Subgroups — C₇×#34898 #13212114

Order 1792.

1804 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2577	C₂	1	2	yes	maximal, complemented
2	C₇×#2575	C₂	1	2	yes	maximal, complemented
3	C₇×#2570	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2565	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2562	C₂	1	1	yes	maximal, characteristic
6	C₇×#2536	C₂	1	1	yes	maximal, characteristic
7	C₇×#2524	C₂	1	2	yes	maximal, complemented
8	C₇×#2496	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2495	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2468	C₂	1	2	yes	maximal
11	C₇×#2423	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2421	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2402	C₂	1	2	yes	maximal, complemented
14	C₇×#2395	C₂	1	2	yes	maximal
15	C₄×C₇×#125	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₇×#126	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2298	C₂	1	2	yes	maximal, complemented
20	C₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic
24	C₂×C₇×#126	C₂²	1	2	yes	—
25	C₂×C₇×#125	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₇×#117	C₂²	1	2	yes	—
35	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
37	C₇×#400	C₂²	1	2	yes	—
38	C₇×#400	C₂²	1	2	yes	—
39	C₇×#400	C₂²	1	2	yes	—
40	C₇×#400	C₂²	1	2	yes	—
41	C₇×#400	C₂²	1	2	yes	—
42	C₇×#399	C₂²	1	2	yes	—
43	C₇×#398	C₂²	1	2	yes	—
44	C₇×#398	C₂²	1	2	yes	—
45	C₇×#398	C₂²	1	2	yes	—
46	C₇×#398	C₂²	1	2	yes	—
47	C₇×#398	C₂²	1	2	yes	—
48	C₇×#397	C₂²	1	2	yes	—
49	C₇×#397	C₂²	1	2	yes	—
50	C₇×#397	C₂²	1	2	yes	—
51	C₇×#394	C₂²	1	2	yes	—
52	C₇×#394	C₂²	1	2	yes	—
53	C₇×#391	C₂²	1	1	yes	characteristic
54	C₇×#391	C₂²	1	1	yes	characteristic
55	C₇×#389	C₂²	1	1	yes	characteristic
56	C₇×#389	C₂²	1	1	yes	characteristic
57	C₇×#389	C₂²	1	1	yes	characteristic
58	C₇×#389	C₂²	1	1	yes	characteristic
59	C₇×#388	C₂²	1	2	yes	—
60	C₇×#388	C₂²	1	2	yes	—
61	C₇×#388	C₂²	1	2	yes	—
62	C₇×#388	C₂²	1	2	yes	—
63	C₇×#388	C₂²	1	2	yes	—
64	C₇×#388	C₂²	1	2	yes	—
65	C₇×#388	C₂²	1	2	yes	—
66	C₇×#387	C₂²	1	2	yes	—
67	C₇×#387	C₂²	1	2	yes	—
68	C₇×#387	C₂²	1	2	yes	—
69	C₇×#387	C₂²	1	2	yes	—
70	C₇×#387	C₂²	1	2	yes	—
71	C₇×#387	C₂²	1	2	yes	—
72	C₇×#387	C₂²	1	2	yes	—
73	C₇×#387	C₂²	1	2	yes	—
74	C₇×#387	C₂²	1	2	yes	—
75	C₇×#387	C₂²	1	2	yes	—
76	C₇×#387	C₂²	1	2	yes	—
77	C₇×#385	C₂²	1	2	yes	—
78	C₇×#385	C₂²	1	2	yes	—
79	C₇×#384	C₂²	1	1	yes	characteristic
80	C₇×#384	C₂²	1	1	yes	characteristic
81	C₇×#383	C₂²	1	2	yes	—
82	C₇×#383	C₂²	1	2	yes	—
83	C₇×#382	C₂²	1	1	yes	characteristic
84	C₇×#382	C₂²	1	1	yes	characteristic
85	C₇×#382	C₂²	1	2	yes	—
86	C₇×#382	C₂²	1	1	yes	characteristic
87	C₇×#381	C₂²	1	2	yes	—
88	C₇×#380	C₂²	1	1	yes	characteristic
89	C₇×#380	C₂²	1	1	yes	characteristic
90	C₇×#380	C₂²	1	2	yes	—
91	C₇×#380	C₂²	1	1	yes	characteristic
92	C₇×#380	C₂²	1	1	yes	characteristic
