Finite Group Databasebeta

← #6777783

Subgroups — #6777783

Order 512.

1224 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38976C211yesmaximal, characteristic
2#35656C211yesmaximal, characteristic
3#33091C211yesmaximal, characteristic
4#32656C211yesmaximal, characteristic
5#32625C211yesmaximal, characteristic
6#32602C211yesmaximal, characteristic
7#32557C211yesmaximal, characteristic
8#32313C211yesmaximal, characteristic
9#32082C211yesmaximal, characteristic
10#31575C211yesmaximal, characteristic
11#30744C211yesmaximal, characteristic
12#30140C211yesmaximal, characteristic
13#30078C211yesmaximal, characteristic
14#29573C211yesmaximal, characteristic
15#29549C211yesmaximal, characteristic
16#29509C211yesmaximal, characteristic
17#29439C211yesmaximal, characteristic
18#29379C211yesmaximal, characteristic
19#29371C211yesmaximal, characteristic
20#29034C211yesmaximal, characteristic
21#28904C211yesmaximal, characteristic
22#28030C211yesmaximal, characteristic
23#27570C211yesmaximal, characteristic
24#27487C211yesmaximal, characteristic
25#27209C211yesmaximal, characteristic
26#26255C211yesmaximal, characteristic
27#26171C211yesmaximal, characteristic
28#22833C211yesmaximal, characteristic
29#22270C211yesmaximal, characteristic
30#22164C211yesmaximal, characteristic
31#21132C211yesmaximal, characteristic
32C2×#494C2211yescharacteristic
33C2×#462C2211yescharacteristic
34C2×C4×Q16C2211yescharacteristic
35#2859C2211yescharacteristic
36#2766—21no—
37#2766—21no—
38#2719—21no—
39#2719—21no—
40#2645C2211yescharacteristic
41#2645C2211yescharacteristic
42#2590—21no—
43#2588—21no—
44#2582C2211yescharacteristic
45#2582C2211yescharacteristic
46#2581C2211yescharacteristic
47#2570C2211yescharacteristic
48#2568C2211yescharacteristic
49#2546C2211yescharacteristic
50#2533—21no—
51#2533—21no—
52#2528—21no—
53#2528—21no—
54#2524—21no—
55#2520—21no—
56#2514—21no—
57#2514C2211yescharacteristic
58#2511—21no—
59#2511C2211yescharacteristic
60#2508—21no—
61#2506—21no—
62#2506C2211yescharacteristic
63#2506C2211yescharacteristic
64#2446C2211yescharacteristic
65#2446C2211yescharacteristic
66#2446C2211yescharacteristic
67#2446C2211yescharacteristic
68#2355C2211yescharacteristic
69Q8×C4⋊C4C2211yescharacteristic
70#2327C2211yescharacteristic
71#2327C2211yescharacteristic
72#2320C2211yescharacteristic
73#2320C2211yescharacteristic
74#2320C2211yescharacteristic
75C4×C4⋊Q8C2211yescharacteristic
76C4×C4⋊Q8C2211yescharacteristic
77#2295C2211yescharacteristic
78#2295C2211yescharacteristic
79#2276C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2100C2211yescharacteristic
83#2099C2211yescharacteristic
84#2097C2211yescharacteristic
85#2097C2211yescharacteristic
86#2096C2211yescharacteristic
87#2096C2211yescharacteristic
88#2096C2211yescharacteristic
89#2095C2211yescharacteristic
90#2088C2211yescharacteristic
91#2087C2211yescharacteristic
92#2085C2211yescharacteristic
93#2084C2211yescharacteristic
94#2084C2211yescharacteristic
95#2083C2211yescharacteristic
96#2074C2211yescharacteristic
97#2072C2211yescharacteristic
98#2072C2211yescharacteristic
99#2072C2211yescharacteristic
100#2068C2211yescharacteristic
101#2068C2211yescharacteristic
102#2066C2211yescharacteristic
103#2066C2211yescharacteristic
104#2066C2211yescharacteristic
105#2066C2211yescharacteristic
106#2056C2211yescharacteristic
107#2056C2211yescharacteristic
108#2056C2211yescharacteristic
109#2056C2211yescharacteristic
110#2043C2211yescharacteristic
111#2043C2211yescharacteristic
112#2043C2211yescharacteristic
113#2043C2211yescharacteristic
114#2043C2211yescharacteristic
115#2043C2211yescharacteristic
116#2016C2211yescharacteristic
117#2016C2211yescharacteristic
118#2016C2211yescharacteristic
119#2016C2211yescharacteristic
120#1985C2211yescharacteristic
121#1984C2211yescharacteristic
122#1981C2211yescharacteristic
123#1971C2211yescharacteristic
124#1971C2211yescharacteristic
125#1969C2211yescharacteristic
126#1969C2211yescharacteristic
127#1969C2211yescharacteristic
128#1956C2211yescharacteristic
129#1956C2211yescharacteristic
130#1949C2211yescharacteristic
131#1942C2211yescharacteristic
132#1942C2211yescharacteristic
133#1941C2211yescharacteristic
134#1935C2211yescharacteristic
135#1935C2211yescharacteristic
136#1935C2211yescharacteristic
