Subgroups — C₇×#11256 #13188472

Order 1792.

814 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#107	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#340	C₂	1	2	yes	maximal
3	C₂×C₇×#340	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×#336	C₂	1	1	yes	maximal, characteristic
5	C₇×C₄⋊#95	C₂	1	2	yes	maximal
6	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
7	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
8	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
11	C₂×C₇×#107	—	2	2	no	—
12	C₂×C₇×#107	—	2	4	no	—
13	C₂×C₇×#95	—	2	2	no	—
14	C₂×C₇×#95	—	2	2	no	—
15	C₇×#340	—	2	4	no	—
16	C₇×#340	C₄	1	4	yes	complemented
17	C₇×#336	—	2	2	no	—
18	#11256	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂³×C₄×C₇	—	2	2	no	—
20	C₂³×C₄×C₇	—	2	2	no	—
21	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
24	C₂²×C₇×C₈	—	2	2	no	—
25	C₂²×C₇×C₈	—	2	2	no	—
26	C₂²×C₇×C₈	—	2	1	no	—
27	C₂²×C₇×C₈	—	2	2	no	—
28	C₂²×C₇×C₈	—	2	2	no	—
29	C₂²×C₇×C₈	—	2	1	no	—
30	C₂²×C₇×C₈	C₂×C₄	1	2	yes	—
31	C₂²×C₇×C₈	D₄	1	2	yes	—
32	C₂²×C₇×C₈	Q₈	1	2	yes	—
33	C₂²×C₇×C₈	Q₈	1	2	yes	—
34	C₂×C₇×C₄⋊C₄	—	2	2	no	—
35	C₂×C₇×C₄⋊C₄	—	2	2	no	—
36	C₂×C₇×C₄⋊C₄	—	2	2	no	—
37	C₂×C₇×C₄⋊C₄	—	2	2	no	—
38	C₂×C₇×C₄⋊C₄	—	2	2	no	—
39	C₂×C₇×C₄⋊C₄	—	2	2	no	—
40	C₂×C₇×C₄⋊C₄	—	2	2	no	—
41	C₂×C₇×C₄⋊C₄	—	2	2	no	—
42	C₂×C₇×C₄⋊C₄	—	2	2	no	—
43	C₂×C₇×C₄⋊C₄	—	2	2	no	—
44	C₂×C₇×C₄⋊C₄	C₂×C₄	1	4	yes	—
45	C₂×C₇×C₄⋊C₄	D₄	1	4	yes	—
46	C₂×C₄²×C₇	—	2	1	no	—
47	C₂×C₄²×C₇	—	2	2	no	—
48	C₂×C₄²×C₇	—	2	2	no	—
49	C₂×C₄²×C₇	—	2	1	no	—
50	C₇×#107	—	2	8	no	—
51	C₇×#95	—	4	4	no	—
52	C₇×#95	—	4	4	no	—
53	C₂²×#107	C₂×C₇	1	1	yes	characteristic
54	C₂×#340	C₂×C₇	1	2	yes	—
55	C₂×#340	C₂×C₇	1	1	yes	characteristic
56	C₂×#336	C₂×C₇	1	1	yes	characteristic
57	C₄⋊#95	C₂×C₇	1	2	yes	—
58	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₇	—	2	1	no	—
60	C₂²×C₄×C₇	—	2	1	no	—
61	C₂²×C₄×C₇	—	2	2	no	—
62	C₂²×C₄×C₇	—	2	2	no	—
63	C₂²×C₄×C₇	—	2	1	no	—
64	C₂²×C₄×C₇	—	2	1	no	—
65	C₂²×C₄×C₇	—	2	2	no	—
66	C₂²×C₄×C₇	—	2	2	no	—
67	C₂²×C₄×C₇	—	2	4	no	—
68	C₂²×C₄×C₇	—	2	4	no	—
69	C₂²×C₄×C₇	—	4	2	no	—
70	C₂²×C₄×C₇	—	4	2	no	—
71	C₂²×C₄×C₇	—	4	2	no	—
72	C₂²×C₄×C₇	—	4	2	no	—
73	C₂²×C₄×C₇	—	4	2	no	—
74	C₂²×C₄×C₇	—	4	2	no	—
75	C₂²×C₄×C₇	—	4	2	no	—
76	C₂²×C₄×C₇	—	4	2	no	—
77	C₂²×C₄×C₇	—	4	2	no	—
78	C₂²×C₄×C₇	—	4	2	no	—
79	C₂²×C₄×C₇	—	4	2	no	—
80	C₂²×C₄×C₇	—	4	2	no	—
