Subgroups — C₇×#34914 #13212130

Order 1792.

2458 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#529	C₂	1	2	yes	maximal, complemented
2	C₇×#2560	C₂	1	2	yes	maximal, complemented
3	C₇×#2559	C₂	1	2	yes	maximal, complemented
4	C₇×#2558	C₂	1	2	yes	maximal, complemented
5	C₇×#2557	C₂	1	2	yes	maximal, complemented
6	C₇×#2512	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2506	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2496	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2491	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2445	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2428	C₂	1	1	yes	maximal, characteristic
13	C₇×#2422	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2398	C₂	1	2	yes	maximal, complemented
15	C₇×#2392	C₂	1	2	yes	maximal, complemented
16	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₇×#127	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2290	C₂	1	2	yes	maximal, complemented
22	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#127	C₂²	1	1	yes	characteristic
26	C₇×#529	—	2	16	no	—
27	C₂×C₇×#126	C₂²	1	2	yes	—
28	C₂×C₇×#126	C₂²	1	2	yes	—
29	C₂×C₇×#125	C₂²	1	2	yes	—
30	C₂×C₇×#124	C₂²	1	2	yes	—
31	C₂×C₇×#123	C₂²	1	2	yes	—
32	C₂×C₇×#123	C₂²	1	2	yes	—
33	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₇×#121	C₂²	1	1	yes	characteristic
35	C₂×C₇×#121	C₂²	1	1	yes	characteristic
36	C₂×C₇×#121	C₂²	1	2	yes	—
37	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
38	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
39	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
40	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
41	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
42	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₇×#117	C₂²	1	1	yes	characteristic
47	C₂×C₇×#117	C₂²	1	2	yes	—
48	C₂×C₇×#117	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₇	C₂²	1	2	yes	—
50	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
51	C₇×#400	C₂²	1	2	yes	—
52	C₇×#400	C₂²	1	2	yes	—
53	C₇×#398	C₂²	1	2	yes	—
54	C₇×#397	C₂²	1	2	yes	—
55	C₇×#397	C₂²	1	2	yes	—
56	C₇×#397	C₂²	1	2	yes	—
57	C₇×#396	C₂²	1	2	yes	—
58	C₇×#396	C₂²	1	2	yes	—
59	C₇×#394	C₂²	1	2	yes	—
60	C₇×#394	C₂²	1	2	yes	—
61	C₇×#394	C₂²	1	2	yes	—
62	C₇×#394	C₂²	1	2	yes	—
63	C₇×#394	C₂²	1	2	yes	—
64	C₇×#393	C₂²	1	2	yes	—
65	C₇×#393	C₂²	1	2	yes	—
66	C₇×#392	C₂²	1	2	yes	—
67	C₇×#391	C₂²	1	2	yes	—
68	C₇×#390	C₂²	1	1	yes	characteristic
69	C₇×#390	C₂²	1	1	yes	characteristic
70	C₇×#390	C₂²	1	1	yes	characteristic
71	C₇×#390	C₂²	1	1	yes	characteristic
72	C₇×#390	C₂²	1	1	yes	characteristic
73	C₇×#390	C₂²	1	1	yes	characteristic
74	C₇×#390	C₂²	1	2	yes	—
75	C₇×#390	C₂²	1	2	yes	—
76	C₇×#389	C₂²	1	1	yes	characteristic
77	C₇×#389	C₂²	1	1	yes	characteristic
78	C₇×#389	C₂²	1	1	yes	characteristic
79	C₇×#389	C₂²	1	1	yes	characteristic
80	C₇×#389	C₂²	1	1	yes	characteristic
81	C₇×#389	C₂²	1	1	yes	characteristic
82	C₇×#389	C₂²	1	2	yes	—
83	C₇×#388	C₂²	1	2	yes	—
84	C₇×#388	C₂²	1	2	yes	—
85	C₇×#388	C₂²	1	2	yes	—
86	C₇×#388	C₂²	1	2	yes	—
87	C₇×#388	C₂²	1	2	yes	—
88	C₇×#388	C₂²	1	2	yes	—
89	C₇×#387	C₂²	1	2	yes	—
90	C₇×#387	C₂²	1	2	yes	—
91	C₇×#386	C₂²	1	2	yes	—
92	C₇×#386	C₂²	1	2	yes	—
93	C₇×#386	C₂²	1	2	yes	—
94	C₇×#386	C₂²	1	2	yes	—
95	C₇×#385	C₂²	1	2	yes	—
96	C₇×#385	C₂²	1	2	yes	—
97	C₇×#384	C₂²	1	1	yes	characteristic
98	C₇×#384	C₂²	1	1	yes	characteristic
99	C₇×#380	C₂²	1	1	yes	characteristic
100	C₇×#380	C₂²	1	1	yes	characteristic
101	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
