Finite Group Databasebeta

← #6608796

Subgroups — #6608796

Order 512.

1776 conjugacy classes of subgroups.

The subgroup lattice has 1376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36291C211yesmaximal, characteristic, complemented
2#36263C211yesmaximal, characteristic, complemented
3#33269C211yesmaximal, characteristic, complemented
4#33143C211yesmaximal, characteristic, complemented
5#33052C211yesmaximal, characteristic, complemented
6#29477C211yesmaximal, characteristic, complemented
7#29476C211yesmaximal, characteristic, complemented
8#29445C211yesmaximal, characteristic, complemented
9#29444C211yesmaximal, characteristic, complemented
10#29303C211yesmaximal, characteristic, complemented
11#28966C211yesmaximal, characteristic, complemented
12#28916C211yesmaximal, characteristic, complemented
13#28890C211yesmaximal, characteristic, complemented
14#28862C211yesmaximal, characteristic, complemented
15#28310C211yesmaximal, characteristic, complemented
16#28071C211yesmaximal, characteristic, complemented
17#28043C211yesmaximal, characteristic, complemented
18#26968C211yesmaximal, characteristic, complemented
19#26827C211yesmaximal, characteristic, complemented
20#25252C211yesmaximal, characteristic, complemented
21#25252C211yesmaximal, characteristic, complemented
22#25124C211yesmaximal, characteristic, complemented
23#25124C211yesmaximal, characteristic, complemented
24#22918C211yesmaximal, characteristic, complemented
25#22918C211yesmaximal, characteristic, complemented
26#22870C211yesmaximal, characteristic, complemented
27#22870C211yesmaximal, characteristic, complemented
28C4×#469C211yesmaximal, characteristic, complemented
29#21277C211yesmaximal, characteristic, complemented
30C2×#1936C211yesmaximal, characteristic, complemented
31#20491C211yesmaximal, characteristic, complemented
32C2×#553—21no—
33C2×#490C2211yescharacteristic, complemented
34C2×#481C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#469C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#447C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×C4×D8C2211yescharacteristic
41C2×C4×D8C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C2×#435C2211yescharacteristic
44C22×#102C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C2×C4×M16C2211yescharacteristic, complemented
47C22×#97C2211yescharacteristic
48#2860C2211yescharacteristic
49#2860C2211yescharacteristic, complemented
50#2856C2211yescharacteristic
51#2854C2211yescharacteristic
52#2854C2211yescharacteristic, complemented
53#2851C2211yescharacteristic
54#2602—21no—
55#2601—21no—
56#2595—21no—
57#2591—21no—
58#2559—21no—
59#2558—21no—
60#2543—21no—
61#2516—21no—
62#2513C2211yescharacteristic
63#2506C2211yescharacteristic, complemented
64#2496C2211yescharacteristic, complemented
65#2490C2211yescharacteristic
66#2487C2211yescharacteristic
67#2480—21no—
68#2471—21no—
69#2467—21no—
70#2454C2211yescharacteristic
71#2445C2211yescharacteristic, complemented
72#2428C2211yescharacteristic, complemented
73#2420C2211yescharacteristic
74#2418—21no—
75#2416C2211yescharacteristic
76#2416C2211yescharacteristic
77#2408C2211yescharacteristic
78#2364—21no—
79#2361C2211yescharacteristic
80#2361C2211yescharacteristic
81#2358—21no—
82#2345C2211yescharacteristic
83#2342—21no—
84D4×C22⋊C4C2211yescharacteristic
85C4×#121C2211yescharacteristic
86C4×#121C2211yescharacteristic, complemented
87#2293C2211yescharacteristic
88#2293C2211yescharacteristic, complemented
89C2×#390C2211yescharacteristic
90C2×#389C2211yescharacteristic
91C42×D4C2211yescharacteristic
92#2094C2211yescharacteristic
93#2094C2211yescharacteristic
94#2088C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2077C2211yescharacteristic, complemented
99#2077C2211yescharacteristic, complemented
100#2067C2211yescharacteristic, complemented
101#2067C2211yescharacteristic, complemented
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic
104#2059C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2054C2211yescharacteristic
107#2054C2211yescharacteristic
108#2034C2211yescharacteristic
109#2034C2211yescharacteristic
110#2033C2211yescharacteristic, complemented
111#2033C2211yescharacteristic, complemented
112#2011C2211yescharacteristic
113#2011C2211yescharacteristic
114#1999C2211yescharacteristic
115#1999C2211yescharacteristic
116#1992C2211yescharacteristic, complemented
117#1972C2211yescharacteristic
118#1972C2211yescharacteristic
119#1972C2211yescharacteristic
120#1972C2211yescharacteristic
121#1972C2211yescharacteristic
122#1972C2211yescharacteristic
