Subgroups — C₇²×C₂²⋊(C₁₉⋊C₃) #26014037

Order 11172.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×C₁₉⋊C₃	—	4	1	no	maximal, Hall
3	C₂×C₇²×C₁₉	—	3	1	no	—
4	C₇×C₂²⋊(C₁₉⋊C₃)	C₇	1	8	yes	maximal, direct product factor
5	C₇²×C₁₉	A₄	1	1	yes	characteristic, complemented, Hall
6	C₇²×A₄	—	19	1	no	maximal, Hall
7	C₂²×C₇×C₁₉	C₃×C₇	1	8	yes	complemented
8	C₇×C₁₉⋊C₃	—	4	8	no	—
9	C₂×C₇×C₁₉	—	3	8	no	—
10	C₂²⋊(C₁₉⋊C₃)	C₇²	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₇²	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₇²	—	76	1	no	Hall
13	C₇×C₁₉	C₇×A₄	1	8	yes	complemented
14	C₂×C₇²	—	3	1	no	—
15	C₇×A₄	—	19	8	no	—
16	C₂²×C₁₉	C₃×C₇²	1	1	yes	characteristic, complemented, Hall
17	C₁₉⋊C₃	—	4	1	no	Hall
18	C₇²	C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₁₉	—	3	1	no	—
20	C₂²×C₇	C₇×C₁₉⋊C₃	1	8	yes	complemented
21	C₃×C₇	—	76	8	no	—
22	C₁₉	C₇²×A₄	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₇	—	3	8	no	—
24	A₄	—	19	1	no	Hall
25	C₇	C₇×C₂²⋊(C₁₉⋊C₃)	1	8	yes	direct product factor
26	C₂²	C₇²×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₃	—	76	1	no	Sylow
28	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₇²	C₂²⋊(C₁₉⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₉	C₃×C₇²
Frattini	C₁	G
Fitting, socle	C₂²×C₇²×C₁₉	C₃
LCS	G ▷ C₂²×C₁₉
UCS	C₁ ◁ C₇²

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.