Subgroups — #14557922

Order 2368.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596930	C₂	1	2	yes	maximal, complemented
2	C₂×D₂₉₆	C₂	1	2	yes	maximal, complemented
3	#11924533	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924524	C₂	1	1	yes	maximal, characteristic, complemented
5	#97×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₄₈	—	2	2	no	—
7	C₂×D₁₄₈	C₂²	1	1	yes	characteristic
8	C₂×D₁₄₈	C₂²	1	2	yes	—
9	C₂×Dic₇₄	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₃₇	C₂²	1	2	yes	—
11	C₄²×C₃₇	C₂²	1	1	yes	characteristic
12	#10596938	—	2	2	no	—
13	D₂₉₆	—	2	4	no	—
14	#10596930	—	2	4	no	—
15	C₂²×D₃₇	—	2	1	no	—
16	C₂²×D₃₇	—	2	2	no	—
17	C₂×C₄×C₃₇	D₄	1	2	yes	—
18	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
19	C₂×Dic₃₇	—	2	1	no	—
20	D₁₄₈	—	2	2	no	—
21	D₁₄₈	—	2	2	no	—
22	D₁₄₈	—	2	2	no	—
23	D₁₄₈	—	4	4	no	—
24	Dic₇₄	—	2	2	no	—
25	C₈×C₃₇	D₄	1	4	yes	complemented
26	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
27	C₂×D₃₇	—	4	2	no	—
28	C₂×D₃₇	—	4	1	no	—
29	C₂×D₃₇	—	4	4	no	—
30	C₂×D₃₇	—	4	2	no	—
31	C₄×C₃₇	—	2	2	no	—
32	C₄×C₃₇	C₂×D₄	1	2	yes	—
33	Dic₃₇	—	4	1	no	—
34	C₂×C₃₇	#127	1	1	yes	characteristic
35	C₂×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
36	D₃₇	—	8	2	no	—
37	D₃₇	—	8	1	no	—
38	#496	—	37	1	no	maximal, Sylow
39	C₃₇	#496	1	1	yes	characteristic, complemented, Sylow
40	C₂×SD₁₆	—	37	2	no	—
41	C₂×D₈	—	37	2	no	—
42	#127	—	37	1	no	—
43	#124	—	37	1	no	—
44	#97	D₃₇	1	1	yes	characteristic, complemented
45	C₂×Q₈	—	37	1	no	—
46	C₂×D₄	—	37	1	no	—
47	C₂×D₄	—	37	2	no	—
48	C₂×D₄	—	74	2	no	—
49	SD₁₆	—	74	4	no	—
50	D₈	—	74	4	no	—
51	C₂×C₈	C₂×D₃₇	1	2	yes	—
52	C₂²⋊C₄	—	74	2	no	—
53	C₄²	C₂×D₃₇	1	1	yes	characteristic
54	C₂³	—	74	1	no	—
55	C₂³	—	74	2	no	—
56	Q₈	—	74	2	no	—
57	D₄	—	74	2	no	—
58	D₄	—	74	2	no	—
59	D₄	—	74	2	no	—
60	D₄	—	148	4	no	—
61	C₂×C₄	—	74	1	no	—
62	C₂×C₄	D₁₄₈	1	2	yes	—
63	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
64	C₈	D₁₄₈	1	4	yes	complemented
65	C₂²	—	148	1	no	—
66	C₂²	—	148	2	no	—
67	C₂²	—	148	4	no	—
68	C₂²	—	148	2	no	—
69	C₂²	C₂×D₁₄₈	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	148	1	no	—
72	C₄	C₂×D₁₄₈	1	2	yes	—
73	C₂	—	296	2	no	—
74	C₂	—	296	1	no	—
75	C₂	#11924533	1	1	yes	characteristic
76	C₂	#11924564	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₄₈
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	#97×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
hypercenter	#97	D₃₇
hypocenter	C₃₇	#496
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
1. C₂×#10596930	C₂	semidirect
2. C₂×D₂₉₆	C₂	semidirect
3. #11924533	C₂	semidirect
4. #11924524	C₂	semidirect
5. #97×C₃₇	C₂	semidirect
25. C₈×C₃₇	D₄	semidirect
39. C₃₇	#496	semidirect
44. #97	D₃₇	semidirect
64. C₈	D₁₄₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10596930	2
C₂×D₂₉₆	2
#11924533	2
#11924524	2
#97×C₃₇	2
#496	37