Finite Group Databasebeta

← #7338775

Subgroups — #7338775

Order 512.

1598 conjugacy classes of subgroups.

The subgroup lattice has 1331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59030C211yesmaximal, characteristic
2#45684C211yesmaximal, characteristic, complemented
3#32086C211yesmaximal, characteristic, complemented
4#31973C211yesmaximal, characteristic, complemented
5#31776C211yesmaximal, characteristic, complemented
6#31493C211yesmaximal, characteristic, complemented
7#31320C211yesmaximal, characteristic, complemented
8#31298C211yesmaximal, characteristic, complemented
9#31294C211yesmaximal, characteristic, complemented
10#31294C211yesmaximal, characteristic, complemented
11#31126C211yesmaximal, characteristic, complemented
12#30950C211yesmaximal, characteristic, complemented
13#30807C211yesmaximal, characteristic, complemented
14#30783C211yesmaximal, characteristic, complemented
15#29956C211yesmaximal, characteristic, complemented
16#29693C211yesmaximal, characteristic, complemented
17#29104C211yesmaximal, characteristic, complemented
18#28944C211yesmaximal, characteristic, complemented
19#28068C211yesmaximal, characteristic, complemented
20#27771C211yesmaximal, characteristic, complemented
21#27525C211yesmaximal, characteristic, complemented
22#27256C211yesmaximal, characteristic, complemented
23#27095C211yesmaximal, characteristic, complemented
24#27031C211yesmaximal, characteristic, complemented
25#26760C211yesmaximal, characteristic, complemented
26#26471C211yesmaximal, characteristic, complemented
27#25960C211yesmaximal, characteristic, complemented
28#25885C211yesmaximal, characteristic
29#25675C211yesmaximal, characteristic, complemented
30#24033C211yesmaximal, characteristic
31#22357C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#499C2211yescharacteristic, complemented
35C2×#488C2211yescharacteristic, complemented
36C2×#486C2211yescharacteristic
37C2×#481C2211yescharacteristic
38C2×#479C2211yescharacteristic, complemented
39C2×#478C2211yescharacteristic, complemented
40C2×#474C2211yescharacteristic
41C22×#102C2211yescharacteristic
42#2851C2211yescharacteristic, complemented
43#2851C2211yescharacteristic, complemented
44#2834—21no—
45#2771—21no—
46#2770—21no—
47#2770—21no—
48#2762—21no—
49#2762—21no—
50#2717—21no—
51#2691—21no—
52#2685—21no—
53#2550C2211yescharacteristic, complemented
54#2550C2211yescharacteristic, complemented
55#2547C2211yescharacteristic
56#2544C2211yescharacteristic
57#2534—21no—
58#2508C2211yescharacteristic, complemented
59#2508C2211yescharacteristic, complemented
60#2495C2211yescharacteristic, complemented
61#2495C2211yescharacteristic, complemented
62#2494C2211yescharacteristic, complemented
63#2494C2211yescharacteristic, complemented
64#2490C2211yescharacteristic
65#2487C2211yescharacteristic
66#2476—21no—
67#2454C2211yescharacteristic
68#2445C2211yescharacteristic
69#2442C2211yescharacteristic, complemented
70#2442C2211yescharacteristic, complemented
71#2435C2211yescharacteristic
72#2435C2211yescharacteristic
73#2426C2211yescharacteristic
74#2418—21no—
75#2417C2211yescharacteristic
76#2411—21no—
77#2405—21no—
78#2379—21no—
79#2367C2211yescharacteristic
80#2361C2211yescharacteristic
81D4×C22⋊C4—21no—
82D4×C22⋊C4C2211yescharacteristic
83C4×#123C2211yescharacteristic
84C2×#390C2211yescharacteristic
85#2092C2211yescharacteristic
86#2092C2211yescharacteristic
87#2092C2211yescharacteristic, complemented
88#2092C2211yescharacteristic, complemented
89#2087C2211yescharacteristic, complemented
90#2087C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2077C2211yescharacteristic, complemented
93#2076C2211yescharacteristic, complemented
94#2073C2211yescharacteristic
95#2073C2211yescharacteristic, complemented
96#2073C2211yescharacteristic, complemented
97#2068C2211yescharacteristic, complemented
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic, complemented
101#2067C2211yescharacteristic, complemented
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic, complemented
104#2065C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2059C2211yescharacteristic, complemented
107#2058C2211yescharacteristic, complemented
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic, complemented
111#2042C2211yescharacteristic, complemented
112#2042C2211yescharacteristic, complemented
113#2042C2211yescharacteristic, complemented
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic
