Finite Group Databasebeta

← #7203734

Subgroups — #7203734

Order 512.

1580 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45609C211yesmaximal, characteristic, complemented
2#36404C211yesmaximal, characteristic, complemented
3#33006C211yesmaximal, characteristic, complemented
4#32958C211yesmaximal, characteristic, complemented
5#32786C211yesmaximal, characteristic, complemented
6#32742C211yesmaximal, characteristic, complemented
7#32357C211yesmaximal, characteristic, complemented
8#32007C211yesmaximal, characteristic, complemented
9#31675C211yesmaximal, characteristic, complemented
10#31561C211yesmaximal, characteristic, complemented
11#31543C211yesmaximal, characteristic, complemented
12#31400C211yesmaximal, characteristic, complemented
13#31376C211yesmaximal, characteristic, complemented
14#31279C211yesmaximal, characteristic, complemented
15#31090C211yesmaximal, characteristic, complemented
16#31046C211yesmaximal, characteristic, complemented
17#30673C211yesmaximal, characteristic, complemented
18#30398C211yesmaximal, characteristic, complemented
19#27422C211yesmaximal, characteristic, complemented
20#27374C211yesmaximal, characteristic, complemented
21#26805C211yesmaximal, characteristic, complemented
22#26660C211yesmaximal, characteristic, complemented
23#26412C211yesmaximal, characteristic, complemented
24#26358C211yesmaximal, characteristic, complemented
25#26315C211yesmaximal, characteristic, complemented
26#26152C211yesmaximal, characteristic, complemented
27#25533C211yesmaximal, characteristic, complemented
28#25019C211yesmaximal, characteristic, complemented
29#24943C211yesmaximal, characteristic, complemented
30#24100C211yesmaximal, characteristic, complemented
31#23331C211yesmaximal, characteristic, complemented
32C2×#547C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#480C2211yescharacteristic
37C2×#477C2211yescharacteristic
38C2×#476C2211yescharacteristic
39C2×#466C2211yescharacteristic
40C2×#449C2211yescharacteristic
41C2×#428C2211yescharacteristic
42#2857C2211yescharacteristic
43#2857C2211yescharacteristic
44#2855—21no—
45#2854C2211yescharacteristic
46#2832—21no—
47#2783—21no—
48#2706—21no—
49#2696—21no—
50#2692—21no—
51#2681—21no—
52#2676—21no—
53#2568C2211yescharacteristic
54#2563C2211yescharacteristic
55#2538C2211yescharacteristic
56#2535C2211yescharacteristic
57#2508C2211yescharacteristic
58#2491C2211yescharacteristic
59#2487C2211yescharacteristic
60#2485C2211yescharacteristic
61#2470—21no—
62#2470—21no—
63#2457—21no—
64#2457—21no—
65#2452C2211yescharacteristic
66#2440C2211yescharacteristic
67#2439C2211yescharacteristic
68#2422C2211yescharacteristic
69#2420C2211yescharacteristic
70#2420C2211yescharacteristic
71#2416C2211yescharacteristic
72#2415—21no—
73#2414C2211yescharacteristic
74#2407—21no—
75#2407C2211yescharacteristic
76#2407C2211yescharacteristic
77#2379—21no—
78#2360C2211yescharacteristic
79#2360C2211yescharacteristic
80#2354C2211yescharacteristic
81#2352C2211yescharacteristic
82#2352C2211yescharacteristic
83C4×#121C2211yescharacteristic
84#2297—21no—
85#2101C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2097C2211yescharacteristic
91#2092C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2084C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2076C2211yescharacteristic
102#2075C2211yescharacteristic
103#2075C2211yescharacteristic
104#2075C2211yescharacteristic
105#2075C2211yescharacteristic
106#2073C2211yescharacteristic
107#2071C2211yescharacteristic
108#2068C2211yescharacteristic
109#2066C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic
113#2058C2211yescharacteristic
114#2057C2211yescharacteristic
115#2057C2211yescharacteristic
116#2057C2211yescharacteristic
117#2057C2211yescharacteristic
118#2054C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic
127#2024C2211yescharacteristic
128#2023C2211yescharacteristic
129#2023C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#1999C2211yescharacteristic
133#1993C2211yescharacteristic
134#1988C2211yescharacteristic
135#1973C2211yescharacteristic
136#1955C2211yescharacteristic
137#1954C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1936C2211yescharacteristic
141#1934C2211yescharacteristic
142#1933C2211yescharacteristic
143#1928C2211yescharacteristic
144#1926C2211yescharacteristic
145#1925C2211yescharacteristic
146#1924C2211yescharacteristic
147#1923C2211yescharacteristic
148#1919C2211yescharacteristic
149#1919C2211yescharacteristic
150#1918C2211yescharacteristic
151#1917C2211yescharacteristic
152#1916C2211yescharacteristic
153#1895C2211yescharacteristic
154#1895C2211yescharacteristic
155#1894C2211yescharacteristic
156#1892C2211yescharacteristic
