Subgroups — C₇×#61473 #13238689

Order 1792.

1770 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3516	C₂	1	2	yes	maximal, complemented
2	C₇×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3377	C₂	1	2	yes	maximal, complemented
5	C₇×#3339	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3327	C₂	1	2	yes	maximal, complemented
9	C₇×#3320	C₂	1	2	yes	maximal, complemented
10	C₇×#3316	C₂	1	2	yes	maximal, complemented
11	C₇×D₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3285	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3285	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3177	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×#3121	C₂	1	2	yes	maximal, complemented
18	C₇×#3120	C₂	1	2	yes	maximal, complemented
19	C₇×#3117	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×#2950	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#135	C₂²	1	1	yes	characteristic
25	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
26	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
27	C₇×#557	C₂²	1	2	yes	—
28	C₇×#556	—	2	2	no	—
29	C₇×#556	C₂²	1	2	yes	—
30	C₇×#554	—	2	2	no	—
31	C₇×#554	C₂²	1	2	yes	—
32	C₇×#553	—	2	2	no	—
33	C₇×#553	C₂²	1	2	yes	—
34	C₇×#552	—	2	2	no	—
35	C₇×#552	C₂²	1	2	yes	—
36	C₇×D₄×Q₈	C₂²	1	2	yes	—
37	C₇×#548	C₂²	1	2	yes	—
38	C₇×#548	C₂²	1	2	yes	—
39	C₇×#542	—	2	2	no	—
40	C₇×#542	C₂²	1	2	yes	—
41	C₇×#541	—	2	2	no	—
42	C₇×#541	C₂²	1	2	yes	—
43	C₇×#529	—	2	2	no	—
44	C₇×#529	—	2	2	no	—
45	C₇×#529	C₂²	1	2	yes	—
46	C₇×#529	C₂²	1	1	yes	characteristic
47	C₇×#520	C₂²	1	2	yes	—
48	C₇×#519	C₂²	1	2	yes	—
49	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
50	C₇×#500	C₂²	1	1	yes	characteristic
51	C₇×#499	C₂²	1	1	yes	characteristic
52	C₇×#499	C₂²	1	1	yes	characteristic
53	C₇×#495	C₂²	1	1	yes	characteristic
54	C₇×#495	C₂²	1	1	yes	characteristic
55	C₇×#494	C₂²	1	1	yes	characteristic
56	C₇×#491	C₂²	1	2	yes	—
57	C₇×#489	C₂²	1	2	yes	—
58	C₇×#488	C₂²	1	2	yes	—
59	C₇×#485	C₂²	1	2	yes	—
60	C₇×#484	C₂²	1	2	yes	—
61	C₇×#484	C₂²	1	2	yes	—
62	C₇×#483	C₂²	1	2	yes	—
63	C₇×#482	C₂²	1	2	yes	—
64	C₇×#481	C₂²	1	2	yes	—
65	C₇×#479	C₂²	1	2	yes	—
66	C₇×#479	C₂²	1	2	yes	—
67	C₇×#479	C₂²	1	2	yes	—
68	C₇×#478	C₂²	1	2	yes	—
69	C₇×#477	C₂²	1	2	yes	—
70	C₇×#475	C₂²	1	2	yes	—
71	C₇×#470	C₂²	1	2	yes	—
72	C₇×#468	C₂²	1	2	yes	—
73	C₇×#467	C₂²	1	1	yes	characteristic
74	C₇×#467	C₂²	1	1	yes	characteristic
75	C₇×#467	C₂²	1	1	yes	characteristic
76	C₇×#467	C₂²	1	1	yes	characteristic
77	C₇×#466	C₂²	1	1	yes	characteristic
78	C₇×#466	C₂²	1	1	yes	characteristic
79	C₇×#465	C₂²	1	2	yes	—
80	C₇×#464	C₂²	1	2	yes	—
81	C₇×#464	C₂²	1	2	yes	—
82	C₇×#464	C₂²	1	2	yes	—
83	C₇×#464	C₂²	1	2	yes	—
84	C₇×#462	C₂²	1	2	yes	—
85	C₇×#461	C₂²	1	2	yes	—
86	C₇×#452	C₂²	1	2	yes	—
87	C₇×#452	C₂²	1	2	yes	—
88	C₇×#451	C₂²	1	2	yes	—
89	C₇×#451	C₂²	1	2	yes	—
90	C₇×#448	C₂²	1	2	yes	—
91	C₇×#448	C₂²	1	2	yes	—
92	C₇×#446	C₂²	1	1	yes	characteristic
93	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
94	C₇×#441	C₂²	1	2	yes	—
95	C₇×#441	C₂²	1	2	yes	—
96	C₇×#441	C₂²	1	2	yes	—
97	C₇×#440	C₂²	1	2	yes	—
98	C₇×#440	C₂²	1	2	yes	—
99	C₇×#440	C₂²	1	2	yes	—
100	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
101	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
102	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
103	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
104	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
105	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
106	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
107	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
108	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
109	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
110	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
111	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
112	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
113	C₇×#436	C₂²	1	1	yes	characteristic
114	C₇×#435	C₂²	1	1	yes	characteristic
115	C₇×#435	C₂²	1	1	yes	characteristic
116	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
117	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
