Finite Group Databasebeta

← #7337769

Subgroups — #7337769

Order 512.

1497 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59120C211yesmaximal, characteristic, complemented
2#45602C211yesmaximal, characteristic, complemented
3#32051C211yesmaximal, characteristic, complemented
4#31942C211yesmaximal, characteristic, complemented
5#31849C211yesmaximal, characteristic, complemented
6#31727C211yesmaximal, characteristic, complemented
7#31643C211yesmaximal, characteristic, complemented
8#31466C211yesmaximal, characteristic, complemented
9#31389C211yesmaximal, characteristic, complemented
10#31356C211yesmaximal, characteristic, complemented
11#31150C211yesmaximal, characteristic, complemented
12#30951C211yesmaximal, characteristic, complemented
13#30781C211yesmaximal, characteristic, complemented
14#30592C211yesmaximal, characteristic, complemented
15#29974C211yesmaximal, characteristic, complemented
16#29662C211yesmaximal, characteristic, complemented
17#29331C211yesmaximal, characteristic, complemented
18#28912C211yesmaximal, characteristic, complemented
19#27814C211yesmaximal, characteristic, complemented
20#27701C211yesmaximal, characteristic, complemented
21#26926C211yesmaximal, characteristic, complemented
22#26821C211yesmaximal, characteristic, complemented
23#26733C211yesmaximal, characteristic, complemented
24#26664C211yesmaximal, characteristic, complemented
25#26410C211yesmaximal, characteristic, complemented
26#26159C211yesmaximal, characteristic, complemented
27#26116C211yesmaximal, characteristic, complemented
28#25675C211yesmaximal, characteristic, complemented
29#25539C211yesmaximal, characteristic, complemented
30#24125C211yesmaximal, characteristic, complemented
31#22357C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#499C2211yescharacteristic
35C2×#488C2211yescharacteristic
36C2×#480C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#460C2211yescharacteristic
40C2×#459C2211yescharacteristic
41C2×C4×SD16C2211yescharacteristic
42#2856C2211yescharacteristic
43#2851C2211yescharacteristic
44#2830—21no—
45#2740—21no—
46#2718—21no—
47#2708—21no—
48#2706—21no—
49#2696—21no—
50#2686—21no—
51#2676—21no—
52#2671—21no—
53#2570C2211yescharacteristic
54#2563C2211yescharacteristic
55#2552C2211yescharacteristic
56#2535C2211yescharacteristic
57#2519—21no—
58#2504C2211yescharacteristic
59#2500C2211yescharacteristic
60#2491C2211yescharacteristic
61#2490C2211yescharacteristic
62#2479—21no—
63#2475—21no—
64#2468—21no—
65#2455—21no—
66#2454C2211yescharacteristic
67#2454C2211yescharacteristic
68#2448C2211yescharacteristic
69#2445C2211yescharacteristic
70#2442C2211yescharacteristic
71#2440C2211yescharacteristic
72#2428C2211yescharacteristic
73#2426C2211yescharacteristic
74#2423C2211yescharacteristic
75#2420C2211yescharacteristic
76#2416C2211yescharacteristic
77#2414C2211yescharacteristic
78#2377—21no—
79#2362C2211yescharacteristic
80#2361C2211yescharacteristic
81#2354—21no—
82#2351C2211yescharacteristic
83C4×#123C2211yescharacteristic
84#2296C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2100C2211yescharacteristic
90#2100C2211yescharacteristic
91#2094C2211yescharacteristic
92#2092C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2087C2211yescharacteristic
97#2086C2211yescharacteristic
98#2083C2211yescharacteristic
99#2076C2211yescharacteristic
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2055C2211yescharacteristic
109#2054C2211yescharacteristic
110#2054C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic
115#2035C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2033C2211yescharacteristic
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic
121#2025C2211yescharacteristic
122#2024C2211yescharacteristic
123#2023C2211yescharacteristic
124#2012C2211yescharacteristic
125#2012C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#2000C2211yescharacteristic
129#1999C2211yescharacteristic
130#1999C2211yescharacteristic
131#1999C2211yescharacteristic
132#1999C2211yescharacteristic
133#1991C2211yescharacteristic
134#1991C2211yescharacteristic
135#1990C2211yescharacteristic
136#1987C2211yescharacteristic
137#1970C2211yescharacteristic
138#1970C2211yescharacteristic
139#1958C2211yescharacteristic
140#1954C2211yescharacteristic
141#1949C2211yescharacteristic
142#1939C2211yescharacteristic
143#1934C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic
151#1926C2211yescharacteristic
152#1925C2211yescharacteristic
153#1923C2211yescharacteristic
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic
156#1923C2211yescharacteristic
157#1920C2211yescharacteristic
158#1918C2211yescharacteristic
159#1916C2211yescharacteristic
160#1916C2211yescharacteristic
161#1893C2211yescharacteristic
162#1893C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1877C2211yescharacteristic