81	C₂²×C₄×C₇	D₈	1	2	yes	—
82	C₂²×C₄×C₇	Q₁₆	1	2	yes	—
83	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₇	#41	1	2	yes	—
89	C₂²×C₄×C₇	#41	1	2	yes	—
90	C₂²×C₄×C₇	#41	1	2	yes	—
91	C₂²×C₄×C₇	#41	1	1	yes	characteristic
92	C₂²×C₄×C₇	#41	1	1	yes	characteristic
93	C₂×C₇×C₈	—	2	4	no	—
94	C₂×C₇×C₈	—	2	2	no	—
95	C₂×C₇×C₈	—	2	4	no	—
96	C₂×C₇×C₈	—	2	2	no	—
97	C₂×C₇×C₈	—	2	4	no	—
98	C₂×C₇×C₈	—	2	2	no	—
99	C₂×C₇×C₈	—	4	1	no	—
100	C₂×C₇×C₈	—	4	1	no	—
101	C₂×C₇×C₈	—	4	2	no	—
102	C₂×C₇×C₈	C₄⋊C₄	1	4	yes	—
103	C₇×C₄⋊C₄	—	2	4	no	—
104	C₇×C₄⋊C₄	—	2	4	no	—
105	C₇×C₄⋊C₄	—	2	4	no	—
106	C₇×C₄⋊C₄	—	2	4	no	—
107	C₇×C₄⋊C₄	—	4	2	no	—
108	C₇×C₄⋊C₄	—	4	2	no	—
109	C₇×C₄⋊C₄	—	4	2	no	—
110	C₇×C₄⋊C₄	—	4	2	no	—
111	C₄²×C₇	—	4	1	no	—
112	C₄²×C₇	—	4	1	no	—
113	C₄²×C₇	—	4	2	no	—
114	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
115	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
116	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
117	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
118	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
119	C₂×#107	—	2	2	no	—
120	C₂×#107	—	2	4	no	—
121	C₂×#95	—	2	2	no	—
122	C₂×#95	—	2	2	no	—
123	#340	—	2	4	no	—
124	#340	C₄×C₇	1	4	yes	complemented
125	#336	—	2	2	no	—
126	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
127	C₂³×C₇	#121	1	2	yes	—
128	C₂³×C₇	#121	1	1	yes	characteristic
129	C₂³×C₇	#123	1	2	yes	—
130	C₂³×C₇	C₄⋊Q₈	1	1	yes	characteristic
131	C₂³×C₇	C₂×D₈	1	1	yes	characteristic
132	C₂³×C₇	C₂×Q₁₆	1	1	yes	characteristic
133	C₂³×C₇	#135	1	1	yes	characteristic
134	C₂³×C₇	#135	1	1	yes	characteristic
135	C₂³×C₇	AGL(1,ℤ/8)	1	2	yes	—
136	C₂³×C₇	#137	1	2	yes	—
137	C₂×C₄×C₇	—	2	2	no	—
138	C₂×C₄×C₇	—	2	2	no	—
139	C₂×C₄×C₇	—	2	4	no	—
140	C₂×C₄×C₇	—	2	4	no	—
141	C₂×C₄×C₇	—	4	1	no	—
142	C₂×C₄×C₇	—	4	1	no	—
143	C₂×C₄×C₇	—	4	1	no	—
144	C₂×C₄×C₇	—	4	1	no	—
145	C₂×C₄×C₇	—	4	2	no	—
146	C₂×C₄×C₇	—	4	2	no	—
147	C₂×C₄×C₇	—	4	4	no	—
148	C₂×C₄×C₇	—	4	4	no	—
149	C₂×C₄×C₇	—	4	4	no	—
150	C₂×C₄×C₇	—	4	4	no	—
151	C₂×C₄×C₇	—	4	4	no	—
152	C₂×C₄×C₇	—	4	4	no	—
153	C₂×C₄×C₇	—	8	2	no	—
154	C₂×C₄×C₇	—	8	2	no	—
155	C₂×C₄×C₇	—	8	2	no	—
156	C₂×C₄×C₇	—	8	2	no	—
157	C₂×C₄×C₇	—	8	2	no	—
158	C₂×C₄×C₇	—	8	2	no	—
159	C₂×C₄×C₇	—	8	2	no	—
160	C₂×C₄×C₇	—	8	2	no	—
161	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₇	#117	1	2	yes	—
