Finite Group Databasebeta

← #6672256

Subgroups — #6672256

Order 512.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3240C211yesmaximal, characteristic, complemented
2C22×#479C211yesmaximal, characteristic, complemented
3#36131C211yesmaximal, characteristic, complemented
4#34708C211yesmaximal, characteristic
5#32960C211yesmaximal, characteristic, complemented
6#31139C211yesmaximal, characteristic, complemented
7#31137C211yesmaximal, characteristic, complemented
8#31109C211yesmaximal, characteristic, complemented
9#31101C211yesmaximal, characteristic, complemented
10#30972C211yesmaximal, characteristic, complemented
11#30964C211yesmaximal, characteristic, complemented
12#30830C211yesmaximal, characteristic, complemented
13#30822C211yesmaximal, characteristic, complemented
14#29871C211yesmaximal, characteristic, complemented
15#29693C211yesmaximal, characteristic, complemented
16#28517C211yesmaximal, characteristic, complemented
17#28208C211yesmaximal, characteristic, complemented
18#27266C211yesmaximal, characteristic, complemented
19#27266C211yesmaximal, characteristic, complemented
20#26140C211yesmaximal, characteristic
21#26136C211yesmaximal, characteristic
22#26071C211yesmaximal, characteristic, complemented
23#26068C211yesmaximal, characteristic, complemented
24#24875C211yesmaximal, characteristic, complemented
25#24871C211yesmaximal, characteristic, complemented
26#24839C211yesmaximal, characteristic, complemented
27#24707C211yesmaximal, characteristic, complemented
28#24306C211yesmaximal, characteristic, complemented
29#24305C211yesmaximal, characteristic, complemented
30#22750C211yesmaximal, characteristic, complemented
31#22121C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C22×#125C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36#3240—28no—
37C2×#501C2211yescharacteristic
38C2×#501C2211yescharacteristic
39C2×#489C2211yescharacteristic
40C2×#489C2211yescharacteristic
41C2×#485C2211yescharacteristic
42C2×#485C2211yescharacteristic
43C2×#482C2211yescharacteristic
44C2×#482C2211yescharacteristic
45C2×#479—28no—
46C2×#479C2211yescharacteristic
47C2×#479C2211yescharacteristic
48C2×#479C2211yescharacteristic
49C2×#479C2211yescharacteristic
50C2×#479C2211yescharacteristic
51C2×#479C2211yescharacteristic
52C2×#479C2211yescharacteristic
53C2×#479C2211yescharacteristic
54C2×#479C2211yescharacteristic
55C2×#479C2211yescharacteristic
56C2×#478C2211yescharacteristic
57C2×#478C2211yescharacteristic
58C2×#478C2211yescharacteristic
59C2×#432C2211yescharacteristic
60C22×#107C2211yescharacteristic
61C22×#106C2211yescharacteristic
62C22×C4⋊C8C2211yescharacteristic
63C22×#103C2211yescharacteristic
64C22×#103C2211yescharacteristic
65#2859C2211yescharacteristic
66#2851C2211yescharacteristic
67#2851C2211yescharacteristic
68#2556—21no—
69#2556—21no—
70#2550C2211yescharacteristic
71#2550C2211yescharacteristic
72#2481—21no—
73#2469—21no—
74#2462—21no—
75#2462—21no—
76#2458—21no—
77#2453C2211yescharacteristic
78#2449—21no—
79#2449—21no—
80#2448C2211yescharacteristic
81#2443—21no—
82#2442C2211yescharacteristic
83#2441C2211yescharacteristic
84#2441C2211yescharacteristic
85#2440C2211yescharacteristic
86#2440C2211yescharacteristic
87#2436C2211yescharacteristic
88#2426C2211yescharacteristic
89#2421C2211yescharacteristic
90#2416C2211yescharacteristic
91#2409C2211yescharacteristic
92#2398—21no—
93#2396—21no—
94#2360—21no—
95#2360—21no—
96#2352C2211yescharacteristic
97#2352C2211yescharacteristic
98C4×#125C2211yescharacteristic
99C4×#124C2211yescharacteristic
100C4×C22⋊Q8C2211yescharacteristic
101C4×#121—21no—
102C4×#121C2211yescharacteristic
103#2295C2211yescharacteristic
104#2290—21no—
105C42×D4C2211yescharacteristic
106#2097C2211yescharacteristic
107#2097C2211yescharacteristic
108#2092C2211yescharacteristic
109#2092C2211yescharacteristic
110#2088C2211yescharacteristic
111#2087C2211yescharacteristic
112#2085C2211yescharacteristic
113#2085C2211yescharacteristic
114#2085C2211yescharacteristic
115#2085C2211yescharacteristic
116#2084C2211yescharacteristic
117#2083C2211yescharacteristic
118#2077C2211yescharacteristic
119#2076C2211yescharacteristic
120#2074C2211yescharacteristic
121#2074C2211yescharacteristic
122#2072C2211yescharacteristic
123#2072C2211yescharacteristic
124#2067C2211yescharacteristic
125#2065C2211yescharacteristic
126#2059C2211yescharacteristic
127#2059C2211yescharacteristic
128#2059C2211yescharacteristic
129#2059C2211yescharacteristic