169#1875C2211yescharacteristic
170#1875C2211yescharacteristic
171#1875C2211yescharacteristic
172#1875C2211yescharacteristic
173#1874C2211yescharacteristic
174#1874C2211yescharacteristic
175#1872C2211yescharacteristic
176#1869C2211yescharacteristic
177#1865C2211yescharacteristic
178#1864C2211yescharacteristic
179#1863C2211yescharacteristic
180#1863C2211yescharacteristic
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1853C2211yescharacteristic
186#1850C2211yescharacteristic
187#1835C2211yescharacteristic
188#1825C2211yescharacteristic
189#1825C2211yescharacteristic
190#1824C2211yescharacteristic
191#1805C2211yescharacteristic
192#1805C2211yescharacteristic
193#1803C2211yescharacteristic
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic
196#1797C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201C4×C22⋊C8C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#552—42no—
209#552—42no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212#529—42no—
213#529—42no—
214C2×#126—21no—
215C2×#126—21no—
216C2×#125—21no—
217C2×#125C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×#123D411yescharacteristic
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117—21no—
249C2×#117—21no—
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C42C2311yescharacteristic
255#499—42no—
256#488—42no—
257#480—42no—
258#478—42no—
259#465—42no—
260#460—42no—
261#459—42no—
262C4×SD16—42no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
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×#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×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312#400—21no—
313#400—21no—
314#399—21no—
315#399—21no—
316#399—21no—
317#399—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#395—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#393—21no—
347#393—21no—
348#393—21no—
349#392—21no—
350#392—21no—
351#392—21no—
352#391C2311yescharacteristic
353#390—21no—
354#390—21no—
355#390—21no—
356#390—21no—
357#390—21no—
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#389—21no—
368#389—21no—
369#389—21no—
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
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#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388D411yescharacteristic
393#388D411yescharacteristic
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387D411yescharacteristic
401#387D411yescharacteristic
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386D411yescharacteristic
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385D411yescharacteristic
422#384—21no—
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#382—21no—
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#381—21no—
431#381D411yescharacteristic
432#380—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
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
490C22×Q8—21no—
491C22×Q8C2411yescharacteristic
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C2×D411yescharacteristic
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C2×D411yescharacteristic
510C23×C4C2×D411yescharacteristic
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×D8—41no—
520C2×D8—41no—
521C2×D8—41no—
522C2×D8—41no—
523C2×D8—41no—
524C2×D8—41no—
525C22×C8—41no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538#127—41no—
539#127—41no—
540#126—44no—
541#126—44no—
542#125—22no—
543#125—22no—
544#125—41no—
545#125—41no—
546#125—41no—
547#125—41no—
548#125—44no—
549#124—22no—
550#124—41no—
551#124—82no—
552#123—24no—
553#123—44no—
554#123—44no—
555#123—82no—
556C22⋊Q8—22no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—41no—
560C22⋊Q8—82no—
561#121—22no—
562#121—41no—
563#121—41no—
564#121—41no—
565#121—44no—
566#121—41no—
567#121—41no—
568#121—41no—
569#121—41no—
570#121—41no—
571#121—41no—
572#121—41no—
573#121—41no—
574#121—82no—
575#121—82no—
576#121—82no—
577C4×Q8—22no—
578C4×Q8—22no—
579C4×Q8—22no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×Q8—41no—
583C4×D4—22no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—44no—
592C4×D4—44no—
593#117—22no—
594#117—41no—
595#117—41no—
596#117—41no—
597#117—44no—
598#117—44no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—22no—
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—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
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×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⋊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⋊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×C22⋊C4C2×D411yescharacteristic
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—41no—
701C2×C42—41no—
702C2×C42C2×D411yescharacteristic
703C2×C42C2×D411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709#107—22no—
710#107—41no—
711#107—41no—
