Subgroups — #13320644

Order 1792.

890 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3461	C₂	1	1	yes	maximal, characteristic
2	#11739966	C₂	1	1	yes	maximal, characteristic, complemented
3	#11739962	C₂	1	1	yes	maximal, characteristic, complemented
4	#11729581	C₂	1	1	yes	maximal, characteristic, complemented
5	#11729580	C₂	1	1	yes	maximal, characteristic, complemented
6	#11729579	C₂	1	1	yes	maximal, characteristic, complemented
7	#11729578	C₂	1	1	yes	maximal, characteristic, complemented
8	#11729507	C₂	1	1	yes	maximal, characteristic, complemented
9	#11729506	C₂	1	1	yes	maximal, characteristic, complemented
10	#11729505	C₂	1	1	yes	maximal, characteristic, complemented
11	#11729504	C₂	1	1	yes	maximal, characteristic, complemented
12	#11729395	C₂	1	1	yes	maximal, characteristic, complemented
13	#11729394	C₂	1	1	yes	maximal, characteristic, complemented
14	#11729377	C₂	1	1	yes	maximal, characteristic, complemented
15	#11729376	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#544	C₄	1	1	yes	characteristic
17	C₇×#542	—	2	1	no	—
18	C₇×#542	C₄	1	1	yes	characteristic
19	C₇×#542	C₄	1	1	yes	characteristic
20	C₇×#541	—	2	1	no	—
21	C₇×#541	C₄	1	1	yes	characteristic
22	C₇×#541	C₄	1	1	yes	characteristic
23	C₇×#539	—	2	1	no	—
24	C₇×#539	—	2	1	no	—
25	C₇×#537	C₄	1	1	yes	characteristic
26	C₇×#536	C₄	1	1	yes	characteristic
27	C₇×#536	C₄	1	1	yes	characteristic
28	C₇×#533	—	2	1	no	—
29	C₇×#533	C₂²	1	1	yes	characteristic
30	C₇×#533	C₂²	1	1	yes	characteristic
31	C₇×#529	—	2	1	no	—
32	C₇×#529	—	2	1	no	—
33	C₇×#529	—	2	1	no	—
34	C₇×#529	C₂²	1	1	yes	characteristic
35	C₇×#529	C₂²	1	1	yes	characteristic
36	C₄×C₇×#41	C₂²	1	1	yes	characteristic
37	C₄×C₇×#41	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
39	#89796	—	2	1	no	—
40	#89796	—	2	1	no	—
41	#89784	—	2	1	no	—
42	#89784	—	2	1	no	—
43	#89783	—	2	1	no	—
44	#89783	—	2	1	no	—
45	#89783	—	2	1	no	—
46	#89783	—	2	1	no	—
47	#89698	C₂²	1	1	yes	characteristic
48	#89698	C₂²	1	1	yes	characteristic
49	#89697	C₂²	1	1	yes	characteristic
50	#89697	C₂²	1	1	yes	characteristic
51	#89697	C₂²	1	1	yes	characteristic
52	#89697	C₂²	1	1	yes	characteristic
53	#89696	C₂²	1	1	yes	characteristic
54	#89696	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
56	C₄×#1136	C₂²	1	1	yes	characteristic
57	C₄×#1136	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
59	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
60	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
61	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
62	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
63	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
64	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
65	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
66	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
67	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
68	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
69	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
