Subgroups — #17981492

Order 4352.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545888	C₂	1	2	yes	maximal
2	#14543892	C₂	1	1	yes	maximal, characteristic
3	#11763891	C₄	1	4	yes	complemented
4	C₂×#10587467	C₄	1	1	yes	characteristic
5	C₂×#10587467	C₂²	1	1	yes	characteristic
6	C₁₆×Dic₁₇	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic
8	C₈×Dic₁₇	C₈	1	1	yes	characteristic
9	C₂×#63214	C₂×C₄	1	1	yes	characteristic
10	#10587467	C₈	1	2	yes	—
11	#10587467	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
13	C₄×Dic₁₇	C₁₆	1	1	yes	characteristic
14	C₂×#3622	C₁₆	1	1	yes	characteristic
15	C₁₆×C₁₇	C₁₆	1	2	yes	—
16	#63214	C₄²	1	1	yes	characteristic
17	#63214	C₂×C₈	1	1	yes	characteristic
18	#7511	—	17	1	no	maximal, Sylow
19	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
20	C₂×Dic₁₇	—	2	1	no	—
21	C₈×C₁₇	C₄×C₈	1	1	yes	characteristic
22	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
23	#3622	—	2	1	no	—
24	M₁₂₈	—	17	2	no	—
25	#1397	—	17	1	no	—
26	C₂²×C₁₇	M₆₄	1	1	yes	characteristic
27	C₄×C₁₇	C₄×C₁₆	1	1	yes	characteristic
28	C₄×C₁₇	M₆₄	1	1	yes	characteristic
29	Dic₁₇	—	4	1	no	—
30	C₂×C₃₂	—	17	1	no	—
31	C₂×C₃₂	—	17	1	no	—
32	C₄×C₁₆	—	17	1	no	—
33	C₆₄	—	17	4	no	—
34	C₂×C₁₇	—	2	1	no	—
35	C₂×C₁₇	#1397	1	1	yes	characteristic
36	C₂×C₁₆	—	17	1	no	—
37	C₂×C₁₆	#3633	1	1	yes	characteristic
38	C₄×C₈	—	17	1	no	—
39	C₃₂	—	17	2	no	—
40	C₃₂	—	17	2	no	—
41	C₁₇	#7511	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₈	—	17	1	no	—
43	C₂×C₈	C₂×#3633	1	1	yes	characteristic
44	C₄²	—	17	1	no	—
45	C₁₆	—	17	1	no	—
46	C₁₆	—	17	1	no	—
47	C₁₆	#63241	1	2	yes	—
48	C₂×C₄	—	34	1	no	—
49	C₂×C₄	#10587665	1	1	yes	characteristic
50	C₈	—	34	1	no	—
51	C₈	C₄×#3633	1	1	yes	characteristic
52	C₈	C₂×#63241	1	1	yes	characteristic
53	C₂²	#11763918	1	1	yes	characteristic
54	C₄	—	68	1	no	—
55	C₄	C₄×#63241	1	1	yes	characteristic
56	C₄	#11763918	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#14545870	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×#3633
commutator	C₄×C₁₇	C₄×C₁₆
Frattini	C₂×C₈	C₂×#3633
Fitting	C₂×C₁₆×C₁₇	C₈
socle	C₂×C₁₇	#1397
prime radical	C₂²×C₁₇	M₆₄
cosocle	C₂×#10587467	C₂²
hypercenter	C₂×C₁₆	#3633
hypocenter	C₁₇	#7511
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
3. #11763891	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
#14545888	2
#14543892	2
#7511	17