Finite Group Databasebeta

← #6993166

Subgroups — #6993166

Order 512.

1535 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39297C211yesmaximal, characteristic, complemented
2#37424C211yesmaximal, characteristic, complemented
3#32804C211yesmaximal, characteristic, complemented
4#32797C211yesmaximal, characteristic, complemented
5#31311C211yesmaximal, characteristic, complemented
6#31298C211yesmaximal, characteristic, complemented
7#31297C211yesmaximal, characteristic, complemented
8#31294C211yesmaximal, characteristic, complemented
9#30535C211yesmaximal, characteristic, complemented
10#30533C211yesmaximal, characteristic, complemented
11#30528C211yesmaximal, characteristic, complemented
12#30523C211yesmaximal, characteristic, complemented
13#30349C211yesmaximal, characteristic, complemented
14#30340C211yesmaximal, characteristic, complemented
15#30069C211yesmaximal, characteristic, complemented
16#30065C211yesmaximal, characteristic, complemented
17#29699C211yesmaximal, characteristic, complemented
18#28758C211yesmaximal, characteristic, complemented
19#28751C211yesmaximal, characteristic, complemented
20#28434C211yesmaximal, characteristic, complemented
21#28399C211yesmaximal, characteristic, complemented
22#27786C211yesmaximal, characteristic, complemented
23#27772C211yesmaximal, characteristic, complemented
24#25865C211yesmaximal, characteristic, complemented
25#25286C211yesmaximal, characteristic, complemented
26#25279C211yesmaximal, characteristic, complemented
27#24647C211yesmaximal, characteristic, complemented
28#24636C211yesmaximal, characteristic, complemented
29#24218C211yesmaximal, characteristic
30#23584C211yesmaximal, characteristic, complemented
31#22644C211yesmaximal, characteristic, complemented
32C2×#541C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#489C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#488C2211yescharacteristic, complemented
38C2×#487C2211yescharacteristic, complemented
39C2×#486C2211yescharacteristic
40C2×#477C2211yescharacteristic, complemented
41C2×#475C2211yescharacteristic, complemented
42C2×#463C2211yescharacteristic
43C2×#459C2211yescharacteristic
44C2×#449C2211yescharacteristic
45C2×#447C2211yescharacteristic
46C2×#440C2211yescharacteristic, complemented
47C2×C4×SD16C2211yescharacteristic, complemented
48#2861C2211yescharacteristic
49#2860C2211yescharacteristic, complemented
50#2858C2211yescharacteristic
51#2808—21no—
52#2759—21no—
53#2745—21no—
54#2740—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#2644C2211yescharacteristic, complemented
65#2641C2211yescharacteristic
66#2628C2211yescharacteristic
67#2592—21no—
68#2577—21no—
69#2563C2211yescharacteristic, complemented
70#2550C2211yescharacteristic, complemented
71#2548C2211yescharacteristic
72#2548C2211yescharacteristic
73#2545C2211yescharacteristic
74#2545C2211yescharacteristic
75#2521—21no—
76#2495C2211yescharacteristic
77#2494C2211yescharacteristic
78#2491C2211yescharacteristic
79#2490C2211yescharacteristic
80#2469—21no—
81#2435C2211yescharacteristic
82#2435C2211yescharacteristic
83#2432C2211yescharacteristic
84#2432C2211yescharacteristic
85#2365C2211yescharacteristic, complemented
86#2357C2211yescharacteristic, complemented
87#2331C2211yescharacteristic, complemented
88#2324C2211yescharacteristic
89C4×#125C2211yescharacteristic, complemented
90#2298C2211yescharacteristic
91#2097C2211yescharacteristic, complemented
92#2092C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic, complemented
95#2068C2211yescharacteristic, complemented
96#2067C2211yescharacteristic
97#2065C2211yescharacteristic
98#2065C2211yescharacteristic, complemented
99#2059C2211yescharacteristic, complemented
100#2059C2211yescharacteristic, complemented
101#2059C2211yescharacteristic, complemented
102#2055C2211yescharacteristic, complemented
103#2054C2211yescharacteristic
104#2054C2211yescharacteristic
105#2054C2211yescharacteristic, complemented
106#2043C2211yescharacteristic, complemented
107#2043C2211yescharacteristic, complemented
108#2043C2211yescharacteristic, complemented
109#2043C2211yescharacteristic, complemented
110#2043C2211yescharacteristic, complemented
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic, complemented
