Finite Group Databasebeta

← #7611415

Subgroups — #7611415

Order 512.

1776 conjugacy classes of subgroups.

The subgroup lattice has 1379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59330C211yesmaximal, characteristic, complemented
2#59143C211yesmaximal, characteristic
3#32165C211yesmaximal, characteristic, complemented
4#32165C211yesmaximal, characteristic, complemented
5#31577C211yesmaximal, characteristic, complemented
6#31574C211yesmaximal, characteristic, complemented
7#28898C211yesmaximal, characteristic, complemented
8#28877C211yesmaximal, characteristic, complemented
9#28361C211yesmaximal, characteristic, complemented
10#28361C211yesmaximal, characteristic, complemented
11#27766C211yesmaximal, characteristic, complemented
12#27763C211yesmaximal, characteristic, complemented
13#27751C211yesmaximal, characteristic, complemented
14#27652C211yesmaximal, characteristic, complemented
15#26538C211yesmaximal, characteristic, complemented
16#26334C211yesmaximal, characteristic, complemented
17#25310C211yesmaximal, characteristic, complemented
18#24649C211yesmaximal, characteristic, complemented
19#24538C211yesmaximal, characteristic, complemented
20#24538C211yesmaximal, characteristic, complemented
21#24495C211yesmaximal, characteristic, complemented
22#24493C211yesmaximal, characteristic, complemented
23#24211C211yesmaximal, characteristic
24#24202C211yesmaximal, characteristic, complemented
25#23106C211yesmaximal, characteristic, complemented
26#22584C211yesmaximal, characteristic, complemented
27#22580C211yesmaximal, characteristic, complemented
28#22549C211yesmaximal, characteristic, complemented
29#21600C211yesmaximal, characteristic, complemented
30#21539C211yesmaximal, characteristic, complemented
31#21203C211yesmaximal, characteristic
32C2×#559C2211yescharacteristic
33C22×#127C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#485C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#460C2211yescharacteristic
38C2×#460C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#446C2211yescharacteristic, complemented
42C2×#441C2211yescharacteristic, complemented
43C2×#418C2211yescharacteristic
44C2×#418C2211yescharacteristic
45C2×#418C2211yescharacteristic
46C2×#418C2211yescharacteristic
47C2×C4×M16C2211yescharacteristic
48#2747—21no—
49#2709—21no—
50#2709—21no—
51#2690—21no—
52#2581C2211yescharacteristic, complemented
53#2577—21no—
54#2570C2211yescharacteristic, complemented
55#2570C2211yescharacteristic, complemented
56#2552C2211yescharacteristic, complemented
57#2548C2211yescharacteristic
58#2548C2211yescharacteristic
59#2544—21no—
60#2544C2211yescharacteristic
61#2544C2211yescharacteristic
62#2533—21no—
63#2530—21no—
64#2524—21no—
65#2520—21no—
66#2511C2211yescharacteristic, complemented
67#2511C2211yescharacteristic, complemented
68#2499C2211yescharacteristic
69#2499C2211yescharacteristic
70#2445—21no—
71#2445C2211yescharacteristic
72#2445C2211yescharacteristic
73#2435—21no—
74#2435C2211yescharacteristic
75#2435C2211yescharacteristic
76#2405—21no—
77#2405—21no—
78#2371—21no—
79#2366C2211yescharacteristic
80#2356C2211yescharacteristic, complemented
81#2355C2211yescharacteristic, complemented
82#2347C2211yescharacteristic
83#2346C2211yescharacteristic
84D4×C22⋊C4—21no—
85D4×C22⋊C4C2211yescharacteristic
86D4×C22⋊C4C2211yescharacteristic
87C4×C22⋊Q8C2211yescharacteristic
88C4×C22⋊Q8C2211yescharacteristic
89C4×C22⋊Q8C2211yescharacteristic
90#2285C2211yescharacteristic
91#2094C2211yescharacteristic, complemented
92#2094C2211yescharacteristic, complemented
93#2092C2211yescharacteristic, complemented
94#2092C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2073C2211yescharacteristic, complemented
98#2073C2211yescharacteristic, complemented
99#2072C2211yescharacteristic, complemented
100#2072C2211yescharacteristic, complemented
101#2071C2211yescharacteristic, complemented
102#2071C2211yescharacteristic, complemented
103#2067C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2065C2211yescharacteristic, complemented
106#2065C2211yescharacteristic, complemented
107#2055C2211yescharacteristic, complemented
108#2055C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2055C2211yescharacteristic, complemented
111#2042C2211yescharacteristic, complemented
112#2042C2211yescharacteristic, complemented
113#2042C2211yescharacteristic, complemented
114#2042C2211yescharacteristic, complemented
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#2015C2211yescharacteristic, complemented
118#2015C2211yescharacteristic, complemented
119#2015C2211yescharacteristic, complemented
120#2015C2211yescharacteristic, complemented
121#2014C2211yescharacteristic
122#2014C2211yescharacteristic
123#1985C2211yescharacteristic, complemented
124#1983C2211yescharacteristic, complemented
