Subgroups — C₇⋊Dic₁₁₉₇ #45691537

Order 33516.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₉×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊Dic₁₃₃)	—	3	1	no	maximal
3	C₇²×C₉×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₉	D₃	1	1	yes	characteristic
5	Dic₁₁₉₇	—	7	8	no	maximal
6	C₇⋊Dic₁₃₃	—	9	1	no	Hall
7	C₃×C₇²×C₁₉	Dic₃	1	1	yes	characteristic
8	C₂×C₇×C₉×C₁₉	D₇	1	8	yes	—
9	C₂×C₇²×C₁₉	D₉	1	1	yes	characteristic
10	C₇⋊Dic₆₃	—	19	1	no	maximal, Hall
11	Dic₃₉₉	—	21	8	no	—
12	C₇×C₉×C₁₉	Dic₇	1	8	yes	complemented
13	C₇²×C₁₉	Dic₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇²×C₉	D₁₉	1	1	yes	characteristic
15	C₂×C₃×C₇×C₁₉	D₂₁	1	8	yes	—
16	Dic₁₇₁	—	49	1	no	Hall
17	C₃⋊(C₇⋊Dic₇)	—	57	1	no	—
18	Dic₁₃₃	—	63	8	no	—
19	C₇²×C₉	Dic₁₉	1	1	yes	characteristic, complemented, Hall
20	C₃×C₇×C₁₉	Dic₂₁	1	8	yes	—
21	C₂×C₉×C₁₉	C₇⋊D₇	1	1	yes	characteristic
22	C₂×C₃×C₇²	D₅₇	1	1	yes	characteristic
23	C₂×C₇×C₁₉	D₆₃	1	8	yes	—
24	Dic₆₃	—	133	8	no	—
25	Dic₅₇	—	147	1	no	—
26	C₇⋊Dic₇	—	171	1	no	Hall
27	C₉×C₁₉	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Hall
28	C₃×C₇²	Dic₅₇	1	1	yes	characteristic
29	C₇×C₁₉	Dic₆₃	1	8	yes	complemented
30	C₂×C₇×C₉	D₁₃₃	1	8	yes	—
31	C₂×C₃×C₁₉	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
32	C₂×C₇²	D₁₇₁	1	1	yes	characteristic
33	Dic₂₁	—	399	8	no	—
34	Dic₁₉	—	441	1	no	Hall
35	C₇×C₉	Dic₁₃₃	1	8	yes	complemented
36	C₃×C₁₉	C₃⋊(C₇⋊Dic₇)	1	1	yes	characteristic
37	C₇²	Dic₁₇₁	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃×C₇	D₃₉₉	1	8	yes	—
39	C₂×C₁₉	C₇⋊D₆₃	1	1	yes	characteristic
40	Dic₉	—	931	1	no	Hall
41	Dic₇	—	1197	8	no	—
42	C₃×C₇	Dic₃₉₉	1	8	yes	—
43	C₁₉	C₇⋊Dic₆₃	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₉	C₇⋊D₁₃₃	1	1	yes	characteristic
45	C₂×C₇	D₁₁₉₇	1	8	yes	—
46	Dic₃	—	2793	1	no	—
47	C₉	C₇⋊Dic₁₃₃	1	1	yes	characteristic, complemented, Sylow
48	C₇	Dic₁₁₉₇	1	8	yes	complemented
49	C₂×C₃	C₃⋊(C₇⋊D₁₃₃)	1	1	yes	characteristic
50	C₄	—	8379	1	no	Sylow
51	C₃	C₃⋊(C₇⋊Dic₁₃₃)	1	1	yes	characteristic
52	C₂	C₇⋊D₁₁₉₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	C₇⋊D₁₁₉₇
commutator, hypocenter	C₇²×C₉×C₁₉	C₄
Frattini	C₂×C₃	C₃⋊(C₇⋊D₁₃₃)
Fitting, cosocle	C₂×C₇²×C₉×C₁₉	C₂
socle, prime radical	C₂×C₃×C₇²×C₁₉	D₃
LCS	G ▷ C₇²×C₉×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₇²×C₉×C₁₉	C₄	semidirect
12. C₇×C₉×C₁₉	Dic₇	semidirect
13. C₇²×C₁₉	Dic₉	semidirect
19. C₇²×C₉	Dic₁₉	semidirect
27. C₉×C₁₉	C₇⋊Dic₇	semidirect
29. C₇×C₁₉	Dic₆₃	semidirect
35. C₇×C₉	Dic₁₃₃	semidirect
37. C₇²	Dic₁₇₁	semidirect
43. C₁₉	C₇⋊Dic₆₃	semidirect
47. C₉	C₇⋊Dic₁₃₃	semidirect
48. C₇	Dic₁₁₉₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇²×C₉×C₁₉	2
C₃⋊(C₇⋊Dic₁₃₃)	3
Dic₁₁₉₇	7
C₇⋊Dic₆₃	19

Subgroups — C7⋊Dic1197 #45691537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊Dic₁₁₉₇ #45691537