Finite Group Databasebeta

← #7063242

Subgroups — #7063242

Order 512.

1757 conjugacy classes of subgroups.

The subgroup lattice has 1404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59198C211yesmaximal, characteristic, complemented
2#39862C211yesmaximal, characteristic
3#32207C211yesmaximal, characteristic, complemented
4#32032C211yesmaximal, characteristic, complemented
5#32026C211yesmaximal, characteristic, complemented
6#31800C211yesmaximal, characteristic, complemented
7#31760C211yesmaximal, characteristic, complemented
8#31494C211yesmaximal, characteristic, complemented
9#31320C211yesmaximal, characteristic, complemented
10#30631C211yesmaximal, characteristic, complemented
11#29048C211yesmaximal, characteristic, complemented
12#28597C211yesmaximal, characteristic, complemented
13#28101C211yesmaximal, characteristic, complemented
14#28082C211yesmaximal, characteristic, complemented
15#27411C211yesmaximal, characteristic, complemented
16#27331C211yesmaximal, characteristic, complemented
17#27270C211yesmaximal, characteristic, complemented
18#26242C211yesmaximal, characteristic, complemented
19#26202C211yesmaximal, characteristic, complemented
20#26009C211yesmaximal, characteristic, complemented
21#25236C211yesmaximal, characteristic, complemented
22#24879C211yesmaximal, characteristic, complemented
23#24557C211yesmaximal, characteristic, complemented
24#24553C211yesmaximal, characteristic, complemented
25#24488C211yesmaximal, characteristic, complemented
26#24101C211yesmaximal, characteristic, complemented
27#23482C211yesmaximal, characteristic, complemented
28#22846C211yesmaximal, characteristic, complemented
29#22624C211yesmaximal, characteristic, complemented
30#22493C211yesmaximal, characteristic, complemented
31#21763C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#551—21no—
34C2×#525C2211yescharacteristic
35C2×#486C2211yescharacteristic, complemented
36C2×#481C2211yescharacteristic
37C2×#481C2211yescharacteristic
38C2×#483C2211yescharacteristic, complemented
39C2×#435C2211yescharacteristic
40C2×C8×D4C2211yescharacteristic
41C2×#428C2211yescharacteristic
42C2×#417C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#407C2211yescharacteristic
45C22×C22⋊C8C2211yescharacteristic
46#2847C2211yescharacteristic
47#2722—21no—
48#2717—21no—
49#2706—21no—
50#2703—21no—
51#2678—21no—
52#2669—21no—
53#2636—21no—
54#2603—21no—
55#2547C2211yescharacteristic
56#2541C2211yescharacteristic
57#2540C2211yescharacteristic
58#2535—21no—
59#2496C2211yescharacteristic
60#2496C2211yescharacteristic
61#2490C2211yescharacteristic
62#2489C2211yescharacteristic
63#2486C2211yescharacteristic
64#2486C2211yescharacteristic
65#2486C2211yescharacteristic
66#2483—21no—
67#2440C2211yescharacteristic
68#2440C2211yescharacteristic
69#2438—21no—
70#2438—21no—
71#2431C2211yescharacteristic
72#2428C2211yescharacteristic
73#2427C2211yescharacteristic
74#2419—21no—
75#2419—21no—
76#2417C2211yescharacteristic
77#2416C2211yescharacteristic
78#2407C2211yescharacteristic
79D4×C4⋊C4C2211yescharacteristic
80D4×C4⋊C4C2211yescharacteristic
81#2346C2211yescharacteristic
82#2344C2211yescharacteristic
83#2344C2211yescharacteristic
84#2328—21no—
85C4×#120C2211yescharacteristic
86C2×#380C2211yescharacteristic
87C2×#380C2211yescharacteristic
88#2100C2211yescharacteristic, complemented
89#2094C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2087C2211yescharacteristic, complemented
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2072C2211yescharacteristic, complemented
97#2071C2211yescharacteristic, complemented
98#2068C2211yescharacteristic, complemented
99#2066C2211yescharacteristic, complemented
100#2065C2211yescharacteristic, complemented
101#2065C2211yescharacteristic, complemented
102#2059C2211yescharacteristic, complemented
103#2059C2211yescharacteristic, complemented
104#2058C2211yescharacteristic, complemented
105#2042C2211yescharacteristic, complemented
106#2042C2211yescharacteristic, complemented
107#2041C2211yescharacteristic, complemented
108#2041C2211yescharacteristic, complemented
109#2036C2211yescharacteristic
110#2036C2211yescharacteristic
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic, complemented
114#2035C2211yescharacteristic, complemented
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic, complemented
124#2033C2211yescharacteristic, complemented
125#2033C2211yescharacteristic, complemented
126#2033C2211yescharacteristic, complemented
127#2024C2211yescharacteristic, complemented
128#1992C2211yescharacteristic, complemented
129#1989C2211yescharacteristic, complemented
130#1988C2211yescharacteristic, complemented
131#1983C2211yescharacteristic, complemented
132#1982C2211yescharacteristic, complemented
133#1959C2211yescharacteristic, complemented
134#1955C2211yescharacteristic
135#1948C2211yescharacteristic, complemented
136#1944C2211yescharacteristic, complemented
137#1941C2211yescharacteristic, complemented
138#1936C2211yescharacteristic, complemented
