Subgroups — C₇×#34916 #13212132

Order 1792.

1750 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2590	C₂	1	2	yes	maximal, complemented
2	C₇×#2589	C₂	1	2	yes	maximal
3	C₇×#2588	C₂	1	2	yes	maximal, complemented
4	C₇×#2587	C₂	1	2	yes	maximal
5	C₇×#2511	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2507	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2497	C₂	1	1	yes	maximal, characteristic
8	C₇×#2492	C₂	1	1	yes	maximal, characteristic
9	C₇×#2451	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2429	C₂	1	1	yes	maximal, characteristic
12	C₇×#2423	C₂	1	1	yes	maximal, characteristic
13	C₇×#2402	C₂	1	2	yes	maximal, complemented
14	C₇×#2396	C₂	1	2	yes	maximal
15	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
18	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
19	C₇×#2298	C₂	1	2	yes	maximal
20	C₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2295	C₂	1	2	yes	maximal, complemented
22	C₄²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₇×#117	C₂	1	1	yes	maximal, characteristic
24	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₄⋊Q₈	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	2	yes	—
29	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×#117	C₂²	1	1	yes	characteristic
34	C₂×C₇×#117	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
36	C₇×#400	C₂²	1	2	yes	—
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×#399	C₂²	1	2	yes	—
42	C₇×#398	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×#396	C₂²	1	2	yes	—
49	C₇×#396	C₂²	1	2	yes	—
50	C₇×#395	C₂²	1	2	yes	—
51	C₇×#393	C₂²	1	2	yes	—
52	C₇×#391	C₂²	1	1	yes	characteristic
53	C₇×#391	C₂²	1	1	yes	characteristic
54	C₇×#391	C₂²	1	1	yes	characteristic
55	C₇×#391	C₂²	1	1	yes	characteristic
56	C₇×#391	C₂²	1	1	yes	characteristic
57	C₇×#391	C₂²	1	2	yes	—
58	C₇×#391	C₂²	1	1	yes	characteristic
59	C₇×#391	C₂²	1	2	yes	—
60	C₇×#391	C₂²	1	2	yes	—
61	C₇×#389	C₂²	1	1	yes	characteristic
62	C₇×#389	C₂²	1	1	yes	characteristic
63	C₇×#389	C₂²	1	2	yes	—
64	C₇×#389	C₂²	1	1	yes	characteristic
65	C₇×#389	C₂²	1	1	yes	characteristic
66	C₇×#389	C₂²	1	1	yes	characteristic
67	C₇×#389	C₂²	1	1	yes	characteristic
68	C₇×#389	C₂²	1	2	yes	—
69	C₇×#389	C₂²	1	2	yes	—
70	C₇×#389	C₂²	1	2	yes	—
71	C₇×#389	C₂²	1	2	yes	—
72	C₇×#388	C₂²	1	2	yes	—
73	C₇×#388	C₂²	1	2	yes	—
74	C₇×#388	C₂²	1	2	yes	—
75	C₇×#388	C₂²	1	2	yes	—
76	C₇×#387	C₂²	1	2	yes	—
77	C₇×#387	C₂²	1	2	yes	—
78	C₇×#387	C₂²	1	2	yes	—
79	C₇×#387	C₂²	1	2	yes	—
80	C₇×#387	C₂²	1	2	yes	—
81	C₇×#387	C₂²	1	2	yes	—
82	C₇×#387	C₂²	1	2	yes	—
83	C₇×#387	C₂²	1	2	yes	—
84	C₇×#387	C₂²	1	2	yes	—
85	C₇×#387	C₂²	1	2	yes	—
86	C₇×#387	C₂²	1	2	yes	—
87	C₇×#387	C₂²	1	2	yes	—
88	C₇×#385	C₂²	1	2	yes	—
89	C₇×#385	C₂²	1	2	yes	—
90	C₇×#384	C₂²	1	1	yes	characteristic
91	C₇×#384	C₂²	1	1	yes	characteristic
92	C₇×#380	C₂²	1	1	yes	characteristic
93	C₇×#380	C₂²	1	1	yes	characteristic
94	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
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	2	yes	—
109	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
