Subgroups — C₂×Q₈⋊C₉ #3692

Order 144.

29 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈⋊C₉	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂×C₃×Q₈	C₃	1	1	yes	maximal, characteristic
3	C₂²×C₉	—	4	1	no	maximal
4	C₃×Q₈	—	3	1	no	—
5	C₃×Q₈	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₄	—	3	1	no	—
7	C₂×C₉	—	4	2	no	—
8	C₂×C₉	—	4	1	no	—
9	C₂×Q₈	C₉	1	1	yes	characteristic, complemented, Sylow
10	C₂²×C₃	A₄	1	1	yes	characteristic
11	C₃×C₄	—	3	1	no	—
12	C₃×C₄	—	3	1	no	—
13	C₉	—	4	1	no	Sylow
14	Q₈	—	3	1	no	—
15	Q₈	C₂×C₉	1	1	yes	characteristic, complemented
16	C₂×C₄	—	3	1	no	—
17	C₂×C₃	SL(2,𝔽₃)	1	2	yes	—
18	C₂×C₃	C₂×A₄	1	1	yes	characteristic
19	C₂²	C₂²⋊C₉	1	1	yes	characteristic
20	C₄	—	3	1	no	—
21	C₄	—	3	1	no	—
22	C₃	C₂×SL(2,𝔽₃)	1	1	yes	characteristic
23	C₂	Q₈⋊C₉	1	2	yes	direct product factor
24	C₂	C₂×C₂²⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical, hypercenter	C₂²×C₃	A₄
commutator, hypocenter	Q₈	C₂×C₉
Frattini	C₂×C₃	C₂×A₄
Fitting	C₂×C₃×Q₈	C₃
cosocle	C₃×Q₈	C₂×C₃
LCS	G ▷ Q₈
UCS	C₁ ◁ C₂²×C₃

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.