118	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
119	C₇×#433	C₂²	1	1	yes	characteristic
120	C₇×#433	C₂²	1	1	yes	characteristic
121	C₇×#432	C₂²	1	1	yes	characteristic
122	C₇×#427	C₂²	1	1	yes	characteristic
123	C₂×C₇×#107	C₂²	1	1	yes	characteristic
124	C₂×C₇×#107	C₂²	1	1	yes	characteristic
125	C₇×#419	C₂²	1	2	yes	—
126	C₇×#417	C₂²	1	2	yes	—
127	C₂×C₇×#103	C₂²	1	2	yes	—
128	C₇×#405	C₂²	1	1	yes	characteristic
129	C₇×#405	C₂²	1	1	yes	characteristic
130	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
131	#61473	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂×C₇×#41	C₂³	1	2	yes	—
133	C₂²×C₇×Q₈	C₂³	1	2	yes	—
134	C₂²×C₇×Q₈	C₂³	1	2	yes	—
135	C₇×#135	—	2	4	no	—
136	C₂×C₇×Q₁₆	—	2	4	no	—
137	C₂×C₇×Q₁₆	—	2	4	no	—
138	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
139	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
141	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
142	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
143	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
145	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
146	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
147	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
148	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
150	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
151	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
152	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
153	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
154	C₇×C₄⋊Q₈	—	2	2	no	—
155	C₇×C₄⋊Q₈	—	2	2	no	—
156	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₇×#126	—	2	2	no	—
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	—	2	2	no	—
164	C₇×#126	—	2	2	no	—
165	C₇×#126	—	2	2	no	—
166	C₇×#126	D₄	1	1	yes	characteristic
167	C₇×#126	D₄	1	1	yes	characteristic
168	C₇×#125	—	2	2	no	—
169	C₇×#125	—	2	2	no	—
170	C₇×#125	—	2	2	no	—
171	C₇×#125	—	2	2	no	—
172	C₇×#125	—	2	2	no	—
173	C₇×#125	—	2	2	no	—
174	C₇×#125	D₄	1	1	yes	characteristic
175	C₇×#125	C₂³	1	2	yes	—
176	C₇×#125	C₂³	1	2	yes	—
177	C₇×#124	—	2	2	no	—
178	C₇×#124	—	2	2	no	—
179	C₇×#124	—	2	2	no	—
180	C₇×#124	D₄	1	1	yes	characteristic
181	C₇×#124	C₂³	1	2	yes	—
182	C₇×#124	C₂³	1	2	yes	—
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	D₄	1	1	yes	characteristic
188	C₇×#123	D₄	1	1	yes	characteristic
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	—	2	2	no	—
194	C₇×C₂²⋊Q₈	—	2	2	no	—
195	C₇×C₂²⋊Q₈	—	2	2	no	—
196	C₇×C₂²⋊Q₈	—	2	2	no	—
197	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
198	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₇×#121	—	2	2	no	—
203	C₇×#121	—	2	2	no	—
204	C₇×#121	—	2	2	no	—
205	C₇×#121	D₄	1	1	yes	characteristic
206	C₇×#121	C₂³	1	2	yes	—
207	C₇×#121	C₂³	1	2	yes	—
208	C₄×C₇×Q₈	—	2	2	no	—
209	C₄×C₇×Q₈	—	2	2	no	—
210	C₄×C₇×Q₈	—	2	2	no	—
211	C₄×C₇×Q₈	—	2	2	no	—
212	C₄×C₇×Q₈	—	2	2	no	—
213	C₄×C₇×Q₈	C₂³	1	2	yes	—
214	C₄×C₇×Q₈	C₂³	1	2	yes	—
215	C₄×C₇×Q₈	C₂³	1	2	yes	—
216	C₄×C₇×Q₈	C₂³	1	2	yes	—
217	C₄×C₇×Q₈	C₂³	1	2	yes	—
218	C₄×C₇×Q₈	C₂³	1	2	yes	—
219	C₄×C₇×Q₈	C₂³	1	2	yes	—
220	C₄×C₇×Q₈	C₂³	1	2	yes	—
221	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
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	2	no	—
226	C₄×C₇×D₄	—	2	2	no	—
227	C₄×C₇×D₄	—	2	2	no	—
228	C₄×C₇×D₄	—	2	2	no	—
229	C₄×C₇×D₄	—	2	2	no	—
230	C₄×C₇×D₄	C₂³	1	2	yes	—
231	C₄×C₇×D₄	C₂³	1	2	yes	—
232	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
233	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
234	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
235	C₇×#117	—	2	2	no	—
236	C₇×#117	—	2	2	no	—
237	C₇×#117	—	2	2	no	—
238	C₇×#117	—	2	2	no	—
239	C₇×#117	—	2	2	no	—
240	C₇×#117	—	2	2	no	—
241	C₇×#117	C₂³	1	2	yes	—
242	C₇×#117	C₂³	1	1	yes	characteristic
243	C₇×#117	C₂³	1	1	yes	characteristic
244	C₂×C₇×C₄⋊C₄	—	2	2	no	—
245	C₂×C₇×C₄⋊C₄	—	2	2	no	—
246	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
247	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
248	C₂×C₄²×C₇	—	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×#103	C₂³	1	2	yes	—
271	C₇×#103	C₂³	1	2	yes	—
272	C₇×#103	C₂³	1	2	yes	—
273	C₇×#103	C₂³	1	2	yes	—