110	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
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	C₇×#376	C₂²	1	1	yes	characteristic
118	C₇×#376	C₂²	1	1	yes	characteristic
119	C₇×#376	C₂²	1	2	yes	—
120	C₄³×C₇	C₂²	1	1	yes	characteristic
121	C₄³×C₇	C₂²	1	1	yes	characteristic
122	C₄³×C₇	C₂²	1	2	yes	—
123	#34916	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
125	C₂²×C₇×Q₈	C₂³	1	2	yes	—
126	C₂²×C₇×Q₈	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	C₇×C₄⋊Q₈	—	2	4	no	—
131	C₇×C₄⋊Q₈	—	2	4	no	—
132	C₇×C₂²⋊Q₈	—	2	4	no	—
133	C₇×C₂²⋊Q₈	—	2	4	no	—
134	C₄×C₇×Q₈	—	2	4	no	—
135	C₄×C₇×Q₈	—	2	4	no	—
136	C₄×C₇×Q₈	—	2	4	no	—
137	C₄×C₇×Q₈	—	2	4	no	—
138	C₄×C₇×Q₈	—	2	8	no	—
139	C₇×#117	—	2	4	no	—
140	C₇×#117	Q₈	1	8	yes	complemented
141	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
155	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
177	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₇	—	2	4	no	—
179	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₇	C₂³	1	2	yes	—
185	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₇	C₂³	1	2	yes	—
189	C₂×C₄²×C₇	C₂³	1	2	yes	—
190	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇	C₂³	1	2	yes	—
192	C₂×C₄²×C₇	C₂³	1	2	yes	—
193	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇	C₂³	1	2	yes	—
198	C₂×C₄²×C₇	C₂³	1	2	yes	—
199	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
203	C₇×#95	C₂³	1	1	yes	characteristic
204	C₇×#95	C₂³	1	1	yes	characteristic
205	C₇×#95	C₂³	1	1	yes	characteristic
206	C₇×#95	C₂³	1	1	yes	characteristic
207	C₇×#95	C₂³	1	1	yes	characteristic
208	C₇×#95	C₂³	1	1	yes	characteristic
209	C₇×#95	C₂³	1	1	yes	characteristic
210	C₇×#95	C₂³	1	1	yes	characteristic
211	C₇×#95	C₂³	1	2	yes	—
212	C₇×#95	C₂³	1	2	yes	—
213	C₇×#95	C₂³	1	2	yes	—
214	C₇×#95	C₂³	1	2	yes	—
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	#2590	C₂×C₇	1	2	yes	complemented
236	#2589	C₂×C₇	1	2	yes	—
237	#2588	C₂×C₇	1	2	yes	complemented
238	#2587	C₂×C₇	1	2	yes	—
239	#2511	C₂×C₇	1	1	yes	characteristic, complemented
240	#2507	C₂×C₇	1	1	yes	characteristic, complemented
241	#2497	C₂×C₇	1	1	yes	characteristic
242	#2492	C₂×C₇	1	1	yes	characteristic
243	#2451	C₂×C₇	1	1	yes	characteristic, complemented
244	#2446	C₂×C₇	1	1	yes	characteristic, complemented
245	#2429	C₂×C₇	1	1	yes	characteristic
246	#2423	C₂×C₇	1	1	yes	characteristic
247	#2402	C₂×C₇	1	2	yes	complemented
248	#2396	C₂×C₇	1	2	yes	—
249	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
250	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
251	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic
252	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic
253	#2298	C₂×C₇	1	2	yes	—
254	#2295	C₂×C₇	1	2	yes	complemented
255	#2295	C₂×C₇	1	1	yes	characteristic, complemented
256	C₄²×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
257	C₄×#117	C₂×C₇	1	1	yes	characteristic
258	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
259	C₂×C₇×Q₈	—	2	2	no	—
260	C₂×C₇×Q₈	—	2	2	no	—
261	C₂×C₇×Q₈	—	2	4	no	—
