Subgroups — C₇×#61471 #13238687

Order 1792.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3513	C₂	1	2	yes	maximal, complemented
2	C₇×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3370	C₂	1	2	yes	maximal, complemented
5	C₇×#3339	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3336	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3334	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3322	C₂	1	2	yes	maximal, complemented
9	C₇×#3310	C₂	1	2	yes	maximal, complemented
10	C₇×#3306	C₂	1	2	yes	maximal, complemented
11	C₇×#3280	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3280	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×D₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3176	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3175	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3168	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3119	C₂	1	2	yes	maximal, complemented
18	C₇×#3118	C₂	1	2	yes	maximal, complemented
19	C₇×#3114	C₂	1	2	yes	maximal, complemented
20	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2951	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2948	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#135	C₂²	1	1	yes	characteristic
25	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
26	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
27	C₇×#559	C₂²	1	2	yes	complemented
28	C₇×#554	C₂²	1	2	yes	complemented
29	C₇×#553	—	2	2	no	—
30	C₇×#553	C₂²	1	2	yes	complemented
31	C₇×#552	C₂²	1	2	yes	—
32	C₇×#551	—	2	2	no	—
33	C₇×#551	—	2	2	no	—
34	C₇×#547	C₂²	1	2	yes	complemented
35	C₇×#546	—	2	2	no	—
36	C₇×#546	C₂²	1	2	yes	complemented
37	C₇×#546	C₂²	1	2	yes	complemented
38	C₇×D₄²	C₂²	1	2	yes	—
39	C₇×#542	C₂²	1	2	yes	complemented
40	C₇×#540	C₂²	1	2	yes	complemented
41	C₇×#539	—	2	2	no	—
42	C₇×#538	—	2	2	no	—
43	C₇×#529	C₂²	1	1	yes	characteristic
44	C₇×#529	C₂²	1	2	yes	complemented
45	C₇×#525	—	2	2	no	—
46	C₂×C₇×#123	—	2	2	no	—
47	C₇×#520	C₂²	1	2	yes	complemented
48	C₇×#518	C₂²	1	2	yes	complemented
49	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
50	C₇×#500	C₂²	1	1	yes	characteristic, complemented
51	C₇×#499	C₂²	1	1	yes	characteristic, complemented
52	C₇×#499	C₂²	1	1	yes	characteristic, complemented
53	C₇×#495	C₂²	1	1	yes	characteristic, complemented
54	C₇×#495	C₂²	1	1	yes	characteristic, complemented
55	C₇×#493	C₂²	1	1	yes	characteristic
56	C₇×#490	C₂²	1	2	yes	complemented
57	C₇×#489	C₂²	1	2	yes	complemented
58	C₇×#488	C₂²	1	2	yes	complemented
59	C₇×#485	C₂²	1	2	yes	complemented
60	C₇×#483	C₂²	1	2	yes	complemented
61	C₇×#482	C₂²	1	2	yes	complemented
62	C₇×#481	C₂²	1	2	yes	complemented
63	C₇×#480	C₂²	1	2	yes	complemented
64	C₇×#480	C₂²	1	2	yes	complemented
65	C₇×#479	C₂²	1	2	yes	complemented
66	C₇×#478	C₂²	1	2	yes	complemented
67	C₇×#478	C₂²	1	2	yes	complemented
68	C₇×#478	C₂²	1	2	yes	complemented
69	C₇×#476	C₂²	1	2	yes	complemented
70	C₇×#474	C₂²	1	2	yes	complemented
71	C₇×#469	C₂²	1	2	yes	complemented
72	C₇×#468	C₂²	1	2	yes	complemented
73	C₇×#467	C₂²	1	1	yes	characteristic, complemented
74	C₇×#467	C₂²	1	1	yes	characteristic, complemented
75	C₇×#466	C₂²	1	1	yes	characteristic
76	C₇×#466	C₂²	1	1	yes	characteristic
77	C₇×#466	C₂²	1	1	yes	characteristic, complemented
78	C₇×#466	C₂²	1	1	yes	characteristic, complemented
79	C₇×#465	C₂²	1	2	yes	complemented
80	C₇×#463	C₂²	1	2	yes	complemented
81	C₇×#463	C₂²	1	2	yes	complemented
82	C₇×#463	C₂²	1	2	yes	complemented
83	C₇×#463	C₂²	1	2	yes	complemented
84	C₇×#460	C₂²	1	2	yes	complemented
85	C₇×#459	C₂²	1	2	yes	—
86	C₇×#450	C₂²	1	2	yes	complemented
87	C₇×#450	C₂²	1	2	yes	complemented
88	C₇×#449	C₂²	1	2	yes	complemented
89	C₇×#449	C₂²	1	2	yes	complemented
90	C₇×#447	C₂²	1	2	yes	—
91	C₇×#447	C₂²	1	2	yes	—
92	C₇×#446	C₂²	1	1	yes	characteristic, complemented
93	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
94	C₇×#442	C₂²	1	2	yes	complemented
95	C₇×#442	C₂²	1	2	yes	complemented
96	C₇×#442	C₂²	1	2	yes	complemented
97	C₇×#440	C₂²	1	2	yes	complemented
98	C₇×#440	C₂²	1	2	yes	complemented
99	C₇×#440	C₂²	1	2	yes	complemented
100	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
103	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
104	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
105	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
106	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
107	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
108	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
109	C₄×C₇×D₈	C₂²	1	2	yes	complemented
110	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₇×D₈	C₂²	1	2	yes	complemented
112	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
113	C₇×#436	C₂²	1	1	yes	characteristic, complemented
114	C₇×#435	C₂²	1	1	yes	characteristic
115	C₇×#435	C₂²	1	1	yes	characteristic, complemented
116	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
117	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
118	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
119	C₇×#433	C₂²	1	1	yes	characteristic, complemented
120	C₇×#433	C₂²	1	1	yes	characteristic, complemented
121	C₇×#432	C₂²	1	1	yes	characteristic, complemented
122	C₇×#427	C₂²	1	1	yes	characteristic, complemented
123	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
