Subgroups — #14557627

Order 2368.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₄₈	C₂	1	1	yes	maximal, characteristic
2	#11924501	C₂	1	2	yes	maximal
3	#11924459	C₂	1	2	yes	maximal
4	C₈×Dic₃₇	C₂	1	1	yes	maximal, characteristic
5	#107×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₇₄	C₂²	1	2	yes	—
7	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
9	#10596936	—	2	2	no	—
10	C₄×Dic₃₇	—	2	2	no	—
11	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
12	C₂×#64436	C₂²	1	1	yes	characteristic
13	Dic₁₄₈	C₄	1	4	yes	complemented
14	C₂×C₄×C₃₇	—	2	2	no	—
15	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
16	C₂×Dic₃₇	—	2	2	no	—
17	C₂×Dic₃₇	D₄	1	1	yes	characteristic
18	C₂×Dic₃₇	D₄	1	1	yes	characteristic
19	Dic₇₄	—	2	2	no	—
20	Dic₇₄	C₂×C₄	1	4	yes	—
21	C₈×C₃₇	C₂×C₄	1	2	yes	—
22	#64436	—	2	1	no	—
23	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
24	C₄×C₃₇	—	4	2	no	—
25	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
26	C₄×C₃₇	#41	1	1	yes	characteristic
27	Dic₃₇	—	2	4	no	—
28	Dic₃₇	—	2	1	no	—
29	Dic₃₇	Q₁₆	1	2	yes	complemented
30	C₂×C₃₇	C₄×D₄	1	1	yes	characteristic
31	C₂×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
32	C₂×C₃₇	#135	1	1	yes	characteristic
33	C₄×Q₁₆	—	37	1	no	maximal, Sylow
34	C₃₇	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₁₆	—	37	1	no	—
36	C₄×Q₈	—	37	2	no	—
37	#107	D₃₇	1	1	yes	characteristic
38	#103	—	37	2	no	—
39	C₄×C₈	—	37	1	no	—
40	C₂×Q₈	—	37	2	no	—
41	Q₁₆	—	37	4	no	—
42	C₂×C₈	—	37	1	no	—
43	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
44	C₄⋊C₄	—	74	2	no	—
45	C₄⋊C₄	C₂×D₃₇	1	2	yes	—
46	C₄²	—	37	1	no	—
47	C₄²	—	74	2	no	—
48	Q₈	—	37	4	no	—
49	Q₈	—	74	2	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	37	1	no	—
52	C₂×C₄	—	37	1	no	—
53	C₂×C₄	—	74	2	no	—
54	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
55	C₈	—	74	1	no	—
56	C₈	C₄×D₃₇	1	2	yes	—
57	C₂²	D₄×D₃₇	1	1	yes	characteristic
58	C₄	—	4	2	no	—
59	C₄	—	37	2	no	—
60	C₄	—	74	4	no	—
61	C₄	—	74	1	no	—
62	C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
63	C₄	#10596966	1	1	yes	characteristic
64	C₂	#11924498	1	1	yes	characteristic
65	C₂	Q₁₆×D₃₇	1	1	yes	characteristic
66	C₂	#11924555	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₇
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	#107×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₄
cosocle	C₂×C₄×C₃₇	C₂³
hypercenter	#107	D₃₇
hypocenter	C₃₇	C₄×Q₁₆
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
13. Dic₁₄₈	C₄	semidirect
29. Dic₃₇	Q₁₆	semidirect
34. C₃₇	C₄×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₄₈	2
#11924501	2
#11924459	2
C₈×Dic₃₇	2
#107×C₃₇	2
C₄×Q₁₆	37