Subgroups — #11763668

Order 1088.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587574	C₂	1	1	yes	maximal, characteristic
2	#10587544	C₂	1	1	yes	maximal, characteristic
3	#10587544	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₄	—	2	1	no	—
5	C₂×#3624	—	2	1	no	—
6	C₂×#3624	—	2	1	no	—
7	C₄⋊C₄×C₁₇	C₄	1	1	yes	characteristic
8	C₄⋊Dic₁₇	C₄	1	1	yes	characteristic
9	#63225	—	2	1	no	—
10	C₄×Dic₁₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₇	—	2	1	no	—
12	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₁₇	—	2	1	no	—
14	C₂×Dic₁₇	D₄	1	1	yes	characteristic
15	C₂×Dic₁₇	D₄	1	1	yes	characteristic
16	Dic₃₄	—	4	1	no	—
17	Dic₃₄	—	4	1	no	—
18	#3624	—	4	1	no	—
19	#3624	—	4	1	no	—
20	C₂²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₇	—	2	1	no	—
22	C₄×C₁₇	—	4	1	no	—
23	Dic₁₇	—	4	1	no	—
24	Dic₁₇	D₈	1	1	yes	characteristic
25	Dic₁₇	SD₁₆	1	1	yes	characteristic
26	Dic₁₇	SD₁₆	1	1	yes	characteristic
27	Dic₁₇	Q₁₆	1	1	yes	characteristic
28	#332	—	17	1	no	maximal, Sylow
29	C₂×C₁₇	#101	1	1	yes	characteristic
30	C₂×C₁₇	#102	1	1	yes	characteristic
31	C₂×C₁₇	#103	1	1	yes	characteristic
32	C₄⋊Q₈	—	17	1	no	—
33	C₄⋊C₈	—	17	1	no	—
34	C₄⋊C₈	—	17	1	no	—
35	C₁₇	#332	1	1	yes	characteristic, complemented, Sylow
36	C₂×Q₈	—	34	1	no	—
37	C₂×C₈	—	34	1	no	—
38	C₂×C₈	—	34	1	no	—
39	C₄⋊C₄	—	17	1	no	—
40	C₄⋊C₄	—	34	1	no	—
41	C₄⋊C₄	#595	1	1	yes	characteristic
42	C₄²	—	17	1	no	—
43	Q₈	—	68	1	no	—
44	Q₈	—	68	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	17	1	no	—
47	C₂×C₄	—	17	1	no	—
48	C₂×C₄	—	34	1	no	—
49	C₂×C₄	C₂×#595	1	1	yes	characteristic
50	C₈	—	68	1	no	—
51	C₈	—	68	1	no	—
52	C₂²	C₂²⋊#595	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	4	1	no	—
55	C₄	—	17	1	no	—
56	C₄	—	17	1	no	—
57	C₄	—	17	1	no	—
58	C₄	—	17	1	no	—
59	C₄	—	68	1	no	—
60	C₂	#10587545	1	1	yes	characteristic
61	C₂	#10587547	1	1	yes	characteristic
62	C₂	#10587549	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#595
commutator	C₂×C₄×C₁₇	C₂×C₄
Frattini	C₂×C₄	C₂×#595
Fitting	C₄⋊C₄×C₁₇	C₄
socle, prime radical	C₂²×C₁₇	C₂²⋊C₄
cosocle	C₄×Dic₁₇	C₂²
hypercenter	C₄⋊C₄	#595
hypocenter	C₁₇	#332
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
35. C₁₇	#332	semidirect

Maximal subgroups

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

subgroup	index
#10587574	2
#10587544	2
#332	17