125	C₇×#418	C₂²	1	2	yes	complemented
126	C₇×#417	C₂²	1	2	yes	complemented
127	C₂×C₇×#102	C₂²	1	2	yes	complemented
128	C₇×#405	C₂²	1	1	yes	characteristic, complemented
129	C₇×#405	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
131	#61471	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂×C₇×#41	—	2	2	no	—
133	C₂×C₇×#41	C₂³	1	2	yes	—
134	C₂²×C₇×D₄	—	2	2	no	—
135	C₂²×C₇×D₄	C₂³	1	2	yes	—
136	C₂²×C₇×D₄	C₂³	1	2	yes	—
137	C₂³×C₄×C₇	—	2	2	no	—
138	C₇×#135	—	2	4	no	—
139	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
141	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
142	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
143	C₂×C₇×D₈	—	2	4	no	—
144	C₂×C₇×D₈	—	2	4	no	—
145	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
146	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
147	C₂×C₇×D₈	C₂³	1	2	yes	—
148	C₂×C₇×D₈	C₂³	1	2	yes	—
149	C₂×C₇×D₈	C₂³	1	2	yes	—
150	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
151	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
152	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
153	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
154	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
155	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
156	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
157	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₇×#127	C₂³	1	2	yes	—
159	C₇×#126	—	2	2	no	—
160	C₇×#126	—	2	2	no	—
161	C₇×#126	—	2	2	no	—
162	C₇×#126	—	2	2	no	—
163	C₇×#126	D₄	1	1	yes	characteristic
164	C₇×#126	D₄	1	1	yes	characteristic
165	C₇×#125	—	2	2	no	—
166	C₇×#125	D₄	1	1	yes	characteristic
167	C₇×#125	C₂³	1	2	yes	—
168	C₇×#125	C₂³	1	2	yes	—
169	C₇×#124	—	2	2	no	—
170	C₇×#124	—	2	2	no	—
171	C₇×#124	D₄	1	1	yes	characteristic
172	C₇×#124	C₂³	1	2	yes	—
173	C₇×#124	C₂³	1	2	yes	—
174	C₇×#123	—	2	2	no	—
175	C₇×#123	—	2	2	no	—
176	C₇×#123	—	2	2	no	—
177	C₇×#123	—	2	2	no	—
178	C₇×#123	—	2	2	no	—
179	C₇×#123	—	2	2	no	—
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	D₄	1	1	yes	characteristic
187	C₇×#123	D₄	1	1	yes	characteristic
188	C₇×C₂²⋊Q₈	—	2	2	no	—
189	C₇×C₂²⋊Q₈	—	2	2	no	—
190	C₇×C₂²⋊Q₈	—	2	2	no	—
191	C₇×C₂²⋊Q₈	—	2	2	no	—
192	C₇×C₂²⋊Q₈	—	2	2	no	—
193	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
194	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₇×#121	—	2	2	no	—
197	C₇×#121	—	2	2	no	—
198	C₇×#121	—	2	2	no	—
199	C₇×#121	—	2	2	no	—
200	C₇×#121	—	2	2	no	—
201	C₇×#121	—	2	2	no	—
202	C₇×#121	D₄	1	1	yes	characteristic
203	C₇×#121	C₂³	1	2	yes	—
204	C₇×#121	C₂³	1	2	yes	—
205	C₇×#121	C₂³	1	2	yes	—
206	C₇×#121	C₂³	1	2	yes	—
207	C₇×#120	—	2	2	no	—
208	C₇×#120	—	2	2	no	—
209	C₇×#120	—	2	2	no	—
210	C₇×#120	—	2	2	no	—
211	C₄×C₇×Q₈	C₂³	1	2	yes	—
212	C₄×C₇×Q₈	C₂³	1	2	yes	—
213	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
214	C₄×C₇×D₄	—	2	2	no	—
215	C₄×C₇×D₄	—	2	2	no	—
216	C₄×C₇×D₄	—	2	2	no	—
217	C₄×C₇×D₄	—	2	2	no	—
218	C₄×C₇×D₄	—	2	2	no	—
219	C₄×C₇×D₄	—	2	2	no	—
220	C₄×C₇×D₄	—	2	2	no	—
221	C₄×C₇×D₄	—	2	2	no	—
222	C₄×C₇×D₄	—	2	2	no	—
223	C₄×C₇×D₄	C₂³	1	2	yes	—
224	C₄×C₇×D₄	C₂³	1	2	yes	—
225	C₄×C₇×D₄	C₂³	1	2	yes	—
226	C₄×C₇×D₄	C₂³	1	2	yes	—
227	C₄×C₇×D₄	C₂³	1	2	yes	—
228	C₄×C₇×D₄	C₂³	1	2	yes	—
229	C₄×C₇×D₄	C₂³	1	2	yes	—
230	C₄×C₇×D₄	C₂³	1	2	yes	—
231	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
232	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
233	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
234	C₇×#117	—	2	2	no	—
235	C₇×#117	—	2	2	no	—
236	C₇×#117	—	2	2	no	—
237	C₇×#117	C₂³	1	2	yes	—
238	C₇×#117	C₂³	1	1	yes	characteristic
239	C₇×#117	C₂³	1	1	yes	characteristic
240	C₂×C₇×C₄⋊C₄	—	2	2	no	—
241	C₂×C₇×C₄⋊C₄	—	2	2	no	—
242	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
243	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
244	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
250	C₇×#107	C₂³	1	1	yes	characteristic
251	C₇×#107	C₂³	1	1	yes	characteristic
252	C₇×#107	C₂³	1	1	yes	characteristic
253	C₇×#107	C₂³	1	2	yes	—
254	C₇×#107	C₂³	1	2	yes	—
255	C₇×#107	C₂³	1	2	yes	—
256	C₇×#107	C₂³	1	1	yes	characteristic
257	C₇×#106	C₂³	1	2	yes	—
258	C₇×#106	C₂³	1	2	yes	—
259	C₇×#106	C₂³	1	2	yes	—
260	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₇×#103	C₂³	1	2	yes	—
267	C₇×#103	C₂³	1	2	yes	—
268	C₇×#103	C₂³	1	2	yes	—
269	C₇×#103	C₂³	1	2	yes	—
270	C₇×#102	C₂³	1	2	yes	—
271	C₇×#102	C₂³	1	2	yes	—
272	C₇×#102	C₂³	1	2	yes	—
273	C₇×#102	C₂³	1	2	yes	—
274	C₇×#102	C₂³	1	2	yes	—
275	C₇×#102	C₂³	1	2	yes	—
276	C₇×#102	C₂³	1	2	yes	—
277	C₇×#102	C₂³	1	2	yes	—
278	C₇×#102	C₂³	1	2	yes	—
279	C₇×#102	C₂³	1	2	yes	—
280	C₇×#102	C₂³	1	2	yes	—
281	C₇×#102	C₂³	1	2	yes	—
282	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₇×#97	C₂³	1	1	yes	characteristic
289	C₇×#97	C₂³	1	1	yes	characteristic
290	C₇×#97	C₂³	1	1	yes	characteristic
291	C₇×#97	C₂³	1	1	yes	characteristic
292	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
293	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
294	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
295	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
296	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
297	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
298	#3513	C₂×C₇	1	2	yes	complemented
299	#3396	C₂×C₇	1	1	yes	characteristic, complemented
