Finite Group Databasebeta

← #6686545

Subgroups — #6686545

Order 512.

1721 conjugacy classes of subgroups.

The subgroup lattice has 1313 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3243C211yesmaximal, characteristic, complemented
2C2×#3172C211yesmaximal, characteristic, complemented
3#37766C211yesmaximal, characteristic
4#37757C211yesmaximal, characteristic, complemented
5#33218C211yesmaximal, characteristic, complemented
6#30688C211yesmaximal, characteristic, complemented
7#30687C211yesmaximal, characteristic, complemented
8#30682C211yesmaximal, characteristic, complemented
9#30681C211yesmaximal, characteristic, complemented
10#30587C211yesmaximal, characteristic, complemented
11#30582C211yesmaximal, characteristic
12#30580C211yesmaximal, characteristic, complemented
13#30573C211yesmaximal, characteristic
14#30288C211yesmaximal, characteristic, complemented
15#29856C211yesmaximal, characteristic, complemented
16#28697C211yesmaximal, characteristic, complemented
17#28629C211yesmaximal, characteristic, complemented
18#26560C211yesmaximal, characteristic, complemented
19#26559C211yesmaximal, characteristic, complemented
20#26553C211yesmaximal, characteristic, complemented
21#26550C211yesmaximal, characteristic, complemented
22#26381C211yesmaximal, characteristic, complemented
23#26378C211yesmaximal, characteristic, complemented
24#26372C211yesmaximal, characteristic, complemented
25#26371C211yesmaximal, characteristic, complemented
26#25822C211yesmaximal, characteristic, complemented
27#25675C211yesmaximal, characteristic, complemented
28#25674C211yesmaximal, characteristic, complemented
29#25613C211yesmaximal, characteristic, complemented
30#22233C211yesmaximal, characteristic, complemented
31#21106C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#529C2211yescharacteristic
36#3243—28no—
37#3172—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#500C2211yescharacteristic
41C2×#499C2211yescharacteristic
42C2×#497C2211yescharacteristic
43C2×#491C2211yescharacteristic
44C2×#489C2211yescharacteristic
45C2×#488C2211yescharacteristic
46C2×#487C2211yescharacteristic
47C2×#484C2211yescharacteristic
48C2×#485C2211yescharacteristic
49C2×#482C2211yescharacteristic
50C2×#480C2211yescharacteristic
51C2×#479C2211yescharacteristic
52C2×#477C2211yescharacteristic
53C2×#478C2211yescharacteristic
54C2×#474C2211yescharacteristic
55C2×#470C2211yescharacteristic
56C2×#470C2211yescharacteristic
57C2×#468C2211yescharacteristic
58C2×#468C2211yescharacteristic
59C2×C4×Q16C2211yescharacteristic
60C2×C4×Q16C2211yescharacteristic
61C2×C4×SD16C2211yescharacteristic
62C2×C4×SD16C2211yescharacteristic
63C2×#433C2211yescharacteristic
64C2×C4×M16C2211yescharacteristic
65#2857C2211yescharacteristic
66#2851C2211yescharacteristic
67#2729—21no—
68#2728—21no—
69#2722—21no—
70#2719—21no—
71#2718—21no—
72#2690—21no—
73#2680—21no—
74#2672—21no—
75#2660C2211yescharacteristic
76#2642C2211yescharacteristic
77#2629C2211yescharacteristic
78#2621C2211yescharacteristic
79#2537C2211yescharacteristic
80#2536C2211yescharacteristic
81#2492C2211yescharacteristic
82#2489C2211yescharacteristic
83#2477—21no—
84#2475—21no—
85#2474—21no—
86#2468—21no—
87#2453C2211yescharacteristic
88#2451C2211yescharacteristic
89#2446—21no—
90#2438—21no—
91#2425—21no—
92#2423C2211yescharacteristic
93#2422C2211yescharacteristic
94#2421—21no—
95#2421C2211yescharacteristic
96#2420C2211yescharacteristic
97#2417C2211yescharacteristic
98#2415C2211yescharacteristic
99#2362C2211yescharacteristic
100#2360C2211yescharacteristic
101Q8×C4⋊C4C2211yescharacteristic
102#2349C2211yescharacteristic
103#2331C2211yescharacteristic
104#2326C2211yescharacteristic
105#2290C2211yescharacteristic
106#2097C2211yescharacteristic
107#2097C2211yescharacteristic
108#2097C2211yescharacteristic
109#2097C2211yescharacteristic
110#2096C2211yescharacteristic
111#2096C2211yescharacteristic
112#2095C2211yescharacteristic
113#2095C2211yescharacteristic
114#2085C2211yescharacteristic
115#2085C2211yescharacteristic
116#2083C2211yescharacteristic
117#2083C2211yescharacteristic
118#2068C2211yescharacteristic
119#2068C2211yescharacteristic
120#2066C2211yescharacteristic
121#2066C2211yescharacteristic
122#2059C2211yescharacteristic
123#2059C2211yescharacteristic
124#2058C2211yescharacteristic
125#2057C2211yescharacteristic
