Finite Group Databasebeta

← #6851015

Subgroups — #6851015

Order 512.

1473 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39689C211yesmaximal, characteristic, complemented
2#35257C211yesmaximal, characteristic
3#32958C211yesmaximal, characteristic
4#31888C211yesmaximal, characteristic, complemented
5#31874C211yesmaximal, characteristic, complemented
6#31548C211yesmaximal, characteristic, complemented
7#31526C211yesmaximal, characteristic, complemented
8#31248C211yesmaximal, characteristic, complemented
9#31239C211yesmaximal, characteristic, complemented
10#30970C211yesmaximal, characteristic, complemented
11#30957C211yesmaximal, characteristic, complemented
12#29964C211yesmaximal, characteristic
13#29961C211yesmaximal, characteristic
14#29309C211yesmaximal, characteristic, complemented
15#29302C211yesmaximal, characteristic, complemented
16#29251C211yesmaximal, characteristic, complemented
17#29241C211yesmaximal, characteristic, complemented
18#28969C211yesmaximal, characteristic, complemented
19#28952C211yesmaximal, characteristic, complemented
20#27025C211yesmaximal, characteristic, complemented
21#27022C211yesmaximal, characteristic, complemented
22#26497C211yesmaximal, characteristic, complemented
23#26495C211yesmaximal, characteristic, complemented
24#26397C211yesmaximal, characteristic, complemented
25#26395C211yesmaximal, characteristic, complemented
26#25821C211yesmaximal, characteristic, complemented
27#24311C211yesmaximal, characteristic, complemented
28#22631C211yesmaximal, characteristic, complemented
29#22059C211yesmaximal, characteristic
30#22057C211yesmaximal, characteristic
31#21457C211yesmaximal, characteristic
32C2×#544C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#500C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#477C2211yescharacteristic
38C2×#477C2211yescharacteristic
39C2×#476C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#441C2211yescharacteristic
42C2×#440C2211yescharacteristic
43#2857—21no—
44#2857C2211yescharacteristic
45#2851—21no—
46#2802—21no—
47#2792—21no—
48#2729—21no—
49#2720—21no—
50#2629—21no—
51#2629C2211yescharacteristic
52#2628—21no—
53#2628C2211yescharacteristic
54#2588—21no—
55#2574—21no—
56#2565C2211yescharacteristic
57#2551C2211yescharacteristic
58#2550—21no—
59#2522—21no—
60#2508C2211yescharacteristic
61#2506C2211yescharacteristic
62#2454C2211yescharacteristic
63#2454C2211yescharacteristic
64#2453C2211yescharacteristic
65#2453C2211yescharacteristic
66#2452C2211yescharacteristic
67#2452C2211yescharacteristic
68#2451C2211yescharacteristic
69#2451C2211yescharacteristic
70#2451C2211yescharacteristic
71#2451C2211yescharacteristic
72#2450—21no—
73#2450—21no—
74#2449—21no—
75#2449—21no—
76#2370C2211yescharacteristic
77Q8×C4⋊C4C2211yescharacteristic
78#2323C2211yescharacteristic
79#2323C2211yescharacteristic
80#2317C2211yescharacteristic
81#2311C2211yescharacteristic
82#2311C2211yescharacteristic
83C4×C22⋊Q8C2211yescharacteristic
84#2296C2211yescharacteristic
85C2×#389C2211yescharacteristic
86#2097C2211yescharacteristic
87#2095C2211yescharacteristic
88#2093C2211yescharacteristic
89#2092C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2087C2211yescharacteristic
93#2087C2211yescharacteristic
94#2084C2211yescharacteristic
95#2084C2211yescharacteristic
96#2084C2211yescharacteristic
97#2083C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2068C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic
108#2066C2211yescharacteristic
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2057C2211yescharacteristic
116#2057C2211yescharacteristic
117#2057C2211yescharacteristic
118#2057C2211yescharacteristic
119#2057C2211yescharacteristic
120#2026C2211yescharacteristic
121#2026C2211yescharacteristic
122#2025C2211yescharacteristic
123#2024C2211yescharacteristic
124#2024C2211yescharacteristic
125#2023C2211yescharacteristic
126#1993C2211yescharacteristic
127#1991C2211yescharacteristic
128#1989C2211yescharacteristic
129#1988C2211yescharacteristic
130#1973C2211yescharacteristic
131#1971C2211yescharacteristic
132#1969C2211yescharacteristic
133#1968C2211yescharacteristic
134#1944C2211yescharacteristic
135#1944C2211yescharacteristic
136#1944C2211yescharacteristic
137#1944C2211yescharacteristic
138#1944C2211yescharacteristic
139#1943C2211yescharacteristic
140#1942C2211yescharacteristic
141#1941C2211yescharacteristic
142#1940C2211yescharacteristic
143#1939C2211yescharacteristic
144#1936C2211yescharacteristic
145#1935C2211yescharacteristic
146#1934C2211yescharacteristic
