Subgroups — #15673535

Order 2944.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092441	C₂	1	2	yes	maximal
2	#13092182	C₂	1	4	yes	maximal
3	C₂×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₃	C₂²	1	2	yes	—
5	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
6	C₂×#67267	C₂²	1	4	yes	—
7	C₄×C₈×C₂₃	C₄	1	2	yes	—
8	C₄×C₈×C₂₃	C₄	1	2	yes	—
9	C₄⋊(C₂₃⋊C₈)	—	2	4	no	—
10	C₂²×C₄×C₂₃	Q₈	1	2	yes	—
11	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
12	C₂×C₈×C₂₃	—	2	4	no	—
13	C₂×C₈×C₂₃	C₂×C₄	1	4	yes	—
14	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
15	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
16	C₄²×C₂₃	D₄	1	2	yes	—
17	#67267	—	2	8	no	—
18	C₂×C₂₃⋊C₈	—	2	4	no	—
19	C₂³×C₂₃	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₄×C₂₃	—	2	4	no	—
21	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
22	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
25	C₂×C₄×C₂₃	#41	1	4	yes	—
26	C₈×C₂₃	—	2	4	no	—
27	C₂₃⋊C₈	—	4	4	no	—
28	#1837	—	23	1	no	maximal, Sylow
29	C₂²×C₂₃	—	2	2	no	—
30	C₂²×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
31	C₂²×C₂₃	#125	1	2	yes	—
32	C₄×C₂₃	—	2	2	no	—
33	C₄×C₂₃	#108	1	4	yes	—
34	C₄×C₂₃	#117	1	2	yes	—
35	C₄×C₂₃	#124	1	2	yes	—
36	#423	—	23	2	no	—
37	C₂×C₄×C₈	D₂₃	1	1	yes	characteristic
38	#341	—	23	4	no	—
39	C₂×C₂₃	—	2	2	no	—
40	C₂×C₂₃	#382	1	1	yes	characteristic
41	C₂×C₂₃	C₂×#108	1	2	yes	—
42	C₂×M₁₆	—	23	4	no	—
43	C₂²×C₈	C₂×D₂₃	1	2	yes	—
44	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
45	C₄⋊C₈	—	46	4	no	—
46	C₄×C₈	Dic₂₃	1	2	yes	—
47	C₄×C₈	Dic₂₃	1	2	yes	—
48	C₂₃	#1837	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₄	Dic₄₆	1	2	yes	—
50	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
51	M₁₆	—	46	8	no	—
52	C₂×C₈	—	2	4	no	—
53	C₂×C₈	—	46	4	no	—
54	C₂×C₈	C₂×Dic₂₃	1	4	yes	—
55	C₄²	D₉₂	1	2	yes	—
56	C₄²	C₂×Dic₂₃	1	1	yes	characteristic
57	C₄²	C₂×Dic₂₃	1	1	yes	characteristic
58	C₂³	C₂×Dic₄₆	1	1	yes	characteristic
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	C₄⋊Dic₂₃	1	2	yes	—
61	C₂×C₄	C₄⋊Dic₂₃	1	2	yes	—
62	C₂×C₄	C₂×D₉₂	1	1	yes	characteristic
63	C₂×C₄	#67288	1	4	yes	—
64	C₂×C₄	C₂²×Dic₂₃	1	1	yes	characteristic
65	C₈	—	2	4	no	—
66	C₈	—	92	4	no	—
67	C₂²	—	2	2	no	—
68	C₂²	#10625041	1	2	yes	—
69	C₂²	C₂×C₄⋊Dic₂₃	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	#10625001	1	4	yes	—
72	C₄	#10625046	1	2	yes	—
73	C₄	#10625097	1	2	yes	—
74	C₂	—	2	2	no	—
75	C₂	#13092283	1	1	yes	characteristic
76	C₂	C₂×#10625001	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₉₂
commutator	C₂×C₄×C₂₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₃
Fitting	C₂×C₄×C₈×C₂₃	C₂
socle	C₂²×C₂₃	C₂×C₄⋊C₄
prime radical	C₂³×C₂₃	C₂×Q₈
cosocle	C₂²×C₄×C₂₃	C₂³
hypercenter	C₂×C₄×C₈	D₂₃
hypocenter	C₂₃	#1837
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
48. C₂₃	#1837	semidirect

Maximal subgroups

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

subgroup	index
#13092441	2
#13092182	2
C₂×C₄×C₈×C₂₃	2
#1837	23