Finite Group Databasebeta

← #7333218

Subgroups — #7333218

Order 512.

1360 conjugacy classes of subgroups.

The subgroup lattice has 1181 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59153C211yesmaximal, characteristic
2#45719C211yesmaximal, characteristic, complemented
3#32691C211yesmaximal, characteristic, complemented
4#32567C211yesmaximal, characteristic, complemented
5#32433C211yesmaximal, characteristic, complemented
6#32368C211yesmaximal, characteristic, complemented
7#32245C211yesmaximal, characteristic, complemented
8#31689C211yesmaximal, characteristic, complemented
9#31479C211yesmaximal, characteristic, complemented
10#31447C211yesmaximal, characteristic, complemented
11#31107C211yesmaximal, characteristic, complemented
12#30975C211yesmaximal, characteristic, complemented
13#30965C211yesmaximal, characteristic, complemented
14#30784C211yesmaximal, characteristic, complemented
15#30167C211yesmaximal, characteristic
16#29645C211yesmaximal, characteristic, complemented
17#29480C211yesmaximal, characteristic
18#29091C211yesmaximal, characteristic, complemented
19#28820C211yesmaximal, characteristic, complemented
20#28799C211yesmaximal, characteristic, complemented
21#27152C211yesmaximal, characteristic, complemented
22#27125C211yesmaximal, characteristic
23#27041C211yesmaximal, characteristic
24#26869C211yesmaximal, characteristic, complemented
25#26796C211yesmaximal, characteristic
26#26572C211yesmaximal, characteristic
27#26499C211yesmaximal, characteristic, complemented
28#25843C211yesmaximal, characteristic, complemented
29#25817C211yesmaximal, characteristic, complemented
30#24343C211yesmaximal, characteristic, complemented
31#22323C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#501C2211yescharacteristic
36C2×#499C2211yescharacteristic
37C2×#485C2211yescharacteristic
38C2×#485C2211yescharacteristic
39C2×#475C2211yescharacteristic
40C2×#478C2211yescharacteristic
41C2×#440C2211yescharacteristic
42#2855C2211yescharacteristic
43#2851C2211yescharacteristic
44#2833—21no—
45#2794—21no—
46#2771—21no—
47#2770—21no—
48#2766—21no—
49#2765—21no—
50#2720—21no—
51#2692—21no—
52#2683—21no—
53#2584C2211yescharacteristic
54#2584C2211yescharacteristic
55#2581C2211yescharacteristic
56#2571C2211yescharacteristic
57#2566C2211yescharacteristic
58#2552C2211yescharacteristic
59#2551C2211yescharacteristic
60#2550C2211yescharacteristic
61#2514C2211yescharacteristic
62#2511C2211yescharacteristic
63#2506C2211yescharacteristic
64#2497C2211yescharacteristic
65#2494C2211yescharacteristic
66#2489C2211yescharacteristic
67#2465—21no—
68#2465—21no—
69#2453C2211yescharacteristic
70#2452—21no—
71#2452C2211yescharacteristic
72#2452C2211yescharacteristic
73#2449—21no—
74#2441C2211yescharacteristic
75#2439C2211yescharacteristic
76#2429—21no—
77#2423C2211yescharacteristic
78#2382—21no—
79#2370C2211yescharacteristic
80#2363C2211yescharacteristic
81#2363C2211yescharacteristic
82#2360—21no—
83C4×C22⋊Q8C2211yescharacteristic
84C4×#121C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2095C2211yescharacteristic
89#2094C2211yescharacteristic
90#2088C2211yescharacteristic
91#2087C2211yescharacteristic
92#2087C2211yescharacteristic
93#2086C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2084C2211yescharacteristic
97#2084C2211yescharacteristic
98#2077C2211yescharacteristic
99#2076C2211yescharacteristic
100#2075C2211yescharacteristic
101#2074C2211yescharacteristic
102#2073C2211yescharacteristic
103#2071C2211yescharacteristic
104#2067C2211yescharacteristic
105#2066C2211yescharacteristic
106#2066C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2058C2211yescharacteristic
118#2058C2211yescharacteristic
119#2057C2211yescharacteristic
120#2057C2211yescharacteristic
121#2055C2211yescharacteristic
122#2035C2211yescharacteristic
123#2034C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2026C2211yescharacteristic
127#2026C2211yescharacteristic
128#2026C2211yescharacteristic
129#2025C2211yescharacteristic
130#2024C2211yescharacteristic
131#2024C2211yescharacteristic
132#2000C2211yescharacteristic
133#1993C2211yescharacteristic
134#1993C2211yescharacteristic
135#1993C2211yescharacteristic
136#1989C2211yescharacteristic
137#1985C2211yescharacteristic
138#1984C2211yescharacteristic
139#1973C2211yescharacteristic
140#1968C2211yescharacteristic
141#1949C2211yescharacteristic
142#1948C2211yescharacteristic
143#1947C2211yescharacteristic
144#1947C2211yescharacteristic
145#1943C2211yescharacteristic
146#1943C2211yescharacteristic
147#1943C2211yescharacteristic
148#1942C2211yescharacteristic
149#1942C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic
152#1935C2211yescharacteristic
153#1935C2211yescharacteristic
154#1933C2211yescharacteristic
155#1928C2211yescharacteristic
156#1928C2211yescharacteristic
157#1928C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1924C2211yescharacteristic
