Subgroups — #16789017

Order 3328.

478 conjugacy classes of subgroups.

The subgroup lattice has 194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131037	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718216	C₂	1	2	yes	maximal
3	C₂×C₁₆×#261	C₂	1	2	yes	maximal
4	#13130492	C₂	1	1	yes	maximal, characteristic
5	C₄×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#88100	C₄	1	2	yes	—
7	C₂×C₈×#261	C₂²	1	2	yes	—
8	C₂×D₁₃⋊C₁₆	C₂²	1	2	yes	—
9	#11719057	C₄	1	1	yes	characteristic
10	#11719047	C₄	1	1	yes	characteristic
11	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
13	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
14	#11718258	C₄	1	2	yes	complemented
15	#11718231	C₄	1	2	yes	complemented
16	#11718216	C₄	1	8	yes	complemented
17	C₁₆×#261	C₄	1	8	yes	complemented
18	C₄×C₁₃×C₁₆	C₄	1	1	yes	characteristic, complemented
19	C₁₆×Dic₁₃	C₄	1	1	yes	characteristic, complemented
20	C₁₆×Dic₁₃	C₄	1	1	yes	characteristic, complemented
21	C₄×#6090	C₄	1	1	yes	characteristic, complemented
22	C₂×C₄×#261	C₂×C₄	1	2	yes	—
23	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
24	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
26	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
27	(C₂×#261)⋊C₄	C₈	1	4	yes	—
28	#88110	C₈	1	4	yes	—
29	C₂×#6092	C₂×C₄	1	4	yes	—
30	#88100	C₈	1	8	yes	—
31	C₈×#261	C₂×C₄	1	4	yes	—
32	C₈×#261	C₂×C₄	1	4	yes	—
33	D₁₃⋊C₁₆	C₂×C₄	1	4	yes	—
34	D₁₃⋊C₁₆	C₂×C₄	1	4	yes	—
35	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
36	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
37	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
39	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂×#6090	C₂×C₄	1	1	yes	characteristic
41	C₂×#6090	C₂×C₄	1	1	yes	characteristic
42	C₄×#1055	C₂×C₄	1	1	yes	characteristic
43	C₁₆×D₁₃	C₂×C₄	1	4	yes	—
44	C₁₆×D₁₃	C₂×C₄	1	4	yes	—
45	#12539	—	13	1	no	maximal, Sylow
46	C₂²×#261	C₂×C₈	1	4	yes	—
47	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
48	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
49	C₂×#1057	C₂×C₈	1	4	yes	—
50	C₄×#261	C₄²	1	4	yes	—
51	C₄×#261	C₂×C₈	1	4	yes	—
52	D₁₃⋊C₈	C₄²	1	4	yes	—
53	D₁₃⋊C₈	C₂×C₈	1	4	yes	—
54	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
55	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
56	C₄²×C₁₃	C₄²	1	1	yes	characteristic
57	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
58	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
59	C₂×#1055	C₄²	1	1	yes	characteristic
60	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
61	C₈×D₁₃	C₂×C₈	1	4	yes	—
62	C₈×D₁₃	C₂²×C₄	1	2	yes	—
63	C₈×D₁₃	C₂²×C₄	1	2	yes	—
64	#6092	C₄²	1	8	yes	—
65	C₁₃×C₁₆	C₄²	1	2	yes	—
66	C₁₃×C₁₆	C₄²	1	2	yes	—
67	#6090	C₄²	1	2	yes	—
68	#6090	C₄²	1	2	yes	—
69	C₂×#346	—	13	2	no	—
70	C₂×#346	—	13	1	no	—
71	C₂×C₄×C₁₆	—	13	2	no	—
72	C₂×C₄×C₁₆	—	13	1	no	—
73	#1726	—	13	1	no	—
74	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
75	C₂×#261	—	2	8	no	—
76	C₂×#261	C₄×C₈	1	8	yes	—
77	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
78	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
79	C₂×Dic₁₃	C₄×C₈	1	2	yes	—
80	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
81	C₄×D₁₃	—	2	4	no	—
82	C₄×D₁₃	C₂×C₄²	1	2	yes	—
83	C₄×D₁₃	C₂²×C₈	1	2	yes	—
84	#1057	C₄×C₈	1	8	yes	—
85	C₈×C₁₃	C₄×C₈	1	2	yes	—
86	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
87	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
88	#1055	C₄×C₈	1	2	yes	—
89	#1055	C₂×C₄²	1	2	yes	—
90	C₂²×C₁₆	—	13	2	no	—
91	C₂²×C₁₆	—	13	1	no	—
