Subgroups — #13058605

Order 1344.

452 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊C₄×D₂₁	C₂	1	1	yes	maximal, characteristic
2	C₇×#889	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#6452	C₂	1	1	yes	maximal, characteristic, complemented
4	#10620999	C₂	1	1	yes	maximal, characteristic
5	#10620966	C₂	1	1	yes	maximal, characteristic
6	#10620966	C₂	1	1	yes	maximal, characteristic
7	#10620966	C₂	1	1	yes	maximal, characteristic
8	#10620966	C₂	1	1	yes	maximal, characteristic
9	C₄×D₂₁⋊C₄	C₂	1	1	yes	maximal, characteristic
10	#10620941	C₂	1	1	yes	maximal, characteristic, complemented
11	#10620940	C₂	1	1	yes	maximal, characteristic, complemented
12	#10620908	C₂	1	1	yes	maximal, characteristic, complemented
13	#10620905	C₂	1	1	yes	maximal, characteristic, complemented
14	#10620897	C₂	1	1	yes	maximal, characteristic, complemented
15	#10620896	C₂	1	1	yes	maximal, characteristic, complemented
16	D₇×#125	—	3	1	no	maximal, Hall
17	C₂×C₄×D₂₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₂₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₂₁	C₂²	1	1	yes	characteristic
20	C₂×D₂₁⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×D₂₁⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×D₂₁⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×D₂₁⋊C₄	C₂²	1	1	yes	characteristic
24	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₄⋊Dic₂₁	C₂²	1	1	yes	characteristic
26	#66629	C₂²	1	1	yes	characteristic
27	#66629	C₂²	1	1	yes	characteristic
28	C₇×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
29	C₇×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
30	C₇×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
31	C₇×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
32	C₇×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₇×Dic₃	C₂²	1	1	yes	characteristic
34	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
35	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic
40	Dic₃⋊Dic₇	C₂²	1	1	yes	characteristic
41	Dic₃⋊Dic₇	C₂²	1	1	yes	characteristic
42	Dic₃⋊Dic₇	C₂²	1	1	yes	characteristic
43	Dic₃⋊Dic₇	C₂²	1	1	yes	characteristic
44	#66577	C₂²	1	1	yes	characteristic
45	#66577	C₂²	1	1	yes	characteristic
46	Dic₇⋊Dic₃	C₂²	1	1	yes	characteristic
47	Dic₇⋊Dic₃	C₂²	1	1	yes	characteristic
48	Dic₇⋊Dic₃	C₂²	1	1	yes	characteristic
49	Dic₇⋊Dic₃	C₂²	1	1	yes	characteristic
50	Dic₃×Dic₇	C₂²	1	1	yes	characteristic
51	Dic₃×Dic₇	C₂²	1	1	yes	characteristic
52	C₇×#125	—	3	1	no	—
