Finite Group Databasebeta

← #6733003

Subgroups — #6733003

Order 512.

1378 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39407C211yesmaximal, characteristic, complemented
2#36298C211yesmaximal, characteristic
3#33073C211yesmaximal, characteristic, complemented
4#31992C211yesmaximal, characteristic, complemented
5#31876C211yesmaximal, characteristic, complemented
6#31604C211yesmaximal, characteristic, complemented
7#31496C211yesmaximal, characteristic
8#31472C211yesmaximal, characteristic, complemented
9#31089C211yesmaximal, characteristic, complemented
10#30824C211yesmaximal, characteristic, complemented
11#30657C211yesmaximal, characteristic
12#30383C211yesmaximal, characteristic, complemented
13#30149C211yesmaximal, characteristic, complemented
14#28082C211yesmaximal, characteristic
15#28000C211yesmaximal, characteristic, complemented
16#27475C211yesmaximal, characteristic, complemented
17#27379C211yesmaximal, characteristic, complemented
18#27344C211yesmaximal, characteristic
19#27051C211yesmaximal, characteristic, complemented
20#27030C211yesmaximal, characteristic
21#26884C211yesmaximal, characteristic, complemented
22#26875C211yesmaximal, characteristic, complemented
23#26780C211yesmaximal, characteristic, complemented
24#26458C211yesmaximal, characteristic, complemented
25#26408C211yesmaximal, characteristic
26#26090C211yesmaximal, characteristic, complemented
27#25990C211yesmaximal, characteristic, complemented
28#23226C211yesmaximal, characteristic, complemented
29#22934C211yesmaximal, characteristic, complemented
30#22351C211yesmaximal, characteristic, complemented
31#21615C211yesmaximal, characteristic, complemented
32C2×#541—21no—
33C2×#489C2211yescharacteristic
34C2×#483C2211yescharacteristic
35C2×#475C2211yescharacteristic
36#2865—21no—
37#2860C2211yescharacteristic
38#2859C2211yescharacteristic
39#2719—21no—
40#2713—21no—
41#2698—21no—
42#2689—21no—
43#2634—21no—
44#2552C2211yescharacteristic
45#2551C2211yescharacteristic
46#2525—21no—
47#2522—21no—
48#2516—21no—
49#2507C2211yescharacteristic
50#2506C2211yescharacteristic
51#2506C2211yescharacteristic
52#2506C2211yescharacteristic
53#2496C2211yescharacteristic
54#2496C2211yescharacteristic
55#2496C2211yescharacteristic
56#2490C2211yescharacteristic
57#2479—21no—
58#2478—21no—
59#2478—21no—
60#2468—21no—
61#2462—21no—
62#2453C2211yescharacteristic
63#2448C2211yescharacteristic
64#2440C2211yescharacteristic
65#2440C2211yescharacteristic
66#2426C2211yescharacteristic
67#2423C2211yescharacteristic
68#2370C2211yescharacteristic
69#2367C2211yescharacteristic
70#2365C2211yescharacteristic
71#2361C2211yescharacteristic
72#2360C2211yescharacteristic
73#2354C2211yescharacteristic
74#2344C2211yescharacteristic
75#2344C2211yescharacteristic
76C4×C4⋊Q8C2211yescharacteristic
77C4×#126C2211yescharacteristic
78#2293—21no—
79C42×Q8C2211yescharacteristic
80#2100C2211yescharacteristic
81#2100C2211yescharacteristic
82#2099C2211yescharacteristic
83#2094C2211yescharacteristic
84#2094C2211yescharacteristic
85#2088C2211yescharacteristic
86#2088C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2086C2211yescharacteristic
92#2084C2211yescharacteristic
93#2084C2211yescharacteristic
94#2083C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2072C2211yescharacteristic
98#2072C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2068C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2066C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2058C2211yescharacteristic
111#2058C2211yescharacteristic
112#2058C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2023C2211yescharacteristic
120#1992C2211yescharacteristic
121#1989C2211yescharacteristic
122#1988C2211yescharacteristic
123#1987C2211yescharacteristic
124#1983C2211yescharacteristic
125#1948C2211yescharacteristic
126#1948C2211yescharacteristic
127#1948C2211yescharacteristic
128#1947C2211yescharacteristic
129#1947C2211yescharacteristic
130#1944C2211yescharacteristic
131#1944C2211yescharacteristic
132#1943C2211yescharacteristic
133#1943C2211yescharacteristic
134#1942C2211yescharacteristic
135#1940C2211yescharacteristic
136#1939C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1935C2211yescharacteristic
141#1933C2211yescharacteristic
142#1928C2211yescharacteristic
143#1927C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic
149#1923C2211yescharacteristic
150#1921C2211yescharacteristic
151#1921C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1920C2211yescharacteristic
155#1920C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1920C2211yescharacteristic
160#1919C2211yescharacteristic
161#1919C2211yescharacteristic
