Finite Group Databasebeta

← #7572616

Subgroups — #7572616

Order 512.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45223C211yesmaximal, characteristic, complemented
2#35963C211yesmaximal, characteristic
3#31894C211yesmaximal, characteristic
4#31878C211yesmaximal, characteristic
5#30951C211yesmaximal, characteristic
6#30951C211yesmaximal, characteristic
7#29324C211yesmaximal, characteristic, complemented
8#29185C211yesmaximal, characteristic, complemented
9#28951C211yesmaximal, characteristic
10#28949C211yesmaximal, characteristic
11#28811C211yesmaximal, characteristic, complemented
12#28804C211yesmaximal, characteristic, complemented
13#27026C211yesmaximal, characteristic
14#27006C211yesmaximal, characteristic
15#26886C211yesmaximal, characteristic, complemented
16#26865C211yesmaximal, characteristic, complemented
17#26865C211yesmaximal, characteristic, complemented
18#26858C211yesmaximal, characteristic, complemented
19#26457C211yesmaximal, characteristic, complemented
20#26457C211yesmaximal, characteristic, complemented
21#26449C211yesmaximal, characteristic, complemented
22#26447C211yesmaximal, characteristic, complemented
23#26090C211yesmaximal, characteristic
24#26037C211yesmaximal, characteristic
25#23260C211yesmaximal, characteristic, complemented
26#23164C211yesmaximal, characteristic, complemented
27#23160C211yesmaximal, characteristic, complemented
28#23076C211yesmaximal, characteristic
29#23065C211yesmaximal, characteristic
30#21620C211yesmaximal, characteristic
31#21619C211yesmaximal, characteristic
32C2×#499C2211yescharacteristic
33C2×#499C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#478C2211yescharacteristic
36#2802—21no—
37#2791—21no—
38#2791—21no—
39#2726—21no—
40#2667—21no—
41#2647C2211yescharacteristic
42#2590—21no—
43#2589—21no—
44#2587—21no—
45#2585—21no—
46#2569—21no—
47#2552—21no—
48#2552C2211yescharacteristic
49#2552C2211yescharacteristic
50#2552C2211yescharacteristic
51#2552C2211yescharacteristic
52#2552C2211yescharacteristic
53#2550C2211yescharacteristic
54#2507C2211yescharacteristic
55#2507C2211yescharacteristic
56#2506—21no—
57#2506C2211yescharacteristic
58#2506C2211yescharacteristic
59#2497—21no—
60#2454C2211yescharacteristic
61#2454C2211yescharacteristic
62#2454C2211yescharacteristic
63#2452C2211yescharacteristic
64#2438—21no—
65#2423—21no—
66#2402C2211yescharacteristic
67#2396—21no—
68#2370C2211yescharacteristic
69#2370C2211yescharacteristic
70#2370C2211yescharacteristic
71#2370C2211yescharacteristic
72#2370C2211yescharacteristic
73#2370C2211yescharacteristic
74#2370C2211yescharacteristic
75#2365C2211yescharacteristic
76#2357C2211yescharacteristic
77#2354C2211yescharacteristic
78#2330C2211yescharacteristic
79#2330C2211yescharacteristic
80#2275C2211yescharacteristic
81#2094C2211yescharacteristic
82#2094C2211yescharacteristic
83#2088C2211yescharacteristic
84#2088C2211yescharacteristic
85#2088C2211yescharacteristic
86#2088C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2087C2211yescharacteristic
91#2084C2211yescharacteristic
92#2083C2211yescharacteristic
93#2083C2211yescharacteristic
94#2083C2211yescharacteristic
95#2067C2211yescharacteristic
96#2065C2211yescharacteristic
97#2065C2211yescharacteristic
98#2065C2211yescharacteristic
99#2059C2211yescharacteristic
100#2059C2211yescharacteristic
101#2059C2211yescharacteristic
102#2059C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2058C2211yescharacteristic
110#2058C2211yescharacteristic
111#2025C2211yescharacteristic
112#2025C2211yescharacteristic
113#1992C2211yescharacteristic
