Subgroups — #17981333

Order 4352.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545867	C₂	1	2	yes	maximal
2	C₁₆×#3624	C₂	1	1	yes	maximal, characteristic
3	C₂×#10587528	C₄	1	4	yes	—
4	#11763695	C₂²	1	1	yes	characteristic
5	C₈×#3624	C₄	1	1	yes	characteristic
6	C₁₆×Dic₁₇	C₄	1	1	yes	characteristic
7	C₄×#3624	C₈	1	2	yes	—
8	C₂×#63216	C₂×C₄	1	2	yes	—
9	#10587528	C₈	1	8	yes	complemented
10	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic
11	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂×#63214	C₈	1	1	yes	characteristic
13	C₂×#3624	C₁₆	1	4	yes	—
14	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
15	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
16	C₂×#3622	C₄²	1	1	yes	characteristic
17	#63216	C₂×C₈	1	4	yes	—
18	C₁₆×C₁₇	C₁₆	1	2	yes	—
19	#63214	C₁₆	1	2	yes	—
20	C₈×C₃₂	—	17	1	no	maximal, Sylow
21	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
22	C₂×Dic₁₇	C₂×C₁₆	1	2	yes	—
23	#3624	C₃₂	1	8	yes	complemented
24	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
25	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
26	#3622	C₄×C₈	1	2	yes	—
27	C₄×C₃₂	—	17	2	no	—
28	C₈×C₁₆	—	17	1	no	—
29	C₂²×C₁₇	C₄×C₁₆	1	1	yes	characteristic
30	C₄×C₁₇	C₈²	1	1	yes	characteristic
31	C₄×C₁₇	C₄×C₁₆	1	1	yes	characteristic
32	Dic₁₇	C₂×C₃₂	1	4	yes	—
33	C₂×C₃₂	—	17	4	no	—
34	C₄×C₁₆	—	17	1	no	—
35	C₄×C₁₆	—	17	1	no	—
36	C₈²	—	17	1	no	—
37	C₂×C₁₇	C₈×C₁₆	1	1	yes	characteristic
38	C₂×C₁₇	C₄×C₃₂	1	2	yes	—
39	C₂×C₁₆	—	17	2	no	—
40	C₂×C₁₆	—	17	1	no	—
41	C₂×C₁₆	#3633	1	1	yes	characteristic
42	C₄×C₈	—	17	2	no	—
43	C₄×C₈	—	17	1	no	—
44	C₃₂	—	17	8	no	—
45	C₁₇	C₈×C₃₂	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₈	—	17	4	no	—
47	C₂×C₈	—	17	1	no	—
48	C₂×C₈	C₂×#3633	1	1	yes	characteristic
49	C₄²	—	17	1	no	—
50	C₁₆	—	17	4	no	—
51	C₁₆	—	17	2	no	—
52	C₁₆	#63241	1	2	yes	—
53	C₂×C₄	—	17	2	no	—
54	C₂×C₄	C₄×#3633	1	1	yes	characteristic
55	C₈	—	17	8	no	—
56	C₈	—	17	2	no	—
57	C₈	#10587665	1	1	yes	characteristic
58	C₈	C₂×#63241	1	1	yes	characteristic
59	C₂²	#11763902	1	1	yes	characteristic
60	C₄	—	17	4	no	—
61	C₄	C₈×#3633	1	1	yes	characteristic
62	C₄	C₄×#63241	1	1	yes	characteristic
63	C₂	C₈×#63241	1	1	yes	characteristic
64	C₂	#14545868	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₁₆	#3633
commutator, hypocenter	C₁₇	C₈×C₃₂
Frattini	C₂×C₈	C₂×#3633
Fitting	C₂×C₁₆×C₁₇	C₈
socle, prime radical	C₂²×C₁₇	C₄×C₁₆
cosocle	#11763695	C₂²
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
9. #10587528	C₈	semidirect
23. #3624	C₃₂	semidirect
45. C₁₇	C₈×C₃₂	semidirect

Maximal subgroups

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

subgroup	index
#14545867	2
C₁₆×#3624	2
C₈×C₃₂	17