Subgroups — #13092211

Order 1472.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625107	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#99	C₂	1	1	yes	maximal, characteristic
3	#10625016	C₂	1	1	yes	maximal, characteristic
4	C₂×D₄×C₂₃	C₂²	1	1	yes	characteristic
5	C₂×Dic₄₆	C₄	1	1	yes	characteristic, complemented
6	C₂²⋊C₄×C₂₃	—	2	1	no	—
7	C₂²⋊Dic₂₃	—	2	1	no	—
8	C₂²⋊Dic₂₃	—	2	1	no	—
9	C₂²⋊Dic₂₃	—	2	1	no	—
10	C₄×Dic₂₃	C₄	1	1	yes	characteristic, complemented
11	C₂³×C₂₃	D₄	1	1	yes	characteristic
12	C₂³×C₂₃	D₄	1	1	yes	characteristic
13	D₄×C₂₃	—	4	1	no	—
14	C₂×C₄×C₂₃	—	4	1	no	—
15	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₂₃	—	2	1	no	—
17	C₂×Dic₂₃	—	2	1	no	—
18	C₂×Dic₂₃	—	4	1	no	—
19	Dic₄₆	—	4	1	no	—
20	C₂²×C₂₃	—	2	1	no	—
21	C₂²×C₂₃	—	2	1	no	—
22	C₂²×C₂₃	—	4	1	no	—
23	C₂²×C₂₃	—	4	1	no	—
24	C₂²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₄×C₂₃	—	2	1	no	—
26	C₄×C₂₃	—	8	1	no	—
27	Dic₂₃	—	4	1	no	—
28	Dic₂₃	—	4	1	no	—
29	Dic₂₃	—	8	1	no	—
30	#354	—	23	1	no	maximal, Sylow
31	C₂×C₂₃	—	2	1	no	—
32	C₂×C₂₃	—	4	1	no	—
33	C₂×C₂₃	—	4	1	no	—
34	C₂×C₂₃	#99	1	1	yes	characteristic
35	#124	—	23	1	no	—
36	#99	—	23	1	no	—
37	#99	D₂₃	1	1	yes	characteristic
38	C₂₃	#354	1	1	yes	characteristic, complemented, Sylow
39	C₂×Q₈	—	23	1	no	—
40	C₂×D₄	C₂×D₂₃	1	1	yes	characteristic
41	C₂²⋊C₄	—	2	1	no	—
42	C₂²⋊C₄	—	46	1	no	—
43	C₂²⋊C₄	—	46	1	no	—
44	C₂²⋊C₄	—	46	1	no	—
45	C₄²	—	23	1	no	—
46	C₂³	D₉₂	1	1	yes	characteristic
47	C₂³	C₂²⋊D₂₃	1	1	yes	characteristic
48	Q₈	—	92	1	no	—
49	D₄	—	4	1	no	—
50	C₂×C₄	—	4	1	no	—
51	C₂×C₄	—	46	1	no	—
52	C₂×C₄	—	46	1	no	—
53	C₂×C₄	—	92	1	no	—
54	C₂×C₄	C₄×D₂₃	1	1	yes	characteristic
55	C₂²	—	2	1	no	—
56	C₂²	—	2	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	—	4	1	no	—
59	C₂²	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
60	C₄	—	2	1	no	—
61	C₄	—	8	1	no	—
62	C₄	—	92	1	no	—
63	C₄	—	92	1	no	—
64	C₄	—	184	1	no	—
65	C₂	—	2	1	no	—
66	C₂	—	4	1	no	—
67	C₂	—	4	1	no	—
68	C₂	#10624988	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10624988
commutator	C₂×C₄×C₂₃	C₂×C₄
Frattini	C₂×D₄	C₂×D₂₃
Fitting	C₂₃×#99	C₂
socle	C₂×C₂₃	#99
prime radical, cosocle	C₂×D₄×C₂₃	C₂²
hypercenter	#99	D₂₃
hypocenter	C₂₃	#354
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂²×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×D₄ ◁ #99

Complements

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

N	H ≅ G/N	type
5. C₂×Dic₄₆	C₄	semidirect
10. C₄×Dic₂₃	C₄	semidirect
38. C₂₃	#354	semidirect

Maximal subgroups

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

subgroup	index
#10625107	2
C₂₃×#99	2
#10625016	2
#354	23