274	C₇×#103	C₂³	1	2	yes	—
275	C₇×#103	C₂³	1	2	yes	—
276	C₇×#103	C₂³	1	2	yes	—
277	C₇×#103	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	#3516	C₂×C₇	1	2	yes	complemented
299	#3393	C₂×C₇	1	1	yes	characteristic, complemented
300	#3383	C₂×C₇	1	1	yes	characteristic, complemented
301	#3377	C₂×C₇	1	2	yes	complemented
302	#3339	C₂×C₇	1	1	yes	characteristic, complemented
303	#3338	C₂×C₇	1	1	yes	characteristic, complemented
304	#3336	C₂×C₇	1	1	yes	characteristic, complemented
305	#3327	C₂×C₇	1	2	yes	complemented
306	#3320	C₂×C₇	1	2	yes	complemented
307	#3316	C₂×C₇	1	2	yes	complemented
308	D₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
309	#3285	C₂×C₇	1	1	yes	characteristic, complemented
310	#3285	C₂×C₇	1	1	yes	characteristic, complemented
311	#3177	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	#3121	C₂×C₇	1	2	yes	complemented
315	#3120	C₂×C₇	1	2	yes	complemented
316	#3117	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	#2950	C₂×C₇	1	1	yes	characteristic, complemented
320	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
321	C₇×#41	—	2	4	no	—
322	C₇×#41	—	4	2	no	—
323	C₂×C₇×Q₈	—	2	2	no	—
324	C₂×C₇×Q₈	—	2	2	no	—
325	C₂×C₇×Q₈	—	2	2	no	—
326	C₂×C₇×Q₈	—	2	4	no	—
327	C₂×C₇×Q₈	—	2	4	no	—
328	C₂×C₇×Q₈	—	4	2	no	—
329	C₂×C₇×Q₈	—	4	2	no	—
330	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
331	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
332	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
333	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
338	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
339	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
340	C₂×C₇×D₄	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₇	—	2	2	no	—
342	C₂²×C₄×C₇	—	2	2	no	—
343	C₂²×C₄×C₇	—	2	2	no	—
344	C₂²×C₄×C₇	—	2	2	no	—
345	C₂²×C₄×C₇	—	2	2	no	—
346	C₂²×C₄×C₇	—	2	2	no	—
347	C₂²×C₄×C₇	—	2	2	no	—
348	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
353	C₇×Q₁₆	—	2	4	no	—
354	C₇×Q₁₆	—	2	4	no	—
355	C₇×Q₁₆	—	2	2	no	—
356	C₇×Q₁₆	—	2	2	no	—
357	C₇×Q₁₆	—	4	2	no	—
358	C₇×Q₁₆	#41	1	4	yes	—
359	C₇×SD₁₆	—	2	4	no	—
360	C₇×SD₁₆	—	4	2	no	—
361	C₇×SD₁₆	—	4	2	no	—
362	C₇×D₈	—	2	2	no	—
363	C₇×M₁₆	—	4	1	no	—
364	C₇×M₁₆	—	4	1	no	—
365	C₂×C₇×C₈	—	2	2	no	—
366	C₂×C₇×C₈	—	2	2	no	—
367	C₂×C₇×C₈	—	2	2	no	—
368	C₂×C₇×C₈	—	4	1	no	—
369	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
370	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
371	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
372	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
373	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
374	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
375	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
376	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
377	C₇×C₄⋊C₄	—	2	2	no	—
378	C₇×C₄⋊C₄	—	2	2	no	—
379	C₇×C₄⋊C₄	—	2	2	no	—
380	C₇×C₄⋊C₄	—	2	2	no	—
381	C₇×C₄⋊C₄	—	2	2	no	—
382	C₇×C₄⋊C₄	—	2	2	no	—
383	C₇×C₄⋊C₄	—	2	2	no	—
384	C₇×C₄⋊C₄	—	2	2	no	—
385	C₇×C₄⋊C₄	—	2	2	no	—
386	C₇×C₄⋊C₄	—	2	2	no	—
387	C₇×C₄⋊C₄	—	2	2	no	—
388	C₇×C₄⋊C₄	—	2	2	no	—
389	C₇×C₄⋊C₄	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
399	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
400	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	2	yes	—
409	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
410	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
411	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
412	C₇×C₂²⋊C₄	—	2	2	no	—
413	C₇×C₂²⋊C₄	—	2	2	no	—
414	C₇×C₂²⋊C₄	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
426	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
427	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
428	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
429	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
430	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
431	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
432	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
433	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
434	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₇	—	2	2	no	—