119#2042C2211yescharacteristic, complemented
120#2041C2211yescharacteristic
121#2041C2211yescharacteristic
122#2041C2211yescharacteristic
123#2036C2211yescharacteristic
124#2036C2211yescharacteristic
125#2036C2211yescharacteristic
126#2035C2211yescharacteristic
127#2035C2211yescharacteristic
128#2035C2211yescharacteristic
129#2026C2211yescharacteristic, complemented
130#2025C2211yescharacteristic
131#2025C2211yescharacteristic, complemented
132#2023C2211yescharacteristic
133#2023C2211yescharacteristic, complemented
134#2013C2211yescharacteristic, complemented
135#2013C2211yescharacteristic, complemented
136#2013C2211yescharacteristic, complemented
137#2012C2211yescharacteristic
138#2012C2211yescharacteristic
139#2012C2211yescharacteristic
140#2012C2211yescharacteristic
141#2012C2211yescharacteristic
142#2012C2211yescharacteristic, complemented
143#2012C2211yescharacteristic, complemented
144#2011C2211yescharacteristic
145#2000C2211yescharacteristic
146#2000C2211yescharacteristic
147#1983C2211yescharacteristic
148#1983C2211yescharacteristic
149#1983C2211yescharacteristic
150#1983C2211yescharacteristic
151#1983C2211yescharacteristic
152#1983C2211yescharacteristic, complemented
153#1983C2211yescharacteristic, complemented
154#1982C2211yescharacteristic
155#1981C2211yescharacteristic, complemented
156#1981C2211yescharacteristic, complemented
157#1972C2211yescharacteristic
158#1970C2211yescharacteristic
159#1970C2211yescharacteristic, complemented
160#1968C2211yescharacteristic, complemented
161#1961C2211yescharacteristic
162#1960C2211yescharacteristic, complemented
163#1958C2211yescharacteristic
164#1958C2211yescharacteristic
165#1958C2211yescharacteristic
166#1958C2211yescharacteristic, complemented
167#1940C2211yescharacteristic, complemented
168#1939C2211yescharacteristic, complemented
169#1936C2211yescharacteristic, complemented
170#1934C2211yescharacteristic
171#1934C2211yescharacteristic
172#1933C2211yescharacteristic, complemented
173#1928C2211yescharacteristic, complemented
174#1927C2211yescharacteristic, complemented
175#1926C2211yescharacteristic
176#1926C2211yescharacteristic
177#1926C2211yescharacteristic, complemented
178#1925C2211yescharacteristic
179#1925C2211yescharacteristic
180#1925C2211yescharacteristic, complemented
181#1924C2211yescharacteristic
182#1923C2211yescharacteristic
183#1923C2211yescharacteristic
184#1923C2211yescharacteristic
185#1840C2211yescharacteristic, complemented
186#1839C2211yescharacteristic, 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#1768C2211yescharacteristic, complemented
199C4×C4⋊C8C2211yescharacteristic, complemented
200#1763C2211yescharacteristic, complemented
201C4×#103C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
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×C4⋊Q8C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#126—21no—
223C2×#126—21no—
224C2×#126—21no—
225C2×#125—21no—
226C2×#125—21no—
227C2×#125C2311yescharacteristic
228C2×#125C2311yescharacteristic
229C2×#124—21no—
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#124C2311yescharacteristic
237C2×#124C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×#121—21no—
241C2×#121—21no—
242C2×#121C2311yescharacteristic
243C2×#120—21no—
244C2×#120—21no—
245C2×C4×Q8—21no—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117C2311yescharacteristic
250#489—42no—
251#489—42no—
252#488—42no—
253#488—42no—
254#487—42no—
255#486—42no—
256#477—42no—
257#475—42no—
258#463—42no—
259#459—42no—
260#449—42no—
261#447—42no—
262#440—42no—
263C4×SD16—42no—
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
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×#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×#103C2311yescharacteristic
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×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330#401—21no—
331#400—21no—
332#400—21no—
333#399—21no—
334#399—21no—
335#399—21no—
336#399—21no—
337#399—21no—
338#398—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#395—21no—
351#395—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#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#393—21no—
372#393—21no—
373#393—21no—
374#391—21no—
375#391—21no—
376#391—21no—
377#391—21no—
