Finite Group Databasebeta

← #6622440

Subgroups — #6622440

Order 512.

1304 conjugacy classes of subgroups.

The subgroup lattice has 1149 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39296C211yesmaximal, characteristic
2#39283C211yesmaximal, characteristic
3#33276C211yesmaximal, characteristic, complemented
4#33270C211yesmaximal, characteristic, complemented
5#33046C211yesmaximal, characteristic
6#29525C211yesmaximal, characteristic, complemented
7#29522C211yesmaximal, characteristic, complemented
8#29509C211yesmaximal, characteristic, complemented
9#29501C211yesmaximal, characteristic, complemented
10#29053C211yesmaximal, characteristic
11#29049C211yesmaximal, characteristic
12#28986C211yesmaximal, characteristic
13#28985C211yesmaximal, characteristic
14#28925C211yesmaximal, characteristic
15#28920C211yesmaximal, characteristic
16#28868C211yesmaximal, characteristic
17#28863C211yesmaximal, characteristic
18#28796C211yesmaximal, characteristic, complemented
19#28417C211yesmaximal, characteristic, complemented
20#27782C211yesmaximal, characteristic, complemented
21#27742C211yesmaximal, characteristic, complemented
22#24718C211yesmaximal, characteristic
23#24664C211yesmaximal, characteristic
24#23221C211yesmaximal, characteristic, complemented
25#23110C211yesmaximal, characteristic, complemented
26#22981C211yesmaximal, characteristic, complemented
27#22761C211yesmaximal, characteristic, complemented
28#21657C211yesmaximal, characteristic, complemented
29#21645C211yesmaximal, characteristic, complemented
30#21537C211yesmaximal, characteristic
31#20475C211yesmaximal, characteristic
32C2×#491C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#475C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#462C2211yescharacteristic
38C2×C4×Q16C2211yescharacteristic
39C2×#433C2211yescharacteristic
40C2×#405C2211yescharacteristic
41#2863C2211yescharacteristic
42#2863C2211yescharacteristic
43#2810—21no—
44#2802—21no—
45#2798—21no—
46#2777—21no—
47#2772—21no—
48#2766—21no—
49#2762—21no—
50#2759—21no—
51#2645C2211yescharacteristic
52#2645C2211yescharacteristic
53#2628C2211yescharacteristic
54#2621C2211yescharacteristic
55#2605—21no—
56#2596—21no—
57#2596—21no—
58#2594—21no—
59#2590—21no—
60#2585—21no—
61#2570C2211yescharacteristic
62#2568C2211yescharacteristic
63#2550C2211yescharacteristic
64#2546C2211yescharacteristic
65#2532—21no—
66#2514—21no—
67#2495C2211yescharacteristic
68#2494C2211yescharacteristic
69#2492C2211yescharacteristic
70#2489C2211yescharacteristic
71#2429C2211yescharacteristic
72#2429C2211yescharacteristic
73#2423C2211yescharacteristic
74#2421C2211yescharacteristic
75#2369C2211yescharacteristic
76#2365C2211yescharacteristic
77#2356C2211yescharacteristic
78#2351C2211yescharacteristic
79#2331C2211yescharacteristic
80#2327C2211yescharacteristic
81#2323C2211yescharacteristic
82#2323C2211yescharacteristic
83C4×C4⋊Q8C2211yescharacteristic
84C4×#125C2211yescharacteristic
85#2298C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2097C2211yescharacteristic
89#2097C2211yescharacteristic
90#2085C2211yescharacteristic
91#2084C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2074C2211yescharacteristic
95#2072C2211yescharacteristic
96#2059C2211yescharacteristic
97#2058C2211yescharacteristic
98#2043C2211yescharacteristic
99#2043C2211yescharacteristic
100#2036C2211yescharacteristic
101#2036C2211yescharacteristic
102#2035C2211yescharacteristic
103#2035C2211yescharacteristic
104#2026C2211yescharacteristic
105#2024C2211yescharacteristic
106#2016C2211yescharacteristic
107#2016C2211yescharacteristic
108#2001C2211yescharacteristic
109#2001C2211yescharacteristic
110#1993C2211yescharacteristic
111#1993C2211yescharacteristic
112#1992C2211yescharacteristic
113#1987C2211yescharacteristic
114#1981C2211yescharacteristic
115#1971C2211yescharacteristic
116#1971C2211yescharacteristic
117#1971C2211yescharacteristic
118#1971C2211yescharacteristic
119#1971C2211yescharacteristic
120#1969C2211yescharacteristic
121#1969C2211yescharacteristic
122#1960C2211yescharacteristic
123#1960C2211yescharacteristic
124#1960C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1944C2211yescharacteristic
128#1944C2211yescharacteristic
129#1944C2211yescharacteristic
130#1943C2211yescharacteristic
131#1943C2211yescharacteristic
132#1941C2211yescharacteristic
133#1941C2211yescharacteristic
134#1935C2211yescharacteristic
135#1935C2211yescharacteristic
136#1935C2211yescharacteristic
137#1935C2211yescharacteristic
138#1935C2211yescharacteristic
139#1935C2211yescharacteristic
140#1935C2211yescharacteristic
