Subgroups — #14526954

Order 2176.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763173	C₂	1	1	yes	maximal, characteristic
2	#11762602	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#353	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#127	C₂²	1	1	yes	characteristic
5	#10587556	C₄	1	1	yes	characteristic, complemented
6	C₁₇×#99	—	2	1	no	—
7	#10587505	—	2	1	no	—
8	#10587503	—	2	1	no	—
9	#10587503	—	2	1	no	—
10	#10587474	C₄	1	1	yes	characteristic, complemented
11	C₂×D₄×C₁₇	—	4	1	no	—
12	C₂×D₄×C₁₇	D₄	1	1	yes	characteristic
13	C₂×D₄×C₁₇	D₄	1	1	yes	characteristic
14	C₂²⋊C₄×C₁₇	—	4	1	no	—
15	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂²⋊Dic₁₇	—	4	1	no	—
17	C₄⋊Dic₁₇	—	2	1	no	—
18	#63225	—	4	1	no	—
19	C₂×#3622	—	2	1	no	—
20	C₂³×C₁₇	—	2	1	no	—
21	C₂³×C₁₇	—	2	1	no	—
22	D₄×C₁₇	—	4	1	no	—
23	D₄×C₁₇	—	4	1	no	—
24	D₄×C₁₇	—	8	2	no	—
25	C₂×C₄×C₁₇	—	2	1	no	—
26	C₂×C₄×C₁₇	—	8	1	no	—
27	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₁₇	—	4	1	no	—
29	C₂×Dic₁₇	—	8	1	no	—
30	#3622	—	4	1	no	—
31	#1412	—	17	1	no	maximal, Sylow
32	C₂²×C₁₇	—	4	1	no	—
33	C₂²×C₁₇	—	4	1	no	—
34	C₂²×C₁₇	—	8	1	no	—
35	C₂²×C₁₇	—	8	1	no	—
36	C₂²×C₁₇	#99	1	1	yes	characteristic
37	C₄×C₁₇	—	2	1	no	—
38	C₄×C₁₇	—	4	1	no	—
39	C₄×C₁₇	—	16	1	no	—
40	Dic₁₇	—	8	1	no	—
41	Dic₁₇	—	16	1	no	—
42	#490	—	17	1	no	—
43	#353	—	17	1	no	—
44	#353	D₁₇	1	1	yes	characteristic
45	C₂×C₁₇	—	2	1	no	—
46	C₂×C₁₇	—	8	1	no	—
47	C₂×C₁₇	—	8	1	no	—
48	C₂×C₁₇	#354	1	1	yes	characteristic
49	#127	C₂×D₁₇	1	1	yes	characteristic
50	#125	—	17	1	no	—
51	#102	—	34	1	no	—
52	#102	—	34	1	no	—
53	#99	—	2	1	no	—
54	#99	—	34	1	no	—
55	#97	—	17	1	no	—
56	C₁₇	#1412	1	1	yes	characteristic, complemented, Sylow
57	C₂×D₄	—	4	1	no	—
58	C₂×D₄	D₆₈	1	1	yes	characteristic
59	C₂×D₄	C₂²⋊D₁₇	1	1	yes	characteristic
60	C₂×C₈	—	34	1	no	—
61	C₄⋊C₄	—	34	1	no	—
62	C₄⋊C₄	—	68	1	no	—
63	C₂²⋊C₄	—	4	1	no	—
64	C₂²⋊C₄	—	68	1	no	—
65	C₄²	C₄×D₁₇	1	1	yes	characteristic
66	C₂³	—	2	1	no	—
67	C₂³	—	2	1	no	—
68	D₄	—	4	1	no	—
69	D₄	—	4	1	no	—
70	D₄	—	8	2	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	8	1	no	—
73	C₂×C₄	—	68	1	no	—
74	C₂×C₄	—	136	1	no	—
75	C₂×C₄	#63227	1	1	yes	characteristic
76	C₈	—	68	1	no	—
77	C₂²	—	4	1	no	—
78	C₂²	—	4	1	no	—
79	C₂²	—	8	1	no	—
80	C₂²	—	8	1	no	—
81	C₂²	#10587477	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	4	1	no	—
84	C₄	—	16	1	no	—
85	C₄	—	272	1	no	—
86	C₄	—	136	1	no	—
87	C₂	—	2	1	no	—
88	C₂	—	8	1	no	—
89	C₂	—	8	1	no	—
90	C₂	#11762603	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11762603
commutator	C₄²×C₁₇	C₂×C₄
Frattini	#127	C₂×D₁₇
Fitting	C₁₇×#353	C₂
socle	C₂×C₁₇	#354
prime radical, cosocle	C₁₇×#127	C₂²
hypercenter	#353	D₁₇
hypocenter	C₁₇	#1412
LCS	G ▷ C₄²×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #127 ◁ #353

Complements

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

N	H ≅ G/N	type
5. #10587556	C₄	semidirect
10. #10587474	C₄	semidirect
56. C₁₇	#1412	semidirect

Maximal subgroups

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

subgroup	index
#11763173	2
#11762602	2
C₁₇×#353	2
#1412	17