Finite Group Databasebeta

← #6679839

Subgroups — #6679839

Order 512.

1449 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42665C211yesmaximal, characteristic, complemented
2#35816C211yesmaximal, characteristic
3#32916C211yesmaximal, characteristic
4#31826C211yesmaximal, characteristic, complemented
5#31822C211yesmaximal, characteristic, complemented
6#31762C211yesmaximal, characteristic, complemented
7#31758C211yesmaximal, characteristic, complemented
8#31543C211yesmaximal, characteristic, complemented
9#31539C211yesmaximal, characteristic, complemented
10#31380C211yesmaximal, characteristic, complemented
11#31368C211yesmaximal, characteristic, complemented
12#29946C211yesmaximal, characteristic, complemented
13#29856C211yesmaximal, characteristic, complemented
14#27819C211yesmaximal, characteristic, complemented
15#27580C211yesmaximal, characteristic, complemented
16#27569C211yesmaximal, characteristic, complemented
17#27252C211yesmaximal, characteristic
18#27247C211yesmaximal, characteristic
19#26055C211yesmaximal, characteristic, complemented
20#25943C211yesmaximal, characteristic, complemented
21#25331C211yesmaximal, characteristic, complemented
22#25301C211yesmaximal, characteristic, complemented
23#25073C211yesmaximal, characteristic, complemented
24#24924C211yesmaximal, characteristic
25#24920C211yesmaximal, characteristic
26#24832C211yesmaximal, characteristic, complemented
27#24826C211yesmaximal, characteristic, complemented
28#23004C211yesmaximal, characteristic, complemented
29#22527C211yesmaximal, characteristic, complemented
30#22105C211yesmaximal, characteristic, complemented
31#20746C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#491C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×#462C2211yescharacteristic
38C2×#461C2211yescharacteristic
39C2×#452C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#446C2211yescharacteristic
42C2×#441C2211yescharacteristic
43C2×#441C2211yescharacteristic
44C2×#433C2211yescharacteristic
45#2839—21no—
46#2799—21no—
47#2798—21no—
48#2767—21no—
49#2754—21no—
50#2654—21no—
51#2650—21no—
52#2629—21no—
53#2629C2211yescharacteristic
54#2621C2211yescharacteristic
55#2568C2211yescharacteristic
56#2568C2211yescharacteristic
57#2566—21no—
58#2566C2211yescharacteristic
59#2565C2211yescharacteristic
60#2550C2211yescharacteristic
61#2538—21no—
62#2538C2211yescharacteristic
63#2520—21no—
64#2511C2211yescharacteristic
65#2511C2211yescharacteristic
66#2492C2211yescharacteristic
67#2489C2211yescharacteristic
68#2454—21no—
69#2454C2211yescharacteristic
70#2452—21no—
71#2452C2211yescharacteristic
72#2442—21no—
73#2442C2211yescharacteristic
74#2440—21no—
75#2440C2211yescharacteristic
76#2423C2211yescharacteristic
77#2421C2211yescharacteristic
78#2396—21no—
79#2396C2211yescharacteristic
80#2365C2211yescharacteristic
81#2355C2211yescharacteristic
82#2351C2211yescharacteristic
83Q8×C4⋊C4C2211yescharacteristic
84Q8×C4⋊C4C2211yescharacteristic
85#2341C2211yescharacteristic
86#2341C2211yescharacteristic
87#2314C2211yescharacteristic
88#2101C2211yescharacteristic
89#2100C2211yescharacteristic
90#2099C2211yescharacteristic
91#2099C2211yescharacteristic
92#2094C2211yescharacteristic
93#2092C2211yescharacteristic
94#2088C2211yescharacteristic
95#2086C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2084C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2076C2211yescharacteristic
103#2075C2211yescharacteristic
104#2074C2211yescharacteristic
105#2072C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2068C2211yescharacteristic
109#2068C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2059C2211yescharacteristic
113#2057C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2026C2211yescharacteristic
123#2026C2211yescharacteristic
124#2025C2211yescharacteristic
125#2024C2211yescharacteristic
126#2024C2211yescharacteristic
127#2023C2211yescharacteristic
128#1993C2211yescharacteristic
129#1993C2211yescharacteristic
130#1992C2211yescharacteristic
131#1992C2211yescharacteristic
132#1991C2211yescharacteristic
133#1989C2211yescharacteristic
134#1989C2211yescharacteristic
135#1989C2211yescharacteristic
136#1987C2211yescharacteristic
137#1985C2211yescharacteristic
138#1973C2211yescharacteristic
139#1973C2211yescharacteristic
140#1956C2211yescharacteristic
141#1948C2211yescharacteristic
142#1947C2211yescharacteristic
143#1940C2211yescharacteristic
144#1940C2211yescharacteristic
145#1940C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1935C2211yescharacteristic
149#1935C2211yescharacteristic
150#1935C2211yescharacteristic
151#1935C2211yescharacteristic
