Subgroups — C₇×#62043 #13239259

Order 1792.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1124 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
2	C₇×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3395	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3328	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3327	C₂	1	2	yes	maximal, complemented
9	C₇×#3315	C₂	1	2	yes	maximal, complemented
10	C₇×#3304	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×D₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3278	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3276	C₂	1	2	yes	maximal, complemented
14	C₇×#3270	C₂	1	2	yes	maximal, complemented
15	C₇×#3258	C₂	1	2	yes	maximal, complemented
16	C₇×#3255	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3223	C₂	1	2	yes	maximal, complemented
18	C₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3121	C₂	1	2	yes	maximal, complemented
20	C₇×#3104	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3044	C₂	1	2	yes	maximal, complemented
22	C₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#137	C₂²	1	2	yes	—
25	C₂×C₇×#137	C₂²	1	2	yes	—
26	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
27	C₇×#562	—	2	2	no	—
28	C₇×#559	—	2	1	no	—
29	C₇×#559	C₂²	1	1	yes	characteristic
30	C₇×#557	—	2	1	no	—
31	C₇×#557	C₂²	1	1	yes	characteristic
32	C₇×#557	C₂²	1	1	yes	characteristic
33	C₇×#557	C₂²	1	1	yes	characteristic
34	C₇×#556	—	2	1	no	—
35	C₇×#556	C₂²	1	1	yes	characteristic
36	C₇×#554	—	2	1	no	—
37	C₇×#552	—	2	2	no	—
38	C₇×#552	C₂²	1	2	yes	—
39	C₇×#550	C₂²	1	1	yes	characteristic
40	C₇×D₄×Q₈	C₂²	1	2	yes	—
41	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
42	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
43	C₇×#548	C₂²	1	2	yes	—
44	C₇×#547	C₂²	1	2	yes	—
45	C₇×#542	—	2	1	no	—
46	C₇×#542	C₂²	1	2	yes	—
47	C₇×#541	—	2	2	no	—
48	C₇×#541	C₂²	1	2	yes	—
49	C₇×#540	—	2	1	no	—
50	C₇×#539	—	2	2	no	—
51	C₇×#536	C₂²	1	2	yes	—
52	C₇×#533	—	2	1	no	—
53	C₇×#533	C₂²	1	1	yes	characteristic
54	C₇×#533	C₂²	1	1	yes	characteristic
55	C₇×#532	C₂²	1	1	yes	characteristic
56	C₇×#529	—	2	1	no	—
57	C₇×#529	C₂²	1	1	yes	characteristic
58	C₇×#519	C₂²	1	2	yes	—
59	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
60	C₇×#497	C₂²	1	2	yes	—
61	C₇×#494	C₂²	1	1	yes	characteristic
62	C₇×#494	C₂²	1	2	yes	—
63	C₇×#492	C₂²	1	1	yes	characteristic
64	C₇×#491	C₂²	1	2	yes	—
65	C₇×#488	C₂²	1	2	yes	—
66	C₇×#487	C₂²	1	1	yes	characteristic
67	C₇×#486	C₂²	1	1	yes	characteristic
68	C₇×#485	C₂²	1	2	yes	—
69	C₇×#484	C₂²	1	1	yes	characteristic
70	C₇×#484	C₂²	1	1	yes	characteristic
71	C₇×#482	C₂²	1	2	yes	—
72	C₇×#479	C₂²	1	2	yes	—
73	C₇×#478	C₂²	1	2	yes	—
74	C₇×#477	C₂²	1	1	yes	characteristic
75	C₇×#477	C₂²	1	1	yes	characteristic
76	C₇×#475	C₂²	1	2	yes	—
77	C₇×#475	C₂²	1	1	yes	characteristic
78	C₇×#475	C₂²	1	1	yes	characteristic
79	C₇×#470	C₂²	1	2	yes	—
80	C₇×#470	C₂²	1	2	yes	—
81	C₇×#470	C₂²	1	2	yes	—
82	C₇×#468	C₂²	1	2	yes	—
83	C₇×#467	C₂²	1	2	yes	—
84	C₇×#465	C₂²	1	2	yes	—
85	C₇×#464	C₂²	1	2	yes	—
86	C₇×#464	C₂²	1	2	yes	—
87	C₇×#464	C₂²	1	2	yes	—
88	C₇×#464	C₂²	1	2	yes	—
89	C₇×#464	C₂²	1	2	yes	—
90	C₇×#464	C₂²	1	2	yes	—
91	C₇×#462	C₂²	1	1	yes	characteristic
92	C₇×#462	C₂²	1	2	yes	—
93	C₇×#462	C₂²	1	1	yes	characteristic
94	C₇×#462	C₂²	1	1	yes	characteristic
95	C₇×#462	C₂²	1	2	yes	—
96	C₇×#462	C₂²	1	2	yes	—
97	C₇×#462	C₂²	1	1	yes	characteristic
98	C₇×#462	C₂²	1	1	yes	characteristic
99	C₇×#462	C₂²	1	1	yes	characteristic
100	C₇×#462	C₂²	1	2	yes	—
101	C₇×#461	C₂²	1	2	yes	—
102	C₇×#460	C₂²	1	1	yes	characteristic
103	C₇×#460	C₂²	1	1	yes	characteristic
104	C₇×#452	C₂²	1	2	yes	—
105	C₇×#452	C₂²	1	2	yes	—
106	C₇×#452	C₂²	1	2	yes	—
107	C₇×#452	C₂²	1	2	yes	—
108	C₇×#451	C₂²	1	2	yes	—
109	C₇×#451	C₂²	1	2	yes	—
110	C₇×#451	C₂²	1	1	yes	characteristic
111	C₇×#451	C₂²	1	1	yes	characteristic
112	C₇×#451	C₂²	1	2	yes	—
113	C₇×#448	C₂²	1	2	yes	—
114	C₇×#446	C₂²	1	1	yes	characteristic
115	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
116	C₇×#441	C₂²	1	2	yes	—
117	C₇×#440	C₂²	1	2	yes	—
118	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
119	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
121	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
