Subgroups — Q₈×C₁₁×C₃₂ #14590852

Order 2816.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₄⋊C₃₂	C₂	1	3	yes	maximal
3	C₄×C₁₁×C₃₂	C₂	1	3	yes	maximal
4	C₈×Q₈×C₁₁	C₄	1	1	yes	characteristic
5	C₂×C₁₁×C₃₂	C₂²	1	3	yes	—
6	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
7	C₁₁×C₄⋊C₁₆	C₄	1	3	yes	—
8	C₄×C₁₁×C₁₆	C₂²	1	3	yes	—
9	C₄×Q₈×C₁₁	C₈	1	1	yes	characteristic
10	C₂×C₁₁×C₁₆	C₂×C₄	1	3	yes	—
11	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
12	C₁₁×C₄⋊C₈	C₈	1	3	yes	—
13	C₄×C₈×C₁₁	C₂×C₄	1	3	yes	—
14	C₁₁×C₃₂	—	2	3	no	—
15	C₁₁×C₃₂	Q₈	1	2	yes	direct product factor
16	Q₈×C₃₂	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×Q₈×C₁₁	C₁₆	1	1	yes	characteristic
18	C₂×C₈×C₁₁	C₂×C₈	1	3	yes	—
19	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
20	C₁₁×C₄⋊C₄	C₁₆	1	3	yes	—
21	C₄²×C₁₁	C₂×C₈	1	3	yes	—
22	C₁₁×C₁₆	—	2	3	no	—
23	C₁₁×C₁₆	C₂×Q₈	1	1	yes	characteristic
24	C₁₁×C₁₆	#41	1	1	yes	characteristic
25	Q₈×C₁₆	C₂×C₁₁	1	1	yes	characteristic
26	C₄⋊C₃₂	C₂×C₁₁	1	3	yes	—
27	C₄×C₃₂	C₂×C₁₁	1	3	yes	—
28	Q₈×C₁₁	C₃₂	1	4	yes	direct product factor
29	C₂×C₄×C₁₁	C₂×C₁₆	1	3	yes	—
30	C₂×C₄×C₁₁	C₂×C₁₆	1	3	yes	—
31	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
32	C₈×C₁₁	—	2	3	no	—
33	C₈×C₁₁	C₄×Q₈	1	1	yes	characteristic
34	C₈×C₁₁	#131	1	1	yes	characteristic
35	C₈×Q₈	C₄×C₁₁	1	1	yes	characteristic
36	C₂×C₃₂	C₂²×C₁₁	1	3	yes	—
37	C₂×C₃₂	C₂²×C₁₁	1	1	yes	characteristic
38	C₄⋊C₁₆	C₄×C₁₁	1	3	yes	—
39	C₄×C₁₆	C₂²×C₁₁	1	3	yes	—
40	C₂²×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
41	C₄×C₁₁	—	2	3	no	—
42	C₄×C₁₁	C₂×C₃₂	1	6	yes	—
43	C₄×C₁₁	C₈×Q₈	1	1	yes	characteristic
44	C₄×C₁₁	#504	1	1	yes	characteristic
45	C₄×Q₈	C₈×C₁₁	1	1	yes	characteristic
46	C₂×C₁₆	C₂×C₄×C₁₁	1	3	yes	—
47	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
48	C₄⋊C₈	C₈×C₁₁	1	3	yes	—
49	C₄×C₈	C₂×C₄×C₁₁	1	3	yes	—
50	C₃₂	—	2	3	no	—
51	C₃₂	Q₈×C₁₁	1	2	yes	direct product factor
52	C₂×C₁₁	Q₈×C₁₆	1	1	yes	characteristic
53	C₂×C₁₁	C₂²×C₃₂	1	1	yes	characteristic
54	C₂×C₁₁	#2258	1	1	yes	characteristic
55	C₂×Q₈	C₁₁×C₁₆	1	1	yes	characteristic
56	C₂×C₈	C₂×C₈×C₁₁	1	3	yes	—
57	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
58	C₄⋊C₄	C₁₁×C₁₆	1	3	yes	—
59	C₄²	C₂×C₈×C₁₁	1	3	yes	—
60	C₁₆	—	2	3	no	—
61	C₁₆	C₂×Q₈×C₁₁	1	1	yes	characteristic
62	C₁₆	C₁₁×#41	1	1	yes	characteristic
63	C₁₁	Q₈×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
64	Q₈	C₁₁×C₃₂	1	4	yes	direct product factor
65	C₂×C₄	C₂×C₁₁×C₁₆	1	3	yes	—
66	C₂×C₄	C₂×C₁₁×C₁₆	1	3	yes	—
67	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
68	C₈	—	2	3	no	—
69	C₈	C₄×Q₈×C₁₁	1	1	yes	characteristic
70	C₈	C₁₁×#131	1	1	yes	characteristic
71	C₂²	C₂²×C₁₁×C₁₆	1	1	yes	characteristic
72	C₄	—	2	3	no	—
73	C₄	C₂×C₁₁×C₃₂	1	6	yes	—
74	C₄	C₈×Q₈×C₁₁	1	1	yes	characteristic
75	C₄	C₁₁×#504	1	1	yes	characteristic
76	C₂	Q₈×C₁₁×C₁₆	1	1	yes	characteristic
77	C₂	C₂²×C₁₁×C₃₂	1	1	yes	characteristic
78	C₂	C₁₁×#2258	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₁×C₃₂	C₂²
commutator	C₂	C₂²×C₁₁×C₃₂
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₁
socle, prime radical	C₂²×C₁₁	C₂²×C₁₆
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁×C₃₂ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₁₁×C₃₂	Q₈	direct (N × H)
16. Q₈×C₃₂	C₁₁	direct (N × H)
28. Q₈×C₁₁	C₃₂	direct (N × H)
51. C₃₂	Q₈×C₁₁	direct (N × H)
63. C₁₁	Q₈×C₃₂	direct (N × H)
64. Q₈	C₁₁×C₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×C₁₁×C₁₆	2
C₁₁×C₄⋊C₃₂	2
C₄×C₁₁×C₃₂	2
Q₈×C₃₂	11

Subgroups — Q8×C11×C32 #14590852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₁₁×C₃₂ #14590852