Subgroups — C₇²×D₃₈₇ #49181609

Order 37926.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₉×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₁₂₉	—	3	1	no	maximal
3	C₃×C₇²×C₄₃	D₃	1	1	yes	characteristic
4	C₇×D₃₈₇	C₇	1	8	yes	maximal, direct product factor
5	C₇²×D₄₃	—	9	1	no	Hall
6	C₇×C₉×C₄₃	C₂×C₇	1	8	yes	complemented
7	C₇²×C₄₃	D₉	1	1	yes	characteristic, complemented, Hall
8	C₇×D₁₂₉	—	3	8	no	—
9	C₃×C₇×C₄₃	D₃×C₇	1	8	yes	—
10	C₇²×D₉	—	43	1	no	maximal, Hall
11	D₃₈₇	C₇²	1	1	yes	characteristic, direct product factor, Hall
12	C₇×D₄₃	—	9	8	no	—
13	C₇²×C₉	D₄₃	1	1	yes	characteristic, complemented, Hall
14	C₉×C₄₃	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
15	C₇×C₄₃	C₇×D₉	1	8	yes	complemented
16	D₃×C₇²	—	129	1	no	—
17	D₁₂₉	—	3	1	no	—
18	C₃×C₇²	D₁₂₉	1	1	yes	characteristic
19	C₃×C₄₃	D₃×C₇²	1	1	yes	characteristic
20	C₇×D₉	—	43	8	no	—
21	C₂×C₇²	—	387	1	no	Hall
22	D₄₃	—	9	1	no	Hall
23	C₇×C₉	C₇×D₄₃	1	8	yes	complemented
24	C₇²	D₃₈₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₄₃	C₇²×D₉	1	1	yes	characteristic, complemented, Sylow
26	D₃×C₇	—	129	8	no	—
27	C₃×C₇	C₇×D₁₂₉	1	8	yes	—
28	D₉	—	43	1	no	Hall
29	C₂×C₇	—	387	8	no	—
30	C₉	C₇²×D₄₃	1	1	yes	characteristic, complemented, Sylow
31	C₇	C₇×D₃₈₇	1	8	yes	direct product factor
32	D₃	—	129	1	no	—
33	C₃	C₇²×D₁₂₉	1	1	yes	characteristic
34	C₂	—	387	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇²	D₃₈₇
commutator, cosocle, hypocenter	C₉×C₄₃	C₂×C₇²
Frattini	C₃	C₇²×D₁₂₉
Fitting	C₇²×C₉×C₄₃	C₂
socle	C₃×C₇²×C₄₃	D₃
LCS	G ▷ C₉×C₄₃
UCS	C₁ ◁ C₇²

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.