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1877C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1873C2211yescharacteristic
166#1872C2211yescharacteristic
167#1870C2211yescharacteristic
168#1870C2211yescharacteristic
169#1869C2211yescharacteristic
170#1869C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1865C2211yescharacteristic
174#1864C2211yescharacteristic
175#1863C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1853C2211yescharacteristic
183#1852C2211yescharacteristic
184#1852C2211yescharacteristic
185#1851C2211yescharacteristic
186#1850C2211yescharacteristic
187#1846C2211yescharacteristic
188#1825C2211yescharacteristic
189#1824C2211yescharacteristic
190#1824C2211yescharacteristic
191#1817C2211yescharacteristic
192#1807C2211yescharacteristic
193#1804C2211yescharacteristic
194#1803C2211yescharacteristic
195#1802C2211yescharacteristic
196#1797C2211yescharacteristic
197#1788C2211yescharacteristic
198#1788C2211yescharacteristic
199#1788C2211yescharacteristic
200#1776C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×#41—21no—
204C22×#41C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#547—42no—
210#547—42no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#124—21no—
215C2×#123—21no—
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121—21no—
227C2×#121D411yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C4×#41—42no—
234C4×#41—42no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117—21no—
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C42—21no—
253C22×C42C2311yescharacteristic
254#482—42no—
255#482—42no—
256#480—42no—
257#477—42no—
258#476—42no—
259#466—42no—
260#449—42no—
261#428—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#399—21no—
317#398—21no—
318#398—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#395—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#393—21no—
340#393—21no—
341#393—21no—
342#393—21no—
343#393—21no—
344#392—21no—
345#392—21no—
346#392—21no—
347#392—21no—
348#391—21no—
349#391—21no—
350#391—21no—
351#391—21no—
352#391—21no—
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#390—21no—
356#390—21no—
357#390—21no—
358#390D411yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389D411yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388D411yescharacteristic
389#388D411yescharacteristic
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—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#386—21no—
407#386—21no—
408#386D411yescharacteristic
409#386D411yescharacteristic
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#382—21no—
421#382—21no—
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#381—21no—
426#381—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380D411yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
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#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—44no—
497C2×#41—44no—
498C2×#41—82no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8C2411yescharacteristic
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4C2×D411yescharacteristic
510C22×D4C2×D411yescharacteristic
511C22×D4C2×D411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C2×SD16—22no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×D8—22no—
530C2×D8—41no—
531C2×D8—41no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C22×C8—41no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C4⋊Q8—41no—
547C4⋊Q8—41no—
548C4⋊Q8—41no—
549C4⋊Q8—41no—
550C4⋊Q8—41no—
551C4⋊Q8—41no—
552#124—44no—
553#123—44no—
554#123—44no—
555#123—82no—
556#123—82no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—41no—
560C22⋊Q8—41no—
561C22⋊Q8—44no—
562C22⋊Q8—82no—
563C22⋊Q8—82no—
564C22⋊Q8—82no—
565C22⋊Q8—82no—
566#121—22no—
567#121—22no—
568#121—42no—
569#121—41no—
570#121—41no—
571#121—41no—
572#121—41no—
573#121—41no—
574#121—41no—
575#121—41no—
576#121—41no—
577#121—82no—
578C4×Q8—22no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—44no—
595C4×D4—44no—
596#117—22no—
597#117—44no—
598#117—41no—
599#117—41no—
600#117—41no—
601#117—82no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
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—41no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—41no—
700C2×C42—41no—
701C2×C42—44no—
702C2×C42C2×D411yescharacteristic
703C2×C42C2×D411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708#107—22no—
709#107—22no—
710#107—41no—
711#107—41no—
712#107—41no—
713#107—41no—
714#107—41no—
715#106—22no—
716#106—41no—
717#106—41no—
718#106—41no—
719#106—41no—
720#106—41no—
721#106—41no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724C4⋊C8—41no—
725C4⋊C8—41no—
726#103—22no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755C22⋊C8—41no—
