Subgroups — #11762913

Order 1088.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Dic₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#63231	C₂	1	1	yes	maximal, characteristic
3	#10587573	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#103	C₂	1	1	yes	maximal, characteristic
5	#10587487	C₂	1	1	yes	maximal, characteristic
6	#10587486	C₂	1	1	yes	maximal, characteristic
7	#10587479	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₁₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₃₄	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₁₇	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
12	#63231	C₄	1	4	yes	complemented
13	C₄⋊Dic₁₇	—	2	1	no	—
14	C₄⋊Dic₁₇	C₂²	1	1	yes	characteristic
15	#63225	—	2	1	no	—
16	C₄×Dic₁₇	—	2	1	no	—
17	C₄×Dic₁₇	—	2	1	no	—
18	C₄×Dic₁₇	C₂²	1	1	yes	characteristic
19	C₂×#3622	C₂²	1	1	yes	characteristic
20	Q₈×C₁₇	—	2	1	no	—
21	Q₈×C₁₇	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₁₇	—	2	1	no	—
23	C₂×C₄×C₁₇	—	2	1	no	—
24	C₂×C₄×C₁₇	C₂³	1	1	yes	characteristic
25	C₂×Dic₁₇	—	2	1	no	—
26	C₂×Dic₁₇	—	2	1	no	—
27	C₂×Dic₁₇	D₄	1	1	yes	characteristic
28	C₂×Dic₁₇	D₄	1	1	yes	characteristic
29	Dic₃₄	—	2	1	no	—
30	Dic₃₄	C₂×C₄	1	2	yes	—
31	C₈×C₁₇	—	2	1	no	—
32	#3622	C₂×C₄	1	2	yes	—
33	C₂²×C₁₇	C₂×D₄	1	1	yes	characteristic
34	C₄×C₁₇	—	2	2	no	—
35	C₄×C₁₇	—	4	1	no	—
36	C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₁₇	#41	1	1	yes	characteristic
38	Dic₁₇	—	2	2	no	—
39	Dic₁₇	—	2	1	no	—
40	Dic₁₇	—	2	1	no	—
41	Dic₁₇	—	4	1	no	—
42	#441	—	17	1	no	maximal, Sylow
43	C₂×C₁₇	C₄×D₄	1	1	yes	characteristic
44	C₂×C₁₇	#137	1	1	yes	characteristic
45	C₂×C₁₇	#137	1	1	yes	characteristic
46	C₂×Q₁₆	—	17	1	no	—
47	C₄×Q₈	—	17	1	no	—
48	C₄×Q₈	—	17	1	no	—
49	#106	—	17	1	no	—
50	#103	—	17	1	no	—
51	#103	D₁₇	1	1	yes	characteristic
52	#97	—	17	1	no	—
53	C₁₇	#441	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	17	1	no	—
55	C₂×Q₈	C₂×D₁₇	1	1	yes	characteristic
56	Q₁₆	—	17	4	no	—
57	C₂×C₈	—	17	1	no	—
58	C₂×C₈	C₂×D₁₇	1	1	yes	characteristic
59	C₄⋊C₄	—	17	1	no	—
60	C₄⋊C₄	—	34	1	no	—
61	C₄⋊C₄	—	34	1	no	—
62	C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
63	C₄²	—	17	1	no	—
64	C₄²	—	34	1	no	—
65	C₄²	—	34	1	no	—
66	Q₈	—	2	1	no	—
67	Q₈	—	17	2	no	—
68	Q₈	—	34	1	no	—
69	Q₈	C₄×D₁₇	1	2	yes	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	17	1	no	—
73	C₂×C₄	—	17	1	no	—
74	C₂×C₄	—	34	1	no	—
75	C₂×C₄	—	34	1	no	—
76	C₂×C₄	C₂²×D₁₇	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	17	2	no	—
79	C₂²	D₄×D₁₇	1	1	yes	characteristic
80	C₄	—	2	2	no	—
81	C₄	—	4	1	no	—
82	C₄	—	34	2	no	—
83	C₄	—	34	1	no	—
84	C₄	—	34	1	no	—
85	C₄	—	68	1	no	—
86	C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
87	C₄	#63254	1	1	yes	characteristic
88	C₂	#10587567	1	1	yes	characteristic
89	C₂	#10587601	1	1	yes	characteristic
90	C₂	#10587604	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₇
commutator	C₄×C₁₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₇
Fitting	C₁₇×#103	C₂
socle, prime radical	C₂²×C₁₇	C₂×D₄
cosocle	C₂×C₄×C₁₇	C₂³
hypercenter	#103	D₁₇
hypocenter	C₁₇	#441
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
12. #63231	C₄	semidirect
53. C₁₇	#441	semidirect

Maximal subgroups

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

subgroup	index
Q₈×Dic₁₇	2
C₂×#63231	2
#10587573	2
C₁₇×#103	2
#10587487	2
#10587486	2
#10587479	2
#441	17