139#1936C2211yescharacteristic, complemented
140#1935C2211yescharacteristic, complemented
141#1933C2211yescharacteristic, complemented
142#1928C2211yescharacteristic, complemented
143#1927C2211yescharacteristic, complemented
144#1926C2211yescharacteristic, complemented
145#1926C2211yescharacteristic, complemented
146#1924C2211yescharacteristic
147#1923C2211yescharacteristic
148#1921C2211yescharacteristic, complemented
149#1920C2211yescharacteristic, complemented
150#1920C2211yescharacteristic, complemented
151#1919C2211yescharacteristic, complemented
152#1918C2211yescharacteristic, complemented
153#1918C2211yescharacteristic, complemented
154#1895C2211yescharacteristic
155#1895C2211yescharacteristic
156#1893C2211yescharacteristic
157#1893C2211yescharacteristic
158#1893C2211yescharacteristic
159#1893C2211yescharacteristic
160#1893C2211yescharacteristic, complemented
161#1893C2211yescharacteristic, complemented
162#1892C2211yescharacteristic
163#1892C2211yescharacteristic
164#1892C2211yescharacteristic, complemented
165#1874C2211yescharacteristic
166#1874C2211yescharacteristic
167#1874C2211yescharacteristic
168#1874C2211yescharacteristic
169#1874C2211yescharacteristic, complemented
170#1874C2211yescharacteristic, complemented
171#1872C2211yescharacteristic
172#1872C2211yescharacteristic
173#1870C2211yescharacteristic
174#1869C2211yescharacteristic
175#1869C2211yescharacteristic
176#1864C2211yescharacteristic, complemented
177#1864C2211yescharacteristic, complemented
178#1853C2211yescharacteristic
179#1853C2211yescharacteristic, complemented
180#1853C2211yescharacteristic, complemented
181#1852C2211yescharacteristic
182#1851C2211yescharacteristic
183#1850C2211yescharacteristic
184#1825C2211yescharacteristic
185#1825C2211yescharacteristic
186#1824C2211yescharacteristic
187#1824C2211yescharacteristic
188#1824C2211yescharacteristic, complemented
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1807C2211yescharacteristic
192#1807C2211yescharacteristic
193#1802C2211yescharacteristic, complemented
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1776C2211yescharacteristic, complemented
197C4×#107C2211yescharacteristic, complemented
198#1762C2211yescharacteristic, complemented
199#1753C2211yescharacteristic
200#1752C2211yescharacteristic
201#1736C2211yescharacteristic
202C2×#340C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#553—24no—
211#553—42no—
212#551—48no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×#127—21no—
215C2×#127C2311yescharacteristic
216C2×#126—21no—
217C2×#126—21no—
218C2×#126—21no—
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#124C2311yescharacteristic
222#525—24no—
223#525—42no—
224C2×#123—21no—
225C2×#123—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×#123—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#120—21no—
245C2×#120—21no—
246C2×#120D411yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4—21no—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×#117—21no—
257C2×#117—21no—
258C2×#117C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C22⋊C4—21no—
266C22×C22⋊C4—21no—
267#486—42no—
268#483—42no—
269#481—42no—
270#481—42no—
271#435—42no—
272C8×D4—42no—
273#428—24no—
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289#417—42no—
290#417—42no—
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
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
315#407—42no—
316C2×C22⋊C8—42no—
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
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×#97C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331#400—21no—
332#400—21no—
333#400—21no—
334#399—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#396—21no—
352#396—21no—
353#395—21no—
354#395—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—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#391C2311yescharacteristic
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#389—21no—
377#389—21no—
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386D411yescharacteristic
407#386D411yescharacteristic
408#386D411yescharacteristic
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385D411yescharacteristic
417#385D411yescharacteristic
418#385D411yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#382—21no—
422#382—21no—
423#381—21no—
424#381—21no—
425#381—21no—
426#381—21no—
427#381—21no—
428#380—21no—
429#380—21no—
430#380—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#379D411yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457#376—21no—
458C2×#95—21no—
459C2×#95—21no—
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
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#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C25C2×D411yescharacteristic
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C22×Q8—21no—
502C22×Q8C2411yescharacteristic
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—21no—
512C22×D4—21no—
513C22×D4C2×D411yescharacteristic