123#1970C2211yescharacteristic
124#1970C2211yescharacteristic
125#1961C2211yescharacteristic, complemented
126#1944C2211yescharacteristic, complemented
127#1944C2211yescharacteristic, complemented
128#1943C2211yescharacteristic, complemented
129#1943C2211yescharacteristic, complemented
130#1943C2211yescharacteristic, complemented
131#1943C2211yescharacteristic, complemented
132#1941C2211yescharacteristic, complemented
133#1941C2211yescharacteristic, complemented
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic, complemented
145#1936C2211yescharacteristic, complemented
146#1936C2211yescharacteristic, complemented
147#1936C2211yescharacteristic, complemented
148#1936C2211yescharacteristic, complemented
149#1936C2211yescharacteristic, complemented
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic, complemented
153#1934C2211yescharacteristic, complemented
154#1926C2211yescharacteristic, complemented
155#1926C2211yescharacteristic, complemented
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic
158#1920C2211yescharacteristic, complemented
159#1920C2211yescharacteristic, complemented
160#1919C2211yescharacteristic, complemented
161#1919C2211yescharacteristic, complemented
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic
164#1895C2211yescharacteristic, complemented
165#1895C2211yescharacteristic, complemented
166#1893C2211yescharacteristic
167#1893C2211yescharacteristic
168#1893C2211yescharacteristic
169#1893C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1864C2211yescharacteristic, complemented
175#1864C2211yescharacteristic, complemented
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1853C2211yescharacteristic
179#1853C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1836C2211yescharacteristic, complemented
183#1809C2211yescharacteristic, complemented
184#1809C2211yescharacteristic, complemented
185C4×#106C2211yescharacteristic, complemented
186C4×#106C2211yescharacteristic, complemented
187#1771C2211yescharacteristic, complemented
188#1771C2211yescharacteristic, complemented
189#1767C2211yescharacteristic, complemented
190C4×#102C2211yescharacteristic
191C4×#102C2211yescharacteristic
192C4×#102C2211yescharacteristic, complemented
193C4×#102C2211yescharacteristic, complemented
194#1753C2211yescharacteristic, complemented
195#1753C2211yescharacteristic, complemented
196C8×C22⋊C4C2211yescharacteristic
197C8×C22⋊C4C2211yescharacteristic
198#1749C2211yescharacteristic
199#1749C2211yescharacteristic, complemented
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C4×#97C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#553—48no—
213C2×#127C2311yescharacteristic
214C2×#126—21no—
215C2×#126—21no—
216C2×#126—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×#121—21no—
223C2×#121—21no—
224C2×#121—21no—
225C2×#121—21no—
226C2×#121—21no—
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#120—21no—
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4D411yescharacteristic
239C2×C4×D4D411yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117—21no—
247C22×C4⋊C4—21no—
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253C22×C22⋊C4—21no—
254C22×C42C2311yescharacteristic
255C22×C42C2311yescharacteristic
256#490—42no—
257#481—24no—
258#481—24no—
259#469—24no—
260#469—42no—
261#447—24no—
262#447—24no—
263C4×D8—24no—
264C4×D8—42no—
265#435—24no—
266#435—24no—
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×#102—24no—
282C2×#102—42no—
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C4×M16—42no—
312C2×#97—42no—
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325#400—21no—
326#400—21no—
327#400—21no—
328#399—21no—
329#399—21no—
330#398—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#392—21no—
348#392—21no—
349#390—21no—
350#390—21no—
351#390—21no—
352#390—21no—
353#390—21no—
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#389—21no—
369#389—21no—
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#389C2311yescharacteristic
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#388—21no—
403#388—21no—
404#388—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#386—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#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#384C2311yescharacteristic
432#382C2311yescharacteristic
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⋊C4D411yescharacteristic
445C4×C4⋊C4D411yescharacteristic
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⋊C4—21no—
456C4×C22⋊C4D411yescharacteristic
457C4×C22⋊C4D411yescharacteristic
