Finite Group Databasebeta

← #7300768

Subgroups — #7300768

Order 512.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1181 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40021C211yesmaximal, characteristic, complemented
2#39192C211yesmaximal, characteristic, complemented
3#32825C211yesmaximal, characteristic, complemented
4#32659C211yesmaximal, characteristic, complemented
5#32623C211yesmaximal, characteristic
6#32614C211yesmaximal, characteristic, complemented
7#32561C211yesmaximal, characteristic, complemented
8#32527C211yesmaximal, characteristic, complemented
9#32474C211yesmaximal, characteristic, complemented
10#32452C211yesmaximal, characteristic, complemented
11#32361C211yesmaximal, characteristic, complemented
12#32188C211yesmaximal, characteristic
13#32097C211yesmaximal, characteristic, complemented
14#31966C211yesmaximal, characteristic, complemented
15#31899C211yesmaximal, characteristic, complemented
16#29574C211yesmaximal, characteristic, complemented
17#29556C211yesmaximal, characteristic, complemented
18#29536C211yesmaximal, characteristic, complemented
19#29018C211yesmaximal, characteristic, complemented
20#28885C211yesmaximal, characteristic
21#28059C211yesmaximal, characteristic, complemented
22#28029C211yesmaximal, characteristic, complemented
23#27150C211yesmaximal, characteristic, complemented
24#27090C211yesmaximal, characteristic, complemented
25#26887C211yesmaximal, characteristic, complemented
26#26779C211yesmaximal, characteristic, complemented
27#26332C211yesmaximal, characteristic, complemented
28#26328C211yesmaximal, characteristic, complemented
29#25074C211yesmaximal, characteristic, complemented
30#25002C211yesmaximal, characteristic, complemented
31#22311C211yesmaximal, characteristic, complemented
32#2861C2211yescharacteristic
33#2859C2211yescharacteristic
34#2801—21no—
35#2772—21no—
36#2772—21no—
37#2757—21no—
38#2731—21no—
39#2725—21no—
40#2725—21no—
41#2718—21no—
42#2653—21no—
43#2625—21no—
44#2592C2211yescharacteristic
45#2582C2211yescharacteristic
46#2580C2211yescharacteristic
47#2566C2211yescharacteristic
48#2548C2211yescharacteristic
49#2544C2211yescharacteristic
50#2538C2211yescharacteristic
51#2538C2211yescharacteristic
52#2514C2211yescharacteristic
53#2513C2211yescharacteristic
54#2513C2211yescharacteristic
55#2512C2211yescharacteristic
56#2512C2211yescharacteristic
57#2512C2211yescharacteristic
58#2509C2211yescharacteristic
59#2509C2211yescharacteristic
60#2507C2211yescharacteristic
61#2507C2211yescharacteristic
62#2496—21no—
63#2479—21no—
64#2470—21no—
65#2448C2211yescharacteristic
66#2445C2211yescharacteristic
67#2429—21no—
68#2370C2211yescharacteristic
69#2367C2211yescharacteristic
70#2355C2211yescharacteristic
71Q8×C4⋊C4C2211yescharacteristic
72#2337—21no—
73#2323—21no—
74C4×C4⋊Q8C2211yescharacteristic
75#2293C2211yescharacteristic
76#2293C2211yescharacteristic
77#2100C2211yescharacteristic
78#2099C2211yescharacteristic
79#2099C2211yescharacteristic
80#2097C2211yescharacteristic
81#2096C2211yescharacteristic
82#2096C2211yescharacteristic
83#2094C2211yescharacteristic
84#2093C2211yescharacteristic
85#2092C2211yescharacteristic
86#2092C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2085C2211yescharacteristic
90#2085C2211yescharacteristic
91#2084C2211yescharacteristic
92#2073C2211yescharacteristic
93#2072C2211yescharacteristic
94#2071C2211yescharacteristic
95#2071C2211yescharacteristic
96#2071C2211yescharacteristic
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic
99#2068C2211yescharacteristic
100#2068C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2054C2211yescharacteristic
115#2054C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic
120#2041C2211yescharacteristic
121#2025C2211yescharacteristic
122#2012C2211yescharacteristic
123#2012C2211yescharacteristic
124#2011C2211yescharacteristic
125#1985C2211yescharacteristic
126#1985C2211yescharacteristic
127#1985C2211yescharacteristic
128#1985C2211yescharacteristic
129#1983C2211yescharacteristic
130#1982C2211yescharacteristic
131#1972C2211yescharacteristic
132#1972C2211yescharacteristic
133#1972C2211yescharacteristic
134#1970C2211yescharacteristic
135#1968C2211yescharacteristic
136#1961C2211yescharacteristic
137#1959C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1948C2211yescharacteristic
141#1948C2211yescharacteristic
142#1943C2211yescharacteristic
143#1941C2211yescharacteristic
144#1941C2211yescharacteristic
145#1939C2211yescharacteristic
146#1939C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1935C2211yescharacteristic
150#1935C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1933C2211yescharacteristic