300	#3380	C₂×C₇	1	1	yes	characteristic, complemented
301	#3370	C₂×C₇	1	2	yes	complemented
302	#3339	C₂×C₇	1	1	yes	characteristic, complemented
303	#3336	C₂×C₇	1	1	yes	characteristic, complemented
304	#3334	C₂×C₇	1	1	yes	characteristic, complemented
305	#3322	C₂×C₇	1	2	yes	complemented
306	#3310	C₂×C₇	1	2	yes	complemented
307	#3306	C₂×C₇	1	2	yes	complemented
308	#3280	C₂×C₇	1	1	yes	characteristic, complemented
309	#3280	C₂×C₇	1	1	yes	characteristic, complemented
310	D₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
311	#3176	C₂×C₇	1	1	yes	characteristic, complemented
312	#3175	C₂×C₇	1	1	yes	characteristic, complemented
313	#3168	C₂×C₇	1	1	yes	characteristic, complemented
314	#3119	C₂×C₇	1	2	yes	complemented
315	#3118	C₂×C₇	1	2	yes	complemented
316	#3114	C₂×C₇	1	2	yes	complemented
317	#2966	C₂×C₇	1	1	yes	characteristic, complemented
318	#2951	C₂×C₇	1	1	yes	characteristic, complemented
319	#2948	C₂×C₇	1	1	yes	characteristic, complemented
320	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
321	C₂⁴×C₇	—	2	2	no	—
322	C₂⁴×C₇	—	2	2	no	—
323	C₇×#41	—	2	4	no	—
324	C₇×#41	—	4	2	no	—
325	C₇×#41	—	8	4	no	—
326	C₂×C₇×Q₈	—	2	2	no	—
327	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
328	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
329	C₂×C₇×D₄	—	2	4	no	—
330	C₂×C₇×D₄	—	2	4	no	—
331	C₂×C₇×D₄	—	2	2	no	—
332	C₂×C₇×D₄	—	2	2	no	—
333	C₂×C₇×D₄	—	2	2	no	—
334	C₂×C₇×D₄	—	2	2	no	—
335	C₂×C₇×D₄	—	2	2	no	—
336	C₂×C₇×D₄	—	2	2	no	—
337	C₂×C₇×D₄	—	2	2	no	—
338	C₂×C₇×D₄	—	2	2	no	—
339	C₂×C₇×D₄	—	2	2	no	—
340	C₂×C₇×D₄	—	4	2	no	—
341	C₂×C₇×D₄	—	4	2	no	—
342	C₂×C₇×D₄	—	8	4	no	—
343	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
344	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
345	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
346	C₂×C₇×D₄	C₂⁴	1	2	yes	—
347	C₂×C₇×D₄	C₂⁴	1	2	yes	—
348	C₂×C₇×D₄	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₇	—	2	2	no	—
350	C₂²×C₄×C₇	—	2	2	no	—
351	C₂²×C₄×C₇	—	2	2	no	—
352	C₂²×C₄×C₇	—	2	2	no	—
353	C₂²×C₄×C₇	—	2	2	no	—
354	C₂²×C₄×C₇	—	2	2	no	—
355	C₂²×C₄×C₇	—	2	2	no	—
356	C₂²×C₄×C₇	—	2	2	no	—
357	C₂²×C₄×C₇	—	2	2	no	—
358	C₂²×C₄×C₇	—	2	2	no	—
359	C₂²×C₄×C₇	—	2	2	no	—
360	C₂²×C₄×C₇	—	8	4	no	—
361	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
366	C₇×Q₁₆	—	2	2	no	—
367	C₇×SD₁₆	—	2	4	no	—
368	C₇×SD₁₆	—	4	2	no	—
369	C₇×SD₁₆	—	4	2	no	—
370	C₇×D₈	—	2	4	no	—
371	C₇×D₈	—	2	4	no	—
372	C₇×D₈	—	2	2	no	—
373	C₇×D₈	—	2	2	no	—
374	C₇×D₈	—	4	2	no	—
375	C₇×D₈	#41	1	4	yes	complemented
376	C₇×M₁₆	—	4	1	no	—
377	C₇×M₁₆	—	4	1	no	—
378	C₂×C₇×C₈	—	2	2	no	—
379	C₂×C₇×C₈	—	2	2	no	—
380	C₂×C₇×C₈	—	2	2	no	—
381	C₂×C₇×C₈	—	4	1	no	—
382	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
383	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
384	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
385	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
386	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
387	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
388	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
389	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
390	C₇×C₄⋊C₄	—	2	2	no	—
391	C₇×C₄⋊C₄	—	2	2	no	—
392	C₇×C₄⋊C₄	—	2	2	no	—
393	C₇×C₄⋊C₄	—	2	2	no	—
394	C₇×C₄⋊C₄	—	2	2	no	—
395	C₇×C₄⋊C₄	—	2	2	no	—
396	C₇×C₄⋊C₄	—	2	2	no	—
397	C₇×C₄⋊C₄	—	2	2	no	—
398	C₇×C₄⋊C₄	—	2	2	no	—
399	C₇×C₄⋊C₄	—	2	2	no	—
400	C₇×C₄⋊C₄	—	2	2	no	—
401	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
402	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
403	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
404	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
405	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
406	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
407	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
408	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
410	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
412	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
413	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
414	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
415	C₇×C₂²⋊C₄	—	2	2	no	—
416	C₇×C₂²⋊C₄	—	2	2	no	—
417	C₇×C₂²⋊C₄	—	2	2	no	—
418	C₇×C₂²⋊C₄	—	2	2	no	—
419	C₇×C₂²⋊C₄	—	2	2	no	—
420	C₇×C₂²⋊C₄	—	2	2	no	—
421	C₇×C₂²⋊C₄	—	2	2	no	—
422	C₇×C₂²⋊C₄	—	2	2	no	—
423	C₇×C₂²⋊C₄	—	2	2	no	—
424	C₇×C₂²⋊C₄	—	2	2	no	—
425	C₇×C₂²⋊C₄	—	2	2	no	—
426	C₇×C₂²⋊C₄	—	2	2	no	—
427	C₇×C₂²⋊C₄	—	2	2	no	—
428	C₇×C₂²⋊C₄	—	2	2	no	—
429	C₇×C₂²⋊C₄	—	2	2	no	—
430	C₇×C₂²⋊C₄	—	2	2	no	—
431	C₇×C₂²⋊C₄	—	2	2	no	—
432	C₇×C₂²⋊C₄	—	2	2	no	—
433	C₇×C₂²⋊C₄	—	2	2	no	—
434	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
435	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
436	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
437	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
438	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
439	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
440	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
441	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
442	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
443	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₇	—	2	2	no	—
445	C₄²×C₇	—	2	2	no	—
446	C₄²×C₇	—	2	2	no	—
447	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₇	C₂⁴	1	1	yes	characteristic
