Subgroups — C₂×M₃₂×Dic₁₃ #16015548

Order 3328.

918 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88052	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	M₃₂×Dic₁₃	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718094	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₆×Dic₁₃	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄×Dic₁₃	C₄	1	1	yes	characteristic
9	C₂³×#1055	C₄	1	1	yes	characteristic
10	C₂×C₁₃×M₃₂	C₄	1	8	yes	complemented
11	C₂×C₁₃×M₃₂	C₂²	1	4	yes	—
12	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
13	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
14	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
15	C₂×C₈×Dic₁₃	C₄	1	4	yes	—
16	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₈×Dic₁₃	C₂²	1	4	yes	—
19	C₂×#88052	C₄	1	8	yes	complemented
20	C₂×#88052	C₂²	1	4	yes	—
21	C₂²×#6090	C₂²	1	2	yes	—
22	#11718094	C₂²	1	8	yes	complemented
23	C₁₆×Dic₁₃	C₂²	1	8	yes	complemented
24	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂³×Dic₁₃	C₈	1	2	yes	—
26	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
28	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
29	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
30	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
31	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
32	C₂×C₄×Dic₁₃	C₈	1	4	yes	—
33	C₂×C₄×Dic₁₃	C₈	1	2	yes	—
34	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×Dic₁₃	C₂×C₄	1	4	yes	—
36	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×#1055	C₈	1	8	yes	—
38	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
39	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
40	C₂²×#1055	C₂×C₄	1	4	yes	—
41	C₁₃×M₃₂	C₂×C₄	1	16	yes	complemented
42	C₂×C₁₃×C₁₆	C₂×C₄	1	8	yes	complemented
43	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
44	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
45	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
46	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
47	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
48	C₈×Dic₁₃	C₂³	1	2	yes	—
49	C₈×Dic₁₃	C₂³	1	2	yes	—
50	#88052	C₂×C₄	1	16	yes	complemented
51	C₂×#6090	C₂×C₄	1	8	yes	complemented
52	C₂×#6090	C₂³	1	4	yes	—
53	C₂×C₄×M₃₂	—	13	1	no	maximal, Sylow
54	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
56	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
57	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
58	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
59	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
60	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
61	C₂²×Dic₁₃	—	2	8	no	—
62	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
63	C₂²×Dic₁₃	C₂×C₈	1	8	yes	—
64	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
65	C₂×C₈×C₁₃	C₄²	1	8	yes	—
66	C₂×C₈×C₁₃	C₄²	1	4	yes	—
67	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
68	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
70	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
71	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
72	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
73	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
74	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
75	C₄×Dic₁₃	C₂×C₈	1	8	yes	—
76	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
77	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
78	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
79	C₂×#1055	C₂×C₈	1	16	yes	—
80	C₂×#1055	C₂×C₈	1	4	yes	—
81	C₂×#1055	C₂×C₈	1	4	yes	—
82	C₂×#1055	C₂²×C₄	1	2	yes	—
83	C₂×#1055	C₂²×C₄	1	2	yes	—
84	C₁₃×C₁₆	C₂²×C₄	1	8	yes	complemented
85	#6090	C₂²×C₄	1	8	yes	complemented
86	C₂²×M₃₂	—	13	1	no	—
87	C₂²×M₃₂	D₁₃	1	1	yes	characteristic
88	C₂²×C₄×C₈	—	13	1	no	—
89	C₄×M₃₂	—	13	8	no	—
90	C₂×#346	—	13	2	no	—
91	C₂×C₄×C₁₆	—	13	2	no	—
92	C₂³×C₁₃	—	2	4	no	—
93	C₂³×C₁₃	C₄×C₈	1	4	yes	—
94	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
95	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
96	C₂×C₄×C₁₃	C₄×C₈	1	8	yes	—
97	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	—
98	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
99	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
100	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
101	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
102	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
103	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
104	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
105	C₂×Dic₁₃	—	2	4	no	—
106	C₂×Dic₁₃	—	2	16	no	—
107	C₂×Dic₁₃	M₃₂	1	8	yes	direct product factor
108	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
109	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
110	C₈×C₁₃	C₂×C₄²	1	2	yes	—
111	C₈×C₁₃	C₂×C₄²	1	4	yes	—
112	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
113	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
114	#1055	C₂²×C₈	1	4	yes	—
115	#1055	C₂²×C₈	1	4	yes	—
116	C₂³×C₈	—	13	1	no	—
