Finite Group Databasebeta

← #6866033

Subgroups — #6866033

Order 512.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39153C211yesmaximal, characteristic, complemented
2#35237C211yesmaximal, characteristic
3#32959C211yesmaximal, characteristic, complemented
4#32294C211yesmaximal, characteristic, complemented
5#32292C211yesmaximal, characteristic, complemented
6#32066C211yesmaximal, characteristic, complemented
7#32060C211yesmaximal, characteristic, complemented
8#31310C211yesmaximal, characteristic, complemented
9#31290C211yesmaximal, characteristic, complemented
10#30547C211yesmaximal, characteristic, complemented
11#30527C211yesmaximal, characteristic, complemented
12#30138C211yesmaximal, characteristic, complemented
13#30138C211yesmaximal, characteristic, complemented
14#29504C211yesmaximal, characteristic, complemented
15#29504C211yesmaximal, characteristic, complemented
16#29265C211yesmaximal, characteristic, complemented
17#29263C211yesmaximal, characteristic, complemented
18#28549C211yesmaximal, characteristic, complemented
19#28435C211yesmaximal, characteristic, complemented
20#27826C211yesmaximal, characteristic, complemented
21#27780C211yesmaximal, characteristic, complemented
22#25676C211yesmaximal, characteristic, complemented
23#25466C211yesmaximal, characteristic, complemented
24#25288C211yesmaximal, characteristic, complemented
25#24695C211yesmaximal, characteristic, complemented
26#24644C211yesmaximal, characteristic, complemented
27#24154C211yesmaximal, characteristic, complemented
28#22635C211yesmaximal, characteristic, complemented
29#22232C211yesmaximal, characteristic, complemented
30#22230C211yesmaximal, characteristic, complemented
31#21453C211yesmaximal, characteristic, complemented
32C2×#532C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C2×#501C2211yescharacteristic, complemented
35C2×#490C2211yescharacteristic
36C2×#490C2211yescharacteristic, complemented
37C2×#486C2211yescharacteristic
38C2×#475C2211yescharacteristic, complemented
39C2×#478C2211yescharacteristic
40C2×#478C2211yescharacteristic
41C2×#460C2211yescharacteristic, complemented
42C2×#450C2211yescharacteristic
43C2×#440C2211yescharacteristic
44C2×#440C2211yescharacteristic
45#2851C2211yescharacteristic
46#2847—21no—
47#2847—21no—
48#2789—21no—
49#2788—21no—
50#2787—21no—
51#2767—21no—
52#2645C2211yescharacteristic, complemented
53#2645C2211yescharacteristic, complemented
54#2631—21no—
55#2631—21no—
56#2573—21no—
57#2565C2211yescharacteristic, complemented
58#2563C2211yescharacteristic
59#2563C2211yescharacteristic
60#2550C2211yescharacteristic, complemented
61#2541C2211yescharacteristic
62#2541C2211yescharacteristic
63#2535—21no—
64#2535—21no—
65#2533—21no—
66#2527—21no—
67#2514—21no—
68#2504C2211yescharacteristic
69#2504C2211yescharacteristic
70#2497C2211yescharacteristic
71#2494C2211yescharacteristic
72#2492C2211yescharacteristic
73#2489C2211yescharacteristic
74#2433C2211yescharacteristic
75#2433C2211yescharacteristic
76#2404—21no—
77#2404—21no—
78#2370C2211yescharacteristic, complemented
79#2356C2211yescharacteristic, complemented
80#2331C2211yescharacteristic, complemented
81#2330C2211yescharacteristic, complemented
82#2328C2211yescharacteristic
83#2328C2211yescharacteristic
84#2328C2211yescharacteristic
85#2328C2211yescharacteristic
86C4×C22⋊Q8C2211yescharacteristic
87#2283C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2094C2211yescharacteristic
93#2093C2211yescharacteristic, complemented
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2074C2211yescharacteristic, complemented
99#2074C2211yescharacteristic, complemented
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic, complemented
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic, complemented
104#2055C2211yescharacteristic
105#2055C2211yescharacteristic
106#2055C2211yescharacteristic, complemented
107#2055C2211yescharacteristic, complemented
108#2041C2211yescharacteristic
109#2041C2211yescharacteristic
110#2041C2211yescharacteristic
111#2041C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic, complemented
120#2023C2211yescharacteristic
121#2023C2211yescharacteristic, complemented
122#2014C2211yescharacteristic
