Subgroups — #11763680

Order 1088.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587677	C₂	1	1	yes	maximal, characteristic
2	D₁₇⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄²×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×D₁₇	—	2	1	no	—
5	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
6	C₂²⋊#595	—	2	1	no	—
7	#63247	—	2	1	no	—
8	C₄⋊#595	C₄	1	2	yes	complemented
9	C₄×#595	—	2	1	no	—
10	#63243	C₄	1	2	yes	complemented
11	#63242	—	2	1	no	—
12	C₄²×C₁₇	C₄	1	1	yes	characteristic, complemented
13	C₄×Dic₁₇	—	2	1	no	—
14	C₄×Dic₁₇	C₄	1	1	yes	characteristic, complemented
15	C₂²×D₁₇	D₄	1	1	yes	characteristic
16	C₂×#595	—	2	2	no	—
17	C₂×C₄×C₁₇	—	2	1	no	—
18	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₁₇	—	2	1	no	—
20	C₂×Dic₁₇	D₄	1	1	yes	characteristic
21	C₄×D₁₇	—	2	4	no	—
22	C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
23	C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
24	C₄×D₁₇	D₄	1	1	yes	characteristic
25	C₄×D₁₇	Q₈	1	1	yes	characteristic
26	#3624	—	2	2	no	—
27	C₂²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×D₁₇	—	2	2	no	—
29	C₂×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×D₁₇	C₄⋊C₄	1	1	yes	characteristic
31	#595	—	4	2	no	—
32	C₄×C₁₇	—	2	2	no	—
33	C₄×C₁₇	C₄²	1	1	yes	characteristic
34	C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
35	Dic₁₇	—	2	2	no	—
36	Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
37	Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
38	#339	—	17	1	no	maximal, Sylow
39	C₂×C₁₇	—	2	1	no	—
40	C₂×C₁₇	#95	1	1	yes	characteristic
41	D₁₇	—	2	1	no	—
42	D₁₇	#104	1	2	yes	—
43	C₂×M₁₆	—	17	1	no	—
44	#117	—	17	1	no	—
45	C₂×C₄²	—	17	1	no	—
46	C₁₇	#339	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₄	—	17	1	no	—
48	C₂²×C₄	—	34	1	no	—
49	M₁₆	—	17	2	no	—
50	M₁₆	—	34	1	no	—
51	C₂×C₈	—	34	1	no	—
52	C₄⋊C₄	—	17	2	no	—
53	C₂²⋊C₄	—	34	1	no	—
54	C₄²	—	17	1	no	—
55	C₄²	—	34	1	no	—
56	C₄²	—	34	1	no	—
57	C₄²	#595	1	1	yes	characteristic, complemented
58	C₂³	—	17	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	17	1	no	—
61	C₂×C₄	—	17	1	no	—
62	C₂×C₄	—	17	1	no	—
63	C₂×C₄	—	17	1	no	—
64	C₂×C₄	—	17	1	no	—
65	C₂×C₄	—	34	4	no	—
66	C₂×C₄	—	34	1	no	—
67	C₂×C₄	—	34	2	no	—
68	C₂×C₄	C₂×#595	1	1	yes	characteristic
69	C₈	—	34	2	no	—
70	C₂²	—	17	1	no	—
71	C₂²	—	17	1	no	—
72	C₂²	—	34	2	no	—
73	C₂²	C₂²⋊#595	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	17	1	no	—
76	C₄	—	17	1	no	—
77	C₄	—	34	2	no	—
78	C₄	—	68	2	no	—
79	C₄	C₄×#595	1	1	yes	characteristic
80	C₄	C₄⋊#595	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	—	17	2	no	—
83	C₂	—	34	1	no	—
84	C₂	(C₂×#595)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊#595
commutator	C₄×C₁₇	C₄²
Frattini	C₂×C₄	C₂×#595
Fitting	C₄²×C₁₇	C₄
socle	C₂×C₁₇	#95
prime radical	C₂²×D₁₇	D₄
cosocle	C₂×C₄×D₁₇	C₂²
hypercenter	C₄²	#595
hypocenter	C₁₇	#339
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
8. C₄⋊#595	C₄	semidirect
10. #63243	C₄	semidirect
12. C₄²×C₁₇	C₄	semidirect
14. C₄×Dic₁₇	C₄	semidirect
46. C₁₇	#339	semidirect
57. C₄²	#595	semidirect

Maximal subgroups

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

subgroup	index
#10587677	2
D₁₇⋊M₁₆	2
C₄²×D₁₇	2
#339	17