Subgroups — #15752274

Order 3328.

574 conjugacy classes of subgroups.

The subgroup lattice has 144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13114581	C₂	1	2	yes	maximal
2	C₄×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718046	C₂	1	2	yes	maximal
4	C₂×C₈×#1055	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×Dic₁₃	C₄	1	4	yes	—
9	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×#1055	C₂²	1	2	yes	—
11	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
12	C₈²×C₁₃	C₄	1	4	yes	complemented
13	#11718142	C₄	1	8	yes	—
14	#11718046	C₄	1	8	yes	complemented
15	C₈×#1055	C₄	1	4	yes	complemented
16	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
17	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
19	C₂×C₄×Dic₁₃	C₂×C₄	1	4	yes	—
20	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
21	C₂²×#1055	C₂×C₄	1	4	yes	—
22	C₂²×#1055	C₂×C₄	1	2	yes	—
23	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
24	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
25	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
26	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
27	C₈×Dic₁₃	C₈	1	16	yes	complemented
28	C₄×#1055	C₂×C₄	1	4	yes	—
29	C₄×#1055	C₂×C₄	1	4	yes	—
30	C₄×#1055	C₂×C₄	1	4	yes	—
31	#7841	—	13	1	no	maximal, Sylow
32	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
34	C₂²×Dic₁₃	C₄²	1	4	yes	—
35	C₂×C₈×C₁₃	—	2	8	no	—
36	C₂×C₈×C₁₃	C₄²	1	8	yes	—
37	C₂×C₈×C₁₃	C₄²	1	4	yes	—
38	C₂×C₈×C₁₃	C₂×C₈	1	8	yes	—
39	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
40	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
42	C₄×Dic₁₃	—	2	8	no	—
43	C₄×Dic₁₃	C₂×C₈	1	8	yes	—
44	C₂×#1055	—	2	8	no	—
45	C₂×#1055	C₄²	1	8	yes	—
46	C₂×#1055	C₄²	1	4	yes	—
47	C₂×#1055	C₂×C₈	1	8	yes	—
48	#1744	—	13	2	no	—
49	C₄²×C₈	—	13	1	no	—
50	C₂×#322	—	13	2	no	—
51	C₂×C₈²	—	13	1	no	—
52	C₂×C₈²	D₁₃	1	1	yes	characteristic
53	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
54	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
55	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
56	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
57	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
58	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
59	C₂×C₄×C₁₃	#131	1	8	yes	—
60	C₂×Dic₁₃	—	2	8	no	—
61	C₂×Dic₁₃	C₄×C₈	1	8	yes	—
62	C₈×C₁₃	—	2	8	no	—
63	C₈×C₁₃	C₄×C₈	1	8	yes	—
64	#1055	—	2	8	no	—
65	#1055	C₄×C₈	1	8	yes	—
66	C₂×C₄×C₈	—	13	4	no	—
67	C₂×C₄×C₈	—	13	2	no	—
68	C₂×C₄×C₈	—	13	1	no	—
69	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
70	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
71	C₄³	—	13	1	no	—
72	#336	—	13	8	no	—
73	#322	—	13	8	no	—
74	C₈²	—	13	4	no	—
75	C₈²	Dic₁₃	1	4	yes	complemented
76	C₂²×C₁₃	C₄³	1	1	yes	characteristic
77	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
78	C₂²×C₁₃	#405	1	4	yes	—
79	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
80	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
81	C₄×C₁₃	#405	1	4	yes	—
82	C₄×C₁₃	#405	1	4	yes	—
83	Dic₁₃	—	2	8	no	—
84	C₂²×C₈	—	13	2	no	—
85	C₂²×C₈	—	13	4	no	—
86	C₂²×C₈	C₄×D₁₃	1	4	yes	—
87	C₂²×C₈	C₄×D₁₃	1	2	yes	—
88	C₂×C₄²	—	13	2	no	—
89	C₂×C₄²	—	13	4	no	—
90	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
91	C₄×C₈	—	13	16	no	—
92	C₄×C₈	—	13	4	no	—
93	C₄×C₈	—	13	4	no	—
94	C₄×C₈	—	13	4	no	—
95	C₄×C₈	C₄×D₁₃	1	2	yes	—
96	C₄×C₈	C₄×D₁₃	1	4	yes	—
97	C₄×C₈	C₂×Dic₁₃	1	4	yes	—
98	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
99	C₂×C₁₃	#1450	1	4	yes	—
100	C₂×C₁₃	C₄²×C₈	1	1	yes	characteristic
101	C₂×C₁₃	#1726	1	2	yes	—
102	C₂²×C₄	—	13	4	no	—
103	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
104	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
105	C₂×C₈	—	2	8	no	—
106	C₂×C₈	—	13	4	no	—
107	C₂×C₈	—	13	8	no	—
108	C₂×C₈	—	13	8	no	—
109	C₂×C₈	—	26	8	no	—
110	C₂×C₈	C₈×D₁₃	1	8	yes	—
111	C₂×C₈	C₄×Dic₁₃	1	8	yes	—
112	C₂×C₈	C₄×Dic₁₃	1	4	yes	—
113	C₄²	—	13	8	no	—
114	C₄²	—	26	8	no	—
115	C₄²	C₂×C₄×D₁₃	1	2	yes	—
116	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
117	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
118	C₁₃	#7841	1	1	yes	characteristic, complemented, Sylow
119	C₂³	C₄²×D₁₃	1	1	yes	characteristic
120	C₂×C₄	—	13	8	no	—
121	C₂×C₄	—	26	8	no	—
122	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
123	C₂×C₄	C₄²×D₁₃	1	2	yes	—
124	C₂×C₄	C₂×C₈×D₁₃	1	4	yes	—
125	C₂×C₄	#88155	1	8	yes	—
126	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
127	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
128	C₈	—	2	8	no	—
129	C₈	—	13	8	no	—
130	C₈	—	26	8	no	—
131	C₈	C₈×Dic₁₃	1	8	yes	—
132	C₂²	C₄×C₈×D₁₃	1	2	yes	—
133	C₂²	#11718350	1	4	yes	—
134	C₂²	C₄²×Dic₁₃	1	1	yes	characteristic
135	C₄	—	26	8	no	—
136	C₄	C₄×C₈×D₁₃	1	2	yes	—
137	C₄	#11718350	1	4	yes	—
138	C₄	C₂×C₈×Dic₁₃	1	2	yes	—
139	C₄	#11718762	1	4	yes	—
140	C₂	#13113118	1	4	yes	—
141	C₂	C₄×C₈×Dic₁₃	1	1	yes	characteristic
142	C₂	#13114522	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₈	C₂×D₁₃
commutator	C₂×C₁₃	C₄²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₈²×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₄²
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×C₈²	D₁₃
hypocenter	C₁₃	#7841
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄×C₈ ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
12. C₈²×C₁₃	C₄	semidirect
14. #11718046	C₄	semidirect
15. C₈×#1055	C₄	semidirect
27. C₈×Dic₁₃	C₈	semidirect
75. C₈²	Dic₁₃	semidirect
118. C₁₃	#7841	semidirect

Maximal subgroups

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

subgroup	index
#13114581	2
C₄×C₈×Dic₁₃	2
C₂×#11718046	2
C₂×C₈×#1055	2
C₂×C₈²×C₁₃	2
#7841	13