262	C₂×C₇×Q₈	—	2	2	no	—
263	C₂×C₇×Q₈	—	2	2	no	—
264	C₂×C₇×Q₈	—	2	4	no	—
265	C₂×C₇×Q₈	—	2	2	no	—
266	C₂×C₇×Q₈	—	4	2	no	—
267	C₂×C₇×Q₈	#41	1	4	yes	—
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	—	4	1	no	—
275	C₂²×C₄×C₇	—	4	1	no	—
276	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
277	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
299	C₇×C₄⋊C₄	—	2	2	no	—
300	C₇×C₄⋊C₄	—	2	2	no	—
301	C₇×C₄⋊C₄	—	2	4	no	—
302	C₇×C₄⋊C₄	—	2	4	no	—
303	C₇×C₄⋊C₄	—	2	4	no	—
304	C₇×C₄⋊C₄	—	2	4	no	—
305	C₇×C₄⋊C₄	—	2	4	no	—
306	C₇×C₄⋊C₄	—	2	2	no	—
307	C₇×C₄⋊C₄	—	2	2	no	—
308	C₇×C₄⋊C₄	—	2	2	no	—
309	C₇×C₄⋊C₄	—	2	4	no	—
310	C₇×C₄⋊C₄	—	2	4	no	—
311	C₇×C₄⋊C₄	—	2	2	no	—
312	C₇×C₄⋊C₄	—	2	4	no	—
313	C₇×C₄⋊C₄	—	2	4	no	—
314	C₇×C₄⋊C₄	—	2	4	no	—
315	C₇×C₄⋊C₄	—	2	4	no	—
316	C₇×C₄⋊C₄	—	2	4	no	—
317	C₇×C₄⋊C₄	—	2	2	no	—
318	C₇×C₄⋊C₄	—	4	2	no	—
319	C₇×C₄⋊C₄	—	4	2	no	—
320	C₇×C₄⋊C₄	—	4	2	no	—
321	C₇×C₄⋊C₄	—	4	2	no	—
322	C₇×C₄⋊C₄	—	4	2	no	—
323	C₇×C₄⋊C₄	—	4	2	no	—
324	C₇×C₄⋊C₄	—	4	2	no	—
325	C₇×C₄⋊C₄	C₂×Q₈	1	4	yes	—
326	C₇×C₄⋊C₄	C₂×Q₈	1	4	yes	—
327	C₇×C₄⋊C₄	#41	1	4	yes	—
328	C₇×C₂²⋊C₄	—	2	2	no	—
329	C₇×C₂²⋊C₄	—	2	2	no	—
330	C₇×C₂²⋊C₄	—	2	4	no	—
331	C₇×C₂²⋊C₄	—	2	4	no	—
332	C₇×C₂²⋊C₄	—	4	2	no	—
333	C₇×C₂²⋊C₄	—	4	2	no	—
334	C₇×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
335	C₇×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
336	C₄²×C₇	—	2	2	no	—
337	C₄²×C₇	—	2	2	no	—
338	C₄²×C₇	—	2	2	no	—
339	C₄²×C₇	—	2	2	no	—
340	C₄²×C₇	—	2	4	no	—
341	C₄²×C₇	—	2	4	no	—
342	C₄²×C₇	—	2	2	no	—
343	C₄²×C₇	—	2	2	no	—
344	C₄²×C₇	—	2	4	no	—
345	C₄²×C₇	—	2	4	no	—
346	C₄²×C₇	—	2	4	no	—
347	C₄²×C₇	—	2	4	no	—
348	C₄²×C₇	—	2	2	no	—
349	C₄²×C₇	—	2	2	no	—
350	C₄²×C₇	—	4	1	no	—
351	C₄²×C₇	—	4	1	no	—
352	C₄²×C₇	—	4	2	no	—
353	C₄²×C₇	—	4	2	no	—
354	C₄²×C₇	—	4	1	no	—
355	C₄²×C₇	—	4	1	no	—
356	C₄²×C₇	C₂×Q₈	1	4	yes	—
357	C₄²×C₇	C₂×Q₈	1	4	yes	—
358	C₄²×C₇	#41	1	4	yes	—
359	C₄²×C₇	#41	1	4	yes	—
360	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
361	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
362	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
363	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
364	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
365	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
366	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
367	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
368	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
369	C₂×#117	C₂²×C₇	1	1	yes	characteristic
370	C₂×#117	C₂²×C₇	1	1	yes	characteristic
371	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
372	#400	C₂²×C₇	1	2	yes	—
373	#400	C₂²×C₇	1	2	yes	—
374	#400	C₂²×C₇	1	2	yes	—
375	#400	C₂²×C₇	1	2	yes	—
376	#400	C₂²×C₇	1	2	yes	—
377	#399	C₂²×C₇	1	2	yes	—
378	#398	C₂²×C₇	1	2	yes	—
379	#398	C₂²×C₇	1	2	yes	—
380	#398	C₂²×C₇	1	2	yes	—
381	#398	C₂²×C₇	1	2	yes	—
382	#398	C₂²×C₇	1	2	yes	—
383	#398	C₂²×C₇	1	2	yes	—
384	#396	C₂²×C₇	1	2	yes	—
385	#396	C₂²×C₇	1	2	yes	—
386	#395	C₂²×C₇	1	2	yes	—
387	#393	C₂²×C₇	1	2	yes	—
