Finite Group Databasebeta

← #7536532

Subgroups — #7536532

Order 512.

1713 conjugacy classes of subgroups.

The subgroup lattice has 1376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59145C211yesmaximal, characteristic
2#36552C211yesmaximal, characteristic, complemented
3#32190C211yesmaximal, characteristic, complemented
4#32164C211yesmaximal, characteristic, complemented
5#31918C211yesmaximal, characteristic, complemented
6#31904C211yesmaximal, characteristic, complemented
7#28747C211yesmaximal, characteristic, complemented
8#28360C211yesmaximal, characteristic, complemented
9#28360C211yesmaximal, characteristic, complemented
10#27763C211yesmaximal, characteristic, complemented
11#27207C211yesmaximal, characteristic, complemented
12#27196C211yesmaximal, characteristic, complemented
13#26542C211yesmaximal, characteristic, complemented
14#26330C211yesmaximal, characteristic, complemented
15#25728C211yesmaximal, characteristic, complemented
16#25641C211yesmaximal, characteristic, complemented
17#25377C211yesmaximal, characteristic, complemented
18#25102C211yesmaximal, characteristic, complemented
19#25096C211yesmaximal, characteristic, complemented
20#24759C211yesmaximal, characteristic, complemented
21#24641C211yesmaximal, characteristic, complemented
22#24628C211yesmaximal, characteristic, complemented
23#24548C211yesmaximal, characteristic, complemented
24#24546C211yesmaximal, characteristic, complemented
25#23192C211yesmaximal, characteristic, complemented
26#22955C211yesmaximal, characteristic, complemented
27#22882C211yesmaximal, characteristic, complemented
28#22867C211yesmaximal, characteristic, complemented
29#22546C211yesmaximal, characteristic, complemented
30#21578C211yesmaximal, characteristic, complemented
31#21258C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#497C2211yescharacteristic
35C2×#497C2211yescharacteristic
36C2×#480C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#460C2211yescharacteristic
41C2×#461C2211yescharacteristic
42C2×#452C2211yescharacteristic
43C2×#452C2211yescharacteristic
44C2×#452C2211yescharacteristic
45C2×#452C2211yescharacteristic
46C2×#446C2211yescharacteristic
47C2×#441C2211yescharacteristic
48C2×C4×SD16C2211yescharacteristic
49C2×#423C2211yescharacteristic
50C2×#417C2211yescharacteristic
51C2×#417C2211yescharacteristic
52C2×#417C2211yescharacteristic
53C2×#417C2211yescharacteristic
54#2857C2211yescharacteristic
55#2851—21no—
56#2703—21no—
57#2676—21no—
58#2592C2211yescharacteristic
59#2590—21no—
60#2590—21no—
61#2568C2211yescharacteristic
62#2552C2211yescharacteristic
63#2545C2211yescharacteristic
64#2544C2211yescharacteristic
65#2541C2211yescharacteristic
66#2511C2211yescharacteristic
67#2511C2211yescharacteristic
68#2508—21no—
69#2505—21no—
70#2505—21no—
71#2502C2211yescharacteristic
72#2502C2211yescharacteristic
73#2464—21no—
74#2459—21no—
75#2457—21no—
76#2456—21no—
77#2453—21no—
78#2446C2211yescharacteristic
79#2445C2211yescharacteristic
80#2431C2211yescharacteristic
81#2431C2211yescharacteristic
82#2425—21no—
83#2367C2211yescharacteristic
84#2365C2211yescharacteristic
85#2364—21no—
86#2360C2211yescharacteristic
87#2360C2211yescharacteristic
88#2355C2211yescharacteristic
89#2355C2211yescharacteristic
90Q8×C4⋊C4C2211yescharacteristic
91#2341C2211yescharacteristic
92#2339C2211yescharacteristic
93C4×C22⋊Q8—21no—
94C4×C22⋊Q8C2211yescharacteristic
95C4×#121C2211yescharacteristic
96C2×C4×C4⋊C4C2211yescharacteristic
97#2095C2211yescharacteristic
98#2095C2211yescharacteristic
99#2093C2211yescharacteristic
100#2093C2211yescharacteristic
101#2072C2211yescharacteristic
102#2072C2211yescharacteristic
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic
105#2068C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2067C2211yescharacteristic
109#2056C2211yescharacteristic
110#2056C2211yescharacteristic
111#2056C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic
117#2042C2211yescharacteristic
118#2041C2211yescharacteristic
119#2016C2211yescharacteristic
