Finite Group Databasebeta

← #6811908

Subgroups — #6811908

Order 512.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1299 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3388C211yesmaximal, characteristic, complemented
2C2×#3183C211yesmaximal, characteristic
3#39880C211yesmaximal, characteristic, complemented
4#39139C211yesmaximal, characteristic, complemented
5#33218C211yesmaximal, characteristic, complemented
6#30819C211yesmaximal, characteristic, complemented
7#30818C211yesmaximal, characteristic, complemented
8#30812C211yesmaximal, characteristic, complemented
9#30811C211yesmaximal, characteristic, complemented
10#30691C211yesmaximal, characteristic
11#30686C211yesmaximal, characteristic, complemented
12#30684C211yesmaximal, characteristic, complemented
13#30679C211yesmaximal, characteristic
14#29693C211yesmaximal, characteristic, complemented
15#29692C211yesmaximal, characteristic, complemented
16#28822C211yesmaximal, characteristic, complemented
17#28814C211yesmaximal, characteristic, complemented
18#28545C211yesmaximal, characteristic, complemented
19#28275C211yesmaximal, characteristic, complemented
20#27801C211yesmaximal, characteristic, complemented
21#27795C211yesmaximal, characteristic, complemented
22#26261C211yesmaximal, characteristic, complemented
23#26251C211yesmaximal, characteristic, complemented
24#25045C211yesmaximal, characteristic, complemented
25#25037C211yesmaximal, characteristic, complemented
26#24692C211yesmaximal, characteristic, complemented
27#24691C211yesmaximal, characteristic, complemented
28#24347C211yesmaximal, characteristic, complemented
29#24344C211yesmaximal, characteristic, complemented
30#22819C211yesmaximal, characteristic, complemented
31#21600C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×#529C2211yescharacteristic
36#3388—28no—
37#3183—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#499C2211yescharacteristic
41C2×#499C2211yescharacteristic
42C2×#495C2211yescharacteristic
43C2×#488C2211yescharacteristic
44C2×#488C2211yescharacteristic
45C2×#479C2211yescharacteristic
46C2×#479C2211yescharacteristic
47C2×#477C2211yescharacteristic
48C2×#475C2211yescharacteristic
49C2×#478C2211yescharacteristic
50C2×#478C2211yescharacteristic
51C2×#478C2211yescharacteristic
52C2×#476C2211yescharacteristic
53C2×#470C2211yescharacteristic
54C2×#469C2211yescharacteristic
55C2×#468C2211yescharacteristic
56C2×#468C2211yescharacteristic
57C2×#446C2211yescharacteristic
58C2×#442C2211yescharacteristic
59C2×#441C2211yescharacteristic
60C2×#440C2211yescharacteristic
61C2×#440C2211yescharacteristic
62C2×#440C2211yescharacteristic
63C2×C4×SD16C2211yescharacteristic
64C2×C4×M16C2211yescharacteristic
65#2857C2211yescharacteristic
66#2851C2211yescharacteristic
67#2721—21no—
68#2721—21no—
69#2698—21no—
70#2694—21no—
71#2694—21no—
72#2689—21no—
73#2687—21no—
74#2680—21no—
75#2638—21no—
76#2621—21no—
77#2581C2211yescharacteristic
78#2565C2211yescharacteristic
79#2552C2211yescharacteristic
80#2552C2211yescharacteristic
81#2552C2211yescharacteristic
82#2550C2211yescharacteristic
83#2542—21no—
84#2542C2211yescharacteristic
85#2538C2211yescharacteristic
86#2536—21no—
87#2499—21no—
88#2492C2211yescharacteristic
89#2490C2211yescharacteristic
90#2490C2211yescharacteristic
91#2489C2211yescharacteristic
92#2484—21no—
93#2448C2211yescharacteristic
94#2448C2211yescharacteristic
95#2447C2211yescharacteristic
96#2447C2211yescharacteristic
97#2423C2211yescharacteristic
98#2423C2211yescharacteristic
99#2422C2211yescharacteristic
100#2420C2211yescharacteristic
101#2357C2211yescharacteristic
102#2355C2211yescharacteristic
103#2323—21no—
104#2322—21no—
105C4×C22⋊Q8C2211yescharacteristic
106#2096C2211yescharacteristic
107#2095C2211yescharacteristic
108#2093C2211yescharacteristic
109#2092C2211yescharacteristic
110#2074C2211yescharacteristic
111#2072C2211yescharacteristic
112#2071C2211yescharacteristic
113#2071C2211yescharacteristic
114#2068C2211yescharacteristic
115#2067C2211yescharacteristic
116#2066C2211yescharacteristic
117#2065C2211yescharacteristic
118#2059C2211yescharacteristic
119#2059C2211yescharacteristic
120#2059C2211yescharacteristic
121#2059C2211yescharacteristic
122#2059C2211yescharacteristic
