Subgroups — #14526953

Order 2176.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11762608	C₂	1	2	yes	maximal
2	C₁₇×#494	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₁₆×C₁₇	—	2	2	no	—
4	C₁₇×C₄⋊Q₈	C₄	1	1	yes	characteristic
5	C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
7	#10587507	—	2	2	no	—
8	C₂×Q₈×C₁₇	—	2	1	no	—
9	C₂×Q₈×C₁₇	D₄	1	2	yes	—
10	Q₁₆×C₁₇	—	4	4	no	—
11	C₂×C₈×C₁₇	—	2	1	no	—
12	C₄⋊C₄×C₁₇	—	4	1	no	—
13	C₄⋊C₄×C₁₇	—	4	1	no	—
14	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
15	#63223	—	4	2	no	—
16	Q₈×C₁₇	—	4	2	no	—
17	Q₈×C₁₇	—	4	2	no	—
18	C₂×C₄×C₁₇	—	2	1	no	—
19	C₂×C₄×C₁₇	—	2	2	no	—
20	C₂×C₄×C₁₇	—	4	1	no	—
21	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₁₇	—	2	2	no	—
23	#3622	—	8	2	no	—
24	#1411	—	17	1	no	maximal, Sylow
25	C₂²×C₁₇	#99	1	1	yes	characteristic
26	C₄×C₁₇	—	2	2	no	—
27	C₄×C₁₇	—	2	1	no	—
28	C₄×C₁₇	—	4	2	no	—
29	C₄×C₁₇	—	8	1	no	—
30	#494	D₁₇	1	1	yes	characteristic
31	#356	—	17	2	no	—
32	C₂×C₁₇	—	2	1	no	—
33	C₂×C₁₇	#353	1	1	yes	characteristic
34	C₂×Q₁₆	—	2	2	no	—
35	C₄⋊Q₈	Dic₁₇	1	1	yes	characteristic
36	C₄⋊Q₈	C₂×D₁₇	1	1	yes	characteristic
37	#101	—	34	2	no	—
38	C₄×C₈	Dic₁₇	1	1	yes	characteristic
39	C₁₇	#1411	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	2	1	no	—
41	C₂×Q₈	C₂²⋊D₁₇	1	2	yes	—
42	Q₁₆	—	4	4	no	—
43	M₁₆	—	68	2	no	—
44	C₂×C₈	—	2	1	no	—
45	C₄⋊C₄	—	4	1	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₄²	C₂×Dic₁₇	1	1	yes	characteristic
48	Q₈	—	4	2	no	—
49	Q₈	—	4	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	4	1	no	—
53	C₂×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
54	C₈	—	2	2	no	—
55	C₈	—	136	2	no	—
56	C₂²	#10587505	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	2	1	no	—
59	C₄	—	4	2	no	—
60	C₄	—	8	1	no	—
61	C₂	—	2	1	no	—
62	C₂	#11762602	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11762602
commutator	C₄²×C₁₇	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₁₇
Fitting	C₁₇×#494	C₂
socle	C₂×C₁₇	#353
prime radical	C₂²×C₁₇	#99
cosocle	C₁₇×C₄⋊Q₈	C₂²
hypercenter	#494	D₁₇
hypocenter	C₁₇	#1411
LCS	G ▷ C₄²×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #494

Complements

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

N	H ≅ G/N	type
39. C₁₇	#1411	semidirect

Maximal subgroups

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

subgroup	index
#11762608	2
C₁₇×#494	2
#1411	17