Subgroups — #16018479

Order 3328.

558 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125420	C₂	1	1	yes	maximal, characteristic, complemented
2	#13125413	C₂	1	1	yes	maximal, characteristic
3	#13117118	C₂	1	1	yes	maximal, characteristic, complemented
4	#13117063	C₂	1	1	yes	maximal, characteristic, complemented
5	#13117059	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116929	C₂	1	4	yes	maximal, complemented
7	SD₃₂×Dic₁₃	C₂	1	4	yes	maximal, complemented
8	C₄×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2248	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719433	—	2	1	no	—
11	#11719421	—	2	1	no	—
12	C₂×C₁₃×SD₃₂	C₂²	1	4	yes	—
13	C₁₃×#494	C₂²	1	1	yes	characteristic
14	C₁₃×#493	C₂²	1	1	yes	characteristic
15	#11718849	—	2	1	no	—
16	#11718849	C₂²	1	2	yes	—
17	Q₁₆×Dic₁₃	—	2	1	no	—
18	Q₁₆×Dic₁₃	C₂²	1	2	yes	—
19	#11718818	—	2	1	no	—
20	#11718818	C₂²	1	2	yes	—
21	D₈×Dic₁₃	—	2	1	no	—
22	D₈×Dic₁₃	C₂²	1	2	yes	—
23	#11718742	—	2	1	no	—
24	#11718731	—	2	1	no	—
25	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
26	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
27	#11718343	C₂²	1	1	yes	characteristic
28	#11718343	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
30	#11718156	C₂²	1	4	yes	—
31	#11718154	C₂²	1	4	yes	—
32	#11718097	C₂²	1	4	yes	—
33	C₁₆×Dic₁₃	C₂²	1	2	yes	—
34	C₄×#6090	C₂²	1	1	yes	characteristic
35	C₂×#6129	—	4	1	no	—
36	C₂×C₁₃×Q₁₆	—	2	1	no	—
37	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
38	C₂×C₁₃×D₈	—	2	1	no	—
39	C₂×C₁₃×D₈	C₂³	1	2	yes	—
40	C₁₃×C₄⋊Q₈	—	2	1	no	—
41	C₁₃×#127	—	2	1	no	—
42	#88200	—	2	2	no	—
43	Q₈×Dic₁₃	—	2	2	no	—
44	#88192	—	2	2	no	—
45	#88192	—	4	1	no	—
46	#88190	—	4	1	no	—
47	D₄×Dic₁₃	—	2	2	no	—
48	D₄×Dic₁₃	—	4	1	no	—
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	—	4	1	no	—
53	#88144	—	4	1	no	—
54	#88141	—	4	1	no	—
55	C₄²×D₁₃	D₄	1	1	yes	characteristic
56	#88123	—	2	1	no	—
57	#88123	—	2	1	no	—
58	C₁₃×SD₃₂	—	2	8	no	—
59	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
60	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	#88075	—	2	2	no	—
62	#88075	—	2	2	no	—
63	#88072	—	2	2	no	—
64	#88072	—	2	2	no	—
65	#88058	—	2	1	no	—
66	#88058	—	2	1	no	—
67	#88058	C₂³	1	2	yes	—
68	#88058	C₂³	1	2	yes	—
69	C₈×Dic₁₃	D₄	1	1	yes	characteristic
70	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
71	C₂×#6090	C₂³	1	2	yes	—
72	C₄×#1055	D₄	1	1	yes	characteristic
73	C₁₆×D₁₃	—	2	4	no	—
74	#33736	—	13	1	no	maximal, Sylow
75	C₂×Q₈×C₁₃	—	2	2	no	—
76	C₂×D₄×C₁₃	—	2	2	no	—
77	C₂×D₄×C₁₃	—	4	1	no	—
