Subgroups — D₇×#14555917 #44538947

Order 31570.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#14555917	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₇×C₄₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×#14555917	—	7	1	no	maximal, Hall
4	C₇×C₁₁×C₄₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	D₇×C₄₁⋊C₅	—	11	1	no	maximal, Hall
6	#14555917	D₇	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₄₁⋊C₅	—	11	1	no	Hall
8	C₂×C₁₁×C₄₁	—	7	1	no	Hall
9	D₇×C₁₁⋊C₅	—	41	1	no	maximal, Hall
10	D₇×C₄₁	C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
11	C₁₁×C₄₁	C₅×D₇	1	1	yes	characteristic, complemented, Hall
12	C₂×C₄₁⋊C₅	—	77	1	no	Hall
13	C₇×C₁₁⋊C₅	—	41	1	no	Hall
14	C₇×C₄₁	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
15	C₄₁⋊C₅	—	11	1	no	Hall
16	C₁₁×D₇	C₄₁⋊C₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₁⋊C₅	—	287	1	no	Hall
18	C₂×C₄₁	—	7	1	no	Hall
19	C₇×C₁₁	C₂×C₄₁⋊C₅	1	1	yes	characteristic, complemented, Hall
20	C₅×D₇	—	451	1	no	Hall
21	C₁₁⋊C₅	—	41	1	no	Hall
22	C₄₁	D₇×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
23	C₅×C₇	—	451	1	no	Hall
24	C₂×C₁₁	—	7	1	no	Hall
25	D₇	#14555917	1	1	yes	characteristic, direct product factor, Hall
26	C₁₁	D₇×C₄₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₅	—	3157	1	no	Hall
28	C₇	C₂×#14555917	1	1	yes	characteristic, complemented, Sylow
29	C₅	—	451	1	no	Sylow
30	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₁×C₄₁	C₂×C₅
LCS	G ▷ C₇×C₁₁×C₄₁
UCS	C₁

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.