Finite Group Databasebeta

← #6571205

Subgroups — #6571205

Order 512.

1713 conjugacy classes of subgroups.

The subgroup lattice has 1343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39153C211yesmaximal, characteristic, complemented
2#34364C211yesmaximal, characteristic
3#30138C211yesmaximal, characteristic, complemented
4#30138C211yesmaximal, characteristic, complemented
5#29940C211yesmaximal, characteristic, complemented
6#29504C211yesmaximal, characteristic, complemented
7#29504C211yesmaximal, characteristic, complemented
8#28214C211yesmaximal, characteristic, complemented
9#28210C211yesmaximal, characteristic, complemented
10#27541C211yesmaximal, characteristic, complemented
11#27536C211yesmaximal, characteristic, complemented
12#27525C211yesmaximal, characteristic, complemented
13#27520C211yesmaximal, characteristic, complemented
14#27245C211yesmaximal, characteristic, complemented
15#27238C211yesmaximal, characteristic, complemented
16#27227C211yesmaximal, characteristic, complemented
17#27224C211yesmaximal, characteristic, complemented
18#26475C211yesmaximal, characteristic, complemented
19#26472C211yesmaximal, characteristic, complemented
20#25860C211yesmaximal, characteristic
21#25332C211yesmaximal, characteristic, complemented
22#25332C211yesmaximal, characteristic, complemented
23#24211C211yesmaximal, characteristic
24#23830C211yesmaximal, characteristic, complemented
25#23828C211yesmaximal, characteristic, complemented
26#23765C211yesmaximal, characteristic, complemented
27#23231C211yesmaximal, characteristic, complemented
28#23229C211yesmaximal, characteristic, complemented
29#23106C211yesmaximal, characteristic, complemented
30#23106C211yesmaximal, characteristic, complemented
31#22635C211yesmaximal, characteristic, complemented
32C22×#127C2211yescharacteristic
33C2×#490C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#478C2211yescharacteristic, complemented
36C2×#478C2211yescharacteristic, complemented
37C2×#476C2211yescharacteristic, complemented
38C2×#474C2211yescharacteristic, complemented
39C2×#460C2211yescharacteristic
40C2×#460C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#450C2211yescharacteristic
43#2851C2211yescharacteristic
44#2789—21no—
45#2788—21no—
46#2787—21no—
47#2767—21no—
48#2645C2211yescharacteristic, complemented
49#2645C2211yescharacteristic, complemented
50#2573—21no—
51#2565C2211yescharacteristic, complemented
52#2550C2211yescharacteristic, complemented
53#2533—21no—
54#2527—21no—
55#2514—21no—
56#2497C2211yescharacteristic
57#2494C2211yescharacteristic
58#2492C2211yescharacteristic
59#2489C2211yescharacteristic
60#2380—21no—
61#2380—21no—
62#2370C2211yescharacteristic, complemented
63#2366C2211yescharacteristic
64#2366C2211yescharacteristic
65#2366C2211yescharacteristic
66#2366C2211yescharacteristic
67#2356C2211yescharacteristic, complemented
68D4×C22⋊C4—21no—
69D4×C22⋊C4—21no—
70D4×C22⋊C4C2211yescharacteristic
71D4×C22⋊C4C2211yescharacteristic
72D4×C22⋊C4C2211yescharacteristic
73D4×C22⋊C4C2211yescharacteristic
74#2331C2211yescharacteristic, complemented
75#2330C2211yescharacteristic, complemented
76#2328—21no—
77#2328—21no—
78#2328C2211yescharacteristic
79#2328C2211yescharacteristic
80#2328C2211yescharacteristic
81#2328C2211yescharacteristic
82#2308—21no—
83#2308—21no—
84C4×C22⋊Q8C2211yescharacteristic
85#2283C2211yescharacteristic
86#2283C2211yescharacteristic
87#2101C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2076C2211yescharacteristic
98#2076C2211yescharacteristic
99#2075C2211yescharacteristic
100#2074C2211yescharacteristic, complemented
101#2073C2211yescharacteristic, complemented
102#2073C2211yescharacteristic, complemented
103#2071C2211yescharacteristic, complemented
104#2071C2211yescharacteristic, complemented
105#2067C2211yescharacteristic, complemented
106#2067C2211yescharacteristic, complemented
107#2065C2211yescharacteristic, complemented
108#2065C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2055C2211yescharacteristic, complemented
111#2055C2211yescharacteristic, complemented
112#2055C2211yescharacteristic, complemented
113#2041C2211yescharacteristic
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#2041C2211yescharacteristic
118#2041C2211yescharacteristic
119#2036C2211yescharacteristic
120#2035C2211yescharacteristic
121#2025C2211yescharacteristic, complemented
122#2025C2211yescharacteristic, complemented