130#2058C2211yescharacteristic
131#2057C2211yescharacteristic
132#2042C2211yescharacteristic
133#2042C2211yescharacteristic
134#2042C2211yescharacteristic
135#2042C2211yescharacteristic
136#2036C2211yescharacteristic
137#2036C2211yescharacteristic
138#2035C2211yescharacteristic
139#2035C2211yescharacteristic
140#2034C2211yescharacteristic
141#2033C2211yescharacteristic
142#2025C2211yescharacteristic
143#2025C2211yescharacteristic
144#2024C2211yescharacteristic
145#2024C2211yescharacteristic
146#1989C2211yescharacteristic
147#1989C2211yescharacteristic
148#1989C2211yescharacteristic
149#1959C2211yescharacteristic
150#1959C2211yescharacteristic
151#1949C2211yescharacteristic
152#1944C2211yescharacteristic
153#1944C2211yescharacteristic
154#1943C2211yescharacteristic
155#1943C2211yescharacteristic
156#1935C2211yescharacteristic
157#1935C2211yescharacteristic
158#1935C2211yescharacteristic
159#1935C2211yescharacteristic
160#1928C2211yescharacteristic
161#1928C2211yescharacteristic
162#1927C2211yescharacteristic
163#1927C2211yescharacteristic
164#1926C2211yescharacteristic
165#1925C2211yescharacteristic
166#1924C2211yescharacteristic
167#1924C2211yescharacteristic
168#1921C2211yescharacteristic
169#1920C2211yescharacteristic
170#1917C2211yescharacteristic
171#1917C2211yescharacteristic
172#1893C2211yescharacteristic
173#1893C2211yescharacteristic
174#1874C2211yescharacteristic
175#1874C2211yescharacteristic
176#1873C2211yescharacteristic
177#1873C2211yescharacteristic
178#1869C2211yescharacteristic
179#1869C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1854C2211yescharacteristic
185#1854C2211yescharacteristic
186#1853C2211yescharacteristic
187#1853C2211yescharacteristic
188#1852C2211yescharacteristic
189#1852C2211yescharacteristic
190#1847C2211yescharacteristic
191#1847C2211yescharacteristic
192#1831C2211yescharacteristic
193#1808C2211yescharacteristic
194#1807C2211yescharacteristic
195#1805C2211yescharacteristic
196#1805C2211yescharacteristic
197#1804C2211yescharacteristic
198#1797C2211yescharacteristic
199#1797C2211yescharacteristic
200#1787C2211yescharacteristic
201#1787C2211yescharacteristic
202#1767C2211yescharacteristic
203#1752C2211yescharacteristic
204#1752C2211yescharacteristic
205C23×Q8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#533—24no—
209#533—42no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212#529—24no—
213#529—42no—
214C2×#126—21no—
215C2×#125—24no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#125—42no—
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#125C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×C4×Q8—21no—
238C2×C4×Q8—21no—
239C2×C4×Q8—21no—
240C2×C4×Q8—21no—
241C2×C4×Q8—24no—
242C2×C4×Q8—42no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4D411yescharacteristic
250C2×C4×D4D411yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×#117—21no—
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C22×C4⋊C4—21no—
257C22×C4⋊C4—21no—
258C22×C4⋊C4—21no—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C42—21no—
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265#501—24no—
266#501—24no—
267#489—24no—
268#489—24no—
269#485—24no—
270#485—24no—
271#482—24no—
272#482—24no—
273#479—24no—
274#479—24no—
275#479—24no—
276#479—24no—
277#479—24no—
278#479—24no—
279#479—24no—
280#479—24no—
281#479—42no—
282#479D418yescomplemented
283#478—24no—
284#478—24no—
285#478—42no—
286#432—24no—
287C2×#107—24no—
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#106—24no—
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×C4⋊C8—24no—
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×#103—24no—
317C2×#103—24no—
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×C22⋊C8C2311yescharacteristic
343C2×C22⋊C8C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×C22⋊C8C2311yescharacteristic
346C2×C22⋊C8C2311yescharacteristic
347C2×C22⋊C8C2311yescharacteristic
348C2×#97C2311yescharacteristic
349C2×#97C2311yescharacteristic
350C2×#97C2311yescharacteristic
351C2×#97C2311yescharacteristic
352#400—21no—
353#400—21no—
354#400—21no—
355#399—21no—
356#399—21no—
357#399—21no—
358#398—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#397—21no—
365#397—21no—
366#396—21no—
367#396—21no—
368#396—21no—
369#396—21no—
370#395—21no—
371#395—21no—
372#395—21no—
373#395—21no—
374#395—21no—
375#394—21no—
376#394—21no—
377#393—21no—
378#393—21no—
379#393—21no—
380#391—21no—
381#391—21no—
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#390—21no—
