Subgroups — #15767964

Order 3328.

510 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13115642	C₂	1	1	yes	maximal, characteristic
2	#13115641	C₂	1	1	yes	maximal, characteristic
3	#13115641	C₂	1	1	yes	maximal, characteristic
4	#13114992	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114963	C₂	1	1	yes	maximal, characteristic, complemented
6	#13112663	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#88128	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×#107	—	2	2	no	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#384	C₂²	1	1	yes	characteristic
12	C₁₃×#384	C₂²	1	1	yes	characteristic
13	C₂×#88061	—	2	2	no	—
14	C₂×#88049	—	2	2	no	—
15	C₂×#88049	—	2	2	no	—
16	C₂×#88048	—	2	2	no	—
17	#11718596	C₂²	1	1	yes	characteristic
18	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
19	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
20	#11718121	—	2	2	no	—
21	C₂²×D₅₂	—	2	1	no	—
22	C₂²×D₅₂	—	2	1	no	—
23	C₂²×D₅₂	—	2	1	no	—
24	C₂²×C₈×C₁₃	D₄	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
31	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
32	C₂×C₄⋊Dic₁₃	—	2	1	no	—
33	C₂×C₄⋊Dic₁₃	—	2	1	no	—
34	C₂×C₄⋊Dic₁₃	—	2	1	no	—
35	C₂²×#1055	D₄	1	2	yes	—
36	C₂²×#1055	D₄	1	2	yes	—
37	#88128	—	2	1	no	—
38	#88128	—	2	1	no	—
39	#88128	—	2	1	no	—
40	#88128	Q₈	1	2	yes	—
41	C₁₃×#107	—	4	4	no	—
42	C₄×C₈×C₁₃	—	2	1	no	—
43	C₄×C₈×C₁₃	—	2	1	no	—
44	#88061	—	4	4	no	—
45	#88049	—	4	4	no	—
46	#88049	—	4	4	no	—
47	#88048	—	4	4	no	—
48	C₄×#1055	—	2	1	no	—
49	C₄×#1055	—	2	1	no	—
50	C₄×#1055	—	2	1	no	—
51	C₄×#1055	—	2	1	no	—
52	#10672	—	13	1	no	maximal, Sylow
53	C₂³×D₁₃	—	4	1	no	—
54	C₂²×C₄×C₁₃	—	4	1	no	—
55	C₂²×C₄×C₁₃	—	4	1	no	—
56	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₂²×Dic₁₃	—	4	1	no	—
60	C₂×D₅₂	—	2	2	no	—
61	C₂×D₅₂	—	2	2	no	—
62	C₂×D₅₂	—	2	2	no	—
63	C₂×D₅₂	—	4	2	no	—
64	C₂×D₅₂	—	4	2	no	—
65	C₂×D₅₂	—	4	2	no	—
66	C₂×D₅₂	—	4	2	no	—
67	C₂×D₅₂	—	4	2	no	—
68	C₂×D₅₂	—	4	2	no	—
69	C₂×D₅₂	—	4	1	no	—
70	C₂×D₅₂	—	4	1	no	—
71	C₂×D₅₂	—	4	1	no	—
72	C₂×C₈×C₁₃	—	2	2	no	—
73	C₂×C₈×C₁₃	—	2	2	no	—
74	C₂×C₈×C₁₃	SD₁₆	1	4	yes	—
75	C₁₃×C₄⋊C₄	—	4	2	no	—
76	C₁₃×C₄⋊C₄	—	4	2	no	—
77	C₁₃×C₄⋊C₄	—	4	2	no	—
78	C₁₃×C₄⋊C₄	—	4	2	no	—
79	C₁₃×C₄⋊C₄	—	4	2	no	—
80	C₁₃×C₄⋊C₄	—	4	2	no	—
81	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
82	C₄²×C₁₃	#41	1	1	yes	characteristic
83	C₄²×C₁₃	#41	1	1	yes	characteristic
84	C₄²×C₁₃	#41	1	1	yes	characteristic
85	C₄⋊Dic₁₃	—	4	2	no	—
86	C₄⋊Dic₁₃	—	4	2	no	—
87	C₄⋊Dic₁₃	—	4	2	no	—
88	C₂×#1055	—	2	2	no	—
