Subgroups — #16776913

Order 3328.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#6092	C₂	1	2	yes	maximal
2	C₁₆×#1055	C₂	1	1	yes	maximal, characteristic
3	C₄×#6092	C₄	1	4	yes	—
4	C₄×C₁₃×C₁₆	C₄	1	1	yes	characteristic
5	C₄×#6090	C₄	1	1	yes	characteristic
6	C₈×#1055	C₂²	1	1	yes	characteristic
7	C₂×#6092	C₈	1	8	yes	—
8	C₂×C₁₃×C₁₆	C₈	1	2	yes	—
9	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₂×#6090	C₈	1	2	yes	—
11	C₄×#1055	C₂×C₄	1	2	yes	—
12	#7052	—	13	1	no	maximal, Sylow
13	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
14	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₁₃	C₄²	1	1	yes	characteristic
16	C₂×#1055	C₂×C₈	1	4	yes	—
17	#6092	—	2	8	no	—
18	C₁₃×C₁₆	C₁₆	1	4	yes	complemented
19	#6090	C₁₆	1	4	yes	complemented
20	C₈×C₁₆	—	13	2	no	—
21	C₈×C₁₆	—	13	1	no	—
22	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
23	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
24	C₈×C₁₃	C₂×C₁₆	1	2	yes	—
25	C₈×C₁₃	C₂×C₁₆	1	2	yes	—
26	#1055	M₃₂	1	8	yes	—
27	C₄×C₁₆	—	13	4	no	—
28	C₄×C₁₆	—	13	1	no	—
29	C₄×C₁₆	#261	1	1	yes	characteristic
30	C₈²	—	13	1	no	—
31	C₂²×C₁₃	C₈²	1	1	yes	characteristic
32	C₄×C₁₃	C₄×C₁₆	1	1	yes	characteristic
33	C₄×C₁₃	C₄×C₁₆	1	1	yes	characteristic
34	C₄×C₁₃	#346	1	4	yes	—
35	C₂×C₁₆	—	13	2	no	—
36	C₂×C₁₆	—	13	8	no	—
37	C₂×C₁₆	#1057	1	2	yes	—
38	C₄×C₈	—	13	2	no	—
39	C₄×C₈	C₂×#261	1	1	yes	characteristic
40	C₂×C₁₃	C₈×C₁₆	1	1	yes	characteristic
41	C₂×C₁₃	#1311	1	2	yes	—
42	C₂×C₈	—	13	4	no	—
43	C₂×C₈	D₁₃⋊C₈	1	1	yes	characteristic
44	C₂×C₈	C₂×#1057	1	1	yes	characteristic
45	C₄²	C₄×#261	1	1	yes	characteristic
46	C₁₆	—	13	4	no	—
47	C₁₆	—	26	8	no	—
48	C₁₆	#6092	1	4	yes	complemented
49	C₁₃	#7052	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₄	C₈×#261	1	2	yes	—
51	C₂×C₄	C₄×#1057	1	1	yes	characteristic
52	C₈	—	13	8	no	—
53	C₈	D₁₃⋊C₁₆	1	2	yes	—
54	C₈	C₂×#6092	1	2	yes	—
55	C₂²	C₈×#1057	1	1	yes	characteristic
56	C₄	#11718216	1	4	yes	—
57	C₄	C₄×#6092	1	1	yes	characteristic
58	C₄	#11718257	1	1	yes	characteristic
59	C₂	C₈×#6092	1	1	yes	characteristic
60	C₂	#13129747	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×#261
commutator	C₂×C₁₃	C₈×C₁₆
Fitting	C₄×C₁₃×C₁₆	C₄
socle, prime radical	C₂²×C₁₃	C₈²
cosocle	C₈×#1055	C₂²
hypercenter	C₄×C₁₆	#261
hypocenter	C₁₃	#7052
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
18. C₁₃×C₁₆	C₁₆	semidirect
19. #6090	C₁₆	semidirect
48. C₁₆	#6092	semidirect
49. C₁₃	#7052	semidirect

Maximal subgroups

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

subgroup	index
C₈×#6092	2
C₁₆×#1055	2
#7052	13