Subgroups — #17981340

Order 4352.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545870	C₂	1	2	yes	maximal
2	#14543695	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	1	yes	characteristic
8	C₄×#3624	C₈	1	1	yes	characteristic
9	C₂×#63216	C₂×C₄	1	2	yes	—
10	#10587528	C₈	1	8	yes	complemented
11	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic
12	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂×#63214	C₈	1	1	yes	characteristic
14	C₂×#3624	—	2	1	no	—
15	C₂×#3624	—	2	1	no	—
16	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
17	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
18	C₂×#3622	C₄²	1	1	yes	characteristic
19	#63216	C₂×C₈	1	4	yes	—
20	C₁₆×C₁₇	—	2	1	no	—
21	#63214	—	2	1	no	—
22	#7330	—	17	1	no	maximal, Sylow
23	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
24	C₂×Dic₁₇	M₃₂	1	1	yes	characteristic
25	C₂×Dic₁₇	M₃₂	1	1	yes	characteristic
26	#3624	—	4	1	no	—
27	#3624	—	4	1	no	—
28	C₈×C₁₇	M₃₂	1	1	yes	characteristic
29	C₈×C₁₇	M₃₂	1	1	yes	characteristic
30	#3622	C₄×C₈	1	2	yes	—
31	#1397	—	17	2	no	—
32	#1311	—	17	1	no	—
33	C₂²×C₁₇	#346	1	1	yes	characteristic
34	C₄×C₁₇	C₈²	1	1	yes	characteristic
35	C₄×C₁₇	#346	1	1	yes	characteristic
36	Dic₁₇	—	2	1	no	—
37	Dic₁₇	—	2	1	no	—
38	C₂×C₃₂	—	17	4	no	—
39	C₄×C₁₆	—	17	1	no	—
40	C₄×C₁₆	—	17	1	no	—
41	C₈²	—	17	1	no	—
42	C₂×C₁₇	#1311	1	1	yes	characteristic
43	C₂×C₁₇	#1398	1	1	yes	characteristic
44	C₂×C₁₇	#1398	1	1	yes	characteristic
45	C₂×C₁₆	—	17	2	no	—
46	C₂×C₁₆	—	17	1	no	—
47	C₂×C₁₆	#3633	1	1	yes	characteristic
48	C₄×C₈	—	17	1	no	—
49	C₄×C₈	—	17	1	no	—
50	C₄×C₈	—	17	1	no	—
51	C₃₂	—	17	8	no	—
52	C₁₇	#7330	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₈	—	17	1	no	—
54	C₂×C₈	—	34	1	no	—
55	C₂×C₈	—	34	1	no	—
56	C₂×C₈	C₂×#3633	1	1	yes	characteristic
57	C₄²	—	17	1	no	—
58	C₁₆	—	2	1	no	—
59	C₁₆	—	17	4	no	—
60	C₁₆	—	34	1	no	—
61	C₂×C₄	—	17	1	no	—
62	C₂×C₄	—	17	1	no	—
63	C₂×C₄	C₄×#3633	1	1	yes	characteristic
64	C₈	—	17	2	no	—
65	C₈	—	68	1	no	—
66	C₈	—	68	1	no	—
67	C₈	#10587666	1	1	yes	characteristic
68	C₈	#10587670	1	1	yes	characteristic
69	C₂²	#11763904	1	1	yes	characteristic
70	C₄	—	34	1	no	—
71	C₄	—	34	1	no	—
72	C₄	C₈×#3633	1	1	yes	characteristic
73	C₄	#11763903	1	1	yes	characteristic
74	C₂	#14545800	1	1	yes	characteristic
75	C₂	#14545874	1	1	yes	characteristic
76	C₂	#14545875	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#3633
commutator	C₄×C₁₇	C₈²
Frattini	C₂×C₈	C₂×#3633
Fitting	C₂×C₁₆×C₁₇	C₈
socle, prime radical	C₂²×C₁₇	#346
cosocle	#11763695	C₂²
hypercenter	C₂×C₁₆	#3633
hypocenter	C₁₇	#7330
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
10. #10587528	C₈	semidirect
52. C₁₇	#7330	semidirect

Maximal subgroups

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

subgroup	index
#14545870	2
#14543695	2
#7330	17