122	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
123	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
124	C₇×#436	C₂²	1	2	yes	—
125	C₇×#436	C₂²	1	1	yes	characteristic
126	C₇×#435	C₂²	1	2	yes	—
127	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
128	C₇×#433	C₂²	1	2	yes	—
129	C₇×#431	C₂²	1	1	yes	characteristic
130	C₇×#424	C₂²	1	2	yes	—
131	C₇×#423	C₂²	1	1	yes	characteristic
132	C₇×#419	C₂²	1	2	yes	—
133	C₇×#417	C₂²	1	2	yes	—
134	C₇×#416	C₂²	1	2	yes	—
135	#62043	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	C₂³	1	2	yes	—
137	C₂×C₇×#41	C₂³	1	2	yes	—
138	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
139	C₂²×C₇×Q₈	C₂³	1	2	yes	—
140	C₂²×C₇×Q₈	C₂³	1	2	yes	—
141	C₇×#137	—	4	4	no	—
142	C₇×#137	—	4	4	no	—
143	C₂×C₇×Q₁₆	—	4	4	no	—
144	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
146	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
149	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
150	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
151	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
152	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
153	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
154	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
155	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
157	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
158	C₂×C₇×M₁₆	C₂³	1	2	yes	—
159	C₂×C₇×M₁₆	C₂³	1	2	yes	—
160	C₂²×C₇×C₈	C₂³	1	2	yes	—
161	C₇×C₄⋊Q₈	—	2	1	no	—
162	C₇×C₄⋊Q₈	—	2	1	no	—
163	C₇×C₄⋊Q₈	—	2	2	no	—
164	C₇×C₄⋊Q₈	—	2	1	no	—
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×C₄⋊Q₈	C₂³	1	2	yes	—
169	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₇×#127	—	2	1	no	—
173	C₇×#127	C₂³	1	1	yes	characteristic
174	C₇×#126	—	2	2	no	—
175	C₇×#126	—	2	2	no	—
176	C₇×#126	—	2	2	no	—
177	C₇×#126	—	2	2	no	—
178	C₇×#126	—	2	2	no	—
179	C₇×#126	D₄	1	2	yes	—
180	C₇×#125	—	2	1	no	—
181	C₇×#125	—	2	2	no	—
182	C₇×#125	—	2	2	no	—
183	C₇×#125	—	2	1	no	—
184	C₇×#125	—	2	2	no	—
185	C₇×#125	—	2	2	no	—
186	C₇×#125	—	2	2	no	—
187	C₇×#125	—	2	2	no	—
188	C₇×#125	—	2	1	no	—
189	C₇×#125	—	2	1	no	—
190	C₇×#125	D₄	1	1	yes	characteristic
191	C₇×#125	C₂³	1	2	yes	—
192	C₇×#124	—	2	1	no	—
193	C₇×#124	—	2	1	no	—
194	C₇×#124	—	2	2	no	—
195	C₇×#124	—	2	2	no	—
196	C₇×#124	D₄	1	1	yes	characteristic
197	C₇×#124	C₂³	1	2	yes	—
198	C₇×#124	C₂³	1	2	yes	—
199	C₇×#123	—	2	2	no	—
200	C₇×#123	—	2	2	no	—
201	C₇×#123	—	2	2	no	—
202	C₇×#123	—	2	2	no	—
203	C₇×#123	—	2	2	no	—
204	C₇×#123	—	2	2	no	—
205	C₇×#123	—	2	2	no	—
206	C₇×#123	D₄	1	2	yes	—
207	C₇×C₂²⋊Q₈	—	2	1	no	—
208	C₇×C₂²⋊Q₈	—	2	1	no	—
209	C₇×C₂²⋊Q₈	—	2	2	no	—
210	C₇×C₂²⋊Q₈	—	2	2	no	—
211	C₇×C₂²⋊Q₈	—	2	2	no	—
212	C₇×C₂²⋊Q₈	—	2	2	no	—
213	C₇×C₂²⋊Q₈	—	2	2	no	—
214	C₇×C₂²⋊Q₈	—	2	2	no	—
215	C₇×C₂²⋊Q₈	—	2	2	no	—
216	C₇×C₂²⋊Q₈	—	2	2	no	—
217	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
218	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₇×#121	—	2	2	no	—
225	C₇×#121	—	2	2	no	—
226	C₇×#121	—	2	1	no	—
227	C₇×#121	—	2	1	no	—
228	C₇×#121	—	2	2	no	—
229	C₇×#121	D₄	1	1	yes	characteristic
230	C₇×#121	C₂³	1	2	yes	—
231	C₄×C₇×Q₈	—	2	1	no	—
232	C₄×C₇×Q₈	—	2	1	no	—
233	C₄×C₇×Q₈	—	2	2	no	—
234	C₄×C₇×Q₈	—	2	2	no	—
235	C₄×C₇×Q₈	—	2	1	no	—
236	C₄×C₇×Q₈	—	2	1	no	—
237	C₄×C₇×Q₈	—	2	1	no	—
238	C₄×C₇×Q₈	—	2	1	no	—
239	C₄×C₇×Q₈	—	2	1	no	—
240	C₄×C₇×Q₈	—	2	1	no	—
241	C₄×C₇×Q₈	C₂³	1	2	yes	—
242	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
243	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
244	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
245	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
246	C₄×C₇×Q₈	C₂³	1	2	yes	—
247	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
248	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
249	C₄×C₇×Q₈	C₂³	1	2	yes	—
250	C₄×C₇×Q₈	C₂³	1	2	yes	—
251	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
252	C₄×C₇×D₄	—	2	2	no	—
253	C₄×C₇×D₄	—	2	1	no	—
254	C₄×C₇×D₄	—	2	1	no	—
255	C₄×C₇×D₄	—	2	1	no	—
256	C₄×C₇×D₄	—	2	1	no	—
257	C₄×C₇×D₄	—	2	2	no	—
258	C₄×C₇×D₄	—	2	1	no	—
259	C₄×C₇×D₄	—	2	1	no	—
260	C₄×C₇×D₄	C₂³	1	2	yes	—
261	C₄×C₇×D₄	C₂³	1	2	yes	—
262	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
