Subgroups — #14539308

Order 2176.

348 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763366	C₂	1	2	yes	maximal
2	#11763218	C₂	1	8	yes	maximal, complemented
3	#11762847	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	#10587612	C₂²	1	4	yes	—
8	#10587610	—	2	4	no	—
9	#10587556	C₂²	1	4	yes	—
10	#10587555	C₂²	1	4	yes	—
11	C₄×Dic₃₄	—	2	4	no	—
12	C₁₇×#97	C₂²	1	4	yes	—
13	#10587489	C₂²	1	8	yes	—
14	#10587488	C₂²	1	8	yes	—
15	C₂²×C₄×C₁₇	D₄	1	2	yes	—
16	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
17	C₂×Dic₃₄	—	2	4	no	—
18	C₂×C₈×C₁₇	Q₈	1	8	yes	complemented
19	C₂×C₈×C₁₇	C₂³	1	4	yes	—
20	C₄²×C₁₇	D₄	1	2	yes	—
21	C₄²×C₁₇	C₂³	1	2	yes	—
22	C₂²⋊Dic₁₇	—	2	4	no	—
23	C₄⋊Dic₁₇	—	2	4	no	—
24	C₄⋊Dic₁₇	C₂³	1	8	yes	—
25	#63225	—	2	8	no	—
26	C₄×Dic₁₇	—	2	4	no	—
27	C₂³×C₁₇	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₁₇	—	4	2	no	—
29	C₂×C₄×C₁₇	C₂×D₄	1	4	yes	—
30	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₁₇	C₂×Q₈	1	4	yes	—
32	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
33	C₂×Dic₁₇	—	2	8	no	—
34	Dic₃₄	—	4	8	no	—
35	C₈×C₁₇	C₂×Q₈	1	8	yes	—
36	#3162	—	17	1	no	maximal, Sylow
37	C₂²×C₁₇	—	2	2	no	—
38	C₂²×C₁₇	C₄⋊Q₈	1	2	yes	—
39	C₂²×C₁₇	C₂²×D₄	1	1	yes	characteristic
40	C₄×C₁₇	—	2	4	no	—
41	C₄×C₁₇	C₄⋊Q₈	1	2	yes	—
42	C₄×C₁₇	C₂²×Q₈	1	2	yes	—
43	Dic₁₇	—	4	8	no	—
44	#533	—	17	2	no	—
45	#501	—	17	8	no	—
46	#427	—	17	4	no	—
47	C₂×#97	D₁₇	1	1	yes	characteristic
48	C₂×C₁₇	—	2	2	no	—
49	C₂×C₁₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
50	C₂×C₁₇	#575	1	2	yes	—
51	C₂²×C₈	C₂×D₁₇	1	2	yes	—
52	C₄⋊Q₈	—	17	4	no	—
53	#125	—	17	4	no	—
54	C₂²⋊Q₈	—	34	4	no	—
55	C₄×Q₈	—	34	4	no	—
56	#117	—	17	4	no	—
57	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
58	#107	—	17	8	no	—
59	#106	—	17	8	no	—
60	#97	C₂×D₁₇	1	4	yes	—
61	C₁₇	#3162	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	34	4	no	—
63	C₂²×C₄	D₆₈	1	2	yes	—
64	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
65	C₂×C₈	Dic₃₄	1	8	yes	complemented
66	C₂×C₈	C₂²×D₁₇	1	4	yes	—
67	C₄⋊C₄	—	17	8	no	—
68	C₄⋊C₄	—	34	8	no	—
69	C₄⋊C₄	—	34	4	no	—
70	C₂²⋊C₄	—	34	4	no	—
71	C₄²	—	34	4	no	—
72	C₄²	D₆₈	1	2	yes	—
73	C₄²	C₂²×D₁₇	1	2	yes	—
74	C₂³	C₂×D₆₈	1	1	yes	characteristic
75	Q₈	—	68	8	no	—
76	C₂×C₄	—	4	2	no	—
77	C₂×C₄	—	34	8	no	—
78	C₂×C₄	C₂×Dic₃₄	1	4	yes	—
79	C₂×C₄	C₂×D₆₈	1	4	yes	—
80	C₂×C₄	C₂×D₆₈	1	1	yes	characteristic
81	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
82	C₈	C₂×Dic₃₄	1	8	yes	—
83	C₂²	—	2	2	no	—
84	C₂²	#10587555	1	2	yes	—
85	C₂²	C₂²×D₆₈	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	—	68	8	no	—
88	C₄	#10587555	1	2	yes	—
89	C₄	C₂²×Dic₃₄	1	2	yes	—
90	C₂	—	2	2	no	—
91	C₂	C₂×#10587555	1	1	yes	characteristic
92	C₂	#11763609	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₆₈
commutator, cosocle	C₂×C₄×C₁₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₇
Fitting	C₂×C₁₇×#97	C₂
socle	C₂²×C₁₇	C₂²×D₄
prime radical	C₂³×C₁₇	C₂×D₄
hypercenter	C₂×#97	D₁₇
hypocenter	C₁₇	#3162
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
2. #11763218	C₂	semidirect
18. C₂×C₈×C₁₇	Q₈	semidirect
61. C₁₇	#3162	semidirect
65. C₂×C₈	Dic₃₄	semidirect

Maximal subgroups

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

subgroup	index
#11763366	2
#11763218	2
#11762847	2
C₂×C₁₇×#97	2
#3162	17