Subgroups — #13320717

Order 1792.

958 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3475	C₂	1	1	yes	maximal, characteristic
2	#11739962	C₂	1	1	yes	maximal, characteristic, complemented
3	#11739960	C₂	1	1	yes	maximal, characteristic, complemented
4	#11729581	C₂	1	1	yes	maximal, characteristic, complemented
5	#11729579	C₂	1	1	yes	maximal, characteristic, complemented
6	#11729507	C₂	1	1	yes	maximal, characteristic, complemented
7	#11729506	C₂	1	1	yes	maximal, characteristic, complemented
8	#11729505	C₂	1	1	yes	maximal, characteristic, complemented
9	#11729504	C₂	1	1	yes	maximal, characteristic, complemented
10	#11729395	C₂	1	1	yes	maximal, characteristic, complemented
11	#11729394	C₂	1	1	yes	maximal, characteristic, complemented
12	#11729393	C₂	1	1	yes	maximal, characteristic, complemented
13	#11729392	C₂	1	1	yes	maximal, characteristic, complemented
14	#11729353	C₂	1	1	yes	maximal, characteristic, complemented
15	#11729351	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#556	C₄	1	1	yes	characteristic
17	C₇×#555	C₄	1	1	yes	characteristic
18	C₇×#554	C₄	1	1	yes	characteristic
19	C₇×#553	—	2	1	no	—
20	C₇×#552	—	2	1	no	—
21	C₇×#552	C₄	1	1	yes	characteristic
22	C₇×#552	C₄	1	1	yes	characteristic
23	C₇×#551	—	2	1	no	—
24	C₇×#551	—	2	1	no	—
25	C₇×#547	C₄	1	1	yes	characteristic
26	C₇×#546	C₄	1	1	yes	characteristic
27	C₇×#546	C₄	1	1	yes	characteristic
28	C₇×#533	C₂²	1	1	yes	characteristic
29	C₇×#529	—	2	1	no	—
30	C₇×#529	—	2	1	no	—
31	C₇×#529	C₂²	1	1	yes	characteristic
32	C₇×#529	C₂²	1	1	yes	characteristic
33	C₇×#525	—	2	1	no	—
34	C₄×C₇×#41	C₂²	1	1	yes	characteristic
35	C₄×C₇×#41	C₂²	1	1	yes	characteristic
36	C₄×C₇×#41	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₇×#117	—	2	1	no	—
39	#90006	—	2	1	no	—
40	#89796	—	2	1	no	—
41	#89784	—	2	1	no	—
42	#89783	—	2	1	no	—
43	#89783	—	2	1	no	—
44	#89772	—	2	1	no	—
45	#89772	—	2	1	no	—
46	#89769	—	2	1	no	—
47	#89698	C₂²	1	1	yes	characteristic
48	#89698	C₂²	1	1	yes	characteristic, complemented
49	#89697	C₂²	1	1	yes	characteristic
50	#89697	C₂²	1	1	yes	characteristic
51	#89697	C₂²	1	1	yes	characteristic, complemented
52	#89697	C₂²	1	1	yes	characteristic, complemented
53	#89697	C₂²	1	1	yes	characteristic, complemented
54	#89696	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
56	C₄×#1136	C₂²	1	1	yes	characteristic
57	C₄×#1136	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
60	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
61	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
62	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
63	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
64	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
65	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
66	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
67	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
68	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
69	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
70	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
71	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
72	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
73	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
74	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
75	#17513	—	7	1	no	maximal, Sylow
76	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
77	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
78	C₂×C₇×#41	D₄	1	1	yes	characteristic
79	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
80	C₂³×C₄×C₇	—	2	1	no	—