125#1983C2211yescharacteristic, complemented
126#1983C2211yescharacteristic, complemented
127#1983C2211yescharacteristic, complemented
128#1982C2211yescharacteristic
129#1982C2211yescharacteristic
130#1973C2211yescharacteristic, complemented
131#1973C2211yescharacteristic, complemented
132#1969C2211yescharacteristic, complemented
133#1968C2211yescharacteristic, complemented
134#1968C2211yescharacteristic, complemented
135#1961C2211yescharacteristic
136#1961C2211yescharacteristic
137#1961C2211yescharacteristic
138#1961C2211yescharacteristic
139#1959C2211yescharacteristic, complemented
140#1959C2211yescharacteristic, complemented
141#1958C2211yescharacteristic, complemented
142#1958C2211yescharacteristic, complemented
143#1957C2211yescharacteristic
144#1957C2211yescharacteristic
145#1957C2211yescharacteristic
146#1957C2211yescharacteristic
147#1949C2211yescharacteristic, complemented
148#1949C2211yescharacteristic, complemented
149#1941C2211yescharacteristic, complemented
150#1940C2211yescharacteristic, complemented
151#1936C2211yescharacteristic, complemented
152#1936C2211yescharacteristic, complemented
153#1934C2211yescharacteristic, complemented
154#1934C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1933C2211yescharacteristic, complemented
157#1926C2211yescharacteristic, complemented
158#1926C2211yescharacteristic, complemented
159#1926C2211yescharacteristic, complemented
160#1926C2211yescharacteristic, complemented
161#1925C2211yescharacteristic, complemented
162#1925C2211yescharacteristic, complemented
163#1925C2211yescharacteristic, complemented
164#1925C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1894C2211yescharacteristic
168#1894C2211yescharacteristic
169#1877C2211yescharacteristic, complemented
170#1877C2211yescharacteristic, complemented
171#1877C2211yescharacteristic, complemented
172#1877C2211yescharacteristic, complemented
173#1864C2211yescharacteristic, complemented
174#1864C2211yescharacteristic, complemented
175#1862C2211yescharacteristic, complemented
176#1862C2211yescharacteristic, complemented
177#1851C2211yescharacteristic
178#1851C2211yescharacteristic
179#1825C2211yescharacteristic
180#1825C2211yescharacteristic
181#1809C2211yescharacteristic
182#1805C2211yescharacteristic, complemented
183#1805C2211yescharacteristic, complemented
184#1804C2211yescharacteristic, complemented
185#1804C2211yescharacteristic, complemented
186#1802C2211yescharacteristic, complemented
187#1802C2211yescharacteristic, complemented
188#1797C2211yescharacteristic
189#1786C2211yescharacteristic
190#1786C2211yescharacteristic
191#1776C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194C8×C4⋊C4C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197#1762C2211yescharacteristic, complemented
198#1762C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic, complemented
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic
203C23×D4—21no—
204C23×D4—21no—
205C23×D4C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214#559—24no—
215#559—42no—
216C2×#127—24no—
217C2×#127—21no—
218C2×#127—21no—
219C2×#127—42no—
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#125—21no—
225C2×#124—21no—
226C2×#124—21no—
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#123—21no—
232C2×#123—21no—
233C2×#123—21no—
234C2×#123—21no—
235C2×C22⋊Q8D411yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C22⋊C4—21no—
250C22×C22⋊C4—21no—
251C22×C42C2311yescharacteristic
252#485—42no—
253#485—42no—
254#470—24no—
255#460—24no—
256#460—42no—
257#450—42no—
258#450—42no—
259#446—42no—
260#441—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274#418—24no—
275#418—24no—
276#418—42no—
277#418—42no—
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C4×M16—42no—
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#400—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—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#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#391—21no—
360#391D411yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#390—21no—
368#390—21no—
369#390—21no—
370#390—21no—
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#389—21no—
380#389D411yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#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#387D411yescharacteristic
412#387D411yescharacteristic
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#385D411yescharacteristic
428#385D411yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#383—21no—
434#383—21no—
435#382—21no—
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#380—21no—
441#380—21no—
442#380D411yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#379—21no—
446#379—21no—
447#379—21no—
448#379—21no—
449#379—21no—
450#379—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4—21no—