93	C₇×#380	C₂²	1	1	yes	characteristic
94	C₇×#380	C₂²	1	1	yes	characteristic
95	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
97	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
98	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
99	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
100	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
108	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₇×C₄⋊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	1	yes	characteristic
119	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
120	C₇×#376	C₂²	1	2	yes	—
121	C₄³×C₇	C₂²	1	1	yes	characteristic
122	C₄³×C₇	C₂²	1	2	yes	—
123	#34898	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
125	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
132	C₇×#126	—	2	8	no	—
133	C₇×#125	—	2	4	no	—
134	C₇×C₂²⋊Q₈	—	2	4	no	—
135	C₇×C₂²⋊Q₈	—	2	4	no	—
136	C₄×C₇×Q₈	—	2	4	no	—
137	C₄×C₇×Q₈	—	2	4	no	—
138	C₄×C₇×Q₈	—	2	4	no	—
139	C₄×C₇×D₄	—	2	4	no	—
140	C₄×C₇×D₄	—	2	4	no	—
141	C₄×C₇×D₄	—	2	4	no	—
142	C₇×#117	—	2	8	no	—
143	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
168	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₇	—	2	4	no	—
183	C₂×C₄²×C₇	—	2	4	no	—
184	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₇	C₂³	1	2	yes	—
187	C₂×C₄²×C₇	C₂³	1	2	yes	—
188	C₂×C₄²×C₇	C₂³	1	2	yes	—
189	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇	C₂³	1	2	yes	—
195	C₂×C₄²×C₇	C₂³	1	2	yes	—
196	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₇	C₂³	1	2	yes	—
200	C₂×C₄²×C₇	C₂³	1	2	yes	—
201	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₇	C₂³	1	2	yes	—
203	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
205	C₇×#95	C₂³	1	2	yes	—
206	C₇×#95	C₂³	1	2	yes	—
207	C₇×#95	C₂³	1	2	yes	—
208	C₇×#95	C₂³	1	2	yes	—
209	C₇×#95	C₂³	1	1	yes	characteristic
210	C₇×#95	C₂³	1	1	yes	characteristic
211	C₇×#95	C₂³	1	1	yes	characteristic
212	C₇×#95	C₂³	1	1	yes	characteristic
213	C₇×#95	C₂³	1	1	yes	characteristic
214	C₇×#95	C₂³	1	1	yes	characteristic
215	C₇×#95	C₂³	1	2	yes	—
216	C₇×#95	C₂³	1	2	yes	—
217	C₇×#95	C₂³	1	2	yes	—
218	C₇×#95	C₂³	1	2	yes	—
219	C₇×#95	C₂³	1	2	yes	—
220	C₇×#95	C₂³	1	2	yes	—
221	C₇×#95	C₂³	1	2	yes	—
222	C₇×#95	C₂³	1	2	yes	—
223	C₇×#95	C₂³	1	2	yes	—
224	C₇×#95	C₂³	1	2	yes	—
225	C₇×#95	C₂³	1	2	yes	—
226	C₇×#95	C₂³	1	2	yes	—
227	C₇×#95	C₂³	1	2	yes	—
228	C₇×#95	C₂³	1	2	yes	—
229	C₇×#95	C₂³	1	2	yes	—
230	C₇×#95	C₂³	1	2	yes	—
231	C₇×#95	C₂³	1	2	yes	—
232	C₇×#95	C₂³	1	2	yes	—
233	C₇×#95	C₂³	1	2	yes	—
234	C₇×#95	C₂³	1	2	yes	—
235	C₇×#95	C₂³	1	2	yes	—
236	#2577	C₂×C₇	1	2	yes	complemented
237	#2575	C₂×C₇	1	2	yes	complemented
238	#2570	C₂×C₇	1	1	yes	characteristic, complemented
239	#2565	C₂×C₇	1	1	yes	characteristic, complemented
240	#2562	C₂×C₇	1	1	yes	characteristic
241	#2536	C₂×C₇	1	1	yes	characteristic
