Finite Group Databasebeta

← #7188254

Subgroups — #7188254

Order 512.

1152 conjugacy classes of subgroups.

The subgroup lattice has 1043 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45280C211yesmaximal, characteristic
2#45202C211yesmaximal, characteristic
3#32523C211yesmaximal, characteristic
4#32522C211yesmaximal, characteristic
5#32513C211yesmaximal, characteristic
6#32508C211yesmaximal, characteristic
7#32154C211yesmaximal, characteristic
8#32149C211yesmaximal, characteristic
9#32145C211yesmaximal, characteristic
10#32144C211yesmaximal, characteristic
11#29294C211yesmaximal, characteristic
12#29293C211yesmaximal, characteristic
13#28807C211yesmaximal, characteristic
14#28806C211yesmaximal, characteristic
15#26882C211yesmaximal, characteristic
16#26872C211yesmaximal, characteristic
17#26870C211yesmaximal, characteristic
18#26869C211yesmaximal, characteristic
19#26514C211yesmaximal, characteristic
20#26511C211yesmaximal, characteristic
21#26457C211yesmaximal, characteristic
22#26455C211yesmaximal, characteristic
23#26451C211yesmaximal, characteristic
24#26450C211yesmaximal, characteristic
25#26449C211yesmaximal, characteristic
26#26443C211yesmaximal, characteristic
27#23845C211yesmaximal, characteristic
28#23169C211yesmaximal, characteristic
29#23166C211yesmaximal, characteristic
30#22306C211yesmaximal, characteristic
31#22255C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33#2809—21no—
34#2802—21no—
35#2802—21no—
36#2799—21no—
37#2791—21no—
38#2791—21no—
39#2774—21no—
40#2755—21no—
41#2588—21no—
42#2588—21no—
43#2582—21no—
44#2571C2211yescharacteristic
45#2570C2211yescharacteristic
46#2552C2211yescharacteristic
47#2552C2211yescharacteristic
48#2550C2211yescharacteristic
49#2550C2211yescharacteristic
50#2550C2211yescharacteristic
51#2550C2211yescharacteristic
52#2511—21no—
53#2509—21no—
54#2509C2211yescharacteristic
55#2509C2211yescharacteristic
56#2509C2211yescharacteristic
57#2508—21no—
58#2508C2211yescharacteristic
59#2508C2211yescharacteristic
60#2507C2211yescharacteristic
61#2507C2211yescharacteristic
62#2506C2211yescharacteristic
63#2462—21no—
64#2453—21no—
65#2402C2211yescharacteristic
66#2370C2211yescharacteristic
67#2370C2211yescharacteristic
68#2370C2211yescharacteristic
69#2370C2211yescharacteristic
70#2370C2211yescharacteristic
71#2369C2211yescharacteristic
72#2365C2211yescharacteristic
73#2365C2211yescharacteristic
74#2331C2211yescharacteristic
75#2331C2211yescharacteristic
76#2330C2211yescharacteristic
77#2330C2211yescharacteristic
78#2101C2211yescharacteristic
79#2101C2211yescharacteristic
80#2101C2211yescharacteristic
81#2099C2211yescharacteristic
82#2088C2211yescharacteristic
83#2088C2211yescharacteristic
84#2088C2211yescharacteristic
85#2088C2211yescharacteristic
86#2088C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2087C2211yescharacteristic
91#2087C2211yescharacteristic
92#2087C2211yescharacteristic
93#2087C2211yescharacteristic
94#2086C2211yescharacteristic
95#2086C2211yescharacteristic
96#2086C2211yescharacteristic
97#2086C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2084C2211yescharacteristic
104#2084C2211yescharacteristic
105#2083C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2058C2211yescharacteristic
115#2058C2211yescharacteristic
