Subgroups — C₇×C₁₁²×#157 #44479172

Order 30492.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₇×C₁₁²	—	6	2	no	—
4	C₁₁²×#157	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₄×C₇×C₁₁²	—	9	1	no	maximal, Hall
6	C₇×C₁₁×#157	C₁₁	1	12	yes	maximal, direct product factor
7	C₃×C₇×C₁₁²	—	2	2	no	—
8	C₁₁²×C₃⋊D₃	C₂×C₇	1	1	yes	characteristic
9	C₂×C₇×C₁₁²	—	9	1	no	—
10	C₇×C₁₁×C₃⋊D₃	C₂×C₁₁	1	12	yes	—
11	C₃²×C₁₁²	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₁²	#157	1	1	yes	characteristic, direct product factor, Hall
13	D₃×C₁₁²	—	6	2	no	—
14	C₃²×C₇×C₁₁	C₄×C₁₁	1	12	yes	complemented
15	C₄×C₁₁²	—	9	1	no	Hall
16	D₃×C₇×C₁₁	—	6	24	no	—
17	C₁₁×#157	C₇×C₁₁	1	12	yes	direct product factor
18	C₃×C₁₁²	—	2	2	no	—
19	C₄×C₇×C₁₁	—	9	12	no	—
20	C₇×#157	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₁₁²	—	9	1	no	—
22	C₃×C₇×C₁₁	—	2	24	no	—
23	C₁₁×C₃⋊D₃	C₂×C₇×C₁₁	1	12	yes	—
24	C₂×C₇×C₁₁	—	9	12	no	—
25	C₇×C₃⋊D₃	C₂×C₁₁²	1	1	yes	characteristic
26	C₁₁²	C₇×#157	1	1	yes	characteristic, direct product factor, Sylow
27	C₃²×C₁₁	C₄×C₇×C₁₁	1	12	yes	complemented
28	C₇×C₁₁	C₁₁×#157	1	12	yes	direct product factor
29	D₃×C₁₁	—	6	24	no	—
30	C₃²×C₇	C₄×C₁₁²	1	1	yes	characteristic, complemented, Hall
31	C₄×C₁₁	—	9	12	no	—
32	D₃×C₇	—	6	2	no	—
33	#157	C₇×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
34	C₃×C₁₁	—	2	24	no	—
35	C₄×C₇	—	9	1	no	Hall
36	C₂×C₁₁	—	9	12	no	—
37	C₃×C₇	—	2	2	no	—
38	C₃⋊D₃	C₂×C₇×C₁₁²	1	1	yes	characteristic
39	C₂×C₇	—	9	1	no	—
40	C₁₁	C₇×C₁₁×#157	1	12	yes	direct product factor
41	C₃²	C₄×C₇×C₁₁²	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₁₁²×#157	1	1	yes	characteristic, direct product factor, Sylow
43	D₃	—	6	2	no	—
44	C₄	—	9	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₁₁²	#157
commutator, hypocenter	C₃²	C₄×C₇×C₁₁²
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁²	C₄
prime radical	C₇×C₁₁²×C₃⋊D₃	C₂
cosocle	C₃⋊D₃	C₂×C₇×C₁₁²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₇×C₁₁²

Complements

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

N	H ≅ G/N	type
2. C₃²×C₇×C₁₁²	C₄	semidirect
4. C₁₁²×#157	C₇	direct (N × H)
6. C₇×C₁₁×#157	C₁₁	direct (N × H)
11. C₃²×C₁₁²	C₄×C₇	semidirect
12. C₇×C₁₁²	#157	direct (N × H)
14. C₃²×C₇×C₁₁	C₄×C₁₁	semidirect
17. C₁₁×#157	C₇×C₁₁	direct (N × H)
20. C₇×#157	C₁₁²	direct (N × H)
26. C₁₁²	C₇×#157	direct (N × H)
27. C₃²×C₁₁	C₄×C₇×C₁₁	semidirect
28. C₇×C₁₁	C₁₁×#157	direct (N × H)
30. C₃²×C₇	C₄×C₁₁²	semidirect
33. #157	C₇×C₁₁²	direct (N × H)
40. C₁₁	C₇×C₁₁×#157	direct (N × H)
41. C₃²	C₄×C₇×C₁₁²	semidirect
42. C₇	C₁₁²×#157	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×C₁₁²×C₃⋊D₃	2
C₁₁²×#157	7
C₄×C₇×C₁₁²	9
C₇×C₁₁×#157	11

Subgroups — C7×C112×#157 #44479172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₁²×#157 #44479172