Subgroups — C₂²×#64625 #11929314

Order 1248.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#64625	C₂	1	12	yes	maximal, direct product factor
4	C₂²×Dic₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂²⋊D₁₃	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₁₃	—	2	4	no	—
7	C₂³×C₃×C₁₃	C₂²	1	1	yes	characteristic
8	C₂³×C₃×C₁₃	C₂²	1	6	yes	complemented
9	C₂²×D₃₉	—	2	4	no	—
10	C₂²×D₃₉	C₂²	1	6	yes	complemented
11	#64625	C₂²	1	16	yes	direct product factor
12	C₂×Dic₃₉	C₂²	1	6	yes	complemented
13	C₂⁴×C₁₃	D₃	1	1	yes	characteristic, complemented
14	C₂³×D₁₃	—	3	1	no	—
15	C₂×C₂²⋊D₁₃	—	3	12	no	—
16	C₂²×Dic₁₃	—	3	1	no	—
17	C₂²×C₃×C₁₃	—	2	12	no	—
18	C₂²×C₃×C₁₃	D₄	1	4	yes	complemented
19	C₂²×C₃×C₁₃	C₂³	1	3	yes	—
20	C₂²×C₃×C₁₃	C₂³	1	4	yes	complemented
21	C₂×D₃₉	—	2	12	no	—
22	C₂×D₃₉	C₂³	1	4	yes	complemented
23	Dic₃₉	C₂³	1	4	yes	complemented
24	C₂³×C₁₃	—	2	4	no	—
25	C₂³×C₁₃	C₂×D₃	1	1	yes	characteristic
26	C₂³×C₁₃	C₂×D₃	1	6	yes	complemented
27	C₂²×D₁₃	—	3	6	no	—
28	C₂²×D₁₃	—	6	4	no	—
29	C₂²⋊D₁₃	—	3	16	no	—
30	C₂×Dic₁₃	—	3	6	no	—
31	C₂²×#67	—	13	1	no	maximal, Hall
32	C₂×C₃×C₁₃	—	2	4	no	—
33	C₂×C₃×C₁₃	C₂×D₄	1	6	yes	complemented
34	C₂×C₃×C₁₃	C₂⁴	1	1	yes	characteristic
35	D₃₉	—	2	4	no	—
36	C₂²×C₁₃	—	2	12	no	—
37	C₂²×C₁₃	#67	1	4	yes	complemented
38	C₂²×C₁₃	C₂²×D₃	1	3	yes	—
39	C₂²×C₁₃	C₂²×D₃	1	4	yes	complemented
40	C₂×D₁₃	—	3	4	no	—
41	C₂×D₁₃	—	6	12	no	—
42	Dic₁₃	—	3	4	no	—
43	C₂⁴×C₃	D₁₃	1	1	yes	characteristic, complemented
44	C₂³×D₃	—	13	1	no	—
45	C₂×#67	—	13	12	no	—
46	C₂²×Dic₃	—	13	1	no	—
47	C₃×C₁₃	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
48	C₂²×D₄	—	39	1	no	Sylow
49	C₂×C₁₃	—	2	4	no	—
50	C₂×C₁₃	C₂×#67	1	6	yes	complemented
51	C₂×C₁₃	C₂³×D₃	1	1	yes	characteristic
52	D₁₃	—	6	4	no	—
53	C₂³×C₃	—	2	4	no	—
54	C₂³×C₃	C₂×D₁₃	1	1	yes	characteristic
55	C₂³×C₃	C₂×D₁₃	1	6	yes	complemented
56	C₂²×D₃	—	13	6	no	—
57	C₂²×D₃	—	26	4	no	—
58	#67	—	13	16	no	—
59	C₂×Dic₃	—	13	6	no	—
60	C₂⁴	—	39	1	no	—
61	C₂⁴	D₃₉	1	1	yes	characteristic, complemented
62	C₂×D₄	—	39	12	no	—
63	C₂²×C₄	—	39	1	no	—
64	C₁₃	C₂²×#67	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₃	—	2	12	no	—
