Finite Group Databasebeta

← #7306173

Subgroups — #7306173

Order 512.

1707 conjugacy classes of subgroups.

The subgroup lattice has 1395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59148C211yesmaximal, characteristic, complemented
2#39409C211yesmaximal, characteristic, complemented
3#32614C211yesmaximal, characteristic, complemented
4#32605C211yesmaximal, characteristic, complemented
5#32167C211yesmaximal, characteristic, complemented
6#32108C211yesmaximal, characteristic, complemented
7#32103C211yesmaximal, characteristic, complemented
8#31972C211yesmaximal, characteristic, complemented
9#31926C211yesmaximal, characteristic, complemented
10#31288C211yesmaximal, characteristic, complemented
11#31008C211yesmaximal, characteristic, complemented
12#31008C211yesmaximal, characteristic, complemented
13#30743C211yesmaximal, characteristic, complemented
14#30453C211yesmaximal, characteristic, complemented
15#30018C211yesmaximal, characteristic, complemented
16#29623C211yesmaximal, characteristic, complemented
17#29413C211yesmaximal, characteristic, complemented
18#27518C211yesmaximal, characteristic, complemented
19#26761C211yesmaximal, characteristic, complemented
20#26612C211yesmaximal, characteristic, complemented
21#26602C211yesmaximal, characteristic, complemented
22#26164C211yesmaximal, characteristic, complemented
23#25367C211yesmaximal, characteristic, complemented
24#25148C211yesmaximal, characteristic
25#24910C211yesmaximal, characteristic, complemented
26#24910C211yesmaximal, characteristic, complemented
27#24740C211yesmaximal, characteristic, complemented
28#24215C211yesmaximal, characteristic, complemented
29#24205C211yesmaximal, characteristic, complemented
30#24185C211yesmaximal, characteristic, complemented
31#23341C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#539—21no—
34C22×#124C2211yescharacteristic
35C2×#492C2211yescharacteristic, complemented
36C2×#463C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#463C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×#461C2211yescharacteristic, complemented
41C2×#459C2211yescharacteristic
42C2×#448C2211yescharacteristic
43C2×#448C2211yescharacteristic
44C2×#447C2211yescharacteristic
45C2×#447C2211yescharacteristic
46C2×#440C2211yescharacteristic, complemented
47C2×#440C2211yescharacteristic, complemented
48C2×C4×D8C2211yescharacteristic
49#2854C2211yescharacteristic
50#2728—21no—
51#2715—21no—
52#2707—21no—
53#2700—21no—
54#2693—21no—
55#2691—21no—
56#2630—21no—
57#2592C2211yescharacteristic
58#2547C2211yescharacteristic
59#2545C2211yescharacteristic
60#2545C2211yescharacteristic
61#2538C2211yescharacteristic, complemented
62#2538C2211yescharacteristic, complemented
63#2521—21no—
64#2512C2211yescharacteristic, complemented
65#2506C2211yescharacteristic, complemented
66#2506C2211yescharacteristic, complemented
67#2496C2211yescharacteristic
68#2481—21no—
69#2480—21no—
70#2480—21no—
71#2474—21no—
72#2460—21no—
73#2448C2211yescharacteristic
74#2447C2211yescharacteristic
75#2445C2211yescharacteristic, complemented
76#2437—21no—
77#2435C2211yescharacteristic
78#2434C2211yescharacteristic
79#2428C2211yescharacteristic
80#2422C2211yescharacteristic
81#2422C2211yescharacteristic
82#2367C2211yescharacteristic
83#2366C2211yescharacteristic, complemented
84D4×C4⋊C4C2211yescharacteristic, complemented
85#2342—21no—
86Q8×C22⋊C4C2211yescharacteristic
87D4×C22⋊C4C2211yescharacteristic
88C4×C22⋊Q8C2211yescharacteristic
89C4×C22⋊Q8C2211yescharacteristic
90C4×#121C2211yescharacteristic
91#2096C2211yescharacteristic, complemented
92#2095C2211yescharacteristic, complemented
93#2095C2211yescharacteristic, complemented
94#2087C2211yescharacteristic, complemented
95#2075C2211yescharacteristic
96#2075C2211yescharacteristic
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2068C2211yescharacteristic, complemented
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2066C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic, complemented
107#2055C2211yescharacteristic, complemented
108#2055C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2055C2211yescharacteristic, complemented
111#2043C2211yescharacteristic, complemented
112#2043C2211yescharacteristic, complemented
113#2043C2211yescharacteristic, complemented
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic