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#389—21no—
390#389—21no—
391#389—21no—
392#389—21no—
393#389—21no—
394#389—21no—
395#389—21no—
396#389—21no—
397#389—21no—
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#382C2311yescharacteristic
451#382C2311yescharacteristic
452#382C2311yescharacteristic
453#382C2311yescharacteristic
454#380—21no—
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461C4×C4⋊C4—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4—21no—
465C4×C4⋊C4D411yescharacteristic
466C4×C4⋊C4D411yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C22⋊C4—21no—
472C4×C22⋊C4—21no—
473C4×C22⋊C4—21no—
474C4×C22⋊C4—21no—
475C4×C22⋊C4—21no—
476C4×C22⋊C4—21no—
477C4×C22⋊C4D411yescharacteristic
478C4×C22⋊C4D411yescharacteristic
479C4×C22⋊C4D411yescharacteristic
480C4×C22⋊C4D411yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482C4×C22⋊C4C2311yescharacteristic
483#376—21no—
484C43C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
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×Q8—21no—
518C22×Q8—22no—
519C22×Q8—22no—
520C22×Q8—22no—
521C22×Q8—22no—
522C22×Q8—41no—
523C22×Q8—41no—
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×D4—21no—
527C22×D4—21no—
528C22×D4C2×D411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4C2×D411yescharacteristic
536C23×C4C2×D411yescharacteristic
537C23×C4C2×D411yescharacteristic
538C23×C4C2×D411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C22×C8—22no—
542C22×C8—22no—
543C22×C8—22no—
544C22×C8—22no—
545C22×C8—41no—
546C22×C8—41no—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C4⋊Q8—22no—
556C4⋊Q8—22no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559#126—44no—
560#125—22no—
561#125—22no—
562#125—22no—
563#125—22no—
564#125—22no—
565#125—22no—
566#125—22no—
567#125—22no—
568#125—41no—
569#125—41no—
570#125—41no—
571#125—44no—
572#125—44no—
573#125C2×D414yes—
574#124—22no—
575#124—22no—
576#124—41no—
577#124—41no—
578#123—44no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—44no—
582C22⋊Q8—44no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—44no—
586C22⋊Q8—44no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—41no—
591#121—44no—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—44no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×Q8—44no—
601C4×Q8—44no—
602C4×Q8—44no—
603C4×Q8C2×D414yes—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—44no—
609C4×D4—42no—
610C4×D4—42no—
611C4×D4—44no—
612#117—22no—
613#117—22no—
614#117—44no—
615#117—41no—
616#117—41no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—21no—
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—41no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—44no—
661C2×C4⋊C4—44no—
662C2×C4⋊C4—44no—
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C42—21no—
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—44no—
720C2×C42C2×D411yescharacteristic
721C2×C42C2×D411yescharacteristic
722C2×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D411yescharacteristic
726C2×C42C2×D411yescharacteristic
727C2×C42C2×D411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733#107—22no—
734#107—22no—
735#107—22no—
736#107—22no—
737#107—22no—
738#107—22no—
739#107—41no—
740#107—41no—
741#107—41no—
742#107C2×D414yes—
743#106—22no—
744#106—22no—
745#106—22no—
746#106—22no—
747#106—22no—
748#106—22no—
749#106—41no—
750#106—41no—
751#106—41no—
752#106C2×D414yes—
753C4⋊C8—22no—
754C4⋊C8—22no—
755C4⋊C8—22no—
756C4⋊C8—22no—
757C4⋊C8—22no—
758C4⋊C8C2×D414yes—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103C2×D414yes—
774#103C2×D414yes—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783C22⋊C8—22no—
784C22⋊C8—22no—
785C22⋊C8—22no—
786C22⋊C8—22no—
787C22⋊C8—41no—
788C22⋊C8—41no—
789#97—22no—
790#97—22no—
791#97—41no—
792#97—41no—
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#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834C24—21no—
835C24C22×D411yescharacteristic
836C24C22×D411yescharacteristic
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—28no—
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—42no—
849C2×Q8—42no—
850C2×Q8—42no—
851C2×Q8—42no—
852C2×Q8—44no—
853C2×Q8—44no—
854C2×Q8—44no—
855C2×Q8—42no—
856C2×Q8—42no—
857C2×Q8—42no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×Q8C22×D412yes—
861C2×Q82−1+412yes—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—81no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—22no—
