Subgroups — D₇×Dic₂₁ #11924245

Order 1176.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×D₇	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊Dic₇)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×Dic₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×Dic₇	—	3	1	no	maximal, Hall
5	C₂×C₃×C₇²	C₂²	1	1	yes	characteristic
6	C₃×C₇×D₇	C₄	1	2	yes	complemented
7	C₂×C₇×D₇	D₃	1	1	yes	characteristic
8	C₇⋊Dic₇	—	3	1	no	—
9	C₇×Dic₇	—	3	1	no	—
10	C₂×Dic₂₁	—	7	1	no	maximal
11	Dic₃×D₇	—	7	1	no	maximal
12	C₃×C₇²	C₂×C₄	1	1	yes	characteristic, complemented, Hall
13	C₂×C₇²	C₂×D₃	1	1	yes	characteristic
14	C₇×D₇	Dic₃	1	2	yes	complemented
15	C₂²×C₃×C₇	—	7	1	no	—
16	C₂×C₃×D₇	D₇	1	1	yes	characteristic
17	Dic₂₁	—	7	1	no	—
18	Dic₂₁	—	7	1	no	—
19	Dic₂₁	—	14	3	no	—
20	Dic₂₁	D₇	1	1	yes	characteristic, direct product factor
21	C₇×Dic₃	—	7	1	no	—
22	C₂×Dic₇	—	21	1	no	—
23	C₄×D₇	—	21	1	no	—
24	C₇²	C₂×Dic₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×C₇	—	2	3	no	—
26	C₂×C₃×C₇	—	7	2	no	—
27	C₂×C₃×C₇	C₂×D₇	1	1	yes	characteristic
28	C₂×C₃×C₇	C₂×D₇	1	1	yes	characteristic
29	C₃×D₇	Dic₇	1	2	yes	complemented
30	C₂²×C₇	—	7	1	no	—
31	C₂×D₇	D₂₁	1	1	yes	characteristic
32	C₄×C₇	—	21	1	no	—
33	Dic₇	—	3	1	no	—
34	Dic₇	—	21	1	no	—
35	Dic₇	—	21	1	no	—
36	Dic₇	—	42	3	no	—
37	C₂×Dic₃	—	49	1	no	Hall
38	C₃×C₇	—	2	3	no	—
39	C₃×C₇	C₄×D₇	1	1	yes	characteristic, complemented
40	C₃×C₇	C₂×Dic₇	1	1	yes	characteristic, complemented
41	C₂×C₇	—	2	3	no	—
42	C₂×C₇	—	7	2	no	—
43	C₂×C₇	D₃×D₇	1	1	yes	characteristic
44	C₂×C₇	C₂×D₂₁	1	1	yes	characteristic
45	D₇	Dic₂₁	1	2	yes	direct product factor
46	C₂²×C₃	—	7	1	no	—
47	Dic₃	—	7	1	no	—
48	Dic₃	—	49	1	no	—
49	C₂×C₄	—	147	1	no	Sylow
50	C₇	—	2	3	no	—
51	C₇	Dic₃×D₇	1	1	yes	characteristic, complemented
52	C₇	C₂×Dic₂₁	1	1	yes	characteristic, complemented
53	C₂×C₃	—	7	2	no	—
54	C₂×C₃	D₇²	1	1	yes	characteristic
55	C₂²	—	7	1	no	—
56	C₄	—	21	1	no	—
57	C₄	—	147	1	no	—
58	C₃	D₇×Dic₇	1	1	yes	characteristic, complemented, Sylow
59	C₂	—	7	2	no	—
60	C₂	D₇×D₂₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇×D₂₁
commutator, hypocenter	C₃×C₇²	C₂×C₄
Fitting, socle, cosocle	C₂×C₃×C₇²	C₂²
prime radical	C₂×C₃×C₇×D₇	C₂
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₇⋊Dic₇)	C₂	semidirect
3. C₇×Dic₂₁	C₂	semidirect
6. C₃×C₇×D₇	C₄	semidirect
12. C₃×C₇²	C₂×C₄	semidirect
14. C₇×D₇	Dic₃	semidirect
20. Dic₂₁	D₇	direct (N × H)
24. C₇²	C₂×Dic₃	semidirect
29. C₃×D₇	Dic₇	semidirect
39. C₃×C₇	C₄×D₇	semidirect
40. C₃×C₇	C₂×Dic₇	semidirect
45. D₇	Dic₂₁	direct (N × H)
51. C₇	Dic₃×D₇	semidirect
52. C₇	C₂×Dic₂₁	semidirect
58. C₃	D₇×Dic₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×D₇	2
C₃⋊(C₇⋊Dic₇)	2
C₇×Dic₂₁	2
D₇×Dic₇	3
C₂×Dic₂₁	7
Dic₃×D₇	7

Subgroups — D7×Dic21 #11924245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×Dic₂₁ #11924245