Subgroups — D₇₇⋊D₅₉ #31827862

Order 18172.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×D₇₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₄₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₆₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₁×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₁×D₅₉	—	7	1	no	maximal, Hall
6	D₇×D₅₉	—	11	1	no	maximal, Hall
7	D₆₄₉	D₇	1	1	yes	characteristic, complemented
8	C₁₁×D₅₉	—	7	1	no	—
9	D₁₁×C₅₉	—	7	1	no	—
10	D₄₁₃	D₁₁	1	1	yes	characteristic, complemented
11	C₇×D₅₉	—	11	1	no	—
12	D₇×C₅₉	—	11	1	no	—
13	C₁₁×C₅₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
14	C₇×C₅₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
15	D₇×D₁₁	—	59	1	no	maximal, Hall
16	C₂×D₅₉	—	77	1	no	Hall
17	D₇₇	D₅₉	1	1	yes	characteristic, complemented
18	C₇×D₁₁	—	59	1	no	—
19	C₁₁×D₇	—	59	1	no	—
20	C₂×C₅₉	—	77	1	no	—
21	D₅₉	—	7	1	no	—
22	D₅₉	—	11	1	no	—
23	C₇×C₁₁	C₂×D₅₉	1	1	yes	characteristic, complemented, Hall
24	C₅₉	D₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
25	C₂×D₁₁	—	413	1	no	Hall
26	C₂×D₇	—	649	1	no	Hall
27	C₂×C₁₁	—	413	1	no	—
28	D₁₁	—	7	1	no	—
29	D₁₁	—	59	1	no	—
30	C₂×C₇	—	649	1	no	—
31	D₇	—	11	1	no	—
32	D₇	—	59	1	no	—
33	C₁₁	D₇×D₅₉	1	1	yes	characteristic, complemented, Sylow
34	C₇	D₁₁×D₅₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	4543	1	no	Sylow
36	C₂	—	77	1	no	—
37	C₂	—	649	1	no	—
38	C₂	—	413	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₁×C₅₉	C₂²
LCS	G ▷ C₇×C₁₁×C₅₉
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.