137#1935C2211yescharacteristic
138#1933C2211yescharacteristic
139#1933C2211yescharacteristic
140#1933C2211yescharacteristic
141#1933C2211yescharacteristic
142#1928C2211yescharacteristic
143#1928C2211yescharacteristic
144#1927C2211yescharacteristic
145#1927C2211yescharacteristic
146#1927C2211yescharacteristic
147#1927C2211yescharacteristic
148#1927C2211yescharacteristic
149#1927C2211yescharacteristic
150#1921C2211yescharacteristic
151#1921C2211yescharacteristic
152#1921C2211yescharacteristic
153#1920C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1917C2211yescharacteristic
157#1916C2211yescharacteristic
158#1916C2211yescharacteristic
159#1916C2211yescharacteristic
160#1878C2211yescharacteristic
161#1878C2211yescharacteristic
162#1878C2211yescharacteristic
163#1878C2211yescharacteristic
164#1878C2211yescharacteristic
165#1878C2211yescharacteristic
166#1878C2211yescharacteristic
167#1878C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1865C2211yescharacteristic
183#1865C2211yescharacteristic
184#1865C2211yescharacteristic
185#1865C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1863C2211yescharacteristic
189#1863C2211yescharacteristic
190#1840C2211yescharacteristic
191#1839C2211yescharacteristic
192#1834C2211yescharacteristic
193#1832C2211yescharacteristic
194#1805C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1771C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic
198#1768C2211yescharacteristic
199#1763C2211yescharacteristic
200#1763C2211yescharacteristic
201#1746C2211yescharacteristic
202#1744C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#125—21no—
214C2×#125—21no—
215C2×#125—21no—
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226#494—24no—
227#462—24no—
228C4×Q16—24no—
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#97C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
274C2×C4×C8C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277#401—21no—
278#401—21no—
279#401—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#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—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#395—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#391D411yescharacteristic
317#391D411yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
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#389—21no—
346#389—21no—
347#389—21no—
348#389D411yescharacteristic
349#389D411yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#387—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#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#387D411yescharacteristic
400#387D411yescharacteristic
401#387D411yescharacteristic
402#387D411yescharacteristic
403#384—21no—
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#383—21no—
409#383—21no—
410#383—21no—
411#383—21no—
412#382—21no—
413#382—21no—
414#382—21no—
415#382—21no—
416#382—21no—
417#382—21no—
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
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⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438#376—21no—
439#376—21no—
440#376C2311yescharacteristic
441#376C2311yescharacteristic
442C43C2311yescharacteristic
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#336C2311yescharacteristic
464#336C2311yescharacteristic
465#336C2311yescharacteristic
466#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
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
484C22×Q8C2411yescharacteristic
485C22×Q8C2411yescharacteristic
486C22×Q8C2411yescharacteristic
487C2×Q16—22no—
488C2×Q16—22no—
489C2×Q16—22no—
490C2×Q16—22no—
491C2×Q16—41no—
492C2×Q16—41no—
493C2×Q16—41no—
494C2×Q16—41no—
495C2×Q16—41no—
496C2×Q16—41no—
497C2×Q16—41no—
498C2×Q16—41no—
499C2×Q16—41no—
500C2×Q16—41no—
501C2×Q16—41no—
502C2×Q16—41no—
503C2×Q16—41no—
504C2×Q16#4114yes—
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C4⋊Q8—22no—
514C4⋊Q8—22no—
515C4⋊Q8—22no—
516C4⋊Q8—41no—
517C4⋊Q8—41no—
518C4⋊Q8—41no—
519C4⋊Q8—41no—
520C4⋊Q8—41no—
521#125—82no—
522#125—82no—
523#125—82no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×Q8—22no—
527C4×Q8—41no—
528C4×Q8—41no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×Q8—41no—
532C4×Q8—41no—
533C4×Q8—41no—
534C4×Q8—41no—
535C4×Q8—41no—
536C4×Q8—41no—