141#1935C2211yescharacteristic
142#1935C2211yescharacteristic
143#1935C2211yescharacteristic
144#1933C2211yescharacteristic
145#1933C2211yescharacteristic
146#1933C2211yescharacteristic
147#1933C2211yescharacteristic
148#1933C2211yescharacteristic
149#1933C2211yescharacteristic
150#1933C2211yescharacteristic
151#1933C2211yescharacteristic
152#1928C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1927C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1920C2211yescharacteristic
159#1919C2211yescharacteristic
160#1894C2211yescharacteristic
161#1894C2211yescharacteristic
162#1892C2211yescharacteristic
163#1892C2211yescharacteristic
164#1892C2211yescharacteristic
165#1892C2211yescharacteristic
166#1878C2211yescharacteristic
167#1878C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1863C2211yescharacteristic
174#1836C2211yescharacteristic
175#1835C2211yescharacteristic
176#1835C2211yescharacteristic
177#1809C2211yescharacteristic
178#1805C2211yescharacteristic
179#1805C2211yescharacteristic
180C4×#106C2211yescharacteristic
181#1771C2211yescharacteristic
182#1771C2211yescharacteristic
183#1770C2211yescharacteristic
184#1770C2211yescharacteristic
185#1763C2211yescharacteristic
186#1763C2211yescharacteristic
187#1763C2211yescharacteristic
188#1763C2211yescharacteristic
189#1763C2211yescharacteristic
190#1763C2211yescharacteristic
191#1763C2211yescharacteristic
192#1763C2211yescharacteristic
193C4×#103C2211yescharacteristic
194C4×#103C2211yescharacteristic
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1752C2211yescharacteristic
198#1752C2211yescharacteristic
199#1746C2211yescharacteristic
200#1745C2211yescharacteristic
201#1726C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×#117C2311yescharacteristic
225#491—24no—
226#487—24no—
227#487—24no—
228#475—24no—
229#470—24no—
230#462—24no—
231C4×Q16—24no—
232#433—24no—
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272#405—24no—
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287#401—21no—
288#401—21no—
289#401—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#399—21no—
305#399—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#396—21no—
322#396—21no—
323#395—21no—
324#395—21no—
325#393—21no—
326#393—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
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#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388D411yescharacteristic
385#388D411yescharacteristic
386#388D411yescharacteristic
387#388D411yescharacteristic
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387D411yescharacteristic
414#387D411yescharacteristic
415#387D411yescharacteristic
416#387D411yescharacteristic
417#384C2311yescharacteristic
418#383—21no—
419#383—21no—
420#383—21no—
421#383—21no—
422#382—21no—
423#382—21no—
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450#376—21no—
451#376C2311yescharacteristic
452C43C2311yescharacteristic
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#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8C2411yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×Q8C2411yescharacteristic
492C22×Q8C2411yescharacteristic
493C23×C4C2411yescharacteristic
494C2×Q16—22no—
495C2×Q16—22no—
496C2×Q16—22no—
497C2×Q16—22no—
498C2×Q16—41no—
499C2×Q16—41no—
500C2×Q16—41no—
501C2×Q16—41no—
502C2×Q16—41no—
503C2×M16—22no—
504C2×M16—22no—
505C2×M16—41no—
506C22×C8—22no—
507C22×C8—41no—
508C22×C8—41no—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C4⋊Q8—22no—
518C4⋊Q8—22no—
519C4⋊Q8—22no—
520C4⋊Q8—22no—
521C4⋊Q8—22no—
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527#125—22no—
528#125—41no—
529C22⋊Q8—22no—
530C22⋊Q8—22no—
531C22⋊Q8—41no—
532C22⋊Q8—41no—
533C22⋊Q8—41no—
534C22⋊Q8—41no—
535C22⋊Q8—41no—
536C22⋊Q8—41no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×Q8—41no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×Q8—41no—
549#117—22no—
550#117—22no—
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—21no—
584C2×C4⋊C4—21no—
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×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⋊C4C2×D411yescharacteristic
612C2×C22⋊C4C2×D411yescharacteristic
613C2×C22⋊C4C2×D411yescharacteristic
614C2×C22⋊C4C2×D411yescharacteristic
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42C2×D411yescharacteristic
630C2×C42C2×D411yescharacteristic
631C2×C42C2×D411yescharacteristic
632C2×C42C2×D411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639#107—22no—
640#107—41no—
641#107—41no—
642#106—22no—
643#106—22no—
644#106—22no—
645#106—41no—
646#106—41no—