117	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
118	C₂²×C₄²	—	13	1	no	—
119	C₂×M₃₂	—	13	8	no	—
120	C₂×M₃₂	—	13	4	no	—
121	C₂×M₃₂	Dic₁₃	1	8	yes	direct product factor
122	C₂×M₃₂	C₂×D₁₃	1	4	yes	—
123	C₂²×C₁₆	—	13	2	no	—
124	C₂²×C₁₆	C₂×D₁₃	1	2	yes	—
125	C₂×C₄×C₈	—	13	1	no	—
126	C₂×C₄×C₈	—	13	1	no	—
127	C₂×C₄×C₈	—	13	4	no	—
128	C₂×C₄×C₈	—	13	4	no	—
129	C₂×C₄×C₈	—	13	1	no	—
130	C₂×C₄×C₈	—	13	1	no	—
131	#346	—	13	8	no	—
132	C₄×C₁₆	—	13	8	no	—
133	C₂²×C₁₃	—	2	8	no	—
134	C₂²×C₁₃	—	2	4	no	—
135	C₂²×C₁₃	C₂×C₄×C₈	1	4	yes	—
136	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
137	C₂²×C₁₃	C₂×M₃₂	1	4	yes	—
138	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
139	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
140	C₄×C₁₃	C₂×C₄×C₈	1	4	yes	—
141	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
142	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
143	Dic₁₃	—	2	4	no	—
144	Dic₁₃	C₂×M₃₂	1	8	yes	direct product factor
145	C₂³×C₄	—	13	2	no	—
146	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
147	C₂²×C₈	—	13	8	no	—
148	C₂²×C₈	—	13	4	no	—
149	C₂²×C₈	—	13	1	no	—
150	C₂²×C₈	—	13	1	no	—
151	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
152	C₂²×C₈	C₄×D₁₃	1	2	yes	—
153	C₂²×C₈	C₄×D₁₃	1	4	yes	—
154	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
155	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
156	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
157	C₂×C₄²	—	13	2	no	—
158	C₂×C₄²	—	13	4	no	—
159	C₂×C₄²	—	13	1	no	—
160	C₂×C₄²	—	13	4	no	—
161	C₂×C₄²	—	13	1	no	—
162	M₃₂	—	13	16	no	—
163	M₃₂	C₂×Dic₁₃	1	16	yes	direct product factor
164	C₂×C₁₆	—	13	8	no	—
165	C₂×C₁₆	—	13	4	no	—
166	C₂×C₁₆	C₂×Dic₁₃	1	8	yes	complemented
167	C₂×C₁₆	C₂²×D₁₃	1	4	yes	—
168	C₄×C₈	—	13	4	no	—
169	C₄×C₈	—	13	4	no	—
170	C₄×C₈	—	13	2	no	—
171	C₄×C₈	—	13	2	no	—
172	C₄×C₈	—	13	2	no	—
173	C₄×C₈	—	13	2	no	—
174	C₂×C₁₃	—	2	4	no	—
175	C₂×C₁₃	C₄×M₃₂	1	4	yes	complemented
176	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
177	C₂×C₁₃	C₂²×M₃₂	1	2	yes	—
178	C₂⁴	C₈×D₁₃	1	1	yes	characteristic
179	C₂²×C₄	—	13	2	no	—
180	C₂²×C₄	—	13	8	no	—
181	C₂²×C₄	—	13	2	no	—
182	C₂²×C₄	—	26	8	no	—
183	C₂²×C₄	C₈×D₁₃	1	4	yes	—
184	C₂²×C₄	C₈×D₁₃	1	2	yes	—
185	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
186	C₂²×C₄	C₄×Dic₁₃	1	4	yes	—
187	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
188	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
189	C₂×C₈	—	13	16	no	—
190	C₂×C₈	—	13	4	no	—
191	C₂×C₈	—	13	4	no	—
192	C₂×C₈	—	13	2	no	—
193	C₂×C₈	—	13	2	no	—
194	C₂×C₈	C₄×Dic₁₃	1	4	yes	—
195	C₂×C₈	C₄×Dic₁₃	1	8	yes	—
196	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
197	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
198	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
199	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
200	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
201	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
202	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
203	C₄²	—	13	2	no	—
204	C₄²	—	13	8	no	—
205	C₄²	—	13	2	no	—
206	C₄²	—	13	2	no	—
207	C₄²	—	13	2	no	—
208	C₁₆	—	13	8	no	—
209	C₁₆	C₂²×Dic₁₃	1	8	yes	complemented
210	C₁₃	C₂×C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
211	C₂³	—	2	4	no	—
212	C₂³	C₈×Dic₁₃	1	4	yes	—
213	C₂³	C₂×C₈×D₁₃	1	2	yes	—
214	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
215	C₂×C₄	—	13	4	no	—
216	C₂×C₄	—	13	8	no	—
217	C₂×C₄	—	13	4	no	—
218	C₂×C₄	—	26	16	no	—
219	C₂×C₄	—	26	4	no	—
220	C₂×C₄	C₈×Dic₁₃	1	8	yes	—
221	C₂×C₄	C₈×Dic₁₃	1	4	yes	—
222	C₂×C₄	C₂×C₈×D₁₃	1	4	yes	—
223	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
224	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
225	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
226	C₂×C₄	C₂×C₄×Dic₁₃	1	4	yes	—
227	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
228	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
229	C₈	—	13	4	no	—
230	C₈	—	13	4	no	—
231	C₈	C₂×C₄×Dic₁₃	1	4	yes	—
232	C₈	C₂×C₄×Dic₁₃	1	2	yes	—
233	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
234	C₈	C₂³×Dic₁₃	1	1	yes	characteristic
235	C₂²	—	2	8	no	—
236	C₂²	—	2	4	no	—
237	C₂²	D₁₃×M₃₂	1	4	yes	—
238	C₂²	C₂×C₈×Dic₁₃	1	4	yes	—
239	C₂²	C₂×C₈×Dic₁₃	1	2	yes	—
240	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
241	C₄	—	13	8	no	—
242	C₄	—	26	4	no	—
243	C₄	C₂×C₈×Dic₁₃	1	4	yes	—
244	C₄	C₂×C₈×Dic₁₃	1	2	yes	—
245	C₄	C₂²×C₈×D₁₃	1	1	yes	characteristic
246	C₄	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
247	C₂	—	2	4	no	—
248	C₂	M₃₂×Dic₁₃	1	4	yes	direct product factor
249	C₂	C₂²×C₈×Dic₁₃	1	1	yes	characteristic
250	C₂	C₂×D₁₃×M₃₂	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂²×D₁₃
commutator	C₂×C₁₃	C₂²×C₄×C₈
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂²×C₁₃×M₃₂	C₂
socle	C₂³×C₁₃	C₂²×C₈
prime radical	C₂⁴×C₁₃	C₂×C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂²×M₃₂	D₁₃
hypocenter	C₁₃	C₂×C₄×M₃₂
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂²×M₃₂