458C4×C22⋊C4D411yescharacteristic
459C4×C22⋊C4D411yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C2×#95—21no—
463C43C2311yescharacteristic
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#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C25—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C2×D411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C2×D411yescharacteristic
523C23×C4C2×D411yescharacteristic
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8—41no—
540C2×M16—22no—
541C2×M16—22no—
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C2×M16—41no—
546C22×C8—22no—
547C22×C8—22no—
548C22×C8—22no—
549C22×C8—22no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560#127—41no—
561#127—41no—
562#126—44no—
563#126—44no—
564#126—82no—
565#125—41no—
566#125—41no—
567#125—44no—
568#123—44no—
569#123—44no—
570#123—82no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121—44no—
578#121—41no—
579#121—41no—
580#121—44no—
581#121—44no—
582#121—44no—
583#121—44no—
584#121—41no—
585#121—41no—
586#121—41no—
587#121—41no—
588#120—44no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—24no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—42no—
601C4×D4—44no—
602C4×D4—44no—
603C4×D4—44no—
604C4×D4—82no—
605#117—44no—
606#117—82no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
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—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—44no—
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×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—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—44no—
695C2×C22⋊C4—82no—
696C2×C22⋊C4—82no—
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—41no—
708C2×C42—41no—
709C2×C42—41no—
710C2×C42—41no—
711C2×C42C2×D411yescharacteristic
712C2×C42C2×D411yescharacteristic
713C2×C42C2×D411yescharacteristic
714C2×C42C2×D411yescharacteristic
715C2×C42C2×D411yescharacteristic
716C2×C42C2×D411yescharacteristic
717C2×C42C2×D411yescharacteristic
718C2×C42C2×D411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724#107—22no—
725#107—41no—
726#107—41no—
727#107—41no—
728#106—22no—
729#106—22no—
730#106—22no—
731#106—22no—
732#106—22no—
733#106—41no—
734#106—41no—
735#106—41no—
736C4⋊C8—22no—
737C4⋊C8—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
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—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102#4114yes—
762C22⋊C8—22no—
763C22⋊C8—22no—
764C22⋊C8#4114yes—
765C22⋊C8#4114yes—
766#97—22no—
767#97—22no—
768#97—22no—
769#97—22no—
770#97—41no—
771#97—41no—
772#97—41no—
773#97—41no—
774C4×C8—22no—
775C4×C8—22no—
776C4×C8—41no—
777C4×C8—41no—
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#95—21no—
803#95—21no—
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—42no—
815C24—42no—
816C24—42no—
817C24—42no—
818C24—81no—
819C24—81no—
820C24—81no—
821C24C22×D411yescharacteristic
822C24C22×D411yescharacteristic
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—22no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—44no—
850C2×D4—44no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—82no—
868C2×D4—82no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4C2×#4112yes—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—22no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C2×#4112yes—
949C22×C4C2×#4112yes—
950C22×C4C2511yescharacteristic
951D8—44no—
952D8—44no—
953D8—82no—
954D8—82no—
955M16—44no—
956M16—44no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—44no—
976C2×C8—44no—
977C2×C8C2×#4112yes—
978C2×C8C2×#4112yes—
979C2×C8C2×#4112yes—
980C2×C8C2×#4112yes—
981C2×C8C2×#4112yes—
982C2×C8H(5,𝔽2)12yes—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—41no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4C2×#4112yes—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—41no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
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—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4AGL(1,ℤ/8)14yes—
1081C42—22no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—41no—
1093C42—41no—
1094C42—41no—
1095C42—41no—
1096C42—41no—
1097C42—41no—
1098C42—41no—
1099C42—42no—
1100C42—42no—
1101C42—81no—
1102C42—81no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—22no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—84no—
1143C23—84no—
1144C23—84no—
1145C23—84no—
1146C23—162no—
1147C23—162no—
1148C23—162no—
1149C23#53212yes—
1150C23C2×AGL(1,ℤ/8)12yes—
1151C23#57512yes—
