Subgroups — #18009740

Order 4736.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558444	C₂	1	2	yes	maximal
2	#14557902	C₂	1	1	yes	maximal, characteristic
3	#11924597	—	2	2	no	—
4	#11924536	C₂²	1	1	yes	characteristic
5	#11924528	C₄	1	1	yes	characteristic
6	#11924461	—	2	2	no	—
7	#97×C₃₇	C₄	1	1	yes	characteristic
8	C₂×Dic₇₄	D₄	1	2	yes	—
9	#10596957	—	4	2	no	—
10	C₂×C₈×C₃₇	—	2	1	no	—
11	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₄⋊Dic₃₇	—	2	1	no	—
13	C₄⋊Dic₃₇	—	4	1	no	—
14	#10596936	—	4	1	no	—
15	C₂×C₄×C₃₇	—	2	1	no	—
16	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
17	C₂×Dic₃₇	—	2	2	no	—
18	C₂×Dic₃₇	—	4	1	no	—
19	Dic₇₄	—	4	2	no	—
20	#64438	—	8	2	no	—
21	C₈×C₃₇	—	4	1	no	—
22	C₂²×C₃₇	#99	1	1	yes	characteristic
23	C₄×C₃₇	—	2	1	no	—
24	C₄×C₃₇	—	4	1	no	—
25	Dic₃₇	—	4	2	no	—
26	Dic₃₇	—	8	1	no	—
27	#1413	—	37	1	no	maximal, Sylow
28	C₂×C₃₇	—	2	1	no	—
29	C₂×C₃₇	#354	1	1	yes	characteristic
30	#491	—	37	1	no	—
31	#356	—	37	2	no	—
32	C₃₇	#1413	1	1	yes	characteristic, complemented, Sylow
33	C₄⋊Q₈	—	37	1	no	—
34	#125	—	37	1	no	—
35	#103	—	74	2	no	—
36	#101	—	74	2	no	—
37	#97	#3866	1	1	yes	characteristic
38	C₂×Q₈	—	37	2	no	—
39	M₁₆	—	148	2	no	—
40	C₂×C₈	—	2	1	no	—
41	C₄⋊C₄	—	74	1	no	—
42	C₄⋊C₄	—	148	1	no	—
43	C₄⋊C₄	—	148	1	no	—
44	C₄²	C₂×#3866	1	1	yes	characteristic
45	Q₈	—	148	2	no	—
46	C₂×C₄	—	2	1	no	—
47	C₂×C₄	—	74	2	no	—
48	C₂×C₄	—	148	1	no	—
49	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
50	C₈	—	4	1	no	—
51	C₈	—	296	2	no	—
52	C₂²	#11924595	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	4	1	no	—
55	C₄	—	296	1	no	—
56	C₄	—	148	2	no	—
57	C₂	—	2	1	no	—
58	C₂	#14558440	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14558440
commutator	C₄²×C₃₇	C₂×C₄
Frattini	C₄²	C₂×#3866
Fitting	#97×C₃₇	C₄
socle	C₂×C₃₇	#354
prime radical	C₂²×C₃₇	#99
cosocle	#11924536	C₂²
hypercenter	#97	#3866
hypocenter	C₃₇	#1413
LCS	G ▷ C₄²×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
32. C₃₇	#1413	semidirect

Maximal subgroups

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

subgroup	index
#14558444	2
#14557902	2
#1413	37