116#2058C2211yescharacteristic
117#2057C2211yescharacteristic
118#1993C2211yescharacteristic
119#1992C2211yescharacteristic
120#1991C2211yescharacteristic
121#1991C2211yescharacteristic
122#1991C2211yescharacteristic
123#1990C2211yescharacteristic
124#1989C2211yescharacteristic
125#1989C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1989C2211yescharacteristic
129#1989C2211yescharacteristic
130#1989C2211yescharacteristic
131#1988C2211yescharacteristic
132#1988C2211yescharacteristic
133#1987C2211yescharacteristic
134#1987C2211yescharacteristic
135#1987C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1949C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1948C2211yescharacteristic
144#1947C2211yescharacteristic
145#1947C2211yescharacteristic
146#1947C2211yescharacteristic
147#1947C2211yescharacteristic
148#1944C2211yescharacteristic
149#1944C2211yescharacteristic
150#1943C2211yescharacteristic
151#1943C2211yescharacteristic
152#1942C2211yescharacteristic
153#1942C2211yescharacteristic
154#1942C2211yescharacteristic
155#1941C2211yescharacteristic
156#1940C2211yescharacteristic
157#1940C2211yescharacteristic
158#1939C2211yescharacteristic
159#1939C2211yescharacteristic
160#1939C2211yescharacteristic
161#1939C2211yescharacteristic
162#1921C2211yescharacteristic
163#1921C2211yescharacteristic
164#1921C2211yescharacteristic
165#1921C2211yescharacteristic
166#1921C2211yescharacteristic
167#1920C2211yescharacteristic
168#1920C2211yescharacteristic
169#1920C2211yescharacteristic
170#1920C2211yescharacteristic
171#1920C2211yescharacteristic
172#1920C2211yescharacteristic
173#1919C2211yescharacteristic
174#1919C2211yescharacteristic
175#1919C2211yescharacteristic
176#1919C2211yescharacteristic
177#1919C2211yescharacteristic
178#1919C2211yescharacteristic
179#1919C2211yescharacteristic
180#1918C2211yescharacteristic
181#1918C2211yescharacteristic
182#1918C2211yescharacteristic
183#1918C2211yescharacteristic
184#1918C2211yescharacteristic
185#1918C2211yescharacteristic
186#1917C2211yescharacteristic
187#1917C2211yescharacteristic
188#1916C2211yescharacteristic
189#1916C2211yescharacteristic
190#1843C2211yescharacteristic
191#1836C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195#1776C2211yescharacteristic
196C4×#107C2211yescharacteristic
197C4×#106C2211yescharacteristic
198C4×#106C2211yescharacteristic
199C4×#106C2211yescharacteristic
200#1771C2211yescharacteristic
201#1771C2211yescharacteristic
202#1746C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×#125—21no—
207C2×#125C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×C4×Q8—21no—
213C2×C4×Q8—21no—
214#501Q818yescomplemented
215C2×#107C2311yescharacteristic
216C2×#107C2311yescharacteristic
217C2×#107C2311yescharacteristic
218C2×#107C2311yescharacteristic
219C2×#107C2311yescharacteristic
220C2×#107C2311yescharacteristic
221C2×#107C2311yescharacteristic
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#106C2311yescharacteristic
226C2×#106C2311yescharacteristic
227C2×#106C2311yescharacteristic
228C2×#106C2311yescharacteristic
229C2×#106C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×C4⋊C8C2311yescharacteristic
236C2×C4⋊C8C2311yescharacteristic
237C2×C4⋊C8C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×#97C2311yescharacteristic
