Subgroups — C₂²×#64604 #11929240

Order 1248.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#64604	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₂²⋊D₁₃	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×D₃₉	—	2	4	no	—
8	C₂²×D₃₉	C₂²	1	6	yes	complemented
9	C₂²×D₃×C₁₃	—	2	4	no	—
10	C₂²×D₃×C₁₃	C₂²	1	6	yes	complemented
11	C₂×C₃×Dic₁₃	C₂²	1	6	yes	complemented
12	#64604	C₂²	1	16	yes	direct product factor
13	C₂⁴×C₁₃	—	3	1	no	—
14	C₂³×D₁₃	—	3	1	no	—
15	C₂×C₂²⋊D₁₃	—	3	12	no	—
16	C₂²×Dic₁₃	D₃	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₁₃	D₄	1	4	yes	complemented
18	C₂²×C₃×C₁₃	C₂³	1	3	yes	—
19	C₂×D₃₉	—	2	12	no	—
20	C₂×D₃₉	C₂³	1	4	yes	complemented
21	C₂×D₃×C₁₃	—	2	12	no	—
22	C₂×D₃×C₁₃	C₂³	1	4	yes	complemented
23	C₃×Dic₁₃	C₂³	1	4	yes	complemented
24	C₂³×C₁₃	—	3	6	no	—
25	C₂³×C₁₃	—	6	4	no	—
26	C₂³×C₁₃	C₂×D₃	1	1	yes	characteristic
27	C₂²×D₁₃	—	3	6	no	—
28	C₂²×D₁₃	—	6	4	no	—
29	C₂²⋊D₁₃	—	3	16	no	—
30	C₂×Dic₁₃	C₂×D₃	1	6	yes	complemented
31	C₂²×D₁₂	—	13	1	no	maximal, Hall
32	C₂×C₃×C₁₃	C₂×D₄	1	6	yes	complemented
33	C₂×C₃×C₁₃	C₂⁴	1	1	yes	characteristic
34	D₃₉	—	2	4	no	—
35	D₃×C₁₃	—	2	4	no	—
36	C₂²×C₁₃	—	3	4	no	—
37	C₂²×C₁₃	—	6	12	no	—
38	C₂²×C₁₃	D₁₂	1	4	yes	complemented
39	C₂²×C₁₃	C₂²×D₃	1	3	yes	—
40	C₂×D₁₃	—	3	4	no	—
41	C₂×D₁₃	—	6	12	no	—
42	Dic₁₃	C₂²×D₃	1	4	yes	complemented
43	C₂³×D₃	—	13	1	no	—
44	C₂³×D₃	D₁₃	1	1	yes	characteristic, complemented
45	C₂²×C₃×C₄	—	13	1	no	—
46	C₂×D₁₂	—	13	12	no	—
47	C₃×C₁₃	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
48	C₂²×D₄	—	39	1	no	Sylow
49	C₂×C₁₃	—	6	4	no	—
50	C₂×C₁₃	C₂×D₁₂	1	6	yes	complemented
51	C₂×C₁₃	C₂³×D₃	1	1	yes	characteristic
52	D₁₃	—	6	4	no	—
53	C₂³×C₃	C₂×D₁₃	1	1	yes	characteristic
54	C₂²×D₃	—	2	4	no	—
55	C₂²×D₃	—	13	6	no	—
56	C₂²×D₃	—	26	4	no	—
57	C₂²×D₃	C₂×D₁₃	1	6	yes	complemented
58	C₂×C₃×C₄	—	13	6	no	—
59	D₁₂	—	13	16	no	—
60	C₂⁴	—	3	1	no	—
61	C₂⁴	—	39	1	no	—
62	C₂×D₄	—	39	12	no	—
63	C₂²×C₄	—	13	1	no	—
64	C₁₃	C₂²×D₁₂	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₃	C₂²⋊D₁₃	1	4	yes	complemented
66	C₂²×C₃	C₂²×D₁₃	1	3	yes	—
67	C₂×D₃	—	2	12	no	—
68	C₂×D₃	—	13	4	no	—
69	C₂×D₃	—	26	12	no	—
70	C₂×D₃	C₂²×D₁₃	1	4	yes	complemented
71	C₃×C₄	—	13	4	no	—
72	C₂³	—	3	6	no	—
73	C₂³	—	6	4	no	—
74	C₂³	—	39	6	no	—
75	C₂³	—	78	4	no	—
76	C₂³	D₃×D₁₃	1	1	yes	characteristic
77	D₄	—	39	16	no	—
78	C₂×C₄	—	13	6	no	—
79	C₂×C₃	C₂×C₂²⋊D₁₃	1	6	yes	complemented
80	C₂×C₃	C₂³×D₁₃	1	1	yes	characteristic
81	D₃	—	2	4	no	—
82	D₃	—	26	4	no	—
83	C₂²	—	3	4	no	—
84	C₂²	—	6	12	no	—
85	C₂²	—	39	4	no	—
86	C₂²	—	78	12	no	—
87	C₂²	#64604	1	4	yes	direct product factor
88	C₂²	C₂×D₃×D₁₃	1	3	yes	—
89	C₄	—	13	4	no	—
90	C₃	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	6	4	no	—
92	C₂	—	78	4	no	—
93	C₂	C₂×#64604	1	6	yes	direct product factor
94	C₂	C₂²×D₃×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³	D₃×D₁₃
commutator, cosocle	C₂×C₃×C₁₃	C₂⁴
Frattini	C₂	C₂²×D₃×D₁₃
Fitting, socle	C₂³×C₃×C₁₃	C₂²
hypocenter	C₃×C₁₃	C₂²×D₄
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. C₂³×D₃₉	C₂	semidirect
2. C₂³×D₃×C₁₃	C₂	semidirect
3. C₂²×C₃×Dic₁₃	C₂	semidirect
4. C₂×#64604	C₂	direct (N × H)
8. C₂²×D₃₉	C₂²	semidirect
10. C₂²×D₃×C₁₃	C₂²	semidirect
11. C₂×C₃×Dic₁₃	C₂²	semidirect
12. #64604	C₂²	direct (N × H)
16. C₂²×Dic₁₃	D₃	semidirect
17. C₂²×C₃×C₁₃	D₄	semidirect
20. C₂×D₃₉	C₂³	semidirect
22. C₂×D₃×C₁₃	C₂³	semidirect
23. C₃×Dic₁₃	C₂³	semidirect
30. C₂×Dic₁₃	C₂×D₃	semidirect
32. C₂×C₃×C₁₃	C₂×D₄	semidirect
38. C₂²×C₁₃	D₁₂	semidirect
42. Dic₁₃	C₂²×D₃	semidirect
44. C₂³×D₃	D₁₃	semidirect
47. C₃×C₁₃	C₂²×D₄	semidirect
50. C₂×C₁₃	C₂×D₁₂	semidirect
57. C₂²×D₃	C₂×D₁₃	semidirect
64. C₁₃	C₂²×D₁₂	semidirect
65. C₂²×C₃	C₂²⋊D₁₃	semidirect
70. C₂×D₃	C₂²×D₁₃	semidirect
79. C₂×C₃	C₂×C₂²⋊D₁₃	semidirect
87. C₂²	#64604	direct (N × H)
90. C₃	C₂²×C₂²⋊D₁₃	semidirect
93. C₂	C₂×#64604	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₃₉	2
C₂³×D₃×C₁₃	2
C₂²×C₃×Dic₁₃	2
C₂×#64604	2
C₂²×C₂²⋊D₁₃	3
C₂²×D₁₂	13

Subgroups — C22×#64604 #11929240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#64604 #11929240