Subgroups — #11763654

Order 1088.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊#3624	C₂	1	2	yes	maximal
3	C₂²×C₄×C₁₇	C₄	1	1	yes	characteristic
4	C₂²×Dic₁₇	C₄	1	1	yes	characteristic
5	C₂²×Dic₁₇	C₂²	1	1	yes	characteristic
6	C₂×#3624	—	2	2	no	—
7	C₄⋊Dic₁₇	—	2	2	no	—
8	C₂³×C₁₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₇	—	2	1	no	—
10	C₂×C₄×C₁₇	—	2	1	no	—
11	C₂×C₄×C₁₇	C₈	1	2	yes	complemented
12	C₂×Dic₁₇	—	2	1	no	—
13	C₂×Dic₁₇	—	4	1	no	—
14	C₂×Dic₁₇	—	4	1	no	—
15	C₂×Dic₁₇	D₄	1	2	yes	—
16	#3624	—	4	2	no	—
17	C₂²×C₁₇	—	2	1	no	—
18	C₂²×C₁₇	—	2	1	no	—
19	C₂²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₂²×C₁₇	C₂×C₈	1	1	yes	characteristic
21	C₂²×C₁₇	M₁₆	1	1	yes	characteristic
22	C₄×C₁₇	—	2	2	no	—
23	Dic₁₇	—	2	2	no	—
24	Dic₁₇	—	4	1	no	—
25	#324	—	17	1	no	maximal, Sylow
26	C₂×C₁₇	—	2	1	no	—
27	C₂×C₁₇	—	2	1	no	—
28	C₂×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
29	C₂×C₁₇	#99	1	1	yes	characteristic
30	C₂×C₁₇	#101	1	1	yes	characteristic
31	C₂×C₄⋊C₄	—	17	1	no	—
32	C₂²⋊C₈	—	17	2	no	—
33	C₁₇	#324	1	1	yes	characteristic, complemented, Sylow
34	C₂²×C₄	—	17	1	no	—
35	C₂²×C₄	—	17	1	no	—
36	C₂²×C₄	#595	1	1	yes	characteristic
37	C₂×C₈	—	34	2	no	—
38	C₄⋊C₄	—	34	2	no	—
39	C₂³	C₂×#595	1	1	yes	characteristic
40	C₂×C₄	—	2	1	no	—
41	C₂×C₄	—	2	1	no	—
42	C₂×C₄	—	17	2	no	—
43	C₂×C₄	—	34	1	no	—
44	C₂×C₄	—	68	1	no	—
45	C₂×C₄	—	68	1	no	—
46	C₂×C₄	#3624	1	2	yes	complemented
47	C₈	—	68	2	no	—
48	C₂²	—	2	1	no	—
49	C₂²	—	2	1	no	—
50	C₂²	C₂×#3624	1	1	yes	characteristic
51	C₂²	#63247	1	1	yes	characteristic
52	C₂²	C₂²⋊#595	1	1	yes	characteristic
53	C₄	—	2	2	no	—
54	C₄	—	34	2	no	—
55	C₄	—	68	1	no	—
56	C₂	—	2	1	no	—
57	C₂	—	2	1	no	—
58	C₂	#10587539	1	1	yes	characteristic
59	C₂	#10587545	1	1	yes	characteristic
60	C₂	C₂²⋊#3624	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#595
commutator	C₂²×C₁₇	C₂×C₈
Frattini	C₂³	C₂×#595
Fitting	C₂²×C₄×C₁₇	C₄
socle	C₂²×C₁₇	C₂²⋊C₄
prime radical	C₂³×C₁₇	C₂×C₄
cosocle	C₂²×Dic₁₇	C₂²
hypercenter	C₂²×C₄	#595
hypocenter	C₁₇	#324
LCS	G ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
11. C₂×C₄×C₁₇	C₈	semidirect
33. C₁₇	#324	semidirect
46. C₂×C₄	#3624	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊Dic₁₇	2
C₂²⋊#3624	2
#324	17