126#2056C2211yescharacteristic
127#2056C2211yescharacteristic
128#2055C2211yescharacteristic
129#2055C2211yescharacteristic
130#2036C2211yescharacteristic
131#2036C2211yescharacteristic
132#2036C2211yescharacteristic
133#2036C2211yescharacteristic
134#2036C2211yescharacteristic
135#2036C2211yescharacteristic
136#2036C2211yescharacteristic
137#2035C2211yescharacteristic
138#2035C2211yescharacteristic
139#2035C2211yescharacteristic
140#2034C2211yescharacteristic
141#2033C2211yescharacteristic
142#2001C2211yescharacteristic
143#2001C2211yescharacteristic
144#2000C2211yescharacteristic
145#2000C2211yescharacteristic
146#1993C2211yescharacteristic
147#1992C2211yescharacteristic
148#1991C2211yescharacteristic
149#1990C2211yescharacteristic
150#1958C2211yescharacteristic
151#1956C2211yescharacteristic
152#1949C2211yescharacteristic
153#1949C2211yescharacteristic
154#1947C2211yescharacteristic
155#1947C2211yescharacteristic
156#1942C2211yescharacteristic
157#1942C2211yescharacteristic
158#1941C2211yescharacteristic
159#1941C2211yescharacteristic
160#1928C2211yescharacteristic
161#1927C2211yescharacteristic
162#1926C2211yescharacteristic
163#1925C2211yescharacteristic
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic
166#1916C2211yescharacteristic
167#1916C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1870C2211yescharacteristic
177#1870C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1862C2211yescharacteristic
189#1862C2211yescharacteristic
190#1854C2211yescharacteristic
191#1854C2211yescharacteristic
192#1853C2211yescharacteristic
193#1852C2211yescharacteristic
194#1851C2211yescharacteristic
195#1851C2211yescharacteristic
196#1847C2211yescharacteristic
197#1809C2211yescharacteristic
198#1809C2211yescharacteristic
199#1809C2211yescharacteristic
200#1809C2211yescharacteristic
201#1768C2211yescharacteristic
202#1750C2211yescharacteristic
203C4×C22⋊C8C2211yescharacteristic
204#1746C2211yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211#544—24no—
212#544—42no—
213#542—24no—
214#542—42no—
215#533—24no—
216#533—42no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222#529—24no—
223#529—42no—
224C2×#126—21no—
225C2×#126—21no—
226C2×#125—21no—
227C2×#125—21no—
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#124—21no—
232C2×#124C2311yescharacteristic
233C2×#123—21no—
234C2×#123—21no—
235C2×#123—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2311yescharacteristic
247C2×#121—21no—
248C2×#121C2311yescharacteristic
249C2×#121C2311yescharacteristic
250C2×C4×Q8—21no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×D4—21no—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×#117—21no—
262C2×#117—21no—
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C42C2311yescharacteristic
267#501—24no—
268#501—24no—
269#500—24no—
270#499—42no—
271#497—24no—
272#491—24no—
273#489D418yescomplemented
274#488—24no—
275#487—42no—
276#485—24no—
277#484—24no—
278#482—24no—
279#480—24no—
280#479—24no—
281#478—24no—
282#477—24no—
283#474—24no—
284#470—24no—
285#470—24no—
286#468—24no—
287#468—24no—
288C4×Q16—24no—
289C4×Q16—24no—
290C4×SD16—24no—
291C4×SD16—24no—
292#433—24no—
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×#106C2311yescharacteristic
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×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×C22⋊C8C2311yescharacteristic
342C2×C22⋊C8C2311yescharacteristic
343C2×C22⋊C8C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×C22⋊C8C2311yescharacteristic
346C2×C22⋊C8C2311yescharacteristic
347C4×M16—24no—
348C2×#97C2311yescharacteristic
349C2×#97C2311yescharacteristic
350C2×C4×C8C2311yescharacteristic
351C2×C4×C8C2311yescharacteristic
352C2×C4×C8C2311yescharacteristic
353C2×C4×C8C2311yescharacteristic
354#400—21no—
355#400—21no—
356#400—21no—
357#400—21no—
358#400—21no—
359#400—21no—
360#400—21no—
361#400—21no—
362#399—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#398—21no—
373#398—21no—
374#397—21no—
375#397—21no—
376#397—21no—
377#397—21no—
378#397—21no—
379#397—21no—
380#397—21no—
381#396—21no—
382#396—21no—
383#396—21no—
384#395—21no—
385#395—21no—
386#395—21no—
387#394—21no—
388#394—21no—
389#394—21no—
390#394—21no—
391#394—21no—
392#394—21no—
393#393—21no—
394#391—21no—
395#391—21no—
396#391—21no—
397#391—21no—
398#391—21no—
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#390C2311yescharacteristic
