Finite Group Databasebeta

← #6627339

Subgroups — #6627339

Order 512.

1985 conjugacy classes of subgroups.

The subgroup lattice has 1394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3401C211yesmaximal, characteristic, complemented
2C22×#446C211yesmaximal, characteristic, complemented
3#36580C211yesmaximal, characteristic, complemented
4#36579C211yesmaximal, characteristic, complemented
5#33184C211yesmaximal, characteristic, complemented
6#33183C211yesmaximal, characteristic
7#33173C211yesmaximal, characteristic, complemented
8#28747C211yesmaximal, characteristic, complemented
9#28746C211yesmaximal, characteristic, complemented
10#28742C211yesmaximal, characteristic, complemented
11#28278C211yesmaximal, characteristic, complemented
12#28276C211yesmaximal, characteristic, complemented
13#28270C211yesmaximal, characteristic, complemented
14#25311C211yesmaximal, characteristic, complemented
15#25310C211yesmaximal, characteristic, complemented
16#25309C211yesmaximal, characteristic, complemented
17#25308C211yesmaximal, characteristic, complemented
18#25299C211yesmaximal, characteristic, complemented
19#25298C211yesmaximal, characteristic, complemented
20#24755C211yesmaximal, characteristic, complemented
21#24755C211yesmaximal, characteristic, complemented
22#24754C211yesmaximal, characteristic, complemented
23#24754C211yesmaximal, characteristic, complemented
24#24753C211yesmaximal, characteristic, complemented
25#24751C211yesmaximal, characteristic, complemented
26#22730C211yesmaximal, characteristic, complemented
27#22549C211yesmaximal, characteristic, complemented
28#22548C211yesmaximal, characteristic, complemented
29#21527C211yesmaximal, characteristic, complemented
30#21526C211yesmaximal, characteristic, complemented
31C4×#465C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×#556C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#3401—28no—
36C2×#497C2211yescharacteristic
37C2×#496C2211yescharacteristic
38C2×#495C2211yescharacteristic
39C2×#467C2211yescharacteristic
40C2×#467C2211yescharacteristic
41C2×#466C2211yescharacteristic
42C2×#466C2211yescharacteristic
43C2×#465C2211yescharacteristic
44C2×#465C2211yescharacteristic
45C2×#465C2211yescharacteristic
46C2×#465C2211yescharacteristic
47C2×#465C2211yescharacteristic
48C2×#464C2211yescharacteristic
49C2×#464C2211yescharacteristic
50C2×#460C2211yescharacteristic
51C2×#463C2211yescharacteristic
52C2×#463C2211yescharacteristic
53C2×#461C2211yescharacteristic
54C2×#446—28no—
55C2×#446C2211yescharacteristic
56C2×#446C2211yescharacteristic
57C2×#446C2211yescharacteristic
58C2×#446C2211yescharacteristic
59C2×#446C2211yescharacteristic
60C2×#446C2211yescharacteristic
61C2×#446C2211yescharacteristic
62C2×#446C2211yescharacteristic
63C2×#442C2211yescharacteristic
64C2×#441C2211yescharacteristic
65C2×C4×SD16C2211yescharacteristic
66C22×C4⋊C8C2211yescharacteristic
67C22×C4⋊C8C2211yescharacteristic
68C22×C4⋊C8C2211yescharacteristic
69C22×#97C2211yescharacteristic
70C22×#97C2211yescharacteristic
71C22×C4×C8C2211yescharacteristic
72#2857C2211yescharacteristic
73#2856C2211yescharacteristic
74#2850C2211yescharacteristic
75#2850C2211yescharacteristic
76#2850C2211yescharacteristic
77#2850C2211yescharacteristic
78#2592C2211yescharacteristic
79#2592C2211yescharacteristic
80#2592C2211yescharacteristic
81#2592C2211yescharacteristic
82#2582C2211yescharacteristic
83#2581C2211yescharacteristic
84#2581C2211yescharacteristic
85#2580C2211yescharacteristic
86#2580C2211yescharacteristic
