Subgroups — C₇⋊D₇×C₃⋊D₃₉ #37525647

Order 22932.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇²×C₃⋊D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₃⋊(C₇⋊D₉₁))	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₉×C₇⋊D₇	—	3	4	no	maximal
5	C₃²×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃⋊(C₇⋊D₉₁)	—	3	4	no	—
7	C₇²×D₃₉	—	3	4	no	—
8	C₃×C₁₃×C₇⋊D₇	D₃	1	4	yes	complemented
9	D₇×C₃⋊D₃₉	—	7	8	no	maximal
10	D₁₃×C₇⋊D₇	—	9	1	no	Hall
11	C₃×C₇²×C₁₃	C₂×D₃	1	4	yes	complemented
12	C₃⋊D₃×C₇⋊D₇	—	13	1	no	maximal, Hall
13	C₃⋊D₂₇₃	—	7	8	no	—
14	C₇×C₃⋊D₃₉	D₇	1	8	yes	complemented
15	C₃²×C₁₃×D₇	—	7	8	no	—
16	C₇⋊D₉₁	—	9	1	no	—
17	C₁₃×C₇⋊D₇	C₃⋊D₃	1	1	yes	characteristic, complemented
18	C₇²×D₁₃	—	9	1	no	—
19	D₇×D₃₉	—	21	32	no	—
20	C₃⋊(C₃⋊(C₇⋊D₇))	—	13	1	no	—
21	C₇²×C₃⋊D₃	—	13	1	no	—
22	C₃²×C₇⋊D₇	D₁₃	1	1	yes	characteristic, complemented
23	C₃²×C₇×C₁₃	C₂×D₇	1	8	yes	complemented
24	C₇²×C₁₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
25	D₃×C₇⋊D₇	—	39	4	no	—
26	D₂₇₃	—	21	32	no	—
27	C₇×D₃₉	—	3	32	no	—
28	C₃×C₁₃×D₇	—	7	32	no	—
29	C₂×C₃⋊D₃₉	—	49	1	no	Hall
30	C₃²×C₇²	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
31	D₇×D₁₃	—	63	8	no	—
32	C₃⋊(C₇⋊D₇)	—	39	4	no	—
33	D₃×C₇²	—	39	4	no	—
34	C₃×C₇⋊D₇	D₃₉	1	4	yes	complemented
35	C₃×C₇×C₁₃	D₃×D₇	1	32	yes	complemented
36	D₇×C₃⋊D₃	—	91	8	no	—
37	C₂×C₃²×C₁₃	—	49	1	no	—
38	C₃⋊D₃₉	—	49	1	no	—
39	C₃⋊D₃₉	C₇⋊D₇	1	1	yes	characteristic, direct product factor
40	C₂×C₇⋊D₇	—	117	1	no	Hall
41	D₉₁	—	63	8	no	—
42	C₇×D₁₃	—	9	8	no	—
43	C₁₃×D₇	—	7	8	no	—
44	C₂×D₃₉	—	147	4	no	—
45	C₃×C₇²	C₂×D₃₉	1	4	yes	complemented
46	C₃⋊D₂₁	—	91	8	no	—
47	C₇×C₃⋊D₃	—	13	8	no	—
48	C₃²×D₇	—	7	8	no	—
49	C₃²×C₁₃	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
50	C₂×C₇²	—	117	1	no	—
51	C₇⋊D₇	—	117	1	no	—
52	C₇⋊D₇	C₃⋊D₃₉	1	1	yes	characteristic, direct product factor
53	C₇×C₁₃	D₇×C₃⋊D₃	1	8	yes	complemented
54	D₃×D₇	—	273	32	no	—
55	C₂×C₃×C₁₃	—	49	4	no	—
56	D₃₉	—	3	4	no	—
57	D₃₉	—	147	4	no	—
58	C₃²×C₇	D₇×D₁₃	1	8	yes	complemented
