Finite Group Databasebeta

← #6990375

Subgroups — #6990375

Order 512.

1496 conjugacy classes of subgroups.

The subgroup lattice has 1329 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38277C211yesmaximal, characteristic, complemented
2#37424C211yesmaximal, characteristic
3#32827C211yesmaximal, characteristic, complemented
4#32822C211yesmaximal, characteristic, complemented
5#31311C211yesmaximal, characteristic, complemented
6#31298C211yesmaximal, characteristic, complemented
7#31297C211yesmaximal, characteristic, complemented
8#31294C211yesmaximal, characteristic, complemented
9#31012C211yesmaximal, characteristic, complemented
10#30997C211yesmaximal, characteristic, complemented
11#30996C211yesmaximal, characteristic, complemented
12#30991C211yesmaximal, characteristic, complemented
13#30223C211yesmaximal, characteristic, complemented
14#30221C211yesmaximal, characteristic, complemented
15#29805C211yesmaximal, characteristic, complemented
16#29801C211yesmaximal, characteristic, complemented
17#29699C211yesmaximal, characteristic, complemented
18#29569C211yesmaximal, characteristic, complemented
19#29557C211yesmaximal, characteristic, complemented
20#28424C211yesmaximal, characteristic, complemented
21#28402C211yesmaximal, characteristic, complemented
22#27766C211yesmaximal, characteristic, complemented
23#27752C211yesmaximal, characteristic, complemented
24#25865C211yesmaximal, characteristic
25#25287C211yesmaximal, characteristic, complemented
26#25277C211yesmaximal, characteristic, complemented
27#24747C211yesmaximal, characteristic, complemented
28#24736C211yesmaximal, characteristic, complemented
29#24220C211yesmaximal, characteristic
30#23586C211yesmaximal, characteristic, complemented
31#22637C211yesmaximal, characteristic, complemented
32C2×#541C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#477C2211yescharacteristic, complemented
37C2×#475C2211yescharacteristic, complemented
38C2×#464C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#464C2211yescharacteristic, complemented
42C2×#462C2211yescharacteristic, complemented
43C2×#460C2211yescharacteristic
44C2×#452C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#441C2211yescharacteristic, complemented
47C2×C4×Q16C2211yescharacteristic, complemented
48#2864C2211yescharacteristic, complemented
49#2861C2211yescharacteristic
50#2858C2211yescharacteristic
51#2776—21no—
52#2773—21no—
53#2762—21no—
54#2754—21no—
55#2711—21no—
56#2711—21no—
57#2711—21no—
58#2711—21no—
59#2685—21no—
60#2685—21no—
61#2685—21no—
62#2685—21no—
63#2658C2211yescharacteristic
64#2647C2211yescharacteristic, complemented
65#2641C2211yescharacteristic
66#2628C2211yescharacteristic
67#2596—21no—
68#2570C2211yescharacteristic, complemented
69#2568C2211yescharacteristic, complemented
70#2548C2211yescharacteristic
71#2548C2211yescharacteristic
72#2545C2211yescharacteristic
73#2545C2211yescharacteristic
74#2533—21no—
75#2532—21no—
76#2520—21no—
77#2495C2211yescharacteristic
78#2494C2211yescharacteristic
79#2435C2211yescharacteristic
80#2435C2211yescharacteristic
81#2432C2211yescharacteristic
82#2432C2211yescharacteristic
83#2423C2211yescharacteristic
84#2421C2211yescharacteristic
85#2369C2211yescharacteristic, complemented
86#2351C2211yescharacteristic, complemented
87#2323C2211yescharacteristic
88#2320C2211yescharacteristic, complemented
89#2298C2211yescharacteristic
90#2295C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2092C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic, complemented
95#2074C2211yescharacteristic, complemented
96#2073C2211yescharacteristic
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic, complemented
99#2068C2211yescharacteristic, complemented
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic, complemented
103#2066C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic, complemented
107#2059C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2059C2211yescharacteristic, complemented
110#2043C2211yescharacteristic, complemented
111#2043C2211yescharacteristic, complemented
112#2043C2211yescharacteristic, complemented
