Finite Group Databasebeta

← #6486540

Subgroups — #6486540

Order 512.

1239 conjugacy classes of subgroups.

The subgroup lattice has 1073 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35187C211yesmaximal, characteristic
2#35115C211yesmaximal, characteristic
3#33270C211yesmaximal, characteristic
4#33270C211yesmaximal, characteristic
5#33264C211yesmaximal, characteristic
6#33259C211yesmaximal, characteristic
7#30387C211yesmaximal, characteristic
8#30387C211yesmaximal, characteristic
9#30387C211yesmaximal, characteristic
10#30382C211yesmaximal, characteristic
11#28840C211yesmaximal, characteristic
12#28685C211yesmaximal, characteristic
13#28546C211yesmaximal, characteristic
14#28278C211yesmaximal, characteristic
15#28045C211yesmaximal, characteristic
16#28042C211yesmaximal, characteristic
17#28035C211yesmaximal, characteristic
18#28033C211yesmaximal, characteristic
19#28016C211yesmaximal, characteristic
20#28012C211yesmaximal, characteristic
21#27999C211yesmaximal, characteristic
22#27991C211yesmaximal, characteristic
23#27745C211yesmaximal, characteristic
24#27742C211yesmaximal, characteristic
25#25488C211yesmaximal, characteristic
26#25483C211yesmaximal, characteristic
27#22121C211yesmaximal, characteristic
28#22119C211yesmaximal, characteristic
29C4×#501C211yesmaximal, characteristic
30#21287C211yesmaximal, characteristic
31#20520C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#477C2211yescharacteristic
35C2×#446C2211yescharacteristic
36C2×#446C2211yescharacteristic
37C2×#441C2211yescharacteristic
38#2864C2211yescharacteristic
39#2864C2211yescharacteristic
40#2864C2211yescharacteristic
41#2863C2211yescharacteristic
42#2863C2211yescharacteristic
43#2863C2211yescharacteristic
44#2863C2211yescharacteristic
45#2859C2211yescharacteristic
46#2655—21no—
47#2655—21no—
48#2655—21no—
49#2634—21no—
50#2584C2211yescharacteristic
51#2582C2211yescharacteristic
52#2581C2211yescharacteristic
53#2571C2211yescharacteristic
54#2570C2211yescharacteristic
55#2568C2211yescharacteristic
56#2565C2211yescharacteristic
57#2546C2211yescharacteristic
58#2533—21no—
59#2528—21no—
60#2524—21no—
61#2524—21no—
62#2524—21no—
63#2514—21no—
64#2514C2211yescharacteristic
65#2514C2211yescharacteristic
66#2514C2211yescharacteristic
67#2511C2211yescharacteristic
68#2509C2211yescharacteristic
69#2508C2211yescharacteristic
70#2508C2211yescharacteristic
71#2506C2211yescharacteristic
72#2462—21no—
73#2446—21no—
74#2336—21no—
75#2336—21no—
76#2327—21no—
77#2320—21no—
78C4×C4⋊Q8C2211yescharacteristic
79C4×#125C2211yescharacteristic
80#2295C2211yescharacteristic
81#2295C2211yescharacteristic
82C42×Q8C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2100C2211yescharacteristic
87#2097C2211yescharacteristic
88#2097C2211yescharacteristic
89#2097C2211yescharacteristic
90#2095C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2087C2211yescharacteristic
95#2087C2211yescharacteristic
96#2087C2211yescharacteristic
97#2086C2211yescharacteristic
98#2086C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2084C2211yescharacteristic
103#2074C2211yescharacteristic
104#2074C2211yescharacteristic
105#2074C2211yescharacteristic
106#2072C2211yescharacteristic
107#2068C2211yescharacteristic
108#2068C2211yescharacteristic
109#2068C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2066C2211yescharacteristic
113#2066C2211yescharacteristic
114#2066C2211yescharacteristic
115#1993C2211yescharacteristic
116#1992C2211yescharacteristic
117#1989C2211yescharacteristic
118#1987C2211yescharacteristic
119#1971C2211yescharacteristic
120#1971C2211yescharacteristic
121#1971C2211yescharacteristic
122#1969C2211yescharacteristic
123#1969C2211yescharacteristic
