Finite Group Databasebeta

← #7589060

Subgroups — #7589060

Order 512.

1277 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45174C211yesmaximal, characteristic
2#35919C211yesmaximal, characteristic
3#32497C211yesmaximal, characteristic, complemented
4#32160C211yesmaximal, characteristic, complemented
5#32114C211yesmaximal, characteristic
6#30795C211yesmaximal, characteristic
7#29525C211yesmaximal, characteristic, complemented
8#29438C211yesmaximal, characteristic, complemented
9#29049C211yesmaximal, characteristic
10#28985C211yesmaximal, characteristic
11#28892C211yesmaximal, characteristic, complemented
12#27459C211yesmaximal, characteristic
13#27444C211yesmaximal, characteristic, complemented
14#27164C211yesmaximal, characteristic
15#27142C211yesmaximal, characteristic, complemented
16#27082C211yesmaximal, characteristic, complemented
17#27028C211yesmaximal, characteristic, complemented
18#26807C211yesmaximal, characteristic
19#26789C211yesmaximal, characteristic
20#26718C211yesmaximal, characteristic, complemented
21#26621C211yesmaximal, characteristic
22#26489C211yesmaximal, characteristic, complemented
23#26473C211yesmaximal, characteristic, complemented
24#26418C211yesmaximal, characteristic
25#23289C211yesmaximal, characteristic
26#23168C211yesmaximal, characteristic, complemented
27#23074C211yesmaximal, characteristic, complemented
28#22934C211yesmaximal, characteristic
29#22932C211yesmaximal, characteristic
30#21626C211yesmaximal, characteristic, complemented
31#21135C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#484C2211yescharacteristic
34C2×#483C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#475C2211yescharacteristic
37C2×C4×Q16C2211yescharacteristic
38#2788—21no—
39#2776—21no—
40#2767—21no—
41#2758—21no—
42#2655—21no—
43#2645C2211yescharacteristic
44#2588—21no—
45#2577—21no—
46#2575—21no—
47#2550C2211yescharacteristic
48#2528—21no—
49#2527—21no—
50#2523—21no—
51#2514—21no—
52#2514C2211yescharacteristic
53#2514C2211yescharacteristic
54#2506C2211yescharacteristic
55#2495C2211yescharacteristic
56#2494—21no—
57#2492C2211yescharacteristic
58#2492C2211yescharacteristic
59#2489C2211yescharacteristic
60#2475—21no—
61#2453—21no—
62#2453C2211yescharacteristic
63#2451C2211yescharacteristic
64#2446C2211yescharacteristic
65#2442C2211yescharacteristic
66#2429C2211yescharacteristic
67#2423C2211yescharacteristic
68#2401C2211yescharacteristic
69#2396—21no—
70#2370C2211yescharacteristic
71#2370C2211yescharacteristic
72#2365C2211yescharacteristic
73#2365C2211yescharacteristic
74#2360C2211yescharacteristic
75#2360C2211yescharacteristic
76#2360C2211yescharacteristic
77#2355C2211yescharacteristic
78#2345C2211yescharacteristic
79#2344C2211yescharacteristic
80#2331C2211yescharacteristic
81#2320C2211yescharacteristic
82#2276C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2100C2211yescharacteristic
86#2097C2211yescharacteristic
87#2087C2211yescharacteristic
88#2086C2211yescharacteristic
89#2085C2211yescharacteristic
90#2077C2211yescharacteristic
91#2076C2211yescharacteristic
92#2072C2211yescharacteristic
93#2068C2211yescharacteristic
94#2068C2211yescharacteristic
95#2068C2211yescharacteristic
96#2068C2211yescharacteristic
97#2068C2211yescharacteristic
98#2066C2211yescharacteristic
99#2059C2211yescharacteristic
100#2058C2211yescharacteristic
101#2057C2211yescharacteristic
102#2056C2211yescharacteristic
103#2056C2211yescharacteristic
104#2043C2211yescharacteristic
105#2036C2211yescharacteristic
106#2035C2211yescharacteristic
107#2026C2211yescharacteristic
108#2026C2211yescharacteristic
109#2026C2211yescharacteristic
110#2024C2211yescharacteristic
111#2024C2211yescharacteristic
112#2016C2211yescharacteristic
113#2001C2211yescharacteristic
114#2001C2211yescharacteristic
115#1992C2211yescharacteristic
116#1989C2211yescharacteristic
117#1987C2211yescharacteristic
118#1987C2211yescharacteristic
119#1981C2211yescharacteristic
120#1971C2211yescharacteristic
121#1971C2211yescharacteristic
122#1969C2211yescharacteristic
123#1960C2211yescharacteristic
124#1949C2211yescharacteristic
125#1949C2211yescharacteristic
126#1947C2211yescharacteristic
127#1944C2211yescharacteristic
128#1944C2211yescharacteristic
129#1943C2211yescharacteristic
130#1942C2211yescharacteristic
131#1941C2211yescharacteristic
132#1940C2211yescharacteristic
133#1935C2211yescharacteristic
134#1935C2211yescharacteristic
135#1935C2211yescharacteristic
136#1935C2211yescharacteristic
137#1935C2211yescharacteristic
138#1933C2211yescharacteristic
139#1928C2211yescharacteristic
140#1928C2211yescharacteristic
141#1928C2211yescharacteristic
142#1928C2211yescharacteristic