102	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
111	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
112	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
113	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
114	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₇×#376	C₂²	1	1	yes	characteristic
121	C₇×#376	C₂²	1	1	yes	characteristic
122	C₄³×C₇	C₂²	1	1	yes	characteristic
123	C₄³×C₇	C₂²	1	1	yes	characteristic
124	#34914	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂²×C₇×Q₈	C₂³	1	2	yes	—
126	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
127	C₂²×C₇×D₄	C₂³	1	2	yes	—
128	C₂²×C₇×D₄	C₂³	1	2	yes	—
129	C₂²×C₇×D₄	C₂³	1	2	yes	—
130	C₂²×C₇×D₄	C₂³	1	2	yes	—
131	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₇	C₂³	1	2	yes	—
134	C₂³×C₄×C₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
139	C₇×C₄⋊Q₈	—	2	4	no	—
140	C₇×#127	—	2	4	no	—
141	C₇×#126	—	2	8	no	—
142	C₇×#126	—	2	8	no	—
143	C₇×#125	—	2	8	no	—
144	C₇×#124	—	2	8	no	—
145	C₇×#123	—	2	8	no	—
146	C₇×#123	—	2	8	no	—
147	C₇×C₂²⋊Q₈	—	2	8	no	—
148	C₇×#121	—	2	4	no	—
149	C₇×#121	—	2	4	no	—
150	C₇×#121	—	2	8	no	—
151	C₄×C₇×Q₈	—	2	8	no	—
152	C₄×C₇×D₄	—	2	4	no	—
153	C₄×C₇×D₄	—	2	8	no	—
154	C₄×C₇×D₄	—	2	8	no	—
155	C₄×C₇×D₄	—	2	4	no	—
156	C₄×C₇×D₄	—	2	8	no	—
157	C₄×C₇×D₄	—	2	4	no	—
158	C₄×C₇×D₄	—	2	4	no	—
159	C₄×C₇×D₄	—	2	8	no	—
160	C₇×#117	—	2	8	no	—
161	C₇×#117	—	2	4	no	—
162	C₇×#117	D₄	1	8	yes	complemented
163	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₇	—	2	8	no	—
209	C₂×C₄²×C₇	—	2	4	no	—
210	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₇	C₂³	1	2	yes	—
215	C₂×C₄²×C₇	C₂³	1	2	yes	—
216	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₇	C₂³	1	2	yes	—
221	C₂×C₄²×C₇	C₂³	1	2	yes	—
222	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
230	C₇×#95	C₂³	1	1	yes	characteristic
231	C₇×#95	C₂³	1	1	yes	characteristic
232	C₇×#95	C₂³	1	1	yes	characteristic
233	C₇×#95	C₂³	1	1	yes	characteristic
234	C₇×#95	C₂³	1	1	yes	characteristic
235	C₇×#95	C₂³	1	1	yes	characteristic
236	C₇×#95	C₂³	1	1	yes	characteristic
237	C₇×#95	C₂³	1	1	yes	characteristic
238	C₇×#95	C₂³	1	2	yes	—
239	C₇×#95	C₂³	1	2	yes	—
240	C₇×#95	C₂³	1	2	yes	—
241	C₇×#95	C₂³	1	2	yes	—
242	C₇×#95	C₂³	1	2	yes	—
243	C₇×#95	C₂³	1	2	yes	—
244	C₇×#95	C₂³	1	2	yes	—
245	C₇×#95	C₂³	1	2	yes	—
246	C₇×#95	C₂³	1	2	yes	—
247	C₇×#95	C₂³	1	2	yes	—
248	C₇×#95	C₂³	1	2	yes	—
249	C₇×#95	C₂³	1	2	yes	—
250	C₂×#529	C₂×C₇	1	2	yes	complemented
251	#2560	C₂×C₇	1	2	yes	complemented
252	#2559	C₂×C₇	1	2	yes	complemented
253	#2558	C₂×C₇	1	2	yes	complemented
254	#2557	C₂×C₇	1	2	yes	complemented
255	#2512	C₂×C₇	1	1	yes	characteristic, complemented
256	#2506	C₂×C₇	1	1	yes	characteristic, complemented
257	#2496	C₂×C₇	1	1	yes	characteristic, complemented
258	#2491	C₂×C₇	1	1	yes	characteristic, complemented
259	#2452	C₂×C₇	1	1	yes	characteristic, complemented
260	#2445	C₂×C₇	1	1	yes	characteristic, complemented
261	#2428	C₂×C₇	1	1	yes	characteristic
262	#2422	C₂×C₇	1	1	yes	characteristic, complemented
263	#2398	C₂×C₇	1	2	yes	complemented
264	#2392	C₂×C₇	1	2	yes	complemented
265	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
266	C₄×#127	C₂×C₇	1	1	yes	characteristic, complemented
267	C₄×#121	C₂×C₇	1	1	yes	characteristic, complemented
268	C₄×#121	C₂×C₇	1	1	yes	characteristic, complemented
269	#2293	C₂×C₇	1	1	yes	characteristic, complemented
270	#2290	C₂×C₇	1	2	yes	complemented
271	C₄²×D₄	C₂×C₇	1	1	yes	characteristic, complemented
272	C₄×#117	C₂×C₇	1	1	yes	characteristic, complemented
