Subgroups — #14543901

Order 2176.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763741	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10587467	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763226	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#131	C₄	1	1	yes	characteristic
5	#10587483	—	2	1	no	—
6	#10587483	C₄	1	1	yes	characteristic
7	C₂×#63214	—	2	1	no	—
8	C₂×#63214	C₂²	1	1	yes	characteristic
9	#10587467	—	2	1	no	—
10	#10587467	—	2	1	no	—
11	#41×C₁₇	C₈	1	1	yes	characteristic
12	M₁₆×C₁₇	—	2	1	no	—
13	M₁₆×C₁₇	C₈	1	1	yes	characteristic
14	C₂×C₈×C₁₇	—	2	1	no	—
15	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
16	#63214	—	2	1	no	—
17	#63214	D₄	1	1	yes	characteristic
18	#63214	D₄	1	1	yes	characteristic
19	Q₈×C₁₇	C₁₆	1	1	yes	characteristic
20	D₄×C₁₇	—	2	1	no	—
21	D₄×C₁₇	C₁₆	1	1	yes	characteristic
22	C₂×C₄×C₁₇	—	2	1	no	—
23	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
24	C₈×C₁₇	—	2	1	no	—
25	C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₁₇	M₁₆	1	1	yes	characteristic
27	#1401	—	17	1	no	maximal, Sylow
28	C₂²×C₁₇	—	2	1	no	—
29	C₂²×C₁₇	M₃₂	1	1	yes	characteristic
30	C₄×C₁₇	—	2	1	no	—
31	C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
33	#504	—	17	1	no	—
34	M₆₄	—	17	1	no	—
35	C₂×C₃₂	—	17	1	no	—
36	C₂×C₁₇	—	2	1	no	—
37	C₂×C₁₇	—	4	1	no	—
38	C₂×C₁₇	C₂²⋊C₁₆	1	1	yes	characteristic
39	#131	#595	1	1	yes	characteristic
40	M₃₂	—	17	1	no	—
41	M₃₂	—	34	1	no	—
42	C₂×C₁₆	—	17	1	no	—
43	C₂×C₁₆	—	34	1	no	—
44	C₃₂	—	34	1	no	—
45	C₃₂	—	34	1	no	—
46	C₁₇	#1401	1	1	yes	characteristic, complemented, Sylow
47	#41	#3624	1	1	yes	characteristic
48	M₁₆	—	2	1	no	—
49	M₁₆	#3624	1	1	yes	characteristic
50	C₂×C₈	—	2	1	no	—
51	C₂×C₈	C₂×#595	1	1	yes	characteristic
52	C₁₆	—	17	1	no	—
53	C₁₆	—	17	1	no	—
54	C₁₆	—	34	1	no	—
55	Q₈	#63216	1	1	yes	characteristic
56	D₄	—	2	1	no	—
57	D₄	#63216	1	1	yes	characteristic
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	C₂×#3624	1	1	yes	characteristic
60	C₈	—	2	1	no	—
61	C₈	#63247	1	1	yes	characteristic
62	C₈	C₂²⋊#595	1	1	yes	characteristic
63	C₂²	—	2	1	no	—
64	C₂²	#10587538	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	C₂×#63216	1	1	yes	characteristic
67	C₄	C₂²⋊#3624	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	1	no	—
70	C₂	C₂²⋊#63216	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#595
commutator	C₄×C₁₇	C₂×C₁₆
Frattini	C₂×C₈	C₂×#595
Fitting	C₁₇×#131	C₄
socle	C₂×C₁₇	C₂²⋊C₁₆
prime radical	#41×C₁₇	C₈
cosocle	C₂×#63214	C₂²
hypercenter	#131	#595
hypocenter	C₁₇	#1401
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #131

Complements

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

N	H ≅ G/N	type
1. #11763741	C₂	semidirect
2. C₂×#10587467	C₂	semidirect
46. C₁₇	#1401	semidirect

Maximal subgroups

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

subgroup	index
#11763741	2
C₂×#10587467	2
#11763226	2
#1401	17