Subgroups — D₇×Dic₇ #87638

Order 392.

41 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₇	C₂	1	1	yes	maximal, characteristic
2	C₇⋊Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇²	C₂²	1	1	yes	characteristic
5	C₇×D₇	C₄	1	2	yes	complemented
6	C₂×Dic₇	—	7	1	no	maximal
7	C₄×D₇	—	7	1	no	maximal
8	C₇²	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
9	C₂²×C₇	—	7	1	no	—
10	C₂×D₇	D₇	1	1	yes	characteristic
11	C₄×C₇	—	7	1	no	—
12	Dic₇	—	7	1	no	—
13	Dic₇	—	7	1	no	—
14	Dic₇	—	14	3	no	—
15	Dic₇	D₇	1	1	yes	characteristic, direct product factor
16	C₂×C₇	—	2	3	no	—
17	C₂×C₇	—	7	2	no	—
18	C₂×C₇	C₂×D₇	1	1	yes	characteristic
19	C₂×C₇	C₂×D₇	1	1	yes	characteristic
20	D₇	Dic₇	1	2	yes	direct product factor
21	C₂×C₄	—	49	1	no	Sylow
22	C₇	—	2	3	no	—
23	C₇	C₄×D₇	1	1	yes	characteristic, complemented
24	C₇	C₂×Dic₇	1	1	yes	characteristic, complemented
25	C₂²	—	7	1	no	—
26	C₄	—	7	1	no	—
27	C₄	—	49	1	no	—
28	C₂	—	7	2	no	—
29	C₂	D₇²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇²
commutator, hypocenter	C₇²	C₂×C₄
Fitting, socle, cosocle	C₂×C₇²	C₂²
prime radical	C₂×C₇×D₇	C₂
LCS	G ▷ C₇²
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.