123#2059C2211yescharacteristic
124#2059C2211yescharacteristic
125#2058C2211yescharacteristic
126#2056C2211yescharacteristic
127#2056C2211yescharacteristic
128#2054C2211yescharacteristic
129#2054C2211yescharacteristic
130#2042C2211yescharacteristic
131#2042C2211yescharacteristic
132#2042C2211yescharacteristic
133#2042C2211yescharacteristic
134#2036C2211yescharacteristic
135#2035C2211yescharacteristic
136#2035C2211yescharacteristic
137#2035C2211yescharacteristic
138#2034C2211yescharacteristic
139#2033C2211yescharacteristic
140#2033C2211yescharacteristic
141#2033C2211yescharacteristic
142#2026C2211yescharacteristic
143#2026C2211yescharacteristic
144#2025C2211yescharacteristic
145#2023C2211yescharacteristic
146#1993C2211yescharacteristic
147#1992C2211yescharacteristic
148#1985C2211yescharacteristic
149#1973C2211yescharacteristic
150#1973C2211yescharacteristic
151#1973C2211yescharacteristic
152#1968C2211yescharacteristic
153#1968C2211yescharacteristic
154#1968C2211yescharacteristic
155#1949C2211yescharacteristic
156#1948C2211yescharacteristic
157#1948C2211yescharacteristic
158#1948C2211yescharacteristic
159#1944C2211yescharacteristic
160#1942C2211yescharacteristic
161#1942C2211yescharacteristic
162#1942C2211yescharacteristic
163#1941C2211yescharacteristic
164#1941C2211yescharacteristic
165#1940C2211yescharacteristic
166#1928C2211yescharacteristic
167#1928C2211yescharacteristic
168#1927C2211yescharacteristic
169#1927C2211yescharacteristic
170#1926C2211yescharacteristic
171#1926C2211yescharacteristic
172#1926C2211yescharacteristic
173#1925C2211yescharacteristic
174#1916C2211yescharacteristic
175#1916C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1878C2211yescharacteristic
179#1878C2211yescharacteristic
180#1864C2211yescharacteristic
181#1863C2211yescharacteristic
182#1863C2211yescharacteristic
183#1862C2211yescharacteristic
184#1851C2211yescharacteristic
185#1851C2211yescharacteristic
186#1847C2211yescharacteristic
187#1847C2211yescharacteristic
188#1845C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1809C2211yescharacteristic
192#1809C2211yescharacteristic
193#1805C2211yescharacteristic
194#1804C2211yescharacteristic
195#1803C2211yescharacteristic
196#1802C2211yescharacteristic
197#1797C2211yescharacteristic
198#1776C2211yescharacteristic
199C4×#107C2211yescharacteristic
200#1771C2211yescharacteristic
201#1771C2211yescharacteristic
202C8×C4⋊C4C2211yescharacteristic
203#1753C2211yescharacteristic
204#1753C2211yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211#557—24no—
212#557—42no—
213#554—24no—
214#554—42no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218#529—24no—
219#529—24no—
220#529—42no—
221#529—42no—
222C2×#126—21no—
223C2×#126—21no—
224C2×#125—21no—
225C2×#125—21no—
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#123—21no—
235C2×#123—21no—
236C2×#123—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8D411yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×C4×Q8—21no—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×D4—21no—
256C2×C4×D4—21no—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×#117—21no—
262C2×#117—21no—
263C22×C4⋊C4—21no—
264C22×C42C2311yescharacteristic
265#501—24no—
266#501—24no—
267#499—24no—
268#499—24no—
269#495—24no—
270#488—24no—
271#488—24no—
272#479—24no—
273#479—24no—
274#478—24no—
275#478—24no—
276#478—42no—
277#477—42no—
278#476—24no—
279#475—24no—
280#470—24no—
281#469—24no—
282#468—24no—
283#468—24no—
284#446—24no—
285#442—24no—
286#441—24no—
287#440—24no—
288#440—24no—
289#440D418yes—
290C4×SD16—24no—
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×C22⋊C8C2311yescharacteristic
342C2×C22⋊C8C2311yescharacteristic
343C4×M16—24no—
344C2×#97C2311yescharacteristic
345C2×#97C2311yescharacteristic
346C2×#97C2311yescharacteristic
347C2×#97C2311yescharacteristic
348C2×C4×C8C2311yescharacteristic
349C2×C4×C8C2311yescharacteristic
350C2×C4×C8C2311yescharacteristic
351C2×C4×C8C2311yescharacteristic
352#400—21no—
353#400—21no—
354#400—21no—
355#399—21no—
356#399—21no—
357#399—21no—
358#399—21no—
359#399—21no—
360#399—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#398—21no—
365#398—21no—
366#398—21no—
367#398—21no—
368#398—21no—
