Subgroups — Q₈⋊(C₂₃⋊C₁₆) #15671376

Order 2944.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₂₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₈×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₄×Q₈×C₂₃	C₄	1	1	yes	characteristic
5	C₂₃×C₄⋊C₈	—	2	1	no	—
6	C₂₃×C₄⋊C₈	C₄	1	1	yes	characteristic
7	C₄×C₈×C₂₃	—	2	1	no	—
8	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×C₂₃⋊C₁₆	—	2	1	no	—
10	C₂×C₂₃⋊C₁₆	—	2	1	no	—
11	C₂×Q₈×C₂₃	C₈	1	1	yes	characteristic
12	C₂×C₈×C₂₃	—	2	1	no	—
13	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
14	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
15	C₄⋊C₄×C₂₃	—	2	1	no	—
16	C₄⋊C₄×C₂₃	C₈	1	1	yes	characteristic
17	C₄²×C₂₃	—	2	1	no	—
18	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
19	C₂₃⋊C₁₆	—	2	2	no	—
20	C₂₃⋊C₁₆	—	4	1	no	—
21	Q₈×C₂₃	—	2	1	no	—
22	Q₈×C₂₃	C₁₆	1	2	yes	complemented
23	C₂×C₄×C₂₃	—	2	1	no	—
24	C₂×C₄×C₂₃	—	2	1	no	—
25	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₂₃	M₁₆	1	1	yes	characteristic
28	C₈×C₂₃	—	2	1	no	—
29	C₈×C₂₃	—	4	1	no	—
30	C₈×C₂₃	SD₁₆	1	1	yes	characteristic
31	C₈×C₂₃	Q₁₆	1	1	yes	characteristic
32	Q₈⋊C₁₆	—	23	1	no	maximal, Sylow
33	C₂²×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
34	C₄×C₂₃	—	2	2	no	—
35	C₄×C₂₃	—	2	1	no	—
36	C₄×C₂₃	—	4	1	no	—
37	C₄×C₂₃	#103	1	1	yes	characteristic
38	C₄×C₂₃	#104	1	1	yes	characteristic
39	C₄×C₂₃	C₂×C₁₆	1	1	yes	characteristic
40	C₄×C₂₃	M₃₂	1	1	yes	characteristic
41	C₈×Q₈	D₂₃	1	1	yes	characteristic
42	C₄⋊C₁₆	—	23	1	no	—
43	C₄×C₁₆	—	23	1	no	—
44	C₂×C₂₃	Q₈⋊C₈	1	1	yes	characteristic
45	C₂×C₂₃	C₂²⋊C₁₆	1	1	yes	characteristic
46	C₂×C₂₃	#350	1	1	yes	characteristic
47	C₄×Q₈	Dic₂₃	1	1	yes	characteristic
48	C₂×C₁₆	—	46	1	no	—
49	C₂×C₁₆	—	46	1	no	—
50	C₄⋊C₈	—	2	1	no	—
51	C₄⋊C₈	Dic₂₃	1	1	yes	characteristic
52	C₄×C₈	—	2	1	no	—
53	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
54	C₂₃	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₈	C₂₃⋊C₈	1	1	yes	characteristic
56	C₂×C₈	—	2	1	no	—
57	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
59	C₄⋊C₄	—	2	1	no	—
60	C₄⋊C₄	C₂₃⋊C₈	1	1	yes	characteristic
61	C₄²	—	2	1	no	—
62	C₄²	C₂×Dic₂₃	1	1	yes	characteristic
63	C₁₆	—	46	2	no	—
64	C₁₆	—	92	1	no	—
65	Q₈	—	2	1	no	—
66	Q₈	C₂₃⋊C₁₆	1	2	yes	complemented
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	C₂×C₂₃⋊C₈	1	1	yes	characteristic
70	C₂×C₄	#67267	1	1	yes	characteristic
71	C₂×C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	4	1	no	—
74	C₈	#67274	1	1	yes	characteristic
75	C₈	#67275	1	1	yes	characteristic
76	C₂²	C₂²⋊(C₂₃⋊C₈)	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	2	1	no	—
79	C₄	—	4	1	no	—
80	C₄	C₂×C₂₃⋊C₁₆	1	1	yes	characteristic
81	C₄	#10624994	1	1	yes	characteristic
82	C₄	#10625017	1	1	yes	characteristic
83	C₄	#10625019	1	1	yes	characteristic
84	C₂	Q₈⋊(C₂₃⋊C₈)	1	1	yes	characteristic
85	C₂	C₂²⋊(C₂₃⋊C₁₆)	1	1	yes	characteristic
86	C₂	#13092201	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₂₃
commutator	C₄×C₂₃	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₂₃
Fitting	C₈×Q₈×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	C₂²⋊C₈
cosocle	C₄×C₈×C₂₃	C₂²
hypercenter	C₈×Q₈	D₂₃
hypocenter	C₂₃	Q₈⋊C₁₆
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×Q₈

Complements

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

N	H ≅ G/N	type
22. Q₈×C₂₃	C₁₆	semidirect
54. C₂₃	Q₈⋊C₁₆	semidirect
66. Q₈	C₂₃⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊(C₂₃⋊C₁₆)	2
C₄×C₂₃⋊C₁₆	2
C₈×Q₈×C₂₃	2
Q₈⋊C₁₆	23

Subgroups — Q8⋊(C23⋊C16) #15671376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈⋊(C₂₃⋊C₁₆) #15671376