511yescharacteristic
1096C4#355711yescharacteristic
1097C2—81no—
1098C2#3779911yescharacteristic
1099C2#6127111yescharacteristic
1100C2#6128111yescharacteristic
1101C2#6193511yescharacteristic
1102C2#6194311yescharacteristic
1103C2#6215711yescharacteristic
1104C2#6218211yescharacteristic
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
4. #32498C2semidirect
5. #32477C2semidirect
6. #32392C2semidirect
7. #32376C2semidirect
14. #28837C2semidirect
15. #28652C2semidirect
16. #27380C2semidirect
17. #27366C2semidirect
22. #26528C2semidirect
23. #26517C2semidirect
24. #26320C2semidirect
25. #26285C2semidirect
26. #26104C2semidirect
27. #26088C2semidirect
28. #23233C2semidirect
29. #22729C2semidirect

Maximal subgroups

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

subgroupindex
#424552
#358182
#331572
#324982
#324772
#323922
#323762
#322962
#322802
#299342
#298562
#288372
#286522
#273802
#273662
#271202
#271032
#270602
#270432
#265282
#265172
#263202
#262852
#261042
#260882
#232332
#227292
#221092
#213692