Finite Group Databasebeta

← #6830451

Subgroups — #6830451

Order 512.

1664 conjugacy classes of subgroups.

The subgroup lattice has 1392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42951C211yesmaximal, characteristic
2#42506C211yesmaximal, characteristic, complemented
3#33045C211yesmaximal, characteristic, complemented
4#31976C211yesmaximal, characteristic, complemented
5#31966C211yesmaximal, characteristic, complemented
6#31674C211yesmaximal, characteristic, complemented
7#31666C211yesmaximal, characteristic, complemented
8#31378C211yesmaximal, characteristic, complemented
9#31376C211yesmaximal, characteristic, complemented
10#31313C211yesmaximal, characteristic, complemented
11#31310C211yesmaximal, characteristic, complemented
12#29961C211yesmaximal, characteristic, complemented
13#29765C211yesmaximal, characteristic, complemented
14#29032C211yesmaximal, characteristic, complemented
15#29029C211yesmaximal, characteristic, complemented
16#28866C211yesmaximal, characteristic, complemented
17#28844C211yesmaximal, characteristic, complemented
18#28107C211yesmaximal, characteristic, complemented
19#28101C211yesmaximal, characteristic, complemented
20#27270C211yesmaximal, characteristic, complemented
21#27254C211yesmaximal, characteristic, complemented
22#26202C211yesmaximal, characteristic, complemented
23#26198C211yesmaximal, characteristic, complemented
24#25263C211yesmaximal, characteristic, complemented
25#25245C211yesmaximal, characteristic, complemented
26#24037C211yesmaximal, characteristic, complemented
27#24034C211yesmaximal, characteristic, complemented
28#22432C211yesmaximal, characteristic, complemented
29#22419C211yesmaximal, characteristic, complemented
30#21496C211yesmaximal, characteristic, complemented
31#21087C211yesmaximal, characteristic, complemented
32C2×#550C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#482C2211yescharacteristic, complemented
37C2×#436C2211yescharacteristic, complemented
38C2×#435C2211yescharacteristic
39C2×#435C2211yescharacteristic
40C2×#417C2211yescharacteristic
41C2×#417C2211yescharacteristic, complemented
42C2×#416C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C2×#405C2211yescharacteristic, complemented
45#2834—21no—
46#2813—21no—
47#2792—21no—
48#2765—21no—
49#2765—21no—
50#2688—21no—
51#2680—21no—
52#2673—21no—
53#2669—21no—
54#2668—21no—
55#2638—21no—
56#2638—21no—
57#2630—21no—
58#2628C2211yescharacteristic, complemented
59#2619C2211yescharacteristic
60#2617—21no—
61#2534—21no—
62#2507C2211yescharacteristic, complemented
63#2507C2211yescharacteristic, complemented
64#2494C2211yescharacteristic
65#2494C2211yescharacteristic, complemented
66#2486C2211yescharacteristic
67#2486C2211yescharacteristic
68#2485C2211yescharacteristic
69#2485C2211yescharacteristic, complemented
70#2455—21no—
71#2448C2211yescharacteristic
72#2445C2211yescharacteristic
73#2440C2211yescharacteristic
74#2440C2211yescharacteristic, complemented
75#2433C2211yescharacteristic
76#2431C2211yescharacteristic
77#2421C2211yescharacteristic
78#2420C2211yescharacteristic
79#2416C2211yescharacteristic
80#2416C2211yescharacteristic
81#2408C2211yescharacteristic
82#2407C2211yescharacteristic
83#2392C2211yescharacteristic
84D4×C4⋊C4C2211yescharacteristic
85D4×C4⋊C4C2211yescharacteristic, complemented
86#2317C2211yescharacteristic, complemented
87#2311C2211yescharacteristic
88#2100C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2092C2211yescharacteristic
92#2088C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2077C2211yescharacteristic, complemented
97#2076C2211yescharacteristic, complemented
98#2075C2211yescharacteristic
99#2075C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic, complemented
107#2066C2211yescharacteristic, complemented
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic, complemented
111#2065C2211yescharacteristic, complemented
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#2041C2211yescharacteristic
118#2036C2211yescharacteristic
119#2035C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2024C2211yescharacteristic, complemented
127#2023C2211yescharacteristic
128#1993C2211yescharacteristic, complemented
129#1983C2211yescharacteristic
130#1982C2211yescharacteristic
131#1961C2211yescharacteristic
132#1959C2211yescharacteristic
