Subgroups — #11928667

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Dic₁₃	C₂	1	1	yes	maximal, characteristic
2	#10597671	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#217	C₂	1	1	yes	maximal, characteristic
4	#10597611	C₂	1	2	yes	maximal, complemented
5	Dic₃×Dic₁₃	C₂	1	2	yes	maximal, complemented
6	#88131	—	3	1	no	maximal, Hall
7	C₂³×C₃×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×Dic₃₉	C₂²	1	2	yes	—
9	C₂×Dic₃×C₁₃	C₂²	1	2	yes	—
10	C₂×C₃×Dic₁₃	C₄	1	4	yes	complemented
11	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
13	C₂²×Dic₁₃	D₃	1	1	yes	characteristic
14	C₁₃×C₂²⋊C₄	—	3	1	no	—
15	C₂²⋊Dic₁₃	—	3	1	no	—
16	#6101	—	3	2	no	—
17	C₄×Dic₁₃	—	3	2	no	—
18	C₂²×C₃×C₁₃	—	2	2	no	—
19	C₂²×C₃×C₁₃	C₂×C₄	1	2	yes	—
20	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
21	Dic₃₉	—	2	2	no	—
22	C₃×Dic₁₃	C₂×C₄	1	2	yes	—
23	C₃×Dic₁₃	C₂×C₄	1	2	yes	—
24	Dic₃×C₁₃	—	2	2	no	—
25	C₂³×C₁₃	C₂×D₃	1	1	yes	characteristic
26	C₂×C₄×C₁₃	—	3	2	no	—
27	C₂×Dic₁₃	—	3	2	no	—
28	C₂×Dic₁₃	Dic₃	1	4	yes	complemented
29	C₂×Dic₁₃	C₂×D₃	1	1	yes	characteristic
30	C₂×Dic₁₃	C₂×D₃	1	1	yes	characteristic
31	#926	—	13	1	no	maximal, Hall
32	C₂×C₃×C₁₃	—	2	2	no	—
33	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₃×C₁₃	#41	1	2	yes	—
35	C₂²×C₁₃	—	2	2	no	—
36	C₂²×C₁₃	C₂×Dic₃	1	2	yes	—
37	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
38	C₄×C₁₃	—	6	2	no	—
39	Dic₁₃	—	6	2	no	—
40	Dic₁₃	C₂×Dic₃	1	2	yes	—
41	Dic₁₃	C₂×Dic₃	1	2	yes	—
42	C₂²×C₃×C₄	—	13	1	no	—
43	#217	—	13	1	no	—
44	#217	D₁₃	1	1	yes	characteristic
45	C₄⋊Dic₃	—	13	2	no	—
46	C₄×Dic₃	—	13	2	no	—
47	C₃×C₁₃	#117	1	1	yes	characteristic, complemented, Hall
48	#117	—	39	1	no	Sylow
49	C₂×C₁₃	—	2	2	no	—
50	C₂×C₁₃	#235	1	2	yes	—
51	C₂×C₁₃	C₂²×Dic₃	1	1	yes	characteristic
52	C₂³×C₃	C₂×D₁₃	1	1	yes	characteristic
53	C₂×C₃×C₄	—	13	4	no	—
54	C₂×C₃×C₄	—	13	1	no	—
55	C₂×C₃×C₄	—	13	1	no	—
56	C₂×Dic₃	—	13	2	no	—
57	C₂×Dic₃	C₂×D₁₃	1	2	yes	—
58	C₂²×C₄	—	13	1	no	—
59	C₄⋊C₄	—	39	2	no	—
60	C₂²⋊C₄	—	3	1	no	—
61	C₂²⋊C₄	—	39	1	no	—
62	C₄²	—	39	2	no	—
63	C₁₃	#926	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₃	—	2	2	no	—
65	C₂²×C₃	C₄×D₁₃	1	2	yes	—
66	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
67	C₃×C₄	—	13	2	no	—
68	C₃×C₄	—	13	2	no	—
69	Dic₃	—	2	2	no	—
70	Dic₃	—	26	2	no	—
71	C₂³	D₃×D₁₃	1	1	yes	characteristic
72	C₂×C₄	—	3	2	no	—
73	C₂×C₄	—	13	4	no	—
74	C₂×C₄	—	13	1	no	—
75	C₂×C₄	—	13	1	no	—
76	C₂×C₄	—	39	2	no	—
77	C₂×C₃	—	2	2	no	—
78	C₂×C₃	C₂×C₄×D₁₃	1	1	yes	characteristic
79	C₂×C₃	#6129	1	2	yes	—
80	C₂²	—	2	2	no	—
81	C₂²	Dic₃×D₁₃	1	2	yes	—
82	C₂²	C₂×D₃×D₁₃	1	1	yes	characteristic
83	C₄	—	6	2	no	—
84	C₄	—	13	2	no	—
85	C₄	—	13	2	no	—
86	C₄	—	78	2	no	—
87	C₃	#88131	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	2	2	no	—
89	C₂	C₂×Dic₃×D₁₃	1	1	yes	characteristic
90	C₂	#10597748	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂×D₃×D₁₃
commutator	C₂×C₃×C₁₃	C₂²×C₄
Fitting, prime radical	C₂³×C₃×C₁₃	C₂²
socle, cosocle	C₂²×C₃×C₁₃	C₂³
hypercenter	C₂³	D₃×D₁₃
hypocenter	C₃×C₁₃	#117
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₂³

Complements

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

N	H ≅ G/N	type
4. #10597611	C₂	semidirect
5. Dic₃×Dic₁₃	C₂	semidirect
10. C₂×C₃×Dic₁₃	C₄	semidirect
28. C₂×Dic₁₃	Dic₃	semidirect
47. C₃×C₁₃	#117	semidirect
63. C₁₃	#926	semidirect
87. C₃	#88131	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×Dic₁₃	2
#10597671	2
C₁₃×#217	2
#10597611	2
Dic₃×Dic₁₃	2
#88131	3
#926	13