Finite Group Databasebeta

← #7459768

Subgroups — #7459768

Order 512.

1446 conjugacy classes of subgroups.

The subgroup lattice has 1293 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53115C211yesmaximal, characteristic, complemented
2#42681C211yesmaximal, characteristic, complemented
3#32589C211yesmaximal, characteristic, complemented
4#32584C211yesmaximal, characteristic, complemented
5#31958C211yesmaximal, characteristic, complemented
6#31933C211yesmaximal, characteristic, complemented
7#31372C211yesmaximal, characteristic, complemented
8#31361C211yesmaximal, characteristic, complemented
9#31335C211yesmaximal, characteristic, complemented
10#31332C211yesmaximal, characteristic, complemented
11#31145C211yesmaximal, characteristic, complemented
12#31123C211yesmaximal, characteristic, complemented
13#31098C211yesmaximal, characteristic, complemented
14#31082C211yesmaximal, characteristic, complemented
15#30315C211yesmaximal, characteristic, complemented
16#30209C211yesmaximal, characteristic, complemented
17#29588C211yesmaximal, characteristic, complemented
18#29564C211yesmaximal, characteristic, complemented
19#28785C211yesmaximal, characteristic, complemented
20#28780C211yesmaximal, characteristic, complemented
21#27712C211yesmaximal, characteristic, complemented
22#27709C211yesmaximal, characteristic, complemented
23#26984C211yesmaximal, characteristic, complemented
24#26977C211yesmaximal, characteristic, complemented
25#25554C211yesmaximal, characteristic, complemented
26#25538C211yesmaximal, characteristic, complemented
27#25048C211yesmaximal, characteristic, complemented
28#25042C211yesmaximal, characteristic, complemented
29#24347C211yesmaximal, characteristic, complemented
30#24339C211yesmaximal, characteristic, complemented
31#23277C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#474C2211yescharacteristic
38C2×#469C2211yescharacteristic
39C2×#466C2211yescharacteristic
40C2×#442C2211yescharacteristic
41C2×#442C2211yescharacteristic
42#2837—21no—
43#2826—21no—
44#2816—21no—
45#2816—21no—
46#2813—21no—
47#2743—21no—
48#2701—21no—
49#2700—21no—
50#2700—21no—
51#2696—21no—
52#2674—21no—
53#2674—21no—
54#2671—21no—
55#2660C2211yescharacteristic
56#2647C2211yescharacteristic
57#2641C2211yescharacteristic
58#2625—21no—
59#2618—21no—
60#2580C2211yescharacteristic
61#2562C2211yescharacteristic
62#2546C2211yescharacteristic
63#2538C2211yescharacteristic
64#2501C2211yescharacteristic
65#2500C2211yescharacteristic
66#2484—21no—
67#2442C2211yescharacteristic
68#2441C2211yescharacteristic
69#2441C2211yescharacteristic
70#2441C2211yescharacteristic
71#2439C2211yescharacteristic
72#2439C2211yescharacteristic
73#2428C2211yescharacteristic
74#2428C2211yescharacteristic
75#2422C2211yescharacteristic
76#2422C2211yescharacteristic
77#2420C2211yescharacteristic
78#2420C2211yescharacteristic
79#2420C2211yescharacteristic
80#2420C2211yescharacteristic
81#2416C2211yescharacteristic
82#2414C2211yescharacteristic
83#2398C2211yescharacteristic
84#2319C2211yescharacteristic
85#2101C2211yescharacteristic
86#2100C2211yescharacteristic
87#2099C2211yescharacteristic
88#2094C2211yescharacteristic
89#2088C2211yescharacteristic
90#2087C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2085C2211yescharacteristic
95#2084C2211yescharacteristic
96#2084C2211yescharacteristic
97#2083C2211yescharacteristic
98#2075C2211yescharacteristic
99#2075C2211yescharacteristic
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2058C2211yescharacteristic
112#2058C2211yescharacteristic
113#2057C2211yescharacteristic
114#2041C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2025C2211yescharacteristic
124#2025C2211yescharacteristic
125#2025C2211yescharacteristic
126#2025C2211yescharacteristic
127#2023C2211yescharacteristic
128#2023C2211yescharacteristic
129#2023C2211yescharacteristic
130#2011C2211yescharacteristic
131#1999C2211yescharacteristic
132#1999C2211yescharacteristic
133#1993C2211yescharacteristic
134#1992C2211yescharacteristic
135#1992C2211yescharacteristic
136#1991C2211yescharacteristic
137#1985C2211yescharacteristic
138#1985C2211yescharacteristic
139#1972C2211yescharacteristic
140#1970C2211yescharacteristic
141#1961C2211yescharacteristic
142#1957C2211yescharacteristic
143#1944C2211yescharacteristic
144#1943C2211yescharacteristic
145#1943C2211yescharacteristic