242	#2524	C₂×C₇	1	2	yes	complemented
243	#2496	C₂×C₇	1	1	yes	characteristic, complemented
244	#2495	C₂×C₇	1	1	yes	characteristic, complemented
245	#2468	C₂×C₇	1	2	yes	—
246	#2423	C₂×C₇	1	1	yes	characteristic, complemented
247	#2421	C₂×C₇	1	1	yes	characteristic, complemented
248	#2402	C₂×C₇	1	2	yes	complemented
249	#2395	C₂×C₇	1	2	yes	—
250	C₄×#125	C₂×C₇	1	1	yes	characteristic, complemented
251	C₄×#126	C₂×C₇	1	2	yes	complemented
252	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
253	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
254	#2298	C₂×C₇	1	2	yes	complemented
255	#2285	C₂×C₇	1	1	yes	characteristic, complemented
256	#2283	C₂×C₇	1	1	yes	characteristic, complemented
257	C₄²×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
258	C₄²×D₄	C₂×C₇	1	1	yes	characteristic
259	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
260	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
261	C₂×C₇×Q₈	—	2	2	no	—
262	C₂×C₇×Q₈	—	2	2	no	—
263	C₂×C₇×Q₈	#41	1	4	yes	—
264	C₂×C₇×D₄	—	2	2	no	—
265	C₂×C₇×D₄	—	2	2	no	—
266	C₂×C₇×D₄	—	2	2	no	—
267	C₂²×C₄×C₇	—	2	2	no	—
268	C₂²×C₄×C₇	—	2	2	no	—
269	C₂²×C₄×C₇	—	2	2	no	—
270	C₂²×C₄×C₇	—	2	2	no	—
271	C₂²×C₄×C₇	—	2	2	no	—
272	C₂²×C₄×C₇	—	2	2	no	—
273	C₂²×C₄×C₇	—	2	2	no	—
274	C₂²×C₄×C₇	—	2	2	no	—
275	C₂²×C₄×C₇	—	2	2	no	—
276	C₂²×C₄×C₇	—	2	2	no	—
277	C₂²×C₄×C₇	—	2	2	no	—
278	C₂²×C₄×C₇	—	2	2	no	—
279	C₂²×C₄×C₇	—	2	2	no	—
280	C₂²×C₄×C₇	—	2	2	no	—
281	C₂²×C₄×C₇	—	2	2	no	—
282	C₂²×C₄×C₇	—	4	1	no	—
283	C₂²×C₄×C₇	—	4	1	no	—
284	C₂²×C₄×C₇	#41	1	4	yes	—
285	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
306	C₇×C₄⋊C₄	—	2	4	no	—
307	C₇×C₄⋊C₄	—	2	4	no	—
308	C₇×C₄⋊C₄	—	2	2	no	—
309	C₇×C₄⋊C₄	—	2	2	no	—
310	C₇×C₄⋊C₄	—	2	2	no	—
311	C₇×C₄⋊C₄	—	2	4	no	—
312	C₇×C₄⋊C₄	—	2	4	no	—
313	C₇×C₄⋊C₄	—	2	4	no	—
314	C₇×C₄⋊C₄	—	2	2	no	—
315	C₇×C₄⋊C₄	—	2	2	no	—
316	C₇×C₄⋊C₄	—	2	2	no	—
317	C₇×C₄⋊C₄	—	2	2	no	—
318	C₇×C₄⋊C₄	—	2	2	no	—
319	C₇×C₄⋊C₄	—	2	4	no	—
320	C₇×C₄⋊C₄	—	2	4	no	—
321	C₇×C₄⋊C₄	—	2	4	no	—
322	C₇×C₄⋊C₄	—	2	4	no	—
323	C₇×C₄⋊C₄	—	2	2	no	—
324	C₇×C₄⋊C₄	—	2	2	no	—
325	C₇×C₄⋊C₄	—	2	4	no	—
326	C₇×C₄⋊C₄	—	2	4	no	—
327	C₇×C₄⋊C₄	—	2	4	no	—
328	C₇×C₄⋊C₄	—	4	2	no	—
329	C₇×C₄⋊C₄	—	4	2	no	—
330	C₇×C₄⋊C₄	—	4	2	no	—
331	C₇×C₂²⋊C₄	—	2	4	no	—
332	C₇×C₂²⋊C₄	—	2	4	no	—
333	C₇×C₂²⋊C₄	—	2	2	no	—
334	C₇×C₂²⋊C₄	—	2	4	no	—
335	C₇×C₂²⋊C₄	—	2	4	no	—
336	C₇×C₂²⋊C₄	—	2	2	no	—
337	C₇×C₂²⋊C₄	—	2	2	no	—
338	C₇×C₂²⋊C₄	—	2	2	no	—
339	C₇×C₂²⋊C₄	—	2	2	no	—
340	C₇×C₂²⋊C₄	—	2	4	no	—
341	C₇×C₂²⋊C₄	—	2	4	no	—
342	C₇×C₂²⋊C₄	—	4	2	no	—
343	C₇×C₂²⋊C₄	—	4	2	no	—
344	C₇×C₂²⋊C₄	#41	1	4	yes	—
345	C₄²×C₇	—	2	2	no	—
346	C₄²×C₇	—	2	2	no	—
347	C₄²×C₇	—	2	2	no	—
348	C₄²×C₇	—	2	2	no	—
349	C₄²×C₇	—	2	2	no	—
350	C₄²×C₇	—	2	2	no	—
351	C₄²×C₇	—	2	4	no	—
352	C₄²×C₇	—	2	4	no	—
353	C₄²×C₇	—	2	2	no	—
354	C₄²×C₇	—	2	2	no	—
355	C₄²×C₇	—	2	4	no	—
356	C₄²×C₇	—	2	2	no	—
