Finite Group Databasebeta

← #7575703

Subgroups — #7575703

Order 512.

1695 conjugacy classes of subgroups.

The subgroup lattice has 1389 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45020C211yesmaximal, characteristic, complemented
2#35847C211yesmaximal, characteristic, complemented
3#32674C211yesmaximal, characteristic, complemented
4#32642C211yesmaximal, characteristic, complemented
5#31331C211yesmaximal, characteristic, complemented
6#31318C211yesmaximal, characteristic, complemented
7#29570C211yesmaximal, characteristic, complemented
8#29566C211yesmaximal, characteristic, complemented
9#28932C211yesmaximal, characteristic, complemented
10#28930C211yesmaximal, characteristic, complemented
11#27790C211yesmaximal, characteristic, complemented
12#27788C211yesmaximal, characteristic, complemented
13#27336C211yesmaximal, characteristic, complemented
14#27331C211yesmaximal, characteristic, complemented
15#27253C211yesmaximal, characteristic, complemented
16#27240C211yesmaximal, characteristic, complemented
17#26747C211yesmaximal, characteristic, complemented
18#26736C211yesmaximal, characteristic, complemented
19#25946C211yesmaximal, characteristic, complemented
20#25843C211yesmaximal, characteristic, complemented
21#25162C211yesmaximal, characteristic, complemented
22#25148C211yesmaximal, characteristic, complemented
23#24434C211yesmaximal, characteristic, complemented
24#24428C211yesmaximal, characteristic, complemented
25#23274C211yesmaximal, characteristic, complemented
26#22872C211yesmaximal, characteristic, complemented
27#22870C211yesmaximal, characteristic, complemented
28#22564C211yesmaximal, characteristic, complemented
29#22562C211yesmaximal, characteristic, complemented
30#21134C211yesmaximal, characteristic, complemented
31#21129C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#499C2211yescharacteristic, complemented
35C2×#490C2211yescharacteristic, complemented
36C2×#478C2211yescharacteristic
37C2×#466C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#459C2211yescharacteristic
40C2×#449C2211yescharacteristic
41C2×#449C2211yescharacteristic
42C2×#447C2211yescharacteristic
43C2×#447C2211yescharacteristic
44C2×C4×D8C2211yescharacteristic
45C2×C4×D8C2211yescharacteristic
46C2×#416C2211yescharacteristic
47C22×#102C2211yescharacteristic
48#2803—21no—
49#2781—21no—
50#2699—21no—
51#2686—21no—
52#2640C2211yescharacteristic
53#2639—21no—
54#2610—21no—
55#2592C2211yescharacteristic
56#2584C2211yescharacteristic, complemented
57#2561—21no—
58#2548C2211yescharacteristic, complemented
59#2547C2211yescharacteristic
60#2526—21no—
61#2504—21no—
62#2490C2211yescharacteristic
63#2490C2211yescharacteristic
64#2490C2211yescharacteristic
65#2490C2211yescharacteristic, complemented
66#2489C2211yescharacteristic
67#2489C2211yescharacteristic
68#2488—21no—
69#2488—21no—
70#2472—21no—
71#2472—21no—
72#2428C2211yescharacteristic
73#2428C2211yescharacteristic, complemented
74#2420—21no—
75#2416C2211yescharacteristic
76#2414—21no—
77#2414C2211yescharacteristic
78#2398C2211yescharacteristic
79C2×#397—21no—
80#2363C2211yescharacteristic, complemented
81#2361C2211yescharacteristic
82#2346C2211yescharacteristic, complemented
83#2344C2211yescharacteristic
84#2339C2211yescharacteristic
85#2339C2211yescharacteristic
86D4×C22⋊C4C2211yescharacteristic
87D4×C22⋊C4C2211yescharacteristic
88#2319C2211yescharacteristic, complemented
89#2319C2211yescharacteristic, complemented
90#2275C2211yescharacteristic
91#2077C2211yescharacteristic
92#2075C2211yescharacteristic, complemented
93#2068C2211yescharacteristic, complemented
94#2067C2211yescharacteristic
95#2059C2211yescharacteristic, complemented
96#2059C2211yescharacteristic, complemented
97#2058C2211yescharacteristic, complemented
98#2057C2211yescharacteristic, complemented
99#2055C2211yescharacteristic, complemented
100#2054C2211yescharacteristic
101#2042C2211yescharacteristic
102#2042C2211yescharacteristic
103#2036C2211yescharacteristic
104#2034C2211yescharacteristic
105#2034C2211yescharacteristic, complemented
106#2034C2211yescharacteristic, complemented
107#2033C2211yescharacteristic
108#2033C2211yescharacteristic
109#2033C2211yescharacteristic
110#2033C2211yescharacteristic, complemented
111#2026C2211yescharacteristic, complemented
112#2025C2211yescharacteristic
113#2025C2211yescharacteristic, complemented
114#2025C2211yescharacteristic, complemented
115#2023C2211yescharacteristic, complemented
