Subgroups — #14543810

Order 2176.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763670	C₂	1	1	yes	maximal, characteristic
2	#11763670	C₂	1	1	yes	maximal, characteristic
3	#11762584	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#3624	—	2	1	no	—
5	C₄⋊#3624	—	2	1	no	—
6	C₂×C₁₆×C₁₇	C₄	1	1	yes	characteristic
7	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
8	C₂×#63214	C₄	1	1	yes	characteristic
9	C₂×#3624	—	4	1	no	—
10	C₂×#3624	—	4	1	no	—
11	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₄×Dic₁₇	D₄	1	1	yes	characteristic
13	C₂×#3622	Q₈	1	1	yes	characteristic
14	C₁₆×C₁₇	—	2	1	no	—
15	#63214	C₈	1	2	yes	complemented
16	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
17	C₂×Dic₁₇	SD₁₆	1	1	yes	characteristic
18	C₂×Dic₁₇	SD₁₆	1	1	yes	characteristic
19	#3624	—	8	1	no	—
20	#3624	—	8	1	no	—
21	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
22	C₈×C₁₇	M₁₆	1	1	yes	characteristic
23	#3622	—	2	1	no	—
24	#1368	—	17	1	no	maximal, Sylow
25	C₂²×C₁₇	#106	1	1	yes	characteristic
26	C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₁₇	#108	1	1	yes	characteristic
28	Dic₁₇	—	2	1	no	—
29	Dic₁₇	—	2	1	no	—
30	#346	—	17	1	no	—
31	#334	—	17	1	no	—
32	#334	—	17	1	no	—
33	C₂×C₁₇	#334	1	1	yes	characteristic
34	C₂×C₁₇	#365	1	1	yes	characteristic
35	C₂×C₁₇	#365	1	1	yes	characteristic
36	C₂×C₁₆	—	17	1	no	—
37	C₂×C₁₆	#595	1	1	yes	characteristic
38	C₄⋊C₈	—	34	1	no	—
39	C₄⋊C₈	—	34	1	no	—
40	C₄×C₈	—	17	1	no	—
41	C₁₇	#1368	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₈	—	17	1	no	—
43	C₂×C₈	—	68	1	no	—
44	C₂×C₈	—	68	1	no	—
45	C₂×C₈	C₂×#595	1	1	yes	characteristic
46	C₄²	—	17	1	no	—
47	C₁₆	—	2	1	no	—
48	C₁₆	—	17	2	no	—
49	C₂×C₄	—	17	1	no	—
50	C₂×C₄	—	17	1	no	—
51	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
52	C₈	—	34	1	no	—
53	C₈	—	136	1	no	—
54	C₈	—	136	1	no	—
55	C₈	#63242	1	1	yes	characteristic
56	C₈	#63247	1	1	yes	characteristic
57	C₂²	#10587533	1	1	yes	characteristic
58	C₄	—	34	1	no	—
59	C₄	—	34	1	no	—
60	C₄	#10587536	1	1	yes	characteristic
61	C₄	#10587544	1	1	yes	characteristic
62	C₂	#11763671	1	1	yes	characteristic
63	C₂	#11763733	1	1	yes	characteristic
64	C₂	#11763734	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10587533
commutator	C₈×C₁₇	C₂×C₈
Frattini	C₂×C₈	C₂×#595
Fitting	C₂×C₁₆×C₁₇	C₄
socle, prime radical	C₂²×C₁₇	#106
cosocle	C₈×Dic₁₇	C₂²
hypercenter	C₂×C₁₆	#595
hypocenter	C₁₇	#1368
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
15. #63214	C₈	semidirect
41. C₁₇	#1368	semidirect

Maximal subgroups

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

subgroup	index
#11763670	2
#11762584	2
#1368	17