114#1992C2211yescharacteristic
115#1991C2211yescharacteristic
116#1990C2211yescharacteristic
117#1989C2211yescharacteristic
118#1989C2211yescharacteristic
119#1989C2211yescharacteristic
120#1989C2211yescharacteristic
121#1989C2211yescharacteristic
122#1989C2211yescharacteristic
123#1989C2211yescharacteristic
124#1988C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1948C2211yescharacteristic
128#1948C2211yescharacteristic
129#1948C2211yescharacteristic
130#1948C2211yescharacteristic
131#1947C2211yescharacteristic
132#1947C2211yescharacteristic
133#1944C2211yescharacteristic
134#1943C2211yescharacteristic
135#1943C2211yescharacteristic
136#1942C2211yescharacteristic
137#1942C2211yescharacteristic
138#1941C2211yescharacteristic
139#1941C2211yescharacteristic
140#1941C2211yescharacteristic
141#1940C2211yescharacteristic
142#1940C2211yescharacteristic
143#1939C2211yescharacteristic
144#1939C2211yescharacteristic
145#1936C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1926C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1920C2211yescharacteristic
160#1920C2211yescharacteristic
161#1920C2211yescharacteristic
162#1920C2211yescharacteristic
163#1920C2211yescharacteristic
164#1920C2211yescharacteristic
165#1920C2211yescharacteristic
166#1919C2211yescharacteristic
167#1919C2211yescharacteristic
168#1919C2211yescharacteristic
169#1919C2211yescharacteristic
170#1919C2211yescharacteristic
171#1918C2211yescharacteristic
172#1918C2211yescharacteristic
173#1917C2211yescharacteristic
174#1916C2211yescharacteristic
175#1916C2211yescharacteristic
176#1916C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1844C2211yescharacteristic
182#1836C2211yescharacteristic
183#1802C2211yescharacteristic
184#1802C2211yescharacteristic
185#1776C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188C4×#107C2211yescharacteristic
189C4×#107C2211yescharacteristic
190C4×#107C2211yescharacteristic
191C4×#106C2211yescharacteristic
192C4×#106C2211yescharacteristic
193#1771C2211yescharacteristic
194#1770C2211yescharacteristic
195C8×C4⋊C4C2211yescharacteristic
196C8×C4⋊C4C2211yescharacteristic
197#1768C2211yescharacteristic
198#1768C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×#125—21no—
205C2×#125—21no—
206C2×#125—21no—
207C2×#125C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×C22⋊Q8—21no—
215C2×C4×Q8—21no—
216C2×C4×D4C2311yescharacteristic
217C2×C4×D4C2311yescharacteristic
218C2×C4×D4C2311yescharacteristic
219C2×#117—21no—
220#499—24no—
221#499—24no—
222#478—24no—
223#478Q818yescomplemented
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#97C2311yescharacteristic
261C2×#97C2311yescharacteristic
262C2×#97C2311yescharacteristic
263C2×C4×C8C2311yescharacteristic
264C2×C4×C8C2311yescharacteristic
265C2×C4×C8C2311yescharacteristic
266C2×C4×C8C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268#400—21no—
269#400—21no—
270#400—21no—
271#400—21no—
272#400D411yescharacteristic
273#400D411yescharacteristic
274#400D411yescharacteristic
275#400D411yescharacteristic
276#399—21no—
277#399—21no—
278#399—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#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398D411yescharacteristic
299#398D411yescharacteristic
300#398D411yescharacteristic
301#398D411yescharacteristic
302#396—21no—
303#396—21no—
304#396—21no—
305#396—21no—
306#395—21no—
307#393—21no—
308#391—21no—
309#391—21no—
310#390C2311yescharacteristic
311#390C2311yescharacteristic
312#390C2311yescharacteristic
313#390C2311yescharacteristic
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#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
