Subgroups — #11763685

Order 1088.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63243	C₂	1	2	yes	maximal
2	C₂×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
4	C₂×#3624	—	2	2	no	—
5	#63243	—	2	2	no	—
6	#63243	C₄	1	4	yes	—
7	C₂×C₈×C₁₇	C₄	1	1	yes	characteristic
8	C₂×#3622	C₄	1	1	yes	characteristic
9	C₈×D₁₇	—	2	2	no	—
10	C₂²×D₁₇	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₁₇	D₄	1	1	yes	characteristic
13	C₄×D₁₇	C₂×C₄	1	2	yes	—
14	C₄×D₁₇	D₄	1	2	yes	—
15	#3624	—	2	4	no	—
16	C₈×C₁₇	—	2	1	no	—
17	#3622	—	2	1	no	—
18	C₂²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
19	C₂×D₁₇	—	2	1	no	—
20	C₂×D₁₇	—	2	1	no	—
21	C₂×D₁₇	C₄⋊C₄	1	2	yes	—
22	C₄×C₁₇	C₄²	1	1	yes	characteristic
23	C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₁₇	C₂²⋊C₄	1	2	yes	—
25	#341	—	17	1	no	maximal, Sylow
26	C₂×C₁₇	#95	1	1	yes	characteristic
27	C₂×C₁₇	#108	1	1	yes	characteristic
28	C₂×C₁₇	#108	1	1	yes	characteristic
29	D₁₇	—	2	2	no	—
30	C₂×M₁₆	—	17	2	no	—
31	C₂²×C₈	—	17	1	no	—
32	C₁₇	#341	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₄	—	17	1	no	—
34	M₁₆	—	17	4	no	—
35	M₁₆	—	34	2	no	—
36	C₂×C₈	—	17	1	no	—
37	C₂×C₈	—	34	2	no	—
38	C₂×C₈	—	34	2	no	—
39	C₂×C₈	#595	1	1	yes	characteristic
40	C₂³	—	17	1	no	—
41	C₂×C₄	—	17	1	no	—
42	C₂×C₄	—	17	2	no	—
43	C₂×C₄	—	17	2	no	—
44	C₂×C₄	C₂×#595	1	1	yes	characteristic
45	C₈	—	2	1	no	—
46	C₈	—	34	4	no	—
47	C₈	—	34	1	no	—
48	C₂²	—	17	2	no	—
49	C₂²	—	34	1	no	—
50	C₂²	—	34	1	no	—
51	C₂²	C₄⋊#595	1	1	yes	characteristic
52	C₄	—	17	2	no	—
53	C₄	C₄×#595	1	1	yes	characteristic
54	C₄	C₂²⋊#595	1	1	yes	characteristic
55	C₂	—	34	2	no	—
56	C₂	#10587535	1	1	yes	characteristic
57	C₂	#10587536	1	1	yes	characteristic
58	C₂	(C₂×#595)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#595
commutator	C₄×C₁₇	C₄²
Frattini	C₂×C₄	C₂×#595
Fitting	C₂×C₈×C₁₇	C₄
socle	C₂²×C₁₇	C₄⋊C₄
prime radical	C₂²×D₁₇	Q₈
cosocle	C₂×C₄×D₁₇	C₂²
hypercenter	C₂×C₈	#595
hypocenter	C₁₇	#341
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
32. C₁₇	#341	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63243	2
C₂×C₈×D₁₇	2
#341	17