Finite Group Databasebeta

← #6611263

Subgroups — #6611263

Order 512.

1484 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37878C211yesmaximal, characteristic
2#37690C211yesmaximal, characteristic
3#33292C211yesmaximal, characteristic, complemented
4#33219C211yesmaximal, characteristic, complemented
5#33207C211yesmaximal, characteristic, complemented
6#29215C211yesmaximal, characteristic, complemented
7#28803C211yesmaximal, characteristic, complemented
8#28802C211yesmaximal, characteristic, complemented
9#28793C211yesmaximal, characteristic, complemented
10#28791C211yesmaximal, characteristic, complemented
11#28783C211yesmaximal, characteristic, complemented
12#28782C211yesmaximal, characteristic, complemented
13#28780C211yesmaximal, characteristic, complemented
14#28779C211yesmaximal, characteristic, complemented
15#28774C211yesmaximal, characteristic, complemented
16#28774C211yesmaximal, characteristic, complemented
17#28773C211yesmaximal, characteristic, complemented
18#28771C211yesmaximal, characteristic, complemented
19#28696C211yesmaximal, characteristic, complemented
20#27957C211yesmaximal, characteristic, complemented
21#27955C211yesmaximal, characteristic, complemented
22#25820C211yesmaximal, characteristic, complemented
23#25818C211yesmaximal, characteristic, complemented
24#22710C211yesmaximal, characteristic
25#22710C211yesmaximal, characteristic
26#22708C211yesmaximal, characteristic
27#22706C211yesmaximal, characteristic
28#21730C211yesmaximal, characteristic, complemented
29#21326C211yesmaximal, characteristic, complemented
30#21318C211yesmaximal, characteristic, complemented
31#20484C211yesmaximal, characteristic
32C2×#544C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#501C2211yescharacteristic
36C2×#498C2211yescharacteristic
37C2×#435C2211yescharacteristic
38C2×C8×D4C2211yescharacteristic
39C2×#405C2211yescharacteristic
40C22×C4×C8C2211yescharacteristic
41#2857C2211yescharacteristic
42#2857C2211yescharacteristic
43#2748—21no—
44#2742—21no—
45#2704—21no—
46#2704—21no—
47#2692—21no—
48#2692—21no—
49#2683—21no—
50#2677—21no—
51#2660C2211yescharacteristic
52#2660C2211yescharacteristic
53#2629C2211yescharacteristic
54#2628C2211yescharacteristic
55#2590—21no—
56#2589—21no—
57#2586—21no—
58#2570C2211yescharacteristic
59#2556—21no—
60#2552C2211yescharacteristic
61#2551C2211yescharacteristic
62#2550C2211yescharacteristic
63#2465—21no—
64#2462—21no—
65#2451—21no—
66#2441C2211yescharacteristic
67#2441C2211yescharacteristic
68#2441C2211yescharacteristic
69#2440C2211yescharacteristic
70#2440C2211yescharacteristic
71#2439C2211yescharacteristic
72#2439C2211yescharacteristic
73#2439C2211yescharacteristic
74#2429—21no—
75#2354C2211yescharacteristic
76#2354C2211yescharacteristic
77#2352C2211yescharacteristic
78#2352C2211yescharacteristic
79#2331C2211yescharacteristic
80#2330C2211yescharacteristic
81#2317C2211yescharacteristic
82#2290C2211yescharacteristic
83#2285C2211yescharacteristic
84#2085C2211yescharacteristic
85#2085C2211yescharacteristic
86#2085C2211yescharacteristic
87#2085C2211yescharacteristic
88#2084C2211yescharacteristic
89#2084C2211yescharacteristic
90#2084C2211yescharacteristic
91#2084C2211yescharacteristic
92#2084C2211yescharacteristic
93#2084C2211yescharacteristic
94#2083C2211yescharacteristic
95#2083C2211yescharacteristic
96#2059C2211yescharacteristic
97#2059C2211yescharacteristic
98#2059C2211yescharacteristic
99#2059C2211yescharacteristic
100#2058C2211yescharacteristic
101#2058C2211yescharacteristic
102#2058C2211yescharacteristic
103#2058C2211yescharacteristic
104#2058C2211yescharacteristic
105#2058C2211yescharacteristic
106#2057C2211yescharacteristic
107#2057C2211yescharacteristic
108#1993C2211yescharacteristic
109#1993C2211yescharacteristic
110#1993C2211yescharacteristic
111#1993C2211yescharacteristic
112#1992C2211yescharacteristic
113#1992C2211yescharacteristic
114#1992C2211yescharacteristic