81	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
82	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
83	C₇×#126	—	2	1	no	—
84	C₇×#126	—	2	1	no	—
85	C₇×#126	—	2	1	no	—
86	C₇×#126	—	2	1	no	—
87	C₇×#126	—	2	1	no	—
88	C₇×#126	—	2	1	no	—
89	C₇×#125	—	2	1	no	—
90	C₇×#125	—	2	1	no	—
91	C₇×#125	—	2	1	no	—
92	C₇×#125	C₂×C₄	1	1	yes	characteristic
93	C₇×#125	C₂×C₄	1	1	yes	characteristic
94	C₇×#124	—	2	1	no	—
95	C₇×#124	—	2	1	no	—
96	C₇×#124	C₂×C₄	1	1	yes	characteristic
97	C₇×#124	C₂×C₄	1	1	yes	characteristic
98	C₇×#123	—	2	1	no	—
99	C₇×#123	—	2	1	no	—
100	C₇×#123	—	2	1	no	—
101	C₇×#123	—	2	1	no	—
102	C₇×#123	—	2	1	no	—
103	C₇×#123	—	2	1	no	—
104	C₇×#123	—	2	1	no	—
105	C₇×#123	—	2	1	no	—
106	C₇×C₂²⋊Q₈	—	2	1	no	—
107	C₇×C₂²⋊Q₈	—	2	1	no	—
108	C₇×C₂²⋊Q₈	—	2	1	no	—
109	C₇×C₂²⋊Q₈	—	2	1	no	—
110	C₇×C₂²⋊Q₈	—	2	1	no	—
111	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
112	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
113	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
114	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
115	C₇×#121	—	2	1	no	—
116	C₇×#121	—	2	1	no	—
117	C₇×#121	—	2	1	no	—
118	C₇×#121	—	2	1	no	—
119	C₇×#121	C₂×C₄	1	1	yes	characteristic
120	C₇×#121	C₂×C₄	1	1	yes	characteristic
121	C₇×#120	—	2	1	no	—
122	C₇×#120	—	2	1	no	—
123	C₄×C₇×Q₈	—	2	1	no	—
124	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
125	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
126	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
127	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
128	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
129	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
130	C₄×C₇×D₄	—	2	1	no	—
131	C₄×C₇×D₄	—	2	1	no	—
132	C₄×C₇×D₄	—	2	1	no	—
133	C₄×C₇×D₄	—	2	1	no	—
134	C₄×C₇×D₄	—	2	1	no	—
135	C₄×C₇×D₄	—	2	1	no	—
136	C₄×C₇×D₄	—	2	1	no	—
137	C₄×C₇×D₄	—	2	1	no	—
138	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
139	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
140	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
141	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
142	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
143	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
144	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
145	C₄×C₇×D₄	D₄	1	1	yes	characteristic
146	C₄×C₇×D₄	D₄	1	1	yes	characteristic
147	C₄×C₇×D₄	D₄	1	1	yes	characteristic
148	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
149	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
150	C₇×#117	—	2	1	no	—
151	C₇×#117	—	2	1	no	—
152	C₇×#117	—	2	1	no	—
153	C₇×#117	—	2	1	no	—
154	C₇×#117	—	2	1	no	—
155	C₇×#117	—	2	1	no	—
156	C₇×#117	—	2	1	no	—
157	C₇×#117	—	2	1	no	—
158	C₇×#117	—	2	1	no	—
159	C₇×#117	C₂×C₄	1	1	yes	characteristic
160	C₇×#117	C₂×C₄	1	1	yes	characteristic
161	C₇×#117	D₄	1	1	yes	characteristic
162	C₇×#117	D₄	1	1	yes	characteristic
163	C₇×#117	D₄	1	1	yes	characteristic
164	C₂×C₇×C₄⋊C₄	—	2	1	no	—
165	C₂×C₇×C₄⋊C₄	—	2	1	no	—
166	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
167	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
168	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
169	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
170	C₂×C₄²×C₇	—	2	1	no	—
171	C₂×C₄²×C₇	—	2	1	no	—
172	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
175	C₂×#1136	—	2	1	no	—
176	C₂×#1136	—	2	1	no	—
177	C₂×#1136	—	2	1	no	—
178	C₂²×C₇⋊C₈	—	2	1	no	—
179	C₂²×C₇⋊C₈	—	2	1	no	—
180	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
181	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
