Subgroups — #13092146

Order 1472.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₉₂	C₂	1	1	yes	maximal, characteristic
2	C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₂₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₉₂	C₄	1	1	yes	characteristic
5	C₂×C₄×D₂₃	—	2	1	no	—
6	C₂×C₈×C₂₃	—	2	1	no	—
7	C₄²×C₂₃	C₂²	1	1	yes	characteristic
8	(C₂×D₂₃)⋊C₄	—	2	1	no	—
9	C₄⋊Dic₂₃	C₄	1	1	yes	characteristic
10	C₂×C₂₃⋊C₈	—	2	1	no	—
11	C₂²×D₂₃	—	2	1	no	—
12	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
14	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
15	C₂×Dic₂₃	—	2	1	no	—
16	D₉₂	—	2	1	no	—
17	D₉₂	C₈	1	2	yes	complemented
18	C₄×D₂₃	—	4	1	no	—
19	C₄×D₂₃	—	4	1	no	—
20	C₈×C₂₃	—	2	2	no	—
21	C₂₃⋊C₈	—	4	1	no	—
22	C₂²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×D₂₃	—	2	2	no	—
24	C₂×D₂₃	—	4	1	no	—
25	C₂×D₂₃	—	4	1	no	—
26	C₄×C₂₃	—	2	1	no	—
27	C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
28	C₄×C₂₃	M₁₆	1	1	yes	characteristic
29	C₄×C₂₃	D₈	1	1	yes	characteristic
30	C₄×C₂₃	SD₁₆	1	1	yes	characteristic
31	Dic₂₃	—	4	1	no	—
32	D₄⋊C₈	—	23	1	no	maximal, Sylow
33	C₂×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
34	C₂×C₂₃	#102	1	1	yes	characteristic
35	C₂×C₂₃	#104	1	1	yes	characteristic
36	D₂₃	—	4	2	no	—
37	C₄×D₄	—	23	1	no	—
38	C₄⋊C₈	—	23	1	no	—
39	C₄×C₈	D₂₃	1	1	yes	characteristic, complemented
40	C₂₃	D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
41	C₂×D₄	—	23	1	no	—
42	C₂²×C₄	—	46	1	no	—
43	C₂×C₈	—	2	1	no	—
44	C₂×C₈	—	46	1	no	—
45	C₄⋊C₄	—	23	1	no	—
46	C₂²⋊C₄	—	46	1	no	—
47	C₄²	C₂×D₂₃	1	1	yes	characteristic
48	C₂³	—	46	1	no	—
49	D₄	—	23	2	no	—
50	D₄	—	46	1	no	—
51	C₂×C₄	—	46	1	no	—
52	C₂×C₄	—	92	1	no	—
53	C₂×C₄	—	92	1	no	—
54	C₂×C₄	C₄×D₂₃	1	1	yes	characteristic
55	C₂×C₄	D₉₂	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
57	C₈	—	2	2	no	—
58	C₈	—	92	1	no	—
59	C₂²	—	46	2	no	—
60	C₂²	—	92	1	no	—
61	C₂²	—	92	1	no	—
62	C₂²	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	—	92	1	no	—
65	C₄	C₈×D₂₃	1	1	yes	characteristic
66	C₄	#67262	1	1	yes	characteristic
67	C₄	#67263	1	1	yes	characteristic
68	C₄	D₁₈₄	1	1	yes	characteristic
69	C₂	—	92	2	no	—
70	C₂	#10624987	1	1	yes	characteristic
71	C₂	(C₂×D₂₃)⋊C₈	1	1	yes	characteristic
72	C₂	#10625003	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₉₂
commutator	C₄×C₂₃	C₂×C₈
Frattini	C₄²	C₂×D₂₃
Fitting	C₄×C₈×C₂₃	C₂
socle	C₂²×C₂₃	C₂²⋊C₄
prime radical	C₂×D₉₂	C₄
cosocle	C₄²×C₂₃	C₂²
hypercenter	C₄×C₈	D₂₃
hypocenter	C₂₃	D₄⋊C₈
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₄×C₈×C₂₃	C₂	semidirect
3. C₄⋊(C₂₃⋊C₈)	C₂	semidirect
17. D₉₂	C₈	semidirect
39. C₄×C₈	D₂₃	semidirect
40. C₂₃	D₄⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₉₂	2
C₄×C₈×C₂₃	2
C₄⋊(C₂₃⋊C₈)	2
D₄⋊C₈	23