Subgroups — #14220050

Order 1792.

1664 conjugacy classes of subgroups.

The subgroup lattice has 1090 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	#11740777	C₂	1	1	yes	maximal, characteristic, complemented
3	#11740776	C₂	1	1	yes	maximal, characteristic, complemented
4	#11740776	C₂	1	2	yes	maximal, complemented
5	#11740775	C₂	1	1	yes	maximal, characteristic, complemented
6	#11740774	C₂	1	2	yes	maximal, complemented
7	#11740773	C₂	1	1	yes	maximal, characteristic, complemented
8	#11740578	C₂	1	2	yes	maximal, complemented
9	#11740578	C₂	1	2	yes	maximal, complemented
10	#11740577	C₂	1	1	yes	maximal, characteristic, complemented
11	#11740576	C₂	1	1	yes	maximal, characteristic, complemented
12	#11740576	C₂	1	2	yes	maximal, complemented
13	#11740574	C₂	1	1	yes	maximal, characteristic, complemented
14	#11740574	C₂	1	2	yes	maximal, complemented
15	#11740573	C₂	1	2	yes	maximal, complemented
16	#11740572	C₂	1	2	yes	maximal, complemented
17	#11740571	C₂	1	1	yes	maximal, characteristic, complemented
18	#11739968	C₂	1	1	yes	maximal, characteristic, complemented
19	#11739966	C₂	1	1	yes	maximal, characteristic, complemented
20	#11739963	C₂	1	1	yes	maximal, characteristic, complemented
21	#11739962	C₂	1	1	yes	maximal, characteristic, complemented
22	#11739882	C₂	1	1	yes	maximal, characteristic, complemented
23	Q₈×#1136	C₂	1	1	yes	maximal, characteristic, complemented
24	C₇×#544	C₄	1	1	yes	characteristic
25	C₇×#542	C₄	1	1	yes	characteristic
26	C₇×#542	C₄	1	1	yes	characteristic
27	C₇×#542	C₄	1	2	yes	—
28	C₇×#541	C₄	1	1	yes	characteristic
29	C₇×#541	C₄	1	1	yes	characteristic
30	C₇×#541	C₄	1	2	yes	—
31	C₇×#539	C₄	1	2	yes	—
32	C₇×#539	C₄	1	2	yes	—
33	C₇×#537	C₄	1	1	yes	characteristic
34	C₇×#536	C₄	1	1	yes	characteristic
35	C₇×#536	C₄	1	1	yes	characteristic
36	C₇×#533	C₂²	1	1	yes	characteristic
37	C₇×#533	C₂²	1	2	yes	—
38	C₇×#533	C₂²	1	1	yes	characteristic
39	C₇×#529	C₂²	1	1	yes	characteristic
40	C₇×#529	C₂²	1	2	yes	—
41	C₇×#529	C₂²	1	2	yes	—
42	C₇×#529	C₂²	1	1	yes	characteristic
43	C₇×#529	C₂²	1	2	yes	—
44	C₄×C₇×#41	C₂²	1	1	yes	characteristic
45	C₄×C₇×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
47	#89796	C₂²	1	1	yes	characteristic
48	#89796	C₂²	1	1	yes	characteristic
49	#89796	C₂²	1	1	yes	characteristic
50	#89796	C₂²	1	1	yes	characteristic
51	#89796	C₂²	1	2	yes	—
52	#89796	C₂²	1	2	yes	—
53	#89796	C₂²	1	1	yes	characteristic
54	#89796	C₂²	1	2	yes	—
55	#89796	C₂²	1	2	yes	—
56	#89796	C₂²	1	2	yes	—
57	#89796	C₂²	1	2	yes	—
58	#89796	C₂²	1	2	yes	—
59	#89796	C₂²	1	2	yes	—
60	#89796	C₂²	1	1	yes	characteristic
61	#89796	C₂²	1	2	yes	—
62	#89796	C₂²	1	2	yes	—
63	#89796	C₂²	1	1	yes	characteristic
64	#89796	C₂²	1	2	yes	—
65	#89796	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	2	yes	—
69	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
70	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
71	Q₈×C₇⋊C₈	C₂²	1	2	yes	—
72	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
73	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
74	#89784	C₂²	1	1	yes	characteristic
75	#89784	C₂²	1	1	yes	characteristic
76	#89784	C₂²	1	2	yes	—
77	#89784	C₂²	1	1	yes	characteristic
78	#89784	C₂²	1	2	yes	—
79	#89784	C₂²	1	2	yes	—
80	#89784	C₂²	1	1	yes	characteristic
81	#89784	C₂²	1	2	yes	—
82	#89784	C₂²	1	2	yes	—
83	#89783	C₂²	1	1	yes	characteristic
84	#89783	C₂²	1	1	yes	characteristic
85	#89783	C₂²	1	1	yes	characteristic
86	#89783	C₂²	1	1	yes	characteristic
87	#89783	C₂²	1	2	yes	—
88	#89783	C₂²	1	2	yes	—
89	#89783	C₂²	1	2	yes	—
90	#89783	C₂²	1	2	yes	—
91	#89783	C₂²	1	2	yes	—
92	#89783	C₂²	1	2	yes	—
93	#89783	C₂²	1	2	yes	—
94	#89783	C₂²	1	2	yes	—
95	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
96	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
97	D₄×C₇⋊C₈	C₂²	1	2	yes	—
98	D₄×C₇⋊C₈	C₂²	1	2	yes	—
99	#89772	C₂²	1	2	yes	—
100	#89772	C₂²	1	2	yes	—
101	#89772	C₂²	1	2	yes	—
102	#89772	C₂²	1	2	yes	—
103	#89772	C₂²	1	2	yes	—
104	#89772	C₂²	1	2	yes	—
105	#89772	C₂²	1	2	yes	—
106	#89772	C₂²	1	2	yes	—
107	#89771	C₂²	1	2	yes	—
108	#89771	C₂²	1	2	yes	—
109	#89771	C₂²	1	2	yes	—
110	#89771	C₂²	1	2	yes	—
111	#89769	C₂²	1	2	yes	—
112	#89769	C₂²	1	2	yes	—
113	#89769	C₂²	1	2	yes	—
114	#89769	C₂²	1	2	yes	—
115	#89698	C₂²	1	1	yes	characteristic
116	#89698	C₂²	1	2	yes	—
117	#89698	C₂²	1	1	yes	characteristic
118	#89698	C₂²	1	2	yes	—
119	#89697	C₂²	1	1	yes	characteristic
120	#89697	C₂²	1	1	yes	characteristic
121	#89697	C₂²	1	1	yes	characteristic
122	#89697	C₂²	1	1	yes	characteristic
123	#89697	C₂²	1	2	yes	—
124	#89697	C₂²	1	2	yes	—
125	#89696	C₂²	1	1	yes	characteristic
126	#89696	C₂²	1	1	yes	characteristic
127	#89696	C₂²	1	2	yes	—
128	#89696	C₂²	1	2	yes	—
129	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
130	C₄×#1136	C₂²	1	1	yes	characteristic
131	C₄×#1136	C₂²	1	1	yes	characteristic
132	C₄×#1136	C₂²	1	2	yes	—
133	C₂×#6377	C₂²	1	2	yes	—
134	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
135	#60344	—	7	1	no	maximal, Sylow
136	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
137	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
138	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
