Subgroups — C₂₃×#1377 #15668996

Order 2944.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×M₃₂	C₂	1	2	yes	maximal
2	C₂×C₂₃×#97	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₂₃	C₄	1	1	yes	characteristic
4	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
5	C₂×C₄²×C₂₃	C₄	1	1	yes	characteristic
6	C₂₃×M₃₂	—	2	2	no	—
7	C₂₃×M₃₂	C₄	1	4	yes	complemented
8	C₂×C₁₆×C₂₃	—	2	2	no	—
9	C₂₃×#97	—	2	2	no	—
10	C₂²×C₄×C₂₃	C₈	1	2	yes	—
11	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₂₃	—	2	1	no	—
13	C₂×C₈×C₂₃	—	2	1	no	—
14	C₂×C₈×C₂₃	C₈	1	2	yes	—
15	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
16	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
17	C₂×C₈×C₂₃	D₄	1	2	yes	—
18	C₂×C₈×C₂₃	Q₈	1	1	yes	characteristic
19	C₄²×C₂₃	—	2	1	no	—
20	C₄²×C₂₃	—	2	1	no	—
21	C₁₆×C₂₃	—	2	4	no	—
22	C₂³×C₂₃	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₂₃	—	2	2	no	—
24	C₂×C₄×C₂₃	—	4	2	no	—
25	C₂×C₄×C₂₃	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₂₃	M₁₆	1	1	yes	characteristic
30	C₂×C₄×C₂₃	M₁₆	1	1	yes	characteristic
31	C₈×C₂₃	—	2	2	no	—
32	C₈×C₂₃	C₂²⋊C₄	1	2	yes	—
33	C₈×C₂₃	C₄⋊C₄	1	2	yes	—
34	#1377	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂²×C₂₃	—	2	2	no	—
36	C₂²×C₂₃	C₄×C₈	1	1	yes	characteristic
37	C₂²×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
38	C₂²×C₂₃	C₄⋊C₈	1	1	yes	characteristic
39	C₄×C₂₃	—	4	2	no	—
40	C₄×C₂₃	#95	1	1	yes	characteristic
41	C₄×C₂₃	#97	1	1	yes	characteristic
42	C₄×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
43	C₄×C₂₃	C₄⋊C₈	1	1	yes	characteristic
44	C₂×M₃₂	C₂×C₂₃	1	2	yes	—
45	C₂×#97	C₂×C₂₃	1	1	yes	characteristic
46	C₂×C₂₃	—	2	1	no	—
47	C₂×C₂₃	—	2	1	no	—
48	C₂×C₂₃	#336	1	1	yes	characteristic
49	C₂×C₂₃	#349	1	2	yes	—
50	C₂²×C₈	C₄×C₂₃	1	1	yes	characteristic
51	C₂²×C₈	C₂²×C₂₃	1	1	yes	characteristic
52	C₂×C₄²	C₄×C₂₃	1	1	yes	characteristic
53	M₃₂	—	2	2	no	—
54	M₃₂	C₄×C₂₃	1	4	yes	complemented
55	C₂×C₁₆	—	2	2	no	—
56	#97	—	2	2	no	—
57	C₂₃	#1377	1	1	yes	characteristic, direct product factor, Sylow
58	C₂²×C₄	C₈×C₂₃	1	2	yes	—
59	C₂²×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	C₈×C₂₃	1	2	yes	—
63	C₂×C₈	C₂×C₄×C₂₃	1	2	yes	—
64	C₂×C₈	D₄×C₂₃	1	1	yes	characteristic
65	C₂×C₈	D₄×C₂₃	1	2	yes	—
66	C₂×C₈	Q₈×C₂₃	1	1	yes	characteristic
67	C₄²	—	2	1	no	—
68	C₄²	—	2	1	no	—
69	C₁₆	—	2	4	no	—
70	C₂³	C₂×C₈×C₂₃	1	1	yes	characteristic
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	4	2	no	—
73	C₂×C₄	C₄²×C₂₃	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
75	C₂×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
76	C₂×C₄	C₂×C₈×C₂₃	1	1	yes	characteristic
77	C₂×C₄	M₁₆×C₂₃	1	1	yes	characteristic
78	C₂×C₄	M₁₆×C₂₃	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	C₂²⋊C₄×C₂₃	1	2	yes	—
81	C₈	C₄⋊C₄×C₂₃	1	2	yes	—
82	C₂²	—	2	2	no	—
83	C₂²	C₄×C₈×C₂₃	1	1	yes	characteristic
84	C₂²	C₂₃×C₂²⋊C₈	1	1	yes	characteristic
85	C₂²	C₂₃×C₄⋊C₈	1	1	yes	characteristic
86	C₄	—	4	2	no	—
87	C₄	C₂₃×#95	1	1	yes	characteristic
88	C₄	C₂₃×#97	1	1	yes	characteristic
89	C₄	C₂₃×C₂²⋊C₈	1	1	yes	characteristic
90	C₄	C₂₃×C₄⋊C₈	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	C₂₃×#336	1	1	yes	characteristic
94	C₂	C₂₃×#349	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²⋊C₄
commutator	C₂²	C₄×C₈×C₂₃
Frattini, cosocle	C₂²×C₈	C₂²×C₂₃
socle	C₂²×C₂₃	C₂²⋊C₈
prime radical	C₂³×C₂₃	C₂×C₈
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₂₃×M₃₂	C₄	semidirect
34. #1377	C₂₃	direct (N × H)
54. M₃₂	C₄×C₂₃	semidirect
57. C₂₃	#1377	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×M₃₂	2
C₂×C₂₃×#97	2
#1377	23

Subgroups — C23×#1377 #15668996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1377 #15668996