Subgroups — C₇×#61464 #13238680

Order 1792.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3481	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3351	C₂	1	2	yes	maximal, complemented
9	C₇×#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3325	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3323	C₂	1	2	yes	maximal, complemented
12	C₇×#3322	C₂	1	2	yes	maximal, complemented
13	C₇×#3273	C₂	1	2	yes	maximal, complemented
14	C₇×#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3183	C₂	1	2	yes	maximal, complemented
16	C₇×#3182	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3114	C₂	1	2	yes	maximal, complemented
19	C₇×#3111	C₂	1	2	yes	maximal, complemented
20	C₇×#3109	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2971	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₇×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
24	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₇×#559	C₂²	1	1	yes	characteristic, complemented
27	C₇×#556	C₂²	1	1	yes	characteristic, complemented
28	C₇×#555	C₂²	1	1	yes	characteristic
29	C₇×#554	C₂²	1	1	yes	characteristic, complemented
30	C₇×#554	C₂²	1	1	yes	characteristic, complemented
31	C₇×#554	C₂²	1	1	yes	characteristic, complemented
32	C₇×#553	—	2	1	no	—
33	C₇×#553	—	2	1	no	—
34	C₇×#553	C₂²	1	2	yes	—
35	C₇×#552	—	2	1	no	—
36	C₇×#552	C₂²	1	2	yes	complemented
37	C₇×#551	—	2	2	no	—
38	C₇×#551	—	2	2	no	—
39	C₇×#547	C₂²	1	1	yes	characteristic
40	C₇×#546	—	2	1	no	—
41	C₇×#546	C₂²	1	2	yes	—
42	C₇×#546	C₂²	1	2	yes	complemented
43	C₇×D₄²	C₂²	1	1	yes	characteristic, complemented
44	C₇×#533	C₂²	1	1	yes	characteristic, complemented
45	C₇×#532	C₂²	1	1	yes	characteristic
46	C₇×#529	—	2	1	no	—
47	C₇×#529	—	2	2	no	—
48	C₇×#529	C₂²	1	2	yes	complemented
49	C₇×#529	C₂²	1	2	yes	complemented
50	C₇×#525	—	2	1	no	—
51	C₇×#525	—	2	2	no	—
52	C₄×C₇×#41	C₂²	1	1	yes	characteristic
53	C₄×C₇×#41	C₂²	1	1	yes	characteristic
54	C₄×C₇×#41	C₂²	1	2	yes	complemented
55	C₂×C₄×C₇×D₄	—	2	1	no	—
56	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
58	C₂×C₇×#117	—	2	1	no	—
59	C₇×#500	C₂²	1	1	yes	characteristic, complemented
60	C₇×#499	C₂²	1	2	yes	complemented
61	C₇×#495	C₂²	1	2	yes	complemented
62	C₇×#492	C₂²	1	1	yes	characteristic, complemented
63	C₇×#488	C₂²	1	2	yes	complemented
64	C₇×#488	C₂²	1	2	yes	complemented
65	C₇×#487	C₂²	1	1	yes	characteristic, complemented
66	C₇×#486	C₂²	1	1	yes	characteristic, complemented
67	C₇×#485	C₂²	1	2	yes	complemented
68	C₇×#485	C₂²	1	2	yes	complemented
69	C₇×#483	C₂²	1	2	yes	complemented
70	C₇×#482	C₂²	1	2	yes	complemented
71	C₇×#481	C₂²	1	2	yes	complemented
72	C₇×#480	C₂²	1	2	yes	complemented
73	C₇×#479	C₂²	1	2	yes	complemented
74	C₇×#478	C₂²	1	2	yes	complemented
75	C₇×#478	C₂²	1	2	yes	complemented
76	C₇×#478	C₂²	1	2	yes	complemented
77	C₇×#477	C₂²	1	1	yes	characteristic, complemented
78	C₇×#476	C₂²	1	1	yes	characteristic, complemented
79	C₇×#476	C₂²	1	1	yes	characteristic, complemented
80	C₇×#476	C₂²	1	1	yes	characteristic, complemented
81	C₇×#470	C₂²	1	2	yes	complemented
82	C₇×#469	C₂²	1	2	yes	—
83	C₇×#468	C₂²	1	2	yes	complemented
84	C₇×#468	C₂²	1	2	yes	complemented
85	C₇×#468	C₂²	1	2	yes	complemented
86	C₇×#468	C₂²	1	2	yes	complemented
87	C₇×#464	C₂²	1	2	yes	complemented
88	C₇×#463	C₂²	1	2	yes	—
89	C₇×#463	C₂²	1	2	yes	complemented
90	C₇×#463	C₂²	1	2	yes	complemented
91	C₇×#462	C₂²	1	1	yes	characteristic, complemented
92	C₇×#461	C₂²	1	1	yes	characteristic, complemented
93	C₇×#459	C₂²	1	1	yes	characteristic
94	C₇×#459	C₂²	1	1	yes	characteristic
95	C₇×#452	C₂²	1	2	yes	—
96	C₇×#452	C₂²	1	2	yes	complemented
97	C₇×#450	C₂²	1	2	yes	complemented
98	C₇×#449	C₂²	1	2	yes	—
99	C₇×#447	C₂²	1	2	yes	—
100	C₇×#447	C₂²	1	2	yes	complemented
101	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
102	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
103	C₇×#442	C₂²	1	1	yes	characteristic
104	C₇×#442	C₂²	1	1	yes	characteristic
105	C₇×#442	C₂²	1	2	yes	complemented
106	C₇×#442	C₂²	1	2	yes	complemented
107	C₇×#441	C₂²	1	2	yes	complemented
108	C₇×#440	C₂²	1	2	yes	complemented
109	C₇×#440	C₂²	1	2	yes	complemented
110	C₇×#440	C₂²	1	1	yes	characteristic, complemented
111	C₇×#440	C₂²	1	1	yes	characteristic, complemented
112	C₇×#440	C₂²	1	2	yes	complemented
113	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
114	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
116	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
118	C₄×C₇×D₈	C₂²	1	2	yes	—
119	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
120	C₄×C₇×D₈	C₂²	1	2	yes	complemented
121	C₇×#436	C₂²	1	1	yes	characteristic, complemented
122	C₇×#436	C₂²	1	2	yes	complemented
123	C₇×#436	C₂²	1	2	yes	complemented
124	C₇×#436	C₂²	1	1	yes	characteristic, complemented
125	C₇×#432	C₂²	1	1	yes	characteristic, complemented
126	C₇×#432	C₂²	1	2	yes	complemented
127	C₇×#428	C₂²	1	1	yes	characteristic, complemented
128	C₇×#428	C₂²	1	2	yes	complemented
129	C₇×#418	C₂²	1	1	yes	characteristic, complemented
130	C₇×#418	C₂²	1	2	yes	complemented
131	C₇×#417	C₂²	1	1	yes	characteristic
132	C₇×#417	C₂²	1	2	yes	complemented
133	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
