Subgroups — #11928467

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃₉	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597612	C₂	1	2	yes	maximal, complemented
5	#10597610	C₂	1	2	yes	maximal
6	#88126	—	3	1	no	maximal, Hall
7	C₂²×D₃₉	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₃₉	C₂²	1	1	yes	characteristic
10	C₄×D₃₉	C₄	1	4	yes	complemented
11	C₂×Dic₃×C₁₃	C₂²	1	2	yes	—
12	C₂×C₃×Dic₁₃	C₂²	1	2	yes	—
13	C₂×C₄×D₁₃	—	3	1	no	—
14	C₄²×C₁₃	—	3	1	no	—
15	#6103	—	3	2	no	—
16	#6101	—	3	2	no	—
17	C₄×Dic₁₃	D₃	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
19	C₂×D₃₉	—	2	2	no	—
20	C₂×D₃₉	C₂×C₄	1	2	yes	—
21	C₃×C₄×C₁₃	C₂×C₄	1	2	yes	—
22	Dic₃₉	C₂×C₄	1	2	yes	—
23	C₃×Dic₁₃	—	2	2	no	—
24	Dic₃×C₁₃	—	2	2	no	—
25	C₂²×D₁₃	—	3	1	no	—
26	C₂×C₄×C₁₃	—	3	2	no	—
27	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
28	C₂×Dic₁₃	—	3	1	no	—
29	C₂×Dic₁₃	C₂×D₃	1	2	yes	—
30	C₄×D₁₃	—	3	4	no	—
31	#872	—	13	1	no	maximal, Hall
32	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₃×C₁₃	#41	1	2	yes	—
34	D₃₉	—	2	2	no	—
35	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
36	C₂×D₁₃	—	3	2	no	—
37	C₂×D₁₃	—	6	2	no	—
38	C₄×C₁₃	—	6	2	no	—
39	C₄×C₁₃	C₄×D₃	1	2	yes	—
40	Dic₁₃	—	2	2	no	—
41	Dic₁₃	—	3	2	no	—
42	C₂×C₄×D₃	—	13	1	no	—
43	C₃×C₄²	—	13	1	no	—
44	(C₂×D₃)⋊C₄	—	13	2	no	—
45	Dic₃⋊C₄	—	13	2	no	—
46	C₄×Dic₃	D₁₃	1	1	yes	characteristic, complemented
47	C₃×C₁₃	#117	1	1	yes	characteristic, complemented, Hall
48	#117	—	39	1	no	Sylow
49	C₂×C₁₃	C₂×C₄×D₃	1	1	yes	characteristic
50	C₂×C₁₃	#235	1	2	yes	—
51	D₁₃	—	6	2	no	—
52	C₂²×D₃	—	13	1	no	—
53	C₂×C₃×C₄	—	13	2	no	—
54	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
55	C₂×Dic₃	—	13	1	no	—
56	C₂×Dic₃	C₂×D₁₃	1	2	yes	—
57	C₄×D₃	—	13	4	no	—
58	C₂²×C₄	—	39	1	no	—
59	C₄⋊C₄	—	39	2	no	—
60	C₂²⋊C₄	—	39	2	no	—
61	C₄²	—	3	1	no	—
62	C₄²	—	13	1	no	—
63	C₁₃	#872	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
65	C₂×D₃	—	13	2	no	—
66	C₂×D₃	—	26	2	no	—
67	C₃×C₄	—	26	2	no	—
68	C₃×C₄	C₄×D₁₃	1	2	yes	—
69	Dic₃	—	2	2	no	—
70	Dic₃	—	13	2	no	—
71	C₂³	—	39	1	no	—
72	C₂×C₄	—	3	2	no	—
73	C₂×C₄	—	13	2	no	—
74	C₂×C₄	—	39	1	no	—
75	C₂×C₄	—	39	4	no	—
76	C₂×C₄	D₃×D₁₃	1	1	yes	characteristic
77	C₂×C₃	C₂×C₄×D₁₃	1	1	yes	characteristic
78	C₂×C₃	#6127	1	2	yes	—
79	D₃	—	26	2	no	—
80	C₂²	—	39	2	no	—
81	C₂²	—	78	2	no	—
82	C₂²	C₂×D₃×D₁₃	1	1	yes	characteristic
83	C₄	—	6	2	no	—
84	C₄	—	26	2	no	—
85	C₄	—	39	2	no	—
86	C₄	#64601	1	2	yes	—
87	C₃	#88126	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	78	2	no	—
89	C₂	#10597737	1	2	yes	—
90	C₂	C₂×#64601	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₃×D₁₃
commutator	C₂×C₃×C₁₃	C₂²×C₄
Frattini	C₂²	C₂×D₃×D₁₃
Fitting	C₂×C₃×C₄×C₁₃	C₂²
socle, cosocle	C₂²×C₃×C₁₃	C₂³
prime radical	C₂²×D₃₉	C₂²
hypocenter	C₃×C₁₃	#117
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₄×Dic₃×C₁₃	C₂	semidirect
3. C₃×C₄×Dic₁₃	C₂	semidirect
4. #10597612	C₂	semidirect
10. C₄×D₃₉	C₄	semidirect
17. C₄×Dic₁₃	D₃	semidirect
46. C₄×Dic₃	D₁₃	semidirect
47. C₃×C₁₃	#117	semidirect
63. C₁₃	#872	semidirect
87. C₃	#88126	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₃₉	2
C₄×Dic₃×C₁₃	2
C₃×C₄×Dic₁₃	2
#10597612	2
#10597610	2
#88126	3
#872	13