Finite Group Databasebeta

← #7607555

Subgroups — #7607555

Order 512.

1813 conjugacy classes of subgroups.

The subgroup lattice has 1400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59216C211yesmaximal, characteristic, complemented
2#59051C211yesmaximal, characteristic
3#32035C211yesmaximal, characteristic, complemented
4#32026C211yesmaximal, characteristic, complemented
5#31392C211yesmaximal, characteristic, complemented
6#31386C211yesmaximal, characteristic, complemented
7#29064C211yesmaximal, characteristic, complemented
8#29051C211yesmaximal, characteristic, complemented
9#27760C211yesmaximal, characteristic, complemented
10#27633C211yesmaximal, characteristic, complemented
11#27049C211yesmaximal, characteristic, complemented
12#27046C211yesmaximal, characteristic, complemented
13#26950C211yesmaximal, characteristic, complemented
14#26947C211yesmaximal, characteristic, complemented
15#26521C211yesmaximal, characteristic, complemented
16#26248C211yesmaximal, characteristic, complemented
17#25402C211yesmaximal, characteristic, complemented
18#25402C211yesmaximal, characteristic, complemented
19#25387C211yesmaximal, characteristic, complemented
20#25243C211yesmaximal, characteristic, complemented
21#25232C211yesmaximal, characteristic, complemented
22#24742C211yesmaximal, characteristic, complemented
23#24156C211yesmaximal, characteristic, complemented
24#24132C211yesmaximal, characteristic, complemented
25#23141C211yesmaximal, characteristic, complemented
26#23134C211yesmaximal, characteristic, complemented
27#22977C211yesmaximal, characteristic, complemented
28#22495C211yesmaximal, characteristic, complemented
29#21528C211yesmaximal, characteristic, complemented
30#21489C211yesmaximal, characteristic, complemented
31#21408C211yesmaximal, characteristic, complemented
32C2×#550—21no—
33C2×#547C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#480C2211yescharacteristic
37C2×#477C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#460C2211yescharacteristic
42C2×#460C2211yescharacteristic
43C2×#460C2211yescharacteristic
44C2×#440C2211yescharacteristic
45C2×#435C2211yescharacteristic
46C2×#435C2211yescharacteristic
47C2×C8×D4C2211yescharacteristic
48C22×#97C2211yescharacteristic
49#2739—21no—
50#2701—21no—
51#2673—21no—
52#2673—21no—
53#2606—21no—
54#2570C2211yescharacteristic
55#2541C2211yescharacteristic
56#2541C2211yescharacteristic
57#2541C2211yescharacteristic
58#2541C2211yescharacteristic
59#2538C2211yescharacteristic
60#2536C2211yescharacteristic
61#2536C2211yescharacteristic
62#2526—21no—
63#2525—21no—
64#2518—21no—
65#2515—21no—
66#2497C2211yescharacteristic
67#2495C2211yescharacteristic
68#2486C2211yescharacteristic
69#2485C2211yescharacteristic
70#2456—21no—
71#2456—21no—
72#2431—21no—
73#2428C2211yescharacteristic
74#2428C2211yescharacteristic
75#2426—21no—
76#2416C2211yescharacteristic
77#2416C2211yescharacteristic
78#2407—21no—
79#2374—21no—
80#2365C2211yescharacteristic
81#2362C2211yescharacteristic
82#2361C2211yescharacteristic
83#2361C2211yescharacteristic
84#2360C2211yescharacteristic
85#2352C2211yescharacteristic
86#2351C2211yescharacteristic
87C4×C22⋊Q8C2211yescharacteristic
88C4×#121C2211yescharacteristic
89C4×#121C2211yescharacteristic
90#2283C2211yescharacteristic
91#2101C2211yescharacteristic
92#2100C2211yescharacteristic
93#2087C2211yescharacteristic
94#2086C2211yescharacteristic
95#2077C2211yescharacteristic
96#2075C2211yescharacteristic
97#2073C2211yescharacteristic
98#2071C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2041C2211yescharacteristic
102#2041C2211yescharacteristic
103#2041C2211yescharacteristic
104#2041C2211yescharacteristic
105#2034C2211yescharacteristic
106#2034C2211yescharacteristic
107#2034C2211yescharacteristic
108#2034C2211yescharacteristic
109#2034C2211yescharacteristic
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2033C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2000C2211yescharacteristic
118#2000C2211yescharacteristic
119#2000C2211yescharacteristic
120#2000C2211yescharacteristic