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#390—21no—
389#390—21no—
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#389—21no—
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
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#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388D411yescharacteristic
428#388D411yescharacteristic
429#388D411yescharacteristic
430#388D411yescharacteristic
431#387—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387D411yescharacteristic
439#387D411yescharacteristic
440#387D411yescharacteristic
441#387D411yescharacteristic
442#386—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#383—21no—
449#382C2311yescharacteristic
450#382C2311yescharacteristic
451#382C2311yescharacteristic
452#381—21no—
453#380—21no—
454#380—21no—
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#379—21no—
459#379—21no—
460#379—21no—
461#379—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C22⋊C4—21no—
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
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×Q8—21no—
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—21no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2411yescharacteristic
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C4⋊Q8—22no—
555C4⋊Q8—22no—
556C4⋊Q8—22no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564#127—22no—
565#127—22no—
566#127—41no—
567#127—41no—
568#126—44no—
569#126—44no—
570#126—82no—
571#125—22no—
572#125—41no—
573#125—41no—
574#125—41no—
575#125—44no—
576#125—44no—
577#124—22no—
578#124—22no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124—41no—
586#124—41no—
587#124—41no—
588#124—41no—
589#124—41no—
590#124—41no—
591#124—41no—
592#124—41no—
593#124—82no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598#121—22no—
599#121—41no—
600#121—44no—
601#121—44no—
602#120—44no—
603#120—44no—
604C4×Q8—22no—
605C4×Q8—22no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—82no—
609C4×D4—22no—
610C4×D4—22no—
611#117—22no—
612#117—22no—
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⋊C4—21no—
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42C2×D411yescharacteristic
710C2×C42C2×D411yescharacteristic
711C2×C42C2×D411yescharacteristic
712C2×C42C2×D411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719#107—41no—
720#107—41no—
721#107—41no—
722#106—41no—
723#106—41no—
724#106—41no—
725C4⋊C8—22no—
726C4⋊C8—22no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731#103—22no—
732#103—22no—
733#103—22no—
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#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#102—22no—
753#102—22no—
754#102—22no—
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—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779#97—22no—
780#97—41no—
781C4×C8—22no—
782C4×C8—41no—
783C4×C8—41no—
784C4×C8—41no—
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#95—21no—
808#95—21no—
809#95—21no—
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
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—42no—
827C24—81no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24C22×D411yescharacteristic
834#41—82no—
835#41—82no—
836#41—82no—
837#41—82no—
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—42no—
857C2×Q8—42no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×Q8—81no—
861C2×Q8—81no—
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—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—82no—
904C2×D4—82no—
905C2×D4—82no—
906C2×D4—82no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C2511yescharacteristic
949SD16—44no—
950SD16—44no—
951SD16—82no—
952D8—82no—
953D8—82no—
954D8—82no—
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—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4H(5,𝔽2)12yes—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
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—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—41no—
1088C42—41no—
1089C42—41no—
1090C42—41no—
1091C42—42no—
1092C42—42no—
1093C42—42no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C42H(5,𝔽2)12yes—
1099C42H(5,𝔽2)12yes—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—84no—
1136C23—162no—
1137C23—162no—
1138C23—162no—
1139C23—162no—
1140C23—162no—
