Finite Group Databasebeta

← #6803044

Subgroups — #6803044

Order 512.

1656 conjugacy classes of subgroups.

The subgroup lattice has 1397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39718C211yesmaximal, characteristic, complemented
2#35180C211yesmaximal, characteristic, complemented
3#33110C211yesmaximal, characteristic, complemented
4#32678C211yesmaximal, characteristic, complemented
5#32675C211yesmaximal, characteristic, complemented
6#32674C211yesmaximal, characteristic, complemented
7#32671C211yesmaximal, characteristic, complemented
8#32624C211yesmaximal, characteristic, complemented
9#32612C211yesmaximal, characteristic, complemented
10#32605C211yesmaximal, characteristic, complemented
11#32601C211yesmaximal, characteristic, complemented
12#29729C211yesmaximal, characteristic, complemented
13#29725C211yesmaximal, characteristic, complemented
14#28747C211yesmaximal, characteristic, complemented
15#28746C211yesmaximal, characteristic, complemented
16#28327C211yesmaximal, characteristic, complemented
17#28325C211yesmaximal, characteristic, complemented
18#28131C211yesmaximal, characteristic, complemented
19#28127C211yesmaximal, characteristic, complemented
20#26333C211yesmaximal, characteristic, complemented
21#26332C211yesmaximal, characteristic, complemented
22#25727C211yesmaximal, characteristic, complemented
23#25642C211yesmaximal, characteristic, complemented
24#25641C211yesmaximal, characteristic, complemented
25#25308C211yesmaximal, characteristic, complemented
26#25304C211yesmaximal, characteristic, complemented
27#24210C211yesmaximal, characteristic, complemented
28#22511C211yesmaximal, characteristic, complemented
29#22059C211yesmaximal, characteristic, complemented
30#22053C211yesmaximal, characteristic, complemented
31#21578C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×#497C2211yescharacteristic
36C2×#496C2211yescharacteristic
37C2×#484C2211yescharacteristic
38C2×#481C2211yescharacteristic
39C2×#480C2211yescharacteristic
40C2×#461C2211yescharacteristic
41C2×#459C2211yescharacteristic
42C2×#452C2211yescharacteristic
43C2×#452C2211yescharacteristic
44C2×#449C2211yescharacteristic
45C2×#449C2211yescharacteristic
46C2×#449C2211yescharacteristic
47C2×#449C2211yescharacteristic
48C2×#446C2211yescharacteristic
49C2×#446C2211yescharacteristic
50#2850—21no—
51#2850—21no—
52#2850C2211yescharacteristic
53#2731—21no—
54#2730—21no—
55#2696—21no—
56#2674—21no—
57#2639—21no—
58#2639—21no—
59#2620C2211yescharacteristic
60#2619C2211yescharacteristic
61#2592C2211yescharacteristic
62#2592C2211yescharacteristic
63#2592C2211yescharacteristic
64#2592C2211yescharacteristic
65#2592C2211yescharacteristic
66#2592C2211yescharacteristic
67#2581C2211yescharacteristic
68#2580C2211yescharacteristic
69#2568C2211yescharacteristic
70#2568C2211yescharacteristic
71#2563—21no—
72#2562—21no—
73#2562—21no—
74#2558—21no—
75#2548C2211yescharacteristic
76#2548C2211yescharacteristic
77#2548C2211yescharacteristic
78#2547—21no—
79#2538C2211yescharacteristic
80#2463—21no—
81#2461—21no—
82#2460—21no—
83#2355C2211yescharacteristic
84#2324C2211yescharacteristic
85#2323C2211yescharacteristic
86#2311C2211yescharacteristic
87#2311C2211yescharacteristic
88#2311C2211yescharacteristic
89#2311C2211yescharacteristic
90C4×#121C2211yescharacteristic
91C2×C4×C4⋊C4C2211yescharacteristic
92#2097C2211yescharacteristic
93#2095C2211yescharacteristic
94#2093C2211yescharacteristic
95#2092C2211yescharacteristic
96#2074C2211yescharacteristic
97#2073C2211yescharacteristic
98#2072C2211yescharacteristic
99#2071C2211yescharacteristic
100#2068C2211yescharacteristic
101#2067C2211yescharacteristic
102#2066C2211yescharacteristic
103#2065C2211yescharacteristic
104#2056C2211yescharacteristic
105#2056C2211yescharacteristic
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2054C2211yescharacteristic
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic
115#2054C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2015C2211yescharacteristic
119#2015C2211yescharacteristic
120#2015C2211yescharacteristic
