Subgroups — C₂×#14558462 #18010951

Order 4736.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924607	C₂	1	2	yes	maximal
2	#14558462	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×D₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596953	—	2	2	no	—
5	#11924607	—	2	2	no	—
6	#11924607	C₂²	1	4	yes	—
7	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
8	C₂×#10596925	C₄	1	1	yes	characteristic
9	C₁₆×D₃₇	C₄	1	2	yes	—
10	C₁₆×D₃₇	C₂²	1	2	yes	—
11	C₂×C₁₆×C₃₇	C₄	1	1	yes	characteristic
12	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
13	C₂×#64438	—	4	2	no	—
14	#10596953	—	2	4	no	—
15	#10596953	—	4	2	no	—
16	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂×#64436	Q₈	1	1	yes	characteristic
18	C₈×D₃₇	C₂×C₄	1	1	yes	characteristic
19	C₈×D₃₇	D₄	1	1	yes	characteristic
20	C₈×D₃₇	Q₈	1	1	yes	characteristic
21	C₈×D₃₇	C₂³	1	1	yes	characteristic
22	C₁₆×C₃₇	C₂×C₄	1	2	yes	—
23	#10596925	C₂×C₄	1	2	yes	—
24	C₂²×D₃₇	Q₁₆	1	1	yes	characteristic
25	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
26	C₂×Dic₃₇	D₈	1	1	yes	characteristic
27	C₄×D₃₇	C₄⋊C₄	1	1	yes	characteristic
28	C₄×D₃₇	D₈	1	1	yes	characteristic
29	C₄×D₃₇	Q₁₆	1	1	yes	characteristic
30	C₄×D₃₇	C₂×D₄	1	1	yes	characteristic
31	#64438	—	4	4	no	—
32	C₈×C₃₇	C₄⋊C₄	1	1	yes	characteristic
33	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
34	#64436	C₄⋊C₄	1	1	yes	characteristic
35	#64436	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₃₇	#107	1	1	yes	characteristic
37	C₂×D₃₇	—	2	2	no	—
38	C₂×D₃₇	#107	1	1	yes	characteristic
39	C₂×D₃₇	C₂×Q₁₆	1	1	yes	characteristic
40	C₄×C₃₇	#107	1	1	yes	characteristic
41	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
42	Dic₃₇	#107	1	1	yes	characteristic
43	Dic₃₇	C₂×D₈	1	1	yes	characteristic
44	C₂×#368	—	37	1	no	maximal, Sylow
45	C₂×C₃₇	#368	1	2	yes	complemented
46	C₂×C₃₇	C₂×#107	1	1	yes	characteristic
47	D₃₇	—	2	1	no	—
48	D₃₇	—	2	1	no	—
49	C₂²×C₁₆	—	37	1	no	—
50	C₂×#108	—	37	2	no	—
51	#368	—	37	4	no	—
52	C₃₇	C₂×#368	1	1	yes	characteristic, complemented, Sylow
53	C₂×M₁₆	—	74	2	no	—
54	C₂²×C₈	—	37	1	no	—
55	C₂×C₁₆	—	37	1	no	—
56	C₂×C₁₆	—	37	2	no	—
57	C₂×C₁₆	—	37	2	no	—
58	C₂×C₁₆	#3866	1	1	yes	characteristic
59	#108	—	37	4	no	—
60	#108	—	74	2	no	—
61	C₂²×C₄	—	37	1	no	—
62	M₁₆	—	74	4	no	—
63	M₁₆	—	148	2	no	—
64	C₂×C₈	—	37	1	no	—
65	C₂×C₈	—	37	1	no	—
66	C₂×C₈	—	37	1	no	—
67	C₂×C₈	—	37	1	no	—
68	C₂×C₈	—	37	1	no	—
69	C₂×C₈	—	148	2	no	—
70	C₂×C₈	C₂×#3866	1	1	yes	characteristic
71	C₁₆	—	37	2	no	—
72	C₁₆	C₂×#3866	1	2	yes	—
73	C₂³	—	37	1	no	—
74	C₂×C₄	—	37	1	no	—
75	C₂×C₄	—	37	1	no	—
76	C₂×C₄	—	37	1	no	—
77	C₂×C₄	—	37	1	no	—
78	C₂×C₄	—	37	1	no	—
79	C₂×C₄	C₄⋊#3866	1	1	yes	characteristic
80	C₈	—	37	1	no	—
81	C₈	—	37	1	no	—
82	C₈	—	148	4	no	—
83	C₈	C₄⋊#3866	1	1	yes	characteristic
84	C₈	C₂²×#3866	1	1	yes	characteristic
85	C₂²	—	37	1	no	—
86	C₂²	—	37	1	no	—
87	C₂²	—	74	2	no	—
88	C₂²	#11924605	1	1	yes	characteristic
89	C₄	—	37	1	no	—
90	C₄	—	37	1	no	—
91	C₄	#11924605	1	1	yes	characteristic
92	C₄	C₂×C₄⋊#3866	1	1	yes	characteristic
93	C₂	—	74	1	no	—
94	C₂	—	74	1	no	—
95	C₂	#14558462	1	2	yes	direct product factor
96	C₂	C₂×#11924605	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11924605
commutator	C₈×C₃₇	C₂²×C₄
Frattini	C₈	C₂²×#3866
Fitting	C₂×C₁₆×C₃₇	C₄
socle	C₂²×C₃₇	#107
prime radical	C₂²×D₃₇	Q₁₆
cosocle	C₈×D₃₇	C₂³
hypercenter	C₂×C₁₆	#3866
hypocenter	C₃₇	C₂×#368
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #14558462	C₂	direct (N × H)
45. C₂×C₃₇	#368	semidirect
52. C₃₇	C₂×#368	semidirect
95. C₂	#14558462	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×#11924607	2
#14558462	2
C₂×C₁₆×D₃₇	2
C₂×#368	37

Subgroups — C2×#14558462 #18010951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14558462 #18010951