182	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
183	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
184	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
185	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
186	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
187	C₄⋊(C₇⋊C₈)	—	2	1	no	—
188	C₄⋊(C₇⋊C₈)	—	2	1	no	—
189	C₄⋊(C₇⋊C₈)	—	2	1	no	—
190	C₄⋊(C₇⋊C₈)	—	2	1	no	—
191	C₄⋊(C₇⋊C₈)	—	2	1	no	—
192	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
193	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
194	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
195	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
196	#6377	—	2	1	no	—
197	#6377	—	2	1	no	—
198	#6377	—	2	1	no	—
199	#6377	—	2	1	no	—
200	C₄×C₇⋊C₈	—	2	1	no	—
201	C₄×C₇⋊C₈	—	2	1	no	—
202	C₄×C₇⋊C₈	—	2	1	no	—
203	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
204	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
205	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
206	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
207	#3475	D₇	1	1	yes	characteristic
208	#2965	—	7	1	no	—
209	#2925	—	7	1	no	—
210	#1497	—	7	1	no	—
211	#1495	—	7	1	no	—
212	#1494	—	7	1	no	—
213	#1490	—	7	1	no	—
214	#1489	—	7	1	no	—
215	#1488	—	7	1	no	—
216	#1485	—	7	1	no	—
217	#1483	—	7	1	no	—
218	#1482	—	7	1	no	—
219	#1478	—	7	1	no	—
220	#1477	—	7	1	no	—
221	#1476	—	7	1	no	—
222	C₂⁴×C₇	—	2	1	no	—
223	C₇×#41	—	2	2	no	—
224	C₇×#41	—	2	2	no	—
225	C₇×#41	—	4	1	no	—
226	C₇×#41	—	4	1	no	—
227	C₇×#41	—	4	1	no	—
228	C₇×#41	—	4	1	no	—
229	C₂×C₇×Q₈	—	2	1	no	—
230	C₂×C₇×Q₈	C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
232	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
233	C₂×C₇×D₄	—	2	2	no	—
234	C₂×C₇×D₄	—	2	1	no	—
235	C₂×C₇×D₄	—	2	1	no	—
236	C₂×C₇×D₄	—	2	1	no	—
237	C₂×C₇×D₄	—	2	1	no	—
238	C₂×C₇×D₄	—	2	1	no	—
239	C₂×C₇×D₄	—	4	1	no	—
240	C₂×C₇×D₄	C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₇×D₄	C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₇×D₄	C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
244	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
245	C₂²×C₄×C₇	—	2	1	no	—
246	C₂²×C₄×C₇	—	2	1	no	—
247	C₂²×C₄×C₇	—	2	1	no	—
248	C₂²×C₄×C₇	—	2	1	no	—
249	C₂²×C₄×C₇	—	2	1	no	—
250	C₂²×C₄×C₇	—	2	1	no	—
251	C₂²×C₄×C₇	—	2	1	no	—
252	C₂²×C₄×C₇	—	2	1	no	—
253	C₂²×C₄×C₇	—	2	1	no	—
254	C₂²×C₄×C₇	—	4	2	no	—
255	C₂²×C₄×C₇	—	4	2	no	—
256	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
257	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
258	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
259	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
265	C₇×C₄⋊C₄	—	2	1	no	—
266	C₇×C₄⋊C₄	—	2	1	no	—
267	C₇×C₄⋊C₄	—	2	1	no	—
268	C₇×C₄⋊C₄	—	2	1	no	—
269	C₇×C₄⋊C₄	—	2	1	no	—
270	C₇×C₄⋊C₄	—	2	1	no	—
271	C₇×C₄⋊C₄	—	2	1	no	—
272	C₇×C₄⋊C₄	—	2	1	no	—
273	C₇×C₄⋊C₄	—	2	1	no	—
274	C₇×C₄⋊C₄	—	2	1	no	—
275	C₇×C₄⋊C₄	—	2	1	no	—
276	C₇×C₄⋊C₄	—	2	1	no	—
277	C₇×C₄⋊C₄	—	2	1	no	—
278	C₇×C₄⋊C₄	—	2	1	no	—
279	C₇×C₄⋊C₄	—	2	1	no	—
280	C₇×C₄⋊C₄	—	2	1	no	—
281	C₇×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
282	C₇×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
283	C₇×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
284	C₇×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
285	C₇×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
286	C₇×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
287	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
288	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
289	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
