Subgroups — #11763113

Order 1088.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#125	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₃₄	C₂	1	1	yes	maximal, characteristic
3	#10587481	C₂	1	1	yes	maximal, characteristic
4	#10587481	C₂	1	1	yes	maximal, characteristic
5	#10587479	C₂	1	1	yes	maximal, characteristic
6	#10587478	C₂	1	1	yes	maximal, characteristic
7	C₄⋊#3622	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₄	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₁₇	—	2	1	no	—
10	C₄⋊C₄×C₁₇	—	2	1	no	—
11	C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
13	C₄²×C₁₇	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₁₇	C₂²	1	1	yes	characteristic
15	#63225	—	2	1	no	—
16	C₄×Dic₁₇	—	2	1	no	—
17	C₂×#3622	C₂²	1	1	yes	characteristic
18	C₂×#3622	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₁₇	—	2	1	no	—
20	C₂×C₄×C₁₇	—	2	1	no	—
21	C₂×C₄×C₁₇	D₄	1	1	yes	characteristic
22	C₂×C₄×C₁₇	D₄	1	1	yes	characteristic
23	C₂×C₄×C₁₇	C₂³	1	1	yes	characteristic
24	C₂×Dic₁₇	—	2	1	no	—
25	C₂×Dic₁₇	—	2	1	no	—
26	Dic₃₄	—	2	1	no	—
27	Dic₃₄	Q₈	1	2	yes	—
28	#3622	—	2	1	no	—
29	#3622	—	2	1	no	—
30	C₂²×C₁₇	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₇	—	2	1	no	—
32	C₄×C₁₇	—	2	1	no	—
33	C₄×C₁₇	—	4	1	no	—
34	C₄×C₁₇	—	4	1	no	—
35	C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
36	C₄×C₁₇	#41	1	1	yes	characteristic
37	Dic₁₇	—	2	2	no	—
38	Dic₁₇	—	4	1	no	—
39	#479	—	17	1	no	maximal, Sylow
40	C₂×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
41	C₂×C₁₇	#135	1	1	yes	characteristic
42	C₂×C₁₇	#137	1	1	yes	characteristic
43	#125	D₁₇	1	1	yes	characteristic
44	C₄×Q₈	—	17	1	no	—
45	#107	—	17	1	no	—
46	#106	—	17	1	no	—
47	C₄⋊C₈	—	17	1	no	—
48	#103	—	17	1	no	—
49	#103	—	17	1	no	—
50	C₁₇	#479	1	1	yes	characteristic, complemented, Sylow
51	C₂×Q₈	—	17	1	no	—
52	C₂×C₈	—	17	1	no	—
53	C₂×C₈	—	17	1	no	—
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	2	1	no	—
56	C₄⋊C₄	—	17	1	no	—
57	C₄⋊C₄	—	34	1	no	—
58	C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
60	C₄²	—	34	1	no	—
61	C₄²	C₂×D₁₇	1	1	yes	characteristic
62	Q₈	—	17	2	no	—
63	Q₈	—	34	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	34	1	no	—
67	C₂×C₄	—	34	1	no	—
68	C₂×C₄	C₂²⋊D₁₇	1	1	yes	characteristic
69	C₂×C₄	C₂²⋊D₁₇	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₁₇	1	1	yes	characteristic
71	C₈	—	34	1	no	—
72	C₈	—	34	1	no	—
73	C₂²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	34	2	no	—
79	C₄	—	68	1	no	—
80	C₄	Q₈×D₁₇	1	1	yes	characteristic
81	C₄	#63256	1	1	yes	characteristic
82	C₂	#10587632	1	1	yes	characteristic
83	C₂	#10587636	1	1	yes	characteristic
84	C₂	#10587637	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₇
commutator, cosocle	C₂×C₄×C₁₇	C₂³
Frattini	C₂×C₄	C₂²×D₁₇
Fitting	C₁₇×#125	C₂
socle, prime radical	C₂²×C₁₇	C₂×D₄
hypercenter	#125	D₁₇
hypocenter	C₁₇	#479
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
50. C₁₇	#479	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#125	2
C₄×Dic₃₄	2
#10587481	2
#10587479	2
#10587478	2
C₄⋊#3622	2
#479	17