Subgroups — #17948321

Order 4352.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543697	C₂	1	2	yes	maximal
2	#14526700	C₂	1	1	yes	maximal, characteristic
3	C₄×#63216	C₄	1	4	yes	—
4	C₄×#63214	C₄	1	1	yes	characteristic
5	C₈×#3622	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₁₇	C₄	1	1	yes	characteristic
7	C₂×#63216	—	2	4	no	—
8	C₂×C₁₆×C₁₇	C₈	1	2	yes	—
9	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
10	C₂×#63214	C₈	1	2	yes	—
11	C₄×#3622	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
13	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
14	C₄²×C₁₇	C₄²	1	1	yes	characteristic
15	C₂×#3622	M₁₆	1	4	yes	—
16	#63216	—	4	4	no	—
17	C₁₆×C₁₇	C₁₆	1	4	yes	complemented
18	#63214	—	2	2	no	—
19	#7053	—	17	1	no	maximal, Sylow
20	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
21	C₂×C₄×C₁₇	#97	1	2	yes	—
22	C₈×C₁₇	C₂×C₁₆	1	2	yes	—
23	C₈×C₁₇	M₃₂	1	2	yes	—
24	#3622	—	2	4	no	—
25	#1312	—	17	2	no	—
26	#1311	—	17	1	no	—
27	C₂²×C₁₇	#322	1	1	yes	characteristic
28	C₄×C₁₇	C₄×C₁₆	1	1	yes	characteristic
29	C₄×C₁₇	#346	1	1	yes	characteristic
30	C₄×C₁₇	#347	1	4	yes	—
31	C₄×C₁₆	—	17	4	no	—
32	C₄×C₁₆	—	17	1	no	—
33	C₄×C₁₆	#595	1	1	yes	characteristic
34	C₈²	—	17	1	no	—
35	C₂×C₁₇	#1312	1	1	yes	characteristic
36	C₂×C₁₇	#1313	1	2	yes	—
37	C₂×C₁₆	—	17	2	no	—
38	C₂×C₁₆	—	34	4	no	—
39	C₂×C₁₆	#3624	1	2	yes	—
40	C₄×C₈	—	17	2	no	—
41	C₄×C₈	C₂×#595	1	1	yes	characteristic
42	C₁₇	#7053	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₈	—	17	4	no	—
44	C₂×C₈	#63242	1	1	yes	characteristic
45	C₂×C₈	C₂×#3624	1	1	yes	characteristic
46	C₄²	C₄×#595	1	1	yes	characteristic
47	C₁₆	—	34	2	no	—
48	C₁₆	—	68	4	no	—
49	C₁₆	#63216	1	4	yes	complemented
50	C₂×C₄	#10587532	1	2	yes	—
51	C₂×C₄	C₄×#3624	1	1	yes	characteristic
52	C₈	—	34	4	no	—
53	C₈	#10587530	1	2	yes	—
54	C₈	C₂×#63216	1	2	yes	—
55	C₂²	#11763650	1	1	yes	characteristic
56	C₄	C₄×#63216	1	1	yes	characteristic
57	C₄	#11763698	1	1	yes	characteristic
58	C₄	#11763700	1	4	yes	—
59	C₂	#14543697	1	1	yes	characteristic
60	C₂	#14543701	1	2	yes	—

	subgroup	G/H
center	C₄²	C₄×#595
commutator	C₄×C₁₇	C₄×C₁₆
Frattini	C₄×C₈	C₂×#595
Fitting	C₄×C₁₆×C₁₇	C₄
socle, prime radical	C₂²×C₁₇	#322
cosocle	C₈×#3622	C₂²
hypercenter	C₄×C₁₆	#595
hypocenter	C₁₇	#7053
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
17. C₁₆×C₁₇	C₁₆	semidirect
42. C₁₇	#7053	semidirect
49. C₁₆	#63216	semidirect

Maximal subgroups

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

subgroup	index
#14543697	2
#14526700	2
#7053	17