Subgroups — C₇×#61857 #13239073

Order 1792.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3389	C₂	1	2	yes	maximal, complemented
4	C₇×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3386	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3385	C₂	1	2	yes	maximal, complemented
7	C₇×#3383	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×Q₈×D₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3375	C₂	1	2	yes	maximal, complemented
10	C₇×#3373	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3370	C₂	1	2	yes	maximal, complemented
12	C₇×#3368	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3365	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3358	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3243	C₂	1	2	yes	maximal, complemented
16	C₇×#3241	C₂	1	2	yes	maximal, complemented
17	C₇×#3239	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3124	C₂	1	2	yes	maximal, complemented
20	C₇×#3119	C₂	1	2	yes	maximal, complemented
21	C₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#3102	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2985	C₂	1	1	yes	maximal, characteristic, complemented
24	C₇×#562	—	2	2	no	—
25	C₇×#559	C₂²	1	1	yes	characteristic
26	C₇×#559	C₂²	1	2	yes	—
27	C₇×Q₈²	C₂²	1	2	yes	—
28	C₇×#557	C₂²	1	1	yes	characteristic
29	C₇×#557	C₂²	1	1	yes	characteristic
30	C₇×#557	C₂²	1	1	yes	characteristic
31	C₇×#554	—	2	2	no	—
32	C₇×#554	C₂²	1	2	yes	—
33	C₇×#554	C₂²	1	2	yes	—
34	C₇×#550	C₂²	1	1	yes	characteristic
35	C₇×D₄×Q₈	—	2	1	no	—
36	C₇×D₄×Q₈	—	2	1	no	—
37	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
38	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
39	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
40	C₇×#548	—	2	1	no	—
41	C₇×#547	—	2	1	no	—
42	C₇×#544	—	2	2	no	—
43	C₇×#544	C₂²	1	2	yes	—
44	C₇×#542	—	2	1	no	—
45	C₇×#542	C₂²	1	2	yes	—
46	C₇×#540	C₂²	1	2	yes	—
47	C₇×#539	—	2	2	no	—
48	C₇×#536	—	2	1	no	—
49	C₇×#533	—	2	1	no	—
50	C₇×#533	C₂²	1	1	yes	characteristic
51	C₇×#532	C₂²	1	1	yes	characteristic
52	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
53	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
54	C₇×#529	C₂²	1	1	yes	characteristic
55	C₇×#520	C₂²	1	2	yes	—
56	C₄×C₇×#41	C₂²	1	1	yes	characteristic
57	C₇×#501	C₂²	1	2	yes	—
58	C₇×#501	C₂²	1	2	yes	—
59	C₇×#501	C₂²	1	2	yes	—
60	C₇×#500	C₂²	1	1	yes	characteristic
61	C₇×#500	C₂²	1	1	yes	characteristic
62	C₇×#500	C₂²	1	2	yes	—
63	C₇×#499	C₂²	1	2	yes	—
64	C₇×#490	C₂²	1	2	yes	—
65	C₇×#489	C₂²	1	2	yes	—
66	C₇×#489	C₂²	1	2	yes	—
67	C₇×#488	C₂²	1	2	yes	—
68	C₇×#486	C₂²	1	1	yes	characteristic
69	C₇×#486	C₂²	1	1	yes	characteristic
70	C₇×#486	C₂²	1	2	yes	—
71	C₇×#485	C₂²	1	1	yes	characteristic
72	C₇×#484	C₂²	1	2	yes	—
73	C₇×#482	C₂²	1	1	yes	characteristic
74	C₇×#482	C₂²	1	2	yes	—
75	C₇×#481	C₂²	1	2	yes	—
76	C₇×#480	C₂²	1	2	yes	—
77	C₇×#480	C₂²	1	2	yes	—
78	C₇×#479	C₂²	1	2	yes	—
79	C₇×#479	C₂²	1	1	yes	characteristic
80	C₇×#479	C₂²	1	2	yes	—
81	C₇×#478	C₂²	1	2	yes	—
82	C₇×#478	C₂²	1	2	yes	—
83	C₇×#478	C₂²	1	2	yes	—
84	C₇×#478	C₂²	1	1	yes	characteristic
85	C₇×#478	C₂²	1	2	yes	—
86	C₇×#477	C₂²	1	2	yes	—
87	C₇×#477	C₂²	1	2	yes	—
88	C₇×#476	C₂²	1	2	yes	—
89	C₇×#475	C₂²	1	1	yes	characteristic
90	C₇×#475	C₂²	1	1	yes	characteristic
91	C₇×#475	C₂²	1	1	yes	characteristic
92	C₇×#474	C₂²	1	2	yes	—
93	C₇×#474	C₂²	1	2	yes	—
94	C₇×#474	C₂²	1	1	yes	characteristic
95	C₇×#474	C₂²	1	1	yes	characteristic
96	C₇×#474	C₂²	1	2	yes	—
97	C₇×#474	C₂²	1	2	yes	—
98	C₇×#474	C₂²	1	1	yes	characteristic
99	C₇×#474	C₂²	1	2	yes	—
100	C₇×#464	C₂²	1	1	yes	characteristic
101	C₇×#464	C₂²	1	2	yes	—
102	C₇×#463	C₂²	1	1	yes	characteristic
103	C₇×#463	C₂²	1	2	yes	—
104	C₇×#460	C₂²	1	1	yes	characteristic
105	C₇×#460	C₂²	1	2	yes	—
106	C₇×#459	C₂²	1	2	yes	—
107	C₇×#459	C₂²	1	1	yes	characteristic
108	C₇×#452	C₂²	1	1	yes	characteristic
109	C₇×#449	C₂²	1	1	yes	characteristic
110	C₇×#449	C₂²	1	2	yes	—
111	C₇×#446	C₂²	1	1	yes	characteristic
112	C₇×#446	C₂²	1	2	yes	—
113	C₇×#446	C₂²	1	1	yes	characteristic
114	C₇×#446	C₂²	1	2	yes	—
115	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
116	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
117	C₇×#442	C₂²	1	2	yes	—
118	C₇×#442	C₂²	1	2	yes	—
119	C₇×#440	C₂²	1	2	yes	—
120	C₇×#440	C₂²	1	2	yes	—
