Subgroups — #17949387

Order 4352.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543817	C₂	1	1	yes	maximal, characteristic
2	#14543817	C₂	1	1	yes	maximal, characteristic
3	#14526917	C₂	1	1	yes	maximal, characteristic
4	#11763672	—	2	1	no	—
5	#11763672	—	2	1	no	—
6	C₂×#10587465	C₄	1	1	yes	characteristic
7	C₁₆×Dic₁₇	C₂²	1	1	yes	characteristic
8	C₂×C₁₇×C₃₂	C₄	1	1	yes	characteristic
9	C₄⋊#3624	—	4	1	no	—
10	C₄⋊#3624	—	4	1	no	—
11	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₈×Dic₁₇	D₄	1	1	yes	characteristic
13	C₂×#63214	Q₈	1	1	yes	characteristic
14	C₁₇×C₃₂	—	2	1	no	—
15	#10587465	C₈	1	2	yes	complemented
16	C₂×#3624	—	8	1	no	—
17	C₂×#3624	—	8	1	no	—
18	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
19	C₄×Dic₁₇	D₈	1	1	yes	characteristic
20	C₂×#3622	Q₁₆	1	1	yes	characteristic
21	C₁₆×C₁₇	C₂×C₈	1	1	yes	characteristic
22	C₁₆×C₁₇	M₁₆	1	1	yes	characteristic
23	#63214	—	2	1	no	—
24	#7463	—	17	1	no	maximal, Sylow
25	C₂×C₄×C₁₇	#107	1	1	yes	characteristic
26	C₂×Dic₁₇	SD₃₂	1	1	yes	characteristic
27	C₂×Dic₁₇	SD₃₂	1	1	yes	characteristic
28	#3624	—	16	1	no	—
29	#3624	—	16	1	no	—
30	C₈×C₁₇	C₄⋊C₈	1	1	yes	characteristic
31	C₈×C₁₇	#108	1	1	yes	characteristic
32	#3622	—	2	1	no	—
33	#1397	—	17	1	no	—
34	#1372	—	17	1	no	—
35	#1372	—	17	1	no	—
36	C₂²×C₁₇	#367	1	1	yes	characteristic
37	C₄×C₁₇	#335	1	1	yes	characteristic
38	C₄×C₁₇	#368	1	1	yes	characteristic
39	Dic₁₇	—	2	1	no	—
40	Dic₁₇	—	2	1	no	—
41	C₂×C₃₂	—	17	1	no	—
42	C₂×C₃₂	#595	1	1	yes	characteristic
43	C₄×C₁₆	—	17	1	no	—
44	#335	—	34	1	no	—
45	#335	—	34	1	no	—
46	C₂×C₁₇	#1372	1	1	yes	characteristic
47	C₂×C₁₇	#1426	1	1	yes	characteristic
48	C₂×C₁₇	#1426	1	1	yes	characteristic
49	C₂×C₁₆	—	17	1	no	—
50	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
51	C₄⋊C₈	—	68	1	no	—
52	C₄⋊C₈	—	68	1	no	—
53	C₄×C₈	—	17	1	no	—
54	C₃₂	—	2	1	no	—
55	C₃₂	—	17	2	no	—
56	C₁₇	#7463	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₈	—	17	1	no	—
58	C₂×C₈	—	136	1	no	—
59	C₂×C₈	—	136	1	no	—
60	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
61	C₄²	—	17	1	no	—
62	C₁₆	—	34	1	no	—
63	C₁₆	#63242	1	1	yes	characteristic
64	C₁₆	#63247	1	1	yes	characteristic
65	C₂×C₄	—	17	1	no	—
66	C₂×C₄	—	17	1	no	—
67	C₂×C₄	#10587534	1	1	yes	characteristic
68	C₈	—	272	1	no	—
69	C₈	—	272	1	no	—
70	C₈	—	34	1	no	—
71	C₈	#10587535	1	1	yes	characteristic
72	C₈	#10587544	1	1	yes	characteristic
73	C₂²	#11763736	1	1	yes	characteristic
74	C₄	—	34	1	no	—
75	C₄	—	34	1	no	—
76	C₄	#11763673	1	1	yes	characteristic
77	C₄	#11763737	1	1	yes	characteristic
78	C₂	#14543818	1	1	yes	characteristic
79	C₂	#14543949	1	1	yes	characteristic
80	C₂	#14543950	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11763736
commutator	C₁₆×C₁₇	C₂×C₈
Frattini	C₂×C₁₆	C₂×#595
Fitting	C₂×C₁₇×C₃₂	C₄
socle, prime radical	C₂²×C₁₇	#367
cosocle	C₁₆×Dic₁₇	C₂²
hypercenter	C₂×C₃₂	#595
hypocenter	C₁₇	#7463
LCS	G ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
15. #10587465	C₈	semidirect
56. C₁₇	#7463	semidirect

Maximal subgroups

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

subgroup	index
#14543817	2
#14526917	2
#7463	17