Finite Group Databasebeta

← #6820083

Subgroups — #6820083

Order 512.

1667 conjugacy classes of subgroups.

The subgroup lattice has 1389 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40035C211yesmaximal, characteristic, complemented
2#39383C211yesmaximal, characteristic, complemented
3#33185C211yesmaximal, characteristic, complemented
4#32600C211yesmaximal, characteristic, complemented
5#32596C211yesmaximal, characteristic, complemented
6#32404C211yesmaximal, characteristic, complemented
7#32400C211yesmaximal, characteristic, complemented
8#31913C211yesmaximal, characteristic, complemented
9#31909C211yesmaximal, characteristic, complemented
10#30752C211yesmaximal, characteristic, complemented
11#30749C211yesmaximal, characteristic, complemented
12#29758C211yesmaximal, characteristic, complemented
13#29718C211yesmaximal, characteristic, complemented
14#28893C211yesmaximal, characteristic, complemented
15#28891C211yesmaximal, characteristic, complemented
16#28885C211yesmaximal, characteristic, complemented
17#28881C211yesmaximal, characteristic, complemented
18#28365C211yesmaximal, characteristic, complemented
19#28353C211yesmaximal, characteristic, complemented
20#27760C211yesmaximal, characteristic, complemented
21#27760C211yesmaximal, characteristic, complemented
22#25295C211yesmaximal, characteristic, complemented
23#25292C211yesmaximal, characteristic, complemented
24#25230C211yesmaximal, characteristic, complemented
25#25228C211yesmaximal, characteristic, complemented
26#25097C211yesmaximal, characteristic, complemented
27#25093C211yesmaximal, characteristic, complemented
28#23143C211yesmaximal, characteristic, complemented
29#23141C211yesmaximal, characteristic, complemented
30#21596C211yesmaximal, characteristic, complemented
31#21095C211yesmaximal, characteristic, complemented
32C2×#538—21no—
33C2×#496C2211yescharacteristic, complemented
34C2×#482C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#469C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#460C2211yescharacteristic
41C2×#459C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#447C2211yescharacteristic
44C2×C8×Q8C2211yescharacteristic, complemented
45C2×#418C2211yescharacteristic
46C2×#418C2211yescharacteristic
47C2×C4×M16C2211yescharacteristic
48#2856C2211yescharacteristic
49#2850C2211yescharacteristic
50#2786—21no—
51#2757—21no—
52#2746—21no—
53#2733—21no—
54#2728—21no—
55#2714—21no—
56#2714—21no—
57#2682—21no—
58#2654—21no—
59#2617—21no—
60#2594—21no—
61#2582C2211yescharacteristic, complemented
62#2577—21no—
63#2570C2211yescharacteristic, complemented
64#2570C2211yescharacteristic, complemented
65#2548C2211yescharacteristic
66#2548C2211yescharacteristic
67#2541C2211yescharacteristic
68#2541C2211yescharacteristic
69#2538C2211yescharacteristic, complemented
70#2514C2211yescharacteristic, complemented
71#2513C2211yescharacteristic, complemented
72#2512C2211yescharacteristic
73#2512C2211yescharacteristic
74#2500C2211yescharacteristic
75#2499C2211yescharacteristic
76#2448C2211yescharacteristic, complemented
77#2447C2211yescharacteristic, complemented
78#2445C2211yescharacteristic
79#2445C2211yescharacteristic
80#2433C2211yescharacteristic
81#2433C2211yescharacteristic
82#2424—21no—
83#2424—21no—
84#2363C2211yescharacteristic
85#2362C2211yescharacteristic
86#2361C2211yescharacteristic
87#2361C2211yescharacteristic
88#2332—21no—
89C4×C22⋊Q8C2211yescharacteristic
90#2296C2211yescharacteristic
91C2×#390C2211yescharacteristic
92#2094C2211yescharacteristic
93#2093C2211yescharacteristic
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2084C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2071C2211yescharacteristic, complemented
103#2071C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic, complemented
107#2067C2211yescharacteristic, complemented
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic, complemented
110#2065C2211yescharacteristic, complemented
111#2065C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic, complemented
116#2054C2211yescharacteristic
117#2054C2211yescharacteristic
118#2054C2211yescharacteristic
119#2054C2211yescharacteristic, complemented
