Subgroups — #14543698

Order 2176.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763695	C₂	1	1	yes	maximal, characteristic
2	C₈×#3624	C₂	1	1	yes	maximal, characteristic
3	C₁₆×Dic₁₇	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	C₈	1	2	yes	—
11	C₂×#3624	C₈	1	2	yes	—
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	—	2	2	no	—
16	C₁₆×C₁₇	—	2	1	no	—
17	#63214	—	2	1	no	—
18	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
19	C₂×Dic₁₇	C₂×C₈	1	1	yes	characteristic
20	C₂×Dic₁₇	C₂×C₈	1	1	yes	characteristic
21	#3624	—	2	2	no	—
22	#3624	C₁₆	1	4	yes	complemented
23	C₈×C₁₇	M₁₆	1	1	yes	characteristic
24	C₈×C₁₇	M₁₆	1	1	yes	characteristic
25	#3622	M₁₆	1	2	yes	—
26	#1312	—	17	1	no	maximal, Sylow
27	C₂²×C₁₇	C₄×C₈	1	1	yes	characteristic
28	C₄×C₁₇	#97	1	1	yes	characteristic
29	C₄×C₁₇	#97	1	1	yes	characteristic
30	Dic₁₇	C₂×C₁₆	1	2	yes	—
31	Dic₁₇	M₃₂	1	2	yes	—
32	C₄×C₁₆	—	17	1	no	—
33	C₄×C₁₆	—	17	1	no	—
34	C₈²	—	17	1	no	—
35	C₂×C₁₇	#322	1	1	yes	characteristic
36	C₂×C₁₇	C₄×C₁₆	1	1	yes	characteristic
37	C₂×C₁₇	#346	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	#1312	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₈	—	17	2	no	—
46	C₂×C₈	—	17	1	no	—
47	C₂×C₈	—	17	2	no	—
48	C₂×C₈	C₂×#595	1	1	yes	characteristic
49	C₄²	—	17	1	no	—
50	C₁₆	—	2	1	no	—
51	C₁₆	—	34	2	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	4	no	—
57	C₈	—	17	2	no	—
58	C₈	—	34	2	no	—
59	C₈	#63243	1	1	yes	characteristic
60	C₈	#63247	1	1	yes	characteristic
61	C₂²	C₈×#595	1	1	yes	characteristic
62	C₄	—	17	2	no	—
63	C₄	—	17	2	no	—
64	C₄	#10587532	1	1	yes	characteristic
65	C₄	#10587542	1	1	yes	characteristic
66	C₂	#11763651	1	1	yes	characteristic
67	C₂	C₁₆×#595	1	1	yes	characteristic
68	C₂	#11763696	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#595
commutator	C₂×C₁₇	C₄×C₁₆
Fitting	C₂×C₁₆×C₁₇	C₄
socle, prime radical	C₂²×C₁₇	C₄×C₈
cosocle	C₈×Dic₁₇	C₂²
hypercenter	C₂×C₁₆	#595
hypocenter	C₁₇	#1312
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
22. #3624	C₁₆	semidirect
44. C₁₇	#1312	semidirect

Maximal subgroups

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

subgroup	index
#11763695	2
C₈×#3624	2
C₁₆×Dic₁₇	2
#1312	17