290	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
291	C₇×C₂²⋊C₄	—	2	1	no	—
292	C₇×C₂²⋊C₄	—	2	1	no	—
293	C₇×C₂²⋊C₄	—	2	1	no	—
294	C₇×C₂²⋊C₄	—	2	1	no	—
295	C₇×C₂²⋊C₄	—	2	1	no	—
296	C₇×C₂²⋊C₄	—	2	1	no	—
297	C₇×C₂²⋊C₄	—	2	1	no	—
298	C₇×C₂²⋊C₄	—	2	1	no	—
299	C₇×C₂²⋊C₄	—	2	1	no	—
300	C₇×C₂²⋊C₄	—	2	1	no	—
301	C₇×C₂²⋊C₄	—	2	1	no	—
302	C₇×C₂²⋊C₄	—	2	1	no	—
303	C₇×C₂²⋊C₄	—	2	1	no	—
304	C₇×C₂²⋊C₄	—	2	1	no	—
305	C₇×C₂²⋊C₄	—	2	1	no	—
306	C₇×C₂²⋊C₄	—	2	1	no	—
307	C₇×C₂²⋊C₄	—	2	1	no	—
308	C₇×C₂²⋊C₄	—	2	1	no	—
309	C₇×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
310	C₇×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
311	C₇×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
312	C₇×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
313	C₇×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
314	C₇×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
315	C₄²×C₇	—	2	1	no	—
316	C₄²×C₇	—	2	1	no	—
317	C₄²×C₇	—	2	1	no	—
318	C₄²×C₇	—	2	1	no	—
319	C₄²×C₇	—	2	1	no	—
320	C₄²×C₇	—	2	1	no	—
321	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
322	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
323	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
324	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₇	C₂⁴	1	1	yes	characteristic
331	#1136	—	4	2	no	—
332	#1136	—	4	2	no	—
333	#1136	—	4	2	no	—
334	C₂×C₇⋊C₈	—	2	1	no	—
335	C₂×C₇⋊C₈	—	2	1	no	—
336	C₂×C₇⋊C₈	—	2	1	no	—
337	C₂×C₇⋊C₈	—	2	1	no	—
338	C₂×C₇⋊C₈	—	2	1	no	—
339	C₂×C₇⋊C₈	—	2	1	no	—
340	C₂×C₇⋊C₈	—	2	1	no	—
341	C₂×C₇⋊C₈	—	2	1	no	—
342	C₂×C₇⋊C₈	—	4	2	no	—
343	C₂×C₇⋊C₈	—	4	2	no	—
344	#556	Dic₇	1	1	yes	characteristic
345	#555	Dic₇	1	1	yes	characteristic
346	#554	Dic₇	1	1	yes	characteristic
347	#553	—	2	1	no	—
348	#552	—	2	1	no	—
349	#552	Dic₇	1	1	yes	characteristic
350	#552	Dic₇	1	1	yes	characteristic
351	#551	—	2	1	no	—
352	#551	—	2	1	no	—
353	#547	Dic₇	1	1	yes	characteristic
354	#546	Dic₇	1	1	yes	characteristic
355	#546	Dic₇	1	1	yes	characteristic
356	#533	C₂×D₇	1	1	yes	characteristic
357	#529	—	2	1	no	—
358	#529	—	2	1	no	—
359	#529	C₂×D₇	1	1	yes	characteristic
360	#529	C₂×D₇	1	1	yes	characteristic
361	#525	—	2	1	no	—
362	C₄×#41	C₂×D₇	1	1	yes	characteristic
363	C₄×#41	C₂×D₇	1	1	yes	characteristic
364	C₄×#41	C₂×D₇	1	1	yes	characteristic
365	C₂×C₄×D₄	C₂×D₇	1	1	yes	characteristic
366	C₂×#117	—	2	1	no	—
367	#446	—	14	1	no	—
368	#436	—	14	1	no	—
369	#435	—	14	1	no	—
370	#435	—	14	1	no	—
371	#433	—	14	1	no	—
372	#433	—	14	1	no	—
373	#432	—	7	1	no	—
374	#432	—	7	1	no	—
375	#431	—	7	1	no	—
376	#431	—	7	1	no	—
377	#431	—	7	1	no	—
378	#431	—	7	1	no	—
379	#431	—	7	1	no	—
380	#423	—	7	1	no	—
381	C₂×C₄⋊C₈	—	7	1	no	—
382	#408	—	14	1	no	—
383	#405	—	14	1	no	—
384	C₄×M₁₆	—	7	1	no	—
385	C₄×M₁₆	—	7	1	no	—
386	C₂×C₄×C₈	—	7	1	no	—
387	Q₈⋊C₈	—	7	1	no	—
388	Q₈⋊C₈	—	7	1	no	—
389	Q₈⋊C₈	—	7	1	no	—
390	Q₈⋊C₈	—	7	1	no	—
391	Q₈⋊C₈	—	7	1	no	—
392	Q₈⋊C₈	—	7	1	no	—
393	Q₈⋊C₈	—	7	1	no	—
394	Q₈⋊C₈	—	7	1	no	—
395	D₄⋊C₈	—	7	1	no	—
396	D₄⋊C₈	—	7	1	no	—
397	D₄⋊C₈	—	7	1	no	—
398	D₄⋊C₈	—	7	1	no	—
399	D₄⋊C₈	—	7	1	no	—
400	D₄⋊C₈	—	7	1	no	—
401	D₄⋊C₈	—	7	1	no	—
402	D₄⋊C₈	—	7	1	no	—
403	C₂³×C₇	—	2	1	no	—
404	C₂³×C₇	—	2	1	no	—
405	C₂³×C₇	—	4	2	no	—
406	C₂³×C₇	—	4	2	no	—
407	C₂³×C₇	—	8	1	no	—
408	C₂³×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
409	C₂³×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
410	C₂³×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
411	C₇×Q₈	—	2	1	no	—
412	C₇×Q₈	—	2	1	no	—
413	C₇×Q₈	—	2	1	no	—
414	C₇×Q₈	—	2	1	no	—
415	C₇×Q₈	—	4	1	no	—
416	C₇×Q₈	—	8	1	no	—
417	C₇×D₄	—	2	1	no	—
