Subgroups — #18010521

Order 4736.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558538	C₂	1	2	yes	maximal
2	#14558409	C₂	1	4	yes	maximal
3	C₄×C₈×D₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596953	C₂²	1	4	yes	—
5	#11924603	—	2	4	no	—
6	C₂×C₈×D₃₇	C₂²	1	2	yes	—
7	C₄²×D₃₇	C₂²	1	1	yes	characteristic
8	C₄×#64436	C₄	1	1	yes	characteristic
9	C₈×Dic₃₇	C₄	1	2	yes	—
10	C₄×C₈×C₃₇	C₄	1	1	yes	characteristic
11	C₂×C₄×D₃₇	Q₈	1	2	yes	—
12	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
13	C₂×#64438	—	2	4	no	—
14	#10596953	—	2	8	no	—
15	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
16	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₃₇	D₄	1	2	yes	—
19	C₂×#64436	C₂×C₄	1	2	yes	—
20	C₈×D₃₇	—	2	4	no	—
21	C₂²×D₃₇	C₂×Q₈	1	1	yes	characteristic
22	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
24	C₂×Dic₃₇	C₄⋊C₄	1	2	yes	—
25	C₂×Dic₃₇	C₂×D₄	1	1	yes	characteristic
26	C₄×D₃₇	—	2	4	no	—
27	C₄×D₃₇	#41	1	4	yes	—
28	#64438	—	4	4	no	—
29	C₈×C₃₇	—	2	2	no	—
30	#64436	—	2	2	no	—
31	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₂×D₃₇	—	2	2	no	—
33	C₂×D₃₇	#125	1	2	yes	—
34	C₄×C₃₇	—	2	2	no	—
35	C₄×C₃₇	#117	1	2	yes	—
36	Dic₃₇	#108	1	4	yes	—
37	Dic₃₇	#124	1	2	yes	—
38	#1837	—	37	1	no	maximal, Sylow
39	C₂×C₃₇	#382	1	1	yes	characteristic
40	C₂×C₃₇	C₂×#108	1	2	yes	—
41	D₃₇	—	2	2	no	—
42	#423	—	37	2	no	—
43	C₂×C₄×C₈	—	37	1	no	—
44	#341	—	37	4	no	—
45	C₃₇	#1837	1	1	yes	characteristic, complemented, Sylow
46	C₂×M₁₆	—	37	4	no	—
47	C₂²×C₈	—	37	2	no	—
48	C₂×C₄²	—	37	1	no	—
49	C₄⋊C₈	—	74	4	no	—
50	C₄×C₈	—	37	2	no	—
51	C₄×C₈	—	37	1	no	—
52	C₄×C₈	#3866	1	1	yes	characteristic
53	C₂²×C₄	—	37	1	no	—
54	C₂²×C₄	—	37	2	no	—
55	M₁₆	—	74	8	no	—
56	C₂×C₈	—	37	2	no	—
57	C₂×C₈	—	74	4	no	—
58	C₂×C₈	—	74	4	no	—
59	C₂×C₈	C₂×#3866	1	2	yes	—
60	C₄²	—	37	2	no	—
61	C₄²	—	37	1	no	—
62	C₄²	C₂×#3866	1	1	yes	characteristic
63	C₂³	—	37	1	no	—
64	C₂×C₄	—	37	1	no	—
65	C₂×C₄	—	37	2	no	—
66	C₂×C₄	—	37	4	no	—
67	C₂×C₄	—	74	4	no	—
68	C₂×C₄	C₄⋊#3866	1	2	yes	—
69	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₈	—	74	2	no	—
72	C₈	—	148	4	no	—
73	C₂²	—	37	2	no	—
74	C₂²	—	74	2	no	—
75	C₂²	C₂×C₄⋊#3866	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	37	2	no	—
78	C₄	—	37	4	no	—
79	C₄	#11924615	1	2	yes	—
80	C₂	—	74	2	no	—
81	C₂	#14558477	1	1	yes	characteristic
82	C₂	D₃₇⋊#108	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	#1837
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
45. C₃₇	#1837	semidirect

Maximal subgroups

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

subgroup	index
#14558538	2
#14558409	2
C₄×C₈×D₃₇	2
#1837	37