Subgroups — #17981142

Order 4352.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545848	C₂	1	2	yes	maximal
2	C₁₆×#3624	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#63241	—	2	2	no	—
4	#11763695	C₄	1	1	yes	characteristic
5	C₈×#3624	C₂²	1	1	yes	characteristic
6	C₁₆×Dic₁₇	C₄	1	1	yes	characteristic
7	C₂×#63241	—	4	2	no	—
8	C₄×#3624	D₄	1	1	yes	characteristic
9	C₄×#3624	Q₈	1	1	yes	characteristic
10	C₂×#63216	—	2	1	no	—
11	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic
12	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂×#63214	C₈	1	1	yes	characteristic
14	C₂×#3624	—	2	1	no	—
15	C₂×#3624	D₈	1	1	yes	characteristic
16	C₂×#3624	Q₁₆	1	1	yes	characteristic
17	#63241	—	8	2	no	—
18	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
19	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
20	C₂×#3622	M₁₆	1	1	yes	characteristic
21	#63216	—	2	2	no	—
22	C₁₆×C₁₇	—	2	1	no	—
23	#63214	C₁₆	1	2	yes	complemented
24	#7100	—	17	1	no	maximal, Sylow
25	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
26	C₂×Dic₁₇	#107	1	1	yes	characteristic
27	C₂×Dic₁₇	#108	1	1	yes	characteristic
28	#3624	—	2	2	no	—
29	#3624	—	2	1	no	—
30	#3624	D₁₆	1	1	yes	characteristic
31	#3624	Q₃₂	1	1	yes	characteristic
32	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
33	C₈×C₁₇	M₃₂	1	1	yes	characteristic
34	#3622	—	2	1	no	—
35	#1370	—	17	2	no	—
36	C₈×C₁₆	—	17	1	no	—
37	C₂²×C₁₇	#335	1	1	yes	characteristic
38	C₄×C₁₇	C₄⋊C₁₆	1	1	yes	characteristic
39	C₄×C₁₇	#364	1	1	yes	characteristic
40	Dic₁₇	—	2	1	no	—
41	Dic₁₇	#366	1	1	yes	characteristic
42	Dic₁₇	#368	1	1	yes	characteristic
43	C₄⋊C₁₆	—	34	2	no	—
44	C₄×C₁₆	—	17	1	no	—
45	C₄×C₁₆	—	17	1	no	—
46	C₈²	—	17	1	no	—
47	C₂×C₁₇	#1370	1	1	yes	characteristic
48	C₂×C₁₇	#1371	1	1	yes	characteristic
49	C₂×C₁₇	#1373	1	1	yes	characteristic
50	C₂×C₁₆	—	17	1	no	—
51	C₂×C₁₆	—	34	1	no	—
52	C₂×C₁₆	—	68	2	no	—
53	C₂×C₁₆	#3633	1	1	yes	characteristic
54	C₄×C₈	—	17	1	no	—
55	C₄×C₈	—	17	1	no	—
56	C₄×C₈	—	17	1	no	—
57	C₁₇	#7100	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₈	—	17	1	no	—
59	C₂×C₈	—	17	1	no	—
60	C₂×C₈	—	17	1	no	—
61	C₂×C₈	—	34	1	no	—
62	C₂×C₈	C₂×#3633	1	1	yes	characteristic
63	C₄²	—	17	1	no	—
64	C₁₆	—	2	1	no	—
65	C₁₆	—	17	2	no	—
66	C₁₆	—	34	2	no	—
67	C₁₆	—	136	2	no	—
68	C₂×C₄	—	17	1	no	—
69	C₂×C₄	—	17	1	no	—
70	C₂×C₄	C₄⋊#3633	1	1	yes	characteristic
71	C₈	—	17	1	no	—
72	C₈	—	17	1	no	—
73	C₈	—	34	1	no	—
74	C₈	—	34	2	no	—
75	C₈	—	34	1	no	—
76	C₈	#10587665	1	1	yes	characteristic
77	C₈	#10587670	1	1	yes	characteristic
78	C₂²	#11763899	1	1	yes	characteristic
79	C₄	—	17	1	no	—
80	C₄	—	17	1	no	—
81	C₄	—	34	1	no	—
82	C₄	#11763912	1	1	yes	characteristic
83	C₄	#11763913	1	1	yes	characteristic
84	C₂	#14545849	1	1	yes	characteristic
85	C₂	#14545850	1	1	yes	characteristic
86	C₂	#14545853	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11763899
commutator	C₈×C₁₇	C₂×C₁₆
Frattini	C₂×C₈	C₂×#3633
Fitting	C₂×C₁₆×C₁₇	C₈
socle, prime radical	C₂²×C₁₇	#335
cosocle	C₈×#3624	C₂²
hypercenter	C₂×C₁₆	#3633
hypocenter	C₁₇	#7100
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
23. #63214	C₁₆	semidirect
57. C₁₇	#7100	semidirect

Maximal subgroups

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

subgroup	index
#14545848	2
C₁₆×#3624	2
#7100	17