1152C23C23×D411yescharacteristic
1153D4—22no—
1154D4—22no—
1155D4—44no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—84no—
1171D4—84no—
1172D4—84no—
1173D4—84no—
1174D4—84no—
1175D4—162no—
1176D4—162no—
1177D4—162no—
1178D4—162no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—22no—
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—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—82no—
1257C2×C4—84no—
1258C2×C4—84no—
1259C2×C4—82no—
1260C2×C4—82no—
1261C2×C4—82no—
1262C2×C4—84no—
1263C2×C4—162no—
1264C2×C4—162no—
1265C2×C4—162no—
1266C2×C4—162no—
1267C2×C4#53212yes—
1268C2×C4C2×AGL(1,ℤ/8)12yes—
1269C2×C4C2×AGL(1,ℤ/8)12yes—
1270C2×C4C22×#4111yescharacteristic
1271C2×C4C22×#4111yescharacteristic
1272C2×C4C22×#4111yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4#58511yescharacteristic
1275C2×C4#58511yescharacteristic
1276C8—22no—
1277C8—22no—
1278C8—22no—
1279C8—22no—
1280C8—22no—
1281C8—22no—
1282C8—41no—
1283C8—41no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—41no—
1291C22—42no—
1292C22—41no—
1293C22—41no—
1294C22—42no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—42no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—168no—
1326C22#317114yes—
1327C22C2×#53211yescharacteristic
1328C22D4×#4111yescharacteristic
1329C22#349611yescharacteristic
1330C22C22×AGL(1,ℤ/8)11yescharacteristic
1331C22C2×#57511yescharacteristic
1332C22#358511yescharacteristic
1333C22#358511yescharacteristic
1334C4—22no—
1335C4—22no—
1336C4—22no—
1337C4—41no—
1338C4—42no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4#347511yescharacteristic
1359C4#348111yescharacteristic
1360C4#351311yescharacteristic
1361C4#352111yescharacteristic
1362C2—24no—
1363C2—81no—
1364C2—82no—
1365C2—161no—
1366C2—161no—
1367C2—161no—
1368C2#3626611yescharacteristic
1369C2C2×#317111yescharacteristic
1370C2#6072511yescharacteristic
1371C2#6145111yescharacteristic
1372C2#6145611yescharacteristic
1373C2#6229811yescharacteristic
1374C2#6229911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36291C2semidirect
2. #36263C2semidirect
3. #33269C2semidirect
4. #33143C2semidirect
5. #33052C2semidirect
6. #29477C2semidirect
7. #29476C2semidirect
8. #29445C2semidirect
9. #29444C2semidirect
10. #29303C2semidirect
11. #28966C2semidirect
12. #28916C2semidirect
13. #28890C2semidirect
14. #28862C2semidirect
15. #28310C2semidirect
16. #28071C2semidirect
17. #28043C2semidirect
18. #26968C2semidirect
19. #26827C2semidirect
20. #25252C2semidirect
21. #25252C2semidirect
22. #25124C2semidirect
23. #25124C2semidirect
24. #22918C2semidirect
25. #22918C2semidirect
26. #22870C2semidirect
27. #22870C2semidirect
28. C4×#469C2semidirect
29. #21277C2semidirect
30. C2×#1936C2semidirect
31. #20491C2semidirect
33. C2×#490C22semidirect
46. C2×C4×M16C22semidirect
49. #2860C22semidirect
52. #2854C22semidirect
63. #2506C22semidirect
64. #2496C22semidirect
71. #2445C22semidirect
72. #2428C22semidirect
86. C4×#121C22semidirect
88. #2293C22semidirect
94. #2088C22semidirect
95. #2088C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
98. #2077C22semidirect
99. #2077C22semidirect
100. #2067C22semidirect
101. #2067C22semidirect
104. #2059C22semidirect
105. #2059C22semidirect
110. #2033C22semidirect
111. #2033C22semidirect
116. #1992C22semidirect
125. #1961C22semidirect
126. #1944C22semidirect
127. #1944C22semidirect
128. #1943C22semidirect
129. #1943C22semidirect
130. #1943C22semidirect
131. #1943C22semidirect
132. #1941C22semidirect
133. #1941C22semidirect
144. #1936C22semidirect
145. #1936C22semidirect
146. #1936C22semidirect
147. #1936C22semidirect
148. #1936C22semidirect
149. #1936C22semidirect
152. #1934C22semidirect
153. #1934C22semidirect
154. #1926C22semidirect
155. #1926C22semidirect
158. #1920C22semidirect
159. #1920C22semidirect
160. #1919C22semidirect
161. #1919C22semidirect
164. #1895C22semidirect
165. #1895C22semidirect
174. #1864C22semidirect
175. #1864C22semidirect
182. #1836C22semidirect
183. #1809C22semidirect
184. #1809C22semidirect
185. C4×#106C22semidirect
186. C4×#106C22semidirect
187. #1771C22semidirect
188. #1771C22semidirect
189. #1767C22semidirect
192. C4×#102C22semidirect
193. C4×#102C22semidirect
194. #1753C22semidirect
195. #1753C22semidirect
199. #1749C22semidirect
202. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
#362912
#362632
#332692
#331432
#330522
#294772
#294762
#294452
#294442
#293032
#289662
#289162
#288902
#288622
#283102
#280712
#280432
#269682
#268272
#252522
#251242
#229182
#228702
C4×#4692
#212772
C2×#19362
#204912