Subgroups — #16018274

Order 3328.

578 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125347	C₂	1	1	yes	maximal, characteristic
2	D₁₃×#494	C₂	1	1	yes	maximal, characteristic
3	#13117080	C₂	1	4	yes	maximal, complemented
4	#13117065	C₂	1	1	yes	maximal, characteristic, complemented
5	#13117064	C₂	1	1	yes	maximal, characteristic, complemented
6	#13117063	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116554	C₂	1	4	yes	maximal
8	C₄×#88038	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2241	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×Q₁₆×D₁₃	—	2	1	no	—
11	C₂×Q₁₆×D₁₃	C₂²	1	2	yes	—
12	#11719433	—	2	1	no	—
13	D₁₃×C₄⋊Q₈	—	2	1	no	—
14	C₁₃×#500	C₂²	1	1	yes	characteristic
15	C₁₃×#494	C₂²	1	1	yes	characteristic
16	#11718842	—	2	1	no	—
17	#11718842	C₂²	1	2	yes	—
18	#11718753	—	2	1	no	—
19	#11718740	—	2	1	no	—
20	C₂×#88038	C₂²	1	2	yes	—
21	#11718541	—	2	1	no	—
22	#11718541	C₂²	1	2	yes	—
23	#11718539	—	2	1	no	—
24	#11718539	C₂²	1	2	yes	—
25	#11718360	C₂²	1	1	yes	characteristic
26	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
27	#11718343	C₂²	1	1	yes	characteristic
28	C₁₃×#358	C₂²	1	4	yes	—
29	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
30	#11718156	C₂²	1	4	yes	—
31	#11718095	C₂²	1	4	yes	—
32	#11718094	C₂²	1	2	yes	—
33	#11718084	C₂²	1	4	yes	—
34	C₄×#6090	C₂²	1	1	yes	characteristic
35	C₂×Q₈×D₁₃	—	2	2	no	—
36	C₂×C₁₃×Q₁₆	—	2	1	no	—
37	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
38	C₁₃×C₄⋊Q₈	—	2	1	no	—
39	C₁₃×C₄⋊Q₈	—	2	1	no	—
40	#88200	—	4	1	no	—
41	Q₈×Dic₁₃	—	4	1	no	—
42	#88198	—	2	2	no	—
43	C₂×#6107	—	2	2	no	—
44	C₂×#6107	—	2	2	no	—
45	Q₁₆×D₁₃	—	2	8	no	—
46	Q₁₆×D₁₃	—	4	4	no	—
47	C₂×Dic₅₂	—	2	1	no	—
48	C₂×Dic₅₂	C₂³	1	2	yes	—
49	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
50	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
51	#88151	—	4	1	no	—
52	#88146	—	2	2	no	—
53	C₄⋊C₄×D₁₃	—	4	1	no	—
54	C₄⋊C₄×D₁₃	—	4	1	no	—
55	#88144	—	2	2	no	—
56	#88142	—	4	1	no	—
57	#88142	—	4	1	no	—
58	#88141	—	4	1	no	—
59	C₄²×D₁₃	D₄	1	1	yes	characteristic
60	#88123	—	2	1	no	—
61	#88123	—	2	1	no	—
62	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
63	C₁₃×#107	—	2	1	no	—
64	C₁₃×#107	C₂³	1	2	yes	—
65	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	#88058	—	2	1	no	—
67	#88058	C₂³	1	2	yes	—
68	C₈×Dic₁₃	D₄	1	1	yes	characteristic
69	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
70	C₂×#6090	C₂³	1	2	yes	—
71	#88048	—	2	2	no	—
72	#88048	—	2	2	no	—
73	C₄×#1055	D₄	1	1	yes	characteristic
74	#88038	—	2	4	no	—
75	#33705	—	13	1	no	maximal, Sylow