70	Q₈⋊(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	#17506	—	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	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
79	C₇×C₄⋊Q₈	—	2	1	no	—
80	C₇×C₄⋊Q₈	—	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×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
84	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
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×#126	—	2	1	no	—
90	C₇×#126	—	2	1	no	—
91	C₇×#126	—	2	1	no	—
92	C₇×#126	—	2	1	no	—
93	C₇×#125	—	2	1	no	—
94	C₇×#125	—	2	1	no	—
95	C₇×#125	—	2	1	no	—
96	C₇×#125	—	2	1	no	—
97	C₇×#125	—	2	1	no	—
98	C₇×#125	—	2	1	no	—
99	C₇×#125	—	2	1	no	—
100	C₇×#125	C₂×C₄	1	1	yes	characteristic
101	C₇×#125	C₂×C₄	1	1	yes	characteristic
102	C₇×#124	—	2	1	no	—
103	C₇×#124	—	2	1	no	—
104	C₇×#124	—	2	1	no	—
105	C₇×#124	C₂×C₄	1	1	yes	characteristic
106	C₇×#124	C₂×C₄	1	1	yes	characteristic
107	C₇×#123	—	2	1	no	—
108	C₇×#123	—	2	1	no	—
109	C₇×#123	—	2	1	no	—
110	C₇×#123	—	2	1	no	—
111	C₇×#123	—	2	1	no	—
112	C₇×#123	—	2	1	no	—
113	C₇×#123	—	2	1	no	—
114	C₇×#123	—	2	1	no	—
115	C₇×C₂²⋊Q₈	—	2	1	no	—
116	C₇×C₂²⋊Q₈	—	2	1	no	—
117	C₇×C₂²⋊Q₈	—	2	1	no	—
118	C₇×C₂²⋊Q₈	—	2	1	no	—
119	C₇×C₂²⋊Q₈	—	2	1	no	—
120	C₇×C₂²⋊Q₈	—	2	1	no	—
121	C₇×C₂²⋊Q₈	—	2	1	no	—
122	C₇×C₂²⋊Q₈	—	2	1	no	—
123	C₇×C₂²⋊Q₈	—	2	1	no	—
124	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
125	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
126	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
127	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
128	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
129	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
130	C₇×#121	—	2	1	no	—
131	C₇×#121	—	2	1	no	—
132	C₇×#121	—	2	1	no	—
133	C₇×#121	C₂×C₄	1	1	yes	characteristic
134	C₇×#121	C₂×C₄	1	1	yes	characteristic
135	C₄×C₇×Q₈	—	2	1	no	—
136	C₄×C₇×Q₈	—	2	1	no	—
137	C₄×C₇×Q₈	—	2	1	no	—
138	C₄×C₇×Q₈	—	2	1	no	—
139	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
140	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
141	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
142	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
143	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
144	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
145	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
146	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
147	C₄×C₇×D₄	—	2	1	no	—
148	C₄×C₇×D₄	—	2	1	no	—
149	C₄×C₇×D₄	—	2	1	no	—
150	C₄×C₇×D₄	—	2	1	no	—
151	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
152	C₄×C₇×D₄	D₄	1	1	yes	characteristic
153	C₄×C₇×D₄	D₄	1	1	yes	characteristic
154	C₄×C₇×D₄	D₄	1	1	yes	characteristic
155	C₄×C₇×D₄	D₄	1	1	yes	characteristic
156	C₄×C₇×D₄	D₄	1	1	yes	characteristic
157	C₄×C₇×D₄	D₄	1	1	yes	characteristic
158	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
159	C₇×#117	—	2	1	no	—
160	C₇×#117	—	2	1	no	—
161	C₇×#117	—	2	1	no	—
162	C₇×#117	—	2	1	no	—
163	C₇×#117	—	2	1	no	—
164	C₇×#117	C₂×C₄	1	1	yes	characteristic
165	C₇×#117	C₂×C₄	1	1	yes	characteristic