246C2×#97C2311yescharacteristic
247C2×#97C2311yescharacteristic
248C2×C4×C8C2311yescharacteristic
249C2×C4×C8C2311yescharacteristic
250C2×C4×C8C2311yescharacteristic
251#400—21no—
252#400—21no—
253#400—21no—
254#400—21no—
255#400—21no—
256#400—21no—
257#400—21no—
258#400—21no—
259#400—21no—
260#400—21no—
261#400—21no—
262#400—21no—
263#400D411yescharacteristic
264#400D411yescharacteristic
265#400D411yescharacteristic
266#400D411yescharacteristic
267#398—21no—
268#398—21no—
269#398—21no—
270#398—21no—
271#398—21no—
272#398—21no—
273#398—21no—
274#398—21no—
275#398—21no—
276#398—21no—
277#398—21no—
278#398—21no—
279#398—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#398D411yescharacteristic
284#398D411yescharacteristic
285#398D411yescharacteristic
286#398D411yescharacteristic
287#395—21no—
288#395—21no—
289#395—21no—
290#395—21no—
291#391—21no—
292#391—21no—
293#391—21no—
294#391—21no—
295#391—21no—
296#391—21no—
297#391—21no—
298#391—21no—
299#391—21no—
300#391—21no—
301#391—21no—
302#391—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#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
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#389C2311yescharacteristic
348#389C2311yescharacteristic
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#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#384—21no—
382#384—21no—
383#384C2311yescharacteristic
384#384C2311yescharacteristic
385#384C2311yescharacteristic
386#382—21no—
387#382—21no—
388#382—21no—
389#382C2311yescharacteristic
390#382C2311yescharacteristic
391#382C2311yescharacteristic
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394C4×C4⋊C4—21no—
395C4×C4⋊C4—21no—
396C4×C4⋊C4—21no—
397C4×C4⋊C4—21no—
398C4×C4⋊C4—21no—
399C4×C4⋊C4—21no—
400C4×C4⋊C4C2311yescharacteristic
401C4×C4⋊C4C2311yescharacteristic
402C4×C4⋊C4C2311yescharacteristic
403C4×C4⋊C4C2311yescharacteristic
404C4×C4⋊C4C2311yescharacteristic
405C4×C4⋊C4C2311yescharacteristic
406C4×C4⋊C4C2311yescharacteristic
407C4×C4⋊C4C2311yescharacteristic
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422#376C2311yescharacteristic
423#340C2311yescharacteristic
424#340C2311yescharacteristic
425#340C2311yescharacteristic
426#340C2311yescharacteristic
427#340C2311yescharacteristic
428#340C2311yescharacteristic
429#340C2311yescharacteristic
430#340C2311yescharacteristic
431#340C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
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#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479C22×Q8—21no—
480C22×Q8—21no—
481C22×Q8—21no—
482C22×C8C2411yescharacteristic
483C22×C8C2411yescharacteristic
484C22×C8C2411yescharacteristic
485C22×C8C2411yescharacteristic
486C22×C8C2411yescharacteristic
487C22×C8C2411yescharacteristic
488C22×C8C2411yescharacteristic
489C22×C8C2411yescharacteristic
490C4⋊Q8—22no—
491C4⋊Q8—22no—
492C4⋊Q8—22no—
493C4⋊Q8—41no—
494C4⋊Q8—41no—
495C4⋊Q8C2×Q814yes—
496#125—22no—
497#125—22no—
498#125—22no—
499#125—22no—
500#125—22no—
501#125—41no—
502#125—41no—
503#125—41no—
504#125—41no—
505#125—82no—
506#125C2×Q814yes—
507C4×Q8—82no—
508C4×Q8—82no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
553C2×C4⋊C4C2×D411yescharacteristic
554C2×C4⋊C4C2×D411yescharacteristic