146#1941C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1926C2211yescharacteristic
154#1925C2211yescharacteristic
155#1924C2211yescharacteristic
156#1924C2211yescharacteristic
157#1923C2211yescharacteristic
158#1923C2211yescharacteristic
159#1920C2211yescharacteristic
160#1919C2211yescharacteristic
161#1895C2211yescharacteristic
162#1893C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1875C2211yescharacteristic
168#1875C2211yescharacteristic
169#1875C2211yescharacteristic
170#1874C2211yescharacteristic
171#1870C2211yescharacteristic
172#1869C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1853C2211yescharacteristic
185#1847C2211yescharacteristic
186#1846C2211yescharacteristic
187#1836C2211yescharacteristic
188#1834C2211yescharacteristic
189#1825C2211yescharacteristic
190#1824C2211yescharacteristic
191#1809C2211yescharacteristic
192#1807C2211yescharacteristic
193#1804C2211yescharacteristic
194#1802C2211yescharacteristic
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1752C2211yescharacteristic
198#1752C2211yescharacteristic
199#1746C2211yescharacteristic
200#1746C2211yescharacteristic
201#1736C2211yescharacteristic
202#1735C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207#555—42no—
208#555—42no—
209#554—42no—
210#554—42no—
211C2×C4⋊Q8—21no—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#124—21no—
219C2×#124—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C4⋊C4—21no—
250C22×C4⋊C4C2311yescharacteristic
251#482—42no—
252#482—42no—
253#478—42no—
254#474—42no—
255#469—42no—
256#466—42no—
257#442—42no—
258#442—42no—
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400D411yescharacteristic
312#400D411yescharacteristic
313#399—21no—
314#399—21no—
315#399—21no—
316#399—21no—
317#399—21no—
318#399—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397D411yescharacteristic
333#397D411yescharacteristic
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#395—21no—
343#395—21no—
344#394—21no—
345#394—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#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394D411yescharacteristic
362#394D411yescharacteristic
363#393—21no—
364#393—21no—
365#393—21no—
366#393D411yescharacteristic
367#393D411yescharacteristic
368#392—21no—
369#392—21no—
370#392—21no—
371#391—21no—
372#391—21no—
373#391—21no—
374#390—21no—
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#389—21no—
384#389—21no—
385#389—21no—
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#387—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#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#381—21no—
431#381—21no—
432#381—21no—
433#381—21no—
434#381—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
449#376C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
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#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8C2×D411yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4C2×D411yescharacteristic
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—41no—
518C2×D8—41no—
519C2×M16—22no—
520C2×M16—41no—
521C2×M16—41no—
522C22×C8—22no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C4⋊Q8—22no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—82no—
538#127—41no—
539#127—41no—
540#125—22no—
541#125—41no—
542#125—41no—
543#125—41no—
544#125—41no—
545#125—41no—
546#124—44no—
547#124—44no—
548#123—82no—
549#123—82no—
550#123—82no—
551#123—82no—
552C22⋊Q8—44no—
553C22⋊Q8—44no—
554C22⋊Q8—44no—
555C22⋊Q8—82no—
556#121—22no—
557#121—22no—
558#121—41no—
559#121—41no—
560#121—44no—
561#121—41no—
562#121—41no—
563#121—41no—
564#121—41no—
565#121—41no—
566#121—41no—
567#121—41no—
568#121—41no—
569#121—82no—
570#121—82no—
571#121—82no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586#117—22no—
587#117—22no—
588#117—41no—
589#117—41no—
590#117—44no—
591#117—41no—
592#117—41no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
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—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—44no—
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697#107—22no—
698#107—41no—
699#107—41no—
700#107—41no—
701#107—41no—
702#107—41no—
703#106—22no—
704#106—41no—
705#106—41no—
706#106—41no—
707#106—41no—
708#106—41no—
709#106—41no—
710#106—41no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733C22⋊C8—22no—
734C22⋊C8—22no—
735C22⋊C8—41no—
736C22⋊C8—41no—
737C22⋊C8—41no—
