Subgroups — #14558508

Order 2368.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596953	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#11924593	C₂	1	4	yes	maximal, complemented
4	C₂×#10596966	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₃₇	C₄	1	1	yes	characteristic
6	#10596966	—	2	2	no	—
7	#10596966	—	2	2	no	—
8	C₂×D₁₄₈	C₄	1	2	yes	—
9	C₂×D₁₄₈	C₄	1	1	yes	characteristic
10	C₂×C₄×D₃₇	C₂²	1	2	yes	—
11	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
12	C₂×#64438	C₂²	1	2	yes	—
13	C₂×#64438	C₂²	1	2	yes	—
14	#10596953	—	2	2	no	—
15	D₃₇⋊C₈	—	2	2	no	—
16	C₂²×D₃₇	C₂×C₄	1	2	yes	—
17	C₂²×D₃₇	C₂×C₄	1	1	yes	characteristic
18	Q₈×C₃₇	—	2	2	no	—
19	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
22	D₁₄₈	—	2	4	no	—
23	D₁₄₈	—	2	2	no	—
24	C₄×D₃₇	—	2	2	no	—
25	C₄×D₃₇	—	2	2	no	—
26	C₄×D₃₇	D₄	1	2	yes	—
27	C₄×D₃₇	D₄	1	2	yes	—
28	#64438	—	2	2	no	—
29	#64438	—	2	2	no	—
30	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×D₃₇	—	2	2	no	—
32	C₂×D₃₇	—	2	2	no	—
33	C₂×D₃₇	—	2	4	no	—
34	C₂×D₃₇	C₂²⋊C₄	1	2	yes	—
35	C₄×C₃₇	—	2	2	no	—
36	C₄×C₃₇	C₂²⋊C₄	1	2	yes	—
37	Dic₃₇	C₂×D₄	1	1	yes	characteristic
38	Dic₃₇	C₂×D₄	1	1	yes	characteristic
39	C₂×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₃₇	#131	1	2	yes	—
41	D₃₇	—	2	2	no	—
42	D₃₇	—	4	2	no	—
43	#408	—	37	1	no	maximal, Sylow
44	C₃₇	#408	1	1	yes	characteristic, complemented, Sylow
45	C₂×#41	—	37	1	no	—
46	C₂×M₁₆	—	37	1	no	—
47	C₂²×C₈	—	37	1	no	—
48	C₂²⋊C₈	—	37	4	no	—
49	#41	—	74	2	no	—
50	#41	—	74	2	no	—
51	C₂×Q₈	#3866	1	1	yes	characteristic
52	C₂×D₄	—	37	2	no	—
53	C₂×D₄	—	37	1	no	—
54	C₂²×C₄	—	37	1	no	—
55	C₂²×C₄	—	37	2	no	—
56	M₁₆	—	74	2	no	—
57	C₂×C₈	—	37	2	no	—
58	C₂×C₈	—	37	2	no	—
59	C₂×C₈	—	74	2	no	—
60	C₂³	—	37	1	no	—
61	C₂³	—	37	2	no	—
62	Q₈	—	2	2	no	—
63	D₄	—	74	4	no	—
64	D₄	—	74	2	no	—
65	C₂×C₄	—	37	1	no	—
66	C₂×C₄	—	37	2	no	—
67	C₂×C₄	—	37	2	no	—
68	C₂×C₄	—	74	2	no	—
69	C₂×C₄	—	74	2	no	—
70	C₂×C₄	C₂×#3866	1	2	yes	—
71	C₂×C₄	C₂×#3866	1	1	yes	characteristic
72	C₈	—	74	2	no	—
73	C₈	—	74	2	no	—
74	C₂²	—	37	2	no	—
75	C₂²	—	74	2	no	—
76	C₂²	—	74	2	no	—
77	C₂²	—	74	4	no	—
78	C₂²	C₂²×#3866	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	—	37	1	no	—
81	C₄	—	37	1	no	—
82	C₄	C₂²⋊#3866	1	2	yes	—
83	C₂	—	74	2	no	—
84	C₂	—	148	2	no	—
85	C₂	C₂×C₂²⋊#3866	1	1	yes	characteristic
86	C₂	#11924624	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#3866
commutator, socle	C₂²×C₃₇	C₂²×C₄
Fitting	C₂×Q₈×C₃₇	C₄
prime radical	C₂×#10596966	C₂
cosocle	C₂×Dic₃₇	C₂³
hypercenter	C₂×Q₈	#3866
hypocenter	C₃₇	#408
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#10596953	C₂	semidirect
2. C₂×D₃₇⋊C₈	C₂	semidirect
3. #11924593	C₂	semidirect
44. C₃₇	#408	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10596953	2
C₂×D₃₇⋊C₈	2
#11924593	2
C₂×#10596966	2
#408	37