418	C₇×D₄	—	2	1	no	—
419	C₇×D₄	—	2	1	no	—
420	C₇×D₄	—	4	1	no	—
421	C₇×D₄	—	4	1	no	—
422	C₇×D₄	—	4	1	no	—
423	C₇×D₄	—	4	2	no	—
424	C₇×D₄	—	4	2	no	—
425	C₇×D₄	—	4	2	no	—
426	C₇×D₄	—	8	1	no	—
427	C₇×D₄	—	8	1	no	—
428	C₇×D₄	#131	1	2	yes	—
429	C₂×C₄×C₇	—	2	1	no	—
430	C₂×C₄×C₇	—	2	1	no	—
431	C₂×C₄×C₇	—	2	1	no	—
432	C₂×C₄×C₇	—	2	1	no	—
433	C₂×C₄×C₇	—	2	1	no	—
434	C₂×C₄×C₇	—	2	1	no	—
435	C₂×C₄×C₇	—	2	1	no	—
436	C₂×C₄×C₇	—	2	1	no	—
437	C₂×C₄×C₇	—	2	1	no	—
438	C₂×C₄×C₇	—	2	1	no	—
439	C₂×C₄×C₇	—	2	1	no	—
440	C₂×C₄×C₇	—	2	1	no	—
441	C₂×C₄×C₇	—	2	1	no	—
442	C₂×C₄×C₇	—	2	1	no	—
443	C₂×C₄×C₇	—	2	1	no	—
444	C₂×C₄×C₇	—	2	1	no	—
445	C₂×C₄×C₇	—	2	1	no	—
446	C₂×C₄×C₇	—	2	1	no	—
447	C₂×C₄×C₇	—	4	1	no	—
448	C₂×C₄×C₇	—	4	1	no	—
449	C₂×C₄×C₇	—	4	1	no	—
450	C₂×C₄×C₇	—	4	2	no	—
451	C₂×C₄×C₇	—	4	2	no	—
452	C₂×C₄×C₇	—	4	2	no	—
453	C₂×C₄×C₇	—	4	2	no	—
454	C₂×C₄×C₇	—	4	2	no	—
455	C₂×C₄×C₇	—	4	1	no	—
456	C₂×C₄×C₇	—	4	1	no	—
457	C₂×C₄×C₇	—	4	1	no	—
458	C₂×C₄×C₇	—	4	1	no	—
459	C₂×C₄×C₇	—	8	1	no	—
460	C₂×C₄×C₇	—	8	1	no	—
461	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
462	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
463	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
464	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
465	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
466	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
467	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
468	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
469	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
470	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
471	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
473	C₇⋊C₈	—	2	2	no	—
474	C₇⋊C₈	—	4	1	no	—
475	C₇⋊C₈	—	4	1	no	—
476	C₇⋊C₈	—	4	1	no	—
477	C₇⋊C₈	—	4	1	no	—
478	C₇⋊C₈	—	4	1	no	—
479	C₇⋊C₈	—	4	1	no	—
480	C₇⋊C₈	—	4	1	no	—
481	C₂×#41	C₂×Dic₇	1	1	yes	characteristic
482	C₂×#41	C₂×Dic₇	1	1	yes	characteristic
483	C₂×#41	C₂²⋊D₇	1	1	yes	characteristic
484	C₂²×D₄	C₂×Dic₇	1	1	yes	characteristic
485	C₂³×C₄	—	2	1	no	—
486	C₂×M₁₆	—	14	1	no	—
487	C₂×M₁₆	—	14	1	no	—
488	C₂×M₁₆	—	14	1	no	—
489	C₂²×C₈	—	14	1	no	—
490	C₂²×C₈	—	14	1	no	—
491	C₄⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
492	C₄⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
493	#126	—	2	1	no	—
494	#126	—	2	1	no	—
495	#126	—	2	1	no	—
496	#126	—	2	1	no	—
497	#126	—	2	1	no	—
498	#126	—	2	1	no	—
499	#125	—	2	1	no	—
500	#125	—	2	1	no	—
501	#125	—	2	1	no	—
502	#125	C₂×Dic₇	1	1	yes	characteristic
503	#125	C₂×Dic₇	1	1	yes	characteristic
504	#124	—	2	1	no	—
505	#124	—	2	1	no	—
506	#124	C₂×Dic₇	1	1	yes	characteristic
507	#124	C₂×Dic₇	1	1	yes	characteristic
508	#123	—	2	1	no	—
509	#123	—	2	1	no	—
510	#123	—	2	1	no	—
511	#123	—	2	1	no	—
512	#123	—	2	1	no	—
513	#123	—	2	1	no	—
514	#123	—	2	1	no	—
515	#123	—	2	1	no	—
516	C₂²⋊Q₈	—	2	1	no	—
517	C₂²⋊Q₈	—	2	1	no	—
518	C₂²⋊Q₈	—	2	1	no	—
519	C₂²⋊Q₈	—	2	1	no	—
520	C₂²⋊Q₈	—	2	1	no	—
521	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
522	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
523	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
524	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
525	#121	—	2	1	no	—
526	#121	—	2	1	no	—
527	#121	—	2	1	no	—
528	#121	—	2	1	no	—
529	#121	C₂×Dic₇	1	1	yes	characteristic
530	#121	C₂×Dic₇	1	1	yes	characteristic
531	#120	—	2	1	no	—
532	#120	—	2	1	no	—
533	C₄×Q₈	—	2	1	no	—
534	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
535	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
536	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
