Finite Group Databasebeta

← #7272496

Subgroups — #7272496

Order 512.

1205 conjugacy classes of subgroups.

The subgroup lattice has 1157 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42955C211yesmaximal, characteristic, complemented
2#42467C211yesmaximal, characteristic
3#32779C211yesmaximal, characteristic
4#32640C211yesmaximal, characteristic, complemented
5#32635C211yesmaximal, characteristic, complemented
6#32354C211yesmaximal, characteristic, complemented
7#32353C211yesmaximal, characteristic, complemented
8#32231C211yesmaximal, characteristic, complemented
9#32227C211yesmaximal, characteristic, complemented
10#32147C211yesmaximal, characteristic, complemented
11#32138C211yesmaximal, characteristic, complemented
12#31766C211yesmaximal, characteristic, complemented
13#31750C211yesmaximal, characteristic, complemented
14#31372C211yesmaximal, characteristic, complemented
15#31364C211yesmaximal, characteristic, complemented
16#29343C211yesmaximal, characteristic
17#28056C211yesmaximal, characteristic, complemented
18#28044C211yesmaximal, characteristic, complemented
19#27886C211yesmaximal, characteristic, complemented
20#27826C211yesmaximal, characteristic, complemented
21#27819C211yesmaximal, characteristic, complemented
22#27619C211yesmaximal, characteristic, complemented
23#27354C211yesmaximal, characteristic, complemented
24#27340C211yesmaximal, characteristic, complemented
25#27186C211yesmaximal, characteristic, complemented
26#27170C211yesmaximal, characteristic, complemented
27#26768C211yesmaximal, characteristic, complemented
28#26753C211yesmaximal, characteristic, complemented
29#26289C211yesmaximal, characteristic, complemented
30#26284C211yesmaximal, characteristic, complemented
31#22324C211yesmaximal, characteristic, complemented
32#2843—21no—
33#2830—21no—
34#2768—21no—
35#2768—21no—
36#2763—21no—
37#2751—21no—
38#2742—21no—
39#2715—21no—
40#2712—21no—
41#2705—21no—
42#2666—21no—
43#2666—21no—
44#2662—21no—
45#2630—21no—
46#2628C2211yescharacteristic
47#2619C2211yescharacteristic
48#2584C2211yescharacteristic
49#2584C2211yescharacteristic
50#2571—21no—
51#2566C2211yescharacteristic
52#2563C2211yescharacteristic
53#2550C2211yescharacteristic
54#2550C2211yescharacteristic
55#2550C2211yescharacteristic
56#2548C2211yescharacteristic
57#2512C2211yescharacteristic
58#2512C2211yescharacteristic
59#2508C2211yescharacteristic
60#2508C2211yescharacteristic
61#2508C2211yescharacteristic
62#2508C2211yescharacteristic
63#2491C2211yescharacteristic
64#2490C2211yescharacteristic
65#2468—21no—
66#2442C2211yescharacteristic
67#2442C2211yescharacteristic
68#2422C2211yescharacteristic
69#2420C2211yescharacteristic
70#2396C2211yescharacteristic
71#2366C2211yescharacteristic
72#2355C2211yescharacteristic
73#2347C2211yescharacteristic
74#2347C2211yescharacteristic
75#2317C2211yescharacteristic
76#2314C2211yescharacteristic
77#2101C2211yescharacteristic
78#2101C2211yescharacteristic
79#2101C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2099C2211yescharacteristic
85#2092C2211yescharacteristic
86#2092C2211yescharacteristic
87#2087C2211yescharacteristic
88#2086C2211yescharacteristic
89#2085C2211yescharacteristic
90#2085C2211yescharacteristic
91#2085C2211yescharacteristic
92#2084C2211yescharacteristic
93#2083C2211yescharacteristic
94#2083C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2076C2211yescharacteristic
98#2075C2211yescharacteristic
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2058C2211yescharacteristic
110#2057C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2041C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic
121#2025C2211yescharacteristic
122#2025C2211yescharacteristic
123#2023C2211yescharacteristic
124#2023C2211yescharacteristic
125#1993C2211yescharacteristic
126#1993C2211yescharacteristic
127#1992C2211yescharacteristic
128#1991C2211yescharacteristic
129#1991C2211yescharacteristic