121#2015C2211yescharacteristic
122#2014C2211yescharacteristic
123#2014C2211yescharacteristic
124#2012C2211yescharacteristic
125#2012C2211yescharacteristic
126#2012C2211yescharacteristic
127#2012C2211yescharacteristic
128#2012C2211yescharacteristic
129#2012C2211yescharacteristic
130#2011C2211yescharacteristic
131#2011C2211yescharacteristic
132#1985C2211yescharacteristic
133#1985C2211yescharacteristic
134#1985C2211yescharacteristic
135#1985C2211yescharacteristic
136#1984C2211yescharacteristic
137#1984C2211yescharacteristic
138#1983C2211yescharacteristic
139#1983C2211yescharacteristic
140#1982C2211yescharacteristic
141#1981C2211yescharacteristic
142#1973C2211yescharacteristic
143#1973C2211yescharacteristic
144#1973C2211yescharacteristic
145#1972C2211yescharacteristic
146#1972C2211yescharacteristic
147#1971C2211yescharacteristic
148#1970C2211yescharacteristic
149#1970C2211yescharacteristic
150#1969C2211yescharacteristic
151#1968C2211yescharacteristic
152#1968C2211yescharacteristic
153#1968C2211yescharacteristic
154#1961C2211yescharacteristic
155#1960C2211yescharacteristic
156#1949C2211yescharacteristic
157#1949C2211yescharacteristic
158#1936C2211yescharacteristic
159#1935C2211yescharacteristic
160#1934C2211yescharacteristic
161#1933C2211yescharacteristic
162#1928C2211yescharacteristic
163#1927C2211yescharacteristic
164#1927C2211yescharacteristic
165#1927C2211yescharacteristic
166#1927C2211yescharacteristic
167#1927C2211yescharacteristic
168#1926C2211yescharacteristic
169#1926C2211yescharacteristic
170#1926C2211yescharacteristic
171#1926C2211yescharacteristic
172#1926C2211yescharacteristic
173#1925C2211yescharacteristic
174#1925C2211yescharacteristic
175#1925C2211yescharacteristic
176#1921C2211yescharacteristic
177#1921C2211yescharacteristic
178#1880C2211yescharacteristic
179#1880C2211yescharacteristic
180#1879C2211yescharacteristic
181#1879C2211yescharacteristic
182#1878C2211yescharacteristic
183#1878C2211yescharacteristic
184#1877C2211yescharacteristic
185#1877C2211yescharacteristic
186#1874C2211yescharacteristic
187#1874C2211yescharacteristic
188#1872C2211yescharacteristic
189#1853C2211yescharacteristic
190#1823C2211yescharacteristic
191#1798C2211yescharacteristic
192#1798C2211yescharacteristic
193#1797C2211yescharacteristic
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1776C2211yescharacteristic
197#1776C2211yescharacteristic
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic
202#1749C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217#559—42no—
218#559—42no—
219#533—42no—
220#533—42no—
221#532—42no—
222#532—42no—
223C2×C4⋊Q8D411yescharacteristic
224C2×C4⋊Q8D411yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×#127C2311yescharacteristic
227C2×#127C2311yescharacteristic
228C2×#125D411yescharacteristic
229C2×#125D411yescharacteristic
230C2×#124—21no—
231C2×#124—21no—
232C2×#124—21no—
233C2×#124—21no—
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#124C2311yescharacteristic
237C2×#124C2311yescharacteristic
238C2×#123—21no—
239C2×#123—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8D411yescharacteristic
242C2×C22⋊Q8D411yescharacteristic
243C2×C22⋊Q8D411yescharacteristic
244C2×C22⋊Q8D411yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×#121—21no—
247C2×#121—21no—
248C2×#121C2311yescharacteristic
249C2×#121C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×D4—21no—
256C2×C4×D4—21no—
257C2×C4×D4—21no—
258C2×C4×D4—21no—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C42—21no—
266C22×C42C2311yescharacteristic
267#497—42no—
268#496—42no—
269#484—42no—
270#481—42no—
271#480—24no—
272#461—42no—
273#459—42no—
274#452—24no—
275#452—42no—
276#449—24no—
277#449—42no—
278#449—42no—
279#449—42no—
280#446—42no—
281#446—42no—
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
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#399—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#395—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#393—21no—
366#393—21no—
367#393—21no—
368#393—21no—
369#393—21no—
370#393—21no—
371#393—21no—
372#392—21no—