273	C₂⁴×C₇	C₂⁴	1	2	yes	—
274	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
275	C₂⁴×C₇	C₂⁴	1	2	yes	—
276	C₂×C₇×Q₈	—	2	4	no	—
277	C₂×C₇×Q₈	—	2	4	no	—
278	C₂×C₇×Q₈	—	4	2	no	—
279	C₂×C₇×D₄	—	2	4	no	—
280	C₂×C₇×D₄	—	2	4	no	—
281	C₂×C₇×D₄	—	2	4	no	—
282	C₂×C₇×D₄	—	2	4	no	—
283	C₂×C₇×D₄	—	2	4	no	—
284	C₂×C₇×D₄	—	2	4	no	—
285	C₂×C₇×D₄	—	2	2	no	—
286	C₂×C₇×D₄	—	2	2	no	—
287	C₂×C₇×D₄	—	2	4	no	—
288	C₂×C₇×D₄	—	2	2	no	—
289	C₂×C₇×D₄	—	2	4	no	—
290	C₂×C₇×D₄	—	2	2	no	—
291	C₂×C₇×D₄	—	2	2	no	—
292	C₂×C₇×D₄	—	4	2	no	—
293	C₂×C₇×D₄	—	4	2	no	—
294	C₂×C₇×D₄	—	4	2	no	—
295	C₂×C₇×D₄	—	4	2	no	—
296	C₂×C₇×D₄	#41	1	4	yes	—
297	C₂²×C₄×C₇	—	2	2	no	—
298	C₂²×C₄×C₇	—	2	2	no	—
299	C₂²×C₄×C₇	—	2	4	no	—
300	C₂²×C₄×C₇	—	2	4	no	—
301	C₂²×C₄×C₇	—	2	4	no	—
302	C₂²×C₄×C₇	—	2	4	no	—
303	C₂²×C₄×C₇	—	2	4	no	—
304	C₂²×C₄×C₇	—	2	2	no	—
305	C₂²×C₄×C₇	—	2	2	no	—
306	C₂²×C₄×C₇	—	2	4	no	—
307	C₂²×C₄×C₇	—	2	4	no	—
308	C₂²×C₄×C₇	—	2	4	no	—
309	C₂²×C₄×C₇	—	2	4	no	—
310	C₂²×C₄×C₇	—	2	4	no	—
311	C₂²×C₄×C₇	—	2	2	no	—
312	C₂²×C₄×C₇	—	2	2	no	—
313	C₂²×C₄×C₇	—	4	1	no	—
314	C₂²×C₄×C₇	—	4	1	no	—
315	C₂²×C₄×C₇	—	4	2	no	—
316	C₂²×C₄×C₇	—	4	2	no	—
317	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
318	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
338	C₇×C₄⋊C₄	—	2	4	no	—
339	C₇×C₄⋊C₄	—	2	4	no	—
340	C₇×C₄⋊C₄	—	2	4	no	—
341	C₇×C₄⋊C₄	—	2	4	no	—
342	C₇×C₄⋊C₄	—	2	4	no	—
343	C₇×C₄⋊C₄	—	2	4	no	—
344	C₇×C₄⋊C₄	—	2	4	no	—
345	C₇×C₄⋊C₄	—	2	4	no	—
346	C₇×C₄⋊C₄	—	2	2	no	—
347	C₇×C₄⋊C₄	—	2	2	no	—
348	C₇×C₄⋊C₄	—	2	4	no	—
349	C₇×C₄⋊C₄	—	2	2	no	—
350	C₇×C₄⋊C₄	—	2	2	no	—
351	C₇×C₄⋊C₄	—	2	2	no	—
352	C₇×C₄⋊C₄	—	2	2	no	—
353	C₇×C₄⋊C₄	—	2	4	no	—
354	C₇×C₄⋊C₄	—	2	2	no	—
355	C₇×C₄⋊C₄	—	4	2	no	—
356	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
357	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
358	C₇×C₄⋊C₄	#41	1	4	yes	—
359	C₇×C₂²⋊C₄	—	2	4	no	—
360	C₇×C₂²⋊C₄	—	2	4	no	—
361	C₇×C₂²⋊C₄	—	2	4	no	—
362	C₇×C₂²⋊C₄	—	2	4	no	—
363	C₇×C₂²⋊C₄	—	2	4	no	—
364	C₇×C₂²⋊C₄	—	2	4	no	—
365	C₇×C₂²⋊C₄	—	2	4	no	—
366	C₇×C₂²⋊C₄	—	2	4	no	—
367	C₇×C₂²⋊C₄	—	2	4	no	—
368	C₇×C₂²⋊C₄	—	2	4	no	—
369	C₇×C₂²⋊C₄	—	2	2	no	—
370	C₇×C₂²⋊C₄	—	2	2	no	—
371	C₇×C₂²⋊C₄	—	2	4	no	—
372	C₇×C₂²⋊C₄	—	2	4	no	—
373	C₇×C₂²⋊C₄	—	2	4	no	—
374	C₇×C₂²⋊C₄	—	2	4	no	—
375	C₇×C₂²⋊C₄	—	2	4	no	—
376	C₇×C₂²⋊C₄	—	2	4	no	—
377	C₇×C₂²⋊C₄	—	4	2	no	—
378	C₇×C₂²⋊C₄	—	4	2	no	—
379	C₇×C₂²⋊C₄	—	4	2	no	—
380	C₇×C₂²⋊C₄	—	4	2	no	—
381	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
382	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
383	C₄²×C₇	—	2	4	no	—
384	C₄²×C₇	—	2	4	no	—
385	C₄²×C₇	—	2	4	no	—
386	C₄²×C₇	—	2	4	no	—
387	C₄²×C₇	—	2	2	no	—
388	C₄²×C₇	—	2	2	no	—
389	C₄²×C₇	—	2	2	no	—
390	C₄²×C₇	—	2	2	no	—
391	C₄²×C₇	—	2	2	no	—
392	C₄²×C₇	—	2	2	no	—
393	C₄²×C₇	—	2	2	no	—
394	C₄²×C₇	—	2	2	no	—
395	C₄²×C₇	—	4	1	no	—
396	C₄²×C₇	—	4	1	no	—
397	C₄²×C₇	—	4	1	no	—
398	C₄²×C₇	—	4	1	no	—
399	C₄²×C₇	C₂×D₄	1	4	yes	—
400	C₄²×C₇	C₂×D₄	1	4	yes	—
401	C₄²×C₇	#41	1	4	yes	—
402	C₄²×C₇	#41	1	4	yes	—
403	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
404	C₂×#127	C₂²×C₇	1	1	yes	characteristic
405	#529	—	2	16	no	—
406	C₂×#126	C₂²×C₇	1	2	yes	—
407	C₂×#126	C₂²×C₇	1	2	yes	—
408	C₂×#125	C₂²×C₇	1	2	yes	—
409	C₂×#124	C₂²×C₇	1	2	yes	—
410	C₂×#123	C₂²×C₇	1	2	yes	—
411	C₂×#123	C₂²×C₇	1	2	yes	—
412	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
413	C₂×#121	C₂²×C₇	1	2	yes	—
414	C₂×#121	C₂²×C₇	1	1	yes	characteristic
415	C₂×#121	C₂²×C₇	1	1	yes	characteristic
416	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
