Subgroups — C₇×#34691 #13211907

Order 1792.

2464 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2473	C₂	1	2	yes	maximal, complemented
4	C₇×#2465	C₂	1	2	yes	maximal, complemented
5	C₇×#2462	C₂	1	2	yes	maximal, complemented
6	C₇×#2451	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2449	C₂	1	2	yes	maximal
8	C₇×#2446	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2440	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2434	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2429	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2423	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2417	C₂	1	1	yes	maximal, characteristic
14	C₇×#2409	C₂	1	1	yes	maximal, characteristic
15	C₇×#2399	C₂	1	2	yes	maximal, complemented
16	C₇×#2396	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₇×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
20	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2290	C₂	1	2	yes	maximal
23	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic
24	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
25	C₇×#533	—	2	8	no	—
26	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×#125	C₂²	1	2	yes	—
30	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₂×C₄×C₇×Q₈	—	2	8	no	—
37	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
38	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
39	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
42	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₇×#117	C₂²	1	2	yes	—
49	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
51	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
52	C₂²×C₄²×C₇	C₂²	1	2	yes	—
53	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
54	C₇×#400	C₂²	1	2	yes	—
55	C₇×#399	C₂²	1	2	yes	—
56	C₇×#398	C₂²	1	2	yes	—
57	C₇×#398	C₂²	1	2	yes	—
58	C₇×#398	C₂²	1	2	yes	—
59	C₇×#398	C₂²	1	2	yes	—
60	C₇×#398	C₂²	1	2	yes	—
61	C₇×#398	C₂²	1	2	yes	—
62	C₇×#396	C₂²	1	2	yes	—
63	C₇×#396	C₂²	1	2	yes	—
64	C₇×#395	C₂²	1	2	yes	—
65	C₇×#395	C₂²	1	2	yes	—
66	C₇×#395	C₂²	1	2	yes	—
67	C₇×#395	C₂²	1	2	yes	—
68	C₇×#395	C₂²	1	2	yes	—
69	C₇×#393	C₂²	1	2	yes	—
70	C₇×#391	C₂²	1	1	yes	characteristic
71	C₇×#391	C₂²	1	1	yes	characteristic
72	C₇×#391	C₂²	1	1	yes	characteristic
73	C₇×#391	C₂²	1	1	yes	characteristic
74	C₇×#391	C₂²	1	1	yes	characteristic
75	C₇×#391	C₂²	1	1	yes	characteristic
76	C₇×#391	C₂²	1	2	yes	—
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	2	yes	—
81	C₇×#389	C₂²	1	1	yes	characteristic
82	C₇×#389	C₂²	1	2	yes	—
83	C₇×#389	C₂²	1	2	yes	—
84	C₇×#388	C₂²	1	2	yes	—
85	C₇×#388	C₂²	1	2	yes	—
86	C₇×#387	C₂²	1	2	yes	—
87	C₇×#387	C₂²	1	2	yes	—
88	C₇×#387	C₂²	1	2	yes	—
89	C₇×#387	C₂²	1	2	yes	—
90	C₇×#387	C₂²	1	2	yes	—
91	C₇×#387	C₂²	1	2	yes	—
92	C₇×#387	C₂²	1	2	yes	—
93	C₇×#387	C₂²	1	2	yes	—
94	C₇×#386	C₂²	1	2	yes	—
95	C₇×#386	C₂²	1	2	yes	—
96	C₇×#385	C₂²	1	2	yes	—
97	C₇×#385	C₂²	1	2	yes	—
98	C₇×#385	C₂²	1	2	yes	—
99	C₇×#385	C₂²	1	2	yes	—
100	C₇×#385	C₂²	1	2	yes	—
101	C₇×#385	C₂²	1	2	yes	—
102	C₇×#384	C₂²	1	1	yes	characteristic
103	C₇×#380	C₂²	1	1	yes	characteristic
104	C₇×#380	C₂²	1	1	yes	characteristic
105	C₇×#380	C₂²	1	2	yes	—
106	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
107	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
108	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
109	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
111	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
