Subgroups — #14558514

Order 2368.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924615	C₂	1	2	yes	maximal, complemented
2	#11924595	C₂	1	4	yes	maximal, complemented
3	C₂×#10596966	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₃₇	C₄	1	1	yes	characteristic, complemented
5	#10596966	—	2	2	no	—
6	#10596966	—	2	2	no	—
7	C₂×D₁₄₈	C₄	1	1	yes	characteristic, complemented
8	C₂×D₁₄₈	C₂²	1	2	yes	—
9	C₂×C₄×D₃₇	C₄	1	2	yes	complemented
10	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
11	C₂²⋊#3866	C₂²	1	4	yes	—
12	C₄⋊#3866	—	2	2	no	—
13	C₄×#3866	—	2	2	no	—
14	C₂²×D₃₇	C₂×C₄	1	2	yes	—
15	C₂²×D₃₇	C₂³	1	1	yes	characteristic
16	C₂×#3866	—	2	4	no	—
17	Q₈×C₃₇	—	2	2	no	—
18	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
21	D₁₄₈	—	2	4	no	—
22	D₁₄₈	—	2	2	no	—
23	C₄×D₃₇	—	2	2	no	—
24	C₄×D₃₇	—	2	2	no	—
25	C₄×D₃₇	D₄	1	2	yes	—
26	C₄×D₃₇	D₄	1	2	yes	—
27	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×D₃₇	—	2	2	no	—
29	C₂×D₃₇	—	4	1	no	—
30	C₂×D₃₇	—	4	2	no	—
31	C₂×D₃₇	C₂×D₄	1	2	yes	—
32	#3866	—	4	4	no	—
33	C₄×C₃₇	—	2	2	no	—
34	C₄×C₃₇	C₂²⋊C₄	1	2	yes	—
35	Dic₃₇	C₂²⋊C₄	1	1	yes	characteristic
36	Dic₃₇	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₃₇	—	2	1	no	—
38	C₂×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	D₃₇	—	2	2	no	—
40	D₃₇	—	4	2	no	—
41	#410	—	37	1	no	maximal, Sylow
42	C₃₇	#410	1	1	yes	characteristic, complemented, Sylow
43	C₂×#41	—	37	1	no	—
44	#117	—	37	2	no	—
45	#99	—	37	4	no	—
46	#41	—	74	2	no	—
47	#41	—	74	2	no	—
48	C₂×Q₈	#3866	1	1	yes	characteristic, complemented
49	C₂×D₄	—	37	2	no	—
50	C₂×D₄	—	37	1	no	—
51	C₂²×C₄	—	37	1	no	—
52	C₂²×C₄	—	37	2	no	—
53	C₄⋊C₄	—	74	2	no	—
54	C₂²⋊C₄	—	37	4	no	—
55	C₄²	—	74	2	no	—
56	C₂³	—	37	1	no	—
57	C₂³	—	37	2	no	—
58	Q₈	—	2	2	no	—
59	D₄	—	74	4	no	—
60	D₄	—	74	2	no	—
61	C₂×C₄	—	37	1	no	—
62	C₂×C₄	—	37	2	no	—
63	C₂×C₄	—	37	2	no	—
64	C₂×C₄	—	74	2	no	—
65	C₂×C₄	—	74	2	no	—
66	C₂×C₄	—	74	4	no	—
67	C₂×C₄	C₂×#3866	1	2	yes	—
68	C₂×C₄	C₂×#3866	1	1	yes	characteristic
69	C₂²	—	37	2	no	—
70	C₂²	—	74	2	no	—
71	C₂²	—	148	1	no	—
72	C₂²	—	148	2	no	—
73	C₂²	C₂²×#3866	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	37	1	no	—
76	C₄	—	37	1	no	—
77	C₄	—	148	4	no	—
78	C₄	C₂²⋊#3866	1	2	yes	—
79	C₂	—	2	1	no	—
80	C₂	—	74	2	no	—
81	C₂	—	148	2	no	—
82	C₂	C₂×C₂²⋊#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊#3866
commutator	C₂²×C₃₇	C₂²×C₄
Frattini	C₂²	C₂²×#3866
Fitting	C₂×Q₈×C₃₇	C₄
socle	C₂×C₃₇	C₂×C₂²⋊C₄
prime radical	C₂×#10596966	C₂
cosocle	C₂²×D₃₇	C₂³
hypercenter	C₂×Q₈	#3866
hypocenter	C₃₇	#410
LCS	G ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. #11924615	C₂	semidirect
2. #11924595	C₂	semidirect
4. C₂×Q₈×C₃₇	C₄	semidirect
7. C₂×D₁₄₈	C₄	semidirect
9. C₂×C₄×D₃₇	C₄	semidirect
42. C₃₇	#410	semidirect
48. C₂×Q₈	#3866	semidirect

Maximal subgroups

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

subgroup	index
#11924615	2
#11924595	2
C₂×#10596966	2
#410	37