407#389—21no—
408#389—21no—
409#389—21no—
410#389—21no—
411#389—21no—
412#389—21no—
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#388—21no—
422#388—21no—
423#388—21no—
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#388D411yescharacteristic
433#388D411yescharacteristic
434#387—21no—
435#387—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#387D411yescharacteristic
445#387D411yescharacteristic
446#386—21no—
447#386—21no—
448#386D411yescharacteristic
449#386D411yescharacteristic
450#385—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#385D411yescharacteristic
459#385D411yescharacteristic
460#384—21no—
461#384C2311yescharacteristic
462#384C2311yescharacteristic
463#384C2311yescharacteristic
464#382—21no—
465#382C2311yescharacteristic
466#382C2311yescharacteristic
467#382C2311yescharacteristic
468#381—21no—
469#380—21no—
470#380—21no—
471#380—21no—
472#380—21no—
473#380C2311yescharacteristic
474#380C2311yescharacteristic
475#380C2311yescharacteristic
476#380C2311yescharacteristic
477#380C2311yescharacteristic
478#380C2311yescharacteristic
479C4×C4⋊C4—21no—
480C4×C4⋊C4—21no—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C22⋊C4—21no—
485C4×C22⋊C4C2311yescharacteristic
486C4×C22⋊C4C2311yescharacteristic
487#376C2311yescharacteristic
488C2×#95—21no—
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×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×D4—21no—
522C22×D4—21no—
523C22×D4C2×D411yescharacteristic
524C22×D4C2411yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2×D411yescharacteristic
530C23×C4C2×D411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—22no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×M16—22no—
546C2×M16—22no—
547C2×M16—22no—
548C2×M16—22no—
549C2×M16—41no—
550C2×M16—41no—
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C4⋊Q8—22no—
560C4⋊Q8—22no—
561C4⋊Q8—22no—
562C4⋊Q8—22no—
563C4⋊Q8—22no—
564C4⋊Q8—22no—
565C4⋊Q8—41no—
566C4⋊Q8—44no—
567C4⋊Q8C2×D414yes—
568#126—44no—
569#126—44no—
570#125—22no—
571#125—22no—
572#125—22no—
573#125—22no—
574#125—22no—
575#125—41no—
576#125—44no—
577#125—44no—
578#124—22no—
579#124—44no—
580#124C2×D414yes—
581#123—44no—
582#123—44no—
583#123—82no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—22no—
588C22⋊Q8—44no—
589C22⋊Q8—44no—
590C22⋊Q8—44no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—44no—
600C22⋊Q8—82no—
601#121—22no—
602#121—22no—
603#121—41no—
604#121—41no—
605#121—82no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—44no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—44no—
626#117—22no—
627#117—22no—
628#117—22no—
629#117—44no—
630#117—41no—
631#117—44no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—22no—
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—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C42—22no—
719C2×C42—22no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42C2×D411yescharacteristic
729C2×C42C2×D411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735#107—22no—
736#107—22no—
737#107—22no—
738#107—22no—
739#107—22no—
740#107—22no—
741#107—22no—
742#107—22no—
743#107—41no—
744#107—41no—
745#107—41no—
746#107—41no—
747#106—22no—
748#106—22no—
749#106—22no—
750#106—22no—
751#106—41no—
752#106—41no—
753#106—41no—
754#106—41no—
755C4⋊C8—22no—
756C4⋊C8—22no—
757C4⋊C8—22no—
758C4⋊C8—22no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103C2×D414yes—
776#103C2×D414yes—
777#102—22no—
778#102—22no—
779#102—41no—
780#102—41no—
781#102C2×D414yes—
782#102C2×D414yes—
783C22⋊C8—22no—
784C22⋊C8—22no—
785C22⋊C8—22no—
786C22⋊C8—22no—
787C22⋊C8—41no—
788C22⋊C8—41no—
789#97—22no—
790#97C2×D414yes—
791C4×C8—22no—
792C4×C8—22no—
793C4×C8—22no—
794C4×C8—22no—
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#95—21no—
829#95—21no—
830#95—21no—
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841C24—21no—
842C24C22×D411yescharacteristic
843C24C22×D411yescharacteristic
844C2×Q8—24no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—42no—
863C2×Q8—42no—
864C2×Q8—81no—
865C2×Q8—81no—
866C2×Q8—81no—
867C2×Q8—81no—
868C2×Q8—81no—
869C2×Q8—81no—
870C2×Q8C22×D412yes—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4C22×D412yes—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—22no—
890C22×C4—22no—