112	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
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	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
121	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
122	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
123	C₇×#376	C₂²	1	2	yes	—
124	C₄³×C₇	C₂²	1	1	yes	characteristic
125	#34691	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂²×C₇×Q₈	—	2	4	no	—
127	C₂²×C₇×Q₈	—	2	4	no	—
128	C₂²×C₇×Q₈	—	2	4	no	—
129	C₂²×C₇×Q₈	C₂³	1	2	yes	—
130	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
131	C₂²×C₇×Q₈	C₂³	1	2	yes	—
132	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
133	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
134	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₇	C₂³	1	2	yes	—
139	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
143	C₇×C₄⋊Q₈	—	2	4	no	—
144	C₇×C₄⋊Q₈	—	2	4	no	—
145	C₇×C₄⋊Q₈	—	2	4	no	—
146	C₇×#125	—	2	8	no	—
147	C₇×C₂²⋊Q₈	—	2	4	no	—
148	C₇×C₂²⋊Q₈	—	2	4	no	—
149	C₇×C₂²⋊Q₈	—	2	4	no	—
150	C₇×C₂²⋊Q₈	—	2	4	no	—
151	C₇×C₂²⋊Q₈	—	2	8	no	—
152	C₇×C₂²⋊Q₈	—	2	8	no	—
153	C₄×C₇×Q₈	—	2	4	no	—
154	C₄×C₇×Q₈	—	2	8	no	—
155	C₄×C₇×Q₈	—	2	4	no	—
156	C₄×C₇×Q₈	—	2	4	no	—
157	C₄×C₇×Q₈	—	2	8	no	—
158	C₄×C₇×Q₈	—	2	8	no	—
159	C₄×C₇×Q₈	—	2	4	no	—
160	C₄×C₇×Q₈	D₄	1	8	yes	complemented
161	C₄×C₇×D₄	—	2	4	no	—
162	C₄×C₇×D₄	—	2	4	no	—
163	C₄×C₇×D₄	Q₈	1	8	yes	complemented
164	C₇×#117	—	2	8	no	—
165	C₂×C₇×C₄⋊C₄	—	2	8	no	—
166	C₂×C₇×C₄⋊C₄	—	2	4	no	—
167	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	4	no	—
209	C₂×C₄²×C₇	—	2	8	no	—
210	C₂×C₄²×C₇	—	2	4	no	—
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	1	yes	characteristic
215	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₇	C₂³	1	2	yes	—
219	C₂×C₄²×C₇	C₂³	1	2	yes	—
220	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₇	C₂³	1	2	yes	—
223	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₇	C₂³	1	2	yes	—
225	C₂×C₄²×C₇	C₂³	1	2	yes	—
226	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₇	C₂³	1	2	yes	—
229	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
239	C₇×#95	C₂³	1	1	yes	characteristic
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	C₇×#95	C₂³	1	2	yes	—
251	C₇×#95	C₂³	1	2	yes	—
252	C₇×#95	C₂³	1	2	yes	—
253	C₇×#95	C₂³	1	2	yes	—
254	C₇×#95	C₂³	1	2	yes	—
255	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
256	C₂²×C₄×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
257	#2473	C₂×C₇	1	2	yes	complemented
258	#2465	C₂×C₇	1	2	yes	complemented
259	#2462	C₂×C₇	1	2	yes	complemented
260	#2451	C₂×C₇	1	1	yes	characteristic, complemented
261	#2449	C₂×C₇	1	2	yes	—
262	#2446	C₂×C₇	1	1	yes	characteristic, complemented
263	#2440	C₂×C₇	1	1	yes	characteristic, complemented
264	#2434	C₂×C₇	1	1	yes	characteristic, complemented
265	#2429	C₂×C₇	1	1	yes	characteristic, complemented
266	#2423	C₂×C₇	1	1	yes	characteristic, complemented
267	#2417	C₂×C₇	1	1	yes	characteristic
268	#2409	C₂×C₇	1	1	yes	characteristic
269	#2399	C₂×C₇	1	2	yes	complemented
270	#2396	C₂×C₇	1	2	yes	complemented
271	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
272	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
273	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
274	C₄×C₂²⋊Q₈	C₂×C₇	1	2	yes	complemented
275	#2295	C₂×C₇	1	1	yes	characteristic, complemented
276	#2290	C₂×C₇	1	2	yes	—
277	C₄²×D₄	C₂×C₇	1	1	yes	characteristic
278	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