76	C₂×Q₈×C₁₃	—	2	2	no	—
77	C₂×Q₈×C₁₃	—	4	1	no	—
78	Q₈×D₁₃	—	4	4	no	—
79	Q₈×D₁₃	—	4	4	no	—
80	C₂×C₄×D₁₃	—	4	2	no	—
81	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
82	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
83	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
84	C₂×Dic₂₆	—	2	2	no	—
85	C₂×Dic₂₆	—	4	1	no	—
86	C₂×Dic₂₆	—	4	2	no	—
87	C₁₃×Q₁₆	—	2	4	no	—
88	C₁₃×Q₁₆	—	4	2	no	—
89	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
91	C₁₃×C₄⋊C₄	—	2	2	no	—
92	C₁₃×C₄⋊C₄	—	4	1	no	—
93	C₁₃×C₄⋊C₄	—	4	1	no	—
94	C₁₃×C₄⋊C₄	—	4	1	no	—
95	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
96	#6107	—	4	4	no	—
97	#6107	—	4	4	no	—
98	#6103	—	4	2	no	—
99	C₄⋊Dic₁₃	—	2	2	no	—
100	C₄⋊Dic₁₃	—	4	1	no	—
101	C₄⋊Dic₁₃	—	4	1	no	—
102	C₄⋊Dic₁₃	—	4	1	no	—
103	C₄⋊Dic₁₃	—	4	2	no	—
104	#6101	—	4	2	no	—
105	#6101	—	4	2	no	—
106	#6101	—	4	2	no	—
107	C₄×Dic₁₃	—	4	2	no	—
108	C₄×Dic₁₃	D₈	1	1	yes	characteristic
109	C₄×Dic₁₃	D₈	1	1	yes	characteristic
110	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂×#1055	C₂×D₄	1	1	yes	characteristic
112	C₂×#1055	C₂×D₄	1	1	yes	characteristic
113	Dic₅₂	—	2	4	no	—
114	Dic₅₂	—	4	2	no	—
115	C₈×D₁₃	SD₁₆	1	4	yes	—
116	C₈×D₁₃	#41	1	4	yes	—
117	C₁₃×C₁₆	—	2	2	no	—
118	#6090	—	2	2	no	—
119	#3160	—	13	1	no	—
120	C₂×#494	—	13	1	no	—
121	#2245	—	13	4	no	—
122	#2241	—	13	1	no	—
123	#2241	—	13	1	no	—
124	#2241	—	13	1	no	—
125	#2241	D₁₃	1	1	yes	characteristic, complemented
126	#2141	—	13	4	no	—
127	C₄×M₃₂	—	13	1	no	—
128	C₂²×D₁₃	C₂×D₈	1	1	yes	characteristic
129	Q₈×C₁₃	—	4	2	no	—
130	Q₈×C₁₃	—	4	2	no	—
131	Q₈×C₁₃	—	8	2	no	—
132	C₂×C₄×C₁₃	—	4	2	no	—
133	C₂×C₄×C₁₃	—	4	2	no	—
134	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
135	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
136	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
137	C₂×Dic₁₃	—	4	2	no	—
138	C₂×Dic₁₃	—	4	2	no	—
139	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
140	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
141	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
142	C₄×D₁₃	—	2	2	no	—
143	C₄×D₁₃	—	2	2	no	—
144	C₄×D₁₃	—	8	4	no	—
145	C₄×D₁₃	#124	1	2	yes	—
146	C₄×D₁₃	C₂×SD₁₆	1	2	yes	—
147	Dic₂₆	—	4	2	no	—
148	Dic₂₆	—	4	2	no	—
149	Dic₂₆	—	8	2	no	—
150	Dic₂₆	—	8	4	no	—
151	C₈×C₁₃	C₂×SD₁₆	1	2	yes	—
152	C₈×C₁₃	C₂×#41	1	2	yes	—
153	#1055	#124	1	2	yes	—
154	#1055	C₂×SD₁₆	1	2	yes	—
155	C₂²×Q₁₆	—	13	2	no	—
156	C₂²×Q₁₆	—	26	1	no	—
157	#533	—	26	1	no	—
158	C₂×C₄⋊Q₈	—	26	1	no	—
159	C₂×M₃₂	—	13	2	no	—
160	#500	—	13	1	no	—
161	#500	C₂×D₁₃	1	1	yes	characteristic