1141C23—162no—
1142C23C23×D411yescharacteristic
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—84no—
1156Q8—162no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—84no—
1174D4—84no—
1175D4—162no—
1176D4—162no—
1177D4—162no—
1178D4—162no—
1179D4—162no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
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—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—84no—
1258C2×C4—162no—
1259C2×C4#53512yes—
1260C2×C4#53512yes—
1261C2×C4C2×H(5,𝔽2)11yescharacteristic
1262C2×C4C2×H(5,𝔽2)11yescharacteristic
1263C2×C4C2×H(5,𝔽2)11yescharacteristic
1264C2×C4#58511yescharacteristic
1265C2×C4#58511yescharacteristic
1266C2×C4#58511yescharacteristic
1267C8—41no—
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C8—41no—
1272C8—41no—
1273C8—41no—
1274C8—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—168no—
1311C22C2×#53511yescharacteristic
1312C22#348811yescharacteristic
1313C22#350011yescharacteristic
1314C22#358411yescharacteristic
1315C22#358411yescharacteristic
1316C22#358411yescharacteristic
1317C22#358511yescharacteristic
1318C4—22no—
1319C4—22no—
1320C4—41no—
1321C4—41no—
1322C4—42no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4#354011yescharacteristic
1344C4#354011yescharacteristic
1345C4#354611yescharacteristic
1346C4#354611yescharacteristic
1347C2—81no—
1348C2—161no—
1349C2—161no—
1350C2—161no—
1351C2—161no—
1352C2#4298711yescharacteristic
1353C2#6081911yescharacteristic
1354C2#6083411yescharacteristic
1355C2#6201111yescharacteristic
1356C2#6206111yescharacteristic
1357C2#6255511yescharacteristic
1358C2#6261311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24218C2
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. #39297C2semidirect
2. #37424C2semidirect
3. #32804C2semidirect
4. #32797C2semidirect
5. #31311C2semidirect
6. #31298C2semidirect
7. #31297C2semidirect
8. #31294C2semidirect
9. #30535C2semidirect
10. #30533C2semidirect
11. #30528C2semidirect
12. #30523C2semidirect
13. #30349C2semidirect
14. #30340C2semidirect
15. #30069C2semidirect
16. #30065C2semidirect
17. #29699C2semidirect
18. #28758C2semidirect
19. #28751C2semidirect
20. #28434C2semidirect
21. #28399C2semidirect
22. #27786C2semidirect
23. #27772C2semidirect
24. #25865C2semidirect
25. #25286C2semidirect
26. #25279C2semidirect
27. #24647C2semidirect
28. #24636C2semidirect
30. #23584C2semidirect
31. #22644C2semidirect
37. C2×#488C22semidirect
38. C2×#487C22semidirect
40. C2×#477C22semidirect
41. C2×#475C22semidirect
46. C2×#440C22semidirect
47. C2×C4×SD16C22semidirect
49. #2860C22semidirect
64. #2644C22semidirect
69. #2563C22semidirect
70. #2550C22semidirect
85. #2365C22semidirect
86. #2357C22semidirect
87. #2331C22semidirect
89. C4×#125C22semidirect
91. #2097C22semidirect
94. #2092C22semidirect
95. #2068C22semidirect
98. #2065C22semidirect
99. #2059C22semidirect
100. #2059C22semidirect
101. #2059C22semidirect
102. #2055C22semidirect
105. #2054C22semidirect
106. #2043C22semidirect
107. #2043C22semidirect
108. #2043C22semidirect
109. #2043C22semidirect
110. #2043C22semidirect
118. #2042C22semidirect
119. #2042C22semidirect
129. #2026C22semidirect
131. #2025C22semidirect
133. #2023C22semidirect
134. #2013C22semidirect
135. #2013C22semidirect
136. #2013C22semidirect
142. #2012C22semidirect
143. #2012C22semidirect
152. #1983C22semidirect
153. #1983C22semidirect
155. #1981C22semidirect
156. #1981C22semidirect
159. #1970C22semidirect
160. #1968C22semidirect
162. #1960C22semidirect
166. #1958C22semidirect
167. #1940C22semidirect
168. #1939C22semidirect
169. #1936C22semidirect
172. #1933C22semidirect
173. #1928C22semidirect
174. #1927C22semidirect
177. #1926C22semidirect
180. #1925C22semidirect
185. #1840C22semidirect
186. #1839C22semidirect
187. #1805C22semidirect
188. #1805C22semidirect
196. #1771C22semidirect
197. C8×C4⋊C4C22semidirect
198. #1768C22semidirect
199. C4×C4⋊C8C22semidirect
200. #1763C22semidirect
201. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#392972
#374242
#328042
#327972
#313112
#312982
#312972
#312942
#305352
#305332
#305282
#305232
#303492
#303402
#300692
#300652
#296992
#287582
#287512
#284342
#283992
#277862
#277722
#258652
#252862
#252792
#246472
#246362
#242182
#235842
#226442