134	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
135	#61464	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	1	no	—
137	C₂×C₇×#41	D₄	1	1	yes	characteristic
138	C₂×C₇×#41	C₂³	1	1	yes	characteristic
139	C₂×C₇×#41	C₂³	1	2	yes	—
140	C₂²×C₇×D₄	—	2	1	no	—
141	C₂²×C₇×D₄	C₂³	1	2	yes	—
142	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₇	—	2	1	no	—
144	C₂³×C₄×C₇	—	2	2	no	—
145	C₇×AGL(1,ℤ/8)	—	2	8	no	—
146	C₇×AGL(1,ℤ/8)	—	2	4	no	—
147	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
149	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
150	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
152	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
154	C₂×C₇×D₈	C₂³	1	2	yes	—
155	C₂×C₇×D₈	C₂³	1	2	yes	—
156	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
157	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₇×M₁₆	C₂³	1	2	yes	—
159	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
160	C₂×C₇×M₁₆	C₂³	1	2	yes	—
161	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₇×#127	C₂³	1	1	yes	characteristic
165	C₇×#126	—	2	2	no	—
166	C₇×#126	—	2	2	no	—
167	C₇×#126	—	2	2	no	—
168	C₇×#126	—	2	2	no	—
169	C₇×#126	—	2	2	no	—
170	C₇×#125	—	2	2	no	—
171	C₇×#125	—	2	1	no	—
172	C₇×#125	—	2	1	no	—
173	C₇×#125	C₂³	1	2	yes	—
174	C₇×#125	C₂³	1	2	yes	—
175	C₇×#124	—	2	1	no	—
176	C₇×#124	—	2	2	no	—
177	C₇×#124	—	2	1	no	—
178	C₇×#124	C₂³	1	2	yes	—
179	C₇×#124	C₂³	1	2	yes	—
180	C₇×#123	—	2	2	no	—
181	C₇×#123	—	2	2	no	—
182	C₇×#123	—	2	2	no	—
183	C₇×#123	—	2	2	no	—
184	C₇×#123	—	2	2	no	—
185	C₇×#123	—	2	2	no	—
186	C₇×#123	—	2	2	no	—
187	C₇×#123	—	2	2	no	—
188	C₇×C₂²⋊Q₈	—	2	1	no	—
189	C₇×C₂²⋊Q₈	—	2	1	no	—
190	C₇×C₂²⋊Q₈	—	2	1	no	—
191	C₇×C₂²⋊Q₈	—	2	1	no	—
192	C₇×C₂²⋊Q₈	—	2	2	no	—
193	C₇×C₂²⋊Q₈	—	2	2	no	—
194	C₇×C₂²⋊Q₈	—	2	2	no	—
195	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₇×#121	—	2	2	no	—
199	C₇×#121	—	2	1	no	—
200	C₇×#121	—	2	1	no	—
201	C₇×#121	—	2	1	no	—
202	C₇×#121	—	2	1	no	—
203	C₇×#121	—	2	2	no	—
204	C₇×#121	—	2	2	no	—
205	C₇×#121	C₂³	1	2	yes	—
206	C₇×#121	C₂³	1	2	yes	—
207	C₇×#121	C₂³	1	2	yes	—
208	C₇×#120	—	2	2	no	—
209	C₇×#120	—	2	2	no	—
210	C₇×#120	—	2	2	no	—
211	C₄×C₇×Q₈	—	2	1	no	—
212	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
213	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
214	C₄×C₇×Q₈	C₂³	1	2	yes	—
215	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
216	C₄×C₇×Q₈	C₂³	1	2	yes	—
217	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
218	C₄×C₇×D₄	—	2	1	no	—
219	C₄×C₇×D₄	—	2	2	no	—
220	C₄×C₇×D₄	—	2	1	no	—
221	C₄×C₇×D₄	—	2	1	no	—
222	C₄×C₇×D₄	—	2	2	no	—
223	C₄×C₇×D₄	—	2	2	no	—
224	C₄×C₇×D₄	—	2	2	no	—
225	C₄×C₇×D₄	—	2	1	no	—
226	C₄×C₇×D₄	—	2	2	no	—
227	C₄×C₇×D₄	—	2	1	no	—
228	C₄×C₇×D₄	—	2	2	no	—
229	C₄×C₇×D₄	—	2	1	no	—
230	C₄×C₇×D₄	—	2	2	no	—
231	C₄×C₇×D₄	—	2	1	no	—
232	C₄×C₇×D₄	D₄	1	1	yes	characteristic
233	C₄×C₇×D₄	D₄	1	2	yes	—
234	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
235	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
236	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
237	C₄×C₇×D₄	C₂³	1	2	yes	—
238	C₄×C₇×D₄	C₂³	1	2	yes	—
239	C₄×C₇×D₄	C₂³	1	2	yes	—
240	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
241	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
242	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
243	C₄×C₇×D₄	C₂³	1	2	yes	—
244	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
245	C₄×C₇×D₄	C₂³	1	2	yes	—
246	C₇×#117	—	2	1	no	—
247	C₇×#117	—	2	1	no	—
248	C₇×#117	—	2	1	no	—
249	C₇×#117	—	2	2	no	—
250	C₇×#117	—	2	2	no	—
251	C₇×#117	—	2	1	no	—
252	C₇×#117	—	2	2	no	—
253	C₇×#117	—	2	2	no	—
254	C₇×#117	D₄	1	1	yes	characteristic
255	C₇×#117	D₄	1	2	yes	—
256	C₇×#117	C₂³	1	2	yes	—
257	C₇×#117	C₂³	1	1	yes	characteristic
258	C₂×C₇×C₄⋊C₄	—	2	1	no	—
259	C₂×C₇×C₄⋊C₄	—	2	1	no	—
260	C₂×C₇×C₄⋊C₄	—	2	1	no	—
261	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²×C₇	—	2	2	no	—
268	C₂×C₄²×C₇	—	2	1	no	—
269	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
270	C₂×C₄²×C₇	C₂³	1	2	yes	—
271	C₇×#107	C₂³	1	1	yes	characteristic
272	C₇×#107	C₂³	1	2	yes	—
273	C₇×#107	C₂³	1	2	yes	—
274	C₇×#107	C₂³	1	2	yes	—
275	C₇×#107	C₂³	1	1	yes	characteristic
276	C₇×#106	C₂³	1	2	yes	—
277	C₇×#106	C₂³	1	2	yes	—
278	C₇×#106	C₂³	1	2	yes	—
279	C₇×#106	C₂³	1	1	yes	characteristic
280	C₇×#106	C₂³	1	1	yes	characteristic
281	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₇×C₄⋊C₈	C₂³	1	2	yes	—
284	C₇×C₄⋊C₈	C₂³	1	2	yes	—
285	C₇×#103	C₂³	1	2	yes	—
286	C₇×#103	C₂³	1	2	yes	—
287	C₇×#103	C₂³	1	2	yes	—
288	C₇×#103	C₂³	1	2	yes	—
289	C₇×#103	C₂³	1	1	yes	characteristic
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#103	C₂³	1	1	yes	characteristic
292	C₇×#102	C₂³	1	2	yes	—
293	C₇×#102	C₂³	1	2	yes	—
294	C₇×#102	C₂³	1	2	yes	—
295	C₇×#102	C₂³	1	2	yes	—
296	C₇×#102	C₂³	1	1	yes	characteristic
297	C₇×#102	C₂³	1	2	yes	—
298	C₇×#102	C₂³	1	2	yes	—
299	C₇×#102	C₂³	1	1	yes	characteristic
300	C₇×#102	C₂³	1	1	yes	characteristic
301	C₇×#102	C₂³	1	1	yes	characteristic
302	C₇×#102	C₂³	1	2	yes	—
303	C₇×#102	C₂³	1	1	yes	characteristic
304	C₇×#102	C₂³	1	1	yes	characteristic