163	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₇	C₄×Q₈	1	1	yes	characteristic
165	C₂×C₄×C₇	#120	1	1	yes	characteristic
166	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
167	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
168	C₂×C₄×C₇	C₂²⋊Q₈	1	1	yes	characteristic
169	C₂×C₄×C₇	#123	1	1	yes	characteristic
170	C₂×C₄×C₇	#123	1	2	yes	—
171	C₂×C₄×C₇	#124	1	1	yes	characteristic
172	C₂×C₄×C₇	#124	1	1	yes	characteristic
173	C₂×C₄×C₇	#124	1	2	yes	—
174	C₂×C₄×C₇	#125	1	2	yes	—
175	C₂×C₄×C₇	#125	1	2	yes	—
176	C₂×C₄×C₇	#125	1	1	yes	characteristic
177	C₂×C₄×C₇	#126	1	2	yes	—
178	C₂×C₄×C₇	#126	1	2	yes	—
179	C₇×C₈	—	2	4	no	—
180	C₇×C₈	—	4	2	no	—
181	C₂³×C₄	—	2	2	no	—
182	C₂³×C₄	—	2	2	no	—
183	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
184	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
185	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
186	C₂²×C₈	—	2	2	no	—
187	C₂²×C₈	—	2	2	no	—
188	C₂²×C₈	—	2	1	no	—
189	C₂²×C₈	—	2	2	no	—
190	C₂²×C₈	—	2	2	no	—
191	C₂²×C₈	—	2	1	no	—
192	C₂²×C₈	C₂×C₄×C₇	1	2	yes	—
193	C₂²×C₈	C₇×D₄	1	2	yes	—
194	C₂²×C₈	C₇×Q₈	1	2	yes	—
195	C₂²×C₈	C₇×Q₈	1	2	yes	—
196	C₂×C₄⋊C₄	—	2	2	no	—
197	C₂×C₄⋊C₄	—	2	2	no	—
198	C₂×C₄⋊C₄	—	2	2	no	—
199	C₂×C₄⋊C₄	—	2	2	no	—
200	C₂×C₄⋊C₄	—	2	2	no	—
201	C₂×C₄⋊C₄	—	2	2	no	—
202	C₂×C₄⋊C₄	—	2	2	no	—
203	C₂×C₄⋊C₄	—	2	2	no	—
204	C₂×C₄⋊C₄	—	2	2	no	—
205	C₂×C₄⋊C₄	—	2	2	no	—
206	C₂×C₄⋊C₄	C₂×C₄×C₇	1	4	yes	—
207	C₂×C₄⋊C₄	C₇×D₄	1	4	yes	—
208	C₂×C₄²	—	2	1	no	—
209	C₂×C₄²	—	2	2	no	—
210	C₂×C₄²	—	2	2	no	—
211	C₂×C₄²	—	2	1	no	—
212	#107	—	2	8	no	—
213	#95	—	4	4	no	—
214	#95	—	4	4	no	—
215	C₂²×C₇	#388	1	2	yes	—
216	C₂²×C₇	#389	1	1	yes	characteristic
217	C₂²×C₇	#394	1	1	yes	characteristic
218	C₂²×C₇	#397	1	1	yes	characteristic
219	C₂²×C₇	#398	1	2	yes	—
220	C₂²×C₇	C₄×D₈	1	1	yes	characteristic
221	C₂²×C₇	C₄×Q₁₆	1	1	yes	characteristic
222	C₂²×C₇	#440	1	2	yes	—
223	C₂²×C₇	#459	1	2	yes	—
224	C₂²×C₇	#462	1	2	yes	—
225	C₂²×C₇	#463	1	2	yes	—
226	C₂²×C₇	#464	1	2	yes	—
227	C₂²×C₇	#466	1	1	yes	characteristic
228	C₂²×C₇	#467	1	1	yes	characteristic
229	C₂²×C₇	#469	1	1	yes	characteristic
230	C₂²×C₇	#470	1	1	yes	characteristic
231	C₂²×C₇	#480	1	2	yes	—
232	C₂²×C₇	#482	1	2	yes	—
233	C₂²×C₇	#484	1	2	yes	—
234	C₂²×C₇	#485	1	2	yes	—
235	C₂²×C₇	#499	1	1	yes	characteristic
236	C₂²×C₇	#500	1	1	yes	characteristic
237	C₂²×C₇	#501	1	2	yes	—
238	C₄×C₇	—	4	2	no	—
239	C₄×C₇	—	4	2	no	—