123#2014C2211yescharacteristic
124#2014C2211yescharacteristic
125#2014C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#1993C2211yescharacteristic, complemented
129#1993C2211yescharacteristic, complemented
130#1991C2211yescharacteristic, complemented
131#1988C2211yescharacteristic, complemented
132#1982C2211yescharacteristic
133#1982C2211yescharacteristic
134#1982C2211yescharacteristic
135#1982C2211yescharacteristic
136#1982C2211yescharacteristic, complemented
137#1973C2211yescharacteristic
138#1973C2211yescharacteristic, complemented
139#1968C2211yescharacteristic
140#1968C2211yescharacteristic, complemented
141#1961C2211yescharacteristic
142#1961C2211yescharacteristic, complemented
143#1957C2211yescharacteristic
144#1949C2211yescharacteristic, complemented
145#1949C2211yescharacteristic, complemented
146#1949C2211yescharacteristic, complemented
147#1949C2211yescharacteristic, complemented
148#1940C2211yescharacteristic, complemented
149#1940C2211yescharacteristic, complemented
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic, complemented
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic, complemented
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic, complemented
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic, complemented
160#1925C2211yescharacteristic, complemented
161#1925C2211yescharacteristic, complemented
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic, complemented
169#1877C2211yescharacteristic, complemented
170#1872C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic, complemented
174#1864C2211yescharacteristic, complemented
175#1864C2211yescharacteristic, complemented
176#1864C2211yescharacteristic, complemented
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic, complemented
182#1862C2211yescharacteristic, complemented
183#1853C2211yescharacteristic
184#1852C2211yescharacteristic
185#1852C2211yescharacteristic
186#1847C2211yescharacteristic, complemented
187#1846C2211yescharacteristic, complemented
188#1832C2211yescharacteristic, complemented
189#1832C2211yescharacteristic, complemented
190#1804C2211yescharacteristic
191#1804C2211yescharacteristic
192#1797C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1771C2211yescharacteristic, complemented
197#1771C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1749C2211yescharacteristic
201#1746C2211yescharacteristic, complemented
202#1746C2211yescharacteristic, complemented
203C22×#41—21no—
204C23×D4C2311yescharacteristic
205C24×C4—21no—
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210#532—42no—
211#532—42no—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121—21no—
224C2×#121—21no—
225C2×#121—21no—
226C2×#121—21no—
227C2×#121—21no—
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C2×#120—21no—
232C2×#120—21no—
233C2×#120—21no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—42no—
239C2×C4×D4—42no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C22⋊C4—21no—
248C22×C42C2311yescharacteristic
249#501—42no—
250#490—24no—
251#490—42no—
252#486—24no—
253#478—42no—
254#478—42no—
255#475—42no—
256#460—42no—
257#450—24no—
258#440—42no—
259#440—42no—
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320#401—21no—
321#401—21no—
322#401—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#396—21no—
342#395—21no—
343#393—21no—
344#393—21no—
345#393—21no—
346#393—21no—
347#393—21no—
348#392—21no—
349#392—21no—
350#392—21no—
351#392—21no—
352#392—21no—
353#392—21no—
354#392—21no—
355#392—21no—
356#391—21no—
357#391—21no—
358#391—21no—
359#391—21no—
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
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#387—21no—
389#387—21no—
390#387—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#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—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#385—21no—
424#385—21no—
425#385—21no—
426#384C2311yescharacteristic
427#383—21no—
428#383D411yescharacteristic
429#383D411yescharacteristic
430#382—21no—
431#382D411yescharacteristic
432#382D411yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#381D411yescharacteristic
440#381D411yescharacteristic
441#380—21no—
442#380—21no—