124#1969C2211yescharacteristic
125#1949C2211yescharacteristic
126#1948C2211yescharacteristic
127#1944C2211yescharacteristic
128#1944C2211yescharacteristic
129#1944C2211yescharacteristic
130#1944C2211yescharacteristic
131#1944C2211yescharacteristic
132#1944C2211yescharacteristic
133#1944C2211yescharacteristic
134#1943C2211yescharacteristic
135#1943C2211yescharacteristic
136#1943C2211yescharacteristic
137#1943C2211yescharacteristic
138#1943C2211yescharacteristic
139#1943C2211yescharacteristic
140#1943C2211yescharacteristic
141#1943C2211yescharacteristic
142#1942C2211yescharacteristic
143#1942C2211yescharacteristic
144#1941C2211yescharacteristic
145#1941C2211yescharacteristic
146#1941C2211yescharacteristic
147#1941C2211yescharacteristic
148#1941C2211yescharacteristic
149#1935C2211yescharacteristic
150#1935C2211yescharacteristic
151#1935C2211yescharacteristic
152#1935C2211yescharacteristic
153#1935C2211yescharacteristic
154#1935C2211yescharacteristic
155#1935C2211yescharacteristic
156#1935C2211yescharacteristic
157#1935C2211yescharacteristic
158#1935C2211yescharacteristic
159#1933C2211yescharacteristic
160#1933C2211yescharacteristic
161#1933C2211yescharacteristic
162#1933C2211yescharacteristic
163#1933C2211yescharacteristic
164#1933C2211yescharacteristic
165#1928C2211yescharacteristic
166#1927C2211yescharacteristic
167#1927C2211yescharacteristic
168#1927C2211yescharacteristic
169#1921C2211yescharacteristic
170#1920C2211yescharacteristic
171#1918C2211yescharacteristic
172#1918C2211yescharacteristic
173#1847C2211yescharacteristic
174#1847C2211yescharacteristic
175#1847C2211yescharacteristic
176#1846C2211yescharacteristic
177#1846C2211yescharacteristic
178#1836C2211yescharacteristic
179#1836C2211yescharacteristic
180#1835C2211yescharacteristic
181#1835C2211yescharacteristic
182#1805C2211yescharacteristic
183#1803C2211yescharacteristic
184#1776C2211yescharacteristic
185C4×#107C2211yescharacteristic
186C4×#107C2211yescharacteristic
187C4×#106C2211yescharacteristic
188C4×#106C2211yescharacteristic
189#1771C2211yescharacteristic
190#1771C2211yescharacteristic
191#1771C2211yescharacteristic
192#1771C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194C8×C4⋊C4C2211yescharacteristic
195#1767C2211yescharacteristic
196#1767C2211yescharacteristic
197#1767C2211yescharacteristic
198#1763C2211yescharacteristic
199#1763C2211yescharacteristic
200C4×#97C2211yescharacteristic
201C4×#97C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C2×C4⋊Q8—21no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×#125—21no—
207C2×#125—21no—
208C2×#125C2311yescharacteristic
209C2×C4×Q8—21no—
210C2×C4×Q8D411yescharacteristic
211C2×C4×Q8D411yescharacteristic
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215#501—24no—
216#479—24no—
217#477—24no—
218#446—24no—
219#446—24no—
220#441—24no—
221C2×#107C2311yescharacteristic
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
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×#97C2311yescharacteristic
261C2×#97C2311yescharacteristic
262C2×#97C2311yescharacteristic
263C2×#97C2311yescharacteristic
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
276#401—21no—
277#401—21no—
278#401—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#400—21no—
293#400—21no—
294#400—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#395—21no—
307#395—21no—
308#391—21no—
309#391—21no—
310#391—21no—
311#391—21no—
312#391—21no—
313#391C2311yescharacteristic
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
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#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
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#387—21no—
400#387—21no—