450	C₄²×C₇	C₂⁴	1	1	yes	characteristic
451	C₄²×C₇	C₂⁴	1	1	yes	characteristic
452	C₄²×C₇	C₂⁴	1	1	yes	characteristic
453	C₂×#135	C₂²×C₇	1	1	yes	characteristic
454	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
455	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
456	#559	C₂²×C₇	1	2	yes	complemented
457	#554	C₂²×C₇	1	2	yes	complemented
458	#553	—	2	2	no	—
459	#553	C₂²×C₇	1	2	yes	complemented
460	#552	C₂²×C₇	1	2	yes	—
461	#551	—	2	2	no	—
462	#551	—	2	2	no	—
463	#547	C₂²×C₇	1	2	yes	complemented
464	#546	—	2	2	no	—
465	#546	C₂²×C₇	1	2	yes	complemented
466	#546	C₂²×C₇	1	2	yes	complemented
467	D₄²	C₂²×C₇	1	2	yes	—
468	#542	C₂²×C₇	1	2	yes	complemented
469	#540	C₂²×C₇	1	2	yes	complemented
470	#539	—	2	2	no	—
471	#538	—	2	2	no	—
472	#529	C₂²×C₇	1	1	yes	characteristic
473	#529	C₂²×C₇	1	2	yes	complemented
474	#525	—	2	2	no	—
475	C₂×#123	—	2	2	no	—
476	#520	C₂²×C₇	1	2	yes	complemented
477	#518	C₂²×C₇	1	2	yes	complemented
478	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
479	#500	C₂²×C₇	1	1	yes	characteristic, complemented
480	#499	C₂²×C₇	1	1	yes	characteristic, complemented
481	#499	C₂²×C₇	1	1	yes	characteristic, complemented
482	#495	C₂²×C₇	1	1	yes	characteristic, complemented
483	#495	C₂²×C₇	1	1	yes	characteristic, complemented
484	#493	C₂²×C₇	1	1	yes	characteristic
485	#490	C₂²×C₇	1	2	yes	complemented
486	#489	C₂²×C₇	1	2	yes	complemented
487	#488	C₂²×C₇	1	2	yes	complemented
488	#485	C₂²×C₇	1	2	yes	complemented
489	#483	C₂²×C₇	1	2	yes	complemented
490	#482	C₂²×C₇	1	2	yes	complemented
491	#481	C₂²×C₇	1	2	yes	complemented
492	#480	C₂²×C₇	1	2	yes	complemented
493	#480	C₂²×C₇	1	2	yes	complemented
494	#479	C₂²×C₇	1	2	yes	complemented
495	#478	C₂²×C₇	1	2	yes	complemented
496	#478	C₂²×C₇	1	2	yes	complemented
497	#478	C₂²×C₇	1	2	yes	complemented
498	#476	C₂²×C₇	1	2	yes	complemented
499	#474	C₂²×C₇	1	2	yes	complemented
500	#469	C₂²×C₇	1	2	yes	complemented
501	#468	C₂²×C₇	1	2	yes	complemented
502	#467	C₂²×C₇	1	1	yes	characteristic, complemented
503	#467	C₂²×C₇	1	1	yes	characteristic, complemented
504	#466	C₂²×C₇	1	1	yes	characteristic
505	#466	C₂²×C₇	1	1	yes	characteristic
506	#466	C₂²×C₇	1	1	yes	characteristic, complemented
507	#466	C₂²×C₇	1	1	yes	characteristic, complemented
508	#465	C₂²×C₇	1	2	yes	complemented
509	#463	C₂²×C₇	1	2	yes	complemented
510	#463	C₂²×C₇	1	2	yes	complemented
511	#463	C₂²×C₇	1	2	yes	complemented
512	#463	C₂²×C₇	1	2	yes	complemented
513	#460	C₂²×C₇	1	2	yes	complemented
514	#459	C₂²×C₇	1	2	yes	—
515	#450	C₂²×C₇	1	2	yes	complemented
516	#450	C₂²×C₇	1	2	yes	complemented
517	#449	C₂²×C₇	1	2	yes	complemented
518	#449	C₂²×C₇	1	2	yes	complemented
519	#447	C₂²×C₇	1	2	yes	—
520	#447	C₂²×C₇	1	2	yes	—
521	#446	C₂²×C₇	1	1	yes	characteristic, complemented
522	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
523	#442	C₂²×C₇	1	2	yes	complemented
524	#442	C₂²×C₇	1	2	yes	complemented
525	#442	C₂²×C₇	1	2	yes	complemented
526	#440	C₂²×C₇	1	2	yes	complemented
527	#440	C₂²×C₇	1	2	yes	complemented
528	#440	C₂²×C₇	1	2	yes	complemented
529	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
530	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
531	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
532	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
533	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
534	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
535	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
536	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
537	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
538	C₄×D₈	C₂²×C₇	1	2	yes	complemented
539	C₄×D₈	C₂²×C₇	1	2	yes	complemented
540	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
541	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
542	#436	C₂²×C₇	1	1	yes	characteristic, complemented
543	#435	C₂²×C₇	1	1	yes	characteristic
544	#435	C₂²×C₇	1	1	yes	characteristic, complemented
545	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
546	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
547	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
548	#433	C₂²×C₇	1	1	yes	characteristic, complemented
549	#433	C₂²×C₇	1	1	yes	characteristic, complemented
550	#432	C₂²×C₇	1	1	yes	characteristic, complemented
551	#427	C₂²×C₇	1	1	yes	characteristic, complemented
552	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
553	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
554	#418	C₂²×C₇	1	2	yes	complemented
555	#417	C₂²×C₇	1	2	yes	complemented
556	C₂×#102	C₂²×C₇	1	2	yes	complemented
557	#405	C₂²×C₇	1	1	yes	characteristic, complemented
558	#405	C₂²×C₇	1	1	yes	characteristic, complemented
559	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
560	C₂³×C₇	—	2	2	no	—
561	C₂³×C₇	—	2	2	no	—
562	C₂³×C₇	—	2	2	no	—
563	C₂³×C₇	—	4	4	no	—
564	C₂³×C₇	—	4	4	no	—
565	C₂³×C₇	—	4	4	no	—
566	C₂³×C₇	—	8	2	no	—
567	C₂³×C₇	—	8	2	no	—
568	C₂³×C₇	—	8	2	no	—
569	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
570	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
571	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
572	C₇×Q₈	—	2	2	no	—
573	C₇×Q₈	—	2	2	no	—
574	C₇×Q₈	—	4	1	no	—
575	C₇×Q₈	—	8	2	no	—
576	C₇×D₄	—	2	2	no	—
577	C₇×D₄	—	2	2	no	—
578	C₇×D₄	—	2	2	no	—
579	C₇×D₄	—	2	2	no	—
