Subgroups — #14557927

Order 2368.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₄₈	C₂	1	2	yes	maximal, complemented
2	C₂×#10596930	C₂	1	2	yes	maximal
3	#11924536	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924524	C₂	1	1	yes	maximal, characteristic
5	#97×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₄₈	C₂²	1	1	yes	characteristic
7	C₂×Dic₇₄	C₂²	1	1	yes	characteristic
8	C₂×Dic₇₄	C₂²	1	2	yes	—
9	C₂×C₈×C₃₇	C₂²	1	2	yes	—
10	C₄²×C₃₇	C₂²	1	1	yes	characteristic
11	#10596938	—	2	2	no	—
12	C₄⋊Dic₃₇	—	2	2	no	—
13	Dic₁₄₈	—	2	4	no	—
14	#10596930	—	2	4	no	—
15	C₂²×D₃₇	—	2	1	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	C₂×Dic₃₇	—	2	1	no	—
20	D₁₄₈	—	2	2	no	—
21	Dic₇₄	—	2	2	no	—
22	Dic₇₄	—	2	2	no	—
23	Dic₇₄	—	2	2	no	—
24	C₈×C₃₇	D₄	1	4	yes	—
25	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
26	C₂×D₃₇	—	4	1	no	—
27	C₂×D₃₇	—	4	2	no	—
28	C₄×C₃₇	—	2	2	no	—
29	C₄×C₃₇	C₂×D₄	1	2	yes	—
30	Dic₃₇	—	4	2	no	—
31	Dic₃₇	—	4	1	no	—
32	C₂×C₃₇	#127	1	1	yes	characteristic
33	C₂×C₃₇	#137	1	2	yes	—
34	D₃₇	—	8	1	no	—
35	#497	—	37	1	no	maximal, Sylow
36	C₃₇	#497	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₁₆	—	37	2	no	—
38	C₂×SD₁₆	—	37	2	no	—
39	C₄⋊Q₈	—	37	1	no	—
40	#124	—	37	1	no	—
41	#97	D₃₇	1	1	yes	characteristic, complemented
42	C₂×Q₈	—	37	1	no	—
43	C₂×Q₈	—	37	2	no	—
44	C₂×D₄	—	37	1	no	—
45	Q₁₆	—	74	4	no	—
46	SD₁₆	—	74	4	no	—
47	C₂×C₈	C₂×D₃₇	1	2	yes	—
48	C₄⋊C₄	—	74	2	no	—
49	C₂²⋊C₄	—	74	2	no	—
50	C₄²	C₂×D₃₇	1	1	yes	characteristic
51	C₂³	—	74	1	no	—
52	Q₈	—	74	2	no	—
53	Q₈	—	74	2	no	—
54	Q₈	—	74	2	no	—
55	D₄	—	74	2	no	—
56	C₂×C₄	—	74	1	no	—
57	C₂×C₄	—	74	2	no	—
58	C₂×C₄	D₁₄₈	1	2	yes	—
59	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
60	C₈	D₁₄₈	1	4	yes	—
61	C₂²	—	148	1	no	—
62	C₂²	—	148	2	no	—
63	C₂²	C₂×D₁₄₈	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	148	1	no	—
66	C₄	—	148	2	no	—
67	C₄	C₂×D₁₄₈	1	2	yes	—
68	C₂	—	296	1	no	—
69	C₂	#11924533	1	1	yes	characteristic
70	C₂	#11924569	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
prime radical	C₂×D₁₄₈	C₂²
hypercenter	#97	D₃₇
hypocenter	C₃₇	#497
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×Dic₁₄₈	C₂	semidirect
3. #11924536	C₂	semidirect
5. #97×C₃₇	C₂	semidirect
36. C₃₇	#497	semidirect
41. #97	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
#11924536	2
#11924524	2
#97×C₃₇	2
#497	37