147#1933C2211yescharacteristic
148#1928C2211yescharacteristic
149#1927C2211yescharacteristic
150#1926C2211yescharacteristic
151#1925C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1920C2211yescharacteristic
156#1917C2211yescharacteristic
157#1917C2211yescharacteristic
158#1917C2211yescharacteristic
159#1916C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1878C2211yescharacteristic
163#1878C2211yescharacteristic
164#1878C2211yescharacteristic
165#1877C2211yescharacteristic
166#1873C2211yescharacteristic
167#1872C2211yescharacteristic
168#1872C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1864C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1853C2211yescharacteristic
183#1853C2211yescharacteristic
184#1852C2211yescharacteristic
185#1852C2211yescharacteristic
186#1852C2211yescharacteristic
187#1852C2211yescharacteristic
188#1803C2211yescharacteristic
189#1802C2211yescharacteristic
190#1798C2211yescharacteristic
191#1798C2211yescharacteristic
192#1797C2211yescharacteristic
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1771C2211yescharacteristic
197#1770C2211yescharacteristic
198#1763C2211yescharacteristic
199#1762C2211yescharacteristic
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic
202#1749C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206#544—42no—
207#544—42no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#125—21no—
215C2×#125—21no—
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C4×#41—42no—
226C4×#41—42no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×#117—21no—
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C22×C4⋊C4—21no—
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C42—21no—
244C22×C42C2311yescharacteristic
245#501—42no—
246#500—42no—
247#479—42no—
248#477—42no—
249#477—42no—
250#476—42no—
251#452Q818yescomplemented
252#441—42no—
253#440—42no—
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#399—21no—
314#399—21no—
315#399—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#396—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#395—21no—
335#395—21no—
336#395—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#393—21no—
342#393—21no—
343#393—21no—
344#391—21no—
345#391—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389D411yescharacteristic
372#389D411yescharacteristic
373#389D411yescharacteristic
374#389D411yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385D411yescharacteristic
423#385D411yescharacteristic
424#385D411yescharacteristic
425#385D411yescharacteristic
426#384—21no—
427#384—21no—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#382—21no—
431#382—21no—
432#382C2311yescharacteristic
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C22⋊C4—21no—
454C2×#95—21no—
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41C2×Q814yes—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×D4—21no—
504C22×D4C2411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2411yescharacteristic
513C2×Q16—41no—
514C2×Q16—41no—
515C2×Q16C2×Q814yes—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16C2×Q814yes—
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C4⋊Q8—22no—
528C4⋊Q8—22no—
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8—44no—
536C4⋊Q8—82no—
537#125—22no—
538#125—22no—
539#125—41no—
540#125—41no—
541#125—41no—
542#125—41no—
543#125—44no—
544#125—82no—
545C22⋊Q8—22no—
546C22⋊Q8—44no—
547C22⋊Q8—44no—
548C22⋊Q8—82no—
549C22⋊Q8—82no—
550C22⋊Q8—82no—
551C22⋊Q8C2×Q814yes—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—44no—
567C4×D4—44no—
568#117—22no—
569#117—22no—
570#117—41no—
571#117—41no—
572#117—41no—
573#117—41no—
574#117—44no—
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—41no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—82no—
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊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×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—41no—
673C2×C42—41no—
674C2×C42—44no—
675C2×C42C2×D411yescharacteristic
676C2×C42C2×D411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683#107—22no—
684#107—22no—
685#107—22no—
686#107—41no—
687#107—41no—
688#107—41no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#107—41no—
694#106—22no—
695#106—22no—
696#106—22no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707#103—22no—
708#103—22no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103C2×Q814yes—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102C2×Q814yes—
727C22⋊C8—22no—
728C22⋊C8—22no—
729C22⋊C8—22no—
730C22⋊C8C2×Q814yes—
731#97—41no—