436	C₄²×C₇	—	2	2	no	—
437	C₄²×C₇	—	2	2	no	—
438	C₄²×C₇	—	2	2	no	—
439	C₄²×C₇	—	2	2	no	—
440	C₄²×C₇	—	2	2	no	—
441	C₄²×C₇	—	2	2	no	—
442	C₄²×C₇	—	2	2	no	—
443	C₄²×C₇	—	2	2	no	—
444	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₇	C₂⁴	1	1	yes	characteristic
447	C₄²×C₇	C₂⁴	1	1	yes	characteristic
448	C₄²×C₇	C₂⁴	1	1	yes	characteristic
449	C₄²×C₇	C₂⁴	1	1	yes	characteristic
450	C₂×#135	C₂²×C₇	1	1	yes	characteristic
451	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
452	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
453	#557	C₂²×C₇	1	2	yes	—
454	#556	—	2	2	no	—
455	#556	C₂²×C₇	1	2	yes	—
456	#554	—	2	2	no	—
457	#554	C₂²×C₇	1	2	yes	—
458	#553	—	2	2	no	—
459	#553	C₂²×C₇	1	2	yes	—
460	#552	—	2	2	no	—
461	#552	C₂²×C₇	1	2	yes	—
462	D₄×Q₈	C₂²×C₇	1	2	yes	—
463	#548	C₂²×C₇	1	2	yes	—
464	#548	C₂²×C₇	1	2	yes	—
465	#542	—	2	2	no	—
466	#542	C₂²×C₇	1	2	yes	—
467	#541	—	2	2	no	—
468	#541	C₂²×C₇	1	2	yes	—
469	#529	—	2	2	no	—
470	#529	—	2	2	no	—
471	#529	C₂²×C₇	1	2	yes	—
472	#529	C₂²×C₇	1	1	yes	characteristic
473	#520	C₂²×C₇	1	2	yes	—
474	#519	C₂²×C₇	1	2	yes	—
475	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
476	#500	C₂²×C₇	1	1	yes	characteristic
477	#499	C₂²×C₇	1	1	yes	characteristic
478	#499	C₂²×C₇	1	1	yes	characteristic
479	#495	C₂²×C₇	1	1	yes	characteristic
480	#495	C₂²×C₇	1	1	yes	characteristic
481	#494	C₂²×C₇	1	1	yes	characteristic
482	#491	C₂²×C₇	1	2	yes	—
483	#489	C₂²×C₇	1	2	yes	—
484	#488	C₂²×C₇	1	2	yes	—
485	#485	C₂²×C₇	1	2	yes	—
486	#484	C₂²×C₇	1	2	yes	—
487	#484	C₂²×C₇	1	2	yes	—
488	#483	C₂²×C₇	1	2	yes	—
489	#482	C₂²×C₇	1	2	yes	—
490	#481	C₂²×C₇	1	2	yes	—
491	#479	C₂²×C₇	1	2	yes	—
492	#479	C₂²×C₇	1	2	yes	—
493	#479	C₂²×C₇	1	2	yes	—
494	#478	C₂²×C₇	1	2	yes	—
495	#477	C₂²×C₇	1	2	yes	—
496	#475	C₂²×C₇	1	2	yes	—
497	#470	C₂²×C₇	1	2	yes	—
498	#468	C₂²×C₇	1	2	yes	—
499	#467	C₂²×C₇	1	1	yes	characteristic
500	#467	C₂²×C₇	1	1	yes	characteristic
501	#467	C₂²×C₇	1	1	yes	characteristic
502	#467	C₂²×C₇	1	1	yes	characteristic
503	#466	C₂²×C₇	1	1	yes	characteristic
504	#466	C₂²×C₇	1	1	yes	characteristic
505	#465	C₂²×C₇	1	2	yes	—
506	#464	C₂²×C₇	1	2	yes	—
507	#464	C₂²×C₇	1	2	yes	—
508	#464	C₂²×C₇	1	2	yes	—
509	#464	C₂²×C₇	1	2	yes	—
510	#462	C₂²×C₇	1	2	yes	—
511	#461	C₂²×C₇	1	2	yes	—
512	#452	C₂²×C₇	1	2	yes	—
513	#452	C₂²×C₇	1	2	yes	—
514	#451	C₂²×C₇	1	2	yes	—
515	#451	C₂²×C₇	1	2	yes	—
516	#448	C₂²×C₇	1	2	yes	—
517	#448	C₂²×C₇	1	2	yes	—
518	#446	C₂²×C₇	1	1	yes	characteristic
519	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
520	#441	C₂²×C₇	1	2	yes	—
521	#441	C₂²×C₇	1	2	yes	—
522	#441	C₂²×C₇	1	2	yes	—
523	#440	C₂²×C₇	1	2	yes	—
524	#440	C₂²×C₇	1	2	yes	—
525	#440	C₂²×C₇	1	2	yes	—
526	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
527	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
528	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
529	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
530	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
531	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
532	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
533	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
534	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
535	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
536	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
537	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
538	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
539	#436	C₂²×C₇	1	1	yes	characteristic
540	#435	C₂²×C₇	1	1	yes	characteristic
541	#435	C₂²×C₇	1	1	yes	characteristic
542	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
543	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
544	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
545	#433	C₂²×C₇	1	1	yes	characteristic
546	#433	C₂²×C₇	1	1	yes	characteristic
547	#432	C₂²×C₇	1	1	yes	characteristic
548	#427	C₂²×C₇	1	1	yes	characteristic
549	C₂×#107	C₂²×C₇	1	1	yes	characteristic
550	C₂×#107	C₂²×C₇	1	1	yes	characteristic
551	#419	C₂²×C₇	1	2	yes	—
552	#417	C₂²×C₇	1	2	yes	—
553	C₂×#103	C₂²×C₇	1	2	yes	—
554	#405	C₂²×C₇	1	1	yes	characteristic
555	#405	C₂²×C₇	1	1	yes	characteristic