120#2041C2211yescharacteristic
121#2041C2211yescharacteristic
122#2041C2211yescharacteristic, complemented
123#2041C2211yescharacteristic, complemented
124#2014C2211yescharacteristic
125#2014C2211yescharacteristic
126#2014C2211yescharacteristic
127#2012C2211yescharacteristic
128#2012C2211yescharacteristic
129#2011C2211yescharacteristic
130#2011C2211yescharacteristic
131#2011C2211yescharacteristic
132#1984C2211yescharacteristic, complemented
133#1982C2211yescharacteristic
134#1982C2211yescharacteristic
135#1973C2211yescharacteristic
136#1972C2211yescharacteristic
137#1970C2211yescharacteristic
138#1970C2211yescharacteristic, complemented
139#1970C2211yescharacteristic, complemented
140#1968C2211yescharacteristic
141#1968C2211yescharacteristic, complemented
142#1968C2211yescharacteristic, complemented
143#1961C2211yescharacteristic
144#1961C2211yescharacteristic
145#1961C2211yescharacteristic, complemented
146#1959C2211yescharacteristic, complemented
147#1957C2211yescharacteristic
148#1957C2211yescharacteristic
149#1948C2211yescharacteristic, complemented
150#1947C2211yescharacteristic, complemented
151#1939C2211yescharacteristic, complemented
152#1936C2211yescharacteristic
153#1936C2211yescharacteristic
154#1936C2211yescharacteristic
155#1936C2211yescharacteristic
156#1936C2211yescharacteristic, complemented
157#1935C2211yescharacteristic, complemented
158#1934C2211yescharacteristic
159#1934C2211yescharacteristic
160#1934C2211yescharacteristic
161#1934C2211yescharacteristic
162#1934C2211yescharacteristic, complemented
163#1934C2211yescharacteristic, complemented
164#1927C2211yescharacteristic, complemented
165#1926C2211yescharacteristic
166#1925C2211yescharacteristic
167#1925C2211yescharacteristic, complemented
168#1921C2211yescharacteristic, complemented
169#1920C2211yescharacteristic, complemented
170#1920C2211yescharacteristic, complemented
171#1918C2211yescharacteristic, complemented
172#1917C2211yescharacteristic, complemented
173#1917C2211yescharacteristic, complemented
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic, complemented
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic, complemented
178#1879C2211yescharacteristic, complemented
179#1879C2211yescharacteristic, complemented
180#1877C2211yescharacteristic, complemented
181#1877C2211yescharacteristic, complemented
182#1875C2211yescharacteristic
183#1875C2211yescharacteristic
184#1874C2211yescharacteristic
185#1872C2211yescharacteristic
186#1851C2211yescharacteristic
187#1851C2211yescharacteristic
188#1847C2211yescharacteristic, complemented
189#1804C2211yescharacteristic, complemented
190#1804C2211yescharacteristic, complemented
191#1797C2211yescharacteristic
192#1771C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194#1770C2211yescharacteristic, complemented
195#1762C2211yescharacteristic, complemented
196#1762C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic, complemented
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1736C2211yescharacteristic
202#1736C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214#538—48no—
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#126—21no—
221C2×#126—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225C2×#123—21no—
226C2×#123—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8D411yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#120—21no—
240C2×#120—21no—
241C2×#120—21no—
242C2×#120—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255C22×C42C2311yescharacteristic
256#496—42no—
257#482—42no—
258#482—42no—
259#469—24no—
260#469—42no—
261#468—24no—
262#468—42no—
263#460—42no—
264#459—42no—
265#450—42no—
266#447—42no—
267C8×Q8—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282#418—24no—
283#418—42no—
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C4×M16—42no—
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#401—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#399—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#392—21no—
360#392—21no—
361#392—21no—
362#392—21no—
363#392—21no—
364#392—21no—
365#392—21no—
366#392—21no—
367#391—21no—
368#391D411yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#390—21no—
374#390—21no—