89	C₂×#1055	—	2	2	no	—
90	C₂×#1055	—	2	2	no	—
91	C₂×#1055	—	2	2	no	—
92	C₂×#1055	—	2	2	no	—
93	C₂×#1055	D₈	1	4	yes	—
94	#1957	—	13	1	no	—
95	#1957	—	13	1	no	—
96	#1957	—	13	1	no	—
97	#1845	D₁₃	1	1	yes	characteristic, complemented
98	#1844	—	13	1	no	—
99	#1834	—	13	1	no	—
100	#1273	—	13	1	no	—
101	C₂³×C₁₃	#127	1	1	yes	characteristic
102	C₂²×D₁₃	—	4	2	no	—
103	C₂²×D₁₃	—	8	1	no	—
104	C₂²×D₁₃	—	8	1	no	—
105	C₂²×D₁₃	—	8	1	no	—
106	C₂²×D₁₃	—	8	1	no	—
107	C₂²×D₁₃	—	8	1	no	—
108	C₂²×D₁₃	—	8	1	no	—
109	C₂×C₄×C₁₃	—	8	1	no	—
110	C₂×C₄×C₁₃	—	8	1	no	—
111	C₂×C₄×C₁₃	—	8	1	no	—
112	C₂×C₄×C₁₃	—	8	1	no	—
113	C₂×C₄×C₁₃	—	8	1	no	—
114	C₂×C₄×C₁₃	—	8	1	no	—
115	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
116	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
117	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
118	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
119	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
120	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
121	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
122	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
123	C₂×C₄×C₁₃	#135	1	2	yes	—
124	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
125	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
126	C₂×C₄×C₁₃	#137	1	2	yes	—
127	C₂×Dic₁₃	—	8	1	no	—
128	C₂×Dic₁₃	—	8	1	no	—
129	C₂×Dic₁₃	—	8	1	no	—
130	D₅₂	—	4	4	no	—
131	D₅₂	—	4	4	no	—
132	D₅₂	—	4	4	no	—
133	D₅₂	—	8	2	no	—
134	D₅₂	—	8	2	no	—
135	D₅₂	—	8	2	no	—
136	C₈×C₁₃	—	2	4	no	—
137	#1055	—	2	4	no	—
138	#1055	—	4	2	no	—
139	C₂×#127	—	13	1	no	—
140	C₂×#107	—	2	2	no	—
141	C₂×#106	—	26	2	no	—
142	C₂×#102	—	26	2	no	—
143	C₂×#102	—	26	2	no	—
144	C₂×#102	—	26	2	no	—
145	C₂×C₄×C₈	—	13	1	no	—
146	C₂×C₄×C₈	—	13	1	no	—
147	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
148	#384	—	13	1	no	—
149	#384	C₂×D₁₃	1	1	yes	characteristic
150	#384	C₂×D₁₃	1	1	yes	characteristic
151	#340	—	26	2	no	—
152	C₂²×C₁₃	#399	1	1	yes	characteristic
153	C₂²×C₁₃	#492	1	1	yes	characteristic
154	C₂²×C₁₃	#493	1	1	yes	characteristic
155	C₂²×C₁₃	#495	1	1	yes	characteristic
156	C₂²×C₁₃	#496	1	1	yes	characteristic
157	C₂²×C₁₃	#496	1	1	yes	characteristic
158	C₂²×C₁₃	#497	1	1	yes	characteristic
159	C₂×D₁₃	—	8	2	no	—
160	C₂×D₁₃	—	8	2	no	—
161	C₂×D₁₃	—	8	2	no	—
162	C₂×D₁₃	—	16	1	no	—
163	C₂×D₁₃	—	16	1	no	—
164	C₂×D₁₃	—	16	1	no	—
165	C₂×D₁₃	—	16	1	no	—
166	C₄×C₁₃	—	16	1	no	—
167	C₄×C₁₃	—	16	1	no	—
168	C₄×C₁₃	#474	1	2	yes	—
169	C₄×C₁₃	#476	1	2	yes	—
