Finite Group Databasebeta

← #6565368

Subgroups — #6565368

Order 512.

1446 conjugacy classes of subgroups.

The subgroup lattice has 1276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39560C211yesmaximal, characteristic, complemented
2#37969C211yesmaximal, characteristic, complemented
3#30368C211yesmaximal, characteristic, complemented
4#30364C211yesmaximal, characteristic, complemented
5#29738C211yesmaximal, characteristic
6#29468C211yesmaximal, characteristic, complemented
7#29460C211yesmaximal, characteristic, complemented
8#28999C211yesmaximal, characteristic, complemented
9#28975C211yesmaximal, characteristic, complemented
10#28865C211yesmaximal, characteristic, complemented
11#28849C211yesmaximal, characteristic, complemented
12#28769C211yesmaximal, characteristic, complemented
13#28091C211yesmaximal, characteristic, complemented
14#28079C211yesmaximal, characteristic, complemented
15#27928C211yesmaximal, characteristic, complemented
16#27886C211yesmaximal, characteristic, complemented
17#27878C211yesmaximal, characteristic, complemented
18#27854C211yesmaximal, characteristic, complemented
19#27840C211yesmaximal, characteristic, complemented
20#27720C211yesmaximal, characteristic, complemented
21#27704C211yesmaximal, characteristic, complemented
22#24565C211yesmaximal, characteristic, complemented
23#24565C211yesmaximal, characteristic, complemented
24#23767C211yesmaximal, characteristic, complemented
25#23760C211yesmaximal, characteristic, complemented
26#23641C211yesmaximal, characteristic, complemented
27#23132C211yesmaximal, characteristic, complemented
28#22946C211yesmaximal, characteristic, complemented
29#22926C211yesmaximal, characteristic, complemented
30#22616C211yesmaximal, characteristic, complemented
31#20531C211yesmaximal, characteristic, complemented
32C2×#482C2211yescharacteristic
33C2×#482C2211yescharacteristic
34C2×#466C2211yescharacteristic
35C2×#427C2211yescharacteristic
36C2×#408C2211yescharacteristic
37C2×#408C2211yescharacteristic
38#2857C2211yescharacteristic
39#2854C2211yescharacteristic
40#2778—21no—
41#2763—21no—
42#2759—21no—
43#2756—21no—
44#2753—21no—
45#2730—21no—
46#2706—21no—
47#2696—21no—
48#2628C2211yescharacteristic
49#2624C2211yescharacteristic
50#2615C2211yescharacteristic
51#2615C2211yescharacteristic
52#2610—21no—
53#2602—21no—
54#2598—21no—
55#2589—21no—
56#2532—21no—
57#2500C2211yescharacteristic
58#2500C2211yescharacteristic
59#2497C2211yescharacteristic
60#2497C2211yescharacteristic
61#2495C2211yescharacteristic
62#2494C2211yescharacteristic
63#2491C2211yescharacteristic
64#2491C2211yescharacteristic
65#2463—21no—
66#2461—21no—
67#2461—21no—
68#2440C2211yescharacteristic
69#2440C2211yescharacteristic
70#2422C2211yescharacteristic
71#2422C2211yescharacteristic
72#2361C2211yescharacteristic
73#2361C2211yescharacteristic
74#2347C2211yescharacteristic
75#2346C2211yescharacteristic
76#2324C2211yescharacteristic
77#2314C2211yescharacteristic
78#2311C2211yescharacteristic
79#2311C2211yescharacteristic
80C4×#121C2211yescharacteristic
81#2297C2211yescharacteristic
82#2285C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2100C2211yescharacteristic
86#2100C2211yescharacteristic
87#2094C2211yescharacteristic
88#2094C2211yescharacteristic
89#2092C2211yescharacteristic
90#2092C2211yescharacteristic
91#2083C2211yescharacteristic
92#2083C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2076C2211yescharacteristic
100#2076C2211yescharacteristic
101#2076C2211yescharacteristic
102#2076C2211yescharacteristic
103#2076C2211yescharacteristic
104#2076C2211yescharacteristic
105#2075C2211yescharacteristic
106#2075C2211yescharacteristic
107#2071C2211yescharacteristic
108#2071C2211yescharacteristic
109#2057C2211yescharacteristic
110#2057C2211yescharacteristic
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2033C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2023C2211yescharacteristic
120#2023C2211yescharacteristic
121#1999C2211yescharacteristic
122#1999C2211yescharacteristic
123#1993C2211yescharacteristic
124#1990C2211yescharacteristic
125#1990C2211yescharacteristic
126#1990C2211yescharacteristic
127#1970C2211yescharacteristic
128#1970C2211yescharacteristic
129#1944C2211yescharacteristic
130#1944C2211yescharacteristic
131#1944C2211yescharacteristic
132#1942C2211yescharacteristic
133#1942C2211yescharacteristic
134#1942C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1934C2211yescharacteristic
143#1925C2211yescharacteristic
144#1925C2211yescharacteristic
145#1921C2211yescharacteristic
146#1921C2211yescharacteristic
147#1921C2211yescharacteristic
148#1921C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1920C2211yescharacteristic
152#1919C2211yescharacteristic
153#1918C2211yescharacteristic
154#1918C2211yescharacteristic
155#1895C2211yescharacteristic
156#1895C2211yescharacteristic
157#1895C2211yescharacteristic
158#1895C2211yescharacteristic
159#1893C2211yescharacteristic