123#2023C2211yescharacteristic, complemented
124#2023C2211yescharacteristic, complemented
125#2014C2211yescharacteristic
126#2014C2211yescharacteristic
127#1989C2211yescharacteristic, complemented
128#1989C2211yescharacteristic, complemented
129#1982C2211yescharacteristic
130#1982C2211yescharacteristic
131#1973C2211yescharacteristic, complemented
132#1973C2211yescharacteristic, complemented
133#1968C2211yescharacteristic, complemented
134#1968C2211yescharacteristic, complemented
135#1961C2211yescharacteristic
136#1961C2211yescharacteristic
137#1949C2211yescharacteristic, complemented
138#1949C2211yescharacteristic, complemented
139#1940C2211yescharacteristic, complemented
140#1940C2211yescharacteristic, complemented
141#1936C2211yescharacteristic, complemented
142#1936C2211yescharacteristic, complemented
143#1934C2211yescharacteristic, complemented
144#1934C2211yescharacteristic, complemented
145#1926C2211yescharacteristic, complemented
146#1926C2211yescharacteristic, complemented
147#1926C2211yescharacteristic, complemented
148#1926C2211yescharacteristic, complemented
149#1925C2211yescharacteristic, complemented
150#1925C2211yescharacteristic, complemented
151#1925C2211yescharacteristic, complemented
152#1925C2211yescharacteristic, complemented
153#1924C2211yescharacteristic
154#1924C2211yescharacteristic
155#1923C2211yescharacteristic
156#1923C2211yescharacteristic
157#1877C2211yescharacteristic, complemented
158#1877C2211yescharacteristic, complemented
159#1877C2211yescharacteristic, complemented
160#1877C2211yescharacteristic, complemented
161#1877C2211yescharacteristic, complemented
162#1877C2211yescharacteristic, complemented
163#1877C2211yescharacteristic, complemented
164#1877C2211yescharacteristic, complemented
165#1864C2211yescharacteristic, complemented
166#1864C2211yescharacteristic, complemented
167#1864C2211yescharacteristic, complemented
168#1864C2211yescharacteristic, complemented
169#1862C2211yescharacteristic, complemented
170#1862C2211yescharacteristic, complemented
171#1862C2211yescharacteristic, complemented
172#1862C2211yescharacteristic, complemented
173#1832C2211yescharacteristic, complemented
174#1832C2211yescharacteristic, complemented
175#1804C2211yescharacteristic, complemented
176#1804C2211yescharacteristic, complemented
177#1802C2211yescharacteristic, complemented
178#1802C2211yescharacteristic, complemented
179#1797C2211yescharacteristic
180#1786C2211yescharacteristic
181#1786C2211yescharacteristic
182#1786C2211yescharacteristic
183#1786C2211yescharacteristic
184#1786C2211yescharacteristic
185#1786C2211yescharacteristic
186#1776C2211yescharacteristic, complemented
187#1776C2211yescharacteristic, complemented
188#1771C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1763C2211yescharacteristic, complemented
191#1763C2211yescharacteristic, complemented
192#1762C2211yescharacteristic, complemented
193#1762C2211yescharacteristic, complemented
194#1762C2211yescharacteristic, complemented
195#1762C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic, complemented
200#1749C2211yescharacteristic
201#1746C2211yescharacteristic, complemented
202#1746C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4—21no—
205C23×D4C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127—24no—
213C2×#127—24no—
214C2×#127—21no—
215C2×#127—21no—
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4—21no—
225C2×C4×D4—21no—
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C22×C22⋊C4—21no—
237C22×C22⋊C4—21no—
238C22×C22⋊C4—21no—
239C22×C22⋊C4—21no—
240C22×C42C2311yescharacteristic
241#490—24no—
242#490—24no—
243#478—42no—
244#478—42no—
245#476—42no—
246#474—42no—
247#460—24no—
248#460—24no—
249#450—42no—
250#450—42no—
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307#401—21no—
308#401—21no—
309#401—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#397—21no—
323#397—21no—
324#396—21no—
325#395—21no—
326#393—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#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
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#387—21no—
364#387—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#386—21no—
379#386—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
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#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#384C2311yescharacteristic
414#383—21no—
415#383—21no—
416#383D411yescharacteristic
417#383D411yescharacteristic
