Subgroups — #14545867

Order 2176.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587528	C₂	1	2	yes	maximal
2	#11763695	C₂	1	1	yes	maximal, characteristic
3	C₂×#63216	C₄	1	1	yes	characteristic
4	C₂×#63216	C₂²	1	1	yes	characteristic
5	#10587528	C₄	1	4	yes	complemented
6	C₈×Dic₁₇	C₄	1	1	yes	characteristic
7	C₂×C₈×C₁₇	C₈	1	1	yes	characteristic
8	C₄×Dic₁₇	C₈	1	1	yes	characteristic
9	C₂×#3622	C₂×C₄	1	1	yes	characteristic
10	#63216	C₈	1	2	yes	—
11	#63216	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
13	C₂×Dic₁₇	C₁₆	1	2	yes	—
14	C₈×C₁₇	C₁₆	1	2	yes	—
15	#3622	C₄²	1	1	yes	characteristic
16	#3622	C₂×C₈	1	1	yes	characteristic
17	C₄×C₃₂	—	17	1	no	maximal, Sylow
18	C₂²×C₁₇	C₂×C₁₆	1	1	yes	characteristic
19	C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
20	C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
21	Dic₁₇	C₃₂	1	4	yes	complemented
22	C₂×C₃₂	—	17	2	no	—
23	C₄×C₁₆	—	17	1	no	—
24	C₂×C₁₇	C₄×C₁₆	1	1	yes	characteristic
25	C₂×C₁₇	C₂×C₃₂	1	2	yes	—
26	C₂×C₁₆	—	17	1	no	—
27	C₂×C₁₆	—	17	1	no	—
28	C₄×C₈	—	17	1	no	—
29	C₃₂	—	17	4	no	—
30	C₁₇	C₄×C₃₂	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₈	—	17	1	no	—
32	C₂×C₈	#3633	1	1	yes	characteristic
33	C₄²	—	17	1	no	—
34	C₁₆	—	17	2	no	—
35	C₁₆	—	17	2	no	—
36	C₂×C₄	—	17	2	no	—
37	C₂×C₄	C₂×#3633	1	1	yes	characteristic
38	C₈	—	17	1	no	—
39	C₈	—	17	1	no	—
40	C₈	#63241	1	2	yes	—
41	C₂²	#10587665	1	1	yes	characteristic
42	C₄	—	17	4	no	—
43	C₄	C₄×#3633	1	1	yes	characteristic
44	C₄	C₂×#63241	1	1	yes	characteristic
45	C₂	C₄×#63241	1	1	yes	characteristic
46	C₂	#11763916	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₈	#3633
commutator, hypocenter	C₁₇	C₄×C₃₂
Frattini	C₂×C₄	C₂×#3633
Fitting	C₂×C₈×C₁₇	C₈
socle, prime radical	C₂²×C₁₇	C₂×C₁₆
cosocle	C₂×#63216	C₂²
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
5. #10587528	C₄	semidirect
21. Dic₁₇	C₃₂	semidirect
30. 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
C₂×#10587528	2
#11763695	2
C₄×C₃₂	17