Subgroups — #14557975

Order 2368.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924559	C₂	1	1	yes	maximal, characteristic
2	Q₁₆×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#11924482	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924481	C₂	1	1	yes	maximal, characteristic, complemented
5	#11924479	C₂	1	1	yes	maximal, characteristic, complemented
6	#11924475	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₃₂×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#10596966	—	2	1	no	—
9	Q₈×D₃₇	—	2	1	no	—
10	Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
11	Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
12	#10596942	—	2	1	no	—
13	#10596941	—	2	1	no	—
14	Dic₁₄₈	C₂²	1	1	yes	characteristic
15	D₂₉₆	C₂²	1	1	yes	characteristic
16	C₈×D₃₇	C₂²	1	1	yes	characteristic
17	C₁₆×C₃₇	C₂²	1	1	yes	characteristic
18	#10596925	C₂²	1	1	yes	characteristic
19	Q₈×C₃₇	—	2	1	no	—
20	Q₈×C₃₇	—	2	1	no	—
21	D₁₄₈	—	2	1	no	—
22	D₁₄₈	—	4	1	no	—
23	C₄×D₃₇	—	4	1	no	—
24	C₄×D₃₇	—	4	1	no	—
25	C₄×D₃₇	D₄	1	1	yes	characteristic
26	Dic₇₄	—	2	1	no	—
27	Dic₇₄	—	4	1	no	—
28	C₈×C₃₇	C₂³	1	1	yes	characteristic
29	#64436	D₄	1	1	yes	characteristic
30	C₂×D₃₇	—	4	1	no	—
31	C₂×D₃₇	D₈	1	1	yes	characteristic
32	C₄×C₃₇	—	4	1	no	—
33	C₄×C₃₇	—	4	1	no	—
34	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
35	Dic₃₇	—	4	1	no	—
36	Dic₃₇	D₈	1	1	yes	characteristic
37	C₂×C₃₇	C₂×D₈	1	1	yes	characteristic
38	D₃₇	—	2	1	no	—
39	D₃₇	—	8	1	no	—
40	#510	—	37	1	no	maximal, Sylow
41	C₃₇	#510	1	1	yes	characteristic, complemented, Sylow
42	#135	—	37	1	no	—
43	C₂×Q₁₆	—	37	1	no	—
44	Q₃₂	—	37	1	no	—
45	Q₃₂	D₃₇	1	1	yes	characteristic, complemented
46	SD₃₂	—	37	1	no	—
47	SD₃₂	—	37	1	no	—
48	M₃₂	—	37	1	no	—
49	#41	—	74	1	no	—
50	C₂×Q₈	—	74	1	no	—
51	Q₁₆	—	37	1	no	—
52	Q₁₆	—	74	1	no	—
53	Q₁₆	C₂×D₃₇	1	1	yes	characteristic
54	Q₁₆	C₂×D₃₇	1	1	yes	characteristic
55	SD₁₆	—	74	1	no	—
56	D₈	—	37	1	no	—
57	C₂×C₈	—	37	1	no	—
58	C₁₆	—	37	1	no	—
59	C₁₆	C₂×D₃₇	1	1	yes	characteristic
60	Q₈	—	2	1	no	—
61	Q₈	—	2	1	no	—
62	Q₈	—	74	1	no	—
63	Q₈	—	148	1	no	—
64	D₄	—	74	1	no	—
65	D₄	—	148	1	no	—
66	C₂×C₄	—	37	1	no	—
67	C₂×C₄	—	148	1	no	—
68	C₂×C₄	—	148	1	no	—
69	C₈	—	37	1	no	—
70	C₈	C₂²×D₃₇	1	1	yes	characteristic
71	C₂²	—	37	1	no	—
72	C₂²	—	148	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	4	1	no	—
75	C₄	—	37	1	no	—
76	C₄	—	148	1	no	—
77	C₄	D₄×D₃₇	1	1	yes	characteristic
78	C₂	—	296	1	no	—
79	C₂	—	74	1	no	—
80	C₂	D₈×D₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₃₇
commutator, cosocle	C₈×C₃₇	C₂³
Frattini	C₈	C₂²×D₃₇
Fitting	Q₃₂×C₃₇	C₂
socle	C₂×C₃₇	C₂×D₈
prime radical	#11924559	C₂
hypercenter	Q₃₂	D₃₇
hypocenter	C₃₇	#510
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. Q₁₆×D₃₇	C₂	semidirect
3. #11924482	C₂	semidirect
4. #11924481	C₂	semidirect
5. #11924479	C₂	semidirect
6. #11924475	C₂	semidirect
7. Q₃₂×C₃₇	C₂	semidirect
41. C₃₇	#510	semidirect
45. Q₃₂	D₃₇	semidirect

Maximal subgroups

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

subgroup	index
#11924559	2
Q₁₆×D₃₇	2
#11924482	2
#11924481	2
#11924479	2
#11924475	2
Q₃₂×C₃₇	2
#510	37