Finite Group Databasebeta

← #7586833

Subgroups — #7586833

Order 512.

1673 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45006C211yesmaximal, characteristic, complemented
2#36051C211yesmaximal, characteristic, complemented
3#32589C211yesmaximal, characteristic, complemented
4#32584C211yesmaximal, characteristic, complemented
5#32041C211yesmaximal, characteristic, complemented
6#30501C211yesmaximal, characteristic, complemented
7#29570C211yesmaximal, characteristic, complemented
8#29566C211yesmaximal, characteristic, complemented
9#29059C211yesmaximal, characteristic, complemented
10#29056C211yesmaximal, characteristic, complemented
11#27122C211yesmaximal, characteristic, complemented
12#27119C211yesmaximal, characteristic, complemented
13#26977C211yesmaximal, characteristic, complemented
14#26976C211yesmaximal, characteristic, complemented
15#26939C211yesmaximal, characteristic, complemented
16#26938C211yesmaximal, characteristic, complemented
17#26669C211yesmaximal, characteristic, complemented
18#26664C211yesmaximal, characteristic, complemented
19#25172C211yesmaximal, characteristic, complemented
20#25168C211yesmaximal, characteristic, complemented
21#24204C211yesmaximal, characteristic, complemented
22#24198C211yesmaximal, characteristic, complemented
23#24093C211yesmaximal, characteristic, complemented
24#23976C211yesmaximal, characteristic, complemented
25#23277C211yesmaximal, characteristic, complemented
26#23033C211yesmaximal, characteristic, complemented
27#23031C211yesmaximal, characteristic, complemented
28#22868C211yesmaximal, characteristic, complemented
29#22864C211yesmaximal, characteristic, complemented
30#21126C211yesmaximal, characteristic, complemented
31#21126C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic, complemented
33C2×#555C2211yescharacteristic
34C2×#482C2211yescharacteristic, complemented
35C2×#466C2211yescharacteristic
36C2×#465C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#459C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#442C2211yescharacteristic
43C2×#442C2211yescharacteristic
44C2×#442C2211yescharacteristic
45C2×#440C2211yescharacteristic
46C2×#427C2211yescharacteristic, complemented
47C2×#418C2211yescharacteristic
48#2749—21no—
49#2743—21no—
50#2696—21no—
51#2685—21no—
52#2661—21no—
53#2640C2211yescharacteristic, complemented
54#2580C2211yescharacteristic
55#2578—21no—
56#2561—21no—
57#2557—21no—
58#2557—21no—
59#2546C2211yescharacteristic, complemented
60#2543—21no—
61#2540C2211yescharacteristic
62#2538C2211yescharacteristic
63#2498—21no—
64#2496C2211yescharacteristic
65#2495C2211yescharacteristic
66#2491—21no—
67#2491—21no—
68#2485C2211yescharacteristic
69#2480—21no—
70#2428C2211yescharacteristic
71#2428C2211yescharacteristic, complemented
72#2427C2211yescharacteristic
73#2427C2211yescharacteristic, complemented
74#2422C2211yescharacteristic
75#2420C2211yescharacteristic
76#2412—21no—
77#2408C2211yescharacteristic
78#2398C2211yescharacteristic
79#2395—21no—
80#2363C2211yescharacteristic
81#2363C2211yescharacteristic
82#2363C2211yescharacteristic
83#2363C2211yescharacteristic, complemented
84#2362C2211yescharacteristic
85#2362C2211yescharacteristic, complemented
86D4×C22⋊C4C2211yescharacteristic
87D4×C22⋊C4C2211yescharacteristic
88#2319C2211yescharacteristic
89#2319C2211yescharacteristic
90#2275C2211yescharacteristic, complemented
91#2101C2211yescharacteristic, complemented
92#2100C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2087C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2084C2211yescharacteristic, complemented
97#2065C2211yescharacteristic
98#2065C2211yescharacteristic
99#2058C2211yescharacteristic, complemented
100#2057C2211yescharacteristic, complemented
101#2042C2211yescharacteristic, complemented
102#2042C2211yescharacteristic, complemented
103#2042C2211yescharacteristic, complemented
104#2041C2211yescharacteristic, complemented
105#2036C2211yescharacteristic
106#2035C2211yescharacteristic
107#2035C2211yescharacteristic, complemented
108#2034C2211yescharacteristic
109#2034C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic, complemented
112#2033C2211yescharacteristic
113#2023C2211yescharacteristic