357	C₄²×C₇	—	2	4	no	—
358	C₄²×C₇	—	2	4	no	—
359	C₄²×C₇	—	2	4	no	—
360	C₄²×C₇	—	2	2	no	—
361	C₄²×C₇	—	2	4	no	—
362	C₄²×C₇	—	4	1	no	—
363	C₄²×C₇	—	4	2	no	—
364	C₄²×C₇	#41	1	4	yes	—
365	C₄²×C₇	#41	1	4	yes	—
366	C₂×#126	C₂²×C₇	1	2	yes	—
367	C₂×#125	C₂²×C₇	1	1	yes	characteristic
368	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
369	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
370	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
371	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
372	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
373	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
375	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
376	C₂×#117	C₂²×C₇	1	2	yes	—
377	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
378	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
379	#400	C₂²×C₇	1	2	yes	—
380	#400	C₂²×C₇	1	2	yes	—
381	#400	C₂²×C₇	1	2	yes	—
382	#400	C₂²×C₇	1	2	yes	—
383	#400	C₂²×C₇	1	2	yes	—
384	#399	C₂²×C₇	1	2	yes	—
385	#398	C₂²×C₇	1	2	yes	—
386	#398	C₂²×C₇	1	2	yes	—
387	#398	C₂²×C₇	1	2	yes	—
388	#398	C₂²×C₇	1	2	yes	—
389	#398	C₂²×C₇	1	2	yes	—
390	#397	C₂²×C₇	1	2	yes	—
391	#397	C₂²×C₇	1	2	yes	—
392	#397	C₂²×C₇	1	2	yes	—
393	#394	C₂²×C₇	1	2	yes	—
394	#394	C₂²×C₇	1	2	yes	—
395	#391	C₂²×C₇	1	1	yes	characteristic
396	#391	C₂²×C₇	1	1	yes	characteristic
397	#389	C₂²×C₇	1	1	yes	characteristic
398	#389	C₂²×C₇	1	1	yes	characteristic
399	#389	C₂²×C₇	1	1	yes	characteristic
400	#389	C₂²×C₇	1	1	yes	characteristic
401	#388	C₂²×C₇	1	2	yes	—
402	#388	C₂²×C₇	1	2	yes	—
403	#388	C₂²×C₇	1	2	yes	—
404	#388	C₂²×C₇	1	2	yes	—
405	#388	C₂²×C₇	1	2	yes	—
406	#388	C₂²×C₇	1	2	yes	—
407	#388	C₂²×C₇	1	2	yes	—
408	#387	C₂²×C₇	1	2	yes	—
409	#387	C₂²×C₇	1	2	yes	—
410	#387	C₂²×C₇	1	2	yes	—
411	#387	C₂²×C₇	1	2	yes	—
412	#387	C₂²×C₇	1	2	yes	—
413	#387	C₂²×C₇	1	2	yes	—
414	#387	C₂²×C₇	1	2	yes	—
415	#387	C₂²×C₇	1	2	yes	—
416	#387	C₂²×C₇	1	2	yes	—
417	#387	C₂²×C₇	1	2	yes	—
418	#387	C₂²×C₇	1	2	yes	—
419	#385	C₂²×C₇	1	2	yes	—
420	#385	C₂²×C₇	1	2	yes	—
421	#384	C₂²×C₇	1	1	yes	characteristic
422	#384	C₂²×C₇	1	1	yes	characteristic
423	#383	C₂²×C₇	1	2	yes	—
424	#383	C₂²×C₇	1	2	yes	—
425	#382	C₂²×C₇	1	1	yes	characteristic
426	#382	C₂²×C₇	1	1	yes	characteristic
427	#382	C₂²×C₇	1	1	yes	characteristic
428	#382	C₂²×C₇	1	2	yes	—
429	#381	C₂²×C₇	1	2	yes	—
430	#380	C₂²×C₇	1	1	yes	characteristic
431	#380	C₂²×C₇	1	1	yes	characteristic
432	#380	C₂²×C₇	1	1	yes	characteristic
433	#380	C₂²×C₇	1	1	yes	characteristic
434	#380	C₂²×C₇	1	2	yes	—
435	#380	C₂²×C₇	1	1	yes	characteristic
436	#380	C₂²×C₇	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
438	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
439	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
440	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