305	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₇×#97	C₂³	1	1	yes	characteristic
309	C₇×#97	C₂³	1	1	yes	characteristic
310	C₇×#97	C₂³	1	2	yes	—
311	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
312	C₄×C₇×C₈	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₇×C₈	C₂³	1	2	yes	—
315	#3481	C₂×C₇	1	1	yes	characteristic, complemented
316	#3475	C₂×C₇	1	1	yes	characteristic, complemented
317	#3394	C₂×C₇	1	1	yes	characteristic, complemented
318	#3380	C₂×C₇	1	1	yes	characteristic, complemented
319	#3361	C₂×C₇	1	1	yes	characteristic, complemented
320	#3360	C₂×C₇	1	1	yes	characteristic, complemented
321	#3357	C₂×C₇	1	1	yes	characteristic, complemented
322	#3351	C₂×C₇	1	2	yes	complemented
323	#3331	C₂×C₇	1	1	yes	characteristic, complemented
324	#3325	C₂×C₇	1	1	yes	characteristic, complemented
325	#3323	C₂×C₇	1	2	yes	complemented
326	#3322	C₂×C₇	1	2	yes	complemented
327	#3273	C₂×C₇	1	2	yes	complemented
328	#3272	C₂×C₇	1	1	yes	characteristic, complemented
329	#3183	C₂×C₇	1	2	yes	complemented
330	#3182	C₂×C₇	1	1	yes	characteristic, complemented
331	#3116	C₂×C₇	1	1	yes	characteristic, complemented
332	#3114	C₂×C₇	1	2	yes	complemented
333	#3111	C₂×C₇	1	2	yes	complemented
334	#3109	C₂×C₇	1	1	yes	characteristic, complemented
335	#2971	C₂×C₇	1	1	yes	characteristic, complemented
336	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic, complemented
337	C₄×AGL(1,ℤ/8)	C₂×C₇	1	2	yes	complemented
338	C₂⁴×C₇	—	2	1	no	—
339	C₂⁴×C₇	—	2	2	no	—
340	C₇×#41	—	2	4	no	—
341	C₇×#41	—	2	2	no	—
342	C₇×#41	—	4	2	no	—
343	C₇×#41	—	4	1	no	—
344	C₇×#41	—	4	2	no	—
345	C₇×#41	—	8	2	no	—
346	C₂×C₇×Q₈	—	2	1	no	—
347	C₂×C₇×Q₈	—	2	1	no	—
348	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
349	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
350	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
351	C₂×C₇×D₄	—	2	2	no	—
352	C₂×C₇×D₄	—	2	4	no	—
353	C₂×C₇×D₄	—	2	1	no	—
354	C₂×C₇×D₄	—	2	2	no	—
355	C₂×C₇×D₄	—	2	2	no	—
356	C₂×C₇×D₄	—	2	2	no	—
357	C₂×C₇×D₄	—	2	2	no	—
358	C₂×C₇×D₄	—	2	2	no	—
359	C₂×C₇×D₄	—	2	1	no	—
360	C₂×C₇×D₄	—	2	1	no	—
361	C₂×C₇×D₄	—	2	1	no	—
362	C₂×C₇×D₄	—	4	2	no	—
363	C₂×C₇×D₄	—	4	1	no	—
364	C₂×C₇×D₄	—	4	4	no	—
365	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
366	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
367	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
368	C₂×C₇×D₄	C₂⁴	1	2	yes	—
369	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
370	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₇	—	2	1	no	—
372	C₂²×C₄×C₇	—	2	2	no	—
373	C₂²×C₄×C₇	—	2	1	no	—
374	C₂²×C₄×C₇	—	2	1	no	—
375	C₂²×C₄×C₇	—	2	2	no	—
376	C₂²×C₄×C₇	—	2	1	no	—
377	C₂²×C₄×C₇	—	2	1	no	—
378	C₂²×C₄×C₇	—	2	1	no	—
379	C₂²×C₄×C₇	—	2	1	no	—
380	C₂²×C₄×C₇	—	2	1	no	—
381	C₂²×C₄×C₇	—	2	2	no	—
382	C₂²×C₄×C₇	—	2	2	no	—
383	C₂²×C₄×C₇	—	2	2	no	—
384	C₂²×C₄×C₇	—	2	2	no	—
385	C₂²×C₄×C₇	—	4	4	no	—
386	C₂²×C₄×C₇	—	8	4	no	—
387	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
389	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
391	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
392	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
393	C₇×Q₁₆	—	4	2	no	—
394	C₇×SD₁₆	—	2	2	no	—
395	C₇×SD₁₆	—	2	4	no	—
396	C₇×SD₁₆	—	2	4	no	—
397	C₇×SD₁₆	—	2	2	no	—
398	C₇×SD₁₆	—	4	2	no	—
399	C₇×D₈	—	2	4	no	—
400	C₇×D₈	—	2	2	no	—
401	C₇×D₈	—	4	2	no	—
402	C₇×D₈	#41	1	4	yes	complemented
403	C₇×M₁₆	—	2	2	no	—
404	C₇×M₁₆	—	2	4	no	—
405	C₇×M₁₆	—	4	2	no	—
406	C₇×M₁₆	—	4	1	no	—
407	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
408	C₂×C₇×C₈	C₂⁴	1	2	yes	—
409	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
410	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
411	C₂×C₇×C₈	C₂⁴	1	2	yes	—
412	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
413	C₇×C₄⋊C₄	—	2	1	no	—
414	C₇×C₄⋊C₄	—	2	1	no	—
415	C₇×C₄⋊C₄	—	2	2	no	—
416	C₇×C₄⋊C₄	—	2	2	no	—
417	C₇×C₄⋊C₄	—	2	1	no	—
418	C₇×C₄⋊C₄	—	2	2	no	—
419	C₇×C₄⋊C₄	—	2	2	no	—
420	C₇×C₄⋊C₄	—	2	1	no	—
421	C₇×C₄⋊C₄	—	2	1	no	—
422	C₇×C₄⋊C₄	—	2	2	no	—
423	C₇×C₄⋊C₄	—	2	2	no	—
424	C₇×C₄⋊C₄	—	2	1	no	—
425	C₇×C₄⋊C₄	—	2	2	no	—
426	C₇×C₄⋊C₄	—	2	2	no	—
427	C₇×C₄⋊C₄	—	2	2	no	—
428	C₇×C₄⋊C₄	—	2	2	no	—
429	C₇×C₄⋊C₄	—	2	1	no	—
430	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
431	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
432	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
433	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
434	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
435	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
436	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
437	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
438	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
439	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
440	C₇×C₂²⋊C₄	—	2	2	no	—
441	C₇×C₂²⋊C₄	—	2	2	no	—
442	C₇×C₂²⋊C₄	—	2	1	no	—
443	C₇×C₂²⋊C₄	—	2	2	no	—
444	C₇×C₂²⋊C₄	—	2	2	no	—
445	C₇×C₂²⋊C₄	—	2	1	no	—
446	C₇×C₂²⋊C₄	—	2	1	no	—
447	C₇×C₂²⋊C₄	—	2	2	no	—
448	C₇×C₂²⋊C₄	—	2	2	no	—
449	C₇×C₂²⋊C₄	—	2	2	no	—
450	C₇×C₂²⋊C₄	—	2	2	no	—
451	C₇×C₂²⋊C₄	—	2	2	no	—
452	C₇×C₂²⋊C₄	—	2	2	no	—
453	C₇×C₂²⋊C₄	—	2	2	no	—
454	C₇×C₂²⋊C₄	—	2	1	no	—
455	C₇×C₂²⋊C₄	—	2	1	no	—
