Finite Group Databasebeta

← #6940659

Subgroups — #6940659

Order 512.

1643 conjugacy classes of subgroups.

The subgroup lattice has 1321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36294C211yesmaximal, characteristic, complemented
2#36264C211yesmaximal, characteristic, complemented
3#32859C211yesmaximal, characteristic, complemented
4#32823C211yesmaximal, characteristic, complemented
5#32533C211yesmaximal, characteristic, complemented
6#32484C211yesmaximal, characteristic, complemented
7#31977C211yesmaximal, characteristic, complemented
8#31973C211yesmaximal, characteristic, complemented
9#31913C211yesmaximal, characteristic, complemented
10#31879C211yesmaximal, characteristic, complemented
11#31241C211yesmaximal, characteristic, complemented
12#31150C211yesmaximal, characteristic, complemented
13#30153C211yesmaximal, characteristic, complemented
14#30126C211yesmaximal, characteristic, complemented
15#30000C211yesmaximal, characteristic, complemented
16#29825C211yesmaximal, characteristic, complemented
17#29770C211yesmaximal, characteristic, complemented
18#29536C211yesmaximal, characteristic, complemented
19#28286C211yesmaximal, characteristic, complemented
20#26348C211yesmaximal, characteristic, complemented
21#26338C211yesmaximal, characteristic, complemented
22#25994C211yesmaximal, characteristic, complemented
23#25952C211yesmaximal, characteristic, complemented
24#25214C211yesmaximal, characteristic, complemented
25#25076C211yesmaximal, characteristic
26#24603C211yesmaximal, characteristic, complemented
27#24531C211yesmaximal, characteristic, complemented
28#24500C211yesmaximal, characteristic, complemented
29#24478C211yesmaximal, characteristic, complemented
30C2×#2065C211yesmaximal, characteristic, complemented
31#21972C211yesmaximal, characteristic, complemented
32C2×#551—21no—
33C2×#481C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#478C2211yescharacteristic, complemented
36C2×#476C2211yescharacteristic, complemented
37C2×#466C2211yescharacteristic
38C2×#459C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#431C2211yescharacteristic
41C22×#106C2211yescharacteristic
42C22×C4⋊C8C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2864C2211yescharacteristic, complemented
46#2860C2211yescharacteristic
47#2860C2211yescharacteristic, complemented
48#2858C2211yescharacteristic
49#2854C2211yescharacteristic
50#2854C2211yescharacteristic
51#2610—21no—
52#2603—21no—
53#2596—21no—
54#2554—21no—
55#2530—21no—
56#2529—21no—
57#2513C2211yescharacteristic, complemented
58#2512C2211yescharacteristic
59#2509C2211yescharacteristic, complemented
60#2508C2211yescharacteristic, complemented
61#2504C2211yescharacteristic
62#2498—21no—
63#2481—21no—
64#2478—21no—
65#2472—21no—
66#2461—21no—
67#2454C2211yescharacteristic, complemented
68#2452C2211yescharacteristic
69#2445C2211yescharacteristic
70#2445C2211yescharacteristic
71#2442C2211yescharacteristic
72#2440C2211yescharacteristic
73#2433C2211yescharacteristic
74#2411—21no—
75#2361C2211yescharacteristic
76#2361C2211yescharacteristic
77#2359—21no—
78#2358—21no—
79#2352—21no—
80#2345C2211yescharacteristic
81D4×C22⋊C4C2211yescharacteristic
82C4×#127C2211yescharacteristic
83C4×#125C2211yescharacteristic, complemented
84#2293C2211yescharacteristic
85#2293C2211yescharacteristic, complemented
86C2×#390C2211yescharacteristic
87C2×#389C2211yescharacteristic
88C4×#117C2211yescharacteristic
89#2100C2211yescharacteristic, complemented
90#2094C2211yescharacteristic, complemented
91#2092C2211yescharacteristic
92#2092C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2087C2211yescharacteristic, complemented
98#2087C2211yescharacteristic, complemented
99#2086C2211yescharacteristic, complemented
100#2086C2211yescharacteristic, complemented
101#2085C2211yescharacteristic, complemented
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic
104#2073C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic, complemented
110#2067C2211yescharacteristic, complemented
111#2067C2211yescharacteristic, complemented
112#2067C2211yescharacteristic, complemented
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#2065C2211yescharacteristic
116#2065C2211yescharacteristic
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic
120#2065C2211yescharacteristic
121#2065C2211yescharacteristic
122#2065C2211yescharacteristic
123#2065C2211yescharacteristic
124#2065C2211yescharacteristic, complemented
125#2065C2211yescharacteristic, complemented
126#2065C2211yescharacteristic, complemented
127#2065C2211yescharacteristic, complemented
128#2065C2211yescharacteristic, complemented
129#2059C2211yescharacteristic, complemented
