Subgroups — #14558579

Order 2368.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924624	C₂	1	2	yes	maximal, complemented
2	#11924606	C₂	1	1	yes	maximal, characteristic, complemented
3	#11924601	C₂	1	2	yes	maximal, complemented
4	#11924590	C₂	1	1	yes	maximal, characteristic, complemented
5	#11924559	C₂	1	1	yes	maximal, characteristic
6	#10596966	C₂²	1	2	yes	—
7	C₄×#3866	C₂²	1	1	yes	characteristic
8	#10596953	—	2	2	no	—
9	#10596953	C₂²	1	2	yes	—
10	D₃₇⋊C₈	—	2	2	no	—
11	D₃₇⋊C₈	C₂²	1	1	yes	characteristic
12	Q₁₆×C₃₇	C₄	1	1	yes	characteristic, complemented
13	#10596941	C₄	1	2	yes	complemented
14	D₂₉₆	C₄	1	1	yes	characteristic, complemented
15	C₈×D₃₇	C₂²	1	1	yes	characteristic
16	C₂×#3866	—	2	1	no	—
17	Q₈×C₃₇	C₂×C₄	1	2	yes	—
18	D₁₄₈	—	2	2	no	—
19	D₁₄₈	C₂×C₄	1	2	yes	—
20	C₄×D₃₇	—	2	2	no	—
21	C₄×D₃₇	C₂³	1	1	yes	characteristic
22	#64438	—	2	2	no	—
23	#64438	D₄	1	2	yes	—
24	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
25	#64436	C₂×C₄	1	1	yes	characteristic
26	C₂×D₃₇	—	2	2	no	—
27	C₂×D₃₇	#41	1	1	yes	characteristic
28	#3866	—	4	1	no	—
29	C₄×C₃₇	—	2	2	no	—
30	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
31	Dic₃₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₃₇	C₄×D₄	1	1	yes	characteristic
33	D₃₇	—	2	1	no	—
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	—	37	1	no	—
42	#41	—	37	2	no	—
43	Q₁₆	#3866	1	1	yes	characteristic, complemented
44	SD₁₆	—	37	2	no	—
45	D₈	—	37	1	no	—
46	M₁₆	—	37	2	no	—
47	M₁₆	—	74	2	no	—
48	C₂×C₈	—	37	1	no	—
49	C₂×C₈	—	37	1	no	—
50	C₂×C₈	—	74	2	no	—
51	C₄²	—	37	1	no	—
52	Q₈	C₂×#3866	1	2	yes	—
53	D₄	—	37	2	no	—
54	D₄	—	74	2	no	—
55	C₂×C₄	—	37	1	no	—
56	C₂×C₄	—	74	2	no	—
57	C₂×C₄	—	74	1	no	—
58	C₈	—	37	2	no	—
59	C₈	—	37	1	no	—
60	C₈	—	74	2	no	—
61	C₈	C₂×#3866	1	1	yes	characteristic
62	C₂²	—	37	1	no	—
63	C₂²	—	74	2	no	—
64	C₄	—	2	2	no	—
65	C₄	—	37	1	no	—
66	C₄	—	148	1	no	—
67	C₄	C₂²×#3866	1	1	yes	characteristic
68	C₂	—	74	1	no	—
69	C₂	—	148	2	no	—
70	C₂	D₄×#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#3866
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₄	C₂²×#3866
Fitting	Q₁₆×C₃₇	C₄
socle	C₂×C₃₇	C₄×D₄
prime radical	#11924559	C₂
cosocle	C₄×D₃₇	C₂³
hypercenter	Q₁₆	#3866
hypocenter	C₃₇	#444
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #11924624	C₂	semidirect
2. #11924606	C₂	semidirect
3. #11924601	C₂	semidirect
4. #11924590	C₂	semidirect
12. Q₁₆×C₃₇	C₄	semidirect
13. #10596941	C₄	semidirect
14. D₂₉₆	C₄	semidirect
36. C₃₇	#444	semidirect
43. Q₁₆	#3866	semidirect

Maximal subgroups

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

subgroup	index
#11924624	2
#11924606	2
#11924601	2
#11924590	2
#11924559	2
#444	37