Subgroups — #14528537

Order 2176.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#3622	C₂	1	1	yes	maximal, characteristic
2	#11762655	C₂	1	1	yes	maximal, characteristic
3	#11762563	C₂	1	4	yes	maximal
4	C₂×C₁₇×#97	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₁₇	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₁₇	C₂²	1	2	yes	—
8	C₂²×#3622	C₂²	1	2	yes	—
9	C₁₇×#97	C₄	1	4	yes	complemented
10	#10587502	C₄	1	4	yes	—
11	C₄×#3622	C₄	1	4	yes	complemented
12	C₂²×C₄×C₁₇	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
14	C₂²×Dic₁₇	C₂×C₄	1	4	yes	—
15	C₂×C₈×C₁₇	—	2	4	no	—
16	C₂×C₈×C₁₇	C₂×C₄	1	4	yes	—
17	C₄²×C₁₇	C₂×C₄	1	2	yes	—
18	C₄²×C₁₇	C₂×C₄	1	2	yes	—
19	C₄×Dic₁₇	—	2	4	no	—
20	C₂×#3622	—	2	4	no	—
21	C₂×#3622	C₂×C₄	1	4	yes	—
22	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₇	—	2	4	no	—
24	C₂×C₄×C₁₇	C₄²	1	4	yes	—
25	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₇	#41	1	4	yes	—
28	C₂×Dic₁₇	—	2	4	no	—
29	C₂×Dic₁₇	—	2	8	no	—
30	C₈×C₁₇	—	2	4	no	—
31	#3622	—	2	4	no	—
32	#1746	—	17	1	no	maximal, Sylow
33	C₂²×C₁₇	C₂×C₄²	1	1	yes	characteristic
34	C₂²×C₁₇	#117	1	2	yes	—
35	C₂²×C₁₇	#131	1	4	yes	—
36	C₄×C₁₇	—	2	4	no	—
37	C₄×C₁₇	#117	1	2	yes	—
38	C₄×C₁₇	#117	1	2	yes	—
39	Dic₁₇	—	4	4	no	—
40	C₂×#97	D₁₇	1	1	yes	characteristic
41	C₂×C₄×C₈	—	17	1	no	—
42	#376	—	17	1	no	—
43	#336	—	17	4	no	—
44	C₂×C₁₇	#376	1	1	yes	characteristic
45	C₂×C₁₇	#405	1	2	yes	—
46	C₂×C₁₇	#433	1	4	yes	—
47	C₂²×C₈	—	17	2	no	—
48	C₂²×C₈	C₂×D₁₇	1	2	yes	—
49	C₂×C₄²	—	17	2	no	—
50	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
51	#97	Dic₁₇	1	4	yes	complemented
52	C₄×C₈	—	17	4	no	—
53	#95	—	17	4	no	—
54	C₁₇	#1746	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₄	—	17	4	no	—
56	C₂²×C₄	C₄×D₁₇	1	2	yes	—
57	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
58	C₂×C₈	—	2	4	no	—
59	C₂×C₈	—	17	4	no	—
60	C₂×C₈	—	34	4	no	—
61	C₂×C₈	C₂×Dic₁₇	1	4	yes	—
62	C₄²	—	34	4	no	—
63	C₄²	C₄×D₁₇	1	2	yes	—
64	C₄²	C₂×Dic₁₇	1	2	yes	—
65	C₂³	C₂×C₄×D₁₇	1	1	yes	characteristic
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	34	4	no	—
68	C₂×C₄	—	34	8	no	—
69	C₂×C₄	C₄×Dic₁₇	1	4	yes	—
70	C₂×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
71	C₂×C₄	#63252	1	4	yes	—
72	C₂×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
73	C₈	—	2	4	no	—
74	C₈	—	34	4	no	—
75	C₂²	#10587558	1	2	yes	—
76	C₂²	#10587593	1	4	yes	—
77	C₂²	C₂×C₄×Dic₁₇	1	1	yes	characteristic
78	C₄	—	2	4	no	—
79	C₄	—	68	4	no	—
80	C₄	#10587558	1	2	yes	—
81	C₄	#10587612	1	2	yes	—
82	C₂	#11762655	1	1	yes	characteristic
83	C₂	#11762767	1	2	yes	—
84	C₂	#11762871	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₇
commutator	C₂²×C₁₇	C₂×C₄²
Fitting	C₂×C₁₇×#97	C₂
socle, prime radical	C₂³×C₁₇	C₂²×C₄
cosocle	C₂²×C₄×C₁₇	C₂³
hypercenter	C₂×#97	D₁₇
hypocenter	C₁₇	#1746
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
9. C₁₇×#97	C₄	semidirect
11. C₄×#3622	C₄	semidirect
51. #97	Dic₁₇	semidirect
54. C₁₇	#1746	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#3622	2
#11762655	2
#11762563	2
C₂×C₁₇×#97	2
#1746	17