87#2568C2211yescharacteristic
88#2548C2211yescharacteristic
89#2538C2211yescharacteristic
90#2481—21no—
91#2481—21no—
92#2469—21no—
93#2469—21no—
94#2458—21no—
95#2458—21no—
96#2448—21no—
97#2443—21no—
98#2443—21no—
99#2436—21no—
100#2421—21no—
101#2409—21no—
102#2367—21no—
103#2362—21no—
104#2361—21no—
105#2355C2211yescharacteristic
106#2355C2211yescharacteristic
107#2352—21no—
108C4×C22⋊Q8C2211yescharacteristic
109C4×C22⋊Q8C2211yescharacteristic
110C4×C22⋊Q8C2211yescharacteristic
111C4×#121C2211yescharacteristic
112C4×#121C2211yescharacteristic
113C4×#121C2211yescharacteristic
114#2068C2211yescharacteristic
115#2068C2211yescharacteristic
116#2067C2211yescharacteristic
117#2067C2211yescharacteristic
118#2066C2211yescharacteristic
119#2066C2211yescharacteristic
120#2066C2211yescharacteristic
121#2066C2211yescharacteristic
122#2065C2211yescharacteristic
123#2065C2211yescharacteristic
124#2065C2211yescharacteristic
125#2065C2211yescharacteristic
126#2056C2211yescharacteristic
127#2056C2211yescharacteristic
128#2055C2211yescharacteristic
129#2055C2211yescharacteristic
130#2055C2211yescharacteristic
131#2055C2211yescharacteristic
132#2055C2211yescharacteristic
133#2055C2211yescharacteristic
134#2055C2211yescharacteristic
135#2055C2211yescharacteristic
136#2054C2211yescharacteristic
137#2054C2211yescharacteristic
138#1983C2211yescharacteristic
139#1983C2211yescharacteristic
140#1983C2211yescharacteristic
141#1983C2211yescharacteristic
142#1982C2211yescharacteristic
143#1981C2211yescharacteristic
144#1973C2211yescharacteristic
145#1973C2211yescharacteristic
146#1973C2211yescharacteristic
147#1973C2211yescharacteristic
148#1972C2211yescharacteristic
149#1972C2211yescharacteristic
150#1972C2211yescharacteristic
151#1971C2211yescharacteristic
152#1971C2211yescharacteristic
153#1971C2211yescharacteristic
154#1970C2211yescharacteristic
155#1969C2211yescharacteristic
156#1968C2211yescharacteristic
157#1968C2211yescharacteristic
158#1968C2211yescharacteristic
159#1961C2211yescharacteristic
160#1960C2211yescharacteristic
161#1959C2211yescharacteristic
162#1959C2211yescharacteristic
163#1958C2211yescharacteristic
164#1958C2211yescharacteristic
165#1949C2211yescharacteristic
166#1949C2211yescharacteristic
167#1949C2211yescharacteristic
168#1949C2211yescharacteristic
169#1948C2211yescharacteristic
170#1948C2211yescharacteristic
171#1943C2211yescharacteristic
172#1943C2211yescharacteristic
173#1941C2211yescharacteristic
174#1936C2211yescharacteristic
175#1936C2211yescharacteristic
176#1935C2211yescharacteristic
177#1935C2211yescharacteristic
178#1934C2211yescharacteristic
179#1933C2211yescharacteristic
180#1893C2211yescharacteristic
181#1893C2211yescharacteristic
182#1893C2211yescharacteristic
183#1892C2211yescharacteristic
184#1892C2211yescharacteristic
185#1892C2211yescharacteristic
186#1847C2211yescharacteristic
187#1847C2211yescharacteristic
188#1846C2211yescharacteristic
189#1807C2211yescharacteristic
190#1805C2211yescharacteristic
191#1805C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic
194#1803C2211yescharacteristic
195#1802C2211yescharacteristic
196#1776C2211yescharacteristic
197#1776C2211yescharacteristic
198C4×#106C2211yescharacteristic
199#1763C2211yescharacteristic
200#1763C2211yescharacteristic
201#1762C2211yescharacteristic
202#1762C2211yescharacteristic
203C4×#103C2211yescharacteristic
204C4×#102C2211yescharacteristic
205C23×Q8D411yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C23×C8C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#559—24no—