369#398—21no—
370#398—21no—
371#398—21no—
372#397—21no—
373#397—21no—
374#397—21no—
375#397—21no—
376#397—21no—
377#397—21no—
378#397—21no—
379#397—21no—
380#397—21no—
381#397—21no—
382#397—21no—
383#396—21no—
384#396—21no—
385#395—21no—
386#395—21no—
387#394—21no—
388#394—21no—
389#394—21no—
390#394—21no—
391#393—21no—
392#391—21no—
393#391—21no—
394#391—21no—
395#391D411yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#390—21no—
403#390—21no—
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#389—21no—
411#389—21no—
412#389—21no—
413#389—21no—
414#389—21no—
415#389D411yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#387D411yescharacteristic
447#387D411yescharacteristic
448#386—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#385D411yescharacteristic
455#385D411yescharacteristic
456#384—21no—
457#384—21no—
458#384—21no—
459#384C2311yescharacteristic
460#384C2311yescharacteristic
461#384C2311yescharacteristic
462#384C2311yescharacteristic
463#382—21no—
464#382—21no—
465#382C2311yescharacteristic
466#382C2311yescharacteristic
467#381—21no—
468#381—21no—
469#381—21no—
470#381—21no—
471#380—21no—
472#380—21no—
473#380D411yescharacteristic
474#380C2311yescharacteristic
475#380C2311yescharacteristic
476#380C2311yescharacteristic
477#380C2311yescharacteristic
478C4×C4⋊C4—21no—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C22⋊C4—21no—
487C4×C22⋊C4C2311yescharacteristic
488C4×C22⋊C4C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C22×Q8—21no—
516C22×Q8—21no—
517C22×Q8C2×D411yescharacteristic
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×D4—21no—
521C22×D4—21no—
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4C2×D411yescharacteristic
529C23×C4C2×D411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—41no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16C2×D414yes—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—41no—
543C2×M16—22no—
544C2×M16—22no—
545C2×M16—22no—
546C2×M16—22no—
547C2×M16—22no—
548C2×M16—41no—
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C4⋊Q8—22no—
558C4⋊Q8—22no—
559C4⋊Q8—22no—
560C4⋊Q8—41no—
561C4⋊Q8—44no—
562#126—44no—
563#126—44no—
564#125—22no—
565#125—22no—
566#125—22no—
567#125—22no—
568#125—22no—
569#125—22no—
570#125—22no—
571#125—41no—
572#125—41no—
573#125—41no—
574#125—41no—
575#125—41no—
576#125—44no—
577#125—44no—
578#124—22no—
579#124—22no—
580#124—41no—
581#124—41no—
582#123—44no—
583#123—44no—
584#123—44no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—42no—
588C22⋊Q8—44no—
589C22⋊Q8—44no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—44no—
593C22⋊Q8—44no—
594C22⋊Q8—82no—
595C22⋊Q8—82no—
596C22⋊Q8—82no—
597#121—22no—
598#121—22no—
599#121—41no—
600#121—41no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—22no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—44no—
611C4×Q8C2×D414yes—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—44no—
620C4×D4—44no—
621C4×D4C2×D414yes—
622#117—44no—
623#117—44no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—44no—
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C42—21no—
715C2×C42—22no—
716C2×C42—22no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732#107—22no—
733#107—22no—
734#107—22no—
735#107—22no—
736#107—22no—
737#107—41no—
738#107—41no—
739#107—41no—
740#107—41no—
741#107C2×D414yes—
742#106—22no—
743#106—22no—
744#106—22no—
745#106—22no—
746#106—22no—
747#106—22no—
748#106—22no—
749#106—22no—
750#106—41no—
751#106—41no—
752C4⋊C8—22no—
753C4⋊C8—22no—
754C4⋊C8—22no—
755C4⋊C8—22no—
756C4⋊C8—22no—
757C4⋊C8—22no—
758#103—22no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—41no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103C2×D414yes—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102C2×D414yes—
782C22⋊C8—41no—
783C22⋊C8—41no—
784#97—22no—
785#97—22no—
786#97—22no—
787#97C2×D414yes—
788C4×C8—22no—
789C4×C8—22no—
790C4×C8—22no—
791C4×C8—22no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834C24—21no—
835C24—21no—
836C24C22×D411yescharacteristic
837C2×Q8—22no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—41no—
850C2×Q8—41no—
851C2×Q8—42no—
852C2×Q8—42no—
853C2×Q8—42no—
854C2×Q8—42no—
855C2×Q8—81no—
856C2×Q8—81no—
