Subgroups — #16807059

Order 3328.

682 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131199	C₂	1	4	yes	maximal, complemented
2	#13131195	C₂	1	4	yes	maximal, complemented
3	#13131170	C₂	1	2	yes	maximal, complemented
4	#13131065	C₂	1	2	yes	maximal
5	C₄×#88106	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
8	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄²×D₁₃	C₄	1	1	yes	characteristic
10	C₂×#88106	C₂²	1	4	yes	—
11	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
15	C₄×C₈×D₁₃	C₄	1	2	yes	—
16	C₄×C₈×D₁₃	C₄	1	2	yes	—
17	C₄×C₈×D₁₃	C₂²	1	2	yes	—
18	C₄×C₈×D₁₃	C₂²	1	2	yes	—
19	#11718260	C₂²	1	8	yes	complemented
20	#11718259	C₂²	1	8	yes	—
21	#11718231	C₂²	1	4	yes	complemented
22	C₄×#6092	C₂²	1	4	yes	complemented
23	C₂²×C₄×D₁₃	C₈	1	2	yes	—
24	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×Dic₁₃	C₈	1	2	yes	—
29	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
31	C₂²×#1055	C₂³	1	1	yes	characteristic
32	C₂×C₈×D₁₃	—	2	4	no	—
33	C₂×C₈×D₁₃	—	2	4	no	—
34	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
35	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
36	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
37	C₂×C₈×D₁₃	C₂³	1	2	yes	—
38	C₄²×D₁₃	C₈	1	2	yes	—
39	C₄²×D₁₃	C₈	1	2	yes	—
40	C₄²×D₁₃	C₂×C₄	1	2	yes	—
41	C₄²×D₁₃	C₂×C₄	1	2	yes	—
42	#88106	—	2	8	no	—
43	C₂×#6092	C₂³	1	8	yes	—
44	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
45	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
46	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
47	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
48	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
49	C₈×Dic₁₃	C₂³	1	2	yes	—
50	C₄×#1055	C₂×C₄	1	1	yes	characteristic
51	C₄×#1055	C₂×C₄	1	1	yes	characteristic
52	C₄×#1055	C₂³	1	1	yes	characteristic
53	C₄×#1055	C₂³	1	1	yes	characteristic
54	#33418	—	13	1	no	maximal, Sylow
55	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
57	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
58	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
59	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
60	C₂×C₄×D₁₃	—	2	2	no	—
61	C₂×C₄×D₁₃	—	2	2	no	—
62	C₂×C₄×D₁₃	—	2	8	no	—
63	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
64	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
65	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
66	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
67	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
68	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
69	C₂×C₈×C₁₃	—	2	2	no	—
70	C₂×C₈×C₁₃	—	2	2	no	—
71	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
72	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
73	C₄²×C₁₃	C₂×C₈	1	2	yes	—
74	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
75	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
77	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
78	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
79	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
80	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
81	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
82	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