113#2043C2211yescharacteristic, complemented
114#2043C2211yescharacteristic, complemented
115#2043C2211yescharacteristic, complemented
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic
121#2042C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2042C2211yescharacteristic
125#2042C2211yescharacteristic, complemented
126#2042C2211yescharacteristic, complemented
127#2042C2211yescharacteristic, complemented
128#2041C2211yescharacteristic
129#2041C2211yescharacteristic
130#2041C2211yescharacteristic
131#2036C2211yescharacteristic
132#2036C2211yescharacteristic
133#2036C2211yescharacteristic
134#2035C2211yescharacteristic
135#2035C2211yescharacteristic
136#2035C2211yescharacteristic
137#2026C2211yescharacteristic, complemented
138#2016C2211yescharacteristic, complemented
139#2016C2211yescharacteristic, complemented
140#2015C2211yescharacteristic
141#2015C2211yescharacteristic
142#2015C2211yescharacteristic
143#2015C2211yescharacteristic, complemented
144#2014C2211yescharacteristic
145#2001C2211yescharacteristic
146#2001C2211yescharacteristic
147#1983C2211yescharacteristic
148#1983C2211yescharacteristic
149#1983C2211yescharacteristic
150#1983C2211yescharacteristic, complemented
151#1982C2211yescharacteristic
152#1981C2211yescharacteristic, complemented
153#1973C2211yescharacteristic
154#1969C2211yescharacteristic, complemented
155#1968C2211yescharacteristic
156#1968C2211yescharacteristic, complemented
157#1961C2211yescharacteristic
158#1960C2211yescharacteristic, complemented
159#1959C2211yescharacteristic
160#1958C2211yescharacteristic
161#1958C2211yescharacteristic
162#1958C2211yescharacteristic
163#1958C2211yescharacteristic
164#1958C2211yescharacteristic, complemented
165#1958C2211yescharacteristic, complemented
166#1956C2211yescharacteristic, complemented
167#1940C2211yescharacteristic, complemented
168#1939C2211yescharacteristic, complemented
169#1936C2211yescharacteristic, complemented
170#1934C2211yescharacteristic
171#1934C2211yescharacteristic
172#1933C2211yescharacteristic, complemented
173#1927C2211yescharacteristic, complemented
174#1926C2211yescharacteristic
175#1925C2211yescharacteristic
176#1925C2211yescharacteristic, complemented
177#1924C2211yescharacteristic
178#1923C2211yescharacteristic
179#1923C2211yescharacteristic
180#1923C2211yescharacteristic
181#1880C2211yescharacteristic
182#1880C2211yescharacteristic
183#1880C2211yescharacteristic, complemented
184#1878C2211yescharacteristic, complemented
185#1832C2211yescharacteristic, complemented
186#1831C2211yescharacteristic, complemented
187#1805C2211yescharacteristic, complemented
188#1805C2211yescharacteristic, complemented
189#1798C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1771C2211yescharacteristic, complemented
197C8×C4⋊C4C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199C4×#103C2211yescharacteristic, complemented
200#1750C2211yescharacteristic
201#1746C2211yescharacteristic, complemented
202#1744C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211#541—42no—
212#541—42no—
213#535—42no—
214#535—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#126—21no—
222C2×#126—21no—
223C2×#125—21no—
224C2×#125—21no—
225C2×#125C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×#121—21no—
238C2×#121—21no—
239C2×#120—21no—
240C2×#120—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×#117C2311yescharacteristic
247#489—42no—
248#486—42no—
249#477—42no—
250#475—42no—
251#464—42no—
252#464—42no—
253#464—42no—
254#464—42no—
255#462—42no—
256#460—42no—
257#452—42no—
258#450—42no—
259#441—42no—
260C4×Q16—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#401—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#399—21no—
337#399—21no—
338#399—21no—
339#399—21no—
340#399—21no—
341#399—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#395—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#393—21no—
371#391—21no—
372#391—21no—
373#391—21no—
374#391—21no—
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#390—21no—
381#390—21no—
382#390—21no—
383#390—21no—
384#390—21no—
385#390—21no—
386#390—21no—
387#390—21no—