133#1957C2211yescharacteristic
134#1954C2211yescharacteristic
135#1944C2211yescharacteristic, complemented
136#1942C2211yescharacteristic, complemented
137#1939C2211yescharacteristic, complemented
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic, complemented
142#1936C2211yescharacteristic, complemented
143#1935C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic, complemented
150#1933C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1926C2211yescharacteristic
153#1925C2211yescharacteristic, complemented
154#1924C2211yescharacteristic
155#1924C2211yescharacteristic, complemented
156#1919C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic
160#1895C2211yescharacteristic
161#1895C2211yescharacteristic, complemented
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic
164#1893C2211yescharacteristic, complemented
165#1892C2211yescharacteristic
166#1874C2211yescharacteristic
167#1874C2211yescharacteristic
168#1874C2211yescharacteristic
169#1874C2211yescharacteristic
170#1874C2211yescharacteristic, complemented
171#1872C2211yescharacteristic
172#1869C2211yescharacteristic
173#1869C2211yescharacteristic, complemented
174#1865C2211yescharacteristic, complemented
175#1864C2211yescharacteristic
176#1863C2211yescharacteristic, complemented
177#1862C2211yescharacteristic
178#1853C2211yescharacteristic, complemented
179#1852C2211yescharacteristic, complemented
180#1835C2211yescharacteristic, complemented
181#1824C2211yescharacteristic, complemented
182#1823C2211yescharacteristic
183#1809C2211yescharacteristic, complemented
184#1807C2211yescharacteristic
185#1803C2211yescharacteristic, complemented
186#1802C2211yescharacteristic
187#1798C2211yescharacteristic, complemented
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic, complemented
191#1788C2211yescharacteristic, complemented
192#1788C2211yescharacteristic, complemented
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1771C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198C4×#103C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200C8×C22⋊C4C2211yescharacteristic
201#1736C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#550—24no—
211#550—42no—
212#546—24no—
213#546—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×#127—21no—
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121—21no—
227C2×#121—21no—
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—21no—
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120—21no—
238C2×#120—21no—
239C2×#120—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255#486—42no—
256#482—42no—
257#482—42no—
258#436—42no—
259#435—42no—
260#435—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273#417—42no—
274#417—42no—
275#416—24no—
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#102—42no—
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317#405—42no—
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324#401—21no—
325#401—21no—
326#400—21no—
327#400—21no—
328#399—21no—
329#399—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398D411yescharacteristic
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397D411yescharacteristic
349#396—21no—
350#396—21no—
351#396D411yescharacteristic
352#396D411yescharacteristic
353#395—21no—
354#395—21no—
355#395—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#394—21no—
366#394—21no—
367#394D411yescharacteristic
368#394D411yescharacteristic
369#394D411yescharacteristic
370#393—21no—
371#392—21no—
372#392—21no—
373#392—21no—
374#392—21no—
375#392—21no—
376#392—21no—
377#392—21no—
378#392—21no—
379#392D411yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#389—21no—
389#389—21no—
390#389—21no—
391#389—21no—
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#384—21no—
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#382—21no—
440#382C2311yescharacteristic
441#382C2311yescharacteristic
442#381—21no—
443#381—21no—
444#381—21no—
445#380—21no—
446#380—21no—
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#379—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
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#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41#4114yes—
506C22×Q8—21no—
507C22×Q8C2411yescharacteristic
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×D411yescharacteristic