263	C₇×#117	—	2	1	no	—
264	C₇×#117	—	2	1	no	—
265	C₇×#117	—	2	2	no	—
266	C₇×#117	—	2	2	no	—
267	C₇×#117	—	2	2	no	—
268	C₇×#117	C₂³	1	2	yes	—
269	C₇×#117	C₂³	1	2	yes	—
270	C₂×C₇×C₄⋊C₄	—	2	1	no	—
271	C₂×C₇×C₄⋊C₄	—	2	2	no	—
272	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₇	—	2	1	no	—
274	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
275	C₇×#107	C₂³	1	1	yes	characteristic
276	C₇×#107	C₂³	1	1	yes	characteristic
277	C₇×#107	C₂³	1	1	yes	characteristic
278	C₇×#107	C₂³	1	1	yes	characteristic
279	C₇×#106	C₂³	1	2	yes	—
280	C₇×#106	C₂³	1	2	yes	—
281	C₇×C₄⋊C₈	C₂³	1	2	yes	—
282	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₇×C₄⋊C₈	C₂³	1	2	yes	—
287	C₇×C₄⋊C₈	C₂³	1	2	yes	—
288	C₇×#103	C₂³	1	2	yes	—
289	C₇×#103	C₂³	1	2	yes	—
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#103	C₂³	1	1	yes	characteristic
292	C₇×#103	C₂³	1	2	yes	—
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	1	yes	characteristic
296	C₇×#103	C₂³	1	1	yes	characteristic
297	C₇×#103	C₂³	1	1	yes	characteristic
298	C₇×#103	C₂³	1	1	yes	characteristic
299	C₇×#103	C₂³	1	1	yes	characteristic
300	C₇×#103	C₂³	1	1	yes	characteristic
301	C₇×#103	C₂³	1	1	yes	characteristic
302	C₇×#103	C₂³	1	2	yes	—
303	C₇×#103	C₂³	1	2	yes	—
304	C₇×#102	C₂³	1	2	yes	—
305	C₇×#102	C₂³	1	2	yes	—
306	C₇×#102	C₂³	1	2	yes	—
307	C₇×#102	C₂³	1	2	yes	—
308	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₇×#97	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
315	C₄×C₇×C₈	C₂³	1	2	yes	—
316	#3554	C₂×C₇	1	1	yes	characteristic
317	#3523	C₂×C₇	1	1	yes	characteristic, complemented
318	#3400	C₂×C₇	1	1	yes	characteristic, complemented
319	#3395	C₂×C₇	1	1	yes	characteristic, complemented
320	#3374	C₂×C₇	1	1	yes	characteristic, complemented
321	#3365	C₂×C₇	1	1	yes	characteristic, complemented
322	#3328	C₂×C₇	1	1	yes	characteristic, complemented
323	#3327	C₂×C₇	1	2	yes	complemented
324	#3315	C₂×C₇	1	2	yes	complemented
325	#3304	C₂×C₇	1	1	yes	characteristic, complemented
326	D₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
327	#3278	C₂×C₇	1	1	yes	characteristic, complemented
328	#3276	C₂×C₇	1	2	yes	complemented
329	#3270	C₂×C₇	1	2	yes	complemented
330	#3258	C₂×C₇	1	2	yes	complemented
331	#3255	C₂×C₇	1	1	yes	characteristic, complemented
332	#3223	C₂×C₇	1	2	yes	complemented
333	#3210	C₂×C₇	1	1	yes	characteristic, complemented
334	#3121	C₂×C₇	1	2	yes	complemented
335	#3104	C₂×C₇	1	1	yes	characteristic, complemented
336	#3044	C₂×C₇	1	2	yes	complemented
337	#3037	C₂×C₇	1	1	yes	characteristic, complemented
338	#2993	C₂×C₇	1	1	yes	characteristic, complemented
339	C₇×#41	—	4	2	no	—
340	C₇×#41	—	4	2	no	—
341	C₇×#41	—	4	2	no	—
342	C₇×#41	—	4	2	no	—
343	C₂×C₇×Q₈	—	2	1	no	—
344	C₂×C₇×Q₈	—	2	2	no	—
345	C₂×C₇×Q₈	—	2	1	no	—
346	C₂×C₇×Q₈	—	2	1	no	—
347	C₂×C₇×Q₈	—	2	2	no	—
348	C₂×C₇×Q₈	—	2	4	no	—
349	C₂×C₇×Q₈	—	2	2	no	—
350	C₂×C₇×Q₈	—	4	2	no	—
351	C₂×C₇×Q₈	—	4	1	no	—
352	C₂×C₇×Q₈	—	4	2	no	—
353	C₂×C₇×Q₈	—	4	2	no	—
354	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
355	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
356	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
357	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
358	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
359	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
360	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
361	C₂×C₇×D₄	—	2	2	no	—
362	C₂×C₇×D₄	—	2	2	no	—
363	C₂×C₇×D₄	—	2	2	no	—
364	C₂×C₇×D₄	—	2	1	no	—
365	C₂×C₇×D₄	—	2	1	no	—
366	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
367	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
368	C₂×C₇×D₄	C₂⁴	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
380	C₇×Q₁₆	—	2	2	no	—
381	C₇×Q₁₆	—	2	4	no	—
382	C₇×Q₁₆	—	2	2	no	—
383	C₇×Q₁₆	—	4	2	no	—
384	C₇×Q₁₆	—	4	2	no	—
385	C₇×Q₁₆	—	4	1	no	—
386	C₇×Q₁₆	—	4	2	no	—
387	C₇×Q₁₆	—	4	1	no	—
388	C₇×Q₁₆	—	4	2	no	—
389	C₇×Q₁₆	—	4	2	no	—
390	C₇×SD₁₆	—	2	4	no	—
391	C₇×SD₁₆	—	4	2	no	—
392	C₇×SD₁₆	—	4	2	no	—
393	C₇×SD₁₆	—	4	2	no	—
394	C₇×M₁₆	—	4	2	no	—
395	C₇×M₁₆	—	4	2	no	—
396	C₂×C₇×C₈	—	4	2	no	—
397	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
398	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