121	C₇×#440	C₂²	1	2	yes	—
122	C₇×#440	C₂²	1	2	yes	—
123	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
124	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
125	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
126	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
127	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
128	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
129	C₄×C₇×D₈	C₂²	1	2	yes	—
130	C₄×C₇×D₈	C₂²	1	2	yes	—
131	C₇×#433	C₂²	1	2	yes	—
132	C₇×#433	C₂²	1	2	yes	—
133	C₇×#432	C₂²	1	1	yes	characteristic
134	C₇×#431	C₂²	1	1	yes	characteristic
135	#61857	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	1	no	—
137	C₂×C₇×#41	—	2	1	no	—
138	C₂×C₇×#41	C₂³	1	1	yes	characteristic
139	C₂²×C₇×Q₈	—	2	1	no	—
140	C₂²×C₇×Q₈	—	2	1	no	—
141	C₂²×C₇×Q₈	—	2	1	no	—
142	C₂²×C₇×Q₈	—	2	1	no	—
143	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
146	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
148	C₂×C₇×D₈	C₂³	1	2	yes	—
149	C₇×C₄⋊Q₈	—	2	1	no	—
150	C₇×C₄⋊Q₈	—	2	1	no	—
151	C₇×C₄⋊Q₈	—	2	1	no	—
152	C₇×C₄⋊Q₈	—	2	2	no	—
153	C₇×C₄⋊Q₈	—	2	2	no	—
154	C₇×C₄⋊Q₈	—	2	2	no	—
155	C₇×C₄⋊Q₈	—	2	2	no	—
156	C₇×C₄⋊Q₈	—	2	1	no	—
157	C₇×C₄⋊Q₈	—	2	1	no	—
158	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
159	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
160	C₇×C₄⋊Q₈	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×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₇×#127	C₂³	1	1	yes	characteristic
168	C₇×#127	C₂³	1	2	yes	—
169	C₇×#126	—	2	2	no	—
170	C₇×#126	—	2	1	no	—
171	C₇×#125	—	2	2	no	—
172	C₇×#125	—	2	2	no	—
173	C₇×#125	—	2	2	no	—
174	C₇×#125	—	2	2	no	—
175	C₇×#125	D₄	1	2	yes	—
176	C₇×#125	C₂³	1	2	yes	—
177	C₇×#125	C₂³	1	2	yes	—
178	C₇×#125	C₂³	1	2	yes	—
179	C₇×#125	C₂³	1	1	yes	characteristic
180	C₇×#124	—	2	1	no	—
181	C₇×#124	—	2	2	no	—
182	C₇×#124	—	2	2	no	—
183	C₇×#124	—	2	1	no	—
184	C₇×#124	C₂³	1	2	yes	—
185	C₇×#124	C₂³	1	1	yes	characteristic
186	C₇×#123	—	2	1	no	—
187	C₇×#123	—	2	2	no	—
188	C₇×#123	—	2	2	no	—
189	C₇×#123	—	2	2	no	—
190	C₇×#123	—	2	2	no	—
191	C₇×#123	—	2	2	no	—
192	C₇×#123	—	2	2	no	—
193	C₇×C₂²⋊Q₈	—	2	2	no	—
194	C₇×C₂²⋊Q₈	—	2	2	no	—
195	C₇×C₂²⋊Q₈	—	2	1	no	—
196	C₇×C₂²⋊Q₈	—	2	1	no	—
197	C₇×C₂²⋊Q₈	—	2	2	no	—
198	C₇×C₂²⋊Q₈	—	2	2	no	—
199	C₇×C₂²⋊Q₈	—	2	2	no	—
200	C₇×C₂²⋊Q₈	—	2	2	no	—
201	C₇×C₂²⋊Q₈	—	2	1	no	—
202	C₇×C₂²⋊Q₈	—	2	2	no	—
203	C₇×C₂²⋊Q₈	—	2	2	no	—
204	C₇×C₂²⋊Q₈	—	2	2	no	—
205	C₇×C₂²⋊Q₈	—	2	2	no	—
206	C₇×C₂²⋊Q₈	—	2	2	no	—
207	C₇×C₂²⋊Q₈	—	2	2	no	—
208	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
211	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₇×#121	—	2	1	no	—
213	C₇×#121	—	2	2	no	—
214	C₇×#121	—	2	1	no	—
215	C₇×#121	—	2	2	no	—
216	C₇×#121	—	2	2	no	—
217	C₇×#121	C₂³	1	2	yes	—
218	C₇×#121	C₂³	1	1	yes	characteristic
219	C₄×C₇×Q₈	—	2	2	no	—
220	C₄×C₇×Q₈	—	2	1	no	—
221	C₄×C₇×Q₈	—	2	1	no	—
222	C₄×C₇×Q₈	—	2	1	no	—
223	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
224	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
225	C₄×C₇×Q₈	C₂³	1	2	yes	—
226	C₄×C₇×Q₈	C₂³	1	2	yes	—
227	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
228	C₄×C₇×Q₈	C₂³	1	2	yes	—
229	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
230	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
231	C₄×C₇×Q₈	C₂³	1	2	yes	—
232	C₄×C₇×D₄	—	2	1	no	—
233	C₄×C₇×D₄	—	2	1	no	—
234	C₄×C₇×D₄	—	2	1	no	—
235	C₄×C₇×D₄	—	2	2	no	—
236	C₄×C₇×D₄	—	2	1	no	—
237	C₄×C₇×D₄	—	2	2	no	—
238	C₄×C₇×D₄	—	2	2	no	—
239	C₄×C₇×D₄	—	2	1	no	—
240	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
241	C₄×C₇×D₄	C₂³	1	2	yes	—
242	C₄×C₇×D₄	C₂³	1	2	yes	—
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	C₄×C₇×D₄	C₂³	1	2	yes	—
247	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
248	C₄×C₇×D₄	C₂³	1	2	yes	—
249	C₇×#117	—	2	2	no	—
250	C₇×#117	—	2	1	no	—
251	C₇×#117	—	2	1	no	—
252	C₇×#117	C₂³	1	1	yes	characteristic
253	C₇×#117	C₂³	1	2	yes	—
254	C₂×C₇×C₄⋊C₄	—	2	1	no	—
255	C₂×C₇×C₄⋊C₄	—	2	2	no	—
256	C₂×C₇×C₄⋊C₄	—	2	2	no	—
257	C₂×C₇×C₄⋊C₄	—	2	2	no	—
258	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
259	C₂×C₄²×C₇	—	2	1	no	—
260	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
261	C₇×#107	C₂³	1	2	yes	—
262	C₇×#107	C₂³	1	2	yes	—
263	C₇×#107	C₂³	1	2	yes	—
264	C₇×#107	C₂³	1	2	yes	—