78	C₂×D₄×C₁₃	—	4	1	no	—
79	C₂×C₂²⋊D₁₃	—	4	2	no	—
80	C₂²×Dic₁₃	—	4	2	no	—
81	#6129	—	8	4	no	—
82	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
83	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
84	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
85	C₂×Dic₂₆	—	4	1	no	—
86	C₂×Dic₂₆	—	4	1	no	—
87	C₁₃×Q₁₆	—	2	4	no	—
88	C₁₃×Q₁₆	—	4	2	no	—
89	C₁₃×D₈	—	2	4	no	—
90	C₁₃×D₈	—	4	2	no	—
91	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
93	C₁₃×C₄⋊C₄	—	4	1	no	—
94	C₁₃×C₄⋊C₄	—	4	1	no	—
95	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂²⋊Dic₁₃	—	4	2	no	—
97	C₂²⋊Dic₁₃	—	4	2	no	—
98	#6103	—	4	2	no	—
99	C₄⋊Dic₁₃	—	2	2	no	—
100	C₄⋊Dic₁₃	—	2	2	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	C₄×Dic₁₃	—	4	2	no	—
106	C₄×Dic₁₃	D₈	1	1	yes	characteristic
107	C₄×Dic₁₃	D₈	1	1	yes	characteristic
108	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂×#1055	C₂×D₄	1	1	yes	characteristic
110	C₂×#1055	C₂×D₄	1	1	yes	characteristic
111	C₈×D₁₃	—	2	2	no	—
112	C₈×D₁₃	—	2	2	no	—
113	C₁₃×C₁₆	#41	1	4	yes	complemented
114	#6090	—	2	2	no	—
115	#3170	—	13	1	no	—
116	#3169	—	13	1	no	—
117	#2254	—	13	1	no	—
118	#2248	D₁₃	1	1	yes	characteristic, complemented
119	#2241	—	13	1	no	—
120	#2240	—	13	1	no	—
121	#2217	—	13	4	no	—
122	C₄×SD₃₂	—	13	4	no	—
123	C₂×C₄×C₁₆	—	13	1	no	—
124	C₂³×C₁₃	—	4	2	no	—
125	C₂²×D₁₃	C₂×D₈	1	1	yes	characteristic
126	Q₈×C₁₃	—	4	2	no	—
127	Q₈×C₁₃	—	4	2	no	—
128	D₄×C₁₃	—	4	2	no	—
129	D₄×C₁₃	—	4	2	no	—
130	D₄×C₁₃	—	8	2	no	—
131	D₄×C₁₃	—	8	2	no	—
132	C₂×C₄×C₁₃	—	4	2	no	—
133	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
134	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
135	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
136	C₂²⋊D₁₃	—	8	4	no	—
137	C₂×Dic₁₃	—	4	2	no	—
138	C₂×Dic₁₃	—	4	2	no	—
139	C₂×Dic₁₃	—	8	4	no	—
140	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
141	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
142	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
143	C₄×D₁₃	—	2	1	no	—
144	C₄×D₁₃	—	2	1	no	—
145	C₄×D₁₃	—	2	2	no	—
146	C₄×D₁₃	SD₃₂	1	4	yes	complemented
147	Dic₂₆	—	8	2	no	—
148	Dic₂₆	—	8	2	no	—
149	C₈×C₁₃	#135	1	2	yes	—
150	C₈×C₁₃	C₂×#41	1	2	yes	—
151	#1055	—	2	1	no	—
152	#1055	—	2	1	no	—
153	#533	—	26	1	no	—
154	#532	—	26	1	no	—
155	C₂×SD₃₂	C₂×D₁₃	1	4	yes	—
156	C₂²×C₁₆	—	13	2	no	—
157	#500	—	13	1	no	—
158	#500	—	13	1	no	—
159	#494	C₂×D₁₃	1	1	yes	characteristic
160	#493	C₂×D₁₃	1	1	yes	characteristic
161	#487	—	26	1	no	—
162	#486	—	26	1	no	—
163	#467	—	13	2	no	—
164	#467	—	26	1	no	—
165	#466	—	13	2	no	—