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#389—21no—
395#389—21no—
396#389—21no—
397#389—21no—
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388D411yescharacteristic
422#388D411yescharacteristic
423#388D411yescharacteristic
424#388D411yescharacteristic
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387D411yescharacteristic
440#387D411yescharacteristic
441#387D411yescharacteristic
442#387D411yescharacteristic
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#384C2311yescharacteristic
448#383—21no—
449#383—21no—
450#382—21no—
451#382—21no—
452#382C2311yescharacteristic
453#382C2311yescharacteristic
454#382C2311yescharacteristic
455#382C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#379—21no—
460#379—21no—
461#379—21no—
462#379—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4—21no—
465C4×C4⋊C4—21no—
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473#376—21no—
474#376C2311yescharacteristic
475C43C2311yescharacteristic
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—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—21no—
524C23×C4C2411yescharacteristic
525C2×Q16—22no—
526C2×Q16—22no—
527C2×Q16—22no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×Q16—41no—
531C2×Q16—41no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C4⋊Q8—22no—
552C4⋊Q8—22no—
553C4⋊Q8—41no—
554C4⋊Q8—41no—
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559#127—22no—
560#127—22no—
561#127—41no—
562#127—41no—
563#126—44no—
564#126—44no—
565#125—41no—
566#125—41no—
567#125—44no—
568#125—44no—
569#124—22no—
570#124—22no—
571#124—41no—
572#124—41no—
573#124—41no—
574#124—41no—
575#124—41no—
576#124—41no—
577#124—41no—
578#124—41no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585C22⋊Q8—22no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591#121—44no—
592#121—44no—
593#120—44no—
594#120—44no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—22no—
598C4×Q8—22no—
599C4×Q8—22no—
600C4×Q8—22no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—41no—
604C4×Q8—41no—
605#117—22no—
606#117—22no—
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—21no—
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⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42C2×D411yescharacteristic
699C2×C42C2×D411yescharacteristic
700C2×C42C2×D411yescharacteristic
701C2×C42C2×D411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708#107—41no—
709#107—41no—
710#107—41no—
711#106—41no—
712#106—41no—
713#106—41no—
714C4⋊C8—22no—
715C4⋊C8—22no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768#97—22no—
769#97—41no—
770C4×C8—22no—
771C4×C8—41no—
772C4×C8—41no—
773C4×C8—41no—
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#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#95—21no—
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
818#95C2×D411yescharacteristic
819C24—21no—
820C24—21no—
821C24—21no—
822C24—42no—
823C24—81no—
824C24—81no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24C22×D411yescharacteristic
830#41—82no—
831#41—82no—
832#41—82no—
833#41—82no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—42no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×Q8H(5,𝔽2)12yes—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—81no—
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—82no—
896C2×D4—82no—
897C2×D4—82no—
898C2×D4—82no—
899C2×D4—81no—
900C2×D4—81no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
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—42no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C2511yescharacteristic
937Q16—44no—
938Q16—44no—
939Q16—82no—
940SD16—82no—
941SD16—82no—
942SD16—82no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C22⋊C4—22no—
1020C22⋊C4—22no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—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—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—41no—
1070C42—41no—
1071C42—41no—
1072C42—41no—
1073C42—42no—
1074C42—42no—
1075C42—42no—
1076C42—42no—
1077C42—42no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C42H(5,𝔽2)12yes—
1082C42H(5,𝔽2)12yes—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—84no—
