Subgroups — #15671694

Order 2944.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092470	C₂	1	2	yes	maximal
2	#13092139	C₂	1	2	yes	maximal, complemented
3	#13092138	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₂₃	C₄	1	2	yes	—
7	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
8	C₂₃×#97	C₄	1	2	yes	—
9	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
11	C₂²⋊(C₂₃⋊C₈)	C₄	1	4	yes	—
12	C₄⋊(C₂₃⋊C₈)	C₄	1	4	yes	—
13	C₄×C₂₃⋊C₈	C₂²	1	2	yes	—
14	C₄×C₂₃⋊C₈	C₂²	1	2	yes	—
15	C₂²×C₄×C₂₃	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
17	M₁₆×C₂₃	—	2	4	no	—
18	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
20	C₄²×C₂₃	C₂×C₄	1	2	yes	—
21	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₂₃	C₂³	1	1	yes	characteristic
23	C₂×C₂₃⋊C₈	C₂×C₄	1	4	yes	—
24	C₂×C₂₃⋊C₈	C₂×C₄	1	4	yes	—
25	C₂³×C₂₃	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₂₃	—	2	2	no	—
27	C₂×C₄×C₂₃	—	2	4	no	—
28	C₂×C₄×C₂₃	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₂₃	C₄²	1	2	yes	—
30	C₂×C₄×C₂₃	C₂²×C₄	1	2	yes	—
31	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₂₃	—	2	2	no	—
33	C₈×C₂₃	M₁₆	1	4	yes	—
34	C₂₃⋊C₈	—	2	4	no	—
35	C₂₃⋊C₈	—	2	4	no	—
36	#1453	—	23	1	no	maximal, Sylow
37	C₂²×C₂₃	—	2	1	no	—
38	C₂²×C₂₃	—	2	2	no	—
39	C₂²×C₂₃	C₂×C₄²	1	1	yes	characteristic
40	C₄×C₂₃	—	2	1	no	—
41	C₄×C₂₃	—	2	2	no	—
42	C₄×C₂₃	C₂×M₁₆	1	2	yes	—
43	C₄×C₂₃	#131	1	4	yes	—
44	#431	—	23	2	no	—
45	C₄×M₁₆	D₂₃	1	1	yes	characteristic
46	#322	—	23	1	no	—
47	#322	—	23	2	no	—
48	C₈²	—	23	1	no	—
49	C₂×C₂₃	—	4	1	no	—
50	C₂×C₂₃	C₄×M₁₆	1	1	yes	characteristic
51	C₂×C₂₃	#405	1	2	yes	—
52	C₂×M₁₆	Dic₂₃	1	2	yes	—
53	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
54	C₄⋊C₈	—	23	4	no	—
55	C₂²⋊C₈	—	23	4	no	—
56	#97	Dic₂₃	1	2	yes	—
57	C₄×C₈	—	23	2	no	—
58	C₄×C₈	—	23	2	no	—
59	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
60	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
61	C₂₃	#1453	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₄	C₄×D₂₃	1	2	yes	—
63	C₂²×C₄	C₂×Dic₂₃	1	1	yes	characteristic
64	M₁₆	—	2	4	no	—
65	C₂×C₈	—	23	4	no	—
66	C₂×C₈	—	23	4	no	—
67	C₂×C₈	C₂×Dic₂₃	1	2	yes	—
68	C₂×C₈	C₂×Dic₂₃	1	2	yes	—
69	C₄²	C₄×D₂₃	1	2	yes	—
70	C₄²	C₂×Dic₂₃	1	1	yes	characteristic
71	C₄²	C₂²×D₂₃	1	1	yes	characteristic
72	C₂³	C₄×Dic₂₃	1	1	yes	characteristic
73	C₂×C₄	—	2	4	no	—
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	C₄×Dic₂₃	1	1	yes	characteristic
76	C₂×C₄	C₄×Dic₂₃	1	2	yes	—
77	C₂×C₄	C₂×C₄×D₂₃	1	2	yes	—
78	C₂×C₄	C₂²×Dic₂₃	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	—	46	4	no	—
81	C₈	—	46	4	no	—
82	C₈	#67267	1	4	yes	—
83	C₂²	—	2	1	no	—
84	C₂²	—	2	2	no	—
85	C₂²	C₂×C₄×Dic₂₃	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	2	2	no	—
88	C₄	#10625078	1	4	yes	—
89	C₄	C₂×#67267	1	2	yes	—
90	C₂	—	4	1	no	—
91	C₂	C₄×#67267	1	1	yes	characteristic
92	C₂	#13092375	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₂₃
commutator, socle	C₂²×C₂₃	C₂×C₄²
Fitting	C₄×M₁₆×C₂₃	C₂
prime radical	C₂³×C₂₃	C₄²
cosocle	C₄²×C₂₃	C₂³
hypercenter	C₄×M₁₆	D₂₃
hypocenter	C₂₃	#1453
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄² ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. #13092139	C₂	semidirect
3. #13092138	C₂	semidirect
4. C₈×C₂₃⋊C₈	C₂	semidirect
61. C₂₃	#1453	semidirect

Maximal subgroups

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

subgroup	index
#13092470	2
#13092139	2
#13092138	2
C₈×C₂₃⋊C₈	2
C₄×M₁₆×C₂₃	2
#1453	23