115#1992C2211yescharacteristic
116#1991C2211yescharacteristic
117#1991C2211yescharacteristic
118#1991C2211yescharacteristic
119#1991C2211yescharacteristic
120#1991C2211yescharacteristic
121#1991C2211yescharacteristic
122#1990C2211yescharacteristic
123#1990C2211yescharacteristic
124#1990C2211yescharacteristic
125#1990C2211yescharacteristic
126#1990C2211yescharacteristic
127#1990C2211yescharacteristic
128#1990C2211yescharacteristic
129#1990C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1948C2211yescharacteristic
135#1948C2211yescharacteristic
136#1948C2211yescharacteristic
137#1948C2211yescharacteristic
138#1944C2211yescharacteristic
139#1944C2211yescharacteristic
140#1943C2211yescharacteristic
141#1943C2211yescharacteristic
142#1942C2211yescharacteristic
143#1942C2211yescharacteristic
144#1941C2211yescharacteristic
145#1941C2211yescharacteristic
146#1941C2211yescharacteristic
147#1941C2211yescharacteristic
148#1941C2211yescharacteristic
149#1941C2211yescharacteristic
150#1854C2211yescharacteristic
151#1854C2211yescharacteristic
152#1854C2211yescharacteristic
153#1854C2211yescharacteristic
154#1854C2211yescharacteristic
155#1854C2211yescharacteristic
156#1854C2211yescharacteristic
157#1854C2211yescharacteristic
158#1854C2211yescharacteristic
159#1854C2211yescharacteristic
160#1854C2211yescharacteristic
161#1854C2211yescharacteristic
162#1853C2211yescharacteristic
163#1853C2211yescharacteristic
164#1853C2211yescharacteristic
165#1853C2211yescharacteristic
166#1847C2211yescharacteristic
167#1847C2211yescharacteristic
168#1844C2211yescharacteristic
169#1836C2211yescharacteristic
170#1836C2211yescharacteristic
171#1835C2211yescharacteristic
172#1834C2211yescharacteristic
173#1809C2211yescharacteristic
174#1809C2211yescharacteristic
175#1808C2211yescharacteristic
176#1807C2211yescharacteristic
177#1807C2211yescharacteristic
178#1807C2211yescharacteristic
179#1807C2211yescharacteristic
180#1807C2211yescharacteristic
181#1776C2211yescharacteristic
182#1776C2211yescharacteristic
183C4×#107C2211yescharacteristic
184C4×#106C2211yescharacteristic
185#1771C2211yescharacteristic
186C8×C4⋊C4C2211yescharacteristic
187#1768C2211yescharacteristic
188#1753C2211yescharacteristic
189#1752C2211yescharacteristic
190C8×C22⋊C4C2211yescharacteristic
191C8×C22⋊C4C2211yescharacteristic
192#1750C2211yescharacteristic
193#1749C2211yescharacteristic
194#1736C2211yescharacteristic
195#1736C2211yescharacteristic
196#1735C2211yescharacteristic
197#1735C2211yescharacteristic
198#1735C2211yescharacteristic
199#1735C2211yescharacteristic
200#1735C2211yescharacteristic
201C2×#340C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207#544—24no—
208#544—42no—
209#533—24no—
210#533—42no—
211C2×C4⋊Q8—21no—
212C2×C4⋊Q8—21no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#125—21no—
220C2×#125—21no—
221C2×#125C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#125C2311yescharacteristic
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C4×Q8—21no—
234C2×C4×Q8—21no—
235C2×C4×D4C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C42C2311yescharacteristic
246#501—24no—
247#501—42no—
248#498—42no—
249#435Q818yescomplemented
250C8×D4Q818yescomplemented
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281#405—42no—
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×C4×C8—42no—
288C2×C4×C8C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295#400—21no—
296#400—21no—
297#399—21no—
298#399—21no—
299#399—21no—
300#399—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#396—21no—
319#396—21no—
320#396—21no—
321#395—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#393—21no—
332#393—21no—
333#393—21no—
334#393—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#390—21no—
344#390—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#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388D411yescharacteristic
376#388D411yescharacteristic
