Subgroups — D₇₇⋊D₇₉ #37566652

Order 24332.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×D₇₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₅₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₈₆₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₁×C₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₁×D₇₉	—	7	1	no	maximal, Hall
6	D₇×D₇₉	—	11	1	no	maximal, Hall
7	D₈₆₉	D₇	1	1	yes	characteristic, complemented
8	C₁₁×D₇₉	—	7	1	no	—
9	D₁₁×C₇₉	—	7	1	no	—
10	D₅₅₃	D₁₁	1	1	yes	characteristic, complemented
11	C₇×D₇₉	—	11	1	no	—
12	D₇×C₇₉	—	11	1	no	—
13	C₁₁×C₇₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
14	C₇×C₇₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×D₇₉	—	77	1	no	Hall
16	D₇×D₁₁	—	79	1	no	maximal, Hall
17	C₂×C₇₉	—	77	1	no	—
18	D₇₉	—	7	1	no	—
19	D₇₉	—	11	1	no	—
20	D₇₇	D₇₉	1	1	yes	characteristic, complemented
21	C₇×D₁₁	—	79	1	no	—
22	C₁₁×D₇	—	79	1	no	—
23	C₇₉	D₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
24	C₇×C₁₁	C₂×D₇₉	1	1	yes	characteristic, complemented, Hall
25	C₂×D₁₁	—	553	1	no	Hall
26	C₂×D₇	—	869	1	no	Hall
27	C₂×C₁₁	—	553	1	no	—
28	D₁₁	—	7	1	no	—
29	D₁₁	—	79	1	no	—
30	C₂×C₇	—	869	1	no	—
31	D₇	—	11	1	no	—
32	D₇	—	79	1	no	—
33	C₁₁	D₇×D₇₉	1	1	yes	characteristic, complemented, Sylow
34	C₇	D₁₁×D₇₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	6083	1	no	Sylow
36	C₂	—	553	1	no	—
37	C₂	—	77	1	no	—
38	C₂	—	869	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₁×C₇₉	C₂²
LCS	G ▷ C₇×C₁₁×C₇₉
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.