418#382—21no—
419#382D411yescharacteristic
420#382D411yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#381—21no—
426#381D411yescharacteristic
427#381D411yescharacteristic
428#380D411yescharacteristic
429#380D411yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#379—21no—
436#379—21no—
437#379—21no—
438#379—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454#376—21no—
455#376—21no—
456#376C2311yescharacteristic
457#376C2311yescharacteristic
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#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C25—21no—
492C22×Q8—21no—
493C22×Q8C2411yescharacteristic
494C22×D4—28no—
495C22×D4—28no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—82no—
519C22×D4—82no—
520C22×D4—82no—
521C22×D4—82no—
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4C2×D411yescharacteristic
535C23×C4C2×D411yescharacteristic
536C23×C4C2411yescharacteristic
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C4⋊Q8—22no—
558C4⋊Q8—41no—
559#127—28no—
560#127—28no—
561#127—22no—
562#127—22no—
563#127—22no—
564#127—22no—
565#127—22no—
566#127—22no—
567#127#4114yes—
568#127#4114yes—
569#125—22no—
570#125—22no—
571#125—22no—
572#125—41no—
573C22⋊Q8—22no—
574C22⋊Q8—41no—
575C4×Q8—22no—
576C4×Q8—22no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—82no—
594C4×D4—82no—
595C4×D4—82no—
596C4×D4—82no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—82no—
659C2×C22⋊C4—82no—
660C2×C22⋊C4—82no—
661C2×C22⋊C4—82no—
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C42—22no—
667C2×C42—22no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42C2×D411yescharacteristic
677C2×C42C2×D411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684#107—22no—
685#107—41no—
686#107—41no—
687#107—41no—
688#106—22no—
689#106—41no—
690#106—41no—
691#106—41no—
692C4⋊C8—22no—
693C4⋊C8—22no—
694C4⋊C8—41no—
695C4⋊C8—41no—
696C4⋊C8—41no—
697C4⋊C8—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#102—22no—
703#102—22no—
704#102—22no—
705#102—22no—
706#102—22no—
707#102—22no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730C22⋊C8—41no—
731C22⋊C8—41no—
732C22⋊C8—41no—
733C22⋊C8—41no—
734#97—22no—
735#97—22no—
736#97—41no—
737#97—41no—
738C4×C8—41no—
739C4×C8—41no—
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#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793C24—24no—
794C24—24no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—42no—
800C24—42no—
801C24—42no—
802C24—42no—
803C24—81no—
804C24—81no—
805C24—81no—
806C24—81no—
807C24—81no—
808C24—81no—
809C24—81no—
810C24—81no—
811C24C22×D411yescharacteristic
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—42no—
819C2×Q8—81no—
820C2×Q8—81no—
821C2×D4—24no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—24no—
829C2×D4—24no—
830C2×D4—24no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—82no—
872C2×D4—82no—
873C2×D4—82no—
874C2×D4—82no—
875C2×D4—82no—
876C2×D4—82no—
877C2×D4—82no—
878C2×D4—82no—
879C2×D4—816no—
880C2×D4—816no—
881C2×D4C2×#4112yes—
882C2×D4C2×#4112yes—
883C2×D4C2×#4112yes—
884C2×D4C2×#4112yes—
885C22×C4—22no—
886C22×C4—21no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C2511yescharacteristic
947SD16—82no—
948SD16—82no—
949SD16—82no—
950SD16—82no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4H(5,𝔽2)12yes—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C42—22no—
1052C42—22no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—42no—
1064C42—42no—
1065C42—42no—
1066C42—81no—
1067C42—81no—
1068C42—81no—
1069C42—81no—
1070C42—81no—
1071C42C2×#4112yes—
1072C42C2×#4112yes—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—48no—
1084C23—48no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—84no—
1110C23—84no—
1111C23—84no—
1112C23—84no—
1113C23—162no—
1114C23—162no—
1115C23—162no—
1116C23—162no—
1117C23—162no—
1118C23—162no—
1119C23—162no—
1120C23—162no—
1121C23#57712yes—
1122C23C23×D411yescharacteristic
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—162no—
1128D4—22no—
1129D4—22no—
1130D4—22no—
1131D4—22no—
1132D4—22no—
1133D4—22no—
1134D4—22no—
1135D4—22no—
1136D4—48no—
1137D4—48no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—84no—
1147D4—84no—
1148D4—84no—
1149D4—84no—
1150D4—84no—
1151D4—84no—
1152D4—84no—
1153D4—84no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—44no—
