Subgroups — #15753342

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	C₄²×#1055	C₂	1	2	yes	maximal
2	#13112663	C₂	1	4	yes	maximal
3	C₄²×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₃	C₄	1	2	yes	—
5	C₂×C₄×C₈×C₁₃	C₄	1	2	yes	—
6	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
7	C₄³×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×#1055	C₄	1	4	yes	—
9	C₂×C₄×#1055	C₄	1	4	yes	—
10	C₂×C₄×#1055	C₂²	1	4	yes	—
11	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
12	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
13	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
14	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
17	C₂²×#1055	C₂×C₄	1	8	yes	—
18	C₄×C₈×C₁₃	—	2	4	no	—
19	C₄×C₈×C₁₃	—	2	4	no	—
20	C₄×C₈×C₁₃	C₈	1	8	yes	complemented
21	C₄×#1055	—	2	8	no	—
22	C₄×#1055	—	2	8	no	—
23	C₄×#1055	C₈	1	16	yes	complemented
24	#8131	—	13	1	no	maximal, Sylow
25	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
26	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
27	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
28	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
29	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₃	—	2	4	no	—
31	C₂×C₈×C₁₃	—	2	4	no	—
32	C₂×C₈×C₁₃	C₂×C₈	1	8	yes	—
33	C₄²×C₁₃	C₂×C₈	1	8	yes	—
34	C₄²×C₁₃	C₂×C₈	1	4	yes	—
35	C₄²×C₁₃	M₁₆	1	8	yes	—
36	C₄²×C₁₃	M₁₆	1	4	yes	—
37	C₄²×C₁₃	#41	1	4	yes	—
38	C₂×#1055	—	2	8	no	—
39	C₂×#1055	—	2	8	no	—
40	C₂×#1055	C₂×C₈	1	16	yes	—
41	C₄²×C₈	—	13	2	no	—
42	C₄²×C₈	D₁₃	1	1	yes	characteristic
43	#1273	—	13	4	no	—
44	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
45	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
46	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	—
47	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
48	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	—
49	C₂×C₄×C₁₃	#97	1	4	yes	—
50	C₂×C₄×C₁₃	#97	1	4	yes	—
51	C₂×C₄×C₁₃	#97	1	4	yes	—
52	C₂×C₄×C₁₃	#117	1	4	yes	—
53	C₂×C₄×C₁₃	#117	1	2	yes	—
54	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
55	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
56	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
57	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
58	C₈×C₁₃	—	2	8	no	—
59	#1055	—	2	16	no	—
60	C₂×C₄×C₈	—	13	4	no	—
61	C₂×C₄×C₈	—	13	4	no	—
62	C₂×C₄×C₈	—	13	4	no	—
63	C₂×C₄×C₈	Dic₁₃	1	2	yes	—
64	C₂×C₄×C₈	Dic₁₃	1	2	yes	—
65	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
66	C₄³	C₂×D₁₃	1	1	yes	characteristic
67	C₂²×C₁₃	#376	1	1	yes	characteristic
68	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
69	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
70	C₂²×C₁₃	C₂×#97	1	2	yes	—
71	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
72	C₄×C₁₃	C₈²	1	4	yes	—
73	C₄×C₁₃	#322	1	8	yes	—
74	C₄×C₁₃	#322	1	4	yes	—
75	C₄×C₁₃	#431	1	4	yes	—
76	C₄×C₁₃	#431	1	8	yes	—
77	C₂²×C₈	—	13	8	no	—
78	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
79	C₂×C₄²	C₄×D₁₃	1	2	yes	—
80	C₂×C₄²	C₄×D₁₃	1	2	yes	—
81	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
82	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
83	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
84	C₄×C₈	—	2	4	no	—
85	C₄×C₈	—	2	4	no	—
86	C₄×C₈	—	13	16	no	—
87	C₄×C₈	—	26	8	no	—
88	C₄×C₈	—	26	8	no	—
89	C₄×C₈	#1055	1	8	yes	complemented
90	C₂×C₁₃	C₂×C₈²	1	1	yes	characteristic
91	C₂×C₁₃	C₂×#322	1	1	yes	characteristic
92	C₂×C₁₃	C₂×#322	1	2	yes	—
93	C₂×C₁₃	#1744	1	2	yes	—
94	C₂×C₁₃	#1744	1	1	yes	characteristic
95	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
96	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
97	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
98	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
99	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
100	C₂×C₈	—	2	4	no	—
101	C₂×C₈	—	2	4	no	—
102	C₂×C₈	—	13	16	no	—
103	C₂×C₈	—	26	8	no	—
104	C₂×C₈	—	26	8	no	—
105	C₂×C₈	C₂×#1055	1	8	yes	—
106	C₄²	C₈×D₁₃	1	8	yes	—
107	C₄²	#6094	1	8	yes	—
108	C₄²	C₂×#1055	1	4	yes	—
109	C₄²	#6099	1	4	yes	—
110	C₄²	#6127	1	4	yes	—
111	C₁₃	#8131	1	1	yes	characteristic, complemented, Sylow
112	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
113	C₂×C₄	C₄×#1055	1	2	yes	—
114	C₂×C₄	C₄×#1055	1	2	yes	—
115	C₂×C₄	#88043	1	4	yes	—
116	C₂×C₄	C₈×Dic₁₃	1	4	yes	—
117	C₂×C₄	C₈×Dic₁₃	1	4	yes	—
118	C₂×C₄	#88055	1	4	yes	—
119	C₂×C₄	#88055	1	4	yes	—
120	C₂×C₄	#88126	1	4	yes	—
121	C₂×C₄	C₂×C₈×D₁₃	1	4	yes	—
122	C₂×C₄	C₂×#6094	1	4	yes	—
123	C₂×C₄	C₂²×#1055	1	2	yes	—
124	C₂×C₄	C₂×#6099	1	2	yes	—
125	C₂×C₄	#88180	1	2	yes	—
126	C₈	—	2	8	no	—
127	C₈	—	26	16	no	—
128	C₂²	C₂×C₄×#1055	1	1	yes	characteristic
129	C₂²	C₂×#88043	1	1	yes	characteristic
130	C₂²	#11718593	1	1	yes	characteristic
131	C₂²	C₂×C₈×Dic₁₃	1	2	yes	—
132	C₂²	C₂×#88055	1	2	yes	—
133	C₄	C₈×#1055	1	4	yes	—
134	C₄	#11718046	1	8	yes	—
135	C₄	#11718047	1	4	yes	—
136	C₄	#11718346	1	8	yes	—
137	C₄	#11718586	1	4	yes	—
138	C₂	C₂×C₈×#1055	1	1	yes	characteristic
139	C₂	C₂×#11718047	1	1	yes	characteristic
140	C₂	C₂×#11718046	1	2	yes	—
141	C₂	#13114581	1	2	yes	—
142	C₂	#13114582	1	1	yes	characteristic

	subgroup	G/H
center	C₄³	C₂×D₁₃
commutator	C₂×C₁₃	C₂×C₈²
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₄²×C₈×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₄²
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₄²×C₈	D₁₃
hypocenter	C₁₃	#8131
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄³ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
20. C₄×C₈×C₁₃	C₈	semidirect
23. C₄×#1055	C₈	semidirect
89. C₄×C₈	#1055	semidirect
111. C₁₃	#8131	semidirect

Maximal subgroups

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

subgroup	index
C₄²×#1055	2
#13112663	2
C₄²×C₈×C₁₃	2
#8131	13