Finite Group Databasebeta

← #6798463

Subgroups — #6798463

Order 512.

1388 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39494C211yesmaximal, characteristic, complemented
2#39377C211yesmaximal, characteristic
3#33294C211yesmaximal, characteristic, complemented
4#31373C211yesmaximal, characteristic, complemented
5#31372C211yesmaximal, characteristic, complemented
6#31371C211yesmaximal, characteristic, complemented
7#31370C211yesmaximal, characteristic, complemented
8#31369C211yesmaximal, characteristic, complemented
9#31368C211yesmaximal, characteristic, complemented
10#31367C211yesmaximal, characteristic, complemented
11#31366C211yesmaximal, characteristic, complemented
12#29885C211yesmaximal, characteristic, complemented
13#29885C211yesmaximal, characteristic, complemented
14#29146C211yesmaximal, characteristic, complemented
15#28694C211yesmaximal, characteristic, complemented
16#27971C211yesmaximal, characteristic, complemented
17#27971C211yesmaximal, characteristic, complemented
18#26121C211yesmaximal, characteristic, complemented
19#26120C211yesmaximal, characteristic, complemented
20#26119C211yesmaximal, characteristic, complemented
21#26118C211yesmaximal, characteristic, complemented
22#25684C211yesmaximal, characteristic, complemented
23#25684C211yesmaximal, characteristic, complemented
24#24984C211yesmaximal, characteristic, complemented
25#24983C211yesmaximal, characteristic, complemented
26#24982C211yesmaximal, characteristic
27#24981C211yesmaximal, characteristic
28#21871C211yesmaximal, characteristic, complemented
29#21871C211yesmaximal, characteristic, complemented
30#21648C211yesmaximal, characteristic, complemented
31#21267C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#501C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#433C2211yescharacteristic
38C2×#433C2211yescharacteristic
39#2868C2211yescharacteristic
40#2859C2211yescharacteristic
41#2802—21no—
42#2802—21no—
43#2780—21no—
44#2780—21no—
45#2718—21no—
46#2718—21no—
47#2674—21no—
48#2674—21no—
49#2629C2211yescharacteristic
50#2629C2211yescharacteristic
51#2628C2211yescharacteristic
52#2628C2211yescharacteristic
53#2587—21no—
54#2587—21no—
55#2570C2211yescharacteristic
56#2570C2211yescharacteristic
57#2538C2211yescharacteristic
58#2537C2211yescharacteristic
59#2522—21no—
60#2522—21no—
61#2501—21no—
62#2496—21no—
63#2491—21no—
64#2442C2211yescharacteristic
65#2442C2211yescharacteristic
66#2441C2211yescharacteristic
67#2441C2211yescharacteristic
68#2440—21no—
69#2423C2211yescharacteristic
70#2423C2211yescharacteristic
71#2422C2211yescharacteristic
72#2422C2211yescharacteristic
73#2352C2211yescharacteristic
74#2352C2211yescharacteristic
75Q8×C4⋊C4C2211yescharacteristic
76D4×C4⋊C4C2211yescharacteristic
77#2317C2211yescharacteristic
78#2317C2211yescharacteristic
79C4×#125C2211yescharacteristic
80C4×#124C2211yescharacteristic
81#2293C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2100C2211yescharacteristic
87#2100C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2087C2211yescharacteristic
95#2087C2211yescharacteristic
96#2086C2211yescharacteristic
97#2086C2211yescharacteristic
98#2084C2211yescharacteristic
99#2084C2211yescharacteristic
100#2083C2211yescharacteristic
101#2083C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2077C2211yescharacteristic
106#2076C2211yescharacteristic
107#2076C2211yescharacteristic
108#2075C2211yescharacteristic
109#2075C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2026C2211yescharacteristic
119#2026C2211yescharacteristic
120#2025C2211yescharacteristic
121#2025C2211yescharacteristic
122#1993C2211yescharacteristic
123#1993C2211yescharacteristic
124#1992C2211yescharacteristic
125#1992C2211yescharacteristic
126#1992C2211yescharacteristic
127#1992C2211yescharacteristic
128#1991C2211yescharacteristic
129#1990C2211yescharacteristic
130#1990C2211yescharacteristic
131#1990C2211yescharacteristic
132#1990C2211yescharacteristic
133#1959C2211yescharacteristic
134#1959C2211yescharacteristic
135#1958C2211yescharacteristic
136#1955C2211yescharacteristic
137#1955C2211yescharacteristic
138#1948C2211yescharacteristic
139#1948C2211yescharacteristic
140#1947C2211yescharacteristic
141#1947C2211yescharacteristic
142#1940C2211yescharacteristic
143#1940C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1935C2211yescharacteristic
147#1935C2211yescharacteristic
148#1924C2211yescharacteristic
149#1924C2211yescharacteristic
150#1924C2211yescharacteristic
151#1924C2211yescharacteristic
152#1875C2211yescharacteristic