130#2058C2211yescharacteristic, complemented
131#2057C2211yescharacteristic, complemented
132#2054C2211yescharacteristic
133#2054C2211yescharacteristic
134#2054C2211yescharacteristic
135#2054C2211yescharacteristic
136#2054C2211yescharacteristic
137#2054C2211yescharacteristic, complemented
138#2054C2211yescharacteristic, complemented
139#2054C2211yescharacteristic, complemented
140#2041C2211yescharacteristic
141#2041C2211yescharacteristic
142#2041C2211yescharacteristic
143#2025C2211yescharacteristic
144#2011C2211yescharacteristic
145#1987C2211yescharacteristic, complemented
146#1982C2211yescharacteristic
147#1982C2211yescharacteristic
148#1982C2211yescharacteristic
149#1970C2211yescharacteristic
150#1970C2211yescharacteristic
151#1949C2211yescharacteristic, complemented
152#1949C2211yescharacteristic, complemented
153#1948C2211yescharacteristic, complemented
154#1947C2211yescharacteristic, complemented
155#1941C2211yescharacteristic, complemented
156#1941C2211yescharacteristic, complemented
157#1939C2211yescharacteristic, complemented
158#1939C2211yescharacteristic, complemented
159#1939C2211yescharacteristic, complemented
160#1939C2211yescharacteristic, complemented
161#1934C2211yescharacteristic
162#1934C2211yescharacteristic
163#1934C2211yescharacteristic, complemented
164#1934C2211yescharacteristic, complemented
165#1926C2211yescharacteristic
166#1926C2211yescharacteristic
167#1926C2211yescharacteristic, complemented
168#1925C2211yescharacteristic
169#1921C2211yescharacteristic, complemented
170#1921C2211yescharacteristic, complemented
171#1920C2211yescharacteristic, complemented
172#1919C2211yescharacteristic, complemented
173#1893C2211yescharacteristic
174#1893C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic, complemented
179#1874C2211yescharacteristic
180#1874C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic, complemented
183#1864C2211yescharacteristic, complemented
184#1862C2211yescharacteristic
185#1853C2211yescharacteristic
186#1852C2211yescharacteristic
187#1850C2211yescharacteristic
188#1850C2211yescharacteristic
189#1850C2211yescharacteristic
190#1850C2211yescharacteristic
191#1842C2211yescharacteristic, complemented
192#1842C2211yescharacteristic, complemented
193#1831C2211yescharacteristic, complemented
194#1831C2211yescharacteristic, complemented
195#1824C2211yescharacteristic
196#1808C2211yescharacteristic
197#1804C2211yescharacteristic
198#1804C2211yescharacteristic
199#1804C2211yescharacteristic
200#1804C2211yescharacteristic, complemented
201#1786C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#551—48no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#126—21no—
214C2×#126—21no—
215C2×#126—21no—
216C2×#125C2311yescharacteristic
217C2×#124—21no—
218C2×#124—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#120—21no—
228C2×#120—21no—
229C2×C4×D4—21no—
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117—21no—
238C2×#117—21no—
239C2×#117D411yescharacteristic
240C2×#117D411yescharacteristic
241C22×C4⋊C4—21no—
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C22⋊C4—21no—
246C22×C22⋊C4—21no—
247C22×C22⋊C4—21no—
248C22×C42C2311yescharacteristic
249#481—42no—
250#478—42no—
251#478—42no—
252#476—42no—
253#466—42no—
254#459—42no—
255#447—42no—
256#431—42no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#106—42no—
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8—42no—
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×#102—42no—
287C2×#102—42no—
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×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#399—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#395—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#393—21no—
340#392—21no—
341#392—21no—
342#390—21no—
343#390—21no—
344#390—21no—
345#390—21no—
346#390—21no—
347#390—21no—
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#389—21no—
365#389—21no—
366#389—21no—
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
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#388—21no—
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#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—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#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#384C2311yescharacteristic
429#382—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#380—21no—
434#380—21no—
435#380—21no—
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#379—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4D411yescharacteristic
442C4×C4⋊C4D411yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4D411yescharacteristic