162	#499	—	13	2	no	—
163	#499	—	26	1	no	—
164	#498	—	26	1	no	—
165	#494	—	13	2	no	—
166	#494	—	13	1	no	—
167	#494	—	26	1	no	—
168	#494	—	26	1	no	—
169	#494	C₂×D₁₃	1	1	yes	characteristic
170	#427	—	13	2	no	—
171	#427	—	26	1	no	—
172	C₂×C₄×C₈	—	13	1	no	—
173	#358	—	13	4	no	—
174	#358	—	13	4	no	—
175	#358	—	13	4	no	—
176	#358	C₂×D₁₃	1	4	yes	—
177	#346	—	13	2	no	—
178	C₄×C₁₆	—	13	1	no	—
179	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
180	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
181	C₂×D₁₃	—	2	1	no	—
182	C₂×D₁₃	—	2	1	no	—
183	C₂×D₁₃	#486	1	2	yes	—
184	C₄×C₁₃	—	8	2	no	—
185	C₄×C₁₃	—	8	2	no	—
186	C₄×C₁₃	#510	1	2	yes	—
187	C₄×C₁₃	#510	1	2	yes	—
188	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
189	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
190	Dic₁₃	—	2	1	no	—
191	Dic₁₃	—	2	1	no	—
192	Dic₁₃	—	8	2	no	—
193	Dic₁₃	—	8	2	no	—
194	Dic₁₃	#486	1	2	yes	—
195	C₂²×Q₈	—	26	2	no	—
196	C₂×Q₁₆	—	2	1	no	—
197	C₂×Q₁₆	—	13	2	no	—
198	C₂×Q₁₆	—	26	8	no	—
199	C₂×Q₁₆	—	26	2	no	—
200	C₂×Q₁₆	—	26	2	no	—
201	C₂×Q₁₆	—	26	1	no	—
202	C₂×Q₁₆	—	52	4	no	—
203	C₂×Q₁₆	C₂²×D₁₃	1	2	yes	—
204	C₂²×C₈	—	13	1	no	—
205	C₂²×C₈	—	13	1	no	—
206	C₄⋊Q₈	—	2	1	no	—
207	C₄⋊Q₈	—	2	1	no	—
208	C₄⋊Q₈	—	26	2	no	—
209	C₄⋊Q₈	—	26	1	no	—
210	C₄⋊Q₈	—	26	1	no	—
211	C₄⋊Q₈	—	52	1	no	—
212	C₄⋊Q₈	—	52	1	no	—
213	#125	—	26	2	no	—
214	C₂²⋊Q₈	—	52	1	no	—
215	C₂²⋊Q₈	—	52	1	no	—
216	C₄×Q₈	—	52	1	no	—
217	C₄×Q₈	—	52	1	no	—
218	#117	—	26	2	no	—
219	C₂×C₄⋊C₄	—	52	1	no	—
220	C₂×C₄⋊C₄	—	52	1	no	—
221	C₂×C₄²	—	13	1	no	—
222	M₃₂	—	26	4	no	—
223	C₂×C₁₆	—	13	2	no	—
224	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
225	#107	—	2	1	no	—
226	#107	—	13	2	no	—
227	#107	—	26	1	no	—
228	#107	C₂²×D₁₃	1	2	yes	—
229	#106	—	26	2	no	—
230	#106	—	26	2	no	—
231	C₄×C₈	—	13	1	no	—
232	C₄×C₈	—	13	1	no	—
233	C₄×C₈	—	13	1	no	—
234	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
235	C₂×C₁₃	C₂×#486	1	1	yes	characteristic
236	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
237	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
238	D₁₃	—	2	2	no	—
239	C₂×Q₈	—	2	2	no	—
240	C₂×Q₈	—	4	1	no	—
241	C₂×Q₈	—	26	2	no	—
242	C₂×Q₈	—	52	2	no	—
243	C₂×Q₈	—	52	4	no	—
244	C₂×Q₈	—	52	4	no	—
245	C₂×Q₈	—	52	1	no	—
246	C₂²×C₄	—	13	1	no	—
247	C₂²×C₄	—	13	1	no	—
248	C₂²×C₄	—	13	1	no	—
249	C₂²×C₄	—	52	2	no	—
250	Q₁₆	—	2	4	no	—
251	Q₁₆	—	4	2	no	—
252	Q₁₆	—	26	4	no	—
253	Q₁₆	—	52	4	no	—
254	Q₁₆	—	52	4	no	—
255	Q₁₆	—	52	2	no	—
256	C₂×C₈	—	13	1	no	—
257	C₂×C₈	—	13	1	no	—
258	C₂×C₈	—	13	4	no	—
259	C₂×C₈	—	13	4	no	—
