Subgroups — C₂×#26041109 #37535513

Order 23168.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19153752	C₂	1	2	yes	maximal
2	#26041109	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₁₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#15668433	—	2	2	no	—
5	#19153752	—	2	2	no	—
6	#19153752	C₂²	1	4	yes	—
7	C₂²×C₈×C₁₈₁	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₁₈₁	C₄	1	2	yes	—
9	C₂×C₁₆×C₁₈₁	C₄	1	2	yes	—
10	C₂×C₁₆×C₁₈₁	C₂²	1	2	yes	—
11	#15668433	—	2	4	no	—
12	#15668433	—	4	2	no	—
13	C₂×#13089678	—	4	2	no	—
14	C₂²×C₄×C₁₈₁	D₄	1	1	yes	characteristic
15	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₈₁	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₈₁	Q₈	1	1	yes	characteristic
19	C₂×C₈×C₁₈₁	Q₈	1	1	yes	characteristic
20	C₂×C₈×C₁₈₁	C₂³	1	1	yes	characteristic
21	C₁₆×C₁₈₁	C₂×C₄	1	4	yes	—
22	#13089678	—	4	4	no	—
23	C₂³×C₁₈₁	Q₁₆	1	1	yes	characteristic
24	C₂×C₄×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₈₁	D₈	1	1	yes	characteristic
27	C₂×C₄×C₁₈₁	D₈	1	1	yes	characteristic
28	C₂×C₄×C₁₈₁	Q₁₆	1	1	yes	characteristic
29	C₂×C₄×C₁₈₁	C₂×D₄	1	1	yes	characteristic
30	C₈×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
31	C₈×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
32	C₈×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₁₈₁	C₂×Q₈	1	1	yes	characteristic
34	C₂²×C₁₈₁	—	2	2	no	—
35	C₂²×C₁₈₁	#107	1	1	yes	characteristic
36	C₂²×C₁₈₁	#107	1	1	yes	characteristic
37	C₂²×C₁₈₁	C₂×Q₁₆	1	1	yes	characteristic
38	C₄×C₁₈₁	#107	1	1	yes	characteristic
39	C₄×C₁₈₁	#107	1	1	yes	characteristic
40	C₄×C₁₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₄×C₁₈₁	C₂×D₈	1	1	yes	characteristic
42	C₂×C₁₈₁	—	2	1	no	—
43	C₂×C₁₈₁	—	2	1	no	—
44	C₂×C₁₈₁	#368	1	2	yes	complemented
45	C₂×C₁₈₁	C₂×#107	1	1	yes	characteristic
46	C₁₈₁	C₂×#368	1	1	yes	characteristic, complemented, Sylow
47	C₂×#368	—	181	1	no	maximal, Sylow
48	C₂²×C₁₆	D₁₈₁	1	1	yes	characteristic
49	C₂×#108	—	181	2	no	—
50	#368	—	181	4	no	—
51	C₂×M₁₆	—	362	2	no	—
52	C₂²×C₈	C₂×D₁₈₁	1	1	yes	characteristic
53	C₂×C₁₆	Dic₁₈₁	1	2	yes	—
54	C₂×C₁₆	Dic₁₈₁	1	2	yes	—
55	C₂×C₁₆	C₂×D₁₈₁	1	2	yes	—
56	#108	—	362	2	no	—
57	#108	—	181	4	no	—
58	C₂²×C₄	D₇₂₄	1	1	yes	characteristic
59	M₁₆	—	362	4	no	—
60	M₁₆	—	724	2	no	—
61	C₂×C₈	—	724	2	no	—
62	C₂×C₈	C₂×Dic₁₈₁	1	1	yes	characteristic
63	C₂×C₈	C₂×Dic₁₈₁	1	1	yes	characteristic
64	C₂×C₈	D₇₂₄	1	1	yes	characteristic
65	C₂×C₈	Dic₃₆₂	1	1	yes	characteristic
66	C₂×C₈	Dic₃₆₂	1	1	yes	characteristic
67	C₂×C₈	C₂²×D₁₈₁	1	1	yes	characteristic
68	C₁₆	C₂×Dic₁₈₁	1	4	yes	—
69	C₂³	Dic₇₂₄	1	1	yes	characteristic
70	C₂×C₄	C₄⋊Dic₁₈₁	1	1	yes	characteristic
71	C₂×C₄	C₄⋊Dic₁₈₁	1	1	yes	characteristic
72	C₂×C₄	D₁₄₄₈	1	1	yes	characteristic
73	C₂×C₄	D₁₄₄₈	1	1	yes	characteristic
74	C₂×C₄	Dic₇₂₄	1	1	yes	characteristic
75	C₂×C₄	C₂×D₇₂₄	1	1	yes	characteristic
76	C₈	—	724	4	no	—
77	C₈	C₄⋊Dic₁₈₁	1	1	yes	characteristic
78	C₈	C₄⋊Dic₁₈₁	1	1	yes	characteristic
79	C₈	C₂²×Dic₁₈₁	1	1	yes	characteristic
80	C₈	C₂×Dic₃₆₂	1	1	yes	characteristic
81	C₂²	—	2	2	no	—
82	C₂²	#19153750	1	1	yes	characteristic
83	C₂²	#19153750	1	1	yes	characteristic
84	C₂²	C₂×Dic₇₂₄	1	1	yes	characteristic
85	C₄	#19153750	1	1	yes	characteristic
86	C₄	#19153750	1	1	yes	characteristic
87	C₄	C₂×C₄⋊Dic₁₈₁	1	1	yes	characteristic
88	C₄	C₂×D₁₄₄₈	1	1	yes	characteristic
89	C₂	—	2	1	no	—
90	C₂	—	2	1	no	—
91	C₂	#26041109	1	2	yes	direct product factor
92	C₂	C₂×#19153750	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₄₄₈
commutator	C₈×C₁₈₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₈₁
Fitting	C₂²×C₁₆×C₁₈₁	C₂
socle	C₂²×C₁₈₁	#107
prime radical	C₂³×C₁₈₁	Q₁₆
cosocle	C₂×C₈×C₁₈₁	C₂³
hypercenter	C₂²×C₁₆	D₁₈₁
hypocenter	C₁₈₁	C₂×#368
LCS	G ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
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. #26041109	C₂	direct (N × H)
44. C₂×C₁₈₁	#368	semidirect
46. C₁₈₁	C₂×#368	semidirect
91. C₂	#26041109	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×#19153752	2
#26041109	2
C₂²×C₁₆×C₁₈₁	2
C₂×#368	181

Subgroups — C2×#26041109 #37535513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26041109 #37535513