220#559—24no—
221#556—24no—
222#556—24no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×#127C2311yescharacteristic
225C2×#126—21no—
226C2×#126—21no—
227C2×#124—21no—
228C2×#124—21no—
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#123—21no—
234C2×#123—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×#121—21no—
241C2×#121—21no—
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×C4×Q8—24no—
246C2×C4×Q8—24no—
247C2×C4×Q8D411yescharacteristic
248C2×C4×Q8D411yescharacteristic
249C2×C4×Q8D411yescharacteristic
250C2×C4×Q8D411yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×D4—21no—
259C2×C4×D4—21no—
260C2×C4×D4—21no—
261C2×C4×D4—21no—
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×#117—21no—
266C22×C4⋊C4D411yescharacteristic
267C22×C4⋊C4D411yescharacteristic
268C22×C4⋊C4D411yescharacteristic
269C22×C42C2311yescharacteristic
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272#497—24no—
273#496—24no—
274#495—24no—
275#467—24no—
276#467—42no—
277#466—24no—
278#466—42no—
279#465—24no—
280#465—42no—
281#465—42no—
282#465—42no—
283#465—42no—
284#464—24no—
285#464—24no—
286#463—24no—
287#463—24no—
288#461—24no—
289#460—24no—
290#446—24no—
291#446—24no—
292#446—24no—
293#446—24no—
294#446—24no—
295#446—24no—
296#446—24no—
297#446D418yescomplemented
298#442—24no—
299#441—24no—
300C4×SD16—24no—
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×C4⋊C8—24no—
313C2×C4⋊C8—24no—
314C2×C4⋊C8—24no—
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320C2×C4⋊C8C2311yescharacteristic
321C2×C4⋊C8C2311yescharacteristic
322C2×C4⋊C8C2311yescharacteristic
323C2×C4⋊C8C2311yescharacteristic
324C2×C4⋊C8C2311yescharacteristic
325C2×C4⋊C8C2311yescharacteristic
326C2×C4⋊C8C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#103C2311yescharacteristic
341C2×#103C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×#102C2311yescharacteristic
351C2×#102C2311yescharacteristic
352C2×#102C2311yescharacteristic
353C2×#102C2311yescharacteristic
354C2×#102C2311yescharacteristic
355C2×#102C2311yescharacteristic
356C2×#102C2311yescharacteristic
357C2×#97—24no—
358C2×#97—24no—
359C2×#97C2311yescharacteristic
360C2×#97C2311yescharacteristic
361C2×#97C2311yescharacteristic
362C2×#97C2311yescharacteristic
363C2×#97C2311yescharacteristic
364C2×#97C2311yescharacteristic
365C2×#97C2311yescharacteristic
366C2×#97C2311yescharacteristic
367C2×C4×C8—24no—
368C2×C4×C8C2311yescharacteristic
369C2×C4×C8C2311yescharacteristic
370C2×C4×C8C2311yescharacteristic
371C2×C4×C8C2311yescharacteristic
372#400—21no—
373#400—21no—
374#400—21no—
375#400—21no—
376#399—21no—
377#399—21no—
378#398—21no—
379#398—21no—
380#397—21no—
381#397—21no—
382#397—21no—
383#397—21no—
384#396—21no—
385#396—21no—
386#395—21no—
387#395—21no—
388#394—21no—
389#394—21no—
390#393—21no—
391#393—21no—
392#393—21no—
393#393—21no—
394#393—21no—
395#393—21no—
396#391—21no—
397#391—21no—
398#391—21no—
399#391—21no—
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#391C2311yescharacteristic
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#390—21no—
410#390—21no—
411#390—21no—
412#390C2311yescharacteristic
413#390C2311yescharacteristic
414#390C2311yescharacteristic
415#390C2311yescharacteristic
416#390C2311yescharacteristic
417#390C2311yescharacteristic
418#390C2311yescharacteristic
419#390C2311yescharacteristic
420#390C2311yescharacteristic
421#389—21no—
422#389—21no—
423#389—21no—
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#388—21no—
441#388—21no—
442#388—21no—
