Subgroups — C₂×#10625006 #13092396

Order 1472.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₄₆	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#67267	C₂	1	1	yes	maximal, characteristic
4	#10625006	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
6	C₂²×Dic₂₃	C₄	1	2	yes	—
7	C₂×Dic₄₆	—	2	1	no	—
8	C₂×Dic₄₆	—	2	1	no	—
9	C₂×Dic₄₆	—	2	1	no	—
10	C₂×Dic₄₆	—	2	1	no	—
11	C₂×Dic₄₆	C₄	1	2	yes	—
12	C₂×Dic₄₆	C₂²	1	2	yes	—
13	M₁₆×C₂₃	—	2	1	no	—
14	M₁₆×C₂₃	C₂²	1	2	yes	—
15	C₂×C₈×C₂₃	—	2	1	no	—
16	#67267	—	2	1	no	—
17	#67267	C₂²	1	2	yes	—
18	C₂×C₂₃⋊C₈	—	2	1	no	—
19	C₂³×C₂₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
22	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
23	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
24	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
25	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
26	C₂×Dic₂₃	—	2	2	no	—
27	C₂×Dic₂₃	—	2	2	no	—
28	C₂×Dic₂₃	C₂×C₄	1	4	yes	—
29	Dic₄₆	—	2	2	no	—
30	Dic₄₆	—	2	2	no	—
31	Dic₄₆	—	2	2	no	—
32	Dic₄₆	—	2	2	no	—
33	C₈×C₂₃	—	2	2	no	—
34	C₂₃⋊C₈	—	2	2	no	—
35	C₂²×C₂₃	—	2	2	no	—
36	C₂²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
37	C₂²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
38	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
39	C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
40	C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
41	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
42	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
43	Dic₂₃	—	2	4	no	—
44	C₂×#101	—	23	1	no	maximal, Sylow
45	C₂×C₂₃	—	2	1	no	—
46	C₂×C₂₃	—	2	1	no	—
47	C₂×C₂₃	#101	1	2	yes	complemented
48	C₂×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×Q₈	—	23	1	no	—
50	C₂×M₁₆	—	23	1	no	—
51	C₂×M₁₆	D₂₃	1	1	yes	characteristic
52	#101	—	23	4	no	—
53	C₂₃	C₂×#101	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	23	2	no	—
55	C₂×Q₈	—	23	2	no	—
56	C₂×Q₈	—	46	1	no	—
57	C₂×Q₈	—	46	1	no	—
58	C₂×Q₈	—	46	1	no	—
59	C₂×Q₈	—	46	1	no	—
60	C₂²×C₄	—	23	2	no	—
61	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
62	M₁₆	—	2	1	no	—
63	M₁₆	—	23	2	no	—
64	M₁₆	—	46	1	no	—
65	M₁₆	C₂×D₂₃	1	2	yes	—
66	C₂×C₈	—	2	1	no	—
67	C₂×C₈	—	46	1	no	—
68	C₂³	C₄×D₂₃	1	1	yes	characteristic
69	Q₈	—	46	2	no	—
70	Q₈	—	46	2	no	—
71	Q₈	—	46	2	no	—
72	Q₈	—	46	2	no	—
73	C₂×C₄	—	23	4	no	—
74	C₂×C₄	—	46	2	no	—
75	C₂×C₄	—	46	2	no	—
76	C₂×C₄	C₄×D₂₃	1	1	yes	characteristic
77	C₂×C₄	D₉₂	1	1	yes	characteristic
78	C₂×C₄	D₉₂	1	1	yes	characteristic
79	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
80	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
81	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
82	C₈	—	2	2	no	—
83	C₈	—	46	2	no	—
84	C₂²	—	2	2	no	—
85	C₂²	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
86	C₂²	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
87	C₂²	C₂×C₄×D₂₃	1	1	yes	characteristic
88	C₄	—	46	4	no	—
89	C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
90	C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
91	C₄	C₂×D₉₂	1	1	yes	characteristic
92	C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
93	C₂	—	2	1	no	—
94	C₂	—	2	1	no	—
95	C₂	#10625006	1	2	yes	direct product factor
96	C₂	C₂×(C₂×D₂₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₂₃)⋊C₄
commutator	C₂²×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂×M₁₆×C₂₃	C₂
socle	C₂²×C₂₃	C₂²⋊C₄
prime radical	C₂³×C₂₃	C₂×C₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₂×M₁₆	D₂₃
hypocenter	C₂₃	C₂×#101
LCS	G ▷ C₂²×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. #10625006	C₂	direct (N × H)
47. C₂×C₂₃	#101	semidirect
53. C₂₃	C₂×#101	semidirect
95. C₂	#10625006	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₄₆	2
C₂×M₁₆×C₂₃	2
C₂×#67267	2
#10625006	2
C₂×#101	23

Subgroups — C2×#10625006 #13092396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10625006 #13092396