388	#391	C₂²×C₇	1	2	yes	—
389	#391	C₂²×C₇	1	1	yes	characteristic
390	#391	C₂²×C₇	1	1	yes	characteristic
391	#391	C₂²×C₇	1	2	yes	—
392	#391	C₂²×C₇	1	2	yes	—
393	#391	C₂²×C₇	1	1	yes	characteristic
394	#391	C₂²×C₇	1	1	yes	characteristic
395	#391	C₂²×C₇	1	1	yes	characteristic
396	#391	C₂²×C₇	1	1	yes	characteristic
397	#389	C₂²×C₇	1	2	yes	—
398	#389	C₂²×C₇	1	2	yes	—
399	#389	C₂²×C₇	1	2	yes	—
400	#389	C₂²×C₇	1	1	yes	characteristic
401	#389	C₂²×C₇	1	1	yes	characteristic
402	#389	C₂²×C₇	1	2	yes	—
403	#389	C₂²×C₇	1	2	yes	—
404	#389	C₂²×C₇	1	1	yes	characteristic
405	#389	C₂²×C₇	1	1	yes	characteristic
406	#389	C₂²×C₇	1	1	yes	characteristic
407	#389	C₂²×C₇	1	1	yes	characteristic
408	#388	C₂²×C₇	1	2	yes	—
409	#388	C₂²×C₇	1	2	yes	—
410	#388	C₂²×C₇	1	2	yes	—
411	#388	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	#387	C₂²×C₇	1	2	yes	—
420	#387	C₂²×C₇	1	2	yes	—
421	#387	C₂²×C₇	1	2	yes	—
422	#387	C₂²×C₇	1	2	yes	—
423	#387	C₂²×C₇	1	2	yes	—
424	#385	C₂²×C₇	1	2	yes	—
425	#385	C₂²×C₇	1	2	yes	—
426	#384	C₂²×C₇	1	1	yes	characteristic
427	#384	C₂²×C₇	1	1	yes	characteristic
428	#380	C₂²×C₇	1	1	yes	characteristic
429	#380	C₂²×C₇	1	1	yes	characteristic
430	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
431	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
432	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
433	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
434	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
435	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
436	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
438	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
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	2	yes	—
442	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
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	1	yes	characteristic
446	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
447	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
448	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
449	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
450	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
451	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
452	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
453	#376	C₂²×C₇	1	1	yes	characteristic
454	#376	C₂²×C₇	1	1	yes	characteristic
455	#376	C₂²×C₇	1	2	yes	—
456	C₄³	C₂²×C₇	1	1	yes	characteristic
457	C₄³	C₂²×C₇	1	1	yes	characteristic
458	C₄³	C₂²×C₇	1	2	yes	—
459	C₂³×C₇	—	2	1	no	—
460	C₂³×C₇	—	2	1	no	—
461	C₂³×C₇	—	2	1	no	—
462	C₂³×C₇	—	2	1	no	—
463	C₂³×C₇	—	2	1	no	—
464	C₂³×C₇	—	2	1	no	—
465	C₂³×C₇	C₂²×Q₈	1	2	yes	—
466	C₂³×C₇	C₂⁵	1	1	yes	characteristic
467	C₇×Q₈	—	2	8	no	—
468	C₇×Q₈	—	4	8	no	—
469	C₇×Q₈	—	4	4	no	—
470	C₂×C₄×C₇	—	2	1	no	—
471	C₂×C₄×C₇	—	2	1	no	—
472	C₂×C₄×C₇	—	2	1	no	—
473	C₂×C₄×C₇	—	2	1	no	—
474	C₂×C₄×C₇	—	2	1	no	—
475	C₂×C₄×C₇	—	2	1	no	—
476	C₂×C₄×C₇	—	2	2	no	—
477	C₂×C₄×C₇	—	2	2	no	—
478	C₂×C₄×C₇	—	2	2	no	—
479	C₂×C₄×C₇	—	2	1	no	—
480	C₂×C₄×C₇	—	2	1	no	—