647#106—41no—
648C4⋊C8—22no—
649C4⋊C8#4114yes—
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—22no—
659#103—22no—
660#103—22no—
661#103—22no—
662#103—22no—
663#103—22no—
664#103—22no—
665#103—22no—
666#103—22no—
667#103—41no—
668#103—41no—
669#103—41no—
670#103—41no—
671#103—41no—
672#103—41no—
673#103—41no—
674#103—41no—
675#103#4114yes—
676C22⋊C8—22no—
677C22⋊C8—22no—
678#97—22no—
679#97—22no—
680#97—22no—
681#97—22no—
682#97—41no—
683#97—41no—
684#97—41no—
685#97—41no—
686#97—41no—
687C4×C8—22no—
688C4×C8—22no—
689C4×C8—22no—
690C4×C8—41no—
691C4×C8#4114yes—
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#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#95—21no—
747#95—21no—
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
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760C24C22×D411yescharacteristic
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—42no—
785C2×Q8—42no—
786C2×Q8—81no—
787C2×Q8—81no—
788C2×Q8—81no—
789C2×Q8—81no—
790C2×Q8C2×#4112yes—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C2511yescharacteristic
827Q16—44no—
828Q16—82no—
829Q16—82no—
830M16—44no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—44no—
851C2×C8C2×#4112yes—
852C2×C8C2×#4112yes—
853C2×C8C2×#4112yes—
854C2×C8C2×#4112yes—
855C2×C8C2×#4112yes—
856C4⋊C4—22no—
857C4⋊C4—22no—
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—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—41no—
882C4⋊C4—41no—
883C4⋊C4—41no—
884C4⋊C4—41no—
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—42no—
901C4⋊C4—42no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4C2×#4112yes—
920C22⋊C4—22no—
921C22⋊C4—22no—
922C22⋊C4—41no—
923C22⋊C4—41no—
924C22⋊C4—41no—
925C22⋊C4—41no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—41no—
945C42—41no—
946C42—41no—
947C42—41no—
948C42—42no—
949C42—42no—
950C42—42no—
951C42—81no—
952C42—81no—
953C42—81no—
954C42—81no—
955C42—81no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42—81no—
960C42C2×#4112yes—
961C42C2×#4112yes—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23C23×D411yescharacteristic
970Q8—22no—
971Q8—22no—
972Q8—41no—
973Q8—41no—
974Q8—41no—
975Q8—41no—
976Q8—41no—
977Q8—41no—
978Q8—41no—
979Q8—41no—
980Q8—41no—
981Q8—41no—
982Q8—41no—
983Q8—41no—
984Q8—41no—
985Q8—41no—
986Q8—162no—
987Q8—162no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4#53212yes—
1078C2×C4#53212yes—
1079C2×C4C22×#4111yescharacteristic
1080C2×C4C22×#4111yescharacteristic
1081C2×C4C22×#4111yescharacteristic
1082C2×C4#58511yescharacteristic
1083C2×C4#58511yescharacteristic
1084C2×C4#58511yescharacteristic
1085C8—22no—
1086C8—22no—
1087C8—22no—
1088C8—22no—
1089C8—22no—
1090C8—41no—
1091C8—41no—
1092C8—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—41no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22C2×#53211yescharacteristic
1101C22D4×#4111yescharacteristic
1102C22#350011yescharacteristic
1103C22#358611yescharacteristic
1104C22#358611yescharacteristic
1105C22#358611yescharacteristic
1106C22#358611yescharacteristic
1107C4—22no—
1108C4—22no—
1109C4—41no—
1110C4—41no—
1111C4—41no—
1112C4—41no—
1113C4—41no—
1114C4—41no—
1115C4—42no—
1116C4—41no—
1117C4—41no—
1118C4—41no—
1119C4—41no—
1120C4—41no—
1121C4—42no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C4—81no—
1127C4—81no—
1128C4—81no—
1129C4—81no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C4—81no—
1135C4—81no—
1136C4#347511yescharacteristic
1137C4#348011yescharacteristic
1138C4#349311yescharacteristic
1139C4#352111yescharacteristic
1140C2—81no—
1141C2#3647011yescharacteristic
1142C2#6069911yescharacteristic
1143C2#6072011yescharacteristic
1144C2#6151111yescharacteristic
1145C2#6151411yescharacteristic
1146C2#6256511yescharacteristic
1147C2#6257211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
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
3. #33276C2semidirect
4. #33270C2semidirect
6. #29525C2semidirect
7. #29522C2semidirect
8. #29509C2semidirect
9. #29501C2semidirect
18. #28796C2semidirect
19. #28417C2semidirect
20. #27782C2semidirect
21. #27742C2semidirect
24. #23221C2semidirect
25. #23110C2semidirect
26. #22981C2semidirect
27. #22761C2semidirect
28. #21657C2semidirect
29. #21645C2semidirect

Maximal subgroups

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

subgroupindex
#392962
#392832
#332762
#332702
#330462
#295252
#295222
#295092
#295012
#290532
#290492
#289862
#289852
#289252
#289202
#288682
#288632
#287962
#284172
#277822
#277422
#247182
#246642
#232212
#231102
#229812
#227612
#216572
#216452
#215372
#204752