83	C₂×#1055	M₁₆	1	4	yes	—
84	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
85	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
86	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
87	C₂×#1055	#41	1	4	yes	—
88	C₂×#1055	C₂⁴	1	1	yes	characteristic
89	C₈×D₁₃	—	2	4	no	—
90	C₈×D₁₃	—	2	4	no	—
91	C₈×D₁₃	—	2	4	no	—
92	C₈×D₁₃	—	2	4	no	—
93	#6092	—	2	8	no	—
94	C₂²×C₄×C₈	—	13	1	no	—
95	#2163	—	13	4	no	—
96	#2162	—	13	4	no	—
97	#2150	—	13	2	no	—
98	#2112	—	13	2	no	—
99	C₄×M₃₂	—	13	2	no	—
100	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
101	C₂²×D₁₃	—	2	2	no	—
102	C₂²×D₁₃	—	2	4	no	—
103	C₂²×D₁₃	C₂²×C₈	1	2	yes	—
104	C₂×C₄×C₁₃	—	2	4	no	—
105	C₂×C₄×C₁₃	#117	1	2	yes	—
106	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
107	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
108	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
109	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
110	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
111	C₂×Dic₁₃	—	2	2	no	—
112	C₂×Dic₁₃	—	2	4	no	—
113	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
114	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
115	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
116	C₄×D₁₃	—	2	4	no	—
117	C₄×D₁₃	—	2	2	no	—
118	C₄×D₁₃	—	2	2	no	—
119	C₄×D₁₃	—	2	4	no	—
120	C₄×D₁₃	—	2	4	no	—
121	C₄×D₁₃	—	2	4	no	—
122	C₄×D₁₃	M₃₂	1	8	yes	complemented
123	C₈×C₁₃	—	2	2	no	—
124	C₈×C₁₃	—	2	2	no	—
125	#1055	#117	1	2	yes	—
126	#1055	C₂×M₁₆	1	2	yes	—
127	#1055	C₂×M₁₆	1	2	yes	—
128	#1055	C₂×#41	1	2	yes	—
129	C₂³×C₈	—	13	1	no	—
130	C₂³×C₈	—	13	1	no	—
131	C₂²×C₄²	—	13	1	no	—
132	C₂×M₃₂	—	13	4	no	—
133	C₂×C₄×C₈	—	13	1	no	—
134	C₂×C₄×C₈	—	13	1	no	—
135	C₂×C₄×C₈	—	13	1	no	—
136	C₂×C₄×C₈	—	13	2	no	—
137	C₂×C₄×C₈	—	13	2	no	—
138	C₂×C₄×C₈	—	13	2	no	—
139	C₂×C₄×C₈	—	13	2	no	—
140	C₂×C₄×C₈	#261	1	1	yes	characteristic
141	C₄⋊C₁₆	—	13	8	no	—
142	C₂²⋊C₁₆	—	13	8	no	—
143	#346	—	13	4	no	—
144	C₄×C₁₆	—	13	4	no	—
145	C₂²×C₁₃	—	2	2	no	—
146	C₂²×C₁₃	#431	1	2	yes	—
147	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
148	C₂×D₁₃	—	2	8	no	—
149	C₂×D₁₃	—	2	2	no	—
150	C₂×D₁₃	—	2	2	no	—
151	C₂×D₁₃	C₂×M₃₂	1	4	yes	—
152	C₄×C₁₃	—	2	2	no	—
153	C₄×C₁₃	#431	1	2	yes	—
154	C₄×C₁₃	C₂×M₃₂	1	4	yes	—
155	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
156	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
157	Dic₁₃	—	2	2	no	—
158	Dic₁₃	—	2	2	no	—
159	Dic₁₃	C₂×M₃₂	1	4	yes	—
160	C₂³×C₄	—	13	2	no	—
161	C₂³×C₄	—	13	1	no	—
162	C₂²×C₈	—	13	1	no	—
163	C₂²×C₈	—	13	1	no	—
164	C₂²×C₈	—	13	2	no	—
165	C₂²×C₈	—	13	2	no	—
166	C₂²×C₈	—	13	2	no	—
167	C₂²×C₈	—	13	2	no	—
168	C₂²×C₈	—	26	4	no	—
169	C₂²×C₈	—	26	4	no	—
170	C₂²×C₈	C₂×#261	1	1	yes	characteristic
171	C₂²×C₈	C₂×#261	1	1	yes	characteristic
172	C₂×C₄²	—	13	2	no	—
173	C₂×C₄²	—	13	1	no	—
174	C₂×C₄²	—	13	2	no	—
175	C₂×C₄²	—	13	2	no	—
176	C₂×C₄²	—	13	2	no	—
177	C₂×C₄²	—	13	2	no	—
178	C₂×C₄²	C₂×#261	1	1	yes	characteristic
179	M₃₂	—	26	8	no	—
180	C₂×C₁₆	—	13	8	no	—
181	C₄×C₈	—	13	2	no	—
182	C₄×C₈	—	13	2	no	—
183	C₄×C₈	—	13	2	no	—
184	C₄×C₈	—	13	2	no	—
185	C₄×C₈	—	13	1	no	—
186	C₄×C₈	—	13	1	no	—
187	C₄×C₈	—	13	1	no	—
188	C₄×C₈	—	13	1	no	—
189	C₄×C₈	C₂×#261	1	2	yes	—
