Finite Group Databasebeta

← #6739164

Subgroups — #6739164

Order 512.

1319 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40120C211yesmaximal, characteristic, complemented
2#36462C211yesmaximal, characteristic
3#33068C211yesmaximal, characteristic, complemented
4#32511C211yesmaximal, characteristic, complemented
5#32328C211yesmaximal, characteristic, complemented
6#32196C211yesmaximal, characteristic, complemented
7#31895C211yesmaximal, characteristic, complemented
8#31495C211yesmaximal, characteristic
9#31121C211yesmaximal, characteristic
10#30975C211yesmaximal, characteristic, complemented
11#30794C211yesmaximal, characteristic, complemented
12#30383C211yesmaximal, characteristic, complemented
13#30154C211yesmaximal, characteristic, complemented
14#29036C211yesmaximal, characteristic, complemented
15#28850C211yesmaximal, characteristic, complemented
16#27466C211yesmaximal, characteristic, complemented
17#27383C211yesmaximal, characteristic, complemented
18#27183C211yesmaximal, characteristic, complemented
19#27124C211yesmaximal, characteristic, complemented
20#27122C211yesmaximal, characteristic, complemented
21#26877C211yesmaximal, characteristic, complemented
22#26771C211yesmaximal, characteristic, complemented
23#26716C211yesmaximal, characteristic, complemented
24#26530C211yesmaximal, characteristic, complemented
25#26421C211yesmaximal, characteristic, complemented
26#26037C211yesmaximal, characteristic, complemented
27#25999C211yesmaximal, characteristic, complemented
28#23169C211yesmaximal, characteristic, complemented
29#22933C211yesmaximal, characteristic, complemented
30#22351C211yesmaximal, characteristic, complemented
31#21617C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#482C2211yescharacteristic
34C2×#478C2211yescharacteristic
35#2860C2211yescharacteristic
36#2859C2211yescharacteristic
37#2850—21no—
38#2783—21no—
39#2769—21no—
40#2769—21no—
41#2721—21no—
42#2664—21no—
43#2572—21no—
44#2560—21no—
45#2559—21no—
46#2554—21no—
47#2552C2211yescharacteristic
48#2552C2211yescharacteristic
49#2519—21no—
50#2518—21no—
51#2508C2211yescharacteristic
52#2508C2211yescharacteristic
53#2507C2211yescharacteristic
54#2506—21no—
55#2506C2211yescharacteristic
56#2497C2211yescharacteristic
57#2496C2211yescharacteristic
58#2495C2211yescharacteristic
59#2491C2211yescharacteristic
60#2459—21no—
61#2452C2211yescharacteristic
62#2445C2211yescharacteristic
63#2441C2211yescharacteristic
64#2441C2211yescharacteristic
65#2428C2211yescharacteristic
66#2420C2211yescharacteristic
67#2370C2211yescharacteristic
68#2369C2211yescharacteristic
69#2366C2211yescharacteristic
70#2363C2211yescharacteristic
71#2363C2211yescharacteristic
72#2357C2211yescharacteristic
73#2347C2211yescharacteristic
74#2347C2211yescharacteristic
75#2336—21no—
76C4×#125C2211yescharacteristic
77C4×#126C2211yescharacteristic
78C4×#123—21no—
79C42×D4C2211yescharacteristic
80#2101C2211yescharacteristic
81#2100C2211yescharacteristic
82#2099C2211yescharacteristic
83#2094C2211yescharacteristic
84#2094C2211yescharacteristic
85#2088C2211yescharacteristic
86#2088C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2087C2211yescharacteristic
91#2087C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2084C2211yescharacteristic
95#2084C2211yescharacteristic
96#2083C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2073C2211yescharacteristic
100#2071C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2059C2211yescharacteristic
109#2058C2211yescharacteristic
110#2058C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2025C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic
120#1989C2211yescharacteristic
121#1989C2211yescharacteristic
122#1988C2211yescharacteristic
123#1982C2211yescharacteristic
124#1957C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1948C2211yescharacteristic
128#1948C2211yescharacteristic
129#1948C2211yescharacteristic
130#1944C2211yescharacteristic
131#1944C2211yescharacteristic
132#1944C2211yescharacteristic
133#1942C2211yescharacteristic
134#1941C2211yescharacteristic
135#1940C2211yescharacteristic
136#1939C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic
149#1923C2211yescharacteristic
150#1921C2211yescharacteristic
151#1921C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1920C2211yescharacteristic
155#1920C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1919C2211yescharacteristic
159#1918C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1918C2211yescharacteristic
164#1918C2211yescharacteristic
165#1917C2211yescharacteristic
166#1917C2211yescharacteristic
167#1917C2211yescharacteristic