556	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
557	C₂³×C₇	—	2	2	no	—
558	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
559	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
560	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
561	C₇×Q₈	—	2	2	no	—
562	C₇×Q₈	—	2	2	no	—
563	C₇×Q₈	—	2	2	no	—
564	C₇×Q₈	—	2	2	no	—
565	C₇×Q₈	—	2	2	no	—
566	C₇×Q₈	—	4	1	no	—
567	C₇×Q₈	—	4	4	no	—
568	C₇×Q₈	—	4	4	no	—
569	C₇×Q₈	—	8	2	no	—
570	C₇×Q₈	C₂×#41	1	4	yes	—
571	C₇×D₄	—	2	2	no	—
572	C₇×D₄	—	2	2	no	—
573	C₇×D₄	—	2	2	no	—
574	C₇×D₄	—	2	2	no	—
575	C₇×D₄	—	4	1	no	—
576	C₇×D₄	—	4	4	no	—
577	C₇×D₄	—	4	4	no	—
578	C₇×D₄	—	8	2	no	—
579	C₂×C₄×C₇	—	2	2	no	—
580	C₂×C₄×C₇	—	2	2	no	—
581	C₂×C₄×C₇	—	2	1	no	—
582	C₂×C₄×C₇	—	2	1	no	—
583	C₂×C₄×C₇	—	2	1	no	—
584	C₂×C₄×C₇	—	2	1	no	—
585	C₂×C₄×C₇	—	2	1	no	—
586	C₂×C₄×C₇	—	2	1	no	—
587	C₂×C₄×C₇	—	2	2	no	—
588	C₂×C₄×C₇	—	2	2	no	—
589	C₂×C₄×C₇	—	2	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	—	4	1	no	—
594	C₂×C₄×C₇	—	4	4	no	—
595	C₂×C₄×C₇	—	4	4	no	—
596	C₂×C₄×C₇	—	4	4	no	—
597	C₂×C₄×C₇	—	8	2	no	—
598	C₂×C₄×C₇	—	8	2	no	—
599	C₂×C₄×C₇	—	8	2	no	—
600	C₂×C₄×C₇	—	8	2	no	—
601	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
602	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
603	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
604	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
605	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
606	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
607	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
608	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
609	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
610	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
611	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
612	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
613	C₇×C₈	—	2	1	no	—
614	C₇×C₈	—	2	1	no	—
615	C₇×C₈	—	2	1	no	—
616	C₇×C₈	—	2	1	no	—
617	C₇×C₈	—	2	1	no	—
618	C₇×C₈	—	2	1	no	—
619	C₇×C₈	—	2	1	no	—
620	C₇×C₈	C₂×#41	1	2	yes	—
621	C₂×#41	C₂³×C₇	1	2	yes	—
622	C₂²×Q₈	C₂³×C₇	1	2	yes	—
623	C₂²×Q₈	C₂³×C₇	1	2	yes	—
624	#135	—	2	4	no	—
625	C₂×Q₁₆	—	2	4	no	—
626	C₂×Q₁₆	—	2	4	no	—
627	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
628	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
629	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
630	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
631	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
632	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
633	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
634	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
635	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
636	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
637	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
638	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
639	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
640	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
641	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
642	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
643	C₄⋊Q₈	—	2	2	no	—
644	C₄⋊Q₈	—	2	2	no	—
645	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
646	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
647	#126	—	2	2	no	—
648	#126	—	2	2	no	—
649	#126	—	2	2	no	—
650	#126	—	2	2	no	—
651	#126	—	2	2	no	—
652	#126	—	2	2	no	—
653	#126	—	2	2	no	—
654	#126	—	2	2	no	—
655	#126	C₇×D₄	1	1	yes	characteristic
656	#126	C₇×D₄	1	1	yes	characteristic
657	#125	—	2	2	no	—
658	#125	—	2	2	no	—
659	#125	—	2	2	no	—
660	#125	—	2	2	no	—
661	#125	—	2	2	no	—
662	#125	—	2	2	no	—
663	#125	C₇×D₄	1	1	yes	characteristic
664	#125	C₂³×C₇	1	2	yes	—
665	#125	C₂³×C₇	1	2	yes	—
666	#124	—	2	2	no	—
667	#124	—	2	2	no	—
668	#124	—	2	2	no	—
669	#124	C₇×D₄	1	1	yes	characteristic
670	#124	C₂³×C₇	1	2	yes	—
671	#124	C₂³×C₇	1	2	yes	—
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	C₇×D₄	1	1	yes	characteristic
677	#123	C₇×D₄	1	1	yes	characteristic
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
687	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
