Subgroups — C₂×C₇²×C₃⋊D₃₃ #34085077

Order 19404.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₃⋊D₃₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇²×D₃₃	—	3	4	no	maximal
4	C₃²×C₇²×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇²×D₃₃	—	3	8	no	—
6	C₂×C₃×C₇²×C₁₁	D₃	1	4	yes	complemented
7	C₂×C₇×C₃⋊D₃₃	C₇	1	8	yes	maximal, direct product factor
8	C₂×C₇²×D₁₁	—	9	1	no	Hall
9	C₂×C₇²×C₃⋊D₃	—	11	1	no	maximal, Hall
10	C₃×C₇²×C₁₁	C₂×D₃	1	4	yes	complemented
11	C₂×C₃²×C₇×C₁₁	C₂×C₇	1	8	yes	complemented
12	C₇×C₃⋊D₃₃	C₂×C₇	1	16	yes	direct product factor
13	C₂×C₇²×C₁₁	C₃⋊D₃	1	1	yes	characteristic, complemented
14	C₇²×D₁₁	—	9	2	no	—
15	C₂×C₇×D₃₃	—	3	32	no	—
16	C₂×C₃²×C₇²	D₁₁	1	1	yes	characteristic, complemented
17	C₇²×C₃⋊D₃	—	11	2	no	—
18	C₃²×C₇×C₁₁	C₂²×C₇	1	8	yes	complemented
19	C₂×D₃×C₇²	—	33	4	no	—
20	C₇²×C₁₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₇×C₁₁	D₃×C₇	1	32	yes	complemented
22	C₇×D₃₃	—	3	64	no	—
23	C₃²×C₇²	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃⋊D₃₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇×D₁₁	—	9	8	no	—
26	C₂×C₃×C₇²	D₃₃	1	4	yes	complemented
27	D₃×C₇²	—	33	8	no	—
28	C₂×C₇×C₃⋊D₃	—	11	8	no	—
29	C₃×C₇×C₁₁	C₂×D₃×C₇	1	32	yes	complemented
30	C₂×C₃²×C₁₁	C₂×C₇²	1	1	yes	characteristic, complemented
31	C₃⋊D₃₃	C₂×C₇²	1	2	yes	direct product factor
32	C₂²×C₇²	—	99	1	no	Hall
33	C₂×C₇×C₁₁	C₇×C₃⋊D₃	1	8	yes	complemented
34	C₇×D₁₁	—	9	16	no	—
35	C₃×C₇²	C₂×D₃₃	1	4	yes	complemented
36	C₂×D₃₃	—	3	4	no	—
37	C₂×C₃²×C₇	C₇×D₁₁	1	8	yes	complemented
38	C₇×C₃⋊D₃	—	11	16	no	—
39	C₃²×C₁₁	C₂²×C₇²	1	1	yes	characteristic, complemented, Hall
40	C₂×C₇²	—	99	2	no	—
41	C₂×C₇²	C₃⋊D₃₃	1	1	yes	characteristic, direct product factor
42	C₂×D₃×C₇	—	33	32	no	—
43	C₇×C₁₁	C₂×C₇×C₃⋊D₃	1	8	yes	complemented
44	C₂×C₃×C₁₁	D₃×C₇²	1	4	yes	complemented
45	D₃₃	—	3	8	no	—
46	C₃²×C₇	C₂×C₇×D₁₁	1	8	yes	complemented
47	C₇²	C₂×C₃⋊D₃₃	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×D₁₁	—	9	1	no	Hall
49	C₂×C₃×C₇	C₇×D₃₃	1	32	yes	complemented
50	D₃×C₇	—	33	64	no	—
51	C₂×C₃⋊D₃	—	11	1	no	Hall
52	C₃×C₁₁	C₂×D₃×C₇²	1	4	yes	complemented
53	C₂²×C₇	—	99	8	no	—
54	C₂×C₁₁	C₇²×C₃⋊D₃	1	1	yes	characteristic, complemented
55	D₁₁	—	9	2	no	—
56	C₃×C₇	C₂×C₇×D₃₃	1	32	yes	complemented
57	C₂×C₃²	C₇²×D₁₁	1	1	yes	characteristic, complemented
58	C₃⋊D₃	—	11	2	no	—
59	C₂×C₇	—	99	16	no	—
60	C₂×C₇	C₇×C₃⋊D₃₃	1	8	yes	direct product factor
61	C₂×D₃	—	33	4	no	—
62	C₁₁	C₂×C₇²×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
63	C₃²	C₂×C₇²×D₁₁	1	1	yes	characteristic, complemented, Sylow
64	C₇	C₂×C₇×C₃⋊D₃₃	1	8	yes	direct product factor
65	C₂×C₃	C₇²×D₃₃	1	4	yes	complemented
66	D₃	—	33	8	no	—
67	C₂²	—	99	1	no	Sylow
68	C₃	C₂×C₇²×D₃₃	1	4	yes	complemented
69	C₂	—	99	2	no	—
70	C₂	C₇²×C₃⋊D₃₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇²	C₃⋊D₃₃
commutator, cosocle, hypocenter	C₃²×C₁₁	C₂²×C₇²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇²×C₁₁	C₂
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₂×C₇²

