Subgroups — C₇×#61872 #13239088

Order 1792.

1722 conjugacy classes of subgroups.

The subgroup lattice has 998 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×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3389	C₂	1	2	yes	maximal, complemented
4	C₇×#3388	C₂	1	2	yes	maximal, complemented
5	C₇×#3384	C₂	1	2	yes	maximal, complemented
6	C₇×#3384	C₂	1	2	yes	maximal, complemented
7	C₇×#3373	C₂	1	2	yes	maximal, complemented
8	C₇×#3370	C₂	1	2	yes	maximal, complemented
9	C₇×#3370	C₂	1	2	yes	maximal, complemented
10	C₇×#3366	C₂	1	2	yes	maximal, complemented
11	C₇×#3244	C₂	1	2	yes	maximal, complemented
12	C₇×#3241	C₂	1	2	yes	maximal, complemented
13	C₇×#3240	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3235	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3122	C₂	1	2	yes	maximal, complemented
16	C₇×#3118	C₂	1	2	yes	maximal, complemented
17	C₇×#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3109	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#562	—	2	2	no	—
21	C₇×#559	C₂²	1	1	yes	characteristic, complemented
22	C₇×#559	C₂²	1	2	yes	complemented
23	C₇×#557	C₂²	1	1	yes	characteristic, complemented
24	C₇×#554	—	2	1	no	—
25	C₇×#554	—	2	2	no	—
26	C₇×#554	C₂²	1	2	yes	—
27	C₇×#554	C₂²	1	2	yes	—
28	C₇×#554	C₂²	1	2	yes	—
29	C₇×#554	C₂²	1	2	yes	complemented
30	C₇×#550	C₂²	1	1	yes	characteristic, complemented
31	C₇×D₄×Q₈	—	2	1	no	—
32	C₇×D₄×Q₈	C₂²	1	2	yes	—
33	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₇×#548	—	2	1	no	—
35	C₇×#547	—	2	1	no	—
36	C₇×#544	C₂²	1	2	yes	—
37	C₇×#543	—	2	1	no	—
38	C₇×#543	—	2	1	no	—
39	C₇×#542	—	2	1	no	—
40	C₇×#542	C₂²	1	2	yes	—
41	C₇×#540	C₂²	1	2	yes	—
42	C₇×#539	—	2	2	no	—
43	C₇×#536	—	2	1	no	—
44	C₇×#533	C₂²	1	1	yes	characteristic
45	C₇×#533	C₂²	1	1	yes	characteristic
46	C₇×#532	C₂²	1	1	yes	characteristic
47	C₇×#529	C₂²	1	1	yes	characteristic
48	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
49	C₇×#518	C₂²	1	2	yes	—
50	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
51	C₇×#501	C₂²	1	2	yes	complemented
52	C₇×#501	C₂²	1	1	yes	characteristic, complemented
53	C₇×#501	C₂²	1	1	yes	characteristic, complemented
54	C₇×#501	C₂²	1	2	yes	complemented
55	C₇×#501	C₂²	1	2	yes	complemented
56	C₇×#499	C₂²	1	2	yes	complemented
57	C₇×#498	C₂²	1	2	yes	complemented
58	C₇×#490	C₂²	1	2	yes	complemented
59	C₇×#490	C₂²	1	2	yes	complemented
60	C₇×#489	C₂²	1	1	yes	characteristic, complemented
61	C₇×#489	C₂²	1	1	yes	characteristic, complemented
62	C₇×#489	C₂²	1	2	yes	complemented