688	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
689	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
690	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
691	#121	—	2	2	no	—
692	#121	—	2	2	no	—
693	#121	—	2	2	no	—
694	#121	C₇×D₄	1	1	yes	characteristic
695	#121	C₂³×C₇	1	2	yes	—
696	#121	C₂³×C₇	1	2	yes	—
697	C₄×Q₈	—	2	2	no	—
698	C₄×Q₈	—	2	2	no	—
699	C₄×Q₈	—	2	2	no	—
700	C₄×Q₈	—	2	2	no	—
701	C₄×Q₈	—	2	2	no	—
702	C₄×Q₈	C₂³×C₇	1	2	yes	—
703	C₄×Q₈	C₂³×C₇	1	2	yes	—
704	C₄×Q₈	C₂³×C₇	1	2	yes	—
705	C₄×Q₈	C₂³×C₇	1	2	yes	—
706	C₄×Q₈	C₂³×C₇	1	2	yes	—
707	C₄×Q₈	C₂³×C₇	1	2	yes	—
708	C₄×Q₈	C₂³×C₇	1	2	yes	—
709	C₄×Q₈	C₂³×C₇	1	2	yes	—
710	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
711	C₄×D₄	—	2	2	no	—
712	C₄×D₄	—	2	2	no	—
713	C₄×D₄	—	2	2	no	—
714	C₄×D₄	—	2	2	no	—
715	C₄×D₄	—	2	2	no	—
716	C₄×D₄	—	2	2	no	—
717	C₄×D₄	—	2	2	no	—
718	C₄×D₄	—	2	2	no	—
719	C₄×D₄	C₂³×C₇	1	2	yes	—
720	C₄×D₄	C₂³×C₇	1	2	yes	—
721	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
722	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
723	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
724	#117	—	2	2	no	—
725	#117	—	2	2	no	—
726	#117	—	2	2	no	—
727	#117	—	2	2	no	—
728	#117	—	2	2	no	—
729	#117	—	2	2	no	—
730	#117	C₂³×C₇	1	2	yes	—
731	#117	C₂³×C₇	1	1	yes	characteristic
732	#117	C₂³×C₇	1	1	yes	characteristic
733	C₂×C₄⋊C₄	—	2	2	no	—
734	C₂×C₄⋊C₄	—	2	2	no	—
735	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
736	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
737	C₂×C₄²	—	2	2	no	—
738	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
739	#107	C₂³×C₇	1	1	yes	characteristic
740	#107	C₂³×C₇	1	1	yes	characteristic
741	#107	C₂³×C₇	1	1	yes	characteristic
742	#107	C₂³×C₇	1	2	yes	—
743	#107	C₂³×C₇	1	2	yes	—
744	#107	C₂³×C₇	1	1	yes	characteristic
745	#107	C₂³×C₇	1	2	yes	—
746	#106	C₂³×C₇	1	2	yes	—
747	#106	C₂³×C₇	1	2	yes	—
748	#106	C₂³×C₇	1	2	yes	—
749	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
750	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
751	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
752	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
753	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
754	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
755	#103	C₂³×C₇	1	2	yes	—
756	#103	C₂³×C₇	1	2	yes	—
757	#103	C₂³×C₇	1	2	yes	—
758	#103	C₂³×C₇	1	2	yes	—
759	#103	C₂³×C₇	1	2	yes	—
760	#103	C₂³×C₇	1	2	yes	—
761	#103	C₂³×C₇	1	2	yes	—
762	#103	C₂³×C₇	1	2	yes	—
763	#103	C₂³×C₇	1	2	yes	—
764	#103	C₂³×C₇	1	2	yes	—
765	#103	C₂³×C₇	1	2	yes	—
766	#103	C₂³×C₇	1	2	yes	—
767	#102	C₂³×C₇	1	2	yes	—
768	#102	C₂³×C₇	1	2	yes	—
769	#102	C₂³×C₇	1	2	yes	—
770	#102	C₂³×C₇	1	2	yes	—
771	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
772	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
773	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
774	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
775	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
776	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
777	#97	C₂³×C₇	1	1	yes	characteristic
778	#97	C₂³×C₇	1	1	yes	characteristic
779	#97	C₂³×C₇	1	1	yes	characteristic
780	#97	C₂³×C₇	1	1	yes	characteristic
781	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
782	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
783	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
784	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
785	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
786	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
787	C₂²×C₇	—	2	1	no	—
788	C₂²×C₇	—	2	1	no	—
789	C₂²×C₇	—	2	1	no	—
790	C₂²×C₇	—	2	1	no	—
791	C₂²×C₇	—	2	1	no	—
792	C₂²×C₇	—	2	1	no	—
793	C₂²×C₇	—	2	1	no	—
794	C₂²×C₇	—	2	1	no	—
795	C₂²×C₇	—	4	2	no	—
796	C₂²×C₇	—	4	2	no	—
797	C₂²×C₇	—	4	2	no	—
798	C₂²×C₇	#578	1	2	yes	—
799	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
800	C₄×C₇	—	2	1	no	—
801	C₄×C₇	—	2	1	no	—
802	C₄×C₇	—	2	1	no	—
803	C₄×C₇	—	2	1	no	—
804	C₄×C₇	—	2	1	no	—
805	C₄×C₇	—	2	1	no	—
806	C₄×C₇	—	2	1	no	—
807	C₄×C₇	—	2	4	no	—
808	C₄×C₇	—	2	1	no	—
809	C₄×C₇	—	2	1	no	—