1112C23—162no—
1113C23—162no—
1114C23—162no—
1115C23—162no—
1116C23—162no—
1117C23—162no—
1118C23C23×D411yescharacteristic
1119Q8—22no—
1120Q8—22no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—162no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—84no—
1149D4—84no—
1150D4—162no—
1151D4—162no—
1152D4—162no—
1153D4—162no—
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—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—84no—
1235C2×C4#53512yes—
1236C2×C4#53512yes—
1237C2×C4C2×H(5,𝔽2)11yescharacteristic
1238C2×C4C2×H(5,𝔽2)11yescharacteristic
1239C2×C4C2×H(5,𝔽2)11yescharacteristic
1240C2×C4#58511yescharacteristic
1241C2×C4#58511yescharacteristic
1242C2×C4#58511yescharacteristic
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—168no—
1280C22C2×#53511yescharacteristic
1281C22#348811yescharacteristic
1282C22#350011yescharacteristic
1283C22#358411yescharacteristic
1284C22#358411yescharacteristic
1285C22#358411yescharacteristic
1286C22#358611yescharacteristic
1287C4—22no—
1288C4—22no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—42no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4#354211yescharacteristic
1314C4#354211yescharacteristic
1315C4#355111yescharacteristic
1316C4#355111yescharacteristic
1317C2—81no—
1318C2—161no—
1319C2—161no—
1320C2—161no—
1321C2#4296211yescharacteristic
1322C2#6081911yescharacteristic
1323C2#6083511yescharacteristic
1324C2#6203011yescharacteristic
1325C2#6206111yescharacteristic
1326C2#6255511yescharacteristic
1327C2#6260011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38277C2semidirect
3. #32827C2semidirect
4. #32822C2semidirect
5. #31311C2semidirect
6. #31298C2semidirect
7. #31297C2semidirect
8. #31294C2semidirect
9. #31012C2semidirect
10. #30997C2semidirect
11. #30996C2semidirect
12. #30991C2semidirect
13. #30223C2semidirect
14. #30221C2semidirect
15. #29805C2semidirect
16. #29801C2semidirect
17. #29699C2semidirect
18. #29569C2semidirect
19. #29557C2semidirect
20. #28424C2semidirect
21. #28402C2semidirect
22. #27766C2semidirect
23. #27752C2semidirect
25. #25287C2semidirect
26. #25277C2semidirect
27. #24747C2semidirect
28. #24736C2semidirect
30. #23586C2semidirect
31. #22637C2semidirect
36. C2×#477C22semidirect
37. C2×#475C22semidirect
41. C2×#464C22semidirect
42. C2×#462C22semidirect
46. C2×#441C22semidirect
47. C2×C4×Q16C22semidirect
48. #2864C22semidirect
64. #2647C22semidirect
68. #2570C22semidirect
69. #2568C22semidirect
85. #2369C22semidirect
86. #2351C22semidirect
88. #2320C22semidirect
90. #2295C22semidirect
91. #2097C22semidirect
94. #2092C22semidirect
95. #2074C22semidirect
98. #2071C22semidirect
99. #2068C22semidirect
102. #2067C22semidirect
103. #2066C22semidirect
106. #2065C22semidirect
107. #2059C22semidirect
108. #2059C22semidirect
109. #2059C22semidirect
110. #2043C22semidirect
111. #2043C22semidirect
112. #2043C22semidirect
113. #2043C22semidirect
114. #2043C22semidirect
115. #2043C22semidirect
125. #2042C22semidirect
126. #2042C22semidirect
127. #2042C22semidirect
137. #2026C22semidirect
138. #2016C22semidirect
139. #2016C22semidirect
143. #2015C22semidirect
150. #1983C22semidirect
152. #1981C22semidirect
154. #1969C22semidirect
156. #1968C22semidirect
158. #1960C22semidirect
164. #1958C22semidirect
165. #1958C22semidirect
166. #1956C22semidirect
167. #1940C22semidirect
168. #1939C22semidirect
169. #1936C22semidirect
172. #1933C22semidirect
173. #1927C22semidirect
176. #1925C22semidirect
183. #1880C22semidirect
184. #1878C22semidirect
185. #1832C22semidirect
186. #1831C22semidirect
187. #1805C22semidirect
188. #1805C22semidirect
196. #1771C22semidirect
197. C8×C4⋊C4C22semidirect
198. #1763C22semidirect
199. C4×#103C22semidirect
201. #1746C22semidirect
202. #1744C22semidirect

Maximal subgroups

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

subgroupindex
#382772
#374242
#328272
#328222
#313112
#312982
#312972
#312942
#310122
#309972
#309962
#309912
#302232
#302212
#298052
#298012
#296992
#295692
#295572
#284242
#284022
#277662
#277522
#258652
#252872
#252772
#247472
#247362
#242202
#235862
#226372