170	C₄×C₁₃	#478	1	2	yes	—
171	C₄×C₁₃	#480	1	2	yes	—
172	C₄×C₁₃	#481	1	2	yes	—
173	C₄×C₁₃	#482	1	2	yes	—
174	Dic₁₃	—	16	1	no	—
175	C₂²×D₄	—	26	1	no	—
176	C₂²×D₄	—	26	1	no	—
177	C₂²×D₄	—	26	1	no	—
178	C₂²×C₈	—	13	2	no	—
179	C₂²×C₈	—	13	2	no	—
180	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
181	#127	—	13	2	no	—
182	#127	—	26	1	no	—
183	#127	—	26	1	no	—
184	#127	—	26	1	no	—
185	C₂×C₄⋊C₄	—	2	1	no	—
186	C₂×C₄⋊C₄	—	2	1	no	—
187	C₂×C₄⋊C₄	—	2	1	no	—
188	C₂×C₄⋊C₄	—	2	1	no	—
189	C₂×C₄⋊C₄	—	2	1	no	—
190	C₂×C₄⋊C₄	—	2	1	no	—
191	C₂×C₄⋊C₄	—	26	1	no	—
192	C₂×C₄⋊C₄	—	26	1	no	—
193	C₂×C₄⋊C₄	—	26	1	no	—
194	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
195	#107	—	4	4	no	—
196	#106	—	52	4	no	—
197	#102	—	52	4	no	—
198	#102	—	52	4	no	—
199	#102	—	52	4	no	—
200	C₄×C₈	—	2	1	no	—
201	C₄×C₈	—	2	1	no	—
202	C₄×C₈	—	26	1	no	—
203	C₄×C₈	—	26	1	no	—
204	C₄×C₈	—	26	1	no	—
205	C₄×C₈	—	26	1	no	—
206	C₂×C₁₃	#1706	1	1	yes	characteristic
207	C₂×C₁₃	#1714	1	1	yes	characteristic
208	C₂×C₁₃	#1720	1	1	yes	characteristic
209	C₂×C₁₃	#1721	1	1	yes	characteristic
210	C₂×C₁₃	#2092	1	1	yes	characteristic
211	C₂×C₁₃	#2093	1	1	yes	characteristic
212	C₂×C₁₃	#2094	1	1	yes	characteristic
213	D₁₃	—	16	2	no	—
214	C₂⁴	—	52	1	no	—
215	C₂×D₄	—	26	2	no	—
216	C₂×D₄	—	26	2	no	—
217	C₂×D₄	—	26	2	no	—
218	C₂×D₄	—	52	1	no	—
219	C₂×D₄	—	52	1	no	—
220	C₂×D₄	—	52	2	no	—
221	C₂×D₄	—	52	2	no	—
222	C₂×D₄	—	52	2	no	—
223	C₂×D₄	—	52	2	no	—
224	C₂×D₄	—	52	1	no	—
225	C₂×D₄	—	52	2	no	—
226	C₂×D₄	—	52	2	no	—
227	C₂²×C₄	—	4	1	no	—
228	C₂²×C₄	—	4	1	no	—
229	C₂²×C₄	—	52	1	no	—
230	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
231	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
232	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
233	C₂×C₈	—	2	2	no	—
234	C₂×C₈	—	2	2	no	—
235	C₂×C₈	—	13	4	no	—
236	C₂×C₈	—	26	2	no	—
237	C₂×C₈	—	26	2	no	—
238	C₂×C₈	—	26	2	no	—
239	C₂×C₈	—	26	2	no	—
240	C₂×C₈	—	26	2	no	—
241	C₂×C₈	#6106	1	4	yes	—
242	C₄⋊C₄	—	4	2	no	—
243	C₄⋊C₄	—	4	2	no	—
244	C₄⋊C₄	—	4	2	no	—
245	C₄⋊C₄	—	4	2	no	—
246	C₄⋊C₄	—	4	2	no	—
247	C₄⋊C₄	—	4	2	no	—
248	C₄⋊C₄	—	52	2	no	—
249	C₄⋊C₄	—	52	2	no	—
250	C₄⋊C₄	—	52	2	no	—
251	C₄²	#6127	1	1	yes	characteristic
252	C₄²	#6127	1	1	yes	characteristic
253	C₄²	Q₈×D₁₃	1	1	yes	characteristic
254	C₄²	#6131	1	1	yes	characteristic
255	C₁₃	#10672	1	1	yes	characteristic, complemented, Sylow
256	C₂³	—	52	2	no	—
257	C₂³	—	104	1	no	—
258	C₂³	—	104	1	no	—
259	C₂³	—	104	1	no	—
260	C₂³	—	104	1	no	—
261	C₂³	—	104	1	no	—
262	C₂³	—	104	1	no	—
