Finite Group Databasebeta

← #7572968

Subgroups — #7572968

Order 512.

1242 conjugacy classes of subgroups.

The subgroup lattice has 1067 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59671C211yesmaximal, characteristic
2#36475C211yesmaximal, characteristic
3#32513C211yesmaximal, characteristic
4#32508C211yesmaximal, characteristic
5#32143C211yesmaximal, characteristic
6#32135C211yesmaximal, characteristic
7#29316C211yesmaximal, characteristic
8#29180C211yesmaximal, characteristic
9#28832C211yesmaximal, characteristic
10#28794C211yesmaximal, characteristic
11#27994C211yesmaximal, characteristic
12#27991C211yesmaximal, characteristic
13#27308C211yesmaximal, characteristic
14#27308C211yesmaximal, characteristic
15#27298C211yesmaximal, characteristic
16#27297C211yesmaximal, characteristic
17#26864C211yesmaximal, characteristic
18#26860C211yesmaximal, characteristic
19#26516C211yesmaximal, characteristic
20#26514C211yesmaximal, characteristic
21#26114C211yesmaximal, characteristic
22#26050C211yesmaximal, characteristic
23#26050C211yesmaximal, characteristic
24#26047C211yesmaximal, characteristic
25#23253C211yesmaximal, characteristic
26#22967C211yesmaximal, characteristic
27#22967C211yesmaximal, characteristic
28#22967C211yesmaximal, characteristic
29#22965C211yesmaximal, characteristic
30C4×#479C211yesmaximal, characteristic
31C4×#479C211yesmaximal, characteristic
32C2×#479C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#477C2211yescharacteristic
36#2864—21no—
37#2864C2211yescharacteristic
38#2805—21no—
39#2802—21no—
40#2590—21no—
41#2588—21no—
42#2570—21no—
43#2570—21no—
44#2570C2211yescharacteristic
45#2570C2211yescharacteristic
46#2570C2211yescharacteristic
47#2552C2211yescharacteristic
48#2550C2211yescharacteristic
49#2550C2211yescharacteristic
50#2520—21no—
51#2511—21no—
52#2509—21no—
53#2509C2211yescharacteristic
54#2509C2211yescharacteristic
55#2509C2211yescharacteristic
56#2509C2211yescharacteristic
57#2508—21no—
58#2508C2211yescharacteristic
59#2507—21no—
60#2507C2211yescharacteristic
61#2506—21no—
62#2506—21no—
63#2506C2211yescharacteristic
64#2506C2211yescharacteristic
65#2370—21no—
66#2370C2211yescharacteristic
67#2370C2211yescharacteristic
68#2370C2211yescharacteristic
69#2369C2211yescharacteristic
70#2351C2211yescharacteristic
71#2351C2211yescharacteristic
72#2351C2211yescharacteristic
73#2351C2211yescharacteristic
74Q8×C4⋊C4C2211yescharacteristic
75Q8×C4⋊C4C2211yescharacteristic
76C4×#125—21no—
77C4×#125C2211yescharacteristic
78C4×#125C2211yescharacteristic
79C4×#125C2211yescharacteristic
80C42×Q8C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2087C2211yescharacteristic
93#2087C2211yescharacteristic
94#2087C2211yescharacteristic
95#2086C2211yescharacteristic
96#2086C2211yescharacteristic
97#2086C2211yescharacteristic
98#2086C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2085C2211yescharacteristic
104#2084C2211yescharacteristic
105#2084C2211yescharacteristic
106#2084C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2058C2211yescharacteristic
112#2058C2211yescharacteristic
113#1991C2211yescharacteristic
114#1991C2211yescharacteristic
115#1991C2211yescharacteristic
116#1990C2211yescharacteristic
117#1989C2211yescharacteristic
118#1989C2211yescharacteristic
119#1949C2211yescharacteristic
120#1949C2211yescharacteristic
121#1949C2211yescharacteristic
122#1949C2211yescharacteristic
123#1949C2211yescharacteristic