155#1928C2211yescharacteristic
156#1927C2211yescharacteristic
157#1927C2211yescharacteristic
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic
163#1926C2211yescharacteristic
164#1925C2211yescharacteristic
165#1925C2211yescharacteristic
166#1925C2211yescharacteristic
167#1921C2211yescharacteristic
168#1920C2211yescharacteristic
169#1920C2211yescharacteristic
170#1920C2211yescharacteristic
171#1920C2211yescharacteristic
172#1919C2211yescharacteristic
173#1919C2211yescharacteristic
174#1919C2211yescharacteristic
175#1917C2211yescharacteristic
176#1917C2211yescharacteristic
177#1917C2211yescharacteristic
178#1917C2211yescharacteristic
179#1880C2211yescharacteristic
180#1879C2211yescharacteristic
181#1879C2211yescharacteristic
182#1879C2211yescharacteristic
183#1879C2211yescharacteristic
184#1877C2211yescharacteristic
185#1865C2211yescharacteristic
186#1864C2211yescharacteristic
187#1864C2211yescharacteristic
188#1864C2211yescharacteristic
189#1864C2211yescharacteristic
190#1862C2211yescharacteristic
191#1847C2211yescharacteristic
192#1836C2211yescharacteristic
193#1831C2211yescharacteristic
194#1805C2211yescharacteristic
195#1802C2211yescharacteristic
196#1776C2211yescharacteristic
197#1776C2211yescharacteristic
198#1770C2211yescharacteristic
199#1770C2211yescharacteristic
200#1763C2211yescharacteristic
201#1762C2211yescharacteristic
202#1744C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C2×C4⋊Q8D411yescharacteristic
207C2×#127C2311yescharacteristic
208C2×#126—21no—
209C2×#126—21no—
210C2×#126—21no—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×#124—21no—
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#123—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C4×Q8—21no—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×#117—21no—
227C2×#117—21no—
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×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279#401—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#399—21no—
286#399—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#396—21no—
303#396—21no—
304#396—21no—
305#396—21no—
306#396—21no—
307#396—21no—
308#396—21no—
309#396—21no—
310#396—21no—
311#394—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#394—21no—
316#394—21no—
317#393—21no—
318#393—21no—
319#391—21no—
320#391—21no—
321#391D411yescharacteristic
322#391D411yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#390—21no—
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389D411yescharacteristic
354#389D411yescharacteristic
355#389D411yescharacteristic
356#389D411yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#384D411yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#383—21no—
416#382—21no—
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#380—21no—
421#380—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C43C2311yescharacteristic
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#336C2311yescharacteristic
463#336C2311yescharacteristic
464#336C2311yescharacteristic
465#336C2311yescharacteristic
466#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478C22×Q8C2×D411yescharacteristic
479C22×Q8C2×D411yescharacteristic
480C22×Q8C2411yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4C2411yescharacteristic
484C22×D4C2411yescharacteristic
485C22×D4C2411yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C2×SD16—41no—
490C2×SD16—41no—
491C2×SD16—41no—
492C2×D8—22no—
493C2×D8—41no—
494C2×D8—41no—
495C2×D8—41no—
496C2×D8—41no—
497C2×D8—41no—
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C4⋊Q8—42no—
507#127—41no—
508#127—41no—
509#126—82no—
510#126—82no—
511#126—82no—
512#125—41no—
513#125—41no—
514#125—82no—
515#124—41no—
516#124—41no—
517#124—41no—
518#124—41no—
519#124—44no—
520#123—82no—
521C22⋊Q8—44no—
522C22⋊Q8—82no—
523C4×Q8—41no—
524C4×Q8—41no—
525C4×Q8—41no—
526C4×Q8—41no—
527C4×Q8—41no—
528C4×Q8—41no—
529C4×Q8—82no—
530C4×D4—41no—
531C4×D4—41no—
532C4×D4—41no—
533C4×D4—41no—
534C4×D4—41no—
535C4×D4—41no—
536#117—82no—
537#117—82no—
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⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
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×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42C2×D411yescharacteristic
636C2×C42C2×D411yescharacteristic
637C2×C42C2×D411yescharacteristic
638C2×C42C2×D411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646#107—41no—
647#107—41no—
648#107—41no—
649#107—41no—
650#106—22no—
651#106—41no—
652#106—41no—
653#106—41no—
654#106—41no—
655#106—41no—
656#106—41no—
657#106—41no—
658#106—41no—
659C4⋊C8—41no—
660C4⋊C8—41no—
661C4⋊C8—41no—
662C4⋊C8—41no—
663C4⋊C8—41no—
664C4⋊C8—41no—
665#103—22no—
