Subgroups — #14543920

Order 2176.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763720	C₂	1	2	yes	maximal, complemented
2	#11763182	C₂	1	1	yes	maximal, characteristic
3	C₂×#63219	—	2	2	no	—
4	#10587560	C₄	1	1	yes	characteristic
5	#10587555	C₂²	1	1	yes	characteristic
6	#10587545	—	2	2	no	—
7	C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
8	C₂×D₆₈	—	2	1	no	—
9	C₂×D₆₈	—	4	1	no	—
10	C₂×Dic₃₄	D₄	1	2	yes	—
11	#63247	—	4	2	no	—
12	C₂×C₈×C₁₇	—	2	1	no	—
13	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
14	C₄⋊Dic₁₇	—	4	1	no	—
15	#63219	—	4	4	no	—
16	C₂²×D₁₇	—	4	1	no	—
17	C₂×C₄×C₁₇	—	2	1	no	—
18	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×Dic₁₇	—	2	2	no	—
20	D₆₈	—	4	2	no	—
21	D₆₈	—	8	2	no	—
22	Dic₃₄	—	4	2	no	—
23	#3624	—	8	2	no	—
24	C₈×C₁₇	—	2	2	no	—
25	#1410	—	17	1	no	maximal, Sylow
26	C₂²×C₁₇	#99	1	1	yes	characteristic
27	C₂×D₁₇	—	8	2	no	—
28	C₂×D₁₇	—	8	1	no	—
29	C₄×C₁₇	—	2	2	no	—
30	C₄×C₁₇	—	2	1	no	—
31	Dic₁₇	—	4	2	no	—
32	#492	—	17	1	no	—
33	#356	—	17	2	no	—
34	C₂×C₁₇	—	2	1	no	—
35	C₂×C₁₇	#353	1	1	yes	characteristic
36	D₁₇	—	16	1	no	—
37	C₂×SD₁₆	—	34	2	no	—
38	C₄⋊Q₈	—	17	1	no	—
39	#127	—	17	1	no	—
40	#101	—	34	2	no	—
41	C₄×C₈	#595	1	1	yes	characteristic
42	C₁₇	#1410	1	1	yes	characteristic, complemented, Sylow
43	C₂×Q₈	—	17	2	no	—
44	C₂×D₄	—	34	1	no	—
45	C₂×D₄	—	68	1	no	—
46	SD₁₆	—	68	4	no	—
47	M₁₆	—	68	2	no	—
48	C₂×C₈	—	2	1	no	—
49	C₄⋊C₄	—	68	1	no	—
50	C₄²	C₂×#595	1	1	yes	characteristic
51	C₂³	—	68	1	no	—
52	Q₈	—	68	2	no	—
53	D₄	—	68	2	no	—
54	D₄	—	136	2	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	34	2	no	—
57	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₈	—	136	2	no	—
60	C₂²	—	136	2	no	—
61	C₂²	—	136	1	no	—
62	C₂²	#10587539	1	1	yes	characteristic
63	C₄	—	2	2	no	—
64	C₄	—	2	1	no	—
65	C₄	—	68	2	no	—
66	C₂	—	2	1	no	—
67	C₂	—	272	1	no	—
68	C₂	#11763714	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11763714
commutator	C₄²×C₁₇	C₂×C₄
Frattini	C₄²	C₂×#595
Fitting	C₄×C₈×C₁₇	C₄
socle	C₂×C₁₇	#353
prime radical	#10587560	C₄
cosocle	#10587555	C₂²
hypercenter	C₄×C₈	#595
hypocenter	C₁₇	#1410
LCS	G ▷ C₄²×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. #11763720	C₂	semidirect
42. C₁₇	#1410	semidirect

Maximal subgroups

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

subgroup	index
#11763720	2
#11763182	2
#1410	17