Subgroups — #14543808

Order 2176.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763670	C₂	1	2	yes	maximal
2	#11762584	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#3624	—	2	2	no	—
4	C₂×C₁₆×C₁₇	C₄	1	1	yes	characteristic
5	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
6	C₂×#63214	C₄	1	1	yes	characteristic
7	C₂×#3624	—	4	2	no	—
8	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
9	C₄×Dic₁₇	D₄	1	1	yes	characteristic
10	C₂×#3622	Q₈	1	1	yes	characteristic
11	C₁₆×C₁₇	C₈	1	2	yes	complemented
12	#63214	—	2	1	no	—
13	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
14	C₂×Dic₁₇	SD₁₆	1	2	yes	—
15	#3624	—	8	2	no	—
16	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
17	C₈×C₁₇	M₁₆	1	1	yes	characteristic
18	#3622	—	2	1	no	—
19	#1368	—	17	1	no	maximal, Sylow
20	C₂²×C₁₇	#106	1	1	yes	characteristic
21	C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₁₇	#108	1	1	yes	characteristic
23	Dic₁₇	—	2	2	no	—
24	#346	—	17	1	no	—
25	#334	—	17	2	no	—
26	C₂×C₁₇	#334	1	1	yes	characteristic
27	C₂×C₁₇	#365	1	2	yes	—
28	C₂×C₁₆	—	17	1	no	—
29	C₂×C₁₆	#595	1	1	yes	characteristic
30	C₄⋊C₈	—	34	2	no	—
31	C₄×C₈	—	17	1	no	—
32	C₁₇	#1368	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₈	—	17	1	no	—
34	C₂×C₈	—	68	2	no	—
35	C₂×C₈	C₂×#595	1	1	yes	characteristic
36	C₄²	—	17	1	no	—
37	C₁₆	—	34	1	no	—
38	C₁₆	#3624	1	2	yes	complemented
39	C₂×C₄	—	17	2	no	—
40	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
41	C₈	—	34	1	no	—
42	C₈	—	136	2	no	—
43	C₈	#63243	1	1	yes	characteristic
44	C₈	C₂×#3624	1	1	yes	characteristic
45	C₂²	#10587533	1	1	yes	characteristic
46	C₄	—	34	2	no	—
47	C₄	#10587535	1	1	yes	characteristic
48	C₄	C₄⋊#3624	1	1	yes	characteristic
49	C₂	#11763670	1	1	yes	characteristic
50	C₂	#11763733	1	2	yes	—

	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
11. C₁₆×C₁₇	C₈	semidirect
32. C₁₇	#1368	semidirect
38. C₁₆	#3624	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