Subgroups — C₂×D₁₆×Dic₁₃ #16016180

Order 3328.

806 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×Dic₁₃	C₂	1	2	yes	maximal, complemented
2	D₁₆×Dic₁₃	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718096	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11718154	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
8	C₂×D₄×Dic₁₃	—	2	2	no	—
9	C₂×C₁₃×D₁₆	C₄	1	8	yes	complemented
10	C₂×C₁₃×D₁₆	C₂²	1	4	yes	—
11	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
12	C₂×#88072	—	2	2	no	—
13	D₈×Dic₁₃	—	2	4	no	—
14	D₈×Dic₁₃	C₂²	1	8	yes	complemented
15	C₂×#88058	C₂²	1	2	yes	—
16	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
17	C₂²×#6090	C₂²	1	1	yes	characteristic
18	#11718154	C₂²	1	8	yes	complemented
19	#11718096	C₂²	1	4	yes	complemented
20	C₁₆×Dic₁₃	C₂²	1	4	yes	complemented
21	C₂²×D₄×C₁₃	—	2	2	no	—
22	C₂³×Dic₁₃	—	4	2	no	—
23	C₂×C₁₃×D₈	—	2	2	no	—
24	C₂×C₁₃×D₈	—	2	4	no	—
25	C₂×C₁₃×D₈	C₂×C₄	1	8	yes	complemented
26	C₂×C₁₃×D₈	C₂³	1	4	yes	—
27	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×C₂²⋊Dic₁₃	—	4	2	no	—
29	D₄×Dic₁₃	—	2	8	no	—
30	D₄×Dic₁₃	—	4	4	no	—
31	C₂×C₄⋊Dic₁₃	—	2	2	no	—
32	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
33	C₂²×#1055	D₄	1	1	yes	characteristic
34	C₁₃×D₁₆	C₂×C₄	1	16	yes	complemented
35	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	complemented
36	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
37	#88072	—	2	8	no	—
38	#88058	—	2	2	no	—
39	#88058	C₂³	1	4	yes	—
40	C₈×Dic₁₃	D₄	1	2	yes	—
41	C₈×Dic₁₃	C₂³	1	2	yes	—
42	C₂×#6090	—	2	2	no	—
43	C₂×#6090	C₂³	1	2	yes	—
44	C₂×C₄×D₁₆	—	13	1	no	maximal, Sylow
45	C₂⁴×C₁₃	—	4	2	no	—
46	C₂×D₄×C₁₃	—	2	8	no	—
47	C₂×D₄×C₁₃	—	2	4	no	—
48	C₂×D₄×C₁₃	—	4	2	no	—
49	C₂×D₄×C₁₃	—	4	4	no	—
50	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
51	C₂²×Dic₁₃	—	4	2	no	—
52	C₂²×Dic₁₃	—	4	8	no	—
53	C₂²×Dic₁₃	—	8	8	no	—
54	C₂²×Dic₁₃	D₈	1	1	yes	characteristic
55	C₂²×Dic₁₃	D₈	1	1	yes	characteristic
56	C₁₃×D₈	—	2	8	no	—
57	C₁₃×D₈	—	2	4	no	—
58	C₁₃×D₈	C₂²×C₄	1	8	yes	complemented
59	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
60	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
61	C₂×C₈×C₁₃	#41	1	2	yes	—
62	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
63	C₂²⋊Dic₁₃	—	4	8	no	—
64	C₄⋊Dic₁₃	—	2	4	no	—
65	C₄⋊Dic₁₃	—	4	2	no	—
66	C₄×Dic₁₃	D₈	1	2	yes	—
67	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
68	C₂×#1055	—	2	2	no	—
69	C₂×#1055	C₂×D₄	1	2	yes	—
70	C₁₃×C₁₆	C₂²×C₄	1	4	yes	complemented
71	#6090	—	2	2	no	—
72	C₂²×D₁₆	D₁₃	1	1	yes	characteristic
73	C₂×C₄×D₈	—	13	2	no	—
74	C₄×D₁₆	—	13	8	no	—
75	C₂×#366	—	13	1	no	—
76	C₂×#357	—	13	2	no	—
77	C₂×C₄×C₁₆	—	13	1	no	—
78	C₂³×C₁₃	—	4	4	no	—
79	C₂³×C₁₃	—	4	8	no	—
80	C₂³×C₁₃	—	8	4	no	—
81	C₂³×C₁₃	—	8	4	no	—
82	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
83	D₄×C₁₃	—	2	8	no	—
84	D₄×C₁₃	—	4	4	no	—
85	D₄×C₁₃	—	4	8	no	—
86	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
