Finite Group Databasebeta

← #6852144

Subgroups — #6852144

Order 512.

1457 conjugacy classes of subgroups.

The subgroup lattice has 1189 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39591C211yesmaximal, characteristic
2#35281C211yesmaximal, characteristic
3#33152C211yesmaximal, characteristic
4#32694C211yesmaximal, characteristic, complemented
5#32690C211yesmaximal, characteristic, complemented
6#32688C211yesmaximal, characteristic, complemented
7#32683C211yesmaximal, characteristic, complemented
8#32591C211yesmaximal, characteristic, complemented
9#32586C211yesmaximal, characteristic, complemented
10#32579C211yesmaximal, characteristic, complemented
11#32566C211yesmaximal, characteristic, complemented
12#29979C211yesmaximal, characteristic
13#29977C211yesmaximal, characteristic
14#29311C211yesmaximal, characteristic
15#29309C211yesmaximal, characteristic
16#29253C211yesmaximal, characteristic
17#29251C211yesmaximal, characteristic
18#28686C211yesmaximal, characteristic, complemented
19#28686C211yesmaximal, characteristic, complemented
20#26295C211yesmaximal, characteristic, complemented
21#26293C211yesmaximal, characteristic, complemented
22#25848C211yesmaximal, characteristic, complemented
23#25848C211yesmaximal, characteristic, complemented
24#25816C211yesmaximal, characteristic
25#25487C211yesmaximal, characteristic, complemented
26#25487C211yesmaximal, characteristic, complemented
27#24301C211yesmaximal, characteristic
28#22511C211yesmaximal, characteristic
29#22094C211yesmaximal, characteristic
30#22092C211yesmaximal, characteristic
31#21583C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C22×C4⋊Q8C2211yescharacteristic
35C2×#501C2211yescharacteristic
36C2×#501C2211yescharacteristic
37C2×#485C2211yescharacteristic
38C2×#475C2211yescharacteristic
39C2×#475C2211yescharacteristic
40C2×#446C2211yescharacteristic
41C2×#446C2211yescharacteristic
42#2868—21no—
43#2862—21no—
44#2851C2211yescharacteristic
45#2734—21no—
46#2729—21no—
47#2720—21no—
48#2713—21no—
49#2660—21no—
50#2660—21no—
51#2629C2211yescharacteristic
52#2628C2211yescharacteristic
53#2584C2211yescharacteristic
54#2584C2211yescharacteristic
55#2582C2211yescharacteristic
56#2581C2211yescharacteristic
57#2581C2211yescharacteristic
58#2567C2211yescharacteristic
59#2567C2211yescharacteristic
60#2567C2211yescharacteristic
61#2567C2211yescharacteristic
62#2567C2211yescharacteristic
63#2556—21no—
64#2546C2211yescharacteristic
65#2546C2211yescharacteristic
66#2546C2211yescharacteristic
67#2546C2211yescharacteristic
68#2506—21no—
69#2502—21no—
70#2502—21no—
71#2465—21no—
72#2462—21no—
73#2434—21no—
74#2434—21no—
75#2355C2211yescharacteristic
76#2323C2211yescharacteristic
77#2323C2211yescharacteristic
78#2317C2211yescharacteristic
79#2317C2211yescharacteristic
80#2317C2211yescharacteristic
81#2317C2211yescharacteristic
82C4×C22⋊Q8C2211yescharacteristic
83C4×#117C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2100C2211yescharacteristic
87#2099C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2087C2211yescharacteristic
97#2087C2211yescharacteristic
98#2086C2211yescharacteristic
99#2086C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2084C2211yescharacteristic
103#2083C2211yescharacteristic
104#2068C2211yescharacteristic
105#2068C2211yescharacteristic
106#2066C2211yescharacteristic
107#2066C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2058C2211yescharacteristic
113#2058C2211yescharacteristic
114#2058C2211yescharacteristic
115#2058C2211yescharacteristic
116#2058C2211yescharacteristic
117#2058C2211yescharacteristic
118#2058C2211yescharacteristic
119#2058C2211yescharacteristic
120#2057C2211yescharacteristic
121#2057C2211yescharacteristic
122#2024C2211yescharacteristic
123#2024C2211yescharacteristic
124#1993C2211yescharacteristic
125#1993C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1988C2211yescharacteristic
129#1988C2211yescharacteristic
130#1985C2211yescharacteristic
131#1985C2211yescharacteristic
132#1985C2211yescharacteristic
133#1985C2211yescharacteristic
134#1984C2211yescharacteristic
135#1984C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1944C2211yescharacteristic
139#1944C2211yescharacteristic
140#1943C2211yescharacteristic
141#1943C2211yescharacteristic
142#1943C2211yescharacteristic
143#1943C2211yescharacteristic
144#1942C2211yescharacteristic
145#1942C2211yescharacteristic
146#1941C2211yescharacteristic
147#1941C2211yescharacteristic
148#1941C2211yescharacteristic
149#1941C2211yescharacteristic
150#1935C2211yescharacteristic
151#1935C2211yescharacteristic
152#1933C2211yescharacteristic
153#1933C2211yescharacteristic
154#1928C2211yescharacteristic
155#1927C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1921C2211yescharacteristic
159#1921C2211yescharacteristic
160#1920C2211yescharacteristic
161#1920C2211yescharacteristic
162#1920C2211yescharacteristic