265	C₇×#107	C₂³	1	1	yes	characteristic
266	C₇×#107	C₂³	1	2	yes	—
267	C₇×#107	C₂³	1	2	yes	—
268	C₇×#107	C₂³	1	2	yes	—
269	C₇×#107	C₂³	1	1	yes	characteristic
270	C₇×#106	C₂³	1	2	yes	—
271	C₇×#106	C₂³	1	2	yes	—
272	C₇×#106	C₂³	1	2	yes	—
273	C₇×#106	C₂³	1	1	yes	characteristic
274	C₇×#106	C₂³	1	1	yes	characteristic
275	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₇×C₄⋊C₈	C₂³	1	2	yes	—
278	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₇×C₄⋊C₈	C₂³	1	2	yes	—
281	C₇×C₄⋊C₈	C₂³	1	2	yes	—
282	C₇×C₄⋊C₈	C₂³	1	2	yes	—
283	C₇×#103	C₂³	1	2	yes	—
284	C₇×#103	C₂³	1	2	yes	—
285	C₇×#103	C₂³	1	2	yes	—
286	C₇×#103	C₂³	1	1	yes	characteristic
287	C₇×#103	C₂³	1	1	yes	characteristic
288	C₇×#103	C₂³	1	1	yes	characteristic
289	C₇×#103	C₂³	1	1	yes	characteristic
290	C₇×#102	C₂³	1	1	yes	characteristic
291	C₇×#102	C₂³	1	2	yes	—
292	C₇×#102	C₂³	1	2	yes	—
293	C₇×#102	C₂³	1	2	yes	—
294	C₇×#102	C₂³	1	1	yes	characteristic
295	C₇×#102	C₂³	1	2	yes	—
296	C₇×#102	C₂³	1	2	yes	—
297	C₇×#102	C₂³	1	2	yes	—
298	C₇×#102	C₂³	1	2	yes	—
299	C₇×#102	C₂³	1	2	yes	—
300	C₇×#102	C₂³	1	1	yes	characteristic
301	C₇×#102	C₂³	1	2	yes	—
302	C₇×#102	C₂³	1	1	yes	characteristic
303	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₇×#97	C₂³	1	2	yes	—
307	C₇×#97	C₂³	1	2	yes	—
308	C₇×#97	C₂³	1	2	yes	—
309	C₄×C₇×C₈	C₂³	1	2	yes	—
310	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
311	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
312	C₄×C₇×C₈	C₂³	1	2	yes	—
313	#3554	C₂×C₇	1	1	yes	characteristic, complemented
314	#3503	C₂×C₇	1	1	yes	characteristic, complemented
315	#3389	C₂×C₇	1	2	yes	complemented
316	#3386	C₂×C₇	1	1	yes	characteristic, complemented
317	#3386	C₂×C₇	1	1	yes	characteristic, complemented
318	#3385	C₂×C₇	1	2	yes	complemented
319	#3383	C₂×C₇	1	1	yes	characteristic, complemented
320	Q₈×D₈	C₂×C₇	1	1	yes	characteristic, complemented
321	#3375	C₂×C₇	1	2	yes	complemented
322	#3373	C₂×C₇	1	1	yes	characteristic, complemented
323	#3370	C₂×C₇	1	2	yes	complemented
324	#3368	C₂×C₇	1	1	yes	characteristic, complemented
325	#3365	C₂×C₇	1	1	yes	characteristic, complemented
326	#3358	C₂×C₇	1	1	yes	characteristic, complemented
327	#3243	C₂×C₇	1	2	yes	complemented
328	#3241	C₂×C₇	1	2	yes	complemented
329	#3239	C₂×C₇	1	1	yes	characteristic, complemented
330	#3226	C₂×C₇	1	1	yes	characteristic, complemented
331	#3124	C₂×C₇	1	2	yes	complemented
332	#3119	C₂×C₇	1	2	yes	complemented
333	#3115	C₂×C₇	1	1	yes	characteristic, complemented
334	#3102	C₂×C₇	1	1	yes	characteristic, complemented
335	#2985	C₂×C₇	1	1	yes	characteristic, complemented
336	C₇×#41	—	2	2	no	—
337	C₇×#41	—	2	2	no	—
338	C₇×#41	—	8	2	no	—
339	C₇×#41	—	8	2	no	—
340	C₂×C₇×Q₈	—	2	1	no	—
341	C₂×C₇×Q₈	—	2	1	no	—
342	C₂×C₇×Q₈	—	2	1	no	—
343	C₂×C₇×Q₈	—	2	2	no	—
344	C₂×C₇×Q₈	—	2	2	no	—
345	C₂×C₇×Q₈	—	2	2	no	—
346	C₂×C₇×Q₈	—	2	2	no	—
347	C₂×C₇×Q₈	—	8	2	no	—
348	C₂×C₇×Q₈	—	8	2	no	—
349	C₂×C₇×Q₈	—	8	2	no	—
350	C₂×C₇×Q₈	—	8	2	no	—
351	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
352	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
353	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
354	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
355	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
356	C₂×C₇×D₄	—	2	1	no	—
357	C₂×C₇×D₄	—	2	1	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	2	no	—
362	C₂×C₇×D₄	—	2	2	no	—
363	C₂×C₇×D₄	C₂⁴	1	2	yes	—
364	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
365	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₇	—	2	1	no	—
367	C₂²×C₄×C₇	—	2	2	no	—
368	C₂²×C₄×C₇	—	2	1	no	—
369	C₂²×C₄×C₇	—	2	1	no	—
370	C₂²×C₄×C₇	—	2	1	no	—
371	C₂²×C₄×C₇	—	2	2	no	—
372	C₂²×C₄×C₇	—	2	2	no	—
373	C₂²×C₄×C₇	—	2	2	no	—
374	C₂²×C₄×C₇	—	2	2	no	—
375	C₂²×C₄×C₇	—	2	2	no	—
376	C₂²×C₄×C₇	—	2	2	no	—
377	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
380	C₇×Q₁₆	—	2	2	no	—
381	C₇×SD₁₆	—	2	2	no	—
382	C₇×SD₁₆	—	2	4	no	—
383	C₇×SD₁₆	—	2	2	no	—
384	C₇×D₈	—	2	2	no	—
385	C₇×D₈	—	2	4	no	—
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	C₂×C₇×C₈	C₂⁴	1	2	yes	—
391	C₂×C₇×C₈	C₂⁴	1	2	yes	—
392	C₇×C₄⋊C₄	—	2	1	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	1	no	—
400	C₇×C₄⋊C₄	—	2	1	no	—
401	C₇×C₄⋊C₄	—	2	2	no	—
402	C₇×C₄⋊C₄	—	2	2	no	—
403	C₇×C₄⋊C₄	—	2	1	no	—