417	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
418	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
419	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
420	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
421	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
422	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
423	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
424	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
425	C₂×#117	C₂²×C₇	1	1	yes	characteristic
426	C₂×#117	C₂²×C₇	1	2	yes	—
427	C₂×#117	C₂²×C₇	1	1	yes	characteristic
428	C₂²×C₄²	C₂²×C₇	1	2	yes	—
429	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
430	#400	C₂²×C₇	1	2	yes	—
431	#400	C₂²×C₇	1	2	yes	—
432	#398	C₂²×C₇	1	2	yes	—
433	#397	C₂²×C₇	1	2	yes	—
434	#397	C₂²×C₇	1	2	yes	—
435	#397	C₂²×C₇	1	2	yes	—
436	#396	C₂²×C₇	1	2	yes	—
437	#396	C₂²×C₇	1	2	yes	—
438	#394	C₂²×C₇	1	2	yes	—
439	#394	C₂²×C₇	1	2	yes	—
440	#394	C₂²×C₇	1	2	yes	—
441	#394	C₂²×C₇	1	2	yes	—
442	#394	C₂²×C₇	1	2	yes	—
443	#393	C₂²×C₇	1	2	yes	—
444	#393	C₂²×C₇	1	2	yes	—
445	#392	C₂²×C₇	1	2	yes	—
446	#391	C₂²×C₇	1	2	yes	—
447	#390	C₂²×C₇	1	2	yes	—
448	#390	C₂²×C₇	1	1	yes	characteristic
449	#390	C₂²×C₇	1	1	yes	characteristic
450	#390	C₂²×C₇	1	2	yes	—
451	#390	C₂²×C₇	1	1	yes	characteristic
452	#390	C₂²×C₇	1	1	yes	characteristic
453	#390	C₂²×C₇	1	1	yes	characteristic
454	#390	C₂²×C₇	1	1	yes	characteristic
455	#389	C₂²×C₇	1	1	yes	characteristic
456	#389	C₂²×C₇	1	1	yes	characteristic
457	#389	C₂²×C₇	1	2	yes	—
458	#389	C₂²×C₇	1	1	yes	characteristic
459	#389	C₂²×C₇	1	1	yes	characteristic
460	#389	C₂²×C₇	1	1	yes	characteristic
461	#389	C₂²×C₇	1	1	yes	characteristic
462	#388	C₂²×C₇	1	2	yes	—
463	#388	C₂²×C₇	1	2	yes	—
464	#388	C₂²×C₇	1	2	yes	—
465	#388	C₂²×C₇	1	2	yes	—
466	#388	C₂²×C₇	1	2	yes	—
467	#388	C₂²×C₇	1	2	yes	—
468	#387	C₂²×C₇	1	2	yes	—
469	#387	C₂²×C₇	1	2	yes	—
470	#386	C₂²×C₇	1	2	yes	—
471	#386	C₂²×C₇	1	2	yes	—
472	#386	C₂²×C₇	1	2	yes	—
473	#386	C₂²×C₇	1	2	yes	—
474	#385	C₂²×C₇	1	2	yes	—
475	#385	C₂²×C₇	1	2	yes	—
476	#384	C₂²×C₇	1	1	yes	characteristic
477	#384	C₂²×C₇	1	1	yes	characteristic
478	#380	C₂²×C₇	1	1	yes	characteristic
479	#380	C₂²×C₇	1	1	yes	characteristic
480	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
481	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
482	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
483	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
484	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
485	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
486	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
487	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
488	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
489	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
490	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
491	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
492	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
493	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
494	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
495	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
496	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
497	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
498	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
499	#376	C₂²×C₇	1	1	yes	characteristic
500	#376	C₂²×C₇	1	1	yes	characteristic
501	C₄³	C₂²×C₇	1	1	yes	characteristic
502	C₄³	C₂²×C₇	1	1	yes	characteristic