455C4×C4⋊C4—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470#376—21no—
471#376—21no—
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C25—21no—
498C22×Q8C2×D411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—22no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—44no—
524C22×D4—44no—
525C22×D4—44no—
526C22×D4—82no—
527C22×D4—82no—
528C22×D4—82no—
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4C2×D411yescharacteristic
538C23×C4C2×D411yescharacteristic
539C23×C4C2411yescharacteristic
540C2×Q16—22no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×M16—22no—
556C2×M16—41no—
557C2×M16—41no—
558C2×M16—41no—
559C2×M16—41no—
560C2×M16#4114yes—
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569#127—22no—
570#127—22no—
571#127—22no—
572#127—22no—
573#127—22no—
574#127—41no—
575#127—41no—
576#127—44no—
577#127—44no—
578#127#4114yes—
579#125—44no—
580#124—22no—
581#124—22no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124—41no—
586#124—41no—
587#124—41no—
588#124—44no—
589#124—82no—
590#123—44no—
591#123—44no—
592#123—82no—
593#123—82no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—42no—
599C4×Q8—22no—
600C4×Q8—22no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—44no—
614C4×D4—82no—
615#117—22no—
616#117—22no—
617#117—22no—
618#117—22no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—82no—
691C2×C22⋊C4—82no—
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C42—22no—
697C2×C42—22no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42C2×D411yescharacteristic
709C2×C42C2×D411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#107—41no—
717#107—41no—
718#107—41no—
719#106—22no—
720#106—41no—
721#106—41no—
722#106—41no—
723C4⋊C8—22no—
724C4⋊C8—22no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729#103—22no—
730#103—22no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
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—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
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—41no—
766#102—41no—
767C22⋊C8—22no—
768C22⋊C8—22no—
769#97—22no—
770#97—22no—
771#97—41no—
772#97—41no—
773C4×C8—41no—
774C4×C8—41no—
775C4×C8—41no—
776C4×C8—41no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—42no—
826C24—42no—
827C24—42no—
828C24—42no—
829C24—42no—
830C24—42no—
831C24—42no—
832C24—42no—
833C24—81no—
834C24—81no—
835C24—81no—
836C24—81no—
837C24—81no—
838C24—81no—
839C24C22×D411yescharacteristic
840C2×Q8—22no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—41no—
854C2×Q8—41no—
855C2×D4—24no—
856C2×D4—24no—
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—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—82no—
904C2×D4—82no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—816no—
916C2×D4—816no—
917C2×D4C2×#4112yes—
918C2×D4C2×#4112yes—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—41no—
940C22×C4—41no—
941C22×C4—42no—
942C22×C4—42no—
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×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
967C22×C4H(5,𝔽2)12yes—
968C22×C4C2511yescharacteristic
969Q16—44no—
970SD16—82no—
971SD16—82no—
972SD16—82no—
973SD16—82no—
974M16—44no—
975M16—44no—
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—21no—
998C2×C8C2×#4112yes—
999C2×C8C2×#4112yes—
1000C4⋊C4—22no—
1001C4⋊C4—22no—
1002C4⋊C4—22no—
1003C4⋊C4—22no—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
1006C4⋊C4—22no—
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—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—41no—
1028C4⋊C4—41no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
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⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C42—22no—
1086C42—22no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—42no—
1098C42—42no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—42no—
1103C42—81no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
1107C42C2×#4112yes—
1108C42H(5,𝔽2)12yes—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—22no—
1116C23—22no—
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—41no—
1143C23—84no—
1144C23—84no—
1145C23—84no—
1146C23—84no—
1147C23—84no—
1148C23—84no—
1149C23—84no—
1150C23—84no—
1151C23—162no—
1152C23—162no—
1153C23—162no—
1154C23—162no—
1155C23—162no—
1156C23—162no—
1157C23#55012yes—
1158C23C23×D411yescharacteristic
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—82no—
1168D4—22no—
1169D4—22no—
1170D4—22no—
1171D4—22no—
1172D4—48no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—84no—
1186D4—84no—
1187D4—84no—
1188D4—84no—
1189D4—84no—
1190D4—84no—
1191D4—84no—
1192D4—84no—
1193D4—84no—
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—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