116#2036C2211yescharacteristic, complemented
117#2036C2211yescharacteristic, complemented
118#2036C2211yescharacteristic, complemented
119#2035C2211yescharacteristic, complemented
120#2035C2211yescharacteristic, complemented
121#2035C2211yescharacteristic, complemented
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2025C2211yescharacteristic
129#2025C2211yescharacteristic
130#2025C2211yescharacteristic, complemented
131#2025C2211yescharacteristic, complemented
132#2024C2211yescharacteristic, complemented
133#1991C2211yescharacteristic, complemented
134#1983C2211yescharacteristic
135#1983C2211yescharacteristic, complemented
136#1982C2211yescharacteristic
137#1958C2211yescharacteristic
138#1958C2211yescharacteristic, complemented
139#1958C2211yescharacteristic, complemented
140#1954C2211yescharacteristic
141#1949C2211yescharacteristic, complemented
142#1942C2211yescharacteristic, complemented
143#1941C2211yescharacteristic, complemented
144#1939C2211yescharacteristic, complemented
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic, complemented
149#1934C2211yescharacteristic, complemented
150#1934C2211yescharacteristic, complemented
151#1934C2211yescharacteristic, complemented
152#1933C2211yescharacteristic, complemented
153#1927C2211yescharacteristic, complemented
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic, complemented
156#1925C2211yescharacteristic, complemented
157#1923C2211yescharacteristic, complemented
158#1923C2211yescharacteristic, complemented
159#1923C2211yescharacteristic, complemented
160#1923C2211yescharacteristic, complemented
161#1920C2211yescharacteristic, complemented
162#1920C2211yescharacteristic, complemented
163#1919C2211yescharacteristic, complemented
164#1918C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1893C2211yescharacteristic
168#1892C2211yescharacteristic, complemented
169#1872C2211yescharacteristic, complemented
170#1869C2211yescharacteristic
171#1865C2211yescharacteristic, complemented
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic, complemented
175#1864C2211yescharacteristic, complemented
176#1863C2211yescharacteristic, complemented
177#1862C2211yescharacteristic, complemented
178#1862C2211yescharacteristic, complemented
179#1853C2211yescharacteristic, complemented
180#1852C2211yescharacteristic, complemented
181#1852C2211yescharacteristic, complemented
182#1850C2211yescharacteristic, complemented
183#1824C2211yescharacteristic, complemented
184#1824C2211yescharacteristic, complemented
185#1807C2211yescharacteristic, complemented
186#1805C2211yescharacteristic, complemented
187#1804C2211yescharacteristic, complemented
188#1804C2211yescharacteristic, complemented
189#1797C2211yescharacteristic, complemented
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197C4×#107C2211yescharacteristic, complemented
198C8×C4⋊C4C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic, complemented
202C4×C22⋊C8C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C23×C8C2311yescharacteristic
207D42—42no—
208D42—42no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211#529—42no—
212#529—42no—
213C2×#126—21no—
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#123—21no—
222C2×#123—21no—
223C2×#123D411yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121—21no—
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#120—21no—
230C2×#120—21no—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117—21no—
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C22⋊C4—21no—
242C22×C22⋊C4—21no—
243C22×C22⋊C4—21no—
244C22×C42C2311yescharacteristic
245#499—42no—
246#488—42no—
247#486—42no—
248#481—42no—
249#479—42no—
250#478—42no—
251#474—42no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#102—42no—
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#401—21no—
315#401—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#399—21no—
324#399—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#395—21no—
343#395—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#391—21no—
355#391—21no—
356#391—21no—
357#391C2311yescharacteristic
358#390—21no—
359#390—21no—
360#390—21no—
361#390—21no—
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#389—21no—
370#389—21no—
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388D411yescharacteristic
393#388D411yescharacteristic
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387D411yescharacteristic
403#387D411yescharacteristic
