Finite Group Databasebeta

← #7549509

Subgroups — #7549509

Order 512.

1591 conjugacy classes of subgroups.

The subgroup lattice has 1319 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45187C211yesmaximal, characteristic
2#35720C211yesmaximal, characteristic, complemented
3#32213C211yesmaximal, characteristic, complemented
4#32190C211yesmaximal, characteristic, complemented
5#31810C211yesmaximal, characteristic, complemented
6#31309C211yesmaximal, characteristic, complemented
7#29029C211yesmaximal, characteristic, complemented
8#28928C211yesmaximal, characteristic, complemented
9#27397C211yesmaximal, characteristic, complemented
10#27271C211yesmaximal, characteristic, complemented
11#27234C211yesmaximal, characteristic, complemented
12#27212C211yesmaximal, characteristic, complemented
13#27027C211yesmaximal, characteristic, complemented
14#26782C211yesmaximal, characteristic, complemented
15#26742C211yesmaximal, characteristic, complemented
16#26349C211yesmaximal, characteristic, complemented
17#26220C211yesmaximal, characteristic, complemented
18#25512C211yesmaximal, characteristic, complemented
19#25283C211yesmaximal, characteristic, complemented
20#25100C211yesmaximal, characteristic, complemented
21#25084C211yesmaximal, characteristic, complemented
22#24785C211yesmaximal, characteristic, complemented
23#24516C211yesmaximal, characteristic, complemented
24#24442C211yesmaximal, characteristic
25#23139C211yesmaximal, characteristic, complemented
26#23107C211yesmaximal, characteristic, complemented
27#22911C211yesmaximal, characteristic, complemented
28#22583C211yesmaximal, characteristic, complemented
29#22419C211yesmaximal, characteristic
30#21398C211yesmaximal, characteristic, complemented
31#21065C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C2×#488C2211yescharacteristic
35C2×#479C2211yescharacteristic, complemented
36C2×#470C2211yescharacteristic
37C2×#470C2211yescharacteristic, complemented
38C2×#467C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C2×#433C2211yescharacteristic
44C2×#427C2211yescharacteristic
45C2×#417C2211yescharacteristic
46C2×#418C2211yescharacteristic
47C22×#102C2211yescharacteristic
48#2711—21no—
49#2694—21no—
50#2685—21no—
51#2685—21no—
52#2652—21no—
53#2625C2211yescharacteristic
54#2590—21no—
55#2575—21no—
56#2558—21no—
57#2545C2211yescharacteristic
58#2517—21no—
59#2511C2211yescharacteristic, complemented
60#2509—21no—
61#2507C2211yescharacteristic, complemented
62#2496C2211yescharacteristic, complemented
63#2490—21no—
64#2490C2211yescharacteristic
65#2489C2211yescharacteristic, complemented
66#2480—21no—
67#2480—21no—
68#2478—21no—
69#2466—21no—
70#2454C2211yescharacteristic
71#2448C2211yescharacteristic
72#2441C2211yescharacteristic
73#2435C2211yescharacteristic
74#2432C2211yescharacteristic
75#2426C2211yescharacteristic
76#2415C2211yescharacteristic
77#2415C2211yescharacteristic
78#2395—21no—
79#2395C2211yescharacteristic
80#2370C2211yescharacteristic, complemented
81#2367C2211yescharacteristic
82#2362C2211yescharacteristic
83#2360C2211yescharacteristic
84#2360C2211yescharacteristic, complemented
85#2355C2211yescharacteristic, complemented
86D4×C4⋊C4C2211yescharacteristic
87#2344C2211yescharacteristic, complemented
88#2341C2211yescharacteristic
89#2309C2211yescharacteristic
90#2274C2211yescharacteristic
91#2099C2211yescharacteristic, complemented
92#2095C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2077C2211yescharacteristic, complemented
95#2072C2211yescharacteristic, complemented
96#2071C2211yescharacteristic
97#2068C2211yescharacteristic, complemented
98#2068C2211yescharacteristic, complemented
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2066C2211yescharacteristic, complemented
102#2065C2211yescharacteristic
103#2059C2211yescharacteristic, complemented
104#2059C2211yescharacteristic, complemented
105#2055C2211yescharacteristic
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2043C2211yescharacteristic, complemented
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2036C2211yescharacteristic, complemented
114#2036C2211yescharacteristic, complemented
115#2036C2211yescharacteristic, complemented
116#2034C2211yescharacteristic
