Finite Group Databasebeta

← #6880080

Subgroups — #6880080

Order 512.

1372 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39292C211yesmaximal, characteristic, complemented
2#39064C211yesmaximal, characteristic, complemented
3#33268C211yesmaximal, characteristic, complemented
4#32428C211yesmaximal, characteristic, complemented
5#32233C211yesmaximal, characteristic, complemented
6#31740C211yesmaximal, characteristic, complemented
7#31686C211yesmaximal, characteristic, complemented
8#31634C211yesmaximal, characteristic, complemented
9#31289C211yesmaximal, characteristic, complemented
10#30807C211yesmaximal, characteristic, complemented
11#30529C211yesmaximal, characteristic
12#30372C211yesmaximal, characteristic, complemented
13#30348C211yesmaximal, characteristic, complemented
14#29512C211yesmaximal, characteristic, complemented
15#29493C211yesmaximal, characteristic, complemented
16#29469C211yesmaximal, characteristic, complemented
17#29437C211yesmaximal, characteristic, complemented
18#29363C211yesmaximal, characteristic, complemented
19#29120C211yesmaximal, characteristic, complemented
20#27544C211yesmaximal, characteristic, complemented
21#27450C211yesmaximal, characteristic, complemented
22#27253C211yesmaximal, characteristic, complemented
23#27215C211yesmaximal, characteristic, complemented
24#27049C211yesmaximal, characteristic, complemented
25#27019C211yesmaximal, characteristic, complemented
26#26738C211yesmaximal, characteristic, complemented
27#26708C211yesmaximal, characteristic, complemented
28#22122C211yesmaximal, characteristic, complemented
29#22055C211yesmaximal, characteristic, complemented
30#21646C211yesmaximal, characteristic, complemented
31#21434C211yesmaximal, characteristic, complemented
32C2×#486C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#449C2211yescharacteristic
35#2863C2211yescharacteristic
36#2860C2211yescharacteristic
37#2798—21no—
38#2749—21no—
39#2740—21no—
40#2737—21no—
41#2727—21no—
42#2700—21no—
43#2696—21no—
44#2689—21no—
45#2644C2211yescharacteristic
46#2640C2211yescharacteristic
47#2628C2211yescharacteristic
48#2624C2211yescharacteristic
49#2600—21no—
50#2596—21no—
51#2564—21no—
52#2560—21no—
53#2550C2211yescharacteristic
54#2542C2211yescharacteristic
55#2511C2211yescharacteristic
56#2497C2211yescharacteristic
57#2496C2211yescharacteristic
58#2491C2211yescharacteristic
59#2490C2211yescharacteristic
60#2465—21no—
61#2463—21no—
62#2452C2211yescharacteristic
63#2448—21no—
64#2447C2211yescharacteristic
65#2445C2211yescharacteristic
66#2440C2211yescharacteristic
67#2431C2211yescharacteristic
68#2419—21no—
69#2369C2211yescharacteristic
70#2361C2211yescharacteristic
71#2357C2211yescharacteristic
72#2339C2211yescharacteristic
73#2330C2211yescharacteristic
74#2324C2211yescharacteristic
75#2319C2211yescharacteristic
76#2311C2211yescharacteristic
77C4×C4⋊Q8C2211yescharacteristic
78C4×#127C2211yescharacteristic
79#2298C2211yescharacteristic
80#2101C2211yescharacteristic
81#2099C2211yescharacteristic
82#2096C2211yescharacteristic
83#2092C2211yescharacteristic
84#2086C2211yescharacteristic
85#2083C2211yescharacteristic
86#2077C2211yescharacteristic
87#2075C2211yescharacteristic
88#2075C2211yescharacteristic
89#2074C2211yescharacteristic
90#2073C2211yescharacteristic
91#2072C2211yescharacteristic
92#2071C2211yescharacteristic
93#2071C2211yescharacteristic
94#2068C2211yescharacteristic
95#2067C2211yescharacteristic
96#2065C2211yescharacteristic
97#2065C2211yescharacteristic
98#2058C2211yescharacteristic
99#2058C2211yescharacteristic
100#2057C2211yescharacteristic
101#2055C2211yescharacteristic
102#2054C2211yescharacteristic
103#2054C2211yescharacteristic
104#2042C2211yescharacteristic
105#2041C2211yescharacteristic
106#2034C2211yescharacteristic
107#2034C2211yescharacteristic
108#2034C2211yescharacteristic
109#2034C2211yescharacteristic
110#2026C2211yescharacteristic
111#2025C2211yescharacteristic
112#2024C2211yescharacteristic
113#2024C2211yescharacteristic
114#2023C2211yescharacteristic
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic
117#2012C2211yescharacteristic
118#2011C2211yescharacteristic
119#1999C2211yescharacteristic
120#1990C2211yescharacteristic
121#1989C2211yescharacteristic
122#1988C2211yescharacteristic
123#1987C2211yescharacteristic
124#1983C2211yescharacteristic
125#1983C2211yescharacteristic
126#1973C2211yescharacteristic
127#1973C2211yescharacteristic
128#1970C2211yescharacteristic
129#1970C2211yescharacteristic
130#1968C2211yescharacteristic
131#1957C2211yescharacteristic
132#1948C2211yescharacteristic
133#1944C2211yescharacteristic
134#1943C2211yescharacteristic
135#1942C2211yescharacteristic
136#1941C2211yescharacteristic
