Subgroups — #11763704

Order 1088.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#63216	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×D₁₇	C₄	1	1	yes	characteristic
4	C₂×C₈×C₁₇	C₄	1	1	yes	characteristic
5	C₂×#3622	C₂²	1	1	yes	characteristic
6	C₈×D₁₇	—	2	2	no	—
7	#63216	—	2	2	no	—
8	C₂²×D₁₇	C₈	1	1	yes	characteristic
9	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₁₇	C₈	1	1	yes	characteristic
11	C₄×D₁₇	—	2	1	no	—
12	C₄×D₁₇	—	2	1	no	—
13	C₈×C₁₇	—	2	1	no	—
14	#3622	D₄	1	2	yes	—
15	C₂²×C₁₇	C₂×C₈	1	1	yes	characteristic
16	C₂×D₁₇	—	2	1	no	—
17	C₂×D₁₇	—	2	1	no	—
18	C₂×D₁₇	C₁₆	1	2	yes	complemented
19	C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₁₇	M₁₆	1	1	yes	characteristic
21	Dic₁₇	—	2	1	no	—
22	C₂²⋊C₁₆	—	17	1	no	maximal, Sylow
23	C₂×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
24	C₂×C₁₇	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₁₇	M₃₂	1	1	yes	characteristic
26	D₁₇	—	2	2	no	—
27	C₂²×C₈	—	17	1	no	—
28	C₂×C₁₆	—	17	2	no	—
29	C₁₇	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₄	—	17	1	no	—
31	C₂×C₈	—	17	1	no	—
32	C₂×C₈	—	34	2	no	—
33	C₂×C₈	#595	1	1	yes	characteristic
34	C₁₆	—	34	2	no	—
35	C₂³	—	17	1	no	—
36	C₂×C₄	—	17	1	no	—
37	C₂×C₄	—	34	1	no	—
38	C₂×C₄	—	34	1	no	—
39	C₂×C₄	C₂×#595	1	1	yes	characteristic
40	C₈	—	2	1	no	—
41	C₈	—	17	2	no	—
42	C₂²	—	17	2	no	—
43	C₂²	—	34	1	no	—
44	C₂²	—	34	1	no	—
45	C₂²	#63242	1	1	yes	characteristic
46	C₄	—	34	1	no	—
47	C₄	#63243	1	1	yes	characteristic
48	C₄	C₂²⋊#595	1	1	yes	characteristic
49	C₂	—	34	2	no	—
50	C₂	#10587529	1	1	yes	characteristic
51	C₂	#10587530	1	1	yes	characteristic
52	C₂	#10587543	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#595
commutator	C₂×C₁₇	C₂×C₁₆
Fitting	C₂×C₈×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₈
prime radical	C₂²×D₁₇	C₈
cosocle	C₂×#3622	C₂²
hypercenter	C₂×C₈	#595
hypocenter	C₁₇	C₂²⋊C₁₆
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#63216	C₂	semidirect
18. C₂×D₁₇	C₁₆	semidirect
29. C₁₇	C₂²⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₁₇	2
C₂×#63216	2
C₂²⋊C₁₆	17