Subgroups — C₇×#61344 #13238560

Order 1792.

1748 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×#3510	C₂	1	1	yes	maximal, characteristic
2	C₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3377	C₂	1	2	yes	maximal, complemented
4	C₇×#3377	C₂	1	2	yes	maximal, complemented
5	C₇×#3375	C₂	1	2	yes	maximal, complemented
6	C₇×#3371	C₂	1	2	yes	maximal, complemented
7	C₇×#3371	C₂	1	2	yes	maximal, complemented
8	C₇×#3369	C₂	1	2	yes	maximal, complemented
9	C₇×#3365	C₂	1	2	yes	maximal, complemented
10	C₇×#3364	C₂	1	2	yes	maximal, complemented
11	C₇×#3140	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3136	C₂	1	1	yes	maximal, characteristic
14	C₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3081	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3043	C₂	1	1	yes	maximal, characteristic
19	C₂×C₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2950	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2949	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#137	C₂²	1	1	yes	characteristic
25	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
26	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
27	C₇×#559	C₂²	1	2	yes	—
28	C₇×#559	C₂²	1	2	yes	—
29	C₇×Q₈²	—	2	1	no	—
30	C₇×Q₈²	C₂²	1	2	yes	complemented
31	C₇×#557	—	2	1	no	—
32	C₇×#557	—	2	1	no	—
33	C₇×#557	—	2	1	no	—
34	C₇×#557	C₂²	1	2	yes	complemented
35	C₇×#557	C₂²	1	2	yes	complemented
36	C₇×#557	C₂²	1	2	yes	complemented
37	C₇×#556	C₂²	1	2	yes	—
38	C₇×#556	C₂²	1	2	yes	—
39	C₇×#551	—	2	2	no	—
40	C₇×#551	—	2	2	no	—
41	C₇×#544	—	2	2	no	—
42	C₇×#544	C₂²	1	1	yes	characteristic
43	C₇×#544	C₂²	1	1	yes	characteristic
44	C₇×#542	—	2	1	no	—
45	C₇×#542	—	2	1	no	—
46	C₇×#536	C₂²	1	1	yes	characteristic
47	C₇×#535	C₂²	1	1	yes	characteristic
48	C₇×#533	—	2	2	no	—
49	C₇×#533	C₂²	1	1	yes	characteristic
50	C₇×#533	C₂²	1	1	yes	characteristic
51	C₇×#529	—	2	1	no	—
52	C₇×#529	—	2	1	no	—
53	C₂×C₇×#124	C₂²	1	1	yes	characteristic
54	C₇×#519	C₂²	1	1	yes	characteristic
55	C₇×#519	C₂²	1	1	yes	characteristic
56	C₇×#519	C₂²	1	1	yes	characteristic
57	C₇×#518	C₂²	1	1	yes	characteristic
58	C₄×C₇×#41	C₂²	1	1	yes	characteristic
59	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
60	C₇×#491	C₂²	1	2	yes	complemented
61	C₇×#490	C₂²	1	2	yes	—
62	C₇×#489	C₂²	1	2	yes	—
63	C₇×#489	C₂²	1	2	yes	—
64	C₇×#489	C₂²	1	2	yes	—
65	C₇×#489	C₂²	1	2	yes	complemented
66	C₇×#488	C₂²	1	2	yes	—
67	C₇×#488	C₂²	1	2	yes	—
68	C₇×#488	C₂²	1	2	yes	—
69	C₇×#488	C₂²	1	2	yes	complemented
70	C₇×#487	C₂²	1	2	yes	complemented
71	C₇×#486	C₂²	1	2	yes	—
72	C₇×#479	C₂²	1	1	yes	characteristic, complemented
73	C₇×#479	C₂²	1	1	yes	characteristic, complemented
74	C₇×#479	C₂²	1	2	yes	complemented
75	C₇×#479	C₂²	1	2	yes	complemented
76	C₇×#478	C₂²	1	2	yes	—
77	C₇×#478	C₂²	1	2	yes	—
78	C₇×#478	C₂²	1	1	yes	characteristic, complemented
79	C₇×#478	C₂²	1	1	yes	characteristic, complemented
80	C₇×#477	C₂²	1	1	yes	characteristic, complemented
81	C₇×#477	C₂²	1	2	yes	complemented
82	C₇×#476	C₂²	1	2	yes	—
83	C₇×#476	C₂²	1	1	yes	characteristic, complemented
84	C₇×#475	C₂²	1	1	yes	characteristic, complemented
85	C₇×#475	C₂²	1	2	yes	complemented
86	C₇×#474	C₂²	1	2	yes	—
87	C₇×#474	C₂²	1	1	yes	characteristic, complemented
88	C₇×#464	C₂²	1	2	yes	—
89	C₇×#464	C₂²	1	2	yes	—
90	C₇×#464	C₂²	1	2	yes	—
91	C₇×#464	C₂²	1	2	yes	—
92	C₇×#464	C₂²	1	2	yes	—
93	C₇×#464	C₂²	1	2	yes	—
94	C₇×#464	C₂²	1	2	yes	complemented
95	C₇×#464	C₂²	1	2	yes	complemented
96	C₇×#462	C₂²	1	2	yes	complemented
97	C₇×#462	C₂²	1	2	yes	complemented
98	C₇×#460	C₂²	1	2	yes	—
99	C₇×#460	C₂²	1	2	yes	—
100	C₇×#446	C₂²	1	2	yes	complemented
101	C₇×#446	C₂²	1	2	yes	complemented
102	C₇×#446	C₂²	1	2	yes	complemented
103	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
104	C₇×#441	C₂²	1	2	yes	complemented
105	C₇×#441	C₂²	1	2	yes	complemented
106	C₇×#441	C₂²	1	2	yes	complemented
107	C₇×#440	C₂²	1	2	yes	—
108	C₇×#440	C₂²	1	2	yes	—
109	C₇×#440	C₂²	1	2	yes	complemented
110	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
111	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
112	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
113	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
114	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
115	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
116	C₇×#428	C₂²	1	1	yes	characteristic
117	C₇×#427	C₂²	1	1	yes	characteristic
118	C₇×#427	C₂²	1	1	yes	characteristic
119	C₇×#424	C₂²	1	1	yes	characteristic
120	C₇×#424	C₂²	1	1	yes	characteristic
121	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
122	C₇×#419	C₂²	1	1	yes	characteristic