139	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
140	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
141	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
142	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
143	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
144	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
145	C₇×#126	C₂×C₄	1	2	yes	—
146	C₇×#126	C₂×C₄	1	2	yes	—
147	C₇×#126	C₂×C₄	1	2	yes	—
148	C₇×#126	C₂×C₄	1	2	yes	—
149	C₇×#126	C₂×C₄	1	2	yes	—
150	C₇×#126	C₂×C₄	1	2	yes	—
151	C₇×#126	C₂×C₄	1	2	yes	—
152	C₇×#126	C₂×C₄	1	2	yes	—
153	C₇×#125	C₂×C₄	1	2	yes	—
154	C₇×#125	C₂×C₄	1	2	yes	—
155	C₇×#125	C₂×C₄	1	1	yes	characteristic
156	C₇×#125	C₂×C₄	1	2	yes	—
157	C₇×#125	C₂×C₄	1	1	yes	characteristic
158	C₇×#125	C₂×C₄	1	2	yes	—
159	C₇×#125	C₂×C₄	1	2	yes	—
160	C₇×#125	C₂×C₄	1	2	yes	—
161	C₇×#125	C₂×C₄	1	2	yes	—
162	C₇×#124	C₂×C₄	1	1	yes	characteristic
163	C₇×#124	C₂×C₄	1	1	yes	characteristic
164	C₇×#124	C₂×C₄	1	2	yes	—
165	C₇×#124	C₂×C₄	1	2	yes	—
166	C₇×#124	C₂×C₄	1	2	yes	—
167	C₇×#123	C₂×C₄	1	2	yes	—
168	C₇×#123	C₂×C₄	1	2	yes	—
169	C₇×#123	C₂×C₄	1	2	yes	—
170	C₇×#123	C₂×C₄	1	2	yes	—
171	C₇×#123	C₂×C₄	1	2	yes	—
172	C₇×#123	C₂×C₄	1	2	yes	—
173	C₇×#123	C₂×C₄	1	2	yes	—
174	C₇×#123	C₂×C₄	1	2	yes	—
175	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
176	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
177	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
178	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
179	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
180	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
181	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
182	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
183	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
184	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
185	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
186	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
187	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
188	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
189	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
190	C₇×#121	C₂×C₄	1	2	yes	—
191	C₇×#121	C₂×C₄	1	2	yes	—
192	C₇×#121	C₂×C₄	1	1	yes	characteristic
193	C₇×#121	C₂×C₄	1	1	yes	characteristic
194	C₇×#121	C₂×C₄	1	2	yes	—
195	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
196	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
197	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
198	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
199	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
200	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
201	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
202	C₄×C₇×Q₈	C₂³	1	2	yes	—
203	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
204	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
205	C₄×C₇×Q₈	C₂³	1	2	yes	—
206	C₄×C₇×Q₈	C₂³	1	2	yes	—
207	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
208	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
209	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
210	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
211	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
212	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
213	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
214	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
215	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
216	C₄×C₇×D₄	C₂³	1	2	yes	—
217	C₄×C₇×D₄	C₂³	1	2	yes	—
218	C₄×C₇×D₄	C₂³	1	2	yes	—
219	C₇×#117	C₂×C₄	1	1	yes	characteristic
220	C₇×#117	C₂×C₄	1	1	yes	characteristic
221	C₇×#117	C₂×C₄	1	1	yes	characteristic
222	C₇×#117	C₂×C₄	1	1	yes	characteristic
223	C₇×#117	C₂×C₄	1	2	yes	—
224	C₇×#117	C₂³	1	2	yes	—
225	C₇×#117	C₂³	1	2	yes	—
226	C₇×#117	C₂³	1	2	yes	—
227	C₇×#117	C₂³	1	2	yes	—
228	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
229	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
230	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₇	C₂³	1	2	yes	—
232	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₇	C₂³	1	2	yes	—
235	C₂×#1136	C₂³	1	1	yes	characteristic
236	C₂×#1136	C₂³	1	1	yes	characteristic
237	C₂×#1136	C₂³	1	1	yes	characteristic
238	C₂×#1136	C₂³	1	2	yes	—
239	C₂×#1136	C₂³	1	1	yes	characteristic
240	C₂×#1136	C₂³	1	2	yes	—
241	C₂×#1136	C₂³	1	2	yes	—
242	C₂×#1136	C₂³	1	2	yes	—
243	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
244	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
245	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
246	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
247	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
248	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
249	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
250	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
251	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
252	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
253	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
254	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
255	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