130#1990C2211yescharacteristic
131#1989C2211yescharacteristic
132#1989C2211yescharacteristic
133#1989C2211yescharacteristic
134#1988C2211yescharacteristic
135#1985C2211yescharacteristic
136#1984C2211yescharacteristic
137#1949C2211yescharacteristic
138#1948C2211yescharacteristic
139#1943C2211yescharacteristic
140#1941C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic
156#1925C2211yescharacteristic
157#1924C2211yescharacteristic
158#1924C2211yescharacteristic
159#1923C2211yescharacteristic
160#1923C2211yescharacteristic
161#1921C2211yescharacteristic
162#1921C2211yescharacteristic
163#1921C2211yescharacteristic
164#1921C2211yescharacteristic
165#1920C2211yescharacteristic
166#1920C2211yescharacteristic
167#1920C2211yescharacteristic
168#1920C2211yescharacteristic
169#1919C2211yescharacteristic
170#1919C2211yescharacteristic
171#1919C2211yescharacteristic
172#1919C2211yescharacteristic
173#1918C2211yescharacteristic
174#1918C2211yescharacteristic
175#1917C2211yescharacteristic
176#1916C2211yescharacteristic
177#1916C2211yescharacteristic
178#1916C2211yescharacteristic
179#1875C2211yescharacteristic
180#1875C2211yescharacteristic
181#1874C2211yescharacteristic
182#1874C2211yescharacteristic
183#1864C2211yescharacteristic
184#1864C2211yescharacteristic
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic
187#1854C2211yescharacteristic
188#1854C2211yescharacteristic
189#1846C2211yescharacteristic
190#1836C2211yescharacteristic
191#1824C2211yescharacteristic
192#1823C2211yescharacteristic
193#1818C2211yescharacteristic
194#1804C2211yescharacteristic
195#1804C2211yescharacteristic
196#1776C2211yescharacteristic
197C4×#107C2211yescharacteristic
198#1771C2211yescharacteristic
199#1770C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1750C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×#127C2311yescharacteristic
206C2×#126—21no—
207C2×#126—21no—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#124—21no—
212C2×#124—21no—
213C2×#123—21no—
214C2×#121C2311yescharacteristic
215C2×#121C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×D4—21no—
218C2×C4×D4C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×#117C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#106C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×C4⋊C8C2311yescharacteristic
236C2×C4⋊C8C2311yescharacteristic
237C2×C4⋊C8C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×#102C2311yescharacteristic
240C2×#102C2311yescharacteristic
241C2×#102C2311yescharacteristic
242C2×#102C2311yescharacteristic
243C2×#102C2311yescharacteristic
244C2×#102C2311yescharacteristic
245C2×#102C2311yescharacteristic
246C2×#102C2311yescharacteristic
247C2×#102C2311yescharacteristic
248C2×#102C2311yescharacteristic
249C2×#102C2311yescharacteristic
250C2×#102C2311yescharacteristic
251C2×#102C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×C22⋊C8C2311yescharacteristic
256C2×C22⋊C8C2311yescharacteristic
257C2×C22⋊C8C2311yescharacteristic
258C2×C22⋊C8C2311yescharacteristic
259C2×#97C2311yescharacteristic
260C2×#97C2311yescharacteristic
261C2×#97C2311yescharacteristic
262C2×C4×C8C2311yescharacteristic
263C2×C4×C8C2311yescharacteristic
264C2×C4×C8C2311yescharacteristic
265#400—21no—
266#400—21no—
267#400—21no—
268#400—21no—
269#400—21no—
270#400—21no—
271#400—21no—
272#400D411yescharacteristic
273#399—21no—
274#399D411yescharacteristic
275#398—21no—
276#398—21no—
277#398—21no—
278#398—21no—
279#398—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#398D411yescharacteristic
287#398D411yescharacteristic
288#397—21no—
289#397—21no—
290#397—21no—
291#397—21no—
292#397—21no—
293#396—21no—
294#396—21no—
295#396—21no—
296#396—21no—
297#396D411yescharacteristic
298#396D411yescharacteristic
299#395—21no—
300#395—21no—
301#395—21no—
302#395—21no—
303#395—21no—
304#395—21no—
305#395D411yescharacteristic
306#394—21no—
307#394—21no—
308#394—21no—