166	C₇×#117	C₂×C₄	1	1	yes	characteristic
167	C₇×#117	C₂×C₄	1	1	yes	characteristic
168	C₂×C₇×C₄⋊C₄	—	2	1	no	—
169	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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	C₂×#1136	—	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)	—	2	1	no	—
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	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
197	#6377	—	2	1	no	—
198	#6377	—	2	1	no	—
199	#6377	—	2	1	no	—
200	#6377	—	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	#3461	D₇	1	1	yes	characteristic
208	#2989	—	7	1	no	—
209	#2965	—	7	1	no	—
210	#1497	—	7	1	no	—
211	#1495	—	7	1	no	—
212	#1494	—	7	1	no	—
213	#1493	—	7	1	no	—
214	#1491	—	7	1	no	—
215	#1489	—	7	1	no	—
216	#1488	—	7	1	no	—
217	#1487	—	7	1	no	—
218	#1485	—	7	1	no	—
219	#1483	—	7	1	no	—
220	#1482	—	7	1	no	—
221	#1481	—	7	1	no	—
222	C₇×#41	—	4	2	no	—
223	C₇×#41	—	4	2	no	—
224	C₂×C₇×Q₈	—	2	1	no	—
225	C₂×C₇×Q₈	—	2	1	no	—
226	C₂×C₇×Q₈	—	2	1	no	—
227	C₂×C₇×Q₈	—	4	2	no	—
228	C₂×C₇×Q₈	C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
230	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
231	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
232	C₂×C₇×D₄	—	2	1	no	—
233	C₂×C₇×D₄	—	2	1	no	—
234	C₂×C₇×D₄	—	2	1	no	—
235	C₂×C₇×D₄	C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₇×D₄	C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₇×D₄	C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
239	C₂²×C₄×C₇	—	2	1	no	—
240	C₂²×C₄×C₇	—	2	1	no	—
241	C₂²×C₄×C₇	—	2	1	no	—
242	C₂²×C₄×C₇	—	2	1	no	—
243	C₂²×C₄×C₇	—	2	1	no	—
244	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
245	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
246	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
247	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
253	C₇×C₄⋊C₄	—	2	1	no	—
254	C₇×C₄⋊C₄	—	2	1	no	—
255	C₇×C₄⋊C₄	—	2	1	no	—
256	C₇×C₄⋊C₄	—	2	1	no	—
257	C₇×C₄⋊C₄	—	2	1	no	—
258	C₇×C₄⋊C₄	—	2	1	no	—
259	C₇×C₄⋊C₄	—	2	1	no	—
260	C₇×C₄⋊C₄	—	2	1	no	—
261	C₇×C₄⋊C₄	—	2	1	no	—
262	C₇×C₄⋊C₄	—	2	1	no	—
263	C₇×C₄⋊C₄	—	2	1	no	—
264	C₇×C₄⋊C₄	—	2	1	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
277	C₇×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
278	C₇×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
279	C₇×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
280	C₇×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
287	C₇×C₂²⋊C₄	—	2	1	no	—
288	C₇×C₂²⋊C₄	—	2	1	no	—
289	C₇×C₂²⋊C₄	—	2	1	no	—
290	C₇×C₂²⋊C₄	—	2	1	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
302	C₇×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
303	C₇×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
304	C₇×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
305	C₇×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
306	C₇×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
307	C₄²×C₇	—	2	1	no	—
308	C₄²×C₇	—	2	1	no	—
309	C₄²×C₇	—	2	1	no	—
310	C₄²×C₇	—	2	1	no	—
311	C₄²×C₇	—	2	1	no	—
312	C₄²×C₇	—	2	1	no	—
313	C₄²×C₇	—	2	1	no	—
