Subgroups — C₃²×(C₇⋊D₇)⋊D₁₃ #37525575

Order 22932.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×D₉₁	C₂	1	2	yes	maximal, complemented
2	C₃²×C₁₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×(C₇⋊D₇)⋊D₁₃	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×C₇⋊D₇	C₂×C₃	1	4	yes	complemented
6	C₃×C₇×D₉₁	C₂×C₃	1	8	yes	complemented
7	C₃²×D₇×D₁₃	—	7	2	no	maximal
8	(C₇⋊D₇)⋊D₁₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇²×C₁₃	C₂²×C₃	1	4	yes	complemented
10	C₃²×D₇²	—	13	1	no	maximal, Hall
11	C₃²×D₉₁	D₇	1	2	yes	complemented
12	C₃²×C₁₃×D₇	—	7	2	no	—
13	C₃²×C₁₃×D₇	—	14	3	no	—
14	C₃²×C₇×D₁₃	—	7	2	no	—
15	C₁₃×C₇⋊D₇	C₂×C₃²	1	1	yes	characteristic, complemented
16	C₇×D₉₁	C₂×C₃²	1	2	yes	complemented
17	C₃×D₇×D₁₃	—	7	8	no	—
18	C₃²×C₇⋊D₇	D₁₃	1	1	yes	characteristic, complemented
19	C₃²×C₇×D₇	—	13	2	no	—
20	C₃²×C₇×C₁₃	—	2	3	no	—
21	C₃²×C₇×C₁₃	C₂×D₇	1	2	yes	complemented
22	C₇²×C₁₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
23	C₃×D₇²	—	13	4	no	—
24	C₃×D₉₁	C₃×D₇	1	8	yes	complemented
25	C₃×C₁₃×D₇	—	7	8	no	—
26	C₃×C₁₃×D₇	—	14	12	no	—
27	C₃×C₇×D₁₃	—	7	8	no	—
28	C₂×C₃²×D₁₃	—	49	1	no	Hall
29	C₃²×C₇²	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
30	D₇×D₁₃	—	7	2	no	—
31	C₃×C₇⋊D₇	C₃×D₁₃	1	4	yes	complemented
32	C₃×C₇×D₇	—	13	8	no	—
33	C₃×C₇×C₁₃	—	2	12	no	—
34	C₃×C₇×C₁₃	C₂×C₃×D₇	1	8	yes	complemented
35	C₂×C₃²×D₇	—	91	2	no	—
36	C₂×C₃²×C₁₃	—	49	1	no	—
37	C₃²×D₁₃	—	7	2	no	—
38	D₇²	—	13	1	no	Hall
39	D₉₁	C₃²×D₇	1	2	yes	complemented
40	C₇×D₁₃	—	7	2	no	—
41	C₁₃×D₇	—	7	2	no	—
42	C₁₃×D₇	—	14	3	no	—
43	C₂×C₃×D₁₃	—	49	4	no	—
44	C₃×C₇²	C₂×C₃×D₁₃	1	4	yes	complemented
45	C₂×C₃²×C₇	—	91	2	no	—
46	C₃²×D₇	—	7	2	no	—
47	C₃²×D₇	—	13	2	no	—
48	C₃²×D₇	—	14	3	no	—
49	C₃²×C₁₃	D₇²	1	1	yes	characteristic, complemented, Hall
50	C₇⋊D₇	C₃²×D₁₃	1	1	yes	characteristic, complemented
51	C₇×D₇	—	13	2	no	—
52	C₇×C₁₃	—	2	3	no	—
53	C₇×C₁₃	C₂×C₃²×D₇	1	2	yes	complemented
54	C₂×C₃×D₇	—	91	8	no	—
55	C₂×C₃×C₁₃	—	49	4	no	—
56	C₃×D₁₃	—	7	8	no	—
57	C₃²×C₇	—	2	3	no	—
58	C₃²×C₇	D₇×D₁₃	1	2	yes	complemented
59	C₂×D₁₃	—	49	1	no	Hall
60	C₇²	C₂×C₃²×D₁₃	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₃×C₇	—	91	8	no	—
62	C₃×D₇	—	7	8	no	—
63	C₃×D₇	—	13	8	no	—
64	C₃×D₇	—	14	12	no	—
65	C₃×C₁₃	C₃×D₇²	1	4	yes	complemented
66	C₂²×C₃²	—	637	1	no	Hall
67	C₂×D₇	—	91	2	no	—
68	C₂×C₁₃	—	49	1	no	—
69	D₁₃	—	7	2	no	—
70	C₃×C₇	—	2	12	no	—
71	C₃×C₇	C₃×D₇×D₁₃	1	8	yes	complemented
72	C₂×C₃²	—	49	1	no	—
73	C₂×C₃²	—	91	2	no	—
74	C₂×C₇	—	91	2	no	—
75	D₇	—	7	2	no	—
76	D₇	—	13	2	no	—
77	D₇	—	14	3	no	—
78	C₁₃	C₃²×D₇²	1	1	yes	characteristic, complemented, Sylow
79	C₂²×C₃	—	637	4	no	—
80	C₃²	(C₇⋊D₇)⋊D₁₃	1	1	yes	characteristic, direct product factor, Sylow
81	C₇	—	2	3	no	—
82	C₇	C₃²×D₇×D₁₃	1	2	yes	complemented
83	C₂×C₃	—	49	4	no	—
84	C₂×C₃	—	91	8	no	—
85	C₂²	—	637	1	no	Sylow
86	C₃	C₃×(C₇⋊D₇)⋊D₁₃	1	4	yes	direct product factor
87	C₂	—	49	1	no	—
88	C₂	—	91	2	no	—