114#2023C2211yescharacteristic
115#2012C2211yescharacteristic
116#2012C2211yescharacteristic
117#2012C2211yescharacteristic
118#2011C2211yescharacteristic
119#2000C2211yescharacteristic
120#1999C2211yescharacteristic
121#1999C2211yescharacteristic
122#1999C2211yescharacteristic
123#1985C2211yescharacteristic, complemented
124#1985C2211yescharacteristic, complemented
125#1973C2211yescharacteristic
126#1972C2211yescharacteristic
127#1970C2211yescharacteristic
128#1968C2211yescharacteristic
129#1961C2211yescharacteristic, complemented
130#1959C2211yescharacteristic, complemented
131#1944C2211yescharacteristic, complemented
132#1943C2211yescharacteristic, complemented
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic, complemented
136#1935C2211yescharacteristic, complemented
137#1934C2211yescharacteristic, complemented
138#1933C2211yescharacteristic, complemented
139#1928C2211yescharacteristic, complemented
140#1927C2211yescharacteristic, complemented
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic, complemented
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic, complemented
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic
149#1923C2211yescharacteristic, complemented
150#1923C2211yescharacteristic, complemented
151#1920C2211yescharacteristic, complemented
152#1920C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1919C2211yescharacteristic, complemented
155#1895C2211yescharacteristic
156#1895C2211yescharacteristic
157#1894C2211yescharacteristic
158#1893C2211yescharacteristic, complemented
159#1880C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1875C2211yescharacteristic
170#1875C2211yescharacteristic
171#1875C2211yescharacteristic, complemented
172#1873C2211yescharacteristic, complemented
173#1870C2211yescharacteristic
174#1869C2211yescharacteristic
175#1865C2211yescharacteristic, complemented
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic, complemented
179#1864C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic, complemented
183#1862C2211yescharacteristic, complemented
184#1862C2211yescharacteristic, complemented
185#1854C2211yescharacteristic
186#1854C2211yescharacteristic
187#1825C2211yescharacteristic
188#1825C2211yescharacteristic, complemented
189#1805C2211yescharacteristic, complemented
190#1802C2211yescharacteristic, complemented
191#1776C2211yescharacteristic, complemented
192#1776C2211yescharacteristic, complemented
193C4×#102C2211yescharacteristic
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic, complemented
197#1753C2211yescharacteristic
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic, complemented
200#1752C2211yescharacteristic, complemented
201#1746C2211yescharacteristic, complemented
202#1746C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#559—42no—
213#559—42no—
214#555—42no—
215#555—42no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#126—21no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#124—21no—
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#123—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×#117—21no—
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C22⋊C4—21no—
258C22×C22⋊C4—21no—
259#482—42no—
260#466—24no—
261#465—24no—
262#463—42no—
263#459—42no—
264#450—24no—
265#447—24no—
266#447—42no—
267#442—24no—
268#442—24no—
269#442—42no—
270#440—42no—
271#427—42no—
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284#418—42no—
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325#400—21no—
326#400—21no—
327#400D411yescharacteristic
328#400D411yescharacteristic
329#399—21no—
330#399—21no—
331#398—21no—
332#398—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397D411yescharacteristic
343#397D411yescharacteristic
344#396—21no—
345#396—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394D411yescharacteristic
355#394D411yescharacteristic
356#393—21no—
357#393—21no—
358#393—21no—
359#393D411yescharacteristic
360#393D411yescharacteristic
361#392—21no—
362#392—21no—
363#392—21no—
364#392—21no—
365#391—21no—
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#390—21no—
369#390—21no—
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