375#390—21no—
376#390—21no—
377#390—21no—
378#390—21no—
379#390—21no—
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#389—21no—
397#389D411yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387D411yescharacteristic
430#387D411yescharacteristic
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385D411yescharacteristic
444#385D411yescharacteristic
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#383—21no—
449#382C2311yescharacteristic
450#382C2311yescharacteristic
451#382C2311yescharacteristic
452#381—21no—
453#380—21no—
454#380D411yescharacteristic
455C4×C4⋊C4—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C22⋊C4—21no—
466C4×C22⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C25—21no—
495C22×Q8C2×D411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C2×D8—41no—
550C2×D8—41no—
551C2×D8—41no—
552C2×D8—41no—
553C2×M16—22no—
554C2×M16—22no—
555C2×M16—41no—
556C2×M16—41no—
557C2×M16—41no—
558C2×M16#4114yes—
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567#127—41no—
568#127—41no—
569#127—41no—
570#127—41no—
571#127—41no—
572#127—41no—
573#127—41no—
574#127—41no—
575#127—41no—
576#127—41no—
577#126—44no—
578#126—44no—
579#124—41no—
580#124—41no—
581#124—44no—
582#124—44no—
583#123—44no—
584#123—44no—
585C22⋊Q8—24no—
586C22⋊Q8—22no—
587C22⋊Q8—22no—
588C22⋊Q8—44no—
589#121—22no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—44no—
596#121—44no—
597#121—44no—
598#121—82no—
599#121—82no—
600#121—82no—
601#120—44no—
602#120—44no—
603#120—82no—
604#120—82no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—44no—
616C4×D4—44no—
617#117—22no—
618#117—22no—
619#117—41no—
620#117—41no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—44no—
703C2×C22⋊C4—82no—
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42—41no—
717C2×C42C2×D411yescharacteristic
718C2×C42C2×D411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725#107—22no—
726#107—41no—
727#107—41no—
728#107—41no—
729#106—22no—
730#106—41no—
731#106—41no—
732#106—41no—
733C4⋊C8—22no—
734C4⋊C8—22no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739#103—22no—
740#103—41no—
741#103—41no—
742#103—41no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771C22⋊C8—22no—
772C22⋊C8—22no—
773#97—22no—
774#97—41no—
775#97—41no—
776#97—41no—
777C4×C8—22no—
778C4×C8—41no—
779C4×C8—41no—
780C4×C8—41no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—42no—
823C24—42no—
824C24—42no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24C22×D411yescharacteristic
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—41no—
837C2×Q8—41no—
838C2×Q8AGL(1,ℤ/8)14yes—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—82no—
886C2×D4—82no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—22no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—41no—
932C22×C4—41no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—41no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C2×#4112yes—
962C22×C4H(5,𝔽2)12yes—
963C22×C4C2511yescharacteristic
964SD16—82no—
965SD16—82no—
966SD16—82no—
967SD16—82no—
968D8—82no—
969D8—82no—
970D8—82no—
971D8—82no—
972M16—44no—
973M16—44no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8C2×#4112yes—
996C2×C8C2×#4112yes—
997C2×C8H(5,𝔽2)12yes—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—22no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—41no—
1026C4⋊C4—41no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—41no—
1104C42—41no—
1105C42—42no—
1106C42—42no—
1107C42—42no—
1108C42—81no—
1109C42—81no—
1110C42—81no—
1111C42—81no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
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—84no—
1154C23—84no—
1155C23—84no—
1156C23—162no—
1157C23—162no—
1158C23—162no—
1159C23—162no—
1160C23#55012yes—
1161C23C23×D411yescharacteristic
1162Q8—44no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—84no—
1188D4—84no—
1189D4—84no—
1190D4—162no—
1191D4—162no—
1192D4—162no—
1193D4—162no—
1194D4—162no—
1195D4—162no—
1196D4—162no—
1197D4—162no—
1198D4—162no—
1199D4—162no—
1200D4—162no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
