Subgroups — #14545804

Order 2176.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763904	C₂	1	1	yes	maximal, characteristic
2	#11763893	C₂	1	1	yes	maximal, characteristic
3	#11763696	C₂	1	1	yes	maximal, characteristic
4	C₄×#3633	C₄	1	2	yes	—
5	#10587665	C₄	1	2	yes	—
6	C₈×#595	C₂²	1	1	yes	characteristic
7	#10587529	C₄	1	1	yes	characteristic
8	C₁₆×D₁₇	C₄	1	1	yes	characteristic
9	C₂×#3633	—	2	2	no	—
10	C₄×#595	C₂×C₄	1	1	yes	characteristic
11	#63242	C₂×C₄	1	1	yes	characteristic
12	#63241	—	2	2	no	—
13	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
14	#63216	C₈	1	2	yes	complemented
15	C₁₆×C₁₇	C₈	1	1	yes	characteristic, complemented
16	#63214	C₈	1	1	yes	characteristic, complemented
17	C₂×#595	M₁₆	1	2	yes	—
18	#3633	—	4	2	no	—
19	C₄×D₁₇	C₄²	1	1	yes	characteristic
20	#3624	M₁₆	1	2	yes	—
21	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
22	#3622	C₂×C₈	1	1	yes	characteristic
23	#1313	—	17	1	no	maximal, Sylow
24	C₂×D₁₇	#97	1	1	yes	characteristic
25	#595	—	2	2	no	—
26	C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
27	Dic₁₇	#97	1	1	yes	characteristic
28	#346	—	17	1	no	—
29	#346	—	17	1	no	—
30	#322	—	17	1	no	—
31	C₂×C₁₇	#322	1	1	yes	characteristic
32	D₁₇	#347	1	2	yes	—
33	C₂×C₁₆	—	17	1	no	—
34	C₂×C₁₆	—	17	1	no	—
35	C₂×C₁₆	—	17	2	no	—
36	C₄×C₈	—	17	1	no	—
37	C₄×C₈	—	17	2	no	—
38	C₁₇	#1313	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₈	—	17	1	no	—
40	C₂×C₈	—	17	1	no	—
41	C₂×C₈	—	34	2	no	—
42	C₄²	—	17	1	no	—
43	C₁₆	—	17	2	no	—
44	C₁₆	—	17	1	no	—
45	C₁₆	—	34	2	no	—
46	C₁₆	#3633	1	1	yes	characteristic, complemented
47	C₂×C₄	—	17	1	no	—
48	C₂×C₄	—	17	2	no	—
49	C₈	—	17	2	no	—
50	C₈	—	17	1	no	—
51	C₈	—	68	2	no	—
52	C₈	C₂×#3633	1	1	yes	characteristic
53	C₂²	—	17	1	no	—
54	C₄	—	17	1	no	—
55	C₄	—	34	2	no	—
56	C₄	C₄×#3633	1	1	yes	characteristic
57	C₂	—	17	2	no	—
58	C₂	#11763893	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×#3633
commutator	C₄×C₁₇	C₄×C₈
Frattini	C₈	C₂×#3633
Fitting	C₁₆×C₁₇	C₈
socle	C₂×C₁₇	#322
prime radical	C₂×D₁₇	#97
cosocle	C₈×#595	C₂²
hypercenter	C₁₆	#3633
hypocenter	C₁₇	#1313
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
14. #63216	C₈	semidirect
15. C₁₆×C₁₇	C₈	semidirect
16. #63214	C₈	semidirect
38. C₁₇	#1313	semidirect
46. C₁₆	#3633	semidirect

Maximal subgroups

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

subgroup	index
#11763904	2
#11763893	2
#11763696	2
#1313	17