Subgroups — #16018134

Order 3328.

544 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125486	C₂	1	1	yes	maximal, characteristic
2	#13117027	C₂	1	2	yes	maximal, complemented
3	#13117000	C₂	1	2	yes	maximal, complemented
4	#13116876	C₂	1	2	yes	maximal, complemented
5	#13116753	C₂	1	2	yes	maximal, complemented
6	#13116698	C₂	1	2	yes	maximal, complemented
7	C₄×#88068	C₂	1	2	yes	maximal, complemented
8	#13116643	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
11	C₁₃×#519	—	2	1	no	—
12	#11719240	—	2	1	no	—
13	C₁₃×#441	—	2	1	no	—
14	C₁₃×#441	—	2	1	no	—
15	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
16	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
17	C₁₃×#427	C₂²	1	1	yes	characteristic
18	C₁₃×#419	—	2	1	no	—
19	C₁₃×#405	C₂²	1	1	yes	characteristic
20	C₂×#88068	C₂²	1	2	yes	—
21	C₂×#88068	C₂²	1	2	yes	—
22	#11718796	—	2	1	no	—
23	#11718776	C₂²	1	2	yes	—
24	#11718374	—	2	1	no	—
25	#11718372	—	2	1	no	—
26	#11718356	C₂²	1	1	yes	characteristic
27	C₄×D₁₀₄	C₂²	1	2	yes	—
28	#11718344	C₂²	1	1	yes	characteristic
29	#11718156	C₂²	1	2	yes	—
30	#11718156	C₂²	1	2	yes	—
31	C₂²⋊#6090	C₂²	1	2	yes	—
32	#11718083	C₂²	1	2	yes	—
33	#11718083	C₂²	1	2	yes	—
34	#11718082	C₂²	1	2	yes	—
35	#11718081	C₂²	1	2	yes	—
36	C₄⋊#6090	C₂²	1	2	yes	—
37	#11718053	C₂²	1	1	yes	characteristic
38	C₄×#6090	C₂²	1	1	yes	characteristic
39	C₂²×Q₈×C₁₃	—	2	1	no	—
40	C₂×C₁₃×Q₁₆	—	2	4	no	—
41	C₂×C₁₃×Q₁₆	—	2	1	no	—
42	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
43	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₄×Q₈×C₁₃	—	2	2	no	—
46	C₄×Q₈×C₁₃	—	2	2	no	—
47	C₄×Q₈×C₁₃	—	4	2	no	—
48	C₁₃×#117	—	2	1	no	—
49	C₁₃×#117	—	4	2	no	—
50	C₁₃×#117	D₄	1	1	yes	characteristic
51	#88184	—	2	2	no	—
52	C₂×D₁₀₄	—	2	1	no	—
53	C₂×D₁₀₄	C₂³	1	2	yes	—
54	#88148	—	4	2	no	—
55	#88138	—	4	2	no	—
56	#88128	—	2	1	no	—
57	C₄×D₅₂	—	2	2	no	—
58	#88124	—	2	1	no	—
59	C₁₃×#107	C₂³	1	2	yes	—
60	C₁₃×#106	—	2	1	no	—
61	C₁₃×#103	—	2	2	no	—
62	C₁₃×#103	—	2	2	no	—
63	C₁₃×#97	D₄	1	1	yes	characteristic
64	C₁₃×#97	D₄	1	1	yes	characteristic
65	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	#88068	—	2	4	no	—
68	#88068	—	2	4	no	—
69	#88061	—	2	2	no	—
70	#88061	—	2	2	no	—
71	#88058	C₂³	1	2	yes	—
72	#88057	—	2	1	no	—
73	C₂×#6090	C₂³	1	2	yes	—
74	C₂×#6090	C₂³	1	2	yes	—
75	#33686	—	13	1	no	maximal, Sylow
76	C₂×Q₈×C₁₃	—	2	4	no	—
77	C₂×Q₈×C₁₃	—	2	2	no	—