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—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—44no—
1233C2×C4—44no—
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—162no—
1271C2×C4—162no—
1272C2×C4—162no—
1273C2×C4—162no—
1274C2×C4#54612yes—
1275C2×C4#54612yes—
1276C2×C4#55012yes—
1277C2×C4#57512yes—
1278C2×C4#57712yes—
1279C2×C4C22×#4111yescharacteristic
1280C2×C4C22×#4111yescharacteristic
1281C2×C4C2×H(5,𝔽2)11yescharacteristic
1282C2×C4C2×H(5,𝔽2)11yescharacteristic
1283C2×C4#58511yescharacteristic
1284C2×C4#58511yescharacteristic
1285C8—22no—
1286C8—22no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C8—41no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
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—81no—
1326C22—81no—
1327C22—81no—
1328C22—168no—
1329C22—168no—
1330C22C2×#54611yescharacteristic
1331C22C2×#55011yescharacteristic
1332C22#350011yescharacteristic
1333C22C2×#57511yescharacteristic
1334C22C2×#57711yescharacteristic
1335C22#358511yescharacteristic
1336C22#358511yescharacteristic
1337C4—22no—
1338C4—22no—
1339C4—22no—
1340C4—22no—
1341C4—22no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4#347511yescharacteristic
1363C4#350511yescharacteristic
1364C4#351311yescharacteristic
1365C4#354211yescharacteristic
1366C2—42no—
1367C2—82no—
1368C2—82no—
1369C2—161no—
1370C2—161no—
1371C2#5980711yescharacteristic
1372C2#6115611yescharacteristic
1373C2#6118411yescharacteristic
1374C2#6140511yescharacteristic
1375C2#6142111yescharacteristic
1376C2#6254411yescharacteristic
1377C2#6256411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59330C2semidirect
3. #32165C2semidirect
4. #32165C2semidirect
5. #31577C2semidirect
6. #31574C2semidirect
7. #28898C2semidirect
8. #28877C2semidirect
9. #28361C2semidirect
10. #28361C2semidirect
11. #27766C2semidirect
12. #27763C2semidirect
13. #27751C2semidirect
14. #27652C2semidirect
15. #26538C2semidirect
16. #26334C2semidirect
17. #25310C2semidirect
18. #24649C2semidirect
19. #24538C2semidirect
20. #24538C2semidirect
21. #24495C2semidirect
22. #24493C2semidirect
24. #24202C2semidirect
25. #23106C2semidirect
26. #22584C2semidirect
27. #22580C2semidirect
28. #22549C2semidirect
29. #21600C2semidirect
30. #21539C2semidirect
41. C2×#446C22semidirect
42. C2×#441C22semidirect
52. #2581C22semidirect
54. #2570C22semidirect
55. #2570C22semidirect
56. #2552C22semidirect
66. #2511C22semidirect
67. #2511C22semidirect
80. #2356C22semidirect
81. #2355C22semidirect
91. #2094C22semidirect
92. #2094C22semidirect
93. #2092C22semidirect
94. #2092C22semidirect
95. #2084C22semidirect
96. #2083C22semidirect
97. #2073C22semidirect
98. #2073C22semidirect
99. #2072C22semidirect
100. #2072C22semidirect
101. #2071C22semidirect
102. #2071C22semidirect
103. #2067C22semidirect
104. #2067C22semidirect
105. #2065C22semidirect
106. #2065C22semidirect
107. #2055C22semidirect
108. #2055C22semidirect
109. #2055C22semidirect
110. #2055C22semidirect
111. #2042C22semidirect
112. #2042C22semidirect
113. #2042C22semidirect
114. #2042C22semidirect
117. #2015C22semidirect
118. #2015C22semidirect
119. #2015C22semidirect
120. #2015C22semidirect
123. #1985C22semidirect
124. #1983C22semidirect
125. #1983C22semidirect
126. #1983C22semidirect
127. #1983C22semidirect
130. #1973C22semidirect
131. #1973C22semidirect
132. #1969C22semidirect
133. #1968C22semidirect
134. #1968C22semidirect
139. #1959C22semidirect
140. #1959C22semidirect
141. #1958C22semidirect
142. #1958C22semidirect
147. #1949C22semidirect
148. #1949C22semidirect
149. #1941C22semidirect
150. #1940C22semidirect
151. #1936C22semidirect
152. #1936C22semidirect
153. #1934C22semidirect
154. #1934C22semidirect
155. #1933C22semidirect
156. #1933C22semidirect
157. #1926C22semidirect
158. #1926C22semidirect
159. #1926C22semidirect
160. #1926C22semidirect
161. #1925C22semidirect
162. #1925C22semidirect
163. #1925C22semidirect
164. #1925C22semidirect
165. #1916C22semidirect
166. #1916C22semidirect
169. #1877C22semidirect
170. #1877C22semidirect
171. #1877C22semidirect
172. #1877C22semidirect
173. #1864C22semidirect
174. #1864C22semidirect
175. #1862C22semidirect
176. #1862C22semidirect
182. #1805C22semidirect
183. #1805C22semidirect
184. #1804C22semidirect
185. #1804C22semidirect
186. #1802C22semidirect
187. #1802C22semidirect
191. #1776C22semidirect
192. #1771C22semidirect
193. #1771C22semidirect
194. C8×C4⋊C4C22semidirect
195. #1763C22semidirect
196. #1763C22semidirect
197. #1762C22semidirect
198. #1762C22semidirect
199. C4×#102C22semidirect
200. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#593302
#591432
#321652
#315772
#315742
#288982
#288772
#283612
#277662
#277632
#277512
#276522
#265382
#263342
#253102
#246492
#245382
#244952
#244932
#242112
#242022
#231062
#225842
#225802
#225492
#216002
#215392
#212032