161#1924C2211yescharacteristic
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic
164#1921C2211yescharacteristic
165#1921C2211yescharacteristic
166#1920C2211yescharacteristic
167#1920C2211yescharacteristic
168#1919C2211yescharacteristic
169#1918C2211yescharacteristic
170#1918C2211yescharacteristic
171#1918C2211yescharacteristic
172#1918C2211yescharacteristic
173#1917C2211yescharacteristic
174#1917C2211yescharacteristic
175#1917C2211yescharacteristic
176#1916C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1865C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1863C2211yescharacteristic
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic
187#1854C2211yescharacteristic
188#1854C2211yescharacteristic
189#1854C2211yescharacteristic
190#1854C2211yescharacteristic
191#1847C2211yescharacteristic
192#1834C2211yescharacteristic
193#1825C2211yescharacteristic
194#1825C2211yescharacteristic
195#1817C2211yescharacteristic
196#1804C2211yescharacteristic
197#1776C2211yescharacteristic
198C4×#106C2211yescharacteristic
199#1771C2211yescharacteristic
200#1770C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1749C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204#554—42no—
205#554—42no—
206#533—42no—
207#533—42no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#125—21no—
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8D411yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×C4×Q8—21no—
229C2×C4×Q8—21no—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C22×C4⋊C4—21no—
239C22×C42C2311yescharacteristic
240#501—42no—
241#501—42no—
242#499—42no—
243#485—42no—
244#485—42no—
245#478—42no—
246#475—42no—
247#440—42no—
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295#401—21no—
296#401—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#399—21no—
308#399—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#395—21no—
327#395—21no—
328#395—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#393—21no—
333#393—21no—
334#393—21no—
335#391—21no—
336#391—21no—
337#391D411yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#390—21no—
344#390—21no—
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389D411yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—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#387D411yescharacteristic
402#387D411yescharacteristic
403#386—21no—
404#386—21no—
405#386—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385D411yescharacteristic
414#385D411yescharacteristic
415#384—21no—
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#383—21no—
420#382—21no—
421#382—21no—
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#381—21no—
426#380D411yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431C4×C4⋊C4—21no—
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
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
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8C2×D411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×D4—21no—
496C22×D4C2411yescharacteristic
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4C2×D411yescharacteristic
501C23×C4C2×D411yescharacteristic
502C23×C4C2411yescharacteristic
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—41no—
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C4⋊Q8—22no—
515C4⋊Q8—22no—
516C4⋊Q8—22no—
517C4⋊Q8—41no—
518C4⋊Q8—41no—
519C4⋊Q8—41no—
520C4⋊Q8—82no—
521#125—22no—
522#125—22no—
523#125—22no—
524#125—41no—
525#125—41no—
526#125—41no—
527#125—41no—
528#125—41no—
529#125—41no—
530#125—41no—
531#125—44no—
532C22⋊Q8—42no—
533C22⋊Q8—44no—
534C22⋊Q8—44no—
535C22⋊Q8—44no—
536C22⋊Q8—44no—
537C22⋊Q8—44no—
538C22⋊Q8—44no—
539C22⋊Q8—41no—
540C22⋊Q8—41no—
541C22⋊Q8—82no—
542#121—22no—
543#121—22no—
544C4×Q8—41no—
545C4×Q8—41no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×Q8—44no—
549C4×Q8—44no—
550C4×D4—22no—
551C4×D4—22no—
552C4×D4—41no—
553C4×D4—41no—
554C4×D4—41no—
555C4×D4—41no—
556C4×D4—82no—
557#117—22no—
558#117—22no—
559#117—41no—
560#117—41no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊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—44no—
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C22⋊C4C2×D411yescharacteristic
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—41no—
653C2×C42—41no—
654C2×C42C2×D411yescharacteristic
655C2×C42C2×D411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662#107—22no—
663#107—22no—
664#107—22no—
665#107—22no—
666#107—22no—
667#107—22no—
668#107—41no—
669#107—41no—
670#107—41no—
671#107—41no—
672#106—22no—
673#106—22no—
674#106—22no—
675#106—22no—
676#106—41no—
677#106—41no—
678#106—41no—
679#106—41no—
680#106—41no—
681C4⋊C8—22no—
682C4⋊C8—22no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685#103—22no—
686#103—22no—
687#103—22no—
688#103—22no—
689#103—41no—
690#103—41no—
691#103—41no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—41no—
697#102—41no—