	subgroup	G/H
center, hypercenter	C₃²	(C₇⋊D₇)⋊D₁₃
commutator, cosocle, hypocenter	C₇²×C₁₃	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₃	C₂²
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×D₉₁	C₂	semidirect
2. C₃²×C₁₃×C₇⋊D₇	C₂	semidirect
3. C₃×(C₇⋊D₇)⋊D₁₃	C₃	direct (N × H)
4. C₃²×C₇²×C₁₃	C₂²	semidirect
5. C₃×C₁₃×C₇⋊D₇	C₂×C₃	semidirect
6. C₃×C₇×D₉₁	C₂×C₃	semidirect
8. (C₇⋊D₇)⋊D₁₃	C₃²	direct (N × H)
9. C₃×C₇²×C₁₃	C₂²×C₃	semidirect
11. C₃²×D₉₁	D₇	semidirect
15. C₁₃×C₇⋊D₇	C₂×C₃²	semidirect
16. C₇×D₉₁	C₂×C₃²	semidirect
18. C₃²×C₇⋊D₇	D₁₃	semidirect
21. C₃²×C₇×C₁₃	C₂×D₇	semidirect
22. C₇²×C₁₃	C₂²×C₃²	semidirect
24. C₃×D₉₁	C₃×D₇	semidirect
29. C₃²×C₇²	C₂×D₁₃	semidirect
31. C₃×C₇⋊D₇	C₃×D₁₃	semidirect
34. C₃×C₇×C₁₃	C₂×C₃×D₇	semidirect
39. D₉₁	C₃²×D₇	semidirect
44. C₃×C₇²	C₂×C₃×D₁₃	semidirect
49. C₃²×C₁₃	D₇²	semidirect
50. C₇⋊D₇	C₃²×D₁₃	semidirect
53. C₇×C₁₃	C₂×C₃²×D₇	semidirect
58. C₃²×C₇	D₇×D₁₃	semidirect
60. C₇²	C₂×C₃²×D₁₃	semidirect
65. C₃×C₁₃	C₃×D₇²	semidirect
71. C₃×C₇	C₃×D₇×D₁₃	semidirect
78. C₁₃	C₃²×D₇²	semidirect
80. C₃²	(C₇⋊D₇)⋊D₁₃	direct (N × H)
82. C₇	C₃²×D₇×D₁₃	semidirect
86. C₃	C₃×(C₇⋊D₇)⋊D₁₃	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×C₇×D₉₁	2
C₃²×C₁₃×C₇⋊D₇	2
C₃×(C₇⋊D₇)⋊D₁₃	3
C₃²×D₇×D₁₃	7
C₃²×D₇²	13

Subgroups — C32×(C7⋊D7)⋊D13 #37525575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×(C₇⋊D₇)⋊D₁₃ #37525575