732#97—41no—
733#97—41no—
734#97—41no—
735C4×C8—41no—
736C4×C8—41no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784C24—21no—
785C24C22×D411yescharacteristic
786#41—44no—
787#41—44no—
788#41—44no—
789#41—44no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—42no—
801C2×Q8—42no—
802C2×Q8—42no—
803C2×Q8—81no—
804C2×Q8—81no—
805C2×Q8—81no—
806C2×Q8—81no—
807C2×Q8—81no—
808C2×Q8—81no—
809C2×Q8—81no—
810C2×Q8—81no—
811C2×Q8—81no—
812C2×Q8C22×Q812yes—
813C2×Q8C22×Q812yes—
814C2×D4—24no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4C22×Q812yes—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—24no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—41no—
845C22×C4—41no—
846C22×C4—41no—
847C22×C4—41no—
848C22×C4—41no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×Q812yes—
877C22×C42−1+412yes—
878C22×C4C2511yescharacteristic
879Q16—44no—
880SD16—44no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8C22×Q812yes—
904C2×C8C22×Q812yes—
905C4⋊C4—24no—
906C4⋊C4—22no—
907C4⋊C4—22no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—41no—
934C4⋊C4—41no—
935C4⋊C4—41no—
936C4⋊C4—41no—
937C4⋊C4—41no—
938C4⋊C4—41no—
939C4⋊C4—41no—
940C4⋊C4—41no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4C22×Q812yes—
980C4⋊C4H(5,𝔽2)12yes—
981C4⋊C4H(5,𝔽2)12yes—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C42—24no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—41no—
1015C42—41no—
1016C42—42no—
1017C42—42no—
1018C42—42no—
1019C42—42no—
1020C42—81no—
1021C42—81no—
1022C42—81no—
1023C42—81no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—22no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23D4×Q812yes—
1038C23C23×D411yescharacteristic
1039Q8—22no—
1040Q8—22no—
1041Q8—22no—
1042Q8—22no—
1043Q8—41no—
1044Q8—41no—
1045Q8—41no—
1046Q8—41no—
1047Q8—162no—
1048Q8—162no—
1049Q8—162no—
1050Q8—162no—
1051D4—22no—
1052D4—22no—
1053D4—48no—
1054D4—41no—
1055D4—41no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—48no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—82no—
1144C2×C4—84no—
1145C2×C4—82no—
1146C2×C4—84no—
1147C2×C4—84no—
1148C2×C4—162no—
1149C2×C4D4×Q812yes—
1150C2×C4#57812yes—
1151C2×C4C23×Q811yescharacteristic
1152C2×C4C2×H(5,𝔽2)11yescharacteristic
1153C2×C4C2×H(5,𝔽2)11yescharacteristic
1154C2×C4C2×2−1+411yescharacteristic
1155C2×C4#58511yescharacteristic
1156C2×C4#58511yescharacteristic
1157C8—22no—
1158C8—22no—
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C8—41no—
1163C8—41no—
1164C8—41no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—41no—
1169C22—41no—
1170C22—41no—
1171C22—41no—
1172C22—42no—
1173C22—42no—
1174C22—42no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22#344911yescharacteristic
1180C22C2×D4×Q811yescharacteristic
1181C22#348411yescharacteristic
1182C22C2×#57811yescharacteristic
1183C22#358511yescharacteristic
1184C22#358511yescharacteristic
1185C22#358611yescharacteristic
1186C4—22no—
1187C4—22no—
1188C4—41no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—42no—
1193C4—42no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—42no—
1198C4—42no—
1199C4—41no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—42no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4#350111yescharacteristic
1215C4#350111yescharacteristic
1216C4#354111yescharacteristic
1217C4#354111yescharacteristic
1218C2—42no—
1219C2—82no—
1220C2#3958811yescharacteristic
1221C2#6097311yescharacteristic
1222C2#6099311yescharacteristic
1223C2#6138011yescharacteristic
1224C2#6138411yescharacteristic
1225C2#6162211yescharacteristic
1226C2#6165311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39689C2semidirect
4. #31888C2semidirect
5. #31874C2semidirect
6. #31548C2semidirect
7. #31526C2semidirect
8. #31248C2semidirect
9. #31239C2semidirect
10. #30970C2semidirect
11. #30957C2semidirect
14. #29309C2semidirect
15. #29302C2semidirect
16. #29251C2semidirect
17. #29241C2semidirect
18. #28969C2semidirect
19. #28952C2semidirect
20. #27025C2semidirect
21. #27022C2semidirect
22. #26497C2semidirect
23. #26495C2semidirect
24. #26397C2semidirect
25. #26395C2semidirect
26. #25821C2semidirect
27. #24311C2semidirect
28. #22631C2semidirect
251. #452Q8semidirect

Maximal subgroups

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

subgroupindex
#396892
#352572
#329582
#318882
#318742
#315482
#315262
#312482
#312392
#309702
#309572
#299642
#299612
#293092
#293022
#292512
#292412
#289692
#289522
#270252
#270222
#264972
#264952
#263972
#263952
#258212
#243112
#226312
#220592
#220572
#214572