120#2016C2211yescharacteristic
121#2015C2211yescharacteristic
122#2015C2211yescharacteristic
123#2015C2211yescharacteristic
124#2014C2211yescharacteristic
125#2014C2211yescharacteristic
126#2014C2211yescharacteristic
127#2014C2211yescharacteristic
128#2014C2211yescharacteristic
129#1985C2211yescharacteristic
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1983C2211yescharacteristic
134#1983C2211yescharacteristic
135#1982C2211yescharacteristic
136#1982C2211yescharacteristic
137#1982C2211yescharacteristic
138#1981C2211yescharacteristic
139#1981C2211yescharacteristic
140#1981C2211yescharacteristic
141#1973C2211yescharacteristic
142#1973C2211yescharacteristic
143#1971C2211yescharacteristic
144#1969C2211yescharacteristic
145#1969C2211yescharacteristic
146#1968C2211yescharacteristic
147#1959C2211yescharacteristic
148#1959C2211yescharacteristic
149#1959C2211yescharacteristic
150#1959C2211yescharacteristic
151#1957C2211yescharacteristic
152#1957C2211yescharacteristic
153#1947C2211yescharacteristic
154#1940C2211yescharacteristic
155#1940C2211yescharacteristic
156#1939C2211yescharacteristic
157#1936C2211yescharacteristic
158#1933C2211yescharacteristic
159#1928C2211yescharacteristic
160#1927C2211yescharacteristic
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic
163#1926C2211yescharacteristic
164#1925C2211yescharacteristic
165#1921C2211yescharacteristic
166#1921C2211yescharacteristic
167#1917C2211yescharacteristic
168#1916C2211yescharacteristic
169#1894C2211yescharacteristic
170#1894C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1874C2211yescharacteristic
182#1865C2211yescharacteristic
183#1864C2211yescharacteristic
184#1853C2211yescharacteristic
185#1851C2211yescharacteristic
186#1851C2211yescharacteristic
187#1823C2211yescharacteristic
188#1803C2211yescharacteristic
189#1803C2211yescharacteristic
190#1802C2211yescharacteristic
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195#1771C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199C4×#103C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1749C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C22×M16C2311yescharacteristic
217#559—24no—
218#559—42no—
219#532—24no—
220#532—42no—
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#127C2311yescharacteristic
225C2×#127C2311yescharacteristic
226C2×#125—21no—
227C2×#124—21no—
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#123—21no—
233C2×#123—21no—
234C2×#123—21no—
235C2×C22⋊Q8D411yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121—21no—
242C2×#121C2311yescharacteristic
243C2×C4×Q8—21no—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4—21no—
252C2×C4×D4—21no—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C42—21no—
259C22×C42C2311yescharacteristic
260#497—24no—
261#497—42no—
262#480—24no—
263#468—42no—
264#468—42no—
265#464—42no—
266#461—42no—
267#460—42no—
268#452—24no—
269#452—24no—
270#452—42no—
271#452—42no—
272#446—42no—
273#441—42no—
274C4×SD16—42no—
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281#423—42no—
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290#417—42no—
291#417—42no—
292#417—42no—
293#417—42no—
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338#400—21no—
339#400—21no—
340#400—21no—
341#400—21no—
342#400—21no—
343#400—21no—
344#400—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#398—21no—
351#398—21no—
352#397—21no—
353#396—21no—
354#396—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#393—21no—
360#392—21no—
361#392—21no—
362#392—21no—
363#392—21no—
364#392—21no—
365#392—21no—
366#391—21no—
367#391D411yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#390—21no—
381#390—21no—
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#389—21no—
388#389—21no—
389#389—21no—
390#389—21no—
391#389—21no—
392#389—21no—
393#389—21no—
394#389—21no—
395#389—21no—
396#389D411yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387D411yescharacteristic
422#387D411yescharacteristic
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385D411yescharacteristic
