Subgroups — #14543793

Order 2176.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763732	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	C₄	1	1	yes	characteristic
6	#10587538	—	2	2	no	—
7	C₄×#3622	C₂²	1	1	yes	characteristic
8	C₂×Q₈×C₁₇	—	2	1	no	—
9	C₂×Dic₃₄	—	2	1	no	—
10	C₄⋊C₄×C₁₇	—	4	1	no	—
11	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
12	#63231	—	4	2	no	—
13	#63231	—	4	2	no	—
14	C₄⋊Dic₁₇	—	4	1	no	—
15	C₂×#3622	D₄	1	2	yes	—
16	#63216	—	4	2	no	—
17	Q₈×C₁₇	—	4	2	no	—
18	C₂×C₄×C₁₇	—	2	1	no	—
19	C₂×C₄×C₁₇	—	4	1	no	—
20	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×Dic₁₇	—	4	1	no	—
22	Dic₃₄	—	4	2	no	—
23	#3622	D₈	1	2	yes	—
24	#3622	SD₁₆	1	2	yes	—
25	#1358	—	17	1	no	maximal, Sylow
26	C₂²×C₁₇	#100	1	1	yes	characteristic
27	C₄×C₁₇	—	2	2	no	—
28	C₄×C₁₇	—	8	1	no	—
29	C₄×C₁₇	#102	1	2	yes	—
30	Dic₁₇	—	8	1	no	—
31	#494	—	17	1	no	—
32	#364	—	17	2	no	—
33	C₂×C₁₇	—	2	1	no	—
34	C₂×C₁₇	#331	1	1	yes	characteristic
35	C₂×Q₁₆	—	34	2	no	—
36	C₄⋊Q₈	—	17	1	no	—
37	C₄⋊Q₈	#595	1	1	yes	characteristic
38	M₃₂	—	34	2	no	—
39	C₄×C₈	—	17	1	no	—
40	C₁₇	#1358	1	1	yes	characteristic, complemented, Sylow
41	C₂×Q₈	—	2	1	no	—
42	C₂×Q₈	—	34	1	no	—
43	Q₁₆	—	68	2	no	—
44	Q₁₆	—	68	2	no	—
45	C₂×C₈	—	17	2	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₄⋊C₄	—	68	1	no	—
48	C₄²	C₂×#595	1	1	yes	characteristic
49	C₁₆	—	68	2	no	—
50	Q₈	—	4	2	no	—
51	Q₈	—	68	2	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	—	68	1	no	—
55	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
56	C₈	—	17	2	no	—
57	C₈	—	17	2	no	—
58	C₂²	#10587553	1	1	yes	characteristic
59	C₄	—	2	2	no	—
60	C₄	—	8	1	no	—
61	C₄	—	136	1	no	—
62	C₄	#10587547	1	2	yes	—
63	C₂	—	2	1	no	—
64	C₂	#11763667	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11763667
commutator	C₄²×C₁₇	C₂×C₄
Frattini	C₄²	C₂×#595
Fitting	C₁₇×C₄⋊Q₈	C₄
socle	C₂×C₁₇	#331
prime radical	C₂²×C₁₇	#100
cosocle	C₄×#3622	C₂²
hypercenter	C₄⋊Q₈	#595
hypocenter	C₁₇	#1358
LCS	G ▷ C₄²×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
40. C₁₇	#1358	semidirect

Maximal subgroups

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

subgroup	index
#11763732	2
#11763188	2
#1358	17