123	C₇×#419	C₂²	1	1	yes	characteristic
124	C₇×#419	C₂²	1	1	yes	characteristic
125	C₇×#418	C₂²	1	1	yes	characteristic
126	C₇×#418	C₂²	1	1	yes	characteristic
127	C₇×#417	C₂²	1	1	yes	characteristic
128	C₇×#416	C₂²	1	1	yes	characteristic
129	C₇×#416	C₂²	1	1	yes	characteristic
130	C₂×C₇×#103	C₂²	1	1	yes	characteristic
131	C₂×C₇×#102	C₂²	1	1	yes	characteristic
132	C₇×#405	C₂²	1	1	yes	characteristic
133	C₇×#405	C₂²	1	1	yes	characteristic
134	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
135	#61344	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	C₂³	1	1	yes	characteristic
137	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
138	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
139	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
140	C₇×#137	—	2	4	no	—
141	C₂×C₇×Q₁₆	—	2	4	no	—
142	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
143	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
144	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
145	C₂×C₇×SD₁₆	—	2	4	no	—
146	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
147	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
148	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
149	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
150	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
151	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
152	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
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	2	no	—
157	C₇×C₄⋊Q₈	—	2	2	no	—
158	C₇×C₄⋊Q₈	—	2	2	no	—
159	C₇×C₄⋊Q₈	—	2	1	no	—
160	C₇×C₄⋊Q₈	—	2	1	no	—
161	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
162	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
163	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₇×#127	C₂³	1	2	yes	—
169	C₇×#126	—	2	2	no	—
170	C₇×#126	—	2	2	no	—
171	C₇×#126	—	2	2	no	—
172	C₇×#126	—	2	2	no	—
173	C₇×#125	—	2	2	no	—
174	C₇×#125	—	2	2	no	—
175	C₇×#125	—	2	2	no	—
176	C₇×#125	—	2	2	no	—
177	C₇×#125	—	2	2	no	—
178	C₇×#125	—	2	2	no	—
179	C₇×#125	—	2	1	no	—
180	C₇×#125	—	2	1	no	—
181	C₇×#125	D₄	1	1	yes	characteristic
182	C₇×#125	D₄	1	1	yes	characteristic
183	C₇×#125	C₂³	1	2	yes	—
184	C₇×#125	C₂³	1	1	yes	characteristic
185	C₇×#125	C₂³	1	1	yes	characteristic
186	C₇×#125	C₂³	1	2	yes	—
187	C₇×#124	—	2	2	no	—
188	C₇×#124	—	2	2	no	—
189	C₇×#124	—	2	1	no	—
190	C₇×#124	—	2	1	no	—
191	C₇×#124	C₂³	1	2	yes	—
192	C₇×#124	C₂³	1	2	yes	—
193	C₇×#124	C₂³	1	2	yes	—
194	C₇×#124	C₂³	1	2	yes	—
195	C₇×#123	—	2	2	no	—
196	C₇×#123	—	2	2	no	—
197	C₇×#123	—	2	2	no	—
198	C₇×#123	—	2	2	no	—
199	C₇×#123	—	2	2	no	—
200	C₇×C₂²⋊Q₈	—	2	2	no	—
201	C₇×C₂²⋊Q₈	—	2	2	no	—
202	C₇×C₂²⋊Q₈	—	2	1	no	—
203	C₇×C₂²⋊Q₈	—	2	1	no	—
204	C₇×C₂²⋊Q₈	—	2	1	no	—
205	C₇×C₂²⋊Q₈	—	2	1	no	—
206	C₇×C₂²⋊Q₈	—	2	2	no	—
207	C₇×C₂²⋊Q₈	—	2	2	no	—
208	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
209	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
210	C₇×#121	—	2	1	no	—
211	C₇×#121	—	2	1	no	—
212	C₇×#120	—	2	2	no	—
213	C₄×C₇×Q₈	—	2	2	no	—
214	C₄×C₇×Q₈	—	2	1	no	—
215	C₄×C₇×Q₈	—	2	1	no	—
216	C₄×C₇×Q₈	—	2	1	no	—
217	C₄×C₇×Q₈	—	2	1	no	—
218	C₄×C₇×Q₈	—	2	1	no	—
219	C₄×C₇×Q₈	—	2	1	no	—
220	C₄×C₇×Q₈	—	2	2	no	—
221	C₄×C₇×Q₈	—	2	2	no	—
222	C₄×C₇×Q₈	—	2	2	no	—
223	C₄×C₇×Q₈	—	2	1	no	—
224	C₄×C₇×Q₈	—	2	1	no	—
225	C₄×C₇×Q₈	—	2	1	no	—
226	C₄×C₇×Q₈	—	2	1	no	—
227	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
228	C₄×C₇×Q₈	C₂³	1	2	yes	—
229	C₄×C₇×Q₈	C₂³	1	2	yes	—
230	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
231	C₄×C₇×Q₈	C₂³	1	2	yes	—
232	C₄×C₇×Q₈	C₂³	1	2	yes	—
233	C₄×C₇×Q₈	C₂³	1	2	yes	—
234	C₄×C₇×Q₈	C₂³	1	2	yes	—
235	C₄×C₇×Q₈	C₂³	1	2	yes	—
236	C₄×C₇×Q₈	C₂³	1	2	yes	—
237	C₄×C₇×Q₈	C₂³	1	2	yes	—
238	C₄×C₇×Q₈	C₂³	1	2	yes	—
239	C₄×C₇×D₄	—	2	1	no	—
240	C₄×C₇×D₄	—	2	1	no	—
241	C₄×C₇×D₄	—	2	1	no	—
242	C₄×C₇×D₄	—	2	1	no	—
243	C₄×C₇×D₄	—	2	2	no	—
244	C₄×C₇×D₄	—	2	2	no	—
245	C₄×C₇×D₄	C₂³	1	2	yes	—
246	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
247	C₄×C₇×D₄	C₂³	1	2	yes	—
248	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
249	C₇×#117	—	2	2	no	—
250	C₇×#117	—	2	2	no	—
251	C₇×#117	—	2	2	no	—
252	C₇×#117	—	2	2	no	—
253	C₇×#117	—	2	2	no	—
254	C₇×#117	—	2	1	no	—
255	C₇×#117	C₂³	1	1	yes	characteristic
256	C₇×#117	C₂³	1	1	yes	characteristic
257	C₇×#117	C₂³	1	1	yes	characteristic
258	C₇×#117	C₂³	1	1	yes	characteristic
259	C₇×#117	C₂³	1	1	yes	characteristic
260	C₂×C₇×C₄⋊C₄	—	2	1	no	—
261	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²×C₇	—	2	1	no	—
266	C₂×C₄²×C₇	—	2	1	no	—
267	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
268	C₇×#107	C₂³	1	1	yes	characteristic
