Subgroups — C₂₃×#2165 #15669784

Order 2944.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#364	C₂	1	2	yes	maximal, complemented
3	C₂₃×#349	C₂	1	2	yes	maximal
4	C₂₃×#347	C₂	1	2	yes	maximal, complemented
5	C₂×M₁₆×C₂₃	C₄	1	1	yes	characteristic
6	C₂×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₄²×C₂₃	C₄	1	1	yes	characteristic
8	C₂₃×M₃₂	C₂²	1	4	yes	—
9	C₂₃×#97	C₄	1	1	yes	characteristic
10	C₂₃×#97	C₂²	1	1	yes	characteristic
11	C₄×C₈×C₂₃	C₄	1	1	yes	characteristic
12	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₂₃	—	2	1	no	—
14	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
15	M₁₆×C₂₃	—	2	2	no	—
16	M₁₆×C₂₃	—	2	2	no	—
17	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
21	C₄²×C₂₃	—	2	1	no	—
22	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
24	C₁₆×C₂₃	—	2	4	no	—
25	C₂³×C₂₃	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₂₃	—	2	1	no	—
27	C₂×C₄×C₂₃	—	2	1	no	—
28	C₂×C₄×C₂₃	—	2	1	no	—
29	C₂×C₄×C₂₃	—	2	1	no	—
30	C₂×C₄×C₂₃	—	4	2	no	—
31	C₂×C₄×C₂₃	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₂₃	—	2	1	no	—
34	C₈×C₂₃	—	2	1	no	—
35	C₈×C₂₃	M₁₆	1	2	yes	—
36	C₈×C₂₃	#41	1	2	yes	—
37	#2165	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₂₃	—	2	1	no	—
39	C₂²×C₂₃	—	4	1	no	—
40	C₂²×C₂₃	C₂×M₁₆	1	1	yes	characteristic
41	C₄×C₂₃	—	2	2	no	—
42	C₄×C₂₃	—	2	1	no	—
43	C₄×C₂₃	—	4	1	no	—
44	C₄×C₂₃	#117	1	1	yes	characteristic
45	C₄×C₂₃	C₂×M₁₆	1	1	yes	characteristic
46	C₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic
47	#364	C₂×C₂₃	1	2	yes	complemented
48	#349	C₂×C₂₃	1	2	yes	—
49	#347	C₂×C₂₃	1	2	yes	complemented
50	C₂×C₂₃	—	2	1	no	—
51	C₂×C₂₃	—	4	1	no	—
52	C₂×C₂₃	#432	1	1	yes	characteristic
53	C₂×M₁₆	C₄×C₂₃	1	1	yes	characteristic
54	C₂×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
55	C₂×C₄²	C₄×C₂₃	1	1	yes	characteristic
56	M₃₂	C₂²×C₂₃	1	4	yes	—
57	#97	C₄×C₂₃	1	1	yes	characteristic
58	#97	C₂²×C₂₃	1	1	yes	characteristic
59	C₄×C₈	C₄×C₂₃	1	1	yes	characteristic
60	C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
61	C₂₃	#2165	1	1	yes	characteristic, direct product factor, Sylow
62	C₂²×C₄	—	2	1	no	—
63	C₂²×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
64	M₁₆	—	2	2	no	—
65	M₁₆	—	2	2	no	—
66	C₂×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
67	C₂×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
68	C₂×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
69	C₂×C₈	C₂³×C₂₃	1	1	yes	characteristic
70	C₄²	—	2	1	no	—
71	C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
72	C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
73	C₁₆	—	2	4	no	—
74	C₂³	M₁₆×C₂₃	1	1	yes	characteristic
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	4	2	no	—
80	C₂×C₄	M₁₆×C₂₃	1	1	yes	characteristic
81	C₂×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	2	1	no	—
84	C₈	M₁₆×C₂₃	1	2	yes	—
85	C₈	#41×C₂₃	1	2	yes	—
86	C₂²	—	2	1	no	—
87	C₂²	—	4	1	no	—
88	C₂²	C₂×M₁₆×C₂₃	1	1	yes	characteristic
89	C₄	—	2	2	no	—
90	C₄	—	2	1	no	—
91	C₄	—	4	1	no	—
92	C₄	C₂₃×#117	1	1	yes	characteristic
93	C₄	C₂×M₁₆×C₂₃	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	4	1	no	—
96	C₂	C₂₃×#432	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₂₃	#117
commutator	C₂×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×C₈	C₂³×C₂₃
socle	C₂×C₂₃	#432
prime radical	C₂³×C₂₃	M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂₃×#97 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#364	C₂	semidirect
4. C₂₃×#347	C₂	semidirect
37. #2165	C₂₃	direct (N × H)
47. #364	C₂×C₂₃	semidirect
49. #347	C₂×C₂₃	semidirect
61. C₂₃	#2165	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×M₁₆×C₂₃	2
C₂₃×#364	2
C₂₃×#349	2
C₂₃×#347	2
#2165	23

Subgroups — C23×#2165 #15669784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#2165 #15669784