163#1920C2211yescharacteristic
164#1919C2211yescharacteristic
165#1919C2211yescharacteristic
166#1919C2211yescharacteristic
167#1918C2211yescharacteristic
168#1918C2211yescharacteristic
169#1918C2211yescharacteristic
170#1873C2211yescharacteristic
171#1872C2211yescharacteristic
172#1872C2211yescharacteristic
173#1865C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1865C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1863C2211yescharacteristic
180#1863C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1853C2211yescharacteristic
185#1853C2211yescharacteristic
186#1853C2211yescharacteristic
187#1853C2211yescharacteristic
188#1852C2211yescharacteristic
189#1852C2211yescharacteristic
190#1825C2211yescharacteristic
191#1825C2211yescharacteristic
192#1825C2211yescharacteristic
193#1798C2211yescharacteristic
194#1798C2211yescharacteristic
195#1797C2211yescharacteristic
196#1776C2211yescharacteristic
197#1776C2211yescharacteristic
198#1763C2211yescharacteristic
199#1763C2211yescharacteristic
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic
202#1749C2211yescharacteristic
203C23×Q8—21no—
204#557—42no—
205#557—42no—
206#533—42no—
207#533—42no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8—21no—
212C2×C4⋊Q8—21no—
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8—42no—
216C2×C4⋊Q8—42no—
217C2×C4⋊Q8D411yescharacteristic
218C2×C4⋊Q8D411yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×#125—21no—
225C2×#125—21no—
226C2×#125D411yescharacteristic
227C2×#125D411yescharacteristic
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×C22⋊Q8D411yescharacteristic
231C2×C22⋊Q8D411yescharacteristic
232C2×C22⋊Q8D411yescharacteristic
233C2×C22⋊Q8D411yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C4×Q8—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C22×C4⋊C4—21no—
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C42C2311yescharacteristic
251#501—42no—
252#501—42no—
253#485Q818yescomplemented
254#475—42no—
255#475—42no—
256#446—42no—
257#446—42no—
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302#400—21no—
303#400—21no—
304#400—21no—
305#399—21no—
306#398—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#398—21no—
318#398—21no—
319#398—21no—
320#396—21no—
321#396—21no—
322#395—21no—
323#395—21no—
324#395—21no—
325#395—21no—
326#395—21no—
327#395—21no—
328#395—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#395—21no—
334#395—21no—
335#395—21no—
336#395—21no—
337#393—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389C2311yescharacteristic
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#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#388—21no—
385#388—21no—
386#388—21no—
387#388—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#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#384—21no—
411#384—21no—
412#384—21no—
413#384—21no—
414#384—21no—
415#384—21no—
416#384—21no—
417#384—21no—
418#384—21no—
419#384C2311yescharacteristic
420#382—21no—
421#382—21no—
422#382—21no—
423#382—21no—
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441#376—21no—
442C43—21no—
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#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—44no—
497C22×Q8—82no—
498C22×Q8—82no—
499C22×Q8C2×D411yescharacteristic
500C22×Q8C2×D411yescharacteristic
501C22×Q8C2×D411yescharacteristic
502C22×Q8C2×D411yescharacteristic
503C22×Q8C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C2×D411yescharacteristic
507C23×C4C2×D411yescharacteristic
508C23×C4C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C4⋊Q8—22no—
518C4⋊Q8—22no—
519C4⋊Q8—22no—
520C4⋊Q8—22no—
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525C4⋊Q8—42no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—42no—
529C4⋊Q8—44no—
530C4⋊Q8—44no—
531C4⋊Q8—44no—
532C4⋊Q8—82no—
533C4⋊Q8—82no—
534C4⋊Q8—82no—
535C4⋊Q8—82no—
536#125—22no—
537#125—22no—
538#125—42no—
539#125—42no—
540#125—41no—
541#125—41no—
542#125—44no—
543#125—44no—
544C22⋊Q8—22no—
545C22⋊Q8—42no—
546C22⋊Q8—42no—
547C22⋊Q8—42no—
548C22⋊Q8—42no—
549C22⋊Q8C2×Q814yes—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—22no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—44no—
565#117—22no—
566#117—22no—
567#117—22no—
568#117—41no—
569#117—41no—
570#117—41no—
571#117—41no—
572#117C2×Q814yes—
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—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—44no—
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—22no—
664C2×C42—22no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42C2×D411yescharacteristic
676C2×C42C2×D411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683#107—22no—
684#107—22no—
685#107—22no—
686#107—41no—
687#107—41no—
688#107—41no—
689#107—41no—
690#107C2×Q814yescomplemented
691#106—22no—
692#106—22no—
693#106—22no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106C2×Q814yescomplemented