153#1875C2211yescharacteristic
154#1874C2211yescharacteristic
155#1874C2211yescharacteristic
156#1873C2211yescharacteristic
157#1873C2211yescharacteristic
158#1872C2211yescharacteristic
159#1872C2211yescharacteristic
160#1865C2211yescharacteristic
161#1865C2211yescharacteristic
162#1864C2211yescharacteristic
163#1864C2211yescharacteristic
164#1863C2211yescharacteristic
165#1863C2211yescharacteristic
166#1862C2211yescharacteristic
167#1862C2211yescharacteristic
168#1836C2211yescharacteristic
169#1836C2211yescharacteristic
170#1836C2211yescharacteristic
171#1836C2211yescharacteristic
172#1836C2211yescharacteristic
173#1836C2211yescharacteristic
174#1835C2211yescharacteristic
175#1825C2211yescharacteristic
176#1825C2211yescharacteristic
177#1825C2211yescharacteristic
178#1825C2211yescharacteristic
179#1824C2211yescharacteristic
180#1824C2211yescharacteristic
181#1823C2211yescharacteristic
182#1823C2211yescharacteristic
183#1805C2211yescharacteristic
184#1805C2211yescharacteristic
185#1805C2211yescharacteristic
186#1805C2211yescharacteristic
187#1804C2211yescharacteristic
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1767C2211yescharacteristic
196#1763C2211yescharacteristic
197#1763C2211yescharacteristic
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic
202C4×#97C2211yescharacteristic
203#542—24no—
204#542—24no—
205#542—42no—
206#542—42no—
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#126—21no—
212C2×#126—21no—
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#124—21no—
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×#121—21no—
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C22×C4⋊C4—21no—
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244#501—42no—
245#501—42no—
246#488—24no—
247#433—42no—
248#433—42no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#399—21no—
302#399—21no—
303#399—21no—
304#399—21no—
305#399—21no—
306#399—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#397—21no—
318#397—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#395—21no—
328#395—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#393—21no—
334#393—21no—
335#391C2311yescharacteristic
336#390—21no—
337#390D411yescharacteristic
338#390D411yescharacteristic
339#390C2311yescharacteristic
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#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389D411yescharacteristic
354#389D411yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388D411yescharacteristic
372#388D411yescharacteristic
373#388D411yescharacteristic
374#388D411yescharacteristic
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#386—21no—
388#386—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#384—21no—
400#384—21no—
401#384—21no—
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#380—21no—
417#380—21no—
418#380—21no—
419#380—21no—
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440C43C2311yescharacteristic
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#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8C2411yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C2×D411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4C2411yescharacteristic
500C23×C4C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C4⋊Q8—22no—
510C4⋊Q8—22no—
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513C4⋊Q8—82no—
514C4⋊Q8—82no—
515#126—44no—
516#126—44no—
517#125—22no—
518#125—22no—
519#125—41no—
520#125—41no—
521#125—41no—
522#125—41no—
523#124—22no—
524#124—44no—
525#124—44no—
526#124#4114yes—
527#123—44no—
528#123—44no—
529#123—82no—
530#123—82no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—44no—
534C22⋊Q8—44no—
535C22⋊Q8—41no—
536C22⋊Q8—41no—
537#121—22no—
538#121—22no—
539#121—41no—
540#121—41no—
541#121—82no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—22no—
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—41no—
555C4×D4—41no—
556#117—22no—
557#117—22no—
558#117—22no—
559#117—22no—
560#117—41no—
561#117—41no—
562#117—41no—
563#117—41no—
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⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—82no—
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42C2×D411yescharacteristic
670C2×C42C2×D411yescharacteristic
671C2×C42C2×D411yescharacteristic
672C2×C42C2×D411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678#107—41no—
679#107—41no—
680#107—41no—
681#107—41no—
682#106—41no—
683#106—41no—
684#106—41no—
685#106—41no—
686C4⋊C8—22no—
687C4⋊C8—22no—
688C4⋊C8—41no—
689C4⋊C8—41no—