240	C₄×C₇	—	8	4	no	—
241	C₄×C₇	—	8	4	no	—
242	C₄×C₇	#382	1	1	yes	characteristic
243	C₄×C₇	#385	1	1	yes	characteristic
244	C₄×C₇	#387	1	2	yes	—
245	C₄×C₇	#393	1	1	yes	characteristic
246	C₄×C₇	#400	1	2	yes	—
247	C₄×C₇	#400	1	1	yes	characteristic
248	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
249	C₂²×C₄	—	2	1	no	—
250	C₂²×C₄	—	2	1	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	C₇×D₈	1	2	yes	—
272	C₂²×C₄	C₇×Q₁₆	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
276	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
278	C₂²×C₄	C₇×#41	1	2	yes	—
279	C₂²×C₄	C₇×#41	1	2	yes	—
280	C₂²×C₄	C₇×#41	1	2	yes	—
281	C₂²×C₄	C₇×#41	1	1	yes	characteristic
282	C₂²×C₄	C₇×#41	1	1	yes	characteristic
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	4	1	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	C₇×C₄⋊C₄	1	4	yes	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₄⋊C₄	—	4	2	no	—
300	C₄⋊C₄	—	4	2	no	—
301	C₄²	—	4	1	no	—
302	C₄²	—	4	1	no	—
303	C₄²	—	4	2	no	—
304	C₂×C₇	#1442	1	1	yes	characteristic
305	C₂×C₇	#1925	1	2	yes	—
306	C₂×C₇	#1928	1	2	yes	—
307	C₂×C₇	#1942	1	1	yes	characteristic
308	C₂×C₇	#1944	1	1	yes	characteristic
309	C₂×C₇	#2054	1	1	yes	characteristic
310	C₂×C₇	#2056	1	1	yes	characteristic
311	C₂×C₇	#2075	1	1	yes	characteristic
312	C₂×C₇	#2076	1	1	yes	characteristic
313	C₂×C₇	#2083	1	2	yes	—
314	C₂×C₇	#2085	1	2	yes	—
315	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
316	C₂³	C₇×#121	1	1	yes	characteristic
317	C₂³	C₇×#121	1	2	yes	—
318	C₂³	C₇×#123	1	2	yes	—
319	C₂³	C₇×C₄⋊Q₈	1	1	yes	characteristic
320	C₂³	C₂×C₇×D₈	1	1	yes	characteristic
321	C₂³	C₂×C₇×Q₁₆	1	1	yes	characteristic
322	C₂³	C₇×#135	1	1	yes	characteristic
323	C₂³	C₇×#135	1	1	yes	characteristic
324	C₂³	C₇×AGL(1,ℤ/8)	1	2	yes	—
325	C₂³	C₇×#137	1	2	yes	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	8	2	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	—	8	2	no	—
345	C₂×C₄	—	8	2	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
351	C₂×C₄	C₇×#117	1	2	yes	—
352	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
353	C₂×C₄	C₄×C₇×Q₈	1	1	yes	characteristic
354	C₂×C₄	C₇×#120	1	1	yes	characteristic
355	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
356	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
357	C₂×C₄	C₇×C₂²⋊Q₈	1	1	yes	characteristic
358	C₂×C₄	C₇×#123	1	1	yes	characteristic