160#1893C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1862C2211yescharacteristic
166#1862C2211yescharacteristic
167#1852C2211yescharacteristic
168#1852C2211yescharacteristic
169#1846C2211yescharacteristic
170#1845C2211yescharacteristic
171#1836C2211yescharacteristic
172#1834C2211yescharacteristic
173#1825C2211yescharacteristic
174#1825C2211yescharacteristic
175#1809C2211yescharacteristic
176#1809C2211yescharacteristic
177#1808C2211yescharacteristic
178#1808C2211yescharacteristic
179#1808C2211yescharacteristic
180#1776C2211yescharacteristic
181#1776C2211yescharacteristic
182#1776C2211yescharacteristic
183C4×#107C2211yescharacteristic
184#1762C2211yescharacteristic
185#1762C2211yescharacteristic
186#1762C2211yescharacteristic
187C4×#102C2211yescharacteristic
188#1753C2211yescharacteristic
189#1753C2211yescharacteristic
190#1753C2211yescharacteristic
191#1753C2211yescharacteristic
192#1752C2211yescharacteristic
193#1752C2211yescharacteristic
194C8×C22⋊C4C2211yescharacteristic
195C8×C22⋊C4C2211yescharacteristic
196#1750C2211yescharacteristic
197#1750C2211yescharacteristic
198#1749C2211yescharacteristic
199C4×C22⋊C8C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#124—21no—
212C2×#124—21no—
213C2×#123—21no—
214C2×#123—21no—
215C2×#123—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×C4×D4—21no—
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×#117—21no—
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C42C2311yescharacteristic
237#482—24no—
238#482—24no—
239#466—24no—
240#427—24no—
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270#408—24no—
271#408—24no—
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288#401—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#399—21no—
294#399—21no—
295#398—21no—
296#398—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#396—21no—
303#396—21no—
304#395—21no—
305#395—21no—
306#395—21no—
307#394—21no—
308#394—21no—
309#394—21no—
310#394—21no—
311#394—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#394—21no—
316#394—21no—
317#393—21no—
318#393—21no—
319#393—21no—
320#393—21no—
321#393—21no—
322#392—21no—
323#392—21no—
324#392—21no—
325#392—21no—
326#392—21no—
327#392—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391D411yescharacteristic
332#391D411yescharacteristic
333#390—21no—
334#390—21no—
335#390—21no—
336#390D411yescharacteristic
337#390D411yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#389—21no—
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386D411yescharacteristic
392#386D411yescharacteristic
393#386D411yescharacteristic
394#386D411yescharacteristic
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#383—21no—
407#383—21no—
408#382—21no—
409#382—21no—
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#380—21no—
413#380—21no—
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
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⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4C2311yescharacteristic
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441#376—21no—
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#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—41no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8C2×D411yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C2×D411yescharacteristic
500C22×D4C2×D411yescharacteristic
501C22×D4C2×D411yescharacteristic
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C2×D411yescharacteristic
509C23×C4C2×D411yescharacteristic
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C2×D8—22no—
514C2×D8—41no—
515C2×D8—41no—
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—41no—
519C2×M16—41no—
520C2×M16—41no—
521C2×M16—41no—
522C22×C8—22no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8—41no—
526C22×C8—41no—
527C22×C8#4114yes—
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540#124—82no—
541#124—82no—
542#123—82no—
543#123—82no—
544#123—82no—
545C22⋊Q8—82no—
546C22⋊Q8—82no—
547C22⋊Q8—82no—
548#121—22no—
549#121—22no—
550#121—22no—
551#121—22no—
552#121—41no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—41no—
557#121—41no—
558#121—41no—
559#121—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—82no—
565C4×D4—82no—
566C4×D4—82no—
567#117—22no—
568#117—22no—
569#117—22no—
570#117—22no—
571#117—41no—
572#117—41no—
573#117—82no—
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—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
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×C42—21no—
670C2×C42—41no—
671C2×C42—41no—
672C2×C42C2×D411yescharacteristic
673C2×C42C2×D411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678#107—22no—
679#107—22no—
680#107—22no—
681#107—22no—
682#107—22no—
683#107—41no—
684#107—41no—
685#107—41no—
686#107—41no—
687#107—41no—
688#107—41no—
689#106—22no—
690#106—22no—
691#106—22no—
692#106—22no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707C22⋊C8—22no—
708C22⋊C8—22no—