92	C₂²×C₁₆	—	13	1	no	—
93	C₂×#97	—	13	1	no	—
94	C₂×#97	—	13	2	no	—
95	C₂×C₄×C₈	—	13	2	no	—
96	C₂×C₄×C₈	—	13	1	no	—
97	#376	—	13	1	no	—
98	#346	—	13	8	no	—
99	#346	—	13	2	no	—
100	#346	—	13	2	no	—
101	C₄×C₁₆	—	13	8	no	—
102	C₄×C₁₆	—	13	1	no	—
103	C₄×C₁₆	—	13	1	no	—
104	C₄×C₁₆	—	13	1	no	—
105	C₄×C₁₆	#261	1	1	yes	characteristic, complemented
106	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
107	C₂×D₁₃	C₂×C₄×C₈	1	2	yes	—
108	C₂×D₁₃	#504	1	4	yes	—
109	#261	—	2	8	no	—
110	C₄×C₁₃	—	2	2	no	—
111	C₄×C₁₃	C₄³	1	1	yes	characteristic
112	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
113	Dic₁₃	—	2	2	no	—
114	Dic₁₃	C₂×C₄×C₈	1	2	yes	—
115	C₂²×C₈	—	13	2	no	—
116	C₂²×C₈	—	13	1	no	—
117	C₂²×C₈	—	13	1	no	—
118	C₂×C₄²	—	13	2	no	—
119	C₂×C₄²	—	13	1	no	—
120	C₂×C₁₆	—	13	4	no	—
121	C₂×C₁₆	—	13	4	no	—
122	C₂×C₁₆	—	13	4	no	—
123	C₂×C₁₆	—	13	1	no	—
124	C₂×C₁₆	—	13	1	no	—
125	C₂×C₁₆	—	13	4	no	—
126	C₂×C₁₆	—	13	4	no	—
127	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
128	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
129	#97	—	13	8	no	—
130	#97	—	13	4	no	—
131	C₄×C₈	—	13	4	no	—
132	C₄×C₈	—	13	4	no	—
133	C₄×C₈	—	13	1	no	—
134	C₄×C₈	—	13	1	no	—
135	C₄×C₈	—	13	1	no	—
136	C₄×C₈	C₂×#261	1	1	yes	characteristic
137	#95	—	13	4	no	—
138	C₂×C₁₃	C₄²×C₈	1	1	yes	characteristic
139	C₂×C₁₃	#2108	1	2	yes	—
140	D₁₃	#2108	1	4	yes	—
141	C₂²×C₄	—	13	1	no	—
142	C₂²×C₄	—	13	4	no	—
143	C₂²×C₄	—	13	2	no	—
144	C₂×C₈	—	13	4	no	—
145	C₂×C₈	—	13	4	no	—
146	C₂×C₈	—	13	4	no	—
147	C₂×C₈	—	13	1	no	—
148	C₂×C₈	—	13	1	no	—
149	C₂×C₈	—	13	4	no	—
150	C₂×C₈	—	13	2	no	—
151	C₂×C₈	—	13	2	no	—
152	C₂×C₈	C₄×#261	1	1	yes	characteristic
153	C₂×C₈	C₂²×#261	1	1	yes	characteristic
154	C₄²	—	13	4	no	—
155	C₄²	—	13	4	no	—
156	C₄²	—	13	2	no	—
157	C₄²	—	13	1	no	—
158	C₄²	C₄×#261	1	1	yes	characteristic
159	C₁₆	—	13	8	no	—
160	C₁₆	—	13	2	no	—
161	C₁₆	—	13	2	no	—
162	C₁₆	C₄×#261	1	2	yes	—
163	C₁₆	C₄×#261	1	2	yes	—
164	C₁₃	#12539	1	1	yes	characteristic, complemented, Sylow
165	C₂³	—	13	1	no	—
166	C₂×C₄	—	13	1	no	—
167	C₂×C₄	—	13	2	no	—
168	C₂×C₄	—	13	2	no	—
169	C₂×C₄	—	13	8	no	—
170	C₂×C₄	—	13	2	no	—
171	C₂×C₄	—	26	4	no	—
172	C₂×C₄	—	26	8	no	—
173	C₂×C₄	C₈×#261	1	2	yes	—
174	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
175	C₈	—	13	8	no	—
176	C₈	—	13	2	no	—
177	C₈	—	13	2	no	—
178	C₈	C₈×#261	1	2	yes	—
179	C₈	C₂×C₄×#261	1	1	yes	characteristic
180	C₈	C₂×C₄×#261	1	1	yes	characteristic
181	C₂²	—	13	4	no	—
182	C₂²	—	13	2	no	—
183	C₂²	C₂×C₈×#261	1	1	yes	characteristic
184	C₄	—	2	2	no	—
185	C₄	—	13	2	no	—
186	C₄	—	26	8	no	—
187	C₄	—	26	2	no	—
188	C₄	C₄²×#261	1	1	yes	characteristic
189	C₄	C₂×C₈×#261	1	1	yes	characteristic
190	C₂	—	13	4	no	—
191	C₂	C₄×C₈×#261	1	1	yes	characteristic
192	C₂	#13131044	1	2	yes	—

	subgroup	G/H
center	C₂×C₁₆	C₂×#261
commutator	C₂×C₁₃	C₄²×C₈
Frattini	C₂×C₈	C₂²×#261
Fitting	C₄×C₁₃×C₁₆	C₄
socle	C₂²×C₁₃	C₂×C₄×C₈
prime radical	C₂²×D₁₃	C₂²×C₈
cosocle	C₂×C₈×D₁₃	C₂³
hypercenter	C₄×C₁₆	#261
hypocenter	C₁₃	#12539
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
14. #11718258	C₄	semidirect
15. #11718231	C₄	semidirect
16. #11718216	C₄	semidirect
17. C₁₆×#261	C₄	semidirect
18. C₄×C₁₃×C₁₆	C₄	semidirect
19. C₁₆×Dic₁₃	C₄	semidirect
20. C₁₆×Dic₁₃	C₄	semidirect
21. C₄×#6090	C₄	semidirect
105. C₄×C₁₆	#261	semidirect
164. C₁₃	#12539	semidirect

Maximal subgroups

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

subgroup	index
#13131037	2
C₂×#11718216	2
C₂×C₁₆×#261	2
#13130492	2
C₄×C₁₆×D₁₃	2
#12539	13