Subgroups — C₁₇×C₂²⋊(C₁₁²⋊C₃) #37590656

Order 24684.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁²×C₁₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×C₁₁²⋊C₃	—	4	1	no	maximal, Hall
3	C₂×C₁₁²×C₁₇	—	3	1	no	—
4	C₁₁²×C₁₇	A₄	1	1	yes	characteristic, complemented, Hall
5	C₂²⋊(C₁₁²⋊C₃)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₁₁×C₁₇	—	3	4	no	—
7	C₂²×C₁₁²	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₁×C₁₇	—	3	12	no	—
9	C₁₁²⋊C₃	—	4	1	no	Hall
10	C₂×C₁₁²	—	3	1	no	—
11	A₄×C₁₇	—	121	1	no	maximal, Hall
12	C₁₁×C₁₇	—	3	4	no	—
13	C₁₁²	A₄×C₁₇	1	1	yes	characteristic, complemented, Sylow
14	C₂²×C₁₇	C₁₁²⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₇	—	484	1	no	Hall
16	C₂²×C₁₁	—	3	4	no	—
17	C₂×C₁₇	—	3	1	no	—
18	C₂×C₁₁	—	3	12	no	—
19	C₁₇	C₂²⋊(C₁₁²⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
20	A₄	—	121	1	no	Hall
21	C₁₁	—	3	4	no	—
22	C₂²	C₁₇×C₁₁²⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₃	—	484	1	no	Sylow
24	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	C₂²⋊(C₁₁²⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₁²	C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂²×C₁₁²×C₁₇	C₃
LCS	G ▷ C₂²×C₁₁²
UCS	C₁ ◁ C₁₇

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.