78	C₂×Q₈×C₁₃	—	4	2	no	—
79	C₂×Q₈×C₁₃	—	4	1	no	—
80	C₂²×C₄×C₁₃	—	4	1	no	—
81	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
82	C₂×C₂²⋊D₁₃	—	4	2	no	—
83	C₂×D₅₂	—	2	2	no	—
84	C₂×D₅₂	—	4	2	no	—
85	C₂×C₄×D₁₃	—	4	2	no	—
86	C₁₃×Q₁₆	—	2	4	no	—
87	C₁₃×Q₁₆	—	2	2	no	—
88	C₁₃×Q₁₆	#41	1	4	yes	—
89	C₁₃×M₁₆	—	4	1	no	—
90	C₂×C₈×C₁₃	—	2	2	no	—
91	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
95	C₁₃×C₄⋊C₄	—	2	2	no	—
96	C₁₃×C₄⋊C₄	—	4	2	no	—
97	C₁₃×C₄⋊C₄	—	4	2	no	—
98	C₁₃×C₄⋊C₄	D₈	1	2	yes	—
99	C₁₃×C₂²⋊C₄	—	4	1	no	—
100	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
101	C₄²×C₁₃	—	4	1	no	—
102	C₄²×C₁₃	—	4	2	no	—
103	C₄²×C₁₃	—	4	2	no	—
104	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
106	#6103	—	4	2	no	—
107	#6103	—	4	2	no	—
108	C₄⋊Dic₁₃	—	2	2	no	—
109	#6101	—	4	2	no	—
110	D₁₀₄	—	2	2	no	—
111	D₁₀₄	—	2	2	no	—
112	D₁₀₄	—	4	2	no	—
113	#6090	—	2	2	no	—
114	#6090	—	2	2	no	—
115	#3176	—	13	1	no	—
116	#2950	D₁₃	1	1	yes	characteristic, complemented
117	#2234	—	13	2	no	—
118	#2229	—	13	2	no	—
119	#2207	—	13	2	no	—
120	#2185	—	13	2	no	—
121	#2175	—	13	2	no	—
122	C₄×SD₃₂	—	13	2	no	—
123	#2164	—	13	1	no	—
124	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
125	C₂²×D₁₃	—	4	2	no	—
126	Q₈×C₁₃	—	2	4	no	—
127	Q₈×C₁₃	—	4	4	no	—
128	Q₈×C₁₃	—	4	2	no	—
129	C₂×C₄×C₁₃	—	2	1	no	—
130	C₂×C₄×C₁₃	—	2	1	no	—
131	C₂×C₄×C₁₃	—	4	4	no	—
132	C₂×C₄×C₁₃	—	4	2	no	—
133	C₂×C₄×C₁₃	—	4	2	no	—
134	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
135	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
136	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
137	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
138	C₂²⋊D₁₃	—	16	2	no	—
139	C₂×Dic₁₃	—	4	2	no	—
140	D₅₂	—	4	2	no	—
141	D₅₂	—	4	2	no	—
142	D₅₂	—	16	2	no	—
143	C₄×D₁₃	—	16	2	no	—
144	C₈×C₁₃	—	2	1	no	—
145	C₈×C₁₃	—	2	1	no	—
146	C₈×C₁₃	—	2	1	no	—
147	C₈×C₁₃	C₂×#41	1	2	yes	—
148	C₂²×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
149	#540	—	26	1	no	—
150	#519	—	2	1	no	—
151	C₂×SD₃₂	—	13	2	no	—
152	C₂×SD₃₂	—	13	2	no	—
153	#499	—	13	1	no	—
154	#493	—	13	1	no	—
155	#490	—	26	1	no	—
156	#469	—	26	1	no	—
157	#466	—	13	2	no	—
158	#442	—	26	1	no	—
159	#441	—	2	1	no	—
160	#441	—	2	1	no	—
161	C₄×Q₁₆	C₂×D₁₃	1	2	yes	—
162	C₄×Q₁₆	C₂×D₁₃	1	2	yes	—
163	C₄×D₈	—	13	2	no	—
164	#427	C₂×D₁₃	1	1	yes	characteristic
165	#419	—	2	1	no	—
