Subgroups — #14543789

Order 2176.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763701	C₂	1	2	yes	maximal
2	#11763177	C₂	1	1	yes	maximal, characteristic
3	C₁₇×C₄⋊Q₈	C₄	1	1	yes	characteristic
4	#10587556	C₄	1	1	yes	characteristic
5	#10587538	—	2	2	no	—
6	#10587506	—	2	2	no	—
7	#10587474	C₂²	1	1	yes	characteristic
8	C₂×Q₈×C₁₇	—	2	1	no	—
9	C₄⋊C₄×C₁₇	—	4	1	no	—
10	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₄⋊Dic₁₇	—	2	1	no	—
12	#63225	—	4	1	no	—
13	C₂×#3622	D₄	1	2	yes	—
14	#63216	—	2	4	no	—
15	Q₈×C₁₇	—	4	2	no	—
16	C₂×C₄×C₁₇	—	2	1	no	—
17	C₂×C₄×C₁₇	—	4	1	no	—
18	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×Dic₁₇	—	4	1	no	—
20	#3622	—	2	2	no	—
21	#1356	—	17	1	no	maximal, Sylow
22	C₂²×C₁₇	#100	1	1	yes	characteristic
23	C₄×C₁₇	—	4	1	no	—
24	C₄×C₁₇	—	8	1	no	—
25	C₄×C₁₇	#104	1	2	yes	—
26	Dic₁₇	—	8	1	no	—
27	#491	—	17	1	no	—
28	#347	—	17	2	no	—
29	C₂×C₁₇	—	2	1	no	—
30	C₂×C₁₇	#329	1	1	yes	characteristic
31	C₄⋊Q₈	#595	1	1	yes	characteristic
32	#125	—	17	1	no	—
33	M₃₂	—	34	2	no	—
34	#103	—	34	2	no	—
35	#97	—	17	1	no	—
36	C₁₇	#1356	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₈	—	2	1	no	—
38	C₂×C₈	—	17	2	no	—
39	C₄⋊C₄	—	4	1	no	—
40	C₄⋊C₄	—	34	1	no	—
41	C₄⋊C₄	—	68	1	no	—
42	C₄²	C₂×#595	1	1	yes	characteristic
43	C₁₆	—	34	4	no	—
44	Q₈	—	4	2	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	4	1	no	—
47	C₂×C₄	—	68	1	no	—
48	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
49	C₈	—	34	2	no	—
50	C₂²	#10587553	1	1	yes	characteristic
51	C₄	—	4	1	no	—
52	C₄	—	8	1	no	—
53	C₄	—	136	1	no	—
54	C₄	#10587548	1	2	yes	—
55	C₂	—	2	1	no	—
56	C₂	#11763664	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11763664
commutator	C₄²×C₁₇	C₂×C₄
Frattini	C₄²	C₂×#595
Fitting	C₁₇×C₄⋊Q₈	C₄
socle	C₂×C₁₇	#329
prime radical	C₂²×C₁₇	#100
cosocle	#10587474	C₂²
hypercenter	C₄⋊Q₈	#595
hypocenter	C₁₇	#1356
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
36. C₁₇	#1356	semidirect

Maximal subgroups

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

subgroup	index
#11763701	2
#11763177	2
#1356	17