709C22⋊C8—22no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—22no—
713C22⋊C8—22no—
714C22⋊C8#4114yes—
715#97—41no—
716#97—41no—
717#97—41no—
718#97—41no—
719C4×C8—41no—
720C4×C8—41no—
721C4×C8—41no—
722C4×C8—41no—
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#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#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765C24—21no—
766C24—21no—
767C24C22×D411yescharacteristic
768C24C22×D411yescharacteristic
769C24C22×D411yescharacteristic
770#41—82no—
771#41—82no—
772#41—82no—
773#41—82no—
774C2×Q8—22no—
775C2×Q8—41no—
776C2×Q8—41no—
777C2×Q8—42no—
778C2×Q8—81no—
779C2×Q8—81no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—41no—
801C2×D4—41no—
802C2×D4—41no—
803C2×D4—41no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—81no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4—81no—
812C2×D4—81no—
813C2×D4—81no—
814C2×D4—81no—
815C2×D4—81no—
816C2×D4—81no—
817C2×D4—81no—
818C2×D4—81no—
819C2×D4—81no—
820C2×D4—81no—
821C2×D4—81no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—41no—
855C22×C4—41no—
856C22×C4—41no—
857C22×C4—41no—
858C22×C4—42no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
864C22×C4—81no—
865C22×C4—81no—
866C22×C4—81no—
867C22×C4—81no—
868C22×C4—81no—
869C22×C4—81no—
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C2×#4112yes—
882C22×C4C2×#4112yes—
883C22×C4C2511yescharacteristic
884D8—82no—
885M16—82no—
886M16—82no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—44no—
908C2×C8—82no—
909C2×C8C2×#4112yes—
910C2×C8C2×#4112yes—
911C2×C8C2×#4112yes—
912C2×C8C2×#4112yes—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—41no—
942C4⋊C4—41no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—41no—
970C22⋊C4—41no—
971C22⋊C4—41no—
972C22⋊C4—41no—
973C22⋊C4—41no—
974C22⋊C4—41no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—21no—
1019C42—41no—
1020C42—41no—
1021C42—42no—
1022C42—42no—
1023C42—42no—
1024C42—42no—
1025C42—81no—
1026C42—81no—
1027C42—81no—
1028C42—81no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23#53212yes—
1064C23C23×D411yescharacteristic
1065Q8—82no—
1066Q8—162no—
1067Q8—162no—
1068D4—41no—
1069D4—41no—
1070D4—41no—
1071D4—41no—
1072D4—41no—
1073D4—41no—
1074D4—41no—
1075D4—41no—
1076D4—82no—
1077D4—82no—
1078D4—82no—
1079D4—84no—
1080D4—84no—
1081D4—84no—
1082D4—162no—
1083D4—162no—
1084D4—162no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—44no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—82no—
1171C2×C4—162no—
1172C2×C4—162no—
1173C2×C4—162no—
1174C2×C4—162no—
1175C2×C4#53212yes—
1176C2×C4#57612yes—
1177C2×C4#57812yes—
1178C2×C4C22×#4111yescharacteristic
1179C2×C4C22×#4111yescharacteristic
1180C2×C4#58511yescharacteristic
1181C2×C4#58511yescharacteristic
1182C2×C4#58511yescharacteristic
1183C2×C4#58511yescharacteristic
1184C8—22no—
1185C8—22no—
1186C8—22no—
1187C8—22no—
1188C8—41no—
1189C8—41no—
1190C8—41no—
1191C8—41no—
1192C22—22no—
1193C22—22no—
1194C22—22no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22C2×#53211yescharacteristic
1228C22#348511yescharacteristic
1229C22#348511yescharacteristic
1230C22C2×#57611yescharacteristic
1231C22C2×#57811yescharacteristic
1232C22#358511yescharacteristic
1233C22#358511yescharacteristic
1234C4—22no—
1235C4—22no—
1236C4—22no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4#349111yescharacteristic
1260C4#351011yescharacteristic
1261C4#352111yescharacteristic
1262C4#352111yescharacteristic
1263C2—42no—
1264C2—81no—
1265C2—81no—
1266C2—161no—
1267C2—161no—
1268C2#3601211yescharacteristic
1269C2#6069811yescharacteristic
1270C2#6071811yescharacteristic
1271C2#6174711yescharacteristic
1272C2#6175211yescharacteristic
1273C2#6180211yescharacteristic
1274C2#6181611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#29738C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2297 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39560C2semidirect
2. #37969C2semidirect
3. #30368C2semidirect
4. #30364C2semidirect
6. #29468C2semidirect
7. #29460C2semidirect
8. #28999C2semidirect
9. #28975C2semidirect
10. #28865C2semidirect
11. #28849C2semidirect
12. #28769C2semidirect
13. #28091C2semidirect
14. #28079C2semidirect
15. #27928C2semidirect
16. #27886C2semidirect
17. #27878C2semidirect
18. #27854C2semidirect
19. #27840C2semidirect
20. #27720C2semidirect
21. #27704C2semidirect
22. #24565C2semidirect
23. #24565C2semidirect
24. #23767C2semidirect
25. #23760C2semidirect
26. #23641C2semidirect
27. #23132C2semidirect
28. #22946C2semidirect
29. #22926C2semidirect
30. #22616C2semidirect
31. #20531C2semidirect

Maximal subgroups

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

subgroupindex
#395602
#379692
#303682
#303642
#297382
#294682
#294602
#289992
#289752
#288652
#288492
#287692
#280912
#280792
#279282
#278862
#278782
#278542
#278402
#277202
#277042
#245652
#237672
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