Finite Group Databasebeta

← #6697965

Subgroups — #6697965

Order 512.

1549 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40106C211yesmaximal, characteristic, complemented
2#36457C211yesmaximal, characteristic
3#33085C211yesmaximal, characteristic, complemented
4#32640C211yesmaximal, characteristic, complemented
5#32617C211yesmaximal, characteristic, complemented
6#32270C211yesmaximal, characteristic, complemented
7#32122C211yesmaximal, characteristic, complemented
8#31766C211yesmaximal, characteristic, complemented
9#31334C211yesmaximal, characteristic, complemented
10#30791C211yesmaximal, characteristic, complemented
11#30680C211yesmaximal, characteristic, complemented
12#30337C211yesmaximal, characteristic, complemented
13#30066C211yesmaximal, characteristic, complemented
14#28077C211yesmaximal, characteristic, complemented
15#27796C211yesmaximal, characteristic, complemented
16#27530C211yesmaximal, characteristic, complemented
17#27330C211yesmaximal, characteristic, complemented
18#27247C211yesmaximal, characteristic, complemented
19#27234C211yesmaximal, characteristic, complemented
20#26788C211yesmaximal, characteristic, complemented
21#25977C211yesmaximal, characteristic, complemented
22#25977C211yesmaximal, characteristic, complemented
23#25847C211yesmaximal, characteristic, complemented
24#24920C211yesmaximal, characteristic, complemented
25#24443C211yesmaximal, characteristic
26#24345C211yesmaximal, characteristic, complemented
27#24045C211yesmaximal, characteristic
28#22867C211yesmaximal, characteristic, complemented
29#22579C211yesmaximal, characteristic, complemented
30#22393C211yesmaximal, characteristic, complemented
31C4×#479C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#479C2211yescharacteristic
38C2×#475C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#441C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#417C2211yescharacteristic
45#2863C2211yescharacteristic
46#2858—21no—
47#2858C2211yescharacteristic
48#2767—21no—
49#2747—21no—
50#2739—21no—
51#2717—21no—
52#2666—21no—
53#2584C2211yescharacteristic
54#2581C2211yescharacteristic
55#2563—21no—
56#2563C2211yescharacteristic
57#2548—21no—
58#2548C2211yescharacteristic
59#2515—21no—
60#2495—21no—
61#2495C2211yescharacteristic
62#2491—21no—
63#2491—21no—
64#2491—21no—
65#2491—21no—
66#2491C2211yescharacteristic
67#2491C2211yescharacteristic
68#2491C2211yescharacteristic
69#2491C2211yescharacteristic
70#2489C2211yescharacteristic
71#2489C2211yescharacteristic
72#2486C2211yescharacteristic
73#2442C2211yescharacteristic
74#2442C2211yescharacteristic
75#2421C2211yescharacteristic
76#2417C2211yescharacteristic
77#2360C2211yescharacteristic
78#2345C2211yescharacteristic
79#2341C2211yescharacteristic
80#2341C2211yescharacteristic
81#2341C2211yescharacteristic
82#2341C2211yescharacteristic
83#2335—21no—
84C4×#125C2211yescharacteristic
85C4×#124—21no—
86C4×#124C2211yescharacteristic
87C42×Q8C2211yescharacteristic
88#2092C2211yescharacteristic
89#2092C2211yescharacteristic
90#2092C2211yescharacteristic
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2076C2211yescharacteristic
94#2076C2211yescharacteristic
95#2075C2211yescharacteristic
96#2073C2211yescharacteristic
97#2067C2211yescharacteristic
98#2065C2211yescharacteristic
99#2065C2211yescharacteristic
100#2065C2211yescharacteristic
101#2065C2211yescharacteristic
102#2058C2211yescharacteristic
103#2058C2211yescharacteristic
104#2058C2211yescharacteristic
105#2058C2211yescharacteristic
106#2057C2211yescharacteristic
107#2057C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2035C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2033C2211yescharacteristic
120#2025C2211yescharacteristic
121#2025C2211yescharacteristic
122#2025C2211yescharacteristic
123#2025C2211yescharacteristic
124#2024C2211yescharacteristic
125#2024C2211yescharacteristic
126#2014C2211yescharacteristic
127#2000C2211yescharacteristic
128#1993C2211yescharacteristic
129#1989C2211yescharacteristic
130#1988C2211yescharacteristic
131#1985C2211yescharacteristic
132#1985C2211yescharacteristic
133#1973C2211yescharacteristic
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1949C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1928C2211yescharacteristic
143#1927C2211yescharacteristic
144#1927C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic
153#1923C2211yescharacteristic
154#1923C2211yescharacteristic
155#1920C2211yescharacteristic
156#1920C2211yescharacteristic
157#1919C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1895C2211yescharacteristic
161#1894C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1878C2211yescharacteristic
165#1878C2211yescharacteristic
166#1878C2211yescharacteristic
167#1878C2211yescharacteristic
168#1874C2211yescharacteristic
169#1870C2211yescharacteristic
