Finite Group Databasebeta

← #6499368

Subgroups — #6499368

Order 512.

1236 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35336C211yesmaximal, characteristic
2#35265C211yesmaximal, characteristic
3#33262C211yesmaximal, characteristic, complemented
4#33262C211yesmaximal, characteristic, complemented
5#33261C211yesmaximal, characteristic, complemented
6#33260C211yesmaximal, characteristic, complemented
7#30312C211yesmaximal, characteristic, complemented
8#30311C211yesmaximal, characteristic, complemented
9#30308C211yesmaximal, characteristic, complemented
10#30307C211yesmaximal, characteristic, complemented
11#29327C211yesmaximal, characteristic, complemented
12#29326C211yesmaximal, characteristic, complemented
13#29324C211yesmaximal, characteristic, complemented
14#29324C211yesmaximal, characteristic, complemented
15#29321C211yesmaximal, characteristic, complemented
16#29318C211yesmaximal, characteristic, complemented
17#29316C211yesmaximal, characteristic, complemented
18#29314C211yesmaximal, characteristic, complemented
19#29309C211yesmaximal, characteristic
20#29309C211yesmaximal, characteristic
21#29307C211yesmaximal, characteristic
22#29306C211yesmaximal, characteristic
23#29305C211yesmaximal, characteristic
24#29303C211yesmaximal, characteristic
25#29300C211yesmaximal, characteristic
26#29298C211yesmaximal, characteristic
27#21992C211yesmaximal, characteristic
28#21992C211yesmaximal, characteristic
29#21991C211yesmaximal, characteristic
30#21990C211yesmaximal, characteristic
31#20468C211yesmaximal, characteristic
32C2×#433C2211yescharacteristic
33C2×#433C2211yescharacteristic
34#2864C2211yescharacteristic
35#2864C2211yescharacteristic
36#2859C2211yescharacteristic
37#2859C2211yescharacteristic
38#2859C2211yescharacteristic
39#2859C2211yescharacteristic
40#2851C2211yescharacteristic
41#2851C2211yescharacteristic
42#2647C2211yescharacteristic
43#2647C2211yescharacteristic
44#2647C2211yescharacteristic
45#2647C2211yescharacteristic
46#2647C2211yescharacteristic
47#2647C2211yescharacteristic
48#2629C2211yescharacteristic
49#2629C2211yescharacteristic
50#2590—21no—
51#2590—21no—
52#2590—21no—
53#2590—21no—
54#2587—21no—
55#2587—21no—
56#2587—21no—
57#2587—21no—
58#2509—21no—
59#2508—21no—
60#2507—21no—
61#2506—21no—
62#2505—21no—
63#2505—21no—
64#2473—21no—
65#2473—21no—
66#2330C2211yescharacteristic
67#2330C2211yescharacteristic
68#2317C2211yescharacteristic
69#2317C2211yescharacteristic
70#2317C2211yescharacteristic
71#2316C2211yescharacteristic
72#2314C2211yescharacteristic
73#2314C2211yescharacteristic
74C4×#125C2211yescharacteristic
75C4×#125C2211yescharacteristic
76#2296C2211yescharacteristic
77C2×#389C2211yescharacteristic
78C4×#117C2211yescharacteristic
79#2085C2211yescharacteristic
80#2085C2211yescharacteristic
81#2085C2211yescharacteristic
82#2085C2211yescharacteristic
83#2085C2211yescharacteristic
84#2085C2211yescharacteristic
85#2085C2211yescharacteristic
86#2085C2211yescharacteristic
87#2084C2211yescharacteristic
88#2084C2211yescharacteristic
89#2084C2211yescharacteristic
90#2084C2211yescharacteristic
91#2083C2211yescharacteristic
92#2083C2211yescharacteristic
93#2083C2211yescharacteristic
94#2083C2211yescharacteristic
95#2059C2211yescharacteristic
96#2059C2211yescharacteristic
97#2059C2211yescharacteristic
98#2059C2211yescharacteristic
99#2059C2211yescharacteristic
100#2059C2211yescharacteristic
101#2059C2211yescharacteristic
102#2059C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#1949C2211yescharacteristic
112#1949C2211yescharacteristic
113#1949C2211yescharacteristic
114#1949C2211yescharacteristic
115#1949C2211yescharacteristic
116#1949C2211yescharacteristic
117#1949C2211yescharacteristic
118#1949C2211yescharacteristic
119#1948C2211yescharacteristic
120#1948C2211yescharacteristic
121#1948C2211yescharacteristic
122#1948C2211yescharacteristic
123#1947C2211yescharacteristic
124#1947C2211yescharacteristic
125#1947C2211yescharacteristic
126#1947C2211yescharacteristic
127#1944C2211yescharacteristic
