Finite Group Databasebeta

← #6569428

Subgroups — #6569428

Order 512.

1471 conjugacy classes of subgroups.

The subgroup lattice has 1273 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36499C211yesmaximal, characteristic, complemented
2#36174C211yesmaximal, characteristic, complemented
3#30323C211yesmaximal, characteristic, complemented
4#30320C211yesmaximal, characteristic, complemented
5#30217C211yesmaximal, characteristic, complemented
6#28997C211yesmaximal, characteristic, complemented
7#28993C211yesmaximal, characteristic, complemented
8#28987C211yesmaximal, characteristic, complemented
9#28983C211yesmaximal, characteristic, complemented
10#28693C211yesmaximal, characteristic, complemented
11#28579C211yesmaximal, characteristic, complemented
12#28576C211yesmaximal, characteristic, complemented
13#28379C211yesmaximal, characteristic, complemented
14#27866C211yesmaximal, characteristic, complemented
15#27859C211yesmaximal, characteristic, complemented
16#27800C211yesmaximal, characteristic, complemented
17#27797C211yesmaximal, characteristic, complemented
18#27796C211yesmaximal, characteristic, complemented
19#27794C211yesmaximal, characteristic, complemented
20#25401C211yesmaximal, characteristic
21#25399C211yesmaximal, characteristic, complemented
22#25355C211yesmaximal, characteristic, complemented
23#25353C211yesmaximal, characteristic, complemented
24#23821C211yesmaximal, characteristic, complemented
25#23764C211yesmaximal, characteristic, complemented
26#23759C211yesmaximal, characteristic, complemented
27#23107C211yesmaximal, characteristic, complemented
28#23105C211yesmaximal, characteristic, complemented
29#23078C211yesmaximal, characteristic, complemented
30#23076C211yesmaximal, characteristic, complemented
31#20556C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#501C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#469C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#467C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C2×#435C2211yescharacteristic
44#2861C2211yescharacteristic
45#2859C2211yescharacteristic
46#2855C2211yescharacteristic
47#2854C2211yescharacteristic
48#2850C2211yescharacteristic
49#2850C2211yescharacteristic
50#2596—21no—
51#2589—21no—
52#2562C2211yescharacteristic
53#2540C2211yescharacteristic
54#2538C2211yescharacteristic
55#2537C2211yescharacteristic
56#2526—21no—
57#2526—21no—
58#2518—21no—
59#2518—21no—
60#2516—21no—
61#2495—21no—
62#2492C2211yescharacteristic
63#2491C2211yescharacteristic
64#2490C2211yescharacteristic
65#2490C2211yescharacteristic
66#2489C2211yescharacteristic
67#2489C2211yescharacteristic
68#2459—21no—
69#2458—21no—
70#2455—21no—
71#2423C2211yescharacteristic
72#2422C2211yescharacteristic
73#2420—21no—
74#2374—21no—
75#2370C2211yescharacteristic
76#2367—21no—
77#2367C2211yescharacteristic
78#2363—21no—
79#2355C2211yescharacteristic
80#2354C2211yescharacteristic
81#2346—21no—
82C4×C4⋊Q8C2211yescharacteristic
83C4×#124C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85C4×#121C2211yescharacteristic
86#2283C2211yescharacteristic
87#2283C2211yescharacteristic
88C42×D4C2211yescharacteristic
89#2101C2211yescharacteristic
90#2101C2211yescharacteristic
91#2097C2211yescharacteristic
92#2092C2211yescharacteristic
93#2085C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2075C2211yescharacteristic
100#2075C2211yescharacteristic
101#2074C2211yescharacteristic
102#2074C2211yescharacteristic
103#2073C2211yescharacteristic
104#2073C2211yescharacteristic
105#2072C2211yescharacteristic
106#2071C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2036C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2035C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic
116#2033C2211yescharacteristic
117#2026C2211yescharacteristic
118#2026C2211yescharacteristic
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic
121#2024C2211yescharacteristic
122#2023C2211yescharacteristic
123#2015C2211yescharacteristic
124#2012C2211yescharacteristic
125#2001C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#1999C2211yescharacteristic
129#1992C2211yescharacteristic
130#1992C2211yescharacteristic
131#1992C2211yescharacteristic
132#1992C2211yescharacteristic
133#1973C2211yescharacteristic
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic
136#1972C2211yescharacteristic
137#1971C2211yescharacteristic
138#1971C2211yescharacteristic
139#1970C2211yescharacteristic
140#1968C2211yescharacteristic
141#1959C2211yescharacteristic
142#1959C2211yescharacteristic
143#1948C2211yescharacteristic
144#1948C2211yescharacteristic
145#1947C2211yescharacteristic
146#1947C2211yescharacteristic
147#1936C2211yescharacteristic
148#1935C2211yescharacteristic
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic
151#1928C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1926C2211yescharacteristic