698#102—41no—
699C22⋊C8—22no—
700C22⋊C8—22no—
701C22⋊C8—41no—
702C22⋊C8—41no—
703#97—22no—
704#97—41no—
705#97—41no—
706#97—41no—
707C4×C8—22no—
708C4×C8—41no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#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#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761C24—21no—
762C24C22×D411yescharacteristic
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—41no—
770C2×Q8—41no—
771C2×Q8—41no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×Q8—81no—
778C2×Q8—81no—
779C2×Q8—81no—
780C2×Q8—81no—
781C2×D4—24no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—81no—
788C2×D4—81no—
789C2×D42−1+412yes—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×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—41no—
812C22×C4—41no—
813C22×C4—41no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—41no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4—81no—
824C22×C4—81no—
825C22×C4—81no—
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C2511yescharacteristic
840SD16—44no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
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×C82−1+412yes—
864C2×C82−1+412yes—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
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—41no—
895C4⋊C4—41no—
896C4⋊C4—41no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—41no—
900C4⋊C4—41no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
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—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
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⋊C4H(5,𝔽2)12yes—
937C4⋊C4H(5,𝔽2)12yes—
938C4⋊C42−1+412yes—
939C22⋊C4—24no—
940C22⋊C4—22no—
941C22⋊C4—41no—
942C22⋊C4—41no—
943C22⋊C4—41no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—41no—
973C42—41no—
974C42—42no—
975C42—42no—
976C42—42no—
977C42—81no—
978C42—81no—
979C42—81no—
980C42—81no—
981C42—81no—
982C42—81no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—22no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23C23×D411yescharacteristic
998Q8—41no—
999Q8—41no—
1000Q8—41no—
1001Q8—41no—
1002Q8—82no—
1003Q8—84no—
1004Q8—84no—
1005Q8—162no—
1006D4—22no—
1007D4—22no—
1008D4—41no—
1009D4—41no—
1010D4—84no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—22no—
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—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
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—82no—
1099C2×C4—82no—
1100C2×C4—84no—
1101C2×C4—162no—
1102C2×C4—162no—
1103C2×C4#57512yes—
1104C2×C4C2×H(5,𝔽2)11yescharacteristic
1105C2×C4C2×H(5,𝔽2)11yescharacteristic
1106C2×C4C2×2−1+411yescharacteristic
1107C2×C4C2×2−1+411yescharacteristic
1108C2×C4C2×2−1+411yescharacteristic
1109C2×C4C2×2−1+411yescharacteristic
1110C8—22no—
1111C8—22no—
1112C8—41no—
1113C8—41no—
1114C8—41no—
1115C8—41no—
1116C8—41no—
1117C8—41no—
1118C22—41no—
1119C22—41no—
1120C22—41no—
1121C22—42no—
1122C22—41no—
1123C22—42no—
1124C22—41no—
1125C22—41no—
1126C22—42no—
1127C22—41no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22#348411yescharacteristic
1133C22#348611yescharacteristic
1134C22#349911yescharacteristic
1135C22C2×#57511yescharacteristic
1136C22#358411yescharacteristic
1137C22#358511yescharacteristic
1138C22#358611yescharacteristic
1139C4—22no—
1140C4—41no—
1141C4—41no—
1142C4—41no—
1143C4—41no—
1144C4—41no—
1145C4—41no—
1146C4—41no—
1147C4—41no—
1148C4—42no—
1149C4—42no—
1150C4—41no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—42no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4#353811yescharacteristic
1168C4#355011yescharacteristic
1169C4#355211yescharacteristic
1170C4#355211yescharacteristic
1171C2—81no—
1172C2—82no—
1173C2#4794511yescharacteristic
1174C2#6159911yescharacteristic
1175C2#6165411yescharacteristic
1176C2#6183411yescharacteristic
1177C2#6185511yescharacteristic
1178C2#6250611yescharacteristic
1179C2#6252311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #45719C2semidirect
3. #32691C2semidirect
4. #32567C2semidirect
5. #32433C2semidirect
6. #32368C2semidirect
7. #32245C2semidirect
8. #31689C2semidirect
9. #31479C2semidirect
10. #31447C2semidirect
11. #31107C2semidirect
12. #30975C2semidirect
13. #30965C2semidirect
14. #30784C2semidirect
16. #29645C2semidirect
18. #29091C2semidirect
19. #28820C2semidirect
20. #28799C2semidirect
21. #27152C2semidirect
24. #26869C2semidirect
27. #26499C2semidirect
28. #25843C2semidirect
29. #25817C2semidirect
30. #24343C2semidirect
31. #22323C2semidirect

Maximal subgroups

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

subgroupindex
#591532
#457192
#326912
#325672
#324332
#323682
#322452
#316892
#314792
#314472
#311072
#309752
#309652
#307842
#301672
#296452
#294802
#290912
#288202
#287992
#271522
#271252
#270412
#268692
#267962
#265722
#264992
#258432
#258172
#243432
#223232