Subgroups — C₃⋊(C₇⋊#13089721) #44479121

Order 30492.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×(C₁₁⋊D₁₁)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊#92150)	—	3	1	no	maximal
3	C₇⋊#13089721	—	3	3	no	maximal
4	C₃×C₇×C₁₁²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×C₁₁⋊D₁₁	D₃	1	1	yes	characteristic
6	C₇×(C₁₁⋊D₁₁)⋊C₃	D₃	1	3	yes	—
7	C₃⋊#13089721	—	7	1	no	maximal, Hall
8	C₇⋊#92150	—	9	1	no	Hall
9	C₇×C₁₁²⋊C₃	Dic₃	1	3	yes	complemented
10	C₃×C₇×C₁₁²	Dic₃	1	1	yes	characteristic, complemented
11	C₃×(C₁₁⋊D₁₁)⋊C₃	D₇	1	1	yes	characteristic
12	C₇×C₁₁⋊D₁₁	C₃⋊D₃	1	1	yes	characteristic
13	C₃⋊#92150	—	21	1	no	—
14	#13089721	—	21	3	no	—
15	C₃×C₁₁²⋊C₃	Dic₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₁₁²	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₁₁⋊D₁₁	D₂₁	1	1	yes	characteristic
18	(C₁₁⋊D₁₁)⋊C₃	D₂₁	1	3	yes	—
19	#92150	—	63	1	no	Hall
20	C₃×C₇×D₁₁	—	66	2	no	—
21	C₃×C₁₁²	Dic₂₁	1	1	yes	characteristic, complemented
22	C₁₁²⋊C₃	Dic₂₁	1	3	yes	complemented
23	C₃⋊Dic₂₁	—	121	1	no	maximal, Hall
24	C₁₁⋊D₁₁	C₃⋊D₂₁	1	1	yes	characteristic
25	C₃×C₇×C₁₁	—	6	2	no	—
26	C₇×D₁₁	—	66	2	no	—
27	C₂×C₃²×C₇	—	121	1	no	—
28	C₁₁²	C₃⋊Dic₂₁	1	1	yes	characteristic, complemented, Sylow
29	Dic₂₁	—	363	3	no	—
30	Dic₂₁	—	363	1	no	—
31	C₇×C₁₁	—	6	2	no	—
32	C₃×D₁₁	—	66	2	no	—
33	C₃²×C₇	—	484	1	no	Hall
34	C₂×C₃×C₇	—	121	3	no	—
35	C₂×C₃×C₇	—	121	1	no	—
36	C₃⋊Dic₃	—	847	1	no	Hall
37	C₃×C₁₁	—	6	2	no	—
38	Dic₇	—	1089	1	no	Hall
39	D₁₁	—	66	2	no	—
40	C₃×C₇	—	484	3	no	—
41	C₃×C₇	#13089721	1	1	yes	characteristic, complemented
42	C₂×C₃²	—	121	1	no	—
43	C₂×C₇	—	121	1	no	—
44	Dic₃	—	2541	3	no	—
45	Dic₃	—	2541	1	no	—
46	C₁₁	—	6	2	no	—
47	C₃²	—	484	1	no	Sylow
48	C₇	C₃⋊#13089721	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃	—	121	3	no	—
50	C₂×C₃	—	121	1	no	—
51	C₄	—	7623	1	no	Sylow
52	C₃	—	484	3	no	—
53	C₃	C₇⋊#13089721	1	1	yes	characteristic, complemented
54	C₂	—	121	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₃×C₇×C₁₁²⋊C₃	C₄
Fitting, socle	C₃×C₇×C₁₁²	Dic₃
prime radical, cosocle	C₃×C₇×(C₁₁⋊D₁₁)⋊C₃	C₂
LCS	G ▷ C₃×C₇×C₁₁²⋊C₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
4. C₃×C₇×C₁₁²⋊C₃	C₄	semidirect
9. C₇×C₁₁²⋊C₃	Dic₃	semidirect
10. C₃×C₇×C₁₁²	Dic₃	semidirect
15. C₃×C₁₁²⋊C₃	Dic₇	semidirect
16. C₇×C₁₁²	C₃⋊Dic₃	semidirect
21. C₃×C₁₁²	Dic₂₁	semidirect
22. C₁₁²⋊C₃	Dic₂₁	semidirect
28. C₁₁²	C₃⋊Dic₂₁	semidirect
41. C₃×C₇	#13089721	semidirect
48. C₇	C₃⋊#13089721	semidirect
53. C₃	C₇⋊#13089721	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×(C₁₁⋊D₁₁)⋊C₃	2
C₃⋊(C₇⋊#92150)	3
C₇⋊#13089721	3
C₃⋊#13089721	7
C₃⋊Dic₂₁	121

Subgroups — C3⋊(C7⋊#13089721) #44479121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₇⋊#13089721) #44479121