152#1926C2211yescharacteristic
153#1925C2211yescharacteristic
154#1924C2211yescharacteristic
155#1924C2211yescharacteristic
156#1924C2211yescharacteristic
157#1924C2211yescharacteristic
158#1920C2211yescharacteristic
159#1918C2211yescharacteristic
160#1917C2211yescharacteristic
161#1917C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1878C2211yescharacteristic
165#1878C2211yescharacteristic
166#1878C2211yescharacteristic
167#1878C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic
176#1865C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1863C2211yescharacteristic
180#1847C2211yescharacteristic
181#1824C2211yescharacteristic
182#1823C2211yescharacteristic
183#1805C2211yescharacteristic
184#1805C2211yescharacteristic
185#1805C2211yescharacteristic
186#1805C2211yescharacteristic
187#1804C2211yescharacteristic
188#1804C2211yescharacteristic
189#1803C2211yescharacteristic
190#1803C2211yescharacteristic
191#1803C2211yescharacteristic
192#1802C2211yescharacteristic
193#1798C2211yescharacteristic
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1770C2211yescharacteristic
197#1763C2211yescharacteristic
198#1763C2211yescharacteristic
199#1763C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208#557—24no—
209#557—42no—
210C2×C4⋊Q8—21no—
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⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224#520—24no—
225#520—42no—
226C2×C4×Q8—21no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C2×#117C2311yescharacteristic
242C22×C4⋊C4—21no—
243C22×C4⋊C4C2311yescharacteristic
244#491—42no—
245#479—42no—
246#477—42no—
247#462—24no—
248#461—42no—
249#452—42no—
250#452—42no—
251#446—42no—
252#441—42no—
253#441—42no—
254#433—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400D411yescharacteristic
318#399—21no—
319#399—21no—
320#399D411yescharacteristic
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398D411yescharacteristic
332#398D411yescharacteristic
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396D411yescharacteristic
346#396D411yescharacteristic
347#395—21no—
348#395—21no—
349#395D411yescharacteristic
350#393—21no—
351#393—21no—
352#393D411yescharacteristic
353#391—21no—
354#391—21no—
355#391—21no—
356#391—21no—
357#391—21no—
358#391—21no—
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#390—21no—
368#390—21no—
369#390—21no—
370#390—21no—
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389—21no—
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—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#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#384—21no—
418#384—21no—
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#382—21no—
424#382—21no—
425#382—21no—
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#380—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8C2×D411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×D4—21no—
506C22×D4C2411yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4C2411yescharacteristic
512C2×Q16—22no—
513C2×Q16—22no—
514C2×Q16—22no—
515C2×Q16—22no—
516C2×Q16—22no—
517C2×Q16—22no—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C4⋊Q8—22no—
533C4⋊Q8—22no—
534C4⋊Q8—22no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—44no—
539#125—22no—
540#125—22no—
541#125—22no—
542#125—41no—
543#125—41no—
544#125—41no—
545#125—44no—
546#125—44no—
547C22⋊Q8—41no—
548C22⋊Q8—41no—
549C22⋊Q8—41no—
550C22⋊Q8—41no—
551C22⋊Q8—82no—
552C22⋊Q8—82no—
553C22⋊Q8—82no—
554C4×Q8—22no—
555C4×Q8—22no—
556C4×Q8—22no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—44no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×Q8#4114yes—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—44no—
577C4×D4—41no—
578C4×D4—44no—
579#117—22no—
580#117—22no—
581#117—44no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—44no—
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⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685#107—41no—
686#107—41no—
687#107—41no—
688#107—41no—
689#106—41no—
690#106—41no—
691#106—41no—
692#106—41no—
693C4⋊C8—22no—
694C4⋊C8—22no—
695C4⋊C8—41no—
696C4⋊C8—41no—
697C4⋊C8—41no—
698C4⋊C8—41no—
699C4⋊C8—41no—
700C4⋊C8—41no—
701#103—22no—
702#103—22no—
703#103—22no—
704#103—22no—
705#103—22no—
706#103—22no—
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#102—22no—
720#102—22no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725C22⋊C8—41no—
726C22⋊C8—41no—
727C22⋊C8—41no—
728C22⋊C8—41no—
729#97—22no—
730#97—41no—
731#97—41no—
732#97—41no—
733#97—41no—
734C4×C8—22no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#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#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785C24—21no—
