Subgroups — C₃×C₃₇×#6862 #41004375

Order 26973.

284 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×C₃²⋊C₉	C₃	1	4	yes	maximal
2	C₃₇×#6862	C₃	1	9	yes	maximal, direct product factor
3	C₃⁴×C₃₇	C₃²	1	1	yes	characteristic
4	C₃²×C₉×C₃₇	—	3	4	no	—
5	C₃₇×C₃²⋊C₉	—	3	8	no	—
6	C₃₇×C₃²⋊C₉	C₃²	1	12	yes	—
7	C₃³×C₃₇	—	3	12	no	—
8	C₃³×C₃₇	H(3,𝔽₃)	1	2	yes	—
9	C₃³×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
10	C₃³×C₃₇	C₃³	1	1	yes	characteristic
11	C₃×C₉×C₃₇	—	3	12	no	—
12	C₃×C₉×C₃₇	—	9	12	no	—
13	C₃×#6862	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃²×C₃₇	—	3	8	no	—
15	C₃²×C₃₇	—	3	4	no	—
16	C₃²×C₃₇	—	9	9	no	—
17	C₃²×C₃₇	#731	1	12	yes	—
18	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
19	C₉×C₃₇	—	9	12	no	—
20	C₃×C₃²⋊C₉	C₃×C₃₇	1	4	yes	—
21	#6862	C₃×C₃₇	1	9	yes	direct product factor
22	C₃×C₃₇	—	9	2	no	—
23	C₃×C₃₇	—	9	1	no	—
24	C₃×C₃₇	#6862	1	9	yes	direct product factor
25	C₃×C₃₇	C₃×#731	1	4	yes	—
26	C₃⁴	C₃²×C₃₇	1	1	yes	characteristic
27	C₃²×C₉	—	3	4	no	—
28	C₃²⋊C₉	—	3	8	no	—
29	C₃²⋊C₉	C₃²×C₃₇	1	12	yes	—
30	C₃₇	C₃×#6862	1	1	yes	characteristic, direct product factor, Sylow
31	C₃³	—	3	12	no	—
32	C₃³	H(3,𝔽₃)×C₃₇	1	2	yes	—
33	C₃³	H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
34	C₃³	C₃³×C₃₇	1	1	yes	characteristic
35	C₃×C₉	—	3	12	no	—
36	C₃×C₉	—	9	12	no	—
37	C₃²	—	3	8	no	—
38	C₃²	—	3	4	no	—
39	C₃²	—	9	9	no	—
40	C₃²	C₃₇×#731	1	12	yes	—
41	C₃²	C₃×H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
42	C₉	—	9	12	no	—
43	C₃	—	9	2	no	—
44	C₃	—	9	1	no	—
45	C₃	C₃₇×#6862	1	9	yes	direct product factor
46	C₃	C₃×C₃₇×#731	1	4	yes	—

	subgroup	G/H
center, socle	C₃³×C₃₇	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₃₇
prime radical	C₃⁴×C₃₇	C₃²
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³×C₃₇ ◁ C₃⁴×C₃₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃₇×#6862	C₃	direct (N × H)
13. C₃×#6862	C₃₇	direct (N × H)
21. #6862	C₃×C₃₇	direct (N × H)
24. C₃×C₃₇	#6862	direct (N × H)
30. C₃₇	C₃×#6862	direct (N × H)
45. C₃	C₃₇×#6862	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₃₇×C₃²⋊C₉	3
C₃₇×#6862	3
C₃×#6862	37

Subgroups — C3×C37×#6862 #41004375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃₇×#6862 #41004375