810	C₄×C₇	—	2	1	no	—
811	C₄×C₇	—	2	1	no	—
812	C₄×C₇	—	4	2	no	—
813	C₄×C₇	—	4	2	no	—
814	C₄×C₇	—	4	2	no	—
815	C₄×C₇	—	4	2	no	—
816	C₄×C₇	—	4	2	no	—
817	C₄×C₇	—	4	2	no	—
818	C₄×C₇	C₂²×#41	1	1	yes	characteristic
819	C₄×C₇	#585	1	1	yes	characteristic
820	#41	—	2	4	no	—
821	#41	—	4	2	no	—
822	C₂×Q₈	—	2	2	no	—
823	C₂×Q₈	—	2	2	no	—
824	C₂×Q₈	—	2	2	no	—
825	C₂×Q₈	—	2	4	no	—
826	C₂×Q₈	—	2	4	no	—
827	C₂×Q₈	—	4	2	no	—
828	C₂×Q₈	—	4	2	no	—
829	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
830	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
831	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
832	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
837	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
838	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
839	C₂×D₄	C₂⁴×C₇	1	2	yes	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
848	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
849	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
851	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
852	Q₁₆	—	2	4	no	—
853	Q₁₆	—	2	4	no	—
854	Q₁₆	—	2	2	no	—
855	Q₁₆	—	2	2	no	—
856	Q₁₆	—	4	2	no	—
857	Q₁₆	C₇×#41	1	4	yes	—
858	SD₁₆	—	2	4	no	—
859	SD₁₆	—	4	2	no	—
860	SD₁₆	—	4	2	no	—
861	D₈	—	2	2	no	—
862	M₁₆	—	4	1	no	—
863	M₁₆	—	4	1	no	—
864	C₂×C₈	—	2	2	no	—
865	C₂×C₈	—	2	2	no	—
866	C₂×C₈	—	2	2	no	—
867	C₂×C₈	—	4	1	no	—
868	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
869	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
870	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
871	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
872	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
873	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
874	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
875	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
898	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
899	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
900	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
901	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
902	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
903	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
904	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
905	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
906	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
907	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
908	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
909	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
910	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
925	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
926	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
927	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
928	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
929	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
930	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
931	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
932	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
933	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
934	C₄²	—	2	2	no	—
935	C₄²	—	2	2	no	—
936	C₄²	—	2	2	no	—
937	C₄²	—	2	2	no	—
938	C₄²	—	2	2	no	—
939	C₄²	—	2	2	no	—
940	C₄²	—	2	2	no	—
941	C₄²	—	2	2	no	—
942	C₄²	—	2	2	no	—
943	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
944	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
945	C₄²	C₂⁴×C₇	1	1	yes	characteristic
946	C₄²	C₂⁴×C₇	1	1	yes	characteristic
947	C₄²	C₂⁴×C₇	1	1	yes	characteristic
948	C₄²	C₂⁴×C₇	1	1	yes	characteristic
949	C₂×C₇	—	2	2	no	—
950	C₂×C₇	—	4	1	no	—
951	C₂×C₇	—	4	1	no	—
952	C₂×C₇	—	8	2	no	—
953	C₂×C₇	D₄×#41	1	1	yes	characteristic
954	C₂×C₇	C₂×#578	1	1	yes	characteristic
955	C₂×C₇	#3584	1	1	yes	characteristic
956	C₂³	—	2	2	no	—
957	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
958	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
959	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
960	Q₈	—	2	2	no	—
961	Q₈	—	2	2	no	—
962	Q₈	—	2	2	no	—
963	Q₈	—	2	2	no	—
964	Q₈	—	2	2	no	—
965	Q₈	—	4	1	no	—
966	Q₈	—	4	4	no	—
