Subgroups — #14557804

Order 2368.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924564	C₂	1	2	yes	maximal, complemented
2	C₂×D₂₉₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#11924542	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924452	C₂	1	2	yes	maximal, complemented
5	#108×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#10596962	C₂²	1	1	yes	characteristic
7	C₂×D₁₄₈	C₂²	1	2	yes	—
8	M₁₆×C₃₇	C₂²	1	2	yes	—
9	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
10	#10596934	C₂²	1	1	yes	characteristic
11	D₂₉₆	—	2	2	no	—
12	D₂₉₆	—	2	1	no	—
13	D₂₉₆	—	2	1	no	—
14	#10596930	—	2	2	no	—
15	#10596929	—	2	1	no	—
16	C₈×D₃₇	—	2	1	no	—
17	C₂²×D₃₇	—	2	2	no	—
18	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
19	C₂²⋊D₃₇	—	2	1	no	—
20	D₁₄₈	—	2	2	no	—
21	D₁₄₈	—	2	2	no	—
22	D₁₄₈	D₄	1	1	yes	characteristic
23	C₄×D₃₇	—	2	1	no	—
24	Dic₇₄	D₄	1	1	yes	characteristic
25	C₈×C₃₇	—	2	2	no	—
26	C₈×C₃₇	D₄	1	1	yes	characteristic
27	C₈×C₃₇	D₄	1	1	yes	characteristic
28	#64436	—	2	1	no	—
29	C₂²×C₃₇	#41	1	1	yes	characteristic
30	C₂×D₃₇	—	2	1	no	—
31	C₂×D₃₇	—	4	2	no	—
32	C₂×D₃₇	—	8	2	no	—
33	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
34	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
35	Dic₃₇	—	2	1	no	—
36	C₂×C₃₇	—	2	1	no	—
37	C₂×C₃₇	#121	1	1	yes	characteristic
38	D₃₇	—	4	1	no	—
39	D₃₇	—	8	2	no	—
40	#472	—	37	1	no	maximal, Sylow
41	C₃₇	#472	1	1	yes	characteristic, complemented, Sylow
42	AGL(1,ℤ/8)	—	37	2	no	—
43	C₂×D₈	—	37	1	no	—
44	#131	—	37	1	no	—
45	#108	D₃₇	1	1	yes	characteristic, complemented
46	#100	—	37	2	no	—
47	#41	—	37	1	no	—
48	C₂×D₄	—	37	2	no	—
49	SD₁₆	—	74	2	no	—
50	D₈	—	74	2	no	—
51	D₈	—	74	1	no	—
52	D₈	—	74	1	no	—
53	M₁₆	—	37	1	no	—
54	M₁₆	—	74	1	no	—
55	M₁₆	C₂×D₃₇	1	2	yes	—
56	C₂×C₈	—	74	1	no	—
57	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
58	C₂³	—	74	2	no	—
59	Q₈	—	37	1	no	—
60	D₄	—	37	1	no	—
61	D₄	—	74	1	no	—
62	D₄	—	74	2	no	—
63	D₄	—	74	2	no	—
64	C₂×C₄	—	74	1	no	—
65	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
66	C₈	—	2	2	no	—
67	C₈	—	74	1	no	—
68	C₈	D₁₄₈	1	1	yes	characteristic
69	C₈	D₁₄₈	1	1	yes	characteristic
70	C₂²	—	296	2	no	—
71	C₂²	—	74	1	no	—
72	C₂²	—	148	2	no	—
73	C₂²	#10596966	1	1	yes	characteristic
74	C₄	—	74	1	no	—
75	C₄	C₂×D₁₄₈	1	1	yes	characteristic
76	C₄	D₄×D₃₇	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	—	296	2	no	—
79	C₂	—	148	1	no	—
80	C₂	#11924511	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11924511
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	#108×C₃₇	C₂
socle	C₂×C₃₇	#121
hypercenter	#108	D₃₇
hypocenter	C₃₇	#472
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
1. #11924564	C₂	semidirect
2. C₂×D₂₉₆	C₂	semidirect
3. #11924542	C₂	semidirect
4. #11924452	C₂	semidirect
5. #108×C₃₇	C₂	semidirect
41. C₃₇	#472	semidirect
45. #108	D₃₇	semidirect

Maximal subgroups

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

subgroup	index
#11924564	2
C₂×D₂₉₆	2
#11924542	2
#11924452	2
#108×C₃₇	2
#472	37