116#2023C2211yescharacteristic, complemented
117#2014C2211yescharacteristic, complemented
118#2012C2211yescharacteristic
119#2012C2211yescharacteristic
120#2011C2211yescharacteristic
121#2000C2211yescharacteristic
122#1999C2211yescharacteristic
123#1989C2211yescharacteristic, complemented
124#1989C2211yescharacteristic, complemented
125#1985C2211yescharacteristic, complemented
126#1984C2211yescharacteristic, complemented
127#1973C2211yescharacteristic, complemented
128#1972C2211yescharacteristic
129#1970C2211yescharacteristic
130#1970C2211yescharacteristic
131#1968C2211yescharacteristic, complemented
132#1968C2211yescharacteristic, complemented
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1935C2211yescharacteristic, complemented
136#1935C2211yescharacteristic, complemented
137#1934C2211yescharacteristic
138#1933C2211yescharacteristic, complemented
139#1928C2211yescharacteristic, complemented
140#1928C2211yescharacteristic, complemented
141#1928C2211yescharacteristic, complemented
142#1927C2211yescharacteristic, complemented
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic, complemented
146#1926C2211yescharacteristic, complemented
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic, complemented
150#1925C2211yescharacteristic, complemented
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic, complemented
153#1923C2211yescharacteristic
154#1923C2211yescharacteristic, complemented
155#1921C2211yescharacteristic, complemented
156#1921C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1893C2211yescharacteristic
160#1893C2211yescharacteristic, complemented
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1877C2211yescharacteristic, complemented
170#1877C2211yescharacteristic, complemented
171#1875C2211yescharacteristic
172#1872C2211yescharacteristic
173#1869C2211yescharacteristic
174#1869C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1854C2211yescharacteristic, complemented
182#1852C2211yescharacteristic
183#1825C2211yescharacteristic, complemented
184#1823C2211yescharacteristic
185#1808C2211yescharacteristic, complemented
186#1807C2211yescharacteristic
187#1788C2211yescharacteristic
188#1786C2211yescharacteristic
189C4×#107C2211yescharacteristic, complemented
190C4×#106C2211yescharacteristic, complemented
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic, complemented
195#1762C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197#1752C2211yescharacteristic
198#1752C2211yescharacteristic, complemented
199C8×C22⋊C4C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic, complemented
201#1746C2211yescharacteristic, complemented
202#1746C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#554—42no—
214#554—42no—
215#546—42no—
216#546—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#124—21no—
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#120—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117—21no—
251C2×#117C2311yescharacteristic
252C22×C4⋊C4—21no—
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257#499—42no—
258#490—42no—
259#478—42no—
260#466—42no—
261#465—42no—
262#459—42no—
263#449—24no—
264#449—42no—
265#447—24no—
266#447—42no—
267C4×D8—24no—
268C4×D8—24no—
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281#416—24no—
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#102—24no—
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×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323#400—21no—
324#400—21no—
325#400D411yescharacteristic
326#400D411yescharacteristic
327#398—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397D411yescharacteristic
340#397D411yescharacteristic
341#396—21no—
342#395—21no—
343#394—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#394D411yescharacteristic
354#394D411yescharacteristic
355#393—21no—
356#393—21no—
357#393—21no—
358#393D411yescharacteristic
359#393D411yescharacteristic
360#392—21no—
361#392—21no—
362#392—21no—
363#391—21no—
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#390—21no—
369#390—21no—
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#389—21no—
386#389—21no—
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#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#387—21no—
411#387—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#385—21no—
426#382—21no—
427#382—21no—
428#382—21no—
429#381—21no—
430#381—21no—
431#381—21no—
432#381—21no—
433#381—21no—