404	C₇×C₄⋊C₄	—	2	1	no	—
405	C₇×C₄⋊C₄	—	2	1	no	—
406	C₇×C₄⋊C₄	—	2	1	no	—
407	C₇×C₄⋊C₄	—	2	1	no	—
408	C₇×C₄⋊C₄	—	2	2	no	—
409	C₇×C₄⋊C₄	—	2	2	no	—
410	C₇×C₄⋊C₄	—	2	2	no	—
411	C₇×C₄⋊C₄	—	2	2	no	—
412	C₇×C₄⋊C₄	—	2	2	no	—
413	C₇×C₄⋊C₄	—	2	2	no	—
414	C₇×C₄⋊C₄	—	2	1	no	—
415	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
416	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
417	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
418	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
419	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
420	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
421	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
422	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
423	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
424	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
425	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
426	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
427	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
428	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
429	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
430	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
431	C₇×C₂²⋊C₄	—	2	1	no	—
432	C₇×C₂²⋊C₄	—	2	1	no	—
433	C₇×C₂²⋊C₄	—	2	1	no	—
434	C₇×C₂²⋊C₄	—	2	1	no	—
435	C₇×C₂²⋊C₄	—	2	2	no	—
436	C₇×C₂²⋊C₄	—	2	2	no	—
437	C₇×C₂²⋊C₄	—	2	1	no	—
438	C₇×C₂²⋊C₄	—	2	1	no	—
439	C₇×C₂²⋊C₄	—	2	1	no	—
440	C₇×C₂²⋊C₄	—	2	2	no	—
441	C₇×C₂²⋊C₄	—	2	2	no	—
442	C₇×C₂²⋊C₄	—	2	2	no	—
443	C₇×C₂²⋊C₄	—	2	1	no	—
444	C₇×C₂²⋊C₄	—	2	2	no	—
445	C₇×C₂²⋊C₄	—	2	2	no	—
446	C₇×C₂²⋊C₄	—	2	2	no	—
447	C₇×C₂²⋊C₄	—	2	2	no	—
448	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
449	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
450	C₄²×C₇	—	2	1	no	—
451	C₄²×C₇	—	2	1	no	—
452	C₄²×C₇	—	2	1	no	—
453	C₄²×C₇	—	2	1	no	—
454	C₄²×C₇	—	2	2	no	—
455	C₄²×C₇	—	2	2	no	—
456	C₄²×C₇	—	2	2	no	—
457	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₇	C₂⁴	1	1	yes	characteristic
460	C₄²×C₇	C₂⁴	1	2	yes	—
461	C₄²×C₇	C₂⁴	1	2	yes	—
462	C₄²×C₇	C₂⁴	1	1	yes	characteristic
463	#562	—	2	2	no	—
464	#559	C₂²×C₇	1	1	yes	characteristic
465	#559	C₂²×C₇	1	2	yes	—
466	Q₈²	C₂²×C₇	1	2	yes	—
467	#557	C₂²×C₇	1	1	yes	characteristic
468	#557	C₂²×C₇	1	1	yes	characteristic
469	#557	C₂²×C₇	1	1	yes	characteristic
470	#554	—	2	2	no	—
471	#554	C₂²×C₇	1	2	yes	—
472	#554	C₂²×C₇	1	2	yes	—
473	#550	C₂²×C₇	1	1	yes	characteristic
474	D₄×Q₈	—	2	1	no	—
475	D₄×Q₈	—	2	1	no	—
476	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
477	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
478	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
479	#548	—	2	1	no	—
480	#547	—	2	1	no	—
481	#544	—	2	2	no	—
482	#544	C₂²×C₇	1	2	yes	—
483	#542	—	2	1	no	—
484	#542	C₂²×C₇	1	2	yes	—
485	#540	C₂²×C₇	1	2	yes	—
486	#539	—	2	2	no	—
487	#536	—	2	1	no	—
488	#533	—	2	1	no	—
489	#533	C₂²×C₇	1	1	yes	characteristic
490	#532	C₂²×C₇	1	1	yes	characteristic
491	C₂×C₄⋊Q₈	—	2	1	no	—
492	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
493	#529	C₂²×C₇	1	1	yes	characteristic
494	#520	C₂²×C₇	1	2	yes	—
495	C₄×#41	C₂²×C₇	1	1	yes	characteristic
496	#501	C₂²×C₇	1	2	yes	—
497	#501	C₂²×C₇	1	2	yes	—
498	#501	C₂²×C₇	1	2	yes	—
499	#500	C₂²×C₇	1	1	yes	characteristic
500	#500	C₂²×C₇	1	2	yes	—
501	#500	C₂²×C₇	1	1	yes	characteristic
502	#499	C₂²×C₇	1	2	yes	—
503	#490	C₂²×C₇	1	2	yes	—
504	#489	C₂²×C₇	1	2	yes	—
505	#489	C₂²×C₇	1	2	yes	—
506	#488	C₂²×C₇	1	2	yes	—
507	#486	C₂²×C₇	1	1	yes	characteristic
508	#486	C₂²×C₇	1	2	yes	—
509	#486	C₂²×C₇	1	1	yes	characteristic
510	#485	C₂²×C₇	1	1	yes	characteristic
511	#484	C₂²×C₇	1	2	yes	—
512	#482	C₂²×C₇	1	1	yes	characteristic
513	#482	C₂²×C₇	1	2	yes	—
514	#481	C₂²×C₇	1	2	yes	—
515	#480	C₂²×C₇	1	2	yes	—
516	#480	C₂²×C₇	1	2	yes	—
517	#479	C₂²×C₇	1	1	yes	characteristic
518	#479	C₂²×C₇	1	2	yes	—
519	#479	C₂²×C₇	1	2	yes	—
520	#478	C₂²×C₇	1	1	yes	characteristic
521	#478	C₂²×C₇	1	2	yes	—
522	#478	C₂²×C₇	1	2	yes	—
523	#478	C₂²×C₇	1	2	yes	—
524	#478	C₂²×C₇	1	2	yes	—
525	#477	C₂²×C₇	1	2	yes	—
526	#477	C₂²×C₇	1	2	yes	—
527	#476	C₂²×C₇	1	2	yes	—
528	#475	C₂²×C₇	1	1	yes	characteristic
529	#475	C₂²×C₇	1	1	yes	characteristic
530	#475	C₂²×C₇	1	1	yes	characteristic
531	#474	C₂²×C₇	1	2	yes	—
