Subgroups — C₂×D₃₄₄₇ #28352006

Order 13788.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₄₄₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₃₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₁₄₉	—	3	1	no	maximal
4	C₉×C₃₈₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₃₈₃	D₃	1	1	yes	characteristic
6	D₁₁₄₉	—	3	2	no	—
7	C₂×D₃₈₃	—	9	1	no	Hall
8	C₃×C₃₈₃	C₂×D₃	1	1	yes	characteristic
9	C₂×C₃₈₃	D₉	1	1	yes	characteristic, complemented
10	D₃₈₃	—	9	2	no	—
11	C₃₈₃	C₂×D₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×D₉	—	383	1	no	maximal, Hall
13	C₂×C₉	D₃₈₃	1	1	yes	characteristic, complemented
14	D₉	—	383	2	no	—
15	C₂×D₃	—	1149	1	no	—
16	C₉	C₂×D₃₈₃	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃	D₁₁₄₉	1	1	yes	characteristic
18	D₃	—	1149	2	no	—
19	C₂²	—	3447	1	no	Sylow
20	C₃	C₂×D₁₁₄₉	1	1	yes	characteristic
21	C₂	—	3447	2	no	—
22	C₂	D₃₄₄₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃₄₄₇
commutator, cosocle, hypocenter	C₉×C₃₈₃	C₂²
Frattini	C₃	C₂×D₁₁₄₉
Fitting	C₂×C₉×C₃₈₃	C₂
socle	C₂×C₃×C₃₈₃	D₃
LCS	G ▷ C₉×C₃₈₃
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.