Subgroups — #14528532

Order 2176.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587474	C₂	1	1	yes	maximal, characteristic
2	C₄²×Dic₁₇	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	C₄	1	4	yes	—
8	C₂×C₄×Dic₁₇	C₂²	1	2	yes	—
9	C₂²×#3622	C₂²	1	2	yes	—
10	C₁₇×#97	C₄	1	4	yes	complemented
11	#10587474	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	C₄×Dic₁₇	—	2	8	no	—
21	C₂×#3622	—	2	4	no	—
22	C₂×#3622	C₂×C₄	1	4	yes	—
23	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₇	—	2	4	no	—
25	C₂×C₄×C₁₇	C₄²	1	4	yes	—
26	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₇	#41	1	4	yes	—
29	C₂×Dic₁₇	—	2	4	no	—
30	C₂×Dic₁₇	—	2	4	no	—
31	C₂×Dic₁₇	M₁₆	1	8	yes	—
32	C₈×C₁₇	—	2	4	no	—
33	#3622	—	2	4	no	—
34	#1745	—	17	1	no	maximal, Sylow
35	C₂²×C₁₇	C₂×C₄²	1	1	yes	characteristic
36	C₂²×C₁₇	#117	1	2	yes	—
37	C₂²×C₁₇	C₂×M₁₆	1	4	yes	—
38	C₄×C₁₇	—	2	4	no	—
39	C₄×C₁₇	#117	1	2	yes	—
40	C₄×C₁₇	#117	1	2	yes	—
41	Dic₁₇	—	2	8	no	—
42	C₂×#97	—	17	1	no	—
43	C₂×#97	D₁₇	1	1	yes	characteristic
44	C₄³	—	17	1	no	—
45	#336	—	17	4	no	—
46	C₂×C₁₇	#376	1	1	yes	characteristic
47	C₂×C₁₇	C₄×M₁₆	1	2	yes	—
48	C₂×C₁₇	#432	1	4	yes	—
49	C₂²×C₈	—	17	2	no	—
50	C₂²×C₈	C₂×D₁₇	1	2	yes	—
51	C₂×C₄²	—	17	4	no	—
52	C₂×C₄²	—	17	2	no	—
53	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
54	#97	—	17	4	no	—
55	#97	Dic₁₇	1	4	yes	complemented
56	C₁₇	#1745	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₄	—	17	4	no	—
58	C₂²×C₄	C₄×D₁₇	1	2	yes	—
59	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
60	C₂×C₈	—	2	4	no	—
61	C₂×C₈	—	17	4	no	—
62	C₂×C₈	—	34	4	no	—
63	C₂×C₈	C₂×Dic₁₇	1	4	yes	—
64	C₄²	—	34	8	no	—
65	C₄²	—	34	4	no	—
66	C₄²	C₄×D₁₇	1	2	yes	—
67	C₄²	C₂×Dic₁₇	1	2	yes	—
68	C₂³	C₂×C₄×D₁₇	1	1	yes	characteristic
69	C₂×C₄	—	2	4	no	—
70	C₂×C₄	—	17	8	no	—
71	C₂×C₄	—	34	4	no	—
72	C₂×C₄	—	34	4	no	—
73	C₂×C₄	C₄×Dic₁₇	1	4	yes	—
74	C₂×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
75	C₂×C₄	#63252	1	4	yes	—
76	C₂×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
77	C₈	—	2	4	no	—
78	C₈	—	34	4	no	—
79	C₂²	#10587558	1	2	yes	—
80	C₂²	M₁₆×D₁₇	1	4	yes	—
81	C₂²	C₂×C₄×Dic₁₇	1	1	yes	characteristic
82	C₄	—	2	4	no	—
83	C₄	—	34	8	no	—
84	C₄	#10587558	1	2	yes	—
85	C₄	#10587612	1	2	yes	—
86	C₂	#11762655	1	1	yes	characteristic
87	C₂	M₁₆×Dic₁₇	1	2	yes	—
88	C₂	#11762864	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	#1745
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
10. C₁₇×#97	C₄	semidirect
11. #10587474	C₄	semidirect
55. #97	Dic₁₇	semidirect
56. C₁₇	#1745	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10587474	2
C₄²×Dic₁₇	2
#11762563	2
C₂×C₁₇×#97	2
#1745	17