Subgroups — #14545884

Order 2176.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763917	C₂	1	2	yes	maximal
2	#11763695	C₂	1	1	yes	maximal, characteristic
3	C₂×#63216	C₄	1	1	yes	characteristic
4	C₂×#63216	C₂²	1	1	yes	characteristic
5	#10587528	—	2	2	no	—
6	C₈×Dic₁₇	C₄	1	1	yes	characteristic
7	C₂×C₈×C₁₇	C₈	1	1	yes	characteristic
8	C₄×Dic₁₇	C₈	1	1	yes	characteristic
9	C₂×#3622	C₂×C₄	1	1	yes	characteristic
10	#63216	—	2	1	no	—
11	#63216	D₄	1	1	yes	characteristic
12	#63216	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
14	C₂×Dic₁₇	—	2	1	no	—
15	C₈×C₁₇	C₁₆	1	2	yes	—
16	#3622	C₄⋊C₄	1	1	yes	characteristic
17	#3622	M₁₆	1	1	yes	characteristic
18	#1422	—	17	1	no	maximal, Sylow
19	C₂²×C₁₇	M₃₂	1	1	yes	characteristic
20	C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
22	Dic₁₇	—	2	2	no	—
23	M₆₄	—	17	2	no	—
24	C₄×C₁₆	—	17	1	no	—
25	C₂×C₁₇	—	2	1	no	—
26	C₂×C₁₇	C₄⋊C₁₆	1	1	yes	characteristic
27	C₂×C₁₆	—	17	1	no	—
28	C₂×C₁₆	—	17	1	no	—
29	C₄×C₈	—	17	1	no	—
30	C₃₂	—	34	2	no	—
31	C₁₇	#1422	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₈	—	17	1	no	—
33	C₂×C₈	#3633	1	1	yes	characteristic
34	C₄²	—	17	1	no	—
35	C₁₆	—	17	1	no	—
36	C₁₆	—	17	1	no	—
37	C₁₆	—	34	1	no	—
38	C₂×C₄	—	34	1	no	—
39	C₂×C₄	C₂×#3633	1	1	yes	characteristic
40	C₈	—	17	1	no	—
41	C₈	—	17	1	no	—
42	C₈	#63241	1	2	yes	—
43	C₂²	#10587666	1	1	yes	characteristic
44	C₄	—	34	2	no	—
45	C₄	C₄⋊#3633	1	1	yes	characteristic
46	C₄	C₂×#63241	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	C₄⋊#63241	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊#3633
commutator	C₄×C₁₇	C₂×C₁₆
Frattini	C₂×C₄	C₂×#3633
Fitting	C₂×C₈×C₁₇	C₈
socle	C₂×C₁₇	C₄⋊C₁₆
prime radical	C₂²×C₁₇	M₃₂
cosocle	C₂×#63216	C₂²
hypercenter	C₂×C₈	#3633
hypocenter	C₁₇	#1422
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
31. C₁₇	#1422	semidirect

Maximal subgroups

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

subgroup	index
#11763917	2
#11763695	2
#1422	17