Subgroups — #13092400

Order 1472.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#67292	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₂₃	C₂	1	2	yes	maximal, complemented
3	C₂₃×#101	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625018	C₂	1	1	yes	maximal, characteristic, complemented
5	#10625005	C₂	1	2	yes	maximal, complemented
6	C₂×Q₈×C₂₃	C₂²	1	1	yes	characteristic
7	#67292	—	2	2	no	—
8	#67292	—	2	2	no	—
9	C₂×D₉₂	C₄	1	2	yes	—
10	C₂×D₉₂	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₂₃	C₄	1	2	yes	—
12	C₂×C₄×D₂₃	C₂²	1	1	yes	characteristic
13	M₁₆×C₂₃	C₂²	1	2	yes	—
14	#67267	C₂²	1	2	yes	—
15	#67262	—	2	2	no	—
16	C₈×D₂₃	—	2	2	no	—
17	C₂²×D₂₃	C₂×C₄	1	2	yes	—
18	C₂²×D₂₃	C₂×C₄	1	1	yes	characteristic
19	Q₈×C₂₃	—	2	2	no	—
20	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
22	C₂×Dic₂₃	C₂×C₄	1	1	yes	characteristic
23	D₉₂	—	2	4	no	—
24	D₉₂	—	2	2	no	—
25	C₄×D₂₃	—	2	2	no	—
26	C₄×D₂₃	—	2	2	no	—
27	C₄×D₂₃	D₄	1	2	yes	—
28	C₄×D₂₃	D₄	1	2	yes	—
29	C₈×C₂₃	—	2	2	no	—
30	C₂₃⋊C₈	—	2	2	no	—
31	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×D₂₃	—	2	2	no	—
33	C₂×D₂₃	—	4	1	no	—
34	C₂×D₂₃	—	4	2	no	—
35	C₂×D₂₃	C₂²⋊C₄	1	2	yes	—
36	C₄×C₂₃	—	2	2	no	—
37	C₄×C₂₃	C₂×D₄	1	2	yes	—
38	Dic₂₃	C₂²⋊C₄	1	1	yes	characteristic
39	Dic₂₃	C₂²⋊C₄	1	1	yes	characteristic
40	#413	—	23	1	no	maximal, Sylow
41	C₂×C₂₃	—	2	1	no	—
42	C₂×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
43	D₂₃	—	2	2	no	—
44	D₂₃	—	4	2	no	—
45	C₂×#41	—	23	1	no	—
46	C₂×M₁₆	—	23	2	no	—
47	#101	—	23	1	no	—
48	#101	D₂₃	1	1	yes	characteristic, complemented
49	#100	—	23	2	no	—
50	C₂₃	#413	1	1	yes	characteristic, complemented, Sylow
51	#41	—	46	2	no	—
52	#41	—	46	2	no	—
53	C₂×Q₈	C₂×D₂₃	1	1	yes	characteristic
54	C₂×D₄	—	23	2	no	—
55	C₂×D₄	—	23	1	no	—
56	C₂²×C₄	—	23	1	no	—
57	C₂²×C₄	—	23	2	no	—
58	M₁₆	—	23	2	no	—
59	M₁₆	—	46	2	no	—
60	M₁₆	C₂×D₂₃	1	2	yes	—
61	C₂×C₈	—	46	2	no	—
62	C₂³	—	23	1	no	—
63	C₂³	—	23	2	no	—
64	Q₈	—	2	2	no	—
65	D₄	—	46	4	no	—
66	D₄	—	46	2	no	—
67	C₂×C₄	—	23	1	no	—
68	C₂×C₄	—	23	2	no	—
69	C₂×C₄	—	23	2	no	—
70	C₂×C₄	—	46	2	no	—
71	C₂×C₄	—	46	2	no	—
72	C₂×C₄	C₄×D₂₃	1	2	yes	—
73	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
74	C₈	—	2	2	no	—
75	C₈	—	46	2	no	—
76	C₂²	—	23	2	no	—
77	C₂²	—	46	2	no	—
78	C₂²	—	92	1	no	—
79	C₂²	—	92	2	no	—
80	C₂²	C₂×C₄×D₂₃	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	23	1	no	—
83	C₄	—	23	1	no	—
84	C₄	D₄×D₂₃	1	2	yes	—
85	C₂	—	2	1	no	—
86	C₂	—	46	2	no	—
87	C₂	—	92	2	no	—
88	C₂	C₂²⋊C₄×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊C₄×D₂₃
commutator	C₂²×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#101	C₂
socle	C₂×C₂₃	C₂×C₂²⋊C₄
prime radical	C₂×#67292	C₂
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	#101	D₂₃
hypocenter	C₂₃	#413
LCS	G ▷ C₂²×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #101

Complements

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

N	H ≅ G/N	type
2. M₁₆×D₂₃	C₂	semidirect
3. C₂₃×#101	C₂	semidirect
4. #10625018	C₂	semidirect
5. #10625005	C₂	semidirect
48. #101	D₂₃	semidirect
50. C₂₃	#413	semidirect

Maximal subgroups

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

subgroup	index
C₂×#67292	2
M₁₆×D₂₃	2
C₂₃×#101	2
#10625018	2
#10625005	2
#413	23