481	C₂×C₄×C₇	—	2	1	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	1	no	—
488	C₂×C₄×C₇	—	2	2	no	—
489	C₂×C₄×C₇	—	2	1	no	—
490	C₂×C₄×C₇	—	2	8	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	2	no	—
496	C₂×C₄×C₇	—	2	2	no	—
497	C₂×C₄×C₇	—	2	1	no	—
498	C₂×C₄×C₇	—	2	1	no	—
499	C₂×C₄×C₇	—	2	2	no	—
500	C₂×C₄×C₇	—	2	2	no	—
501	C₂×C₄×C₇	—	2	2	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	1	no	—
507	C₂×C₄×C₇	—	2	1	no	—
508	C₂×C₄×C₇	—	2	2	no	—
509	C₂×C₄×C₇	—	2	2	no	—
510	C₂×C₄×C₇	—	2	2	no	—
511	C₂×C₄×C₇	—	2	2	no	—
512	C₂×C₄×C₇	—	2	2	no	—
513	C₂×C₄×C₇	—	2	1	no	—
514	C₂×C₄×C₇	—	2	1	no	—
515	C₂×C₄×C₇	—	2	2	no	—
516	C₂×C₄×C₇	—	2	2	no	—
517	C₂×C₄×C₇	—	2	2	no	—
518	C₂×C₄×C₇	—	2	2	no	—
519	C₂×C₄×C₇	—	2	1	no	—
520	C₂×C₄×C₇	—	2	1	no	—
521	C₂×C₄×C₇	—	4	4	no	—
522	C₂×C₄×C₇	—	4	4	no	—
523	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
524	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
525	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
526	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
527	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
528	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
529	C₂×C₄×C₇	C₂×#41	1	2	yes	—
530	C₂×C₄×C₇	C₂×#41	1	4	yes	—
531	C₂×C₄×C₇	C₂×#41	1	4	yes	—
532	C₂×C₄×C₇	C₂×#41	1	2	yes	—
533	C₂×C₄×C₇	C₂×#41	1	2	yes	—
534	C₂×C₄×C₇	C₂×#41	1	2	yes	—
535	C₂×C₄×C₇	C₂×#41	1	2	yes	—
536	C₂×C₄×C₇	C₂×#41	1	2	yes	—
537	C₂×C₄×C₇	C₂×#41	1	2	yes	—
538	C₂×C₄×C₇	C₂×#41	1	2	yes	—
539	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
540	C₂²×Q₈	C₂³×C₇	1	2	yes	—
541	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
545	C₄⋊Q₈	—	2	4	no	—
546	C₄⋊Q₈	—	2	4	no	—
547	C₂²⋊Q₈	—	2	4	no	—
548	C₂²⋊Q₈	—	2	4	no	—
549	C₄×Q₈	—	2	4	no	—
550	C₄×Q₈	—	2	4	no	—
551	C₄×Q₈	—	2	4	no	—
552	C₄×Q₈	—	2	4	no	—
553	C₄×Q₈	—	2	8	no	—
554	#117	—	2	4	no	—
555	#117	C₇×Q₈	1	8	yes	complemented
556	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
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	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
585	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
586	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
587	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
593	C₂×C₄²	—	2	4	no	—
594	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₇	1	2	yes	—
596	C₂×C₄²	C₂³×C₇	1	2	yes	—
597	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₇	1	2	yes	—
600	C₂×C₄²	C₂³×C₇	1	2	yes	—
601	C₂×C₄²	C₂³×C₇	1	2	yes	—
602	C₂×C₄²	C₂³×C₇	1	2	yes	—
603	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₇	1	2	yes	—
613	C₂×C₄²	C₂³×C₇	1	2	yes	—
614	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
618	#95	C₂³×C₇	1	1	yes	characteristic
619	#95	C₂³×C₇	1	1	yes	characteristic
620	#95	C₂³×C₇	1	1	yes	characteristic
621	#95	C₂³×C₇	1	1	yes	characteristic
622	#95	C₂³×C₇	1	1	yes	characteristic
623	#95	C₂³×C₇	1	1	yes	characteristic
624	#95	C₂³×C₇	1	1	yes	characteristic
625	#95	C₂³×C₇	1	1	yes	characteristic
626	#95	C₂³×C₇	1	2	yes	—
627	#95	C₂³×C₇	1	2	yes	—
628	#95	C₂³×C₇	1	2	yes	—
629	#95	C₂³×C₇	1	2	yes	—