121#2042C2211yescharacteristic
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2014C2211yescharacteristic, complemented
127#2013C2211yescharacteristic, complemented
128#2012C2211yescharacteristic
129#2012C2211yescharacteristic
130#2012C2211yescharacteristic
131#2012C2211yescharacteristic
132#2012C2211yescharacteristic
133#2012C2211yescharacteristic
134#2012C2211yescharacteristic
135#2012C2211yescharacteristic
136#2011C2211yescharacteristic
137#2000C2211yescharacteristic
138#2000C2211yescharacteristic
139#1985C2211yescharacteristic, complemented
140#1984C2211yescharacteristic, complemented
141#1983C2211yescharacteristic
142#1983C2211yescharacteristic
143#1981C2211yescharacteristic, complemented
144#1972C2211yescharacteristic
145#1972C2211yescharacteristic
146#1970C2211yescharacteristic
147#1959C2211yescharacteristic
148#1959C2211yescharacteristic
149#1956C2211yescharacteristic, complemented
150#1940C2211yescharacteristic, complemented
151#1939C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1935C2211yescharacteristic, complemented
154#1934C2211yescharacteristic
155#1933C2211yescharacteristic, complemented
156#1933C2211yescharacteristic, complemented
157#1928C2211yescharacteristic, complemented
158#1927C2211yescharacteristic, complemented
159#1926C2211yescharacteristic, complemented
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic, complemented
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic
166#1921C2211yescharacteristic, complemented
167#1920C2211yescharacteristic, complemented
168#1919C2211yescharacteristic, complemented
169#1917C2211yescharacteristic, complemented
170#1917C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1916C2211yescharacteristic, complemented
173#1880C2211yescharacteristic, complemented
174#1880C2211yescharacteristic, complemented
175#1880C2211yescharacteristic, complemented
176#1880C2211yescharacteristic, complemented
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic
180#1879C2211yescharacteristic
181#1877C2211yescharacteristic, complemented
182#1877C2211yescharacteristic, complemented
183#1877C2211yescharacteristic, complemented
184#1877C2211yescharacteristic, complemented
185#1863C2211yescharacteristic, complemented
186#1863C2211yescharacteristic, complemented
187#1863C2211yescharacteristic, complemented
188#1863C2211yescharacteristic, complemented
189#1862C2211yescharacteristic
190#1862C2211yescharacteristic
191#1862C2211yescharacteristic
192#1862C2211yescharacteristic, complemented
193#1817C2211yescharacteristic
194#1803C2211yescharacteristic, complemented
195#1803C2211yescharacteristic, complemented
196#1802C2211yescharacteristic
197#1797C2211yescharacteristic
198#1787C2211yescharacteristic
199#1787C2211yescharacteristic
200#1786C2211yescharacteristic
201#1786C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215#556—42no—
216#556—42no—
217#539—48no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#126—21no—
222C2×#126—21no—
223C2×#126—21no—
224C2×#126—21no—
225C2×#125—21no—
226C2×#125—21no—
227C2×#124—21no—
228C2×#124—21no—
229C2×#124—42no—
230C2×#124—42no—
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#124C2311yescharacteristic
237C2×#123—21no—
238C2×#123—21no—
239C2×#123—21no—
240C2×#123—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8D411yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×#121—21no—
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×#117—21no—
262C22×C4⋊C4—21no—
263C22×C22⋊C4—21no—
264C22×C22⋊C4—21no—
265C22×C22⋊C4—21no—
266C22×C42C2311yescharacteristic
267#492—42no—
268#463—42no—
269#463—42no—
270#463—42no—
271#463—42no—
272#461—42no—
273#459—42no—
274#448—42no—
275#448—42no—
276#447—42no—
277#447—42no—
278#440—42no—
279#440—42no—
280C4×D8—42no—
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×C4×C8C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337#400—21no—
338#400—21no—
339#400—21no—
340#399—21no—
341#398—21no—
342#398—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#396—21no—
362#395—21no—
363#395—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#393—21no—
372#392—21no—
373#391—21no—
374#391—21no—
375#391D411yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#390—21no—
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#389D411yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387D411yescharacteristic