401#387—21no—
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#383—21no—
406#383—21no—
407#383—21no—
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#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4D411yescharacteristic
429C4×C4⋊C4D411yescharacteristic
430C4×C4⋊C4D411yescharacteristic
431C4×C4⋊C4D411yescharacteristic
432C4×C4⋊C4D411yescharacteristic
433C4×C4⋊C4D411yescharacteristic
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×C4⋊C4C2311yescharacteristic
443#376—21no—
444#376—21no—
445C43C2311yescharacteristic
446C43C2311yescharacteristic
447C43C2311yescharacteristic
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#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8C2×D411yescharacteristic
486C22×Q8C2411yescharacteristic
487C22×Q8C2411yescharacteristic
488C2×Q16—22no—
489C2×Q16—22no—
490C2×Q16—22no—
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C4⋊Q8—22no—
500C4⋊Q8—22no—
501C4⋊Q8—44no—
502#125—22no—
503#125—22no—
504#125—44no—
505#125—44no—
506C4×Q8—22no—
507C4×Q8—22no—
508C4×Q8—22no—
509C4×Q8—22no—
510C4×Q8—22no—
511C4×Q8—22no—
512C4×Q8—42no—
513C4×Q8—42no—
514C4×Q8—44no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
551C2×C4⋊C4C2×D411yescharacteristic
552C2×C4⋊C4C2×D411yescharacteristic
553C2×C4⋊C4C2×D411yescharacteristic
554C2×C4⋊C4C2×D411yescharacteristic
555C2×C4⋊C4C2×D411yescharacteristic
556C2×C4⋊C4C2×D411yescharacteristic
557C2×C4⋊C4C2×D411yescharacteristic
558C2×C4⋊C4C2×D411yescharacteristic
559C2×C4⋊C4C2411yescharacteristic
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2411yescharacteristic
562C2×C4⋊C4C2411yescharacteristic
563C2×C4⋊C4C2411yescharacteristic
564C2×C4⋊C4C2411yescharacteristic
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C42—21no—
574C2×C42—21no—
575C2×C42—21no—
576C2×C42—21no—
577C2×C42—21no—
578C2×C42—21no—
579C2×C42—21no—
580C2×C42—21no—
581C2×C42C2×D411yescharacteristic
582C2×C42C2×D411yescharacteristic
583C2×C42C2×D411yescharacteristic
584C2×C42C2×D411yescharacteristic
585C2×C42C2×D411yescharacteristic
586C2×C42C2×D411yescharacteristic
587C2×C42C2×D411yescharacteristic
588C2×C42C2×D411yescharacteristic
589C2×C42C2×D411yescharacteristic
590C2×C42C2×D411yescharacteristic
591C2×C42C2×D411yescharacteristic
592C2×C42C2×D411yescharacteristic
593C2×C42C2411yescharacteristic
594C2×C42C2411yescharacteristic
595C2×C42C2411yescharacteristic
596C2×C42C2411yescharacteristic
597C2×C42C2411yescharacteristic
598C2×C42C2411yescharacteristic
599C2×C42C2411yescharacteristic
600#107—22no—
601#107—22no—
602#107—22no—
603#107—22no—
604#107—22no—
605#107—22no—
606#107—22no—
607#107—41no—
608#107—41no—
609#106—22no—
610#106—22no—
611#106—22no—
612#106—22no—
613#106—22no—
614#106—22no—
615#106—41no—
616#106—41no—
617#106—41no—
618#106—41no—
619C4⋊C8—22no—
620C4⋊C8—22no—
621C4⋊C8—22no—
622C4⋊C8—22no—
623C4⋊C8—22no—
624C4⋊C8#4114yes—
625#103—22no—
626#103—22no—
627#103—22no—
628#103—22no—
629#103—22no—
630#103—22no—
631#103—22no—
632#103—22no—
633#103—41no—
634#103—41no—
635#103—41no—
636#103—41no—
637#103—41no—
638#103—41no—
639#97—22no—
640#97—22no—
641#97—22no—
642#97—22no—
643#97—22no—
644#97—22no—
645#97—41no—
646#97—41no—
647#97—41no—
648#97#4114yes—
649C4×C8—22no—
650C4×C8—22no—
651C4×C8—22no—
652C4×C8—22no—
653C4×C8—22no—
654C4×C8—22no—
655#95—21no—
656#95—21no—
657#95—21no—
658#95—21no—
659#95—21no—
660#95—21no—
661#95—21no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
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#95—21no—
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729C2×Q8—22no—
730C2×Q8—22no—
731C2×Q8—21no—
732C2×Q8—21no—
733C2×Q8—21no—
734C2×Q8—21no—
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—41no—
