Subgroups — #14543842

Order 2176.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587534	C₂	1	2	yes	maximal
2	C₂×C₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊#595	—	2	2	no	—
4	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
5	#10587534	—	2	2	no	—
6	#10587534	C₄	1	4	yes	complemented
7	C₂×C₁₆×C₁₇	C₄	1	1	yes	characteristic, complemented
8	C₂×#63214	C₄	1	1	yes	characteristic, complemented
9	C₁₆×D₁₇	—	2	2	no	—
10	C₂²×#595	—	4	2	no	—
11	C₂×C₄×D₁₇	D₄	1	1	yes	characteristic
12	C₄⋊#595	—	2	4	no	—
13	C₄⋊#595	—	4	2	no	—
14	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂×#3622	Q₈	1	1	yes	characteristic
16	C₈×D₁₇	C₂×C₄	1	2	yes	—
17	C₈×D₁₇	D₄	1	2	yes	—
18	C₁₆×C₁₇	—	2	1	no	—
19	#63214	—	2	1	no	—
20	C₂²×D₁₇	D₈	1	1	yes	characteristic
21	C₂×#595	—	4	4	no	—
22	C₂×#595	—	8	2	no	—
23	C₂×#595	—	8	2	no	—
24	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
25	C₂×Dic₁₇	Q₁₆	1	1	yes	characteristic
26	C₄×D₁₇	C₂²⋊C₄	1	2	yes	—
27	C₄×D₁₇	SD₁₆	1	2	yes	—
28	C₈×C₁₇	C₄²	1	1	yes	characteristic
29	C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
30	#3622	C₄⋊C₄	1	2	yes	—
31	#1380	—	17	1	no	maximal, Sylow
32	C₂²×C₁₇	#107	1	1	yes	characteristic
33	C₂×D₁₇	#102	1	2	yes	—
34	C₂×D₁₇	D₁₆	1	1	yes	characteristic
35	C₂×D₁₇	SD₃₂	1	2	yes	—
36	C₂×D₁₇	Q₃₂	1	1	yes	characteristic
37	#595	—	8	4	no	—
38	C₄×C₁₇	#95	1	1	yes	characteristic
39	C₄×C₁₇	#106	1	1	yes	characteristic
40	Dic₁₇	#103	1	2	yes	—
41	C₂²×C₁₆	—	17	1	no	—
42	C₂×#107	—	17	2	no	—
43	C₂×C₁₇	#340	1	1	yes	characteristic
44	C₂×C₁₇	#366	1	1	yes	characteristic
45	C₂×C₁₇	#367	1	1	yes	characteristic
46	D₁₇	#357	1	2	yes	—
47	D₁₇	#358	1	2	yes	—
48	C₂²×C₈	—	17	1	no	—
49	C₂×C₄⋊C₄	—	34	2	no	—
50	C₂×C₁₆	—	17	1	no	—
51	C₂×C₁₆	—	34	2	no	—
52	C₂×C₁₆	#595	1	1	yes	characteristic, complemented
53	#107	—	17	4	no	—
54	#107	—	34	2	no	—
55	C₁₇	#1380	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₄	—	17	1	no	—
57	C₂²×C₄	—	68	2	no	—
58	C₂×C₈	—	17	1	no	—
59	C₂×C₈	—	17	2	no	—
60	C₂×C₈	—	17	2	no	—
61	C₂×C₈	C₂×#595	1	1	yes	characteristic
62	C₄⋊C₄	—	34	4	no	—
63	C₄⋊C₄	—	68	2	no	—
64	C₁₆	—	2	1	no	—
65	C₁₆	—	34	1	no	—
66	C₂³	—	17	1	no	—
67	C₂×C₄	—	17	1	no	—
68	C₂×C₄	—	17	2	no	—
69	C₂×C₄	—	17	2	no	—
70	C₂×C₄	—	68	4	no	—
71	C₂×C₄	—	136	2	no	—
72	C₂×C₄	—	136	2	no	—
73	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
74	C₈	—	17	2	no	—
75	C₈	C₄×#595	1	1	yes	characteristic
76	C₈	C₂²⋊#595	1	1	yes	characteristic
77	C₂²	—	17	1	no	—
78	C₂²	—	17	1	no	—
79	C₂²	—	17	2	no	—
80	C₂²	—	17	2	no	—
81	C₂²	#10587534	1	1	yes	characteristic
82	C₄	—	17	2	no	—
83	C₄	—	136	4	no	—
84	C₄	#10587533	1	1	yes	characteristic
85	C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
86	C₂	—	17	2	no	—
87	C₂	—	17	2	no	—
88	C₂	#11763683	1	1	yes	characteristic
89	C₂	#11763735	1	1	yes	characteristic
90	C₂	#11763736	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10587534
commutator	C₈×C₁₇	C₄²
Frattini	C₂×C₈	C₂×#595
Fitting	C₂×C₁₆×C₁₇	C₄
socle	C₂²×C₁₇	#107
prime radical	C₂²×D₁₇	D₈
cosocle	C₂×C₈×D₁₇	C₂²
hypercenter	C₂×C₁₆	#595
hypocenter	C₁₇	#1380
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
6. #10587534	C₄	semidirect
7. C₂×C₁₆×C₁₇	C₄	semidirect
8. C₂×#63214	C₄	semidirect
52. C₂×C₁₆	#595	semidirect
55. C₁₇	#1380	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10587534	2
C₂×C₁₆×D₁₇	2
#1380	17