314	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
315	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
316	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
317	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₇	C₂⁴	1	1	yes	characteristic
324	#1136	—	4	2	no	—
325	#1136	—	4	2	no	—
326	#1136	—	8	1	no	—
327	#1136	—	8	1	no	—
328	C₂×C₇⋊C₈	—	2	1	no	—
329	C₂×C₇⋊C₈	—	2	1	no	—
330	C₂×C₇⋊C₈	—	2	1	no	—
331	C₂×C₇⋊C₈	—	2	1	no	—
332	C₂×C₇⋊C₈	—	2	1	no	—
333	C₂×C₇⋊C₈	—	2	1	no	—
334	C₂×C₇⋊C₈	—	2	1	no	—
335	C₂×C₇⋊C₈	—	2	1	no	—
336	C₂×C₇⋊C₈	—	4	2	no	—
337	C₂×C₇⋊C₈	—	8	1	no	—
338	#544	Dic₇	1	1	yes	characteristic
339	#542	—	2	1	no	—
340	#542	Dic₇	1	1	yes	characteristic
341	#542	Dic₇	1	1	yes	characteristic
342	#541	—	2	1	no	—
343	#541	Dic₇	1	1	yes	characteristic
344	#541	Dic₇	1	1	yes	characteristic
345	#539	—	2	1	no	—
346	#539	—	2	1	no	—
347	#537	Dic₇	1	1	yes	characteristic
348	#536	Dic₇	1	1	yes	characteristic
349	#536	Dic₇	1	1	yes	characteristic
350	#533	—	2	1	no	—
351	#533	C₂×D₇	1	1	yes	characteristic
352	#533	C₂×D₇	1	1	yes	characteristic
353	#529	—	2	1	no	—
354	#529	—	2	1	no	—
355	#529	—	2	1	no	—
356	#529	C₂×D₇	1	1	yes	characteristic
357	#529	C₂×D₇	1	1	yes	characteristic
358	C₄×#41	C₂×D₇	1	1	yes	characteristic
359	C₄×#41	C₂×D₇	1	1	yes	characteristic
360	C₂×C₄×Q₈	C₂×D₇	1	1	yes	characteristic
361	#446	—	14	1	no	—
362	#446	—	14	1	no	—
363	#436	—	14	1	no	—
364	#436	—	14	1	no	—
365	#435	—	14	1	no	—
366	#435	—	14	1	no	—
367	#435	—	14	1	no	—
368	#435	—	14	1	no	—
369	#432	—	7	1	no	—
370	#432	—	7	1	no	—
371	#431	—	7	1	no	—
372	#431	—	7	1	no	—
373	#431	—	7	1	no	—
374	#431	—	7	1	no	—
375	#423	—	7	1	no	—
376	#423	—	7	1	no	—
377	C₂×C₄⋊C₈	—	7	1	no	—
378	C₄×M₁₆	—	7	1	no	—
379	C₄×M₁₆	—	7	1	no	—
380	C₂×C₄×C₈	—	7	1	no	—
381	Q₈⋊C₈	—	7	1	no	—
382	Q₈⋊C₈	—	7	1	no	—
383	Q₈⋊C₈	—	7	1	no	—
384	Q₈⋊C₈	—	7	1	no	—
385	Q₈⋊C₈	—	7	1	no	—
386	Q₈⋊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	D₄⋊C₈	—	7	1	no	—
394	D₄⋊C₈	—	7	1	no	—
395	D₄⋊C₈	—	7	1	no	—
396	D₄⋊C₈	—	7	1	no	—
397	C₂³×C₇	—	2	1	no	—
398	C₂³×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
399	C₂³×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
400	C₂³×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
401	C₇×Q₈	—	2	2	no	—
402	C₇×Q₈	—	2	2	no	—
403	C₇×Q₈	—	2	2	no	—
404	C₇×Q₈	—	4	1	no	—
405	C₇×Q₈	—	4	2	no	—
406	C₇×Q₈	—	8	1	no	—
407	C₇×Q₈	—	8	1	no	—
408	C₇×D₄	—	2	2	no	—
409	C₇×D₄	—	4	1	no	—
410	C₇×D₄	—	4	1	no	—
411	C₇×D₄	—	4	1	no	—
412	C₇×D₄	—	4	2	no	—
413	C₇×D₄	—	8	1	no	—
414	C₇×D₄	—	8	1	no	—
415	C₂×C₄×C₇	—	2	2	no	—
416	C₂×C₄×C₇	—	2	2	no	—
417	C₂×C₄×C₇	—	2	2	no	—
418	C₂×C₄×C₇	—	2	1	no	—
419	C₂×C₄×C₇	—	2	1	no	—
420	C₂×C₄×C₇	—	2	1	no	—
421	C₂×C₄×C₇	—	2	1	no	—
422	C₂×C₄×C₇	—	2	1	no	—
423	C₂×C₄×C₇	—	2	1	no	—
424	C₂×C₄×C₇	—	2	1	no	—
425	C₂×C₄×C₇	—	2	1	no	—
426	C₂×C₄×C₇	—	2	1	no	—
427	C₂×C₄×C₇	—	2	1	no	—
428	C₂×C₄×C₇	—	2	1	no	—
429	C₂×C₄×C₇	—	2	1	no	—
430	C₂×C₄×C₇	—	2	1	no	—
431	C₂×C₄×C₇	—	4	1	no	—
432	C₂×C₄×C₇	—	4	1	no	—
433	C₂×C₄×C₇	—	4	1	no	—
434	C₂×C₄×C₇	—	4	2	no	—
435	C₂×C₄×C₇	—	4	2	no	—