170#1870C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1865C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1853C2211yescharacteristic
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic
182#1851C2211yescharacteristic
183#1851C2211yescharacteristic
184#1839C2211yescharacteristic
185#1823C2211yescharacteristic
186#1809C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1805C2211yescharacteristic
190#1805C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195C4×#107C2211yescharacteristic
196C4×#106C2211yescharacteristic
197C4×C4⋊C8C2211yescharacteristic
198#1763C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210Q82—42no—
211Q82—42no—
212#550—42no—
213#550—42no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127—21no—
221C2×#127C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#124—21no—
225C2×#124—21no—
226C2×#124—21no—
227C2×#124—21no—
228C2×#124—21no—
229C2×#124—21no—
230C2×#124—21no—
231C2×#124D411yescharacteristic
232C2×#123—21no—
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121—21no—
236C2×#121—21no—
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×C4×Q8—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251#501—42no—
252#481—42no—
253#479—24no—
254#479—42no—
255#475—42no—
256#468—42no—
257#452—24no—
258#452—42no—
259#441—42no—
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×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277#417—24no—
278#417—42no—
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#396—21no—
333#395—21no—
334#395—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#393—21no—
342#393—21no—
343#393—21no—
344#393—21no—
345#393—21no—
346#393—21no—
347#391D411yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#390—21no—
353#390—21no—
354#390—21no—
355#390—21no—
356#390—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390—21no—
361#390—21no—
362#390—21no—
363#390—21no—
364#390D411yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#389—21no—
374#389—21no—
375#389—21no—
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
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#388D411yescharacteristic
395#388D411yescharacteristic
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#386—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#383—21no—
412#383—21no—
413#382—21no—
414#382—21no—
415#382—21no—
416#382D411yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#381—21no—
420#380—21no—
421#380—21no—
422#380—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C43—21no—
458C43C2311yescharacteristic
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#340C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C22×Q8—21no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8C2×D411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4C2×D411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C2×Q16—22no—
527C2×Q16—22no—
528C2×Q16—22no—
529C2×SD16—22no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×M16—22no—
536C2×M16—41no—
537C2×M16—41no—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C4⋊Q8—22no—
550C4⋊Q8—22no—
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554C4⋊Q8—41no—
555C4⋊Q8—44no—
556C4⋊Q8—44no—
557C4⋊Q8—44no—
558#127—41no—
559#127—41no—
560#127—44no—
561#125—22no—
562#125—41no—
563#125—41no—
564#125—41no—
565#124—42no—
566#124—44no—
567#124—82no—
568#124—82no—
569#124—82no—
570#124—82no—
571#124—82no—
572#124—82no—
573#123—44no—
574C22⋊Q8—22no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578#121—22no—
579#121—22no—
580#121—41no—
581#121—41no—
582#121—44no—
583#121—44no—
584C4×Q8—22no—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—44no—
597C4×Q8—41no—
598C4×Q8—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—44no—
602C2×C4⋊C4—21no—
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—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⋊C4C2411yescharacteristic
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×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⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42C2×D411yescharacteristic
698C2×C42C2×D411yescharacteristic
699C2×C42C2×D411yescharacteristic
700C2×C42C2×D411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706#107—22no—
707#107—22no—
708#107—41no—
709#107—41no—
710#107—41no—
711#106—22no—
712#106—22no—
713#106—22no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718#106—41no—
719C4⋊C8—22no—
720C4⋊C8—41no—
721C4⋊C8—41no—
722C4⋊C8—41no—
723#103—22no—
724#103—22no—
725#103—22no—
726#103—22no—
727#103—22no—
728#103—22no—
729#103—22no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103#4114yes—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749C22⋊C8—22no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755#97—41no—
756#97—41no—
757C4×C8—41no—
758C4×C8—41no—
