Subgroups — C₂⁵×C₂²⋊D₇ #14267673

Order 1792.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁷×C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁶×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂⁴×C₂²⋊D₇	C₂	1	124	yes	maximal, direct product factor
4	C₂⁵×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁶×C₇	—	2	32	no	—
6	C₂⁶×C₇	C₂²	1	1	yes	characteristic
7	C₂⁶×C₇	C₂²	1	62	yes	complemented
8	C₂⁵×D₇	—	2	32	no	—
9	C₂⁵×D₇	C₂²	1	62	yes	complemented
10	C₂³×C₂²⋊D₇	C₂²	1	2480	yes	direct product factor
11	C₂⁴×Dic₇	C₂²	1	62	yes	complemented
12	C₂⁵×D₄	—	7	1	no	maximal, Sylow
13	C₂⁵×C₇	—	2	992	no	—
14	C₂⁵×C₇	D₄	1	32	yes	complemented
15	C₂⁵×C₇	C₂³	1	31	yes	—
16	C₂⁵×C₇	C₂³	1	620	yes	complemented
17	C₂⁴×D₇	—	2	992	no	—
18	C₂⁴×D₇	C₂³	1	620	yes	complemented
19	C₂²×C₂²⋊D₇	C₂³	1	9920	yes	direct product factor
20	C₂³×Dic₇	C₂³	1	620	yes	complemented
21	C₂⁷	—	7	1	no	—
22	C₂⁷	D₇	1	1	yes	characteristic, complemented
23	C₂⁴×D₄	—	7	124	no	—
24	C₂⁵×C₄	—	7	1	no	—
25	C₂⁴×C₇	—	2	4960	no	—
26	C₂⁴×C₇	C₂×D₄	1	496	yes	complemented
27	C₂⁴×C₇	C₂⁴	1	155	yes	—
28	C₂⁴×C₇	C₂⁴	1	1240	yes	complemented
29	C₂³×D₇	—	2	4960	no	—
30	C₂³×D₇	C₂⁴	1	1240	yes	complemented
31	C₂×C₂²⋊D₇	C₂⁴	1	7936	yes	direct product factor
32	C₂²×Dic₇	C₂⁴	1	1240	yes	complemented
33	C₂⁶	—	2	32	no	—
34	C₂⁶	—	7	62	no	—
35	C₂⁶	—	14	32	no	—
36	C₂⁶	C₂×D₇	1	1	yes	characteristic
37	C₂⁶	C₂×D₇	1	62	yes	complemented
38	C₂³×D₄	—	7	2480	no	—
39	C₂⁴×C₄	—	7	62	no	—
40	C₂³×C₇	—	2	4960	no	—
41	C₂³×C₇	C₂²×D₄	1	1240	yes	complemented
42	C₂³×C₇	C₂⁵	1	155	yes	—
43	C₂³×C₇	C₂⁵	1	496	yes	complemented
44	C₂²×D₇	—	2	4960	no	—
45	C₂²×D₇	C₂⁵	1	496	yes	complemented
46	C₂²⋊D₇	C₂⁵	1	1024	yes	direct product factor
47	C₂×Dic₇	C₂⁵	1	496	yes	complemented
48	C₂⁵	—	2	992	no	—
49	C₂⁵	—	7	620	no	—
50	C₂⁵	—	14	992	no	—
51	C₂⁵	C₂²⋊D₇	1	32	yes	direct product factor
52	C₂⁵	C₂²×D₇	1	31	yes	—
53	C₂⁵	C₂²×D₇	1	620	yes	complemented
54	C₂²×D₄	—	7	9920	no	—
55	C₂³×C₄	—	7	620	no	—
56	C₂²×C₇	—	2	992	no	—
57	C₂²×C₇	C₂³×D₄	1	620	yes	complemented
58	C₂²×C₇	C₂⁶	1	31	yes	—
59	C₂²×C₇	C₂⁶	1	32	yes	complemented
60	C₂×D₇	—	2	992	no	—
61	C₂×D₇	C₂⁶	1	32	yes	complemented
62	Dic₇	C₂⁶	1	32	yes	complemented
63	C₂⁴	—	2	4960	no	—
64	C₂⁴	—	7	1240	no	—
65	C₂⁴	—	14	4960	no	—
66	C₂⁴	C₂×C₂²⋊D₇	1	496	yes	direct product factor
67	C₂⁴	C₂³×D₇	1	155	yes	—
68	C₂⁴	C₂³×D₇	1	1240	yes	complemented
69	C₂×D₄	—	7	7936	no	—
70	C₂²×C₄	—	7	1240	no	—
71	C₂×C₇	—	2	32	no	—
72	C₂×C₇	C₂⁴×D₄	1	62	yes	complemented
73	C₂×C₇	C₂⁷	1	1	yes	characteristic
74	D₇	—	2	32	no	—
75	C₂³	—	2	4960	no	—
76	C₂³	—	7	496	no	—
77	C₂³	—	14	4960	no	—
78	C₂³	C₂²×C₂²⋊D₇	1	1240	yes	direct product factor
79	C₂³	C₂⁴×D₇	1	155	yes	—
80	C₂³	C₂⁴×D₇	1	496	yes	complemented
81	D₄	—	7	1024	no	—
82	C₂×C₄	—	7	496	no	—
83	C₇	C₂⁵×D₄	1	1	yes	characteristic, complemented, Sylow
84	C₂²	—	2	992	no	—
85	C₂²	—	7	32	no	—
86	C₂²	—	14	992	no	—
87	C₂²	C₂³×C₂²⋊D₇	1	620	yes	direct product factor
88	C₂²	C₂⁵×D₇	1	31	yes	—
89	C₂²	C₂⁵×D₇	1	32	yes	complemented
90	C₄	—	7	32	no	—
91	C₂	—	2	32	no	—
92	C₂	—	14	32	no	—
93	C₂	C₂⁴×C₂²⋊D₇	1	62	yes	direct product factor
94	C₂	C₂⁶×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁶	C₂×D₇
commutator, cosocle	C₂×C₇	C₂⁷
Frattini	C₂	C₂⁶×D₇
Fitting	C₂⁷×C₇	C₂
socle	C₂⁶×C₇	C₂²
hypercenter	C₂⁷	D₇
hypocenter	C₇	C₂⁵×D₄
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂⁶ ◁ C₂⁷