503	C₂³×C₇	—	2	2	no	—
504	C₂³×C₇	—	2	1	no	—
505	C₂³×C₇	—	2	2	no	—
506	C₂³×C₇	—	2	2	no	—
507	C₂³×C₇	—	2	2	no	—
508	C₂³×C₇	—	2	1	no	—
509	C₂³×C₇	—	2	1	no	—
510	C₂³×C₇	—	2	1	no	—
511	C₂³×C₇	—	2	2	no	—
512	C₂³×C₇	—	2	2	no	—
513	C₂³×C₇	—	2	1	no	—
514	C₂³×C₇	—	2	1	no	—
515	C₂³×C₇	—	2	2	no	—
516	C₂³×C₇	—	2	2	no	—
517	C₂³×C₇	—	2	2	no	—
518	C₂³×C₇	—	2	2	no	—
519	C₂³×C₇	—	2	2	no	—
520	C₂³×C₇	—	2	2	no	—
521	C₂³×C₇	—	2	2	no	—
522	C₂³×C₇	C₂²×D₄	1	2	yes	—
523	C₂³×C₇	C₂×#41	1	4	yes	—
524	C₂³×C₇	C₂⁵	1	1	yes	characteristic
525	C₇×Q₈	—	4	8	no	—
526	C₇×D₄	—	2	8	no	—
527	C₇×D₄	—	4	8	no	—
528	C₇×D₄	—	4	8	no	—
529	C₇×D₄	—	4	8	no	—
530	C₇×D₄	—	4	8	no	—
531	C₇×D₄	—	4	4	no	—
532	C₂×C₄×C₇	—	2	2	no	—
533	C₂×C₄×C₇	—	2	1	no	—
534	C₂×C₄×C₇	—	2	1	no	—
535	C₂×C₄×C₇	—	2	1	no	—
536	C₂×C₄×C₇	—	2	1	no	—
537	C₂×C₄×C₇	—	2	1	no	—
538	C₂×C₄×C₇	—	2	1	no	—
539	C₂×C₄×C₇	—	2	1	no	—
540	C₂×C₄×C₇	—	2	1	no	—
541	C₂×C₄×C₇	—	2	1	no	—
542	C₂×C₄×C₇	—	2	1	no	—
543	C₂×C₄×C₇	—	2	1	no	—
544	C₂×C₄×C₇	—	2	1	no	—
545	C₂×C₄×C₇	—	2	1	no	—
546	C₂×C₄×C₇	—	2	1	no	—
547	C₂×C₄×C₇	—	2	1	no	—
548	C₂×C₄×C₇	—	2	1	no	—
549	C₂×C₄×C₇	—	2	2	no	—
550	C₂×C₄×C₇	—	2	8	no	—
551	C₂×C₄×C₇	—	2	2	no	—
552	C₂×C₄×C₇	—	2	2	no	—
553	C₂×C₄×C₇	—	2	2	no	—
554	C₂×C₄×C₇	—	2	2	no	—
555	C₂×C₄×C₇	—	2	2	no	—
556	C₂×C₄×C₇	—	2	1	no	—
557	C₂×C₄×C₇	—	2	1	no	—
558	C₂×C₄×C₇	—	2	1	no	—
559	C₂×C₄×C₇	—	2	1	no	—
560	C₂×C₄×C₇	—	2	1	no	—
561	C₂×C₄×C₇	—	2	1	no	—
562	C₂×C₄×C₇	—	2	1	no	—
563	C₂×C₄×C₇	—	2	1	no	—
564	C₂×C₄×C₇	—	2	2	no	—
565	C₂×C₄×C₇	—	2	2	no	—
566	C₂×C₄×C₇	—	2	2	no	—
567	C₂×C₄×C₇	—	2	2	no	—
568	C₂×C₄×C₇	—	2	2	no	—
569	C₂×C₄×C₇	—	2	2	no	—
570	C₂×C₄×C₇	—	2	2	no	—
571	C₂×C₄×C₇	—	2	1	no	—
572	C₂×C₄×C₇	—	2	1	no	—
573	C₂×C₄×C₇	—	2	1	no	—
574	C₂×C₄×C₇	—	2	1	no	—
575	C₂×C₄×C₇	—	2	2	no	—
576	C₂×C₄×C₇	—	2	2	no	—
577	C₂×C₄×C₇	—	2	2	no	—
578	C₂×C₄×C₇	—	4	8	no	—
579	C₂×C₄×C₇	—	4	8	no	—
580	C₂×C₄×C₇	—	4	4	no	—
581	C₂×C₄×C₇	—	4	4	no	—
582	C₂×C₄×C₇	—	4	8	no	—
583	C₂×C₄×C₇	—	4	8	no	—
584	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
585	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
586	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
587	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
588	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
589	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
590	C₂×C₄×C₇	C₂×#41	1	2	yes	—
591	C₂×C₄×C₇	C₂×#41	1	2	yes	—
592	C₂×C₄×C₇	C₂×#41	1	2	yes	—
593	C₂×C₄×C₇	C₂×#41	1	4	yes	—
594	C₂×C₄×C₇	C₂×#41	1	2	yes	—
595	C₂×C₄×C₇	C₂×#41	1	2	yes	—
596	C₂×C₄×C₇	C₂×#41	1	2	yes	—
597	C₂×C₄×C₇	C₂×#41	1	2	yes	—
598	C₂×C₄×C₇	C₂×#41	1	2	yes	—
599	C₂²×Q₈	C₂³×C₇	1	2	yes	—
600	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
601	C₂²×D₄	C₂³×C₇	1	2	yes	—
602	C₂²×D₄	C₂³×C₇	1	2	yes	—
603	C₂²×D₄	C₂³×C₇	1	2	yes	—
604	C₂²×D₄	C₂³×C₇	1	2	yes	—
605	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₇	1	2	yes	—
607	C₂³×C₄	C₂³×C₇	1	2	yes	—
608	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₇	1	2	yes	—
610	C₂³×C₄	C₂³×C₇	1	2	yes	—
611	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
613	C₄⋊Q₈	—	2	4	no	—
614	#127	—	2	4	no	—
615	#126	—	2	8	no	—
616	#126	—	2	8	no	—
617	#125	—	2	8	no	—
618	#124	—	2	8	no	—
619	#123	—	2	8	no	—
620	#123	—	2	8	no	—
621	C₂²⋊Q₈	—	2	8	no	—
622	#121	—	2	4	no	—
623	#121	—	2	4	no	—
624	#121	—	2	8	no	—
625	C₄×Q₈	—	2	8	no	—
626	C₄×D₄	—	2	4	no	—
627	C₄×D₄	—	2	8	no	—
628	C₄×D₄	—	2	8	no	—
629	C₄×D₄	—	2	4	no	—
630	C₄×D₄	—	2	8	no	—
631	C₄×D₄	—	2	4	no	—
632	C₄×D₄	—	2	4	no	—
633	C₄×D₄	—	2	8	no	—
634	#117	—	2	8	no	—
635	#117	—	2	4	no	—