117#2026C2211yescharacteristic, complemented
118#2025C2211yescharacteristic
119#2016C2211yescharacteristic, complemented
120#2015C2211yescharacteristic
121#2015C2211yescharacteristic
122#2000C2211yescharacteristic
123#1989C2211yescharacteristic, complemented
124#1989C2211yescharacteristic, complemented
125#1983C2211yescharacteristic
126#1983C2211yescharacteristic
127#1981C2211yescharacteristic, complemented
128#1981C2211yescharacteristic, complemented
129#1973C2211yescharacteristic
130#1971C2211yescharacteristic, complemented
131#1968C2211yescharacteristic
132#1959C2211yescharacteristic
133#1959C2211yescharacteristic
134#1948C2211yescharacteristic, complemented
135#1944C2211yescharacteristic, complemented
136#1939C2211yescharacteristic, complemented
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1935C2211yescharacteristic, complemented
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1933C2211yescharacteristic, complemented
143#1927C2211yescharacteristic, complemented
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1924C2211yescharacteristic, complemented
154#1923C2211yescharacteristic, complemented
155#1919C2211yescharacteristic, complemented
156#1919C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1917C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1895C2211yescharacteristic
162#1894C2211yescharacteristic
163#1892C2211yescharacteristic
164#1880C2211yescharacteristic
165#1878C2211yescharacteristic, complemented
166#1878C2211yescharacteristic, complemented
167#1878C2211yescharacteristic, complemented
168#1878C2211yescharacteristic, complemented
169#1877C2211yescharacteristic
170#1874C2211yescharacteristic
171#1873C2211yescharacteristic
172#1873C2211yescharacteristic
173#1873C2211yescharacteristic
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic
176#1872C2211yescharacteristic, complemented
177#1870C2211yescharacteristic
178#1865C2211yescharacteristic, complemented
179#1865C2211yescharacteristic, complemented
180#1864C2211yescharacteristic
181#1863C2211yescharacteristic, complemented
182#1854C2211yescharacteristic
183#1851C2211yescharacteristic, complemented
184#1850C2211yescharacteristic
185#1824C2211yescharacteristic, complemented
186#1809C2211yescharacteristic, complemented
187#1802C2211yescharacteristic
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1786C2211yescharacteristic
191#1771C2211yescharacteristic, complemented
192#1763C2211yescharacteristic, complemented
193#1763C2211yescharacteristic, complemented
194#1763C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196C4×#103C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic, complemented
201#1736C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#546—24no—
213#546—42no—
214#541—24no—
215#541—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×#126—21no—
218C2×#126—21no—
219C2×#126—21no—
220C2×#125—21no—
221C2×#125—21no—
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121—21no—
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×#117—21no—
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C22⋊C4—21no—
250#488—42no—
251#479—42no—
252#470—24no—
253#470—42no—
254#467—42no—
255#464—24no—
256#452—42no—
257#450—42no—
258#435—42no—
259#433—42no—
260#427—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274#418—42no—
275#417—24no—
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×#102—24no—
295C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400D411yescharacteristic
325#399—21no—
326#399—21no—
327#399—21no—
328#399D411yescharacteristic
329#398—21no—
330#398—21no—
331#398—21no—
332#398D411yescharacteristic
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397D411yescharacteristic
342#397D411yescharacteristic
343#397D411yescharacteristic
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394D411yescharacteristic
358#394D411yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#390—21no—
366#390—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390—21no—
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#382—21no—
431#382—21no—
432#381—21no—
433#380—21no—
434#380—21no—
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441#379—21no—