260	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
261	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	4	1	no	—
264	C₄⋊C₄	—	4	1	no	—
265	C₄⋊C₄	—	4	1	no	—
266	C₄⋊C₄	—	26	2	no	—
267	C₄⋊C₄	—	52	2	no	—
268	C₄⋊C₄	—	52	2	no	—
269	C₄⋊C₄	—	52	2	no	—
270	C₄⋊C₄	—	52	2	no	—
271	C₄⋊C₄	—	52	1	no	—
272	C₄⋊C₄	—	52	1	no	—
273	C₄⋊C₄	—	52	1	no	—
274	C₂²⋊C₄	—	52	2	no	—
275	C₄²	—	13	1	no	—
276	C₄²	—	13	1	no	—
277	C₄²	—	13	1	no	—
278	C₄²	—	52	2	no	—
279	C₄²	D₄×D₁₃	1	1	yes	characteristic
280	C₁₆	—	2	2	no	—
281	C₁₆	—	26	2	no	—
282	C₁₃	#33705	1	1	yes	characteristic, complemented, Sylow
283	C₂³	—	13	1	no	—
284	Q₈	—	4	2	no	—
285	Q₈	—	4	2	no	—
286	Q₈	—	8	2	no	—
287	Q₈	—	52	2	no	—
288	Q₈	—	52	2	no	—
289	Q₈	—	104	4	no	—
290	Q₈	—	104	2	no	—
291	C₂×C₄	—	4	2	no	—
292	C₂×C₄	—	4	2	no	—
293	C₂×C₄	—	13	1	no	—
294	C₂×C₄	—	13	2	no	—
295	C₂×C₄	—	13	2	no	—
296	C₂×C₄	—	13	1	no	—
297	C₂×C₄	—	13	1	no	—
298	C₂×C₄	—	26	2	no	—
299	C₂×C₄	—	26	2	no	—
300	C₂×C₄	—	52	2	no	—
301	C₂×C₄	—	52	2	no	—
302	C₂×C₄	—	104	4	no	—
303	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
304	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
305	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
306	C₈	—	13	2	no	—
307	C₈	—	13	2	no	—
308	C₈	SD₁₆×D₁₃	1	2	yes	—
309	C₈	#41×D₁₃	1	2	yes	—
310	C₂²	—	13	2	no	—
311	C₂²	—	26	1	no	—
312	C₂²	—	26	1	no	—
313	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
314	C₄	—	8	2	no	—
315	C₄	—	8	2	no	—
316	C₄	—	13	2	no	—
317	C₄	—	26	1	no	—
318	C₄	—	26	1	no	—
319	C₄	—	104	2	no	—
320	C₄	—	104	2	no	—
321	C₄	#11718576	1	2	yes	—
322	C₄	#11718579	1	2	yes	—
323	C₄	D₁₃×#124	1	1	yes	characteristic
324	C₄	C₂×SD₁₆×D₁₃	1	1	yes	characteristic
325	C₂	—	26	2	no	—
326	C₂	D₁₃×#486	1	1	yes	characteristic
327	C₂	C₂×#11718576	1	1	yes	characteristic
328	C₂	C₂×#11718579	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₃
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#2241	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₂²×D₁₃	C₂×D₈
hypercenter	#2241	D₁₃
hypocenter	C₁₃	#33705
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2241

Complements

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

N	H ≅ G/N	type
3. #13117080	C₂	semidirect
4. #13117065	C₂	semidirect
5. #13117064	C₂	semidirect
6. #13117063	C₂	semidirect
9. C₁₃×#2241	C₂	semidirect
125. #2241	D₁₃	semidirect
282. C₁₃	#33705	semidirect

Maximal subgroups

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

subgroup	index
#13125347	2
D₁₃×#494	2
#13117080	2
#13117065	2
#13117064	2
#13117063	2
#13116554	2
C₄×#88038	2
C₁₃×#2241	2
#33705	13