53	D₇×C₄⋊C₄	—	3	1	no	—
54	D₇×C₄⋊C₄	—	3	1	no	—
55	D₇×C₄⋊C₄	—	3	1	no	—
56	D₇×C₄⋊C₄	—	3	1	no	—
57	D₇×C₄⋊C₄	—	3	1	no	—
58	D₇×C₄⋊C₄	—	3	1	no	—
59	#6453	—	3	1	no	—
60	#6453	—	3	1	no	—
61	#6452	—	3	1	no	—
62	#6452	—	3	1	no	—
63	#6452	—	3	1	no	—
64	#6452	D₃	1	1	yes	characteristic, complemented
65	C₄²×D₇	—	3	1	no	—
66	#6433	—	3	1	no	—
67	D₃×#125	—	7	1	no	maximal, Hall
68	C₂²×D₂₁	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
72	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
73	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
74	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
75	C₄×D₂₁	—	2	2	no	—
76	C₄×D₂₁	—	2	2	no	—
77	C₄×D₂₁	—	2	2	no	—
78	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
79	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
80	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
81	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
82	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
83	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
84	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
85	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
86	D₂₁⋊C₄	—	2	2	no	—
87	D₂₁⋊C₄	—	2	2	no	—
88	D₂₁⋊C₄	—	2	2	no	—
89	D₂₁⋊C₄	Q₈	1	4	yes	—
90	C₂×C₄×D₇	—	3	1	no	—
91	C₂×C₄×D₇	—	3	1	no	—
92	C₂×C₄×D₇	—	3	1	no	—
93	C₂×C₄×D₇	—	3	1	no	—
94	C₂×C₄×D₇	—	3	1	no	—
95	C₂×C₄×D₇	—	3	1	no	—
96	C₂×C₄×D₇	—	3	1	no	—
97	C₇×C₄⋊C₄	—	3	1	no	—
98	C₇×C₄⋊C₄	—	3	1	no	—
99	C₇×C₄⋊C₄	—	3	1	no	—
100	C₇×C₄⋊C₄	—	3	1	no	—
101	C₇×C₄⋊C₄	—	3	1	no	—
102	C₇×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
103	C₄²×C₇	—	3	1	no	—
104	C₄⋊Dic₇	—	3	1	no	—
105	C₄⋊Dic₇	—	3	1	no	—
106	C₄⋊Dic₇	—	3	1	no	—
107	C₄⋊Dic₇	—	3	1	no	—
108	C₄⋊Dic₇	—	3	1	no	—
109	C₄⋊Dic₇	C₂×D₃	1	1	yes	characteristic
110	Dic₇⋊C₄	—	3	1	no	—
111	Dic₇⋊C₄	—	3	1	no	—
112	Dic₇⋊C₄	—	3	1	no	—
113	Dic₇⋊C₄	—	3	1	no	—
114	Dic₇⋊C₄	—	3	1	no	—
115	Dic₇⋊C₄	—	3	1	no	—
116	Dic₇⋊C₄	—	3	1	no	—
117	Dic₇⋊C₄	—	3	1	no	—
118	Dic₇⋊C₄	C₂×D₃	1	1	yes	characteristic
119	Dic₇⋊C₄	C₂×D₃	1	1	yes	characteristic
120	Dic₇⋊C₄	C₂×D₃	1	1	yes	characteristic
121	Dic₇⋊C₄	C₂×D₃	1	1	yes	characteristic
122	C₄×Dic₇	—	3	1	no	—
123	C₄×Dic₇	—	3	1	no	—
124	C₄×Dic₇	C₂×D₃	1	1	yes	characteristic
125	C₃×#125	—	7	1	no	—
126	D₃×C₄⋊C₄	—	7	1	no	—
127	D₃×C₄⋊C₄	—	7	1	no	—
128	D₃×C₄⋊C₄	—	7	1	no	—
129	D₃×C₄⋊C₄	—	7	1	no	—
130	D₃×C₄⋊C₄	—	7	1	no	—
131	D₃×C₄⋊C₄	—	7	1	no	—
132	#890	—	7	1	no	—
133	#890	—	7	1	no	—
134	#889	—	7	1	no	—
135	#889	—	7	1	no	—
136	#889	—	7	1	no	—
