Subgroups — C₂⁵×C₂²⋊D₆₇ #31769708

Order 17152.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₂²⋊D₆₇	C₂	1	124	yes	maximal, direct product factor
3	C₂⁵×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁷×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁵×D₆₇	—	2	32	no	—
6	C₂⁵×D₆₇	C₂²	1	62	yes	complemented
7	C₂³×C₂²⋊D₆₇	C₂²	1	2480	yes	direct product factor
8	C₂⁴×Dic₆₇	C₂²	1	62	yes	complemented
9	C₂⁶×C₆₇	—	2	32	no	—
10	C₂⁶×C₆₇	C₂²	1	1	yes	characteristic
11	C₂⁶×C₆₇	C₂²	1	62	yes	complemented
12	C₂⁴×D₆₇	—	2	992	no	—
13	C₂⁴×D₆₇	C₂³	1	620	yes	complemented
14	C₂²×C₂²⋊D₆₇	C₂³	1	9920	yes	direct product factor
15	C₂³×Dic₆₇	C₂³	1	620	yes	complemented
16	C₂⁵×C₆₇	—	2	992	no	—
17	C₂⁵×C₆₇	D₄	1	32	yes	complemented
18	C₂⁵×C₆₇	C₂³	1	31	yes	—
19	C₂⁵×C₆₇	C₂³	1	620	yes	complemented
20	C₂³×D₆₇	—	2	4960	no	—
21	C₂³×D₆₇	C₂⁴	1	1240	yes	complemented
22	C₂×C₂²⋊D₆₇	C₂⁴	1	7936	yes	direct product factor
23	C₂²×Dic₆₇	C₂⁴	1	1240	yes	complemented
24	C₂⁴×C₆₇	—	2	4960	no	—
25	C₂⁴×C₆₇	C₂×D₄	1	496	yes	complemented
26	C₂⁴×C₆₇	C₂⁴	1	155	yes	—
27	C₂⁴×C₆₇	C₂⁴	1	1240	yes	complemented
28	C₂³×C₆₇	—	2	4960	no	—
29	C₂³×C₆₇	C₂²×D₄	1	1240	yes	complemented
30	C₂³×C₆₇	C₂⁵	1	155	yes	—
31	C₂³×C₆₇	C₂⁵	1	496	yes	complemented
32	C₂²×D₆₇	—	2	4960	no	—
33	C₂²×D₆₇	C₂⁵	1	496	yes	complemented
34	C₂²⋊D₆₇	C₂⁵	1	1024	yes	direct product factor
35	C₂×Dic₆₇	C₂⁵	1	496	yes	complemented
36	C₂²×C₆₇	—	2	992	no	—
37	C₂²×C₆₇	C₂³×D₄	1	620	yes	complemented
38	C₂²×C₆₇	C₂⁶	1	31	yes	—
39	C₂²×C₆₇	C₂⁶	1	32	yes	complemented
40	C₂×D₆₇	—	2	992	no	—
41	C₂×D₆₇	C₂⁶	1	32	yes	complemented
42	Dic₆₇	C₂⁶	1	32	yes	complemented
43	C₂⁵×D₄	—	67	1	no	maximal, Sylow
44	C₂×C₆₇	—	2	32	no	—
45	C₂×C₆₇	C₂⁴×D₄	1	62	yes	complemented
46	C₂×C₆₇	C₂⁷	1	1	yes	characteristic
47	D₆₇	—	2	32	no	—
48	C₂⁷	—	67	1	no	—
49	C₂⁷	D₆₇	1	1	yes	characteristic, complemented
50	C₂⁴×D₄	—	67	124	no	—
51	C₂⁵×C₄	—	67	1	no	—
52	C₆₇	C₂⁵×D₄	1	1	yes	characteristic, complemented, Sylow
53	C₂⁶	—	2	32	no	—
54	C₂⁶	—	67	62	no	—
55	C₂⁶	—	134	32	no	—
56	C₂⁶	C₂×D₆₇	1	1	yes	characteristic
57	C₂⁶	C₂×D₆₇	1	62	yes	complemented
58	C₂³×D₄	—	67	2480	no	—
59	C₂⁴×C₄	—	67	62	no	—
60	C₂⁵	—	2	992	no	—
61	C₂⁵	—	67	620	no	—
62	C₂⁵	—	134	992	no	—
63	C₂⁵	C₂²⋊D₆₇	1	32	yes	direct product factor
64	C₂⁵	C₂²×D₆₇	1	31	yes	—
65	C₂⁵	C₂²×D₆₇	1	620	yes	complemented
66	C₂²×D₄	—	67	9920	no	—
67	C₂³×C₄	—	67	620	no	—
68	C₂⁴	—	2	4960	no	—
69	C₂⁴	—	67	1240	no	—
70	C₂⁴	—	134	4960	no	—
71	C₂⁴	C₂×C₂²⋊D₆₇	1	496	yes	direct product factor
72	C₂⁴	C₂³×D₆₇	1	155	yes	—
73	C₂⁴	C₂³×D₆₇	1	1240	yes	complemented
74	C₂×D₄	—	67	7936	no	—
75	C₂²×C₄	—	67	1240	no	—
76	C₂³	—	2	4960	no	—
77	C₂³	—	67	496	no	—
78	C₂³	—	134	4960	no	—
79	C₂³	C₂²×C₂²⋊D₆₇	1	1240	yes	direct product factor
80	C₂³	C₂⁴×D₆₇	1	155	yes	—
81	C₂³	C₂⁴×D₆₇	1	496	yes	complemented
82	D₄	—	67	1024	no	—
83	C₂×C₄	—	67	496	no	—
84	C₂²	—	2	992	no	—
85	C₂²	—	67	32	no	—
86	C₂²	—	134	992	no	—
87	C₂²	C₂³×C₂²⋊D₆₇	1	620	yes	direct product factor
88	C₂²	C₂⁵×D₆₇	1	31	yes	—
89	C₂²	C₂⁵×D₆₇	1	32	yes	complemented
90	C₄	—	67	32	no	—
91	C₂	—	2	32	no	—
92	C₂	—	134	32	no	—
93	C₂	C₂⁴×C₂²⋊D₆₇	1	62	yes	direct product factor
94	C₂	C₂⁶×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁶	C₂×D₆₇
commutator, cosocle	C₂×C₆₇	C₂⁷
Frattini	C₂	C₂⁶×D₆₇
Fitting	C₂⁷×C₆₇	C₂
socle	C₂⁶×C₆₇	C₂²
hypercenter	C₂⁷	D₆₇
hypocenter	C₆₇	C₂⁵×D₄
LCS	G ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂⁶ ◁ C₂⁷

