Subgroups — C₂²×#64605 #11929241

Order 1248.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#64605	C₂	1	12	yes	maximal, direct product factor
5	C₂²×Dic₂₆	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×Dic₃₉	C₂²	1	6	yes	—
8	C₂×Dic₃×C₁₃	C₂²	1	6	yes	—
9	C₂×C₃×Dic₁₃	C₂²	1	6	yes	—
10	#64605	C₂²	1	16	yes	direct product factor
11	C₂²×C₄×C₁₃	—	3	1	no	—
12	C₂²×Dic₁₃	—	3	1	no	—
13	C₂²×Dic₁₃	D₃	1	1	yes	characteristic
14	C₂×Dic₂₆	—	3	12	no	—
15	C₂²×C₃×C₁₃	Q₈	1	4	yes	complemented
16	C₂²×C₃×C₁₃	C₂³	1	3	yes	—
17	Dic₃₉	C₂³	1	4	yes	—
18	C₃×Dic₁₃	C₂³	1	4	yes	—
19	Dic₃×C₁₃	C₂³	1	4	yes	—
20	C₂³×C₁₃	C₂×D₃	1	1	yes	characteristic
21	C₂×C₄×C₁₃	—	3	6	no	—
22	C₂×Dic₁₃	—	3	6	no	—
23	C₂×Dic₁₃	C₂×D₃	1	6	yes	—
24	Dic₂₆	—	3	16	no	—
25	C₂²×Dic₆	—	13	1	no	maximal, Hall
26	C₂×C₃×C₁₃	C₂×Q₈	1	6	yes	complemented
27	C₂×C₃×C₁₃	C₂⁴	1	1	yes	characteristic
28	C₂²×C₁₃	Dic₆	1	4	yes	complemented
29	C₂²×C₁₃	C₂²×D₃	1	3	yes	—
30	C₄×C₁₃	—	3	4	no	—
31	Dic₁₃	—	3	4	no	—
32	Dic₁₃	C₂²×D₃	1	4	yes	—
33	C₂²×C₃×C₄	—	13	1	no	—
34	C₂²×Dic₃	—	13	1	no	—
35	C₂²×Dic₃	D₁₃	1	1	yes	characteristic
36	C₂×Dic₆	—	13	12	no	—
37	C₃×C₁₃	C₂²×Q₈	1	1	yes	characteristic, complemented, Hall
38	C₂²×Q₈	—	39	1	no	Sylow
39	C₂×C₁₃	C₂×Dic₆	1	6	yes	complemented
40	C₂×C₁₃	C₂³×D₃	1	1	yes	characteristic
41	C₂³×C₃	C₂×D₁₃	1	1	yes	characteristic
42	C₂×C₃×C₄	—	13	6	no	—
43	C₂×Dic₃	—	13	6	no	—
44	C₂×Dic₃	C₂×D₁₃	1	6	yes	—
45	Dic₆	—	13	16	no	—
46	C₂×Q₈	—	39	12	no	—
47	C₂²×C₄	—	3	1	no	—
48	C₂²×C₄	—	13	1	no	—
49	C₂²×C₄	—	39	1	no	—
50	C₁₃	C₂²×Dic₆	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₃	Dic₂₆	1	4	yes	complemented
52	C₂²×C₃	C₂²×D₁₃	1	3	yes	—
53	C₃×C₄	—	13	4	no	—
54	Dic₃	—	13	4	no	—
55	Dic₃	C₂²×D₁₃	1	4	yes	—
56	C₂³	D₃×D₁₃	1	1	yes	characteristic
57	Q₈	—	39	16	no	—
58	C₂×C₄	—	3	6	no	—
59	C₂×C₄	—	13	6	no	—
60	C₂×C₄	—	39	6	no	—
61	C₂×C₃	C₂×Dic₂₆	1	6	yes	complemented
62	C₂×C₃	C₂³×D₁₃	1	1	yes	characteristic
63	C₂²	#64605	1	4	yes	direct product factor
64	C₂²	C₂×D₃×D₁₃	1	3	yes	—
65	C₄	—	3	4	no	—
66	C₄	—	13	4	no	—
67	C₄	—	39	4	no	—
68	C₃	C₂²×Dic₂₆	1	1	yes	characteristic, complemented, Sylow
69	C₂	C₂×#64605	1	6	yes	direct product factor
70	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, prime radical	C₂³×C₃×C₁₃	C₂²
hypocenter	C₃×C₁₃	C₂²×Q₈
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
4. C₂×#64605	C₂	direct (N × H)
10. #64605	C₂²	direct (N × H)
15. C₂²×C₃×C₁₃	Q₈	semidirect
26. C₂×C₃×C₁₃	C₂×Q₈	semidirect
28. C₂²×C₁₃	Dic₆	semidirect
37. C₃×C₁₃	C₂²×Q₈	semidirect
39. C₂×C₁₃	C₂×Dic₆	semidirect
50. C₁₃	C₂²×Dic₆	semidirect
51. C₂²×C₃	Dic₂₆	semidirect
61. C₂×C₃	C₂×Dic₂₆	semidirect
63. C₂²	#64605	direct (N × H)
68. C₃	C₂²×Dic₂₆	semidirect
69. C₂	C₂×#64605	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₃₉	2
C₂²×Dic₃×C₁₃	2
C₂²×C₃×Dic₁₃	2
C₂×#64605	2
C₂²×Dic₂₆	3
C₂²×Dic₆	13

Subgroups — C22×#64605 #11929241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#64605 #11929241