137	#889	D₇	1	1	yes	characteristic, complemented
138	C₄²×D₃	—	7	1	no	—
139	#870	—	7	1	no	—
140	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
141	C₂×D₂₁	C₂×Q₈	1	2	yes	—
142	C₂×D₂₁	#41	1	2	yes	—
143	C₂×D₂₁	#41	1	2	yes	—
144	C₃×C₄×C₇	—	2	1	no	—
145	C₃×C₄×C₇	—	2	1	no	—
146	C₃×C₄×C₇	—	2	1	no	—
147	Dic₂₁	—	2	1	no	—
148	Dic₂₁	—	2	1	no	—
149	Dic₂₁	—	2	1	no	—
150	C₃×Dic₇	—	2	1	no	—
151	C₃×Dic₇	—	2	1	no	—
152	C₃×Dic₇	—	2	1	no	—
153	C₃×Dic₇	C₂×Q₈	1	2	yes	—
154	C₇×Dic₃	—	2	1	no	—
155	C₇×Dic₃	—	2	1	no	—
156	C₇×Dic₃	—	2	1	no	—
157	C₇×Dic₃	C₂×Q₈	1	2	yes	—
158	C₂×#125	—	21	1	no	Sylow
159	C₂²×D₇	—	3	1	no	—
160	C₂×C₄×C₇	—	3	1	no	—
161	C₂×C₄×C₇	—	3	1	no	—
162	C₂×C₄×C₇	—	3	1	no	—
163	C₂×C₄×C₇	—	3	1	no	—
164	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
165	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
166	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
167	C₂×Dic₇	—	3	1	no	—
168	C₂×Dic₇	—	3	1	no	—
169	C₂×Dic₇	—	3	1	no	—
170	C₂×Dic₇	C₂²×D₃	1	1	yes	characteristic
171	C₂×Dic₇	C₂²×D₃	1	1	yes	characteristic
172	C₂×Dic₇	C₂²×D₃	1	1	yes	characteristic
173	C₂×Dic₇	C₂²×D₃	1	1	yes	characteristic
174	C₄×D₇	—	3	4	no	—
175	C₄×D₇	—	6	2	no	—
176	C₄×D₇	—	6	2	no	—
177	C₄×D₇	—	6	2	no	—
178	C₄×D₇	—	6	2	no	—
179	C₄×D₇	—	6	2	no	—
180	C₄×D₇	—	6	2	no	—
181	C₂×C₄×D₃	—	7	1	no	—
182	C₂×C₄×D₃	—	7	1	no	—
183	C₂×C₄×D₃	—	7	1	no	—
184	C₂×C₄×D₃	—	7	1	no	—
185	C₂×C₄×D₃	—	7	1	no	—
186	C₂×C₄×D₃	—	7	1	no	—
187	C₂×C₄×D₃	—	7	1	no	—
188	C₃×C₄⋊C₄	—	7	1	no	—
189	C₃×C₄⋊C₄	—	7	1	no	—
190	C₃×C₄⋊C₄	—	7	1	no	—
191	C₃×C₄⋊C₄	—	7	1	no	—
192	C₃×C₄⋊C₄	—	7	1	no	—
193	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
194	C₃×C₄²	—	7	1	no	—
195	C₄⋊Dic₃	—	7	1	no	—
196	C₄⋊Dic₃	—	7	1	no	—
197	C₄⋊Dic₃	—	7	1	no	—
198	C₄⋊Dic₃	—	7	1	no	—
199	C₄⋊Dic₃	—	7	1	no	—
200	C₄⋊Dic₃	C₂×D₇	1	1	yes	characteristic
201	Dic₃⋊C₄	—	7	1	no	—
202	Dic₃⋊C₄	—	7	1	no	—
203	Dic₃⋊C₄	—	7	1	no	—
204	Dic₃⋊C₄	—	7	1	no	—
205	Dic₃⋊C₄	—	7	1	no	—
206	Dic₃⋊C₄	—	7	1	no	—
207	Dic₃⋊C₄	—	7	1	no	—
208	Dic₃⋊C₄	—	7	1	no	—
209	Dic₃⋊C₄	C₂×D₇	1	1	yes	characteristic
210	Dic₃⋊C₄	C₂×D₇	1	1	yes	characteristic
211	Dic₃⋊C₄	C₂×D₇	1	1	yes	characteristic
212	Dic₃⋊C₄	C₂×D₇	1	1	yes	characteristic
213	C₄×Dic₃	—	7	1	no	—
214	C₄×Dic₃	—	7	1	no	—
215	C₄×Dic₃	C₂×D₇	1	1	yes	characteristic
216	C₂×C₃×C₇	C₂²×Q₈	1	1	yes	characteristic
217	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
218	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
219	D₂₁	#125	1	4	yes	complemented