441	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
443	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
446	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
447	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
448	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
449	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
450	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
452	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
453	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
454	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
455	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
456	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
457	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
458	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
459	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
460	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
461	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
462	#376	C₂²×C₇	1	2	yes	—
463	C₄³	C₂²×C₇	1	2	yes	—
464	C₄³	C₂²×C₇	1	1	yes	characteristic
465	C₂³×C₇	—	2	1	no	—
466	C₂³×C₇	—	2	1	no	—
467	C₂³×C₇	—	2	1	no	—
468	C₂³×C₇	—	2	1	no	—
469	C₂³×C₇	—	2	1	no	—
470	C₂³×C₇	—	2	1	no	—
471	C₂³×C₇	—	2	1	no	—
472	C₂³×C₇	—	2	1	no	—
473	C₂³×C₇	—	2	1	no	—
474	C₂³×C₇	—	2	1	no	—
475	C₂³×C₇	—	2	1	no	—
476	C₂³×C₇	—	2	1	no	—
477	C₂³×C₇	C₂×#41	1	2	yes	—
478	C₂³×C₇	C₂×#41	1	2	yes	—
479	C₂³×C₇	C₂⁵	1	1	yes	characteristic
480	C₇×Q₈	—	2	8	no	—
481	C₇×D₄	—	2	8	no	—
482	C₂×C₄×C₇	—	2	1	no	—
483	C₂×C₄×C₇	—	2	1	no	—
484	C₂×C₄×C₇	—	2	1	no	—
485	C₂×C₄×C₇	—	2	1	no	—
486	C₂×C₄×C₇	—	2	1	no	—
487	C₂×C₄×C₇	—	2	2	no	—
488	C₂×C₄×C₇	—	2	2	no	—
489	C₂×C₄×C₇	—	2	1	no	—
490	C₂×C₄×C₇	—	2	1	no	—
491	C₂×C₄×C₇	—	2	1	no	—
492	C₂×C₄×C₇	—	2	1	no	—
493	C₂×C₄×C₇	—	2	1	no	—
494	C₂×C₄×C₇	—	2	1	no	—
495	C₂×C₄×C₇	—	2	1	no	—
496	C₂×C₄×C₇	—	2	8	no	—
497	C₂×C₄×C₇	—	2	1	no	—
498	C₂×C₄×C₇	—	2	1	no	—
499	C₂×C₄×C₇	—	2	1	no	—
500	C₂×C₄×C₇	—	2	1	no	—
501	C₂×C₄×C₇	—	2	1	no	—
502	C₂×C₄×C₇	—	2	2	no	—
503	C₂×C₄×C₇	—	2	2	no	—
504	C₂×C₄×C₇	—	2	2	no	—
505	C₂×C₄×C₇	—	2	2	no	—
506	C₂×C₄×C₇	—	2	2	no	—
507	C₂×C₄×C₇	—	2	2	no	—
508	C₂×C₄×C₇	—	2	2	no	—
509	C₂×C₄×C₇	—	2	2	no	—
510	C₂×C₄×C₇	—	2	1	no	—
511	C₂×C₄×C₇	—	2	2	no	—
512	C₂×C₄×C₇	—	2	2	no	—
513	C₂×C₄×C₇	—	2	2	no	—
514	C₂×C₄×C₇	—	2	2	no	—
515	C₂×C₄×C₇	—	2	2	no	—
516	C₂×C₄×C₇	—	2	1	no	—
517	C₂×C₄×C₇	—	2	1	no	—
518	C₂×C₄×C₇	—	2	1	no	—
519	C₂×C₄×C₇	—	2	1	no	—
520	C₂×C₄×C₇	—	2	2	no	—
521	C₂×C₄×C₇	—	2	2	no	—
522	C₂×C₄×C₇	—	2	1	no	—
523	C₂×C₄×C₇	—	2	1	no	—
524	C₂×C₄×C₇	—	2	2	no	—
525	C₂×C₄×C₇	—	2	2	no	—
526	C₂×C₄×C₇	—	2	1	no	—
527	C₂×C₄×C₇	—	2	2	no	—
528	C₂×C₄×C₇	—	2	2	no	—
529	C₂×C₄×C₇	—	2	1	no	—
530	C₂×C₄×C₇	—	2	2	no	—
531	C₂×C₄×C₇	—	2	2	no	—
532	C₂×C₄×C₇	—	2	1	no	—
533	C₂×C₄×C₇	—	4	4	no	—
534	C₂×C₄×C₇	—	4	4	no	—
535	C₂×C₄×C₇	—	4	4	no	—
