Subgroups — C₂×#13092247 #15675189

Order 2944.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625001	C₂	1	2	yes	maximal
2	#13092247	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
5	C₂×#67267	—	2	2	no	—
6	C₂×C₁₆×C₂₃	C₄	1	2	yes	—
7	C₂×C₁₆×C₂₃	C₄	1	2	yes	—
8	C₂×C₁₆×C₂₃	C₂²	1	2	yes	—
9	#10625001	—	2	2	no	—
10	#10625001	C₂²	1	4	yes	—
11	C₂²×C₄×C₂₃	D₄	1	1	yes	characteristic
12	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
15	C₂×C₈×C₂₃	Q₈	1	1	yes	characteristic
16	C₂×C₈×C₂₃	Q₈	1	1	yes	characteristic
17	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
18	#67267	—	2	4	no	—
19	#67267	—	4	2	no	—
20	C₂×C₂₃⋊C₈	—	4	2	no	—
21	C₁₆×C₂₃	C₂×C₄	1	4	yes	—
22	C₂³×C₂₃	Q₁₆	1	1	yes	characteristic
23	C₂×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
26	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
27	C₂×C₄×C₂₃	Q₁₆	1	1	yes	characteristic
28	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
29	C₈×C₂₃	C₄⋊C₄	1	1	yes	characteristic
30	C₈×C₂₃	C₄⋊C₄	1	1	yes	characteristic
31	C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₂₃	C₂×Q₈	1	1	yes	characteristic
33	C₂₃⋊C₈	—	4	4	no	—
34	C₂×#368	—	23	1	no	maximal, Sylow
35	C₂²×C₂₃	—	2	2	no	—
36	C₂²×C₂₃	#107	1	1	yes	characteristic
37	C₂²×C₂₃	#107	1	1	yes	characteristic
38	C₂²×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
39	C₄×C₂₃	#107	1	1	yes	characteristic
40	C₄×C₂₃	#107	1	1	yes	characteristic
41	C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
43	C₂²×C₁₆	D₂₃	1	1	yes	characteristic
44	C₂×#108	—	23	2	no	—
45	#368	—	23	4	no	—
46	C₂×C₂₃	—	2	1	no	—
47	C₂×C₂₃	—	2	1	no	—
48	C₂×C₂₃	#368	1	2	yes	complemented
49	C₂×C₂₃	C₂×#107	1	1	yes	characteristic
50	C₂×M₁₆	—	46	2	no	—
51	C₂²×C₈	C₂×D₂₃	1	1	yes	characteristic
52	C₂×C₁₆	Dic₂₃	1	2	yes	—
53	C₂×C₁₆	Dic₂₃	1	2	yes	—
54	C₂×C₁₆	C₂×D₂₃	1	2	yes	—
55	#108	—	23	4	no	—
56	#108	—	46	2	no	—
57	C₂₃	C₂×#368	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	D₉₂	1	1	yes	characteristic
59	M₁₆	—	46	4	no	—
60	M₁₆	—	92	2	no	—
61	C₂×C₈	—	92	2	no	—
62	C₂×C₈	Dic₄₆	1	1	yes	characteristic
63	C₂×C₈	Dic₄₆	1	1	yes	characteristic
64	C₂×C₈	D₉₂	1	1	yes	characteristic
65	C₂×C₈	C₂×Dic₂₃	1	1	yes	characteristic
66	C₂×C₈	C₂×Dic₂₃	1	1	yes	characteristic
67	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
68	C₁₆	C₂×Dic₂₃	1	4	yes	—
69	C₂³	Dic₉₂	1	1	yes	characteristic
70	C₂×C₄	D₁₈₄	1	1	yes	characteristic
71	C₂×C₄	D₁₈₄	1	1	yes	characteristic
72	C₂×C₄	Dic₉₂	1	1	yes	characteristic
73	C₂×C₄	C₄⋊Dic₂₃	1	1	yes	characteristic
74	C₂×C₄	C₄⋊Dic₂₃	1	1	yes	characteristic
75	C₂×C₄	C₂×D₉₂	1	1	yes	characteristic
76	C₈	—	92	4	no	—
77	C₈	C₄⋊Dic₂₃	1	1	yes	characteristic
78	C₈	C₄⋊Dic₂₃	1	1	yes	characteristic
79	C₈	C₂×Dic₄₆	1	1	yes	characteristic
80	C₈	C₂²×Dic₂₃	1	1	yes	characteristic
81	C₂²	—	2	2	no	—
82	C₂²	#10625000	1	1	yes	characteristic
83	C₂²	#10625000	1	1	yes	characteristic
84	C₂²	C₂×Dic₉₂	1	1	yes	characteristic
85	C₄	#10625000	1	1	yes	characteristic
86	C₄	#10625000	1	1	yes	characteristic
87	C₄	C₂×D₁₈₄	1	1	yes	characteristic
88	C₄	C₂×C₄⋊Dic₂₃	1	1	yes	characteristic
89	C₂	—	2	1	no	—
90	C₂	—	2	1	no	—
91	C₂	#13092247	1	2	yes	direct product factor
92	C₂	C₂×#10625000	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₈₄
commutator	C₈×C₂₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₃
Fitting	C₂²×C₁₆×C₂₃	C₂
socle	C₂²×C₂₃	#107
prime radical	C₂³×C₂₃	Q₁₆
cosocle	C₂×C₈×C₂₃	C₂³
hypercenter	C₂²×C₁₆	D₂₃
hypocenter	C₂₃	C₂×#368
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #13092247	C₂	direct (N × H)
48. C₂×C₂₃	#368	semidirect
57. C₂₃	C₂×#368	semidirect
91. C₂	#13092247	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×#10625001	2
#13092247	2
C₂²×C₁₆×C₂₃	2
C₂×#368	23

Subgroups — C2×#13092247 #15675189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13092247 #15675189