580	C₇×D₄	—	2	2	no	—
581	C₇×D₄	—	2	2	no	—
582	C₇×D₄	—	2	2	no	—
583	C₇×D₄	—	4	1	no	—
584	C₇×D₄	—	4	4	no	—
585	C₇×D₄	—	4	4	no	—
586	C₇×D₄	—	4	4	no	—
587	C₇×D₄	—	4	4	no	—
588	C₇×D₄	—	8	2	no	—
589	C₇×D₄	—	8	2	no	—
590	C₇×D₄	—	8	2	no	—
591	C₇×D₄	—	8	2	no	—
592	C₇×D₄	—	8	2	no	—
593	C₇×D₄	C₂×#41	1	4	yes	—
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	1	no	—
599	C₂×C₄×C₇	—	2	1	no	—
600	C₂×C₄×C₇	—	2	1	no	—
601	C₂×C₄×C₇	—	2	2	no	—
602	C₂×C₄×C₇	—	2	2	no	—
603	C₂×C₄×C₇	—	2	2	no	—
604	C₂×C₄×C₇	—	2	2	no	—
605	C₂×C₄×C₇	—	2	2	no	—
606	C₂×C₄×C₇	—	4	1	no	—
607	C₂×C₄×C₇	—	4	4	no	—
608	C₂×C₄×C₇	—	4	4	no	—
609	C₂×C₄×C₇	—	8	2	no	—
610	C₂×C₄×C₇	—	8	2	no	—
611	C₂×C₄×C₇	—	8	2	no	—
612	C₂×C₄×C₇	—	8	2	no	—
613	C₂×C₄×C₇	—	8	2	no	—
614	C₂×C₄×C₇	—	8	2	no	—
615	C₂×C₄×C₇	—	8	2	no	—
616	C₂×C₄×C₇	—	8	2	no	—
617	C₂×C₄×C₇	—	8	2	no	—
618	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
619	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
620	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
621	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
622	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
623	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
624	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
625	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
626	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
627	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
628	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
629	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
630	C₇×C₈	—	2	1	no	—
631	C₇×C₈	—	2	1	no	—
632	C₇×C₈	—	2	1	no	—
633	C₇×C₈	—	2	1	no	—
634	C₇×C₈	—	2	1	no	—
635	C₇×C₈	—	2	1	no	—
636	C₇×C₈	—	2	1	no	—
637	C₇×C₈	C₂×#41	1	2	yes	—
638	C₂×#41	—	2	2	no	—
639	C₂×#41	C₂³×C₇	1	2	yes	—
640	C₂²×D₄	—	2	2	no	—
641	C₂²×D₄	C₂³×C₇	1	2	yes	—
642	C₂²×D₄	C₂³×C₇	1	2	yes	—
643	C₂³×C₄	—	2	2	no	—
644	#135	—	2	4	no	—
645	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
646	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
647	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
648	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
649	C₂×D₈	—	2	4	no	—
650	C₂×D₈	—	2	4	no	—
651	C₂×D₈	C₂³×C₇	1	2	yes	—
652	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
653	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
654	C₂×D₈	C₂³×C₇	1	2	yes	—
655	C₂×D₈	C₂³×C₇	1	2	yes	—
656	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
657	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
658	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
659	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
660	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
661	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
662	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
663	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
664	#127	C₂³×C₇	1	2	yes	—
665	#126	—	2	2	no	—
666	#126	—	2	2	no	—
667	#126	—	2	2	no	—
668	#126	—	2	2	no	—
669	#126	C₇×D₄	1	1	yes	characteristic
670	#126	C₇×D₄	1	1	yes	characteristic
671	#125	—	2	2	no	—
672	#125	C₇×D₄	1	1	yes	characteristic
673	#125	C₂³×C₇	1	2	yes	—
674	#125	C₂³×C₇	1	2	yes	—
675	#124	—	2	2	no	—
676	#124	—	2	2	no	—
677	#124	C₇×D₄	1	1	yes	characteristic
678	#124	C₂³×C₇	1	2	yes	—
679	#124	C₂³×C₇	1	2	yes	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	#123	—	2	2	no	—
688	#123	—	2	2	no	—
689	#123	—	2	2	no	—
690	#123	—	2	2	no	—
691	#123	—	2	2	no	—
692	#123	C₇×D₄	1	1	yes	characteristic
693	#123	C₇×D₄	1	1	yes	characteristic
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
700	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
701	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
702	#121	—	2	2	no	—
703	#121	—	2	2	no	—
704	#121	—	2	2	no	—
705	#121	—	2	2	no	—
706	#121	—	2	2	no	—
707	#121	—	2	2	no	—
708	#121	C₇×D₄	1	1	yes	characteristic
709	#121	C₂³×C₇	1	2	yes	—
710	#121	C₂³×C₇	1	2	yes	—
711	#121	C₂³×C₇	1	2	yes	—
712	#121	C₂³×C₇	1	2	yes	—
713	#120	—	2	2	no	—
714	#120	—	2	2	no	—
715	#120	—	2	2	no	—
716	#120	—	2	2	no	—
717	C₄×Q₈	C₂³×C₇	1	2	yes	—
718	C₄×Q₈	C₂³×C₇	1	2	yes	—
719	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	—	2	2	no	—
726	C₄×D₄	—	2	2	no	—
727	C₄×D₄	—	2	2	no	—
728	C₄×D₄	—	2	2	no	—
729	C₄×D₄	C₂³×C₇	1	2	yes	—
730	C₄×D₄	C₂³×C₇	1	2	yes	—
731	C₄×D₄	C₂³×C₇	1	2	yes	—
732	C₄×D₄	C₂³×C₇	1	2	yes	—
733	C₄×D₄	C₂³×C₇	1	2	yes	—
734	C₄×D₄	C₂³×C₇	1	2	yes	—
735	C₄×D₄	C₂³×C₇	1	2	yes	—
736	C₄×D₄	C₂³×C₇	1	2	yes	—
737	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
738	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
739	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
740	#117	—	2	2	no	—
741	#117	—	2	2	no	—
742	#117	—	2	2	no	—
743	#117	C₂³×C₇	1	2	yes	—
744	#117	C₂³×C₇	1	1	yes	characteristic
745	#117	C₂³×C₇	1	1	yes	characteristic
746	C₂×C₄⋊C₄	—	2	2	no	—
747	C₂×C₄⋊C₄	—	2	2	no	—
748	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
750	C₂×C₂²⋊C₄	—	2	2	no	—
751	C₂×C₂²⋊C₄	—	2	2	no	—
752	C₂×C₂²⋊C₄	—	2	2	no	—
753	C₂×C₂²⋊C₄	—	2	2	no	—
754	C₂×C₂²⋊C₄	—	2	2	no	—
755	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
756	#107	C₂³×C₇	1	1	yes	characteristic
757	#107	C₂³×C₇	1	1	yes	characteristic
758	#107	C₂³×C₇	1	1	yes	characteristic
759	#107	C₂³×C₇	1	2	yes	—
760	#107	C₂³×C₇	1	2	yes	—
761	#107	C₂³×C₇	1	1	yes	characteristic
762	#107	C₂³×C₇	1	2	yes	—
