Subgroups — C₃×C₃₁×#5997 #32912261

Order 18228.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#5997	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇²×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃₁×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
5	C₇²×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×D₇×C₃₁	—	14	4	no	—
7	C₃×C₇×C₃₁	—	2	4	no	—
8	C₃×#5997	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	D₇×C₃₁	—	14	4	no	—
10	C₃×C₄×C₃₁	—	49	1	no	maximal, Hall
11	C₃×C₇⋊D₇	C₂×C₃₁	1	1	yes	characteristic
12	C₇×C₃₁	—	2	4	no	—
13	#5997	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₃₁	—	49	1	no	—
15	C₃×C₇²	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
16	C₄×C₃₁	—	49	1	no	Hall
17	C₇⋊D₇	C₂×C₃×C₃₁	1	1	yes	characteristic
18	C₃×C₃₁	#5997	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃₁	—	49	1	no	—
20	C₇²	C₃×C₄×C₃₁	1	1	yes	characteristic, complemented, Sylow
21	C₃×D₇	—	14	4	no	—
22	C₃₁	C₃×#5997	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×C₇	—	2	4	no	—
24	D₇	—	14	4	no	—
25	C₃×C₄	—	49	1	no	Hall
26	C₇	—	2	4	no	—
27	C₂×C₃	—	49	1	no	—
28	C₄	—	49	1	no	Sylow
29	C₃	C₃₁×#5997	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	49	1	no	—

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.