Subgroups — #14545868

Order 2176.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763916	C₂	1	2	yes	maximal
2	C₁₆×#595	C₂	1	1	yes	maximal, characteristic
3	C₈×#595	C₄	1	1	yes	characteristic
4	#10587529	C₂²	1	1	yes	characteristic
5	#10587528	C₄	1	4	yes	complemented
6	C₁₆×D₁₇	C₄	1	1	yes	characteristic
7	C₄×#595	C₈	1	1	yes	characteristic
8	#63242	C₈	1	1	yes	characteristic
9	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
10	#63216	C₂×C₄	1	2	yes	—
11	C₁₆×C₁₇	C₈	1	1	yes	characteristic
12	#63214	C₈	1	1	yes	characteristic
13	C₂×#595	C₁₆	1	2	yes	—
14	C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
15	#3624	C₁₆	1	2	yes	—
16	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
17	#3622	C₄²	1	1	yes	characteristic
18	C₄×C₃₂	—	17	1	no	maximal, Sylow
19	C₂×D₁₇	C₂×C₁₆	1	1	yes	characteristic
20	#595	C₃₂	1	4	yes	complemented
21	C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
22	Dic₁₇	C₂×C₁₆	1	1	yes	characteristic
23	C₂×C₃₂	—	17	2	no	—
24	C₄×C₁₆	—	17	1	no	—
25	C₂×C₁₇	C₄×C₁₆	1	1	yes	characteristic
26	D₁₇	C₂×C₃₂	1	2	yes	—
27	C₂×C₁₆	—	17	1	no	—
28	C₂×C₁₆	—	17	1	no	—
29	C₄×C₈	—	17	1	no	—
30	C₃₂	—	17	4	no	—
31	C₁₇	C₄×C₃₂	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₈	—	17	1	no	—
33	C₂×C₈	—	17	1	no	—
34	C₄²	—	17	1	no	—
35	C₁₆	—	17	2	no	—
36	C₁₆	—	17	1	no	—
37	C₁₆	#3633	1	1	yes	characteristic
38	C₂×C₄	—	17	2	no	—
39	C₂×C₄	—	17	1	no	—
40	C₈	—	17	2	no	—
41	C₈	—	17	1	no	—
42	C₈	C₂×#3633	1	1	yes	characteristic
43	C₂²	—	17	1	no	—
44	C₄	—	17	4	no	—
45	C₄	—	17	1	no	—
46	C₄	C₄×#3633	1	1	yes	characteristic
47	C₂	—	17	2	no	—
48	C₂	#11763902	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₁₆	#3633
commutator, hypocenter	C₁₇	C₄×C₃₂
Frattini	C₈	C₂×#3633
Fitting	C₁₆×C₁₇	C₈
socle	C₂×C₁₇	C₄×C₁₆
prime radical	C₂×D₁₇	C₂×C₁₆
cosocle	#10587529	C₂²
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
5. #10587528	C₄	semidirect
20. #595	C₃₂	semidirect
31. C₁₇	C₄×C₃₂	semidirect

Maximal subgroups

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

subgroup	index
#11763916	2
C₁₆×#595	2
C₄×C₃₂	17