Subgroups — #17981500

Order 4352.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545888	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11763891	C₂	1	1	yes	maximal, characteristic, complemented
3	#14545208	C₂	1	1	yes	maximal, characteristic
4	#11763891	—	2	1	no	—
5	#11763891	—	2	1	no	—
6	#11763742	—	2	1	no	—
7	#11763741	C₄	1	1	yes	characteristic
8	#11763740	—	2	1	no	—
9	C₂×#10587467	C₂²	1	1	yes	characteristic
10	#11763227	C₄	1	1	yes	characteristic
11	#10587587	C₈	1	1	yes	characteristic
12	C₁₇×M₃₂	C₈	1	1	yes	characteristic
13	C₂×#63214	C₂×C₄	1	1	yes	characteristic
14	#10587469	—	2	1	no	—
15	C₁₆×D₁₇	—	2	1	no	—
16	#10587467	—	2	1	no	—
17	#10587467	D₄	1	1	yes	characteristic
18	#10587467	D₄	1	1	yes	characteristic
19	#63252	C₁₆	1	1	yes	characteristic
20	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
21	#63223	C₁₆	1	1	yes	characteristic
22	#63218	—	2	1	no	—
23	C₈×D₁₇	—	2	1	no	—
24	C₁₆×C₁₇	—	2	1	no	—
25	#63214	C₂²⋊C₄	1	1	yes	characteristic
26	#63214	M₁₆	1	1	yes	characteristic
27	#7514	—	17	1	no	maximal, Sylow
28	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
29	C₂²⋊D₁₇	—	2	1	no	—
30	D₆₈	C₃₂	1	1	yes	characteristic
31	C₄×D₁₇	—	2	1	no	—
32	Dic₃₄	C₃₂	1	1	yes	characteristic
33	C₈×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
34	C₈×C₁₇	M₃₂	1	1	yes	characteristic
35	#3622	—	2	1	no	—
36	#2258	—	17	1	no	—
37	M₁₂₈	—	17	1	no	—
38	C₂×C₆₄	—	17	1	no	—
39	C₂²×C₁₇	M₆₄	1	1	yes	characteristic
40	C₂×D₁₇	—	2	1	no	—
41	C₄×C₁₇	C₂²⋊C₁₆	1	1	yes	characteristic
42	C₄×C₁₇	C₂×C₃₂	1	1	yes	characteristic
43	Dic₁₇	—	2	1	no	—
44	#504	—	17	1	no	—
45	M₆₄	—	17	1	no	—
46	M₆₄	—	34	1	no	—
47	C₂×C₃₂	—	17	1	no	—
48	C₂×C₃₂	—	34	1	no	—
49	C₆₄	—	34	1	no	—
50	C₆₄	—	34	1	no	—
51	C₂×C₁₇	—	2	1	no	—
52	C₂×C₁₇	C₂²⋊C₃₂	1	1	yes	characteristic
53	D₁₇	—	4	1	no	—
54	#131	—	17	1	no	—
55	M₃₂	—	34	1	no	—
56	M₃₂	#3633	1	1	yes	characteristic
57	C₂×C₁₆	—	17	1	no	—
58	C₂×C₁₆	—	34	1	no	—
59	C₃₂	—	17	1	no	—
60	C₃₂	—	17	1	no	—
61	C₃₂	—	34	1	no	—
62	C₁₇	#7514	1	1	yes	characteristic, complemented, Sylow
63	#41	—	17	1	no	—
64	M₁₆	—	17	1	no	—
65	M₁₆	—	34	1	no	—
66	C₂×C₈	—	34	1	no	—
67	C₂×C₈	C₂×#3633	1	1	yes	characteristic
68	C₁₆	—	2	1	no	—
69	C₁₆	—	17	1	no	—
70	C₁₆	—	17	1	no	—
71	Q₈	—	17	1	no	—
72	D₄	—	17	1	no	—
73	D₄	—	34	1	no	—
74	C₂×C₄	—	34	1	no	—
75	C₂×C₄	#10587665	1	1	yes	characteristic
76	C₈	—	34	1	no	—
77	C₈	#10587666	1	1	yes	characteristic
78	C₈	C₂²⋊#3633	1	1	yes	characteristic
79	C₂²	—	34	1	no	—
80	C₂²	#11763918	1	1	yes	characteristic
81	C₄	—	34	1	no	—
82	C₄	#11763906	1	1	yes	characteristic
83	C₄	#11763916	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	68	1	no	—
86	C₂	#14545877	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#3633
commutator	C₄×C₁₇	C₂×C₃₂
Frattini	C₂×C₈	C₂×#3633
Fitting	C₁₇×M₃₂	C₈
socle	C₂×C₁₇	C₂²⋊C₃₂
prime radical	#63252	C₁₆
cosocle	C₂×#10587467	C₂²
hypercenter	M₃₂	#3633
hypocenter	C₁₇	#7514
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
1. #14545888	C₂	semidirect
2. C₂×#11763891	C₂	semidirect
62. C₁₇	#7514	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×#11763891	2
#14545208	2
#7514	17