279	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
280	C₂×C₇×Q₈	—	2	32	no	—
281	C₂×C₇×Q₈	—	2	4	no	—
282	C₂×C₇×Q₈	—	2	2	no	—
283	C₂×C₇×Q₈	—	2	4	no	—
284	C₂×C₇×Q₈	—	2	2	no	—
285	C₂×C₇×Q₈	—	2	4	no	—
286	C₂×C₇×Q₈	—	2	4	no	—
287	C₂×C₇×Q₈	—	2	2	no	—
288	C₂×C₇×Q₈	—	2	2	no	—
289	C₂×C₇×Q₈	—	2	2	no	—
290	C₂×C₇×Q₈	—	2	4	no	—
291	C₂×C₇×Q₈	—	2	2	no	—
292	C₂×C₇×Q₈	—	2	2	no	—
293	C₂×C₇×Q₈	—	4	2	no	—
294	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
295	C₂×C₇×Q₈	#41	1	4	yes	—
296	C₂×C₇×D₄	—	2	2	no	—
297	C₂×C₇×D₄	—	2	2	no	—
298	C₂×C₇×D₄	C₂×Q₈	1	4	yes	—
299	C₂²×C₄×C₇	—	2	4	no	—
300	C₂²×C₄×C₇	—	2	2	no	—
301	C₂²×C₄×C₇	—	2	4	no	—
302	C₂²×C₄×C₇	—	2	2	no	—
303	C₂²×C₄×C₇	—	2	2	no	—
304	C₂²×C₄×C₇	—	2	4	no	—
305	C₂²×C₄×C₇	—	2	2	no	—
306	C₂²×C₄×C₇	—	2	2	no	—
307	C₂²×C₄×C₇	—	2	2	no	—
308	C₂²×C₄×C₇	—	2	2	no	—
309	C₂²×C₄×C₇	—	2	4	no	—
310	C₂²×C₄×C₇	—	2	2	no	—
311	C₂²×C₄×C₇	—	2	4	no	—
312	C₂²×C₄×C₇	—	2	2	no	—
313	C₂²×C₄×C₇	—	2	2	no	—
314	C₂²×C₄×C₇	—	2	2	no	—
315	C₂²×C₄×C₇	—	2	2	no	—
316	C₂²×C₄×C₇	—	2	2	no	—
317	C₂²×C₄×C₇	—	4	1	no	—
318	C₂²×C₄×C₇	—	4	1	no	—
319	C₂²×C₄×C₇	—	4	2	no	—
320	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
321	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	complemented
322	C₂²×C₄×C₇	#41	1	4	yes	—
323	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
344	C₇×C₄⋊C₄	—	2	4	no	—
345	C₇×C₄⋊C₄	—	2	4	no	—
346	C₇×C₄⋊C₄	—	2	4	no	—
347	C₇×C₄⋊C₄	—	2	4	no	—
348	C₇×C₄⋊C₄	—	2	2	no	—
349	C₇×C₄⋊C₄	—	2	4	no	—
350	C₇×C₄⋊C₄	—	2	4	no	—
351	C₇×C₄⋊C₄	—	2	4	no	—
352	C₇×C₄⋊C₄	—	2	4	no	—
353	C₇×C₄⋊C₄	—	2	4	no	—
354	C₇×C₄⋊C₄	—	2	4	no	—
355	C₇×C₄⋊C₄	—	2	2	no	—
356	C₇×C₄⋊C₄	—	2	2	no	—
357	C₇×C₄⋊C₄	—	2	2	no	—
358	C₇×C₄⋊C₄	—	2	4	no	—
359	C₇×C₄⋊C₄	—	2	2	no	—
360	C₇×C₄⋊C₄	—	2	2	no	—
361	C₇×C₄⋊C₄	—	2	4	no	—
362	C₇×C₄⋊C₄	—	2	4	no	—
363	C₇×C₄⋊C₄	—	2	4	no	—
364	C₇×C₄⋊C₄	—	2	4	no	—
365	C₇×C₄⋊C₄	—	2	4	no	—
366	C₇×C₄⋊C₄	—	2	4	no	—
367	C₇×C₄⋊C₄	—	4	2	no	—
368	C₇×C₄⋊C₄	—	4	2	no	—
369	C₇×C₄⋊C₄	—	4	2	no	—
370	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
371	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
372	C₇×C₄⋊C₄	C₂×Q₈	1	4	yes	complemented
373	C₇×C₂²⋊C₄	—	2	2	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	—	2	4	no	—
378	C₇×C₂²⋊C₄	—	2	2	no	—
379	C₇×C₂²⋊C₄	—	2	2	no	—
380	C₇×C₂²⋊C₄	—	2	4	no	—
381	C₇×C₂²⋊C₄	—	4	2	no	—
382	C₇×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
383	C₇×C₂²⋊C₄	C₂×Q₈	1	4	yes	complemented
384	C₇×C₂²⋊C₄	#41	1	4	yes	—
385	C₄²×C₇	—	2	2	no	—
386	C₄²×C₇	—	2	4	no	—
387	C₄²×C₇	—	2	4	no	—
388	C₄²×C₇	—	2	2	no	—
389	C₄²×C₇	—	2	2	no	—
390	C₄²×C₇	—	2	4	no	—
391	C₄²×C₇	—	2	2	no	—
392	C₄²×C₇	—	2	2	no	—
393	C₄²×C₇	—	2	2	no	—
394	C₄²×C₇	—	2	4	no	—
395	C₄²×C₇	—	2	2	no	—
396	C₄²×C₇	—	2	2	no	—
397	C₄²×C₇	—	2	2	no	—
398	C₄²×C₇	—	2	2	no	—
399	C₄²×C₇	—	2	4	no	—
400	C₄²×C₇	—	4	1	no	—
401	C₄²×C₇	C₂×D₄	1	4	yes	—
402	C₄²×C₇	C₂×D₄	1	8	yes	—
403	C₄²×C₇	C₂×Q₈	1	4	yes	complemented
404	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
405	#533	—	2	8	no	—
406	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
407	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
408	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
409	C₂×#125	C₂²×C₇	1	2	yes	—
410	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
411	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
412	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
413	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
414	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