756#97—41no—
757C4×C8—41no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
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#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797C24—21no—
798C24—21no—
799C24C22×D411yescharacteristic
800C24C22×D411yescharacteristic
801C24C22×D411yescharacteristic
802#41—44no—
803#41—44no—
804#41—44no—
805#41—44no—
806#41—816no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—42no—
813C2×Q8—42no—
814C2×Q8—42no—
815C2×Q8—42no—
816C2×Q8—81no—
817C2×Q8—81no—
818C2×Q8—81no—
819C2×Q8—81no—
820C2×Q8—81no—
821C2×Q82−1+412yes—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—41no—
837C2×D4—42no—
838C2×D4—41no—
839C2×D4—41no—
840C2×D4—41no—
841C2×D4—41no—
842C2×D4—41no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4H(5,𝔽2)12yes—
861C22×C4—24no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—42no—
897C22×C4—41no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C2511yescharacteristic
932SD16—82no—
933D8—82no—
934M16—44no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—82no—
960C4⋊C4—22no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4H(5,𝔽2)12yes—
1014C22⋊C4—24no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—41no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—41no—
1066C42—41no—
1067C42—42no—
1068C42—42no—
1069C42—42no—
1070C42—42no—
1071C42—81no—
1072C42—81no—
1073C42—81no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—22no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23#57512yes—
1109C23C23×D411yescharacteristic
1110Q8—22no—
1111Q8—22no—
1112Q8—41no—
1113Q8—41no—
1114Q8—84no—
1115Q8—162no—
1116Q8—162no—
1117D4—22no—
1118D4—22no—
1119D4—44no—
1120D4—48no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—82no—
1128D4—82no—
1129D4—84no—
1130D4—84no—
1131D4—162no—
1132D4—162no—
1133D4—162no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—22no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—22no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—48no—
1168C2×C4—48no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—82no—
1222C2×C4—82no—
1223C2×C4—84no—
1224C2×C4—84no—
1225C2×C4—84no—
1226C2×C4—162no—
1227C2×C4—162no—
1228C2×C4#57612yes—
1229C2×C4#57712yes—
1230C2×C4C2×H(5,𝔽2)11yescharacteristic
1231C2×C4C2×H(5,𝔽2)11yescharacteristic
1232C2×C4C2×2−1+411yescharacteristic
1233C2×C4#58511yescharacteristic
1234C2×C4#58511yescharacteristic
1235C2×C4#58511yescharacteristic
1236C8—41no—
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C8—41no—
1243C8—41no—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—42no—
1256C22—41no—
1257C22—41no—
1258C22—42no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—42no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22#348411yescharacteristic
1280C22#348511yescharacteristic
1281C22#348911yescharacteristic
1282C22C2×#57511yescharacteristic
1283C22C2×#57611yescharacteristic
1284C22C2×#57711yescharacteristic
1285C22#358611yescharacteristic
1286C4—22no—
1287C4—22no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—42no—
1296C4—41no—
1297C4—42no—
1298C4—41no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4#352911yescharacteristic
1312C4#353311yescharacteristic
1313C4#353511yescharacteristic
1314C4#354111yescharacteristic
1315C2—42no—
1316C2—81no—
1317C2—81no—
1318C2—82no—
1319C2—161no—
1320C2#4544711yescharacteristic
1321C2#6159211yescharacteristic
1322C2#6162011yescharacteristic
1323C2#6171511yescharacteristic
1324C2#6178811yescharacteristic
1325C2#6212911yescharacteristic
1326C2#6218611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
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. #45609C2semidirect
2. #36404C2semidirect
3. #33006C2semidirect
4. #32958C2semidirect
5. #32786C2semidirect
6. #32742C2semidirect
7. #32357C2semidirect
8. #32007C2semidirect
9. #31675C2semidirect
10. #31561C2semidirect
11. #31543C2semidirect
12. #31400C2semidirect
13. #31376C2semidirect
14. #31279C2semidirect
15. #31090C2semidirect
16. #31046C2semidirect
17. #30673C2semidirect
18. #30398C2semidirect
19. #27422C2semidirect
20. #27374C2semidirect
21. #26805C2semidirect
22. #26660C2semidirect
23. #26412C2semidirect
24. #26358C2semidirect
25. #26315C2semidirect
26. #26152C2semidirect
27. #25533C2semidirect
28. #25019C2semidirect
29. #24943C2semidirect
30. #24100C2semidirect
31. #23331C2semidirect

Maximal subgroups

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

subgroupindex
#456092
#364042
#330062
#329582
#327862
#327422
#323572
#320072
#316752
#315612
#315432
#314002
#313762
#312792
#310902
#310462
#306732
#303982
#274222
#273742
#268052
#266602
#264122
#263582
#263152
#261522
#255332
#250192
#249432
#241002
#233312