256	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
257	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
258	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
259	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
260	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
261	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
262	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
263	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
264	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
265	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
266	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
267	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
268	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
269	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
270	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
271	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
272	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
273	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
274	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
275	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
276	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
277	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
278	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
279	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
280	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
281	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
282	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
283	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
284	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
285	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
286	#6377	C₂³	1	1	yes	characteristic
287	#6377	C₂³	1	2	yes	—
288	#6377	C₂³	1	2	yes	—
289	#6377	C₂³	1	2	yes	—
290	#6377	C₂³	1	1	yes	characteristic
291	#6377	C₂³	1	1	yes	characteristic
292	#6377	C₂³	1	2	yes	—
293	#6377	C₂³	1	1	yes	characteristic
294	#6377	C₂³	1	2	yes	—
295	#6377	C₂³	1	2	yes	—
296	#6377	C₂³	1	2	yes	—
297	#6377	C₂³	1	2	yes	—
298	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
299	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
300	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
301	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
302	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
303	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
304	C₄×C₇⋊C₈	C₂³	1	2	yes	—
305	C₄×C₇⋊C₈	C₂³	1	2	yes	—
306	C₄×C₇⋊C₈	C₂³	1	2	yes	—
307	C₄×C₇⋊C₈	C₂³	1	2	yes	—
308	C₄×C₇⋊C₈	C₂³	1	2	yes	—
309	C₄×C₇⋊C₈	C₂³	1	2	yes	—
310	C₄×C₇⋊C₈	C₂³	1	2	yes	—
311	#3461	D₇	1	1	yes	characteristic
312	#2995	—	7	2	no	—
313	#2995	—	7	2	no	—
314	#2994	—	7	1	no	—
315	#2993	—	7	1	no	—
316	#2993	—	7	2	no	—
317	#2991	—	7	1	no	—
318	#2989	—	7	1	no	—
319	#2986	—	7	1	no	—
320	#2985	—	7	1	no	—
321	#2985	—	7	2	no	—
322	#2984	—	7	1	no	—
323	#2970	—	7	1	no	—
324	#2969	—	7	1	no	—
325	#2969	—	7	2	no	—
326	#2968	—	7	2	no	—
327	#2967	—	7	2	no	—
328	#2966	—	7	1	no	—
329	#2965	—	7	1	no	—
330	Q₈×M₁₆	—	7	1	no	—
331	#2962	—	7	1	no	—
332	#2961	—	7	2	no	—
333	#2960	—	7	1	no	—
334	C₇×#41	—	4	2	no	—
335	C₇×#41	—	4	2	no	—
336	C₂×C₇×Q₈	—	4	2	no	—
337	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
338	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
339	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
340	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
341	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
342	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
343	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
344	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
345	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
346	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
347	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
348	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
349	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
350	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
351	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
352	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
353	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
354	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
355	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
356	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
357	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
358	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
359	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
360	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
361	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
365	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
366	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
367	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
368	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
369	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
370	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
371	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