Complements

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

N	H ≅ G/N	type
1. C₇²×C₃⋊D₃₃	C₂	direct (N × H)
2. C₂×C₃²×C₇²×C₁₁	C₂	semidirect
4. C₃²×C₇²×C₁₁	C₂²	semidirect
6. C₂×C₃×C₇²×C₁₁	D₃	semidirect
7. C₂×C₇×C₃⋊D₃₃	C₇	direct (N × H)
10. C₃×C₇²×C₁₁	C₂×D₃	semidirect
11. C₂×C₃²×C₇×C₁₁	C₂×C₇	semidirect
12. C₇×C₃⋊D₃₃	C₂×C₇	direct (N × H)
13. C₂×C₇²×C₁₁	C₃⋊D₃	semidirect
16. C₂×C₃²×C₇²	D₁₁	semidirect
18. C₃²×C₇×C₁₁	C₂²×C₇	semidirect
20. C₇²×C₁₁	C₂×C₃⋊D₃	semidirect
21. C₂×C₃×C₇×C₁₁	D₃×C₇	semidirect
23. C₃²×C₇²	C₂×D₁₁	semidirect
24. C₂×C₃⋊D₃₃	C₇²	direct (N × H)
26. C₂×C₃×C₇²	D₃₃	semidirect
29. C₃×C₇×C₁₁	C₂×D₃×C₇	semidirect
30. C₂×C₃²×C₁₁	C₂×C₇²	semidirect
31. C₃⋊D₃₃	C₂×C₇²	direct (N × H)
33. C₂×C₇×C₁₁	C₇×C₃⋊D₃	semidirect
35. C₃×C₇²	C₂×D₃₃	semidirect
37. C₂×C₃²×C₇	C₇×D₁₁	semidirect
39. C₃²×C₁₁	C₂²×C₇²	semidirect
41. C₂×C₇²	C₃⋊D₃₃	direct (N × H)
43. C₇×C₁₁	C₂×C₇×C₃⋊D₃	semidirect
44. C₂×C₃×C₁₁	D₃×C₇²	semidirect
46. C₃²×C₇	C₂×C₇×D₁₁	semidirect
47. C₇²	C₂×C₃⋊D₃₃	direct (N × H)
49. C₂×C₃×C₇	C₇×D₃₃	semidirect
52. C₃×C₁₁	C₂×D₃×C₇²	semidirect
54. C₂×C₁₁	C₇²×C₃⋊D₃	semidirect
56. C₃×C₇	C₂×C₇×D₃₃	semidirect
57. C₂×C₃²	C₇²×D₁₁	semidirect
60. C₂×C₇	C₇×C₃⋊D₃₃	direct (N × H)
62. C₁₁	C₂×C₇²×C₃⋊D₃	semidirect
63. C₃²	C₂×C₇²×D₁₁	semidirect
64. C₇	C₂×C₇×C₃⋊D₃₃	direct (N × H)
65. C₂×C₃	C₇²×D₃₃	semidirect
68. C₃	C₂×C₇²×D₃₃	semidirect
70. C₂	C₇²×C₃⋊D₃₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×C₃⋊D₃₃	2
C₂×C₃²×C₇²×C₁₁	2
C₂×C₇²×D₃₃	3
C₂×C₇×C₃⋊D₃₃	7
C₂×C₇²×C₃⋊D₃	11

Subgroups — C2×C72×C3⋊D33 #34085077

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇²×C₃⋊D₃₃ #34085077