434#380—21no—
435#380—21no—
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443#379—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459#376—21no—
460#376C2311yescharacteristic
461C2×#95—21no—
462C2×#95—21no—
463C2×#95—21no—
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#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—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8C2×D411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4C2×D411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C2×SD16—22no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—22no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—41no—
551C2×D8—41no—
552C2×D8—41no—
553C2×D8—41no—
554C2×D8—41no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571#127—41no—
572#127—41no—
573#125—22no—
574#125—22no—
575#125—41no—
576#125—41no—
577#125—41no—
578#125—41no—
579#124—41no—
580#124—41no—
581#124—82no—
582#124—82no—
583#123—44no—
584C22⋊Q8—22no—
585C22⋊Q8—44no—
586C22⋊Q8—44no—
587C22⋊Q8—41no—
588C22⋊Q8—44no—
589#121—22no—
590#121—22no—
591#121—22no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—44no—
596#121—41no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—82no—
601#121—82no—
602#121—82no—
603#120—44no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—82no—
623#117—22no—
624#117—41no—
625#117—82no—
626C2×C4⋊C4—22no—
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—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—44no—
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—44no—
702C2×C22⋊C4—82no—
703C2×C22⋊C4—82no—
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727#107—22no—
728#107—22no—
729#107—22no—
730#107—41no—
731#107—41no—
732#107—41no—
733#106—22no—
734#106—41no—
735#106—41no—
736#106—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739#103—22no—
740#103—22no—
741#103—22no—
742#103—41no—
743#103—41no—
744#103—41no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
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#4114yes—
766#102#4114yes—
767C22⋊C8—22no—
768C22⋊C8—22no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773#97—41no—
774#97—41no—
775#97—41no—
776C4×C8—22no—
777C4×C8—22no—
778C4×C8—41no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—42no—
823C24—42no—
824C24—42no—
825C24—42no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
831#41—44no—
832#41—82no—
833#41—82no—
834#41—82no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—41no—
842C2×Q8—41no—
843C2×Q8—41no—
844C2×Q8—42no—
845C2×Q8—81no—
846C2×Q8—81no—
847C2×D4—22no—
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—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—41no—
870C2×D4—41no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—44no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—82no—
890C2×D4—82no—
891C2×D4—82no—
892C2×D4—81no—
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×D4C2×#4112yes—
903C2×D4C2×#4112yes—
904C2×D4H(5,𝔽2)12yes—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—24no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—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—21no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C2511yescharacteristic
969SD16—82no—
970SD16—82no—
971D8—44no—
972D8—44no—
973D8—82no—
974D8—82no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—82no—
998C2×C8—82no—
999C2×C8C2×#4112yes—
1000C2×C8C2×#4112yes—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4C2×#4112yes—
1040C4⋊C4C2×#4112yes—
1041C4⋊C4H(5,𝔽2)12yes—
1042C22⋊C4—24no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
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—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—42no—
1105C42—42no—
1106C42—81no—
1107C42—81no—
1108C42—81no—
1109C42—81no—
1110C42—81no—
1111C42—81no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—22no—
1116C23—22no—
1117C23—21no—
1118C23—21no—
1119C23—22no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—84no—
1154C23—84no—
1155C23—84no—
1156C23—84no—
1157C23—162no—
1158C23—162no—
1159C23—162no—
1160C23#57612yes—
1161C23C23×D411yescharacteristic
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—82no—
1167Q8—162no—
1168D4—22no—
1169D4—22no—
1170D4—22no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—82no—
1184D4—84no—
1185D4—84no—
1186D4—84no—
1187D4—162no—
1188D4—162no—
1189D4—162no—
1190D4—162no—
1191D4—162no—
1192D4—162no—
1193D4#55514yes—