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#388—21no—
404#388—21no—
405#388—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—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#385—21no—
424#385—21no—
425#385—21no—
426#384C2311yescharacteristic
427#383—21no—
428#382C2311yescharacteristic
429#381—21no—
430#381—21no—
431#381—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#379—21no—
442#379—21no—
443#379—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462#376C2311yescharacteristic
463C2×#95—21no—
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#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8—21no—
498C22×Q8C2×D411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4C2×D411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
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×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16—41no—
551C22×C8—22no—
552C22×C8—22no—
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—
564C4⋊Q8—82no—
565#127—22no—
566#127—41no—
567#126—82no—
568#124—22no—
569#124—41no—
570#124—41no—
571#124—41no—
572#124—44no—
573#124—44no—
574#124—44no—
575#123—44no—
576#123—44no—
577#123—82no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—82no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—41no—
590#121—41no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—44no—
596#121—82no—
597#121—82no—
598#120—82no—
599C4×Q8—22no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—44no—
622#117—22no—
623#117—22no—
624#117—41no—
625#117—41no—
626#117—44no—
627#117—41no—
628#117—41no—
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⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—82no—
704C2×C22⋊C4—82no—
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#107—22no—
730#107—22no—
731#107—41no—
732#107—41no—
733#106—22no—
734#106—22no—
735#106—22no—
736#106—22no—
737#106—41no—
738#106—41no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741#103—22no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102#4114yes—
768#102#4114yes—
769C22⋊C8—22no—
770C22⋊C8—22no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775#97—22no—
776#97—22no—
777#97—41no—
778#97—41no—
779C4×C8—41no—
780C4×C8—41no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—42no—
823C24—42no—
824C24—42no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—41no—
838C2×Q8—41no—
839C2×Q8—41no—
840C2×Q8—42no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—41no—
865C2×D4—41no—
866C2×D4—41no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—44no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—82no—
884C2×D4—82no—
885C2×D4—82no—
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×D4C2×#4112yes—
899C2×D4C2×#4112yes—
900C2×D4H(5,𝔽2)12yes—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—24no—
905C22×C4—21no—
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—21no—
925C22×C4—21no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C2511yescharacteristic
962SD16—44no—
963SD16—82no—
964D8—44no—
965D8—44no—
966D8—44no—
967D8—82no—
968M16—82no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—44no—
992C2×C8C2×#4112yes—
993C2×C8C2×#4112yes—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4C2×#4112yes—
1034C4⋊C4C2×#4112yes—
1035C4⋊C4H(5,𝔽2)12yes—
1036C22⋊C4—24no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
1107C42—81no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—22no—
1119C23—22no—
1120C23—21no—
1121C23—21no—
1122C23—22no—
1123C23—21no—
1124C23—21no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—84no—
1151C23—84no—
1152C23—84no—
1153C23—162no—
1154C23—162no—
1155C23—162no—
1156C23—162no—
1157C23C23×D411yescharacteristic
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—82no—
1163Q8—162no—
1164D4—22no—
1165D4—22no—
1166D4—22no—
1167D4—22no—
1168D4—22no—
1169D4—22no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—82no—
1181D4—84no—
1182D4—84no—
1183D4—162no—
1184D4—162no—
1185D4—162no—
1186D4—162no—
1187D4—162no—
1188D4—162no—
1189D4—162no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—22no—
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—22no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—84no—
1271C2×C4—162no—