443#388—21no—
444#388—21no—
445#388—21no—
446#388—21no—
447#388—21no—
448#388—21no—
449#387—21no—
450#387—21no—
451#387—21no—
452#387—21no—
453#387—21no—
454#387—21no—
455#387—21no—
456#387—21no—
457#387—21no—
458#387—21no—
459#387—21no—
460#386—21no—
461#386—21no—
462#386—21no—
463#386—21no—
464#386—21no—
465#386—21no—
466#386—21no—
467#386—21no—
468#386—21no—
469#386—21no—
470#386—21no—
471#385—21no—
472#385—21no—
473#385—21no—
474#385—21no—
475#385—21no—
476#385—21no—
477#385—21no—
478#384C2311yescharacteristic
479#384C2311yescharacteristic
480#382—21no—
481#382C2311yescharacteristic
482#382C2311yescharacteristic
483#382C2311yescharacteristic
484#382C2311yescharacteristic
485#380—21no—
486#380—21no—
487#380—21no—
488#380C2311yescharacteristic
489#380C2311yescharacteristic
490C4×C4⋊C4—21no—
491C4×C4⋊C4—21no—
492C4×C4⋊C4—21no—
493C4×C4⋊C4—21no—
494C4×C4⋊C4—21no—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C22⋊C4—21no—
502C4×C22⋊C4—21no—
503C4×C22⋊C4—21no—
504C4×C22⋊C4—21no—
505C4×C22⋊C4—21no—
506C4×C22⋊C4—21no—
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#340C2311yescharacteristic
512#340C2311yescharacteristic
513#340C2311yescharacteristic
514#340C2311yescharacteristic
515#340C2311yescharacteristic
516#340C2311yescharacteristic
517#340C2311yescharacteristic
518#340C2311yescharacteristic
519#340C2311yescharacteristic
520#340C2311yescharacteristic
521C22×Q8—24no—
522C22×Q8—42no—
523C22×Q8—42no—
524C22×Q8C2×D411yescharacteristic
525C22×Q8C2×D411yescharacteristic
526C22×Q8C2×D411yescharacteristic
527C22×Q8C2×D411yescharacteristic
528C22×Q8C2411yescharacteristic
529C22×Q8C2411yescharacteristic
530C22×Q8C2411yescharacteristic
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4C2411yescharacteristic
537C22×D4C2411yescharacteristic
538C22×D4C2411yescharacteristic
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C2×D411yescharacteristic
543C23×C4C2×D411yescharacteristic
544C23×C4C2×D411yescharacteristic
545C23×C4C2×D411yescharacteristic
546C23×C4C2×D411yescharacteristic
547C23×C4C2×D411yescharacteristic
548C23×C4C2411yescharacteristic
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—22no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—41no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×D8—22no—
571C2×D8—22no—
572C2×D8—22no—
573C2×D8—22no—
574C2×D8—41no—
575C2×D8—41no—
576C22×C8—22no—
577C22×C8—22no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—22no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—22no—
584C22×C8—41no—
585C22×C8—41no—
586C22×C8—41no—
587C22×C8#4114yes—
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C22×C8C2411yescharacteristic
594C22×C8C2411yescharacteristic
595C22×C8C2411yescharacteristic
596C4⋊Q8—22no—
597C4⋊Q8—22no—
598#127—22no—
599#127—22no—
600#126—44no—
601#126—44no—
602#124—22no—
603#124—22no—
604#124—22no—
605#124—22no—
606#124—22no—
607#124—22no—
608#124—22no—
609#124—22no—
610#124—44no—
611#124—44no—
612#123—44no—
613#123—44no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—22no—
619C22⋊Q8—22no—
620C22⋊Q8—44no—
621C22⋊Q8—44no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—22no—
628#121—44no—
629#121—82no—
630C4×Q8—24no—
631C4×Q8—24no—
632C4×Q8—24no—
633C4×Q8—24no—
634C4×Q8—22no—
635C4×Q8—22no—
636C4×Q8—22no—
637C4×Q8—22no—
638C4×Q8—22no—
639C4×Q8—22no—
640C4×Q8—22no—
641C4×Q8—22no—
642C4×Q8—22no—
643C4×Q8—22no—
644C4×Q8—22no—
645C4×Q8—22no—
646C4×Q8C2×D414yes—
647C4×Q8#4114yes—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—44no—
