Subgroups — #11928435

Order 1248.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₃₉	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	Dic₃⋊Dic₁₃	C₂	1	2	yes	maximal
5	Dic₃×Dic₁₃	C₂	1	2	yes	maximal
6	Q₈×Dic₁₃	—	3	1	no	maximal, Hall
7	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×Dic₃₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₃₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₃×C₁₃	C₂²	1	2	yes	—
11	C₁₃×Dic₆	C₄	1	4	yes	complemented
12	C₂×C₃×Dic₁₃	C₂²	1	2	yes	—
13	C₂×Q₈×C₁₃	—	3	1	no	—
14	C₄⋊Dic₁₃	—	3	2	no	—
15	C₄⋊Dic₁₃	D₃	1	1	yes	characteristic
16	C₄×Dic₁₃	—	3	1	no	—
17	C₄×Dic₁₃	—	3	2	no	—
18	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
19	C₃×C₄×C₁₃	C₂×C₄	1	2	yes	—
20	Dic₃₉	—	2	1	no	—
21	Dic₃₉	Q₈	1	2	yes	complemented
22	C₃×Dic₁₃	—	2	2	no	—
23	Dic₃×C₁₃	C₂×C₄	1	4	yes	—
24	Q₈×C₁₃	—	3	4	no	—
25	C₂×C₄×C₁₃	—	3	2	no	—
26	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
27	C₂×Dic₁₃	—	3	1	no	—
28	C₂×Dic₁₃	—	3	1	no	—
29	C₂×Dic₁₃	C₂×D₃	1	2	yes	—
30	#887	—	13	1	no	maximal, Hall
31	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₃×C₁₃	#41	1	1	yes	characteristic
34	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
35	C₄×C₁₃	—	3	4	no	—
36	C₄×C₁₃	C₄×D₃	1	2	yes	—
37	Dic₁₃	—	2	2	no	—
38	Dic₁₃	—	3	2	no	—
39	Dic₁₃	—	6	1	no	—
40	C₂×Dic₆	D₁₃	1	1	yes	characteristic
41	C₃×C₄⋊C₄	—	13	1	no	—
42	Dic₃⋊C₄	—	13	2	no	—
43	C₄×Dic₃	—	13	1	no	—
44	C₄×Dic₃	—	13	2	no	—
45	C₃×C₁₃	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
46	C₄×Q₈	—	39	1	no	Sylow
47	C₂×C₁₃	C₂×C₄×D₃	1	1	yes	characteristic
48	C₂×C₁₃	#237	1	1	yes	characteristic
49	C₂×C₁₃	D₃×Q₈	1	1	yes	characteristic
50	C₂×C₃×C₄	—	13	2	no	—
51	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
52	C₂×Dic₃	—	13	1	no	—
53	C₂×Dic₃	—	13	1	no	—
54	C₂×Dic₃	C₂×D₁₃	1	2	yes	—
55	Dic₆	Dic₁₃	1	4	yes	complemented
56	C₂×Q₈	—	3	1	no	—
57	C₄⋊C₄	—	13	1	no	—
58	C₄⋊C₄	—	39	2	no	—
59	C₄²	—	39	2	no	—
60	C₄²	—	39	1	no	—
61	C₁₃	#887	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
63	C₃×C₄	—	26	2	no	—
64	C₃×C₄	C₂×Dic₁₃	1	2	yes	—
65	Dic₃	—	13	2	no	—
66	Dic₃	—	26	1	no	—
67	Dic₃	C₂×Dic₁₃	1	4	yes	—
68	Q₈	—	3	4	no	—
69	C₂×C₄	—	3	2	no	—
70	C₂×C₄	—	13	2	no	—
71	C₂×C₄	—	39	1	no	—
72	C₂×C₄	—	39	1	no	—
73	C₂×C₄	D₃×D₁₃	1	1	yes	characteristic
74	C₂×C₃	Q₈×D₁₃	1	1	yes	characteristic
75	C₂×C₃	#6131	1	1	yes	characteristic
76	C₂×C₃	C₂²×Dic₁₃	1	1	yes	characteristic
77	C₂²	C₂×D₃×D₁₃	1	1	yes	characteristic
78	C₄	—	3	4	no	—
79	C₄	—	26	2	no	—
80	C₄	—	39	2	no	—
81	C₄	—	78	1	no	—
82	C₄	D₃×Dic₁₃	1	2	yes	—
83	C₃	Q₈×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
84	C₂	#10597732	1	1	yes	characteristic
85	C₂	D₃₉⋊Q₈	1	1	yes	characteristic
86	C₂	C₂×D₃×Dic₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×D₃×D₁₃
commutator	C₂×C₃×C₁₃	C₂²×C₄
Fitting	C₂×C₃×C₄×C₁₃	C₂²
socle, prime radical, cosocle	C₂²×C₃×C₁₃	C₂³
hypercenter	C₂×C₄	D₃×D₁₃
hypocenter	C₃×C₁₃	C₄×Q₈
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
11. C₁₃×Dic₆	C₄	semidirect
21. Dic₃₉	Q₈	semidirect
45. C₃×C₁₃	C₄×Q₈	semidirect
55. Dic₆	Dic₁₃	semidirect
61. C₁₃	#887	semidirect
83. C₃	Q₈×Dic₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×Dic₆	2
C₄×Dic₃₉	2
C₃×C₄⋊Dic₁₃	2
Dic₃⋊Dic₁₃	2
Dic₃×Dic₁₃	2
Q₈×Dic₁₃	3
#887	13