Subgroups — C₇×Dic₃₉₉ #26013876

Order 11172.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇²×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₁₃₃	—	3	1	no	maximal, Hall
3	C₃×C₇²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇²×C₁₉	D₃	1	1	yes	characteristic
5	Dic₃₉₉	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₇×Dic₅₇	—	7	1	no	maximal
7	C₇²×C₁₉	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₇×C₁₉	—	2	3	no	—
9	C₂×C₃×C₇×C₁₉	D₇	1	1	yes	characteristic
10	C₂×C₃×C₇×C₁₉	C₂×C₇	1	1	yes	characteristic
11	C₇×Dic₂₁	—	19	1	no	maximal, Hall
12	Dic₁₃₃	—	3	1	no	—
13	C₇×Dic₁₉	—	21	1	no	—
14	C₃×C₇×C₁₉	—	2	3	no	—
15	C₃×C₇×C₁₉	Dic₇	1	1	yes	characteristic, complemented
16	C₃×C₇×C₁₉	C₄×C₇	1	1	yes	characteristic, complemented
17	C₂×C₃×C₇²	D₁₉	1	1	yes	characteristic
18	C₂×C₇×C₁₉	—	2	3	no	—
19	C₂×C₇×C₁₉	D₃×C₇	1	1	yes	characteristic
20	C₂×C₇×C₁₉	D₂₁	1	1	yes	characteristic
21	Dic₅₇	—	7	1	no	Hall
22	C₇×Dic₇	—	57	1	no	Hall
23	C₃×C₇²	Dic₁₉	1	1	yes	characteristic, complemented, Hall
24	C₇×C₁₉	—	2	3	no	—
25	C₇×C₁₉	C₇×Dic₃	1	1	yes	characteristic, complemented
26	C₇×C₁₉	Dic₂₁	1	1	yes	characteristic, complemented
27	C₂×C₃×C₁₉	C₇×D₇	1	1	yes	characteristic
28	C₂×C₇²	D₅₇	1	1	yes	characteristic
29	Dic₂₁	—	19	1	no	—
30	C₇×Dic₃	—	133	1	no	—
31	Dic₁₉	—	21	1	no	Hall
32	C₃×C₁₉	C₇×Dic₇	1	1	yes	characteristic, complemented, Hall
33	C₇²	Dic₅₇	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃×C₇	—	2	3	no	—
35	C₂×C₃×C₇	C₇×D₁₉	1	1	yes	characteristic
36	C₂×C₃×C₇	D₁₃₃	1	1	yes	characteristic
37	C₂×C₁₉	C₇×D₂₁	1	1	yes	characteristic
38	C₄×C₇	—	399	1	no	—
39	Dic₇	—	57	1	no	—
40	C₃×C₇	—	2	3	no	—
41	C₃×C₇	C₇×Dic₁₉	1	1	yes	characteristic, complemented
42	C₃×C₇	Dic₁₃₃	1	1	yes	characteristic, complemented
43	C₁₉	C₇×Dic₂₁	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₇	—	2	3	no	—
45	C₂×C₇	C₇×D₅₇	1	1	yes	characteristic
46	C₂×C₇	D₃₉₉	1	1	yes	characteristic
47	Dic₃	—	133	1	no	Hall
48	C₇	—	2	3	no	—
49	C₇	C₇×Dic₅₇	1	1	yes	characteristic, complemented
50	C₇	Dic₃₉₉	1	1	yes	characteristic, direct product factor
51	C₂×C₃	C₇×D₁₃₃	1	1	yes	characteristic
52	C₄	—	399	1	no	Sylow
53	C₃	C₇×Dic₁₃₃	1	1	yes	characteristic, complemented, Sylow
54	C₂	C₇×D₃₉₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇	D₃₉₉
commutator, hypocenter	C₃×C₇×C₁₉	C₄×C₇
Frattini	C₂	C₇×D₃₉₉
Fitting, socle, prime radical	C₂×C₃×C₇²×C₁₉	C₂
cosocle	C₂×C₃×C₇×C₁₉	C₂×C₇
LCS	G ▷ C₃×C₇×C₁₉
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
3. C₃×C₇²×C₁₉	C₄	semidirect
5. Dic₃₉₉	C₇	direct (N × H)
7. C₇²×C₁₉	Dic₃	semidirect
15. C₃×C₇×C₁₉	Dic₇	semidirect
16. C₃×C₇×C₁₉	C₄×C₇	semidirect
23. C₃×C₇²	Dic₁₉	semidirect
25. C₇×C₁₉	C₇×Dic₃	semidirect
26. C₇×C₁₉	Dic₂₁	semidirect
32. C₃×C₁₉	C₇×Dic₇	semidirect
33. C₇²	Dic₅₇	semidirect
41. C₃×C₇	C₇×Dic₁₉	semidirect
42. C₃×C₇	Dic₁₃₃	semidirect
43. C₁₉	C₇×Dic₂₁	semidirect
49. C₇	C₇×Dic₅₇	semidirect
50. C₇	Dic₃₉₉	direct (N × H)
53. C₃	C₇×Dic₁₃₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇²×C₁₉	2
C₇×Dic₁₃₃	3
Dic₃₉₉	7
C₇×Dic₅₇	7
C₇×Dic₂₁	19

Subgroups — C7×Dic399 #26013876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×Dic₃₉₉ #26013876