415	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
416	C₂×C₄×Q₈	—	2	8	no	—
417	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
418	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
419	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
420	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
421	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
422	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
423	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
424	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
425	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
428	C₂×#117	C₂²×C₇	1	2	yes	—
429	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
430	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
431	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
432	C₂²×C₄²	C₂²×C₇	1	2	yes	—
433	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
434	#400	C₂²×C₇	1	2	yes	—
435	#399	C₂²×C₇	1	2	yes	—
436	#398	C₂²×C₇	1	2	yes	—
437	#398	C₂²×C₇	1	2	yes	—
438	#398	C₂²×C₇	1	2	yes	—
439	#398	C₂²×C₇	1	2	yes	—
440	#398	C₂²×C₇	1	2	yes	—
441	#398	C₂²×C₇	1	2	yes	—
442	#396	C₂²×C₇	1	2	yes	—
443	#396	C₂²×C₇	1	2	yes	—
444	#395	C₂²×C₇	1	2	yes	—
445	#395	C₂²×C₇	1	2	yes	—
446	#395	C₂²×C₇	1	2	yes	—
447	#395	C₂²×C₇	1	2	yes	—
448	#395	C₂²×C₇	1	2	yes	—
449	#393	C₂²×C₇	1	2	yes	—
450	#391	C₂²×C₇	1	1	yes	characteristic
451	#391	C₂²×C₇	1	1	yes	characteristic
452	#391	C₂²×C₇	1	1	yes	characteristic
453	#391	C₂²×C₇	1	1	yes	characteristic
454	#391	C₂²×C₇	1	1	yes	characteristic
455	#391	C₂²×C₇	1	1	yes	characteristic
456	#391	C₂²×C₇	1	2	yes	—
457	#389	C₂²×C₇	1	2	yes	—
458	#389	C₂²×C₇	1	2	yes	—
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	#389	C₂²×C₇	1	2	yes	—
463	#389	C₂²×C₇	1	1	yes	characteristic
464	#388	C₂²×C₇	1	2	yes	—
465	#388	C₂²×C₇	1	2	yes	—
466	#387	C₂²×C₇	1	2	yes	—
467	#387	C₂²×C₇	1	2	yes	—
468	#387	C₂²×C₇	1	2	yes	—
469	#387	C₂²×C₇	1	2	yes	—
470	#387	C₂²×C₇	1	2	yes	—
471	#387	C₂²×C₇	1	2	yes	—
472	#387	C₂²×C₇	1	2	yes	—
473	#387	C₂²×C₇	1	2	yes	—
474	#386	C₂²×C₇	1	2	yes	—
475	#386	C₂²×C₇	1	2	yes	—
476	#385	C₂²×C₇	1	2	yes	—
477	#385	C₂²×C₇	1	2	yes	—
478	#385	C₂²×C₇	1	2	yes	—
479	#385	C₂²×C₇	1	2	yes	—
480	#385	C₂²×C₇	1	2	yes	—
481	#385	C₂²×C₇	1	2	yes	—
482	#384	C₂²×C₇	1	1	yes	characteristic
483	#380	C₂²×C₇	1	1	yes	characteristic
484	#380	C₂²×C₇	1	1	yes	characteristic
485	#380	C₂²×C₇	1	2	yes	—
486	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
487	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
488	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
489	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
490	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
491	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
492	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
493	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
494	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
495	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
496	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
497	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
498	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
499	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
500	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
501	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
502	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
503	#376	C₂²×C₇	1	2	yes	—
504	C₄³	C₂²×C₇	1	1	yes	characteristic