Complements

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

N	H ≅ G/N	type
3. M₃₂×Dic₁₃	C₂	direct (N × H)
4. C₂×#11718094	C₂	semidirect
5. C₂×C₁₆×Dic₁₃	C₂	semidirect
10. C₂×C₁₃×M₃₂	C₄	semidirect
19. C₂×#88052	C₄	semidirect
22. #11718094	C₂²	semidirect
23. C₁₆×Dic₁₃	C₂²	semidirect
41. C₁₃×M₃₂	C₂×C₄	semidirect
42. C₂×C₁₃×C₁₆	C₂×C₄	semidirect
50. #88052	C₂×C₄	semidirect
51. C₂×#6090	C₂×C₄	semidirect
84. C₁₃×C₁₆	C₂²×C₄	semidirect
85. #6090	C₂²×C₄	semidirect
107. C₂×Dic₁₃	M₃₂	direct (N × H)
121. C₂×M₃₂	Dic₁₃	direct (N × H)
144. Dic₁₃	C₂×M₃₂	direct (N × H)
163. M₃₂	C₂×Dic₁₃	direct (N × H)
166. C₂×C₁₆	C₂×Dic₁₃	semidirect
175. C₂×C₁₃	C₄×M₃₂	semidirect
209. C₁₆	C₂²×Dic₁₃	semidirect
210. C₁₃	C₂×C₄×M₃₂	semidirect
248. C₂	M₃₂×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
C₂²×#88052	2
C₂²×C₈×Dic₁₃	2
M₃₂×Dic₁₃	2
C₂×#11718094	2
C₂×C₁₆×Dic₁₃	2
C₂²×C₁₃×M₃₂	2
C₂×C₄×M₃₂	13

Subgroups — C2×M32×Dic13 #16015548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×M₃₂×Dic₁₃ #16015548