121#2000C2211yescharacteristic
122#2000C2211yescharacteristic
123#1993C2211yescharacteristic
124#1993C2211yescharacteristic
125#1987C2211yescharacteristic
126#1982C2211yescharacteristic
127#1973C2211yescharacteristic
128#1961C2211yescharacteristic
129#1961C2211yescharacteristic
130#1961C2211yescharacteristic
131#1957C2211yescharacteristic
132#1955C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1948C2211yescharacteristic
137#1944C2211yescharacteristic
138#1943C2211yescharacteristic
139#1942C2211yescharacteristic
140#1940C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1935C2211yescharacteristic
144#1934C2211yescharacteristic
145#1926C2211yescharacteristic
146#1925C2211yescharacteristic
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1920C2211yescharacteristic
152#1919C2211yescharacteristic
153#1918C2211yescharacteristic
154#1918C2211yescharacteristic
155#1895C2211yescharacteristic
156#1895C2211yescharacteristic
157#1893C2211yescharacteristic
158#1893C2211yescharacteristic
159#1893C2211yescharacteristic
160#1893C2211yescharacteristic
161#1893C2211yescharacteristic
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic
164#1892C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1875C2211yescharacteristic
170#1875C2211yescharacteristic
171#1874C2211yescharacteristic
172#1874C2211yescharacteristic
173#1872C2211yescharacteristic
174#1872C2211yescharacteristic
175#1869C2211yescharacteristic
176#1869C2211yescharacteristic
177#1865C2211yescharacteristic
178#1863C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic
183#1824C2211yescharacteristic
184#1823C2211yescharacteristic
185#1808C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1797C2211yescharacteristic
189#1776C2211yescharacteristic
190#1771C2211yescharacteristic
191#1763C2211yescharacteristic
192#1763C2211yescharacteristic
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#103C2211yescharacteristic
199#1753C2211yescharacteristic
200#1752C2211yescharacteristic
201#1736C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×#41—21no—
204C22×#41—21no—
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#550—48no—
213#547—24no—
214#547—42no—
215#532—24no—
216#532—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127—21no—
219C2×#127—21no—
220C2×#127—21no—
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#124—21no—
225C2×#123—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×#121—21no—
239C2×#121D411yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×C4×Q8—21no—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4—21no—
256C2×C4×D4—21no—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C42C2311yescharacteristic
268#482—42no—
269#480—42no—
270#477—24no—
271#468—24no—
272#465—24no—
273#465—24no—
274#460—42no—
275#460—42no—
276#460—42no—
277#440—42no—
278#435—42no—
279#435—42no—
280C8×D4—42no—
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×#97—42no—
329C2×#97C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×#97C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×C4×C8C2311yescharacteristic
335#400—21no—
336#400—21no—
337#400—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#392—21no—
358#392—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#391C2311yescharacteristic
369#390—21no—
370#390—21no—
371#390—21no—
372#390—21no—
373#390D411yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389D411yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388D411yescharacteristic
404#388D411yescharacteristic
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386D411yescharacteristic
424#386D411yescharacteristic
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#384C2311yescharacteristic
430#383—21no—
431#383—21no—
432#382—21no—
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#381—21no—
437#381—21no—
438#380D411yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464#376—21no—
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#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497C2×#41—44no—
498C2×#41—44no—
499C2×#41—44no—
500C2×#41—44no—
