Subgroups — C₇×C₉×#92150 #44478951

Order 30492.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×#92150	C₃	1	1	yes	maximal, characteristic
3	C₇×C₉×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×C₁₁⋊D₁₁	C₂×C₃	1	1	yes	characteristic
5	C₉×#92150	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×#92150	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇×C₁₁²	C₃×C₄	1	1	yes	characteristic
8	C₉×C₁₁⋊D₁₁	C₂×C₇	1	1	yes	characteristic
9	C₇×C₁₁⋊D₁₁	C₂×C₉	1	1	yes	characteristic
10	C₃×#92150	C₃×C₇	1	1	yes	characteristic
11	C₇×C₉×D₁₁	—	22	6	no	—
12	C₉×C₁₁²	C₄×C₇	1	1	yes	characteristic, complemented, Hall
13	C₇×C₁₁²	C₄×C₉	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁⋊D₁₁	C₂×C₃×C₇	1	1	yes	characteristic
15	C₇×C₉×C₁₁	—	2	6	no	—
16	#92150	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₇×D₁₁	—	22	6	no	—
18	C₃×C₁₁²	C₃×C₄×C₇	1	1	yes	characteristic
19	C₄×C₇×C₉	—	121	1	no	maximal, Hall
20	C₁₁⋊D₁₁	C₂×C₇×C₉	1	1	yes	characteristic
21	C₃×C₇×C₁₁	—	2	6	no	—
22	C₉×D₁₁	—	22	6	no	—
23	C₇×D₁₁	—	22	6	no	—
24	C₂×C₇×C₉	—	121	1	no	—
25	C₁₁²	C₄×C₇×C₉	1	1	yes	characteristic, complemented, Sylow
26	C₉×C₁₁	—	2	6	no	—
27	C₃×C₄×C₇	—	121	1	no	—
28	C₇×C₁₁	—	2	6	no	—
29	C₃×D₁₁	—	22	6	no	—
30	C₇×C₉	#92150	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃×C₇	—	121	1	no	—
32	C₄×C₉	—	121	1	no	Hall
33	C₃×C₁₁	—	2	6	no	—
34	C₄×C₇	—	121	1	no	Hall
35	D₁₁	—	22	6	no	—
36	C₃×C₇	C₃×#92150	1	1	yes	characteristic
37	C₂×C₉	—	121	1	no	—
38	C₂×C₇	—	121	1	no	—
39	C₃×C₄	—	121	1	no	—
40	C₁₁	—	2	6	no	—
41	C₉	C₇×#92150	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₉×#92150	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	121	1	no	—
44	C₄	—	121	1	no	Sylow
45	C₃	C₃×C₇×#92150	1	1	yes	characteristic
46	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₉	#92150
commutator, hypocenter	C₁₁²	C₄×C₇×C₉
Frattini	C₃	C₃×C₇×#92150
Fitting	C₇×C₉×C₁₁²	C₄
socle	C₃×C₇×C₁₁²	C₃×C₄
prime radical	C₃×C₇×C₁₁⋊D₁₁	C₂×C₃
cosocle	C₃×C₁₁⋊D₁₁	C₂×C₃×C₇
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₇×C₉

Complements

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

N	H ≅ G/N	type
3. C₇×C₉×C₁₁²	C₄	semidirect
5. C₉×#92150	C₇	direct (N × H)
6. C₇×#92150	C₉	direct (N × H)
12. C₉×C₁₁²	C₄×C₇	semidirect
13. C₇×C₁₁²	C₄×C₉	semidirect
16. #92150	C₇×C₉	direct (N × H)
25. C₁₁²	C₄×C₇×C₉	semidirect
30. C₇×C₉	#92150	direct (N × H)
41. C₉	C₇×#92150	direct (N × H)
42. C₇	C₉×#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
C₇×C₉×C₁₁⋊D₁₁	2
C₃×C₇×#92150	3
C₉×#92150	7
C₄×C₇×C₉	121

Subgroups — C7×C9×#92150 #44478951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₉×#92150 #44478951