Subgroups — #17949382

Order 4352.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543815	C₂	1	2	yes	maximal
2	C₃₂×Dic₁₇	C₂	1	1	yes	maximal, characteristic
3	#11763672	—	2	2	no	—
4	C₂×#10587465	C₄	1	1	yes	characteristic
5	C₁₆×Dic₁₇	C₂²	1	1	yes	characteristic
6	C₂×C₁₇×C₃₂	C₄	1	1	yes	characteristic
7	C₄⋊#3624	—	4	2	no	—
8	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
9	C₈×Dic₁₇	D₄	1	1	yes	characteristic
10	C₂×#63214	Q₈	1	1	yes	characteristic
11	C₁₇×C₃₂	—	2	1	no	—
12	#10587465	C₈	1	2	yes	complemented
13	C₂×#3624	—	8	2	no	—
14	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×Dic₁₇	D₈	1	1	yes	characteristic
16	C₂×#3622	Q₁₆	1	1	yes	characteristic
17	C₁₆×C₁₇	C₂×C₈	1	1	yes	characteristic
18	C₁₆×C₁₇	M₁₆	1	1	yes	characteristic
19	#63214	—	2	1	no	—
20	#7461	—	17	1	no	maximal, Sylow
21	C₂×C₄×C₁₇	#107	1	1	yes	characteristic
22	C₂×Dic₁₇	D₁₆	1	1	yes	characteristic
23	C₂×Dic₁₇	Q₃₂	1	1	yes	characteristic
24	#3624	—	16	2	no	—
25	C₈×C₁₇	C₄⋊C₈	1	1	yes	characteristic
26	C₈×C₁₇	#108	1	1	yes	characteristic
27	#3622	—	2	1	no	—
28	C₄×C₃₂	—	17	1	no	—
29	#1371	—	17	2	no	—
30	C₂²×C₁₇	#366	1	1	yes	characteristic
31	C₄×C₁₇	#335	1	1	yes	characteristic
32	C₄×C₁₇	#368	1	1	yes	characteristic
33	Dic₁₇	—	2	1	no	—
34	Dic₁₇	SD₆₄	1	2	yes	—
35	C₂×C₃₂	—	17	1	no	—
36	C₂×C₃₂	#595	1	1	yes	characteristic
37	C₄×C₁₆	—	17	1	no	—
38	#335	—	34	2	no	—
39	C₂×C₁₇	#1371	1	1	yes	characteristic
40	C₂×C₁₇	#1424	1	1	yes	characteristic
41	C₂×C₁₇	#1425	1	1	yes	characteristic
42	C₂×C₁₆	—	17	1	no	—
43	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
44	C₄⋊C₈	—	68	2	no	—
45	C₄×C₈	—	17	1	no	—
46	C₃₂	—	2	1	no	—
47	C₃₂	—	17	2	no	—
48	C₁₇	#7461	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₈	—	17	1	no	—
50	C₂×C₈	—	136	2	no	—
51	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
52	C₄²	—	17	1	no	—
53	C₁₆	—	34	1	no	—
54	C₁₆	#63242	1	1	yes	characteristic
55	C₁₆	#63247	1	1	yes	characteristic
56	C₂×C₄	—	17	1	no	—
57	C₂×C₄	—	17	1	no	—
58	C₂×C₄	#10587534	1	1	yes	characteristic
59	C₈	—	272	2	no	—
60	C₈	—	34	1	no	—
61	C₈	#10587535	1	1	yes	characteristic
62	C₈	#10587544	1	1	yes	characteristic
63	C₂²	#11763735	1	1	yes	characteristic
64	C₄	—	17	2	no	—
65	C₄	—	34	1	no	—
66	C₄	#11763673	1	1	yes	characteristic
67	C₄	#11763738	1	1	yes	characteristic
68	C₂	#14543816	1	1	yes	characteristic
69	C₂	#14543946	1	1	yes	characteristic
70	C₂	#14543947	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11763735
commutator	C₁₆×C₁₇	C₂×C₈
Frattini	C₂×C₁₆	C₂×#595
Fitting	C₂×C₁₇×C₃₂	C₄
socle, prime radical	C₂²×C₁₇	#366
cosocle	C₁₆×Dic₁₇	C₂²
hypercenter	C₂×C₃₂	#595
hypocenter	C₁₇	#7461
LCS	G ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
12. #10587465	C₈	semidirect
48. C₁₇	#7461	semidirect

Maximal subgroups

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

subgroup	index
#14543815	2
C₃₂×Dic₁₇	2
#7461	17