399	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
400	C₂×C₇×C₈	C₂⁴	1	2	yes	—
401	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
402	C₂×C₇×C₈	C₂⁴	1	2	yes	—
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	1	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	—	2	1	no	—
416	C₇×C₄⋊C₄	—	2	2	no	—
417	C₇×C₄⋊C₄	—	2	1	no	—
418	C₇×C₄⋊C₄	—	2	1	no	—
419	C₇×C₄⋊C₄	—	2	2	no	—
420	C₇×C₄⋊C₄	—	2	1	no	—
421	C₇×C₄⋊C₄	—	2	1	no	—
422	C₇×C₄⋊C₄	—	2	1	no	—
423	C₇×C₄⋊C₄	—	2	1	no	—
424	C₇×C₄⋊C₄	—	2	2	no	—
425	C₇×C₄⋊C₄	—	2	1	no	—
426	C₇×C₄⋊C₄	—	2	2	no	—
427	C₇×C₄⋊C₄	—	2	2	no	—
428	C₇×C₄⋊C₄	—	2	2	no	—
429	C₇×C₄⋊C₄	—	2	2	no	—
430	C₇×C₄⋊C₄	—	2	2	no	—
431	C₇×C₄⋊C₄	—	2	1	no	—
432	C₇×C₄⋊C₄	—	2	2	no	—
433	C₇×C₄⋊C₄	—	2	1	no	—
434	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
435	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
436	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
437	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
438	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
439	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
440	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
441	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
442	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
443	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
444	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
445	C₇×C₂²⋊C₄	—	2	2	no	—
446	C₇×C₂²⋊C₄	—	2	2	no	—
447	C₇×C₂²⋊C₄	—	2	1	no	—
448	C₇×C₂²⋊C₄	—	2	1	no	—
449	C₇×C₂²⋊C₄	—	2	2	no	—
450	C₇×C₂²⋊C₄	—	2	2	no	—
451	C₇×C₂²⋊C₄	—	2	2	no	—
452	C₇×C₂²⋊C₄	—	2	2	no	—
453	C₇×C₂²⋊C₄	—	2	2	no	—
454	C₇×C₂²⋊C₄	—	2	2	no	—
455	C₇×C₂²⋊C₄	—	2	2	no	—
456	C₇×C₂²⋊C₄	—	2	2	no	—
457	C₇×C₂²⋊C₄	—	2	2	no	—
458	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
459	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
460	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
461	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
462	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
463	C₄²×C₇	—	2	1	no	—
464	C₄²×C₇	—	2	1	no	—
465	C₄²×C₇	—	2	1	no	—
466	C₄²×C₇	—	2	1	no	—
467	C₄²×C₇	—	2	2	no	—
468	C₄²×C₇	—	2	2	no	—
469	C₄²×C₇	—	2	2	no	—
470	C₄²×C₇	—	2	1	no	—
471	C₄²×C₇	—	2	1	no	—
472	C₄²×C₇	—	2	2	no	—
473	C₄²×C₇	—	2	2	no	—
474	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
475	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
476	C₄²×C₇	C₂⁴	1	1	yes	characteristic
477	C₄²×C₇	C₂⁴	1	2	yes	—
478	C₄²×C₇	C₂⁴	1	1	yes	characteristic
479	C₂×#137	C₂²×C₇	1	2	yes	—
480	C₂×#137	C₂²×C₇	1	2	yes	—
481	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
482	#562	—	2	2	no	—
483	#559	—	2	1	no	—
484	#559	C₂²×C₇	1	1	yes	characteristic
485	#557	—	2	1	no	—
486	#557	C₂²×C₇	1	1	yes	characteristic
487	#557	C₂²×C₇	1	1	yes	characteristic
488	#557	C₂²×C₇	1	1	yes	characteristic
489	#556	—	2	1	no	—
490	#556	C₂²×C₇	1	1	yes	characteristic
491	#554	—	2	1	no	—
492	#552	—	2	2	no	—
493	#552	C₂²×C₇	1	2	yes	—
494	#550	C₂²×C₇	1	1	yes	characteristic
495	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
496	D₄×Q₈	C₂²×C₇	1	2	yes	—
497	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
498	#548	C₂²×C₇	1	2	yes	—
499	#547	C₂²×C₇	1	2	yes	—
500	#542	—	2	1	no	—
501	#542	C₂²×C₇	1	2	yes	—
502	#541	—	2	2	no	—
503	#541	C₂²×C₇	1	2	yes	—
504	#540	—	2	1	no	—
505	#539	—	2	2	no	—
506	#536	C₂²×C₇	1	2	yes	—
507	#533	—	2	1	no	—
508	#533	C₂²×C₇	1	1	yes	characteristic
509	#533	C₂²×C₇	1	1	yes	characteristic
510	#532	C₂²×C₇	1	1	yes	characteristic
511	#529	—	2	1	no	—
512	#529	C₂²×C₇	1	1	yes	characteristic
513	#519	C₂²×C₇	1	2	yes	—
514	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
515	#497	C₂²×C₇	1	2	yes	—
516	#494	C₂²×C₇	1	1	yes	characteristic
517	#494	C₂²×C₇	1	2	yes	—
518	#492	C₂²×C₇	1	1	yes	characteristic
519	#491	C₂²×C₇	1	2	yes	—
520	#488	C₂²×C₇	1	2	yes	—
521	#487	C₂²×C₇	1	1	yes	characteristic
522	#486	C₂²×C₇	1	1	yes	characteristic
523	#485	C₂²×C₇	1	2	yes	—
524	#484	C₂²×C₇	1	1	yes	characteristic
525	#484	C₂²×C₇	1	1	yes	characteristic
526	#482	C₂²×C₇	1	2	yes	—
527	#479	C₂²×C₇	1	2	yes	—
528	#478	C₂²×C₇	1	2	yes	—
529	#477	C₂²×C₇	1	1	yes	characteristic
530	#477	C₂²×C₇	1	1	yes	characteristic
531	#475	C₂²×C₇	1	1	yes	characteristic
