Subgroups — #14543703

Order 2176.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763698	C₂	1	1	yes	maximal, characteristic
2	#11763650	C₂	1	1	yes	maximal, characteristic
3	#11762584	C₂	1	1	yes	maximal, characteristic
4	C₄×#3624	C₄	1	1	yes	characteristic
5	C₄×#3624	C₄	1	1	yes	characteristic
6	C₂×#63216	C₄	1	2	yes	—
7	C₂×C₁₆×C₁₇	C₄	1	1	yes	characteristic
8	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
9	C₂×#63214	C₄	1	1	yes	characteristic
10	C₂×#3624	—	2	1	no	—
11	C₂×#3624	—	2	1	no	—
12	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
14	C₂×#3622	C₂×C₄	1	1	yes	characteristic
15	#63216	C₈	1	4	yes	complemented
16	C₁₆×C₁₇	—	2	1	no	—
17	#63214	—	2	1	no	—
18	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
19	C₂×Dic₁₇	M₁₆	1	1	yes	characteristic
20	C₂×Dic₁₇	M₁₆	1	1	yes	characteristic
21	#3624	—	4	1	no	—
22	#3624	—	4	1	no	—
23	C₈×C₁₇	M₁₆	1	1	yes	characteristic
24	C₈×C₁₇	M₁₆	1	1	yes	characteristic
25	#3622	C₂×C₈	1	2	yes	—
26	#1313	—	17	1	no	maximal, Sylow
27	C₂²×C₁₇	#97	1	1	yes	characteristic
28	C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
29	C₄×C₁₇	#97	1	1	yes	characteristic
30	Dic₁₇	—	2	1	no	—
31	Dic₁₇	—	2	1	no	—
32	#346	—	17	1	no	—
33	#346	—	17	1	no	—
34	#322	—	17	1	no	—
35	C₂×C₁₇	#322	1	1	yes	characteristic
36	C₂×C₁₇	#347	1	1	yes	characteristic
37	C₂×C₁₇	#347	1	1	yes	characteristic
38	C₂×C₁₆	—	17	2	no	—
39	C₂×C₁₆	—	17	1	no	—
40	C₂×C₁₆	#595	1	1	yes	characteristic
41	C₄×C₈	—	17	1	no	—
42	C₄×C₈	—	17	1	no	—
43	C₄×C₈	—	17	1	no	—
44	C₁₇	#1313	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₈	—	17	1	no	—
46	C₂×C₈	—	34	1	no	—
47	C₂×C₈	—	34	1	no	—
48	C₂×C₈	C₂×#595	1	1	yes	characteristic
49	C₄²	—	17	1	no	—
50	C₁₆	—	2	1	no	—
51	C₁₆	—	17	4	no	—
52	C₁₆	—	34	1	no	—
53	C₂×C₄	—	17	1	no	—
54	C₂×C₄	—	17	1	no	—
55	C₂×C₄	C₄×#595	1	1	yes	characteristic
56	C₈	—	17	2	no	—
57	C₈	—	68	1	no	—
58	C₈	—	68	1	no	—
59	C₈	#63243	1	1	yes	characteristic
60	C₈	#63247	1	1	yes	characteristic
61	C₂²	#10587532	1	1	yes	characteristic
62	C₄	—	34	1	no	—
63	C₄	—	34	1	no	—
64	C₄	C₈×#595	1	1	yes	characteristic
65	C₄	#10587542	1	1	yes	characteristic
66	C₂	#11763651	1	1	yes	characteristic
67	C₂	#11763699	1	1	yes	characteristic
68	C₂	#11763700	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#595
commutator	C₄×C₁₇	C₄×C₈
Frattini	C₂×C₈	C₂×#595
Fitting	C₂×C₁₆×C₁₇	C₄
socle, prime radical	C₂²×C₁₇	#97
cosocle	C₈×Dic₁₇	C₂²
hypercenter	C₂×C₁₆	#595
hypocenter	C₁₇	#1313
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
15. #63216	C₈	semidirect
44. C₁₇	#1313	semidirect

Maximal subgroups

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

subgroup	index
#11763698	2
#11763650	2
#11762584	2
#1313	17