763	#106	C₂³×C₇	1	2	yes	—
764	#106	C₂³×C₇	1	2	yes	—
765	#106	C₂³×C₇	1	2	yes	—
766	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
767	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
768	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
769	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
770	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
771	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
772	#103	C₂³×C₇	1	2	yes	—
773	#103	C₂³×C₇	1	2	yes	—
774	#103	C₂³×C₇	1	2	yes	—
775	#103	C₂³×C₇	1	2	yes	—
776	#102	C₂³×C₇	1	2	yes	—
777	#102	C₂³×C₇	1	2	yes	—
778	#102	C₂³×C₇	1	2	yes	—
779	#102	C₂³×C₇	1	2	yes	—
780	#102	C₂³×C₇	1	2	yes	—
781	#102	C₂³×C₇	1	2	yes	—
782	#102	C₂³×C₇	1	2	yes	—
783	#102	C₂³×C₇	1	2	yes	—
784	#102	C₂³×C₇	1	2	yes	—
785	#102	C₂³×C₇	1	2	yes	—
786	#102	C₂³×C₇	1	2	yes	—
787	#102	C₂³×C₇	1	2	yes	—
788	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
789	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
790	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
791	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
792	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
793	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
794	#97	C₂³×C₇	1	1	yes	characteristic
795	#97	C₂³×C₇	1	1	yes	characteristic
796	#97	C₂³×C₇	1	1	yes	characteristic
797	#97	C₂³×C₇	1	1	yes	characteristic
798	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
799	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
800	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
801	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
802	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
803	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
804	C₂²×C₇	—	2	1	no	—
805	C₂²×C₇	—	2	1	no	—
806	C₂²×C₇	—	2	1	no	—
807	C₂²×C₇	—	2	1	no	—
808	C₂²×C₇	—	2	1	no	—
809	C₂²×C₇	—	2	1	no	—
810	C₂²×C₇	—	2	4	no	—
811	C₂²×C₇	—	2	1	no	—
812	C₂²×C₇	—	2	1	no	—
813	C₂²×C₇	—	4	2	no	—
814	C₂²×C₇	—	4	2	no	—
815	C₂²×C₇	—	4	2	no	—
816	C₂²×C₇	—	4	2	no	—
817	C₂²×C₇	—	4	2	no	—
818	C₂²×C₇	—	4	2	no	—
819	C₂²×C₇	—	4	2	no	—
820	C₂²×C₇	—	4	2	no	—
821	C₂²×C₇	—	8	8	no	—
822	C₂²×C₇	—	16	4	no	—
823	C₂²×C₇	#576	1	2	yes	—
824	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
825	C₄×C₇	—	2	1	no	—
826	C₄×C₇	—	2	1	no	—
827	C₄×C₇	—	2	1	no	—
828	C₄×C₇	—	2	1	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	1	no	—
835	C₄×C₇	—	2	1	no	—
836	C₄×C₇	—	4	2	no	—
837	C₄×C₇	—	4	2	no	—
838	C₄×C₇	—	4	2	no	—
839	C₄×C₇	—	4	2	no	—
840	C₄×C₇	—	4	2	no	—
841	C₄×C₇	C₂²×#41	1	1	yes	characteristic
842	C₄×C₇	#585	1	1	yes	characteristic
843	C₂⁴	—	2	2	no	—
844	C₂⁴	—	2	2	no	—
845	#41	—	2	4	no	—
846	#41	—	4	2	no	—
847	#41	—	8	4	no	—
848	C₂×Q₈	—	2	2	no	—
849	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
850	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
851	C₂×D₄	—	2	4	no	—
852	C₂×D₄	—	2	4	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	2	no	—
856	C₂×D₄	—	2	2	no	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	—	2	2	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	2	2	no	—
862	C₂×D₄	—	4	2	no	—
863	C₂×D₄	—	4	2	no	—
864	C₂×D₄	—	8	4	no	—
865	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
866	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
867	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
868	C₂×D₄	C₂⁴×C₇	1	2	yes	—
869	C₂×D₄	C₂⁴×C₇	1	2	yes	—
870	C₂×D₄	C₂⁴×C₇	1	2	yes	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	2	no	—
875	C₂²×C₄	—	2	2	no	—
876	C₂²×C₄	—	2	2	no	—
877	C₂²×C₄	—	2	2	no	—
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	8	4	no	—
883	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
884	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
888	Q₁₆	—	2	2	no	—
889	SD₁₆	—	2	4	no	—
890	SD₁₆	—	4	2	no	—
891	SD₁₆	—	4	2	no	—
892	D₈	—	2	4	no	—
893	D₈	—	2	4	no	—
894	D₈	—	2	2	no	—
895	D₈	—	2	2	no	—
896	D₈	—	4	2	no	—
897	D₈	C₇×#41	1	4	yes	complemented
898	M₁₆	—	4	1	no	—
899	M₁₆	—	4	1	no	—
900	C₂×C₈	—	2	2	no	—
901	C₂×C₈	—	2	2	no	—
902	C₂×C₈	—	2	2	no	—
903	C₂×C₈	—	4	1	no	—
904	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
905	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
906	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
907	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
908	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
909	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
910	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
911	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
924	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
925	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
926	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
927	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
928	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
929	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
930	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
931	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
932	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
933	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
934	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
935	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
936	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