166	#466	—	26	1	no	—
167	C₄×Q₁₆	—	13	2	no	—
168	C₄×Q₁₆	—	26	1	no	—
169	C₄×D₈	—	13	2	no	—
170	C₄×D₈	—	26	1	no	—
171	C₂×C₄×C₈	—	13	1	no	—
172	#367	—	13	4	no	—
173	#358	—	13	4	no	—
174	#357	—	13	4	no	—
175	C₄×C₁₆	—	13	2	no	—
176	C₄×C₁₆	—	13	1	no	—
177	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
178	C₂²×C₁₃	—	8	2	no	—
179	C₂²×C₁₃	—	8	2	no	—
180	C₂²×C₁₃	—	8	2	no	—
181	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
182	C₂×D₁₃	—	2	1	no	—
183	C₂×D₁₃	—	2	1	no	—
184	C₂×D₁₃	C₂×SD₃₂	1	2	yes	—
185	C₄×C₁₃	—	8	2	no	—
186	C₄×C₁₃	C₂×SD₃₂	1	2	yes	—
187	C₄×C₁₃	#508	1	2	yes	—
188	C₄×C₁₃	#532	1	1	yes	characteristic
189	C₄×C₁₃	C₂×#135	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	C₂×SD₃₂	1	2	yes	—
195	C₂×#41	—	52	1	no	—
196	C₂×Q₁₆	—	2	1	no	—
197	C₂×Q₁₆	C₂²×D₁₃	1	2	yes	—
198	C₂×D₈	—	2	1	no	—
199	C₂×D₈	C₂²×D₁₃	1	2	yes	—
200	C₂²×C₈	—	13	1	no	—
201	C₂²×C₈	—	13	1	no	—
202	C₄⋊Q₈	—	2	1	no	—
203	C₄⋊Q₈	—	26	1	no	—
204	C₄⋊Q₈	—	26	1	no	—
205	#127	—	2	1	no	—
206	#125	—	52	1	no	—
207	#124	—	52	1	no	—
208	C₂²⋊Q₈	—	26	2	no	—
209	C₂²⋊Q₈	—	52	1	no	—
210	#121	—	26	2	no	—
211	#121	—	52	1	no	—
212	C₄×Q₈	—	26	2	no	—
213	C₄×Q₈	—	52	1	no	—
214	C₄×D₄	—	26	2	no	—
215	C₄×D₄	—	52	1	no	—
216	#117	—	52	1	no	—
217	C₂×C₄²	—	13	1	no	—
218	SD₃₂	—	2	8	no	—
219	C₂×C₁₆	—	13	2	no	—
220	C₂×C₁₆	—	26	4	no	—
221	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
222	#107	—	13	2	no	—
223	#107	—	13	2	no	—
224	#107	—	26	1	no	—
225	#107	—	26	1	no	—
226	#103	—	26	2	no	—
227	#103	—	26	2	no	—
228	#102	—	26	2	no	—
229	#102	—	26	2	no	—
230	C₄×C₈	—	13	1	no	—
231	C₄×C₈	—	13	1	no	—
232	C₄×C₈	—	13	1	no	—
233	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
234	C₂×C₁₃	—	16	2	no	—
235	C₂×C₁₃	#3169	1	1	yes	characteristic
236	C₂×C₁₃	C₂²×SD₃₂	1	1	yes	characteristic
237	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
238	D₁₃	—	2	2	no	—
239	#41	—	104	4	no	—
240	C₂×Q₈	—	2	2	no	—
241	C₂×Q₈	—	52	1	no	—
242	C₂×Q₈	—	52	1	no	—
243	C₂×D₄	—	2	2	no	—
244	C₂×D₄	—	4	1	no	—
245	C₂×D₄	—	4	1	no	—
246	C₂×D₄	—	52	2	no	—
247	C₂²×C₄	—	13	1	no	—
248	C₂²×C₄	—	13	1	no	—
249	C₂²×C₄	—	13	1	no	—
250	C₂²×C₄	—	52	2	no	—
251	Q₁₆	—	2	4	no	—
252	Q₁₆	—	4	2	no	—
253	D₈	—	2	4	no	—
254	D₈	—	4	2	no	—
255	C₂×C₈	—	13	1	no	—
256	C₂×C₈	—	13	1	no	—
257	C₂×C₈	—	26	2	no	—
258	C₂×C₈	—	26	2	no	—
259	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
260	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
261	C₄⋊C₄	—	4	1	no	—
262	C₄⋊C₄	—	4	1	no	—
263	C₄⋊C₄	—	26	2	no	—
264	C₄⋊C₄	—	26	2	no	—
265	C₄⋊C₄	—	52	2	no	—
266	C₄⋊C₄	—	52	2	no	—