63	C₇×#488	C₂²	1	2	yes	complemented
64	C₇×#486	C₂²	1	2	yes	complemented
65	C₇×#485	C₂²	1	2	yes	—
66	C₇×#483	C₂²	1	1	yes	characteristic
67	C₇×#482	C₂²	1	2	yes	—
68	C₇×#482	C₂²	1	2	yes	—
69	C₇×#482	C₂²	1	2	yes	—
70	C₇×#481	C₂²	1	2	yes	—
71	C₇×#480	C₂²	1	1	yes	characteristic
72	C₇×#479	C₂²	1	2	yes	complemented
73	C₇×#479	C₂²	1	2	yes	complemented
74	C₇×#478	C₂²	1	2	yes	—
75	C₇×#478	C₂²	1	2	yes	—
76	C₇×#478	C₂²	1	2	yes	—
77	C₇×#478	C₂²	1	2	yes	complemented
78	C₇×#478	C₂²	1	2	yes	complemented
79	C₇×#478	C₂²	1	2	yes	complemented
80	C₇×#478	C₂²	1	2	yes	complemented
81	C₇×#476	C₂²	1	2	yes	—
82	C₇×#476	C₂²	1	2	yes	—
83	C₇×#476	C₂²	1	2	yes	complemented
84	C₇×#476	C₂²	1	2	yes	complemented
85	C₇×#476	C₂²	1	2	yes	complemented
86	C₇×#475	C₂²	1	2	yes	complemented
87	C₇×#474	C₂²	1	2	yes	—
88	C₇×#474	C₂²	1	2	yes	complemented
89	C₇×#474	C₂²	1	2	yes	complemented
90	C₇×#463	C₂²	1	2	yes	—
91	C₇×#463	C₂²	1	2	yes	—
92	C₇×#463	C₂²	1	2	yes	—
93	C₇×#459	C₂²	1	2	yes	—
94	C₇×#459	C₂²	1	2	yes	—
95	C₇×#459	C₂²	1	2	yes	—
96	C₇×#450	C₂²	1	1	yes	characteristic
97	C₇×#447	C₂²	1	2	yes	—
98	C₇×#447	C₂²	1	1	yes	characteristic
99	C₇×#446	C₂²	1	2	yes	complemented
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×#442	C₂²	1	2	yes	—
104	C₇×#442	C₂²	1	2	yes	—
105	C₇×#442	C₂²	1	2	yes	—
106	C₇×#442	C₂²	1	2	yes	—
107	C₇×#442	C₂²	1	2	yes	—
108	C₇×#442	C₂²	1	2	yes	—
109	C₇×#440	C₂²	1	2	yes	—
110	C₇×#440	C₂²	1	2	yes	—
111	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
112	C₄×C₇×D₈	C₂²	1	2	yes	—
113	C₄×C₇×D₈	C₂²	1	2	yes	—
114	C₄×C₇×D₈	C₂²	1	2	yes	—
115	C₇×#433	C₂²	1	2	yes	—
116	C₇×#433	C₂²	1	2	yes	—
117	C₇×#432	C₂²	1	1	yes	characteristic
118	C₇×#432	C₂²	1	1	yes	characteristic
119	#61872	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂×C₇×#41	—	2	1	no	—
121	C₂×C₇×#41	—	2	1	no	—
122	C₂²×C₇×Q₈	—	2	2	no	—
123	C₂²×C₇×Q₈	—	2	1	no	—
124	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₇	—	2	1	no	—
126	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
127	C₂×C₇×D₈	C₂³	1	2	yes	—
128	C₂×C₇×D₈	C₂³	1	2	yes	—
129	C₂×C₇×D₈	C₂³	1	2	yes	—
130	C₇×C₄⋊Q₈	—	2	1	no	—
131	C₇×C₄⋊Q₈	—	2	2	no	—
132	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
133	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
134	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
136	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₇×#127	C₂³	1	2	yes	—
141	C₇×#127	C₂³	1	1	yes	characteristic
142	C₇×#126	—	2	2	no	—
143	C₇×#126	—	2	1	no	—
144	C₇×#125	—	2	2	no	—
145	C₇×#125	—	2	2	no	—