436	C₂×C₄×C₇	—	4	1	no	—
437	C₂×C₄×C₇	—	4	1	no	—
438	C₂×C₄×C₇	—	8	1	no	—
439	C₂×C₄×C₇	—	8	1	no	—
440	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
441	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
442	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
443	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
444	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
445	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
446	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
447	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
448	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
449	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
450	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
452	C₇⋊C₈	—	2	2	no	—
453	C₇⋊C₈	—	4	1	no	—
454	C₇⋊C₈	—	4	1	no	—
455	C₇⋊C₈	—	4	1	no	—
456	C₇⋊C₈	—	4	1	no	—
457	C₇⋊C₈	—	4	1	no	—
458	C₇⋊C₈	—	4	1	no	—
459	C₇⋊C₈	—	4	1	no	—
460	C₂×#41	C₂×Dic₇	1	1	yes	characteristic
461	C₂×#41	C₂×Dic₇	1	1	yes	characteristic
462	C₂²×Q₈	C₂×Dic₇	1	1	yes	characteristic
463	C₂×M₁₆	—	14	1	no	—
464	C₂×M₁₆	—	14	1	no	—
465	C₂×M₁₆	—	14	1	no	—
466	C₂×M₁₆	—	14	1	no	—
467	C₂²×C₈	—	14	1	no	—
468	C₂²×C₈	—	14	1	no	—
469	C₄⋊Q₈	—	2	1	no	—
470	C₄⋊Q₈	—	2	1	no	—
471	C₄⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
472	C₄⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
473	C₄⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
474	C₄⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
475	#126	—	2	1	no	—
476	#126	—	2	1	no	—
477	#126	—	2	1	no	—
478	#126	—	2	1	no	—
479	#126	—	2	1	no	—
480	#126	—	2	1	no	—
481	#126	—	2	1	no	—
482	#126	—	2	1	no	—
483	#125	—	2	1	no	—
484	#125	—	2	1	no	—
485	#125	—	2	1	no	—
486	#125	—	2	1	no	—
487	#125	—	2	1	no	—
488	#125	—	2	1	no	—
489	#125	—	2	1	no	—
490	#125	C₂×Dic₇	1	1	yes	characteristic
491	#125	C₂×Dic₇	1	1	yes	characteristic
492	#124	—	2	1	no	—
493	#124	—	2	1	no	—
494	#124	—	2	1	no	—
495	#124	C₂×Dic₇	1	1	yes	characteristic
496	#124	C₂×Dic₇	1	1	yes	characteristic
497	#123	—	2	1	no	—
498	#123	—	2	1	no	—
499	#123	—	2	1	no	—
500	#123	—	2	1	no	—
501	#123	—	2	1	no	—
502	#123	—	2	1	no	—
503	#123	—	2	1	no	—
504	#123	—	2	1	no	—
505	C₂²⋊Q₈	—	2	1	no	—
506	C₂²⋊Q₈	—	2	1	no	—
507	C₂²⋊Q₈	—	2	1	no	—
508	C₂²⋊Q₈	—	2	1	no	—
509	C₂²⋊Q₈	—	2	1	no	—
510	C₂²⋊Q₈	—	2	1	no	—
511	C₂²⋊Q₈	—	2	1	no	—
512	C₂²⋊Q₈	—	2	1	no	—
513	C₂²⋊Q₈	—	2	1	no	—
514	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
515	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
516	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
517	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
518	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
519	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
520	#121	—	2	1	no	—
521	#121	—	2	1	no	—
522	#121	—	2	1	no	—
523	#121	C₂×Dic₇	1	1	yes	characteristic
524	#121	C₂×Dic₇	1	1	yes	characteristic
525	C₄×Q₈	—	2	1	no	—
526	C₄×Q₈	—	2	1	no	—
527	C₄×Q₈	—	2	1	no	—
528	C₄×Q₈	—	2	1	no	—
529	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