527C22×D4C2×D411yescharacteristic
528C22×D4C2×D411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—22no—
545C2×M16—41no—
546C2×M16—41no—
547C2×M16—41no—
548C22×C8—22no—
549C22×C8—22no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8—41no—
553C22×C8—41no—
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564#127—22no—
565#127—41no—
566#127—41no—
567#127—41no—
568#127—44no—
569#124—22no—
570#124—41no—
571#123—44no—
572#123—82no—
573#123—82no—
574#123—82no—
575C22⋊Q8—22no—
576C22⋊Q8—41no—
577C22⋊Q8—82no—
578C22⋊Q8—82no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—44no—
585#121—44no—
586#121—44no—
587#121—41no—
588#121—41no—
589#121—41no—
590#121—41no—
591#121—41no—
592#121—82no—
593#121—82no—
594#120—44no—
595#120—82no—
596#120—82no—
597#120—82no—
598C4×Q8—22no—
599C4×Q8—41no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—44no—
609C4×D4—82no—
610C4×D4—82no—
611#117—22no—
612#117—22no—
613#117—41no—
614#117—41no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
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⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
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—44no—
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718#107—41no—
719#107—41no—
720#107—41no—
721#107—41no—
722#106—41no—
723#106—41no—
724#106—41no—
725#106—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730#103—22no—
731#103—22no—
732#103—22no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
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—
762C22⋊C8—22no—
763C22⋊C8—22no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770#97—22no—
771#97—41no—
772#97—41no—
773C4×C8—22no—
774C4×C8—41no—
775C4×C8—41no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
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#95—21no—
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814C24—21no—
815C24—21no—
816C24—21no—
817C24—42no—
818C24—42no—
819C24—81no—
820C24—81no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24C22×D411yescharacteristic
825C24C22×D411yescharacteristic
826C24C22×D411yescharacteristic
827#41—44no—
828#41—44no—
829#41—44no—
830#41—82no—
831#41—82no—
832#41—82no—
833#41—82no—
834#41—82no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8C2×#4112yes—
844C2×D4—22no—
845C2×D4—22no—
846C2×D4—22no—
847C2×D4—24no—
848C2×D4—22no—
849C2×D4—22no—
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—41no—
868C2×D4—41no—
869C2×D4—41no—
870C2×D4—41no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—44no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—82no—
893C2×D4—82no—
894C2×D4—82no—
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×D4C2×#4112yes—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
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—24no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C2×#4112yes—
973C22×C4H(5,𝔽2)12yes—
974C22×C4C2511yescharacteristic
975M16—44no—
976M16—82no—
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×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—44no—
1001C2×C8—82no—
1002C2×C8H(5,𝔽2)12yes—
1003C4⋊C4—22no—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
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—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—41no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
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—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
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—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—42no—
1110C42—42no—
1111C42—81no—
1112C42—81no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—22no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
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—162no—
1156C23—162no—
1157C23—162no—
1158C23—162no—
1159C23—162no—
1160C23#54612yes—
1161C23#57612yes—
1162C23C23×D411yescharacteristic
1163Q8—22no—
1164Q8—22no—
1165Q8—41no—
1166Q8—41no—
1167Q8—162no—
1168D4—22no—
1169D4—22no—
1170D4—44no—
1171D4—44no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—84no—
1183D4—82no—
1184D4—84no—
1185D4—84no—
1186D4—84no—
1187D4—162no—
1188D4—162no—
1189D4—162no—
1190D4—162no—
1191D4—162no—
1192D4—162no—
1193D4—162no—
1194D4—162no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—22no—
