Subgroups — #16777689

Order 3328.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129943	C₂	1	2	yes	maximal
2	#13112752	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	#7330	—	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	—	2	2	no	—
17	C₁₃×C₁₆	—	2	2	no	—
18	#6090	C₂×C₈	1	4	yes	—
19	#1397	—	13	2	no	—
20	#1311	—	13	1	no	—
21	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
22	C₂×C₄×C₁₃	M₃₂	1	2	yes	—
23	C₈×C₁₃	C₄×C₈	1	2	yes	—
24	C₈×C₁₃	M₃₂	1	2	yes	—
25	#1055	—	4	2	no	—
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	#346	1	1	yes	characteristic
31	C₄×C₁₃	—	2	2	no	—
32	C₄×C₁₃	C₈²	1	1	yes	characteristic
33	C₄×C₁₃	#346	1	1	yes	characteristic
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	#1311	1	1	yes	characteristic
40	C₂×C₁₃	#1398	1	2	yes	—
41	C₂×C₈	—	26	2	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	—	2	2	no	—
46	C₁₆	—	13	4	no	—
47	C₁₃	#7330	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₄	#88098	1	2	yes	—
49	C₂×C₄	C₄×#1057	1	1	yes	characteristic
50	C₈	—	52	2	no	—
51	C₈	C₈×#261	1	2	yes	—
52	C₈	#88106	1	2	yes	—
53	C₂²	#11718258	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	#11718231	1	1	yes	characteristic
56	C₄	C₈×#1057	1	1	yes	characteristic
57	C₂	#13129748	1	1	yes	characteristic
58	C₂	#13129948	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₄×#261
commutator	C₄×C₁₃	C₈²
Frattini	C₄×C₈	C₂×#261
Fitting	C₄×C₁₃×C₁₆	C₄
socle, prime radical	C₂²×C₁₃	#346
cosocle	C₄×#6090	C₂²
hypercenter	C₄×C₁₆	#261
hypocenter	C₁₃	#7330
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
11. #88036	C₈	semidirect
47. C₁₃	#7330	semidirect

Maximal subgroups

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

subgroup	index
#13129943	2
#13112752	2
#7330	13