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1921C2211yescharacteristic
160#1921C2211yescharacteristic
161#1920C2211yescharacteristic
162#1920C2211yescharacteristic
163#1895C2211yescharacteristic
164#1894C2211yescharacteristic
165#1894C2211yescharacteristic
166#1894C2211yescharacteristic
167#1893C2211yescharacteristic
168#1893C2211yescharacteristic
169#1893C2211yescharacteristic
170#1892C2211yescharacteristic
171#1880C2211yescharacteristic
172#1879C2211yescharacteristic
173#1878C2211yescharacteristic
174#1877C2211yescharacteristic
175#1809C2211yescharacteristic
176#1809C2211yescharacteristic
177#1808C2211yescharacteristic
178#1807C2211yescharacteristic
179#1776C2211yescharacteristic
180#1776C2211yescharacteristic
181C4×#107C2211yescharacteristic
182C4×#106C2211yescharacteristic
183#1771C2211yescharacteristic
184#1771C2211yescharacteristic
185#1767C2211yescharacteristic
186#1763C2211yescharacteristic
187#1763C2211yescharacteristic
188#1762C2211yescharacteristic
189#1762C2211yescharacteristic
190#1762C2211yescharacteristic
191#1762C2211yescharacteristic
192C4×#103C2211yescharacteristic
193C4×#103C2211yescharacteristic
194#1753C2211yescharacteristic
195#1753C2211yescharacteristic
196#1752C2211yescharacteristic
197#1752C2211yescharacteristic
198#1749C2211yescharacteristic
199C4×C22⋊C8C2211yescharacteristic
200#1745C2211yescharacteristic
201#1728C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#124—21no—
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#123—21no—
219C2×#123—21no—
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×#121—21no—
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×C4×Q8—21no—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4D411yescharacteristic
234C2×C4×D4D411yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117—21no—
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241#501—42no—
242#501—42no—
243#479—24no—
244#478—24no—
245#469—42no—
246#468—42no—
247#467—42no—
248#465—42no—
249#464—24no—
250#463—24no—
251#435—24no—
252#435—24no—
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#399—21no—
308#399—21no—
309#398—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#396—21no—
316#396—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#393—21no—
325#393—21no—
326#392—21no—
327#391—21no—
328#391—21no—
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#390—21no—
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#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
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#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—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#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#383—21no—
405#383—21no—
406#382—21no—
407#382—21no—
408#382—21no—
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#381—21no—
413#381—21no—
414#381—21no—
415#380—21no—
416#380—21no—
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4D411yescharacteristic
430C4×C4⋊C4D411yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4D411yescharacteristic
448C4×C22⋊C4D411yescharacteristic
449C4×C22⋊C4D411yescharacteristic
450C4×C22⋊C4D411yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453#376—21no—
454#376—21no—
455C43C2311yescharacteristic
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#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8C2411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4C2×D411yescharacteristic
498C22×D4C2411yescharacteristic
499C22×D4C2411yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2×D411yescharacteristic
503C23×C4C2×D411yescharacteristic
504C23×C4C2×D411yescharacteristic
505C23×C4C2×D411yescharacteristic
506C23×C4C2411yescharacteristic
507C23×C4C2411yescharacteristic
508C2×Q16—22no—
509C2×Q16—41no—
510C2×Q16—41no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×D8—22no—
518C2×D8—41no—
519C2×D8—41no—
520C2×M16—22no—
521C2×M16—22no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C22×C8—22no—
527C22×C8—22no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8—41no—
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C4⋊Q8—22no—
541C4⋊Q8—41no—
542#125—22no—
543#125—22no—
544#125—41no—
545#125—41no—
546#125—41no—
547#125—41no—
548#124—22no—
549#124—22no—
550#124—41no—
551#124—41no—
552#124—44no—
553#123—44no—
554#123—82no—
555C22⋊Q8—22no—
556C22⋊Q8—41no—
557C22⋊Q8—41no—
558C22⋊Q8—41no—
559C22⋊Q8—41no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562C22⋊Q8—41no—
563#121—22no—
564#121—41no—
565#121—44no—
566#121—41no—
567#121—41no—
568#121—41no—
569#121—41no—
570#121—41no—
571#121—41no—
572C4×Q8—22no—
573C4×Q8—22no—
574C4×Q8—41no—
575C4×Q8—41no—
576C4×Q8—82no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—42no—
584C4×D4—42no—
585C4×D4—82no—
586#117—44no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊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—21no—
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—41no—