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—41no—
1232C2×C4—41no—
1233C2×C4—41no—
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—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—84no—
1278C2×C4—84no—
1279C2×C4—162no—
1280C2×C4—162no—
1281C2×C4—162no—
1282C2×C4—162no—
1283C2×C4—162no—
1284C2×C4#54612yes—
1285C2×C4#57712yes—
1286C2×C4C22×#4111yescharacteristic
1287C2×C4C2×H(5,𝔽2)11yescharacteristic
1288C2×C4C2×H(5,𝔽2)11yescharacteristic
1289C2×C4#58511yescharacteristic
1290C2×C4#58511yescharacteristic
1291C2×C4#58511yescharacteristic
1292C8—22no—
1293C8—41no—
1294C8—41no—
1295C8—41no—
1296C8—41no—
1297C8—41no—
1298C8—41no—
1299C8—41no—
1300C22—22no—
1301C22—22no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—42no—
1316C22—42no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—42no—
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—168no—
1343C22C2×#54611yescharacteristic
1344C22#349611yescharacteristic
1345C22#350011yescharacteristic
1346C22C2×#57611yescharacteristic
1347C22C2×#57711yescharacteristic
1348C22#358511yescharacteristic
1349C22#358611yescharacteristic
1350C4—22no—
1351C4—22no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—42no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4#345911yescharacteristic
1375C4#349111yescharacteristic
1376C4#353411yescharacteristic
1377C4#356011yescharacteristic
1378C2—42no—
1379C2—42no—
1380C2—81no—
1381C2—82no—
1382C2—161no—
1383C2—161no—
1384C2#3941411yescharacteristic
1385C2#6119111yescharacteristic
1386C2#6119211yescharacteristic
1387C2#6231511yescharacteristic
1388C2#6234511yescharacteristic
1389C2#6255211yescharacteristic
1390C2#6256711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#42951C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42506C2semidirect
3. #33045C2semidirect
4. #31976C2semidirect
5. #31966C2semidirect
6. #31674C2semidirect
7. #31666C2semidirect
8. #31378C2semidirect
9. #31376C2semidirect
10. #31313C2semidirect
11. #31310C2semidirect
12. #29961C2semidirect
13. #29765C2semidirect
14. #29032C2semidirect
15. #29029C2semidirect
16. #28866C2semidirect
17. #28844C2semidirect
18. #28107C2semidirect
19. #28101C2semidirect
20. #27270C2semidirect
21. #27254C2semidirect
22. #26202C2semidirect
23. #26198C2semidirect
24. #25263C2semidirect
25. #25245C2semidirect
26. #24037C2semidirect
27. #24034C2semidirect
28. #22432C2semidirect
29. #22419C2semidirect
30. #21496C2semidirect
31. #21087C2semidirect
36. C2×#482C22semidirect
37. C2×#436C22semidirect
41. C2×#417C22semidirect
44. C2×#405C22semidirect
58. #2628C22semidirect
62. #2507C22semidirect
63. #2507C22semidirect
65. #2494C22semidirect
69. #2485C22semidirect
74. #2440C22semidirect
85. D4×C4⋊C4C22semidirect
86. #2317C22semidirect
88. #2100C22semidirect
89. #2099C22semidirect
90. #2097C22semidirect
92. #2088C22semidirect
93. #2088C22semidirect
94. #2085C22semidirect
95. #2085C22semidirect
96. #2077C22semidirect
97. #2076C22semidirect
101. #2071C22semidirect
102. #2068C22semidirect
106. #2067C22semidirect
107. #2066C22semidirect
110. #2065C22semidirect
111. #2065C22semidirect
126. #2024C22semidirect
128. #1993C22semidirect
135. #1944C22semidirect
136. #1942C22semidirect
137. #1939C22semidirect
141. #1936C22semidirect
142. #1936C22semidirect
143. #1935C22semidirect
144. #1935C22semidirect
149. #1934C22semidirect
150. #1933C22semidirect
151. #1933C22semidirect
153. #1925C22semidirect
155. #1924C22semidirect
156. #1919C22semidirect
157. #1918C22semidirect
161. #1895C22semidirect
164. #1893C22semidirect
170. #1874C22semidirect
173. #1869C22semidirect
174. #1865C22semidirect
176. #1863C22semidirect
178. #1853C22semidirect
179. #1852C22semidirect
180. #1835C22semidirect
181. #1824C22semidirect
183. #1809C22semidirect
185. #1803C22semidirect
187. #1798C22semidirect
190. #1788C22semidirect
191. #1788C22semidirect
192. #1788C22semidirect
196. #1771C22semidirect
198. C4×#103C22semidirect
199. #1753C22semidirect
201. #1736C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#429512
#425062
#330452
#319762
#319662
#316742
#316662
#313782
#313762
#313132
#313102
#299612
#297652
#290322
#290292
#288662
#288442
#281072
#281012
#272702
#272542
#262022
#261982
#252632
#252452
#240372
#240342
#224322
#224192
#214962
#210872