530	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
531	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
532	C₄×Q₈	C₂²⋊D₇	1	1	yes	characteristic
533	C₄×Q₈	C₂²⋊D₇	1	1	yes	characteristic
534	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
535	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
536	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
537	C₄×D₄	—	2	1	no	—
538	C₄×D₄	—	2	1	no	—
539	C₄×D₄	—	2	1	no	—
540	C₄×D₄	—	2	1	no	—
541	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
542	C₄×D₄	C₂²⋊D₇	1	1	yes	characteristic
543	C₄×D₄	C₂²⋊D₇	1	1	yes	characteristic
544	C₄×D₄	C₂²⋊D₇	1	1	yes	characteristic
545	C₄×D₄	C₂²⋊D₇	1	1	yes	characteristic
546	C₄×D₄	C₂²⋊D₇	1	1	yes	characteristic
547	C₄×D₄	C₂²⋊D₇	1	1	yes	characteristic
548	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
549	#117	—	2	1	no	—
550	#117	—	2	1	no	—
551	#117	—	2	1	no	—
552	#117	—	2	1	no	—
553	#117	—	2	1	no	—
554	#117	C₂×Dic₇	1	1	yes	characteristic
555	#117	C₂×Dic₇	1	1	yes	characteristic
556	#117	C₂×Dic₇	1	1	yes	characteristic
557	#117	C₂×Dic₇	1	1	yes	characteristic
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
560	C₂×C₄²	—	2	1	no	—
561	C₂×C₄²	—	2	1	no	—
562	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
563	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
564	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
565	C₄⋊C₈	—	7	1	no	—
566	C₄⋊C₈	—	7	1	no	—
567	C₄⋊C₈	—	7	1	no	—
568	C₄⋊C₈	—	7	1	no	—
569	C₄⋊C₈	—	14	1	no	—
570	C₄⋊C₈	—	14	1	no	—
571	C₄⋊C₈	—	14	1	no	—
572	C₄⋊C₈	—	14	1	no	—
573	C₄⋊C₈	—	14	1	no	—
574	C₄⋊C₈	—	14	1	no	—
575	C₂²⋊C₈	—	14	1	no	—
576	C₂²⋊C₈	—	14	1	no	—
577	C₂²⋊C₈	—	14	1	no	—
578	C₂²⋊C₈	—	14	1	no	—
579	C₂²⋊C₈	—	14	1	no	—
580	C₂²⋊C₈	—	14	1	no	—
581	#97	—	14	1	no	—
582	#97	—	14	1	no	—
583	#97	—	14	1	no	—
584	#97	—	14	1	no	—
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	C₂²×C₇	—	2	1	no	—
592	C₂²×C₇	—	2	1	no	—
593	C₂²×C₇	—	2	1	no	—
594	C₂²×C₇	—	2	1	no	—
595	C₂²×C₇	—	2	1	no	—
596	C₂²×C₇	—	2	1	no	—
597	C₂²×C₇	—	2	1	no	—
598	C₂²×C₇	—	2	1	no	—
599	C₂²×C₇	—	2	1	no	—
600	C₂²×C₇	—	4	1	no	—
601	C₂²×C₇	—	4	1	no	—
602	C₂²×C₇	—	4	1	no	—
603	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
604	C₄×C₇	—	2	1	no	—
605	C₄×C₇	—	2	1	no	—
606	C₄×C₇	—	2	1	no	—
607	C₄×C₇	—	2	1	no	—
608	C₄×C₇	—	2	1	no	—
609	C₄×C₇	—	2	1	no	—
610	C₄×C₇	—	2	1	no	—
611	C₄×C₇	—	2	1	no	—
612	C₄×C₇	—	2	1	no	—
613	C₄×C₇	—	2	1	no	—
614	C₄×C₇	—	4	1	no	—
615	C₄×C₇	—	4	1	no	—
616	C₄×C₇	—	4	1	no	—
617	C₄×C₇	—	4	1	no	—
618	C₄×C₇	—	4	1	no	—
619	C₄×C₇	—	4	1	no	—
620	C₄×C₇	—	4	1	no	—
621	C₄×C₇	#568	1	2	yes	—
622	C₄×C₇	#577	1	1	yes	characteristic
623	C₄×C₇	#578	1	1	yes	characteristic
624	#41	—	4	2	no	—
625	#41	—	4	2	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	4	2	no	—
630	C₂×Q₈	C₂²⋊Dic₇	1	1	yes	characteristic
631	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
632	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
633	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	C₂²⋊Dic₇	1	1	yes	characteristic
638	C₂×D₄	C₂²⋊Dic₇	1	1	yes	characteristic