373#392—21no—
374#391—21no—
375#391—21no—
376#391—21no—
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#390—21no—
389#390—21no—
390#390—21no—
391#390—21no—
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#389—21no—
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#384C2311yescharacteristic
449#382—21no—
450#382—21no—
451#382C2311yescharacteristic
452#382C2311yescharacteristic
453#380—21no—
454#380—21no—
455#380—21no—
456#380—21no—
457#380—21no—
458#380—21no—
459#380—21no—
460#380—21no—
461#380—21no—
462#380C2311yescharacteristic
463C4×C4⋊C4—21no—
464C4×C4⋊C4—21no—
465C4×C4⋊C4—21no—
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C22⋊C4—21no—
474C2×#95—21no—
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C22×Q8C2×D411yescharacteristic
512C22×Q8C2×D411yescharacteristic
513C22×Q8C2×D411yescharacteristic
514C22×Q8C2×D411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C2×D411yescharacteristic
537C23×C4C2×D411yescharacteristic
538C23×C4C2411yescharacteristic
539C2×Q16—22no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×Q16—41no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×D8—22no—
564C2×D8—41no—
565C2×D8—41no—
566C2×D8—41no—
567C2×D8—41no—
568C2×D8—41no—
569C2×D8—41no—
570C2×D8—41no—
571C2×D8—41no—
572C2×D8—41no—
573C2×D8—41no—
574C2×D8—41no—
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C4⋊Q8—22no—
584C4⋊Q8—22no—
585C4⋊Q8—42no—
586C4⋊Q8—42no—
587#127—22no—
588#127—22no—
589#127—41no—
590#127—41no—
591#125—42no—
592#125—42no—
593#124—22no—
594#124—22no—
595#124—41no—
596#124—41no—
597#124—41no—
598#124—41no—
599#124—41no—
600#124—41no—
601#124—44no—
602#124—82no—
603#124—82no—
604#124—82no—
605#123—44no—
606#123—44no—
607C22⋊Q8—22no—
608C22⋊Q8—22no—
609C22⋊Q8—42no—
610C22⋊Q8—42no—
611C22⋊Q8—42no—
612C22⋊Q8—42no—
613C22⋊Q8—82no—
614#121—22no—
615#121—22no—
616#121—22no—
617#121—22no—
618#121—44no—
619#121—44no—
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—41no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—44no—
635C4×D4—44no—
636C4×D4—44no—
637C4×D4—82no—
638#117—41no—
639#117—41no—
640#117—41no—
641#117—41no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—22no—
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—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊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⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—82no—
739C2×C42C2×D411yescharacteristic
740C2×C42C2×D411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747#107—22no—
748#107—22no—
749#107—41no—
750#107—41no—
751#106—41no—
752#106—41no—
753#106—41no—
754#106—41no—
755C4⋊C8—22no—
756C4⋊C8—22no—
757C4⋊C8—41no—
758C4⋊C8—41no—
759C4⋊C8—41no—
760C4⋊C8—41no—
761#103—22no—
762#103—22no—
763#103—41no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
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—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793C22⋊C8—22no—
794C22⋊C8—22no—
795C22⋊C8—22no—
796C22⋊C8#4114yes—
797#97—22no—
798#97—22no—
799#97—41no—
800#97—41no—
801C4×C8—41no—
802C4×C8—41no—
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#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—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24C22×D411yescharacteristic
845#41—82no—
846#41—82no—
847#41—82no—
848#41—82no—
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—41no—
874C2×Q8—41no—
875C2×Q8—41no—
876C2×Q8—41no—
877C2×Q8—41no—
878C2×Q8—41no—
879C2×Q8—41no—
880C2×Q8—41no—
881C2×Q8—41no—
882C2×Q8—41no—
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—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—22no—
936C22×C4—22no—
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—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—41no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
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×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C2×#4112yes—
985C22×C4H(5,𝔽2)12yes—
986C22×C4C2511yescharacteristic
987Q16—82no—
988Q16—82no—
989SD16—82no—
990SD16—82no—
991SD16—82no—
992SD16—82no—
993SD16—82no—