897C22×C4—22no—
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—21no—
907C22×C4—21no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
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×C42−1+412yes—
942C22×C42−1+412yes—
943C22×C4C2511yescharacteristic
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×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—44no—
967C2×C8—44no—
968C2×C8C22×D412yes—
969C2×C8C22×D412yes—
970C4⋊C4—22no—
971C4⋊C4—24no—
972C4⋊C4—24no—
973C4⋊C4—24no—
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—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—21no—
997C4⋊C4—41no—
998C4⋊C4—41no—
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—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4C22×D412yes—
1034C4⋊C4C22×D412yes—
1035C4⋊C4C22×D412yes—
1036C22⋊C4—22no—
1037C22⋊C4—22no—
1038C22⋊C4—22no—
1039C22⋊C4—22no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C42—22no—
1064C42—22no—
1065C42—22no—
1066C42—22no—
1067C42—24no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—41no—
1077C42—41no—
1078C42—41no—
1079C42—41no—
1080C42—42no—
1081C42—42no—
1082C42—42no—
1083C42—42no—
1084C42—42no—
1085C42—42no—
1086C42—81no—
1087C42—81no—
1088C42C22×D412yes—
1089C42H(5,𝔽2)12yes—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23#53612yes—
1109C23#57512yes—
1110C23#57512yes—
1111C23C23×D411yescharacteristic
1112Q8—22no—
1113Q8—22no—
1114Q8—22no—
1115Q8—22no—
1116Q8—48no—
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—84no—
1122Q8—84no—
1123D4—44no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—84no—
1129D4—84no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—22no—
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—44no—
1173C2×C4—44no—
1174C2×C4—48no—
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—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—82no—
1220C2×C4—82no—
1221C2×C4—84no—
1222C2×C4—84no—
1223C2×C4—84no—
1224C2×C4—84no—
1225C2×C4#53612yes—
1226C2×C4D4212yes—
1227C2×C4D4212yes—
1228C2×C4C23×D411yescharacteristic
1229C2×C4C2×H(5,𝔽2)11yescharacteristic
1230C2×C4C2×2−1+411yescharacteristic
1231C2×C4C2×2−1+411yescharacteristic
1232C2×C4C2×2−1+411yescharacteristic
1233C2×C4#58511yescharacteristic
1234C8—22no—
1235C8—22no—
1236C8—41no—
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C22—22no—
1243C22—22no—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—22no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22#324014yescomplemented
1263C22C2×#53611yescharacteristic
1264C22C2×D4211yescharacteristic
1265C22#348911yescharacteristic
1266C22C2×#57511yescharacteristic
1267C22C2×#57511yescharacteristic
1268C22#358411yescharacteristic
1269C22#358611yescharacteristic
1270C4—22no—
1271C4—22no—
1272C4—22no—
1273C4—41no—
1274C4—42no—
1275C4—42no—
1276C4—41no—
1277C4—41no—
1278C4—42no—
1279C4—42no—
1280C4—41no—
1281C4—41no—
1282C4—42no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4#348611yescharacteristic
1298C4#348911yescharacteristic
1299C4#353811yescharacteristic
1300C4#354111yescharacteristic
1301C2—24no—
1302C2—81no—
1303C2—161no—
1304C2#3765111yescharacteristic
1305C2C2×#324011yescharacteristic
1306C2#6089111yescharacteristic
1307C2#6103011yescharacteristic
1308C2#6106811yescharacteristic
1309C2#6212011yescharacteristic
1310C2#6214011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2416C22
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. C2×#3240C2semidirect
2. C22×#479C2semidirect
3. #36131C2semidirect
5. #32960C2semidirect
6. #31139C2semidirect
7. #31137C2semidirect
8. #31109C2semidirect
9. #31101C2semidirect
10. #30972C2semidirect
11. #30964C2semidirect
12. #30830C2semidirect
13. #30822C2semidirect
14. #29871C2semidirect
15. #29693C2semidirect
16. #28517C2semidirect
17. #28208C2semidirect
18. #27266C2semidirect
19. #27266C2semidirect
22. #26071C2semidirect
23. #26068C2semidirect
24. #24875C2semidirect
25. #24871C2semidirect
26. #24839C2semidirect
27. #24707C2semidirect
28. #24306C2semidirect
29. #24305C2semidirect
30. #22750C2semidirect
31. #22121C2semidirect
282. #479D4semidirect
1262. C22#3240semidirect

Maximal subgroups

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

subgroupindex
C2×#32402
C22×#4792
#361312
#347082
#329602
#311392
#311372
#311092
#311012
#309722
#309642
#308302
#308222
#298712
#296932
#285172
#282082
#272662
#261402
#261362
#260712
#260682
#248752
#248712
#248392
#247072
#243062
#243052
#227502
#221212