514C22×D4C2×D411yescharacteristic
515C22×D4C2×D411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—22no—
519C23×C4—22no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—41no—
529C23×C4—41no—
530C23×C4—41no—
531C23×C4—41no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2×D411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C2×M16—22no—
540C2×M16—22no—
541C2×M16—22no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C22×C8—41no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8—41no—
549C22×C8—41no—
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—41no—
565#127—41no—
566#127—44no—
567#126—44no—
568#126—44no—
569#126—44no—
570#125—22no—
571#125—41no—
572#124—41no—
573#124—41no—
574#124—44no—
575#123—44no—
576#123—44no—
577#123—44no—
578#123—44no—
579#123—44no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—44no—
583C22⋊Q8—44no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—44no—
594#121—41no—
595#121—41no—
596#121—41no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—41no—
602#121—41no—
603#121—82no—
604#121—82no—
605#120—24no—
606#120—44no—
607#120—82no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—44no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—44no—
618C4×D4—44no—
619C4×D4—44no—
620C4×D4—44no—
621#117—22no—
622#117—44no—
623#117—44no—
624#117#4114yes—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
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—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
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—41no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
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—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—44no—
710C2×C22⋊C4—44no—
711C2×C22⋊C4C2×D411yescharacteristic
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×C22⋊C4C2×D411yescharacteristic
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732#107—22no—
733#107—22no—
734#107—41no—
735#107—41no—
736#106—22no—
737#106—22no—
738#106—22no—
739#106—41no—
740#106—41no—
741#106—41no—
742#106—41no—
743#106—41no—
744C4⋊C8—41no—
745C4⋊C8—41no—
746C4⋊C8—41no—
747#103—22no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#102—22no—
756#102—22no—
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—
773C22⋊C8—22no—
774C22⋊C8—22no—
775C22⋊C8—22no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782#97—41no—
783#97—41no—
784C4×C8—22no—
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#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822C24—22no—
823C24—22no—
824C24—22no—
825C24—21no—
826C24—21no—
827C24—41no—
828C24—41no—
829C24—41no—
830C24—41no—
831C24C22×D411yescharacteristic
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834C24C22×D411yescharacteristic
835#41—44no—
836#41—44no—
837#41—82no—
838#41—82no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—42no—
846C2×Q8—81no—
847C2×Q8—81no—
848C2×D4—22no—
849C2×D4—22no—
850C2×D4—22no—
851C2×D4—22no—
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—41no—
865C2×D4—41no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
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—81no—
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—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4AGL(1,ℤ/8)14yes—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—22no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
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—22no—
925C22×C4—22no—
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—41no—
939C22×C4—41no—
940C22×C4—41no—
941C22×C4—41no—
942C22×C4—41no—
943C22×C4—41no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—82no—
957C22×C4—82no—
958C22×C4—82no—
959C22×C4—82no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C2×#4112yes—
983C22×C4H(5,𝔽2)12yes—
984C22×C4C2511yescharacteristic
985M16—44no—
986M16—82no—
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—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—82no—
1011C2×C8—82no—
1012C2×C8—82no—
1013C2×C8H(5,𝔽2)12yes—
1014C4⋊C4—22no—
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—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—41no—
1040C4⋊C4—41no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
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—42no—
1055C4⋊C4—42no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4C2×#4112yes—
1066C4⋊C4C2×#4112yes—
1067C22⋊C4—24no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—22no—
1072C22⋊C4—22no—
1073C22⋊C4—22no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—41no—
1078C22⋊C4—41no—
1079C22⋊C4—41no—
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—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C42—24no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—42no—
1119C42—42no—
1120C42—42no—
1121C42—42no—
1122C42—81no—
1123C23—21no—
1124C23—21no—
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—21no—
1145C23—21no—
1146C23—21no—
1147C23—44no—
1148C23—44no—
