Subgroups — C₄₉×Dic₁₂₁ #37557340

Order 23716.

27 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₉×C₁₂₁	C₂	1	1	yes	maximal, characteristic
2	C₄₉×C₁₂₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×Dic₁₂₁	C₇	1	1	yes	maximal, characteristic
4	Dic₁₁×C₄₉	—	11	1	no	maximal
5	C₂×C₇×C₁₂₁	C₂×C₇	1	1	yes	characteristic
6	C₂×C₁₁×C₄₉	D₁₁	1	1	yes	characteristic
7	C₇×C₁₂₁	C₄×C₇	1	1	yes	characteristic
8	C₁₁×C₄₉	Dic₁₁	1	1	yes	characteristic
9	Dic₁₂₁	C₄₉	1	1	yes	characteristic, direct product factor, Hall
10	C₇×Dic₁₁	—	11	1	no	—
11	C₂×C₁₂₁	C₂×C₄₉	1	1	yes	characteristic
12	C₄×C₄₉	—	121	1	no	Hall
13	C₂×C₇×C₁₁	C₇×D₁₁	1	1	yes	characteristic
14	C₁₂₁	C₄×C₄₉	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₄₉	D₁₂₁	1	1	yes	characteristic
16	C₇×C₁₁	C₇×Dic₁₁	1	1	yes	characteristic
17	C₄₉	Dic₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
18	Dic₁₁	—	11	1	no	—
19	C₄×C₇	—	121	1	no	—
20	C₂×C₁₁	D₁₁×C₄₉	1	1	yes	characteristic
21	C₂×C₇	C₇×D₁₂₁	1	1	yes	characteristic
22	C₁₁	Dic₁₁×C₄₉	1	1	yes	characteristic
23	C₇	C₇×Dic₁₂₁	1	1	yes	characteristic
24	C₄	—	121	1	no	Sylow
25	C₂	C₄₉×D₁₂₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄₉	D₁₂₁
commutator, hypocenter	C₁₂₁	C₄×C₄₉
Frattini, socle, prime radical	C₂×C₇×C₁₁	C₇×D₁₁
Fitting	C₂×C₄₉×C₁₂₁	C₂
cosocle	C₂×C₇×C₁₂₁	C₂×C₇
LCS	G ▷ C₁₂₁
UCS	C₁ ◁ C₂×C₄₉

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.