263	C₂³	#88194	1	1	yes	characteristic
264	D₄	—	52	4	no	—
265	D₄	—	52	4	no	—
266	D₄	—	52	4	no	—
267	D₄	—	104	2	no	—
268	D₄	—	104	2	no	—
269	D₄	—	104	2	no	—
270	C₂×C₄	—	8	1	no	—
271	C₂×C₄	—	8	1	no	—
272	C₂×C₄	—	8	1	no	—
273	C₂×C₄	—	8	1	no	—
274	C₂×C₄	—	8	1	no	—
275	C₂×C₄	—	8	1	no	—
276	C₂×C₄	—	104	1	no	—
277	C₂×C₄	—	104	1	no	—
278	C₂×C₄	—	104	1	no	—
279	C₂×C₄	#88148	1	1	yes	characteristic
280	C₂×C₄	#88148	1	1	yes	characteristic
281	C₂×C₄	#88150	1	1	yes	characteristic
282	C₂×C₄	#88150	1	1	yes	characteristic
283	C₂×C₄	D₈×D₁₃	1	2	yes	—
284	C₂×C₄	#88165	1	2	yes	—
285	C₂×C₄	#88172	1	2	yes	—
286	C₂×C₄	#88173	1	2	yes	—
287	C₂×C₄	#88183	1	1	yes	characteristic
288	C₂×C₄	#88186	1	2	yes	—
289	C₂×C₄	C₂×#6106	1	2	yes	—
290	C₂×C₄	#88200	1	1	yes	characteristic
291	C₈	—	2	4	no	—
292	C₈	—	26	4	no	—
293	C₈	—	52	2	no	—
294	C₂²	—	104	2	no	—
295	C₂²	—	104	2	no	—
296	C₂²	—	104	2	no	—
297	C₂²	—	208	1	no	—
298	C₂²	—	208	1	no	—
299	C₂²	—	208	1	no	—
300	C₂²	—	208	1	no	—
301	C₂²	#11718653	1	1	yes	characteristic
302	C₂²	#11718735	1	1	yes	characteristic
303	C₂²	#11718746	1	1	yes	characteristic
304	C₂²	#11718812	1	1	yes	characteristic
305	C₂²	#11718815	1	1	yes	characteristic
306	C₂²	#11718851	1	1	yes	characteristic
307	C₂²	#11718852	1	1	yes	characteristic
308	C₄	—	16	1	no	—
309	C₄	—	16	1	no	—
310	C₄	—	208	1	no	—
311	C₄	#11718543	1	2	yes	—
312	C₄	#11718546	1	2	yes	—
313	C₄	#11718551	1	2	yes	—
314	C₄	#11718552	1	2	yes	—
315	C₄	#11718629	1	2	yes	—
316	C₄	#11718745	1	2	yes	—
317	C₂	—	208	2	no	—
318	C₂	#13114429	1	1	yes	characteristic
319	C₂	#13114459	1	1	yes	characteristic
320	C₂	#13114499	1	1	yes	characteristic
321	C₂	#13114501	1	1	yes	characteristic
322	C₂	#13116354	1	1	yes	characteristic
323	C₂	#13116361	1	1	yes	characteristic
324	C₂	#13116370	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#88194
commutator, cosocle	C₂×C₄²×C₁₃	C₂³
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1845	C₂
socle	C₂³×C₁₃	#127
prime radical	C₂×#88128	C₂²
hypercenter	#1845	D₁₃
hypocenter	C₁₃	#10672
LCS	G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

Complements

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

N	H ≅ G/N	type
4. #13114992	C₂	semidirect
5. #13114963	C₂	semidirect
6. #13112663	C₂	semidirect
7. C₁₃×#1845	C₂	semidirect
97. #1845	D₁₃	semidirect
255. C₁₃	#10672	semidirect

Maximal subgroups

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

subgroup	index
#13115642	2
#13115641	2
#13114992	2
#13114963	2
#13112663	2
C₁₃×#1845	2
#10672	13