372	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
373	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
374	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
375	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
376	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
377	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
378	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
379	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
380	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
381	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
382	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
383	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
384	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
385	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
386	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
387	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
388	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
389	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
390	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
391	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
392	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
393	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
394	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
395	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
396	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
397	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
398	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
399	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
400	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
401	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
402	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
403	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
404	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
405	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
406	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
407	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
408	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
409	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
410	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
411	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
412	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
413	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
414	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
415	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
416	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
417	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
418	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
419	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
420	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
421	C₄²×C₇	C₂²×C₄	1	2	yes	—
422	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
423	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
424	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
425	C₄²×C₇	C₂²×C₄	1	2	yes	—
426	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
427	C₄²×C₇	C₂²×C₄	1	2	yes	—
428	C₄²×C₇	C₂²×C₄	1	2	yes	—
429	C₄²×C₇	C₂⁴	1	1	yes	characteristic
430	C₄²×C₇	C₂⁴	1	1	yes	characteristic
431	C₄²×C₇	C₂⁴	1	1	yes	characteristic
432	C₄²×C₇	C₂⁴	1	2	yes	—
433	C₄²×C₇	C₂⁴	1	1	yes	characteristic
434	C₄²×C₇	C₂⁴	1	2	yes	—
435	C₄²×C₇	C₂⁴	1	2	yes	—
436	#1136	—	2	2	no	—
437	#1136	—	2	2	no	—
438	#1136	—	4	1	no	—
439	#1136	—	4	2	no	—
440	#1136	—	4	2	no	—
441	#1136	—	4	1	no	—
442	#1136	—	4	2	no	—
443	#1136	—	4	2	no	—
444	C₂×C₇⋊C₈	—	2	2	no	—
445	C₂×C₇⋊C₈	—	2	4	no	—
446	C₂×C₇⋊C₈	—	4	2	no	—
447	C₂×C₇⋊C₈	—	4	2	no	—
448	C₂×C₇⋊C₈	—	4	1	no	—
449	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
450	C₂×C₇⋊C₈	C₂⁴	1	2	yes	—
451	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
452	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
453	C₂×C₇⋊C₈	C₂⁴	1	2	yes	—
454	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
455	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
456	C₂×C₇⋊C₈	C₂⁴	1	2	yes	—
457	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
458	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
459	C₂×C₇⋊C₈	C₂⁴	1	2	yes	—
460	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
461	#544	Dic₇	1	1	yes	characteristic
462	#542	Dic₇	1	1	yes	characteristic
463	#542	Dic₇	1	1	yes	characteristic
464	#542	Dic₇	1	2	yes	—
465	#541	Dic₇	1	1	yes	characteristic
466	#541	Dic₇	1	1	yes	characteristic
467	#541	Dic₇	1	2	yes	—
468	#539	Dic₇	1	2	yes	—
469	#539	Dic₇	1	2	yes	—
470	#537	Dic₇	1	1	yes	characteristic
471	#536	Dic₇	1	1	yes	characteristic
472	#536	Dic₇	1	1	yes	characteristic
473	#533	C₂×D₇	1	1	yes	characteristic
474	#533	C₂×D₇	1	2	yes	—
475	#533	C₂×D₇	1	1	yes	characteristic
476	#529	C₂×D₇	1	1	yes	characteristic
477	#529	C₂×D₇	1	2	yes	—
478	#529	C₂×D₇	1	2	yes	—
479	#529	C₂×D₇	1	1	yes	characteristic
480	#529	C₂×D₇	1	2	yes	—
481	C₄×#41	C₂×D₇	1	1	yes	characteristic
482	C₄×#41	C₂×D₇	1	1	yes	characteristic
483	C₂×C₄×Q₈	C₂×D₇	1	1	yes	characteristic
484	#446	—	7	2	no	—
485	#446	—	7	1	no	—
