Subgroups — C₃²×C₅⋊(C₇⋊D₇) #17984403

Order 4410.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅⋊(C₇⋊D₇)	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₇⋊D₇	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇²	C₂×C₃	1	4	yes	complemented
5	C₃²×D₃₅	—	7	8	no	maximal
6	C₅⋊(C₇⋊D₇)	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₇²	D₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₇	D₇	1	8	yes	complemented
9	C₃×C₇⋊D₇	—	5	4	no	—
10	C₅×C₇²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×D₃₅	—	7	32	no	—
12	C₃×C₇²	C₃×D₅	1	4	yes	complemented
13	C₃²×D₇	—	35	8	no	—
14	C₃×C₅×C₇	C₃×D₇	1	32	yes	complemented
15	C₇⋊D₇	—	5	1	no	Hall
16	C₃²×D₅	—	49	1	no	Hall
17	D₃₅	—	7	8	no	—
18	C₃²×C₇	D₃₅	1	8	yes	complemented
19	C₇²	C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
20	C₃²×C₅	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
21	C₃×D₇	—	35	32	no	—
22	C₅×C₇	C₃²×D₇	1	8	yes	complemented
23	C₃×D₅	—	49	4	no	—
24	C₃×C₇	C₃×D₃₅	1	32	yes	complemented
25	C₂×C₃²	—	245	1	no	Hall
26	C₃×C₅	C₃×C₇⋊D₇	1	4	yes	complemented
27	D₇	—	35	8	no	—
28	D₅	—	49	1	no	Hall
29	C₃²	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor, Sylow
30	C₇	C₃²×D₃₅	1	8	yes	complemented
31	C₂×C₃	—	245	4	no	—
32	C₅	C₃²×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
33	C₃	C₃×C₅⋊(C₇⋊D₇)	1	4	yes	direct product factor
34	C₂	—	245	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	C₅⋊(C₇⋊D₇)
commutator, cosocle, hypocenter	C₅×C₇²	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇²	C₂
LCS	G ▷ C₅×C₇²
UCS	C₁ ◁ C₃²

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.