453C4×C22⋊C4D411yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456#376D411yescharacteristic
457#376D411yescharacteristic
458C2×#95—21no—
459C43C2311yescharacteristic
460C43C2311yescharacteristic
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#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C25—21no—
492C22×Q8—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4C2×D411yescharacteristic
518C23×C4C2×D411yescharacteristic
519C23×C4C2411yescharacteristic
520C2×D8—22no—
521C2×D8—41no—
522C2×D8—41no—
523C2×D8—41no—
524C2×D8—41no—
525C2×D8—41no—
526C2×D8—41no—
527C2×D8—41no—
528C2×D8—41no—
529C22×C8—22no—
530C22×C8—22no—
531C22×C8—41no—
532C22×C8—41no—
533C22×C8—41no—
534C22×C8—41no—
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C4⋊Q8—41no—
544C4⋊Q8—41no—
545#127—22no—
546#127—41no—
547#127—41no—
548#127—41no—
549#126—44no—
550#126—44no—
551#126—82no—
552#125—22no—
553#125—41no—
554#124—44no—
555#124—82no—
556#123—44no—
557#123—44no—
558#123—44no—
559#123—44no—
560C22⋊Q8—44no—
561C22⋊Q8—44no—
562#121—22no—
563#121—22no—
564#121—22no—
565#121—22no—
566#120—44no—
567#120—44no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—44no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—44no—
578C4×D4—44no—
579C4×D4—82no—
580#117—24no—
581#117—24no—
582#117—44no—
583#117—82no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
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—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4—82no—
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
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—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—44no—
672C2×C22⋊C4—44no—
673C2×C22⋊C4—82no—
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C42—22no—
679C2×C42—22no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2×D411yescharacteristic
690C2×C42C2×D411yescharacteristic
691C2×C42C2×D411yescharacteristic
692C2×C42C2×D411yescharacteristic
693C2×C42C2×D411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700#107—41no—
701#107—41no—
702#107—41no—
703#107—41no—
704#107—41no—
705#106—22no—
706#106—22no—
707#106—22no—
708#106—41no—
709#106—41no—
710#106—41no—
711#106—41no—
712#106—41no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721C4⋊C8—41no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724C4⋊C8—41no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753C22⋊C8—22no—
754C22⋊C8—22no—
755C4×C8—41no—
756C4×C8—41no—
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#95—21no—
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—42no—
798C24—42no—
799C24—42no—
800C24—42no—
801C24—81no—
802C24—81no—
803C24—81no—
804C24C22×D411yescharacteristic
805C2×Q8—42no—
806C2×Q8—81no—
807C2×Q8—81no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
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—44no—
832C2×D4—44no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—82no—
848C2×D4—82no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D42−1+412yes—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—22no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—41no—
877C22×C4—41no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4AGL(1,ℤ/8)14yes—
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4H(5,𝔽2)12yes—
914C22×C42−1+412yes—
915C22×C4C2511yescharacteristic
916D8—82no—
917D8—82no—
918D8—82no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
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—44no—
944C2×C8—82no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
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—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
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⋊C4H(5,𝔽2)12yes—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
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—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
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#13514yes—
1041C42—22no—
1042C42—22no—
1043C42—22no—
1044C42—22no—
1045C42—22no—
1046C42—22no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—41no—
1060C42—41no—
1061C42—41no—
1062C42—41no—
1063C42—42no—
1064C42—42no—
1065C42—81no—
1066C42—81no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—22no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
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—84no—
1100C23—84no—
1101C23—84no—
1102C23—84no—
1103C23—162no—
1104C23—162no—
1105C23—162no—
1106C23#53712yes—
1107C23C2×#13512yes—
1108C23C2×AGL(1,ℤ/8)12yes—
1109C23C23×D411yescharacteristic
1110Q8—162no—
1111D4—22no—
1112D4—22no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—84no—