146	C₇×#125	D₄	1	2	yes	—
147	C₇×#125	C₂³	1	2	yes	—
148	C₇×#125	C₂³	1	1	yes	characteristic
149	C₇×#125	C₂³	1	2	yes	—
150	C₇×#125	C₂³	1	2	yes	—
151	C₇×#125	C₂³	1	2	yes	—
152	C₇×#124	—	2	1	no	—
153	C₇×#124	—	2	2	no	—
154	C₇×#124	—	2	2	no	—
155	C₇×#124	—	2	1	no	—
156	C₇×#124	C₂³	1	2	yes	—
157	C₇×#124	C₂³	1	1	yes	characteristic
158	C₇×#123	—	2	1	no	—
159	C₇×#123	—	2	2	no	—
160	C₇×#123	—	2	2	no	—
161	C₇×#123	—	2	2	no	—
162	C₇×#123	—	2	2	no	—
163	C₇×#123	—	2	2	no	—
164	C₇×#123	—	2	2	no	—
165	C₇×C₂²⋊Q₈	—	2	2	no	—
166	C₇×C₂²⋊Q₈	—	2	2	no	—
167	C₇×C₂²⋊Q₈	—	2	2	no	—
168	C₇×C₂²⋊Q₈	—	2	2	no	—
169	C₇×C₂²⋊Q₈	—	2	1	no	—
170	C₇×C₂²⋊Q₈	—	2	1	no	—
171	C₇×C₂²⋊Q₈	—	2	2	no	—
172	C₇×C₂²⋊Q₈	—	2	2	no	—
173	C₇×C₂²⋊Q₈	—	2	2	no	—
174	C₇×C₂²⋊Q₈	—	2	2	no	—
175	C₇×C₂²⋊Q₈	—	2	2	no	—
176	C₇×C₂²⋊Q₈	—	2	2	no	—
177	C₇×C₂²⋊Q₈	—	2	2	no	—
178	C₇×C₂²⋊Q₈	—	2	1	no	—
179	C₇×C₂²⋊Q₈	—	2	2	no	—
180	C₇×C₂²⋊Q₈	—	2	2	no	—
181	C₇×C₂²⋊Q₈	—	2	2	no	—
182	C₇×C₂²⋊Q₈	—	2	2	no	—
183	C₇×C₂²⋊Q₈	—	2	2	no	—
184	C₇×C₂²⋊Q₈	—	2	2	no	—
185	C₇×C₂²⋊Q₈	—	2	2	no	—
186	C₇×C₂²⋊Q₈	—	2	2	no	—
187	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
188	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
189	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
190	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
191	C₇×#121	—	2	1	no	—
192	C₇×#121	—	2	2	no	—
193	C₇×#121	—	2	1	no	—
194	C₇×#121	—	2	2	no	—
195	C₇×#121	—	2	2	no	—
196	C₇×#121	C₂³	1	1	yes	characteristic
197	C₇×#121	C₂³	1	2	yes	—
198	C₄×C₇×Q₈	—	2	1	no	—
199	C₄×C₇×Q₈	—	2	1	no	—
200	C₄×C₇×Q₈	—	2	1	no	—
201	C₄×C₇×Q₈	C₂³	1	2	yes	—
202	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
203	C₄×C₇×Q₈	C₂³	1	2	yes	—
204	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
205	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
206	C₄×C₇×D₄	—	2	1	no	—
207	C₄×C₇×D₄	—	2	2	no	—
208	C₄×C₇×D₄	—	2	2	no	—
209	C₄×C₇×D₄	—	2	2	no	—
210	C₄×C₇×D₄	—	2	1	no	—
211	C₄×C₇×D₄	—	2	1	no	—
212	C₄×C₇×D₄	—	2	1	no	—
213	C₄×C₇×D₄	—	2	1	no	—
214	C₄×C₇×D₄	C₂³	1	2	yes	—
215	C₄×C₇×D₄	C₂³	1	2	yes	—
216	C₄×C₇×D₄	C₂³	1	2	yes	—
217	C₄×C₇×D₄	C₂³	1	2	yes	—
218	C₄×C₇×D₄	C₂³	1	2	yes	—
219	C₄×C₇×D₄	C₂³	1	2	yes	—
220	C₄×C₇×D₄	C₂³	1	2	yes	—
221	C₄×C₇×D₄	C₂³	1	2	yes	—
222	C₄×C₇×D₄	C₂³	1	2	yes	—
223	C₄×C₇×D₄	C₂³	1	2	yes	—
224	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
225	C₇×#117	—	2	1	no	—
226	C₇×#117	C₂³	1	2	yes	—
227	C₇×#117	C₂³	1	2	yes	—
228	C₂×C₇×C₄⋊C₄	—	2	2	no	—
229	C₂×C₇×C₄⋊C₄	—	2	2	no	—
230	C₂×C₇×C₄⋊C₄	—	2	2	no	—
231	C₂×C₇×C₄⋊C₄	—	2	2	no	—