532	#474	C₂²×C₇	1	1	yes	characteristic
533	#474	C₂²×C₇	1	1	yes	characteristic
534	#474	C₂²×C₇	1	2	yes	—
535	#474	C₂²×C₇	1	1	yes	characteristic
536	#474	C₂²×C₇	1	2	yes	—
537	#474	C₂²×C₇	1	2	yes	—
538	#474	C₂²×C₇	1	2	yes	—
539	#464	C₂²×C₇	1	1	yes	characteristic
540	#464	C₂²×C₇	1	2	yes	—
541	#463	C₂²×C₇	1	1	yes	characteristic
542	#463	C₂²×C₇	1	2	yes	—
543	#460	C₂²×C₇	1	1	yes	characteristic
544	#460	C₂²×C₇	1	2	yes	—
545	#459	C₂²×C₇	1	2	yes	—
546	#459	C₂²×C₇	1	1	yes	characteristic
547	#452	C₂²×C₇	1	1	yes	characteristic
548	#449	C₂²×C₇	1	1	yes	characteristic
549	#449	C₂²×C₇	1	2	yes	—
550	#446	C₂²×C₇	1	1	yes	characteristic
551	#446	C₂²×C₇	1	2	yes	—
552	#446	C₂²×C₇	1	1	yes	characteristic
553	#446	C₂²×C₇	1	2	yes	—
554	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
555	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
556	#442	C₂²×C₇	1	2	yes	—
557	#442	C₂²×C₇	1	2	yes	—
558	#440	C₂²×C₇	1	2	yes	—
559	#440	C₂²×C₇	1	2	yes	—
560	#440	C₂²×C₇	1	2	yes	—
561	#440	C₂²×C₇	1	2	yes	—
562	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
563	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
564	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
565	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
566	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
567	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
568	C₄×D₈	C₂²×C₇	1	2	yes	—
569	C₄×D₈	C₂²×C₇	1	2	yes	—
570	#433	C₂²×C₇	1	2	yes	—
571	#433	C₂²×C₇	1	2	yes	—
572	#432	C₂²×C₇	1	1	yes	characteristic
573	#431	C₂²×C₇	1	1	yes	characteristic
574	C₂³×C₇	—	2	1	no	—
575	C₂³×C₇	—	2	2	no	—
576	C₂³×C₇	—	2	1	no	—
577	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
578	C₇×Q₈	—	2	2	no	—
579	C₇×Q₈	—	2	2	no	—
580	C₇×Q₈	—	2	1	no	—
581	C₇×Q₈	—	2	1	no	—
582	C₇×Q₈	—	2	1	no	—
583	C₇×Q₈	—	4	2	no	—
584	C₇×Q₈	—	4	2	no	—
585	C₇×Q₈	—	4	2	no	—
586	C₇×Q₈	—	4	2	no	—
587	C₇×Q₈	—	8	2	no	—
588	C₇×Q₈	—	8	2	no	—
589	C₇×Q₈	—	8	2	no	—
590	C₇×Q₈	—	8	2	no	—
591	C₇×Q₈	2₋¹⁺⁴	1	2	yes	—
592	C₇×D₄	—	2	4	no	—
593	C₇×D₄	—	2	1	no	—
594	C₇×D₄	—	2	1	no	—
595	C₇×D₄	—	2	2	no	—
596	C₇×D₄	—	2	2	no	—
597	C₇×D₄	—	2	1	no	—
598	C₇×D₄	—	4	2	no	—
599	C₇×D₄	—	8	1	no	—
600	C₇×D₄	—	8	2	no	—
601	C₇×D₄	—	8	2	no	—
602	C₇×D₄	—	8	1	no	—
603	C₇×D₄	—	8	2	no	—
604	C₇×D₄	2₋¹⁺⁴	1	2	yes	—
605	C₂×C₄×C₇	—	2	4	no	—
606	C₂×C₄×C₇	—	2	1	no	—
607	C₂×C₄×C₇	—	2	2	no	—
608	C₂×C₄×C₇	—	2	1	no	—
609	C₂×C₄×C₇	—	2	1	no	—
610	C₂×C₄×C₇	—	2	1	no	—
611	C₂×C₄×C₇	—	2	1	no	—
612	C₂×C₄×C₇	—	2	1	no	—
613	C₂×C₄×C₇	—	2	1	no	—
614	C₂×C₄×C₇	—	2	2	no	—
615	C₂×C₄×C₇	—	2	2	no	—
616	C₂×C₄×C₇	—	2	2	no	—
617	C₂×C₄×C₇	—	2	1	no	—
618	C₂×C₄×C₇	—	4	1	no	—
619	C₂×C₄×C₇	—	4	2	no	—
620	C₂×C₄×C₇	—	4	2	no	—
621	C₂×C₄×C₇	—	4	2	no	—
622	C₂×C₄×C₇	—	8	2	no	—
623	C₂×C₄×C₇	—	8	2	no	—
624	C₂×C₄×C₇	—	8	2	no	—
625	C₂×C₄×C₇	—	8	2	no	—
626	C₂×C₄×C₇	—	8	2	no	—
627	C₂×C₄×C₇	—	8	2	no	—
628	C₂×C₄×C₇	—	8	2	no	—
629	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
630	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
631	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
632	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
633	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
634	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
635	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
636	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
637	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
638	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
639	C₇×C₈	—	2	1	no	—
640	C₇×C₈	—	2	2	no	—
641	C₇×C₈	—	2	1	no	—
642	C₇×C₈	—	2	2	no	—
643	C₇×C₈	—	2	1	no	—
644	C₇×C₈	—	2	1	no	—
645	C₂×#41	—	2	1	no	—
646	C₂×#41	—	2	1	no	—
647	C₂×#41	C₂³×C₇	1	1	yes	characteristic
648	C₂²×Q₈	—	2	1	no	—
649	C₂²×Q₈	—	2	1	no	—
650	C₂²×Q₈	—	2	1	no	—
651	C₂²×Q₈	—	2	1	no	—
652	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
653	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
654	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
655	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
656	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
657	C₂×D₈	C₂³×C₇	1	2	yes	—
658	C₄⋊Q₈	—	2	1	no	—
659	C₄⋊Q₈	—	2	1	no	—
660	C₄⋊Q₈	—	2	1	no	—
661	C₄⋊Q₈	—	2	2	no	—
662	C₄⋊Q₈	—	2	2	no	—
663	C₄⋊Q₈	—	2	2	no	—
664	C₄⋊Q₈	—	2	2	no	—
665	C₄⋊Q₈	—	2	1	no	—
666	C₄⋊Q₈	—	2	1	no	—