537	C₄×Q₈	C₂²⋊D₇	1	1	yes	characteristic
538	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
539	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
540	C₄×D₄	—	2	1	no	—
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	—	2	1	no	—
543	C₄×D₄	—	2	1	no	—
544	C₄×D₄	—	2	1	no	—
545	C₄×D₄	—	2	1	no	—
546	C₄×D₄	—	2	1	no	—
547	C₄×D₄	—	2	1	no	—
548	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
549	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
550	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
551	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
552	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
553	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
554	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
555	C₄×D₄	C₂²⋊D₇	1	1	yes	characteristic
556	C₄×D₄	C₂²⋊D₇	1	1	yes	characteristic
557	C₄×D₄	C₂²⋊D₇	1	1	yes	characteristic
558	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
559	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
560	#117	—	2	1	no	—
561	#117	—	2	1	no	—
562	#117	—	2	1	no	—
563	#117	—	2	1	no	—
564	#117	—	2	1	no	—
565	#117	—	2	1	no	—
566	#117	—	2	1	no	—
567	#117	—	2	1	no	—
568	#117	—	2	1	no	—
569	#117	C₂×Dic₇	1	1	yes	characteristic
570	#117	C₂×Dic₇	1	1	yes	characteristic
571	#117	C₂²⋊D₇	1	1	yes	characteristic
572	#117	C₂²⋊D₇	1	1	yes	characteristic
573	#117	C₂²⋊D₇	1	1	yes	characteristic
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₄²	—	2	1	no	—
581	C₂×C₄²	—	2	1	no	—
582	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
583	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
584	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
585	C₄⋊C₈	—	7	1	no	—
586	C₄⋊C₈	—	7	1	no	—
587	C₄⋊C₈	—	7	1	no	—
588	C₄⋊C₈	—	7	1	no	—
589	C₄⋊C₈	—	14	1	no	—
590	C₄⋊C₈	—	14	1	no	—
591	C₄⋊C₈	—	14	1	no	—
592	C₄⋊C₈	—	14	1	no	—
593	C₄⋊C₈	—	14	1	no	—
594	C₂²⋊C₈	—	14	1	no	—
595	C₂²⋊C₈	—	14	1	no	—
596	C₂²⋊C₈	—	14	1	no	—
597	C₂²⋊C₈	—	14	1	no	—
598	C₂²⋊C₈	—	14	1	no	—
599	C₂²⋊C₈	—	14	1	no	—
600	C₂²⋊C₈	—	14	1	no	—
601	#97	—	14	1	no	—
602	#97	—	14	1	no	—
603	#97	—	14	1	no	—
604	#97	—	14	1	no	—
605	C₄×C₈	—	7	1	no	—
606	C₄×C₈	—	7	1	no	—
607	C₄×C₈	—	7	1	no	—
608	C₄×C₈	—	7	1	no	—
609	C₄×C₈	—	14	1	no	—
610	C₄×C₈	—	14	1	no	—
611	C₄×C₈	—	14	1	no	—
612	C₂²×C₇	—	2	1	no	—
613	C₂²×C₇	—	2	1	no	—
614	C₂²×C₇	—	2	1	no	—
615	C₂²×C₇	—	2	2	no	—
616	C₂²×C₇	—	2	1	no	—
617	C₂²×C₇	—	2	1	no	—
618	C₂²×C₇	—	2	1	no	—
619	C₂²×C₇	—	2	1	no	—
620	C₂²×C₇	—	2	1	no	—
621	C₂²×C₇	—	2	1	no	—
622	C₂²×C₇	—	4	1	no	—
623	C₂²×C₇	—	4	1	no	—
624	C₂²×C₇	—	4	1	no	—
625	C₂²×C₇	—	4	1	no	—
626	C₂²×C₇	—	4	1	no	—
627	C₂²×C₇	—	8	4	no	—
628	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
629	C₄×C₇	—	2	1	no	—
630	C₄×C₇	—	2	1	no	—
631	C₄×C₇	—	2	1	no	—
632	C₄×C₇	—	2	1	no	—
633	C₄×C₇	—	2	1	no	—
634	C₄×C₇	—	2	1	no	—
635	C₄×C₇	—	2	1	no	—
636	C₄×C₇	—	2	1	no	—
637	C₄×C₇	—	2	1	no	—
638	C₄×C₇	—	2	1	no	—
639	C₄×C₇	—	4	1	no	—
640	C₄×C₇	—	4	1	no	—
641	C₄×C₇	—	4	1	no	—
642	C₄×C₇	—	4	1	no	—
643	C₄×C₇	—	4	1	no	—
644	C₄×C₇	—	4	1	no	—
645	C₄×C₇	C₂×#131	1	1	yes	characteristic
646	C₄×C₇	#568	1	1	yes	characteristic
647	C₄×C₇	#575	1	1	yes	characteristic
648	C₄×C₇	#575	1	1	yes	characteristic
649	C₂⁴	—	2	1	no	—
650	#41	—	2	2	no	—
651	#41	—	2	2	no	—
652	#41	—	4	1	no	—
653	#41	—	4	1	no	—
654	#41	—	4	1	no	—
655	#41	—	4	1	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	C₂²⋊Dic₇	1	1	yes	characteristic
658	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
659	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	4	1	no	—
667	C₂×D₄	C₂²⋊Dic₇	1	1	yes	characteristic