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#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#388—21no—
354#388—21no—
355#388—21no—
356#388—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#385—21no—
382#385—21no—
383#385—21no—
384#385—21no—
385#384—21no—
386#384—21no—
387#384—21no—
388#384—21no—
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#382C2311yescharacteristic
395#381—21no—
396#380—21no—
397#380—21no—
398#380—21no—
399#380—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⋊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
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432#376C2311yescharacteristic
433C2×#95—21no—
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×D4C2411yescharacteristic
484C23×C4—21no—
485C23×C4—21no—
486C23×C4—21no—
487C22×C8C2411yescharacteristic
488C22×C8C2411yescharacteristic
489C22×C8C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C4⋊Q8—22no—
496C4⋊Q8—41no—
497#125—22no—
498#125—22no—
499#125—22no—
500#125—22no—
501#125—22no—
502#125—22no—
503#125—22no—
504#125—41no—
505#125—41no—
506#125—41no—
507#125—41no—
508#125—41no—
509#125—41no—
510#125—82no—
511#125—82no—
512#125—82no—
513#125C2×Q814yes—
514C22⋊Q8—82no—
515C4×Q8—82no—
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—22no—
519C4×D4—41no—
520C4×D4—41no—
521C4×D4C2×Q814yes—
522#117—82no—
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⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42C2411yescharacteristic
622C2×C42C2411yescharacteristic
623C2×C42C2411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628#107—22no—
629#107—22no—
630#107—22no—
631#107—22no—
632#107—22no—
633#107—41no—
634#107—41no—
635#107C2×Q814yes—
636#106—22no—
637#106—22no—
638#106—22no—
639#106—22no—
640#106—41no—
641#106—41no—
642#106—41no—
643#106—41no—
644#106—41no—
645#106—41no—
646#106C2×Q814yes—
647#106#4114yes—
648C4⋊C8—22no—
649C4⋊C8—22no—
650C4⋊C8—41no—
651C4⋊C8—41no—
652C4⋊C8—41no—
653C4⋊C8—41no—
654C4⋊C8—41no—
655C4⋊C8C2×Q814yes—
656#102—22no—
657#102—22no—
658#102—41no—
659#102—41no—
660#102—41no—
661#102—41no—
662#102C2×Q814yes—
663#102C2×Q814yes—
664#97—22no—
665#97—41no—
666#97—41no—
667C4×C8—22no—
668C4×C8—22no—
669C4×C8—22no—
670C4×C8—41no—
671C4×C8—41no—
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#95C2×D411yescharacteristic
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
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725C24—21no—
726C2×Q8—42no—
727C2×Q8—42no—
728C2×Q8—81no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4C22×Q812yes—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—24no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—81no—
754C22×C4—81no—
755C22×C4—81no—
756C22×C4—81no—
757C22×C4—81no—
758C22×C4—81no—
759C22×C4C22×D411yescharacteristic
760C22×C4C22×D411yescharacteristic
761C22×C4C22×D411yescharacteristic
762C22×C4C22×D411yescharacteristic
763C22×C4C22×D411yescharacteristic
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C22×D411yescharacteristic
767C22×C4C22×D411yescharacteristic
768C22×C4C22×D411yescharacteristic
769C22×C4C22×D411yescharacteristic
770C22×C4C22×D411yescharacteristic
771C22×C4C22×D411yescharacteristic
772C22×C4C22×D411yescharacteristic
773C22×C4C2511yescharacteristic
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×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8C22×Q812yes—
796C2×C8C22×Q812yes—
797C2×C8C2×#4112yes—
798C4⋊C4—24no—
799C4⋊C4—24no—
800C4⋊C4—22no—
801C4⋊C4—22no—
802C4⋊C4—22no—