456	C₇×C₂²⋊C₄	—	2	1	no	—
457	C₇×C₂²⋊C₄	—	2	1	no	—
458	C₇×C₂²⋊C₄	—	2	2	no	—
459	C₇×C₂²⋊C₄	—	2	2	no	—
460	C₇×C₂²⋊C₄	—	2	2	no	—
461	C₇×C₂²⋊C₄	—	2	2	no	—
462	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
463	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
464	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
465	C₄²×C₇	—	2	2	no	—
466	C₄²×C₇	—	2	1	no	—
467	C₄²×C₇	—	2	2	no	—
468	C₄²×C₇	—	2	2	no	—
469	C₄²×C₇	—	2	1	no	—
470	C₄²×C₇	—	2	1	no	—
471	C₄²×C₇	C₂×D₄	1	2	yes	—
472	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
473	C₄²×C₇	C₂×D₄	1	2	yes	—
474	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
475	C₄²×C₇	C₂⁴	1	2	yes	—
476	C₄²×C₇	C₂⁴	1	1	yes	characteristic
477	C₄²×C₇	C₂⁴	1	1	yes	characteristic
478	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
479	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
480	#559	C₂²×C₇	1	1	yes	characteristic, complemented
481	#556	C₂²×C₇	1	1	yes	characteristic, complemented
482	#555	C₂²×C₇	1	1	yes	characteristic
483	#554	C₂²×C₇	1	1	yes	characteristic, complemented
484	#554	C₂²×C₇	1	1	yes	characteristic, complemented
485	#554	C₂²×C₇	1	1	yes	characteristic, complemented
486	#553	—	2	1	no	—
487	#553	—	2	1	no	—
488	#553	C₂²×C₇	1	2	yes	—
489	#552	—	2	1	no	—
490	#552	C₂²×C₇	1	2	yes	complemented
491	#551	—	2	2	no	—
492	#551	—	2	2	no	—
493	#547	C₂²×C₇	1	1	yes	characteristic
494	#546	—	2	1	no	—
495	#546	C₂²×C₇	1	2	yes	—
496	#546	C₂²×C₇	1	2	yes	complemented
497	D₄²	C₂²×C₇	1	1	yes	characteristic, complemented
498	#533	C₂²×C₇	1	1	yes	characteristic, complemented
499	#532	C₂²×C₇	1	1	yes	characteristic
500	#529	—	2	1	no	—
501	#529	—	2	2	no	—
502	#529	C₂²×C₇	1	2	yes	complemented
503	#529	C₂²×C₇	1	2	yes	complemented
504	#525	—	2	1	no	—
505	#525	—	2	2	no	—
506	C₄×#41	C₂²×C₇	1	1	yes	characteristic
507	C₄×#41	C₂²×C₇	1	1	yes	characteristic
508	C₄×#41	C₂²×C₇	1	2	yes	complemented
509	C₂×C₄×D₄	—	2	1	no	—
510	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
511	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
512	C₂×#117	—	2	1	no	—
513	#500	C₂²×C₇	1	1	yes	characteristic, complemented
514	#499	C₂²×C₇	1	2	yes	complemented
515	#495	C₂²×C₇	1	2	yes	complemented
516	#492	C₂²×C₇	1	1	yes	characteristic, complemented
517	#488	C₂²×C₇	1	2	yes	complemented
518	#488	C₂²×C₇	1	2	yes	complemented
519	#487	C₂²×C₇	1	1	yes	characteristic, complemented
520	#486	C₂²×C₇	1	1	yes	characteristic, complemented
521	#485	C₂²×C₇	1	2	yes	complemented
522	#485	C₂²×C₇	1	2	yes	complemented
523	#483	C₂²×C₇	1	2	yes	complemented
524	#482	C₂²×C₇	1	2	yes	complemented
525	#481	C₂²×C₇	1	2	yes	complemented
526	#480	C₂²×C₇	1	2	yes	complemented
527	#479	C₂²×C₇	1	2	yes	complemented
528	#478	C₂²×C₇	1	2	yes	complemented
529	#478	C₂²×C₇	1	2	yes	complemented
530	#478	C₂²×C₇	1	2	yes	complemented
531	#477	C₂²×C₇	1	1	yes	characteristic, complemented
532	#476	C₂²×C₇	1	1	yes	characteristic, complemented
533	#476	C₂²×C₇	1	1	yes	characteristic, complemented
534	#476	C₂²×C₇	1	1	yes	characteristic, complemented
535	#470	C₂²×C₇	1	2	yes	complemented
536	#469	C₂²×C₇	1	2	yes	—
537	#468	C₂²×C₇	1	2	yes	complemented
538	#468	C₂²×C₇	1	2	yes	complemented
539	#468	C₂²×C₇	1	2	yes	complemented
540	#468	C₂²×C₇	1	2	yes	complemented
541	#464	C₂²×C₇	1	2	yes	complemented
542	#463	C₂²×C₇	1	2	yes	—
543	#463	C₂²×C₇	1	2	yes	complemented
544	#463	C₂²×C₇	1	2	yes	complemented
545	#462	C₂²×C₇	1	1	yes	characteristic, complemented
546	#461	C₂²×C₇	1	1	yes	characteristic, complemented
547	#459	C₂²×C₇	1	1	yes	characteristic
548	#459	C₂²×C₇	1	1	yes	characteristic
549	#452	C₂²×C₇	1	2	yes	—
550	#452	C₂²×C₇	1	2	yes	complemented
551	#450	C₂²×C₇	1	2	yes	complemented
552	#449	C₂²×C₇	1	2	yes	—
553	#447	C₂²×C₇	1	2	yes	—
554	#447	C₂²×C₇	1	2	yes	complemented
555	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
556	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
557	#442	C₂²×C₇	1	1	yes	characteristic
558	#442	C₂²×C₇	1	1	yes	characteristic
559	#442	C₂²×C₇	1	2	yes	complemented
560	#442	C₂²×C₇	1	2	yes	complemented
561	#441	C₂²×C₇	1	2	yes	complemented
562	#440	C₂²×C₇	1	1	yes	characteristic, complemented
563	#440	C₂²×C₇	1	2	yes	complemented
564	#440	C₂²×C₇	1	2	yes	complemented
565	#440	C₂²×C₇	1	2	yes	complemented
566	#440	C₂²×C₇	1	1	yes	characteristic, complemented
567	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
568	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
569	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
570	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
571	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
572	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
573	C₄×D₈	C₂²×C₇	1	2	yes	—
574	C₄×D₈	C₂²×C₇	1	2	yes	complemented
575	#436	C₂²×C₇	1	1	yes	characteristic, complemented
576	#436	C₂²×C₇	1	2	yes	complemented
577	#436	C₂²×C₇	1	1	yes	characteristic, complemented
578	#436	C₂²×C₇	1	2	yes	complemented
579	#432	C₂²×C₇	1	1	yes	characteristic, complemented
580	#432	C₂²×C₇	1	2	yes	complemented
581	#428	C₂²×C₇	1	1	yes	characteristic, complemented
582	#428	C₂²×C₇	1	2	yes	complemented
583	#418	C₂²×C₇	1	1	yes	characteristic, complemented
584	#418	C₂²×C₇	1	2	yes	complemented