486	#446	—	7	1	no	—
487	#446	—	7	1	no	—
488	#446	—	7	2	no	—
489	#446	—	7	2	no	—
490	#446	—	7	2	no	—
491	#446	—	7	2	no	—
492	#446	—	7	2	no	—
493	#446	—	7	2	no	—
494	#446	—	7	1	no	—
495	#446	—	7	2	no	—
496	#446	—	7	1	no	—
497	#446	—	7	2	no	—
498	#446	—	7	1	no	—
499	#446	—	7	1	no	—
500	#446	—	7	2	no	—
501	#446	—	7	2	no	—
502	#446	—	7	1	no	—
503	C₈×Q₈	—	7	1	no	—
504	C₈×Q₈	—	7	2	no	—
505	C₈×Q₈	—	7	1	no	—
506	C₈×Q₈	—	7	1	no	—
507	C₈×Q₈	—	7	1	no	—
508	C₈×Q₈	—	7	1	no	—
509	C₈×Q₈	—	7	1	no	—
510	C₈×Q₈	—	7	2	no	—
511	#436	—	7	1	no	—
512	#436	—	7	1	no	—
513	#436	—	7	1	no	—
514	#436	—	7	2	no	—
515	#436	—	7	2	no	—
516	#436	—	7	1	no	—
517	#436	—	7	2	no	—
518	#436	—	7	2	no	—
519	#436	—	7	2	no	—
520	#435	—	7	1	no	—
521	#435	—	7	1	no	—
522	#435	—	7	1	no	—
523	#435	—	7	1	no	—
524	#435	—	7	2	no	—
525	#435	—	7	2	no	—
526	#435	—	7	2	no	—
527	#435	—	7	2	no	—
528	#435	—	7	2	no	—
529	#435	—	7	2	no	—
530	#435	—	7	2	no	—
531	#435	—	7	2	no	—
532	C₈×D₄	—	7	2	no	—
533	C₈×D₄	—	7	1	no	—
534	C₈×D₄	—	7	2	no	—
535	C₈×D₄	—	7	1	no	—
536	#433	—	7	2	no	—
537	#433	—	7	2	no	—
538	#433	—	7	2	no	—
539	#433	—	7	2	no	—
540	#433	—	7	2	no	—
541	#433	—	7	2	no	—
542	#433	—	7	2	no	—
543	#433	—	7	2	no	—
544	#432	—	7	1	no	—
545	#432	—	7	2	no	—
546	#432	—	7	1	no	—
547	#432	—	7	2	no	—
548	#431	—	7	1	no	—
549	#431	—	7	1	no	—
550	#431	—	7	1	no	—
551	#431	—	7	2	no	—
552	#431	—	7	2	no	—
553	#431	—	7	1	no	—
554	#424	—	7	2	no	—
555	#424	—	7	2	no	—
556	#424	—	7	2	no	—
557	#424	—	7	2	no	—
558	#423	—	7	1	no	—
559	#423	—	7	2	no	—
560	#423	—	7	1	no	—
561	#423	—	7	2	no	—
562	C₂×C₄⋊C₈	—	7	1	no	—
563	#405	—	7	2	no	—
564	#405	—	7	2	no	—
565	#405	—	7	2	no	—
566	#405	—	7	2	no	—
567	C₄×M₁₆	—	7	1	no	—
568	C₄×M₁₆	—	7	1	no	—
569	C₄×M₁₆	—	7	2	no	—
570	C₂×#97	—	7	2	no	—
571	C₂×C₄×C₈	—	7	1	no	—
572	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
573	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
574	C₂³×C₇	C₂³×C₄	1	2	yes	—
575	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
576	C₇×Q₈	—	2	2	no	—
577	C₇×Q₈	—	2	2	no	—
578	C₇×Q₈	—	2	2	no	—
579	C₇×Q₈	—	4	2	no	—
580	C₇×Q₈	—	4	2	no	—
581	C₇×Q₈	—	4	2	no	—
582	C₇×Q₈	—	4	1	no	—
583	C₇×D₄	—	2	2	no	—
584	C₇×D₄	—	4	2	no	—
585	C₇×D₄	—	4	2	no	—
586	C₇×D₄	—	4	1	no	—
587	C₇×D₄	—	4	1	no	—
588	C₇×D₄	—	4	1	no	—
589	C₇×D₄	—	4	2	no	—
590	C₂×C₄×C₇	—	2	2	no	—
591	C₂×C₄×C₇	—	2	2	no	—
592	C₂×C₄×C₇	—	2	2	no	—
593	C₂×C₄×C₇	—	2	1	no	—
594	C₂×C₄×C₇	—	2	2	no	—
595	C₂×C₄×C₇	—	2	1	no	—
596	C₂×C₄×C₇	—	2	1	no	—
597	C₂×C₄×C₇	—	2	1	no	—
598	C₂×C₄×C₇	—	2	2	no	—
599	C₂×C₄×C₇	—	2	1	no	—
600	C₂×C₄×C₇	—	2	1	no	—
601	C₂×C₄×C₇	—	4	1	no	—
602	C₂×C₄×C₇	—	4	1	no	—
603	C₂×C₄×C₇	—	4	2	no	—
604	C₂×C₄×C₇	—	4	1	no	—
605	C₂×C₄×C₇	—	4	2	no	—
606	C₂×C₄×C₇	—	4	2	no	—
607	C₂×C₄×C₇	—	4	2	no	—
608	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
609	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
610	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
611	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
612	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
613	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
614	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
615	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
616	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
617	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
618	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
619	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
620	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
621	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
622	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
623	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
624	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
625	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
626	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
627	C₇⋊C₈	—	2	1	no	—
628	C₇⋊C₈	—	2	2	no	—
629	C₇⋊C₈	—	2	1	no	—
630	C₇⋊C₈	—	2	1	no	—
631	C₇⋊C₈	—	2	1	no	—
632	C₇⋊C₈	—	2	2	no	—
633	C₇⋊C₈	—	2	2	no	—
634	C₇⋊C₈	—	2	1	no	—
635	C₇⋊C₈	—	2	1	no	—
636	C₇⋊C₈	—	2	1	no	—
637	C₇⋊C₈	—	2	2	no	—
638	C₇⋊C₈	2₋¹⁺⁴	1	2	yes	—
639	C₂×#41	C₂×Dic₇	1	1	yes	characteristic
640	C₂×#41	C₂×Dic₇	1	1	yes	characteristic
641	C₂²×Q₈	C₂×Dic₇	1	1	yes	characteristic
642	C₂×M₁₆	—	7	1	no	—
643	C₂×M₁₆	—	7	1	no	—
644	C₂×M₁₆	—	7	1	no	—
645	C₂×M₁₆	—	7	2	no	—
646	C₂×M₁₆	—	7	1	no	—
647	C₂×M₁₆	—	7	2	no	—
648	C₂×M₁₆	—	7	2	no	—
649	C₂×M₁₆	—	7	2	no	—
650	C₂²×C₈	—	7	1	no	—
651	C₂²×C₈	—	7	2	no	—
652	C₂²×C₈	—	7	1	no	—
653	C₂²×C₈	—	7	2	no	—
654	C₂²×C₈	—	7	2	no	—
655	C₄⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
656	C₄⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
657	C₄⋊Q₈	C₂×Dic₇	1	2	yes	—
658	C₄⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
659	C₄⋊Q₈	C₂×Dic₇	1	2	yes	—
660	C₄⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
661	#126	C₂×Dic₇	1	2	yes	—
662	#126	C₂×Dic₇	1	2	yes	—
663	#126	C₂×Dic₇	1	2	yes	—
664	#126	C₂×Dic₇	1	2	yes	—
665	#126	C₂×Dic₇	1	2	yes	—
666	#126	C₂×Dic₇	1	2	yes	—
667	#126	C₂×Dic₇	1	2	yes	—
668	#126	C₂×Dic₇	1	2	yes	—
669	#125	C₂×Dic₇	1	2	yes	—
670	#125	C₂×Dic₇	1	2	yes	—
671	#125	C₂×Dic₇	1	1	yes	characteristic