536	C₂×C₄×C₇	—	4	4	no	—
537	C₂×C₄×C₇	—	4	4	no	—
538	C₂×C₄×C₇	C₂×#41	1	2	yes	—
539	C₂×C₄×C₇	C₂×#41	1	2	yes	—
540	C₂×C₄×C₇	C₂×#41	1	2	yes	—
541	C₂×C₄×C₇	C₂×#41	1	4	yes	—
542	C₂×C₄×C₇	C₂×#41	1	2	yes	—
543	C₂×C₄×C₇	C₂×#41	1	2	yes	—
544	C₂×C₄×C₇	C₂×#41	1	2	yes	—
545	C₂×C₄×C₇	C₂×#41	1	2	yes	—
546	C₂×C₄×C₇	C₂×#41	1	2	yes	—
547	C₂×C₄×C₇	C₂×#41	1	2	yes	—
548	C₂×C₄×C₇	C₂×#41	1	2	yes	—
549	C₂×C₄×C₇	C₂×#41	1	2	yes	—
550	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
551	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
553	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
554	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
558	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
559	#126	—	2	8	no	—
560	#125	—	2	4	no	—
561	C₂²⋊Q₈	—	2	4	no	—
562	C₂²⋊Q₈	—	2	4	no	—
563	C₄×Q₈	—	2	4	no	—
564	C₄×Q₈	—	2	4	no	—
565	C₄×Q₈	—	2	4	no	—
566	C₄×D₄	—	2	4	no	—
567	C₄×D₄	—	2	4	no	—
568	C₄×D₄	—	2	4	no	—
569	#117	—	2	8	no	—
570	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
601	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
602	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
609	C₂×C₄²	—	2	4	no	—
610	C₂×C₄²	—	2	4	no	—
611	C₂×C₄²	C₂³×C₇	1	2	yes	—
612	C₂×C₄²	C₂³×C₇	1	2	yes	—
613	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₇	1	2	yes	—
616	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₇	1	2	yes	—
618	C₂×C₄²	C₂³×C₇	1	2	yes	—
619	C₂×C₄²	C₂³×C₇	1	2	yes	—
620	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₇	1	2	yes	—
623	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₇	1	2	yes	—
630	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
632	#95	C₂³×C₇	1	2	yes	—
633	#95	C₂³×C₇	1	2	yes	—
634	#95	C₂³×C₇	1	2	yes	—
635	#95	C₂³×C₇	1	2	yes	—
636	#95	C₂³×C₇	1	1	yes	characteristic
637	#95	C₂³×C₇	1	1	yes	characteristic
638	#95	C₂³×C₇	1	1	yes	characteristic
639	#95	C₂³×C₇	1	1	yes	characteristic
640	#95	C₂³×C₇	1	1	yes	characteristic
641	#95	C₂³×C₇	1	1	yes	characteristic
642	#95	C₂³×C₇	1	2	yes	—
643	#95	C₂³×C₇	1	2	yes	—
644	#95	C₂³×C₇	1	2	yes	—
645	#95	C₂³×C₇	1	2	yes	—
646	#95	C₂³×C₇	1	2	yes	—
647	#95	C₂³×C₇	1	2	yes	—
648	#95	C₂³×C₇	1	2	yes	—
649	#95	C₂³×C₇	1	2	yes	—
650	#95	C₂³×C₇	1	2	yes	—
651	#95	C₂³×C₇	1	2	yes	—
652	#95	C₂³×C₇	1	2	yes	—
653	#95	C₂³×C₇	1	2	yes	—
654	#95	C₂³×C₇	1	2	yes	—
655	#95	C₂³×C₇	1	2	yes	—
656	#95	C₂³×C₇	1	2	yes	—
657	#95	C₂³×C₇	1	2	yes	—
658	#95	C₂³×C₇	1	2	yes	—
659	#95	C₂³×C₇	1	2	yes	—
660	#95	C₂³×C₇	1	2	yes	—
661	#95	C₂³×C₇	1	2	yes	—
662	#95	C₂³×C₇	1	2	yes	—
663	C₂²×C₇	—	2	2	no	—
664	C₂²×C₇	—	2	2	no	—
665	C₂²×C₇	—	2	2	no	—
666	C₂²×C₇	—	2	2	no	—
667	C₂²×C₇	—	2	2	no	—
668	C₂²×C₇	—	2	2	no	—
669	C₂²×C₇	—	4	1	no	—
670	C₂²×C₇	—	4	1	no	—
671	C₂²×C₇	—	4	1	no	—
672	C₂²×C₇	—	4	1	no	—
673	C₂²×C₇	—	4	1	no	—
674	C₂²×C₇	—	4	1	no	—
675	C₂²×C₇	—	4	1	no	—
676	C₂²×C₇	—	4	1	no	—
