Subgroups — #18009656

Order 4736.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924607	C₂	1	2	yes	maximal
2	C₂×C₁₆×D₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#10596953	—	2	2	no	—
4	#11924607	—	2	2	no	—
5	#11924607	C₄	1	4	yes	—
6	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
7	C₂×#10596925	C₄	1	1	yes	characteristic
8	C₁₆×D₃₇	—	2	2	no	—
9	C₂×C₁₆×C₃₇	C₄	1	1	yes	characteristic
10	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
11	C₂×#64438	—	4	2	no	—
12	#10596953	—	2	4	no	—
13	#10596953	—	4	2	no	—
14	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂×#64436	Q₈	1	1	yes	characteristic
16	C₈×D₃₇	C₂×C₄	1	2	yes	—
17	C₈×D₃₇	D₄	1	2	yes	—
18	C₁₆×C₃₇	—	2	1	no	—
19	#10596925	—	2	1	no	—
20	C₂²×D₃₇	Q₁₆	1	1	yes	characteristic
21	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
22	C₂×Dic₃₇	D₈	1	1	yes	characteristic
23	C₄×D₃₇	C₂²⋊C₄	1	2	yes	—
24	C₄×D₃₇	SD₁₆	1	2	yes	—
25	#64438	—	4	4	no	—
26	C₈×C₃₇	C₄²	1	1	yes	characteristic
27	C₈×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
28	#64436	C₄⋊C₄	1	2	yes	—
29	C₂²×C₃₇	#107	1	1	yes	characteristic
30	C₂×D₃₇	—	2	1	no	—
31	C₂×D₃₇	—	2	1	no	—
32	C₂×D₃₇	#103	1	2	yes	—
33	C₄×C₃₇	#95	1	1	yes	characteristic
34	C₄×C₃₇	#106	1	1	yes	characteristic
35	Dic₃₇	#102	1	2	yes	—
36	#1381	—	37	1	no	maximal, Sylow
37	C₂×C₃₇	#340	1	1	yes	characteristic
38	C₂×C₃₇	#368	1	1	yes	characteristic
39	C₂×C₃₇	#368	1	1	yes	characteristic
40	D₃₇	—	2	2	no	—
41	C₂²×C₁₆	—	37	1	no	—
42	C₂×#108	—	37	2	no	—
43	C₃₇	#1381	1	1	yes	characteristic, complemented, Sylow
44	C₂×M₁₆	—	74	2	no	—
45	C₂²×C₈	—	37	1	no	—
46	C₂×C₁₆	—	37	1	no	—
47	C₂×C₁₆	—	74	2	no	—
48	C₂×C₁₆	#3866	1	1	yes	characteristic
49	#108	—	37	4	no	—
50	#108	—	74	2	no	—
51	C₂²×C₄	—	37	1	no	—
52	M₁₆	—	74	4	no	—
53	M₁₆	—	148	2	no	—
54	C₂×C₈	—	37	1	no	—
55	C₂×C₈	—	37	2	no	—
56	C₂×C₈	—	37	2	no	—
57	C₂×C₈	—	148	2	no	—
58	C₂×C₈	C₂×#3866	1	1	yes	characteristic
59	C₁₆	—	2	1	no	—
60	C₁₆	—	74	1	no	—
61	C₂³	—	37	1	no	—
62	C₂×C₄	—	37	1	no	—
63	C₂×C₄	—	37	2	no	—
64	C₂×C₄	—	37	2	no	—
65	C₂×C₄	C₄⋊#3866	1	1	yes	characteristic
66	C₈	—	37	2	no	—
67	C₈	—	148	4	no	—
68	C₈	C₄×#3866	1	1	yes	characteristic
69	C₈	C₂²⋊#3866	1	1	yes	characteristic
70	C₂²	—	37	2	no	—
71	C₂²	—	74	1	no	—
72	C₂²	—	74	1	no	—
73	C₂²	#11924605	1	1	yes	characteristic
74	C₄	—	37	2	no	—
75	C₄	(C₂×#3866)⋊C₄	1	1	yes	characteristic
76	C₄	#11924604	1	1	yes	characteristic
77	C₂	—	74	2	no	—
78	C₂	#14558407	1	1	yes	characteristic
79	C₂	#14558461	1	1	yes	characteristic
80	C₂	#14558462	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11924605
commutator	C₈×C₃₇	C₄²
Frattini	C₂×C₈	C₂×#3866
Fitting	C₂×C₁₆×C₃₇	C₄
socle	C₂²×C₃₇	#107
prime radical	C₂²×D₃₇	Q₁₆
cosocle	C₂×C₈×D₃₇	C₂²
hypercenter	C₂×C₁₆	#3866
hypocenter	C₃₇	#1381
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
43. C₃₇	#1381	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
C₂×C₁₆×D₃₇	2
#1381	37