Subgroups — #14557917

Order 2368.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₄₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10596930	C₂	1	2	yes	maximal, complemented
3	C₂×D₂₉₆	C₂	1	1	yes	maximal, characteristic
4	#11924524	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₄₈	C₂²	1	2	yes	—
7	C₂×Dic₇₄	C₂²	1	2	yes	—
8	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
10	C₄²×C₃₇	C₂²	1	1	yes	characteristic
11	#10596938	—	2	4	no	—
12	Dic₁₄₈	—	2	2	no	—
13	D₂₉₆	—	2	2	no	—
14	#10596930	—	2	4	no	—
15	C₂²×D₃₇	—	2	2	no	—
16	C₂×C₄×C₃₇	D₄	1	2	yes	—
17	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
18	C₂×Dic₃₇	—	2	2	no	—
19	D₁₄₈	—	2	2	no	—
20	D₁₄₈	—	2	2	no	—
21	Dic₇₄	—	2	2	no	—
22	Dic₇₄	—	2	2	no	—
23	C₈×C₃₇	D₄	1	2	yes	—
24	C₈×C₃₇	D₄	1	2	yes	—
25	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
26	C₂×D₃₇	—	4	2	no	—
27	C₂×D₃₇	—	4	4	no	—
28	C₄×C₃₇	—	2	2	no	—
29	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
30	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
31	Dic₃₇	—	4	2	no	—
32	C₂×C₃₇	#127	1	1	yes	characteristic
33	C₂×C₃₇	#135	1	2	yes	—
34	D₃₇	—	8	2	no	—
35	#495	—	37	1	no	maximal, Sylow
36	C₃₇	#495	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₁₆	—	37	1	no	—
38	C₂×SD₁₆	—	37	2	no	—
39	C₂×D₈	—	37	1	no	—
40	#124	—	37	2	no	—
41	C₄×C₈	D₃₇	1	1	yes	characteristic, complemented
42	C₂×Q₈	—	37	2	no	—
43	C₂×D₄	—	37	2	no	—
44	Q₁₆	—	74	2	no	—
45	SD₁₆	—	74	4	no	—
46	D₈	—	74	2	no	—
47	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
48	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
49	C₂²⋊C₄	—	74	4	no	—
50	C₄²	C₂×D₃₇	1	1	yes	characteristic
51	C₂³	—	74	2	no	—
52	Q₈	—	74	2	no	—
53	Q₈	—	74	2	no	—
54	D₄	—	74	2	no	—
55	D₄	—	74	2	no	—
56	C₂×C₄	—	74	2	no	—
57	C₂×C₄	D₁₄₈	1	2	yes	—
58	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
59	C₈	D₁₄₈	1	2	yes	—
60	C₈	D₁₄₈	1	2	yes	—
61	C₂²	—	148	2	no	—
62	C₂²	—	148	4	no	—
63	C₂²	C₂×D₁₄₈	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	148	2	no	—
66	C₄	C₂×D₁₄₈	1	1	yes	characteristic
67	C₄	C₂×D₁₄₈	1	1	yes	characteristic
68	C₂	—	296	2	no	—
69	C₂	#11924533	1	1	yes	characteristic
70	C₂	#11924558	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₄₈
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	C₄×C₈×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
prime radical	C₂×D₂₉₆	C₂
hypercenter	C₄×C₈	D₃₇
hypocenter	C₃₇	#495
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₁₄₈	C₂	semidirect
2. C₂×#10596930	C₂	semidirect
4. #11924524	C₂	semidirect
5. C₄×C₈×C₃₇	C₂	semidirect
36. C₃₇	#495	semidirect
41. C₄×C₈	D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₄₈	2
C₂×#10596930	2
C₂×D₂₉₆	2
#11924524	2
C₄×C₈×C₃₇	2
#495	37