443#380—21no—
444#380—21no—
445#380D411yescharacteristic
446#380D411yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462#376—21no—
463#376C2311yescharacteristic
464#376C2311yescharacteristic
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#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—44no—
495C2×#41—82no—
496C2×#41—82no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8C2411yescharacteristic
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—21no—
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—21no—
514C22×D4—21no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—44no—
531C23×C4—82no—
532C23×C4—82no—
533C23×C4C2×D411yescharacteristic
534C23×C4C2×D411yescharacteristic
535C23×C4C2411yescharacteristic
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—
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C4⋊Q8—22no—
557C4⋊Q8—22no—
558C4⋊Q8—22no—
559C4⋊Q8—41no—
560#127—22no—
561#127—22no—
562#127—22no—
563#127—22no—
564#127—22no—
565#127—22no—
566#127—41no—
567#127—41no—
568#127—41no—
569#127—41no—
570#125—22no—
571#125—22no—
572#125—22no—
573#125—41no—
574#124—44no—
575C22⋊Q8—22no—
576C22⋊Q8—41no—
577#121—41no—
578#121—41no—
579#121—41no—
580#121—41no—
581#121—44no—
582#121—82no—
583#121—82no—
584#121—82no—
585#121—82no—
586#120—82no—
587#120—82no—
588#120—82no—
589#120—82no—
590C4×Q8—22no—
591C4×Q8—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—44no—
605C4×D4—44no—
606C4×D4—44no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
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—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—44no—
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C42—22no—
676C2×C42—22no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691#107—41no—
692#107—41no—
693#107—41no—
694#107—41no—
695#107—41no—
696#107—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703C4⋊C8—22no—
704C4⋊C8—22no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102#4114yescomplemented
741C22⋊C8—22no—
742C22⋊C8—41no—
743C22⋊C8—41no—
744C22⋊C8—41no—
745#97—22no—
746#97—22no—
747#97—22no—
748#97—41no—
749C4×C8—22no—
750C4×C8—41no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—42no—
809C24—42no—
810C24—42no—
811C24—42no—
812C24—42no—
813C24—81no—
814C24—81no—
815C24C22×D411yescharacteristic
816#41—816no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—42no—
824C2×Q8—42no—
825C2×Q8—81no—
826C2×Q8—81no—
827C2×Q8—81no—
828C2×Q8—81no—
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—21no—
850C2×D4—21no—
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—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4C2×#4112yes—
895C2×D42−1+412yes—
896C22×C4—22no—
897C22×C4—21no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—41no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—816no—
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C2511yescharacteristic
956SD16—44no—
957SD16—44no—
958SD16—82no—
959SD16—82no—
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—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8C2×#4112yes—
984C4⋊C4—21no—
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—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
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—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4C2×#4112yes—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C42—22no—
1061C42—22no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—42no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42H(5,𝔽2)12yes—
1079C42H(5,𝔽2)12yes—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—22no—
1087C23—22no—
1088C23—48no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—84no—
1116C23—84no—
1117C23—84no—
1118C23—84no—
1119C23—84no—
1120C23—84no—
1121C23#57712yes—
1122C23C23×D411yescharacteristic
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—84no—
1128Q8—162no—
1129D4—22no—
1130D4—22no—
1131D4—22no—
1132D4—22no—
1133D4—48no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—84no—
1147D4—84no—
1148D4—84no—
1149D4—84no—
1150D4—162no—
1151D4—162no—
1152D4—162no—
1153D4—162no—
1154D4—162no—
1155D4—162no—
1156D4—162no—