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386D411yescharacteristic
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385D411yescharacteristic
424#383—21no—
425#383—21no—
426#382—21no—
427#382—21no—
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#381D411yescharacteristic
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#379—21no—
446#379—21no—
447#379—21no—
448#379—21no—
449#379—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C25—21no—
492C22×Q8—21no—
493C22×Q8C2411yescharacteristic
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—44no—
513C22×D4—44no—
514C22×D4—82no—
515C22×D4C2×D411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C22×C8—41no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541#127—22no—
542#127—41no—
543#126—44no—
544#125—22no—
545#125—41no—
546#125—41no—
547#125—41no—
548#125—41no—
549#125—41no—
550#124—22no—
551#124—22no—
552#124—41no—
553#124—41no—
554#124—41no—
555#124—41no—
556#124—44no—
557#123—24no—
558#123—44no—
559#123—82no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562C22⋊Q8—41no—
563C22⋊Q8—41no—
564#121—22no—
565#121—22no—
566#121—22no—
567#121—44no—
568#121—41no—
569#120—44no—
570#120—44no—
571C4×Q8—22no—
572C4×Q8—41no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—44no—
582C4×D4—82no—
583#117—44no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—82no—
665C2×C22⋊C4—82no—
666C2×C22⋊C4—82no—
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—41no—
681C2×C42—41no—
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689#107—22no—
690#107—22no—
691#107—41no—
692#107—41no—
693#107—41no—
694#107—41no—
695#106—22no—
696#106—22no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738C22⋊C8—41no—
739C22⋊C8—41no—
740C22⋊C8—41no—
741C22⋊C8—41no—
742C22⋊C8—41no—
743C22⋊C8—41no—
744C22⋊C8—41no—
745C4×C8—41no—
746C4×C8—41no—
747C4×C8—41no—
748C4×C8—41no—
749C4×C8—41no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794C24—21no—
795C24—21no—
796C24—21no—
797C24—42no—
798C24—42no—
799C24—42no—
800C24—42no—
801C24—42no—
802C24—42no—
803C24—42no—
804C24—81no—
805C24—81no—
806C24—81no—
807C24—81no—
808C24—81no—
809C24—81no—
810C24—81no—
811C24C22×D411yescharacteristic
812C24C22×D411yescharacteristic
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—42no—
820C2×Q8—81no—
821C2×Q8—81no—
822C2×D4—24no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—41no—
840C2×D4—41no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—44no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—82no—
859C2×D4—82no—
860C2×D4—82no—
861C2×D4—82no—
862C2×D4—82no—
863C2×D4—82no—
864C2×D4—82no—
865C2×D4—81no—
866C2×D4—816no—
867C2×D4#13514yes—
868C2×D4H(5,𝔽2)12yes—
869C2×D42−1+412yes—
870C22×C4—21no—
871C22×C4—22no—
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—41no—
897C22×C4—41no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C2511yescharacteristic
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×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—82no—
954C4⋊C4—22no—
955C4⋊C4—22no—
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—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4H(5,𝔽2)12yes—
1007C22⋊C4—24no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
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—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—41no—
1061C42—41no—
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—22no—
1080C23—22no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—84no—
1101C23—84no—
1102C23—84no—
1103C23—84no—
1104C23—84no—
1105C23—84no—
1106C23—84no—
1107C23—162no—
1108C23—162no—
1109C23—162no—
1110C23—162no—
1111C23—162no—
1112C23—162no—
1113C23—162no—
1114C23C2×#13512yes—
1115C23C2×#13512yes—
1116C23C23×D411yescharacteristic
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—162no—
1122D4—22no—
1123D4—22no—
1124D4—22no—
1125D4—22no—
1126D4—44no—
1127D4—48no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—84no—
1137D4—84no—
1138D4—84no—
1139D4—84no—
1140D4—162no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
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—21no—
1163C2×C4—22no—
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—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—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—84no—
1224C2×C4—82no—
1225C2×C4—82no—
1226C2×C4—84no—
1227C2×C4—162no—
1228C2×C4—162no—
1229C2×C4—162no—
1230C2×C4C2×#13512yes—
1231C2×C4C2×H(5,𝔽2)11yescharacteristic
1232C2×C4C2×H(5,𝔽2)11yescharacteristic