505	C₂³×C₇	—	2	1	no	—
506	C₂³×C₇	—	2	1	no	—
507	C₂³×C₇	—	2	1	no	—
508	C₂³×C₇	—	2	1	no	—
509	C₂³×C₇	—	2	1	no	—
510	C₂³×C₇	—	2	1	no	—
511	C₂³×C₇	—	2	1	no	—
512	C₂³×C₇	—	2	1	no	—
513	C₂³×C₇	—	2	1	no	—
514	C₂³×C₇	—	2	1	no	—
515	C₂³×C₇	C₂²×Q₈	1	2	yes	—
516	C₂³×C₇	C₂²×Q₈	1	2	yes	—
517	C₂³×C₇	C₂×#41	1	2	yes	—
518	C₂³×C₇	C₂×#41	1	2	yes	—
519	C₂³×C₇	C₂⁵	1	1	yes	characteristic
520	C₇×Q₈	—	2	16	no	—
521	C₇×Q₈	—	2	8	no	—
522	C₇×Q₈	—	2	8	no	—
523	C₇×Q₈	—	4	8	no	—
524	C₇×Q₈	—	4	4	no	—
525	C₇×D₄	—	2	8	no	—
526	C₂×C₄×C₇	—	2	16	no	—
527	C₂×C₄×C₇	—	2	1	no	—
528	C₂×C₄×C₇	—	2	1	no	—
529	C₂×C₄×C₇	—	2	2	no	—
530	C₂×C₄×C₇	—	2	1	no	—
531	C₂×C₄×C₇	—	2	1	no	—
532	C₂×C₄×C₇	—	2	1	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	2	no	—
538	C₂×C₄×C₇	—	2	2	no	—
539	C₂×C₄×C₇	—	2	2	no	—
540	C₂×C₄×C₇	—	2	2	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	2	no	—
548	C₂×C₄×C₇	—	2	1	no	—
549	C₂×C₄×C₇	—	2	8	no	—
550	C₂×C₄×C₇	—	2	8	no	—
551	C₂×C₄×C₇	—	2	8	no	—
552	C₂×C₄×C₇	—	2	1	no	—
553	C₂×C₄×C₇	—	2	1	no	—
554	C₂×C₄×C₇	—	2	2	no	—
555	C₂×C₄×C₇	—	2	2	no	—
556	C₂×C₄×C₇	—	2	2	no	—
557	C₂×C₄×C₇	—	2	1	no	—
558	C₂×C₄×C₇	—	2	2	no	—
559	C₂×C₄×C₇	—	2	2	no	—
560	C₂×C₄×C₇	—	2	2	no	—
561	C₂×C₄×C₇	—	2	1	no	—
562	C₂×C₄×C₇	—	2	1	no	—
563	C₂×C₄×C₇	—	2	2	no	—
564	C₂×C₄×C₇	—	2	2	no	—
565	C₂×C₄×C₇	—	2	1	no	—
566	C₂×C₄×C₇	—	2	2	no	—
567	C₂×C₄×C₇	—	2	2	no	—
568	C₂×C₄×C₇	—	2	1	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	2	no	—
573	C₂×C₄×C₇	—	2	2	no	—
574	C₂×C₄×C₇	—	2	1	no	—
575	C₂×C₄×C₇	—	2	2	no	—
576	C₂×C₄×C₇	—	4	4	no	—
577	C₂×C₄×C₇	—	4	4	no	—
578	C₂×C₄×C₇	—	4	8	no	—
579	C₂×C₄×C₇	—	4	4	no	—
580	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
581	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
582	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
583	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
584	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
585	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
586	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
587	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
588	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
589	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
590	C₂×C₄×C₇	C₂×#41	1	2	yes	—
591	C₂×C₄×C₇	C₂×#41	1	4	yes	—
592	C₂×C₄×C₇	C₂×#41	1	2	yes	—
593	C₂×C₄×C₇	C₂×#41	1	2	yes	—
594	C₂×C₄×C₇	C₂×#41	1	2	yes	—
595	C₂×C₄×C₇	C₂×#41	1	2	yes	—
596	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
597	C₂²×Q₈	—	2	4	no	—
598	C₂²×Q₈	—	2	4	no	—
599	C₂²×Q₈	—	2	4	no	—
600	C₂²×Q₈	C₂³×C₇	1	2	yes	—
601	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
602	C₂²×Q₈	C₂³×C₇	1	2	yes	—
603	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
604	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
605	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₇	1	2	yes	—
607	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₇	1	2	yes	—
610	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
614	C₄⋊Q₈	—	2	4	no	—
615	C₄⋊Q₈	—	2	4	no	—
616	C₄⋊Q₈	—	2	4	no	—
617	#125	—	2	8	no	—
618	C₂²⋊Q₈	—	2	4	no	—
619	C₂²⋊Q₈	—	2	4	no	—
620	C₂²⋊Q₈	—	2	4	no	—
621	C₂²⋊Q₈	—	2	4	no	—
622	C₂²⋊Q₈	—	2	8	no	—
623	C₂²⋊Q₈	—	2	8	no	—
624	C₄×Q₈	—	2	4	no	—
625	C₄×Q₈	—	2	8	no	—
626	C₄×Q₈	—	2	4	no	—
627	C₄×Q₈	—	2	4	no	—
628	C₄×Q₈	—	2	8	no	—
629	C₄×Q₈	—	2	8	no	—
630	C₄×Q₈	—	2	4	no	—
631	C₄×Q₈	C₇×D₄	1	8	yes	complemented
632	C₄×D₄	—	2	4	no	—
633	C₄×D₄	—	2	4	no	—
634	C₄×D₄	C₇×Q₈	1	8	yes	complemented
635	#117	—	2	8	no	—
636	C₂×C₄⋊C₄	—	2	8	no	—
