Subgroups — #11928145

Order 1248.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
4	#88072	—	3	1	no	maximal, Hall
5	C₂³×C₃×C₁₃	—	2	1	no	—
6	C₃×D₄×C₁₃	—	2	1	no	—
7	C₃×D₄×C₁₃	C₄	1	2	yes	complemented
8	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₃₉	—	2	1	no	—
10	C₃⋊#1055	—	2	1	no	—
11	C₂×D₄×C₁₃	D₃	1	1	yes	characteristic
12	C₄⋊Dic₁₃	—	3	1	no	—
13	C₂×#1055	—	3	1	no	—
14	C₂²×C₃×C₁₃	—	2	2	no	—
15	C₂²×C₃×C₁₃	—	4	1	no	—
16	C₂²×C₃×C₁₃	—	4	1	no	—
17	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
18	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
20	Dic₃₉	—	4	1	no	—
21	C₂³×C₁₃	—	2	1	no	—
22	D₄×C₁₃	—	2	1	no	—
23	D₄×C₁₃	Dic₃	1	2	yes	complemented
24	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
25	C₂×Dic₁₃	—	6	1	no	—
26	#1055	—	6	1	no	—
27	#832	—	13	1	no	maximal, Hall
28	C₂×C₃×C₁₃	—	4	2	no	—
29	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₃×C₁₃	D₈	1	1	yes	characteristic
31	C₂×C₃×C₁₃	SD₁₆	1	1	yes	characteristic
32	C₂²×C₁₃	—	2	2	no	—
33	C₂²×C₁₃	—	4	1	no	—
34	C₂²×C₁₃	—	4	1	no	—
35	C₂²×C₁₃	#67	1	1	yes	characteristic
36	C₄×C₁₃	C₂×Dic₃	1	1	yes	characteristic
37	C₄×C₁₃	#67	1	1	yes	characteristic
38	Dic₁₃	—	12	1	no	—
39	C₂×C₃×D₄	D₁₃	1	1	yes	characteristic
40	C₄⋊Dic₃	—	13	1	no	—
41	C₂×C₃⋊C₈	—	13	1	no	—
42	C₃×C₁₃	#102	1	1	yes	characteristic, complemented, Hall
43	#102	—	39	1	no	Sylow
44	C₂×C₁₃	—	4	2	no	—
45	C₂×C₁₃	#213	1	1	yes	characteristic
46	C₂×C₁₃	#214	1	1	yes	characteristic
47	C₂×C₁₃	#217	1	1	yes	characteristic
48	C₂³×C₃	—	2	1	no	—
49	C₃×D₄	—	2	1	no	—
50	C₃×D₄	Dic₁₃	1	2	yes	complemented
51	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
52	C₂×Dic₃	—	26	1	no	—
53	C₃⋊C₈	—	26	1	no	—
54	C₂×D₄	D₃₉	1	1	yes	characteristic
55	C₂×C₈	—	39	1	no	—
56	C₄⋊C₄	—	39	1	no	—
57	C₁₃	#832	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₃	—	2	2	no	—
59	C₂²×C₃	—	4	1	no	—
60	C₂²×C₃	—	4	1	no	—
61	C₂²×C₃	C₂²⋊D₁₃	1	1	yes	characteristic
62	C₃×C₄	C₂×Dic₁₃	1	1	yes	characteristic
63	C₃×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
64	Dic₃	—	52	1	no	—
65	C₂³	—	2	1	no	—
66	D₄	—	2	1	no	—
67	D₄	Dic₃₉	1	2	yes	complemented
68	C₂×C₄	—	78	1	no	—
69	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
70	C₈	—	78	1	no	—
71	C₂×C₃	—	4	2	no	—
72	C₂×C₃	#6104	1	1	yes	characteristic
73	C₂×C₃	#6105	1	1	yes	characteristic
74	C₂×C₃	C₂²⋊Dic₁₃	1	1	yes	characteristic
75	C₂²	—	2	2	no	—
76	C₂²	—	4	1	no	—
77	C₂²	—	4	1	no	—
78	C₂²	#64625	1	1	yes	characteristic
79	C₄	—	156	1	no	—
80	C₄	C₂×Dic₃₉	1	1	yes	characteristic
81	C₄	#64625	1	1	yes	characteristic
82	C₃	#88072	1	1	yes	characteristic, complemented, Sylow
83	C₂	—	4	2	no	—
84	C₂	#10597667	1	1	yes	characteristic
85	C₂	#10597668	1	1	yes	characteristic
86	C₂	#10597671	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#64625
commutator	C₃×C₄×C₁₃	C₂×C₄
Frattini	C₂×C₄	C₂×D₃₉
Fitting, prime radical	C₂×C₃×D₄×C₁₃	C₂
socle	C₂²×C₃×C₁₃	D₄
cosocle	C₂×C₃×C₄×C₁₃	C₂²
hypercenter	C₂×D₄	D₃₉
hypocenter	C₃×C₁₃	#102
LCS	G ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
2. C₄⋊Dic₃₉	C₂	semidirect
3. C₂×C₃⋊#1055	C₂	semidirect
7. C₃×D₄×C₁₃	C₄	semidirect
23. D₄×C₁₃	Dic₃	semidirect
42. C₃×C₁₃	#102	semidirect
50. C₃×D₄	Dic₁₃	semidirect
57. C₁₃	#832	semidirect
67. D₄	Dic₃₉	semidirect
82. C₃	#88072	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₄×C₁₃	2
C₄⋊Dic₃₉	2
C₂×C₃⋊#1055	2
#88072	3
#832	13