Subgroups — #14543924

Order 2176.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763714	C₂	1	2	yes	maximal
2	#11763175	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#125	C₄	1	1	yes	characteristic, complemented
4	#10587560	C₂²	1	1	yes	characteristic
5	#10587539	—	2	2	no	—
6	#10587480	—	2	2	no	—
7	#10587474	C₄	1	1	yes	characteristic, complemented
8	C₂×D₆₈	—	4	1	no	—
9	C₂×D₆₈	D₄	1	2	yes	—
10	C₂²⋊#595	—	4	2	no	—
11	C₄⋊C₄×C₁₇	—	2	1	no	—
12	C₄⋊C₄×C₁₇	—	4	1	no	—
13	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
14	C₂×#3622	—	2	1	no	—
15	C₂²×D₁₇	—	2	2	no	—
16	C₂×#595	—	8	2	no	—
17	C₂×C₄×C₁₇	—	2	1	no	—
18	C₂×C₄×C₁₇	—	4	1	no	—
19	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
20	D₆₈	—	4	2	no	—
21	D₆₈	—	8	2	no	—
22	#3622	—	4	1	no	—
23	#1412	—	17	1	no	maximal, Sylow
24	C₂²×C₁₇	#99	1	1	yes	characteristic
25	C₂×D₁₇	—	4	2	no	—
26	C₂×D₁₇	—	8	2	no	—
27	#595	—	16	2	no	—
28	C₄×C₁₇	—	2	1	no	—
29	C₄×C₁₇	—	4	1	no	—
30	C₄×C₁₇	—	8	1	no	—
31	#490	—	17	1	no	—
32	#353	—	17	2	no	—
33	C₂×C₁₇	—	2	1	no	—
34	C₂×C₁₇	#354	1	1	yes	characteristic
35	D₁₇	—	8	2	no	—
36	#127	—	17	1	no	—
37	#125	#595	1	1	yes	characteristic, complemented
38	#102	—	34	2	no	—
39	#99	—	34	2	no	—
40	#97	—	17	1	no	—
41	C₁₇	#1412	1	1	yes	characteristic, complemented, Sylow
42	C₂×D₄	—	17	2	no	—
43	C₂×D₄	—	68	1	no	—
44	C₂×C₈	—	34	1	no	—
45	C₄⋊C₄	—	2	1	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₂²⋊C₄	—	68	2	no	—
48	C₄²	C₂×#595	1	1	yes	characteristic
49	C₂³	—	34	2	no	—
50	D₄	—	68	2	no	—
51	D₄	—	136	2	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	—	136	2	no	—
55	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
56	C₈	—	68	1	no	—
57	C₂²	—	68	2	no	—
58	C₂²	—	136	2	no	—
59	C₂²	#10587551	1	1	yes	characteristic
60	C₄	—	2	1	no	—
61	C₄	—	4	1	no	—
62	C₄	—	8	1	no	—
63	C₄	—	272	2	no	—
64	C₂	—	2	1	no	—
65	C₂	—	136	2	no	—
66	C₂	#11763715	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11763715
commutator	C₄²×C₁₇	C₂×C₄
Frattini	C₄²	C₂×#595
Fitting	C₁₇×#125	C₄
socle	C₂×C₁₇	#354
prime radical, cosocle	#10587560	C₂²
hypercenter	#125	#595
hypocenter	C₁₇	#1412
LCS	G ▷ C₄²×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
3. C₁₇×#125	C₄	semidirect
7. #10587474	C₄	semidirect
37. #125	#595	semidirect
41. C₁₇	#1412	semidirect

Maximal subgroups

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

subgroup	index
#11763714	2
#11763175	2
#1412	17