162#1918C2211yescharacteristic
163#1918C2211yescharacteristic
164#1918C2211yescharacteristic
165#1917C2211yescharacteristic
166#1917C2211yescharacteristic
167#1917C2211yescharacteristic
168#1893C2211yescharacteristic
169#1892C2211yescharacteristic
170#1874C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1853C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1850C2211yescharacteristic
183#1850C2211yescharacteristic
184#1844C2211yescharacteristic
185#1831C2211yescharacteristic
186#1823C2211yescharacteristic
187#1807C2211yescharacteristic
188#1803C2211yescharacteristic
189#1803C2211yescharacteristic
190#1803C2211yescharacteristic
191#1802C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195#1776C2211yescharacteristic
196#1771C2211yescharacteristic
197#1767C2211yescharacteristic
198#1763C2211yescharacteristic
199#1763C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1752C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C23×C8C2311yescharacteristic
204#541—48no—
205C2×C4⋊Q8—21no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126—21no—
209C2×#126—21no—
210C2×#126—21no—
211C2×#126—21no—
212C2×#126D411yescharacteristic
213C2×#125—21no—
214C2×#125—21no—
215C2×#125—21no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×C4×Q8—21no—
225C2×C4×Q8—21no—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4C2311yescharacteristic
231C2×#117—21no—
232C2×#117—21no—
233C2×#117—21no—
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236#489—24no—
237#483—24no—
238#475—24no—
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#399—21no—
294#399—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#396—21no—
312#395—21no—
313#395—21no—
314#395—21no—
315#395—21no—
316#394—21no—
317#394—21no—
318#391—21no—
319#391—21no—
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#390—21no—
323#390—21no—
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
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#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
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#388D411yescharacteristic
369#388D411yescharacteristic
370#388D411yescharacteristic
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387D411yescharacteristic
390#387D411yescharacteristic
391#387D411yescharacteristic
392#386—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#383D411yescharacteristic
405#382—21no—
406#381—21no—
407#381—21no—
408#380—21no—
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4C2311yescharacteristic
434C4×C22⋊C4C2311yescharacteristic
435C4×C22⋊C4C2311yescharacteristic
436C43—21no—
437C43C2311yescharacteristic
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#340C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482C22×Q8—21no—
483C22×Q8—21no—
484C22×Q8C2411yescharacteristic
485C22×D4—21no—
486C22×D4C2411yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—21no—
490C23×C4C2411yescharacteristic
491C22×C8—41no—
492C22×C8—41no—
493C22×C8—41no—
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C4⋊Q8—22no—
503C4⋊Q8—22no—
504C4⋊Q8—41no—
505C4⋊Q8—41no—
506C4⋊Q8—44no—
507#126—24no—
508#126—44no—
509#126—44no—
510#126—44no—
511#126—82no—
512#125—22no—
513#125—41no—
514#125—44no—
515#125—44no—
516#125—44no—
517#125—44no—
518#125—44no—
519#124—22no—
520#124—41no—
521C22⋊Q8—22no—
522C22⋊Q8—44no—
523C22⋊Q8—41no—
524C22⋊Q8—44no—
525#121—22no—
526#121—41no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—22no—
530C4×Q8—41no—
531C4×Q8—41no—
532C4×Q8—41no—
533C4×Q8—44no—
534C4×Q8—44no—
535C4×D4—22no—
536C4×D4—41no—
537C4×D4—44no—
538#117—44no—
539#117—82no—
540#117—82no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—22no—
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⋊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—41no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42C2×D411yescharacteristic
642C2×C42C2×D411yescharacteristic
643C2×C42C2×D411yescharacteristic
644C2×C42C2×D411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651#107—22no—
652#107—22no—
653#107—22no—
654#107—22no—
655#107—41no—
656#107—41no—
657#106—22no—
658#106—22no—
659#106—22no—
660#106—22no—
661#106—41no—
662#106—41no—
663#106—41no—
664#106—41no—
665#106—41no—
666#106—41no—
667C4⋊C8—22no—
668C4⋊C8—41no—
669C4⋊C8—41no—
670C4⋊C8—41no—
671C4⋊C8—41no—
672C4⋊C8—41no—
673C4⋊C8—41no—
674#103—22no—
675#103—22no—
676#103—22no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#103#4114yes—
682#102—22no—
683#102—22no—
684#102—41no—
685#102—41no—
686#102—41no—
687#102—41no—
688#102—41no—
689#102—41no—
690C22⋊C8—22no—
691C22⋊C8—41no—
692C22⋊C8—41no—
693#97—22no—
694#97—41no—
695#97—41no—
