Subgroups — #14543804

Order 2176.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763732	C₂	1	1	yes	maximal, characteristic
2	#11763732	C₂	1	1	yes	maximal, characteristic
3	#11763208	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#125	C₄	1	1	yes	characteristic
5	#10587556	C₄	1	1	yes	characteristic
6	#10587538	—	2	1	no	—
7	#10587538	—	2	1	no	—
8	#10587479	—	2	1	no	—
9	#10587478	—	2	1	no	—
10	C₄×#3622	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₁₇	—	2	1	no	—
12	C₄⋊C₄×C₁₇	—	4	1	no	—
13	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
14	C₄⋊Dic₁₇	—	2	1	no	—
15	#63225	—	4	1	no	—
16	C₂×#3622	D₄	1	1	yes	characteristic
17	C₂×#3622	D₄	1	1	yes	characteristic
18	#63216	—	4	1	no	—
19	#63216	—	4	1	no	—
20	C₂×C₄×C₁₇	—	2	1	no	—
21	C₂×C₄×C₁₇	—	4	1	no	—
22	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₁₇	—	4	1	no	—
24	#3622	SD₁₆	1	1	yes	characteristic
25	#3622	SD₁₆	1	1	yes	characteristic
26	#3622	Q₁₆	1	1	yes	characteristic
27	#3622	Q₁₆	1	1	yes	characteristic
28	#1366	—	17	1	no	maximal, Sylow
29	C₂²×C₁₇	#100	1	1	yes	characteristic
30	C₄×C₁₇	—	4	1	no	—
31	C₄×C₁₇	—	8	1	no	—
32	C₄×C₁₇	#103	1	1	yes	characteristic
33	C₄×C₁₇	#103	1	1	yes	characteristic
34	Dic₁₇	—	8	1	no	—
35	#499	—	17	1	no	—
36	#364	—	17	1	no	—
37	#364	—	17	1	no	—
38	C₂×C₁₇	—	2	1	no	—
39	C₂×C₁₇	#333	1	1	yes	characteristic
40	#125	—	17	1	no	—
41	#125	#595	1	1	yes	characteristic
42	M₃₂	—	34	1	no	—
43	M₃₂	—	34	1	no	—
44	#107	—	34	1	no	—
45	#106	—	34	1	no	—
46	C₄×C₈	—	17	1	no	—
47	C₁₇	#1366	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₈	—	17	1	no	—
49	C₂×C₈	—	17	1	no	—
50	C₄⋊C₄	—	2	1	no	—
51	C₄⋊C₄	—	4	1	no	—
52	C₄⋊C₄	—	34	1	no	—
53	C₄⋊C₄	—	68	1	no	—
54	C₄²	C₂×#595	1	1	yes	characteristic
55	C₁₆	—	68	1	no	—
56	C₁₆	—	68	1	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	4	1	no	—
59	C₂×C₄	—	68	1	no	—
60	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
61	C₈	—	17	1	no	—
62	C₈	—	17	1	no	—
63	C₈	—	17	1	no	—
64	C₈	—	17	1	no	—
65	C₂²	#10587553	1	1	yes	characteristic
66	C₄	—	4	1	no	—
67	C₄	—	8	1	no	—
68	C₄	—	136	1	no	—
69	C₄	#10587549	1	1	yes	characteristic
70	C₄	#10587549	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#11763669	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11763669
commutator	C₄²×C₁₇	C₂×C₄
Frattini	C₄²	C₂×#595
Fitting	C₁₇×#125	C₄
socle	C₂×C₁₇	#333
prime radical	C₂²×C₁₇	#100
cosocle	C₄×#3622	C₂²
hypercenter	#125	#595
hypocenter	C₁₇	#1366
LCS	G ▷ C₄²×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
47. C₁₇	#1366	semidirect

Maximal subgroups

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

subgroup	index
#11763732	2
#11763208	2
#1366	17