269	C₇×#107	C₂³	1	2	yes	—
270	C₇×#107	C₂³	1	1	yes	characteristic
271	C₇×#107	C₂³	1	1	yes	characteristic
272	C₇×#107	C₂³	1	1	yes	characteristic
273	C₇×#106	C₂³	1	1	yes	characteristic
274	C₇×#106	C₂³	1	1	yes	characteristic
275	C₇×#106	C₂³	1	2	yes	—
276	C₇×#106	C₂³	1	1	yes	characteristic
277	C₇×#106	C₂³	1	1	yes	characteristic
278	C₇×C₄⋊C₈	C₂³	1	2	yes	—
279	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₇×C₄⋊C₈	C₂³	1	2	yes	—
282	C₇×C₄⋊C₈	C₂³	1	2	yes	—
283	C₇×C₄⋊C₈	C₂³	1	2	yes	—
284	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₇×#103	C₂³	1	2	yes	—
287	C₇×#103	C₂³	1	1	yes	characteristic
288	C₇×#103	C₂³	1	2	yes	—
289	C₇×#103	C₂³	1	1	yes	characteristic
290	C₇×#103	C₂³	1	1	yes	characteristic
291	C₇×#103	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	1	yes	characteristic
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	2	yes	—
296	C₇×#103	C₂³	1	2	yes	—
297	C₇×#103	C₂³	1	2	yes	—
298	C₇×#103	C₂³	1	2	yes	—
299	C₇×#102	C₂³	1	2	yes	—
300	C₇×#102	C₂³	1	2	yes	—
301	C₇×#102	C₂³	1	1	yes	characteristic
302	C₇×#102	C₂³	1	1	yes	characteristic
303	C₇×#102	C₂³	1	2	yes	—
304	C₇×#102	C₂³	1	1	yes	characteristic
305	C₇×#102	C₂³	1	1	yes	characteristic
306	C₇×#102	C₂³	1	2	yes	—
307	C₇×#102	C₂³	1	2	yes	—
308	C₇×#102	C₂³	1	2	yes	—
309	C₇×#102	C₂³	1	2	yes	—
310	C₇×#97	C₂³	1	2	yes	—
311	C₇×#97	C₂³	1	2	yes	—
312	C₇×#97	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	2	yes	—
314	C₄×C₇×C₈	C₂³	1	2	yes	—
315	C₄×C₇×C₈	C₂³	1	2	yes	—
316	#3510	C₂×C₇	1	1	yes	characteristic
317	#3502	C₂×C₇	1	1	yes	characteristic, complemented
318	#3377	C₂×C₇	1	2	yes	complemented
319	#3377	C₂×C₇	1	2	yes	complemented
320	#3375	C₂×C₇	1	2	yes	complemented
321	#3371	C₂×C₇	1	2	yes	complemented
322	#3371	C₂×C₇	1	2	yes	complemented
323	#3369	C₂×C₇	1	2	yes	complemented
324	#3365	C₂×C₇	1	2	yes	complemented
325	#3364	C₂×C₇	1	2	yes	complemented
326	#3140	C₂×C₇	1	1	yes	characteristic, complemented
327	#3137	C₂×C₇	1	1	yes	characteristic, complemented
328	#3136	C₂×C₇	1	1	yes	characteristic
329	#3082	C₂×C₇	1	1	yes	characteristic, complemented
330	#3081	C₂×C₇	1	1	yes	characteristic, complemented
331	#3076	C₂×C₇	1	1	yes	characteristic, complemented
332	#3044	C₂×C₇	1	1	yes	characteristic, complemented
333	#3043	C₂×C₇	1	1	yes	characteristic
334	C₂×#464	C₂×C₇	1	1	yes	characteristic, complemented
335	#2962	C₂×C₇	1	1	yes	characteristic, complemented
336	#2950	C₂×C₇	1	1	yes	characteristic, complemented
337	#2949	C₂×C₇	1	1	yes	characteristic, complemented
338	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
339	C₂⁴×C₇	—	2	1	no	—
340	C₇×#41	—	2	2	no	—
341	C₇×#41	—	2	2	no	—
342	C₂×C₇×Q₈	—	2	1	no	—
343	C₂×C₇×Q₈	—	2	1	no	—
344	C₂×C₇×Q₈	—	2	1	no	—
345	C₂×C₇×Q₈	—	2	1	no	—
346	C₂×C₇×Q₈	—	2	2	no	—
347	C₂×C₇×Q₈	—	2	2	no	—
348	C₂×C₇×Q₈	—	2	2	no	—
349	C₂×C₇×Q₈	—	2	2	no	—
350	C₂×C₇×Q₈	—	2	2	no	—
351	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
352	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
353	C₂×C₇×Q₈	#41	1	4	yes	—
354	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
355	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
356	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
357	C₂×C₇×D₄	—	2	1	no	—
358	C₂×C₇×D₄	—	2	1	no	—
359	C₂×C₇×D₄	—	2	2	no	—
360	C₂×C₇×D₄	—	2	2	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	C₂²×C₄×C₇	—	2	1	no	—
366	C₂²×C₄×C₇	—	2	1	no	—
367	C₂²×C₄×C₇	—	2	1	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	C₂×D₄	1	1	yes	characteristic
374	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
376	C₇×Q₁₆	—	2	4	no	—
377	C₇×Q₁₆	—	2	4	no	—
378	C₇×Q₁₆	—	2	4	no	—
379	C₇×SD₁₆	—	2	4	no	—
380	C₇×SD₁₆	—	2	4	no	—
381	C₇×SD₁₆	—	2	4	no	—
382	C₇×M₁₆	—	2	2	no	—
383	C₇×M₁₆	—	2	2	no	—
384	C₂×C₇×C₈	—	2	2	no	—
385	C₂×C₇×C₈	—	2	2	no	—
386	C₂×C₇×C₈	C₂⁴	1	2	yes	—
387	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
388	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
389	C₂×C₇×C₈	C₂⁴	1	2	yes	—
390	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
391	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
392	C₇×C₄⋊C₄	—	2	2	no	—
393	C₇×C₄⋊C₄	—	2	2	no	—
394	C₇×C₄⋊C₄	—	2	1	no	—
395	C₇×C₄⋊C₄	—	2	1	no	—
396	C₇×C₄⋊C₄	—	2	1	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	—	2	2	no	—
402	C₇×C₄⋊C₄	—	2	2	no	—
403	C₇×C₄⋊C₄	—	2	2	no	—
404	C₇×C₄⋊C₄	—	2	2	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	1	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	1	no	—
414	C₇×C₄⋊C₄	—	2	1	no	—
415	C₇×C₄⋊C₄	—	2	2	no	—
416	C₇×C₄⋊C₄	—	2	2	no	—
417	C₇×C₄⋊C₄	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	1	yes	characteristic
421	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