267	C₄⋊C₄	—	52	1	no	—
268	C₄⋊C₄	—	52	1	no	—
269	C₂²⋊C₄	—	52	2	no	—
270	C₂²⋊C₄	—	52	2	no	—
271	C₂²⋊C₄	—	52	2	no	—
272	C₄²	—	13	1	no	—
273	C₄²	—	13	1	no	—
274	C₄²	—	13	1	no	—
275	C₄²	—	52	2	no	—
276	C₄²	D₄×D₁₃	1	1	yes	characteristic
277	C₁₆	—	26	2	no	—
278	C₁₆	#6129	1	4	yes	complemented
279	C₁₃	#33736	1	1	yes	characteristic, complemented, Sylow
280	C₂³	—	4	2	no	—
281	C₂³	—	13	1	no	—
282	Q₈	—	4	2	no	—
283	Q₈	—	4	2	no	—
284	Q₈	—	104	2	no	—
285	Q₈	—	104	2	no	—
286	D₄	—	4	2	no	—
287	D₄	—	4	2	no	—
288	D₄	—	8	2	no	—
289	D₄	—	8	2	no	—
290	D₄	—	104	4	no	—
291	C₂×C₄	—	4	2	no	—
292	C₂×C₄	—	13	1	no	—
293	C₂×C₄	—	13	4	no	—
294	C₂×C₄	—	13	1	no	—
295	C₂×C₄	—	13	1	no	—
296	C₂×C₄	—	26	1	no	—
297	C₂×C₄	—	26	2	no	—
298	C₂×C₄	—	26	1	no	—
299	C₂×C₄	—	52	2	no	—
300	C₂×C₄	—	52	2	no	—
301	C₂×C₄	—	104	4	no	—
302	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
303	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
304	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
305	C₈	—	26	1	no	—
306	C₈	—	26	1	no	—
307	C₈	#88166	1	2	yes	—
308	C₈	C₂×#6129	1	2	yes	—
309	C₂²	—	8	2	no	—
310	C₂²	—	8	2	no	—
311	C₂²	—	8	2	no	—
312	C₂²	—	13	2	no	—
313	C₂²	—	26	1	no	—
314	C₂²	—	26	1	no	—
315	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
316	C₄	—	8	2	no	—
317	C₄	—	13	2	no	—
318	C₄	—	26	1	no	—
319	C₄	—	26	1	no	—
320	C₄	—	104	2	no	—
321	C₄	—	104	2	no	—
322	C₄	D₁₃×SD₃₂	1	2	yes	—
323	C₄	#11718577	1	2	yes	—
324	C₄	#11719421	1	1	yes	characteristic
325	C₄	C₂×#88166	1	1	yes	characteristic
326	C₂	—	16	2	no	—
327	C₂	—	26	2	no	—
328	C₂	#13125413	1	1	yes	characteristic
329	C₂	C₂×D₁₃×SD₃₂	1	1	yes	characteristic
330	C₂	C₂×#11718577	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×#2248	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	#13125413	C₂
hypercenter	#2248	D₁₃
hypocenter	C₁₃	#33736
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2248

Complements

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

N	H ≅ G/N	type
1. #13125420	C₂	semidirect
3. #13117118	C₂	semidirect
4. #13117063	C₂	semidirect
5. #13117059	C₂	semidirect
6. #13116929	C₂	semidirect
7. SD₃₂×Dic₁₃	C₂	semidirect
8. C₄×C₁₆×D₁₃	C₂	semidirect
9. C₁₃×#2248	C₂	semidirect
113. C₁₃×C₁₆	#41	semidirect
118. #2248	D₁₃	semidirect
146. C₄×D₁₃	SD₃₂	semidirect
278. C₁₆	#6129	semidirect
279. C₁₃	#33736	semidirect

Maximal subgroups

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

subgroup	index
#13125420	2
#13125413	2
#13117118	2
#13117063	2
#13117059	2
#13116929	2
SD₃₂×Dic₁₃	2
C₄×C₁₆×D₁₃	2
C₁₃×#2248	2
#33736	13