143#1928C2211yescharacteristic
144#1928C2211yescharacteristic
145#1927C2211yescharacteristic
146#1927C2211yescharacteristic
147#1927C2211yescharacteristic
148#1927C2211yescharacteristic
149#1924C2211yescharacteristic
150#1923C2211yescharacteristic
151#1923C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1920C2211yescharacteristic
155#1920C2211yescharacteristic
156#1919C2211yescharacteristic
157#1919C2211yescharacteristic
158#1919C2211yescharacteristic
159#1918C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1918C2211yescharacteristic
164#1917C2211yescharacteristic
165#1917C2211yescharacteristic
166#1917C2211yescharacteristic
167#1892C2211yescharacteristic
168#1892C2211yescharacteristic
169#1892C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1872C2211yescharacteristic
175#1865C2211yescharacteristic
176#1865C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1863C2211yescharacteristic
180#1863C2211yescharacteristic
181#1853C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1850C2211yescharacteristic
185#1805C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189C4×#107C2211yescharacteristic
190C4×#106C2211yescharacteristic
191#1771C2211yescharacteristic
192#1771C2211yescharacteristic
193#1768C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197#1763C2211yescharacteristic
198C4×#103C2211yescharacteristic
199#1752C2211yescharacteristic
200#1752C2211yescharacteristic
201#1746C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125—21no—
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×C22⋊Q8C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×C4×Q8—21no—
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×#117—21no—
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224#501—24no—
225#484—24no—
226#483—24no—
227#479—24no—
228#475—24no—
229C4×Q16—24no—
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279#401—21no—
280#401—21no—
281#401—21no—
282#401D411yescharacteristic
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400D411yescharacteristic
297#400D411yescharacteristic
298#400D411yescharacteristic
299#399—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#397—21no—
309#397—21no—
310#397D411yescharacteristic
311#397D411yescharacteristic
312#397D411yescharacteristic
313#396—21no—
314#396D411yescharacteristic
315#395—21no—
316#395—21no—
317#393—21no—
318#393—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
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#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#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#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#384C2311yescharacteristic
399#383—21no—
400#383—21no—
401#383—21no—
402#383—21no—
403#382—21no—
404#382—21no—
405#382—21no—
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#381—21no—
409#380—21no—
410#380—21no—
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442#376—21no—
443#376C2311yescharacteristic
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#340C2311yescharacteristic
471#340C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8C2411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×Q8C2411yescharacteristic
489C23×C4—21no—
490C23×C4—21no—
491C23×C4C2411yescharacteristic
492C2×Q16—22no—
493C2×Q16—22no—
494C2×Q16—41no—
495C2×Q16—41no—
496C2×Q16—41no—
497C2×Q16—41no—
498C22×C8—41no—
499C22×C8—41no—
500C22×C8—41no—
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C4⋊Q8—22no—
510C4⋊Q8—22no—
511C4⋊Q8—22no—
512C4⋊Q8—41no—
513C4⋊Q8—41no—
514C4⋊Q8—41no—
515#125—22no—
516#125—22no—
517#125—41no—
518#125—41no—
519#125—82no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522C22⋊Q8—22no—
523C22⋊Q8—41no—
524C22⋊Q8—41no—
525C22⋊Q8—41no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—22no—
530C4×Q8—22no—
531C4×Q8—41no—
532C4×Q8—41no—
533C4×Q8—41no—
534C4×Q8—41no—
535C4×Q8—41no—
536C4×Q8—82no—
537#117—82no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—22no—
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⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
601C2×C22⋊C4C2×D411yescharacteristic
602C2×C22⋊C4C2×D411yescharacteristic
603C2×C22⋊C4C2×D411yescharacteristic
604C2×C22⋊C4C2×D411yescharacteristic
605C2×C22⋊C4C2×D411yescharacteristic
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42C2411yescharacteristic
623C2×C42C2411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628#107—22no—
629#107—22no—
630#107—22no—
631#107—41no—
632#107—41no—
633#107—41no—
634#107—41no—
635#107#4114yes—
636#106—22no—
637#106—22no—
638#106—22no—
639#106—22no—
640#106—41no—
641#106#4114yes—
642C4⋊C8—22no—
643C4⋊C8—22no—
644C4⋊C8—41no—
645C4⋊C8—41no—
