Subgroups — #15673508

Order 2944.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625015	C₂	1	2	yes	maximal
2	#13092187	C₂	1	4	yes	maximal, complemented
3	C₂₃×#518	C₂	1	1	yes	maximal, characteristic
4	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic
5	C₄×D₄×C₂₃	—	2	4	no	—
6	C₂₃×#117	C₂²	1	2	yes	—
7	C₂×C₂²⋊C₄×C₂₃	C₄	1	4	yes	—
8	C₂×#67267	C₂²	1	4	yes	—
9	#10625015	—	2	4	no	—
10	C₂⁴×C₂₃	C₂×C₄	1	2	yes	—
11	C₂×D₄×C₂₃	—	2	4	no	—
12	C₂×D₄×C₂₃	D₄	1	4	yes	—
13	C₂²×C₄×C₂₃	—	2	4	no	—
14	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
15	C₄⋊C₄×C₂₃	—	2	2	no	—
16	C₂²⋊C₄×C₂₃	—	2	4	no	—
17	C₂²⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
18	C₄²×C₂₃	—	2	2	no	—
19	#67267	—	2	4	no	—
20	#67267	—	2	4	no	—
21	C₂×C₂₃⋊C₈	—	2	4	no	—
22	C₂³×C₂₃	—	2	4	no	—
23	C₂³×C₂₃	—	8	2	no	—
24	C₂³×C₂₃	C₂²⋊C₄	1	4	yes	—
25	C₂³×C₂₃	C₂²×C₄	1	1	yes	characteristic
26	D₄×C₂₃	—	2	8	no	—
27	C₂×C₄×C₂₃	—	2	4	no	—
28	C₂×C₄×C₂₃	—	8	4	no	—
29	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
30	C₂×C₄×C₂₃	#41	1	4	yes	—
31	C₂₃⋊C₈	—	4	4	no	—
32	#1829	—	23	1	no	maximal, Sylow
33	C₂²×C₂₃	—	2	4	no	—
34	C₂²×C₂₃	—	4	1	no	—
35	C₂²×C₂₃	—	4	4	no	—
36	C₂²×C₂₃	—	8	4	no	—
37	C₂²×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₂²×C₂₃	#117	1	2	yes	—
39	C₄×C₂₃	—	4	4	no	—
40	C₄×C₂₃	#123	1	4	yes	—
41	#518	D₂₃	1	1	yes	characteristic
42	C₂×#100	—	23	2	no	—
43	#344	—	23	4	no	—
44	C₂×C₂₃	—	2	1	no	—
45	C₂×C₂₃	—	2	2	no	—
46	C₂×C₂₃	—	4	4	no	—
47	C₂×C₂₃	#381	1	1	yes	characteristic
48	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic
49	C₂×M₁₆	—	23	4	no	—
50	C₄×D₄	—	2	4	no	—
51	#117	C₂×D₂₃	1	2	yes	—
52	C₂×C₂²⋊C₄	Dic₂₃	1	4	yes	—
53	#100	—	46	4	no	—
54	C₂₃	#1829	1	1	yes	characteristic, complemented, Sylow
55	C₂⁴	C₂×Dic₂₃	1	2	yes	—
56	C₂×D₄	—	2	4	no	—
57	C₂×D₄	C₂²⋊D₂₃	1	4	yes	—
58	C₂²×C₄	—	2	4	no	—
59	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
60	M₁₆	—	46	4	no	—
61	M₁₆	—	46	4	no	—
62	C₂×C₈	—	46	4	no	—
63	C₄⋊C₄	—	2	2	no	—
64	C₂²⋊C₄	—	2	4	no	—
65	C₂²⋊C₄	C₂×Dic₂₃	1	4	yes	—
66	C₄²	—	2	2	no	—
67	C₂³	—	2	4	no	—
68	C₂³	—	8	2	no	—
69	C₂³	C₂²⋊Dic₂₃	1	4	yes	—
70	C₂³	C₂²×Dic₂₃	1	1	yes	characteristic
71	D₄	—	2	8	no	—
72	C₂×C₄	—	2	4	no	—
73	C₂×C₄	—	8	4	no	—
74	C₂×C₄	#67288	1	4	yes	—
75	C₂×C₄	C₂×C₂²⋊D₂₃	1	2	yes	—
76	C₈	—	92	4	no	—
77	C₂²	—	2	4	no	—
78	C₂²	—	4	1	no	—
79	C₂²	—	4	4	no	—
80	C₂²	—	8	4	no	—
81	C₂²	#10625097	1	2	yes	—
82	C₂²	C₂×C₂²⋊Dic₂₃	1	1	yes	characteristic
83	C₄	—	4	4	no	—
84	C₄	#10625100	1	4	yes	—
85	C₂	—	2	1	no	—
86	C₂	—	2	2	no	—
87	C₂	—	4	4	no	—
88	C₂	#13092280	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13092280
commutator	C₂³×C₂₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₃
Fitting	C₂₃×#518	C₂
socle	C₂×C₂₃	#381
prime radical	C₂²×D₄×C₂₃	C₂²
cosocle	C₂²×C₄×C₂₃	C₂³
hypercenter	#518	D₂₃
hypocenter	C₂₃	#1829
LCS	G ▷ C₂³×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #518

Complements

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

N	H ≅ G/N	type
2. #13092187	C₂	semidirect
54. C₂₃	#1829	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625015	2
#13092187	2
C₂₃×#518	2
#1829	23