738C22⋊C8—41no—
739#97—22no—
740#97—41no—
741#97—41no—
742#97—41no—
743C4×C8—22no—
744C4×C8—41no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
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#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784C24—21no—
785C24—21no—
786C24—21no—
787C24C22×D411yescharacteristic
788C24C22×D411yescharacteristic
789C2×Q8—41no—
790C2×Q8—41no—
791C2×Q8—41no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8—81no—
795C2×Q8—81no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—41no—
816C2×D4—41no—
817C2×D4—41no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4—81no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—81no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4H(5,𝔽2)12yes—
843C22×C4—21no—
844C22×C4—24no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C2511yescharacteristic
899D8—44no—
900D8—44no—
901M16—82no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—82no—
925C2×C82−1+412yes—
926C2×C82−1+412yes—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4H(5,𝔽2)12yes—
986C22⋊C4—24no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—41no—
992C22⋊C4—41no—
993C22⋊C4—41no—
994C22⋊C4—41no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—42no—
1043C42—42no—
1044C42—81no—
1045C42—81no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—22no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23C23×D411yescharacteristic
1082Q8—82no—
1083Q8—162no—
1084Q8—162no—
1085D4—22no—
1086D4—22no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—82no—
1098D4—162no—
1099D4—162no—
1100D4—162no—
1101D4—162no—
1102D4—162no—
1103D4—162no—
1104D4—162no—
1105D4—162no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—21no—
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—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
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—84no—
1190C2×C4—84no—
1191C2×C4—162no—
1192C2×C4—162no—
1193C2×C4—162no—
1194C2×C4—162no—
1195C2×C4C2×H(5,𝔽2)11yescharacteristic
1196C2×C4C2×H(5,𝔽2)11yescharacteristic
1197C2×C4C2×2−1+411yescharacteristic
1198C2×C4C2×2−1+411yescharacteristic
1199C2×C4#58511yescharacteristic
1200C2×C4#58511yescharacteristic
1201C8—22no—
1202C8—22no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C8—41no—
1208C8—41no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—42no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—42no—
1221C22—41no—
1222C22—41no—
1223C22—42no—
1224C22—41no—
1225C22—41no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22#348411yescharacteristic
1245C22#349911yescharacteristic
1246C22#350011yescharacteristic
1247C22#358411yescharacteristic
1248C22#358511yescharacteristic
1249C22#358511yescharacteristic
1250C22#358511yescharacteristic
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—42no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4#353511yescharacteristic
1277C4#353511yescharacteristic
1278C4#354711yescharacteristic
1279C4#354711yescharacteristic
1280C2—81no—
1281C2—81no—
1282C2—82no—
1283C2—161no—
1284C2—161no—
1285C2#5154111yescharacteristic
1286C2#6161411yescharacteristic
1287C2#6165311yescharacteristic
1288C2#6250111yescharacteristic
1289C2#6251811yescharacteristic
1290C2#6256411yescharacteristic
1291C2#6260111yescharacteristic
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. #53115C2semidirect
2. #42681C2semidirect
3. #32589C2semidirect
4. #32584C2semidirect
5. #31958C2semidirect
6. #31933C2semidirect
7. #31372C2semidirect
8. #31361C2semidirect
9. #31335C2semidirect
10. #31332C2semidirect
11. #31145C2semidirect
12. #31123C2semidirect
13. #31098C2semidirect
14. #31082C2semidirect
15. #30315C2semidirect
16. #30209C2semidirect
17. #29588C2semidirect
18. #29564C2semidirect
19. #28785C2semidirect
20. #28780C2semidirect
21. #27712C2semidirect
22. #27709C2semidirect
23. #26984C2semidirect
24. #26977C2semidirect
25. #25554C2semidirect
26. #25538C2semidirect
27. #25048C2semidirect
28. #25042C2semidirect
29. #24347C2semidirect
30. #24339C2semidirect
31. #23277C2semidirect

Maximal subgroups

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

subgroupindex
#531152
#426812
#325892
#325842
#319582
#319332
#313722
#313612
#313352
#313322
#311452
#311232
#310982
#310822
#303152
#302092
#295882
#295642
#287852
#287802
#277122
#277092
#269842
#269772
#255542
#255382
#250482
#250422
#243472
#243392
#232772