655C4×D4—44no—
656C4×D4—82no—
657C4×D4—82no—
658#117—44no—
659C2×C4⋊C4—24no—
660C2×C4⋊C4—24no—
661C2×C4⋊C4—24no—
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—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2×D411yescharacteristic
686C2×C4⋊C4C2×D411yescharacteristic
687C2×C4⋊C4C2×D411yescharacteristic
688C2×C4⋊C4C2×D411yescharacteristic
689C2×C4⋊C4C2×D411yescharacteristic
690C2×C4⋊C4C2×D411yescharacteristic
691C2×C4⋊C4C2×D411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C42—22no—
740C2×C42—22no—
741C2×C42—22no—
742C2×C42—22no—
743C2×C42—22no—
744C2×C42—22no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42C2×D411yescharacteristic
755C2×C42C2×D411yescharacteristic
756C2×C42C2×D411yescharacteristic
757C2×C42C2×D411yescharacteristic
758C2×C42C2×D411yescharacteristic
759C2×C42C2×D411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766#107—22no—
767#107—22no—
768#107—41no—
769#107—41no—
770#106—22no—
771#106—22no—
772#106—22no—
773#106—41no—
774#106—41no—
775#106—41no—
776#106—41no—
777C4⋊C8—22no—
778C4⋊C8—22no—
779C4⋊C8—22no—
780C4⋊C8—22no—
781C4⋊C8—22no—
782C4⋊C8—22no—
783C4⋊C8—22no—
784C4⋊C8—22no—
785C4⋊C8—22no—
786C4⋊C8C2×D414yes—
787C4⋊C8C2×D414yes—
788C4⋊C8C2×D414yes—
789#103—22no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—41no—
796#103—41no—
797#103—41no—
798#103—41no—
799#103—41no—
800#103—41no—
801#103—41no—
802#103—41no—
803#103—41no—
804#102—22no—
805#102—22no—
806#102—22no—
807#102—22no—
808#102—22no—
809#102—22no—
810#102—41no—
811#102—41no—
812#102—41no—
813#102—41no—
814#102—41no—
815#102—41no—
816#102—41no—
817#102—41no—
818#102—41no—
819#97—22no—
820#97—22no—
821#97—22no—
822#97—22no—
823#97—22no—
824#97—22no—
825#97C2×D414yes—
826#97C2×D414yes—
827C4×C8—22no—
828C4×C8—22no—
829C4×C8—22no—
830C4×C8C2×D414yes—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
853#95—21no—
854#95—21no—
855#95—21no—
856#95—21no—
857#95—21no—
858#95—21no—
859#95—21no—
860#95—21no—
861#95—21no—
862#95—21no—
863#95—21no—
864#95—21no—
865#95—21no—
866#95—21no—
867#95—21no—
868#95—21no—
869#95—21no—
870#95—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24C22×D411yescharacteristic
875C2×Q8—22no—
876C2×Q8—22no—
877C2×Q8—22no—
878C2×Q8—22no—
879C2×Q8—22no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—21no—
898C2×Q8—41no—
899C2×Q8—41no—
900C2×Q8—41no—
901C2×Q8—41no—
902C2×Q8—41no—
903C2×Q8—41no—
904C2×Q8—416no—
905C2×Q8#12114yes—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—81no—
938C2×D4—81no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—22no—
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—41no—
970C22×C4—41no—
971C22×C4—41no—
972C22×C4—41no—
973C22×C4—41no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C2×#4112yes—
997C22×C4H(5,𝔽2)12yes—
998C22×C4C2511yescharacteristic
999Q16—44no—
1000Q16—82no—
1001SD16—44no—
1002SD16—82no—
1003SD16—82no—
1004SD16—82no—
1005SD16—82no—
1006D8—44no—
1007D8—82no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—28no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—44no—
1027C2×C8—44no—
1028C2×C8—44no—
1029C2×C8C22×D412yes—
1030C2×C8C22×D412yes—
1031C2×C8C22×D412yes—
1032C2×C8C22×D412yes—
1033C2×C8C2×#4112yes—
1034C2×C8C2×#4112yes—
1035C2×C82−1+412yes—
1036C4⋊C4—22no—
1037C4⋊C4—22no—
1038C4⋊C4—22no—
1039C4⋊C4—22no—
1040C4⋊C4—22no—
1041C4⋊C4—22no—
1042C4⋊C4—22no—
1043C4⋊C4—22no—
1044C4⋊C4—22no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4#12114yes—
1084C4⋊C4#12114yes—
1085C4⋊C4#12114yes—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C42—22no—