359	C₂×C₄	C₇×#123	1	2	yes	—
360	C₂×C₄	C₇×#124	1	1	yes	characteristic
361	C₂×C₄	C₇×#124	1	1	yes	characteristic
362	C₂×C₄	C₇×#124	1	2	yes	—
363	C₂×C₄	C₇×#125	1	2	yes	—
364	C₂×C₄	C₇×#125	1	2	yes	—
365	C₂×C₄	C₇×#125	1	1	yes	characteristic
366	C₂×C₄	C₇×#126	1	2	yes	—
367	C₂×C₄	C₇×#126	1	2	yes	—
368	C₈	—	2	4	no	—
369	C₈	—	4	2	no	—
370	C₇	#11256	1	1	yes	characteristic, direct product factor, Sylow
371	C₂²	C₇×#388	1	2	yes	—
372	C₂²	C₇×#389	1	1	yes	characteristic
373	C₂²	C₇×#394	1	1	yes	characteristic
374	C₂²	C₇×#397	1	1	yes	characteristic
375	C₂²	C₇×#398	1	2	yes	—
376	C₂²	C₄×C₇×D₈	1	1	yes	characteristic
377	C₂²	C₄×C₇×Q₁₆	1	1	yes	characteristic
378	C₂²	C₇×#440	1	2	yes	—
379	C₂²	C₇×#459	1	2	yes	—
380	C₂²	C₇×#462	1	2	yes	—
381	C₂²	C₇×#463	1	2	yes	—
382	C₂²	C₇×#464	1	2	yes	—
383	C₂²	C₇×#466	1	1	yes	characteristic
384	C₂²	C₇×#467	1	1	yes	characteristic
385	C₂²	C₇×#469	1	1	yes	characteristic
386	C₂²	C₇×#470	1	1	yes	characteristic
387	C₂²	C₇×#480	1	2	yes	—
388	C₂²	C₇×#482	1	2	yes	—
389	C₂²	C₇×#484	1	2	yes	—
390	C₂²	C₇×#485	1	2	yes	—
391	C₂²	C₇×#499	1	1	yes	characteristic
392	C₂²	C₇×#500	1	1	yes	characteristic
393	C₂²	C₇×#501	1	2	yes	—
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	8	4	no	—
397	C₄	—	8	4	no	—
398	C₄	C₇×#382	1	1	yes	characteristic
399	C₄	C₇×#385	1	1	yes	characteristic
400	C₄	C₇×#387	1	2	yes	—
401	C₄	C₇×#393	1	1	yes	characteristic
402	C₄	C₇×#400	1	2	yes	—
403	C₄	C₇×#400	1	1	yes	characteristic
404	C₂	C₇×#1442	1	1	yes	characteristic
405	C₂	C₇×#1925	1	2	yes	—
406	C₂	C₇×#1928	1	2	yes	—
407	C₂	C₇×#1942	1	1	yes	characteristic
408	C₂	C₇×#1944	1	1	yes	characteristic
409	C₂	C₇×#2054	1	1	yes	characteristic
410	C₂	C₇×#2056	1	1	yes	characteristic
411	C₂	C₇×#2075	1	1	yes	characteristic
412	C₂	C₇×#2076	1	1	yes	characteristic
413	C₂	C₇×#2083	1	2	yes	—
414	C₂	C₇×#2085	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₇	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₇
Frattini, cosocle	C₂³×C₄	C₂³×C₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
16. C₇×#340	C₄	semidirect
18. #11256	C₇	direct (N × H)
124. #340	C₄×C₇	semidirect
370. C₇	#11256	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₇×#107	2
C₂×C₇×#340	2
C₂×C₇×#336	2
C₇×C₄⋊#95	2
#11256	7

Subgroups — C7×#11256 #13188472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#11256 #13188472