636	#117	C₇×D₄	1	8	yes	complemented
637	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
661	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
662	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
682	C₂×C₄²	—	2	8	no	—
683	C₂×C₄²	—	2	4	no	—
684	C₂×C₄²	C₂³×C₇	1	2	yes	—
685	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₇	1	2	yes	—
687	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₇	1	2	yes	—
690	C₂×C₄²	C₂³×C₇	1	2	yes	—
691	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
704	#95	C₂³×C₇	1	1	yes	characteristic
705	#95	C₂³×C₇	1	1	yes	characteristic
706	#95	C₂³×C₇	1	1	yes	characteristic
707	#95	C₂³×C₇	1	1	yes	characteristic
708	#95	C₂³×C₇	1	1	yes	characteristic
709	#95	C₂³×C₇	1	1	yes	characteristic
710	#95	C₂³×C₇	1	1	yes	characteristic
711	#95	C₂³×C₇	1	1	yes	characteristic
712	#95	C₂³×C₇	1	2	yes	—
713	#95	C₂³×C₇	1	2	yes	—
714	#95	C₂³×C₇	1	2	yes	—
715	#95	C₂³×C₇	1	2	yes	—
716	#95	C₂³×C₇	1	2	yes	—
717	#95	C₂³×C₇	1	2	yes	—
718	#95	C₂³×C₇	1	2	yes	—
719	#95	C₂³×C₇	1	2	yes	—
720	#95	C₂³×C₇	1	2	yes	—
721	#95	C₂³×C₇	1	2	yes	—
722	#95	C₂³×C₇	1	2	yes	—
723	#95	C₂³×C₇	1	2	yes	—
724	C₂²×C₇	—	2	4	no	—
725	C₂²×C₇	—	2	2	no	—
726	C₂²×C₇	—	2	4	no	—
727	C₂²×C₇	—	2	2	no	—
728	C₂²×C₇	—	2	2	no	—
729	C₂²×C₇	—	2	4	no	—
730	C₂²×C₇	—	4	1	no	—
731	C₂²×C₇	—	4	2	no	—
732	C₂²×C₇	—	4	1	no	—
733	C₂²×C₇	—	4	2	no	—
734	C₂²×C₇	—	4	2	no	—
735	C₂²×C₇	—	4	1	no	—
736	C₂²×C₇	—	4	1	no	—
737	C₂²×C₇	—	4	2	no	—
738	C₂²×C₇	—	4	2	no	—
739	C₂²×C₇	—	4	2	no	—
740	C₂²×C₇	—	4	2	no	—
741	C₂²×C₇	—	4	2	no	—
742	C₂²×C₇	—	4	2	no	—
743	C₂²×C₇	—	4	2	no	—
744	C₂²×C₇	—	4	2	no	—
745	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
746	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
747	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
748	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
749	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
750	C₂²×C₇	#585	1	1	yes	characteristic
751	C₂²×C₇	#585	1	1	yes	characteristic
752	C₄×C₇	—	2	2	no	—
753	C₄×C₇	—	2	2	no	—
754	C₄×C₇	—	2	2	no	—
755	C₄×C₇	—	2	2	no	—
756	C₄×C₇	—	2	4	no	—
757	C₄×C₇	—	2	2	no	—
758	C₄×C₇	—	2	2	no	—
759	C₄×C₇	—	2	2	no	—
760	C₄×C₇	—	2	2	no	—
761	C₄×C₇	—	4	1	no	—
762	C₄×C₇	—	4	2	no	—
763	C₄×C₇	—	4	2	no	—
764	C₄×C₇	—	4	1	no	—
765	C₄×C₇	—	4	2	no	—
766	C₄×C₇	—	4	2	no	—
767	C₄×C₇	—	4	2	no	—
768	C₄×C₇	—	4	1	no	—
769	C₄×C₇	—	4	1	no	—
770	C₄×C₇	#529	1	4	yes	complemented
771	C₄×C₇	#532	1	4	yes	—
772	C₂⁴	C₂⁴×C₇	1	2	yes	—
773	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
774	C₂⁴	C₂⁴×C₇	1	2	yes	—
775	C₂×Q₈	—	2	4	no	—
776	C₂×Q₈	—	2	4	no	—
777	C₂×Q₈	—	4	2	no	—
778	C₂×D₄	—	2	4	no	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	2	4	no	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	2	4	no	—
783	C₂×D₄	—	2	4	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	2	4	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	4	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	2	no	—
791	C₂×D₄	—	4	2	no	—
792	C₂×D₄	—	4	2	no	—
793	C₂×D₄	—	4	2	no	—
794	C₂×D₄	—	4	2	no	—
795	C₂×D₄	C₇×#41	1	4	yes	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	4	no	—
799	C₂²×C₄	—	2	4	no	—
800	C₂²×C₄	—	2	4	no	—
801	C₂²×C₄	—	2	4	no	—
802	C₂²×C₄	—	2	4	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	2	4	no	—
807	C₂²×C₄	—	2	4	no	—
808	C₂²×C₄	—	2	4	no	—
809	C₂²×C₄	—	2	4	no	—
810	C₂²×C₄	—	2	2	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	4	1	no	—
813	C₂²×C₄	—	4	1	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