422	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
423	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
424	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
425	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
426	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
427	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
428	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
429	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
430	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
431	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
432	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
433	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
434	C₇×C₂²⋊C₄	—	2	1	no	—
435	C₇×C₂²⋊C₄	—	2	1	no	—
436	C₇×C₂²⋊C₄	—	2	1	no	—
437	C₇×C₂²⋊C₄	—	2	2	no	—
438	C₇×C₂²⋊C₄	—	2	2	no	—
439	C₇×C₂²⋊C₄	—	2	2	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	1	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	—	2	2	no	—
449	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
450	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
458	C₄²×C₇	—	2	2	no	—
459	C₄²×C₇	—	2	2	no	—
460	C₄²×C₇	—	2	2	no	—
461	C₄²×C₇	—	2	2	no	—
462	C₄²×C₇	—	2	1	no	—
463	C₄²×C₇	—	2	1	no	—
464	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
465	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
466	C₄²×C₇	C₂⁴	1	1	yes	characteristic
467	C₄²×C₇	C₂⁴	1	2	yes	—
468	C₄²×C₇	C₂⁴	1	2	yes	—
469	C₄²×C₇	C₂⁴	1	1	yes	characteristic
470	C₂×#137	C₂²×C₇	1	1	yes	characteristic
471	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
472	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
473	#559	C₂²×C₇	1	2	yes	—
474	#559	C₂²×C₇	1	2	yes	—
475	Q₈²	—	2	1	no	—
476	Q₈²	C₂²×C₇	1	2	yes	complemented
477	#557	—	2	1	no	—
478	#557	—	2	1	no	—
479	#557	—	2	1	no	—
480	#557	C₂²×C₇	1	2	yes	complemented
481	#557	C₂²×C₇	1	2	yes	complemented
482	#557	C₂²×C₇	1	2	yes	complemented
483	#556	C₂²×C₇	1	2	yes	—
484	#556	C₂²×C₇	1	2	yes	—
485	#551	—	2	2	no	—
486	#551	—	2	2	no	—
487	#544	—	2	2	no	—
488	#544	C₂²×C₇	1	1	yes	characteristic
489	#544	C₂²×C₇	1	1	yes	characteristic
490	#542	—	2	1	no	—
491	#542	—	2	1	no	—
492	#536	C₂²×C₇	1	1	yes	characteristic
493	#535	C₂²×C₇	1	1	yes	characteristic
494	#533	—	2	2	no	—
495	#533	C₂²×C₇	1	1	yes	characteristic
496	#533	C₂²×C₇	1	1	yes	characteristic
497	#529	—	2	1	no	—
498	#529	—	2	1	no	—
499	C₂×#124	C₂²×C₇	1	1	yes	characteristic
500	#519	C₂²×C₇	1	1	yes	characteristic
501	#519	C₂²×C₇	1	1	yes	characteristic
502	#519	C₂²×C₇	1	1	yes	characteristic
503	#518	C₂²×C₇	1	1	yes	characteristic
504	C₄×#41	C₂²×C₇	1	1	yes	characteristic
505	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
506	#491	C₂²×C₇	1	2	yes	complemented
507	#490	C₂²×C₇	1	2	yes	—
508	#489	C₂²×C₇	1	2	yes	—
509	#489	C₂²×C₇	1	2	yes	—
510	#489	C₂²×C₇	1	2	yes	—
511	#489	C₂²×C₇	1	2	yes	complemented
512	#488	C₂²×C₇	1	2	yes	—
513	#488	C₂²×C₇	1	2	yes	—
514	#488	C₂²×C₇	1	2	yes	—
515	#488	C₂²×C₇	1	2	yes	complemented
516	#487	C₂²×C₇	1	2	yes	complemented
517	#486	C₂²×C₇	1	2	yes	—
518	#479	C₂²×C₇	1	1	yes	characteristic, complemented
519	#479	C₂²×C₇	1	1	yes	characteristic, complemented
520	#479	C₂²×C₇	1	2	yes	complemented
521	#479	C₂²×C₇	1	2	yes	complemented
522	#478	C₂²×C₇	1	2	yes	—
523	#478	C₂²×C₇	1	2	yes	—
524	#478	C₂²×C₇	1	1	yes	characteristic, complemented
525	#478	C₂²×C₇	1	1	yes	characteristic, complemented
526	#477	C₂²×C₇	1	1	yes	characteristic, complemented
527	#477	C₂²×C₇	1	2	yes	complemented
528	#476	C₂²×C₇	1	2	yes	—
529	#476	C₂²×C₇	1	1	yes	characteristic, complemented
530	#475	C₂²×C₇	1	1	yes	characteristic, complemented
531	#475	C₂²×C₇	1	2	yes	complemented
532	#474	C₂²×C₇	1	2	yes	—
533	#474	C₂²×C₇	1	1	yes	characteristic, complemented
534	#464	C₂²×C₇	1	2	yes	—
535	#464	C₂²×C₇	1	2	yes	—
536	#464	C₂²×C₇	1	2	yes	—
537	#464	C₂²×C₇	1	2	yes	—
538	#464	C₂²×C₇	1	2	yes	—
539	#464	C₂²×C₇	1	2	yes	—
540	#464	C₂²×C₇	1	2	yes	complemented
541	#464	C₂²×C₇	1	2	yes	complemented
542	#462	C₂²×C₇	1	2	yes	complemented
543	#462	C₂²×C₇	1	2	yes	complemented
544	#460	C₂²×C₇	1	2	yes	—
545	#460	C₂²×C₇	1	2	yes	—
546	#446	C₂²×C₇	1	2	yes	complemented
547	#446	C₂²×C₇	1	2	yes	complemented
548	#446	C₂²×C₇	1	2	yes	complemented
549	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
550	#441	C₂²×C₇	1	2	yes	complemented
551	#441	C₂²×C₇	1	2	yes	complemented
552	#441	C₂²×C₇	1	2	yes	complemented
553	#440	C₂²×C₇	1	2	yes	—
554	#440	C₂²×C₇	1	2	yes	—
555	#440	C₂²×C₇	1	2	yes	complemented
556	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
557	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