421#387D411yescharacteristic
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385D411yescharacteristic
440#385D411yescharacteristic
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#381—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380—21no—
451#380D411yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#379—21no—
456#379—21no—
457#379—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
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
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497C25—21no—
498C22×Q8—21no—
499C22×Q8—22no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8C2×D411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C2×D411yescharacteristic
532C23×C4C2×D411yescharacteristic
533C23×C4C2411yescharacteristic
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×D8—41no—
563C2×D8—41no—
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C4⋊Q8—22no—
573C4⋊Q8—41no—
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576#127—22no—
577#127—41no—
578#126—44no—
579#126—44no—
580#126—44no—
581#126—44no—
582#125—44no—
583#125—44no—
584#124—22no—
585#124—22no—
586#124—22no—
587#124—22no—
588#124—22no—
589#124—41no—
590#124—41no—
591#124—41no—
592#124—41no—
593#124—41no—
594#124—41no—
595#124—41no—
596#124—44no—
597#124—44no—
598#123—44no—
599#123—44no—
600#123—44no—
601#123—44no—
602C22⋊Q8—24no—
603C22⋊Q8—44no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606C22⋊Q8—44no—
607C22⋊Q8—44no—
608#121—22no—
609#121—41no—
610#121—44no—
611#121—41no—
612#121—41no—
613C4×Q8—22no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—44no—
634C4×D4—44no—
635#117—44no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—44no—
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—44no—
723C2×C22⋊C4—44no—
724C2×C22⋊C4—44no—
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—41no—
736C2×C42—41no—
737C2×C42C2×D411yescharacteristic
738C2×C42C2×D411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745#107—41no—
746#107—41no—
747#107—41no—
748#107—41no—
749#106—41no—
750#106—41no—
751C4⋊C8—41no—
752C4⋊C8—41no—
753C4⋊C8—41no—
754C4⋊C8—41no—
755C4⋊C8—41no—
756C4⋊C8—41no—
757#103—22no—
758#103—22no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795C22⋊C8—41no—
796C22⋊C8—41no—
797#97—41no—
798#97—41no—
799C4×C8—41no—
800C4×C8—41no—
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#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—42no—
841C24—42no—
842C24—42no—
843C24—42no—
844C24—81no—
845C24—81no—
846C24—81no—
847C24C22×D411yescharacteristic
848C2×Q8—22no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—41no—
867C2×Q8—41no—
868C2×Q8—42no—
869C2×Q8—42no—
870C2×Q8—81no—
871C2×Q8—82no—
872C2×Q8—82no—
873C2×Q8—82no—
874C2×Q8—82no—
875C2×Q8H(5,𝔽2)12yes—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—82no—
911C2×D4—82no—
912C2×D4—82no—
913C2×D4—82no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4H(5,𝔽2)12yes—
918C2×D4H(5,𝔽2)12yes—
919C22×C4—21no—
920C22×C4—22no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—41no—
939C22×C4—41no—
940C22×C4—41no—
941C22×C4—41no—
942C22×C4—41no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C2511yescharacteristic
978SD16—44no—
979SD16—44no—
980SD16—82no—
981SD16—82no—
982SD16—82no—
983SD16—82no—
984D8—44no—
985D8—82no—
986D8—82no—
987D8—82no—
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×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—22no—
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—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—41no—
1036C4⋊C4—41no—
1037C4⋊C4—41no—
1038C4⋊C4—41no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C22⋊C4—24no—
1063C22⋊C4—24no—
1064C22⋊C4—22no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4AGL(1,ℤ/8)14yes—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—41no—
1123C42—41no—
1124C42—42no—
1125C42—42no—
1126C42—42no—
1127C42—42no—
1128C42—81no—
1129C42—81no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—22no—
1137C23—22no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—84no—
1165C23—84no—
1166C23—84no—
1167C23—84no—
1168C23—162no—
1169C23—162no—
1170C23—162no—
1171C23C2×AGL(1,ℤ/8)12yes—
1172C23C23×D411yescharacteristic
1173Q8—22no—
1174Q8—22no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—82no—
1186Q8—84no—
1187D4—22no—
1188D4—22no—
1189D4—22no—