442#379—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—22no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4C2×D411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C2×Q16—22no—
525C2×Q16—22no—
526C2×Q16—41no—
527C2×Q16—41no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×SD16—22no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×M16—22no—
537C2×M16—22no—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C2×M16—41no—
542C22×C8—22no—
543C22×C8—22no—
544C22×C8—41no—
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C4⋊Q8—22no—
554C4⋊Q8—41no—
555#126—44no—
556#126—44no—
557#126—82no—
558#125—22no—
559#125—22no—
560#125—41no—
561#125—41no—
562#125—44no—
563#125—44no—
564#124—22no—
565#124—22no—
566#124—41no—
567#124—41no—
568#124—41no—
569#124—41no—
570#123—44no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8#4114yes—
581#121—22no—
582#121—44no—
583#121—41no—
584#120—44no—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×Q8—22no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—41no—
597C4×D4—82no—
598#117—22no—
599#117—22no—
600#117—22no—
601#117—41no—
602#117—41no—
603#117—41no—
604#117—82no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
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⋊C4—21no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
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—44no—
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#107—22no—
717#107—41no—
718#107—41no—
719#107—41no—
720#106—22no—
721#106—22no—
722#106—41no—
723#106—41no—
724C4⋊C8—22no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729#103—22no—
730#103—22no—
731#103—22no—
732#103—22no—
733#103—22no—
734#103—22no—
735#103—22no—
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#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102#4114yes—
761C22⋊C8—22no—
762C22⋊C8—22no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766#97—41no—
767#97—41no—
768#97—41no—
769C4×C8—41no—
770C4×C8—41no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#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#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812C24—21no—
813C24—21no—
814C24—42no—
815C24—42no—
816C24—81no—
817C24—81no—
818C24—81no—
819C24—81no—
820C24—81no—
821C24C22×D411yescharacteristic
822C24C22×D411yescharacteristic
823#41—44no—
824#41—82no—
825#41—82no—
826#41—82no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
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×Q8C2×#4112yes—
845C2×D4—22no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—41no—
860C2×D4—41no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—82no—
867C2×D4—82no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4C2×#4112yes—
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—21no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C2×#4112yes—
922C22×C4H(5,𝔽2)12yes—
923C22×C4C2511yescharacteristic
924Q16—82no—
925Q16—82no—
926SD16—82no—
927SD16—82no—
928M16—82no—
929M16—82no—
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—44no—
954C2×C8C2×#4112yes—
955C4⋊C4—24no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
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—41no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
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⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4C2×#4112yes—
1011C4⋊C4C2×#4112yes—
1012C4⋊C4H(5,𝔽2)12yes—
1013C22⋊C4—24no—
1014C22⋊C4—22no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—41no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
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—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—42no—
1065C42—42no—
1066C42—42no—
1067C42—42no—
1068C42—81no—
1069C42—81no—
1070C42—81no—
1071C42—81no—
1072C42—81no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—22no—
1089C23—21no—
1090C23—21no—
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—84no—
1105C23—84no—
1106C23—162no—
1107C23—162no—
1108C23—162no—
1109C23—162no—
1110C23—162no—
1111C23#54612yes—
1112C23C23×D411yescharacteristic
1113Q8—22no—
1114Q8—22no—
1115Q8—41no—
1116Q8—41no—
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125D4—22no—
1126D4—22no—
1127D4—44no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—84no—
1135D4—84no—
