Subgroups — #18009535

Order 4736.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#10596927	C₂	1	2	yes	maximal
2	#14557561	C₂	1	1	yes	maximal, characteristic
3	C₂×#10596927	—	2	2	no	—
4	C₂²×#64436	C₂²	1	1	yes	characteristic
5	#11924495	C₄	1	1	yes	characteristic
6	#11924465	—	2	2	no	—
7	C₂×M₁₆×C₃₇	C₄	1	1	yes	characteristic
8	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
9	M₁₆×C₃₇	—	4	1	no	—
10	C₂×C₈×C₃₇	—	2	1	no	—
11	C₂²⋊Dic₃₇	—	2	1	no	—
12	C₄⋊Dic₃₇	C₈	1	2	yes	—
13	C₄×Dic₃₇	—	2	1	no	—
14	C₂×#64436	—	4	1	no	—
15	C₂×#64436	D₄	1	2	yes	—
16	#10596927	—	4	2	no	—
17	C₂³×C₃₇	M₁₆	1	1	yes	characteristic
18	C₂×C₄×C₃₇	—	2	1	no	—
19	C₂×C₄×C₃₇	—	2	1	no	—
20	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
22	C₂×Dic₃₇	—	2	2	no	—
23	C₈×C₃₇	—	4	1	no	—
24	#64436	—	2	2	no	—
25	C₂²×C₃₇	—	2	1	no	—
26	C₂²×C₃₇	—	2	2	no	—
27	C₂²×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
28	C₄×C₃₇	—	2	1	no	—
29	C₄×C₃₇	#99	1	1	yes	characteristic
30	C₄×C₃₇	#101	1	1	yes	characteristic
31	Dic₃₇	—	4	2	no	—
32	#1323	—	37	1	no	maximal, Sylow
33	C₂×C₃₇	—	4	1	no	—
34	C₂×C₃₇	#324	1	1	yes	characteristic
35	C₂×C₃₇	#350	1	2	yes	—
36	#424	—	37	1	no	—
37	C₂²⋊C₁₆	—	37	2	no	—
38	C₃₇	#1323	1	1	yes	characteristic, complemented, Sylow
39	C₂×M₁₆	#3866	1	1	yes	characteristic
40	C₂²×C₈	—	37	1	no	—
41	#117	—	37	1	no	—
42	C₂×C₁₆	—	74	2	no	—
43	C₄⋊C₈	—	74	2	no	—
44	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
45	M₁₆	—	4	1	no	—
46	C₂×C₈	—	2	1	no	—
47	C₂×C₈	—	37	2	no	—
48	C₂×C₈	—	148	1	no	—
49	C₄⋊C₄	—	37	2	no	—
50	C₂²⋊C₄	—	74	1	no	—
51	C₄²	—	74	1	no	—
52	C₁₆	—	148	2	no	—
53	C₂³	#10596953	1	1	yes	characteristic
54	C₂×C₄	—	2	1	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	74	2	no	—
57	C₂×C₄	D₃₇⋊C₈	1	1	yes	characteristic
58	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
59	C₈	—	4	1	no	—
60	C₈	—	74	2	no	—
61	C₂²	—	2	1	no	—
62	C₂²	—	2	2	no	—
63	C₂²	#11924593	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	148	2	no	—
66	C₄	#11924594	1	1	yes	characteristic
67	C₄	#11924597	1	1	yes	characteristic
68	C₂	—	4	1	no	—
69	C₂	#14558379	1	1	yes	characteristic
70	C₂	#14558432	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊#3866
commutator	C₂×C₄×C₃₇	C₂×C₈
Frattini	C₂²×C₄	C₂×#3866
Fitting	C₂×M₁₆×C₃₇	C₄
socle	C₂²×C₃₇	C₂²⋊C₈
prime radical	C₂³×C₃₇	M₁₆
cosocle	C₂²×#64436	C₂²
hypercenter	C₂×M₁₆	#3866
hypocenter	C₃₇	#1323
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
38. C₃₇	#1323	semidirect

Maximal subgroups

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

subgroup	index
C₂²⋊#10596927	2
#14557561	2
#1323	37