Subgroups — C₃₇⋊C₃×#6862 #41005307

Order 26973.

284 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊C₉×C₃₇⋊C₃	C₃	1	4	yes	maximal
2	C₃₇⋊#6862	C₃	1	8	yes	maximal, complemented
3	C₃₇×#6862	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
5	C₃×C₉×C₃₇⋊C₃	—	3	4	no	—
6	C₃²⋊#66524	C₃²	1	8	yes	—
7	#15688502	—	3	8	no	—
8	C₃₇×C₃²⋊C₉	C₃²	1	4	yes	—
9	C₃³×C₃₇	C₃³	1	1	yes	characteristic
10	C₃²×C₃₇⋊C₃	—	3	12	no	—
11	C₃²×C₃₇⋊C₃	H(3,𝔽₃)	1	2	yes	—
12	C₃²×C₃₇⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃×C₉×C₃₇	—	3	4	no	—
14	C₃×#66524	—	3	8	no	—
15	C₉×C₃₇⋊C₃	—	9	12	no	—
16	C₃×#6862	—	37	1	no	maximal, Sylow
17	C₃²×C₃₇	—	3	4	no	—
18	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
19	C₃×C₃₇⋊C₃	—	3	8	no	—
20	C₃×C₃₇⋊C₃	—	9	9	no	—
21	C₃×C₃₇⋊C₃	#731	1	12	yes	—
22	C₉×C₃₇	—	9	4	no	—
23	#66524	—	9	8	no	—
24	C₃×C₃²⋊C₉	—	37	4	no	—
25	#6862	—	37	8	no	—
26	#6862	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
27	C₃×C₃₇	—	9	1	no	—
28	C₃×C₃₇	C₃×#731	1	4	yes	—
29	C₃₇⋊C₃	—	9	2	no	—
30	C₃₇⋊C₃	#6862	1	9	yes	direct product factor
31	C₃⁴	—	37	1	no	—
32	C₃²×C₉	—	111	4	no	—
33	C₃²⋊C₉	—	37	8	no	—
34	C₃²⋊C₉	—	111	8	no	—
35	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	4	yes	—
36	C₃₇	C₃×#6862	1	1	yes	characteristic, complemented, Sylow
37	C₃³	—	37	1	no	—
38	C₃³	—	37	2	no	—
39	C₃³	—	111	12	no	—
40	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
41	C₃×C₉	—	3	4	no	—
42	C₃×C₉	—	333	12	no	—
43	C₃×C₉	—	111	8	no	—
44	C₃²	—	3	4	no	—
45	C₃²	—	37	12	no	—
46	C₃²	—	333	9	no	—
47	C₃²	—	111	8	no	—
48	C₃²	H(3,𝔽₃)×C₃₇⋊C₃	1	1	yes	characteristic
49	C₉	—	9	4	no	—
50	C₉	—	333	8	no	—
51	C₃	—	9	1	no	—
52	C₃	—	37	9	no	—
53	C₃	—	333	2	no	—
54	C₃	#731×C₃₇⋊C₃	1	4	yes	—

	subgroup	G/H
center	C₃²	H(3,𝔽₃)×C₃₇⋊C₃
commutator, cosocle	C₃³×C₃₇	C₃³
Frattini	C₃³	C₃²×C₃₇⋊C₃
Fitting	C₃₇×#6862	C₃
socle	C₃²×C₃₇	C₃×H(3,𝔽₃)
prime radical	C₃³×C₃₇⋊C₃	C₃²
hypercenter	#6862	C₃₇⋊C₃
hypocenter	C₃₇	C₃×#6862
LCS	G ▷ C₃³×C₃₇ ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ #6862

Complements

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

N	H ≅ G/N	type
2. C₃₇⋊#6862	C₃	semidirect
3. C₃₇×#6862	C₃	semidirect
26. #6862	C₃₇⋊C₃	direct (N × H)
30. C₃₇⋊C₃	#6862	direct (N × H)
36. C₃₇	C₃×#6862	semidirect

Maximal subgroups

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

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

Subgroups — C37⋊C3×#6862 #41005307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇⋊C₃×#6862 #41005307