Subgroups — #14544713

Order 2176.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763675	C₂	1	6	yes	maximal
2	#11762654	C₂	1	1	yes	maximal, characteristic
3	C₂²×#3624	C₂²	1	4	yes	—
4	C₂×C₄×Dic₁₇	C₂²	1	3	yes	—
5	C₁₇×#95	C₄	1	1	yes	characteristic
6	#10587502	C₄	1	3	yes	—
7	C₂²×C₄×C₁₇	C₂×C₄	1	3	yes	—
8	C₂²×Dic₁₇	C₂×C₄	1	3	yes	—
9	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
10	C₂×#3624	—	2	12	no	—
11	C₄×Dic₁₇	—	2	6	no	—
12	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₁₇	—	2	3	no	—
14	C₂×C₄×C₁₇	—	2	6	no	—
15	C₂×Dic₁₇	—	2	3	no	—
16	C₂×Dic₁₇	—	2	3	no	—
17	C₂×Dic₁₇	—	2	3	no	—
18	C₂×Dic₁₇	#41	1	6	yes	—
19	#3624	—	4	4	no	—
20	#1840	—	17	1	no	maximal, Sylow
21	C₂²×C₁₇	#117	1	3	yes	—
22	C₂²×C₁₇	#131	1	3	yes	—
23	C₂²×C₁₇	#131	1	1	yes	characteristic
24	C₄×C₁₇	—	4	3	no	—
25	Dic₁₇	—	4	3	no	—
26	Dic₁₇	#126	1	4	yes	—
27	#376	—	17	1	no	—
28	#336	—	17	6	no	—
29	C₂×C₁₇	#383	1	1	yes	characteristic
30	C₂×C₁₇	#433	1	3	yes	—
31	C₂×C₁₇	#433	1	3	yes	—
32	C₂²×C₈	—	17	4	no	—
33	C₂×C₄²	—	17	3	no	—
34	#95	—	17	3	no	—
35	#95	#595	1	1	yes	characteristic
36	C₁₇	#1840	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₄	—	17	1	no	—
38	C₂²×C₄	—	17	3	no	—
39	C₂²×C₄	C₂×#595	1	3	yes	—
40	C₂×C₈	—	34	12	no	—
41	C₄²	—	34	6	no	—
42	C₂³	C₂²×#595	1	1	yes	characteristic
43	C₂×C₄	—	2	3	no	—
44	C₂×C₄	—	2	6	no	—
45	C₂×C₄	—	17	6	no	—
46	C₂×C₄	—	34	3	no	—
47	C₂×C₄	—	34	3	no	—
48	C₂×C₄	—	34	3	no	—
49	C₈	—	68	4	no	—
50	C₂²	#10587677	1	3	yes	—
51	C₂²	#10587678	1	3	yes	—
52	C₂²	#10587680	1	1	yes	characteristic
53	C₄	—	4	3	no	—
54	C₄	—	17	4	no	—
55	C₄	—	68	3	no	—
56	C₂	#11763754	1	1	yes	characteristic
57	C₂	#11763833	1	3	yes	—
58	C₂	#11763834	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#595
commutator, socle, prime radical	C₂³×C₁₇	C₂²×C₄
Fitting	C₁₇×#95	C₄
cosocle	C₂²×Dic₁₇	C₂³
hypercenter	#95	#595
hypocenter	C₁₇	#1840
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
36. C₁₇	#1840	semidirect

Maximal subgroups

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

subgroup	index
#11763675	2
#11762654	2
#1840	17