66	C₂²×C₃	C₂²⋊D₁₃	1	4	yes	complemented
67	C₂²×C₃	C₂²×D₁₃	1	3	yes	—
68	C₂²×C₃	C₂²×D₁₃	1	4	yes	complemented
69	C₂×D₃	—	13	4	no	—
70	C₂×D₃	—	26	12	no	—
71	Dic₃	—	13	4	no	—
72	C₂³	—	2	4	no	—
73	C₂³	—	39	6	no	—
74	C₂³	—	78	4	no	—
75	C₂³	C₂×D₃₉	1	1	yes	characteristic
76	C₂³	C₂×D₃₉	1	6	yes	complemented
77	D₄	—	39	16	no	—
78	C₂×C₄	—	39	6	no	—
79	C₂×C₃	—	2	4	no	—
80	C₂×C₃	C₂×C₂²⋊D₁₃	1	6	yes	complemented
81	C₂×C₃	C₂³×D₁₃	1	1	yes	characteristic
82	D₃	—	26	4	no	—
83	C₂²	—	2	12	no	—
84	C₂²	—	39	4	no	—
85	C₂²	—	78	12	no	—
86	C₂²	#64625	1	4	yes	direct product factor
87	C₂²	C₂²×D₃₉	1	3	yes	—
88	C₂²	C₂²×D₃₉	1	4	yes	complemented
89	C₄	—	39	4	no	—
90	C₃	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	2	4	no	—
92	C₂	—	78	4	no	—
93	C₂	C₂×#64625	1	6	yes	direct product factor
94	C₂	C₂³×D₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₃₉
commutator, cosocle	C₂×C₃×C₁₃	C₂⁴
Frattini	C₂	C₂³×D₃₉
Fitting	C₂⁴×C₃×C₁₃	C₂
socle	C₂³×C₃×C₁₃	C₂²
hypercenter	C₂⁴	D₃₉
hypocenter	C₃×C₁₃	C₂²×D₄
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×C₁₃	C₂	semidirect
2. C₂³×D₃₉	C₂	semidirect
3. C₂×#64625	C₂	direct (N × H)
4. C₂²×Dic₃₉	C₂	semidirect
8. C₂³×C₃×C₁₃	C₂²	semidirect
10. C₂²×D₃₉	C₂²	semidirect
11. #64625	C₂²	direct (N × H)
12. C₂×Dic₃₉	C₂²	semidirect
13. C₂⁴×C₁₃	D₃	semidirect
18. C₂²×C₃×C₁₃	D₄	semidirect
20. C₂²×C₃×C₁₃	C₂³	semidirect
22. C₂×D₃₉	C₂³	semidirect
23. Dic₃₉	C₂³	semidirect
26. C₂³×C₁₃	C₂×D₃	semidirect
33. C₂×C₃×C₁₃	C₂×D₄	semidirect
37. C₂²×C₁₃	#67	semidirect
39. C₂²×C₁₃	C₂²×D₃	semidirect
43. C₂⁴×C₃	D₁₃	semidirect
47. C₃×C₁₃	C₂²×D₄	semidirect
50. C₂×C₁₃	C₂×#67	semidirect
55. C₂³×C₃	C₂×D₁₃	semidirect
61. C₂⁴	D₃₉	semidirect
64. C₁₃	C₂²×#67	semidirect
66. C₂²×C₃	C₂²⋊D₁₃	semidirect
68. C₂²×C₃	C₂²×D₁₃	semidirect
76. C₂³	C₂×D₃₉	semidirect
80. C₂×C₃	C₂×C₂²⋊D₁₃	semidirect
86. C₂²	#64625	direct (N × H)
88. C₂²	C₂²×D₃₉	semidirect
90. C₃	C₂²×C₂²⋊D₁₃	semidirect
93. C₂	C₂×#64625	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₁₃	2
C₂³×D₃₉	2
C₂×#64625	2
C₂²×Dic₃₉	2
C₂²×C₂²⋊D₁₃	3
C₂²×#67	13

Subgroups — C22×#64625 #11929314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#64625 #11929314