Subgroups — #16777682

Order 3328.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#88036	C₂	1	2	yes	maximal
2	C₁₆×#1055	C₂	1	1	yes	maximal, characteristic
3	C₂×#88036	C₄	1	4	yes	—
4	C₄×C₁₃×C₁₆	C₄	1	1	yes	characteristic
5	C₄×#6090	C₂²	1	1	yes	characteristic
6	C₈×#1055	C₄	1	1	yes	characteristic
7	C₂×C₁₃×C₁₆	C₈	1	2	yes	—
8	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
9	C₂×#6090	C₂×C₄	1	2	yes	—
10	C₄×#1055	C₈	1	2	yes	—
11	#88036	C₈	1	8	yes	complemented
12	C₈×C₃₂	—	13	1	no	maximal, Sylow
13	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
14	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
16	C₂×#1055	C₁₆	1	4	yes	—
17	C₁₃×C₁₆	C₁₆	1	4	yes	—
18	#6090	C₂×C₈	1	4	yes	—
19	C₄×C₃₂	—	13	2	no	—
20	C₈×C₁₆	—	13	1	no	—
21	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
22	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
23	C₈×C₁₃	C₄×C₈	1	2	yes	—
24	C₈×C₁₃	C₂×C₁₆	1	2	yes	—
25	#1055	C₃₂	1	8	yes	complemented
26	C₂×C₃₂	—	13	4	no	—
27	C₄×C₁₆	—	13	1	no	—
28	C₄×C₁₆	#261	1	1	yes	characteristic
29	C₈²	—	13	1	no	—
30	C₂²×C₁₃	C₄×C₁₆	1	1	yes	characteristic
31	C₄×C₁₃	C₈²	1	1	yes	characteristic
32	C₄×C₁₃	C₄×C₁₆	1	1	yes	characteristic
33	C₄×C₁₃	C₂×C₃₂	1	4	yes	—
34	C₂×C₁₆	—	13	2	no	—
35	C₂×C₁₆	#1057	1	2	yes	—
36	C₄×C₈	—	13	2	no	—
37	C₄×C₈	C₂×#261	1	1	yes	characteristic
38	C₃₂	—	13	8	no	—
39	C₂×C₁₃	C₈×C₁₆	1	1	yes	characteristic
40	C₂×C₁₃	C₄×C₃₂	1	2	yes	—
41	C₂×C₈	—	13	4	no	—
42	C₂×C₈	C₄×#261	1	1	yes	characteristic
43	C₂×C₈	C₂×#1057	1	1	yes	characteristic
44	C₄²	D₁₃⋊C₈	1	1	yes	characteristic
45	C₁₆	—	13	4	no	—
46	C₁₆	#6092	1	4	yes	—
47	C₁₃	C₈×C₃₂	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₄	D₁₃⋊C₁₆	1	2	yes	—
49	C₂×C₄	C₄×#1057	1	1	yes	characteristic
50	C₈	—	13	8	no	—
51	C₈	C₈×#261	1	2	yes	—
52	C₈	C₂×#6092	1	2	yes	—
53	C₂²	#11718257	1	1	yes	characteristic
54	C₄	D₁₃⋊C₃₂	1	4	yes	—
55	C₄	C₄×#6092	1	1	yes	characteristic
56	C₄	C₈×#1057	1	1	yes	characteristic
57	C₂	C₈×#6092	1	1	yes	characteristic
58	C₂	#13129941	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄×C₁₆	#261
commutator, hypocenter	C₁₃	C₈×C₃₂
Frattini	C₄×C₈	C₂×#261
Fitting	C₄×C₁₃×C₁₆	C₄
socle, prime radical	C₂²×C₁₃	C₄×C₁₆
cosocle	C₄×#6090	C₂²
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
11. #88036	C₈	semidirect
25. #1055	C₃₂	semidirect
47. C₁₃	C₈×C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₄×#88036	2
C₁₆×#1055	2
C₈×C₃₂	13