Subgroups — #18009542

Order 4736.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558429	C₂	1	2	yes	maximal
2	#14557557	C₂	1	1	yes	maximal, characteristic
3	#11924610	—	2	2	no	—
4	C₂×#10596934	C₄	1	1	yes	characteristic
5	C₂×#10596934	C₂²	1	1	yes	characteristic
6	C₄⋊#64436	—	2	2	no	—
7	C₂×C₄²×C₃₇	C₄	1	1	yes	characteristic
8	C₂²×C₄×C₃₇	—	2	1	no	—
9	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
10	C₄²×C₃₇	—	2	1	no	—
11	C₄²×C₃₇	C₈	1	1	yes	characteristic
12	C₄²×C₃₇	C₈	1	1	yes	characteristic
13	#10596934	—	4	1	no	—
14	#10596934	—	4	1	no	—
15	C₂×#64436	—	2	1	no	—
16	C₂×#64436	D₄	1	2	yes	—
17	#10596927	—	4	2	no	—
18	C₂³×C₃₇	M₁₆	1	1	yes	characteristic
19	C₂×C₄×C₃₇	—	2	1	no	—
20	C₂×C₄×C₃₇	—	2	1	no	—
21	C₂×C₄×C₃₇	—	2	1	no	—
22	C₂×C₄×C₃₇	—	2	1	no	—
23	C₂×C₄×C₃₇	—	4	2	no	—
24	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
26	#64436	—	2	2	no	—
27	#64436	—	4	1	no	—
28	C₂²×C₃₇	—	2	1	no	—
29	C₂²×C₃₇	—	4	1	no	—
30	C₂²×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₃₇	—	2	2	no	—
32	C₄×C₃₇	—	2	1	no	—
33	C₄×C₃₇	—	4	1	no	—
34	C₄×C₃₇	#99	1	1	yes	characteristic
35	C₄×C₃₇	#101	1	1	yes	characteristic
36	#1327	—	37	1	no	maximal, Sylow
37	C₂×C₃₇	—	2	1	no	—
38	C₂×C₃₇	—	4	1	no	—
39	C₂×C₃₇	#324	1	1	yes	characteristic
40	#423	—	37	1	no	—
41	#349	—	37	2	no	—
42	C₃₇	#1327	1	1	yes	characteristic, complemented, Sylow
43	C₂×M₁₆	—	37	1	no	—
44	C₂×M₁₆	—	37	1	no	—
45	C₂×C₄²	#3866	1	1	yes	characteristic
46	M₃₂	—	74	2	no	—
47	C₄⋊C₈	—	74	2	no	—
48	C₂²×C₄	—	2	1	no	—
49	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
50	M₁₆	—	148	1	no	—
51	M₁₆	—	148	1	no	—
52	C₂×C₈	—	37	2	no	—
53	C₂×C₈	—	74	1	no	—
54	C₄²	—	2	1	no	—
55	C₄²	#64438	1	1	yes	characteristic
56	C₄²	#64438	1	1	yes	characteristic
57	C₁₆	—	148	2	no	—
58	C₂³	#10596957	1	1	yes	characteristic
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	4	2	no	—
64	C₂×C₄	C₂×#64438	1	1	yes	characteristic
65	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
66	C₈	—	74	2	no	—
67	C₈	—	148	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	—	4	1	no	—
70	C₂²	C₂²⋊#64438	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	2	1	no	—
73	C₄	—	4	1	no	—
74	C₄	#11924595	1	1	yes	characteristic
75	C₄	#11924597	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	4	1	no	—
78	C₂	#14558378	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11924595
commutator	C₂×C₄×C₃₇	C₂×C₈
Frattini	C₂²×C₄	C₂×#3866
Fitting	C₂×C₄²×C₃₇	C₄
socle	C₂×C₃₇	#324
prime radical	C₂³×C₃₇	M₁₆
cosocle	C₂×#10596934	C₂²
hypercenter	C₂×C₄²	#3866
hypocenter	C₃₇	#1327
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
42. C₃₇	#1327	semidirect

Maximal subgroups

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

subgroup	index
#14558429	2
#14557557	2
#1327	37