441#385D411yescharacteristic
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#384C2311yescharacteristic
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#382—21no—
448#382—21no—
449#382—21no—
450#381—21no—
451#380—21no—
452#380—21no—
453#380—21no—
454#380D411yescharacteristic
455#380C2311yescharacteristic
456C4×C4⋊C4—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4—21no—
460C4×C4⋊C4—21no—
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
477C4×C22⋊C4C2311yescharacteristic
478C2×#95—21no—
479C2×#95—21no—
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C22×Q8C2×D411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×Q8C2411yescharacteristic
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C2×D411yescharacteristic
539C23×C4C2×D411yescharacteristic
540C23×C4C2411yescharacteristic
541C2×Q16—22no—
542C2×Q16—22no—
543C2×Q16—22no—
544C2×Q16—22no—
545C2×Q16—41no—
546C2×Q16—41no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
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×SD16—41no—
571C2×M16—22no—
572C2×M16—22no—
573C2×M16—41no—
574C2×M16—41no—
575C2×M16—41no—
576C2×M16—41no—
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C4⋊Q8—22no—
586C4⋊Q8—22no—
587C4⋊Q8—22no—
588C4⋊Q8—41no—
589#127—22no—
590#127—22no—
591#127—41no—
592#127—41no—
593#127—41no—
594#127—41no—
595#125—82no—
596#124—22no—
597#124—22no—
598#124—22no—
599#124—22no—
600#124—41no—
601#124—41no—
602#124—41no—
603#124—44no—
604#124#4114yes—
605#123—44no—
606#123—44no—
607#123—82no—
608C22⋊Q8—24no—
609C22⋊Q8—22no—
610C22⋊Q8—22no—
611C22⋊Q8—22no—
612C22⋊Q8—22no—
613#121—22no—
614#121—22no—
615#121—44no—
616#121—44no—
617#121—44no—
618#121—82no—
619C4×Q8—22no—
620C4×Q8—22no—
621C4×Q8—22no—
622C4×Q8—22no—
623C4×Q8—22no—
624C4×Q8—41no—
625C4×Q8—41no—
626C4×Q8—41no—
627C4×Q8—41no—
628C4×Q8—41no—
629C4×Q8—82no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—44no—
634C4×D4—44no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—44no—
639C4×D4—82no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
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—41no—
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
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×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⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C42—22no—
717C2×C42—22no—
718C2×C42—21no—
719C2×C42—21no—
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×C42—21no—
729C2×C42—82no—
730C2×C42C2×D411yescharacteristic
731C2×C42C2×D411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738#107—22no—
739#107—22no—
740#107—41no—
741#107—41no—
742#106—22no—
743#106—41no—
744C4⋊C8—22no—
745C4⋊C8—22no—
746C4⋊C8—41no—
747C4⋊C8—41no—
748C4⋊C8—41no—
749C4⋊C8—41no—
750C4⋊C8—41no—
751C4⋊C8—41no—
752#103—22no—
753#103—22no—
754#103—22no—
755#103—22no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788C22⋊C8—22no—
789C22⋊C8#4114yes—
790#97—22no—
791#97—22no—
792#97—41no—
793#97—41no—
794C4×C8—41no—
795C4×C8—41no—
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—
842C24—21no—
843C24—21no—
844C24C22×D411yescharacteristic
845#41—44no—
846#41—44no—
847#41—44no—
848#41—44no—
849#41—82no—
850#41—82no—
851#41—82no—
852#41—82no—
853C2×Q8—22no—
854C2×Q8—22no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—41no—
879C2×Q8C2×#4112yes—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4C2×#4112yes—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—22no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—41no—
946C22×C4—41no—
947C22×C4—41no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C2×#4112yes—
983C22×C4H(5,𝔽2)12yes—
984C22×C4C2511yescharacteristic
985Q16—44no—
986Q16—82no—
987Q16—82no—
988Q16—82no—
989SD16—44no—
990SD16—82no—
991SD16—82no—
992SD16—82no—
993SD16—82no—
994SD16—82no—
995M16—82no—
996M16—82no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
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—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8C2×#4112yes—