703C4⋊C8—22no—
704C4⋊C8—22no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709#103—22no—
710#103—22no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103C2×Q814yescomplemented
716#103C2×Q814yescomplemented
717C22⋊C8—22no—
718C22⋊C8—22no—
719C22⋊C8—22no—
720C22⋊C8C2×Q814yes—
721#97—22no—
722#97—22no—
723#97—41no—
724#97—41no—
725C4×C8—41no—
726C4×C8—41no—
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#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772C24C22×D411yescharacteristic
773C2×Q8—22no—
774C2×Q8—22no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—41no—
783C2×Q8—41no—
784C2×Q8—41no—
785C2×Q8—41no—
786C2×Q8—41no—
787C2×Q8—41no—
788C2×Q8—41no—
789C2×Q8—41no—
790C2×Q8—42no—
791C2×Q8—42no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8—42no—
795C2×Q8—42no—
796C2×Q8—42no—
797C2×Q8—42no—
798C2×Q8—42no—
799C2×Q8—81no—
800C2×Q8—81no—
801C2×Q8—81no—
802C2×Q8—81no—
803C2×Q8—81no—
804C2×Q8—81no—
805C2×Q8—816no—
806C2×Q8C22×Q812yes—
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—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4—81no—
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×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×Q812yes—
853C22×C42−1+412yes—
854C22×C4C2511yescharacteristic
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—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8C22×Q812yes—
878C2×C8C22×Q812yes—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—24no—
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—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—41no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
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—
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⋊C4C22×Q812yes—
963C4⋊C4C22×Q812yes—
964C4⋊C4C22×Q812yes—
965C4⋊C42−1+412yes—
966C4⋊C42−1+412yes—
967C22⋊C4—24no—
968C22⋊C4—24no—
969C22⋊C4—24no—
970C22⋊C4—41no—
971C22⋊C4—41no—
972C22⋊C4—41no—
973C22⋊C4—41no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C42—24no—
978C42—22no—
979C42—22no—
980C42—24no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—42no—
992C42—42no—
993C42—42no—
994C42—42no—
995C42—42no—
996C42—42no—
997C42—42no—
998C42—81no—
999C42—81no—
1000C42—81no—
1001C42H(5,𝔽2)12yes—
1002C42H(5,𝔽2)12yes—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23D4×Q812yes—
1010C23C23×D411yescharacteristic
1011Q8—22no—
1012Q8—22no—
1013Q8—41no—
1014Q8—41no—
1015Q8—82no—
1016Q8—82no—
1017Q8—82no—
1018Q8—82no—
1019Q8—84no—
1020Q8—84no—
1021Q8—84no—
1022Q8—84no—
1023Q8—84no—
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—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
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—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—44no—
1070C2×C4—44no—
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—84no—
1114C2×C4—84no—
1115C2×C4#53412yes—
1116C2×C4#53412yes—
1117C2×C4D4×Q812yes—
1118C2×C4#57712yes—
1119C2×C4C23×Q811yescharacteristic
1120C2×C4C2×H(5,𝔽2)11yescharacteristic
1121C2×C4C2×H(5,𝔽2)11yescharacteristic
1122C2×C4C2×2−1+411yescharacteristic
1123C2×C4C2×2−1+411yescharacteristic
1124C2×C4C2×2−1+411yescharacteristic
1125C8—22no—
1126C8—22no—
1127C8—41no—
1128C8—41no—
1129C8—41no—
1130C8—41no—
1131C8—41no—
1132C8—41no—
1133C22—22no—
1134C22—22no—
1135C22—22no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22C2×#53411yescharacteristic
1141C22C2×D4×Q811yescharacteristic
1142C22#348611yescharacteristic
1143C22C2×#57711yescharacteristic
1144C22#358511yescharacteristic
1145C22#358611yescharacteristic
1146C22#358611yescharacteristic
1147C4—22no—
1148C4—22no—
1149C4—22no—
1150C4—22no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4#350311yescharacteristic
1177C4#350311yescharacteristic
1178C4#355211yescharacteristic
1179C4#355211yescharacteristic
1180C2—42no—
1181C2#3959311yescharacteristic
1182C2#6075411yescharacteristic
1183C2#6075711yescharacteristic
1184C2#6138011yescharacteristic
1185C2#6138311yescharacteristic
1186C2#6185811yescharacteristic
1187C2#6187911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#533 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #32694C2semidirect
5. #32690C2semidirect
6. #32688C2semidirect
7. #32683C2semidirect
8. #32591C2semidirect
9. #32586C2semidirect
10. #32579C2semidirect
11. #32566C2semidirect
18. #28686C2semidirect
19. #28686C2semidirect
20. #26295C2semidirect
21. #26293C2semidirect
22. #25848C2semidirect
23. #25848C2semidirect
25. #25487C2semidirect
26. #25487C2semidirect
253. #485Q8semidirect
690. #107C2×Q8semidirect
702. #106C2×Q8semidirect
715. #103C2×Q8semidirect
716. #103C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#395912
#352812
#331522
#326942
#326902
#326882
#326832
#325912
#325862
#325792
#325662
#299792
#299772
#293112
#293092
#292532
#292512
#286862
#262952
#262932
#258482
#258162
#254872
#243012
#225112
#220942
#220922
#215832