59	C₂×D₁₃	—	441	1	no	Hall
60	C₇²	C₂×C₃⋊D₃₉	1	1	yes	characteristic, complemented, Sylow
61	D₂₁	—	273	32	no	—
62	C₃×D₇	—	7	32	no	—
63	D₃×C₇	—	39	32	no	—
64	C₃×C₁₃	D₃×C₇⋊D₇	1	4	yes	complemented
65	C₂×C₃⋊D₃	—	637	1	no	Hall
66	C₂×D₇	—	819	8	no	—
67	C₂×C₁₃	—	49	1	no	—
68	D₁₃	—	9	1	no	—
69	D₁₃	—	441	1	no	—
70	C₃×C₇	D₇×D₃₉	1	32	yes	complemented
71	C₂×C₃²	—	49	1	no	—
72	C₃⋊D₃	—	13	1	no	—
73	C₃⋊D₃	—	637	1	no	—
74	C₂×C₇	—	117	8	no	—
75	D₇	—	7	8	no	—
76	D₇	—	819	8	no	—
77	C₁₃	C₃⋊D₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
78	C₂×D₃	—	1911	4	no	—
79	C₃²	D₁₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
80	C₇	D₇×C₃⋊D₃₉	1	8	yes	complemented
81	C₂×C₃	—	49	4	no	—
82	D₃	—	39	4	no	—
83	D₃	—	1911	4	no	—
84	C₂²	—	5733	1	no	Sylow
85	C₃	D₃₉×C₇⋊D₇	1	4	yes	complemented
86	C₂	—	49	1	no	—
87	C₂	—	5733	1	no	—
88	C₂	—	117	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇²×C₁₃	C₂²
LCS	G ▷ C₃²×C₇²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×C₇⋊D₇	C₂	semidirect
2. C₇²×C₃⋊D₃₉	C₂	semidirect
3. C₃⋊(C₃⋊(C₇⋊D₉₁))	C₂	semidirect
5. C₃²×C₇²×C₁₃	C₂²	semidirect
8. C₃×C₁₃×C₇⋊D₇	D₃	semidirect
11. C₃×C₇²×C₁₃	C₂×D₃	semidirect
14. C₇×C₃⋊D₃₉	D₇	semidirect
17. C₁₃×C₇⋊D₇	C₃⋊D₃	semidirect
22. C₃²×C₇⋊D₇	D₁₃	semidirect
23. C₃²×C₇×C₁₃	C₂×D₇	semidirect
24. C₇²×C₁₃	C₂×C₃⋊D₃	semidirect
30. C₃²×C₇²	C₂×D₁₃	semidirect
34. C₃×C₇⋊D₇	D₃₉	semidirect
35. C₃×C₇×C₁₃	D₃×D₇	semidirect
39. C₃⋊D₃₉	C₇⋊D₇	direct (N × H)
45. C₃×C₇²	C₂×D₃₉	semidirect
49. C₃²×C₁₃	C₂×C₇⋊D₇	semidirect
52. C₇⋊D₇	C₃⋊D₃₉	direct (N × H)
53. C₇×C₁₃	D₇×C₃⋊D₃	semidirect
58. C₃²×C₇	D₇×D₁₃	semidirect
60. C₇²	C₂×C₃⋊D₃₉	semidirect
64. C₃×C₁₃	D₃×C₇⋊D₇	semidirect
70. C₃×C₇	D₇×D₃₉	semidirect
77. C₁₃	C₃⋊D₃×C₇⋊D₇	semidirect
79. C₃²	D₁₃×C₇⋊D₇	semidirect
80. C₇	D₇×C₃⋊D₃₉	semidirect
85. C₃	D₃₉×C₇⋊D₇	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₃×C₇⋊D₇	2
C₇²×C₃⋊D₃₉	2
C₃⋊(C₃⋊(C₇⋊D₉₁))	2
D₃₉×C₇⋊D₇	3
D₇×C₃⋊D₃₉	7
C₃⋊D₃×C₇⋊D₇	13

Subgroups — C7⋊D7×C3⋊D39 #37525647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊D₇×C₃⋊D₃₉ #37525647