Subgroups — #18010537

Order 4736.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924607	C₂	1	4	yes	maximal
2	#14558537	C₂	1	2	yes	maximal
3	C₄×C₈×D₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596953	C₂²	1	4	yes	—
5	#11924607	—	2	8	no	—
6	C₄⋊#64438	—	2	4	no	—
7	C₂×C₈×D₃₇	C₂²	1	2	yes	—
8	C₄²×D₃₇	C₂²	1	1	yes	characteristic
9	C₄×#64436	C₄	1	1	yes	characteristic
10	C₈×Dic₃₇	C₄	1	2	yes	—
11	C₄×C₈×C₃₇	C₄	1	1	yes	characteristic
12	C₂×C₄×D₃₇	Q₈	1	2	yes	—
13	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
14	C₂×#64438	—	2	4	no	—
15	#10596953	—	2	8	no	—
16	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
17	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₃₇	D₄	1	2	yes	—
20	C₂×#64436	C₂×C₄	1	2	yes	—
21	C₈×D₃₇	D₄	1	4	yes	—
22	C₈×D₃₇	Q₈	1	4	yes	—
23	C₂²×D₃₇	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
26	C₂×Dic₃₇	C₄⋊C₄	1	2	yes	—
27	C₂×Dic₃₇	C₂×D₄	1	1	yes	characteristic
28	C₄×D₃₇	—	2	4	no	—
29	C₄×D₃₇	C₂×D₄	1	2	yes	—
30	C₄×D₃₇	C₂×Q₈	1	2	yes	—
31	#64438	—	4	4	no	—
32	C₈×C₃₇	C₄⋊C₄	1	4	yes	—
33	#64436	C₄⋊C₄	1	4	yes	—
34	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×D₃₇	—	2	2	no	—
36	C₂×D₃₇	C₄⋊Q₈	1	2	yes	—
37	C₄×C₃₇	#108	1	4	yes	complemented
38	C₄×C₃₇	C₂×C₄⋊C₄	1	2	yes	—
39	Dic₃₇	—	2	2	no	—
40	Dic₃₇	#127	1	1	yes	characteristic
41	Dic₃₇	C₄⋊Q₈	1	1	yes	characteristic
42	#1848	—	37	1	no	maximal, Sylow
43	C₂×C₃₇	#384	1	1	yes	characteristic
44	C₂×C₃₇	C₂×#108	1	2	yes	—
45	D₃₇	—	2	2	no	—
46	C₂×#108	—	37	4	no	—
47	#423	—	37	2	no	—
48	C₂×C₄×C₈	—	37	1	no	—
49	C₃₇	#1848	1	1	yes	characteristic, complemented, Sylow
50	C₂×M₁₆	—	37	4	no	—
51	C₂²×C₈	—	37	2	no	—
52	C₂×C₄²	—	37	1	no	—
53	#108	—	74	8	no	—
54	C₄⋊C₈	—	74	4	no	—
55	C₄×C₈	—	37	2	no	—
56	C₄×C₈	—	37	1	no	—
57	C₄×C₈	#3866	1	1	yes	characteristic
58	C₂²×C₄	—	37	1	no	—
59	C₂²×C₄	—	37	2	no	—
60	M₁₆	—	74	8	no	—
61	C₂×C₈	—	37	2	no	—
62	C₂×C₈	—	37	4	no	—
63	C₂×C₈	—	37	4	no	—
64	C₂×C₈	—	74	4	no	—
65	C₂×C₈	C₂×#3866	1	2	yes	—
66	C₄²	—	37	2	no	—
67	C₄²	—	37	1	no	—
68	C₄²	C₂×#3866	1	1	yes	characteristic
69	C₂³	—	37	1	no	—
70	C₂×C₄	—	37	1	no	—
71	C₂×C₄	—	37	2	no	—
72	C₂×C₄	—	37	2	no	—
73	C₂×C₄	—	37	2	no	—
74	C₂×C₄	—	74	4	no	—
75	C₂×C₄	C₄⋊#3866	1	2	yes	—
76	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
77	C₈	—	37	4	no	—
78	C₈	—	148	4	no	—
79	C₈	C₄⋊#3866	1	4	yes	—
80	C₂²	—	37	2	no	—
81	C₂²	—	74	2	no	—
82	C₂²	C₂×C₄⋊#3866	1	1	yes	characteristic
83	C₄	—	37	1	no	—
84	C₄	—	37	1	no	—
85	C₄	—	74	2	no	—
86	C₄	#11924607	1	4	yes	complemented
87	C₄	C₂×C₄⋊#3866	1	2	yes	—
88	C₂	—	74	2	no	—
89	C₂	#14558479	1	1	yes	characteristic
90	C₂	C₂×#11924607	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#3866
commutator	C₂×C₄×C₃₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×#3866
Fitting	C₄×C₈×C₃₇	C₄
socle	C₂²×C₃₇	C₂×C₄⋊C₄
prime radical	C₂²×D₃₇	C₂×Q₈
cosocle	C₂×C₄×D₃₇	C₂³
hypercenter	C₄×C₈	#3866
hypocenter	C₃₇	#1848
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
37. C₄×C₃₇	#108	semidirect
49. C₃₇	#1848	semidirect
86. C₄	#11924607	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924607	2
#14558537	2
C₄×C₈×D₃₇	2
#1848	37