220	#125	—	3	1	no	—
221	#125	—	7	1	no	—
222	#125	—	21	1	no	—
223	#125	—	21	1	no	—
224	#125	—	21	1	no	—
225	#125	—	21	1	no	—
226	#125	—	21	1	no	—
227	#125	—	21	1	no	—
228	C₂×C₄⋊C₄	—	21	1	no	—
229	C₂×C₄⋊C₄	—	21	1	no	—
230	C₂×C₄⋊C₄	—	21	1	no	—
231	C₂×C₄⋊C₄	—	21	1	no	—
232	C₂×C₄⋊C₄	—	21	1	no	—
233	C₂×C₄⋊C₄	—	21	1	no	—
234	C₂×C₄²	—	21	1	no	—
235	C₂²×C₇	C₂³×D₃	1	1	yes	characteristic
236	C₂×D₇	—	3	2	no	—
237	C₂×D₇	—	3	2	no	—
238	C₂×D₇	—	3	2	no	—
239	C₄×C₇	—	2	1	no	—
240	C₄×C₇	—	2	1	no	—
241	C₄×C₇	—	2	1	no	—
242	C₄×C₇	—	3	2	no	—
243	C₄×C₇	—	6	1	no	—
244	C₄×C₇	—	6	1	no	—
245	C₄×C₇	—	6	1	no	—
246	Dic₇	—	2	1	no	—
247	Dic₇	—	2	1	no	—
248	Dic₇	—	2	1	no	—
249	Dic₇	—	6	1	no	—
250	Dic₇	—	6	1	no	—
251	Dic₇	—	6	1	no	—
252	Dic₇	D₃×Q₈	1	2	yes	—
253	C₂²×D₃	—	7	1	no	—
254	C₂×C₃×C₄	—	7	1	no	—
255	C₂×C₃×C₄	—	7	1	no	—
256	C₂×C₃×C₄	—	7	1	no	—
257	C₂×C₃×C₄	—	7	1	no	—
258	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
261	C₂×Dic₃	—	7	1	no	—
262	C₂×Dic₃	—	7	1	no	—
263	C₂×Dic₃	—	7	1	no	—
264	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
265	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
266	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
267	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
268	C₄×D₃	—	7	4	no	—
269	C₄×D₃	—	14	2	no	—
270	C₄×D₃	—	14	2	no	—
271	C₄×D₃	—	14	2	no	—
272	C₄×D₃	—	14	2	no	—
273	C₄×D₃	—	14	2	no	—
274	C₄×D₃	—	14	2	no	—
275	C₃×C₇	C₂×#125	1	1	yes	characteristic, complemented, Hall
276	C₂²×C₄	—	21	1	no	—
277	C₂²×C₄	—	21	1	no	—
278	C₂²×C₄	—	21	1	no	—
279	C₂²×C₄	—	21	1	no	—
280	C₂²×C₄	—	21	1	no	—
281	C₂²×C₄	—	21	1	no	—
282	C₂²×C₄	—	21	1	no	—
283	C₄⋊C₄	—	3	1	no	—
284	C₄⋊C₄	—	3	1	no	—
285	C₄⋊C₄	—	3	1	no	—
286	C₄⋊C₄	—	3	1	no	—
287	C₄⋊C₄	—	3	1	no	—
288	C₄⋊C₄	—	7	1	no	—
289	C₄⋊C₄	—	7	1	no	—
290	C₄⋊C₄	—	7	1	no	—
291	C₄⋊C₄	—	7	1	no	—
292	C₄⋊C₄	—	7	1	no	—
293	C₄⋊C₄	—	21	1	no	—
294	C₄⋊C₄	—	21	1	no	—
295	C₄⋊C₄	—	21	1	no	—
296	C₄⋊C₄	—	21	1	no	—
297	C₄⋊C₄	—	21	1	no	—
298	C₄⋊C₄	—	21	1	no	—
299	C₄⋊C₄	—	21	1	no	—
300	C₄⋊C₄	—	21	1	no	—
301	C₄⋊C₄	—	21	1	no	—
302	C₄⋊C₄	—	21	1	no	—
303	C₄⋊C₄	—	21	1	no	—
304	C₄⋊C₄	—	21	1	no	—
305	C₄⋊C₄	—	21	1	no	—
306	C₄⋊C₄	D₃×D₇	1	1	yes	characteristic
307	C₄²	—	3	1	no	—
308	C₄²	—	7	1	no	—
309	C₄²	—	21	1	no	—
310	C₄²	—	21	1	no	—
311	C₂×C₇	C₂×D₃×Q₈	1	1	yes	characteristic
312	C₂×C₇	D₃×#41	1	1	yes	characteristic
313	C₂×C₇	D₃×#41	1	1	yes	characteristic
314	D₇	—	3	4	no	—
315	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
316	C₂×D₃	—	7	2	no	—