630	#95	C₂³×C₇	1	2	yes	—
631	#95	C₂³×C₇	1	2	yes	—
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	2	yes	—
637	#95	C₂³×C₇	1	2	yes	—
638	#95	C₂³×C₇	1	2	yes	—
639	#95	C₂³×C₇	1	2	yes	—
640	#95	C₂³×C₇	1	2	yes	—
641	#95	C₂³×C₇	1	2	yes	—
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	C₂²×C₇	—	2	2	no	—
651	C₂²×C₇	—	2	2	no	—
652	C₂²×C₇	—	2	2	no	—
653	C₂²×C₇	—	4	1	no	—
654	C₂²×C₇	—	4	1	no	—
655	C₂²×C₇	—	4	1	no	—
656	C₂²×C₇	—	4	1	no	—
657	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
658	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
659	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
660	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
661	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
662	C₂²×C₇	#585	1	1	yes	characteristic
663	C₂²×C₇	#585	1	1	yes	characteristic
664	C₄×C₇	—	2	4	no	—
665	C₄×C₇	—	2	2	no	—
666	C₄×C₇	—	2	2	no	—
667	C₄×C₇	—	2	4	no	—
668	C₄×C₇	—	2	2	no	—
669	C₄×C₇	—	2	2	no	—
670	C₄×C₇	—	2	2	no	—
671	C₄×C₇	—	2	2	no	—
672	C₄×C₇	—	2	2	no	—
673	C₄×C₇	—	2	2	no	—
674	C₄×C₇	—	4	1	no	—
675	C₄×C₇	—	4	2	no	—
676	C₄×C₇	—	4	2	no	—
677	C₄×C₇	—	4	2	no	—
678	C₄×C₇	—	4	1	no	—
679	C₄×C₇	—	4	1	no	—
680	C₄×C₇	—	4	2	no	—
681	C₄×C₇	—	4	1	no	—
682	C₄×C₇	—	4	2	no	—
683	C₄×C₇	—	4	2	no	—
684	C₄×C₇	#529	1	4	yes	—
685	C₄×C₇	#533	1	4	yes	—
686	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
687	C₂×Q₈	—	2	2	no	—
688	C₂×Q₈	—	2	2	no	—
689	C₂×Q₈	—	2	4	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	2	2	no	—
692	C₂×Q₈	—	2	4	no	—
693	C₂×Q₈	—	2	2	no	—
694	C₂×Q₈	—	4	2	no	—
695	C₂×Q₈	C₇×#41	1	4	yes	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	4	1	no	—
703	C₂²×C₄	—	4	1	no	—
704	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
705	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₄⋊C₄	—	4	2	no	—
750	C₄⋊C₄	—	4	2	no	—
751	C₄⋊C₄	—	4	2	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₄⋊C₄	C₂×C₇×Q₈	1	4	yes	—
754	C₄⋊C₄	C₂×C₇×Q₈	1	4	yes	—
755	C₄⋊C₄	C₇×#41	1	4	yes	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	C₂×C₇×Q₈	1	4	yes	—
763	C₂²⋊C₄	C₂×C₇×Q₈	1	4	yes	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	4	no	—
769	C₄²	—	2	4	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	4	no	—
773	C₄²	—	2	4	no	—
774	C₄²	—	2	4	no	—
775	C₄²	—	2	4	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	4	1	no	—
779	C₄²	—	4	1	no	—
780	C₄²	—	4	2	no	—
781	C₄²	—	4	2	no	—
782	C₄²	—	4	1	no	—
783	C₄²	—	4	1	no	—
784	C₄²	C₂×C₇×Q₈	1	4	yes	—
785	C₄²	C₂×C₇×Q₈	1	4	yes	—
786	C₄²	C₇×#41	1	4	yes	—
787	C₄²	C₇×#41	1	4	yes	—
788	C₂×C₇	—	4	2	no	—
789	C₂×C₇	C₂×#529	1	1	yes	characteristic
790	C₂×C₇	C₂×#533	1	1	yes	characteristic
791	C₂×C₇	#3455	1	1	yes	characteristic
792	C₂×C₇	#3475	1	1	yes	characteristic
793	C₂×C₇	Q₈×#41	1	1	yes	characteristic
794	C₂×C₇	Q₈×#41	1	1	yes	characteristic
795	C₂×C₇	#3480	1	1	yes	characteristic
796	C₂³	—	2	1	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	C₂²×C₇×Q₈	1	2	yes	—
803	C₂³	C₂⁵×C₇	1	1	yes	characteristic
804	Q₈	—	2	8	no	—
805	Q₈	—	4	8	no	—