309#394—21no—
310#394—21no—
311#394—21no—
312#394—21no—
313#394—21no—
314#393—21no—
315#393—21no—
316#393—21no—
317#393—21no—
318#393D411yescharacteristic
319#392—21no—
320#392—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#390—21no—
326#390—21no—
327#390—21no—
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—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#386—21no—
378#386—21no—
379#386—21no—
380#385—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#384—21no—
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#383—21no—
391#383—21no—
392#382—21no—
393#382—21no—
394#382—21no—
395#382—21no—
396#382—21no—
397#382C2311yescharacteristic
398#382C2311yescharacteristic
399#382C2311yescharacteristic
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#381—21no—
404#380—21no—
405#380—21no—
406#380—21no—
407#380—21no—
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
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×C22⋊C4C2311yescharacteristic
427C4×C22⋊C4C2311yescharacteristic
428#340C2311yescharacteristic
429#340C2311yescharacteristic
430#340C2311yescharacteristic
431#340C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#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×Q8—21no—
479C22×Q8—21no—
480C22×Q8C2×D411yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4C2411yescharacteristic
486C22×D4C2411yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—21no—
490C23×C4C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C4⋊Q8—41no—
500C4⋊Q8—41no—
501C4⋊Q8—41no—
502C4⋊Q8—41no—
503#127—41no—
504#127—41no—
505#126—82no—
506#126—82no—
507#125—41no—
508#125—41no—
509#125—41no—
510#125—41no—
511#125—41no—
512#125—41no—
513#124—82no—
514#124—82no—
515#123—82no—
516#121—41no—
517#121—41no—
518#121—41no—
519#121—41no—
520C4×Q8—41no—
521C4×Q8—41no—
522C4×D4—41no—
523C4×D4—41no—
524C4×D4—41no—
525C4×D4—41no—
526C4×D4—82no—
527#117—22no—
528#117—22no—
529#117—41no—
530#117—41no—
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—41no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
613C2×C22⋊C4C2×D411yescharacteristic
614C2×C22⋊C4C2×D411yescharacteristic
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C22⋊C4C2×D411yescharacteristic
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633#107—22no—
634#107—22no—
635#107—41no—
636#107—41no—
637#107—41no—
638#107—41no—
639#106—22no—
640#106—22no—
641#106—41no—
642#106—41no—
643#106—41no—
644#106—41no—
645C4⋊C8—41no—
646C4⋊C8—41no—
647C4⋊C8—41no—
648C4⋊C8—41no—
649#102—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—41no—
654#102—41no—
655#102—41no—
656#102—41no—
657#102—41no—
658#102—41no—
659#102—41no—
660#102—41no—
661#102—41no—
662#102—41no—
663#102—41no—
664#102—41no—
665C22⋊C8—41no—
666C22⋊C8—41no—
667C22⋊C8—41no—
668C22⋊C8—41no—
669#97—41no—
670#97—41no—
671#97—41no—
672C4×C8—41no—
673C4×C8—41no—
674C4×C8—41no—
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#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
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—
726C24—21no—
727C24C22×D411yescharacteristic
728C2×Q8—41no—
729C2×Q8—41no—
730C2×Q8—41no—
731C2×Q8—81no—
732C2×Q8—81no—
733C2×Q8—81no—
734C2×Q8—81no—
735C2×Q8—81no—
736C2×Q8—81no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—21no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4—81no—
757C2×D4—81no—
758C2×D4—81no—
759C2×D4—81no—
760C2×D4—81no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—42no—
782C22×C4—81no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4—81no—
786C22×C4—81no—
787C22×C4—81no—
788C22×C4—81no—
789C22×C4—81no—
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C2511yescharacteristic
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
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—41no—
855C4⋊C4—41no—
856C4⋊C4—41no—
857C4⋊C4—41no—
858C4⋊C4—41no—
859C4⋊C4—41no—
860C4⋊C4—41no—
861C4⋊C4—41no—
862C4⋊C4—41no—
863C4⋊C4—41no—
