Subgroups — #16922129

Order 4352.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11762528	C₂	1	2	yes	maximal
2	C₄×C₁₇×C₃₂	C₂	1	1	yes	maximal, characteristic
3	#11762528	C₄	1	4	yes	complemented
4	C₂×C₁₇×C₃₂	C₄	1	1	yes	characteristic
5	C₂×C₁₇×C₃₂	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₁₇	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₁₇	C₈	1	1	yes	characteristic
10	C₁₇×C₃₂	C₈	1	2	yes	—
11	C₁₇×C₃₂	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₁₇	C₁₆	1	1	yes	characteristic
13	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
14	C₄²×C₁₇	C₁₆	1	1	yes	characteristic
15	C₁₆×C₁₇	C₁₆	1	2	yes	—
16	C₁₆×C₁₇	C₄²	1	1	yes	characteristic
17	C₁₆×C₁₇	C₂×C₈	1	1	yes	characteristic
18	#7510	—	17	1	no	maximal, Sylow
19	C₂×C₄×C₁₇	C₃₂	1	2	yes	—
20	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
21	C₈×C₁₇	C₃₂	1	2	yes	—
22	C₈×C₁₇	C₄×C₈	1	1	yes	characteristic
23	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
24	C₂×C₆₄	—	17	2	no	—
25	C₄×C₃₂	D₁₇	1	1	yes	characteristic
26	C₂²×C₁₇	C₂×C₃₂	1	1	yes	characteristic
27	C₄×C₁₇	—	2	2	no	—
28	C₄×C₁₇	C₄×C₁₆	1	1	yes	characteristic
29	C₄×C₁₇	C₂×C₃₂	1	1	yes	characteristic
30	C₂×C₃₂	Dic₁₇	1	1	yes	characteristic
31	C₂×C₃₂	C₂×D₁₇	1	1	yes	characteristic
32	C₄×C₁₆	Dic₁₇	1	1	yes	characteristic
33	C₆₄	—	17	4	no	—
34	C₂×C₁₇	C₄×C₃₂	1	1	yes	characteristic
35	C₂×C₁₇	M₁₂₈	1	2	yes	—
36	C₂×C₁₆	#3622	1	1	yes	characteristic
37	C₂×C₁₆	C₂×Dic₁₇	1	1	yes	characteristic
38	C₄×C₈	#3622	1	1	yes	characteristic
39	C₃₂	#3622	1	2	yes	—
40	C₃₂	C₄×D₁₇	1	2	yes	—
41	C₁₇	#7510	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₈	#63214	1	1	yes	characteristic
43	C₂×C₈	C₂×#3622	1	1	yes	characteristic
44	C₄²	#63214	1	1	yes	characteristic
45	C₁₆	#63214	1	2	yes	—
46	C₁₆	C₂×#3622	1	1	yes	characteristic
47	C₁₆	C₄×Dic₁₇	1	1	yes	characteristic
48	C₂×C₄	#10587465	1	2	yes	—
49	C₂×C₄	C₂×#63214	1	1	yes	characteristic
50	C₈	#10587465	1	2	yes	—
51	C₈	C₄×#3622	1	1	yes	characteristic
52	C₈	C₂×#63214	1	1	yes	characteristic
53	C₂²	C₂×#10587465	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	C₄×#63214	1	1	yes	characteristic
56	C₄	C₂×#10587465	1	1	yes	characteristic
57	C₂	C₄×#10587465	1	1	yes	characteristic
58	C₂	#14526995	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₁₇
commutator	C₂×C₁₇	C₄×C₃₂
Fitting	C₄×C₁₇×C₃₂	C₂
socle, prime radical	C₂²×C₁₇	C₂×C₃₂
cosocle	C₂×C₁₇×C₃₂	C₂²
hypercenter	C₄×C₃₂	D₁₇
hypocenter	C₁₇	#7510
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₃₂ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
3. #11762528	C₄	semidirect
41. C₁₇	#7510	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11762528	2
C₄×C₁₇×C₃₂	2
#7510	17