166	#405	C₂×D₁₃	1	1	yes	characteristic
167	#367	—	13	2	no	—
168	#366	—	13	2	no	—
169	C₄⋊C₁₆	—	13	2	no	—
170	#358	—	13	2	no	—
171	#358	—	13	2	no	—
172	#357	—	13	2	no	—
173	#357	—	13	2	no	—
174	C₂²⋊C₁₆	—	13	2	no	—
175	#346	—	13	1	no	—
176	C₄×C₁₆	—	13	1	no	—
177	C₂²×C₁₃	—	2	1	no	—
178	C₂²×C₁₃	—	2	2	no	—
179	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
180	C₂×D₁₃	—	8	2	no	—
181	C₂×D₁₃	—	8	2	no	—
182	C₂×D₁₃	—	8	2	no	—
183	C₄×C₁₃	—	2	1	no	—
184	C₄×C₁₃	—	2	2	no	—
185	C₄×C₁₃	—	2	2	no	—
186	C₄×C₁₃	—	4	4	no	—
187	C₄×C₁₃	—	8	2	no	—
188	C₄×C₁₃	#525	1	1	yes	characteristic
189	C₄×C₁₃	#575	1	1	yes	characteristic
190	Dic₁₃	—	8	2	no	—
191	C₂²×Q₈	—	2	1	no	—
192	C₂×Q₁₆	—	2	4	no	—
193	C₂×Q₁₆	—	2	1	no	—
194	C₂×Q₁₆	C₂²×D₁₃	1	2	yes	—
195	C₂×D₈	—	13	2	no	—
196	C₂×D₈	—	26	1	no	—
197	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
198	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
199	#127	—	26	1	no	—
200	#125	—	26	1	no	—
201	#123	—	52	2	no	—
202	#121	—	26	2	no	—
203	#121	—	52	2	no	—
204	C₄×Q₈	—	2	2	no	—
205	C₄×Q₈	—	2	2	no	—
206	C₄×Q₈	—	4	2	no	—
207	C₄×D₄	—	26	2	no	—
208	#117	—	2	1	no	—
209	#117	—	4	2	no	—
210	#117	C₂²⋊D₁₃	1	1	yes	characteristic
211	SD₃₂	—	26	4	no	—
212	SD₃₂	—	26	4	no	—
213	C₂×C₁₆	—	13	2	no	—
214	C₂×C₁₆	—	13	2	no	—
215	#107	—	13	2	no	—
216	#107	C₂²×D₁₃	1	2	yes	—
217	#106	—	2	1	no	—
218	#106	—	26	1	no	—
219	#103	—	2	2	no	—
220	#103	—	2	2	no	—
221	#102	—	26	2	no	—
222	#102	—	26	2	no	—
223	#97	C₂²⋊D₁₃	1	1	yes	characteristic
224	#97	C₂²⋊D₁₃	1	1	yes	characteristic
225	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
226	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
227	C₂×C₁₃	—	4	1	no	—
228	C₂×C₁₃	#3100	1	1	yes	characteristic
229	C₂×C₁₃	#3416	1	2	yes	—
230	D₁₃	—	16	2	no	—
231	C₂×Q₈	—	2	4	no	—
232	C₂×Q₈	—	2	2	no	—
233	C₂×Q₈	—	4	2	no	—
234	C₂×Q₈	—	4	1	no	—
235	C₂×D₄	—	26	2	no	—
236	C₂×D₄	—	52	2	no	—
237	C₂×D₄	—	52	2	no	—
238	C₂²×C₄	—	4	1	no	—
239	C₂²×C₄	—	52	2	no	—
240	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
241	Q₁₆	—	2	4	no	—
242	Q₁₆	—	2	2	no	—
243	Q₁₆	#6127	1	4	yes	—
244	D₈	—	26	2	no	—
245	D₈	—	26	2	no	—
246	D₈	—	52	2	no	—
247	M₁₆	—	4	1	no	—
248	C₂×C₈	—	2	2	no	—
249	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
250	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
251	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
252	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
