Subgroups — #18009504

Order 4736.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558536	C₂	1	2	yes	maximal
2	#14557556	C₂	1	1	yes	maximal, characteristic
3	C₂×#10596957	C₄	1	4	yes	—
4	#11924603	—	2	2	no	—
5	C₄⋊#64438	—	2	2	no	—
6	C₂×#10596934	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
8	#11924465	—	2	2	no	—
9	C₂×M₁₆×C₃₇	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
11	C₂²×Dic₃₇	C₂×C₄	1	2	yes	—
12	#10596957	—	4	4	no	—
13	C₂×#64438	—	2	4	no	—
14	M₁₆×C₃₇	—	4	1	no	—
15	C₂×C₈×C₃₇	—	2	1	no	—
16	C₄×Dic₃₇	D₄	1	1	yes	characteristic
17	C₄×Dic₃₇	D₄	1	2	yes	—
18	C₄×Dic₃₇	Q₈	1	1	yes	characteristic
19	#10596934	—	4	1	no	—
20	C₂×#64436	—	2	1	no	—
21	C₂³×C₃₇	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₃₇	—	2	1	no	—
23	C₂×C₄×C₃₇	—	2	1	no	—
24	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
26	C₂×Dic₃₇	—	2	2	no	—
27	C₂×Dic₃₇	—	2	2	no	—
28	C₂×Dic₃₇	C₂²⋊C₄	1	2	yes	—
29	C₂×Dic₃₇	C₄⋊C₄	1	2	yes	—
30	#64438	—	4	4	no	—
31	C₈×C₃₇	—	4	1	no	—
32	#64436	—	4	1	no	—
33	C₂²×C₃₇	—	2	2	no	—
34	C₂²×C₃₇	—	2	1	no	—
35	C₂²×C₃₇	#95	1	1	yes	characteristic
36	C₄×C₃₇	—	2	1	no	—
37	C₄×C₃₇	#100	1	1	yes	characteristic
38	C₄×C₃₇	#101	1	1	yes	characteristic
39	Dic₃₇	—	2	2	no	—
40	Dic₃₇	#100	1	2	yes	—
41	Dic₃₇	#101	1	2	yes	—
42	#1309	—	37	1	no	maximal, Sylow
43	C₂×C₃₇	—	4	1	no	—
44	C₂×C₃₇	#343	1	2	yes	—
45	C₂×C₃₇	#343	1	1	yes	characteristic
46	#423	—	37	2	no	—
47	#423	—	37	1	no	—
48	C₃₇	#1309	1	1	yes	characteristic, complemented, Sylow
49	C₂×M₁₆	—	37	4	no	—
50	C₂×M₁₆	—	37	1	no	—
51	C₂×M₁₆	#3866	1	1	yes	characteristic
52	C₂×C₄²	—	37	1	no	—
53	C₄⋊C₈	—	74	2	no	—
54	C₄⋊C₈	—	74	2	no	—
55	C₄⋊C₈	—	74	2	no	—
56	C₂²×C₄	—	37	2	no	—
57	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
58	M₁₆	—	4	1	no	—
59	M₁₆	—	148	1	no	—
60	M₁₆	—	148	4	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	—	74	4	no	—
63	C₂×C₈	—	74	1	no	—
64	C₄²	—	37	1	no	—
65	C₄²	—	37	1	no	—
66	C₄²	—	37	2	no	—
67	C₂³	C₄×#3866	1	1	yes	characteristic
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	37	2	no	—
71	C₂×C₄	—	37	2	no	—
72	C₂×C₄	—	74	2	no	—
73	C₂×C₄	—	74	2	no	—
74	C₂×C₄	C₄⋊#3866	1	1	yes	characteristic
75	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
76	C₈	—	4	1	no	—
77	C₈	—	148	4	no	—
78	C₈	—	148	1	no	—
79	C₂²	—	2	2	no	—
80	C₂²	—	2	1	no	—
81	C₂²	(C₂×#3866)⋊C₄	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	37	2	no	—
84	C₄	—	37	2	no	—
85	C₄	—	74	2	no	—
86	C₄	#11924596	1	1	yes	characteristic
87	C₄	#11924597	1	1	yes	characteristic
88	C₂	—	4	1	no	—
89	C₂	#14558412	1	2	yes	—
90	C₂	#14558413	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×#3866)⋊C₄
commutator, prime radical	C₂³×C₃₇	C₄²
Frattini	C₂²×C₄	C₂×#3866
Fitting	C₂×M₁₆×C₃₇	C₄
socle	C₂²×C₃₇	#95
cosocle	C₂×C₄×Dic₃₇	C₂²
hypercenter	C₂×M₁₆	#3866
hypocenter	C₃₇	#1309
LCS	G ▷ C₂³×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
48. C₃₇	#1309	semidirect

Maximal subgroups

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

subgroup	index
#14558536	2
#14557556	2
#1309	37