555C2×C4⋊C4C2×D411yescharacteristic
556C2×C4⋊C4C2×D411yescharacteristic
557C2×C4⋊C4C2×D411yescharacteristic
558C2×C4⋊C4C2×D411yescharacteristic
559C2×C4⋊C4C2×D411yescharacteristic
560C2×C4⋊C4C2×D411yescharacteristic
561C2×C4⋊C4C2×D411yescharacteristic
562C2×C4⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2411yescharacteristic
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C42—21no—
581C2×C42—21no—
582C2×C42—21no—
583C2×C42—21no—
584C2×C42—21no—
585C2×C42—21no—
586C2×C42—21no—
587C2×C42—21no—
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×C42C2411yescharacteristic
597C2×C42C2411yescharacteristic
598C2×C42C2411yescharacteristic
599C2×C42C2411yescharacteristic
600C2×C42C2411yescharacteristic
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603#107—22no—
604#107—41no—
605#107—41no—
606#107—41no—
607#107—41no—
608#107—41no—
609#107—41no—
610#107—41no—
611#107C2×Q814yes—
612#107C2×Q814yes—
613#106—22no—
614#106—22no—
615#106—22no—
616#106—41no—
617#106—41no—
618#106—41no—
619#106—41no—
620#106—41no—
621#106C2×Q814yes—
622#106C2×Q814yes—
623C4⋊C8—22no—
624C4⋊C8—22no—
625C4⋊C8—41no—
626C4⋊C8—41no—
627C4⋊C8—41no—
628C4⋊C8—41no—
629C4⋊C8—41no—
630C4⋊C8—41no—
631C4⋊C8—41no—
632C4⋊C8—41no—
633#97—41no—
634#97—41no—
635#97C2×Q814yes—
636C4×C8—22no—
637C4×C8—41no—
638C4×C8—41no—
639#95—21no—
640#95—21no—
641#95—21no—
642#95—21no—
643#95—21no—
644#95—21no—
645#95—21no—
646#95—21no—
647#95—21no—
648#95—21no—
649#95—21no—
650#95—21no—
651#95—21no—
652#95—21no—
653#95—21no—
654#95—21no—
655#95—21no—
656#95—21no—
657#95—21no—
658#95—21no—
659#95—21no—
660#95—21no—
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#95C2×D411yescharacteristic
690#95C2×D411yescharacteristic
691#95C2×D411yescharacteristic
692#95C2×D411yescharacteristic
693#95C2×D411yescharacteristic
694#95C2×D411yescharacteristic
695#95C2×D411yescharacteristic
696#95C2×D411yescharacteristic
697#95C2×D411yescharacteristic
698#95C2×D411yescharacteristic
699#95C2×D411yescharacteristic
700#95C2×D411yescharacteristic
701#95C2×D411yescharacteristic
702#95C2×D411yescharacteristic
703#95C2×D411yescharacteristic
704#95C2×D411yescharacteristic
705C2×Q8—24no—
706C2×Q8—42no—
707C2×Q8—42no—
708C2×Q8—42no—
709C2×Q8—81no—
710C2×Q8—81no—
711C2×Q8—81no—
712C2×Q8—81no—
713C2×Q8—81no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4C22×D411yescharacteristic
731C22×C4C22×D411yescharacteristic
732C22×C4C22×D411yescharacteristic
733C22×C4C22×D411yescharacteristic
734C22×C4C22×D411yescharacteristic
735C22×C4C22×D411yescharacteristic
736C22×C4C22×D411yescharacteristic
737C22×C4C22×D411yescharacteristic
738C22×C4C22×D411yescharacteristic
739C22×C4C22×D411yescharacteristic
740C22×C4C22×D411yescharacteristic
741C22×C4C22×D411yescharacteristic
742C22×C4C22×D411yescharacteristic
743C22×C4C22×D411yescharacteristic
744C22×C4C2511yescharacteristic
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8C22×Q812yes—
768C2×C8C22×Q812yes—
769C4⋊C4—24no—
770C4⋊C4—24no—
771C4⋊C4—24no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—21no—
777C4⋊C4—21no—
778C4⋊C4—21no—
779C4⋊C4—21no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—41no—
799C4⋊C4—41no—
800C4⋊C4—41no—
801C4⋊C4—41no—
802C4⋊C4—41no—
803C4⋊C4—41no—
804C4⋊C4—41no—