637	C₂×C₄⋊C₄	—	2	4	no	—
638	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	1	yes	characteristic
670	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
671	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	1	yes	characteristic
677	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
678	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
679	C₂×C₄²	—	2	4	no	—
680	C₂×C₄²	—	2	8	no	—
681	C₂×C₄²	—	2	4	no	—
682	C₂×C₄²	C₂³×C₇	1	2	yes	—
683	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₇	1	2	yes	—
686	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₇	1	2	yes	—
691	C₂×C₄²	C₂³×C₇	1	2	yes	—
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	2	yes	—
697	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₇	1	2	yes	—
699	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
701	#95	C₂³×C₇	1	2	yes	—
702	#95	C₂³×C₇	1	2	yes	—
703	#95	C₂³×C₇	1	2	yes	—
704	#95	C₂³×C₇	1	2	yes	—
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	2	yes	—
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	#95	C₂³×C₇	1	2	yes	—
725	#95	C₂³×C₇	1	2	yes	—
726	C₂²×C₇	—	2	2	no	—
727	C₂²×C₇	—	2	2	no	—
728	C₂²×C₇	—	2	2	no	—
729	C₂²×C₇	—	2	2	no	—
730	C₂²×C₇	—	2	2	no	—
731	C₂²×C₇	—	2	2	no	—
732	C₂²×C₇	—	2	2	no	—
733	C₂²×C₇	—	2	2	no	—
734	C₂²×C₇	—	2	2	no	—
735	C₂²×C₇	—	4	1	no	—
736	C₂²×C₇	—	4	1	no	—
737	C₂²×C₇	—	4	1	no	—
738	C₂²×C₇	—	4	1	no	—
739	C₂²×C₇	#533	1	4	yes	complemented
740	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
741	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
742	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
743	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
744	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
745	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
746	C₂²×C₇	#585	1	1	yes	characteristic
747	C₄×C₇	—	2	4	no	—
748	C₄×C₇	—	2	4	no	—
749	C₄×C₇	—	2	2	no	—
750	C₄×C₇	—	2	2	no	—
751	C₄×C₇	—	2	2	no	—
752	C₄×C₇	—	2	2	no	—
753	C₄×C₇	—	2	2	no	—
754	C₄×C₇	—	2	4	no	—
755	C₄×C₇	—	2	2	no	—
756	C₄×C₇	—	2	2	no	—
757	C₄×C₇	—	2	2	no	—
758	C₄×C₇	—	4	1	no	—
759	C₄×C₇	—	4	2	no	—
760	C₄×C₇	—	4	1	no	—
761	C₄×C₇	—	4	2	no	—
762	C₄×C₇	—	4	1	no	—
763	C₄×C₇	—	4	2	no	—
764	C₄×C₇	—	4	2	no	—
765	C₄×C₇	—	4	2	no	—
766	C₄×C₇	#525	1	4	yes	—
767	C₄×C₇	D₄×Q₈	1	4	yes	—
768	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
769	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
770	C₂×Q₈	—	2	32	no	—
771	C₂×Q₈	—	2	4	no	—
772	C₂×Q₈	—	2	2	no	—
773	C₂×Q₈	—	2	4	no	—
774	C₂×Q₈	—	2	2	no	—
775	C₂×Q₈	—	2	4	no	—
776	C₂×Q₈	—	2	4	no	—
777	C₂×Q₈	—	2	2	no	—
778	C₂×Q₈	—	2	2	no	—
779	C₂×Q₈	—	2	2	no	—
780	C₂×Q₈	—	2	4	no	—
781	C₂×Q₈	—	2	2	no	—
782	C₂×Q₈	—	2	2	no	—
783	C₂×Q₈	—	4	2	no	—
784	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
785	C₂×Q₈	C₇×#41	1	4	yes	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	C₂×C₇×Q₈	1	4	yes	—
789	C₂²×C₄	—	2	4	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	4	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	4	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	4	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	4	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	4	1	no	—
808	C₂²×C₄	—	4	1	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
811	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	complemented
812	C₂²×C₄	C₇×#41	1	4	yes	—
813	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
815	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