1149C23—44no—
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—82no—
1165C23—82no—
1166C23—82no—
1167C23—82no—
1168C23#54612yes—
1169C23C2×AGL(1,ℤ/8)12yes—
1170C23C2×AGL(1,ℤ/8)12yes—
1171C23#57712yes—
1172C23C23×D411yescharacteristic
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—162no—
1178D4—44no—
1179D4—44no—
1180D4—44no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—84no—
1190D4—84no—
1191D4—84no—
1192D4—84no—
1193D4—162no—
1194D4—162no—
1195D4—162no—
1196D4—162no—
1197D4—162no—
1198D4—162no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—22no—
1214C2×C4—22no—
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—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—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—82no—
1287C2×C4—84no—
1288C2×C4—82no—
1289C2×C4—84no—
1290C2×C4—84no—
1291C2×C4—162no—
1292C2×C4—162no—
1293C2×C4—162no—
1294C2×C4—162no—
1295C2×C4—162no—
1296C2×C4#54612yes—
1297C2×C4C2×AGL(1,ℤ/8)12yes—
1298C2×C4C22×#4111yescharacteristic
1299C2×C4C2×H(5,𝔽2)11yescharacteristic
1300C2×C4C2×H(5,𝔽2)11yescharacteristic
1301C2×C4#58511yescharacteristic
1302C2×C4#58511yescharacteristic
1303C2×C4#58511yescharacteristic
1304C8—22no—
1305C8—41no—
1306C8—41no—
1307C8—41no—
1308C8—41no—
1309C8—41no—
1310C8—41no—
1311C8—41no—
1312C22—22no—
1313C22—22no—
1314C22—22no—
1315C22—22no—
1316C22—22no—
1317C22—22no—
1318C22—22no—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—22no—
1323C22—22no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—88no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22C2×#54611yescharacteristic
1356C22#348511yescharacteristic
1357C22#349611yescharacteristic
1358C22C22×AGL(1,ℤ/8)11yescharacteristic
1359C22C2×#57711yescharacteristic
1360C22#358411yescharacteristic
1361C22#358611yescharacteristic
1362C4—22no—
1363C4—22no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—42no—
1372C4—41no—
1373C4—42no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4#349411yescharacteristic
1387C4#351011yescharacteristic
1388C4#353311yescharacteristic
1389C4#354211yescharacteristic
1390C2—42no—
1391C2—42no—
1392C2—42no—
1393C2—42no—
1394C2—161no—
1395C2—161no—
1396C2#4390511yescharacteristic
1397C2#6116111yescharacteristic
1398C2#6117211yescharacteristic
1399C2#6172811yescharacteristic
1400C2#6176311yescharacteristic
1401C2#6225311yescharacteristic
1402C2#6230711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#39862C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59198C2semidirect
3. #32207C2semidirect
4. #32032C2semidirect
5. #32026C2semidirect
6. #31800C2semidirect
7. #31760C2semidirect
8. #31494C2semidirect
9. #31320C2semidirect
10. #30631C2semidirect
11. #29048C2semidirect
12. #28597C2semidirect
13. #28101C2semidirect
14. #28082C2semidirect
15. #27411C2semidirect
16. #27331C2semidirect
17. #27270C2semidirect
18. #26242C2semidirect
19. #26202C2semidirect
20. #26009C2semidirect
21. #25236C2semidirect
22. #24879C2semidirect
23. #24557C2semidirect
24. #24553C2semidirect
25. #24488C2semidirect
26. #24101C2semidirect
27. #23482C2semidirect
28. #22846C2semidirect
29. #22624C2semidirect
30. #22493C2semidirect
31. #21763C2semidirect
35. C2×#486C22semidirect
38. C2×#483C22semidirect
88. #2100C22semidirect
89. #2094C22semidirect
90. #2088C22semidirect
91. #2087C22semidirect
96. #2072C22semidirect
97. #2071C22semidirect
98. #2068C22semidirect
99. #2066C22semidirect
100. #2065C22semidirect
101. #2065C22semidirect
102. #2059C22semidirect
103. #2059C22semidirect
104. #2058C22semidirect
105. #2042C22semidirect
106. #2042C22semidirect
107. #2041C22semidirect
108. #2041C22semidirect
113. #2035C22semidirect
114. #2035C22semidirect
123. #2033C22semidirect
124. #2033C22semidirect
125. #2033C22semidirect
126. #2033C22semidirect
127. #2024C22semidirect
128. #1992C22semidirect
129. #1989C22semidirect
130. #1988C22semidirect
131. #1983C22semidirect
132. #1982C22semidirect
133. #1959C22semidirect
135. #1948C22semidirect
136. #1944C22semidirect
137. #1941C22semidirect
138. #1936C22semidirect
139. #1936C22semidirect
140. #1935C22semidirect
141. #1933C22semidirect
142. #1928C22semidirect
143. #1927C22semidirect
144. #1926C22semidirect
145. #1926C22semidirect
148. #1921C22semidirect
149. #1920C22semidirect
150. #1920C22semidirect
151. #1919C22semidirect
152. #1918C22semidirect
153. #1918C22semidirect
160. #1893C22semidirect
161. #1893C22semidirect
164. #1892C22semidirect
169. #1874C22semidirect
170. #1874C22semidirect
176. #1864C22semidirect
177. #1864C22semidirect
179. #1853C22semidirect
180. #1853C22semidirect
188. #1824C22semidirect
193. #1802C22semidirect
196. #1776C22semidirect
197. C4×#107C22semidirect
198. #1762C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#591982
#398622
#322072
#320322
#320262
#318002
#317602
#314942
#313202
#306312
#290482
#285972
#281012
#280822
#274112
#273312
#272702
#262422
#262022
#260092
#252362
#248792
#245572
#245532
#244882
#241012
#234822
#228462
#226242
#224932
#217632