Subgroups — D₇²×#4294 #45691591

Order 33516.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊D₇×#4294	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₇×#4294	C₂	1	2	yes	maximal, complemented
3	C₃×D₇²×C₁₉	C₃	1	1	yes	maximal, characteristic
4	C₇²×#4294	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
6	C₃×C₇×D₇×C₁₉	C₂×C₃	1	2	yes	—
7	C₂×D₇×#4294	—	7	2	no	maximal
8	D₇²×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic
10	C₂×C₇×#4294	—	7	2	no	—
11	D₇×#4294	—	7	2	no	—
12	D₇×#4294	—	14	3	no	—
13	D₇×#4294	D₇	1	2	yes	direct product factor
14	C₁₉×C₇⋊D₇	C₂×C₉	1	1	yes	characteristic, complemented
15	C₇×D₇×C₁₉	C₂×C₉	1	2	yes	complemented
16	C₉×D₇²	—	19	1	no	maximal, Hall
17	C₂×C₃×D₇×C₁₉	—	7	2	no	—
18	C₇×#4294	—	2	3	no	—
19	C₇×#4294	C₂×D₇	1	2	yes	complemented
20	C₇²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
21	C₉×C₇⋊D₇	—	19	1	no	—
22	C₇×C₉×D₇	—	19	2	no	—
23	C₂×C₃×C₇×C₁₉	—	7	2	no	—
24	C₃×D₇×C₁₉	—	7	2	no	—
25	C₃×D₇×C₁₉	—	14	3	no	—
26	C₃×D₇×C₁₉	C₃×D₇	1	2	yes	—
27	C₂²×#4294	—	49	1	no	Hall
28	C₃×D₇²	C₁₉⋊C₃	1	1	yes	characteristic
29	C₂×D₇×C₁₉	—	7	2	no	—
30	C₇²×C₉	—	19	1	no	Hall
31	C₃×C₇×C₁₉	—	2	3	no	—
32	C₃×C₇×C₁₉	C₂×C₃×D₇	1	2	yes	—
33	C₂×#4294	—	7	2	no	—
34	C₂×#4294	—	49	1	no	—
35	C₃×C₇⋊D₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic
36	C₃×C₇×D₇	C₂×C₁₉⋊C₃	1	2	yes	—
37	C₂×C₇×C₁₉	—	7	2	no	—
38	D₇×C₁₉	—	7	2	no	—
39	D₇×C₁₉	—	14	3	no	—
40	D₇×C₁₉	C₉×D₇	1	2	yes	complemented
41	C₂×C₉×D₇	—	133	2	no	—
42	C₂²×C₃×C₁₉	—	49	1	no	—
43	D₇²	#4294	1	1	yes	characteristic, direct product factor, Hall
44	#4294	D₇²	1	1	yes	characteristic, direct product factor, Hall
45	C₃×C₇²	C₂²×C₁₉⋊C₃	1	1	yes	characteristic
46	C₇×C₁₉	—	2	3	no	—
47	C₇×C₁₉	C₂×C₉×D₇	1	2	yes	complemented
48	C₂×C₇×C₉	—	133	2	no	—
49	C₉×D₇	—	266	3	no	—
50	C₉×D₇	—	19	2	no	—
51	C₉×D₇	—	133	2	no	—
52	C₂×C₃×C₁₉	—	7	2	no	—
53	C₂×C₃×C₁₉	—	49	1	no	—
54	C₇⋊D₇	C₂×#4294	1	1	yes	characteristic, complemented
55	C₇×D₇	C₂×#4294	1	2	yes	complemented
56	C₂×C₃×D₇	—	7	2	no	—
57	C₂²×C₁₉	—	49	1	no	Hall
58	C₇×C₉	—	19	2	no	—
59	C₇×C₉	—	38	3	no	—
60	C₃×C₁₉	C₃×D₇²	1	1	yes	characteristic
61	C₇²	C₂²×#4294	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₃×C₇	—	7	2	no	—
63	C₃×D₇	—	7	2	no	—
64	C₃×D₇	—	14	3	no	—
65	C₃×D₇	D₇×C₁₉⋊C₃	1	2	yes	—
66	C₂×C₁₉	—	7	2	no	—
67	C₂×C₁₉	—	49	1	no	—
68	C₂²×C₉	—	931	1	no	Hall
69	C₂×D₇	—	7	2	no	—
70	C₃×C₇	—	2	3	no	—
71	C₃×C₇	C₂×D₇×C₁₉⋊C₃	1	2	yes	—
72	C₁₉	C₉×D₇²	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₉	—	133	2	no	—
74	C₂×C₉	—	931	1	no	—
75	C₂×C₇	—	7	2	no	—
76	D₇	—	7	2	no	—
77	D₇	—	14	3	no	—
78	D₇	D₇×#4294	1	2	yes	direct product factor
79	C₂²×C₃	—	49	1	no	—
80	C₉	—	19	1	no	Sylow
81	C₇	—	2	3	no	—
82	C₇	C₂×D₇×#4294	1	2	yes	complemented
83	C₂×C₃	—	7	2	no	—
84	C₂×C₃	—	49	1	no	—
85	C₂²	—	49	1	no	Sylow
86	C₃	D₇²×C₁₉⋊C₃	1	1	yes	characteristic
87	C₂	—	7	2	no	—
88	C₂	—	49	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₇²×C₁₉⋊C₃
commutator, hypocenter	C₇²×C₁₉	C₂²×C₉
Fitting, socle, cosocle	C₃×C₇²×C₁₉	C₂²×C₃
prime radical	C₃×D₇²×C₁₉	C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₇⋊D₇×#4294	C₂	semidirect
2. C₇×D₇×#4294	C₂	semidirect
4. C₇²×#4294	C₂²	semidirect
8. D₇²×C₁₉	C₉	semidirect
13. D₇×#4294	D₇	direct (N × H)
14. C₁₉×C₇⋊D₇	C₂×C₉	semidirect
15. C₇×D₇×C₁₉	C₂×C₉	semidirect
19. C₇×#4294	C₂×D₇	semidirect
20. C₇²×C₁₉	C₂²×C₉	semidirect
40. D₇×C₁₉	C₉×D₇	semidirect
43. D₇²	#4294	direct (N × H)
44. #4294	D₇²	direct (N × H)
47. C₇×C₁₉	C₂×C₉×D₇	semidirect
54. C₇⋊D₇	C₂×#4294	semidirect
55. C₇×D₇	C₂×#4294	semidirect
61. C₇²	C₂²×#4294	semidirect
72. C₁₉	C₉×D₇²	semidirect
78. D₇	D₇×#4294	direct (N × H)
82. C₇	C₂×D₇×#4294	semidirect

Maximal subgroups

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

subgroup	index
C₇⋊D₇×#4294	2
C₇×D₇×#4294	2
C₃×D₇²×C₁₉	3
C₂×D₇×#4294	7
C₉×D₇²	19

Subgroups — D72×#4294 #45691591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇²×#4294 #45691591