805C4⋊C4—41no—
806C4⋊C4—41no—
807C4⋊C4—41no—
808C4⋊C4—41no—
809C4⋊C4—41no—
810C4⋊C4—42no—
811C4⋊C4—42no—
812C4⋊C4—42no—
813C4⋊C4—42no—
814C4⋊C4—42no—
815C4⋊C4—42no—
816C4⋊C4—42no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4—42no—
820C4⋊C4—42no—
821C4⋊C4—42no—
822C4⋊C4—81no—
823C4⋊C4—81no—
824C4⋊C4—81no—
825C4⋊C4—81no—
826C4⋊C4—81no—
827C4⋊C4—81no—
828C4⋊C4—81no—
829C4⋊C4—81no—
830C4⋊C4—81no—
831C4⋊C4—81no—
832C4⋊C4—81no—
833C4⋊C4—81no—
834C4⋊C4—81no—
835C4⋊C4—81no—
836C4⋊C4—81no—
837C4⋊C4—81no—
838C4⋊C4—81no—
839C4⋊C4—81no—
840C4⋊C4—81no—
841C4⋊C4—81no—
842C4⋊C4—81no—
843C4⋊C4—81no—
844C4⋊C4—81no—
845C4⋊C4—81no—
846C4⋊C4—81no—
847C4⋊C4—81no—
848C4⋊C4—81no—
849C4⋊C4—81no—
850C4⋊C4C22×Q812yes—
851C4⋊C4C22×Q812yes—
852C4⋊C4C22×Q812yes—
853C4⋊C4C22×Q812yes—
854C4⋊C42−1+412yes—
855C4⋊C42−1+412yes—
856C42—21no—
857C42—21no—
858C42—21no—
859C42—21no—
860C42—21no—
861C42—21no—
862C42—21no—
863C42—21no—
864C42—21no—
865C42—21no—
866C42—21no—
867C42—21no—
868C42—42no—
869C42—81no—
870C42—81no—
871C42—81no—
872C42—81no—
873C42—81no—
874C42—81no—
875C42—81no—
876C42—81no—
877C42—81no—
878C42—81no—
879C42—81no—
880C42—81no—
881C42—81no—
882C42—81no—
883C42—81no—
884C42C22×Q812yes—
885C422−1+412yes—
886C23C23×D411yescharacteristic
887Q8—84no—
888Q8—84no—
889Q8—162no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
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—22no—
935C2×C4—22no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
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×C4D4×Q812yes—
979C2×C4D4×Q812yes—
980C2×C4C23×Q811yescharacteristic
981C2×C4C2×2−1+411yescharacteristic
982C2×C4C2×2−1+411yescharacteristic
983C2×C4C2×2−1+411yescharacteristic
984C2×C4#58511yescharacteristic
985C2×C4#58511yescharacteristic
986C8—22no—
987C8—22no—
988C8—41no—
989C8—41no—
990C8—41no—
991C8—41no—
992C8—41no—
993C8—41no—
994C22C2×D4×Q811yescharacteristic
995C22#348911yescharacteristic
996C22#348911yescharacteristic
997C22#358411yescharacteristic
998C22#358411yescharacteristic
999C22#358511yescharacteristic
1000C22#358611yescharacteristic
1001C4—22no—
1002C4—22no—
1003C4—41no—
1004C4—41no—
1005C4—41no—
1006C4—41no—
1007C4—41no—
1008C4—41no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—41no—
1015C4—41no—
1016C4—41no—
1017C4—42no—
1018C4—41no—
1019C4—41no—
1020C4—41no—
1021C4—81no—
1022C4—81no—
1023C4—81no—
1024C4—81no—
1025C4—81no—
1026C4—81no—
1027C4—81no—
1028C4—81no—
1029C4—81no—
1030C4—81no—
1031C4#350211yescharacteristic
1032C4#350211yescharacteristic
1033C4#355611yescharacteristic
1034C4#355711yescharacteristic
1035C2#4527711yescharacteristic
1036C2#6138511yescharacteristic
1037C2#6138611yescharacteristic
1038C2#6217211yescharacteristic
1039C2#6219711yescharacteristic
1040C2#6221011yescharacteristic
1041C2#6222411yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2402 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
214. #501Q8semidirect

Maximal subgroups

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

subgroupindex
#452802
#452022
#325232
#325222
#325132
#325082
#321542
#321492
#321452
#321442
#292942
#292932
#288072
#288062
#268822
#268722
#268702
#268692
#265142
#265112
#264572
#264552
#264512
#264502
#264492
#264432
#238452
#231692
#231662
#223062
#222552