806	Q₈	—	4	4	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	8	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	4	4	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
861	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
862	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
863	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
864	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
865	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
866	C₂×C₄	C₂×C₇×#41	1	2	yes	—
867	C₂×C₄	C₂×C₇×#41	1	4	yes	—
868	C₂×C₄	C₂×C₇×#41	1	4	yes	—
869	C₂×C₄	C₂×C₇×#41	1	2	yes	—
870	C₂×C₄	C₂×C₇×#41	1	2	yes	—
871	C₂×C₄	C₂×C₇×#41	1	2	yes	—
872	C₂×C₄	C₂×C₇×#41	1	2	yes	—
873	C₂×C₄	C₂×C₇×#41	1	2	yes	—
874	C₂×C₄	C₂×C₇×#41	1	2	yes	—
875	C₂×C₄	C₂×C₇×#41	1	2	yes	—
876	C₇	#34916	1	1	yes	characteristic, direct product factor, Sylow
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	4	1	no	—
884	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
885	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
886	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
887	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
888	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
889	C₂²	C₇×#585	1	1	yes	characteristic
890	C₂²	C₇×#585	1	1	yes	characteristic
891	C₄	—	2	4	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	4	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	2	no	—
911	C₄	C₇×#529	1	4	yes	—
912	C₄	C₇×#533	1	4	yes	—
913	C₂	—	4	2	no	—
914	C₂	C₂×C₇×#529	1	1	yes	characteristic
915	C₂	C₂×C₇×#533	1	1	yes	characteristic
916	C₂	C₇×#3455	1	1	yes	characteristic
917	C₂	C₇×#3475	1	1	yes	characteristic
918	C₂	C₇×Q₈×#41	1	1	yes	characteristic
919	C₂	C₇×Q₈×#41	1	1	yes	characteristic
920	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	C₂⁴×C₇	C₂⁴
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×#2590	C₂	semidirect
3. C₇×#2588	C₂	semidirect
5. C₇×#2511	C₂	semidirect
6. C₇×#2507	C₂	semidirect
9. C₇×#2451	C₂	semidirect
10. C₇×#2446	C₂	semidirect
13. C₇×#2402	C₂	semidirect
15. C₄×C₇×C₄⋊Q₈	C₂	semidirect
16. C₄×C₇×C₄⋊Q₈	C₂	semidirect
20. C₇×#2295	C₂	semidirect
21. C₇×#2295	C₂	semidirect
22. C₄²×C₇×Q₈	C₂	semidirect
123. #34916	C₇	direct (N × H)
140. C₇×#117	Q₈	semidirect
235. #2590	C₂×C₇	semidirect
237. #2588	C₂×C₇	semidirect
239. #2511	C₂×C₇	semidirect
240. #2507	C₂×C₇	semidirect
243. #2451	C₂×C₇	semidirect
244. #2446	C₂×C₇	semidirect
247. #2402	C₂×C₇	semidirect
249. C₄×C₄⋊Q₈	C₂×C₇	semidirect
250. C₄×C₄⋊Q₈	C₂×C₇	semidirect
254. #2295	C₂×C₇	semidirect
255. #2295	C₂×C₇	semidirect
256. C₄²×Q₈	C₂×C₇	semidirect
555. #117	C₇×Q₈	semidirect
876. C₇	#34916	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×#2590	2
C₇×#2589	2
C₇×#2588	2
C₇×#2587	2
C₇×#2511	2
C₇×#2507	2
C₇×#2497	2
C₇×#2492	2
C₇×#2451	2
C₇×#2446	2
C₇×#2429	2
C₇×#2423	2
C₇×#2402	2
C₇×#2396	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×C₂²⋊Q₈	2
C₇×#2298	2
C₇×#2295	2
C₄²×C₇×Q₈	2
C₄×C₇×#117	2
#34916	7

Subgroups — C7×#34916 #13212132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34916 #13212132