677	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
678	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
679	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
680	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
681	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
682	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
683	C₂²×C₇	#585	1	1	yes	characteristic
684	C₄×C₇	—	2	4	no	—
685	C₄×C₇	—	2	2	no	—
686	C₄×C₇	—	2	2	no	—
687	C₄×C₇	—	2	2	no	—
688	C₄×C₇	—	2	2	no	—
689	C₄×C₇	—	2	2	no	—
690	C₄×C₇	—	2	2	no	—
691	C₄×C₇	—	4	1	no	—
692	C₄×C₇	—	4	1	no	—
693	C₄×C₇	—	4	2	no	—
694	C₄×C₇	—	4	2	no	—
695	C₄×C₇	—	4	2	no	—
696	C₄×C₇	—	4	1	no	—
697	C₄×C₇	—	4	2	no	—
698	C₄×C₇	—	4	1	no	—
699	C₄×C₇	—	4	1	no	—
700	C₄×C₇	—	4	2	no	—
701	C₄×C₇	—	4	2	no	—
702	C₄×C₇	—	4	2	no	—
703	C₄×C₇	#529	1	4	yes	—
704	C₄×C₇	#552	1	4	yes	—
705	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
706	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
707	C₂×Q₈	—	2	2	no	—
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	C₇×#41	1	4	yes	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	4	1	no	—
729	C₂²×C₄	—	4	1	no	—
730	C₂²×C₄	C₇×#41	1	4	yes	—
731	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	4	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	4	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	C₇×#41	1	4	yes	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	4	no	—
798	C₄²	—	2	4	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	4	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	4	no	—
804	C₄²	—	2	4	no	—
805	C₄²	—	2	4	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	4	no	—
808	C₄²	—	4	1	no	—
809	C₄²	—	4	2	no	—
810	C₄²	C₇×#41	1	4	yes	—
811	C₄²	C₇×#41	1	4	yes	—
812	C₂×C₇	—	4	2	no	—
813	C₂×C₇	—	4	2	no	—
814	C₂×C₇	C₂×#529	1	1	yes	characteristic
815	C₂×C₇	#3444	1	1	yes	characteristic
816	C₂×C₇	#3461	1	1	yes	characteristic
817	C₂×C₇	C₂×#552	1	1	yes	characteristic
818	C₂×C₇	#3475	1	1	yes	characteristic
819	C₂×C₇	#3480	1	1	yes	characteristic
820	C₂×C₇	#3482	1	1	yes	characteristic
821	C₂³	—	2	1	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	C₂×C₇×#41	1	2	yes	—
834	C₂³	C₂×C₇×#41	1	2	yes	—
835	C₂³	C₂⁵×C₇	1	1	yes	characteristic
836	Q₈	—	2	8	no	—
837	D₄	—	2	8	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	8	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	4	4	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	C₂×C₇×#41	1	2	yes	—
895	C₂×C₄	C₂×C₇×#41	1	2	yes	—
896	C₂×C₄	C₂×C₇×#41	1	2	yes	—
897	C₂×C₄	C₂×C₇×#41	1	4	yes	—
898	C₂×C₄	C₂×C₇×#41	1	2	yes	—
899	C₂×C₄	C₂×C₇×#41	1	2	yes	—
900	C₂×C₄	C₂×C₇×#41	1	2	yes	—
901	C₂×C₄	C₂×C₇×#41	1	2	yes	—
902	C₂×C₄	C₂×C₇×#41	1	2	yes	—
903	C₂×C₄	C₂×C₇×#41	1	2	yes	—
904	C₂×C₄	C₂×C₇×#41	1	2	yes	—
905	C₂×C₄	C₂×C₇×#41	1	2	yes	—
906	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