537C4×Q8—41no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
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⋊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⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42C2×D411yescharacteristic
618C2×C42C2×D411yescharacteristic
619C2×C42C2×D411yescharacteristic
620C2×C42C2×D411yescharacteristic
621C2×C42C2411yescharacteristic
622C2×C42C2411yescharacteristic
623C2×C42C2411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628#107—22no—
629#107—41no—
630#107—41no—
631#107—41no—
632#106—41no—
633#106—41no—
634#106—41no—
635#106—41no—
636#106—41no—
637#106—41no—
638C4⋊C8—22no—
639C4⋊C8—41no—
640C4⋊C8—41no—
641C4⋊C8—41no—
642#103—22no—
643#103—22no—
644#103—22no—
645#103—22no—
646#103—41no—
647#103—41no—
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—
660#103—41no—
661#103—41no—
662#103—41no—
663#103—41no—
664#103—41no—
665#103—41no—
666#103—41no—
667#103—41no—
668#103—41no—
669#103—41no—
670#97—41no—
671#97—41no—
672C4×C8—22no—
673C4×C8—22no—
674C4×C8—41no—
675C4×C8—41no—
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#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#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749C2×Q8—22no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—41no—
779C2×Q8—41no—
780C2×Q8C2×#4112yes—
781C2×Q8C2×#4112yes—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C2511yescharacteristic
813Q16—44no—
814Q16—82no—
815Q16—82no—
816Q16—82no—
817Q16—82no—
818Q16—82no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8C2×#4112yes—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—41no—
871C4⋊C4—41no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C42—22no—
914C42—22no—
915C42—22no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—21no—
926C42—21no—
927C42—21no—
928C42—21no—
929C42—21no—
930C42—41no—
931C42—42no—
932C42—42no—
933C42—42no—
934C42—42no—
935C42—42no—
936C42—42no—
937C42—42no—
938C42—42no—
939C42—42no—
940C42—81no—
941C42—81no—
942C42—81no—
943C42—81no—
944C42—81no—
945C23C23×D411yescharacteristic
946Q8—22no—
947Q8—22no—
948Q8—22no—
949Q8—22no—
950Q8—41no—
951Q8—41no—
952Q8—41no—
953Q8—41no—
954Q8—41no—
955Q8—41no—
956Q8—41no—
957Q8—41no—
958Q8—41no—
959Q8—41no—
960Q8—41no—
961Q8—41no—
962Q8—41no—
963Q8—41no—
964Q8—41no—
965Q8—41no—
966Q8—82no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
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—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
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—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4#57712yes—
1055C2×C4#57812yes—
1056C2×C4#57812yes—
1057C2×C4C22×#4111yescharacteristic
1058C2×C4#58511yescharacteristic
1059C2×C4#58511yescharacteristic
1060C2×C4#58511yescharacteristic
1061C2×C4#58511yescharacteristic
1062C2×C4#58511yescharacteristic
1063C8—22no—
1064C8—41no—
1065C8—41no—
1066C8—41no—
1067C8—41no—
1068C8—41no—
1069C8—41no—
1070C8—41no—
1071C22#344911yescharacteristic
1072C22D4×#4111yescharacteristic
1073C22#348711yescharacteristic
1074C22C2×#57711yescharacteristic
1075C22C2×#57811yescharacteristic
1076C22C2×#57811yescharacteristic
1077C22#358611yescharacteristic
1078C4—22no—
1079C4—22no—
1080C4—22no—
1081C4—41no—
1082C4—41no—
1083C4—41no—
1084C4—41no—
1085C4—41no—
1086C4—41no—
1087C4—41no—
1088C4—41no—
1089C4—41no—
1090C4—41no—
1091C4—42no—
1092C4—42no—
1093C4—41no—
1094C4—81no—
1095C4—81no—
1096C4—81no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—81no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4#349111yescharacteristic
1109C4#352111yescharacteristic
1110C4#356611yescharacteristic
1111C4#356711yescharacteristic
1112C2#3837811yescharacteristic
1113C2#6098311yescharacteristic
1114C2#6100811yescharacteristic
1115C2#6148411yescharacteristic
1116C2#6152611yescharacteristic
1117C2#6191511yescharacteristic
1118C2#6193411yescharacteristic
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

Maximal subgroups

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

subgroupindex
#389762
#356562
#330912
#326562
#326252
#326022
#325572
#323132
#320822
#315752
#307442
#301402
#300782
#295732
#295492
#295092
#294392
#293792
#293712
#290342
#289042
#280302
#275702
#274872
#272092
#262552
#261712
#228332
#222702
#221642
#211322