128#1944C2211yescharacteristic
129#1944C2211yescharacteristic
130#1944C2211yescharacteristic
131#1944C2211yescharacteristic
132#1944C2211yescharacteristic
133#1944C2211yescharacteristic
134#1944C2211yescharacteristic
135#1943C2211yescharacteristic
136#1943C2211yescharacteristic
137#1943C2211yescharacteristic
138#1943C2211yescharacteristic
139#1943C2211yescharacteristic
140#1943C2211yescharacteristic
141#1943C2211yescharacteristic
142#1943C2211yescharacteristic
143#1942C2211yescharacteristic
144#1942C2211yescharacteristic
145#1942C2211yescharacteristic
146#1942C2211yescharacteristic
147#1942C2211yescharacteristic
148#1942C2211yescharacteristic
149#1942C2211yescharacteristic
150#1942C2211yescharacteristic
151#1941C2211yescharacteristic
152#1941C2211yescharacteristic
153#1941C2211yescharacteristic
154#1941C2211yescharacteristic
155#1941C2211yescharacteristic
156#1941C2211yescharacteristic
157#1941C2211yescharacteristic
158#1941C2211yescharacteristic
159#1854C2211yescharacteristic
160#1854C2211yescharacteristic
161#1854C2211yescharacteristic
162#1854C2211yescharacteristic
163#1854C2211yescharacteristic
164#1854C2211yescharacteristic
165#1854C2211yescharacteristic
166#1854C2211yescharacteristic
167#1853C2211yescharacteristic
168#1853C2211yescharacteristic
169#1853C2211yescharacteristic
170#1853C2211yescharacteristic
171#1852C2211yescharacteristic
172#1852C2211yescharacteristic
173#1852C2211yescharacteristic
174#1852C2211yescharacteristic
175#1847C2211yescharacteristic
176#1847C2211yescharacteristic
177#1847C2211yescharacteristic
178#1847C2211yescharacteristic
179#1846C2211yescharacteristic
180#1846C2211yescharacteristic
181#1845C2211yescharacteristic
182#1844C2211yescharacteristic
183#1836C2211yescharacteristic
184#1836C2211yescharacteristic
185#1836C2211yescharacteristic
186#1836C2211yescharacteristic
187#1835C2211yescharacteristic
188#1835C2211yescharacteristic
189#1834C2211yescharacteristic
190#1834C2211yescharacteristic
191#1768C2211yescharacteristic
192#1768C2211yescharacteristic
193#1767C2211yescharacteristic
194C4×C4⋊C8C2211yescharacteristic
195#1750C2211yescharacteristic
196#1750C2211yescharacteristic
197#1749C2211yescharacteristic
198C4×C22⋊C8C2211yescharacteristic
199#1745C2211yescharacteristic
200#1744C2211yescharacteristic
201#1726C2211yescharacteristic
202#1726C2211yescharacteristic
203C2×#125—21no—
204C2×#125—21no—
205C2×#125C2311yescharacteristic
206C2×#125C2311yescharacteristic
207C2×#125C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#117C2311yescharacteristic
210C2×#117C2311yescharacteristic
211C2×#117C2311yescharacteristic
212C2×#117C2311yescharacteristic
213C22×C4⋊C4—21no—
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C42C2311yescharacteristic
217#433Q818yes—
218#433Q818yes—
219C2×#107C2311yescharacteristic
220C2×#107C2311yescharacteristic
221C2×#107C2311yescharacteristic
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C22⋊C8C2311yescharacteristic
256C2×C22⋊C8C2311yescharacteristic
257C2×C22⋊C8C2311yescharacteristic
258C2×C22⋊C8C2311yescharacteristic
259C2×#97C2311yescharacteristic
260C2×#97C2311yescharacteristic
261C2×#97C2311yescharacteristic
262C2×#97C2311yescharacteristic
263C2×#97C2311yescharacteristic
264C2×#97C2311yescharacteristic
265C2×C4×C8C2311yescharacteristic
266C2×C4×C8C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270C2×C4×C8C2311yescharacteristic
271#400—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#396—21no—
300#396—21no—
301#396—21no—
302#396—21no—
303#389—21no—
304#389—21no—
305#389—21no—
306#389—21no—
307#389—21no—
308#389—21no—
309#389—21no—
310#389—21no—
311#389—21no—
312#389—21no—
313#389—21no—
314#389—21no—
315#389—21no—
316#389—21no—
317#389—21no—
318#389—21no—
319#389—21no—
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
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#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#387—21no—
356#387—21no—
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#385—21no—