864C4⋊C4—41no—
865C4⋊C4—42no—
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⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C42−1+412yes—
895C4⋊C42−1+412yes—
896C22⋊C4—24no—
897C22⋊C4—41no—
898C22⋊C4—41no—
899C22⋊C4—41no—
900C22⋊C4—41no—
901C22⋊C4—41no—
902C22⋊C4—41no—
903C22⋊C4—42no—
904C22⋊C4—42no—
905C22⋊C4—42no—
906C22⋊C4—81no—
907C22⋊C4—81no—
908C22⋊C4—81no—
909C22⋊C4—81no—
910C22⋊C4—81no—
911C22⋊C4—81no—
912C22⋊C4—81no—
913C22⋊C4—81no—
914C22⋊C4—81no—
915C22⋊C4—81no—
916C22⋊C4—81no—
917C22⋊C4—81no—
918C22⋊C4—81no—
919C22⋊C4—81no—
920C22⋊C4—81no—
921C22⋊C4—81no—
922C22⋊C4—81no—
923C22⋊C4—81no—
924C22⋊C4—81no—
925C22⋊C4—81no—
926C22⋊C4—81no—
927C42—24no—
928C42—21no—
929C42—21no—
930C42—21no—
931C42—21no—
932C42—21no—
933C42—21no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—42no—
941C42—81no—
942C42—81no—
943C42—81no—
944C42—81no—
945C42—81no—
946C42—81no—
947C42—81no—
948C23—21no—
949C23—21no—
950C23—21no—
951C23—21no—
952C23—21no—
953C23—21no—
954C23—21no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23C23×D411yescharacteristic
970Q8—82no—
971Q8—162no—
972Q8—162no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—41no—
977D4—41no—
978D4—41no—
979D4—41no—
980D4—41no—
981D4—84no—
982D4—162no—
983D4—162no—
984D4—162no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
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—162no—
1071C2×C4—162no—
1072C2×C4—162no—
1073C2×C4C2×2−1+411yescharacteristic
1074C2×C4C2×2−1+411yescharacteristic
1075C2×C4#58511yescharacteristic
1076C2×C4#58511yescharacteristic
1077C2×C4#58511yescharacteristic
1078C2×C4#58511yescharacteristic
1079C8—41no—
1080C8—41no—
1081C8—41no—
1082C8—41no—
1083C8—41no—
1084C8—41no—
1085C8—41no—
1086C8—41no—
1087C22—41no—
1088C22—41no—
1089C22—41no—
1090C22—41no—
1091C22—41no—
1092C22—41no—
1093C22—41no—
1094C22—81no—
1095C22—81no—
1096C22—81no—
1097C22—81no—
1098C22—81no—
1099C22—81no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22#348511yescharacteristic
1109C22#348611yescharacteristic
1110C22#350011yescharacteristic
1111C22#358411yescharacteristic
1112C22#358411yescharacteristic
1113C22#358511yescharacteristic
1114C22#358511yescharacteristic
1115C4—41no—
1116C4—41no—
1117C4—41no—
1118C4—41no—
1119C4—41no—
1120C4—41no—
1121C4—41no—
1122C4—41no—
1123C4—41no—
1124C4—41no—
1125C4—41no—
1126C4—41no—
1127C4—41no—
1128C4—42no—
1129C4—42no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4#356511yescharacteristic
1143C4#356511yescharacteristic
1144C4#356511yescharacteristic
1145C4#356511yescharacteristic
1146C2—81no—
1147C2—161no—
1148C2—161no—
1149C2#4721611yescharacteristic
1150C2#6176211yescharacteristic
1151C2#6180411yescharacteristic
1152C2#6186711yescharacteristic
1153C2#6187611yescharacteristic
1154C2#6260711yescharacteristic
1155C2#6261411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2619C22
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. #42955C2semidirect
4. #32640C2semidirect
5. #32635C2semidirect
6. #32354C2semidirect
7. #32353C2semidirect
8. #32231C2semidirect
9. #32227C2semidirect
10. #32147C2semidirect
11. #32138C2semidirect
12. #31766C2semidirect
13. #31750C2semidirect
14. #31372C2semidirect
15. #31364C2semidirect
17. #28056C2semidirect
18. #28044C2semidirect
19. #27886C2semidirect
20. #27826C2semidirect
21. #27819C2semidirect
22. #27619C2semidirect
23. #27354C2semidirect
24. #27340C2semidirect
25. #27186C2semidirect
26. #27170C2semidirect
27. #26768C2semidirect
28. #26753C2semidirect
29. #26289C2semidirect
30. #26284C2semidirect
31. #22324C2semidirect

Maximal subgroups

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

subgroupindex
#429552
#424672
#327792
#326402
#326352
#323542
#323532
#322312
#322272
#321472
#321382
#317662
#317502
#313722
#313642
#293432
#280562
#280442
#278862
#278262
#278192
#276192
#273542
#273402
#271862
#271702
#267682
#267532
#262892
#262842
#223242