744C2×Q8—42no—
745C2×Q8—42no—
746C2×Q8—42no—
747C22×C4—21no—
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×C4C22×D411yescharacteristic
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C22×D411yescharacteristic
767C22×C4C22×D411yescharacteristic
768C22×C4C22×D411yescharacteristic
769C22×C4C22×D411yescharacteristic
770C22×C4C22×D411yescharacteristic
771C22×C4C22×D411yescharacteristic
772C22×C4C22×D411yescharacteristic
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D411yescharacteristic
775C22×C4C22×D411yescharacteristic
776C22×C4C22×D411yescharacteristic
777C22×C4C2511yescharacteristic
778Q16—44no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
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×C8C2×#4112yes—
797C2×C8C2×#4112yes—
798C2×C8C2×#4112yes—
799C2×C8C2×#4112yes—
800C2×C82−1+412yes—
801C2×C82−1+412yes—
802C2×C82−1+412yes—
803C4⋊C4—22no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
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—41no—
838C4⋊C4—41no—
839C4⋊C4—41no—
840C4⋊C4—42no—
841C4⋊C4—42no—
842C4⋊C4—42no—
843C4⋊C4—42no—
844C4⋊C4—42no—
845C4⋊C4—42no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—42no—
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—
875C42—22no—
876C42—22no—
877C42—21no—
878C42—21no—
879C42—21no—
880C42—21no—
881C42—21no—
882C42—21no—
883C42—21no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42—21no—
889C42—41no—
890C42—41no—
891C42—41no—
892C42—41no—
893C42—41no—
894C42—41no—
895C42—41no—
896C42—41no—
897C42—41no—
898C42—41no—
899C42—42no—
900C42—42no—
901C42—42no—
902C42—42no—
903C42—42no—
904C42—42no—
905C42—81no—
906C42—81no—
907C42C2×#4112yes—
908C42C2×#4112yes—
909C23C23×D411yescharacteristic
910Q8—44no—
911Q8—41no—
912Q8—41no—
913Q8—41no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8—41no—
919Q8—84no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
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—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
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#53212yes—
1007C2×C4#53212yes—
1008C2×C4#57512yes—
1009C2×C4#57512yes—
1010C2×C4C22×#4111yescharacteristic
1011C2×C4C22×#4111yescharacteristic
1012C2×C4C2×2−1+411yescharacteristic
1013C2×C4C2×2−1+411yescharacteristic
1014C2×C4C2×2−1+411yescharacteristic
1015C2×C4#58511yescharacteristic
1016C8—22no—
1017C8—22no—
1018C8—22no—
1019C8—22no—
1020C8—41no—
1021C8—41no—
1022C8—41no—
1023C8#54114yes—
1024C22C2×#53211yescharacteristic
1025C22#349711yescharacteristic
1026C22#349911yescharacteristic
1027C22C2×#57511yescharacteristic
1028C22C2×#57511yescharacteristic
1029C22#358611yescharacteristic
1030C22#358611yescharacteristic
1031C4—22no—
1032C4—22no—
1033C4—22no—
1034C4—22no—
1035C4—41no—
1036C4—41no—
1037C4—41no—
1038C4—41no—
1039C4—41no—
1040C4—41no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4—81no—
1049C4—81no—
1050C4—81no—
1051C4—81no—
1052C4—81no—
1053C4—81no—
1054C4—81no—
1055C4—81no—
1056C4—81no—
1057C4—81no—
1058C4—81no—
1059C4—81no—
1060C4—81no—
1061C4C2×#54111yescharacteristic
1062C4#346111yescharacteristic
1063C4#351511yescharacteristic
1064C4#352311yescharacteristic
1065C2#3520911yescharacteristic
1066C2#6069911yescharacteristic
1067C2#6070211yescharacteristic
1068C2#6239911yescharacteristic
1069C2#6239911yescharacteristic
1070C2#6250511yescharacteristic
1071C2#6250711yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ 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
#351872
#351152
#332702
#332642
#332592
#303872
#303822
#288402
#286852
#285462
#282782
#280452
#280422
#280352
#280332
#280162
#280122
#279992
#279912
#277452
#277422
#254882
#254832
#221212
#221192
C4×#5012
#212872
#205202