646C4⋊C8—41no—
647#103—22no—
648#103—22no—
649#103—22no—
650#103—22no—
651#103—22no—
652#103—22no—
653#103—22no—
654#103—22no—
655#103—22no—
656#103—22no—
657#103—22no—
658#103—41no—
659#103—41no—
660#103—41no—
661#103—41no—
662#103—41no—
663#103—41no—
664#103—41no—
665#103—41no—
666#103—41no—
667C22⋊C8—22no—
668C22⋊C8—22no—
669C22⋊C8—41no—
670#97—22no—
671#97—41no—
672#97—41no—
673#97—41no—
674#97—41no—
675C4×C8—22no—
676C4×C8—41no—
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#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#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
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
746C24C22×D411yescharacteristic
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—42no—
767C2×Q8—81no—
768C2×Q8—81no—
769C2×Q8—81no—
770C2×Q82−1+412yes—
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—21no—
791C22×C4—21no—
792C22×C4—21no—
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
813Q16—44no—
814Q16—82no—
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—
839C2×C8C2×#4112yes—
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—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—41no—
863C4⋊C4—41no—
864C4⋊C4—41no—
865C4⋊C4—41no—
866C4⋊C4—41no—
867C4⋊C4—41no—
868C4⋊C4—42no—
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—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⋊C4C2×#4112yes—
904C4⋊C4C2×#4112yes—
905C22⋊C4—22no—
906C22⋊C4—22no—
907C22⋊C4—22no—
908C22⋊C4—41no—
909C22⋊C4—41no—
910C22⋊C4—41no—
911C22⋊C4—42no—
912C22⋊C4—42no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—81no—
916C22⋊C4—81no—
917C42—21no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—21no—
926C42—21no—
927C42—21no—
928C42—21no—
929C42—42no—
930C42—42no—
931C42—42no—
932C42—42no—
933C42—42no—
934C42—42no—
935C42—81no—
936C42—81no—
937C42—81no—
938C42—81no—
939C42—81no—
940C42—81no—
941C42—81no—
942C42—81no—
943C42—81no—
944C42—81no—
945C23—21no—
946C23—21no—
947C23—21no—
948C23—21no—
949C23—21no—
950C23—21no—
951C23#57812yes—
952C23C23×D411yescharacteristic
953Q8—22no—
954Q8—22no—
955Q8—41no—
956Q8—41no—
957Q8—41no—
958Q8—41no—
959Q8—41no—
960Q8—41no—
961Q8—41no—
962Q8—41no—
963Q8—41no—
964Q8—41no—
965Q8—84no—
966Q8—162no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
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—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
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—84no—
1059C2×C4—162no—
1060C2×C4C22×#4111yescharacteristic
1061C2×C4C22×#4111yescharacteristic
1062C2×C4C2×2−1+411yescharacteristic
1063C2×C4#58511yescharacteristic
1064C2×C4#58511yescharacteristic
1065C2×C4#58511yescharacteristic
1066C8—22no—
1067C8—22no—
1068C8—41no—
1069C8—41no—
1070C8—41no—
1071C8—41no—
1072C8—41no—
1073C8—41no—
1074C22—22no—
1075C22—22no—
1076C22—22no—
1077C22—41no—
1078C22—41no—
1079C22—41no—
1080C22—41no—
1081C22D4×#4111yescharacteristic
1082C22D4×#4111yescharacteristic
1083C22#348911yescharacteristic
1084C22C2×#57811yescharacteristic
1085C22#358511yescharacteristic
1086C22#358611yescharacteristic
1087C22#358611yescharacteristic
1088C4—41no—
1089C4—41no—
1090C4—41no—
1091C4—42no—
1092C4—41no—
1093C4—41no—
1094C4—42no—
1095C4—42no—
1096C4—41no—
1097C4—41no—
1098C4—42no—
1099C4—41no—
1100C4—41no—
1101C4—42no—
1102C4—41no—
1103C4—41no—
1104C4—41no—
1105C4—41no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C4—81no—
1111C4—81no—
1112C4—81no—
1113C4—81no—
1114C4—81no—
1115C4—81no—
1116C4—81no—
1117C4#348011yescharacteristic
1118C4#349511yescharacteristic
1119C4#351611yescharacteristic
1120C4#356811yescharacteristic
1121C2—42no—
1122C2#5918811yescharacteristic
1123C2#6151011yescharacteristic
1124C2#6151411yescharacteristic
1125C2#6152411yescharacteristic
1126C2#6152511yescharacteristic
1127C2#6216811yescharacteristic
1128C2#6222611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2401 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32497C2semidirect
4. #32160C2semidirect
7. #29525C2semidirect
8. #29438C2semidirect
11. #28892C2semidirect
13. #27444C2semidirect
15. #27142C2semidirect
16. #27082C2semidirect
17. #27028C2semidirect
20. #26718C2semidirect
22. #26489C2semidirect
23. #26473C2semidirect
26. #23168C2semidirect
27. #23074C2semidirect
30. #21626C2semidirect
31. #21135C2semidirect

Maximal subgroups

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

subgroupindex
#451742
#359192
#324972
#321602
#321142
#307952
#295252
#294382
#290492
#289852
#288922
#274592
#274442
#271642
#271422
#270822
#270282
#268072
#267892
#267182
#266212
#264892
#264732
#264182
#232892
#231682
#230742
#229342
#229322
#216262
#211352