Subgroups — C₃²×D₁₃×D₄₉ #37524270

Order 22932.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₆₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×C₁₃×D₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₁₃×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₃×D₄₉	C₃	1	4	yes	maximal, direct product factor
5	C₃²×C₁₃×C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₆₃₇	C₂×C₃	1	4	yes	complemented
7	C₃×C₁₃×D₄₉	C₂×C₃	1	4	yes	complemented
8	C₃×D₁₃×C₄₉	C₂×C₃	1	4	yes	complemented
9	C₃²×D₇×D₁₃	—	7	1	no	maximal
10	D₁₃×D₄₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₁₃×C₄₉	C₂²×C₃	1	4	yes	complemented
12	C₂×C₃²×D₄₉	—	13	1	no	maximal, Hall
13	C₃²×D₉₁	—	7	1	no	—
14	C₃²×C₁₃×D₇	—	7	1	no	—
15	C₃²×C₇×D₁₃	D₇	1	1	yes	characteristic
16	D₆₃₇	C₂×C₃²	1	1	yes	characteristic, complemented
17	D₁₃×C₄₉	C₂×C₃²	1	1	yes	characteristic, complemented
18	C₁₃×D₄₉	C₂×C₃²	1	1	yes	characteristic, complemented
19	C₃×D₇×D₁₃	—	7	4	no	—
20	C₂×C₃²×C₄₉	—	13	1	no	—
21	C₃²×D₄₉	—	13	1	no	—
22	C₃²×D₄₉	D₁₃	1	1	yes	characteristic, direct product factor
23	C₃²×C₇×C₁₃	C₂×D₇	1	1	yes	characteristic
24	C₁₃×C₄₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×D₄₉	—	13	4	no	—
26	C₃×D₉₁	—	7	4	no	—
27	C₃×C₁₃×D₇	—	7	4	no	—
28	C₃×C₇×D₁₃	C₃×D₇	1	4	yes	—
29	C₂×C₃²×D₁₃	—	49	1	no	Hall
30	C₃²×C₄₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
31	D₇×D₁₃	—	7	1	no	—
32	C₂×C₃×C₄₉	—	13	4	no	—
33	C₃×D₄₉	—	13	4	no	—
34	C₃×D₄₉	C₃×D₁₃	1	4	yes	direct product factor
35	C₃×C₇×C₁₃	C₂×C₃×D₇	1	4	yes	—
36	C₂×C₃²×D₇	—	91	1	no	—
37	C₂×C₃²×C₁₃	—	49	1	no	—
38	C₃²×D₁₃	—	49	1	no	—
39	C₃²×D₁₃	D₄₉	1	1	yes	characteristic, direct product factor
40	C₂×D₄₉	—	13	1	no	Hall
41	D₉₁	—	7	1	no	—
42	C₇×D₁₃	C₃²×D₇	1	1	yes	characteristic
43	C₁₃×D₇	—	7	1	no	—
44	C₂×C₃×D₁₃	—	49	4	no	—
45	C₃×C₄₉	C₂×C₃×D₁₃	1	4	yes	complemented
46	C₂×C₃²×C₇	—	13	1	no	—
47	C₃²×D₇	—	7	1	no	—
48	C₃²×D₇	—	91	1	no	—
49	C₃²×C₁₃	C₂×D₄₉	1	1	yes	characteristic, complemented, Hall
50	C₂×C₄₉	—	13	1	no	—
51	D₄₉	—	13	1	no	—
52	D₄₉	C₃²×D₁₃	1	1	yes	characteristic, direct product factor
53	C₇×C₁₃	C₂×C₃²×D₇	1	1	yes	characteristic
54	C₂×C₃×D₇	—	91	4	no	—
55	C₂×C₃×C₁₃	—	49	4	no	—
56	C₃×D₁₃	—	49	4	no	—
57	C₃×D₁₃	C₃×D₄₉	1	4	yes	direct product factor
58	C₃²×C₇	D₇×D₁₃	1	1	yes	characteristic
59	C₂×D₁₃	—	49	1	no	Hall
60	C₄₉	C₂×C₃²×D₁₃	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₃×C₇	—	13	4	no	—
62	C₃×D₇	—	7	4	no	—
63	C₃×D₇	—	91	4	no	—
64	C₃×C₁₃	C₂×C₃×D₄₉	1	4	yes	complemented
65	C₂²×C₃²	—	637	1	no	Hall
66	C₂×D₇	—	91	1	no	—
67	C₂×C₁₃	—	49	1	no	—
68	D₁₃	—	49	1	no	—
69	D₁₃	C₃²×D₄₉	1	1	yes	characteristic, direct product factor
70	C₃×C₇	C₃×D₇×D₁₃	1	4	yes	—
71	C₂×C₃²	—	13	1	no	—
72	C₂×C₃²	—	49	1	no	—
73	C₂×C₃²	—	637	1	no	—
74	C₂×C₇	—	13	1	no	—
75	D₇	—	7	1	no	—
76	D₇	—	91	1	no	—
77	C₁₃	C₂×C₃²×D₄₉	1	1	yes	characteristic, complemented, Sylow
78	C₂²×C₃	—	637	4	no	—
79	C₃²	D₁₃×D₄₉	1	1	yes	characteristic, direct product factor, Sylow
80	C₇	C₃²×D₇×D₁₃	1	1	yes	characteristic
81	C₂×C₃	—	13	4	no	—
82	C₂×C₃	—	49	4	no	—
83	C₂×C₃	—	637	4	no	—
84	C₂²	—	637	1	no	Sylow
85	C₃	C₃×D₁₃×D₄₉	1	4	yes	direct product factor
86	C₂	—	13	1	no	—
87	C₂	—	49	1	no	—
88	C₂	—	637	1	no	—