816	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
819	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
820	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
821	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
824	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
834	C₄⋊C₄	—	2	4	no	—
835	C₄⋊C₄	—	2	4	no	—
836	C₄⋊C₄	—	2	4	no	—
837	C₄⋊C₄	—	2	4	no	—
838	C₄⋊C₄	—	2	2	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	2	no	—
848	C₄⋊C₄	—	2	4	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	4	no	—
852	C₄⋊C₄	—	2	4	no	—
853	C₄⋊C₄	—	2	4	no	—
854	C₄⋊C₄	—	2	4	no	—
855	C₄⋊C₄	—	2	4	no	—
856	C₄⋊C₄	—	2	4	no	—
857	C₄⋊C₄	—	4	2	no	—
858	C₄⋊C₄	—	4	2	no	—
859	C₄⋊C₄	—	4	2	no	—
860	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
861	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
862	C₄⋊C₄	C₂×C₇×Q₈	1	4	yes	complemented
863	C₂²⋊C₄	—	2	2	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	—	4	2	no	—
872	C₂²⋊C₄	C₂×C₇×Q₈	1	4	yes	—
873	C₂²⋊C₄	C₂×C₇×Q₈	1	4	yes	complemented
874	C₂²⋊C₄	C₇×#41	1	4	yes	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	4	no	—
877	C₄²	—	2	4	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	—	2	4	no	—
881	C₄²	—	2	2	no	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	4	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	2	no	—
887	C₄²	—	2	2	no	—
888	C₄²	—	2	2	no	—
889	C₄²	—	2	4	no	—
890	C₄²	—	4	1	no	—
891	C₄²	C₂×C₇×D₄	1	4	yes	—
892	C₄²	C₂×C₇×D₄	1	8	yes	—
893	C₄²	C₂×C₇×Q₈	1	4	yes	complemented
894	C₂×C₇	—	2	4	no	—
895	C₂×C₇	—	4	2	no	—
896	C₂×C₇	C₂×#525	1	1	yes	characteristic
897	C₂×C₇	C₂×#533	1	1	yes	characteristic
898	C₂×C₇	#3461	1	1	yes	characteristic
899	C₂×C₇	C₂×D₄×Q₈	1	1	yes	characteristic
900	C₂×C₇	D₄×#41	1	1	yes	characteristic
901	C₂×C₇	Q₈×#41	1	1	yes	characteristic
902	C₂×C₇	#3482	1	1	yes	characteristic
903	C₂³	—	2	1	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	1	no	—
906	C₂³	—	2	1	no	—
907	C₂³	—	2	1	no	—
908	C₂³	—	2	1	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	C₂²×C₇×Q₈	1	2	yes	—
914	C₂³	C₂²×C₇×Q₈	1	2	yes	—
915	C₂³	C₂×C₇×#41	1	2	yes	—
916	C₂³	C₂×C₇×#41	1	2	yes	—
917	C₂³	C₂⁵×C₇	1	1	yes	characteristic
918	Q₈	—	2	16	no	—
919	Q₈	—	2	8	no	—
920	Q₈	—	2	8	no	—
921	Q₈	—	4	8	no	—
922	Q₈	—	4	4	no	—
923	D₄	—	2	8	no	—
924	C₂×C₄	—	2	16	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	8	no	—
948	C₂×C₄	—	2	8	no	—
949	C₂×C₄	—	2	8	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	4	4	no	—
975	C₂×C₄	—	4	4	no	—
976	C₂×C₄	—	4	8	no	—
977	C₂×C₄	—	4	4	no	—
978	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
979	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
980	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
981	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
982	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
983	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
984	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
985	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
986	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
987	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
988	C₂×C₄	C₂×C₇×#41	1	2	yes	—
989	C₂×C₄	C₂×C₇×#41	1	4	yes	—
990	C₂×C₄	C₂×C₇×#41	1	2	yes	—
991	C₂×C₄	C₂×C₇×#41	1	2	yes	—
992	C₂×C₄	C₂×C₇×#41	1	2	yes	—
993	C₂×C₄	C₂×C₇×#41	1	2	yes	—
994	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
995	C₇	#34691	1	1	yes	characteristic, direct product factor, Sylow