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—22no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
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×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C2511yescharacteristic
944Q16—44no—
945Q16—44no—
946SD16—44no—
947SD16—44no—
948M16—44no—
949M16—44no—
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—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8C22×D412yes—
971C2×C8C22×D412yes—
972C2×C82−1+412yes—
973C2×C82−1+412yes—
974C4⋊C4—24no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—22no—
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—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
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—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4C22×D412yes—
1039C4⋊C4C22×D412yes—
1040C22⋊C4—24no—
1041C22⋊C4—24no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
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—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C42—22no—
1071C42—22no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
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—22no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23C23×D411yescharacteristic
1112Q8—22no—
1113Q8—22no—
1114Q8—41no—
1115Q8—41no—
1116Q8—41no—
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—84no—
1125Q8—162no—
1126Q8—162no—
1127D4—22no—
1128D4—22no—
1129D4—41no—
1130D4—41no—
1131D4—82no—
1132D4—84no—
1133D4—162no—
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—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—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—21no—
1161C2×C4—22no—
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—44no—
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—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—82no—
1222C2×C4—84no—
1223C2×C4—162no—
1224C2×C4—162no—
1225C2×C4—162no—
1226C2×C4D4212yes—
1227C2×C4D4212yes—
1228C2×C4#57812yes—
1229C2×C4C23×D411yescharacteristic
1230C2×C4C2×H(5,𝔽2)11yescharacteristic
1231C2×C4C2×2−1+411yescharacteristic
1232C2×C4C2×2−1+411yescharacteristic
1233C2×C4#58511yescharacteristic
1234C2×C4#58511yescharacteristic
1235C8—22no—
1236C8—22no—
1237C8—22no—
1238C8—22no—
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C8—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—42no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—42no—
1257C22—41no—
1258C22—42no—
1259C22—41no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22#344911yescharacteristic
1265C22C2×D4211yescharacteristic
1266C22#349911yescharacteristic
1267C22C2×#57811yescharacteristic
1268C22#358411yescharacteristic
1269C22#358511yescharacteristic
1270C22#358611yescharacteristic
1271C4—22no—
1272C4—22no—
1273C4—22no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—42no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—42no—
1284C4—42no—
1285C4—41no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4#348911yescharacteristic
1299C4#348911yescharacteristic
1300C4#355411yescharacteristic
1301C4#355411yescharacteristic
1302C2—81no—
1303C2—81no—
1304C2—82no—
1305C2#3768011yescharacteristic
1306C2#6095711yescharacteristic
1307C2#6100411yescharacteristic
1308C2#6107411yescharacteristic
1309C2#6107611yescharacteristic
1310C2#6251911yescharacteristic
1311C2#6252311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2537C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3243C2semidirect
2. C2×#3172C2semidirect
4. #37757C2semidirect
5. #33218C2semidirect
6. #30688C2semidirect
7. #30687C2semidirect
8. #30682C2semidirect
9. #30681C2semidirect
10. #30587C2semidirect
12. #30580C2semidirect
14. #30288C2semidirect
15. #29856C2semidirect
16. #28697C2semidirect
17. #28629C2semidirect
18. #26560C2semidirect
19. #26559C2semidirect
20. #26553C2semidirect
21. #26550C2semidirect
22. #26381C2semidirect
23. #26378C2semidirect
24. #26372C2semidirect
25. #26371C2semidirect
26. #25822C2semidirect
27. #25675C2semidirect
28. #25674C2semidirect
29. #25613C2semidirect
30. #22233C2semidirect
31. #21106C2semidirect
273. #489D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32432
C2×#31722
#377662
#377572
#332182
#306882
#306872
#306822
#306812
#305872
#305822
#305802
#305732
#302882
#298562
#286972
#286292
#265602
#265592
#265532
#265502
#263812
#263782
#263722
#263712
#258222
#256752
#256742
#256132
#222332
#211062