667	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
668	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
669	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
670	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
671	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
672	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
673	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
674	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
675	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
676	#127	C₂³×C₇	1	1	yes	characteristic
677	#127	C₂³×C₇	1	2	yes	—
678	#126	—	2	2	no	—
679	#126	—	2	1	no	—
680	#125	—	2	2	no	—
681	#125	—	2	2	no	—
682	#125	—	2	2	no	—
683	#125	—	2	2	no	—
684	#125	C₇×D₄	1	2	yes	—
685	#125	C₂³×C₇	1	1	yes	characteristic
686	#125	C₂³×C₇	1	2	yes	—
687	#125	C₂³×C₇	1	2	yes	—
688	#125	C₂³×C₇	1	2	yes	—
689	#124	—	2	1	no	—
690	#124	—	2	2	no	—
691	#124	—	2	2	no	—
692	#124	—	2	1	no	—
693	#124	C₂³×C₇	1	1	yes	characteristic
694	#124	C₂³×C₇	1	2	yes	—
695	#123	—	2	1	no	—
696	#123	—	2	2	no	—
697	#123	—	2	2	no	—
698	#123	—	2	2	no	—
699	#123	—	2	2	no	—
700	#123	—	2	2	no	—
701	#123	—	2	2	no	—
702	C₂²⋊Q₈	—	2	2	no	—
703	C₂²⋊Q₈	—	2	2	no	—
704	C₂²⋊Q₈	—	2	1	no	—
705	C₂²⋊Q₈	—	2	1	no	—
706	C₂²⋊Q₈	—	2	2	no	—
707	C₂²⋊Q₈	—	2	2	no	—
708	C₂²⋊Q₈	—	2	2	no	—
709	C₂²⋊Q₈	—	2	2	no	—
710	C₂²⋊Q₈	—	2	1	no	—
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	—	2	2	no	—
713	C₂²⋊Q₈	—	2	2	no	—
714	C₂²⋊Q₈	—	2	2	no	—
715	C₂²⋊Q₈	—	2	2	no	—
716	C₂²⋊Q₈	—	2	2	no	—
717	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
718	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
719	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
720	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
721	#121	—	2	1	no	—
722	#121	—	2	2	no	—
723	#121	—	2	1	no	—
724	#121	—	2	2	no	—
725	#121	—	2	2	no	—
726	#121	C₂³×C₇	1	1	yes	characteristic
727	#121	C₂³×C₇	1	2	yes	—
728	C₄×Q₈	—	2	2	no	—
729	C₄×Q₈	—	2	1	no	—
730	C₄×Q₈	—	2	1	no	—
731	C₄×Q₈	—	2	1	no	—
732	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
733	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
734	C₄×Q₈	C₂³×C₇	1	2	yes	—
735	C₄×Q₈	C₂³×C₇	1	2	yes	—
736	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
737	C₄×Q₈	C₂³×C₇	1	2	yes	—
738	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
739	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
740	C₄×Q₈	C₂³×C₇	1	2	yes	—
741	C₄×D₄	—	2	1	no	—
742	C₄×D₄	—	2	1	no	—
743	C₄×D₄	—	2	1	no	—
744	C₄×D₄	—	2	2	no	—
745	C₄×D₄	—	2	1	no	—
746	C₄×D₄	—	2	2	no	—
747	C₄×D₄	—	2	2	no	—
748	C₄×D₄	—	2	1	no	—
749	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
750	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
751	C₄×D₄	C₂³×C₇	1	2	yes	—
752	C₄×D₄	C₂³×C₇	1	2	yes	—
753	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
754	C₄×D₄	C₂³×C₇	1	2	yes	—
755	C₄×D₄	C₂³×C₇	1	2	yes	—
756	C₄×D₄	C₂³×C₇	1	2	yes	—
757	C₄×D₄	C₂³×C₇	1	2	yes	—
758	#117	—	2	2	no	—
759	#117	—	2	1	no	—
760	#117	—	2	1	no	—
761	#117	C₂³×C₇	1	1	yes	characteristic
762	#117	C₂³×C₇	1	2	yes	—
763	C₂×C₄⋊C₄	—	2	1	no	—
764	C₂×C₄⋊C₄	—	2	2	no	—
765	C₂×C₄⋊C₄	—	2	2	no	—
766	C₂×C₄⋊C₄	—	2	2	no	—
767	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
768	C₂×C₄²	—	2	1	no	—
769	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
770	#107	C₂³×C₇	1	2	yes	—
771	#107	C₂³×C₇	1	1	yes	characteristic
772	#107	C₂³×C₇	1	2	yes	—
773	#107	C₂³×C₇	1	2	yes	—
774	#107	C₂³×C₇	1	1	yes	characteristic
775	#107	C₂³×C₇	1	2	yes	—
776	#107	C₂³×C₇	1	2	yes	—
777	#107	C₂³×C₇	1	2	yes	—
778	#107	C₂³×C₇	1	2	yes	—
779	#106	C₂³×C₇	1	2	yes	—
780	#106	C₂³×C₇	1	1	yes	characteristic
781	#106	C₂³×C₇	1	1	yes	characteristic
782	#106	C₂³×C₇	1	2	yes	—
783	#106	C₂³×C₇	1	2	yes	—
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	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
788	C₄⋊C₈	C₂³×C₇	1	2	yes	—
789	C₄⋊C₈	C₂³×C₇	1	2	yes	—
790	C₄⋊C₈	C₂³×C₇	1	2	yes	—
791	C₄⋊C₈	C₂³×C₇	1	2	yes	—
792	#103	C₂³×C₇	1	1	yes	characteristic
793	#103	C₂³×C₇	1	1	yes	characteristic
794	#103	C₂³×C₇	1	1	yes	characteristic
795	#103	C₂³×C₇	1	2	yes	—
796	#103	C₂³×C₇	1	2	yes	—
797	#103	C₂³×C₇	1	1	yes	characteristic
798	#103	C₂³×C₇	1	2	yes	—
799	#102	C₂³×C₇	1	1	yes	characteristic
800	#102	C₂³×C₇	1	2	yes	—
801	#102	C₂³×C₇	1	2	yes	—