996	C₂²	—	2	2	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	1	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	C₇×#533	1	4	yes	complemented
1010	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1011	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
1012	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1013	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1014	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1015	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1016	C₂²	C₇×#585	1	1	yes	characteristic
1017	C₄	—	2	4	no	—
1018	C₄	—	2	4	no	—
1019	C₄	—	2	2	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	2	2	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	2	2	no	—
1024	C₄	—	2	4	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	2	no	—
1028	C₄	—	4	1	no	—
1029	C₄	—	4	2	no	—
1030	C₄	—	4	1	no	—
1031	C₄	—	4	2	no	—
1032	C₄	—	4	1	no	—
1033	C₄	—	4	2	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	2	no	—
1036	C₄	C₇×#525	1	4	yes	—
1037	C₄	C₇×D₄×Q₈	1	4	yes	—
1038	C₂	—	2	4	no	—
1039	C₂	—	4	2	no	—
1040	C₂	C₂×C₇×#525	1	1	yes	characteristic
1041	C₂	C₂×C₇×#533	1	1	yes	characteristic
1042	C₂	C₇×#3461	1	1	yes	characteristic
1043	C₂	C₂×C₇×D₄×Q₈	1	1	yes	characteristic
1044	C₂	C₇×D₄×#41	1	1	yes	characteristic
1045	C₂	C₇×Q₈×#41	1	1	yes	characteristic
1046	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. C₂×C₇×#533	C₂	semidirect
2. C₂²×C₄×C₇×Q₈	C₂	semidirect
3. C₇×#2473	C₂	semidirect
4. C₇×#2465	C₂	semidirect
5. C₇×#2462	C₂	semidirect
6. C₇×#2451	C₂	semidirect
8. C₇×#2446	C₂	semidirect
9. C₇×#2440	C₂	semidirect
10. C₇×#2434	C₂	semidirect
11. C₇×#2429	C₂	semidirect
12. C₇×#2423	C₂	semidirect
15. C₇×#2399	C₂	semidirect
16. C₇×#2396	C₂	semidirect
17. C₄×C₇×C₄⋊Q₈	C₂	semidirect
18. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
19. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
20. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
21. C₇×#2295	C₂	semidirect
125. #34691	C₇	direct (N × H)
160. C₄×C₇×Q₈	D₄	semidirect
163. C₄×C₇×D₄	Q₈	semidirect
255. C₂×#533	C₂×C₇	semidirect
256. C₂²×C₄×Q₈	C₂×C₇	semidirect
257. #2473	C₂×C₇	semidirect
258. #2465	C₂×C₇	semidirect
259. #2462	C₂×C₇	semidirect
260. #2451	C₂×C₇	semidirect
262. #2446	C₂×C₇	semidirect
263. #2440	C₂×C₇	semidirect
264. #2434	C₂×C₇	semidirect
265. #2429	C₂×C₇	semidirect
266. #2423	C₂×C₇	semidirect
269. #2399	C₂×C₇	semidirect
270. #2396	C₂×C₇	semidirect
271. C₄×C₄⋊Q₈	C₂×C₇	semidirect
272. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
273. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
274. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
275. #2295	C₂×C₇	semidirect
321. C₂²×C₄×C₇	C₂×Q₈	semidirect
372. C₇×C₄⋊C₄	C₂×Q₈	semidirect
383. C₇×C₂²⋊C₄	C₂×Q₈	semidirect
403. C₄²×C₇	C₂×Q₈	semidirect
631. C₄×Q₈	C₇×D₄	semidirect
634. C₄×D₄	C₇×Q₈	semidirect
739. C₂²×C₇	#533	semidirect
811. C₂²×C₄	C₂×C₇×Q₈	semidirect
862. C₄⋊C₄	C₂×C₇×Q₈	semidirect
873. C₂²⋊C₄	C₂×C₇×Q₈	semidirect
893. C₄²	C₂×C₇×Q₈	semidirect
995. C₇	#34691	direct (N × H)
1009. C₂²	C₇×#533	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#533	2
C₂²×C₄×C₇×Q₈	2
C₇×#2473	2
C₇×#2465	2
C₇×#2462	2
C₇×#2451	2
C₇×#2449	2
C₇×#2446	2
C₇×#2440	2
C₇×#2434	2
C₇×#2429	2
C₇×#2423	2
C₇×#2417	2
C₇×#2409	2
C₇×#2399	2
C₇×#2396	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×C₂²⋊Q₈	2
C₇×#2295	2
C₇×#2290	2
C₄²×C₇×D₄	2
#34691	7

Subgroups — C7×#34691 #13211907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34691 #13211907