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—21no—
1213C2×C4—21no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
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—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—84no—
1275C2×C4—84no—
1276C2×C4—84no—
1277C2×C4—162no—
1278C2×C4—162no—
1279C2×C4—162no—
1280C2×C4—162no—
1281C2×C4—162no—
1282C2×C4—162no—
1283C2×C4C22×#4111yescharacteristic
1284C2×C4C22×#4111yescharacteristic
1285C2×C4C2×H(5,𝔽2)11yescharacteristic
1286C2×C4C2×H(5,𝔽2)11yescharacteristic
1287C2×C4#58511yescharacteristic
1288C2×C4#58511yescharacteristic
1289C8—22no—
1290C8—22no—
1291C8—41no—
1292C8—41no—
1293C8—41no—
1294C8—41no—
1295C8—41no—
1296C8—41no—
1297C22—24no—
1298C22—22no—
1299C22—22no—
1300C22—22no—
1301C22—41no—
1302C22—42no—
1303C22—41no—
1304C22—42no—
1305C22—42no—
1306C22—41no—
1307C22—42no—
1308C22—42no—
1309C22—41no—
1310C22—42no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—168no—
1340C22D4×#4111yescharacteristic
1341C22D4×#4111yescharacteristic
1342C22#348411yescharacteristic
1343C22C2×#57611yescharacteristic
1344C22#358411yescharacteristic
1345C22#358411yescharacteristic
1346C22#358511yescharacteristic
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—42no—
1351C4—41no—
1352C4—41no—
1353C4—42no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—42no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4C2×#55511yescharacteristic
1372C4#351411yescharacteristic
1373C4#351411yescharacteristic
1374C4#354511yescharacteristic
1375C2—42no—
1376C2—44no—
1377C2—81no—
1378C2—161no—
1379C2—161no—
1380C2—161no—
1381C2#5916011yescharacteristic
1382C2#6147111yescharacteristic
1383C2#6148611yescharacteristic
1384C2#6151911yescharacteristic
1385C2#6153111yescharacteristic
1386C2#6161411yescharacteristic
1387C2#6163911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2398 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45020C2semidirect
2. #35847C2semidirect
3. #32674C2semidirect
4. #32642C2semidirect
5. #31331C2semidirect
6. #31318C2semidirect
7. #29570C2semidirect
8. #29566C2semidirect
9. #28932C2semidirect
10. #28930C2semidirect
11. #27790C2semidirect
12. #27788C2semidirect
13. #27336C2semidirect
14. #27331C2semidirect
15. #27253C2semidirect
16. #27240C2semidirect
17. #26747C2semidirect
18. #26736C2semidirect
19. #25946C2semidirect
20. #25843C2semidirect
21. #25162C2semidirect
22. #25148C2semidirect
23. #24434C2semidirect
24. #24428C2semidirect
25. #23274C2semidirect
26. #22872C2semidirect
27. #22870C2semidirect
28. #22564C2semidirect
29. #22562C2semidirect
30. #21134C2semidirect
31. #21129C2semidirect
34. C2×#499C22semidirect
35. C2×#490C22semidirect
56. #2584C22semidirect
58. #2548C22semidirect
65. #2490C22semidirect
73. #2428C22semidirect
80. #2363C22semidirect
82. #2346C22semidirect
88. #2319C22semidirect
89. #2319C22semidirect
92. #2075C22semidirect
93. #2068C22semidirect
95. #2059C22semidirect
96. #2059C22semidirect
97. #2058C22semidirect
98. #2057C22semidirect
99. #2055C22semidirect
105. #2034C22semidirect
106. #2034C22semidirect
110. #2033C22semidirect
111. #2026C22semidirect
113. #2025C22semidirect
114. #2025C22semidirect
115. #2023C22semidirect
116. #2023C22semidirect
117. #2014C22semidirect
123. #1989C22semidirect
124. #1989C22semidirect
125. #1985C22semidirect
126. #1984C22semidirect
127. #1973C22semidirect
131. #1968C22semidirect
132. #1968C22semidirect
135. #1935C22semidirect
136. #1935C22semidirect
138. #1933C22semidirect
139. #1928C22semidirect
140. #1928C22semidirect
141. #1928C22semidirect
142. #1927C22semidirect
145. #1926C22semidirect
146. #1926C22semidirect
149. #1925C22semidirect
150. #1925C22semidirect
152. #1924C22semidirect
154. #1923C22semidirect
155. #1921C22semidirect
156. #1921C22semidirect
157. #1918C22semidirect
158. #1918C22semidirect
160. #1893C22semidirect
169. #1877C22semidirect
170. #1877C22semidirect
181. #1854C22semidirect
183. #1825C22semidirect
185. #1808C22semidirect
189. C4×#107C22semidirect
190. C4×#106C22semidirect
194. #1762C22semidirect
195. #1762C22semidirect
198. #1752C22semidirect
200. C8×C22⋊C4C22semidirect
201. #1746C22semidirect
202. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#450202
#358472
#326742
#326422
#313312
#313182
#295702
#295662
#289322
#289302
#277902
#277882
#273362
#273312
#272532
#272402
#267472
#267362
#259462
#258432
#251622
#251482
#244342
#244282
#232742
#228722
#228702
#225642
#225622
#211342
#211292