802	#102	C₂³×C₇	1	1	yes	characteristic
803	#102	C₂³×C₇	1	2	yes	—
804	#102	C₂³×C₇	1	1	yes	characteristic
805	#102	C₂³×C₇	1	2	yes	—
806	#102	C₂³×C₇	1	1	yes	characteristic
807	#102	C₂³×C₇	1	2	yes	—
808	#102	C₂³×C₇	1	2	yes	—
809	#102	C₂³×C₇	1	2	yes	—
810	#102	C₂³×C₇	1	2	yes	—
811	#102	C₂³×C₇	1	2	yes	—
812	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
813	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
814	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
815	#97	C₂³×C₇	1	2	yes	—
816	#97	C₂³×C₇	1	2	yes	—
817	#97	C₂³×C₇	1	2	yes	—
818	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
819	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
820	C₄×C₈	C₂³×C₇	1	2	yes	—
821	C₄×C₈	C₂³×C₇	1	2	yes	—
822	C₂²×C₇	—	2	1	no	—
823	C₂²×C₇	—	2	1	no	—
824	C₂²×C₇	—	2	2	no	—
825	C₂²×C₇	—	2	1	no	—
826	C₂²×C₇	—	4	1	no	—
827	C₂²×C₇	—	4	1	no	—
828	C₂²×C₇	—	4	2	no	—
829	C₂²×C₇	—	4	1	no	—
830	C₂²×C₇	—	4	2	no	—
831	C₂²×C₇	—	4	1	no	—
832	C₂²×C₇	—	4	1	no	—
833	C₂²×C₇	—	4	2	no	—
834	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
835	C₄×C₇	—	2	1	no	—
836	C₄×C₇	—	2	1	no	—
837	C₄×C₇	—	2	2	no	—
838	C₄×C₇	—	2	2	no	—
839	C₄×C₇	—	2	1	no	—
840	C₄×C₇	—	2	2	no	—
841	C₄×C₇	—	2	1	no	—
842	C₄×C₇	—	2	2	no	—
843	C₄×C₇	—	2	2	no	—
844	C₄×C₇	—	4	1	no	—
845	C₄×C₇	—	4	1	no	—
846	C₄×C₇	—	4	1	no	—
847	C₄×C₇	—	4	1	no	—
848	C₄×C₇	—	4	1	no	—
849	C₄×C₇	—	4	2	no	—
850	C₄×C₇	—	4	2	no	—
851	C₄×C₇	—	4	2	no	—
852	C₄×C₇	#576	1	2	yes	—
853	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
854	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
855	#41	—	2	2	no	—
856	#41	—	2	2	no	—
857	#41	—	8	2	no	—
858	#41	—	8	2	no	—
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	1	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	—	2	2	no	—
866	C₂×Q₈	—	8	2	no	—
867	C₂×Q₈	—	8	2	no	—
868	C₂×Q₈	—	8	2	no	—
869	C₂×Q₈	—	8	2	no	—
870	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
871	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
872	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
873	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
874	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
875	C₂×D₄	—	2	1	no	—
876	C₂×D₄	—	2	1	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	1	no	—
879	C₂×D₄	—	2	1	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
883	C₂×D₄	C₂⁴×C₇	1	2	yes	—
884	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
885	C₂²×C₄	—	2	1	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	1	no	—
888	C₂²×C₄	—	2	1	no	—
889	C₂²×C₄	—	2	1	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	2	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
897	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
898	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
899	Q₁₆	—	2	2	no	—
900	SD₁₆	—	2	2	no	—
901	SD₁₆	—	2	4	no	—
902	SD₁₆	—	2	2	no	—
903	D₈	—	2	2	no	—
904	D₈	—	2	4	no	—
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	2	yes	—
910	C₂×C₈	C₂⁴×C₇	1	2	yes	—
911	C₄⋊C₄	—	2	1	no	—
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	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
935	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
936	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
937	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
938	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
939	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
940	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
941	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
942	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
943	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
944	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
945	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
946	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
947	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
949	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
950	C₂²⋊C₄	—	2	1	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
968	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	1	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	1	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	2	no	—
976	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
