Subgroups — #14545845

Order 2176.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763898	C₂	1	2	yes	maximal
2	#11763696	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#3633	—	2	2	no	—
4	C₈×#595	C₂²	1	1	yes	characteristic
5	#10587529	C₄	1	1	yes	characteristic
6	C₁₆×D₁₇	C₄	1	1	yes	characteristic
7	C₂×#3633	—	4	2	no	—
8	C₄×#595	D₄	1	1	yes	characteristic
9	#63242	Q₈	1	1	yes	characteristic
10	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
11	#63216	—	2	1	no	—
12	C₁₆×C₁₇	C₈	1	1	yes	characteristic, complemented
13	#63214	C₈	1	1	yes	characteristic, complemented
14	C₂×#595	SD₁₆	1	2	yes	—
15	#3633	—	8	2	no	—
16	C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
17	#3624	—	2	1	no	—
18	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
19	#3622	M₁₆	1	1	yes	characteristic
20	#1368	—	17	1	no	maximal, Sylow
21	C₂×D₁₇	#106	1	1	yes	characteristic
22	#595	—	2	2	no	—
23	C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
24	Dic₁₇	#108	1	1	yes	characteristic
25	#346	—	17	1	no	—
26	#334	—	17	2	no	—
27	C₂×C₁₇	#334	1	1	yes	characteristic
28	D₁₇	#365	1	2	yes	—
29	C₂×C₁₆	—	17	1	no	—
30	C₂×C₁₆	—	17	1	no	—
31	C₄⋊C₈	—	34	2	no	—
32	C₄×C₈	—	17	1	no	—
33	C₁₇	#1368	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₈	—	17	1	no	—
35	C₂×C₈	—	17	1	no	—
36	C₂×C₈	—	68	2	no	—
37	C₄²	—	17	1	no	—
38	C₁₆	—	17	1	no	—
39	C₁₆	—	34	1	no	—
40	C₁₆	#3633	1	1	yes	characteristic, complemented
41	C₂×C₄	—	17	1	no	—
42	C₂×C₄	—	17	2	no	—
43	C₈	—	17	1	no	—
44	C₈	—	34	1	no	—
45	C₈	—	136	2	no	—
46	C₈	C₂×#3633	1	1	yes	characteristic
47	C₂²	—	17	1	no	—
48	C₄	—	17	1	no	—
49	C₄	—	34	2	no	—
50	C₄	C₄⋊#3633	1	1	yes	characteristic
51	C₂	—	17	2	no	—
52	C₂	#11763898	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11763898
commutator	C₈×C₁₇	C₂×C₈
Frattini	C₈	C₂×#3633
Fitting	C₁₆×C₁₇	C₈
socle	C₂×C₁₇	#334
prime radical	C₂×D₁₇	#106
cosocle	C₈×#595	C₂²
hypercenter	C₁₆	#3633
hypocenter	C₁₇	#1368
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₁₇	C₈	semidirect
13. #63214	C₈	semidirect
33. C₁₇	#1368	semidirect
40. C₁₆	#3633	semidirect

Maximal subgroups

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

subgroup	index
#11763898	2
#11763696	2
#1368	17