994SD16—82no—
995D8—82no—
996D8—82no—
997D8—82no—
998D8—82no—
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×C8—21no—
1020C2×C8—21no—
1021C2×C8C2×#4112yes—
1022C2×C8C2×#4112yes—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
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—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—41no—
1048C4⋊C4—41no—
1049C4⋊C4—41no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
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—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
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—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C42—22no—
1115C42—22no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—42no—
1127C42—42no—
1128C42—42no—
1129C42—81no—
1130C42—81no—
1131C42—81no—
1132C42—81no—
1133C42—81no—
1134C42H(5,𝔽2)12yes—
1135C42H(5,𝔽2)12yes—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
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—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#55012yes—
1171C23C23×D411yescharacteristic
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—82no—
1185Q8—82no—
1186Q8—82no—
1187Q8—82no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—84no—
1205D4—84no—
1206D4—84no—
1207D4—84no—
1208D4—84no—
1209D4—84no—
1210D4—162no—
1211D4—162no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
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—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
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—82no—
1290C2×C4—84no—
1291C2×C4—84no—
1292C2×C4—84no—
1293C2×C4—84no—
1294C2×C4—162no—
1295C2×C4—162no—
1296C2×C4#53412yes—
1297C2×C4#53412yes—
1298C2×C4#55012yes—
1299C2×C4C22×#4111yescharacteristic
1300C2×C4C2×H(5,𝔽2)11yescharacteristic
1301C2×C4C2×H(5,𝔽2)11yescharacteristic
1302C2×C4C2×H(5,𝔽2)11yescharacteristic
1303C2×C4#58511yescharacteristic
1304C2×C4#58511yescharacteristic
1305C8—22no—
1306C8—22no—
1307C8—41no—
1308C8—41no—
1309C8—41no—
1310C8—41no—
1311C8—41no—
1312C8—41no—
1313C22—22no—
1314C22—22no—
1315C22—22no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
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—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22C2×#53411yescharacteristic
1349C22C2×#55011yescharacteristic
1350C22#348711yescharacteristic
1351C22#358411yescharacteristic
1352C22#358511yescharacteristic
1353C22#358511yescharacteristic
1354C22#358611yescharacteristic
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4#351411yescharacteristic
1381C4#351411yescharacteristic
1382C4#355811yescharacteristic
1383C4#355811yescharacteristic
1384C2—42no—
1385C2—161no—
1386C2—161no—
1387C2—161no—
1388C2—161no—
1389C2#3913511yescharacteristic
1390C2#6075511yescharacteristic
1391C2#6076011yescharacteristic
1392C2#6141411yescharacteristic
1393C2#6142311yescharacteristic
1394C2#6191911yescharacteristic
1395C2#6194011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#533 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39718C2semidirect
2. #35180C2semidirect
3. #33110C2semidirect
4. #32678C2semidirect
5. #32675C2semidirect
6. #32674C2semidirect
7. #32671C2semidirect
8. #32624C2semidirect
9. #32612C2semidirect
10. #32605C2semidirect
11. #32601C2semidirect
12. #29729C2semidirect
13. #29725C2semidirect
14. #28747C2semidirect
15. #28746C2semidirect
16. #28327C2semidirect
17. #28325C2semidirect
18. #28131C2semidirect
19. #28127C2semidirect
20. #26333C2semidirect
21. #26332C2semidirect
22. #25727C2semidirect
23. #25642C2semidirect
24. #25641C2semidirect
25. #25308C2semidirect
26. #25304C2semidirect
27. #24210C2semidirect
28. #22511C2semidirect
29. #22059C2semidirect
30. #22053C2semidirect
31. #21578C2semidirect

Maximal subgroups

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

subgroupindex
#397182
#351802
#331102
#326782
#326752
#326742
#326712
#326242
#326122
#326052
#326012
#297292
#297252
#287472
#287462
#283272
#283252
#281312
#281272
#263332
#263322
#257272
#256422
#256412
#253082
#253042
#242102
#225112
#220592
#220532
#215782