232	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
234	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
237	C₇×#107	C₂³	1	2	yes	—
238	C₇×#107	C₂³	1	2	yes	—
239	C₇×#107	C₂³	1	2	yes	—
240	C₇×#107	C₂³	1	2	yes	—
241	C₇×#107	C₂³	1	2	yes	—
242	C₇×#106	C₂³	1	2	yes	—
243	C₇×#106	C₂³	1	2	yes	—
244	C₇×#106	C₂³	1	2	yes	—
245	C₇×#106	C₂³	1	2	yes	—
246	C₇×#106	C₂³	1	2	yes	—
247	C₇×#106	C₂³	1	2	yes	—
248	C₇×#106	C₂³	1	2	yes	—
249	C₇×C₄⋊C₈	C₂³	1	2	yes	—
250	C₇×C₄⋊C₈	C₂³	1	2	yes	—
251	C₇×C₄⋊C₈	C₂³	1	2	yes	—
252	C₇×C₄⋊C₈	C₂³	1	2	yes	—
253	C₇×C₄⋊C₈	C₂³	1	2	yes	—
254	C₇×C₄⋊C₈	C₂³	1	2	yes	—
255	C₇×#103	C₂³	1	2	yes	—
256	C₇×#103	C₂³	1	2	yes	—
257	C₇×#103	C₂³	1	2	yes	—
258	C₇×#102	C₂³	1	2	yes	—
259	C₇×#102	C₂³	1	2	yes	—
260	C₇×#102	C₂³	1	2	yes	—
261	C₇×#102	C₂³	1	2	yes	—
262	C₇×#102	C₂³	1	2	yes	—
263	C₇×#102	C₂³	1	2	yes	—
264	C₇×#102	C₂³	1	2	yes	—
265	C₇×#102	C₂³	1	2	yes	—
266	C₇×#102	C₂³	1	2	yes	—
267	C₇×#102	C₂³	1	2	yes	—
268	C₇×#102	C₂³	1	2	yes	—
269	C₇×#102	C₂³	1	2	yes	—
270	C₇×#102	C₂³	1	2	yes	—
271	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₇×#97	C₂³	1	1	yes	characteristic
275	C₇×#97	C₂³	1	1	yes	characteristic
276	C₇×#97	C₂³	1	2	yes	—
277	C₇×#97	C₂³	1	2	yes	—
278	C₇×#97	C₂³	1	2	yes	—
279	C₄×C₇×C₈	C₂³	1	2	yes	—
280	C₄×C₇×C₈	C₂³	1	2	yes	—
281	#3554	C₂×C₇	1	1	yes	characteristic, complemented
282	#3501	C₂×C₇	1	1	yes	characteristic, complemented
283	#3389	C₂×C₇	1	2	yes	complemented
284	#3388	C₂×C₇	1	2	yes	complemented
285	#3384	C₂×C₇	1	2	yes	complemented
286	#3384	C₂×C₇	1	2	yes	complemented
287	#3373	C₂×C₇	1	2	yes	complemented
288	#3370	C₂×C₇	1	2	yes	complemented
289	#3370	C₂×C₇	1	2	yes	complemented
290	#3366	C₂×C₇	1	2	yes	complemented
291	#3244	C₂×C₇	1	2	yes	complemented
292	#3241	C₂×C₇	1	2	yes	complemented
293	#3240	C₂×C₇	1	1	yes	characteristic, complemented
294	#3235	C₂×C₇	1	1	yes	characteristic, complemented
295	#3122	C₂×C₇	1	2	yes	complemented
296	#3118	C₂×C₇	1	2	yes	complemented
297	#3114	C₂×C₇	1	1	yes	characteristic, complemented
298	#3109	C₂×C₇	1	1	yes	characteristic, complemented
299	#2987	C₂×C₇	1	1	yes	characteristic, complemented
300	C₂⁴×C₇	—	2	1	no	—
301	C₇×#41	—	8	2	no	—
302	C₇×#41	—	8	2	no	—
303	C₂×C₇×Q₈	—	2	1	no	—
304	C₂×C₇×Q₈	—	2	1	no	—
305	C₂×C₇×Q₈	—	2	1	no	—
306	C₂×C₇×Q₈	—	2	2	no	—
307	C₂×C₇×Q₈	—	2	2	no	—
308	C₂×C₇×Q₈	—	2	2	no	—
309	C₂×C₇×Q₈	—	8	4	no	—
310	C₂×C₇×Q₈	—	8	2	no	—
311	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
312	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
