Subgroups — #14545802

Order 2176.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#63241	C₂	1	2	yes	maximal
2	C₈×#3624	C₂	1	1	yes	maximal, characteristic
3	C₂×#63241	C₄	1	4	yes	—
4	C₄×#3624	C₄	1	1	yes	characteristic
5	C₄×#3624	C₂²	1	1	yes	characteristic
6	C₈×Dic₁₇	C₄	1	1	yes	characteristic
7	C₂×#3624	C₈	1	2	yes	—
8	C₂×#3624	C₂×C₄	1	2	yes	—
9	#63241	—	2	4	no	—
10	C₂×C₈×C₁₇	C₈	1	1	yes	characteristic
11	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂×#3622	C₈	1	1	yes	characteristic
13	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
14	C₂×Dic₁₇	C₄²	1	1	yes	characteristic
15	C₂×Dic₁₇	C₂×C₈	1	1	yes	characteristic
16	#3624	C₁₆	1	4	yes	complemented
17	#3624	M₁₆	1	4	yes	—
18	C₈×C₁₇	—	2	1	no	—
19	#3622	—	2	1	no	—
20	#1312	—	17	1	no	maximal, Sylow
21	C₂²×C₁₇	C₄×C₈	1	1	yes	characteristic
22	C₄×C₁₇	M₃₂	1	1	yes	characteristic
23	C₄×C₁₇	M₃₂	1	1	yes	characteristic
24	Dic₁₇	#97	1	2	yes	—
25	Dic₁₇	C₂×C₁₆	1	2	yes	—
26	C₄×C₁₆	—	17	2	no	—
27	C₈²	—	17	1	no	—
28	C₂×C₁₇	#322	1	1	yes	characteristic
29	C₂×C₁₇	C₄×C₁₆	1	1	yes	characteristic
30	C₂×C₁₇	#346	1	1	yes	characteristic
31	C₂×C₁₆	—	17	4	no	—
32	C₄×C₈	—	17	1	no	—
33	C₄×C₈	—	17	1	no	—
34	C₄×C₈	—	17	1	no	—
35	C₁₇	#1312	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₈	—	17	2	no	—
37	C₂×C₈	—	17	2	no	—
38	C₂×C₈	—	17	1	no	—
39	C₂×C₈	#3633	1	1	yes	characteristic
40	C₄²	—	17	1	no	—
41	C₁₆	—	34	4	no	—
42	C₂×C₄	—	17	1	no	—
43	C₂×C₄	—	17	1	no	—
44	C₂×C₄	C₂×#3633	1	1	yes	characteristic
45	C₈	—	2	1	no	—
46	C₈	—	17	4	no	—
47	C₈	—	17	4	no	—
48	C₈	—	34	1	no	—
49	C₂²	C₄×#3633	1	1	yes	characteristic
50	C₄	—	17	2	no	—
51	C₄	—	17	2	no	—
52	C₄	#10587666	1	1	yes	characteristic
53	C₄	#10587670	1	1	yes	characteristic
54	C₂	#11763893	1	1	yes	characteristic
55	C₂	#11763902	1	1	yes	characteristic
56	C₂	#11763903	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#3633
commutator	C₂×C₁₇	C₄×C₁₆
Fitting	C₂×C₈×C₁₇	C₈
socle, prime radical	C₂²×C₁₇	C₄×C₈
cosocle	C₄×#3624	C₂²
hypercenter	C₂×C₈	#3633
hypocenter	C₁₇	#1312
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
16. #3624	C₁₆	semidirect
35. C₁₇	#1312	semidirect

Maximal subgroups

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

subgroup	index
C₄×#63241	2
C₈×#3624	2
#1312	17