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—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—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—41no—
1272C2×C4—41no—
1273C2×C4—82no—
1274C2×C4—82no—
1275C2×C4—162no—
1276C2×C4—162no—
1277C2×C4—162no—
1278C2×C4—162no—
1279C2×C4#55012yes—
1280C2×C4C2×AGL(1,ℤ/8)12yes—
1281C2×C4C2×AGL(1,ℤ/8)12yes—
1282C2×C4C2×AGL(1,ℤ/8)12yes—
1283C2×C4C22×#4111yescharacteristic
1284C2×C4C2×H(5,𝔽2)11yescharacteristic
1285C2×C4C2×H(5,𝔽2)11yescharacteristic
1286C2×C4#58511yescharacteristic
1287C2×C4#58511yescharacteristic
1288C2×C4#58511yescharacteristic
1289C8—22no—
1290C8—22no—
1291C8—22no—
1292C8—41no—
1293C8—41no—
1294C8—41no—
1295C8—41no—
1296C8—41no—
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
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—
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—168no—
1340C22C2×#55011yescharacteristic
1341C22#349611yescharacteristic
1342C22#350011yescharacteristic
1343C22C22×AGL(1,ℤ/8)11yescharacteristic
1344C22#358411yescharacteristic
1345C22#358511yescharacteristic
1346C22#358511yescharacteristic
1347C4—22no—
1348C4—22no—
1349C4—22no—
1350C4—22no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4#345511yescharacteristic
1372C4#350511yescharacteristic
1373C4#353411yescharacteristic
1374C4#356011yescharacteristic
1375C2—42no—
1376C2—161no—
1377C2—161no—
1378C2—161no—
1379C2—161no—
1380C2—161no—
1381C2#3938011yescharacteristic
1382C2#6140211yescharacteristic
1383C2#6142411yescharacteristic
1384C2#6225311yescharacteristic
1385C2#6229211yescharacteristic
1386C2#6258811yescharacteristic
1387C2#6261411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
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
1. #40035C2semidirect
2. #39383C2semidirect
3. #33185C2semidirect
4. #32600C2semidirect
5. #32596C2semidirect
6. #32404C2semidirect
7. #32400C2semidirect
8. #31913C2semidirect
9. #31909C2semidirect
10. #30752C2semidirect
11. #30749C2semidirect
12. #29758C2semidirect
13. #29718C2semidirect
14. #28893C2semidirect
15. #28891C2semidirect
16. #28885C2semidirect
17. #28881C2semidirect
18. #28365C2semidirect
19. #28353C2semidirect
20. #27760C2semidirect
21. #27760C2semidirect
22. #25295C2semidirect
23. #25292C2semidirect
24. #25230C2semidirect
25. #25228C2semidirect
26. #25097C2semidirect
27. #25093C2semidirect
28. #23143C2semidirect
29. #23141C2semidirect
30. #21596C2semidirect
31. #21095C2semidirect
33. C2×#496C22semidirect
44. C2×C8×Q8C22semidirect
61. #2582C22semidirect
63. #2570C22semidirect
64. #2570C22semidirect
69. #2538C22semidirect
70. #2514C22semidirect
71. #2513C22semidirect
76. #2448C22semidirect
77. #2447C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
98. #2084C22semidirect
99. #2083C22semidirect
102. #2071C22semidirect
103. #2071C22semidirect
104. #2068C22semidirect
106. #2067C22semidirect
107. #2067C22semidirect
109. #2065C22semidirect
110. #2065C22semidirect
111. #2065C22semidirect
115. #2055C22semidirect
119. #2054C22semidirect
122. #2041C22semidirect
123. #2041C22semidirect
132. #1984C22semidirect
138. #1970C22semidirect
139. #1970C22semidirect
141. #1968C22semidirect
142. #1968C22semidirect
145. #1961C22semidirect
146. #1959C22semidirect
149. #1948C22semidirect
150. #1947C22semidirect
151. #1939C22semidirect
156. #1936C22semidirect
157. #1935C22semidirect
162. #1934C22semidirect
163. #1934C22semidirect
164. #1927C22semidirect
167. #1925C22semidirect
168. #1921C22semidirect
169. #1920C22semidirect
170. #1920C22semidirect
171. #1918C22semidirect
172. #1917C22semidirect
173. #1917C22semidirect
175. #1880C22semidirect
177. #1879C22semidirect
178. #1879C22semidirect
179. #1879C22semidirect
180. #1877C22semidirect
181. #1877C22semidirect
188. #1847C22semidirect
189. #1804C22semidirect
190. #1804C22semidirect
192. #1771C22semidirect
193. #1771C22semidirect
194. #1770C22semidirect
195. #1762C22semidirect
196. #1762C22semidirect
197. C4×#103C22semidirect
198. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#400352
#393832
#331852
#326002
#325962
#324042
#324002
#319132
#319092
#307522
#307492
#297582
#297182
#288932
#288912
#288852
#288812
#283652
#283532
#277602
#252952
#252922
#252302
#252282
#250972
#250932
#231432
#231412
#215962
#210952