585	#417	C₂²×C₇	1	1	yes	characteristic
586	#417	C₂²×C₇	1	2	yes	complemented
587	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
588	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
589	C₂³×C₇	—	2	1	no	—
590	C₂³×C₇	—	2	1	no	—
591	C₂³×C₇	—	2	1	no	—
592	C₂³×C₇	—	2	2	no	—
593	C₂³×C₇	—	4	2	no	—
594	C₂³×C₇	—	4	4	no	—
595	C₂³×C₇	—	4	2	no	—
596	C₂³×C₇	—	4	4	no	—
597	C₂³×C₇	—	8	2	no	—
598	C₂³×C₇	—	8	1	no	—
599	C₂³×C₇	C₂²×D₄	1	2	yes	—
600	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
601	C₇×Q₈	—	2	2	no	—
602	C₇×Q₈	—	2	1	no	—
603	C₇×Q₈	—	2	2	no	—
604	C₇×Q₈	—	2	2	no	—
605	C₇×Q₈	—	2	1	no	—
606	C₇×Q₈	—	8	1	no	—
607	C₇×Q₈	—	8	1	no	—
608	C₇×D₄	—	2	2	no	—
609	C₇×D₄	—	2	1	no	—
610	C₇×D₄	—	2	2	no	—
611	C₇×D₄	—	2	1	no	—
612	C₇×D₄	—	2	1	no	—
613	C₇×D₄	—	2	1	no	—
614	C₇×D₄	—	2	2	no	—
615	C₇×D₄	—	4	2	no	—
616	C₇×D₄	—	4	2	no	—
617	C₇×D₄	—	4	4	no	—
618	C₇×D₄	—	4	4	no	—
619	C₇×D₄	—	4	2	no	—
620	C₇×D₄	—	4	4	no	—
621	C₇×D₄	—	4	2	no	—
622	C₇×D₄	—	8	1	no	—
623	C₇×D₄	—	8	2	no	—
624	C₇×D₄	—	8	2	no	—
625	C₇×D₄	C₂×#41	1	2	yes	—
626	C₇×D₄	C₂×#41	1	2	yes	—
627	C₂×C₄×C₇	—	2	2	no	—
628	C₂×C₄×C₇	—	2	2	no	—
629	C₂×C₄×C₇	—	2	1	no	—
630	C₂×C₄×C₇	—	2	2	no	—
631	C₂×C₄×C₇	—	2	1	no	—
632	C₂×C₄×C₇	—	2	1	no	—
633	C₂×C₄×C₇	—	2	1	no	—
634	C₂×C₄×C₇	—	2	2	no	—
635	C₂×C₄×C₇	—	2	1	no	—
636	C₂×C₄×C₇	—	2	2	no	—
637	C₂×C₄×C₇	—	2	1	no	—
638	C₂×C₄×C₇	—	2	1	no	—
639	C₂×C₄×C₇	—	2	2	no	—
640	C₂×C₄×C₇	—	4	2	no	—
641	C₂×C₄×C₇	—	4	2	no	—
642	C₂×C₄×C₇	—	4	1	no	—
643	C₂×C₄×C₇	—	4	4	no	—
644	C₂×C₄×C₇	—	4	2	no	—
645	C₂×C₄×C₇	—	4	2	no	—
646	C₂×C₄×C₇	—	4	2	no	—
647	C₂×C₄×C₇	—	4	2	no	—
648	C₂×C₄×C₇	—	4	4	no	—
649	C₂×C₄×C₇	—	4	2	no	—
650	C₂×C₄×C₇	—	4	2	no	—
651	C₂×C₄×C₇	—	4	2	no	—
652	C₂×C₄×C₇	—	4	2	no	—
653	C₂×C₄×C₇	—	8	2	no	—
654	C₂×C₄×C₇	—	8	2	no	—
655	C₂×C₄×C₇	—	8	2	no	—
656	C₂×C₄×C₇	—	8	2	no	—
657	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
658	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
659	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
660	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
661	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
662	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
663	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
664	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
665	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
666	C₇×C₈	—	2	1	no	—
667	C₇×C₈	—	2	2	no	—
668	C₇×C₈	—	2	1	no	—
669	C₇×C₈	—	2	2	no	—
670	C₇×C₈	—	2	1	no	—
671	C₇×C₈	C₂×#41	1	2	yes	—
672	C₂×#41	—	2	1	no	—
673	C₂×#41	C₇×D₄	1	1	yes	characteristic
674	C₂×#41	C₂³×C₇	1	1	yes	characteristic
675	C₂×#41	C₂³×C₇	1	2	yes	—
676	C₂²×D₄	—	2	1	no	—
677	C₂²×D₄	C₂³×C₇	1	2	yes	—
678	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
679	C₂³×C₄	—	2	1	no	—
680	C₂³×C₄	—	2	2	no	—
681	AGL(1,ℤ/8)	—	2	8	no	—
682	AGL(1,ℤ/8)	—	2	4	no	—
683	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
684	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
685	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
686	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
688	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
689	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
690	C₂×D₈	C₂³×C₇	1	2	yes	—
691	C₂×D₈	C₂³×C₇	1	2	yes	—
692	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
693	C₂×M₁₆	C₂³×C₇	1	2	yes	—
694	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
695	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
696	C₂×M₁₆	C₂³×C₇	1	2	yes	—
697	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
698	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
699	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
700	#127	C₂³×C₇	1	1	yes	characteristic
701	#126	—	2	2	no	—
702	#126	—	2	2	no	—
703	#126	—	2	2	no	—
704	#126	—	2	2	no	—
705	#126	—	2	2	no	—
706	#125	—	2	2	no	—
707	#125	—	2	1	no	—
708	#125	—	2	1	no	—
709	#125	C₂³×C₇	1	2	yes	—
710	#125	C₂³×C₇	1	2	yes	—
711	#124	—	2	1	no	—
712	#124	—	2	2	no	—
713	#124	—	2	1	no	—
714	#124	C₂³×C₇	1	2	yes	—
715	#124	C₂³×C₇	1	2	yes	—
716	#123	—	2	2	no	—
717	#123	—	2	2	no	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	#123	—	2	2	no	—
721	#123	—	2	2	no	—
722	#123	—	2	2	no	—
723	#123	—	2	2	no	—
724	C₂²⋊Q₈	—	2	1	no	—
725	C₂²⋊Q₈	—	2	1	no	—
726	C₂²⋊Q₈	—	2	1	no	—
727	C₂²⋊Q₈	—	2	1	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
732	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
733	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
734	#121	—	2	2	no	—
735	#121	—	2	1	no	—
736	#121	—	2	1	no	—
737	#121	—	2	1	no	—
738	#121	—	2	1	no	—
739	#121	—	2	2	no	—
740	#121	—	2	2	no	—
741	#121	C₂³×C₇	1	2	yes	—
742	#121	C₂³×C₇	1	2	yes	—
743	#121	C₂³×C₇	1	2	yes	—
744	#120	—	2	2	no	—
745	#120	—	2	2	no	—
746	#120	—	2	2	no	—
747	C₄×Q₈	—	2	1	no	—
748	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
749	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
750	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
751	C₄×Q₈	C₂³×C₇	1	2	yes	—
752	C₄×Q₈	C₂³×C₇	1	2	yes	—
753	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
754	C₄×D₄	—	2	1	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	—	2	1	no	—
