Subgroups — #11763659

Order 1088.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587573	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#3624	C₂	1	1	yes	maximal, characteristic
3	C₄×#3624	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₄	C₄	1	1	yes	characteristic
5	C₂×#3624	—	2	1	no	—
6	C₂×#3624	—	2	1	no	—
7	C₄⋊C₄×C₁₇	C₄	1	1	yes	characteristic
8	#63225	—	2	1	no	—
9	C₄×Dic₁₇	—	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	—	2	1	no	—
17	Dic₃₄	C₈	1	2	yes	complemented
18	#3624	—	2	2	no	—
19	#3624	—	4	1	no	—
20	C₂²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₇	—	4	1	no	—
22	C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
23	C₄×C₁₇	M₁₆	1	1	yes	characteristic
24	Dic₁₇	—	2	2	no	—
25	Dic₁₇	—	2	1	no	—
26	Dic₁₇	SD₁₆	1	1	yes	characteristic
27	Dic₁₇	Q₁₆	1	1	yes	characteristic
28	Q₈⋊C₈	—	17	1	no	maximal, Sylow
29	C₂×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
30	C₂×C₁₇	#103	1	1	yes	characteristic
31	C₂×C₁₇	#104	1	1	yes	characteristic
32	C₄×Q₈	—	17	1	no	—
33	C₄⋊C₈	—	17	1	no	—
34	C₄×C₈	—	17	1	no	—
35	C₁₇	Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
36	C₂×Q₈	—	17	1	no	—
37	C₂×C₈	—	34	1	no	—
38	C₂×C₈	—	34	1	no	—
39	C₄⋊C₄	—	34	1	no	—
40	C₄⋊C₄	#595	1	1	yes	characteristic
41	C₄²	—	17	1	no	—
42	C₄²	—	34	1	no	—
43	Q₈	—	17	2	no	—
44	Q₈	—	34	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	—	34	2	no	—
51	C₈	—	68	1	no	—
52	C₂²	C₂²⋊#595	1	1	yes	characteristic
53	C₄	—	4	1	no	—
54	C₄	—	17	1	no	—
55	C₄	—	17	1	no	—
56	C₄	—	34	2	no	—
57	C₄	—	34	1	no	—
58	C₄	#63242	1	1	yes	characteristic
59	C₄	#63243	1	1	yes	characteristic
60	C₂	#10587543	1	1	yes	characteristic
61	C₂	#10587548	1	1	yes	characteristic
62	C₂	#10587549	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#595
commutator	C₄×C₁₇	C₂×C₈
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	Q₈⋊C₈
LCS	G ▷ C₄×C₁₇ ▷ C₂×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
17. Dic₃₄	C₈	semidirect
35. C₁₇	Q₈⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
#10587573	2
C₄⋊#3624	2
C₄×#3624	2
Q₈⋊C₈	17