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#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387D411yescharacteristic
392#387D411yescharacteristic
393#386—21no—
394#386—21no—
395#386D411yescharacteristic
396#386D411yescharacteristic
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385D411yescharacteristic
402#385D411yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#380—21no—
418#380—21no—
419#380—21no—
420#380—21no—
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
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⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442#376C2311yescharacteristic
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#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489C22×Q8—21no—
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×D4C2×D411yescharacteristic
496C23×C4—21no—
497C23×C4—21no—
498C23×C4C2×D411yescharacteristic
499C23×C4C2×D411yescharacteristic
500C23×C4C2411yescharacteristic
501C23×C4C2411yescharacteristic
502C2×M16—41no—
503C2×M16—41no—
504C2×M16C2×Q814yes—
505C22×C8—41no—
506C22×C8—41no—
507C22×C8—41no—
508C22×C8—41no—
509C22×C8—41no—
510C22×C8—41no—
511C22×C8C2×Q814yes—
512C22×C8C2×Q814yes—
513C22×C8C2×Q814yes—
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8—22no—
525C4⋊Q8—22no—
526C4⋊Q8—22no—
527C4⋊Q8—22no—
528C4⋊Q8—22no—
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534C4⋊Q8—44no—
535C4⋊Q8—82no—
536#125—22no—
537#125—22no—
538#125—22no—
539#125—22no—
540#125—41no—
541#125—41no—
542#125—41no—
543#125—44no—
544#125—82no—
545#125#4114yes—
546C22⋊Q8—44no—
547C22⋊Q8—44no—
548C22⋊Q8—44no—
549C22⋊Q8—44no—
550C22⋊Q8—82no—
551C22⋊Q8—82no—
552C22⋊Q8—82no—
553C22⋊Q8—82no—
554C4×Q8—44no—
555C4×Q8—44no—
556C4×D4C2×Q814yes—
557C4×D4C2×Q814yes—
558#117—22no—
559#117—22no—
560#117—22no—
561#117—22no—
562#117—22no—
563#117—41no—
564#117—41no—
565#117—41no—
566#117—41no—
567#117—41no—
568#117—41no—
569#117—41no—
570#117—41no—
571#117—41no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—22no—
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—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
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×C22⋊C4C2×D411yescharacteristic
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
682#107—22no—
683#107—22no—
684#107—41no—
685#107—41no—
686#107—41no—
687#107—41no—
688#107—41no—
689#107—41no—
690#106—22no—
691#106—22no—
692#106—41no—
693#106—41no—
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#106—41no—
703#106—41no—
704#106—41no—
705#106—41no—
706C4⋊C8C2×Q814yes—
707C4⋊C8C2×Q814yes—
708C22⋊C8C2×Q814yes—
709C22⋊C8C2×Q814yes—
710C22⋊C8C2×Q814yes—
711C22⋊C8C2×Q814yes—
712#97—22no—
713#97—22no—
714#97—41no—
715#97—41no—
716#97C2×Q814yes—
717C4×C8—22no—
718C4×C8—22no—
719C4×C8—41no—
720C4×C8—41no—
721C4×C8—41no—
722C4×C8—41no—
723C4×C8C2×Q814yes—
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#95—21no—
759#95—21no—
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770C24C22×D411yescharacteristic
771C24C22×D411yescharacteristic
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×Q8—42no—
778C2×Q8—42no—
779C2×Q8—81no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×Q8—81no—
784C2×Q8—81no—
785C2×Q8—81no—
786C2×Q8—81no—
787C2×Q8—81no—
788C2×Q8—81no—
789C2×Q8—81no—
790C2×D4—41no—
791C2×D4—41no—
792C2×D4C4⋊Q814yes—
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—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
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—41no—
822C22×C4—41no—
823C22×C4—42no—
824C22×C4—81no—
825C22×C4—81no—
826C22×C4—81no—
827C22×C4—81no—
828C22×C4—81no—
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×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×Q812yes—
842C22×C4C22×Q812yes—
843C22×C4C22×Q812yes—
844C22×C4C22×Q812yes—
845C22×C4C2511yescharacteristic
846M16—44no—
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×C8—44no—