380#385—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#384—21no—
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#384C2311yescharacteristic
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#382—21no—
401#382—21no—
402#382—21no—
403#382C2311yescharacteristic
404#382C2311yescharacteristic
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#380—21no—
412#380—21no—
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
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⋊C4D411yescharacteristic
424C4×C4⋊C4D411yescharacteristic
425C4×C4⋊C4D411yescharacteristic
426C4×C4⋊C4D411yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C22⋊C4D411yescharacteristic
432C4×C22⋊C4D411yescharacteristic
433C4×C22⋊C4D411yescharacteristic
434C4×C22⋊C4D411yescharacteristic
435#376C2311yescharacteristic
436#376C2311yescharacteristic
437C2×#95—21no—
438C43C2311yescharacteristic
439C43C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
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#340C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C2×D411yescharacteristic
483C23×C4C2×D411yescharacteristic
484C23×C4C2411yescharacteristic
485C22×C8C2411yescharacteristic
486C22×C8C2411yescharacteristic
487C22×C8C2411yescharacteristic
488C22×C8C2411yescharacteristic
489C22×C8C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493#125—41no—
494#125—41no—
495#125—41no—
496#125—41no—
497#125—41no—
498#125—41no—
499#125—41no—
500#125—41no—
501#125—82no—
502#125—82no—
503#117—41no—
504#117—41no—
505#117—41no—
506#117—41no—
507#117—41no—
508#117—41no—
509#117C2×Q814yes—
510#117C2×Q814yes—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
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⋊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—41no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—82no—
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4C2×D411yescharacteristic
593C2×C22⋊C4C2×D411yescharacteristic
594C2×C22⋊C4C2×D411yescharacteristic
595C2×C22⋊C4C2×D411yescharacteristic
596C2×C42—21no—
597C2×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42—21no—
601C2×C42—21no—
602C2×C42—41no—
603C2×C42—41no—
604C2×C42C2×D411yescharacteristic
605C2×C42C2×D411yescharacteristic
606C2×C42C2×D411yescharacteristic
607C2×C42C2×D411yescharacteristic
608C2×C42C2×D411yescharacteristic
609C2×C42C2×D411yescharacteristic
610C2×C42C2×D411yescharacteristic
611C2×C42C2×D411yescharacteristic
612C2×C42C2×D411yescharacteristic
613C2×C42C2×D411yescharacteristic
614C2×C42C2411yescharacteristic
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617C2×C42C2411yescharacteristic
618C2×C42C2411yescharacteristic
619C2×C42C2411yescharacteristic
620#107—41no—
621#107—41no—
622#107—41no—
623#107—41no—
624#107—41no—
625#107—41no—
626#107—41no—
627#107—41no—
628#107—41no—
629#107—41no—
630#107—41no—
631#107—41no—
632#107—41no—
633#107—41no—
634#107—41no—
635#107—41no—
636#106—41no—
637#106—41no—
638#106—41no—
639#106—41no—
640#106—41no—
641#106—41no—
642#106—41no—
643#106—41no—
644#106—41no—
645#106—41no—
646#106—41no—
647#106—41no—
648#106—41no—
649#106—41no—
650#106—41no—
651#106—41no—
652C4⋊C8C2×Q814yes—
653C4⋊C8C2×Q814yes—
654C4⋊C8C2×Q814yes—
655C4⋊C8C2×Q814yes—
656C22⋊C8C2×Q814yes—
657C22⋊C8C2×Q814yes—
658C22⋊C8C2×Q814yes—
659C22⋊C8C2×Q814yes—
660#97—41no—
661#97—41no—
662#97—41no—
663#97—41no—
664#97C2×Q814yes—
665#97C2×Q814yes—
666C4×C8—41no—
667C4×C8—41no—
668C4×C8—41no—
669C4×C8—41no—
670C4×C8C2×Q814yes—
671C4×C8C2×Q814yes—
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#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728C24C22×D411yescharacteristic
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—41no—
750C22×C4—41no—
751C22×C4—41no—
752C22×C4—41no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—81no—
758C22×C4—81no—
759C22×C4—81no—
760C22×C4—81no—
761C22×C4C22×D411yescharacteristic
762C22×C4C22×D411yescharacteristic
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×Q812yes—
775C22×C4C22×Q812yes—
776C22×C4C2511yescharacteristic