668	C₂×D₄	C₂²⋊Dic₇	1	1	yes	characteristic
669	C₂×D₄	C₂²⋊Dic₇	1	1	yes	characteristic
670	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
671	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
684	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
685	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
686	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
687	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
688	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
689	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
690	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
691	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
692	M₁₆	—	28	2	no	—
693	M₁₆	—	28	2	no	—
694	M₁₆	—	28	2	no	—
695	C₂×C₈	—	14	1	no	—
696	C₂×C₈	—	14	1	no	—
697	C₂×C₈	—	14	1	no	—
698	C₂×C₈	—	14	1	no	—
699	C₂×C₈	—	14	1	no	—
700	C₂×C₈	—	14	1	no	—
701	C₂×C₈	—	14	1	no	—
702	C₂×C₈	—	14	1	no	—
703	C₂×C₈	—	28	2	no	—
704	C₂×C₈	—	28	2	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
722	C₄⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
723	C₄⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
724	C₄⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
725	C₄⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
726	C₄⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
727	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
728	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
729	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
730	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	1	no	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	1	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
750	C₂²⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
751	C₂²⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
752	C₂²⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
753	C₂²⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
754	C₂²⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
755	C₄²	—	2	1	no	—
756	C₄²	—	2	1	no	—
757	C₄²	—	2	1	no	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	1	no	—
761	C₄²	C₂²×Dic₇	1	1	yes	characteristic
762	C₄²	C₂²×Dic₇	1	1	yes	characteristic
763	C₄²	C₂²×Dic₇	1	1	yes	characteristic
764	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
765	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
766	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
767	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
768	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
769	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
770	C₄²	C₂³×D₇	1	1	yes	characteristic
771	C₂×C₇	—	4	1	no	—
772	C₂×C₇	—	4	1	no	—
773	C₂×C₇	—	4	1	no	—
774	C₂×C₇	—	4	2	no	—
775	C₂×C₇	—	8	1	no	—
776	C₂×C₇	#2880	1	1	yes	characteristic
777	C₂×C₇	#2896	1	1	yes	characteristic
778	C₂×C₇	#2901	1	1	yes	characteristic
779	C₂³	—	2	1	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	4	2	no	—
782	C₂³	—	4	2	no	—
783	C₂³	—	8	1	no	—
784	C₂³	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
785	C₂³	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
786	C₂³	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
787	Q₈	—	2	1	no	—
788	Q₈	—	2	1	no	—
789	Q₈	—	2	1	no	—
790	Q₈	—	2	1	no	—
791	Q₈	—	4	1	no	—
792	Q₈	—	8	1	no	—
793	D₄	—	2	1	no	—
794	D₄	—	2	1	no	—
795	D₄	—	2	1	no	—
796	D₄	—	4	1	no	—
797	D₄	—	4	1	no	—
798	D₄	—	4	1	no	—
799	D₄	—	4	2	no	—
800	D₄	—	4	2	no	—
801	D₄	—	4	2	no	—
802	D₄	—	8	1	no	—
803	D₄	—	8	1	no	—