666#103—41no—
667#103—41no—
668#103—41no—
669#103—41no—
670#103—41no—
671#103—41no—
672#102—22no—
673#102—41no—
674#102—41no—
675#102—41no—
676#102—41no—
677#102—41no—
678#102—41no—
679#102—41no—
680#102—41no—
681#102—41no—
682#102—41no—
683#102—41no—
684#102—41no—
685#102—41no—
686#102—41no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102—41no—
691#97—41no—
692#97—41no—
693#97—41no—
694#97—41no—
695C4×C8—22no—
696C4×C8—41no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741C24—21no—
742C24—21no—
743C24—21no—
744C2×Q8—22no—
745C2×Q8—22no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—41no—
753C2×Q8—41no—
754C2×Q8—41no—
755C2×Q8—41no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—42no—
775C2×D4—81no—
776C2×D4—81no—
777C2×D4—81no—
778C2×D4—81no—
779C2×D4—81no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—81no—
798C22×C4—81no—
799C22×C4—81no—
800C22×C4—81no—
801C22×C4—81no—
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C2511yescharacteristic
817SD16—82no—
818D8—82no—
819D8—82no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C82−1+412yes—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—41no—
871C4⋊C4—41no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4—41no—
875C4⋊C4—41no—
876C4⋊C4—41no—
877C4⋊C4—41no—
878C4⋊C4—41no—
879C4⋊C4—41no—
880C4⋊C4—41no—
881C4⋊C4—41no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C22⋊C4—42no—
910C22⋊C4—42no—
911C22⋊C4—42no—
912C22⋊C4—42no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—42no—
919C22⋊C4—42no—
920C22⋊C4—42no—
921C22⋊C4—42no—
922C22⋊C4—42no—
923C22⋊C4—81no—
924C22⋊C4—81no—
925C22⋊C4—81no—
926C22⋊C4—81no—
927C22⋊C4—81no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C42—22no—
945C42—22no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—41no—
961C42—41no—
962C42—42no—
963C42—42no—
964C42—81no—
965C42—81no—
966C42—81no—
967C42—81no—
968C42—81no—
969C42—81no—
970C42—81no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23C23×D411yescharacteristic
993Q8—44no—
994Q8—41no—
995Q8—41no—
996Q8—41no—
997Q8—41no—
998Q8—82no—
999D4—41no—
1000D4—41no—
1001D4—41no—
1002D4—41no—
1003D4—41no—
1004D4—41no—
1005D4—41no—
1006D4—41no—
1007D4—41no—
1008D4—41no—
1009D4—41no—
1010D4—41no—
1011D4—162no—
1012D4—162no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—84no—
1093C2×C4—84no—
1094C2×C4—162no—
1095C2×C4#57512yes—
1096C2×C4#57712yes—
1097C2×C4C2×2−1+411yescharacteristic
1098C2×C4#58511yescharacteristic
1099C2×C4#58511yescharacteristic
1100C2×C4#58511yescharacteristic
1101C2×C4#58511yescharacteristic
1102C2×C4#58511yescharacteristic
1103C8—22no—
1104C8—41no—
1105C8—41no—
1106C8—41no—
1107C8—41no—
1108C8—41no—
1109C8—41no—
1110C8—41no—
1111C22—81no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22#348511yescharacteristic
1133C22#348711yescharacteristic
1134C22#349711yescharacteristic
1135C22C2×#57511yescharacteristic
1136C22C2×#57711yescharacteristic
1137C22#358511yescharacteristic
1138C22#358511yescharacteristic
1139C4—22no—
1140C4—22no—
1141C4—41no—
1142C4—41no—
1143C4—41no—
1144C4—41no—
1145C4—41no—
1146C4—41no—
1147C4—41no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—41no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4#356411yescharacteristic
1167C4#356511yescharacteristic
1168C4#356611yescharacteristic
1169C4#356611yescharacteristic
1170C2—161no—
1171C2—161no—
1172C2—161no—
1173C2#4782311yescharacteristic
1174C2#6171811yescharacteristic
1175C2#6181511yescharacteristic
1176C2#6189611yescharacteristic
1177C2#6191311yescharacteristic
1178C2#6237011yescharacteristic
1179C2#6238711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2011C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40021C2semidirect
2. #39192C2semidirect
3. #32825C2semidirect
4. #32659C2semidirect
6. #32614C2semidirect
7. #32561C2semidirect
8. #32527C2semidirect
9. #32474C2semidirect
10. #32452C2semidirect
11. #32361C2semidirect
13. #32097C2semidirect
14. #31966C2semidirect
15. #31899C2semidirect
16. #29574C2semidirect
17. #29556C2semidirect
18. #29536C2semidirect
19. #29018C2semidirect
21. #28059C2semidirect
22. #28029C2semidirect
23. #27150C2semidirect
24. #27090C2semidirect
25. #26887C2semidirect
26. #26779C2semidirect
27. #26332C2semidirect
28. #26328C2semidirect
29. #25074C2semidirect
30. #25002C2semidirect
31. #22311C2semidirect

Maximal subgroups

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

subgroupindex
#400212
#391922
#328252
#326592
#326232
#326142
#325612
#325272
#324742
#324522
#323612
#321882
#320972
#319662
#318992
#295742
#295562
#295362
#290182
#288852
#280592
#280292
#271502
#270902
#268872
#267792
#263322
#263282
#250742
#250022
#223112