	subgroup	G/H
center, hypercenter	C₃²	D₁₃×D₄₉
commutator, cosocle, hypocenter	C₁₃×C₄₉	C₂²×C₃²
Frattini	C₇	C₃²×D₇×D₁₃
Fitting	C₃²×C₁₃×C₄₉	C₂²
socle	C₃²×C₇×C₁₃	C₂×D₇
LCS	G ▷ C₁₃×C₄₉
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×D₆₃₇	C₂	semidirect
2. C₃²×C₁₃×D₄₉	C₂	semidirect
3. C₃²×D₁₃×C₄₉	C₂	semidirect
4. C₃×D₁₃×D₄₉	C₃	direct (N × H)
5. C₃²×C₁₃×C₄₉	C₂²	semidirect
6. C₃×D₆₃₇	C₂×C₃	semidirect
7. C₃×C₁₃×D₄₉	C₂×C₃	semidirect
8. C₃×D₁₃×C₄₉	C₂×C₃	semidirect
10. D₁₃×D₄₉	C₃²	direct (N × H)
11. C₃×C₁₃×C₄₉	C₂²×C₃	semidirect
16. D₆₃₇	C₂×C₃²	semidirect
17. D₁₃×C₄₉	C₂×C₃²	semidirect
18. C₁₃×D₄₉	C₂×C₃²	semidirect
22. C₃²×D₄₉	D₁₃	direct (N × H)
24. C₁₃×C₄₉	C₂²×C₃²	semidirect
30. C₃²×C₄₉	C₂×D₁₃	semidirect
34. C₃×D₄₉	C₃×D₁₃	direct (N × H)
39. C₃²×D₁₃	D₄₉	direct (N × H)
45. C₃×C₄₉	C₂×C₃×D₁₃	semidirect
49. C₃²×C₁₃	C₂×D₄₉	semidirect
52. D₄₉	C₃²×D₁₃	direct (N × H)
57. C₃×D₁₃	C₃×D₄₉	direct (N × H)
60. C₄₉	C₂×C₃²×D₁₃	semidirect
64. C₃×C₁₃	C₂×C₃×D₄₉	semidirect
69. D₁₃	C₃²×D₄₉	direct (N × H)
77. C₁₃	C₂×C₃²×D₄₉	semidirect
79. C₃²	D₁₃×D₄₉	direct (N × H)
85. C₃	C₃×D₁₃×D₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×D₆₃₇	2
C₃²×C₁₃×D₄₉	2
C₃²×D₁₃×C₄₉	2
C₃×D₁₃×D₄₉	3
C₃²×D₇×D₁₃	7
C₂×C₃²×D₄₉	13

Subgroups — C32×D13×D49 #37524270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×D₁₃×D₄₉ #37524270