804	D₄	#6511	1	2	yes	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	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	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	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	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	2	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	8	1	no	—
836	C₂×C₄	—	8	1	no	—
837	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
838	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
839	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
840	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
841	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
842	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
843	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
844	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
845	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
846	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
847	C₂×C₄	C₂²×C₂²⋊D₇	1	1	yes	characteristic
848	C₂×C₄	C₂²×C₂²⋊D₇	1	1	yes	characteristic
849	C₈	—	14	2	no	—
850	C₈	—	28	1	no	—
851	C₈	—	28	1	no	—
852	C₈	—	28	1	no	—
853	C₈	—	28	1	no	—
854	C₈	—	28	1	no	—
855	C₈	—	28	1	no	—
856	C₈	—	28	1	no	—
857	C₇	#17513	1	1	yes	characteristic, complemented, Sylow
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	1	no	—
866	C₂²	—	2	1	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	8	4	no	—
874	C₂²	C₂²×C₂²⋊Dic₇	1	1	yes	characteristic
875	C₄	—	2	1	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	1	no	—
878	C₄	—	2	1	no	—
879	C₄	—	2	1	no	—
880	C₄	—	2	1	no	—
881	C₄	—	2	1	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	1	no	—
884	C₄	—	2	1	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	1	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	1	no	—
890	C₄	—	4	1	no	—
891	C₄	C₂×#6511	1	1	yes	characteristic
892	C₄	#90510	1	1	yes	characteristic
893	C₄	#90513	1	1	yes	characteristic
894	C₄	#90513	1	1	yes	characteristic
895	C₂	—	4	1	no	—
896	C₂	—	4	1	no	—
897	C₂	—	4	1	no	—
898	C₂	—	4	2	no	—
899	C₂	—	8	1	no	—
900	C₂	#11741517	1	1	yes	characteristic
901	C₂	#11741520	1	1	yes	characteristic
902	C₂	#11741565	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting, prime radical	C₇×#3475	C₂
socle	C₂²×C₇	C₂²×C₂²⋊C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#3475	D₇
hypocenter	C₇	#17513
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #3475

Complements

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

N	H ≅ G/N	type
2. #11739962	C₂	semidirect
3. #11739960	C₂	semidirect
4. #11729581	C₂	semidirect
5. #11729579	C₂	semidirect
6. #11729507	C₂	semidirect
7. #11729506	C₂	semidirect
8. #11729505	C₂	semidirect
9. #11729504	C₂	semidirect
10. #11729395	C₂	semidirect
11. #11729394	C₂	semidirect
12. #11729393	C₂	semidirect
13. #11729392	C₂	semidirect
14. #11729353	C₂	semidirect
15. #11729351	C₂	semidirect
48. #89698	C₂²	semidirect
51. #89697	C₂²	semidirect
52. #89697	C₂²	semidirect
53. #89697	C₂²	semidirect
54. #89696	C₂²	semidirect
55. C₂×C₄⋊(C₇⋊C₈)	C₂²	semidirect
57. C₄×#1136	C₂²	semidirect
58. C₂×C₄×C₇⋊C₈	C₂²	semidirect
59. Q₈⋊(C₇⋊C₈)	C₂²	semidirect
60. Q₈⋊(C₇⋊C₈)	C₂²	semidirect
61. Q₈⋊(C₇⋊C₈)	C₂²	semidirect
62. Q₈⋊(C₇⋊C₈)	C₂²	semidirect
63. Q₈⋊(C₇⋊C₈)	C₂²	semidirect
64. Q₈⋊(C₇⋊C₈)	C₂²	semidirect
65. Q₈⋊(C₇⋊C₈)	C₂²	semidirect
66. Q₈⋊(C₇⋊C₈)	C₂²	semidirect
857. C₇	#17513	semidirect

Maximal subgroups

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

subgroup	index
C₇×#3475	2
#11739962	2
#11739960	2
#11729581	2
#11729579	2
#11729507	2
#11729506	2
#11729505	2
#11729504	2
#11729395	2
#11729394	2
#11729393	2
#11729392	2
#11729353	2
#11729351	2
#17513	7