957	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
958	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
959	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
960	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
961	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
962	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
963	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
964	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
965	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
966	C₄²	—	2	2	no	—
967	C₄²	—	2	2	no	—
968	C₄²	—	2	2	no	—
969	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
970	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
971	C₄²	C₂⁴×C₇	1	1	yes	characteristic
972	C₄²	C₂⁴×C₇	1	1	yes	characteristic
973	C₄²	C₂⁴×C₇	1	1	yes	characteristic
974	C₄²	C₂⁴×C₇	1	1	yes	characteristic
975	C₂×C₇	—	2	2	no	—
976	C₂×C₇	—	4	1	no	—
977	C₂×C₇	—	4	1	no	—
978	C₂×C₇	—	4	4	no	—
979	C₂×C₇	—	8	2	no	—
980	C₂×C₇	—	8	2	no	—
981	C₂×C₇	D₄×#41	1	1	yes	characteristic
982	C₂×C₇	C₂×#576	1	1	yes	characteristic
983	C₂×C₇	#3584	1	1	yes	characteristic
984	C₂³	—	2	2	no	—
985	C₂³	—	2	2	no	—
986	C₂³	—	2	2	no	—
987	C₂³	—	4	4	no	—
988	C₂³	—	4	4	no	—
989	C₂³	—	4	4	no	—
990	C₂³	—	8	2	no	—
991	C₂³	—	8	2	no	—
992	C₂³	—	8	2	no	—
993	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
994	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
995	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
996	Q₈	—	2	2	no	—
997	Q₈	—	2	2	no	—
998	Q₈	—	4	1	no	—
999	Q₈	—	8	2	no	—
1000	D₄	—	2	2	no	—
1001	D₄	—	2	2	no	—
1002	D₄	—	2	2	no	—
1003	D₄	—	2	2	no	—
1004	D₄	—	2	2	no	—
1005	D₄	—	2	2	no	—
1006	D₄	—	2	2	no	—
1007	D₄	—	4	1	no	—
1008	D₄	—	4	4	no	—
1009	D₄	—	4	4	no	—
1010	D₄	—	4	4	no	—
1011	D₄	—	4	4	no	—
1012	D₄	—	8	2	no	—
1013	D₄	—	8	2	no	—
1014	D₄	—	8	2	no	—
1015	D₄	—	8	2	no	—
1016	D₄	—	8	2	no	—
1017	D₄	C₂×C₇×#41	1	4	yes	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	4	1	no	—
1031	C₂×C₄	—	4	4	no	—
1032	C₂×C₄	—	4	4	no	—
1033	C₂×C₄	—	8	2	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	—	8	2	no	—
1036	C₂×C₄	—	8	2	no	—
1037	C₂×C₄	—	8	2	no	—
1038	C₂×C₄	—	8	2	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	8	2	no	—
1042	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1043	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1044	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1045	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1046	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1047	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1048	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1049	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1050	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1051	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1052	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1053	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1054	C₈	—	2	1	no	—
1055	C₈	—	2	1	no	—
1056	C₈	—	2	1	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	2	1	no	—
1059	C₈	—	2	1	no	—
1060	C₈	—	2	1	no	—
1061	C₈	C₂×C₇×#41	1	2	yes	—
1062	C₇	#61471	1	1	yes	characteristic, direct product factor, Sylow
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	1	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	4	no	—
1072	C₂²	—	4	2	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	8	8	no	—
1081	C₂²	—	16	4	no	—
1082	C₂²	C₇×#576	1	2	yes	—
1083	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1084	C₄	—	2	1	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	1	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	2	1	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	2	no	—
1097	C₄	—	4	2	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	2	no	—
1100	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1101	C₄	C₇×#585	1	1	yes	characteristic
1102	C₂	—	2	2	no	—
1103	C₂	—	4	1	no	—
1104	C₂	—	4	1	no	—
1105	C₂	—	4	4	no	—
1106	C₂	—	8	2	no	—
1107	C₂	—	8	2	no	—
1108	C₂	C₇×D₄×#41	1	1	yes	characteristic
1109	C₂	C₂×C₇×#576	1	1	yes	characteristic
1110	C₂	C₇×#3584	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 ◁ C₇×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3513	C₂	semidirect
2. C₇×#3396	C₂	semidirect
3. C₇×#3380	C₂	semidirect
4. C₇×#3370	C₂	semidirect
5. C₇×#3339	C₂	semidirect
6. C₇×#3336	C₂	semidirect
7. C₇×#3334	C₂	semidirect
8. C₇×#3322	C₂	semidirect
9. C₇×#3310	C₂	semidirect
10. C₇×#3306	C₂	semidirect
11. C₇×#3280	C₂	semidirect
12. C₇×#3280	C₂	semidirect
13. C₇×D₄×D₈	C₂	semidirect
14. C₇×#3176	C₂	semidirect
15. C₇×#3175	C₂	semidirect
16. C₇×#3168	C₂	semidirect
17. C₇×#3119	C₂	semidirect
18. C₇×#3118	C₂	semidirect
19. C₇×#3114	C₂	semidirect
20. C₇×#2966	C₂	semidirect
21. C₇×#2951	C₂	semidirect
22. C₇×#2948	C₂	semidirect
23. C₂×C₄×C₇×D₈	C₂	semidirect
27. C₇×#559	C₂²	semidirect
28. C₇×#554	C₂²	semidirect
30. C₇×#553	C₂²	semidirect
34. C₇×#547	C₂²	semidirect
36. C₇×#546	C₂²	semidirect
37. C₇×#546	C₂²	semidirect
39. C₇×#542	C₂²	semidirect
40. C₇×#540	C₂²	semidirect
44. C₇×#529	C₂²	semidirect
47. C₇×#520	C₂²	semidirect
48. C₇×#518	C₂²	semidirect
49. C₂×C₄×C₇×D₄	C₂²	semidirect
50. C₇×#500	C₂²	semidirect
51. C₇×#499	C₂²	semidirect
52. C₇×#499	C₂²	semidirect
53. C₇×#495	C₂²	semidirect
54. C₇×#495	C₂²	semidirect
56. C₇×#490	C₂²	semidirect