907	C₇	#34898	1	1	yes	characteristic, direct product factor, Sylow
908	C₂²	—	2	2	no	—
909	C₂²	—	2	2	no	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	1	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
923	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
924	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
925	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
926	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
927	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
928	C₂²	C₇×#585	1	1	yes	characteristic
929	C₄	—	2	4	no	—
930	C₄	—	2	2	no	—
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	4	1	no	—
937	C₄	—	4	1	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	1	no	—
943	C₄	—	4	2	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	C₇×#529	1	4	yes	—
949	C₄	C₇×#552	1	4	yes	—
950	C₂	—	4	2	no	—
951	C₂	—	4	2	no	—
952	C₂	C₂×C₇×#529	1	1	yes	characteristic
953	C₂	C₇×#3444	1	1	yes	characteristic
954	C₂	C₇×#3461	1	1	yes	characteristic
955	C₂	C₂×C₇×#552	1	1	yes	characteristic
956	C₂	C₇×#3475	1	1	yes	characteristic
957	C₂	C₇×#3480	1	1	yes	characteristic
958	C₂	C₇×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
socle	C₂³×C₇	C₂⁵
prime radical	C₂²×C₇×D₄	C₂³
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. C₇×#2577	C₂	semidirect
2. C₇×#2575	C₂	semidirect
3. C₇×#2570	C₂	semidirect
4. C₇×#2565	C₂	semidirect
7. C₇×#2524	C₂	semidirect
8. C₇×#2496	C₂	semidirect
9. C₇×#2495	C₂	semidirect
11. C₇×#2423	C₂	semidirect
12. C₇×#2421	C₂	semidirect
13. C₇×#2402	C₂	semidirect
15. C₄×C₇×#125	C₂	semidirect
16. C₄×C₇×#126	C₂	semidirect
17. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
19. C₇×#2298	C₂	semidirect
20. C₇×#2285	C₂	semidirect
21. C₇×#2283	C₂	semidirect
22. C₄²×C₇×Q₈	C₂	semidirect
123. #34898	C₇	direct (N × H)
236. #2577	C₂×C₇	semidirect
237. #2575	C₂×C₇	semidirect
238. #2570	C₂×C₇	semidirect
239. #2565	C₂×C₇	semidirect
242. #2524	C₂×C₇	semidirect
243. #2496	C₂×C₇	semidirect
244. #2495	C₂×C₇	semidirect
246. #2423	C₂×C₇	semidirect
247. #2421	C₂×C₇	semidirect
248. #2402	C₂×C₇	semidirect
250. C₄×#125	C₂×C₇	semidirect
251. C₄×#126	C₂×C₇	semidirect
252. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
253. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
254. #2298	C₂×C₇	semidirect
255. #2285	C₂×C₇	semidirect
256. #2283	C₂×C₇	semidirect
257. C₄²×Q₈	C₂×C₇	semidirect
907. C₇	#34898	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#2577	2
C₇×#2575	2
C₇×#2570	2
C₇×#2565	2
C₇×#2562	2
C₇×#2536	2
C₇×#2524	2
C₇×#2496	2
C₇×#2495	2
C₇×#2468	2
C₇×#2423	2
C₇×#2421	2
C₇×#2402	2
C₇×#2395	2
C₄×C₇×#125	2
C₄×C₇×#126	2
C₄×C₇×C₂²⋊Q₈	2
C₇×#2298	2
C₇×#2285	2
C₇×#2283	2
C₄²×C₇×Q₈	2
C₄²×C₇×D₄	2
#34898	7

Subgroups — C7×#34898 #13212114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34898 #13212114