777C2×C8—21no—
778C2×C8—21no—
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×C8C22×Q812yes—
794C2×C8C22×Q812yes—
795C2×C8C22×Q812yes—
796C2×C8C22×Q812yes—
797C2×C8C22×Q812yes—
798C2×C8C22×Q812yes—
799C2×C8C22×Q812yes—
800C2×C8C22×Q812yes—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
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—41no—
834C4⋊C4—41no—
835C4⋊C4—42no—
836C4⋊C4—42no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—42no—
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—81no—
850C4⋊C4—81no—
851C4⋊C4—81no—
852C4⋊C4—81no—
853C4⋊C4—81no—
854C4⋊C4—81no—
855C4⋊C4—81no—
856C4⋊C4—81no—
857C4⋊C4—81no—
858C4⋊C4—81no—
859C4⋊C4—81no—
860C4⋊C4—81no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
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⋊C4C4⋊Q814yes—
886C4⋊C4C4⋊Q814yes—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—42no—
890C22⋊C4—42no—
891C22⋊C4—81no—
892C22⋊C4—81no—
893C22⋊C4—81no—
894C22⋊C4—81no—
895C22⋊C4C4⋊Q814yes—
896C22⋊C4C4⋊Q814yes—
897C42—21no—
898C42—21no—
899C42—21no—
900C42—21no—
901C42—21no—
902C42—21no—
903C42—21no—
904C42—21no—
905C42—41no—
906C42—41no—
907C42—41no—
908C42—41no—
909C42—41no—
910C42—41no—
911C42—41no—
912C42—41no—
913C42—41no—
914C42—41no—
915C42—42no—
916C42—42no—
917C42—81no—
918C42—81no—
919C42—81no—
920C42—81no—
921C42C22×Q812yes—
922C42C22×Q812yes—
923C42C22×Q812yes—
924C42C22×Q812yes—
925C23—21no—
926C23—21no—
927C23—21no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23C2×C4⋊Q812yes—
932C23C23×D411yescharacteristic
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—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
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—21no—
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—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—82no—
1020C2×C4—82no—
1021C2×C4—84no—
1022C2×C4—162no—
1023C2×C4C2×C4⋊Q812yes—
1024C2×C4C2×C4⋊Q812yes—
1025C2×C4C2×C4⋊Q812yes—
1026C2×C4C2×C4⋊Q812yes—
1027C2×C4C2×C4⋊Q812yes—
1028C2×C4C23×Q811yescharacteristic
1029C2×C4C23×Q811yescharacteristic
1030C2×C4#58511yescharacteristic
1031C2×C4#58511yescharacteristic
1032C2×C4#58511yescharacteristic
1033C2×C4#58511yescharacteristic
1034C8—22no—
1035C8—22no—
1036C8—22no—
1037C8—22no—
1038C8—22no—
1039C8—22no—
1040C8—22no—
1041C8—22no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—41no—
1046C22—41no—
1047C22—41no—
1048C22—41no—
1049C22C22×C4⋊Q811yescharacteristic
1050C22#344911yescharacteristic
1051C22#344911yescharacteristic
1052C22#358411yescharacteristic
1053C22#358411yescharacteristic
1054C22#358511yescharacteristic
1055C22#358611yescharacteristic
1056C4—22no—
1057C4—22no—
1058C4—22no—
1059C4—22no—
1060C4—22no—
1061C4—41no—
1062C4—41no—
1063C4—41no—
1064C4—41no—
1065C4—41no—
1066C4—41no—
1067C4—41no—
1068C4—41no—
1069C4—81no—
1070C4—81no—
1071C4—81no—
1072C4—81no—
1073C4—81no—
1074C4—81no—
1075C4—81no—
1076C4—81no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4#350411yescharacteristic
1086C4#350411yescharacteristic
1087C4#350411yescharacteristic
1088C4#350411yescharacteristic
1089C2—42no—
1090C2#3533511yescharacteristic
1091C2#6066611yescharacteristic
1092C2#6066811yescharacteristic
1093C2#6098411yescharacteristic
1094C2#6098511yescharacteristic
1095C2#6099711yescharacteristic
1096C2#6099911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33262C2semidirect
4. #33262C2semidirect
5. #33261C2semidirect
6. #33260C2semidirect
7. #30312C2semidirect
8. #30311C2semidirect
9. #30308C2semidirect
10. #30307C2semidirect
11. #29327C2semidirect
12. #29326C2semidirect
13. #29324C2semidirect
14. #29324C2semidirect
15. #29321C2semidirect
16. #29318C2semidirect
17. #29316C2semidirect
18. #29314C2semidirect

Maximal subgroups

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

subgroupindex
#353362
#352652
#332622
#332612
#332602
#303122
#303112
#303082
#303072
#293272
#293262
#293242
#293212
#293182
#293162
#293142
#293092
#293072
#293062
#293052
#293032
#293002
#292982
#219922
#219912
#219902
#204682