124#1949C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1948C2211yescharacteristic
128#1947C2211yescharacteristic
129#1942C2211yescharacteristic
130#1942C2211yescharacteristic
131#1942C2211yescharacteristic
132#1942C2211yescharacteristic
133#1942C2211yescharacteristic
134#1942C2211yescharacteristic
135#1942C2211yescharacteristic
136#1941C2211yescharacteristic
137#1941C2211yescharacteristic
138#1941C2211yescharacteristic
139#1941C2211yescharacteristic
140#1941C2211yescharacteristic
141#1939C2211yescharacteristic
142#1939C2211yescharacteristic
143#1939C2211yescharacteristic
144#1939C2211yescharacteristic
145#1921C2211yescharacteristic
146#1921C2211yescharacteristic
147#1921C2211yescharacteristic
148#1920C2211yescharacteristic
149#1920C2211yescharacteristic
150#1920C2211yescharacteristic
151#1919C2211yescharacteristic
152#1919C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1918C2211yescharacteristic
157#1918C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1918C2211yescharacteristic
161#1916C2211yescharacteristic
162#1916C2211yescharacteristic
163#1916C2211yescharacteristic
164#1916C2211yescharacteristic
165#1865C2211yescharacteristic
166#1865C2211yescharacteristic
167#1865C2211yescharacteristic
168#1865C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1863C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1846C2211yescharacteristic
178#1846C2211yescharacteristic
179#1845C2211yescharacteristic
180#1835C2211yescharacteristic
181#1805C2211yescharacteristic
182#1805C2211yescharacteristic
183#1805C2211yescharacteristic
184#1803C2211yescharacteristic
185C4×#107C2211yescharacteristic
186C4×#107C2211yescharacteristic
187C4×#106C2211yescharacteristic
188C4×#106C2211yescharacteristic
189C8×C4⋊C4C2211yescharacteristic
190C8×C4⋊C4C2211yescharacteristic
191C8×C4⋊C4C2211yescharacteristic
192C8×C4⋊C4C2211yescharacteristic
193C4×C4⋊C8C2211yescharacteristic
194C4×C4⋊C8C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×#125—21no—
205C2×#125—21no—
206C2×#125D411yescharacteristic
207C2×#125C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×C4×Q8C2311yescharacteristic
211C2×C4×Q8C2311yescharacteristic
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217#479—24no—
218#479—24no—
219#479Q818yescomplemented
220#477—24no—
221C2×#107C2311yescharacteristic
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×C4×C8C2311yescharacteristic
258C2×C4×C8C2311yescharacteristic
259C2×C4×C8C2311yescharacteristic
260C2×C4×C8C2311yescharacteristic
261C2×C4×C8C2311yescharacteristic
262C2×C4×C8C2311yescharacteristic
263C2×C4×C8C2311yescharacteristic
264C2×C4×C8C2311yescharacteristic
265#400—21no—
266#400—21no—
267#400—21no—
268#400—21no—
269#400—21no—
270#400—21no—
271#400—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#398—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#395—21no—
292#395—21no—
293#391—21no—
294#391—21no—
295#391—21no—
296#391—21no—
297#389—21no—
298#389—21no—
299#389—21no—
300#389—21no—
301#389—21no—
302#389—21no—
303#389—21no—
304#389—21no—
305#389—21no—
306#389—21no—
307#389—21no—
308#389—21no—
309#389—21no—
310#389—21no—
311#389—21no—
312#389—21no—
313#389—21no—
314#389—21no—
315#389—21no—
316#389—21no—
317#389—21no—
318#389—21no—
319#389—21no—
320#389—21no—
321#389D411yescharacteristic
322#389D411yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387D411yescharacteristic
376#387D411yescharacteristic
377#387D411yescharacteristic
378#387D411yescharacteristic
379#384—21no—
380#384—21no—
381#384—21no—