137#1941C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1935C2211yescharacteristic
145#1935C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1933C2211yescharacteristic
150#1933C2211yescharacteristic
151#1933C2211yescharacteristic
152#1928C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic
159#1925C2211yescharacteristic
160#1924C2211yescharacteristic
161#1924C2211yescharacteristic
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic
164#1920C2211yescharacteristic
165#1920C2211yescharacteristic
166#1920C2211yescharacteristic
167#1918C2211yescharacteristic
168#1918C2211yescharacteristic
169#1918C2211yescharacteristic
170#1917C2211yescharacteristic
171#1917C2211yescharacteristic
172#1916C2211yescharacteristic
173#1916C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1877C2211yescharacteristic
180#1874C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1852C2211yescharacteristic
186#1834C2211yescharacteristic
187#1824C2211yescharacteristic
188#1823C2211yescharacteristic
189#1802C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1768C2211yescharacteristic
194#1768C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199#1750C2211yescharacteristic
200#1750C2211yescharacteristic
201#1744C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#126—21no—
212C2×#126—21no—
213C2×#125C2311yescharacteristic
214C2×#124—21no—
215C2×#124C2311yescharacteristic
216C2×#123—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×C4×Q8—21no—
224C2×C4×D4—21no—
225C2×C4×D4—21no—
226C2×C4×D4—21no—
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233#486—24no—
234#478—24no—
235#449—24no—
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#399—21no—
293#399—21no—
294#399—21no—
295#399—21no—
296#398—21no—
297#398—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#396—21no—
309#396—21no—
310#396—21no—
311#395—21no—
312#395—21no—
313#395—21no—
314#394—21no—
315#394—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#393—21no—
321#393—21no—
322#393—21no—
323#393—21no—
324#393—21no—
325#392—21no—
326#392—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#390—21no—
337#390—21no—
338#390—21no—
339#390—21no—
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#388—21no—
369#388—21no—
370#388—21no—
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#388D411yescharacteristic
381#388D411yescharacteristic
382#388D411yescharacteristic
383#388D411yescharacteristic
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387D411yescharacteristic
394#387D411yescharacteristic
395#387D411yescharacteristic
396#387D411yescharacteristic
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#383—21no—
415#382C2311yescharacteristic
416#381—21no—
417#381—21no—
418#381—21no—
419#381—21no—
420#380—21no—
421#380—21no—
422#380—21no—
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C22⋊C4—21no—
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440#376C2311yescharacteristic
441C2×#95—21no—
442C43C2311yescharacteristic
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
481C2×#41—22no—
482C2×#41—41no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8C2411yescharacteristic
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4C2411yescharacteristic
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C2411yescharacteristic
506C2×SD16—22no—
507C2×SD16—41no—
508C2×SD16—41no—
509C2×D8—22no—
510C2×D8—41no—
511C2×D8—41no—
512C2×D8—41no—
513C2×D8—41no—
514C2×D8—41no—
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C4⋊Q8—22no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529#127—22no—
530#127—41no—
531#126—82no—
532#126—82no—
533#125—22no—
534#125—41no—
535#124—41no—
536#124—41no—
537#124—82no—
538#123—82no—
539C22⋊Q8—82no—
540C22⋊Q8—82no—
541C22⋊Q8—82no—
542C22⋊Q8—82no—
543#121—22no—
544#121—41no—
545#121—41no—
546#121—41no—
547C4×Q8—82no—
548C4×D4—22no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—41no—
553C4×D4—41no—
554C4×D4—41no—
555C4×D4—41no—
556C4×D4—82no—
557C4×D4—82no—
558C4×D4—82no—
559#117—41no—
560#117—41no—
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⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C22⋊C4C2×D411yescharacteristic
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2×D411yescharacteristic
654C2×C42C2×D411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661#107—22no—
662#107—41no—
663#107—41no—
664#107—41no—
665#106—22no—
666#106—41no—
667#106—41no—
668#106—41no—
669#106—41no—
670C4⋊C8—22no—
671C4⋊C8—41no—
672C4⋊C8—41no—
673C4⋊C8—41no—
674#103—22no—
675#103—41no—
676#103—41no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—41no—
686#102—41no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102#4114yes—
700C22⋊C8—22no—
701C22⋊C8—41no—
702C22⋊C8—41no—
703C22⋊C8—41no—
