Subgroups — #14543788

Order 2176.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763701	C₂	1	2	yes	maximal, complemented
2	#11763175	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#125	C₄	1	1	yes	characteristic
4	#10587560	C₄	1	1	yes	characteristic
5	#10587538	—	2	2	no	—
6	#10587480	—	2	2	no	—
7	#10587474	C₂²	1	1	yes	characteristic
8	C₂×D₆₈	—	2	1	no	—
9	C₂×D₆₈	—	4	1	no	—
10	C₄⋊C₄×C₁₇	—	2	1	no	—
11	C₄⋊C₄×C₁₇	—	4	1	no	—
12	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂×#3622	D₄	1	2	yes	—
14	#63216	—	2	4	no	—
15	C₂²×D₁₇	—	4	1	no	—
16	C₂×C₄×C₁₇	—	2	1	no	—
17	C₂×C₄×C₁₇	—	4	1	no	—
18	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
19	D₆₈	—	4	2	no	—
20	D₆₈	—	8	2	no	—
21	#3622	—	2	2	no	—
22	#1355	—	17	1	no	maximal, Sylow
23	C₂²×C₁₇	#100	1	1	yes	characteristic
24	C₂×D₁₇	—	8	2	no	—
25	C₂×D₁₇	—	8	1	no	—
26	C₄×C₁₇	—	4	1	no	—
27	C₄×C₁₇	—	8	1	no	—
28	C₄×C₁₇	#104	1	2	yes	—
29	#490	—	17	1	no	—
30	#347	—	17	2	no	—
31	C₂×C₁₇	—	2	1	no	—
32	C₂×C₁₇	#329	1	1	yes	characteristic
33	D₁₇	—	16	1	no	—
34	#127	—	17	1	no	—
35	#125	#595	1	1	yes	characteristic
36	M₃₂	—	34	2	no	—
37	#102	—	34	2	no	—
38	#97	—	17	1	no	—
39	C₁₇	#1355	1	1	yes	characteristic, complemented, Sylow
40	C₂×D₄	—	34	1	no	—
41	C₂×D₄	—	68	1	no	—
42	C₂×C₈	—	17	2	no	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	4	1	no	—
45	C₄²	C₂×#595	1	1	yes	characteristic
46	C₁₆	—	34	4	no	—
47	C₂³	—	68	1	no	—
48	D₄	—	68	2	no	—
49	D₄	—	136	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
53	C₈	—	34	2	no	—
54	C₂²	—	136	2	no	—
55	C₂²	—	136	1	no	—
56	C₂²	#10587553	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	8	1	no	—
59	C₄	#10587550	1	2	yes	—
60	C₂	—	2	1	no	—
61	C₂	—	272	1	no	—
62	C₂	#11763665	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11763665
commutator	C₄²×C₁₇	C₂×C₄
Frattini	C₄²	C₂×#595
Fitting	C₁₇×#125	C₄
socle	C₂×C₁₇	#329
prime radical	#10587560	C₄
cosocle	#10587474	C₂²
hypercenter	#125	#595
hypocenter	C₁₇	#1355
LCS	G ▷ C₄²×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
1. #11763701	C₂	semidirect
39. C₁₇	#1355	semidirect

Maximal subgroups

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

subgroup	index
#11763701	2
#11763175	2
#1355	17