382#384C2311yescharacteristic
383#384C2311yescharacteristic
384#384C2311yescharacteristic
385#382—21no—
386#382—21no—
387#382—21no—
388#382—21no—
389#382—21no—
390#382D411yescharacteristic
391#382C2311yescharacteristic
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#382C2311yescharacteristic
395#382C2311yescharacteristic
396#382C2311yescharacteristic
397#382C2311yescharacteristic
398C4×C4⋊C4—21no—
399C4×C4⋊C4—21no—
400C4×C4⋊C4—21no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C43—21no—
433C43C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482C22×Q8—21no—
483C22×Q8C2411yescharacteristic
484C22×C8C2411yescharacteristic
485C22×C8C2411yescharacteristic
486C22×C8C2411yescharacteristic
487C22×C8C2411yescharacteristic
488C22×C8C2411yescharacteristic
489C22×C8C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C4⋊Q8—22no—
493C4⋊Q8—41no—
494#125—24no—
495#125—22no—
496#125—22no—
497#125—22no—
498#125—41no—
499#125—41no—
500#125—44no—
501#125—44no—
502#125C2×Q814yes—
503C4×Q8—22no—
504C4×Q8—22no—
505C4×Q8—22no—
506C4×Q8—22no—
507C4×Q8—22no—
508C4×Q8—22no—
509C4×Q8—22no—
510C4×Q8—41no—
511C4×Q8—41no—
512C4×Q8—41no—
513C4×Q8—41no—
514C4×Q8—41no—
515C4×Q8—41no—
516C4×Q8C2×Q814yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4C2×D411yescharacteristic
562C2×C4⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C42—21no—
589C2×C42—21no—
590C2×C42—21no—
591C2×C42—21no—
592C2×C42—21no—
593C2×C42—21no—
594C2×C42—21no—
595C2×C42—21no—
596C2×C42—21no—
597C2×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42C2×D411yescharacteristic
607C2×C42C2×D411yescharacteristic
608C2×C42C2×D411yescharacteristic
609C2×C42C2×D411yescharacteristic
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617#107—22no—
618#107—22no—
619#107—22no—
620#107—22no—
621#107—41no—
622#107—41no—
623#107—41no—
624#107—41no—
625#107—41no—
626#107C2×Q814yes—
627#106—22no—
628#106—22no—
629#106—41no—
630#106—41no—
631#106—41no—
632#106—41no—
633#106—41no—
634#106—41no—
635#106—41no—
636#106C2×Q814yes—
637C4⋊C8—22no—
638C4⋊C8—22no—
639C4⋊C8—22no—
640C4⋊C8—22no—
641C4⋊C8—41no—
642C4⋊C8—41no—
643C4⋊C8—41no—
644C4⋊C8C2×Q814yes—
645#103—22no—
646#103—22no—
647#103—22no—
648#103—22no—
649#103—22no—
650#103C2×Q814yes—
651#103C2×Q814yes—
652#103#4114yes—
653C4×C8—22no—
654C4×C8—22no—
655C4×C8—41no—
656C4×C8—41no—
657C4×C8—41no—
658C4×C8—41no—
659C4×C8—41no—
660C4×C8—41no—
661#95—21no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95C2×D411yescharacteristic
711#95C2×D411yescharacteristic
712#95C2×D411yescharacteristic
713#95C2×D411yescharacteristic
714#95C2×D411yescharacteristic
715#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722C2×Q8—21no—
723C2×Q8—21no—
724C2×Q8—21no—
725C2×Q8—42no—
726C2×Q8—81no—
727C2×Q8—81no—
728C2×Q8C22×Q812yes—
729C2×Q8C2×#4112yes—
730C2×Q82−1+412yes—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4C22×D411yescharacteristic
748C22×C4C22×D411yescharacteristic
749C22×C4C22×D411yescharacteristic
750C22×C4C22×D411yescharacteristic
751C22×C4C22×D411yescharacteristic
752C22×C4C22×D411yescharacteristic
753C22×C4C22×D411yescharacteristic
754C22×C4C22×D411yescharacteristic
755C22×C4C22×D411yescharacteristic
756C22×C4C22×D411yescharacteristic
757C22×C4C22×D411yescharacteristic
758C22×C4C22×D411yescharacteristic
759C22×C4C22×D411yescharacteristic
760C22×C4C22×D411yescharacteristic
761C22×C4C2511yescharacteristic
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8C22×Q812yes—
784C2×C8C22×Q812yes—