639	C₂×D₄	C₂²⋊Dic₇	1	1	yes	characteristic
640	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
647	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
648	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
649	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
650	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
651	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
652	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
653	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
654	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
655	M₁₆	—	28	2	no	—
656	M₁₆	—	28	2	no	—
657	M₁₆	—	56	1	no	—
658	M₁₆	—	56	1	no	—
659	C₂×C₈	—	14	1	no	—
660	C₂×C₈	—	14	1	no	—
661	C₂×C₈	—	14	1	no	—
662	C₂×C₈	—	14	1	no	—
663	C₂×C₈	—	14	1	no	—
664	C₂×C₈	—	14	1	no	—
665	C₂×C₈	—	14	1	no	—
666	C₂×C₈	—	14	1	no	—
667	C₂×C₈	—	28	2	no	—
668	C₂×C₈	—	56	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
693	C₄⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
694	C₄⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
695	C₄⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
696	C₄⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
697	C₄⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
698	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
699	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
700	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
701	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
702	C₂²⋊C₄	—	2	1	no	—
703	C₂²⋊C₄	—	2	1	no	—
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	2	1	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	2	1	no	—
712	C₂²⋊C₄	—	2	1	no	—
713	C₂²⋊C₄	—	2	1	no	—
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	1	no	—
716	C₂²⋊C₄	—	2	1	no	—
717	C₂²⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
718	C₂²⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
719	C₂²⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
720	C₂²⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
721	C₂²⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
722	C₂²⋊C₄	C₂²⋊Dic₇	1	1	yes	characteristic
723	C₄²	—	2	1	no	—
724	C₄²	—	2	1	no	—
725	C₄²	—	2	1	no	—
726	C₄²	—	2	1	no	—
727	C₄²	—	2	1	no	—
728	C₄²	—	2	1	no	—
729	C₄²	—	2	1	no	—
730	C₄²	C₂²×Dic₇	1	1	yes	characteristic
731	C₄²	C₂²×Dic₇	1	1	yes	characteristic
732	C₄²	C₂²×Dic₇	1	1	yes	characteristic
733	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
734	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
735	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
736	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
737	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
738	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
739	C₄²	C₂³×D₇	1	1	yes	characteristic
740	C₂×C₇	—	4	1	no	—
741	C₂×C₇	—	4	1	no	—
742	C₂×C₇	—	4	1	no	—
743	C₂×C₇	—	8	1	no	—
744	C₂×C₇	#2879	1	1	yes	characteristic
745	C₂×C₇	#2898	1	1	yes	characteristic
746	C₂×C₇	#2901	1	1	yes	characteristic
747	C₂³	—	2	1	no	—
748	C₂³	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