857C2×Q8C22×D412yes—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4C22×D412yes—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—24no—
888C22×C4—21no—
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—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C2511yescharacteristic
928Q16—44no—
929SD16—28no—
930SD16—44no—
931D8—44no—
932M16—44no—
933M16—44no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8C22×D412yes—
954C2×C8C22×D412yes—
955C2×C82−1+412yes—
956C2×C82−1+412yes—
957C2×C82−1+412yes—
958C4⋊C4—24no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—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—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4C22×D412yes—
1026C4⋊C4C22×D412yes—
1027C22⋊C4—24no—
1028C22⋊C4—22no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C42—22no—
1060C42—22no—
1061C42—24no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—42no—
1073C42—42no—
1074C42—42no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42C22×D412yes—
1080C42H(5,𝔽2)12yes—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—22no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
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—
1102C23C23×D411yescharacteristic
1103Q8—22no—
1104Q8—22no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—82no—
1112Q8—84no—
1113Q8—162no—
1114D4—22no—
1115D4—22no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—84no—
1123D4—84no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—22no—
1152C2×C4—21no—
1153C2×C4—22no—
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—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—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
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—82no—
1207C2×C4—82no—
1208C2×C4—84no—
1209C2×C4—84no—
1210C2×C4—84no—
1211C2×C4—162no—
1212C2×C4D4212yes—
1213C2×C4D4212yes—
1214C2×C4#57512yes—
1215C2×C4C23×D411yescharacteristic
1216C2×C4C2×H(5,𝔽2)11yescharacteristic
1217C2×C4C2×2−1+411yescharacteristic
1218C2×C4C2×2−1+411yescharacteristic
1219C2×C4C2×2−1+411yescharacteristic
1220C2×C4#58511yescharacteristic
1221C8—22no—
1222C8—22no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C8#53614yes—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—42no—
1233C22—42no—
1234C22—41no—
1235C22—41no—
1236C22—42no—
1237C22—41no—
1238C22—41no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22C2×D4211yescharacteristic
1251C22#349711yescharacteristic
1252C22#349911yescharacteristic
1253C22C2×#57511yescharacteristic
1254C22#358411yescharacteristic
1255C22#358511yescharacteristic
1256C22#358611yescharacteristic
1257C4—22no—
1258C4—22no—
1259C4—22no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—42no—
1270C4—42no—
1271C4—41no—
1272C4—42no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4C2×#53611yescharacteristic
1285C4#348911yescharacteristic
1286C4#354711yescharacteristic
1287C4#355011yescharacteristic
1288C2—81no—
1289C2—82no—
1290C2—161no—
1291C2#3934311yescharacteristic
1292C2#6107011yescharacteristic
1293C2#6107311yescharacteristic
1294C2#6239611yescharacteristic
1295C2#6241011yescharacteristic
1296C2#6248411yescharacteristic
1297C2#6249811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#469C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3388C2semidirect
3. #39880C2semidirect
4. #39139C2semidirect
5. #33218C2semidirect
6. #30819C2semidirect
7. #30818C2semidirect
8. #30812C2semidirect
9. #30811C2semidirect
11. #30686C2semidirect
12. #30684C2semidirect
14. #29693C2semidirect
15. #29692C2semidirect
16. #28822C2semidirect
17. #28814C2semidirect
18. #28545C2semidirect
19. #28275C2semidirect
20. #27801C2semidirect
21. #27795C2semidirect
22. #26261C2semidirect
23. #26251C2semidirect
24. #25045C2semidirect
25. #25037C2semidirect
26. #24692C2semidirect
27. #24691C2semidirect
28. #24347C2semidirect
29. #24344C2semidirect
30. #22819C2semidirect
31. #21600C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33882
C2×#31832
#398802
#391392
#332182
#308192
#308182
#308122
#308112
#306912
#306862
#306842
#306792
#296932
#296922
#288222
#288142
#285452
#282752
#278012
#277952
#262612
#262512
#250452
#250372
#246922
#246912
#243472
#243442
#228192
#216002