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#95—21no—
792#95—21no—
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801C24—21no—
802C24—21no—
803C24C22×D411yescharacteristic
804C24C22×D411yescharacteristic
805#41—44no—
806#41—44no—
807#41—82no—
808#41—82no—
809#41—82no—
810#41—82no—
811#41—82no—
812#41—82no—
813C2×Q8—22no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—41no—
824C2×Q8—41no—
825C2×Q8—42no—
826C2×Q8—42no—
827C2×Q8—42no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8—81no—
832C2×Q8—81no—
833C2×Q8—81no—
834C2×Q8C2×#4112yes—
835C2×Q8H(5,𝔽2)12yes—
836C2×Q82−1+412yes—
837C2×D4—22no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
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—21no—
883C22×C4—21no—
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—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C2511yescharacteristic
921Q16—44no—
922SD16—82no—
923SD16—82no—
924M16—82no—
925M16—82no—
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—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×C8C2×#4112yes—
950C4⋊C4—24no—
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—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4C2×#4112yes—
1002C4⋊C4H(5,𝔽2)12yes—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
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—
1041C42—24no—
1042C42—22no—
1043C42—22no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—41no—
1055C42—41no—
1056C42—42no—
1057C42—42no—
1058C42—42no—
1059C42—42no—
1060C42—42no—
1061C42—42no—
1062C42—42no—
1063C42—42no—
1064C42—81no—
1065C42—81no—
1066C42—81no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
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—
1095C23C23×D411yescharacteristic
1096Q8—22no—
1097Q8—22no—
1098Q8—22no—
1099Q8—44no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—162no—
1105Q8—162no—
1106Q8—162no—
1107Q8#54214yes—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—82no—
1117D4—84no—
1118D4—84no—
1119D4—84no—
1120D4—162no—
1121D4—162no—
1122D4—162no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—22no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—21no—
1129C2×C4—22no—
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—22no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
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—21no—
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—41no—
1206C2×C4—41no—
1207C2×C4—84no—
1208C2×C4—84no—
1209C2×C4—162no—
1210C2×C4—162no—
1211C2×C4#57512yes—
1212C2×C4#57712yes—
1213C2×C4C22×#4111yescharacteristic
1214C2×C4C2×H(5,𝔽2)11yescharacteristic
1215C2×C4C2×H(5,𝔽2)11yescharacteristic
1216C2×C4C2×2−1+411yescharacteristic
1217C2×C4#58511yescharacteristic
1218C2×C4#58511yescharacteristic
1219C8—22no—
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C8—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—81no—
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—
1255C22D4×#4111yescharacteristic
1256C22#348411yescharacteristic
1257C22#348911yescharacteristic
1258C22C2×#57511yescharacteristic
1259C22C2×#57711yescharacteristic
1260C22#358511yescharacteristic
1261C22#358611yescharacteristic
1262C4—24no—
1263C4—22no—
1264C4—22no—
1265C4—41no—
1266C4—41no—
1267C4—42no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—42no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4C2×#54211yescharacteristic
1289C4#351411yescharacteristic
1290C4#354511yescharacteristic
1291C4#356111yescharacteristic
1292C2—81no—
1293C2—81no—
1294C2—161no—
1295C2—161no—
1296C2#3771811yescharacteristic
1297C2#6145011yescharacteristic
1298C2#6151811yescharacteristic
1299C2#6158311yescharacteristic
1300C2#6168911yescharacteristic
1301C2#6212311yescharacteristic
1302C2#6216911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#550C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40106C2semidirect
3. #33085C2semidirect
4. #32640C2semidirect
5. #32617C2semidirect
6. #32270C2semidirect
7. #32122C2semidirect
8. #31766C2semidirect
9. #31334C2semidirect
10. #30791C2semidirect
11. #30680C2semidirect
12. #30337C2semidirect
13. #30066C2semidirect
14. #28077C2semidirect
15. #27796C2semidirect
16. #27530C2semidirect
17. #27330C2semidirect
18. #27247C2semidirect
19. #27234C2semidirect
20. #26788C2semidirect
21. #25977C2semidirect
22. #25977C2semidirect
23. #25847C2semidirect
24. #24920C2semidirect
26. #24345C2semidirect
28. #22867C2semidirect
29. #22579C2semidirect
30. #22393C2semidirect
31. C4×#479C2semidirect

Maximal subgroups

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

subgroupindex
#401062
#364572
#330852
#326402
#326172
#322702
#321222
#317662
#313342
#307912
#306802
#303372
#300662
#280772
#277962
#275302
#273302
#272472
#272342
#267882
#259772
#258472
#249202
#244432
#243452
#240452
#228672
#225792
#223932
C4×#4792