1020C2×C8C2×#4112yes—
1021C4⋊C4—22no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—41no—
1044C4⋊C4—41no—
1045C4⋊C4—41no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4#13714yes—
1072C4⋊C4H(5,𝔽2)12yes—
1073C22⋊C4—24no—
1074C22⋊C4—24no—
1075C22⋊C4—22no—
1076C22⋊C4—22no—
1077C22⋊C4—41no—
1078C22⋊C4—41no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C42—22no—
1103C42—22no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—42no—
1115C42—42no—
1116C42—42no—
1117C42—42no—
1118C42—42no—
1119C42—81no—
1120C42—81no—
1121C42—81no—
1122C42—81no—
1123C42—81no—
1124C42—81no—
1125C42C2×#4112yes—
1126C42H(5,𝔽2)12yes—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—22no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23#55012yes—
1155C23C23×D411yescharacteristic
1156Q8—22no—
1157Q8—22no—
1158Q8—44no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173D4—22no—
1174D4—22no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—84no—
1186D4—84no—
1187D4—84no—
1188D4—84no—
1189D4—84no—
1190D4—84no—
1191D4—162no—
1192D4—162no—
1193D4—162no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
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—22no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—22no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—44no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
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—82no—
1272C2×C4—84no—
1273C2×C4—84no—
1274C2×C4—84no—
1275C2×C4—84no—
1276C2×C4—162no—
1277C2×C4—162no—
1278C2×C4—162no—
1279C2×C4#54612yes—
1280C2×C4#54612yes—
1281C2×C4#55012yes—
1282C2×C4C2×#13712yes—
1283C2×C4C2×#13712yes—
1284C2×C4C2×#13712yes—
1285C2×C4C22×#4111yescharacteristic
1286C2×C4C22×#4111yescharacteristic
1287C2×C4C2×H(5,𝔽2)11yescharacteristic
1288C2×C4C2×H(5,𝔽2)11yescharacteristic
1289C2×C4C2×H(5,𝔽2)11yescharacteristic
1290C2×C4#58511yescharacteristic
1291C8—22no—
1292C8—22no—
1293C8—41no—
1294C8—41no—
1295C8—41no—
1296C8—41no—
1297C8—41no—
1298C8—41no—
1299C22—22no—
1300C22—22no—
1301C22—22no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22C2×#54611yescharacteristic
1328C22C2×#55011yescharacteristic
1329C22#348811yescharacteristic
1330C22C22×#13711yescharacteristic
1331C22#358511yescharacteristic
1332C22#358511yescharacteristic
1333C22#358611yescharacteristic
1334C4—22no—
1335C4—22no—
1336C4—22no—
1337C4—22no—
1338C4—22no—
1339C4—22no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—42no—
1344C4—42no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4#348111yescharacteristic
1361C4#351311yescharacteristic
1362C4#351411yescharacteristic
1363C4#354311yescharacteristic
1364C2—42no—
1365C2—82no—
1366C2—161no—
1367C2—161no—
1368C2#5904611yescharacteristic
1369C2#6116211yescharacteristic
1370C2#6118011yescharacteristic
1371C2#6140411yescharacteristic
1372C2#6141411yescharacteristic
1373C2#6196511yescharacteristic
1374C2#6207611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59145C2
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
2. #36552C2semidirect
3. #32190C2semidirect
4. #32164C2semidirect
5. #31918C2semidirect
6. #31904C2semidirect
7. #28747C2semidirect
8. #28360C2semidirect
9. #28360C2semidirect
10. #27763C2semidirect
11. #27207C2semidirect
12. #27196C2semidirect
13. #26542C2semidirect
14. #26330C2semidirect
15. #25728C2semidirect
16. #25641C2semidirect
17. #25377C2semidirect
18. #25102C2semidirect
19. #25096C2semidirect
20. #24759C2semidirect
21. #24641C2semidirect
22. #24628C2semidirect
23. #24548C2semidirect
24. #24546C2semidirect
25. #23192C2semidirect
26. #22955C2semidirect
27. #22882C2semidirect
28. #22867C2semidirect
29. #22546C2semidirect
30. #21578C2semidirect
31. #21258C2semidirect

Maximal subgroups

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

subgroupindex
#591452
#365522
#321902
#321642
#319182
#319042
#287472
#283602
#277632
#272072
#271962
#265422
#263302
#257282
#256412
#253772
#251022
#250962
#247592
#246412
#246282
#245482
#245462
#231922
#229552
#228822
#228672
#225462
#215782
#212582