532	#475	C₂²×C₇	1	1	yes	characteristic
533	#475	C₂²×C₇	1	2	yes	—
534	#470	C₂²×C₇	1	2	yes	—
535	#470	C₂²×C₇	1	2	yes	—
536	#470	C₂²×C₇	1	2	yes	—
537	#468	C₂²×C₇	1	2	yes	—
538	#467	C₂²×C₇	1	2	yes	—
539	#465	C₂²×C₇	1	2	yes	—
540	#464	C₂²×C₇	1	2	yes	—
541	#464	C₂²×C₇	1	2	yes	—
542	#464	C₂²×C₇	1	2	yes	—
543	#464	C₂²×C₇	1	2	yes	—
544	#464	C₂²×C₇	1	2	yes	—
545	#464	C₂²×C₇	1	2	yes	—
546	#462	C₂²×C₇	1	1	yes	characteristic
547	#462	C₂²×C₇	1	1	yes	characteristic
548	#462	C₂²×C₇	1	1	yes	characteristic
549	#462	C₂²×C₇	1	2	yes	—
550	#462	C₂²×C₇	1	1	yes	characteristic
551	#462	C₂²×C₇	1	1	yes	characteristic
552	#462	C₂²×C₇	1	2	yes	—
553	#462	C₂²×C₇	1	2	yes	—
554	#462	C₂²×C₇	1	1	yes	characteristic
555	#462	C₂²×C₇	1	2	yes	—
556	#461	C₂²×C₇	1	2	yes	—
557	#460	C₂²×C₇	1	1	yes	characteristic
558	#460	C₂²×C₇	1	1	yes	characteristic
559	#452	C₂²×C₇	1	2	yes	—
560	#452	C₂²×C₇	1	2	yes	—
561	#452	C₂²×C₇	1	2	yes	—
562	#452	C₂²×C₇	1	2	yes	—
563	#451	C₂²×C₇	1	2	yes	—
564	#451	C₂²×C₇	1	1	yes	characteristic
565	#451	C₂²×C₇	1	1	yes	characteristic
566	#451	C₂²×C₇	1	2	yes	—
567	#451	C₂²×C₇	1	2	yes	—
568	#448	C₂²×C₇	1	2	yes	—
569	#446	C₂²×C₇	1	1	yes	characteristic
570	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
571	#441	C₂²×C₇	1	2	yes	—
572	#440	C₂²×C₇	1	2	yes	—
573	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
574	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
575	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
576	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
577	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
578	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
579	#436	C₂²×C₇	1	1	yes	characteristic
580	#436	C₂²×C₇	1	2	yes	—
581	#435	C₂²×C₇	1	2	yes	—
582	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
583	#433	C₂²×C₇	1	2	yes	—
584	#431	C₂²×C₇	1	1	yes	characteristic
585	#424	C₂²×C₇	1	2	yes	—
586	#423	C₂²×C₇	1	1	yes	characteristic
587	#419	C₂²×C₇	1	2	yes	—
588	#417	C₂²×C₇	1	2	yes	—
589	#416	C₂²×C₇	1	2	yes	—
590	C₂³×C₇	—	2	2	no	—
591	C₂³×C₇	C₂²×D₄	1	2	yes	—
592	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
593	C₇×Q₈	—	2	2	no	—
594	C₇×Q₈	—	2	1	no	—
595	C₇×Q₈	—	2	1	no	—
596	C₇×Q₈	—	2	2	no	—
597	C₇×Q₈	—	2	1	no	—
598	C₇×Q₈	—	2	2	no	—
599	C₇×Q₈	—	2	1	no	—
600	C₇×Q₈	—	2	2	no	—
601	C₇×Q₈	—	2	1	no	—
602	C₇×Q₈	—	2	1	no	—
603	C₇×Q₈	—	2	2	no	—
604	C₇×Q₈	—	2	1	no	—
605	C₇×Q₈	—	4	2	no	—
606	C₇×Q₈	—	4	4	no	—
607	C₇×Q₈	—	4	2	no	—
608	C₇×Q₈	—	8	1	no	—
609	C₇×Q₈	—	8	2	no	—
610	C₇×Q₈	H(5,𝔽₂)	1	2	yes	—
611	C₇×D₄	—	2	2	no	—
612	C₇×D₄	—	2	2	no	—
613	C₇×D₄	—	2	2	no	—
614	C₇×D₄	—	4	2	no	—
615	C₇×D₄	—	4	2	no	—
616	C₇×D₄	—	8	1	no	—
617	C₇×D₄	—	8	2	no	—
618	C₇×D₄	—	8	2	no	—
619	C₇×D₄	—	8	2	no	—
620	C₂×C₄×C₇	—	2	1	no	—
621	C₂×C₄×C₇	—	2	2	no	—
622	C₂×C₄×C₇	—	2	2	no	—
623	C₂×C₄×C₇	—	2	1	no	—
624	C₂×C₄×C₇	—	2	2	no	—
625	C₂×C₄×C₇	—	2	1	no	—
626	C₂×C₄×C₇	—	2	1	no	—
627	C₂×C₄×C₇	—	2	2	no	—
628	C₂×C₄×C₇	—	2	1	no	—
629	C₂×C₄×C₇	—	2	1	no	—
630	C₂×C₄×C₇	—	2	1	no	—
631	C₂×C₄×C₇	—	2	2	no	—
632	C₂×C₄×C₇	—	2	1	no	—
633	C₂×C₄×C₇	—	2	1	no	—
634	C₂×C₄×C₇	—	2	2	no	—
635	C₂×C₄×C₇	—	2	1	no	—
636	C₂×C₄×C₇	—	4	1	no	—
637	C₂×C₄×C₇	—	4	4	no	—
638	C₂×C₄×C₇	—	4	2	no	—
639	C₂×C₄×C₇	—	4	2	no	—
640	C₂×C₄×C₇	—	8	2	no	—
641	C₂×C₄×C₇	—	8	2	no	—
642	C₂×C₄×C₇	—	8	2	no	—
643	C₂×C₄×C₇	—	8	2	no	—
644	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
645	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
646	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
647	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
648	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
649	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
650	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
651	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
652	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
653	C₇×C₈	—	2	1	no	—
654	C₇×C₈	—	2	2	no	—
655	C₇×C₈	—	2	2	no	—
656	C₇×C₈	—	2	1	no	—
657	C₇×C₈	—	2	1	no	—
658	C₇×C₈	—	2	1	no	—
659	C₂×#41	C₂³×C₇	1	2	yes	—
660	C₂×#41	C₂³×C₇	1	2	yes	—
661	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
662	C₂²×Q₈	C₂³×C₇	1	2	yes	—
663	C₂²×Q₈	C₂³×C₇	1	2	yes	—
664	#137	—	4	4	no	—
665	#137	—	4	4	no	—
666	C₂×Q₁₆	—	4	4	no	—
667	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