672	#125	C₂×Dic₇	1	2	yes	—
673	#125	C₂×Dic₇	1	1	yes	characteristic
674	#125	C₂×Dic₇	1	2	yes	—
675	#125	C₂×Dic₇	1	2	yes	—
676	#125	C₂×Dic₇	1	2	yes	—
677	#125	C₂×Dic₇	1	2	yes	—
678	#124	C₂×Dic₇	1	1	yes	characteristic
679	#124	C₂×Dic₇	1	1	yes	characteristic
680	#124	C₂×Dic₇	1	2	yes	—
681	#124	C₂×Dic₇	1	2	yes	—
682	#124	C₂×Dic₇	1	2	yes	—
683	#123	C₂×Dic₇	1	2	yes	—
684	#123	C₂×Dic₇	1	2	yes	—
685	#123	C₂×Dic₇	1	2	yes	—
686	#123	C₂×Dic₇	1	2	yes	—
687	#123	C₂×Dic₇	1	2	yes	—
688	#123	C₂×Dic₇	1	2	yes	—
689	#123	C₂×Dic₇	1	2	yes	—
690	#123	C₂×Dic₇	1	2	yes	—
691	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
692	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
693	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
694	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
695	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
696	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
697	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
698	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
699	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
700	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
701	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
702	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
703	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
704	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
705	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
706	#121	C₂×Dic₇	1	2	yes	—
707	#121	C₂×Dic₇	1	2	yes	—
708	#121	C₂×Dic₇	1	1	yes	characteristic
709	#121	C₂×Dic₇	1	1	yes	characteristic
710	#121	C₂×Dic₇	1	2	yes	—
711	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
712	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
713	C₄×Q₈	C₂×Dic₇	1	2	yes	—
714	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
715	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
716	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
717	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
718	C₄×Q₈	C₂²×D₇	1	2	yes	—
719	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
720	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
721	C₄×Q₈	C₂²×D₇	1	2	yes	—
722	C₄×Q₈	C₂²×D₇	1	2	yes	—
723	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
724	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
725	C₄×D₄	C₂×Dic₇	1	2	yes	—
726	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
727	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
728	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
729	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
730	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
731	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
732	C₄×D₄	C₂²×D₇	1	2	yes	—
733	C₄×D₄	C₂²×D₇	1	2	yes	—
734	C₄×D₄	C₂²×D₇	1	2	yes	—
735	#117	C₂×Dic₇	1	1	yes	characteristic
736	#117	C₂×Dic₇	1	1	yes	characteristic
737	#117	C₂×Dic₇	1	1	yes	characteristic
738	#117	C₂×Dic₇	1	1	yes	characteristic
739	#117	C₂×Dic₇	1	2	yes	—
740	#117	C₂²×D₇	1	2	yes	—
741	#117	C₂²×D₇	1	2	yes	—
742	#117	C₂²×D₇	1	2	yes	—
743	#117	C₂²×D₇	1	2	yes	—
744	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂×Dic₇	1	2	yes	—
746	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
747	C₂×C₄²	C₂²×D₇	1	2	yes	—
748	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
749	C₂×C₄²	C₂²×D₇	1	2	yes	—
750	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
751	C₄⋊C₈	—	7	1	no	—
752	C₄⋊C₈	—	7	1	no	—
753	C₄⋊C₈	—	7	2	no	—
754	C₄⋊C₈	—	7	1	no	—
755	C₄⋊C₈	—	7	2	no	—
756	C₄⋊C₈	—	7	1	no	—
757	C₄⋊C₈	—	7	2	no	—
758	C₄⋊C₈	—	7	2	no	—
759	C₄⋊C₈	—	7	2	no	—
760	C₄⋊C₈	—	7	2	no	—
761	C₄⋊C₈	—	7	2	no	—
762	C₄⋊C₈	—	7	2	no	—
763	C₄⋊C₈	—	7	2	no	—
764	C₄⋊C₈	—	7	1	no	—
765	C₄⋊C₈	—	7	1	no	—
766	C₄⋊C₈	—	7	2	no	—
767	C₄⋊C₈	—	7	2	no	—
768	C₄⋊C₈	—	7	2	no	—
769	C₄⋊C₈	—	7	1	no	—
770	C₄⋊C₈	—	7	1	no	—
771	C₄⋊C₈	—	7	2	no	—
772	C₄⋊C₈	—	7	1	no	—
773	C₄⋊C₈	—	7	1	no	—
774	C₄⋊C₈	—	7	2	no	—
775	C₄⋊C₈	—	7	2	no	—
776	C₂²⋊C₈	—	7	1	no	—
777	C₂²⋊C₈	—	7	2	no	—
778	C₂²⋊C₈	—	7	1	no	—
779	C₂²⋊C₈	—	7	1	no	—
780	C₂²⋊C₈	—	7	2	no	—
781	C₂²⋊C₈	—	7	1	no	—
782	C₂²⋊C₈	—	7	1	no	—
783	C₂²⋊C₈	—	7	2	no	—
784	C₂²⋊C₈	—	7	1	no	—
785	C₂²⋊C₈	—	7	2	no	—
786	C₂²⋊C₈	—	7	2	no	—
787	C₂²⋊C₈	—	7	2	no	—
788	C₂²⋊C₈	—	7	2	no	—
789	#97	—	7	1	no	—
790	#97	—	7	2	no	—
791	#97	—	7	2	no	—
792	#97	—	7	2	no	—
793	#97	—	7	1	no	—
794	#97	—	7	2	no	—
795	#97	—	7	1	no	—
796	#97	—	7	1	no	—
797	#97	—	7	2	no	—
798	#97	—	7	2	no	—
799	#97	—	7	2	no	—
800	#97	—	7	2	no	—
801	C₄×C₈	—	7	1	no	—
802	C₄×C₈	—	7	1	no	—
803	C₄×C₈	—	7	1	no	—
804	C₄×C₈	—	7	1	no	—
805	C₄×C₈	—	7	2	no	—
806	C₄×C₈	—	7	1	no	—
807	C₄×C₈	—	7	1	no	—
808	C₄×C₈	—	7	2	no	—
809	C₄×C₈	—	7	2	no	—
810	C₄×C₈	—	7	2	no	—
811	C₄×C₈	—	7	2	no	—
812	C₄×C₈	—	7	2	no	—
813	C₄×C₈	—	7	2	no	—
814	C₂²×C₇	—	2	1	no	—
815	C₂²×C₇	—	2	2	no	—
816	C₂²×C₇	—	2	1	no	—
817	C₂²×C₇	—	2	1	no	—
818	C₂²×C₇	—	2	1	no	—
819	C₂²×C₇	—	2	1	no	—
820	C₂²×C₇	—	2	1	no	—
821	C₂²×C₇	—	2	2	no	—
822	C₂²×C₇	—	2	1	no	—
823	C₂²×C₇	—	2	1	no	—
824	C₂²×C₇	—	2	1	no	—
825	C₂²×C₇	—	2	2	no	—
826	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
827	C₄×C₇	—	2	1	no	—
828	C₄×C₇	—	2	2	no	—
829	C₄×C₇	—	2	1	no	—
830	C₄×C₇	—	2	1	no	—
831	C₄×C₇	—	2	1	no	—
