Subgroups — C₂⁷×D₇ #14267700

Order 1792.

834398 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁷×C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁶×D₇	C₂	1	254	yes	maximal, direct product factor
3	C₂⁶×C₇	C₂²	1	127	yes	complemented
4	C₂⁵×D₇	C₂²	1	10668	yes	direct product factor
5	C₂⁸	—	7	1	no	maximal, Sylow
6	C₂⁵×C₇	C₂³	1	2667	yes	complemented
7	C₂⁴×D₇	C₂³	1	94488	yes	direct product factor
8	C₂⁷	—	7	254	no	—
9	C₂⁷	D₇	1	1	yes	characteristic, direct product factor
10	C₂⁴×C₇	C₂⁴	1	11811	yes	complemented
11	C₂³×D₇	C₂⁴	1	188976	yes	direct product factor
12	C₂⁶	—	7	10668	no	—
13	C₂⁶	C₂×D₇	1	127	yes	direct product factor
14	C₂³×C₇	C₂⁵	1	11811	yes	complemented
15	C₂²×D₇	C₂⁵	1	85344	yes	direct product factor
16	C₂⁵	—	7	94488	no	—
17	C₂⁵	C₂²×D₇	1	2667	yes	direct product factor
18	C₂²×C₇	C₂⁶	1	2667	yes	complemented
19	C₂×D₇	C₂⁶	1	8128	yes	direct product factor
20	C₂⁴	—	7	188976	no	—
21	C₂⁴	C₂³×D₇	1	11811	yes	direct product factor
22	C₂×C₇	C₂⁷	1	127	yes	complemented
23	D₇	C₂⁷	1	128	yes	direct product factor
24	C₂³	—	7	85344	no	—
25	C₂³	C₂⁴×D₇	1	11811	yes	direct product factor
26	C₇	C₂⁸	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	7	8128	no	—
28	C₂²	C₂⁵×D₇	1	2667	yes	direct product factor
29	C₂	—	7	128	no	—
30	C₂	C₂⁶×D₇	1	127	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁷	D₇
commutator, cosocle, hypocenter	C₇	C₂⁸
Frattini	C₁	G
Fitting, socle	C₂⁷×C₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂⁷

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.