Subgroups — #14557656

Order 2368.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924558	C₂	1	1	yes	maximal, characteristic
2	#11924542	C₂	1	2	yes	maximal, complemented
3	#11924472	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924464	C₂	1	2	yes	maximal, complemented
5	#97×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#10596962	C₂²	1	2	yes	—
7	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
9	C₄²×C₃₇	C₂²	1	1	yes	characteristic
10	#10596934	C₂²	1	2	yes	—
11	Dic₁₄₈	C₄	1	1	yes	characteristic, complemented
12	D₂₉₆	C₄	1	1	yes	characteristic, complemented
13	#10596930	C₄	1	2	yes	complemented
14	#10596929	—	2	2	no	—
15	C₈×D₃₇	—	2	2	no	—
16	C₂×C₄×C₃₇	—	2	1	no	—
17	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
18	C₂²⋊D₃₇	—	2	2	no	—
19	D₁₄₈	C₂×C₄	1	2	yes	—
20	C₄×D₃₇	—	2	2	no	—
21	Dic₇₄	C₂×C₄	1	2	yes	—
22	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
23	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
24	C₈×C₃₇	D₄	1	2	yes	—
25	#64436	—	2	2	no	—
26	C₂²×C₃₇	#41	1	1	yes	characteristic
27	C₂×D₃₇	—	2	2	no	—
28	C₄×C₃₇	—	4	1	no	—
29	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
31	Dic₃₇	—	2	2	no	—
32	C₂×C₃₇	—	2	1	no	—
33	C₂×C₃₇	C₄×D₄	1	1	yes	characteristic
34	D₃₇	—	4	2	no	—
35	#444	—	37	1	no	maximal, Sylow
36	C₃₇	#444	1	1	yes	characteristic, complemented, Sylow
37	#135	—	37	1	no	—
38	#131	—	37	2	no	—
39	#108	—	37	1	no	—
40	#104	—	37	2	no	—
41	#97	D₃₇	1	1	yes	characteristic, complemented
42	#41	—	37	2	no	—
43	Q₁₆	—	37	1	no	—
44	SD₁₆	—	37	2	no	—
45	D₈	—	37	1	no	—
46	M₁₆	—	37	2	no	—
47	M₁₆	—	74	2	no	—
48	C₂×C₈	—	74	2	no	—
49	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
50	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
51	C₄²	C₂×D₃₇	1	1	yes	characteristic
52	Q₈	—	37	2	no	—
53	D₄	—	37	2	no	—
54	D₄	—	74	2	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	74	2	no	—
57	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
58	C₈	—	74	2	no	—
59	C₈	C₄×D₃₇	1	1	yes	characteristic
60	C₈	C₄×D₃₇	1	1	yes	characteristic
61	C₈	D₁₄₈	1	2	yes	—
62	C₂²	—	74	2	no	—
63	C₂²	#10596962	1	1	yes	characteristic
64	C₄	—	4	1	no	—
65	C₄	—	74	2	no	—
66	C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
67	C₄	C₂×D₁₄₈	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	148	2	no	—
70	C₂	C₄×D₁₄₈	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₁₄₈
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	#97×C₃₇	C₂
socle	C₂×C₃₇	C₄×D₄
prime radical	#11924558	C₂
cosocle	C₂×C₄×C₃₇	C₂³
hypercenter	#97	D₃₇
hypocenter	C₃₇	#444
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

Complements

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

N	H ≅ G/N	type
2. #11924542	C₂	semidirect
3. #11924472	C₂	semidirect
4. #11924464	C₂	semidirect
5. #97×C₃₇	C₂	semidirect
11. Dic₁₄₈	C₄	semidirect
12. D₂₉₆	C₄	semidirect
13. #10596930	C₄	semidirect
36. C₃₇	#444	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
#11924558	2
#11924542	2
#11924472	2
#11924464	2
#97×C₃₇	2
#444	37