253	C₄⋊C₄	—	2	2	no	—
254	C₄⋊C₄	—	4	2	no	—
255	C₄⋊C₄	—	4	2	no	—
256	C₄⋊C₄	—	26	2	no	—
257	C₄⋊C₄	—	52	2	no	—
258	C₄⋊C₄	#6104	1	2	yes	—
259	C₂²⋊C₄	—	4	1	no	—
260	C₂²⋊C₄	—	52	2	no	—
261	C₂²⋊C₄	—	52	2	no	—
262	C₂²⋊C₄	#6104	1	2	yes	—
263	C₄²	—	4	1	no	—
264	C₄²	—	4	2	no	—
265	C₄²	—	4	2	no	—
266	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
267	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
268	C₁₆	—	26	2	no	—
269	C₁₆	—	26	2	no	—
270	C₁₃	#33686	1	1	yes	characteristic, complemented, Sylow
271	C₂³	—	52	2	no	—
272	C₂³	C₂×#6104	1	1	yes	characteristic
273	Q₈	—	2	4	no	—
274	Q₈	—	4	4	no	—
275	Q₈	—	4	2	no	—
276	D₄	—	52	2	no	—
277	D₄	—	52	2	no	—
278	D₄	—	208	2	no	—
279	D₄	—	208	2	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	4	4	no	—
283	C₂×C₄	—	4	2	no	—
284	C₂×C₄	—	4	2	no	—
285	C₂×C₄	—	52	2	no	—
286	C₂×C₄	—	208	2	no	—
287	C₂×C₄	C₂×#6104	1	2	yes	—
288	C₂×C₄	C₂×#6104	1	2	yes	—
289	C₂×C₄	C₂×#6104	1	1	yes	characteristic
290	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
291	C₈	—	2	1	no	—
292	C₈	—	2	1	no	—
293	C₈	—	2	1	no	—
294	C₈	C₂×#6127	1	2	yes	—
295	C₂²	—	2	2	no	—
296	C₂²	—	2	1	no	—
297	C₂²	—	104	2	no	—
298	C₂²	—	104	2	no	—
299	C₂²	—	104	2	no	—
300	C₂²	C₂²×#6104	1	1	yes	characteristic
301	C₄	—	2	2	no	—
302	C₄	—	2	2	no	—
303	C₄	—	2	1	no	—
304	C₄	—	4	4	no	—
305	C₄	—	8	2	no	—
306	C₄	—	104	2	no	—
307	C₄	#11719496	1	1	yes	characteristic
308	C₄	#11719527	1	1	yes	characteristic
309	C₂	—	4	1	no	—
310	C₂	—	208	2	no	—
311	C₂	#13124836	1	1	yes	characteristic
312	C₂	#13127980	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#2950	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	#13125486	C₂
hypercenter	#2950	D₁₃
hypocenter	C₁₃	#33686
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405 ◁ #2950

Complements

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

N	H ≅ G/N	type
2. #13117027	C₂	semidirect
3. #13117000	C₂	semidirect
4. #13116876	C₂	semidirect
5. #13116753	C₂	semidirect
6. #13116698	C₂	semidirect
7. C₄×#88068	C₂	semidirect
8. #13116643	C₂	semidirect
9. C₁₃×#2950	C₂	semidirect
116. #2950	D₁₃	semidirect
270. C₁₃	#33686	semidirect

Maximal subgroups

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

subgroup	index
#13125486	2
#13117027	2
#13117000	2
#13116876	2
#13116753	2
#13116698	2
C₄×#88068	2
#13116643	2
C₁₃×#2950	2
#33686	13