558	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
559	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
560	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
561	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
562	#428	C₂²×C₇	1	1	yes	characteristic
563	#427	C₂²×C₇	1	1	yes	characteristic
564	#427	C₂²×C₇	1	1	yes	characteristic
565	#424	C₂²×C₇	1	1	yes	characteristic
566	#424	C₂²×C₇	1	1	yes	characteristic
567	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
568	#419	C₂²×C₇	1	1	yes	characteristic
569	#419	C₂²×C₇	1	1	yes	characteristic
570	#419	C₂²×C₇	1	1	yes	characteristic
571	#418	C₂²×C₇	1	1	yes	characteristic
572	#418	C₂²×C₇	1	1	yes	characteristic
573	#417	C₂²×C₇	1	1	yes	characteristic
574	#416	C₂²×C₇	1	1	yes	characteristic
575	#416	C₂²×C₇	1	1	yes	characteristic
576	C₂×#103	C₂²×C₇	1	1	yes	characteristic
577	C₂×#102	C₂²×C₇	1	1	yes	characteristic
578	#405	C₂²×C₇	1	1	yes	characteristic
579	#405	C₂²×C₇	1	1	yes	characteristic
580	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
581	C₂³×C₇	—	2	2	no	—
582	C₂³×C₇	—	2	1	no	—
583	C₂³×C₇	—	4	2	no	—
584	C₂³×C₇	—	8	1	no	—
585	C₂³×C₇	—	8	1	no	—
586	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
587	C₇×Q₈	—	2	4	no	—
588	C₇×Q₈	—	2	2	no	—
589	C₇×Q₈	—	2	2	no	—
590	C₇×Q₈	—	2	1	no	—
591	C₇×Q₈	—	2	2	no	—
592	C₇×Q₈	—	2	1	no	—
593	C₇×Q₈	—	4	2	no	—
594	C₇×Q₈	—	4	2	no	—
595	C₇×Q₈	—	4	2	no	—
596	C₇×Q₈	—	4	2	no	—
597	C₇×Q₈	—	8	1	no	—
598	C₇×Q₈	—	8	2	no	—
599	C₇×Q₈	—	8	2	no	—
600	C₇×Q₈	C₂×#41	1	4	yes	—
601	C₇×D₄	—	2	2	no	—
602	C₇×D₄	—	2	1	no	—
603	C₇×D₄	—	2	2	no	—
604	C₇×D₄	—	2	1	no	—
605	C₇×D₄	—	4	2	no	—
606	C₇×D₄	—	4	2	no	—
607	C₇×D₄	—	8	2	no	—
608	C₇×D₄	—	8	2	no	—
609	C₂×C₄×C₇	—	2	4	no	—
610	C₂×C₄×C₇	—	2	2	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	1	no	—
615	C₂×C₄×C₇	—	2	1	no	—
616	C₂×C₄×C₇	—	2	1	no	—
617	C₂×C₄×C₇	—	2	2	no	—
618	C₂×C₄×C₇	—	2	1	no	—
619	C₂×C₄×C₇	—	2	2	no	—
620	C₂×C₄×C₇	—	4	1	no	—
621	C₂×C₄×C₇	—	4	1	no	—
622	C₂×C₄×C₇	—	4	2	no	—
623	C₂×C₄×C₇	—	4	2	no	—
624	C₂×C₄×C₇	—	8	1	no	—
625	C₂×C₄×C₇	—	8	2	no	—
626	C₂×C₄×C₇	—	8	1	no	—
627	C₂×C₄×C₇	—	8	2	no	—
628	C₂×C₄×C₇	—	8	1	no	—
629	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
630	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
631	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
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	2	yes	—
635	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
636	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
637	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
638	C₂×C₄×C₇	C₂×#41	1	2	yes	—
639	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
640	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
641	C₇×C₈	—	2	1	no	—
642	C₇×C₈	—	2	1	no	—
643	C₇×C₈	—	2	1	no	—
644	C₇×C₈	—	2	1	no	—
645	C₇×C₈	—	2	2	no	—
646	C₇×C₈	—	2	2	no	—
647	C₂×#41	C₂³×C₇	1	1	yes	characteristic
648	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
649	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
650	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
651	#137	—	2	4	no	—
652	C₂×Q₁₆	—	2	4	no	—
653	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
654	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
655	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
656	C₂×SD₁₆	—	2	4	no	—
657	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
658	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
659	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
660	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
661	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
662	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
663	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
664	C₄⋊Q₈	—	2	2	no	—
665	C₄⋊Q₈	—	2	2	no	—
666	C₄⋊Q₈	—	2	2	no	—
667	C₄⋊Q₈	—	2	2	no	—
668	C₄⋊Q₈	—	2	2	no	—
669	C₄⋊Q₈	—	2	2	no	—
670	C₄⋊Q₈	—	2	1	no	—
671	C₄⋊Q₈	—	2	1	no	—
672	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
673	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
674	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
675	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
676	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
677	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
678	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
679	#127	C₂³×C₇	1	2	yes	—
680	#126	—	2	2	no	—
681	#126	—	2	2	no	—
682	#126	—	2	2	no	—
683	#126	—	2	2	no	—
684	#125	—	2	2	no	—
685	#125	—	2	2	no	—
686	#125	—	2	2	no	—
687	#125	—	2	2	no	—
688	#125	—	2	2	no	—
689	#125	—	2	2	no	—
690	#125	—	2	1	no	—
691	#125	—	2	1	no	—
692	#125	C₇×D₄	1	1	yes	characteristic
693	#125	C₇×D₄	1	1	yes	characteristic
