Subgroups — C₃²×C₇×#92150 #44479179

Order 30492.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×#92150	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₇×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×C₁₁⋊D₁₁	C₂×C₃	1	4	yes	—
5	C₃²×#92150	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×#92150	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇×C₁₁²	C₃×C₄	1	4	yes	complemented
8	C₃²×C₁₁⋊D₁₁	C₂×C₇	1	1	yes	characteristic
9	C₇×C₁₁⋊D₁₁	C₂×C₃²	1	1	yes	characteristic
10	C₃×#92150	C₃×C₇	1	4	yes	direct product factor
11	C₃²×C₇×D₁₁	—	22	6	no	—
12	C₃²×C₁₁²	C₄×C₇	1	1	yes	characteristic, complemented, Hall
13	C₇×C₁₁²	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁⋊D₁₁	C₂×C₃×C₇	1	4	yes	—
15	C₃²×C₇×C₁₁	—	2	6	no	—
16	#92150	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₇×D₁₁	—	22	24	no	—
18	C₃×C₁₁²	C₃×C₄×C₇	1	4	yes	complemented
19	C₃²×C₄×C₇	—	121	1	no	maximal, Hall
20	C₁₁⋊D₁₁	C₂×C₃²×C₇	1	1	yes	characteristic
21	C₃×C₇×C₁₁	—	2	24	no	—
22	C₃²×D₁₁	—	22	6	no	—
23	C₇×D₁₁	—	22	6	no	—
24	C₂×C₃²×C₇	—	121	1	no	—
25	C₁₁²	C₃²×C₄×C₇	1	1	yes	characteristic, complemented, Sylow
26	C₃²×C₁₁	—	2	6	no	—
27	C₃×C₄×C₇	—	121	4	no	—
28	C₇×C₁₁	—	2	6	no	—
29	C₃×D₁₁	—	22	24	no	—
30	C₃²×C₇	#92150	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃×C₇	—	121	4	no	—
32	C₃²×C₄	—	121	1	no	Hall
33	C₃×C₁₁	—	2	24	no	—
34	C₄×C₇	—	121	1	no	Hall
35	D₁₁	—	22	6	no	—
36	C₃×C₇	C₃×#92150	1	4	yes	direct product factor
37	C₂×C₃²	—	121	1	no	—
38	C₂×C₇	—	121	1	no	—
39	C₃×C₄	—	121	4	no	—
40	C₁₁	—	2	6	no	—
41	C₃²	C₇×#92150	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₃²×#92150	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	121	4	no	—
44	C₄	—	121	1	no	Sylow
45	C₃	C₃×C₇×#92150	1	4	yes	direct product factor
46	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₃²×C₇	#92150
commutator, hypocenter	C₁₁²	C₃²×C₄×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁²	C₄
prime radical	C₃²×C₇×C₁₁⋊D₁₁	C₂
cosocle	C₁₁⋊D₁₁	C₂×C₃²×C₇
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₃²×C₇

Complements

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

N	H ≅ G/N	type
2. C₃×C₇×#92150	C₃	direct (N × H)
3. C₃²×C₇×C₁₁²	C₄	semidirect
5. C₃²×#92150	C₇	direct (N × H)
6. C₇×#92150	C₃²	direct (N × H)
7. C₃×C₇×C₁₁²	C₃×C₄	semidirect
10. C₃×#92150	C₃×C₇	direct (N × H)
12. C₃²×C₁₁²	C₄×C₇	semidirect
13. C₇×C₁₁²	C₃²×C₄	semidirect
16. #92150	C₃²×C₇	direct (N × H)
18. C₃×C₁₁²	C₃×C₄×C₇	semidirect
25. C₁₁²	C₃²×C₄×C₇	semidirect
30. C₃²×C₇	#92150	direct (N × H)
36. C₃×C₇	C₃×#92150	direct (N × H)
41. C₃²	C₇×#92150	direct (N × H)
42. C₇	C₃²×#92150	direct (N × H)
45. C₃	C₃×C₇×#92150	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₇×C₁₁⋊D₁₁	2
C₃×C₇×#92150	3
C₃²×#92150	7
C₃²×C₄×C₇	121

Subgroups — C32×C7×#92150 #44479179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×#92150 #44479179