Subgroups — C₂×C₄⋊C₄×C₁₃⋊C₃ #11928721

Order 1248.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₃⋊C₃	C₂	1	2	yes	maximal
2	C₂²×C₄×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×C₁₃⋊C₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₃×C₄⋊C₄	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂³×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₁₃⋊C₃	—	2	4	no	—
7	C₂×C₄×C₁₃⋊C₃	C₄	1	4	yes	complemented
8	C₂×C₄×C₁₃⋊C₃	C₂²	1	4	yes	—
9	C₂×C₄×C₁₃⋊C₃	C₂²	1	2	yes	—
10	C₂²×C₄×C₁₃	C₂×C₃	1	2	yes	—
11	C₂²×C₄×C₁₃	C₂×C₃	1	1	yes	characteristic
12	C₁₃×C₄⋊C₄	C₂×C₃	1	4	yes	complemented
13	C₂²×C₁₃⋊C₃	C₂×C₄	1	2	yes	—
14	C₂²×C₁₃⋊C₃	D₄	1	2	yes	—
15	C₂²×C₁₃⋊C₃	Q₈	1	2	yes	—
16	C₂²×C₁₃⋊C₃	C₂³	1	1	yes	characteristic
17	C₄×C₁₃⋊C₃	—	2	4	no	—
18	C₄×C₁₃⋊C₃	C₂×C₄	1	4	yes	complemented
19	C₂³×C₁₃	C₂²×C₃	1	1	yes	characteristic
20	C₂×C₄×C₁₃	—	2	4	no	—
21	C₂×C₄×C₁₃	C₃×C₄	1	4	yes	complemented
22	C₂×C₄×C₁₃	C₂²×C₃	1	4	yes	—
23	C₂×C₄×C₁₃	C₂²×C₃	1	2	yes	—
24	C₂×C₃×C₄⋊C₄	—	13	1	no	maximal, Hall
25	C₂×C₁₃⋊C₃	C₄⋊C₄	1	4	yes	direct product factor
26	C₂×C₁₃⋊C₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₁₃⋊C₃	C₂×D₄	1	1	yes	characteristic
28	C₂×C₁₃⋊C₃	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₁₃	C₂×C₃×C₄	1	2	yes	—
30	C₂²×C₁₃	C₃×D₄	1	2	yes	—
31	C₂²×C₁₃	C₃×Q₈	1	2	yes	—
32	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
33	C₄×C₁₃	—	2	4	no	—
34	C₄×C₁₃	C₂×C₃×C₄	1	4	yes	complemented
35	C₂²×C₃×C₄	—	13	1	no	—
36	C₂²×C₃×C₄	—	13	2	no	—
37	C₃×C₄⋊C₄	—	13	4	no	—
38	C₁₃⋊C₃	C₂×C₄⋊C₄	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₄⋊C₄	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₁₃	C₃×C₄⋊C₄	1	4	yes	complemented
41	C₂×C₁₃	C₂²×C₃×C₄	1	1	yes	characteristic
42	C₂×C₁₃	C₂×C₃×D₄	1	1	yes	characteristic
43	C₂×C₁₃	C₂×C₃×Q₈	1	1	yes	characteristic
44	C₂³×C₃	—	13	1	no	—
45	C₂×C₃×C₄	—	13	4	no	—
46	C₂×C₃×C₄	—	13	2	no	—
47	C₂×C₃×C₄	—	13	4	no	—
48	C₂×C₃×C₄	—	26	4	no	—
49	C₂²×C₄	C₂×C₁₃⋊C₃	1	2	yes	—
50	C₂²×C₄	C₂×C₁₃⋊C₃	1	1	yes	characteristic
51	C₄⋊C₄	C₂×C₁₃⋊C₃	1	4	yes	direct product factor
52	C₁₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₃	—	13	2	no	—
54	C₂²×C₃	—	13	2	no	—
55	C₂²×C₃	—	13	2	no	—
56	C₂²×C₃	—	13	1	no	—
57	C₃×C₄	—	13	4	no	—
58	C₃×C₄	—	26	4	no	—
59	C₂³	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
60	C₂×C₄	—	2	4	no	—
61	C₂×C₄	C₄×C₁₃⋊C₃	1	4	yes	complemented
62	C₂×C₄	C₂²×C₁₃⋊C₃	1	4	yes	—
63	C₂×C₄	C₂²×C₁₃⋊C₃	1	2	yes	—
64	C₂×C₃	—	13	1	no	—
65	C₂×C₃	—	13	1	no	—
66	C₂×C₃	—	13	1	no	—
67	C₂×C₃	—	13	4	no	—
68	C₂²	C₂×C₄×C₁₃⋊C₃	1	2	yes	—
69	C₂²	D₄×C₁₃⋊C₃	1	2	yes	—
70	C₂²	Q₈×C₁₃⋊C₃	1	2	yes	—
71	C₂²	C₂³×C₁₃⋊C₃	1	1	yes	characteristic
72	C₄	—	2	4	no	—
73	C₄	C₂×C₄×C₁₃⋊C₃	1	4	yes	complemented
74	C₃	—	13	1	no	Sylow
75	C₂	C₄⋊C₄×C₁₃⋊C₃	1	4	yes	direct product factor
76	C₂	C₂²×C₄×C₁₃⋊C₃	1	1	yes	characteristic
77	C₂	C₂×D₄×C₁₃⋊C₃	1	1	yes	characteristic
78	C₂	C₂×Q₈×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₁₃⋊C₃
commutator	C₂×C₁₃	C₂²×C₃×C₄
Frattini	C₂²	C₂³×C₁₃⋊C₃
Fitting	C₂×C₁₃×C₄⋊C₄	C₃
socle	C₂³×C₁₃	C₂²×C₃
prime radical	C₂³×C₁₃⋊C₃	C₂²
cosocle	C₂²×C₁₃	C₂³×C₃
hypercenter	C₂×C₄⋊C₄	C₁₃⋊C₃
hypocenter	C₁₃	C₂×C₃×C₄⋊C₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₄⋊C₄×C₁₃⋊C₃	C₂	direct (N × H)
4. C₂×C₁₃×C₄⋊C₄	C₃	semidirect
7. C₂×C₄×C₁₃⋊C₃	C₄	semidirect
12. C₁₃×C₄⋊C₄	C₂×C₃	semidirect
18. C₄×C₁₃⋊C₃	C₂×C₄	semidirect
21. C₂×C₄×C₁₃	C₃×C₄	semidirect
25. C₂×C₁₃⋊C₃	C₄⋊C₄	direct (N × H)
34. C₄×C₁₃	C₂×C₃×C₄	semidirect
38. C₁₃⋊C₃	C₂×C₄⋊C₄	direct (N × H)
39. C₂×C₄⋊C₄	C₁₃⋊C₃	direct (N × H)
40. C₂×C₁₃	C₃×C₄⋊C₄	semidirect
51. C₄⋊C₄	C₂×C₁₃⋊C₃	direct (N × H)
52. C₁₃	C₂×C₃×C₄⋊C₄	semidirect
61. C₂×C₄	C₄×C₁₃⋊C₃	semidirect
73. C₄	C₂×C₄×C₁₃⋊C₃	semidirect
75. C₂	C₄⋊C₄×C₁₃⋊C₃	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×C₄×C₁₃⋊C₃	2
C₄⋊C₄×C₁₃⋊C₃	2
C₂×C₁₃×C₄⋊C₄	3
C₂×C₃×C₄⋊C₄	13

Subgroups — C2×C4⋊C4×C13⋊C3 #11928721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊C₄×C₁₃⋊C₃ #11928721