1272C2×C4—162no—
1273C2×C4—162no—
1274C2×C4—162no—
1275C2×C4—162no—
1276C2×C4—162no—
1277C2×C4—162no—
1278C2×C4C22×#4111yescharacteristic
1279C2×C4C22×#4111yescharacteristic
1280C2×C4C2×H(5,𝔽2)11yescharacteristic
1281C2×C4C2×H(5,𝔽2)11yescharacteristic
1282C2×C4#58511yescharacteristic
1283C2×C4#58511yescharacteristic
1284C8—22no—
1285C8—22no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C22—41no—
1293C22—41no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—42no—
1302C22—41no—
1303C22—42no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—42no—
1309C22—42no—
1310C22—41no—
1311C22—41no—
1312C22—42no—
1313C22—41no—
1314C22—41no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—168no—
1335C22D4×#4111yescharacteristic
1336C22D4×#4111yescharacteristic
1337C22#348411yescharacteristic
1338C22#358411yescharacteristic
1339C22#358511yescharacteristic
1340C22#358511yescharacteristic
1341C22#358511yescharacteristic
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—42no—
1347C4—41no—
1348C4—41no—
1349C4—42no—
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C4—42no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4#348111yescharacteristic
1367C4#349411yescharacteristic
1368C4#349411yescharacteristic
1369C4#355111yescharacteristic
1370C2—81no—
1371C2—81no—
1372C2—82no—
1373C2—82no—
1374C2—82no—
1375C2—161no—
1376C2#5918411yescharacteristic
1377C2#6150411yescharacteristic
1378C2#6150511yescharacteristic
1379C2#6152711yescharacteristic
1380C2#6152911yescharacteristic
1381C2#6161411yescharacteristic
1382C2#6165311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2398 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45006C2semidirect
2. #36051C2semidirect
3. #32589C2semidirect
4. #32584C2semidirect
5. #32041C2semidirect
6. #30501C2semidirect
7. #29570C2semidirect
8. #29566C2semidirect
9. #29059C2semidirect
10. #29056C2semidirect
11. #27122C2semidirect
12. #27119C2semidirect
13. #26977C2semidirect
14. #26976C2semidirect
15. #26939C2semidirect
16. #26938C2semidirect
17. #26669C2semidirect
18. #26664C2semidirect
19. #25172C2semidirect
20. #25168C2semidirect
21. #24204C2semidirect
22. #24198C2semidirect
23. #24093C2semidirect
24. #23976C2semidirect
25. #23277C2semidirect
26. #23033C2semidirect
27. #23031C2semidirect
28. #22868C2semidirect
29. #22864C2semidirect
30. #21126C2semidirect
31. #21126C2semidirect
32. C2×#559C22semidirect
34. C2×#482C22semidirect
46. C2×#427C22semidirect
53. #2640C22semidirect
59. #2546C22semidirect
71. #2428C22semidirect
73. #2427C22semidirect
83. #2363C22semidirect
85. #2362C22semidirect
90. #2275C22semidirect
91. #2101C22semidirect
92. #2100C22semidirect
93. #2088C22semidirect
94. #2087C22semidirect
95. #2085C22semidirect
96. #2084C22semidirect
99. #2058C22semidirect
100. #2057C22semidirect
101. #2042C22semidirect
102. #2042C22semidirect
103. #2042C22semidirect
104. #2041C22semidirect
107. #2035C22semidirect
111. #2034C22semidirect
123. #1985C22semidirect
124. #1985C22semidirect
129. #1961C22semidirect
130. #1959C22semidirect
131. #1944C22semidirect
132. #1943C22semidirect
135. #1936C22semidirect
136. #1935C22semidirect
137. #1934C22semidirect
138. #1933C22semidirect
139. #1928C22semidirect
140. #1927C22semidirect
143. #1926C22semidirect
146. #1925C22semidirect
149. #1923C22semidirect
150. #1923C22semidirect
151. #1920C22semidirect
152. #1920C22semidirect
153. #1919C22semidirect
154. #1919C22semidirect
158. #1893C22semidirect
171. #1875C22semidirect
172. #1873C22semidirect
175. #1865C22semidirect
178. #1864C22semidirect
179. #1864C22semidirect
182. #1862C22semidirect
183. #1862C22semidirect
184. #1862C22semidirect
188. #1825C22semidirect
189. #1805C22semidirect
190. #1802C22semidirect
191. #1776C22semidirect
192. #1776C22semidirect
195. C4×#102C22semidirect
196. C4×#102C22semidirect
199. #1752C22semidirect
200. #1752C22semidirect
201. #1746C22semidirect
202. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#450062
#360512
#325892
#325842
#320412
#305012
#295702
#295662
#290592
#290562
#271222
#271192
#269772
#269762
#269392
#269382
#266692
#266642
#251722
#251682
#242042
#241982
#240932
#239762
#232772
#230332
#230312
#228682
#228642
#211262