694	#125	C₂³×C₇	1	1	yes	characteristic
695	#125	C₂³×C₇	1	1	yes	characteristic
696	#125	C₂³×C₇	1	2	yes	—
697	#125	C₂³×C₇	1	2	yes	—
698	#124	—	2	2	no	—
699	#124	—	2	2	no	—
700	#124	—	2	1	no	—
701	#124	—	2	1	no	—
702	#124	C₂³×C₇	1	2	yes	—
703	#124	C₂³×C₇	1	2	yes	—
704	#124	C₂³×C₇	1	2	yes	—
705	#124	C₂³×C₇	1	2	yes	—
706	#123	—	2	2	no	—
707	#123	—	2	2	no	—
708	#123	—	2	2	no	—
709	#123	—	2	2	no	—
710	#123	—	2	2	no	—
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	—	2	2	no	—
713	C₂²⋊Q₈	—	2	1	no	—
714	C₂²⋊Q₈	—	2	1	no	—
715	C₂²⋊Q₈	—	2	1	no	—
716	C₂²⋊Q₈	—	2	1	no	—
717	C₂²⋊Q₈	—	2	2	no	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
720	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
721	#121	—	2	1	no	—
722	#121	—	2	1	no	—
723	#120	—	2	2	no	—
724	C₄×Q₈	—	2	2	no	—
725	C₄×Q₈	—	2	1	no	—
726	C₄×Q₈	—	2	1	no	—
727	C₄×Q₈	—	2	1	no	—
728	C₄×Q₈	—	2	1	no	—
729	C₄×Q₈	—	2	1	no	—
730	C₄×Q₈	—	2	1	no	—
731	C₄×Q₈	—	2	2	no	—
732	C₄×Q₈	—	2	2	no	—
733	C₄×Q₈	—	2	2	no	—
734	C₄×Q₈	—	2	1	no	—
735	C₄×Q₈	—	2	1	no	—
736	C₄×Q₈	—	2	1	no	—
737	C₄×Q₈	—	2	1	no	—
738	C₄×Q₈	C₂³×C₇	1	2	yes	—
739	C₄×Q₈	C₂³×C₇	1	2	yes	—
740	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
741	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
742	C₄×Q₈	C₂³×C₇	1	2	yes	—
743	C₄×Q₈	C₂³×C₇	1	2	yes	—
744	C₄×Q₈	C₂³×C₇	1	2	yes	—
745	C₄×Q₈	C₂³×C₇	1	2	yes	—
746	C₄×Q₈	C₂³×C₇	1	2	yes	—
747	C₄×Q₈	C₂³×C₇	1	2	yes	—
748	C₄×Q₈	C₂³×C₇	1	2	yes	—
749	C₄×Q₈	C₂³×C₇	1	2	yes	—
750	C₄×D₄	—	2	1	no	—
751	C₄×D₄	—	2	1	no	—
752	C₄×D₄	—	2	1	no	—
753	C₄×D₄	—	2	1	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
757	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
758	C₄×D₄	C₂³×C₇	1	2	yes	—
759	C₄×D₄	C₂³×C₇	1	2	yes	—
760	#117	—	2	2	no	—
761	#117	—	2	2	no	—
762	#117	—	2	2	no	—
763	#117	—	2	2	no	—
764	#117	—	2	2	no	—
765	#117	—	2	1	no	—
766	#117	C₂³×C₇	1	1	yes	characteristic
767	#117	C₂³×C₇	1	1	yes	characteristic
768	#117	C₂³×C₇	1	1	yes	characteristic
769	#117	C₂³×C₇	1	1	yes	characteristic
770	#117	C₂³×C₇	1	1	yes	characteristic
771	C₂×C₄⋊C₄	—	2	1	no	—
772	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
773	C₂×C₂²⋊C₄	—	2	1	no	—
774	C₂×C₂²⋊C₄	—	2	1	no	—
775	C₂×C₂²⋊C₄	—	2	2	no	—
776	C₂×C₄²	—	2	1	no	—
777	C₂×C₄²	—	2	1	no	—
778	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
779	#107	C₂³×C₇	1	1	yes	characteristic
780	#107	C₂³×C₇	1	1	yes	characteristic
781	#107	C₂³×C₇	1	1	yes	characteristic
782	#107	C₂³×C₇	1	1	yes	characteristic
783	#107	C₂³×C₇	1	2	yes	—
784	#106	C₂³×C₇	1	1	yes	characteristic
785	#106	C₂³×C₇	1	1	yes	characteristic
786	#106	C₂³×C₇	1	1	yes	characteristic
787	#106	C₂³×C₇	1	1	yes	characteristic
788	#106	C₂³×C₇	1	2	yes	—
789	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
790	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
791	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
792	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
793	C₄⋊C₈	C₂³×C₇	1	2	yes	—
794	C₄⋊C₈	C₂³×C₇	1	2	yes	—
795	C₄⋊C₈	C₂³×C₇	1	2	yes	—
796	C₄⋊C₈	C₂³×C₇	1	2	yes	—
797	#103	C₂³×C₇	1	2	yes	—
798	#103	C₂³×C₇	1	2	yes	—
799	#103	C₂³×C₇	1	1	yes	characteristic
800	#103	C₂³×C₇	1	1	yes	characteristic
801	#103	C₂³×C₇	1	1	yes	characteristic
802	#103	C₂³×C₇	1	1	yes	characteristic
803	#103	C₂³×C₇	1	2	yes	—
804	#103	C₂³×C₇	1	2	yes	—
805	#103	C₂³×C₇	1	2	yes	—
806	#103	C₂³×C₇	1	2	yes	—
807	#103	C₂³×C₇	1	2	yes	—
808	#103	C₂³×C₇	1	2	yes	—
809	#103	C₂³×C₇	1	2	yes	—
810	#102	C₂³×C₇	1	2	yes	—
811	#102	C₂³×C₇	1	2	yes	—
812	#102	C₂³×C₇	1	1	yes	characteristic
813	#102	C₂³×C₇	1	1	yes	characteristic
814	#102	C₂³×C₇	1	1	yes	characteristic
815	#102	C₂³×C₇	1	1	yes	characteristic
816	#102	C₂³×C₇	1	2	yes	—
817	#102	C₂³×C₇	1	2	yes	—
818	#102	C₂³×C₇	1	2	yes	—
819	#102	C₂³×C₇	1	2	yes	—
820	#102	C₂³×C₇	1	2	yes	—
821	#97	C₂³×C₇	1	2	yes	—
822	#97	C₂³×C₇	1	2	yes	—
823	#97	C₂³×C₇	1	2	yes	—
824	C₄×C₈	C₂³×C₇	1	2	yes	—
825	C₄×C₈	C₂³×C₇	1	2	yes	—
826	C₄×C₈	C₂³×C₇	1	2	yes	—
827	C₂²×C₇	—	2	1	no	—
828	C₂²×C₇	—	2	1	no	—
829	C₂²×C₇	—	4	1	no	—
830	C₂²×C₇	—	4	2	no	—
831	C₂²×C₇	—	4	1	no	—
832	C₂²×C₇	—	4	2	no	—
833	C₂²×C₇	—	4	1	no	—
834	C₂²×C₇	—	4	2	no	—
835	C₂²×C₇	—	16	2	no	—
836	C₂²×C₇	#548	1	2	yes	—
837	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
838	C₄×C₇	—	2	1	no	—
839	C₄×C₇	—	2	1	no	—
840	C₄×C₇	—	2	2	no	—
841	C₄×C₇	—	2	2	no	—
842	C₄×C₇	—	2	1	no	—
843	C₄×C₇	—	2	1	no	—
844	C₄×C₇	—	2	2	no	—
845	C₄×C₇	—	2	2	no	—
846	C₄×C₇	—	2	4	no	—
847	C₄×C₇	—	4	1	no	—
848	C₄×C₇	—	4	2	no	—
849	C₄×C₇	—	4	1	no	—
850	C₄×C₇	—	4	1	no	—
851	C₄×C₇	—	4	1	no	—
852	C₄×C₇	—	4	1	no	—
853	C₄×C₇	—	4	1	no	—
854	C₄×C₇	—	4	1	no	—
855	C₄×C₇	—	4	2	no	—
