Subgroups — #17992690

Order 4736.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924472	C₂	1	2	yes	maximal
2	C₂²×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#10596934	—	2	2	no	—
4	#11924472	—	2	2	no	—
5	#11924472	C₄	1	4	yes	—
6	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₃₇	—	2	2	no	—
8	C₂×C₁₆×C₃₇	C₄	1	2	yes	—
9	C₂²×C₄×C₃₇	D₄	1	1	yes	characteristic
10	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
11	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₃₇	D₄	1	2	yes	—
13	C₂×C₈×C₃₇	Q₈	1	1	yes	characteristic
14	#10596934	—	2	4	no	—
15	#10596934	—	4	2	no	—
16	C₂×#64436	—	4	2	no	—
17	C₁₆×C₃₇	—	2	2	no	—
18	C₂³×C₃₇	Q₁₆	1	1	yes	characteristic
19	C₂×C₄×C₃₇	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
22	C₂×C₄×C₃₇	SD₁₆	1	2	yes	—
23	C₈×C₃₇	C₄²	1	1	yes	characteristic
24	C₈×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
26	#64436	—	4	4	no	—
27	C₂²×C₃₇	—	2	2	no	—
28	C₂²×C₃₇	#103	1	2	yes	—
29	C₂²×C₃₇	#107	1	1	yes	characteristic
30	C₄×C₃₇	#95	1	1	yes	characteristic
31	C₄×C₃₇	#102	1	2	yes	—
32	C₄×C₃₇	#106	1	1	yes	characteristic
33	#1381	—	37	1	no	maximal, Sylow
34	C₂×C₃₇	—	2	2	no	—
35	C₂×C₃₇	#340	1	1	yes	characteristic
36	C₂×C₃₇	#368	1	2	yes	—
37	C₂²×C₁₆	D₃₇	1	1	yes	characteristic
38	C₂×#108	—	37	2	no	—
39	C₃₇	#1381	1	1	yes	characteristic, complemented, Sylow
40	C₂×M₁₆	—	74	2	no	—
41	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
42	C₂×C₁₆	—	2	2	no	—
43	C₂×C₁₆	Dic₃₇	1	2	yes	—
44	#108	—	37	4	no	—
45	#108	—	74	2	no	—
46	C₂²×C₄	D₁₄₈	1	1	yes	characteristic
47	M₁₆	—	74	4	no	—
48	M₁₆	—	148	2	no	—
49	C₂×C₈	—	148	2	no	—
50	C₂×C₈	Dic₇₄	1	1	yes	characteristic
51	C₂×C₈	C₄×D₃₇	1	2	yes	—
52	C₂×C₈	C₂×Dic₃₇	1	1	yes	characteristic
53	C₂×C₈	C₂²⋊D₃₇	1	2	yes	—
54	C₁₆	—	2	2	no	—
55	C₂³	Dic₁₄₈	1	1	yes	characteristic
56	C₂×C₄	#10596930	1	2	yes	—
57	C₂×C₄	D₂₉₆	1	1	yes	characteristic
58	C₂×C₄	C₄⋊Dic₃₇	1	1	yes	characteristic
59	C₂×C₄	#10596938	1	2	yes	—
60	C₈	—	148	4	no	—
61	C₈	C₄×Dic₃₇	1	1	yes	characteristic
62	C₈	#10596936	1	2	yes	—
63	C₈	C₂²⋊Dic₃₇	1	1	yes	characteristic
64	C₂²	—	2	2	no	—
65	C₂²	#11924461	1	2	yes	—
66	C₂²	#11924470	1	1	yes	characteristic
67	C₄	#11924443	1	1	yes	characteristic
68	C₄	#11924458	1	2	yes	—
69	C₄	#11924468	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	#14557296	1	1	yes	characteristic
72	C₂	#14557363	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₂₉₆
commutator	C₈×C₃₇	C₄²
Frattini	C₂²×C₈	C₂×D₃₇
Fitting	C₂²×C₁₆×C₃₇	C₂
socle	C₂²×C₃₇	#107
prime radical	C₂³×C₃₇	Q₁₆
cosocle	C₂²×C₈×C₃₇	C₂²
hypercenter	C₂²×C₁₆	D₃₇
hypocenter	C₃₇	#1381
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
39. 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×#11924472	2
C₂²×C₁₆×C₃₇	2
#1381	37