168#1893C2211yescharacteristic
169#1893C2211yescharacteristic
170#1875C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1850C2211yescharacteristic
183#1850C2211yescharacteristic
184#1836C2211yescharacteristic
185#1831C2211yescharacteristic
186#1825C2211yescharacteristic
187#1807C2211yescharacteristic
188#1804C2211yescharacteristic
189#1802C2211yescharacteristic
190#1802C2211yescharacteristic
191#1802C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1771C2211yescharacteristic
197#1767C2211yescharacteristic
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201#1752C2211yescharacteristic
202#1735C2211yescharacteristic
203C23×C8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×#127C2311yescharacteristic
206C2×#126—21no—
207C2×#126—21no—
208C2×#126D411yescharacteristic
209C2×#125—21no—
210C2×#125—21no—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#124—21no—
215C2×#123—21no—
216C2×C22⋊Q8—21no—
217C2×#121—21no—
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×C4×D4—21no—
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C22×C42—21no—
228#501—24no—
229#482—24no—
230#478—24no—
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#399—21no—
285#399—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#396—21no—
299#396—21no—
300#396—21no—
301#396—21no—
302#394—21no—
303#394—21no—
304#394—21no—
305#394—21no—
306#394—21no—
307#393—21no—
308#393—21no—
309#392—21no—
310#391—21no—
311#391—21no—
312#390—21no—
313#390—21no—
314#390—21no—
315#390C2311yescharacteristic
316#390C2311yescharacteristic
317#390C2311yescharacteristic
318#390C2311yescharacteristic
319#390C2311yescharacteristic
320#390C2311yescharacteristic
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388D411yescharacteristic
363#388D411yescharacteristic
364#388D411yescharacteristic
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387D411yescharacteristic
378#387D411yescharacteristic
379#387D411yescharacteristic
380#386—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#385—21no—
388#384—21no—
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#384C2311yescharacteristic
393#383—21no—
394#383—21no—
395#383—21no—
396#383D411yescharacteristic
397#382—21no—
398#382—21no—
399#382—21no—
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#381—21no—
403#381—21no—
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4C2311yescharacteristic
434C4×C22⋊C4C2311yescharacteristic
435C4×C22⋊C4C2311yescharacteristic
436C43C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4C2411yescharacteristic
487C22×D4C2411yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—21no—
492C23×C4C2411yescharacteristic
493C22×C8—41no—
494C22×C8—41no—
495C22×C8—41no—
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C4⋊Q8—22no—
505C4⋊Q8—41no—
506#127—22no—
507#127—41no—
508#126—42no—
509#126—82no—
510#126—82no—
511#125—22no—
512#125—22no—
513#125—41no—
514#125—41no—
515#125—44no—
516#125—82no—
517#125—82no—
518#124—82no—
519#123—44no—
520C22⋊Q8—82no—
521#121—22no—
522#121—22no—
523#121—41no—
524#121—41no—
525#121—82no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—41no—
531C4×D4—41no—
532C4×D4—41no—
533C4×D4—41no—
534C4×D4—82no—
535#117—22no—
536#117—22no—
537#117—41no—
538#117—41no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
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⋊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×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4C2×D411yescharacteristic
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C22⋊C4C2×D411yescharacteristic
618C2×C22⋊C4C2×D411yescharacteristic
619C2×C22⋊C4C2×D411yescharacteristic
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—82no—
633C2×C42C2×D411yescharacteristic
634C2×C42C2×D411yescharacteristic
635C2×C42C2×D411yescharacteristic
636C2×C42C2×D411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643#107—22no—
644#107—22no—
645#107—41no—
646#107—41no—
647#107—41no—
648#107#4114yes—
649#106—22no—
650#106—22no—
651#106—22no—
652#106—22no—
653#106—22no—
654#106—41no—
655#106—41no—
656#106—41no—
657#106—41no—
658#106—41no—
659C4⋊C8—22no—
660C4⋊C8—41no—
661C4⋊C8—41no—
662C4⋊C8—41no—
663C4⋊C8—41no—
664C4⋊C8—41no—
665C4⋊C8—41no—
666#102—22no—
667#102—22no—
668#102—22no—
669#102—22no—
670#102—22no—
671#102—22no—
672#102—41no—
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—
682C22⋊C8—22no—
683C22⋊C8—41no—
684C22⋊C8—41no—
685#97—22no—
686#97—41no—
687#97—41no—
688#97—41no—
689C4×C8—41no—
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#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#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738C24—21no—