690C4⋊C8—41no—
691C4⋊C8—41no—
692#103—22no—
693#103—22no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#102—22no—
701#102—22no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708C22⋊C8—41no—
709C22⋊C8—41no—
710C22⋊C8—41no—
711C22⋊C8—41no—
712C22⋊C8—41no—
713C22⋊C8—41no—
714C22⋊C8—41no—
715C22⋊C8—41no—
716#97—22no—
717#97—22no—
718#97—22no—
719#97—22no—
720#97—41no—
721#97—41no—
722C4×C8—22no—
723C4×C8—22no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764C24—21no—
765C24C22×D411yescharacteristic
766C24C22×D411yescharacteristic
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—81no—
775C2×Q8—81no—
776C2×Q8—81no—
777C2×Q8—81no—
778C2×Q8C2×#4112yes—
779C2×D4—22no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—41no—
786C2×D4—41no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—81no—
790C2×D4—81no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4C2×#4112yes—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—81no—
827C22×C4—81no—
828C22×C4—81no—
829C22×C4—81no—
830C22×C4—81no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C2511yescharacteristic
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C22⋊C4—22no—
950C22⋊C4—22no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—22no—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—41no—
987C42—41no—
988C42—41no—
989C42—41no—
990C42—42no—
991C42—42no—
992C42—42no—
993C42—81no—
994C42—81no—
995C42—81no—
996C42—81no—
997C42C2×#4112yes—
998C42H(5,𝔽2)12yes—
999C422−1+412yes—
1000C422−1+412yes—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—22no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23C23×D411yescharacteristic
1023Q8—22no—
1024Q8—22no—
1025Q8—41no—
1026Q8—41no—
1027Q8—162no—
1028Q8—162no—
1029D4—22no—
1030D4—22no—
1031D4—41no—
1032D4—41no—
1033D4—82no—
1034D4—162no—
1035D4—162no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—84no—
1122C2×C4—162no—
1123C2×C4—162no—
1124C2×C4—162no—
1125C2×C4—162no—
1126C2×C4#53612yes—
1127C2×C4#53612yes—
1128C2×C4#54612yes—
1129C2×C4#54612yes—
1130C2×C4C22×#4111yescharacteristic
1131C2×C4C2×H(5,𝔽2)11yescharacteristic
1132C2×C4C2×2−1+411yescharacteristic
1133C2×C4C2×2−1+411yescharacteristic
1134C2×C4#58511yescharacteristic
1135C2×C4#58511yescharacteristic
1136C8—41no—
1137C8—41no—
1138C8—41no—
1139C8—41no—
1140C8—41no—
1141C8—41no—
1142C8—41no—
1143C8—41no—
1144C22—42no—
1145C22—41no—
1146C22—41no—
1147C22—41no—
1148C22—41no—
1149C22—42no—
1150C22—41no—
1151C22—41no—
1152C22—42no—
1153C22—41no—
1154C22—41no—
1155C22—41no—
1156C22—41no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22—41no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22—81no—
1165C22C2×#53611yescharacteristic
1166C22C2×#54611yescharacteristic
1167C22#350011yescharacteristic
1168C22#358511yescharacteristic
1169C22#358511yescharacteristic
1170C22#358611yescharacteristic
1171C22#358611yescharacteristic
1172C4—22no—
1173C4—22no—
1174C4—22no—
1175C4—22no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—41no—
1180C4—41no—
1181C4—41no—
1182C4—42no—
1183C4—41no—
1184C4—41no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4#351511yescharacteristic
1200C4#351511yescharacteristic
1201C4#354711yescharacteristic
1202C4#354711yescharacteristic
1203C2—81no—
1204C2—81no—
1205C2—82no—
1206C2#3895511yescharacteristic
1207C2#6087011yescharacteristic
1208C2#6088611yescharacteristic
1209C2#6122311yescharacteristic
1210C2#6122411yescharacteristic
1211C2#6256611yescharacteristic
1212C2#6256711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2537C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39494C2semidirect
3. #33294C2semidirect
4. #31373C2semidirect
5. #31372C2semidirect
6. #31371C2semidirect
7. #31370C2semidirect
8. #31369C2semidirect
9. #31368C2semidirect
10. #31367C2semidirect
11. #31366C2semidirect
12. #29885C2semidirect
13. #29885C2semidirect
14. #29146C2semidirect
15. #28694C2semidirect
16. #27971C2semidirect
17. #27971C2semidirect
18. #26121C2semidirect
19. #26120C2semidirect
20. #26119C2semidirect
21. #26118C2semidirect
22. #25684C2semidirect
23. #25684C2semidirect
24. #24984C2semidirect
25. #24983C2semidirect
28. #21871C2semidirect
29. #21871C2semidirect
30. #21648C2semidirect
31. #21267C2semidirect

Maximal subgroups

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

subgroupindex
#394942
#393772
#332942
#313732
#313722
#313712
#313702
#313692
#313682
#313672
#313662
#298852
#291462
#286942
#279712
#261212
#261202
#261192
#261182
#256842
#249842
#249832
#249822
#249812
#218712
#216482
#212672