1136D4—162no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
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—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—22no—
1179C2×C4—21no—
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—84no—
1223C2×C4—84no—
1224C2×C4—162no—
1225C2×C4—162no—
1226C2×C4#54612yes—
1227C2×C4C22×#4111yescharacteristic
1228C2×C4C22×#4111yescharacteristic
1229C2×C4C2×H(5,𝔽2)11yescharacteristic
1230C2×C4C2×H(5,𝔽2)11yescharacteristic
1231C2×C4#58511yescharacteristic
1232C2×C4#58511yescharacteristic
1233C8—22no—
1234C8—41no—
1235C8—41no—
1236C8—41no—
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C22—22no—
1242C22—22no—
1243C22—22no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—42no—
1252C22—41no—
1253C22—42no—
1254C22—41no—
1255C22—41no—
1256C22—42no—
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—168no—
1270C22C2×#54611yescharacteristic
1271C22D4×#4111yescharacteristic
1272C22#348811yescharacteristic
1273C22#358411yescharacteristic
1274C22#358511yescharacteristic
1275C22#358611yescharacteristic
1276C22#358611yescharacteristic
1277C4—22no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—42no—
1282C4—41no—
1283C4—42no—
1284C4—41no—
1285C4—41no—
1286C4—42no—
1287C4—41no—
1288C4—41no—
1289C4—42no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4#347511yescharacteristic
1304C4#351411yescharacteristic
1305C4#351911yescharacteristic
1306C4#356011yescharacteristic
1307C2—42no—
1308C2—81no—
1309C2—82no—
1310C2—161no—
1311C2#5909111yescharacteristic
1312C2#6117811yescharacteristic
1313C2#6120711yescharacteristic
1314C2#6151411yescharacteristic
1315C2#6153611yescharacteristic
1316C2#6201211yescharacteristic
1317C2#6207811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35720C2semidirect
3. #32213C2semidirect
4. #32190C2semidirect
5. #31810C2semidirect
6. #31309C2semidirect
7. #29029C2semidirect
8. #28928C2semidirect
9. #27397C2semidirect
10. #27271C2semidirect
11. #27234C2semidirect
12. #27212C2semidirect
13. #27027C2semidirect
14. #26782C2semidirect
15. #26742C2semidirect
16. #26349C2semidirect
17. #26220C2semidirect
18. #25512C2semidirect
19. #25283C2semidirect
20. #25100C2semidirect
21. #25084C2semidirect
22. #24785C2semidirect
23. #24516C2semidirect
25. #23139C2semidirect
26. #23107C2semidirect
27. #22911C2semidirect
28. #22583C2semidirect
30. #21398C2semidirect
31. #21065C2semidirect
35. C2×#479C22semidirect
37. C2×#470C22semidirect
59. #2511C22semidirect
61. #2507C22semidirect
62. #2496C22semidirect
65. #2489C22semidirect
80. #2370C22semidirect
84. #2360C22semidirect
85. #2355C22semidirect
87. #2344C22semidirect
91. #2099C22semidirect
92. #2095C22semidirect
93. #2087C22semidirect
94. #2077C22semidirect
95. #2072C22semidirect
97. #2068C22semidirect
98. #2068C22semidirect
101. #2066C22semidirect
103. #2059C22semidirect
104. #2059C22semidirect
108. #2043C22semidirect
113. #2036C22semidirect
114. #2036C22semidirect
115. #2036C22semidirect
117. #2026C22semidirect
119. #2016C22semidirect
123. #1989C22semidirect
124. #1989C22semidirect
127. #1981C22semidirect
128. #1981C22semidirect
130. #1971C22semidirect
134. #1948C22semidirect
135. #1944C22semidirect
136. #1939C22semidirect
139. #1935C22semidirect
142. #1933C22semidirect
143. #1927C22semidirect
153. #1924C22semidirect
154. #1923C22semidirect
155. #1919C22semidirect
156. #1919C22semidirect
157. #1918C22semidirect
158. #1918C22semidirect
159. #1917C22semidirect
160. #1917C22semidirect
165. #1878C22semidirect
166. #1878C22semidirect
167. #1878C22semidirect
168. #1878C22semidirect
176. #1872C22semidirect
178. #1865C22semidirect
179. #1865C22semidirect
181. #1863C22semidirect
183. #1851C22semidirect
185. #1824C22semidirect
186. #1809C22semidirect
191. #1771C22semidirect
192. #1763C22semidirect
193. #1763C22semidirect
194. #1763C22semidirect
196. C4×#103C22semidirect
197. C4×#103C22semidirect
198. C4×#103C22semidirect
200. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#451872
#357202
#322132
#321902
#318102
#313092
#290292
#289282
#273972
#272712
#272342
#272122
#270272
#267822
#267422
#263492
#262202
#255122
#252832
#251002
#250842
#247852
#245162
#244422
#231392
#231072
#229112
#225832
#224192
#213982
#210652