757	C₄×D₄	—	2	1	no	—
758	C₄×D₄	—	2	2	no	—
759	C₄×D₄	—	2	2	no	—
760	C₄×D₄	—	2	2	no	—
761	C₄×D₄	—	2	1	no	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	—	2	1	no	—
764	C₄×D₄	—	2	2	no	—
765	C₄×D₄	—	2	1	no	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	—	2	1	no	—
768	C₄×D₄	C₇×D₄	1	1	yes	characteristic
769	C₄×D₄	C₇×D₄	1	2	yes	—
770	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
771	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
772	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
773	C₄×D₄	C₂³×C₇	1	2	yes	—
774	C₄×D₄	C₂³×C₇	1	2	yes	—
775	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
776	C₄×D₄	C₂³×C₇	1	2	yes	—
777	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
778	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
779	C₄×D₄	C₂³×C₇	1	2	yes	—
780	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
781	C₄×D₄	C₂³×C₇	1	2	yes	—
782	#117	—	2	1	no	—
783	#117	—	2	1	no	—
784	#117	—	2	1	no	—
785	#117	—	2	2	no	—
786	#117	—	2	2	no	—
787	#117	—	2	1	no	—
788	#117	—	2	2	no	—
789	#117	—	2	2	no	—
790	#117	C₇×D₄	1	1	yes	characteristic
791	#117	C₇×D₄	1	2	yes	—
792	#117	C₂³×C₇	1	1	yes	characteristic
793	#117	C₂³×C₇	1	2	yes	—
794	C₂×C₄⋊C₄	—	2	1	no	—
795	C₂×C₄⋊C₄	—	2	1	no	—
796	C₂×C₄⋊C₄	—	2	1	no	—
797	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
798	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
799	C₂×C₂²⋊C₄	—	2	2	no	—
800	C₂×C₂²⋊C₄	—	2	1	no	—
801	C₂×C₂²⋊C₄	—	2	2	no	—
802	C₂×C₂²⋊C₄	—	2	2	no	—
803	C₂×C₄²	—	2	2	no	—
804	C₂×C₄²	—	2	1	no	—
805	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
806	C₂×C₄²	C₂³×C₇	1	2	yes	—
807	#107	C₂³×C₇	1	1	yes	characteristic
808	#107	C₂³×C₇	1	2	yes	—
809	#107	C₂³×C₇	1	1	yes	characteristic
810	#107	C₂³×C₇	1	2	yes	—
811	#107	C₂³×C₇	1	2	yes	—
812	#106	C₂³×C₇	1	1	yes	characteristic
813	#106	C₂³×C₇	1	1	yes	characteristic
814	#106	C₂³×C₇	1	2	yes	—
815	#106	C₂³×C₇	1	2	yes	—
816	#106	C₂³×C₇	1	2	yes	—
817	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₇	1	2	yes	—
820	C₄⋊C₈	C₂³×C₇	1	2	yes	—
821	#103	C₂³×C₇	1	1	yes	characteristic
822	#103	C₂³×C₇	1	1	yes	characteristic
823	#103	C₂³×C₇	1	2	yes	—
824	#103	C₂³×C₇	1	2	yes	—
825	#103	C₂³×C₇	1	2	yes	—
826	#103	C₂³×C₇	1	2	yes	—
827	#103	C₂³×C₇	1	2	yes	—
828	#102	C₂³×C₇	1	1	yes	characteristic
829	#102	C₂³×C₇	1	1	yes	characteristic
830	#102	C₂³×C₇	1	1	yes	characteristic
831	#102	C₂³×C₇	1	2	yes	—
832	#102	C₂³×C₇	1	2	yes	—
833	#102	C₂³×C₇	1	1	yes	characteristic
834	#102	C₂³×C₇	1	1	yes	characteristic
835	#102	C₂³×C₇	1	2	yes	—
836	#102	C₂³×C₇	1	1	yes	characteristic
837	#102	C₂³×C₇	1	2	yes	—
838	#102	C₂³×C₇	1	2	yes	—
839	#102	C₂³×C₇	1	2	yes	—
840	#102	C₂³×C₇	1	2	yes	—
841	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
842	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
843	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
844	#97	C₂³×C₇	1	1	yes	characteristic
845	#97	C₂³×C₇	1	1	yes	characteristic
846	#97	C₂³×C₇	1	2	yes	—
847	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
848	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
849	C₄×C₈	C₂³×C₇	1	2	yes	—
850	C₄×C₈	C₂³×C₇	1	2	yes	—
851	C₂²×C₇	—	2	2	no	—
852	C₂²×C₇	—	2	1	no	—
853	C₂²×C₇	—	2	2	no	—
854	C₂²×C₇	—	2	1	no	—
855	C₂²×C₇	—	2	2	no	—
856	C₂²×C₇	—	2	2	no	—
857	C₂²×C₇	—	2	1	no	—
858	C₂²×C₇	—	2	2	no	—
859	C₂²×C₇	—	4	1	no	—
860	C₂²×C₇	—	4	1	no	—
861	C₂²×C₇	—	4	1	no	—
862	C₂²×C₇	—	4	1	no	—
863	C₂²×C₇	—	4	2	no	—
864	C₂²×C₇	—	4	1	no	—
865	C₂²×C₇	—	4	1	no	—
866	C₂²×C₇	—	4	2	no	—
867	C₂²×C₇	—	4	1	no	—
868	C₂²×C₇	—	4	2	no	—
869	C₂²×C₇	—	8	4	no	—
870	C₂²×C₇	—	8	8	no	—
871	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
872	C₄×C₇	—	2	1	no	—
873	C₄×C₇	—	2	2	no	—
874	C₄×C₇	—	2	1	no	—
875	C₄×C₇	—	2	2	no	—
876	C₄×C₇	—	2	1	no	—
877	C₄×C₇	—	2	1	no	—
878	C₄×C₇	—	2	2	no	—
879	C₄×C₇	—	4	1	no	—
880	C₄×C₇	—	4	2	no	—
881	C₄×C₇	—	4	2	no	—
882	C₄×C₇	—	4	1	no	—
883	C₄×C₇	—	4	2	no	—
884	C₄×C₇	—	4	1	no	—
885	C₄×C₇	—	4	1	no	—
886	C₄×C₇	—	4	1	no	—
887	C₄×C₇	#575	1	2	yes	—
888	C₄×C₇	C₂²×#41	1	1	yes	characteristic
889	C₄×C₇	#585	1	1	yes	characteristic
890	C₂⁴	—	2	1	no	—
891	C₂⁴	—	2	2	no	—
892	#41	—	2	4	no	—
893	#41	—	2	2	no	—
894	#41	—	4	2	no	—
895	#41	—	4	1	no	—
896	#41	—	4	2	no	—
897	#41	—	8	2	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	1	no	—
900	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
902	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	4	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	1	no	—
914	C₂×D₄	—	4	2	no	—
915	C₂×D₄	—	4	1	no	—
916	C₂×D₄	—	4	4	no	—
917	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
918	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
919	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
920	C₂×D₄	C₂⁴×C₇	1	2	yes	—
921	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
922	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	4	4	no	—
938	C₂²×C₄	—	8	4	no	—
939	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
940	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
941	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
942	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
943	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