668	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
669	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
670	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
671	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
672	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
673	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
674	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
675	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
676	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
677	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
678	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
679	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
680	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
681	C₂×M₁₆	C₂³×C₇	1	2	yes	—
682	C₂×M₁₆	C₂³×C₇	1	2	yes	—
683	C₂²×C₈	C₂³×C₇	1	2	yes	—
684	C₄⋊Q₈	—	2	1	no	—
685	C₄⋊Q₈	—	2	1	no	—
686	C₄⋊Q₈	—	2	2	no	—
687	C₄⋊Q₈	—	2	1	no	—
688	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
689	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
690	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
691	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
692	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
693	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
694	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
695	#127	—	2	1	no	—
696	#127	C₂³×C₇	1	1	yes	characteristic
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	—	2	2	no	—
701	#126	—	2	2	no	—
702	#126	C₇×D₄	1	2	yes	—
703	#125	—	2	1	no	—
704	#125	—	2	2	no	—
705	#125	—	2	2	no	—
706	#125	—	2	1	no	—
707	#125	—	2	2	no	—
708	#125	—	2	2	no	—
709	#125	—	2	2	no	—
710	#125	—	2	2	no	—
711	#125	—	2	1	no	—
712	#125	—	2	1	no	—
713	#125	C₇×D₄	1	1	yes	characteristic
714	#125	C₂³×C₇	1	2	yes	—
715	#124	—	2	1	no	—
716	#124	—	2	1	no	—
717	#124	—	2	2	no	—
718	#124	—	2	2	no	—
719	#124	C₇×D₄	1	1	yes	characteristic
720	#124	C₂³×C₇	1	2	yes	—
721	#124	C₂³×C₇	1	2	yes	—
722	#123	—	2	2	no	—
723	#123	—	2	2	no	—
724	#123	—	2	2	no	—
725	#123	—	2	2	no	—
726	#123	—	2	2	no	—
727	#123	—	2	2	no	—
728	#123	—	2	2	no	—
729	#123	C₇×D₄	1	2	yes	—
730	C₂²⋊Q₈	—	2	1	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
741	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
742	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
743	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
744	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
745	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
746	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
747	#121	—	2	2	no	—
748	#121	—	2	2	no	—
749	#121	—	2	1	no	—
750	#121	—	2	1	no	—
751	#121	—	2	2	no	—
752	#121	C₇×D₄	1	1	yes	characteristic
753	#121	C₂³×C₇	1	2	yes	—
754	C₄×Q₈	—	2	1	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	2	no	—
757	C₄×Q₈	—	2	2	no	—
758	C₄×Q₈	—	2	1	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
765	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
766	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
767	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
768	C₄×Q₈	C₂³×C₇	1	2	yes	—
769	C₄×Q₈	C₂³×C₇	1	2	yes	—
770	C₄×Q₈	C₂³×C₇	1	2	yes	—
771	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
772	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₇	1	2	yes	—
774	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	1	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	2	no	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	C₂³×C₇	1	2	yes	—
784	C₄×D₄	C₂³×C₇	1	2	yes	—
785	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
786	#117	—	2	1	no	—
787	#117	—	2	1	no	—
788	#117	—	2	2	no	—
789	#117	—	2	2	no	—
790	#117	—	2	2	no	—
791	#117	C₂³×C₇	1	2	yes	—
792	#117	C₂³×C₇	1	2	yes	—
793	C₂×C₄⋊C₄	—	2	1	no	—
794	C₂×C₄⋊C₄	—	2	2	no	—
795	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
796	C₂×C₄²	—	2	1	no	—
797	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
798	#107	C₂³×C₇	1	1	yes	characteristic
799	#107	C₂³×C₇	1	1	yes	characteristic
800	#107	C₂³×C₇	1	1	yes	characteristic
801	#107	C₂³×C₇	1	1	yes	characteristic
802	#106	C₂³×C₇	1	2	yes	—
803	#106	C₂³×C₇	1	2	yes	—
804	C₄⋊C₈	C₂³×C₇	1	2	yes	—
805	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