1157D4—162no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—22no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—44no—
1197C2×C4—44no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
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—84no—
1238C2×C4—84no—
1239C2×C4—84no—
1240C2×C4—84no—
1241C2×C4—84no—
1242C2×C4—84no—
1243C2×C4—84no—
1244C2×C4#53512yes—
1245C2×C4#53512yes—
1246C2×C4C22×#4111yescharacteristic
1247C2×C4C2×H(5,𝔽2)11yescharacteristic
1248C2×C4C2×H(5,𝔽2)11yescharacteristic
1249C2×C4C2×2−1+411yescharacteristic
1250C2×C4#58511yescharacteristic
1251C2×C4#58511yescharacteristic
1252C8—22no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C22—22no—
1261C22—22no—
1262C22—22no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—816no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22C2×#53511yescharacteristic
1297C22D4×#4111yescharacteristic
1298C22#348911yescharacteristic
1299C22C2×#57711yescharacteristic
1300C22#358511yescharacteristic
1301C22#358511yescharacteristic
1302C22#358511yescharacteristic
1303C4—22no—
1304C4—22no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—42no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4#350611yescharacteristic
1329C4#352011yescharacteristic
1330C4#354011yescharacteristic
1331C4#354111yescharacteristic
1332C2—42no—
1333C2—82no—
1334C2—82no—
1335C2—161no—
1336C2—161no—
1337C2#3986311yescharacteristic
1338C2#6080611yescharacteristic
1339C2#6081211yescharacteristic
1340C2#6150611yescharacteristic
1341C2#6152111yescharacteristic
1342C2#6216411yescharacteristic
1343C2#6222311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35237C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39153C2semidirect
3. #32959C2semidirect
4. #32294C2semidirect
5. #32292C2semidirect
6. #32066C2semidirect
7. #32060C2semidirect
8. #31310C2semidirect
9. #31290C2semidirect
10. #30547C2semidirect
11. #30527C2semidirect
12. #30138C2semidirect
13. #30138C2semidirect
14. #29504C2semidirect
15. #29504C2semidirect
16. #29265C2semidirect
17. #29263C2semidirect
18. #28549C2semidirect
19. #28435C2semidirect
20. #27826C2semidirect
21. #27780C2semidirect
22. #25676C2semidirect
23. #25466C2semidirect
24. #25288C2semidirect
25. #24695C2semidirect
26. #24644C2semidirect
27. #24154C2semidirect
28. #22635C2semidirect
29. #22232C2semidirect
30. #22230C2semidirect
31. #21453C2semidirect
34. C2×#501C22semidirect
36. C2×#490C22semidirect
38. C2×#475C22semidirect
41. C2×#460C22semidirect
52. #2645C22semidirect
53. #2645C22semidirect
57. #2565C22semidirect
60. #2550C22semidirect
78. #2370C22semidirect
79. #2356C22semidirect
80. #2331C22semidirect
81. #2330C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2097C22semidirect
91. #2097C22semidirect
93. #2093C22semidirect
95. #2092C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
98. #2074C22semidirect
99. #2074C22semidirect
101. #2067C22semidirect
103. #2065C22semidirect
106. #2055C22semidirect
107. #2055C22semidirect
119. #2025C22semidirect
121. #2023C22semidirect
128. #1993C22semidirect
129. #1993C22semidirect
130. #1991C22semidirect
131. #1988C22semidirect
136. #1982C22semidirect
138. #1973C22semidirect
140. #1968C22semidirect
142. #1961C22semidirect
144. #1949C22semidirect
145. #1949C22semidirect
146. #1949C22semidirect
147. #1949C22semidirect
148. #1940C22semidirect
149. #1940C22semidirect
151. #1936C22semidirect
153. #1934C22semidirect
157. #1926C22semidirect
159. #1925C22semidirect
160. #1925C22semidirect
161. #1925C22semidirect
168. #1877C22semidirect
169. #1877C22semidirect
173. #1864C22semidirect
174. #1864C22semidirect
175. #1864C22semidirect
176. #1864C22semidirect
181. #1862C22semidirect
182. #1862C22semidirect
186. #1847C22semidirect
187. #1846C22semidirect
188. #1832C22semidirect
189. #1832C22semidirect
196. #1771C22semidirect
197. #1771C22semidirect
201. #1746C22semidirect
202. #1746C22semidirect
740. #102#41semidirect

Maximal subgroups

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

subgroupindex
#391532
#352372
#329592
#322942
#322922
#320662
#320602
#313102
#312902
#305472
#305272
#301382
#295042
#292652
#292632
#285492
#284352
#278262
#277802
#256762
#254662
#252882
#246952
#246442
#241542
#226352
#222322
#222302
#214532