856	C₄×C₇	#548	1	2	yes	—
857	C₄×C₇	C₂²×#41	1	1	yes	characteristic
858	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
859	C₂⁴	—	2	1	no	—
860	#41	—	2	2	no	—
861	#41	—	2	2	no	—
862	C₂×Q₈	—	2	1	no	—
863	C₂×Q₈	—	2	1	no	—
864	C₂×Q₈	—	2	1	no	—
865	C₂×Q₈	—	2	1	no	—
866	C₂×Q₈	—	2	2	no	—
867	C₂×Q₈	—	2	2	no	—
868	C₂×Q₈	—	2	2	no	—
869	C₂×Q₈	—	2	2	no	—
870	C₂×Q₈	—	2	2	no	—
871	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
872	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
873	C₂×Q₈	C₇×#41	1	4	yes	—
874	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
875	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
876	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
877	C₂×D₄	—	2	1	no	—
878	C₂×D₄	—	2	1	no	—
879	C₂×D₄	—	2	2	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	2	no	—
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	1	no	—
887	C₂²×C₄	—	2	1	no	—
888	C₂²×C₄	—	2	1	no	—
889	C₂²×C₄	—	2	1	no	—
890	C₂²×C₄	—	2	1	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	2	no	—
893	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
894	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
895	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
896	Q₁₆	—	2	4	no	—
897	Q₁₆	—	2	4	no	—
898	Q₁₆	—	2	4	no	—
899	SD₁₆	—	2	4	no	—
900	SD₁₆	—	2	4	no	—
901	SD₁₆	—	2	4	no	—
902	M₁₆	—	2	2	no	—
903	M₁₆	—	2	2	no	—
904	C₂×C₈	—	2	2	no	—
905	C₂×C₈	—	2	2	no	—
906	C₂×C₈	C₂⁴×C₇	1	2	yes	—
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	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	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	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	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	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	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
938	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
939	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
940	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
941	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
942	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
943	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
944	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
945	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
946	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
948	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
949	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
951	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
953	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
970	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	1	no	—
973	C₄²	—	2	1	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	2	1	no	—
983	C₄²	—	2	1	no	—
984	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
985	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
986	C₄²	C₂⁴×C₇	1	1	yes	characteristic
987	C₄²	C₂⁴×C₇	1	2	yes	—
988	C₄²	C₂⁴×C₇	1	2	yes	—
989	C₄²	C₂⁴×C₇	1	1	yes	characteristic
990	C₂×C₇	—	2	2	no	—
991	C₂×C₇	—	8	1	no	—
992	C₂×C₇	—	8	2	no	—
993	C₂×C₇	C₂×#548	1	1	yes	characteristic
994	C₂×C₇	#3584	1	1	yes	characteristic
995	C₂×C₇	#3586	1	1	yes	characteristic
996	C₂³	—	2	2	no	—
997	C₂³	—	2	1	no	—
998	C₂³	—	4	2	no	—
999	C₂³	—	8	1	no	—
1000	C₂³	—	8	1	no	—
1001	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1002	Q₈	—	2	2	no	—
1003	Q₈	—	2	4	no	—
1004	Q₈	—	2	2	no	—
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	2	no	—
1007	Q₈	—	2	1	no	—
1008	Q₈	—	4	2	no	—
1009	Q₈	—	4	2	no	—
1010	Q₈	—	4	2	no	—
1011	Q₈	—	4	2	no	—
1012	Q₈	—	8	1	no	—
1013	Q₈	—	8	2	no	—
1014	Q₈	—	8	2	no	—
1015	Q₈	C₂×C₇×#41	1	4	yes	—
1016	D₄	—	2	2	no	—
1017	D₄	—	2	1	no	—
1018	D₄	—	2	2	no	—
1019	D₄	—	2	1	no	—
1020	D₄	—	4	2	no	—
1021	D₄	—	4	2	no	—
1022	D₄	—	8	2	no	—
1023	D₄	—	8	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	4	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	4	1	no	—
1036	C₂×C₄	—	4	1	no	—
1037	C₂×C₄	—	4	2	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	8	1	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	8	1	no	—
1042	C₂×C₄	—	8	2	no	—
1043	C₂×C₄	—	8	1	no	—
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	2	yes	—
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	2	yes	—
1050	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1051	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1052	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1053	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1054	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1055	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1056	C₈	—	2	1	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	2	1	no	—