832	C₄×C₇	—	2	1	no	—
833	C₄×C₇	—	2	1	no	—
834	C₄×C₇	—	2	2	no	—
835	C₄×C₇	—	2	2	no	—
836	C₄×C₇	—	2	2	no	—
837	C₄×C₇	—	2	1	no	—
838	C₄×C₇	—	2	1	no	—
839	C₄×C₇	—	2	2	no	—
840	C₄×C₇	—	2	2	no	—
841	C₄×C₇	—	2	1	no	—
842	C₄×C₇	—	2	2	no	—
843	C₄×C₇	—	2	1	no	—
844	C₄×C₇	#568	1	2	yes	—
845	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
846	C₄×C₇	#585	1	1	yes	characteristic
847	#41	—	4	2	no	—
848	#41	—	4	2	no	—
849	C₂×Q₈	—	4	2	no	—
850	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
851	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
852	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
853	C₂×Q₈	C₂²×Dic₇	1	2	yes	—
854	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
855	C₂×Q₈	C₂²×Dic₇	1	2	yes	—
856	C₂×Q₈	C₂²×Dic₇	1	2	yes	—
857	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
858	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
859	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
860	C₂×D₄	C₂²×Dic₇	1	2	yes	—
861	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
862	C₂×D₄	C₂²×Dic₇	1	2	yes	—
863	C₂×D₄	C₂²×Dic₇	1	2	yes	—
864	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
865	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
866	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
867	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
868	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
869	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
870	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
871	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
872	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
873	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
874	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
875	C₂²×C₄	C₂³×D₇	1	2	yes	—
876	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
877	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
878	M₁₆	—	14	2	no	—
879	M₁₆	—	14	2	no	—
880	M₁₆	—	28	1	no	—
881	M₁₆	—	28	2	no	—
882	M₁₆	—	28	2	no	—
883	M₁₆	—	28	1	no	—
884	M₁₆	—	28	2	no	—
885	M₁₆	—	28	2	no	—
886	C₂×C₈	—	7	1	no	—
887	C₂×C₈	—	7	1	no	—
888	C₂×C₈	—	7	1	no	—
889	C₂×C₈	—	7	1	no	—
890	C₂×C₈	—	7	1	no	—
891	C₂×C₈	—	7	2	no	—
892	C₂×C₈	—	7	2	no	—
893	C₂×C₈	—	7	1	no	—
894	C₂×C₈	—	7	1	no	—
895	C₂×C₈	—	7	2	no	—
896	C₂×C₈	—	7	1	no	—
897	C₂×C₈	—	7	2	no	—
898	C₂×C₈	—	14	2	no	—
899	C₂×C₈	—	14	4	no	—
900	C₂×C₈	—	28	2	no	—
901	C₂×C₈	—	28	2	no	—
902	C₂×C₈	—	28	1	no	—
903	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
904	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
905	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
906	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
907	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
908	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
909	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
910	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
911	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
912	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
913	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
914	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
915	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
916	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
917	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
918	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
919	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
920	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
921	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
922	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
923	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
924	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
925	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
926	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
927	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
928	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
929	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
930	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
931	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
932	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
933	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
934	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
935	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
936	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
937	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
938	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
939	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
940	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
941	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
942	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
943	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
944	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
945	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
946	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
947	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
948	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
949	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