806	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
807	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
808	C₄⋊C₈	C₂³×C₇	1	2	yes	—
809	C₄⋊C₈	C₂³×C₇	1	2	yes	—
810	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
811	#103	C₂³×C₇	1	1	yes	characteristic
812	#103	C₂³×C₇	1	2	yes	—
813	#103	C₂³×C₇	1	2	yes	—
814	#103	C₂³×C₇	1	2	yes	—
815	#103	C₂³×C₇	1	1	yes	characteristic
816	#103	C₂³×C₇	1	2	yes	—
817	#103	C₂³×C₇	1	2	yes	—
818	#103	C₂³×C₇	1	1	yes	characteristic
819	#103	C₂³×C₇	1	1	yes	characteristic
820	#103	C₂³×C₇	1	2	yes	—
821	#103	C₂³×C₇	1	1	yes	characteristic
822	#103	C₂³×C₇	1	1	yes	characteristic
823	#103	C₂³×C₇	1	1	yes	characteristic
824	#103	C₂³×C₇	1	1	yes	characteristic
825	#103	C₂³×C₇	1	2	yes	—
826	#103	C₂³×C₇	1	2	yes	—
827	#102	C₂³×C₇	1	2	yes	—
828	#102	C₂³×C₇	1	2	yes	—
829	#102	C₂³×C₇	1	2	yes	—
830	#102	C₂³×C₇	1	2	yes	—
831	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
832	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
833	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
834	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
835	#97	C₂³×C₇	1	2	yes	—
836	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
837	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
838	C₄×C₈	C₂³×C₇	1	2	yes	—
839	C₂²×C₇	—	2	1	no	—
840	C₂²×C₇	—	2	2	no	—
841	C₂²×C₇	—	2	2	no	—
842	C₂²×C₇	—	2	1	no	—
843	C₂²×C₇	—	2	1	no	—
844	C₂²×C₇	—	2	2	no	—
845	C₂²×C₇	—	4	2	no	—
846	C₂²×C₇	—	4	2	no	—
847	C₂²×C₇	—	4	2	no	—
848	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
849	C₄×C₇	—	2	1	no	—
850	C₄×C₇	—	2	1	no	—
851	C₄×C₇	—	2	2	no	—
852	C₄×C₇	—	2	1	no	—
853	C₄×C₇	—	2	2	no	—
854	C₄×C₇	—	2	2	no	—
855	C₄×C₇	—	2	1	no	—
856	C₄×C₇	—	2	2	no	—
857	C₄×C₇	—	4	1	no	—
858	C₄×C₇	—	4	1	no	—
859	C₄×C₇	—	4	1	no	—
860	C₄×C₇	—	4	1	no	—
861	C₄×C₇	—	4	1	no	—
862	C₄×C₇	—	4	2	no	—
863	C₄×C₇	—	4	1	no	—
864	C₄×C₇	—	4	2	no	—
865	C₄×C₇	—	4	1	no	—
866	C₄×C₇	—	4	2	no	—
867	C₄×C₇	#578	1	2	yes	—
868	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
869	C₄×C₇	#585	1	1	yes	characteristic
870	#41	—	4	2	no	—
871	#41	—	4	2	no	—
872	#41	—	4	2	no	—
873	#41	—	4	2	no	—
874	C₂×Q₈	—	2	1	no	—
875	C₂×Q₈	—	2	2	no	—
876	C₂×Q₈	—	2	1	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	—	2	4	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	4	2	no	—
882	C₂×Q₈	—	4	1	no	—
883	C₂×Q₈	—	4	2	no	—
884	C₂×Q₈	—	4	2	no	—
885	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
886	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
887	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
888	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
889	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
890	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
891	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
898	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
899	C₂×D₄	C₂⁴×C₇	1	2	yes	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
908	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
909	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
911	Q₁₆	—	2	2	no	—
912	Q₁₆	—	2	4	no	—
913	Q₁₆	—	2	2	no	—
914	Q₁₆	—	4	2	no	—
915	Q₁₆	—	4	2	no	—
916	Q₁₆	—	4	1	no	—
917	Q₁₆	—	4	2	no	—
918	Q₁₆	—	4	1	no	—
919	Q₁₆	—	4	2	no	—
920	Q₁₆	—	4	2	no	—
921	SD₁₆	—	2	4	no	—
922	SD₁₆	—	4	2	no	—
923	SD₁₆	—	4	2	no	—
924	SD₁₆	—	4	2	no	—
925	M₁₆	—	4	2	no	—
926	M₁₆	—	4	2	no	—
927	C₂×C₈	—	4	2	no	—
928	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
929	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
930	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₇	1	2	yes	—
932	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₇	1	2	yes	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
966	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
967	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
968	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
969	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
970	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
990	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
991	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
992	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
