Subgroups — Q₈⋊(C₁₁⋊C₁₆) #13066595

Order 1408.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₁₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₄×Q₈×C₁₁	C₄	1	1	yes	characteristic
5	C₁₁×C₄⋊C₈	—	2	1	no	—
6	C₁₁×C₄⋊C₈	C₄	1	1	yes	characteristic
7	C₄×C₈×C₁₁	—	2	1	no	—
8	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₁⋊C₁₆	—	2	1	no	—
10	C₂×C₁₁⋊C₁₆	—	2	1	no	—
11	C₂×Q₈×C₁₁	C₈	1	1	yes	characteristic
12	C₂×C₈×C₁₁	—	2	1	no	—
13	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
14	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
15	C₁₁×C₄⋊C₄	—	2	1	no	—
16	C₁₁×C₄⋊C₄	C₈	1	1	yes	characteristic
17	C₄²×C₁₁	—	2	1	no	—
18	C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₁₁⋊C₁₆	—	2	2	no	—
20	C₁₁⋊C₁₆	—	4	1	no	—
21	Q₈⋊C₁₆	—	11	1	no	maximal, Sylow
22	Q₈×C₁₁	—	2	1	no	—
23	Q₈×C₁₁	C₁₆	1	2	yes	complemented
24	C₂×C₄×C₁₁	—	2	1	no	—
25	C₂×C₄×C₁₁	—	2	1	no	—
26	C₂×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₁₁	M₁₆	1	1	yes	characteristic
29	C₈×C₁₁	—	2	1	no	—
30	C₈×C₁₁	—	4	1	no	—
31	C₈×C₁₁	SD₁₆	1	1	yes	characteristic
32	C₈×C₁₁	Q₁₆	1	1	yes	characteristic
33	C₈×Q₈	D₁₁	1	1	yes	characteristic
34	C₄⋊C₁₆	—	11	1	no	—
35	C₄×C₁₆	—	11	1	no	—
36	C₂²×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
37	C₄×C₁₁	—	2	2	no	—
38	C₄×C₁₁	—	2	1	no	—
39	C₄×C₁₁	—	4	1	no	—
40	C₄×C₁₁	#103	1	1	yes	characteristic
41	C₄×C₁₁	#104	1	1	yes	characteristic
42	C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
43	C₄×C₁₁	M₃₂	1	1	yes	characteristic
44	C₄×Q₈	Dic₁₁	1	1	yes	characteristic
45	C₂×C₁₆	—	22	1	no	—
46	C₂×C₁₆	—	22	1	no	—
47	C₄⋊C₈	—	2	1	no	—
48	C₄⋊C₈	Dic₁₁	1	1	yes	characteristic
49	C₄×C₈	—	2	1	no	—
50	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
51	C₂×C₁₁	Q₈⋊C₈	1	1	yes	characteristic
52	C₂×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
53	C₂×C₁₁	#350	1	1	yes	characteristic
54	C₂×Q₈	C₁₁⋊C₈	1	1	yes	characteristic
55	C₂×C₈	—	2	1	no	—
56	C₂×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
57	C₂×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
58	C₄⋊C₄	—	2	1	no	—
59	C₄⋊C₄	C₁₁⋊C₈	1	1	yes	characteristic
60	C₄²	—	2	1	no	—
61	C₄²	C₂×Dic₁₁	1	1	yes	characteristic
62	C₁₆	—	22	2	no	—
63	C₁₆	—	44	1	no	—
64	C₁₁	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
65	Q₈	—	2	1	no	—
66	Q₈	C₁₁⋊C₁₆	1	2	yes	complemented
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
70	C₂×C₄	#4318	1	1	yes	characteristic
71	C₂×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	4	1	no	—
74	C₈	#4325	1	1	yes	characteristic
75	C₈	#4326	1	1	yes	characteristic
76	C₂²	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	2	1	no	—
79	C₄	—	4	1	no	—
80	C₄	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
81	C₄	#66876	1	1	yes	characteristic
82	C₄	#66899	1	1	yes	characteristic
83	C₄	#66901	1	1	yes	characteristic
84	C₂	Q₈⋊(C₁₁⋊C₈)	1	1	yes	characteristic
85	C₂	C₂²⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic
86	C₂	#10622199	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₁₁
Fitting	C₈×Q₈×C₁₁	C₂
socle, prime radical	C₂²×C₁₁	C₂²⋊C₈
cosocle	C₄×C₈×C₁₁	C₂²
hypercenter	C₈×Q₈	D₁₁
hypocenter	C₁₁	Q₈⋊C₁₆
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×Q₈

Complements

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

N	H ≅ G/N	type
23. Q₈×C₁₁	C₁₆	semidirect
64. C₁₁	Q₈⋊C₁₆	semidirect
66. Q₈	C₁₁⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₈×Q₈×C₁₁	2
C₄⋊(C₁₁⋊C₁₆)	2
C₄×C₁₁⋊C₁₆	2
Q₈⋊C₁₆	11

Subgroups — Q8⋊(C11⋊C16) #13066595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈⋊(C₁₁⋊C₁₆) #13066595