Subgroups — C₂²×C₇×A₄ #66752

Order 336.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×A₄	C₂	1	3	yes	maximal, direct product factor
2	C₂⁴×C₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂²×C₃×C₇	—	4	1	no	maximal
4	C₇×A₄	C₂²	1	1	yes	characteristic, direct product factor
5	C₂³×C₇	—	3	3	no	—
6	C₂³×C₇	—	3	1	no	—
7	C₂³×C₇	C₂×C₃	1	3	yes	complemented
8	C₂²×A₄	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₇	—	4	3	no	—
10	C₂²×C₇	—	3	3	no	—
11	C₂²×C₇	—	3	2	no	—
12	C₂²×C₇	—	3	3	no	—
13	C₂²×C₇	—	3	3	no	—
14	C₂²×C₇	A₄	1	1	yes	characteristic, direct product factor
15	C₂²×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×A₄	C₂×C₇	1	3	yes	direct product factor
17	C₃×C₇	—	4	1	no	Hall
18	C₂⁴	C₃×C₇	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₇	—	3	3	no	—
20	C₂×C₇	—	3	1	no	—
21	C₂×C₇	C₂×A₄	1	3	yes	direct product factor
22	C₂²×C₃	—	4	1	no	—
23	A₄	C₂²×C₇	1	1	yes	characteristic, direct product factor
24	C₂³	—	3	3	no	—
25	C₂³	—	3	1	no	—
26	C₂³	C₂×C₃×C₇	1	3	yes	complemented
27	C₇	C₂²×A₄	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	4	3	no	—
29	C₂²	—	3	3	no	—
30	C₂²	—	3	2	no	—
31	C₂²	—	3	3	no	—
32	C₂²	—	3	3	no	—
33	C₂²	C₇×A₄	1	1	yes	characteristic, direct product factor
34	C₂²	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
35	C₃	—	4	1	no	Sylow
36	C₂	—	3	1	no	—
37	C₂	—	3	3	no	—
38	C₂	C₂×C₇×A₄	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₇	A₄
commutator, cosocle, hypocenter	C₂²	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂⁴×C₇	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂²×C₇

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.