944	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
945	Q₁₆	—	4	2	no	—
946	SD₁₆	—	2	2	no	—
947	SD₁₆	—	2	4	no	—
948	SD₁₆	—	2	4	no	—
949	SD₁₆	—	2	2	no	—
950	SD₁₆	—	4	2	no	—
951	D₈	—	2	4	no	—
952	D₈	—	2	2	no	—
953	D₈	—	4	2	no	—
954	D₈	C₇×#41	1	4	yes	complemented
955	M₁₆	—	2	4	no	—
956	M₁₆	—	2	2	no	—
957	M₁₆	—	4	2	no	—
958	M₁₆	—	4	1	no	—
959	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
960	C₂×C₈	C₂⁴×C₇	1	2	yes	—
961	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₇	1	2	yes	—
964	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
983	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
984	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
985	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
986	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
987	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
989	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
990	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1015	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1016	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	C₂×C₇×D₄	1	2	yes	—
1024	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1025	C₄²	C₂×C₇×D₄	1	2	yes	—
1026	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1027	C₄²	C₂⁴×C₇	1	2	yes	—
1028	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1029	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1030	C₂×C₇	—	4	2	no	—
1031	C₂×C₇	—	4	1	no	—
1032	C₂×C₇	—	4	2	no	—
1033	C₂×C₇	—	4	2	no	—
1034	C₂×C₇	—	8	2	no	—
1035	C₂×C₇	—	8	1	no	—
1036	C₂×C₇	D₄×#41	1	1	yes	characteristic
1037	C₂×C₇	C₂×#575	1	1	yes	characteristic
1038	C₂×C₇	#3585	1	1	yes	characteristic
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	4	2	no	—
1044	C₂³	—	4	4	no	—
1045	C₂³	—	4	2	no	—
1046	C₂³	—	4	4	no	—
1047	C₂³	—	8	2	no	—
1048	C₂³	—	8	1	no	—
1049	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1050	C₂³	C₂²×C₇×D₄	1	2	yes	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	2	2	no	—
1055	Q₈	—	2	1	no	—
1056	Q₈	—	8	1	no	—
1057	Q₈	—	8	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	4	no	—
1068	D₄	—	4	4	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	4	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	8	1	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	C₂×C₇×#41	1	2	yes	—
1076	D₄	C₂×C₇×#41	1	2	yes	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	1	no	—
1093	C₂×C₄	—	4	4	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	4	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	2	no	—
1107	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1108	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1109	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1110	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1111	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1112	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1113	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1114	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1115	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1116	C₈	—	2	1	no	—
1117	C₈	—	2	2	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	2	no	—
1120	C₈	—	2	1	no	—
1121	C₈	C₂×C₇×#41	1	2	yes	—
1122	C₇	#61464	1	1	yes	characteristic, direct product factor, Sylow
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	8	8	no	—
1142	C₂²	—	8	4	no	—
1143	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	2	no	—
1148	C₄	—	2	1	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	2	no	—
1156	C₄	—	4	2	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	2	no	—
1159	C₄	C₇×#575	1	2	yes	—
1160	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1161	C₄	C₇×#585	1	1	yes	characteristic
1162	C₂	—	4	1	no	—
1163	C₂	—	4	2	no	—
1164	C₂	—	4	2	no	—
1165	C₂	—	4	2	no	—
1166	C₂	—	8	1	no	—
1167	C₂	—	8	2	no	—
1168	C₂	C₇×D₄×#41	1	1	yes	characteristic
1169	C₂	C₂×C₇×#575	1	1	yes	characteristic
1170	C₂	C₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3481	C₂	semidirect
2. C₇×#3475	C₂	semidirect
3. C₇×#3394	C₂	semidirect
4. C₇×#3380	C₂	semidirect
5. C₇×#3361	C₂	semidirect
6. C₇×#3360	C₂	semidirect
7. C₇×#3357	C₂	semidirect
8. C₇×#3351	C₂	semidirect
9. C₇×#3331	C₂	semidirect
10. C₇×#3325	C₂	semidirect
11. C₇×#3323	C₂	semidirect
12. C₇×#3322	C₂	semidirect
13. C₇×#3273	C₂	semidirect
14. C₇×#3272	C₂	semidirect
15. C₇×#3183	C₂	semidirect
16. C₇×#3182	C₂	semidirect
17. C₇×#3116	C₂	semidirect
18. C₇×#3114	C₂	semidirect
19. C₇×#3111	C₂	semidirect
20. C₇×#3109	C₂	semidirect
21. C₇×#2971	C₂	semidirect
22. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
23. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
26. C₇×#559	C₂²	semidirect
27. C₇×#556	C₂²	semidirect
29. C₇×#554	C₂²	semidirect
30. C₇×#554	C₂²	semidirect
31. C₇×#554	C₂²	semidirect
36. C₇×#552	C₂²	semidirect
42. C₇×#546	C₂²	semidirect
43. C₇×D₄²	C₂²	semidirect
44. C₇×#533	C₂²	semidirect
48. C₇×#529	C₂²	semidirect
49. C₇×#529	C₂²	semidirect
54. C₄×C₇×#41	C₂²	semidirect
56. C₂×C₄×C₇×D₄	C₂²	semidirect
57. C₂×C₄×C₇×D₄	C₂²	semidirect
59. C₇×#500	C₂²	semidirect
60. C₇×#499	C₂²	semidirect
61. C₇×#495	C₂²	semidirect