977	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
978	C₄²	C₂⁴×C₇	1	1	yes	characteristic
979	C₄²	C₂⁴×C₇	1	2	yes	—
980	C₄²	C₂⁴×C₇	1	2	yes	—
981	C₄²	C₂⁴×C₇	1	1	yes	characteristic
982	C₂×C₇	—	4	1	no	—
983	C₂×C₇	—	4	2	no	—
984	C₂×C₇	—	8	2	no	—
985	C₂×C₇	—	8	1	no	—
986	C₂×C₇	#3486	1	1	yes	characteristic
987	C₂×C₇	C₂×#576	1	1	yes	characteristic
988	C₂×C₇	#3586	1	1	yes	characteristic
989	C₂³	—	2	1	no	—
990	C₂³	—	2	1	no	—
991	C₂³	—	2	2	no	—
992	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
993	Q₈	—	2	1	no	—
994	Q₈	—	2	2	no	—
995	Q₈	—	2	2	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	2	1	no	—
998	Q₈	—	4	2	no	—
999	Q₈	—	4	2	no	—
1000	Q₈	—	4	2	no	—
1001	Q₈	—	4	2	no	—
1002	Q₈	—	8	2	no	—
1003	Q₈	—	8	2	no	—
1004	Q₈	—	8	2	no	—
1005	Q₈	—	8	2	no	—
1006	Q₈	C₇×2₋¹⁺⁴	1	2	yes	—
1007	D₄	—	2	4	no	—
1008	D₄	—	2	1	no	—
1009	D₄	—	2	1	no	—
1010	D₄	—	2	2	no	—
1011	D₄	—	2	1	no	—
1012	D₄	—	2	2	no	—
1013	D₄	—	4	2	no	—
1014	D₄	—	8	1	no	—
1015	D₄	—	8	2	no	—
1016	D₄	—	8	2	no	—
1017	D₄	—	8	1	no	—
1018	D₄	—	8	2	no	—
1019	D₄	C₇×2₋¹⁺⁴	1	2	yes	—
1020	C₂×C₄	—	2	4	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	4	1	no	—
1034	C₂×C₄	—	4	2	no	—
1035	C₂×C₄	—	4	2	no	—
1036	C₂×C₄	—	4	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	—	8	2	no	—
1043	C₂×C₄	—	8	2	no	—
1044	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
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	2	yes	—
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	2	yes	—
1051	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
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	2	no	—
1056	C₈	—	2	1	no	—
1057	C₈	—	2	2	no	—
1058	C₈	—	2	1	no	—
1059	C₈	—	2	1	no	—
1060	C₇	#61857	1	1	yes	characteristic, direct product factor, Sylow
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	2	no	—
1073	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1074	C₄	—	2	1	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	1	no	—
1078	C₄	—	2	1	no	—
1079	C₄	—	2	2	no	—
1080	C₄	—	2	2	no	—
1081	C₄	—	2	1	no	—
1082	C₄	—	2	2	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	2	no	—
1087	C₄	—	4	2	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	1	no	—
1091	C₄	C₇×#576	1	2	yes	—
1092	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1093	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1094	C₂	—	4	1	no	—
1095	C₂	—	4	2	no	—
1096	C₂	—	8	1	no	—
1097	C₂	—	8	2	no	—
1098	C₂	C₇×#3486	1	1	yes	characteristic
1099	C₂	C₂×C₇×#576	1	1	yes	characteristic
1100	C₂	C₇×#3586	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3554	C₂	semidirect
2. C₇×#3503	C₂	semidirect
3. C₇×#3389	C₂	semidirect
4. C₇×#3386	C₂	semidirect
5. C₇×#3386	C₂	semidirect
6. C₇×#3385	C₂	semidirect
7. C₇×#3383	C₂	semidirect
8. C₇×Q₈×D₈	C₂	semidirect
9. C₇×#3375	C₂	semidirect
10. C₇×#3373	C₂	semidirect
11. C₇×#3370	C₂	semidirect
12. C₇×#3368	C₂	semidirect
13. C₇×#3365	C₂	semidirect
14. C₇×#3358	C₂	semidirect
15. C₇×#3243	C₂	semidirect
16. C₇×#3241	C₂	semidirect
17. C₇×#3239	C₂	semidirect
18. C₇×#3226	C₂	semidirect
19. C₇×#3124	C₂	semidirect
20. C₇×#3119	C₂	semidirect
21. C₇×#3115	C₂	semidirect
22. C₇×#3102	C₂	semidirect
23. C₇×#2985	C₂	semidirect
135. #61857	C₇	direct (N × H)
313. #3554	C₂×C₇	semidirect
314. #3503	C₂×C₇	semidirect
315. #3389	C₂×C₇	semidirect
316. #3386	C₂×C₇	semidirect
317. #3386	C₂×C₇	semidirect
318. #3385	C₂×C₇	semidirect
319. #3383	C₂×C₇	semidirect
320. Q₈×D₈	C₂×C₇	semidirect
321. #3375	C₂×C₇	semidirect
322. #3373	C₂×C₇	semidirect
323. #3370	C₂×C₇	semidirect
324. #3368	C₂×C₇	semidirect
325. #3365	C₂×C₇	semidirect
326. #3358	C₂×C₇	semidirect
327. #3243	C₂×C₇	semidirect
328. #3241	C₂×C₇	semidirect
329. #3239	C₂×C₇	semidirect
330. #3226	C₂×C₇	semidirect
331. #3124	C₂×C₇	semidirect
332. #3119	C₂×C₇	semidirect
333. #3115	C₂×C₇	semidirect
334. #3102	C₂×C₇	semidirect
335. #2985	C₂×C₇	semidirect
1060. C₇	#61857	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×#3554	2
C₇×#3503	2
C₇×#3389	2
C₇×#3386	2
C₇×#3385	2
C₇×#3383	2
C₇×Q₈×D₈	2
C₇×#3375	2
C₇×#3373	2
C₇×#3370	2
C₇×#3368	2
C₇×#3365	2
C₇×#3358	2
C₇×#3243	2
C₇×#3241	2
C₇×#3239	2
C₇×#3226	2
C₇×#3124	2
C₇×#3119	2
C₇×#3115	2
C₇×#3102	2
C₇×#2985	2
#61857	7

Subgroups — C7×#61857 #13239073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61857 #13239073