Subgroups — #37525556

Order 22932.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊(C₇⋊D₉₁))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃⋊(C₇⋊D₉₁)	—	6	2	no	—
4	#14579330	—	9	1	no	maximal, Hall
5	C₃×C₇²×C₁₃	—	2	2	no	—
6	#13183676	—	13	1	no	maximal, Hall
7	C₃⋊D₂₇₃	—	14	4	no	—
8	C₇⋊D₉₁	—	9	1	no	—
9	C₃⋊(C₃⋊(C₇⋊D₇))	—	13	1	no	—
10	C₃²×C₇×C₁₃	—	2	4	no	—
11	C₇²×C₁₃	#157	1	1	yes	characteristic, complemented, Hall
12	D₂₇₃	—	42	16	no	—
13	#90866	—	49	1	no	maximal, Hall
14	C₃²×C₇²	#261	1	1	yes	characteristic, complemented, Hall
15	C₃⋊(C₇⋊D₇)	—	78	2	no	—
16	C₃×C₇×C₁₃	—	2	16	no	—
17	C₃⋊D₃₉	—	49	1	no	—
18	#5997	—	117	1	no	Hall
19	D₉₁	—	126	4	no	—
20	C₃×C₇²	—	2	2	no	—
21	C₃⋊D₂₁	—	182	4	no	—
22	C₃²×C₁₃	#5997	1	1	yes	characteristic, complemented, Hall
23	C₇⋊D₇	—	117	1	no	—
24	C₇×C₁₃	—	2	4	no	—
25	D₃₉	—	294	2	no	—
26	C₃²×C₇	—	2	4	no	—
27	#261	—	441	1	no	Hall
28	C₇²	#90866	1	1	yes	characteristic, complemented, Sylow
29	D₂₁	—	546	16	no	—
30	C₃×C₁₃	—	2	2	no	—
31	#157	—	637	1	no	Hall
32	D₁₃	—	441	1	no	—
33	C₃×C₇	—	2	16	no	—
34	C₃⋊D₃	—	637	1	no	—
35	D₇	—	1638	4	no	—
36	C₁₃	#13183676	1	1	yes	characteristic, complemented, Sylow
37	C₃²	#14579330	1	1	yes	characteristic, complemented, Sylow
38	C₇	—	2	4	no	—
39	D₃	—	3822	2	no	—
40	C₄	—	5733	1	no	Sylow
41	C₃	—	2	2	no	—
42	C₂	—	5733	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₇²×C₁₃	C₄
prime radical, cosocle	C₃⋊(C₃⋊(C₇⋊D₉₁))	C₂
LCS	G ▷ C₃²×C₇²×C₁₃
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.