87	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
88	C₂×C₄×C₁₃	#135	1	2	yes	—
89	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
90	C₂×Dic₁₃	—	2	2	no	—
91	C₂×Dic₁₃	—	4	4	no	—
92	C₂×Dic₁₃	—	8	4	no	—
93	C₂×Dic₁₃	—	8	16	no	—
94	C₂×Dic₁₃	D₁₆	1	4	yes	direct product factor
95	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
96	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
97	C₈×C₁₃	C₄×D₄	1	2	yes	—
98	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
99	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
100	#1055	—	2	2	no	—
101	C₂²×D₈	C₂×D₁₃	1	2	yes	—
102	C₂×C₄×D₄	—	26	2	no	—
103	C₂×D₁₆	Dic₁₃	1	8	yes	direct product factor
104	C₂×D₁₆	C₂×D₁₃	1	4	yes	—
105	C₂²×C₁₆	—	13	1	no	—
106	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
107	C₄×D₈	—	13	8	no	—
108	C₄×D₈	—	26	4	no	—
109	C₂×#107	—	13	2	no	—
110	C₂×#102	—	26	2	no	—
111	C₂×C₄×C₈	—	13	1	no	—
112	#366	—	13	4	no	—
113	#357	—	13	8	no	—
114	C₄×C₁₆	—	13	4	no	—
115	C₂²×C₁₃	—	4	8	no	—
116	C₂²×C₁₃	—	8	4	no	—
117	C₂²×C₁₃	—	8	4	no	—
118	C₂²×C₁₃	—	8	16	no	—
119	C₂²×C₁₃	C₄×D₈	1	2	yes	—
120	C₂²×C₁₃	C₂×D₁₆	1	2	yes	—
121	C₂²×C₁₃	#508	1	2	yes	—
122	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
123	C₄×C₁₃	C₄×D₈	1	2	yes	—
124	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
125	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
126	Dic₁₃	—	2	2	no	—
127	Dic₁₃	—	8	4	no	—
128	Dic₁₃	C₂×D₁₆	1	4	yes	direct product factor
129	C₂²×D₄	—	2	2	no	—
130	C₂³×C₄	—	52	2	no	—
131	C₂×D₈	—	2	2	no	—
132	C₂×D₈	—	2	4	no	—
133	C₂×D₈	C₂×Dic₁₃	1	8	yes	complemented
134	C₂×D₈	C₂²×D₁₃	1	4	yes	—
135	C₂²×C₈	—	13	1	no	—
136	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
137	C₄×D₄	—	26	8	no	—
138	C₄×D₄	—	52	4	no	—
139	C₂×C₄⋊C₄	—	26	2	no	—
140	C₂×C₂²⋊C₄	—	52	2	no	—
141	C₂×C₄²	—	13	1	no	—
142	D₁₆	C₂×Dic₁₃	1	16	yes	direct product factor
143	C₂×C₁₆	—	13	2	no	—
144	C₂×C₁₆	—	26	2	no	—
145	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	complemented
146	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
147	#107	—	13	4	no	—
148	#107	—	26	2	no	—
149	#102	—	26	8	no	—
150	C₄×C₈	—	13	2	no	—
151	C₄×C₈	—	13	2	no	—
152	C₂×C₁₃	—	8	8	no	—
153	C₂×C₁₃	C₄×D₁₆	1	4	yes	complemented
154	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
155	C₂×C₁₃	C₂²×D₁₆	1	1	yes	characteristic
156	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
157	C₂⁴	—	4	2	no	—
158	C₂×D₄	—	2	8	no	—
159	C₂×D₄	—	2	4	no	—
160	C₂×D₄	—	4	2	no	—
161	C₂×D₄	—	4	4	no	—
162	C₂²×C₄	—	13	1	no	—
163	C₂²×C₄	—	13	1	no	—
164	C₂²×C₄	—	52	8	no	—
165	C₂²×C₄	—	52	2	no	—
166	C₂²×C₄	—	104	8	no	—
167	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
168	D₈	—	2	8	no	—
169	D₈	—	2	4	no	—
170	D₈	C₂²×Dic₁₃	1	8	yes	complemented
171	C₂×C₈	—	13	2	no	—
172	C₂×C₈	—	26	2	no	—
173	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
174	C₂×C₈	#6129	1	2	yes	—
175	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