817	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
823	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
824	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
825	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
837	C₄⋊C₄	—	2	4	no	—
838	C₄⋊C₄	—	2	4	no	—
839	C₄⋊C₄	—	2	4	no	—
840	C₄⋊C₄	—	2	4	no	—
841	C₄⋊C₄	—	2	4	no	—
842	C₄⋊C₄	—	2	4	no	—
843	C₄⋊C₄	—	2	4	no	—
844	C₄⋊C₄	—	2	4	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	4	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	4	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	4	2	no	—
855	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
856	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
857	C₄⋊C₄	C₇×#41	1	4	yes	—
858	C₂²⋊C₄	—	2	4	no	—
859	C₂²⋊C₄	—	2	4	no	—
860	C₂²⋊C₄	—	2	4	no	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	2	4	no	—
863	C₂²⋊C₄	—	2	4	no	—
864	C₂²⋊C₄	—	2	4	no	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	4	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	2	4	no	—
873	C₂²⋊C₄	—	2	4	no	—
874	C₂²⋊C₄	—	2	4	no	—
875	C₂²⋊C₄	—	2	4	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	—	4	2	no	—
879	C₂²⋊C₄	—	4	2	no	—
880	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
881	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
882	C₄²	—	2	4	no	—
883	C₄²	—	2	4	no	—
884	C₄²	—	2	4	no	—
885	C₄²	—	2	4	no	—
886	C₄²	—	2	2	no	—
887	C₄²	—	2	2	no	—
888	C₄²	—	2	2	no	—
889	C₄²	—	2	2	no	—
890	C₄²	—	2	2	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	4	1	no	—
895	C₄²	—	4	1	no	—
896	C₄²	—	4	1	no	—
897	C₄²	—	4	1	no	—
898	C₄²	C₂×C₇×D₄	1	4	yes	—
899	C₄²	C₂×C₇×D₄	1	4	yes	—
900	C₄²	C₇×#41	1	4	yes	—
901	C₄²	C₇×#41	1	4	yes	—
902	C₂×C₇	—	4	4	no	—
903	C₂×C₇	—	4	2	no	—
904	C₂×C₇	—	8	2	no	—
905	C₂×C₇	C₂×#529	1	1	yes	characteristic
906	C₂×C₇	C₂×#532	1	1	yes	characteristic
907	C₂×C₇	#3455	1	1	yes	characteristic
908	C₂×C₇	D₄×#41	1	1	yes	characteristic
909	C₂×C₇	D₄×#41	1	1	yes	characteristic
910	C₂×C₇	#3475	1	1	yes	characteristic
911	C₂×C₇	#3480	1	1	yes	characteristic
912	C₂³	—	2	2	no	—
913	C₂³	—	2	1	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	1	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	2	no	—
927	C₂³	—	2	2	no	—
928	C₂³	—	2	2	no	—
929	C₂³	—	2	2	no	—
930	C₂³	—	2	2	no	—
931	C₂³	C₂²×C₇×D₄	1	2	yes	—
932	C₂³	C₂×C₇×#41	1	4	yes	—
933	C₂³	C₂⁵×C₇	1	1	yes	characteristic
934	Q₈	—	4	8	no	—
935	D₄	—	2	8	no	—
936	D₄	—	4	8	no	—
937	D₄	—	4	8	no	—
938	D₄	—	4	8	no	—
939	D₄	—	4	8	no	—
940	D₄	—	4	4	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	8	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	4	8	no	—
988	C₂×C₄	—	4	8	no	—
989	C₂×C₄	—	4	4	no	—
990	C₂×C₄	—	4	4	no	—
991	C₂×C₄	—	4	8	no	—
992	C₂×C₄	—	4	8	no	—
993	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
994	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
995	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
996	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
997	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
998	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
999	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1000	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1001	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1002	C₂×C₄	C₂×C₇×#41	1	4	yes	—
1003	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1004	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1005	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1006	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1007	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1008	C₇	#34914	1	1	yes	characteristic, direct product factor, Sylow