1128D4—84no—
1129D4—84no—
1130D4—84no—
1131D4—84no—
1132D4—162no—
1133D4—162no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—28no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
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—22no—
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—41no—
1175C2×C4—41no—
1176C2×C4—41no—
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—84no—
1210C2×C4—82no—
1211C2×C4—84no—
1212C2×C4—84no—
1213C2×C4—162no—
1214C2×C4—162no—
1215C2×C4—162no—
1216C2×C4—162no—
1217C2×C4#53712yes—
1218C2×C4C2×#13512yes—
1219C2×C4C2×#13512yes—
1220C2×C4C2×AGL(1,ℤ/8)12yes—
1221C2×C4C2×AGL(1,ℤ/8)12yes—
1222C2×C4C2×H(5,𝔽2)11yescharacteristic
1223C2×C4C2×H(5,𝔽2)11yescharacteristic
1224C2×C4C2×2−1+411yescharacteristic
1225C2×C4C2×2−1+411yescharacteristic
1226C2×C4#58511yescharacteristic
1227C2×C4#58511yescharacteristic
1228C8—41no—
1229C8—41no—
1230C8—41no—
1231C8—41no—
1232C8—41no—
1233C8—41no—
1234C8—41no—
1235C8—41no—
1236C22—22no—
1237C22—22no—
1238C22—22no—
1239C22—22no—
1240C22—22no—
1241C22—22no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—168no—
1271C22#324714yes—
1272C22C2×#53711yescharacteristic
1273C22#348811yescharacteristic
1274C22#348911yescharacteristic
1275C22C22×#13511yescharacteristic
1276C22C22×AGL(1,ℤ/8)11yescharacteristic
1277C22#358511yescharacteristic
1278C22#358511yescharacteristic
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—22no—
1284C4—41no—
1285C4—42no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
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—81no—
1304C4#353511yescharacteristic
1305C4#353811yescharacteristic
1306C4#354211yescharacteristic
1307C4#356411yescharacteristic
1308C2—24no—
1309C2—82no—
1310C2—161no—
1311C2—161no—
1312C2—161no—
1313C2#4198411yescharacteristic
1314C2C2×#324711yescharacteristic
1315C2#6093711yescharacteristic
1316C2#6195511yescharacteristic
1317C2#6196311yescharacteristic
1318C2#6210311yescharacteristic
1319C2#6211011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25076C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36294C2semidirect
2. #36264C2semidirect
3. #32859C2semidirect
4. #32823C2semidirect
5. #32533C2semidirect
6. #32484C2semidirect
7. #31977C2semidirect
8. #31973C2semidirect
9. #31913C2semidirect
10. #31879C2semidirect
11. #31241C2semidirect
12. #31150C2semidirect
13. #30153C2semidirect
14. #30126C2semidirect
15. #30000C2semidirect
16. #29825C2semidirect
17. #29770C2semidirect
18. #29536C2semidirect
19. #28286C2semidirect
20. #26348C2semidirect
21. #26338C2semidirect
22. #25994C2semidirect
23. #25952C2semidirect
24. #25214C2semidirect
26. #24603C2semidirect
27. #24531C2semidirect
28. #24500C2semidirect
29. #24478C2semidirect
30. C2×#2065C2semidirect
31. #21972C2semidirect
35. C2×#478C22semidirect
36. C2×#476C22semidirect
45. #2864C22semidirect
47. #2860C22semidirect
57. #2513C22semidirect
59. #2509C22semidirect
60. #2508C22semidirect
67. #2454C22semidirect
83. C4×#125C22semidirect
85. #2293C22semidirect
89. #2100C22semidirect
90. #2094C22semidirect
92. #2092C22semidirect
93. #2088C22semidirect
94. #2088C22semidirect
95. #2088C22semidirect
96. #2088C22semidirect
97. #2087C22semidirect
98. #2087C22semidirect
99. #2086C22semidirect
100. #2086C22semidirect
101. #2085C22semidirect
104. #2073C22semidirect
109. #2067C22semidirect
110. #2067C22semidirect
111. #2067C22semidirect
112. #2067C22semidirect
124. #2065C22semidirect
125. #2065C22semidirect
126. #2065C22semidirect
127. #2065C22semidirect
128. #2065C22semidirect
129. #2059C22semidirect
130. #2058C22semidirect
131. #2057C22semidirect
137. #2054C22semidirect
138. #2054C22semidirect
139. #2054C22semidirect
145. #1987C22semidirect
151. #1949C22semidirect
152. #1949C22semidirect
153. #1948C22semidirect
154. #1947C22semidirect
155. #1941C22semidirect
156. #1941C22semidirect
157. #1939C22semidirect
158. #1939C22semidirect
159. #1939C22semidirect
160. #1939C22semidirect
163. #1934C22semidirect
164. #1934C22semidirect
167. #1926C22semidirect
169. #1921C22semidirect
170. #1921C22semidirect
171. #1920C22semidirect
172. #1919C22semidirect
178. #1879C22semidirect
182. #1864C22semidirect
183. #1864C22semidirect
191. #1842C22semidirect
192. #1842C22semidirect
193. #1831C22semidirect
194. #1831C22semidirect
200. #1804C22semidirect

Maximal subgroups

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

subgroupindex
#362942
#362642
#328592
#328232
#325332
#324842
#319772
#319732
#319132
#318792
#312412
#311502
#301532
#301262
#300002
#298252
#297702
#295362
#282862
#263482
#263382
#259942
#259522
#252142
#250762
#246032
#245312
#245002
#244782
C2×#20652
#219722