Subgroups — #17981498

Order 4352.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545888	C₂	1	2	yes	maximal, complemented
2	C₂×#11763742	C₂	1	1	yes	maximal, characteristic
3	#11763891	—	2	2	no	—
4	#11763742	—	2	2	no	—
5	C₂×#10587467	C₄	1	1	yes	characteristic
6	C₂×#10587467	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×D₁₇	C₄	1	1	yes	characteristic
8	C₂×C₈×D₁₇	C₈	1	1	yes	characteristic
9	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic
10	C₂×#63214	C₂×C₄	1	1	yes	characteristic
11	C₁₆×D₁₇	—	2	1	no	—
12	C₁₆×D₁₇	—	2	1	no	—
13	#10587467	—	2	1	no	—
14	#10587467	D₄	1	2	yes	—
15	C₂×C₄×D₁₇	C₁₆	1	1	yes	characteristic
16	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
17	C₂×#3622	C₁₆	1	1	yes	characteristic
18	C₈×D₁₇	—	2	1	no	—
19	C₈×D₁₇	—	2	1	no	—
20	C₁₆×C₁₇	—	2	1	no	—
21	#63214	C₂²⋊C₄	1	1	yes	characteristic
22	#63214	M₁₆	1	1	yes	characteristic
23	#7513	—	17	1	no	maximal, Sylow
24	C₂²×D₁₇	C₃₂	1	1	yes	characteristic
25	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
26	C₂×Dic₁₇	C₃₂	1	1	yes	characteristic
27	C₄×D₁₇	—	2	1	no	—
28	C₄×D₁₇	—	2	1	no	—
29	C₈×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
30	C₈×C₁₇	M₃₂	1	1	yes	characteristic
31	#3622	—	2	1	no	—
32	C₂×M₆₄	—	17	1	no	—
33	M₁₂₈	—	17	2	no	—
34	C₂²×C₁₇	C₂×C₃₂	1	1	yes	characteristic
35	C₂×D₁₇	—	2	1	no	—
36	C₂×D₁₇	—	4	1	no	—
37	C₄×C₁₇	C₂²⋊C₁₆	1	1	yes	characteristic
38	C₄×C₁₇	M₆₄	1	1	yes	characteristic
39	Dic₁₇	—	2	1	no	—
40	C₂²×C₁₆	—	17	1	no	—
41	M₆₄	—	34	2	no	—
42	C₂×C₃₂	—	17	1	no	—
43	C₂×C₃₂	—	17	1	no	—
44	C₆₄	—	34	2	no	—
45	C₂×C₁₇	—	2	1	no	—
46	C₂×C₁₇	C₂²⋊C₃₂	1	1	yes	characteristic
47	D₁₇	—	4	1	no	—
48	C₂²×C₈	—	17	1	no	—
49	C₂×C₁₆	—	17	1	no	—
50	C₂×C₁₆	—	34	1	no	—
51	C₂×C₁₆	—	34	1	no	—
52	C₂×C₁₆	#3633	1	1	yes	characteristic
53	C₃₂	—	17	2	no	—
54	C₃₂	—	34	1	no	—
55	C₁₇	#7513	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₄	—	17	1	no	—
57	C₂×C₈	—	17	1	no	—
58	C₂×C₈	—	34	1	no	—
59	C₂×C₈	—	34	1	no	—
60	C₂×C₈	C₂×#3633	1	1	yes	characteristic
61	C₁₆	—	2	1	no	—
62	C₁₆	—	17	1	no	—
63	C₁₆	—	17	1	no	—
64	C₂³	—	17	1	no	—
65	C₂×C₄	—	17	1	no	—
66	C₂×C₄	—	34	1	no	—
67	C₂×C₄	—	34	1	no	—
68	C₂×C₄	#10587665	1	1	yes	characteristic
69	C₈	—	34	1	no	—
70	C₈	#10587666	1	1	yes	characteristic
71	C₈	C₂²⋊#3633	1	1	yes	characteristic
72	C₂²	—	34	1	no	—
73	C₂²	—	68	1	no	—
74	C₂²	#11763916	1	1	yes	characteristic
75	C₄	—	34	1	no	—
76	C₄	#11763906	1	1	yes	characteristic
77	C₄	#11763918	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	68	1	no	—
80	C₂	#14545877	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#3633
commutator	C₂²×C₁₇	C₂×C₃₂
Frattini	C₂×C₈	C₂×#3633
Fitting	C₂×C₁₆×C₁₇	C₈
socle	C₂×C₁₇	C₂²⋊C₃₂
prime radical	C₂²×D₁₇	C₃₂
cosocle	C₂×#10587467	C₂²
hypercenter	C₂×C₁₆	#3633
hypocenter	C₁₇	#7513
LCS	G ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #14545888	C₂	semidirect
55. C₁₇	#7513	semidirect

Maximal subgroups

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

subgroup	index
#14545888	2
C₂×#11763742	2
#7513	17