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—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—41no—
828C4⋊C4—41no—
829C4⋊C4—41no—
830C4⋊C4—41no—
831C4⋊C4—41no—
832C4⋊C4—41no—
833C4⋊C4—41no—
834C4⋊C4—41no—
835C4⋊C4—41no—
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—42no—
849C4⋊C4—42no—
850C4⋊C4—42no—
851C4⋊C4—42no—
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—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4C22×Q812yes—
880C4⋊C4C22×Q812yes—
881C4⋊C4C22×Q812yes—
882C4⋊C4C2×#4112yes—
883C4⋊C4C2×#4112yes—
884C4⋊C42−1+412yes—
885C22⋊C4—24no—
886C22⋊C4—42no—
887C22⋊C4—42no—
888C22⋊C4—42no—
889C22⋊C4—81no—
890C22⋊C4—81no—
891C22⋊C4—81no—
892C22⋊C4—81no—
893C22⋊C4—81no—
894C22⋊C4—81no—
895C22⋊C4—81no—
896C42—21no—
897C42—21no—
898C42—21no—
899C42—21no—
900C42—21no—
901C42—21no—
902C42—21no—
903C42—21no—
904C42—21no—
905C42—21no—
906C42—21no—
907C42—21no—
908C42—42no—
909C42—42no—
910C42—81no—
911C42—81no—
912C42—81no—
913C42—81no—
914C42—81no—
915C42—81no—
916C42—81no—
917C42—81no—
918C42—81no—
919C42—81no—
920C42—81no—
921C42—81no—
922C42—81no—
923C42C22×Q812yes—
924C422−1+412yes—
925C23—22no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23C23×D411yescharacteristic
933Q8—84no—
934D4—22no—
935D4—22no—
936D4—41no—
937D4—41no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
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×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—84no—
1023C2×C4—162no—
1024C2×C4—162no—
1025C2×C4D4×Q812yes—
1026C2×C4D4×Q812yes—
1027C2×C4#57712yes—
1028C2×C4C23×Q811yescharacteristic
1029C2×C4C22×#4111yescharacteristic
1030C2×C4C2×2−1+411yescharacteristic
1031C2×C4C2×2−1+411yescharacteristic
1032C2×C4#58511yescharacteristic
1033C2×C4#58511yescharacteristic
1034C8—22no—
1035C8—22no—
1036C8—22no—
1037C8—41no—
1038C8—41no—
1039C8—41no—
1040C8—41no—
1041C8—41no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22C2×D4×Q811yescharacteristic
1050C22D4×#4111yescharacteristic
1051C22#348911yescharacteristic
1052C22C2×#57711yescharacteristic
1053C22#358411yescharacteristic
1054C22#358411yescharacteristic
1055C22#358511yescharacteristic
1056C4—22no—
1057C4—22no—
1058C4—22no—
1059C4—41no—
1060C4—41no—
1061C4—42no—
1062C4—41no—
1063C4—41no—
1064C4—41no—
1065C4—42no—
1066C4—41no—
1067C4—41no—
1068C4—41no—
1069C4—42no—
1070C4—42no—
1071C4—42no—
1072C4—42no—
1073C4—41no—
1074C4—41no—
1075C4—41no—
1076C4—81no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4Q8×#4111yescharacteristic
1086C4#350211yescharacteristic
1087C4#350911yescharacteristic
1088C4#356511yescharacteristic
1089C2—82no—
1090C2#5915211yescharacteristic
1091C2#6137611yescharacteristic
1092C2#6138211yescharacteristic
1093C2#6147611yescharacteristic
1094C2#6153111yescharacteristic
1095C2#6219711yescharacteristic
1096C2#6221211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
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
1. #45223C2semidirect
7. #29324C2semidirect
8. #29185C2semidirect
11. #28811C2semidirect
12. #28804C2semidirect
15. #26886C2semidirect
16. #26865C2semidirect
17. #26865C2semidirect
18. #26858C2semidirect
19. #26457C2semidirect
20. #26457C2semidirect
21. #26449C2semidirect
22. #26447C2semidirect
25. #23260C2semidirect
26. #23164C2semidirect
27. #23160C2semidirect
223. #478Q8semidirect

Maximal subgroups

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

subgroupindex
#452232
#359632
#318942
#318782
#309512
#293242
#291852
#289512
#289492
#288112
#288042
#270262
#270062
#268862
#268652
#268582
#264572
#264492
#264472
#260902
#260372
#232602
#231642
#231602
#230762
#230652
#216202
#216192