Complements

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

N	H ≅ G/N	type
1. C₂⁶×D₆₇	C₂	semidirect
2. C₂⁴×C₂²⋊D₆₇	C₂	direct (N × H)
3. C₂⁵×Dic₆₇	C₂	semidirect
4. C₂⁷×C₆₇	C₂	semidirect
6. C₂⁵×D₆₇	C₂²	semidirect
7. C₂³×C₂²⋊D₆₇	C₂²	direct (N × H)
8. C₂⁴×Dic₆₇	C₂²	semidirect
11. C₂⁶×C₆₇	C₂²	semidirect
13. C₂⁴×D₆₇	C₂³	semidirect
14. C₂²×C₂²⋊D₆₇	C₂³	direct (N × H)
15. C₂³×Dic₆₇	C₂³	semidirect
17. C₂⁵×C₆₇	D₄	semidirect
19. C₂⁵×C₆₇	C₂³	semidirect
21. C₂³×D₆₇	C₂⁴	semidirect
22. C₂×C₂²⋊D₆₇	C₂⁴	direct (N × H)
23. C₂²×Dic₆₇	C₂⁴	semidirect
25. C₂⁴×C₆₇	C₂×D₄	semidirect
27. C₂⁴×C₆₇	C₂⁴	semidirect
29. C₂³×C₆₇	C₂²×D₄	semidirect
31. C₂³×C₆₇	C₂⁵	semidirect
33. C₂²×D₆₇	C₂⁵	semidirect
34. C₂²⋊D₆₇	C₂⁵	direct (N × H)
35. C₂×Dic₆₇	C₂⁵	semidirect
37. C₂²×C₆₇	C₂³×D₄	semidirect
39. C₂²×C₆₇	C₂⁶	semidirect
41. C₂×D₆₇	C₂⁶	semidirect
42. Dic₆₇	C₂⁶	semidirect
45. C₂×C₆₇	C₂⁴×D₄	semidirect
49. C₂⁷	D₆₇	semidirect
52. C₆₇	C₂⁵×D₄	semidirect
57. C₂⁶	C₂×D₆₇	semidirect
63. C₂⁵	C₂²⋊D₆₇	direct (N × H)
65. C₂⁵	C₂²×D₆₇	semidirect
71. C₂⁴	C₂×C₂²⋊D₆₇	direct (N × H)
73. C₂⁴	C₂³×D₆₇	semidirect
79. C₂³	C₂²×C₂²⋊D₆₇	direct (N × H)
81. C₂³	C₂⁴×D₆₇	semidirect
87. C₂²	C₂³×C₂²⋊D₆₇	direct (N × H)
89. C₂²	C₂⁵×D₆₇	semidirect
93. C₂	C₂⁴×C₂²⋊D₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁶×D₆₇	2
C₂⁴×C₂²⋊D₆₇	2
C₂⁵×Dic₆₇	2
C₂⁷×C₆₇	2
C₂⁵×D₄	67

Subgroups — C25×C22⋊D67 #31769708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₂²⋊D₆₇ #31769708