1193C2×C4—44no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—162no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4—162no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4—162no—
1241C2×C4#52512yes—
1242C2×C4#52512yes—
1243C2×C4C22×#4111yescharacteristic
1244C2×C4C22×#4111yescharacteristic
1245C2×C4C2×H(5,𝔽2)11yescharacteristic
1246C2×C4#58511yescharacteristic
1247C2×C4#58511yescharacteristic
1248C2×C4#58511yescharacteristic
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—168no—
1293C22—168no—
1294C22C2×#52511yescharacteristic
1295C22#348811yescharacteristic
1296C22#350011yescharacteristic
1297C22C2×#57711yescharacteristic
1298C22#358511yescharacteristic
1299C22#358511yescharacteristic
1300C22#358511yescharacteristic
1301C4—22no—
1302C4—22no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—42no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4#351411yescharacteristic
1327C4#351411yescharacteristic
1328C4#352111yescharacteristic
1329C4#352111yescharacteristic
1330C2—42no—
1331C2—82no—
1332C2—82no—
1333C2—82no—
1334C2—82no—
1335C2#3607511yescharacteristic
1336C2#6056411yescharacteristic
1337C2#6057911yescharacteristic
1338C2#6200911yescharacteristic
1339C2#6207911yescharacteristic
1340C2#6256411yescharacteristic
1341C2#6259611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39153C2semidirect
3. #30138C2semidirect
4. #30138C2semidirect
5. #29940C2semidirect
6. #29504C2semidirect
7. #29504C2semidirect
8. #28214C2semidirect
9. #28210C2semidirect
10. #27541C2semidirect
11. #27536C2semidirect
12. #27525C2semidirect
13. #27520C2semidirect
14. #27245C2semidirect
15. #27238C2semidirect
16. #27227C2semidirect
17. #27224C2semidirect
18. #26475C2semidirect
19. #26472C2semidirect
21. #25332C2semidirect
22. #25332C2semidirect
24. #23830C2semidirect
25. #23828C2semidirect
26. #23765C2semidirect
27. #23231C2semidirect
28. #23229C2semidirect
29. #23106C2semidirect
30. #23106C2semidirect
31. #22635C2semidirect
35. C2×#478C22semidirect
36. C2×#478C22semidirect
37. C2×#476C22semidirect
38. C2×#474C22semidirect
48. #2645C22semidirect
49. #2645C22semidirect
51. #2565C22semidirect
52. #2550C22semidirect
62. #2370C22semidirect
67. #2356C22semidirect
74. #2331C22semidirect
75. #2330C22semidirect
87. #2101C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2097C22semidirect
91. #2085C22semidirect
92. #2085C22semidirect
93. #2085C22semidirect
100. #2074C22semidirect
101. #2073C22semidirect
102. #2073C22semidirect
103. #2071C22semidirect
104. #2071C22semidirect
105. #2067C22semidirect
106. #2067C22semidirect
107. #2065C22semidirect
108. #2065C22semidirect
109. #2055C22semidirect
110. #2055C22semidirect
111. #2055C22semidirect
112. #2055C22semidirect
121. #2025C22semidirect
122. #2025C22semidirect
123. #2023C22semidirect
124. #2023C22semidirect
127. #1989C22semidirect
128. #1989C22semidirect
131. #1973C22semidirect
132. #1973C22semidirect
133. #1968C22semidirect
134. #1968C22semidirect
137. #1949C22semidirect
138. #1949C22semidirect
139. #1940C22semidirect
140. #1940C22semidirect
141. #1936C22semidirect
142. #1936C22semidirect
143. #1934C22semidirect
144. #1934C22semidirect
145. #1926C22semidirect
146. #1926C22semidirect
147. #1926C22semidirect
148. #1926C22semidirect
149. #1925C22semidirect
150. #1925C22semidirect
151. #1925C22semidirect
152. #1925C22semidirect
157. #1877C22semidirect
158. #1877C22semidirect
159. #1877C22semidirect
160. #1877C22semidirect
161. #1877C22semidirect
162. #1877C22semidirect
163. #1877C22semidirect
164. #1877C22semidirect
165. #1864C22semidirect
166. #1864C22semidirect
167. #1864C22semidirect
168. #1864C22semidirect
169. #1862C22semidirect
170. #1862C22semidirect
171. #1862C22semidirect
172. #1862C22semidirect
173. #1832C22semidirect
174. #1832C22semidirect
175. #1804C22semidirect
176. #1804C22semidirect
177. #1802C22semidirect
178. #1802C22semidirect
186. #1776C22semidirect
187. #1776C22semidirect
188. #1771C22semidirect
189. #1771C22semidirect
190. #1763C22semidirect
191. #1763C22semidirect
192. #1762C22semidirect
193. #1762C22semidirect
194. #1762C22semidirect
195. #1762C22semidirect
196. C4×#102C22semidirect
197. C4×#102C22semidirect
198. C4×#102C22semidirect
199. C4×#102C22semidirect
201. #1746C22semidirect
202. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#391532
#343642
#301382
#299402
#295042
#282142
#282102
#275412
#275362
#275252
#275202
#272452
#272382
#272272
#272242
#264752
#264722
#258602
#253322
#242112
#238302
#238282
#237652
#232312
#232292
#231062
#226352