786C24C22×D411yescharacteristic
787#41—44no—
788#41—44no—
789#41—44no—
790#41—44no—
791C2×Q8—22no—
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—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—41no—
808C2×Q8—41no—
809C2×Q8—42no—
810C2×Q8—42no—
811C2×Q8—42no—
812C2×Q8—81no—
813C2×Q8—81no—
814C2×Q8—81no—
815C2×Q8C2×#4112yes—
816C2×Q8H(5,𝔽2)12yes—
817C2×Q82−1+412yes—
818C2×D4—24no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D42−1+412yes—
827C22×C4—21no—
828C22×C4—24no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
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—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
874Q16—44no—
875Q16—44no—
876SD16—82no—
877SD16—82no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
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—
902C4⋊C4—24no—
903C4⋊C4—22no—
904C4⋊C4—22no—
905C4⋊C4—22no—
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—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
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—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
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⋊C4C2×#4112yes—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—41no—
977C22⋊C4—41no—
978C22⋊C4—41no—
979C22⋊C4—41no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C42—24no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—42no—
1008C42—42no—
1009C42—42no—
1010C42—42no—
1011C42—42no—
1012C42—81no—
1013C42—81no—
1014C42—81no—
1015C42—81no—
1016C42—81no—
1017C42—81no—
1018C42C2×#4112yes—
1019C42H(5,𝔽2)12yes—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—22no—
1027C23—21no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23C23×D411yescharacteristic
1035Q8—22no—
1036Q8—22no—
1037Q8—22no—
1038Q8—41no—
1039Q8—41no—
1040Q8—41no—
1041Q8—41no—
1042Q8—41no—
1043Q8—41no—
1044Q8—41no—
1045Q8—41no—
1046Q8—82no—
1047Q8—84no—
1048Q8—162no—
1049Q8#54214yes—
1050D4—22no—
1051D4—22no—
1052D4—48no—
1053D4—41no—
1054D4—41no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—21no—
1063C2×C4—21no—
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—21no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—48no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—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—162no—
1143C2×C4—162no—
1144C2×C4—162no—
1145C2×C4#54612yes—
1146C2×C4#54612yes—
1147C2×C4C22×#4111yescharacteristic
1148C2×C4C2×H(5,𝔽2)11yescharacteristic
1149C2×C4C2×H(5,𝔽2)11yescharacteristic
1150C2×C4C2×2−1+411yescharacteristic
1151C2×C4C2×2−1+411yescharacteristic
1152C2×C4#58511yescharacteristic
1153C8—41no—
1154C8—41no—
1155C8—41no—
1156C8—41no—
1157C8—41no—
1158C8—41no—
1159C8—41no—
1160C8—41no—
1161C22—42no—
1162C22—41no—
1163C22—41no—
1164C22—41no—
1165C22—41no—
1166C22—41no—
1167C22—42no—
1168C22—41no—
1169C22—42no—
1170C22—41no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22C2×#54611yescharacteristic
1176C22#348611yescharacteristic
1177C22#348811yescharacteristic
1178C22#358511yescharacteristic
1179C22#358611yescharacteristic
1180C22#358611yescharacteristic
1181C22#358611yescharacteristic
1182C4—24no—
1183C4—22no—
1184C4—22no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—42no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4C2×#54211yescharacteristic
1211C4#349511yescharacteristic
1212C4#353611yescharacteristic
1213C4#354111yescharacteristic
1214C2—81no—
1215C2—82no—
1216C2#3766511yescharacteristic
1217C2#6118011yescharacteristic
1218C2#6122111yescharacteristic
1219C2#6187711yescharacteristic
1220C2#6187911yescharacteristic
1221C2#6208611yescharacteristic
1222C2#6209411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42665C2semidirect
4. #31826C2semidirect
5. #31822C2semidirect
6. #31762C2semidirect
7. #31758C2semidirect
8. #31543C2semidirect
9. #31539C2semidirect
10. #31380C2semidirect
11. #31368C2semidirect
12. #29946C2semidirect
13. #29856C2semidirect
14. #27819C2semidirect
15. #27580C2semidirect
16. #27569C2semidirect
19. #26055C2semidirect
20. #25943C2semidirect
21. #25331C2semidirect
22. #25301C2semidirect
23. #25073C2semidirect
26. #24832C2semidirect
27. #24826C2semidirect
28. #23004C2semidirect
29. #22527C2semidirect
30. #22105C2semidirect

Maximal subgroups

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

subgroupindex
#426652
#358162
#329162
#318262
#318222
#317622
#317582
#315432
#315392
#313802
#313682
#299462
#298562
#278192
#275802
#275692
#272522
#272472
#260552
#259432
#253312
#253012
#250732
#249242
#249202
#248322
#248262
#230042
#225272
#221052
#207462