57. C₇×#489	C₂²	semidirect
58. C₇×#488	C₂²	semidirect
59. C₇×#485	C₂²	semidirect
60. C₇×#483	C₂²	semidirect
61. C₇×#482	C₂²	semidirect
62. C₇×#481	C₂²	semidirect
63. C₇×#480	C₂²	semidirect
64. C₇×#480	C₂²	semidirect
65. C₇×#479	C₂²	semidirect
66. C₇×#478	C₂²	semidirect
67. C₇×#478	C₂²	semidirect
68. C₇×#478	C₂²	semidirect
69. C₇×#476	C₂²	semidirect
70. C₇×#474	C₂²	semidirect
71. C₇×#469	C₂²	semidirect
72. C₇×#468	C₂²	semidirect
73. C₇×#467	C₂²	semidirect
74. C₇×#467	C₂²	semidirect
77. C₇×#466	C₂²	semidirect
78. C₇×#466	C₂²	semidirect
79. C₇×#465	C₂²	semidirect
80. C₇×#463	C₂²	semidirect
81. C₇×#463	C₂²	semidirect
82. C₇×#463	C₂²	semidirect
83. C₇×#463	C₂²	semidirect
84. C₇×#460	C₂²	semidirect
86. C₇×#450	C₂²	semidirect
87. C₇×#450	C₂²	semidirect
88. C₇×#449	C₂²	semidirect
89. C₇×#449	C₂²	semidirect
92. C₇×#446	C₂²	semidirect
93. C₇×C₈×Q₈	C₂²	semidirect
94. C₇×#442	C₂²	semidirect
95. C₇×#442	C₂²	semidirect
96. C₇×#442	C₂²	semidirect
97. C₇×#440	C₂²	semidirect
98. C₇×#440	C₂²	semidirect
99. C₇×#440	C₂²	semidirect
100. C₄×C₇×Q₁₆	C₂²	semidirect
101. C₄×C₇×Q₁₆	C₂²	semidirect
102. C₄×C₇×SD₁₆	C₂²	semidirect
107. C₄×C₇×D₈	C₂²	semidirect
108. C₄×C₇×D₈	C₂²	semidirect
109. C₄×C₇×D₈	C₂²	semidirect
110. C₄×C₇×D₈	C₂²	semidirect
111. C₄×C₇×D₈	C₂²	semidirect
112. C₄×C₇×D₈	C₂²	semidirect
113. C₇×#436	C₂²	semidirect
115. C₇×#435	C₂²	semidirect
117. C₇×C₈×D₄	C₂²	semidirect
118. C₇×C₈×D₄	C₂²	semidirect
119. C₇×#433	C₂²	semidirect
120. C₇×#433	C₂²	semidirect
121. C₇×#432	C₂²	semidirect
122. C₇×#427	C₂²	semidirect
123. C₂×C₇×#107	C₂²	semidirect
124. C₂×C₇×#107	C₂²	semidirect
125. C₇×#418	C₂²	semidirect
126. C₇×#417	C₂²	semidirect
127. C₂×C₇×#102	C₂²	semidirect
128. C₇×#405	C₂²	semidirect
129. C₇×#405	C₂²	semidirect
130. C₂×C₄×C₇×C₈	C₂²	semidirect
131. #61471	C₇	direct (N × H)
298. #3513	C₂×C₇	semidirect
299. #3396	C₂×C₇	semidirect
300. #3380	C₂×C₇	semidirect
301. #3370	C₂×C₇	semidirect
302. #3339	C₂×C₇	semidirect
303. #3336	C₂×C₇	semidirect
304. #3334	C₂×C₇	semidirect
305. #3322	C₂×C₇	semidirect
306. #3310	C₂×C₇	semidirect
307. #3306	C₂×C₇	semidirect
308. #3280	C₂×C₇	semidirect
309. #3280	C₂×C₇	semidirect
310. D₄×D₈	C₂×C₇	semidirect
311. #3176	C₂×C₇	semidirect
312. #3175	C₂×C₇	semidirect
313. #3168	C₂×C₇	semidirect
314. #3119	C₂×C₇	semidirect
315. #3118	C₂×C₇	semidirect
316. #3114	C₂×C₇	semidirect
317. #2966	C₂×C₇	semidirect
318. #2951	C₂×C₇	semidirect
319. #2948	C₂×C₇	semidirect
320. C₂×C₄×D₈	C₂×C₇	semidirect
375. C₇×D₈	#41	semidirect
456. #559	C₂²×C₇	semidirect
457. #554	C₂²×C₇	semidirect
459. #553	C₂²×C₇	semidirect
463. #547	C₂²×C₇	semidirect
465. #546	C₂²×C₇	semidirect
466. #546	C₂²×C₇	semidirect
468. #542	C₂²×C₇	semidirect
469. #540	C₂²×C₇	semidirect
473. #529	C₂²×C₇	semidirect
476. #520	C₂²×C₇	semidirect
477. #518	C₂²×C₇	semidirect
478. C₂×C₄×D₄	C₂²×C₇	semidirect
479. #500	C₂²×C₇	semidirect
480. #499	C₂²×C₇	semidirect
481. #499	C₂²×C₇	semidirect
482. #495	C₂²×C₇	semidirect
483. #495	C₂²×C₇	semidirect
485. #490	C₂²×C₇	semidirect
486. #489	C₂²×C₇	semidirect
487. #488	C₂²×C₇	semidirect
488. #485	C₂²×C₇	semidirect
489. #483	C₂²×C₇	semidirect
490. #482	C₂²×C₇	semidirect
491. #481	C₂²×C₇	semidirect
492. #480	C₂²×C₇	semidirect
493. #480	C₂²×C₇	semidirect
494. #479	C₂²×C₇	semidirect
495. #478	C₂²×C₇	semidirect
496. #478	C₂²×C₇	semidirect
497. #478	C₂²×C₇	semidirect
498. #476	C₂²×C₇	semidirect
499. #474	C₂²×C₇	semidirect
500. #469	C₂²×C₇	semidirect
501. #468	C₂²×C₇	semidirect
502. #467	C₂²×C₇	semidirect
503. #467	C₂²×C₇	semidirect
506. #466	C₂²×C₇	semidirect
507. #466	C₂²×C₇	semidirect
508. #465	C₂²×C₇	semidirect
509. #463	C₂²×C₇	semidirect
510. #463	C₂²×C₇	semidirect
511. #463	C₂²×C₇	semidirect
512. #463	C₂²×C₇	semidirect
513. #460	C₂²×C₇	semidirect
515. #450	C₂²×C₇	semidirect
516. #450	C₂²×C₇	semidirect
517. #449	C₂²×C₇	semidirect
518. #449	C₂²×C₇	semidirect
521. #446	C₂²×C₇	semidirect
522. C₈×Q₈	C₂²×C₇	semidirect
523. #442	C₂²×C₇	semidirect
524. #442	C₂²×C₇	semidirect
525. #442	C₂²×C₇	semidirect
526. #440	C₂²×C₇	semidirect
527. #440	C₂²×C₇	semidirect
528. #440	C₂²×C₇	semidirect
529. C₄×Q₁₆	C₂²×C₇	semidirect
530. C₄×Q₁₆	C₂²×C₇	semidirect
531. C₄×SD₁₆	C₂²×C₇	semidirect
536. C₄×D₈	C₂²×C₇	semidirect
537. C₄×D₈	C₂²×C₇	semidirect
538. C₄×D₈	C₂²×C₇	semidirect
539. C₄×D₈	C₂²×C₇	semidirect
540. C₄×D₈	C₂²×C₇	semidirect
541. C₄×D₈	C₂²×C₇	semidirect
542. #436	C₂²×C₇	semidirect
544. #435	C₂²×C₇	semidirect
546. C₈×D₄	C₂²×C₇	semidirect
547. C₈×D₄	C₂²×C₇	semidirect
548. #433	C₂²×C₇	semidirect
549. #433	C₂²×C₇	semidirect
550. #432	C₂²×C₇	semidirect
551. #427	C₂²×C₇	semidirect
552. C₂×#107	C₂²×C₇	semidirect
553. C₂×#107	C₂²×C₇	semidirect
554. #418	C₂²×C₇	semidirect
555. #417	C₂²×C₇	semidirect
556. C₂×#102	C₂²×C₇	semidirect
557. #405	C₂²×C₇	semidirect
558. #405	C₂²×C₇	semidirect
559. C₂×C₄×C₈	C₂²×C₇	semidirect
897. D₈	C₇×#41	semidirect
1062. C₇	#61471	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×#3513	2
C₇×#3396	2
C₇×#3380	2
C₇×#3370	2
C₇×#3339	2
C₇×#3336	2
C₇×#3334	2
C₇×#3322	2
C₇×#3310	2
C₇×#3306	2
C₇×#3280	2
C₇×D₄×D₈	2
C₇×#3176	2
C₇×#3175	2
C₇×#3168	2
C₇×#3119	2
C₇×#3118	2
C₇×#3114	2
C₇×#2966	2
C₇×#2951	2
C₇×#2948	2
C₂×C₄×C₇×D₈	2
#61471	7

Subgroups — C7×#61471 #13238687

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61471 #13238687