Subgroups — #46853604

Order 34916.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22576611	C₂	1	1	yes	maximal, characteristic
2	#22576611	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄₃×Dic₂₉	C₇	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₂₉×C₄₃	C₂×C₇	1	1	yes	characteristic
5	C₂₉×C₄₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
6	C₄×C₄₃⋊C₇	—	29	1	no	maximal, Hall
7	Dic₂₉⋊C₇	—	43	1	no	maximal, Hall
8	C₂×C₄₃⋊C₇	—	29	1	no	—
9	C₂×C₂₉⋊C₇	—	43	1	no	—
10	C₄₃⋊C₇	—	29	1	no	Hall
11	C₂₉⋊C₇	—	43	1	no	Hall
12	C₄×C₄₃	—	29	1	no	Hall
13	Dic₂₉	C₄₃⋊C₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₄₃	D₂₉⋊C₇	1	1	yes	characteristic
15	C₂×C₂₉	C₂×C₄₃⋊C₇	1	1	yes	characteristic
16	C₄₃	Dic₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
17	C₂₉	C₄×C₄₃⋊C₇	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₇	—	1247	1	no	Hall
19	C₂×C₇	—	1247	1	no	—
20	C₇	—	1247	1	no	Sylow
21	C₄	—	29	1	no	Sylow
22	C₂	#31775454	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#31775454
commutator, hypocenter	C₂₉×C₄₃	C₄×C₇
Fitting, socle, cosocle	C₂×C₂₉×C₄₃	C₂×C₇
prime radical	C₂×#22576611	C₂
LCS	G ▷ C₂₉×C₄₃
UCS	C₁ ◁ C₂

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.