704#97—41no—
705#97—41no—
706#97—41no—
707#97—41no—
708C4×C8—22no—
709C4×C8—41no—
710C4×C8—41no—
711C4×C8—41no—
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#95—21no—
734#95—21no—
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#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758C24—21no—
759C24—21no—
760C24—21no—
761C24C22×D411yescharacteristic
762#41—82no—
763#41—82no—
764#41—82no—
765#41—82no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8—81no—
776C2×Q8—81no—
777C2×Q8—81no—
778C2×Q8—81no—
779C2×Q8—81no—
780C2×Q8—81no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4—81no—
812C2×D4—81no—
813C2×D4C2×#4112yes—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C2511yescharacteristic
865SD16—82no—
866D8—82no—
867D8—82no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
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×C8C2×#4112yes—
892C4⋊C4—22no—
893C4⋊C4—22no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
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—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—41no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4C2×#4112yes—
946C22⋊C4—22no—
947C22⋊C4—22no—
948C22⋊C4—41no—
949C22⋊C4—41no—
950C22⋊C4—41no—
951C22⋊C4—41no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C42—22no—
987C42—22no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—41no—
1001C42—41no—
1002C42—81no—
1003C42—81no—
1004C42—81no—
1005C42—81no—
1006C42—81no—
1007C42—81no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—22no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23C23×D411yescharacteristic
1037Q8—41no—
1038Q8—41no—
1039Q8—41no—
1040Q8—41no—
1041Q8—84no—
1042Q8—162no—
1043Q8—162no—
1044D4—22no—
1045D4—22no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—84no—
1057D4—84no—
1058D4—84no—
1059D4—84no—
1060D4—162no—
1061C2×C4—21no—
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—22no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
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—21no—
1097C2×C4—21no—
1098C2×C4—21no—
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—84no—
1142C2×C4—162no—
1143C2×C4—162no—
1144C2×C4—162no—
1145C2×C4—162no—
1146C2×C4—162no—
1147C2×C4#57612yes—
1148C2×C4#57712yes—
1149C2×C4C22×#4111yescharacteristic
1150C2×C4#58511yescharacteristic
1151C2×C4#58511yescharacteristic
1152C2×C4#58511yescharacteristic
1153C2×C4#58511yescharacteristic
1154C2×C4#58511yescharacteristic
1155C8—22no—
1156C8—41no—
1157C8—41no—
1158C8—41no—
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C8—41no—
1163C22—41no—
1164C22—42no—
1165C22—41no—
1166C22—41no—
1167C22—42no—
1168C22—41no—
1169C22—42no—
1170C22—41no—
1171C22—41no—
1172C22—41no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22#344911yescharacteristic
1192C22D4×#4111yescharacteristic
1193C22#350011yescharacteristic
1194C22C2×#57611yescharacteristic
1195C22C2×#57711yescharacteristic
1196C22#358511yescharacteristic
1197C22#358611yescharacteristic
1198C4—22no—
1199C4—22no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—42no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4—81no—
1218C4—81no—
1219C4—81no—
1220C4—81no—
1221C4—81no—
1222C4—81no—
1223C4—81no—
1224C4#351011yescharacteristic
1225C4#352111yescharacteristic
1226C4#356611yescharacteristic
1227C4#356811yescharacteristic
1228C2—81no—
1229C2—82no—
1230C2—161no—
1231C2—161no—
1232C2#3994711yescharacteristic
1233C2#6097311yescharacteristic
1234C2#6100611yescharacteristic
1235C2#6152211yescharacteristic
1236C2#6152311yescharacteristic
1237C2#6261011yescharacteristic
1238C2#6261611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30529C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39292C2semidirect
2. #39064C2semidirect
3. #33268C2semidirect
4. #32428C2semidirect
5. #32233C2semidirect
6. #31740C2semidirect
7. #31686C2semidirect
8. #31634C2semidirect
9. #31289C2semidirect
10. #30807C2semidirect
12. #30372C2semidirect
13. #30348C2semidirect
14. #29512C2semidirect
15. #29493C2semidirect
16. #29469C2semidirect
17. #29437C2semidirect
18. #29363C2semidirect
19. #29120C2semidirect
20. #27544C2semidirect
21. #27450C2semidirect
22. #27253C2semidirect
23. #27215C2semidirect
24. #27049C2semidirect
25. #27019C2semidirect
26. #26738C2semidirect
27. #26708C2semidirect
28. #22122C2semidirect
29. #22055C2semidirect
30. #21646C2semidirect
31. #21434C2semidirect

Maximal subgroups

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

subgroupindex
#392922
#390642
#332682
#324282
#322332
#317402
#316862
#316342
#312892
#308072
#305292
#303722
#303482
#295122
#294932
#294692
#294372
#293632
#291202
#275442
#274502
#272532
#272152
#270492
#270192
#267382
#267082
#221222
#220552
#216462
#214342