Subgroups — #88142

Order 416.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₆	C₂	1	2	yes	maximal
2	C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	#6101	C₂	1	2	yes	maximal
5	C₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₁₃	C₂²	1	2	yes	—
7	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×Dic₁₃	C₂²	1	2	yes	—
9	C₂×Dic₁₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₃	C₂²	1	1	yes	characteristic
11	Dic₂₆	—	2	4	no	—
12	C₂²×C₁₃	C₂³	1	1	yes	characteristic
13	C₄×C₁₃	—	2	2	no	—
14	C₄×C₁₃	Q₈	1	2	yes	complemented
15	Dic₁₃	—	2	2	no	—
16	Dic₁₃	D₄	1	2	yes	—
17	Dic₁₃	Q₈	1	2	yes	complemented
18	C₄⋊Q₈	—	13	1	no	maximal, Sylow
19	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
20	C₂×C₁₃	C₂×Q₈	1	1	yes	characteristic
21	C₂×C₁₃	C₂×Q₈	1	1	yes	characteristic
22	C₂×Q₈	—	13	2	no	—
23	C₄⋊C₄	—	13	2	no	—
24	C₄⋊C₄	—	13	1	no	—
25	C₄⋊C₄	D₁₃	1	1	yes	characteristic
26	C₄²	—	13	1	no	—
27	C₁₃	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
28	Q₈	—	26	4	no	—
29	C₂×C₄	—	13	1	no	—
30	C₂×C₄	—	13	1	no	—
31	C₂×C₄	—	13	2	no	—
32	C₂×C₄	C₂×D₁₃	1	2	yes	—
33	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
34	C₂²	C₂²×D₁₃	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	13	2	no	—
37	C₄	—	13	2	no	—
38	C₄	—	26	2	no	—
39	C₄	Dic₂₆	1	2	yes	complemented
40	C₂	C₂×Dic₂₆	1	1	yes	characteristic
41	C₂	D₄×D₁₃	1	1	yes	characteristic
42	C₂	Q₈×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₁₃
commutator, socle, prime radical, cosocle	C₂²×C₁₃	C₂³
Fitting	C₁₃×C₄⋊C₄	C₂
hypercenter	C₄⋊C₄	D₁₃
hypocenter	C₁₃	C₄⋊Q₈
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

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

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