1233C2×C4C2×2−1+411yescharacteristic
1234C2×C4#58511yescharacteristic
1235C2×C4#58511yescharacteristic
1236C2×C4#58511yescharacteristic
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C22—22no—
1246C22—22no—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—22no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
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—81no—
1280C22—168no—
1281C22—168no—
1282C22#348411yescharacteristic
1283C22#348911yescharacteristic
1284C22#350011yescharacteristic
1285C22C22×#13511yescharacteristic
1286C22#358411yescharacteristic
1287C22#358511yescharacteristic
1288C22#358511yescharacteristic
1289C4—22no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—42no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4#353511yescharacteristic
1315C4#355111yescharacteristic
1316C4#356011yescharacteristic
1317C4#356111yescharacteristic
1318C2—42no—
1319C2—42no—
1320C2—82no—
1321C2—82no—
1322C2—161no—
1323C2#4795611yescharacteristic
1324C2#6156111yescharacteristic
1325C2#6162511yescharacteristic
1326C2#6210311yescharacteristic
1327C2#6217511yescharacteristic
1328C2#6253311yescharacteristic
1329C2#6256411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #45684C2semidirect
3. #32086C2semidirect
4. #31973C2semidirect
5. #31776C2semidirect
6. #31493C2semidirect
7. #31320C2semidirect
8. #31298C2semidirect
9. #31294C2semidirect
10. #31294C2semidirect
11. #31126C2semidirect
12. #30950C2semidirect
13. #30807C2semidirect
14. #30783C2semidirect
15. #29956C2semidirect
16. #29693C2semidirect
17. #29104C2semidirect
18. #28944C2semidirect
19. #28068C2semidirect
20. #27771C2semidirect
21. #27525C2semidirect
22. #27256C2semidirect
23. #27095C2semidirect
24. #27031C2semidirect
25. #26760C2semidirect
26. #26471C2semidirect
27. #25960C2semidirect
29. #25675C2semidirect
31. #22357C2semidirect
34. C2×#499C22semidirect
35. C2×#488C22semidirect
38. C2×#479C22semidirect
39. C2×#478C22semidirect
42. #2851C22semidirect
43. #2851C22semidirect
53. #2550C22semidirect
54. #2550C22semidirect
58. #2508C22semidirect
59. #2508C22semidirect
60. #2495C22semidirect
61. #2495C22semidirect
62. #2494C22semidirect
63. #2494C22semidirect
69. #2442C22semidirect
70. #2442C22semidirect
87. #2092C22semidirect
88. #2092C22semidirect
89. #2087C22semidirect
90. #2087C22semidirect
91. #2085C22semidirect
92. #2077C22semidirect
93. #2076C22semidirect
95. #2073C22semidirect
96. #2073C22semidirect
97. #2068C22semidirect
100. #2067C22semidirect
101. #2067C22semidirect
103. #2065C22semidirect
104. #2065C22semidirect
105. #2059C22semidirect
106. #2059C22semidirect
107. #2058C22semidirect
110. #2042C22semidirect
111. #2042C22semidirect
112. #2042C22semidirect
113. #2042C22semidirect
116. #2036C22semidirect
117. #2036C22semidirect
118. #2036C22semidirect
119. #2035C22semidirect
120. #2035C22semidirect
121. #2035C22semidirect
130. #2025C22semidirect
131. #2025C22semidirect
132. #2024C22semidirect
133. #1991C22semidirect
135. #1983C22semidirect
138. #1958C22semidirect
139. #1958C22semidirect
141. #1949C22semidirect
142. #1942C22semidirect
143. #1941C22semidirect
144. #1939C22semidirect
148. #1934C22semidirect
149. #1934C22semidirect
150. #1934C22semidirect
151. #1934C22semidirect
152. #1933C22semidirect
153. #1927C22semidirect
155. #1926C22semidirect
156. #1925C22semidirect
157. #1923C22semidirect
158. #1923C22semidirect
159. #1923C22semidirect
160. #1923C22semidirect
161. #1920C22semidirect
162. #1920C22semidirect
163. #1919C22semidirect
164. #1918C22semidirect
165. #1916C22semidirect
166. #1916C22semidirect
168. #1892C22semidirect
169. #1872C22semidirect
171. #1865C22semidirect
174. #1864C22semidirect
175. #1864C22semidirect
176. #1863C22semidirect
177. #1862C22semidirect
178. #1862C22semidirect
179. #1853C22semidirect
180. #1852C22semidirect
181. #1852C22semidirect
182. #1850C22semidirect
183. #1824C22semidirect
184. #1824C22semidirect
185. #1807C22semidirect
186. #1805C22semidirect
187. #1804C22semidirect
188. #1804C22semidirect
189. #1797C22semidirect
197. C4×#107C22semidirect
198. C8×C4⋊C4C22semidirect
200. C4×#102C22semidirect
201. C8×C22⋊C4C22semidirect
202. C4×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#590302
#456842
#320862
#319732
#317762
#314932
#313202
#312982
#312942
#311262
#309502
#308072
#307832
#299562
#296932
#291042
#289442
#280682
#277712
#275252
#272562
#270952
#270312
#267602
#264712
#259602
#258852
#256752
#240332
#223572