176	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
177	C₄⋊C₄	—	26	4	no	—
178	C₄⋊C₄	—	52	2	no	—
179	C₂²⋊C₄	—	52	8	no	—
180	C₄²	—	13	2	no	—
181	C₄²	—	13	2	no	—
182	C₁₆	—	26	2	no	—
183	C₁₆	C₂²×Dic₁₃	1	4	yes	complemented
184	C₁₃	C₂×C₄×D₁₆	1	1	yes	characteristic, complemented, Sylow
185	C₂³	—	4	4	no	—
186	C₂³	—	4	8	no	—
187	C₂³	—	8	4	no	—
188	C₂³	—	8	4	no	—
189	C₂³	D₈×D₁₃	1	1	yes	characteristic
190	D₄	—	2	8	no	—
191	D₄	—	4	4	no	—
192	D₄	—	4	8	no	—
193	C₂×C₄	—	13	2	no	—
194	C₂×C₄	—	13	4	no	—
195	C₂×C₄	—	13	2	no	—
196	C₂×C₄	—	26	2	no	—
197	C₂×C₄	—	52	4	no	—
198	C₂×C₄	—	104	16	no	—
199	C₂×C₄	—	104	4	no	—
200	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
201	C₂×C₄	#88166	1	2	yes	—
202	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
203	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
204	C₈	—	26	2	no	—
205	C₈	D₄×Dic₁₃	1	2	yes	—
206	C₈	C₂×#6129	1	1	yes	characteristic
207	C₈	C₂³×Dic₁₃	1	1	yes	characteristic
208	C₂²	—	4	8	no	—
209	C₂²	—	8	4	no	—
210	C₂²	—	8	16	no	—
211	C₂²	—	8	4	no	—
212	C₂²	D₁₃×D₁₆	1	2	yes	—
213	C₂²	#11718573	1	2	yes	—
214	C₂²	D₈×Dic₁₃	1	2	yes	—
215	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
216	C₄	—	13	4	no	—
217	C₄	—	26	2	no	—
218	C₄	—	104	4	no	—
219	C₄	D₈×Dic₁₃	1	2	yes	—
220	C₄	C₂×#88166	1	1	yes	characteristic
221	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
222	C₂	—	8	8	no	—
223	C₂	D₁₆×Dic₁₃	1	4	yes	direct product factor
224	C₂	C₂×D₈×Dic₁₃	1	1	yes	characteristic
225	C₂	C₂×D₁₃×D₁₆	1	1	yes	characteristic
226	C₂	C₂×#11718573	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₈×D₁₃
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting, prime radical	C₂²×C₁₃×D₁₆	C₂
socle	C₂³×C₁₃	C₂×D₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂²×D₁₆	D₁₃
hypocenter	C₁₃	C₂×C₄×D₁₆
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×D₈×Dic₁₃	C₂	semidirect
2. D₁₆×Dic₁₃	C₂	direct (N × H)
3. C₂×#11718096	C₂	semidirect
4. C₂×#11718154	C₂	semidirect
5. C₂×C₁₆×Dic₁₃	C₂	semidirect
9. C₂×C₁₃×D₁₆	C₄	semidirect
14. D₈×Dic₁₃	C₂²	semidirect
18. #11718154	C₂²	semidirect
19. #11718096	C₂²	semidirect
20. C₁₆×Dic₁₃	C₂²	semidirect
25. C₂×C₁₃×D₈	C₂×C₄	semidirect
34. C₁₃×D₁₆	C₂×C₄	semidirect
35. C₂×C₁₃×C₁₆	C₂×C₄	semidirect
58. C₁₃×D₈	C₂²×C₄	semidirect
70. C₁₃×C₁₆	C₂²×C₄	semidirect
94. C₂×Dic₁₃	D₁₆	direct (N × H)
103. C₂×D₁₆	Dic₁₃	direct (N × H)
128. Dic₁₃	C₂×D₁₆	direct (N × H)
133. C₂×D₈	C₂×Dic₁₃	semidirect
142. D₁₆	C₂×Dic₁₃	direct (N × H)
145. C₂×C₁₆	C₂×Dic₁₃	semidirect
153. C₂×C₁₃	C₄×D₁₆	semidirect
170. D₈	C₂²×Dic₁₃	semidirect
183. C₁₆	C₂²×Dic₁₃	semidirect
184. C₁₃	C₂×C₄×D₁₆	semidirect
223. C₂	D₁₆×Dic₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₈×Dic₁₃	2
D₁₆×Dic₁₃	2
C₂×#11718096	2
C₂×#11718154	2
C₂×C₁₆×Dic₁₃	2
C₂²×C₁₃×D₁₆	2
C₂×C₄×D₁₆	13

Subgroups — C2×D16×Dic13 #16016180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₆×Dic₁₃ #16016180