Subgroups — C₁₀₁⋊#64418 #44445950

Order 29694.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₇₀₇	—	3	1	no	maximal, Hall
3	C₇²×C₁₀₁	D₃	1	1	yes	characteristic, complemented, Hall
4	ΓL(1,𝔽₈)×C₁₀₁	—	14	1	no	—
5	D₇₀₇	—	3	1	no	—
6	C₇×D₁₀₁	—	21	1	no	—
7	C₇×C₁₀₁	—	2	1	no	—
8	C₇×C₁₀₁	—	6	1	no	—
9	C₇×C₁₀₁	—	6	1	no	—
10	D₃₀₃	—	49	1	no	maximal, Hall
11	C₃×C₁₀₁	—	98	1	no	Hall
12	#64418	—	101	1	no	maximal, Hall
13	D₁₀₁	—	21	1	no	Hall
14	#3862	D₁₀₁	1	1	yes	characteristic, complemented, Hall
15	C₁₀₁	#64418	1	1	yes	characteristic, complemented, Sylow
16	C₇×D₇	—	303	1	no	Hall
17	C₇²	D₃₀₃	1	1	yes	characteristic, complemented, Sylow
18	ΓL(1,𝔽₈)	—	14	1	no	—
19	C₂×C₇	—	2121	1	no	—
20	D₇	—	303	1	no	—
21	C₇	—	2	1	no	—
22	C₇	—	3	1	no	—
23	C₇	—	6	1	no	—
24	D₃	—	4949	1	no	Hall
25	C₃	—	98	1	no	Sylow
26	C₂	—	2121	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₁₀₁×#3862	C₂
Fitting, socle	C₇²×C₁₀₁	D₃
LCS	G ▷ C₁₀₁×#3862
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.