1059	C₈	—	2	1	no	—
1060	C₈	—	2	2	no	—
1061	C₈	—	2	2	no	—
1062	C₇	#61344	1	1	yes	characteristic, direct product factor, Sylow
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	16	2	no	—
1072	C₂²	C₇×#548	1	2	yes	—
1073	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1074	C₄	—	2	1	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	2	1	no	—
1079	C₄	—	2	1	no	—
1080	C₄	—	2	2	no	—
1081	C₄	—	2	2	no	—
1082	C₄	—	2	4	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	2	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	C₇×#548	1	2	yes	—
1093	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1094	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1095	C₂	—	2	2	no	—
1096	C₂	—	8	2	no	—
1097	C₂	—	8	1	no	—
1098	C₂	C₂×C₇×#548	1	1	yes	characteristic
1099	C₂	C₇×#3584	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
prime radical	C₇×#535	C₂²
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
2. C₇×#3502	C₂	semidirect
3. C₇×#3377	C₂	semidirect
4. C₇×#3377	C₂	semidirect
5. C₇×#3375	C₂	semidirect
6. C₇×#3371	C₂	semidirect
7. C₇×#3371	C₂	semidirect
8. C₇×#3369	C₂	semidirect
9. C₇×#3365	C₂	semidirect
10. C₇×#3364	C₂	semidirect
11. C₇×#3140	C₂	semidirect
12. C₇×#3137	C₂	semidirect
14. C₇×#3082	C₂	semidirect
15. C₇×#3081	C₂	semidirect
16. C₇×#3076	C₂	semidirect
17. C₇×#3044	C₂	semidirect
19. C₂×C₇×#464	C₂	semidirect
20. C₇×#2962	C₂	semidirect
21. C₇×#2950	C₂	semidirect
22. C₇×#2949	C₂	semidirect
23. C₄×C₇×#137	C₂	semidirect
30. C₇×Q₈²	C₂²	semidirect
34. C₇×#557	C₂²	semidirect
35. C₇×#557	C₂²	semidirect
36. C₇×#557	C₂²	semidirect
60. C₇×#491	C₂²	semidirect
65. C₇×#489	C₂²	semidirect
69. C₇×#488	C₂²	semidirect
70. C₇×#487	C₂²	semidirect
72. C₇×#479	C₂²	semidirect
73. C₇×#479	C₂²	semidirect
74. C₇×#479	C₂²	semidirect
75. C₇×#479	C₂²	semidirect
78. C₇×#478	C₂²	semidirect
79. C₇×#478	C₂²	semidirect
80. C₇×#477	C₂²	semidirect
81. C₇×#477	C₂²	semidirect
83. C₇×#476	C₂²	semidirect
84. C₇×#475	C₂²	semidirect
85. C₇×#475	C₂²	semidirect
87. C₇×#474	C₂²	semidirect
94. C₇×#464	C₂²	semidirect
95. C₇×#464	C₂²	semidirect
96. C₇×#462	C₂²	semidirect
97. C₇×#462	C₂²	semidirect
100. C₇×#446	C₂²	semidirect
101. C₇×#446	C₂²	semidirect
102. C₇×#446	C₂²	semidirect
103. C₇×C₈×Q₈	C₂²	semidirect
104. C₇×#441	C₂²	semidirect
105. C₇×#441	C₂²	semidirect
106. C₇×#441	C₂²	semidirect
109. C₇×#440	C₂²	semidirect
110. C₄×C₇×Q₁₆	C₂²	semidirect
111. C₄×C₇×Q₁₆	C₂²	semidirect
112. C₄×C₇×Q₁₆	C₂²	semidirect
115. C₄×C₇×SD₁₆	C₂²	semidirect
135. #61344	C₇	direct (N × H)
317. #3502	C₂×C₇	semidirect
318. #3377	C₂×C₇	semidirect
319. #3377	C₂×C₇	semidirect
320. #3375	C₂×C₇	semidirect
321. #3371	C₂×C₇	semidirect
322. #3371	C₂×C₇	semidirect
323. #3369	C₂×C₇	semidirect
324. #3365	C₂×C₇	semidirect
325. #3364	C₂×C₇	semidirect
326. #3140	C₂×C₇	semidirect
327. #3137	C₂×C₇	semidirect
329. #3082	C₂×C₇	semidirect
330. #3081	C₂×C₇	semidirect
331. #3076	C₂×C₇	semidirect
332. #3044	C₂×C₇	semidirect
334. C₂×#464	C₂×C₇	semidirect
335. #2962	C₂×C₇	semidirect
336. #2950	C₂×C₇	semidirect
337. #2949	C₂×C₇	semidirect
338. C₄×#137	C₂×C₇	semidirect
476. Q₈²	C₂²×C₇	semidirect
480. #557	C₂²×C₇	semidirect
481. #557	C₂²×C₇	semidirect
482. #557	C₂²×C₇	semidirect
506. #491	C₂²×C₇	semidirect
511. #489	C₂²×C₇	semidirect
515. #488	C₂²×C₇	semidirect
516. #487	C₂²×C₇	semidirect
518. #479	C₂²×C₇	semidirect
519. #479	C₂²×C₇	semidirect
520. #479	C₂²×C₇	semidirect
521. #479	C₂²×C₇	semidirect
524. #478	C₂²×C₇	semidirect
525. #478	C₂²×C₇	semidirect
526. #477	C₂²×C₇	semidirect
527. #477	C₂²×C₇	semidirect
529. #476	C₂²×C₇	semidirect
530. #475	C₂²×C₇	semidirect
531. #475	C₂²×C₇	semidirect
533. #474	C₂²×C₇	semidirect
540. #464	C₂²×C₇	semidirect
541. #464	C₂²×C₇	semidirect
542. #462	C₂²×C₇	semidirect
543. #462	C₂²×C₇	semidirect
546. #446	C₂²×C₇	semidirect
547. #446	C₂²×C₇	semidirect
548. #446	C₂²×C₇	semidirect
549. C₈×Q₈	C₂²×C₇	semidirect
550. #441	C₂²×C₇	semidirect
551. #441	C₂²×C₇	semidirect
552. #441	C₂²×C₇	semidirect
555. #440	C₂²×C₇	semidirect
556. C₄×Q₁₆	C₂²×C₇	semidirect
557. C₄×Q₁₆	C₂²×C₇	semidirect
558. C₄×Q₁₆	C₂²×C₇	semidirect
561. C₄×SD₁₆	C₂²×C₇	semidirect
1062. C₇	#61344	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×#3510	2
C₇×#3502	2
C₇×#3377	2
C₇×#3375	2
C₇×#3371	2
C₇×#3369	2
C₇×#3365	2
C₇×#3364	2
C₇×#3140	2
C₇×#3137	2
C₇×#3136	2
C₇×#3082	2
C₇×#3081	2
C₇×#3076	2
C₇×#3044	2
C₇×#3043	2
C₂×C₇×#464	2
C₇×#2962	2
C₇×#2950	2
C₇×#2949	2
C₄×C₇×#137	2
#61344	7

Subgroups — C7×#61344 #13238560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61344 #13238560