Subgroups — #17949548

Order 4352.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543953	C₂	1	2	yes	maximal
2	#14526918	C₂	1	1	yes	maximal, characteristic
3	#11763648	C₄	1	4	yes	complemented
4	C₂×#10587465	C₄	1	1	yes	characteristic
5	C₂×#10587465	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	#10587465	C₈	1	2	yes	—
11	#10587465	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	#7511	—	17	1	no	maximal, Sylow
19	C₂×C₄×C₁₇	—	2	1	no	—
20	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
21	C₈×C₁₇	—	2	1	no	—
22	C₈×C₁₇	C₄×C₈	1	1	yes	characteristic
23	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
24	M₁₂₈	—	17	2	no	—
25	#1397	—	17	1	no	—
26	C₂²×C₁₇	M₆₄	1	1	yes	characteristic
27	C₄×C₁₇	—	4	1	no	—
28	C₄×C₁₇	C₄×C₁₆	1	1	yes	characteristic
29	C₄×C₁₇	M₆₄	1	1	yes	characteristic
30	C₂×C₃₂	—	17	1	no	—
31	C₂×C₃₂	—	17	1	no	—
32	C₄×C₁₆	#595	1	1	yes	characteristic
33	C₆₄	—	17	4	no	—
34	C₂×C₁₇	—	2	1	no	—
35	C₂×C₁₇	#1397	1	1	yes	characteristic
36	C₂×C₁₆	#3624	1	1	yes	characteristic
37	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
38	C₄×C₈	#3624	1	1	yes	characteristic
39	C₃₂	—	17	2	no	—
40	C₃₂	—	17	2	no	—
41	C₁₇	#7511	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₈	#63216	1	1	yes	characteristic
43	C₂×C₈	C₂×#3624	1	1	yes	characteristic
44	C₄²	#63216	1	1	yes	characteristic
45	C₁₆	#63216	1	2	yes	—
46	C₁₆	#63242	1	1	yes	characteristic
47	C₁₆	C₄×#595	1	1	yes	characteristic
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	C₂×#63216	1	1	yes	characteristic
50	C₈	—	2	1	no	—
51	C₈	C₂×#63216	1	1	yes	characteristic
52	C₈	C₄×#3624	1	1	yes	characteristic
53	C₂²	#11763741	1	1	yes	characteristic
54	C₄	—	4	1	no	—
55	C₄	C₄×#63216	1	1	yes	characteristic
56	C₄	#11763741	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#14543891	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₄×#595
commutator	C₄×C₁₇	C₄×C₁₆
Frattini	C₂×C₁₆	C₂×#595
Fitting	C₄×C₁₆×C₁₇	C₄
socle	C₂×C₁₇	#1397
prime radical	C₂²×C₁₇	M₆₄
cosocle	C₂×#10587465	C₂²
hypercenter	C₄×C₁₆	#595
hypocenter	C₁₇	#7511
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
3. #11763648	C₄	semidirect
41. C₁₇	#7511	semidirect

Maximal subgroups

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

subgroup	index
#14543953	2
#14526918	2
#7511	17