993	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1006	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1008	C₄²	C₂⁴×C₇	1	2	yes	—
1009	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1010	C₂×C₇	—	4	1	no	—
1011	C₂×C₇	—	4	2	no	—
1012	C₂×C₇	—	8	2	no	—
1013	C₂×C₇	#3488	1	1	yes	characteristic
1014	C₂×C₇	C₂×#578	1	1	yes	characteristic
1015	C₂×C₇	#3586	1	1	yes	characteristic
1016	C₂³	—	2	2	no	—
1017	C₂³	C₂²×C₇×D₄	1	2	yes	—
1018	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1019	Q₈	—	2	1	no	—
1020	Q₈	—	2	2	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	2	no	—
1025	Q₈	—	2	1	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	1	no	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	2	1	no	—
1031	Q₈	—	4	2	no	—
1032	Q₈	—	4	4	no	—
1033	Q₈	—	4	2	no	—
1034	Q₈	—	8	1	no	—
1035	Q₈	—	8	2	no	—
1036	Q₈	C₇×H(5,𝔽₂)	1	2	yes	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	2	2	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	8	1	no	—
1043	D₄	—	8	2	no	—
1044	D₄	—	8	2	no	—
1045	D₄	—	8	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	4	1	no	—
1063	C₂×C₄	—	4	4	no	—
1064	C₂×C₄	—	4	2	no	—
1065	C₂×C₄	—	4	2	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	—	8	2	no	—
1069	C₂×C₄	—	8	2	no	—
1070	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1071	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1072	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1073	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1074	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1075	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1076	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1077	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1078	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1079	C₈	—	2	1	no	—
1080	C₈	—	2	2	no	—
1081	C₈	—	2	2	no	—
1082	C₈	—	2	1	no	—
1083	C₈	—	2	1	no	—
1084	C₈	—	2	1	no	—
1085	C₇	#62043	1	1	yes	characteristic, direct product factor, Sylow
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	2	no	—
1095	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1096	C₄	—	2	1	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	C₇×#578	1	2	yes	—
1115	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1116	C₄	C₇×#585	1	1	yes	characteristic
1117	C₂	—	4	1	no	—
1118	C₂	—	4	2	no	—
1119	C₂	—	8	2	no	—
1120	C₂	C₇×#3488	1	1	yes	characteristic
1121	C₂	C₂×C₇×#578	1	1	yes	characteristic
1122	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×#3554	C₂
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
2. C₇×#3523	C₂	semidirect
3. C₇×#3400	C₂	semidirect
4. C₇×#3395	C₂	semidirect
5. C₇×#3374	C₂	semidirect
6. C₇×#3365	C₂	semidirect
7. C₇×#3328	C₂	semidirect
8. C₇×#3327	C₂	semidirect
9. C₇×#3315	C₂	semidirect
10. C₇×#3304	C₂	semidirect
11. C₇×D₄×Q₁₆	C₂	semidirect
12. C₇×#3278	C₂	semidirect
13. C₇×#3276	C₂	semidirect
14. C₇×#3270	C₂	semidirect
15. C₇×#3258	C₂	semidirect
16. C₇×#3255	C₂	semidirect
17. C₇×#3223	C₂	semidirect
18. C₇×#3210	C₂	semidirect
19. C₇×#3121	C₂	semidirect
20. C₇×#3104	C₂	semidirect
21. C₇×#3044	C₂	semidirect
22. C₇×#3037	C₂	semidirect
23. C₇×#2993	C₂	semidirect
135. #62043	C₇	direct (N × H)
317. #3523	C₂×C₇	semidirect
318. #3400	C₂×C₇	semidirect
319. #3395	C₂×C₇	semidirect
320. #3374	C₂×C₇	semidirect
321. #3365	C₂×C₇	semidirect
322. #3328	C₂×C₇	semidirect
323. #3327	C₂×C₇	semidirect
324. #3315	C₂×C₇	semidirect
325. #3304	C₂×C₇	semidirect
326. D₄×Q₁₆	C₂×C₇	semidirect
327. #3278	C₂×C₇	semidirect
328. #3276	C₂×C₇	semidirect
329. #3270	C₂×C₇	semidirect
330. #3258	C₂×C₇	semidirect
331. #3255	C₂×C₇	semidirect
332. #3223	C₂×C₇	semidirect
333. #3210	C₂×C₇	semidirect
334. #3121	C₂×C₇	semidirect
335. #3104	C₂×C₇	semidirect
336. #3044	C₂×C₇	semidirect
337. #3037	C₂×C₇	semidirect
338. #2993	C₂×C₇	semidirect
1085. C₇	#62043	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×#3523	2
C₇×#3400	2
C₇×#3395	2
C₇×#3374	2
C₇×#3365	2
C₇×#3328	2
C₇×#3327	2
C₇×#3315	2
C₇×#3304	2
C₇×D₄×Q₁₆	2
C₇×#3278	2
C₇×#3276	2
C₇×#3270	2
C₇×#3258	2
C₇×#3255	2
C₇×#3223	2
C₇×#3210	2
C₇×#3121	2
C₇×#3104	2
C₇×#3044	2
C₇×#3037	2
C₇×#2993	2
#62043	7

Subgroups — C7×#62043 #13239259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62043 #13239259