501C2×#41—82no—
502C2×#41—82no—
503C22×Q8—21no—
504C22×Q8C2411yescharacteristic
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
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×D4C2×D411yescharacteristic
521C22×D4C2×D411yescharacteristic
522C22×D4C2×D411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×M16—22no—
547C2×M16—41no—
548C2×M16—41no—
549C22×C8—22no—
550C22×C8—22no—
551C22×C8—22no—
552C22×C8—41no—
553C22×C8—41no—
554C22×C8—41no—
555C22×C8—41no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C4⋊Q8—22no—
567C4⋊Q8#4114yes—
568#127—22no—
569#127—22no—
570#127—41no—
571#127—41no—
572#127—41no—
573#127—41no—
574#127—44no—
575#127—44no—
576#127—44no—
577#124—44no—
578#123—44no—
579#123—44no—
580#123—44no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—44no—
588#121—24no—
589#121—22no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—44no—
597#121—44no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—41no—
602#121—41no—
603#121—41no—
604#121—41no—
605#121—44no—
606#121—44no—
607#121—44no—
608#121—44no—
609#121—41no—
610#121—41no—
611#121—41no—
612#121—41no—
613#121—82no—
614C4×Q8—22no—
615C4×Q8—22no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—44no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—44no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—44no—
635C4×D4—44no—
636C4×D4—44no—
637#117—41no—
638#117—41no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—41no—
664C2×C4⋊C4—41no—
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42C2×D411yescharacteristic
735C2×C42C2×D411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740#107—22no—
741#107—22no—
742#107—22no—
743#107—22no—
744#107—41no—
745#107—41no—
746#106—22no—
747#106—22no—
748#106—41no—
749C4⋊C8—22no—
750C4⋊C8—22no—
751C4⋊C8—22no—
752C4⋊C8—22no—
753#103—22no—
754#103—22no—
755#103—41no—
756#103—41no—
757#103#4114yescomplemented
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779C22⋊C8—22no—
780C22⋊C8—22no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785C22⋊C8—41no—
786C22⋊C8—41no—
787#97—22no—
788#97—22no—
789#97—41no—
790#97—41no—
791#97—41no—
792C4×C8—41no—
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#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#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829C24—21no—
830C24—21no—
831C24—21no—
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834C24C22×D411yescharacteristic
835#41—816no—
836#41—816no—
837C2×Q8—24no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—42no—
844C2×Q8—42no—
845C2×Q8C2×#4112yes—
846C2×D4—22no—
847C2×D4—22no—
848C2×D4—22no—
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—41no—
868C2×D4—41no—
869C2×D4—41no—
870C2×D4—41no—
871C2×D4—41no—
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—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
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—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4AGL(1,ℤ/8)14yes—
918C22×C4—22no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—22no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
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—21no—
942C22×C4—22no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—41no—
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—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
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×C4C2511yescharacteristic
985SD16—44no—
986SD16—82no—
987SD16—82no—
988M16—82no—
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—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—44no—
1012C2×C8—44no—
1013C2×C8—82no—
1014C2×C8C2×#4112yes—
1015C2×C8H(5,𝔽2)12yes—
1016C4⋊C4—24no—
1017C4⋊C4—22no—
1018C4⋊C4—22no—
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—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—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4C2×#4112yes—
1063C4⋊C4C2×#4112yes—
1064C4⋊C4C2×#4112yes—
1065C22⋊C4—22no—
1066C22⋊C4—22no—
1067C22⋊C4—22no—
1068C22⋊C4—22no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