785C2×C8C2×#4112yes—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4—22no—
792C4⋊C4—22no—
793C4⋊C4—22no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—41no—
821C4⋊C4—41no—
822C4⋊C4—41no—
823C4⋊C4—41no—
824C4⋊C4—41no—
825C4⋊C4—41no—
826C4⋊C4—42no—
827C4⋊C4—42no—
828C4⋊C4—42no—
829C4⋊C4—42no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C4⋊C4—42no—
834C4⋊C4—42no—
835C4⋊C4—42no—
836C4⋊C4—42no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—42no—
840C4⋊C4—42no—
841C4⋊C4—42no—
842C4⋊C4—42no—
843C4⋊C4—42no—
844C4⋊C4—42no—
845C4⋊C4—42no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—81no—
849C4⋊C4—81no—
850C4⋊C4—81no—
851C4⋊C4—81no—
852C4⋊C4—81no—
853C4⋊C4—81no—
854C4⋊C4—81no—
855C4⋊C4—81no—
856C4⋊C4—81no—
857C4⋊C4—81no—
858C4⋊C4—81no—
859C4⋊C4—81no—
860C4⋊C4—81no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4#13514yes—
868C4⋊C4C22×Q812yes—
869C4⋊C4C22×Q812yes—
870C4⋊C4C22×Q812yes—
871C4⋊C4C2×#4112yes—
872C42—24no—
873C42—22no—
874C42—21no—
875C42—21no—
876C42—21no—
877C42—21no—
878C42—21no—
879C42—21no—
880C42—21no—
881C42—21no—
882C42—21no—
883C42—21no—
884C42—21no—
885C42—21no—
886C42—41no—
887C42—41no—
888C42—41no—
889C42—42no—
890C42—42no—
891C42—42no—
892C42—42no—
893C42—42no—
894C42—42no—
895C42—42no—
896C42—42no—
897C42—81no—
898C42—81no—
899C42—81no—
900C42—81no—
901C42—81no—
902C42—81no—
903C42—81no—
904C42—81no—
905C42—81no—
906C42C22×Q812yes—
907C422−1+412yes—
908C23C23×D411yescharacteristic
909Q8—22no—
910Q8—22no—
911Q8—22no—
912Q8—162no—
913Q8#55714yes—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—21no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4D4×Q812yes—
1000C2×C4D4×Q812yes—
1001C2×C4C2×#13512yes—
1002C2×C4C2×#13512yes—
1003C2×C4C2×#13512yes—
1004C2×C4C23×Q811yescharacteristic
1005C2×C4C22×#4111yescharacteristic
1006C2×C4C2×2−1+411yescharacteristic
1007C2×C4C2×2−1+411yescharacteristic
1008C2×C4#58511yescharacteristic
1009C2×C4#58511yescharacteristic
1010C8—22no—
1011C8—22no—
1012C8—22no—
1013C8—41no—
1014C8—41no—
1015C8—41no—
1016C8—41no—
1017C8—41no—
1018C22C2×D4×Q811yescharacteristic
1019C22D4×#4111yescharacteristic
1020C22#348911yescharacteristic
1021C22C22×#13511yescharacteristic
1022C22#358411yescharacteristic
1023C22#358411yescharacteristic
1024C22#358611yescharacteristic
1025C4—24no—
1026C4—22no—
1027C4—22no—
1028C4—22no—
1029C4—22no—
1030C4—22no—
1031C4—41no—
1032C4—41no—
1033C4—41no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—42no—
1038C4—41no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—41no—
1043C4—41no—
1044C4—81no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4—81no—
1049C4—81no—
1050C4—81no—
1051C4—81no—
1052C4—81no—
1053C4—81no—
1054C4—81no—
1055C4C2×#55711yescharacteristic
1056C4#350411yescharacteristic
1057C4#351511yescharacteristic
1058C4#356311yescharacteristic
1059C2#5915411yescharacteristic
1060C2Q8×#13511yescharacteristic
1061C2#6138611yescharacteristic
1062C2#6143011yescharacteristic
1063C2#6155011yescharacteristic
1064C2#6210411yescharacteristic
1065C2#6221011yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#125 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
219. #479Q8semidirect

Maximal subgroups

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

subgroupindex
#596712
#364752
#325132
#325082
#321432
#321352
#293162
#291802
#288322
#287942
#279942
#279912
#273082
#272982
#272972
#268642
#268602
#265162
#265142
#261142
#260502
#260472
#232532
#229672
#229652
C4×#4792