Subgroups — C₇⋊SL(2,ℤ/4) #66651

Order 336.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×A₄	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊Dic₇	—	3	1	no	maximal, Hall
3	C₇×A₄	C₄	1	1	yes	characteristic, complemented
4	Dic₂₁	—	4	1	no	maximal
5	C₂³×C₇	D₃	1	1	yes	characteristic
6	C₂×Dic₇	—	3	1	no	—
7	C₂×Dic₇	—	3	1	no	—
8	SL(2,ℤ/4)	—	7	1	no	maximal, Hall
9	C₂×C₃×C₇	—	4	1	no	—
10	C₂²×C₇	—	3	1	no	—
11	C₂²×C₇	—	3	1	no	—
12	C₂²×C₇	Dic₃	1	1	yes	characteristic, complemented
13	Dic₇	—	6	1	no	—
14	Dic₇	—	6	1	no	—
15	C₂×A₄	D₇	1	1	yes	characteristic
16	C₃×C₇	—	4	1	no	Hall
17	C₂²⋊C₄	—	21	1	no	Sylow
18	C₂×C₇	—	3	1	no	—
19	C₂×C₇	—	3	1	no	—
20	C₂×C₇	S₄	1	1	yes	characteristic
21	A₄	Dic₇	1	1	yes	characteristic, complemented
22	Dic₃	—	28	1	no	—
23	C₂³	D₂₁	1	1	yes	characteristic
24	C₂×C₄	—	21	1	no	—
25	C₂×C₄	—	21	1	no	—
26	C₇	SL(2,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	4	1	no	—
28	C₂²	—	3	1	no	—
29	C₂²	—	3	1	no	—
30	C₂²	Dic₂₁	1	1	yes	characteristic, complemented
31	C₄	—	42	1	no	—
32	C₄	—	42	1	no	—
33	C₃	—	4	1	no	Sylow
34	C₂	—	3	1	no	—
35	C₂	—	3	1	no	—
36	C₂	C₇⋊S₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₇⋊S₄
commutator, hypocenter	C₇×A₄	C₄
Fitting, socle	C₂³×C₇	D₃
prime radical, cosocle	C₂×C₇×A₄	C₂
LCS	G ▷ C₇×A₄
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.