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—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
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—
1105C42—22no—
1106C42—22no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—42no—
1114C42—42no—
1115C42—42no—
1116C42—42no—
1117C42—42no—
1118C42—81no—
1119C42—81no—
1120C42—81no—
1121C42—81no—
1122C42—81no—
1123C42C2×#4112yes—
1124C42H(5,𝔽2)12yes—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
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—
1165C23C2×AGL(1,ℤ/8)12yes—
1166C23C2×AGL(1,ℤ/8)12yes—
1167C23C23×D411yescharacteristic
1168Q8—22no—
1169Q8—22no—
1170Q8—48no—
1171Q8—41no—
1172Q8—41no—
1173D4—44no—
1174D4—44no—
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—82no—
1190D4—84no—
1191D4—84no—
1192D4—84no—
1193D4—84no—
1194D4—84no—
1195D4—84no—
1196D4—84no—
1197D4—162no—
1198D4—162no—
1199D4—162no—
1200D4—162no—
1201D4—162no—
1202D4—162no—
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—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—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
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—44no—
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—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—82no—
1286C2×C4—84no—
1287C2×C4—84no—
1288C2×C4—84no—
1289C2×C4—84no—
1290C2×C4—84no—
1291C2×C4—162no—
1292C2×C4#54612yes—
1293C2×C4#54612yes—
1294C2×C4C2×AGL(1,ℤ/8)12yes—
1295C2×C4C22×#4111yescharacteristic
1296C2×C4C22×#4111yescharacteristic
1297C2×C4C2×H(5,𝔽2)11yescharacteristic
1298C2×C4C2×H(5,𝔽2)11yescharacteristic
1299C2×C4#58511yescharacteristic
1300C2×C4#58511yescharacteristic
1301C8—22no—
1302C8—22no—
1303C8—41no—
1304C8—41no—
1305C8—41no—
1306C8—41no—
1307C8—41no—
1308C8—41no—
1309C22—22no—
1310C22—22no—
1311C22—22no—
1312C22—22no—
1313C22—22no—
1314C22—22no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
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—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22C2×#54611yescharacteristic
1352C22D4×#4111yescharacteristic
1353C22#349611yescharacteristic
1354C22C22×AGL(1,ℤ/8)11yescharacteristic
1355C22#358411yescharacteristic
1356C22#358511yescharacteristic
1357C22#358611yescharacteristic
1358C4—22no—
1359C4—22no—
1360C4—22no—
1361C4—41no—
1362C4—42no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—42no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—42no—
1372C4—42no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4#348011yescharacteristic
1383C4#351711yescharacteristic
1384C4#351911yescharacteristic
1385C4#353911yescharacteristic
1386C2—42no—
1387C2—42no—
1388C2—81no—
1389C2—161no—
1390C2—161no—
1391C2—161no—
1392C2#5977011yescharacteristic
1393C2#6115511yescharacteristic
1394C2#6119011yescharacteristic
1395C2#6145211yescharacteristic
1396C2#6153411yescharacteristic
1397C2#6225311yescharacteristic
1398C2#6233311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59051C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59216C2semidirect
3. #32035C2semidirect
4. #32026C2semidirect
5. #31392C2semidirect
6. #31386C2semidirect
7. #29064C2semidirect
8. #29051C2semidirect
9. #27760C2semidirect
10. #27633C2semidirect
11. #27049C2semidirect
12. #27046C2semidirect
13. #26950C2semidirect
14. #26947C2semidirect
15. #26521C2semidirect
16. #26248C2semidirect
17. #25402C2semidirect
18. #25402C2semidirect
19. #25387C2semidirect
20. #25243C2semidirect
21. #25232C2semidirect
22. #24742C2semidirect
23. #24156C2semidirect
24. #24132C2semidirect
25. #23141C2semidirect
26. #23134C2semidirect
27. #22977C2semidirect
28. #22495C2semidirect
29. #21528C2semidirect
30. #21489C2semidirect
31. #21408C2semidirect
757. #103#41semidirect

Maximal subgroups

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

subgroupindex
#592162
#590512
#320352
#320262
#313922
#313862
#290642
#290512
#277602
#276332
#270492
#270462
#269502
#269472
#265212
#262482
#254022
#253872
#252432
#252322
#247422
#241562
#241322
#231412
#231342
#229772
#224952
#215282
#214892
#214082