190	C₄×C₈	C₂×#261	1	2	yes	—
191	C₂×C₁₃	—	2	2	no	—
192	C₂×C₁₃	C₂×#431	1	1	yes	characteristic
193	C₂×C₁₃	C₂²×M₃₂	1	2	yes	—
194	D₁₃	—	2	4	no	—
195	C₂⁴	—	13	1	no	—
196	C₂²×C₄	—	13	2	no	—
197	C₂²×C₄	—	13	2	no	—
198	C₂²×C₄	—	13	1	no	—
199	C₂²×C₄	—	13	2	no	—
200	C₂²×C₄	—	13	2	no	—
201	C₂²×C₄	—	13	2	no	—
202	C₂²×C₄	—	13	2	no	—
203	C₂²×C₄	—	13	2	no	—
204	C₂²×C₄	—	26	8	no	—
205	C₂²×C₄	—	26	2	no	—
206	C₂²×C₄	—	26	2	no	—
207	C₂²×C₄	D₁₃⋊C₈	1	2	yes	—
208	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
209	C₂×C₈	—	2	2	no	—
210	C₂×C₈	—	2	2	no	—
211	C₂×C₈	—	13	4	no	—
212	C₂×C₈	—	13	4	no	—
213	C₂×C₈	—	13	1	no	—
214	C₂×C₈	—	13	1	no	—
215	C₂×C₈	—	13	1	no	—
216	C₂×C₈	—	13	1	no	—
217	C₂×C₈	—	26	4	no	—
218	C₂×C₈	—	26	4	no	—
219	C₂×C₈	—	26	4	no	—
220	C₂×C₈	—	26	4	no	—
221	C₂×C₈	C₂²×#261	1	2	yes	—
222	C₂×C₈	C₂²×#261	1	2	yes	—
223	C₄²	—	13	1	no	—
224	C₄²	—	13	2	no	—
225	C₄²	—	13	2	no	—
226	C₄²	—	13	2	no	—
227	C₄²	—	13	1	no	—
228	C₄²	—	13	2	no	—
229	C₄²	—	13	2	no	—
230	C₄²	D₁₃⋊C₈	1	2	yes	—
231	C₄²	C₂²×#261	1	1	yes	characteristic
232	C₄²	C₂²×#261	1	1	yes	characteristic
233	C₁₆	—	26	8	no	—
234	C₁₃	#33418	1	1	yes	characteristic, complemented, Sylow
235	C₂³	—	13	2	no	—
236	C₂³	—	26	4	no	—
237	C₂³	—	26	2	no	—
238	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
239	C₂×C₄	—	2	4	no	—
240	C₂×C₄	—	13	2	no	—
241	C₂×C₄	—	13	8	no	—
242	C₂×C₄	—	13	2	no	—
243	C₂×C₄	—	13	2	no	—
244	C₂×C₄	—	26	4	no	—
245	C₂×C₄	—	26	4	no	—
246	C₂×C₄	—	26	4	no	—
247	C₂×C₄	—	26	2	no	—
248	C₂×C₄	—	26	4	no	—
249	C₂×C₄	—	26	4	no	—
250	C₂×C₄	—	26	2	no	—
251	C₂×C₄	—	26	2	no	—
252	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
253	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
254	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
255	C₂×C₄	D₁₃⋊M₁₆	1	2	yes	—
256	C₂×C₄	#88237	1	2	yes	—
257	C₂×C₄	C₂³×#261	1	1	yes	characteristic
258	C₈	—	2	2	no	—
259	C₈	—	2	2	no	—
260	C₈	—	13	2	no	—
261	C₈	—	13	2	no	—
262	C₈	—	13	2	no	—
263	C₈	—	13	2	no	—
264	C₂²	—	2	2	no	—
265	C₂²	—	13	4	no	—
266	C₂²	—	26	8	no	—
267	C₂²	—	26	2	no	—
268	C₂²	—	26	2	no	—
269	C₂²	#11719049	1	2	yes	—
270	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
271	C₄	—	2	2	no	—
272	C₄	—	13	4	no	—
273	C₄	—	26	2	no	—
274	C₄	—	26	2	no	—
275	C₄	#11719049	1	2	yes	—
276	C₄	D₁₃⋊M₃₂	1	4	yes	—
277	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
278	C₄	C₂×#88237	1	1	yes	characteristic
279	C₂	—	2	2	no	—
280	C₂	—	26	4	no	—
281	C₂	C₂×#11719049	1	1	yes	characteristic
282	C₂	C₂×D₁₃⋊M₃₂	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂³×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
prime radical	C₂³×D₁₃	C₂×C₈
cosocle	C₂×#1055	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	#33418
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
1. #13131199	C₂	semidirect
2. #13131195	C₂	semidirect
3. #13131170	C₂	semidirect
5. C₄×#88106	C₂	semidirect
19. #11718260	C₂²	semidirect
21. #11718231	C₂²	semidirect
22. C₄×#6092	C₂²	semidirect
122. C₄×D₁₃	M₃₂	semidirect
234. C₁₃	#33418	semidirect

Maximal subgroups

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

subgroup	index
#13131199	2
#13131195	2
#13131170	2
#13131065	2
C₄×#88106	2
C₂×C₄×C₈×D₁₃	2
#33418	13