1190D4—22no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—84no—
1204D4—84no—
1205D4—84no—
1206D4—162no—
1207D4—162no—
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—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—22no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—84no—
1286C2×C4—82no—
1287C2×C4—82no—
1288C2×C4—84no—
1289C2×C4—84no—
1290C2×C4—162no—
1291C2×C4—162no—
1292C2×C4—162no—
1293C2×C4—162no—
1294C2×C4C2×AGL(1,ℤ/8)12yes—
1295C2×C4C2×AGL(1,ℤ/8)12yes—
1296C2×C4C2×H(5,𝔽2)11yescharacteristic
1297C2×C4C2×H(5,𝔽2)11yescharacteristic
1298C2×C4C2×H(5,𝔽2)11yescharacteristic
1299C2×C4#58511yescharacteristic
1300C2×C4#58511yescharacteristic
1301C2×C4#58511yescharacteristic
1302C8—41no—
1303C8—41no—
1304C8—41no—
1305C8—41no—
1306C8—41no—
1307C8—41no—
1308C8—41no—
1309C8—41no—
1310C22—22no—
1311C22—22no—
1312C22—22no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—168no—
1346C22#348411yescharacteristic
1347C22#348711yescharacteristic
1348C22#348811yescharacteristic
1349C22C22×AGL(1,ℤ/8)11yescharacteristic
1350C22#358411yescharacteristic
1351C22#358411yescharacteristic
1352C22#358611yescharacteristic
1353C4—22no—
1354C4—22no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—42no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4#353311yescharacteristic
1379C4#353411yescharacteristic
1380C4#353411yescharacteristic
1381C4#356011yescharacteristic
1382C2—42no—
1383C2—82no—
1384C2—82no—
1385C2—161no—
1386C2—161no—
1387C2#4784011yescharacteristic
1388C2#6159811yescharacteristic
1389C2#6162611yescharacteristic
1390C2#6188811yescharacteristic
1391C2#6193011yescharacteristic
1392C2#6198911yescharacteristic
1393C2#6204811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25148C2
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. #59148C2semidirect
2. #39409C2semidirect
3. #32614C2semidirect
4. #32605C2semidirect
5. #32167C2semidirect
6. #32108C2semidirect
7. #32103C2semidirect
8. #31972C2semidirect
9. #31926C2semidirect
10. #31288C2semidirect
11. #31008C2semidirect
12. #31008C2semidirect
13. #30743C2semidirect
14. #30453C2semidirect
15. #30018C2semidirect
16. #29623C2semidirect
17. #29413C2semidirect
18. #27518C2semidirect
19. #26761C2semidirect
20. #26612C2semidirect
21. #26602C2semidirect
22. #26164C2semidirect
23. #25367C2semidirect
25. #24910C2semidirect
26. #24910C2semidirect
27. #24740C2semidirect
28. #24215C2semidirect
29. #24205C2semidirect
30. #24185C2semidirect
31. #23341C2semidirect
35. C2×#492C22semidirect
40. C2×#461C22semidirect
46. C2×#440C22semidirect
47. C2×#440C22semidirect
61. #2538C22semidirect
62. #2538C22semidirect
64. #2512C22semidirect
65. #2506C22semidirect
66. #2506C22semidirect
75. #2445C22semidirect
83. #2366C22semidirect
84. D4×C4⋊C4C22semidirect
91. #2096C22semidirect
92. #2095C22semidirect
93. #2095C22semidirect
94. #2087C22semidirect
100. #2068C22semidirect
103. #2066C22semidirect
106. #2065C22semidirect
107. #2055C22semidirect
108. #2055C22semidirect
109. #2055C22semidirect
110. #2055C22semidirect
111. #2043C22semidirect
112. #2043C22semidirect
113. #2043C22semidirect
126. #2014C22semidirect
127. #2013C22semidirect
139. #1985C22semidirect
140. #1984C22semidirect
143. #1981C22semidirect
149. #1956C22semidirect
150. #1940C22semidirect
151. #1939C22semidirect
152. #1935C22semidirect
153. #1935C22semidirect
155. #1933C22semidirect
156. #1933C22semidirect
157. #1928C22semidirect
158. #1927C22semidirect
159. #1926C22semidirect
161. #1925C22semidirect
166. #1921C22semidirect
167. #1920C22semidirect
168. #1919C22semidirect
169. #1917C22semidirect
170. #1917C22semidirect
171. #1916C22semidirect
172. #1916C22semidirect
173. #1880C22semidirect
174. #1880C22semidirect
175. #1880C22semidirect
176. #1880C22semidirect
181. #1877C22semidirect
182. #1877C22semidirect
183. #1877C22semidirect
184. #1877C22semidirect
185. #1863C22semidirect
186. #1863C22semidirect
187. #1863C22semidirect
188. #1863C22semidirect
192. #1862C22semidirect
194. #1803C22semidirect
195. #1803C22semidirect

Maximal subgroups

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

subgroupindex
#591482
#394092
#326142
#326052
#321672
#321082
#321032
#319722
#319262
#312882
#310082
#307432
#304532
#300182
#296232
#294132
#275182
#267612
#266122
#266022
#261642
#253672
#251482
#249102
#247402
#242152
#242052
#241852
#233412