Subgroups — #14543921

Order 2176.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763720	C₂	1	2	yes	maximal
2	#11763188	C₂	1	1	yes	maximal, characteristic
3	C₁₇×C₄⋊Q₈	C₄	1	1	yes	characteristic
4	C₂×#63231	—	2	2	no	—
5	#10587555	C₂²	1	1	yes	characteristic
6	#10587545	—	2	2	no	—
7	C₄×#3622	C₄	1	1	yes	characteristic
8	C₂×Q₈×C₁₇	—	2	1	no	—
9	C₂×Dic₃₄	D₄	1	2	yes	—
10	#63247	—	4	2	no	—
11	C₄⋊C₄×C₁₇	—	4	1	no	—
12	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
13	#63231	—	4	4	no	—
14	C₄⋊Dic₁₇	—	4	1	no	—
15	C₂×#3622	—	2	1	no	—
16	Q₈×C₁₇	—	4	2	no	—
17	C₂×C₄×C₁₇	—	2	1	no	—
18	C₂×C₄×C₁₇	—	4	1	no	—
19	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×Dic₁₇	—	2	2	no	—
21	Dic₃₄	—	4	2	no	—
22	#3624	—	8	2	no	—
23	#3622	—	2	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	—	8	1	no	—
29	Dic₁₇	—	4	2	no	—
30	#494	—	17	1	no	—
31	#356	—	17	2	no	—
32	C₂×C₁₇	—	2	1	no	—
33	C₂×C₁₇	#353	1	1	yes	characteristic
34	C₂×Q₁₆	—	34	2	no	—
35	C₄⋊Q₈	—	17	1	no	—
36	C₄⋊Q₈	#595	1	1	yes	characteristic
37	#101	—	34	2	no	—
38	C₄×C₈	—	17	1	no	—
39	C₁₇	#1411	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	2	1	no	—
41	C₂×Q₈	—	17	2	no	—
42	Q₁₆	—	68	4	no	—
43	M₁₆	—	68	2	no	—
44	C₂×C₈	—	34	1	no	—
45	C₄⋊C₄	—	4	1	no	—
46	C₄⋊C₄	—	68	1	no	—
47	C₄²	C₂×#595	1	1	yes	characteristic
48	Q₈	—	4	2	no	—
49	Q₈	—	68	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	—	34	2	no	—
53	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
54	C₈	—	34	2	no	—
55	C₈	—	136	2	no	—
56	C₂²	#10587551	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	2	1	no	—
59	C₄	—	8	1	no	—
60	C₄	—	68	2	no	—
61	C₂	—	2	1	no	—
62	C₂	#11763713	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11763713
commutator	C₄²×C₁₇	C₂×C₄
Frattini	C₄²	C₂×#595
Fitting	C₁₇×C₄⋊Q₈	C₄
socle	C₂×C₁₇	#353
prime radical	C₂²×C₁₇	#99
cosocle	#10587555	C₂²
hypercenter	C₄⋊Q₈	#595
hypocenter	C₁₇	#1411
LCS	G ▷ C₄²×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

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
#11763720	2
#11763188	2
#1411	17