Subgroups — D₇×D₄₆₉ #27190080

Order 13132.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊D₄₆₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₄₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₇×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇²×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₄₆₉	—	7	1	no	maximal
6	D₇×D₆₇	—	7	1	no	maximal
7	C₂×C₇×C₆₇	—	7	1	no	—
8	D₄₆₉	—	7	1	no	—
9	D₄₆₉	—	7	1	no	—
10	D₄₆₉	—	14	3	no	—
11	D₄₆₉	D₇	1	1	yes	characteristic, direct product factor
12	C₇×D₆₇	—	7	1	no	—
13	D₇×C₆₇	D₇	1	1	yes	characteristic, complemented
14	C₇×C₆₇	—	2	3	no	—
15	C₇×C₆₇	C₂×D₇	1	1	yes	characteristic, complemented
16	C₇×C₆₇	C₂×D₇	1	1	yes	characteristic, complemented
17	C₂×D₆₇	—	49	1	no	Hall
18	D₇²	—	67	1	no	maximal, Hall
19	C₂×C₆₇	—	7	1	no	—
20	D₆₇	—	7	1	no	—
21	D₆₇	—	49	1	no	—
22	C₇⋊D₇	—	67	1	no	—
23	C₇×D₇	—	67	1	no	—
24	C₇×D₇	D₆₇	1	1	yes	characteristic, complemented
25	C₆₇	D₇²	1	1	yes	characteristic, complemented, Sylow
26	C₇²	C₂×D₆₇	1	1	yes	characteristic, complemented, Sylow
27	C₂×D₇	—	469	1	no	—
28	C₂×D₇	—	469	1	no	—
29	C₂×C₇	—	7	1	no	—
30	C₂×C₇	—	469	1	no	—
31	D₇	—	67	1	no	—
32	D₇	—	938	3	no	—
33	D₇	—	469	1	no	—
34	D₇	—	469	1	no	—
35	D₇	D₄₆₉	1	1	yes	characteristic, direct product factor
36	C₇	—	2	3	no	—
37	C₇	D₇×D₆₇	1	1	yes	characteristic, complemented
38	C₇	C₂×D₄₆₉	1	1	yes	characteristic, complemented
39	C₂²	—	3283	1	no	Sylow
40	C₂	—	7	1	no	—
41	C₂	—	3283	1	no	—
42	C₂	—	469	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₆₇	C₂²
LCS	G ▷ C₇²×C₆₇
UCS	C₁

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.