1124C42—22no—
1125C42—22no—
1126C42—22no—
1127C42—22no—
1128C42—22no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—42no—
1136C42—42no—
1137C42—42no—
1138C42—42no—
1139C42—42no—
1140C42—81no—
1141C42—81no—
1142C42—81no—
1143C42—81no—
1144C42C22×D412yes—
1145C42C22×D412yes—
1146C42C22×D412yes—
1147C42C2×#4112yes—
1148C42C2×#4112yes—
1149C42C2×#4112yes—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23#55012yes—
1176C23#57512yes—
1177C23#57712yes—
1178C23C23×D411yescharacteristic
1179Q8—44no—
1180Q8—44no—
1181Q8—44no—
1182Q8—44no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—84no—
1208D4—84no—
1209D4—84no—
1210D4—84no—
1211D4—162no—
1212C2×C4—28no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—44no—
1249C2×C4—44no—
1250C2×C4—44no—
1251C2×C4—44no—
1252C2×C4—44no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—84no—
1293C2×C4—162no—
1294C2×C4—162no—
1295C2×C4C2×#12112yes—
1296C2×C4C2×#12112yes—
1297C2×C4C2×#12112yes—
1298C2×C4C2×#12112yes—
1299C2×C4C2×#12112yes—
1300C2×C4C2×#12112yes—
1301C2×C4#55012yes—
1302C2×C4#57512yes—
1303C2×C4C23×D411yescharacteristic
1304C2×C4C22×#4111yescharacteristic
1305C2×C4C22×#4111yescharacteristic
1306C2×C4C2×H(5,𝔽2)11yescharacteristic
1307C2×C4C2×2−1+411yescharacteristic
1308C2×C4#58511yescharacteristic
1309C8—22no—
1310C8—22no—
1311C8—22no—
1312C8—22no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C8#54814yes—
1317C22—22no—
1318C22—22no—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—22no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22#340114yescomplemented
1345C22C22×#12111yescharacteristic
1346C22C2×#55011yescharacteristic
1347C22#349711yescharacteristic
1348C22C2×#57511yescharacteristic
1349C22C2×#57511yescharacteristic
1350C22C2×#57711yescharacteristic
1351C22#358411yescharacteristic
1352C4—22no—
1353C4—22no—
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—22no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4C2×#54811yescharacteristic
1379C4#348011yescharacteristic
1380C4#348811yescharacteristic
1381C4#352211yescharacteristic
1382C2—24no—
1383C2—161no—
1384C2—161no—
1385C2—161no—
1386C2#3657611yescharacteristic
1387C2#6044411yescharacteristic
1388C2#6045711yescharacteristic
1389C2C2×#340111yescharacteristic
1390C2#6140111yescharacteristic
1391C2#6236711yescharacteristic
1392C2#6237011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#33183C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3401C2semidirect
2. C22×#446C2semidirect
3. #36580C2semidirect
4. #36579C2semidirect
5. #33184C2semidirect
7. #33173C2semidirect
8. #28747C2semidirect
9. #28746C2semidirect
10. #28742C2semidirect
11. #28278C2semidirect
12. #28276C2semidirect
13. #28270C2semidirect
14. #25311C2semidirect
15. #25310C2semidirect
16. #25309C2semidirect
17. #25308C2semidirect
18. #25299C2semidirect
19. #25298C2semidirect
20. #24755C2semidirect
21. #24755C2semidirect
22. #24754C2semidirect
23. #24754C2semidirect
24. #24753C2semidirect
25. #24751C2semidirect
26. #22730C2semidirect
27. #22549C2semidirect
28. #22548C2semidirect
29. #21527C2semidirect
30. #21526C2semidirect
31. C4×#465C2semidirect
297. #446D4semidirect
1344. C22#3401semidirect

Maximal subgroups

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

subgroupindex
C2×#34012
C22×#4462
#365802
#365792
#331842
#331832
#331732
#287472
#287462
#287422
#282782
#282762
#282702
#253112
#253102
#253092
#253082
#252992
#252982
#247552
#247542
#247532
#247512
#227302
#225492
#225482
#215272
#215262
C4×#4652