Complements

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

N	H ≅ G/N	type
1. C₂⁷×C₇	C₂	semidirect
2. C₂⁶×D₇	C₂	semidirect
3. C₂⁴×C₂²⋊D₇	C₂	direct (N × H)
4. C₂⁵×Dic₇	C₂	semidirect
7. C₂⁶×C₇	C₂²	semidirect
9. C₂⁵×D₇	C₂²	semidirect
10. C₂³×C₂²⋊D₇	C₂²	direct (N × H)
11. C₂⁴×Dic₇	C₂²	semidirect
14. C₂⁵×C₇	D₄	semidirect
16. C₂⁵×C₇	C₂³	semidirect
18. C₂⁴×D₇	C₂³	semidirect
19. C₂²×C₂²⋊D₇	C₂³	direct (N × H)
20. C₂³×Dic₇	C₂³	semidirect
22. C₂⁷	D₇	semidirect
26. C₂⁴×C₇	C₂×D₄	semidirect
28. C₂⁴×C₇	C₂⁴	semidirect
30. C₂³×D₇	C₂⁴	semidirect
31. C₂×C₂²⋊D₇	C₂⁴	direct (N × H)
32. C₂²×Dic₇	C₂⁴	semidirect
37. C₂⁶	C₂×D₇	semidirect
41. C₂³×C₇	C₂²×D₄	semidirect
43. C₂³×C₇	C₂⁵	semidirect
45. C₂²×D₇	C₂⁵	semidirect
46. C₂²⋊D₇	C₂⁵	direct (N × H)
47. C₂×Dic₇	C₂⁵	semidirect
51. C₂⁵	C₂²⋊D₇	direct (N × H)
53. C₂⁵	C₂²×D₇	semidirect
57. C₂²×C₇	C₂³×D₄	semidirect
59. C₂²×C₇	C₂⁶	semidirect
61. C₂×D₇	C₂⁶	semidirect
62. Dic₇	C₂⁶	semidirect
66. C₂⁴	C₂×C₂²⋊D₇	direct (N × H)
68. C₂⁴	C₂³×D₇	semidirect
72. C₂×C₇	C₂⁴×D₄	semidirect
78. C₂³	C₂²×C₂²⋊D₇	direct (N × H)
80. C₂³	C₂⁴×D₇	semidirect
83. C₇	C₂⁵×D₄	semidirect
87. C₂²	C₂³×C₂²⋊D₇	direct (N × H)
89. C₂²	C₂⁵×D₇	semidirect
93. C₂	C₂⁴×C₂²⋊D₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁷×C₇	2
C₂⁶×D₇	2
C₂⁴×C₂²⋊D₇	2
C₂⁵×Dic₇	2
C₂⁵×D₄	7

Subgroups — C25×C22⋊D7 #14267673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₂²⋊D₇ #14267673