Subgroups — #14543816

Order 2176.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763672	C₂	1	2	yes	maximal
2	C₁₆×Dic₁₇	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	—	2	1	no	—
12	#63214	C₈	1	2	yes	complemented
13	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
14	C₂×Dic₁₇	D₈	1	1	yes	characteristic
15	C₂×Dic₁₇	Q₁₆	1	1	yes	characteristic
16	#3624	—	8	2	no	—
17	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
18	C₈×C₁₇	M₁₆	1	1	yes	characteristic
19	#3622	—	2	1	no	—
20	#1371	—	17	1	no	maximal, Sylow
21	C₂²×C₁₇	#107	1	1	yes	characteristic
22	C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₁₇	#108	1	1	yes	characteristic
24	Dic₁₇	—	2	1	no	—
25	Dic₁₇	D₁₆	1	1	yes	characteristic
26	Dic₁₇	Q₃₂	1	1	yes	characteristic
27	C₄×C₁₆	—	17	1	no	—
28	#335	—	17	2	no	—
29	C₂×C₁₇	#335	1	1	yes	characteristic
30	C₂×C₁₇	#366	1	1	yes	characteristic
31	C₂×C₁₇	#368	1	1	yes	characteristic
32	C₂×C₁₆	—	17	1	no	—
33	C₂×C₁₆	#595	1	1	yes	characteristic
34	C₄⋊C₈	—	34	2	no	—
35	C₄×C₈	—	17	1	no	—
36	C₁₇	#1371	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₈	—	17	1	no	—
38	C₂×C₈	—	68	2	no	—
39	C₂×C₈	C₂×#595	1	1	yes	characteristic
40	C₄²	—	17	1	no	—
41	C₁₆	—	2	1	no	—
42	C₁₆	—	17	2	no	—
43	C₂×C₄	—	17	1	no	—
44	C₂×C₄	—	17	1	no	—
45	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
46	C₈	—	34	1	no	—
47	C₈	—	136	2	no	—
48	C₈	#63242	1	1	yes	characteristic
49	C₈	#63247	1	1	yes	characteristic
50	C₂²	#10587534	1	1	yes	characteristic
51	C₄	—	17	1	no	—
52	C₄	—	17	1	no	—
53	C₄	—	34	1	no	—
54	C₄	#10587535	1	1	yes	characteristic
55	C₄	#10587544	1	1	yes	characteristic
56	C₂	#11763673	1	1	yes	characteristic
57	C₂	#11763735	1	1	yes	characteristic
58	C₂	#11763738	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10587534
commutator	C₈×C₁₇	C₂×C₈
Frattini	C₂×C₈	C₂×#595
Fitting	C₂×C₁₆×C₁₇	C₄
socle, prime radical	C₂²×C₁₇	#107
cosocle	C₈×Dic₁₇	C₂²
hypercenter	C₂×C₁₆	#595
hypocenter	C₁₇	#1371
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
12. #63214	C₈	semidirect
36. C₁₇	#1371	semidirect

Maximal subgroups

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

subgroup	index
#11763672	2
C₁₆×Dic₁₇	2
#1371	17