950	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
951	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
952	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
953	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
954	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
955	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
956	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
957	C₄²	C₂²×Dic₇	1	1	yes	characteristic
958	C₄²	C₂²×Dic₇	1	1	yes	characteristic
959	C₄²	C₂²×Dic₇	1	2	yes	—
960	C₄²	C₂²×Dic₇	1	1	yes	characteristic
961	C₄²	C₂²×Dic₇	1	1	yes	characteristic
962	C₄²	C₂²×Dic₇	1	1	yes	characteristic
963	C₄²	C₂²×Dic₇	1	2	yes	—
964	C₄²	C₂²×Dic₇	1	1	yes	characteristic
965	C₄²	C₂²×Dic₇	1	2	yes	—
966	C₄²	C₂²×Dic₇	1	2	yes	—
967	C₄²	C₂³×D₇	1	1	yes	characteristic
968	C₄²	C₂³×D₇	1	1	yes	characteristic
969	C₄²	C₂³×D₇	1	2	yes	—
970	C₄²	C₂³×D₇	1	2	yes	—
971	C₄²	C₂³×D₇	1	2	yes	—
972	C₄²	C₂³×D₇	1	1	yes	characteristic
973	C₄²	C₂³×D₇	1	1	yes	characteristic
974	C₂×C₇	—	4	1	no	—
975	C₂×C₇	—	4	1	no	—
976	C₂×C₇	—	4	1	no	—
977	C₂×C₇	—	4	2	no	—
978	C₂×C₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
979	C₂×C₇	C₂×#568	1	1	yes	characteristic
980	C₂×C₇	#3573	1	1	yes	characteristic
981	C₂³	C₂³×Dic₇	1	1	yes	characteristic
982	C₂³	C₂³×Dic₇	1	1	yes	characteristic
983	C₂³	C₂³×Dic₇	1	2	yes	—
984	C₂³	C₂³×Dic₇	1	1	yes	characteristic
985	Q₈	—	2	2	no	—
986	Q₈	—	2	2	no	—
987	Q₈	—	2	2	no	—
988	Q₈	—	4	2	no	—
989	Q₈	—	4	2	no	—
990	Q₈	—	4	2	no	—
991	Q₈	—	4	1	no	—
992	D₄	—	2	2	no	—
993	D₄	—	4	2	no	—
994	D₄	—	4	2	no	—
995	D₄	—	4	1	no	—
996	D₄	—	4	1	no	—
997	D₄	—	4	1	no	—
998	D₄	—	4	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	4	1	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	4	1	no	—
1014	C₂×C₄	—	4	2	no	—
1015	C₂×C₄	—	4	2	no	—
1016	C₂×C₄	—	4	2	no	—
1017	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1018	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1019	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1020	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1021	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1022	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1023	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1024	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1025	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1026	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1027	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1028	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1029	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1030	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1031	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1032	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1033	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1034	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1035	C₂×C₄	C₂⁴×D₇	1	1	yes	characteristic
1036	C₈	—	7	2	no	—
1037	C₈	—	14	1	no	—
1038	C₈	—	14	2	no	—
1039	C₈	—	14	1	no	—
1040	C₈	—	14	1	no	—
1041	C₈	—	14	1	no	—
1042	C₈	—	14	2	no	—
1043	C₈	—	14	1	no	—
1044	C₈	—	14	1	no	—
1045	C₈	—	14	2	no	—
1046	C₈	—	14	1	no	—
1047	C₈	—	14	2	no	—
1048	C₇	#60344	1	1	yes	characteristic, complemented, Sylow
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	2	no	—
1055	C₂²	—	2	1	no	—
1056	C₂²	—	2	1	no	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	C₂⁴×Dic₇	1	1	yes	characteristic
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	2	no	—
1070	C₄	—	2	1	no	—
1071	C₄	—	2	1	no	—
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	2	1	no	—
1079	C₄	#90510	1	2	yes	—
1080	C₄	D₇×2₋¹⁺⁴	1	1	yes	characteristic
1081	C₄	#90620	1	1	yes	characteristic
1082	C₂	—	4	1	no	—
1083	C₂	—	4	1	no	—
1084	C₂	—	4	1	no	—
1085	C₂	—	4	2	no	—
1086	C₂	C₂×#90510	1	1	yes	characteristic
1087	C₂	Dic₇×2₋¹⁺⁴	1	1	yes	characteristic
1088	C₂	#11744364	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₇
commutator, socle	C₂²×C₇	C₂⁴×C₄
Fitting	C₇×#3461	C₂
prime radical	C₇×#537	C₄
cosocle	C₂×C₄×C₇	C₂⁵
hypercenter	#3461	D₇
hypocenter	C₇	#60344
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ #3461

Complements

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

N	H ≅ G/N	type
2. #11740777	C₂	semidirect
3. #11740776	C₂	semidirect
4. #11740776	C₂	semidirect
5. #11740775	C₂	semidirect
6. #11740774	C₂	semidirect
7. #11740773	C₂	semidirect
8. #11740578	C₂	semidirect
9. #11740578	C₂	semidirect
10. #11740577	C₂	semidirect
11. #11740576	C₂	semidirect
12. #11740576	C₂	semidirect
13. #11740574	C₂	semidirect
14. #11740574	C₂	semidirect
15. #11740573	C₂	semidirect
16. #11740572	C₂	semidirect
17. #11740571	C₂	semidirect
18. #11739968	C₂	semidirect
19. #11739966	C₂	semidirect
20. #11739963	C₂	semidirect
21. #11739962	C₂	semidirect
22. #11739882	C₂	semidirect
23. Q₈×#1136	C₂	semidirect
1048. C₇	#60344	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
#11740777	2
#11740776	2
#11740775	2
#11740774	2
#11740773	2
#11740578	2
#11740577	2
#11740576	2
#11740574	2
#11740573	2
#11740572	2
#11740571	2
#11739968	2
#11739966	2
#11739963	2
#11739962	2
#11739882	2
Q₈×#1136	2
#60344	7