864C2×C8—44no—
865C2×C8—44no—
866C2×C8C22×Q812yes—
867C2×C8C22×Q812yes—
868C2×C8C22×Q812yes—
869C2×C8C22×Q812yes—
870C2×C8C22×Q812yes—
871C2×C8C22×Q812yes—
872C2×C8C22×Q812yes—
873C2×C8C22×Q812yes—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—22no—
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—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
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—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
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—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4C4⋊Q814yes—
953C4⋊C4C2×#4112yes—
954C4⋊C4C2×#4112yes—
955C22⋊C4—22no—
956C22⋊C4—22no—
957C22⋊C4—22no—
958C22⋊C4—22no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4C4⋊Q814yes—
976C22⋊C4C4⋊Q814yes—
977C42—22no—
978C42—22no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—42no—
986C42—42no—
987C42—42no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C42—81no—
994C42—81no—
995C42C22×Q812yes—
996C42C22×Q812yes—
997C42C2×#4112yes—
998C42H(5,𝔽2)12yes—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23C2×C4⋊Q812yes—
1012C23C2×C4⋊Q812yes—
1013C23C23×D411yescharacteristic
1014Q8—84no—
1015Q8—84no—
1016Q8—162no—
1017Q8—162no—
1018Q8—162no—
1019Q8—162no—
1020D4—44no—
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—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—44no—
1060C2×C4—44no—
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—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—162no—
1108C2×C4—162no—
1109C2×C4C2×C4⋊Q812yes—
1110C2×C4C2×C4⋊Q812yes—
1111C2×C4C2×C4⋊Q812yes—
1112C2×C4C2×C4⋊Q812yes—
1113C2×C4#54612yes—
1114C2×C4#54612yes—
1115C2×C4#57712yes—
1116C2×C4#57712yes—
1117C2×C4C23×Q811yescharacteristic
1118C2×C4C23×Q811yescharacteristic
1119C2×C4C22×#4111yescharacteristic
1120C2×C4C2×H(5,𝔽2)11yescharacteristic
1121C2×C4#58511yescharacteristic
1122C2×C4#58511yescharacteristic
1123C8—22no—
1124C8—22no—
1125C8—22no—
1126C8—22no—
1127C8—22no—
1128C8—22no—
1129C8—22no—
1130C8—22no—
1131C22—22no—
1132C22—22no—
1133C22—22no—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—41no—
1145C22C22×C4⋊Q811yescharacteristic
1146C22C2×#54611yescharacteristic
1147C22#350011yescharacteristic
1148C22C2×#57711yescharacteristic
1149C22C2×#57711yescharacteristic
1150C22#358411yescharacteristic
1151C22#358411yescharacteristic
1152C4—22no—
1153C4—22no—
1154C4—22no—
1155C4—22no—
1156C4—22no—
1157C4—22no—
1158C4—22no—
1159C4—22no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—42no—
1164C4—41no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4Q8×#4111yescharacteristic
1181C4Q8×#4111yescharacteristic
1182C4#350111yescharacteristic
1183C4#350111yescharacteristic
1184C2—42no—
1185C2—42no—
1186C2#3627611yescharacteristic
1187C2#6066011yescharacteristic
1188C2#6066511yescharacteristic
1189C2#6117211yescharacteristic
1190C2#6117411yescharacteristic
1191C2#6256211yescharacteristic
1192C2#6256311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33292C2semidirect
4. #33219C2semidirect
5. #33207C2semidirect
6. #29215C2semidirect
7. #28803C2semidirect
8. #28802C2semidirect
9. #28793C2semidirect
10. #28791C2semidirect
11. #28783C2semidirect
12. #28782C2semidirect
13. #28780C2semidirect
14. #28779C2semidirect
15. #28774C2semidirect
16. #28774C2semidirect
17. #28773C2semidirect
18. #28771C2semidirect
19. #28696C2semidirect
20. #27957C2semidirect
21. #27955C2semidirect
22. #25820C2semidirect
23. #25818C2semidirect
28. #21730C2semidirect
29. #21326C2semidirect
30. #21318C2semidirect
249. #435Q8semidirect
250. C8×D4Q8semidirect

Maximal subgroups

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

subgroupindex
#378782
#376902
#332922
#332192
#332072
#292152
#288032
#288022
#287932
#287912
#287832
#287822
#287802
#287792
#287742
#287732
#287712
#286962
#279572
#279552
#258202
#258182
#227102
#227082
#227062
#217302
#213262
#213182
#204842