967	Q₈	—	4	4	no	—
968	Q₈	—	8	2	no	—
969	Q₈	C₂×C₇×#41	1	4	yes	—
970	D₄	—	2	2	no	—
971	D₄	—	2	2	no	—
972	D₄	—	2	2	no	—
973	D₄	—	2	2	no	—
974	D₄	—	4	1	no	—
975	D₄	—	4	4	no	—
976	D₄	—	4	4	no	—
977	D₄	—	8	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	4	1	no	—
993	C₂×C₄	—	4	4	no	—
994	C₂×C₄	—	4	4	no	—
995	C₂×C₄	—	4	4	no	—
996	C₂×C₄	—	8	2	no	—
997	C₂×C₄	—	8	2	no	—
998	C₂×C₄	—	8	2	no	—
999	C₂×C₄	—	8	2	no	—
1000	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1001	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1002	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1003	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1004	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1005	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1006	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1007	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1008	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1009	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1010	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1011	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1012	C₈	—	2	1	no	—
1013	C₈	—	2	1	no	—
1014	C₈	—	2	1	no	—
1015	C₈	—	2	1	no	—
1016	C₈	—	2	1	no	—
1017	C₈	—	2	1	no	—
1018	C₈	—	2	1	no	—
1019	C₈	C₂×C₇×#41	1	2	yes	—
1020	C₇	#61473	1	1	yes	characteristic, direct product factor, Sylow
1021	C₂²	—	2	1	no	—
1022	C₂²	—	2	1	no	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	1	no	—
1026	C₂²	—	2	1	no	—
1027	C₂²	—	2	1	no	—
1028	C₂²	—	2	1	no	—
1029	C₂²	—	4	2	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	C₇×#578	1	2	yes	—
1033	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1034	C₄	—	2	1	no	—
1035	C₄	—	2	1	no	—
1036	C₄	—	2	1	no	—
1037	C₄	—	2	1	no	—
1038	C₄	—	2	1	no	—
1039	C₄	—	2	1	no	—
1040	C₄	—	2	1	no	—
1041	C₄	—	2	1	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	1	no	—
1044	C₄	—	2	1	no	—
1045	C₄	—	2	4	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	2	no	—
1048	C₄	—	4	2	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	2	no	—
1051	C₄	—	4	2	no	—
1052	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1053	C₄	C₇×#585	1	1	yes	characteristic
1054	C₂	—	2	2	no	—
1055	C₂	—	4	1	no	—
1056	C₂	—	4	1	no	—
1057	C₂	—	8	2	no	—
1058	C₂	C₇×D₄×#41	1	1	yes	characteristic
1059	C₂	C₂×C₇×#578	1	1	yes	characteristic
1060	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×#3516	C₂	semidirect
2. C₇×#3393	C₂	semidirect
3. C₇×#3383	C₂	semidirect
4. C₇×#3377	C₂	semidirect
5. C₇×#3339	C₂	semidirect
6. C₇×#3338	C₂	semidirect
7. C₇×#3336	C₂	semidirect
8. C₇×#3327	C₂	semidirect
9. C₇×#3320	C₂	semidirect
10. C₇×#3316	C₂	semidirect
11. C₇×D₄×Q₁₆	C₂	semidirect
12. C₇×#3285	C₂	semidirect
13. C₇×#3285	C₂	semidirect
14. C₇×#3177	C₂	semidirect
15. C₇×#3175	C₂	semidirect
16. C₇×#3168	C₂	semidirect
17. C₇×#3121	C₂	semidirect
18. C₇×#3120	C₂	semidirect
19. C₇×#3117	C₂	semidirect
20. C₇×#2966	C₂	semidirect
21. C₇×#2951	C₂	semidirect
22. C₇×#2950	C₂	semidirect
23. C₂×C₄×C₇×Q₁₆	C₂	semidirect
131. #61473	C₇	direct (N × H)
298. #3516	C₂×C₇	semidirect
299. #3393	C₂×C₇	semidirect
300. #3383	C₂×C₇	semidirect
301. #3377	C₂×C₇	semidirect
302. #3339	C₂×C₇	semidirect
303. #3338	C₂×C₇	semidirect
304. #3336	C₂×C₇	semidirect
305. #3327	C₂×C₇	semidirect
306. #3320	C₂×C₇	semidirect
307. #3316	C₂×C₇	semidirect
308. D₄×Q₁₆	C₂×C₇	semidirect
309. #3285	C₂×C₇	semidirect
310. #3285	C₂×C₇	semidirect
311. #3177	C₂×C₇	semidirect
312. #3175	C₂×C₇	semidirect
313. #3168	C₂×C₇	semidirect
314. #3121	C₂×C₇	semidirect
315. #3120	C₂×C₇	semidirect
316. #3117	C₂×C₇	semidirect
317. #2966	C₂×C₇	semidirect
318. #2951	C₂×C₇	semidirect
319. #2950	C₂×C₇	semidirect
320. C₂×C₄×Q₁₆	C₂×C₇	semidirect
1020. C₇	#61473	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×#3516	2
C₇×#3393	2
C₇×#3383	2
C₇×#3377	2
C₇×#3339	2
C₇×#3338	2
C₇×#3336	2
C₇×#3327	2
C₇×#3320	2
C₇×#3316	2
C₇×D₄×Q₁₆	2
C₇×#3285	2
C₇×#3177	2
C₇×#3175	2
C₇×#3168	2
C₇×#3121	2
C₇×#3120	2
C₇×#3117	2
C₇×#2966	2
C₇×#2951	2
C₇×#2950	2
C₂×C₄×C₇×Q₁₆	2
#61473	7

Subgroups — C7×#61473 #13238689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61473 #13238689