Subgroups — #13089757

Order 1456.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×D₇	C₂	1	1	yes	maximal, characteristic
2	C₇⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#1055	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×D₇	C₄	1	1	yes	characteristic
5	C₄×C₇×C₁₃	C₂²	1	1	yes	characteristic
6	C₁₃×Dic₇	C₄	1	1	yes	characteristic
7	#6099	—	7	1	no	maximal, Hall
8	C₂×C₇×C₁₃	C₂×C₄	1	1	yes	characteristic
9	C₁₃×D₇	—	2	1	no	—
10	#1131	—	13	1	no	maximal, Hall
11	C₂×C₄×C₁₃	—	7	1	no	—
12	#1055	—	7	1	no	—
13	#1055	D₇	1	1	yes	characteristic, complemented
14	C₇×C₁₃	M₁₆	1	1	yes	characteristic, complemented, Hall
15	C₄×D₇	D₁₃	1	1	yes	characteristic
16	C₇×C₈	—	13	1	no	—
17	C₇⋊C₈	—	13	1	no	—
18	C₂²×C₁₃	—	7	1	no	—
19	C₄×C₁₃	—	7	1	no	—
20	C₄×C₁₃	C₂×D₇	1	1	yes	characteristic
21	C₂×D₇	Dic₁₃	1	1	yes	characteristic
22	C₄×C₇	C₂×D₁₃	1	1	yes	characteristic
23	Dic₇	Dic₁₃	1	1	yes	characteristic
24	C₂×C₁₃	—	14	1	no	—
25	C₂×C₁₃	C₄×D₇	1	1	yes	characteristic
26	M₁₆	—	91	1	no	Sylow
27	C₂×C₇	C₂×Dic₁₃	1	1	yes	characteristic
28	D₇	—	2	1	no	—
29	C₁₃	#1131	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₄	—	7	1	no	—
31	C₈	—	13	1	no	—
32	C₈	—	91	1	no	—
33	C₇	#6099	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	7	1	no	—
35	C₄	—	7	1	no	—
36	C₄	D₇×D₁₃	1	1	yes	characteristic
37	C₂	—	14	1	no	—
38	C₂	D₇×Dic₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₇×D₁₃
commutator, socle	C₂×C₇×C₁₃	C₂×C₄
Fitting, cosocle	C₄×C₇×C₁₃	C₂²
prime radical	C₂×C₁₃×D₇	C₄
hypocenter	C₇×C₁₃	M₁₆
LCS	G ▷ C₂×C₇×C₁₃ ▷ C₇×C₁₃
UCS	C₁ ◁ 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.