696#97—41no—
697C4×C8—41no—
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#95—21no—
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746C24—21no—
747C24C22×D411yescharacteristic
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—42no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—42no—
757C2×Q8—81no—
758C2×Q8—81no—
759C2×Q8C2×#4112yes—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—42no—
767C2×D4—42no—
768C2×D4—81no—
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—21no—
789C22×C4—21no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—81no—
797C22×C4—81no—
798C22×C4—81no—
799C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
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—
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—82no—
837C2×C8C2×#4112yes—
838C4⋊C4—22no—
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—42no—
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—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
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—
909C4⋊C4C2×#4112yes—
910C4⋊C42−1+412yes—
911C4⋊C42−1+412yes—
912C22⋊C4—22no—
913C22⋊C4—22no—
914C22⋊C4—22no—
915C22⋊C4—41no—
916C22⋊C4—41no—
917C22⋊C4—42no—
918C22⋊C4—42no—
919C22⋊C4—42no—
920C22⋊C4—42no—
921C22⋊C4—42no—
922C22⋊C4—42no—
923C22⋊C4—42no—
924C22⋊C4—42no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4AGL(1,ℤ/8)14yes—
935C42—22no—
936C42—22no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—41no—
950C42—41no—
951C42—42no—
952C42—42no—
953C42—42no—
954C42—42no—
955C42—42no—
956C42—42no—
957C42—42no—
958C42—42no—
959C42—42no—
960C42—42no—
961C42—81no—
962C42—81no—
963C42—81no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23C2×AGL(1,ℤ/8)12yes—
978C23C23×D411yescharacteristic
979Q8—22no—
980Q8—22no—
981Q8—41no—
982Q8—41no—
983Q8—84no—
984Q8—84no—
985D4—41no—
986D4—41no—
987D4—41no—
988D4—41no—
989D4—84no—
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—22no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—22no—
1019C2×C4—22no—
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—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—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—84no—
1076C2×C4—84no—
1077C2×C4—84no—
1078C2×C4C2×AGL(1,ℤ/8)12yes—
1079C2×C4C2×AGL(1,ℤ/8)12yes—
1080C2×C4#57712yes—
1081C2×C4C22×#4111yescharacteristic
1082C2×C4C2×2−1+411yescharacteristic
1083C2×C4C2×2−1+411yescharacteristic
1084C2×C4#58511yescharacteristic
1085C2×C4#58511yescharacteristic
1086C2×C4#58511yescharacteristic
1087C8—22no—
1088C8—41no—
1089C8—41no—
1090C8—41no—
1091C8—41no—
1092C8—41no—
1093C8—41no—
1094C8—41no—
1095C22—22no—
1096C22—22no—
1097C22—22no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—41no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22D4×#4111yescharacteristic
1110C22#348911yescharacteristic
1111C22#348911yescharacteristic
1112C22C22×AGL(1,ℤ/8)11yescharacteristic
1113C22C2×#57711yescharacteristic
1114C22#358611yescharacteristic
1115C22#358611yescharacteristic
1116C4—22no—
1117C4—22no—
1118C4—22no—
1119C4—41no—
1120C4—42no—
1121C4—41no—
1122C4—41no—
1123C4—41no—
1124C4—41no—
1125C4—41no—
1126C4—41no—
1127C4—42no—
1128C4—41no—
1129C4—42no—
1130C4—41no—
1131C4—42no—
1132C4—41no—
1133C4—81no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4#346111yescharacteristic
1145C4#351511yescharacteristic
1146C4#355511yescharacteristic
1147C4#356611yescharacteristic
1148C2—42no—
1149C2—161no—
1150C2#3780711yescharacteristic
1151C2#6145211yescharacteristic
1152C2#6155611yescharacteristic
1153C2#6210711yescharacteristic
1154C2#6212811yescharacteristic
1155C2#6216911yescharacteristic
1156C2#6223411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
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. #39407C2semidirect
3. #33073C2semidirect
4. #31992C2semidirect
5. #31876C2semidirect
6. #31604C2semidirect
8. #31472C2semidirect
9. #31089C2semidirect
10. #30824C2semidirect
12. #30383C2semidirect
13. #30149C2semidirect
15. #28000C2semidirect
16. #27475C2semidirect
17. #27379C2semidirect
19. #27051C2semidirect
21. #26884C2semidirect
22. #26875C2semidirect
23. #26780C2semidirect
24. #26458C2semidirect
26. #26090C2semidirect
27. #25990C2semidirect
28. #23226C2semidirect
29. #22934C2semidirect
30. #22351C2semidirect
31. #21615C2semidirect

Maximal subgroups

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

subgroupindex
#394072
#362982
#330732
#319922
#318762
#316042
#314962
#314722
#310892
#308242
#306572
#303832
#301492
#280822
#280002
#274752
#273792
#273442
#270512
#270302
#268842
#268752
#267802
#264582
#264082
#260902
#259902
#232262
#229342
#223512
#216152