1009	C₂²	—	2	4	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	4	no	—
1015	C₂²	—	4	1	no	—
1016	C₂²	—	4	2	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	2	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	2	no	—
1027	C₂²	—	4	2	no	—
1028	C₂²	—	4	2	no	—
1029	C₂²	—	4	2	no	—
1030	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1031	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1032	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1033	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1034	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1035	C₂²	C₇×#585	1	1	yes	characteristic
1036	C₂²	C₇×#585	1	1	yes	characteristic
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	2	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	4	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	2	2	no	—
1045	C₄	—	2	2	no	—
1046	C₄	—	4	1	no	—
1047	C₄	—	4	2	no	—
1048	C₄	—	4	2	no	—
1049	C₄	—	4	1	no	—
1050	C₄	—	4	2	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	1	no	—
1055	C₄	C₇×#529	1	4	yes	complemented
1056	C₄	C₇×#532	1	4	yes	—
1057	C₂	—	4	4	no	—
1058	C₂	—	4	2	no	—
1059	C₂	—	8	2	no	—
1060	C₂	C₂×C₇×#529	1	1	yes	characteristic
1061	C₂	C₂×C₇×#532	1	1	yes	characteristic
1062	C₂	C₇×#3455	1	1	yes	characteristic
1063	C₂	C₇×D₄×#41	1	1	yes	characteristic
1064	C₂	C₇×D₄×#41	1	1	yes	characteristic
1065	C₂	C₇×#3475	1	1	yes	characteristic
1066	C₂	C₇×#3480	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
socle	C₂³×C₇	C₂⁵
prime radical	C₇×#2428	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#529	C₂	semidirect
2. C₇×#2560	C₂	semidirect
3. C₇×#2559	C₂	semidirect
4. C₇×#2558	C₂	semidirect
5. C₇×#2557	C₂	semidirect
6. C₇×#2512	C₂	semidirect
7. C₇×#2506	C₂	semidirect
8. C₇×#2496	C₂	semidirect
9. C₇×#2491	C₂	semidirect
10. C₇×#2452	C₂	semidirect
11. C₇×#2445	C₂	semidirect
13. C₇×#2422	C₂	semidirect
14. C₇×#2398	C₂	semidirect
15. C₇×#2392	C₂	semidirect
16. C₄×C₇×C₄⋊Q₈	C₂	semidirect
17. C₄×C₇×#127	C₂	semidirect
18. C₄×C₇×#121	C₂	semidirect
19. C₄×C₇×#121	C₂	semidirect
20. C₇×#2293	C₂	semidirect
21. C₇×#2290	C₂	semidirect
22. C₄²×C₇×D₄	C₂	semidirect
23. C₄×C₇×#117	C₂	semidirect
124. #34914	C₇	direct (N × H)
162. C₇×#117	D₄	semidirect
250. C₂×#529	C₂×C₇	semidirect
251. #2560	C₂×C₇	semidirect
252. #2559	C₂×C₇	semidirect
253. #2558	C₂×C₇	semidirect
254. #2557	C₂×C₇	semidirect
255. #2512	C₂×C₇	semidirect
256. #2506	C₂×C₇	semidirect
257. #2496	C₂×C₇	semidirect
258. #2491	C₂×C₇	semidirect
259. #2452	C₂×C₇	semidirect
260. #2445	C₂×C₇	semidirect
262. #2422	C₂×C₇	semidirect
263. #2398	C₂×C₇	semidirect
264. #2392	C₂×C₇	semidirect
265. C₄×C₄⋊Q₈	C₂×C₇	semidirect
266. C₄×#127	C₂×C₇	semidirect
267. C₄×#121	C₂×C₇	semidirect
268. C₄×#121	C₂×C₇	semidirect
269. #2293	C₂×C₇	semidirect
270. #2290	C₂×C₇	semidirect
271. C₄²×D₄	C₂×C₇	semidirect
272. C₄×#117	C₂×C₇	semidirect
636. #117	C₇×D₄	semidirect
770. C₄×C₇	#529	semidirect
1008. C₇	#34914	direct (N × H)
1055. C₄	C₇×#529	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#529	2
C₇×#2560	2
C₇×#2559	2
C₇×#2558	2
C₇×#2557	2
C₇×#2512	2
C₇×#2506	2
C₇×#2496	2
C₇×#2491	2
C₇×#2452	2
C₇×#2445	2
C₇×#2428	2
C₇×#2422	2
C₇×#2398	2
C₇×#2392	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×#127	2
C₄×C₇×#121	2
C₇×#2293	2
C₇×#2290	2
C₄²×C₇×D₄	2
C₄×C₇×#117	2
#34914	7

Subgroups — C7×#34914 #13212130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34914 #13212130