62. C₇×#492	C₂²	semidirect
63. C₇×#488	C₂²	semidirect
64. C₇×#488	C₂²	semidirect
65. C₇×#487	C₂²	semidirect
66. C₇×#486	C₂²	semidirect
67. C₇×#485	C₂²	semidirect
68. C₇×#485	C₂²	semidirect
69. C₇×#483	C₂²	semidirect
70. C₇×#482	C₂²	semidirect
71. C₇×#481	C₂²	semidirect
72. C₇×#480	C₂²	semidirect
73. C₇×#479	C₂²	semidirect
74. C₇×#478	C₂²	semidirect
75. C₇×#478	C₂²	semidirect
76. C₇×#478	C₂²	semidirect
77. C₇×#477	C₂²	semidirect
78. C₇×#476	C₂²	semidirect
79. C₇×#476	C₂²	semidirect
80. C₇×#476	C₂²	semidirect
81. C₇×#470	C₂²	semidirect
83. C₇×#468	C₂²	semidirect
84. C₇×#468	C₂²	semidirect
85. C₇×#468	C₂²	semidirect
86. C₇×#468	C₂²	semidirect
87. C₇×#464	C₂²	semidirect
89. C₇×#463	C₂²	semidirect
90. C₇×#463	C₂²	semidirect
91. C₇×#462	C₂²	semidirect
92. C₇×#461	C₂²	semidirect
96. C₇×#452	C₂²	semidirect
97. C₇×#450	C₂²	semidirect
100. C₇×#447	C₂²	semidirect
101. C₇×C₈×Q₈	C₂²	semidirect
102. C₇×C₈×Q₈	C₂²	semidirect
105. C₇×#442	C₂²	semidirect
106. C₇×#442	C₂²	semidirect
107. C₇×#441	C₂²	semidirect
108. C₇×#440	C₂²	semidirect
109. C₇×#440	C₂²	semidirect
110. C₇×#440	C₂²	semidirect
111. C₇×#440	C₂²	semidirect
112. C₇×#440	C₂²	semidirect
113. C₄×C₇×SD₁₆	C₂²	semidirect
114. C₄×C₇×SD₁₆	C₂²	semidirect
115. C₄×C₇×SD₁₆	C₂²	semidirect
116. C₄×C₇×SD₁₆	C₂²	semidirect
120. C₄×C₇×D₈	C₂²	semidirect
121. C₇×#436	C₂²	semidirect
122. C₇×#436	C₂²	semidirect
123. C₇×#436	C₂²	semidirect
124. C₇×#436	C₂²	semidirect
125. C₇×#432	C₂²	semidirect
126. C₇×#432	C₂²	semidirect
127. C₇×#428	C₂²	semidirect
128. C₇×#428	C₂²	semidirect
129. C₇×#418	C₂²	semidirect
130. C₇×#418	C₂²	semidirect
132. C₇×#417	C₂²	semidirect
133. C₄×C₇×M₁₆	C₂²	semidirect
134. C₄×C₇×M₁₆	C₂²	semidirect
135. #61464	C₇	direct (N × H)
315. #3481	C₂×C₇	semidirect
316. #3475	C₂×C₇	semidirect
317. #3394	C₂×C₇	semidirect
318. #3380	C₂×C₇	semidirect
319. #3361	C₂×C₇	semidirect
320. #3360	C₂×C₇	semidirect
321. #3357	C₂×C₇	semidirect
322. #3351	C₂×C₇	semidirect
323. #3331	C₂×C₇	semidirect
324. #3325	C₂×C₇	semidirect
325. #3323	C₂×C₇	semidirect
326. #3322	C₂×C₇	semidirect
327. #3273	C₂×C₇	semidirect
328. #3272	C₂×C₇	semidirect
329. #3183	C₂×C₇	semidirect
330. #3182	C₂×C₇	semidirect
331. #3116	C₂×C₇	semidirect
332. #3114	C₂×C₇	semidirect
333. #3111	C₂×C₇	semidirect
334. #3109	C₂×C₇	semidirect
335. #2971	C₂×C₇	semidirect
336. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
337. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
402. C₇×D₈	#41	semidirect
480. #559	C₂²×C₇	semidirect
481. #556	C₂²×C₇	semidirect
483. #554	C₂²×C₇	semidirect
484. #554	C₂²×C₇	semidirect
485. #554	C₂²×C₇	semidirect
490. #552	C₂²×C₇	semidirect
496. #546	C₂²×C₇	semidirect
497. D₄²	C₂²×C₇	semidirect
498. #533	C₂²×C₇	semidirect
502. #529	C₂²×C₇	semidirect
503. #529	C₂²×C₇	semidirect
508. C₄×#41	C₂²×C₇	semidirect
510. C₂×C₄×D₄	C₂²×C₇	semidirect
511. C₂×C₄×D₄	C₂²×C₇	semidirect
513. #500	C₂²×C₇	semidirect
514. #499	C₂²×C₇	semidirect
515. #495	C₂²×C₇	semidirect
516. #492	C₂²×C₇	semidirect
517. #488	C₂²×C₇	semidirect
518. #488	C₂²×C₇	semidirect
519. #487	C₂²×C₇	semidirect
520. #486	C₂²×C₇	semidirect
521. #485	C₂²×C₇	semidirect
522. #485	C₂²×C₇	semidirect
523. #483	C₂²×C₇	semidirect
524. #482	C₂²×C₇	semidirect
525. #481	C₂²×C₇	semidirect
526. #480	C₂²×C₇	semidirect
527. #479	C₂²×C₇	semidirect
528. #478	C₂²×C₇	semidirect
529. #478	C₂²×C₇	semidirect
530. #478	C₂²×C₇	semidirect
531. #477	C₂²×C₇	semidirect
532. #476	C₂²×C₇	semidirect
533. #476	C₂²×C₇	semidirect
534. #476	C₂²×C₇	semidirect
535. #470	C₂²×C₇	semidirect
537. #468	C₂²×C₇	semidirect
538. #468	C₂²×C₇	semidirect
539. #468	C₂²×C₇	semidirect
540. #468	C₂²×C₇	semidirect
541. #464	C₂²×C₇	semidirect
543. #463	C₂²×C₇	semidirect
544. #463	C₂²×C₇	semidirect
545. #462	C₂²×C₇	semidirect
546. #461	C₂²×C₇	semidirect
550. #452	C₂²×C₇	semidirect
551. #450	C₂²×C₇	semidirect
554. #447	C₂²×C₇	semidirect
555. C₈×Q₈	C₂²×C₇	semidirect
556. C₈×Q₈	C₂²×C₇	semidirect
559. #442	C₂²×C₇	semidirect
560. #442	C₂²×C₇	semidirect
561. #441	C₂²×C₇	semidirect
562. #440	C₂²×C₇	semidirect
563. #440	C₂²×C₇	semidirect
564. #440	C₂²×C₇	semidirect
565. #440	C₂²×C₇	semidirect
566. #440	C₂²×C₇	semidirect
567. C₄×SD₁₆	C₂²×C₇	semidirect
568. C₄×SD₁₆	C₂²×C₇	semidirect
569. C₄×SD₁₆	C₂²×C₇	semidirect
570. C₄×SD₁₆	C₂²×C₇	semidirect
574. C₄×D₈	C₂²×C₇	semidirect
575. #436	C₂²×C₇	semidirect
576. #436	C₂²×C₇	semidirect
577. #436	C₂²×C₇	semidirect
578. #436	C₂²×C₇	semidirect
579. #432	C₂²×C₇	semidirect
580. #432	C₂²×C₇	semidirect
581. #428	C₂²×C₇	semidirect
582. #428	C₂²×C₇	semidirect
583. #418	C₂²×C₇	semidirect
584. #418	C₂²×C₇	semidirect
586. #417	C₂²×C₇	semidirect
587. C₄×M₁₆	C₂²×C₇	semidirect
588. C₄×M₁₆	C₂²×C₇	semidirect
954. D₈	C₇×#41	semidirect
1122. C₇	#61464	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3481	2
C₇×#3475	2
C₇×#3394	2
C₇×#3380	2
C₇×#3361	2
C₇×#3360	2
C₇×#3357	2
C₇×#3351	2
C₇×#3331	2
C₇×#3325	2
C₇×#3323	2
C₇×#3322	2
C₇×#3273	2
C₇×#3272	2
C₇×#3183	2
C₇×#3182	2
C₇×#3116	2
C₇×#3114	2
C₇×#3111	2
C₇×#3109	2
C₇×#2971	2
C₄×C₇×AGL(1,ℤ/8)	2
#61464	7

Subgroups — C7×#61464 #13238680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61464 #13238680