676C2×C42—41no—
677C2×C42—41no—
678C2×C42—41no—
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692#107—22no—
693#107—22no—
694#107—22no—
695#107—22no—
696#107—41no—
697#107—41no—
698#106—22no—
699#106—22no—
700#106—22no—
701#106—22no—
702#106—41no—
703#106—41no—
704C4⋊C8#4114yes—
705C4⋊C8#4114yes—
706#103—22no—
707#103—22no—
708#103—22no—
709#103—22no—
710#103—22no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730C22⋊C8—22no—
731C22⋊C8—22no—
732C22⋊C8—22no—
733C22⋊C8—22no—
734#97—22no—
735#97—22no—
736#97—41no—
737#97—41no—
738#97—41no—
739#97—41no—
740C4×C8—41no—
741C4×C8—41no—
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#95—21no—
778#95—21no—
779#95—21no—
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786C24—21no—
787C24—21no—
788C24C22×D411yescharacteristic
789C24C22×D411yescharacteristic
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—42no—
803C2×Q8—42no—
804C2×Q8—81no—
805C2×D4—22no—
806C2×D4—22no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—41no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—81no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—81no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—41no—
861C22×C4—41no—
862C22×C4—41no—
863C22×C4—41no—
864C22×C4—41no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C2511yescharacteristic
889Q16—82no—
890SD16—82no—
891SD16—82no—
892D8—82no—
893M16—82no—
894M16—82no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—82no—
916C2×C8—82no—
917C2×C8C2×#4112yes—
918C2×C8C2×#4112yes—
919C2×C8C2×#4112yes—
920C2×C8C2×#4112yes—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—41no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4H(5,𝔽2)12yes—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—41no—
976C22⋊C4—41no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—21no—
1019C42—41no—
1020C42—41no—
1021C42—41no—
1022C42—41no—
1023C42—41no—
1024C42—41no—
1025C42—41no—
1026C42—41no—
1027C42—42no—
1028C42—42no—
1029C42—42no—
1030C42—42no—
1031C42—81no—
1032C42—81no—
1033C42—81no—
1034C42—81no—
1035C42—81no—
1036C42—81no—
1037C42C2×#4112yes—
1038C42C2×#4112yes—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23#57512yes—
1067C23C23×D411yescharacteristic
1068Q8—41no—
1069Q8—41no—
1070Q8—41no—
1071Q8—41no—
1072Q8—41no—
1073Q8—41no—
1074Q8—41no—
1075Q8—41no—
1076Q8—84no—
1077D4—44no—
1078D4—41no—
1079D4—41no—
1080D4—41no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—84no—
1087D4—162no—
1088D4—162no—
1089D4—162no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—82no—
1174C2×C4—84no—
1175C2×C4—82no—
1176C2×C4—82no—
1177C2×C4—82no—
1178C2×C4—162no—
1179C2×C4#53212yes—
1180C2×C4#53212yes—
1181C2×C4#57512yes—
1182C2×C4C22×#4111yescharacteristic
1183C2×C4C22×#4111yescharacteristic
1184C2×C4C2×H(5,𝔽2)11yescharacteristic
1185C2×C4#58511yescharacteristic
1186C2×C4#58511yescharacteristic
1187C2×C4#58511yescharacteristic
1188C8—22no—
1189C8—22no—
1190C8—22no—
1191C8—22no—
1192C8—41no—
1193C8—41no—
1194C8—41no—
1195C8—41no—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22C2×#53211yescharacteristic
1225C22#348511yescharacteristic
1226C22#348811yescharacteristic
1227C22C2×#57511yescharacteristic
1228C22C2×#57511yescharacteristic
1229C22#358511yescharacteristic
1230C22#358611yescharacteristic
1231C4—22no—
1232C4—22no—
1233C4—22no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—42no—
1242C4—41no—
1243C4—41no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4#351411yescharacteristic
1258C4#351411yescharacteristic
1259C4#352411yescharacteristic
1260C4#352411yescharacteristic
1261C2—42no—
1262C2—81no—
1263C2—161no—
1264C2—161no—
1265C2#3605111yescharacteristic
1266C2#6070211yescharacteristic
1267C2#6072111yescharacteristic
1268C2#6171411yescharacteristic
1269C2#6171511yescharacteristic
1270C2#6197211yescharacteristic
1271C2#6197411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25401C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36499C2semidirect
2. #36174C2semidirect
3. #30323C2semidirect
4. #30320C2semidirect
5. #30217C2semidirect
6. #28997C2semidirect
7. #28993C2semidirect
8. #28987C2semidirect
9. #28983C2semidirect
10. #28693C2semidirect
11. #28579C2semidirect
12. #28576C2semidirect
13. #28379C2semidirect
14. #27866C2semidirect
15. #27859C2semidirect
16. #27800C2semidirect
17. #27797C2semidirect
18. #27796C2semidirect
19. #27794C2semidirect
21. #25399C2semidirect
22. #25355C2semidirect
23. #25353C2semidirect
24. #23821C2semidirect
25. #23764C2semidirect
26. #23759C2semidirect
27. #23107C2semidirect
28. #23105C2semidirect
29. #23078C2semidirect
30. #23076C2semidirect
31. #20556C2semidirect

Maximal subgroups

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

subgroupindex
#364992
#361742
#303232
#303202
#302172
#289972
#289932
#289872
#289832
#286932
#285792
#285762
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