317	C₂×D₃	—	7	2	no	—
318	C₂×D₃	—	7	2	no	—
319	C₃×C₄	—	2	1	no	—
320	C₃×C₄	—	2	1	no	—
321	C₃×C₄	—	2	1	no	—
322	C₃×C₄	—	7	2	no	—
323	C₃×C₄	—	14	1	no	—
324	C₃×C₄	—	14	1	no	—
325	C₃×C₄	—	14	1	no	—
326	Dic₃	—	2	1	no	—
327	Dic₃	—	2	1	no	—
328	Dic₃	—	2	1	no	—
329	Dic₃	—	14	1	no	—
330	Dic₃	—	14	1	no	—
331	Dic₃	—	14	1	no	—
332	Dic₃	Q₈×D₇	1	2	yes	—
333	C₂³	—	21	1	no	—
334	C₂×C₄	—	3	1	no	—
335	C₂×C₄	—	3	1	no	—
336	C₂×C₄	—	3	1	no	—
337	C₂×C₄	—	3	1	no	—
338	C₂×C₄	—	7	1	no	—
339	C₂×C₄	—	7	1	no	—
340	C₂×C₄	—	7	1	no	—
341	C₂×C₄	—	7	1	no	—
342	C₂×C₄	—	21	4	no	—
343	C₂×C₄	—	21	1	no	—
344	C₂×C₄	—	21	1	no	—
345	C₂×C₄	—	21	1	no	—
346	C₂×C₄	—	42	2	no	—
347	C₂×C₄	—	42	2	no	—
348	C₂×C₄	—	42	2	no	—
349	C₂×C₄	—	42	2	no	—
350	C₂×C₄	—	42	2	no	—
351	C₂×C₄	—	42	2	no	—
352	C₂×C₄	C₂×D₃×D₇	1	1	yes	characteristic
353	C₂×C₄	C₂×D₃×D₇	1	1	yes	characteristic
354	C₂×C₄	C₂×D₃×D₇	1	1	yes	characteristic
355	C₇	D₃×#125	1	1	yes	characteristic, complemented, Sylow
356	C₂×C₃	C₂×Q₈×D₇	1	1	yes	characteristic
357	C₂×C₃	D₇×#41	1	1	yes	characteristic
358	C₂×C₃	D₇×#41	1	1	yes	characteristic
359	D₃	—	7	4	no	—
360	C₂²	—	21	2	no	—
361	C₂²	—	21	2	no	—
362	C₂²	—	21	2	no	—
363	C₂²	C₂²×D₃×D₇	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	3	2	no	—
368	C₄	—	6	1	no	—
369	C₄	—	6	1	no	—
370	C₄	—	6	1	no	—
371	C₄	—	7	2	no	—
372	C₄	—	14	1	no	—
373	C₄	—	14	1	no	—
374	C₄	—	14	1	no	—
375	C₄	—	42	1	no	—
376	C₄	—	42	1	no	—
377	C₄	—	42	1	no	—
378	C₃	D₇×#125	1	1	yes	characteristic, complemented, Sylow
379	C₂	—	21	4	no	—
380	C₂	#10621563	1	1	yes	characteristic
381	C₂	#10621571	1	1	yes	characteristic
382	C₂	D₃×Q₈×D₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃×D₇
commutator, socle, cosocle	C₂²×C₃×C₇	C₂⁴
Fitting	C₃×C₇×C₄⋊C₄	C₂²
prime radical	C₂²×D₂₁	C₂³
hypercenter	C₄⋊C₄	D₃×D₇
hypocenter	C₃×C₇	C₂×#125
LCS	G ▷ C₂²×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₇×#889	C₂	semidirect
3. C₃×#6452	C₂	semidirect
10. #10620941	C₂	semidirect
11. #10620940	C₂	semidirect
12. #10620908	C₂	semidirect
13. #10620905	C₂	semidirect
14. #10620897	C₂	semidirect
15. #10620896	C₂	semidirect
64. #6452	D₃	semidirect
137. #889	D₇	semidirect
219. D₂₁	#125	semidirect
275. C₃×C₇	C₂×#125	semidirect
355. C₇	D₃×#125	semidirect
378. C₃	D₇×#125	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊C₄×D₂₁	2
C₇×#889	2
C₃×#6452	2
#10620999	2
#10620966	2
C₄×D₂₁⋊C₄	2
#10620941	2
#10620940	2
#10620908	2
#10620905	2
#10620897	2
#10620896	2
D₇×#125	3
D₃×#125	7