Subgroups — #11928981

Order 1248.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10597794	C₂	1	2	yes	maximal, complemented
2	C₃×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#10597669	C₂	1	2	yes	maximal, complemented
4	D₃₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#88173	—	3	1	no	maximal, Hall
7	C₃×Q₈×C₁₃	C₂²	1	2	yes	—
8	D₁₅₆	—	2	2	no	—
9	D₁₅₆	C₂²	1	2	yes	—
10	C₄×D₃₉	—	2	2	no	—
11	C₄×D₃₉	C₂²	1	1	yes	characteristic
12	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₃⋊#1055	C₂²	1	1	yes	characteristic
14	#6131	—	3	2	no	—
15	C₁₃×Q₁₆	D₃	1	1	yes	characteristic, complemented
16	#6106	—	3	2	no	—
17	D₁₀₄	—	3	1	no	—
18	C₈×D₁₃	—	3	1	no	—
19	C₂×D₃₉	—	2	2	no	—
20	C₂×D₃₉	D₄	1	1	yes	characteristic
21	C₃×C₄×C₁₃	—	2	2	no	—
22	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
23	Dic₃₉	D₄	1	1	yes	characteristic
24	Q₈×C₁₃	C₂×D₃	1	2	yes	—
25	D₅₂	—	3	2	no	—
26	D₅₂	—	6	2	no	—
27	C₄×D₁₃	—	3	1	no	—
28	C₄×D₁₃	—	6	2	no	—
29	C₈×C₁₃	C₂×D₃	1	1	yes	characteristic
30	#1055	—	3	1	no	—
31	#919	—	13	1	no	maximal, Hall
32	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
33	D₃₉	—	2	1	no	—
34	D₃₉	—	4	2	no	—
35	C₂×D₁₃	—	3	1	no	—
36	C₂×D₁₃	—	6	2	no	—
37	C₄×C₁₃	—	2	2	no	—
38	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
39	Dic₁₃	—	3	1	no	—
40	#239	—	13	2	no	—
41	C₃×Q₁₆	D₁₃	1	1	yes	characteristic, complemented
42	#215	—	13	2	no	—
43	D₂₄	—	13	1	no	—
44	D₃×C₈	—	13	1	no	—
45	C₃×C₁₃	#135	1	1	yes	characteristic, complemented, Hall
46	#135	—	39	1	no	Sylow
47	C₂×C₁₃	D₃×D₄	1	1	yes	characteristic
48	D₁₃	—	6	1	no	—
49	D₁₃	—	12	2	no	—
50	C₃×Q₈	C₂×D₁₃	1	2	yes	—
51	D₁₂	—	13	2	no	—
52	D₁₂	—	26	2	no	—
53	C₄×D₃	—	13	1	no	—
54	C₄×D₃	—	26	2	no	—
55	C₃×C₈	C₂×D₁₃	1	1	yes	characteristic
56	C₃⋊C₈	—	13	1	no	—
57	#41	—	39	2	no	—
58	Q₁₆	D₃₉	1	1	yes	characteristic, complemented
59	SD₁₆	—	39	2	no	—
60	D₈	—	39	1	no	—
61	C₂×C₈	—	39	1	no	—
62	C₁₃	#919	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₃	—	13	1	no	—
64	C₂×D₃	—	26	2	no	—
65	C₃×C₄	—	2	2	no	—
66	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
67	Dic₃	—	13	1	no	—
68	Q₈	C₂×D₃₉	1	2	yes	—
69	D₄	—	39	2	no	—
70	D₄	—	78	2	no	—
71	C₂×C₄	—	39	1	no	—
72	C₂×C₄	—	78	2	no	—
73	C₈	—	39	1	no	—
74	C₈	C₂×D₃₉	1	1	yes	characteristic
75	C₂×C₃	D₄×D₁₃	1	1	yes	characteristic
76	D₃	—	26	1	no	—
77	D₃	—	52	2	no	—
78	C₂²	—	39	1	no	—
79	C₂²	—	78	2	no	—
80	C₄	—	2	2	no	—
81	C₄	—	39	1	no	—
82	C₄	C₂²×D₃₉	1	1	yes	characteristic
83	C₃	#88173	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	78	1	no	—
85	C₂	—	156	2	no	—
86	C₂	D₄×D₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₃₉
commutator, cosocle	C₃×C₄×C₁₃	C₂³
Frattini	C₄	C₂²×D₃₉
Fitting	C₃×C₁₃×Q₁₆	C₂
socle	C₂×C₃×C₁₃	C₂×D₄
hypercenter	Q₁₆	D₃₉
hypocenter	C₃×C₁₃	#135
LCS	G ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #10597794	C₂	semidirect
2. C₃×C₁₃×Q₁₆	C₂	semidirect
3. #10597669	C₂	semidirect
4. D₃₁₂	C₂	semidirect
5. C₈×D₃₉	C₂	semidirect
15. C₁₃×Q₁₆	D₃	semidirect
41. C₃×Q₁₆	D₁₃	semidirect
45. C₃×C₁₃	#135	semidirect
58. Q₁₆	D₃₉	semidirect
62. C₁₃	#919	semidirect
83. C₃	#88173	semidirect

Maximal subgroups

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

subgroup	index
#10597794	2
C₃×C₁₃×Q₁₆	2
#10597669	2
D₃₁₂	2
C₈×D₃₉	2
#88173	3
#919	13