739C24—21no—
740C24C22×D411yescharacteristic
741C2×Q8—42no—
742C2×Q8—81no—
743C2×Q8—81no—
744C2×D4—21no—
745C2×D4—21no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—42no—
760C2×D4—81no—
761C2×D4—81no—
762C2×D4—81no—
763C2×D4—81no—
764C2×D4—81no—
765C2×D4—81no—
766C2×D4—81no—
767C2×D42−1+412yes—
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—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—81no—
796C22×C4—81no—
797C22×C4—81no—
798C22×C4—81no—
799C22×C4—81no—
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
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—
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—82no—
838C2×C8C2×#4112yes—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—22no—
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—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—41no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
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⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4C2×#4112yes—
902C4⋊C4C2×#4112yes—
903C4⋊C42−1+412yes—
904C22⋊C4—22no—
905C22⋊C4—22no—
906C22⋊C4—41no—
907C22⋊C4—41no—
908C22⋊C4—41no—
909C22⋊C4—41no—
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—
934C42—22no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—41no—
948C42—41no—
949C42—41no—
950C42—42no—
951C42—42no—
952C42—42no—
953C42—42no—
954C42—42no—
955C42—81no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42—81no—
960C42—81no—
961C42—81no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—22no—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23C23×D411yescharacteristic
984Q8—162no—
985D4—22no—
986D4—22no—
987D4—41no—
988D4—41no—
989D4—41no—
990D4—41no—
991D4—41no—
992D4—41no—
993D4—84no—
994D4—162no—
995D4—162no—
996D4—162no—
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—22no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
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—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—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—84no—
1081C2×C4—84no—
1082C2×C4—84no—
1083C2×C4—162no—
1084C2×C4#57512yes—
1085C2×C4#57712yes—
1086C2×C4C22×#4111yescharacteristic
1087C2×C4C2×2−1+411yescharacteristic
1088C2×C4C2×2−1+411yescharacteristic
1089C2×C4#58511yescharacteristic
1090C2×C4#58511yescharacteristic
1091C2×C4#58511yescharacteristic
1092C8—22no—
1093C8—41no—
1094C8—41no—
1095C8—41no—
1096C8—41no—
1097C8—41no—
1098C8—41no—
1099C8—41no—
1100C22—41no—
1101C22—41no—
1102C22—42no—
1103C22—41no—
1104C22—41no—
1105C22—42no—
1106C22—41no—
1107C22—41no—
1108C22—42no—
1109C22—41no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22D4×#4111yescharacteristic
1122C22#348911yescharacteristic
1123C22#348911yescharacteristic
1124C22C2×#57511yescharacteristic
1125C22C2×#57711yescharacteristic
1126C22#358511yescharacteristic
1127C22#358511yescharacteristic
1128C4—22no—
1129C4—22no—
1130C4—41no—
1131C4—41no—
1132C4—41no—
1133C4—41no—
1134C4—41no—
1135C4—41no—
1136C4—42no—
1137C4—42no—
1138C4—41no—
1139C4—41no—
1140C4—41no—
1141C4—41no—
1142C4—41no—
1143C4—42no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4#346111yescharacteristic
1156C4#351611yescharacteristic
1157C4#356311yescharacteristic
1158C4#356611yescharacteristic
1159C2—81no—
1160C2—82no—
1161C2—161no—
1162C2#3781911yescharacteristic
1163C2#6146211yescharacteristic
1164C2#6155111yescharacteristic
1165C2#6212311yescharacteristic
1166C2#6212611yescharacteristic
1167C2#6215611yescharacteristic
1168C2#6223511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2428C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40120C2semidirect
3. #33068C2semidirect
4. #32511C2semidirect
5. #32328C2semidirect
6. #32196C2semidirect
7. #31895C2semidirect
10. #30975C2semidirect
11. #30794C2semidirect
12. #30383C2semidirect
13. #30154C2semidirect
14. #29036C2semidirect
15. #28850C2semidirect
16. #27466C2semidirect
17. #27383C2semidirect
18. #27183C2semidirect
19. #27124C2semidirect
20. #27122C2semidirect
21. #26877C2semidirect
22. #26771C2semidirect
23. #26716C2semidirect
24. #26530C2semidirect
25. #26421C2semidirect
26. #26037C2semidirect
27. #25999C2semidirect
28. #23169C2semidirect
29. #22933C2semidirect
30. #22351C2semidirect
31. #21617C2semidirect

Maximal subgroups

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

subgroupindex
#401202
#364622
#330682
#325112
#323282
#321962
#318952
#314952
#311212
#309752
#307942
#303832
#301542
#290362
#288502
#274662
#273832
#271832
#271242
#271222
#268772
#267712
#267162
#265302
#264212
#260372
#259992
#231692
#229332
#223512
#216172