712#107—41no—
713#106—22no—
714#106—41no—
715#106—41no—
716#106—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721C4⋊C8—41no—
722#103—22no—
723#103—22no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
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—
753C4×C8—41no—
754C4×C8—41no—
755C4×C8—41no—
756C4×C8—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#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794C24—21no—
795C24—21no—
796C24—21no—
797C24C22×D411yescharacteristic
798C24C22×D411yescharacteristic
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—81no—
805C2×Q8—81no—
806C2×Q8—81no—
807C2×Q8H(5,𝔽2)12yes—
808C2×D4—22no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—41no—
828C2×D4—41no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
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—22no—
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—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C2511yescharacteristic
912SD16—44no—
913SD16—82no—
914D8—82no—
915D8—82no—
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—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—82no—
941C4⋊C4—24no—
942C4⋊C4—22no—
943C4⋊C4—22no—
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—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4H(5,𝔽2)12yes—
997C4⋊C42−1+412yes—
998C22⋊C4—24no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
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—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4#13514yes—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—41no—
1054C42—41no—
1055C42—42no—
1056C42—42no—
1057C42—42no—
1058C42—42no—
1059C42—42no—
1060C42—42no—
1061C42—81no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23C2×#13512yes—
1097C23C23×D411yescharacteristic
1098Q8—22no—
1099Q8—22no—
1100Q8—41no—
1101Q8—41no—
1102Q8—162no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—82no—
1116D4—84no—
1117D4—84no—
1118D4—162no—
1119D4—162no—
1120D4—162no—
1121D4—162no—
1122D4—162no—
1123D4—162no—
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—21no—
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—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—22no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
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—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—82no—
1206C2×C4—84no—
1207C2×C4—82no—
1208C2×C4—84no—
1209C2×C4—162no—
1210C2×C4—162no—
1211C2×C4—162no—
1212C2×C4C2×#13512yes—
1213C2×C4C2×#13512yes—
1214C2×C4C2×H(5,𝔽2)11yescharacteristic
1215C2×C4C2×H(5,𝔽2)11yescharacteristic
1216C2×C4C2×2−1+411yescharacteristic
1217C2×C4#58511yescharacteristic
1218C2×C4#58511yescharacteristic
1219C2×C4#58511yescharacteristic
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C22—22no—
1229C22—22no—
1230C22—22no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22#348411yescharacteristic
1264C22#348911yescharacteristic
1265C22#350011yescharacteristic
1266C22C22×#13511yescharacteristic
1267C22#358411yescharacteristic
1268C22#358511yescharacteristic
1269C22#358511yescharacteristic
1270C4—22no—
1271C4—22no—
1272C4—41no—
1273C4—41no—
1274C4—42no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—42no—
1279C4—41no—
1280C4—42no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4#353311yescharacteristic
1296C4#354711yescharacteristic
1297C4#355911yescharacteristic
1298C4#356211yescharacteristic
1299C2—42no—
1300C2—81no—
1301C2—161no—
1302C2—161no—
1303C2—161no—
1304C2#4795411yescharacteristic
1305C2#6156711yescharacteristic
1306C2#6161611yescharacteristic
1307C2#6209811yescharacteristic
1308C2#6219711yescharacteristic
1309C2#6253311yescharacteristic
1310C2#6256411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59120C2semidirect
2. #45602C2semidirect
3. #32051C2semidirect
4. #31942C2semidirect
5. #31849C2semidirect
6. #31727C2semidirect
7. #31643C2semidirect
8. #31466C2semidirect
9. #31389C2semidirect
10. #31356C2semidirect
11. #31150C2semidirect
12. #30951C2semidirect
13. #30781C2semidirect
14. #30592C2semidirect
15. #29974C2semidirect
16. #29662C2semidirect
17. #29331C2semidirect
18. #28912C2semidirect
19. #27814C2semidirect
20. #27701C2semidirect
21. #26926C2semidirect
22. #26821C2semidirect
23. #26733C2semidirect
24. #26664C2semidirect
25. #26410C2semidirect
26. #26159C2semidirect
27. #26116C2semidirect
28. #25675C2semidirect
29. #25539C2semidirect
30. #24125C2semidirect
31. #22357C2semidirect

Maximal subgroups

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

subgroupindex
#591202
#456022
#320512
#319422
#318492
#317272
#316432
#314662
#313892
#313562
#311502
#309512
#307812
#305922
#299742
#296622
#293312
#289122
#278142
#277012
#269262
#268212
#267332
#266642
#264102
#261592
#261162
#256752
#255392
#241252
#223572