749	C₂³	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
750	C₂³	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
751	Q₈	—	2	2	no	—
752	Q₈	—	2	2	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	4	1	no	—
755	Q₈	—	4	2	no	—
756	Q₈	—	8	1	no	—
757	Q₈	—	8	1	no	—
758	D₄	—	2	2	no	—
759	D₄	—	4	1	no	—
760	D₄	—	4	1	no	—
761	D₄	—	4	1	no	—
762	D₄	—	4	2	no	—
763	D₄	—	8	1	no	—
764	D₄	—	8	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	2	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	8	1	no	—
789	C₂×C₄	—	8	1	no	—
790	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
791	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
792	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
793	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
794	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
795	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
796	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
797	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
798	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
799	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
800	C₂×C₄	C₂²×C₂²⋊D₇	1	1	yes	characteristic
801	C₂×C₄	C₂²×C₂²⋊D₇	1	1	yes	characteristic
802	C₈	—	14	2	no	—
803	C₈	—	28	1	no	—
804	C₈	—	28	1	no	—
805	C₈	—	28	1	no	—
806	C₈	—	28	1	no	—
807	C₈	—	28	1	no	—
808	C₈	—	28	1	no	—
809	C₈	—	28	1	no	—
810	C₇	#17506	1	1	yes	characteristic, complemented, Sylow
811	C₂²	—	2	1	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	C₂²×C₂²⋊Dic₇	1	1	yes	characteristic
824	C₄	—	2	1	no	—
825	C₄	—	2	1	no	—
826	C₄	—	2	1	no	—
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	1	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	1	no	—
841	C₄	#90510	1	2	yes	—
842	C₄	#90528	1	1	yes	characteristic
843	C₄	#90529	1	1	yes	characteristic
844	C₂	—	4	1	no	—
845	C₂	—	4	1	no	—
846	C₂	—	4	1	no	—
847	C₂	—	8	1	no	—
848	C₂	#11741519	1	1	yes	characteristic
849	C₂	#11741556	1	1	yes	characteristic
850	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	C₇×#3461	C₂
socle	C₂²×C₇	C₂²×C₂²⋊C₄
prime radical	C₇×#537	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#3461	D₇
hypocenter	C₇	#17506
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #3461

Complements

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

N	H ≅ G/N	type
2. #11739966	C₂	semidirect
3. #11739962	C₂	semidirect
4. #11729581	C₂	semidirect
5. #11729580	C₂	semidirect
6. #11729579	C₂	semidirect
7. #11729578	C₂	semidirect
8. #11729507	C₂	semidirect
9. #11729506	C₂	semidirect
10. #11729505	C₂	semidirect
11. #11729504	C₂	semidirect
12. #11729395	C₂	semidirect
13. #11729394	C₂	semidirect
14. #11729377	C₂	semidirect
15. #11729376	C₂	semidirect
810. C₇	#17506	semidirect

Maximal subgroups

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

subgroup	index
C₇×#3461	2
#11739966	2
#11739962	2
#11729581	2
#11729580	2
#11729579	2
#11729578	2
#11729507	2
#11729506	2
#11729505	2
#11729504	2
#11729395	2
#11729394	2
#11729377	2
#11729376	2
#17506	7