313	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
314	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
315	C₂×C₇×D₄	—	2	4	no	—
316	C₂×C₇×D₄	—	2	1	no	—
317	C₂×C₇×D₄	—	2	2	no	—
318	C₂×C₇×D₄	—	2	1	no	—
319	C₂×C₇×D₄	—	2	1	no	—
320	C₂×C₇×D₄	—	2	1	no	—
321	C₂×C₇×D₄	—	2	2	no	—
322	C₂×C₇×D₄	—	2	2	no	—
323	C₂×C₇×D₄	C₂⁴	1	2	yes	—
324	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
325	C₂×C₇×D₄	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₇	—	2	1	no	—
327	C₂²×C₄×C₇	—	2	2	no	—
328	C₂²×C₄×C₇	—	2	1	no	—
329	C₂²×C₄×C₇	—	2	2	no	—
330	C₂²×C₄×C₇	—	2	2	no	—
331	C₂²×C₄×C₇	—	2	2	no	—
332	C₂²×C₄×C₇	—	2	2	no	—
333	C₂²×C₄×C₇	—	2	2	no	—
334	C₂²×C₄×C₇	—	2	2	no	—
335	C₂²×C₄×C₇	—	2	2	no	—
336	C₂²×C₄×C₇	—	2	2	no	—
337	C₂²×C₄×C₇	—	2	2	no	—
338	C₂²×C₄×C₇	—	8	2	no	—
339	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
342	C₇×SD₁₆	—	2	4	no	—
343	C₇×D₈	—	2	4	no	—
344	C₇×D₈	—	2	4	no	—
345	C₇×D₈	—	2	4	no	—
346	C₂×C₇×C₈	C₂⁴	1	2	yes	—
347	C₂×C₇×C₈	C₂⁴	1	2	yes	—
348	C₂×C₇×C₈	C₂⁴	1	2	yes	—
349	C₂×C₇×C₈	C₂⁴	1	2	yes	—
350	C₇×C₄⋊C₄	—	2	1	no	—
351	C₇×C₄⋊C₄	—	2	2	no	—
352	C₇×C₄⋊C₄	—	2	1	no	—
353	C₇×C₄⋊C₄	—	2	2	no	—
354	C₇×C₄⋊C₄	—	2	2	no	—
355	C₇×C₄⋊C₄	—	2	2	no	—
356	C₇×C₄⋊C₄	—	2	2	no	—
357	C₇×C₄⋊C₄	—	2	2	no	—
358	C₇×C₄⋊C₄	—	2	2	no	—
359	C₇×C₄⋊C₄	—	2	2	no	—
360	C₇×C₄⋊C₄	—	2	2	no	—
361	C₇×C₄⋊C₄	—	2	1	no	—
362	C₇×C₄⋊C₄	—	2	1	no	—
363	C₇×C₄⋊C₄	—	2	1	no	—
364	C₇×C₄⋊C₄	—	2	1	no	—
365	C₇×C₄⋊C₄	—	2	2	no	—
366	C₇×C₄⋊C₄	—	2	2	no	—
367	C₇×C₄⋊C₄	—	2	1	no	—
368	C₇×C₄⋊C₄	—	2	2	no	—
369	C₇×C₄⋊C₄	—	2	1	no	—
370	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
371	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
372	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
373	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
374	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
375	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
376	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
377	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
378	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
379	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
380	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
381	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
382	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
383	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
384	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
385	C₇×C₂²⋊C₄	—	2	2	no	—
386	C₇×C₂²⋊C₄	—	2	1	no	—
387	C₇×C₂²⋊C₄	—	2	2	no	—
388	C₇×C₂²⋊C₄	—	2	2	no	—
389	C₇×C₂²⋊C₄	—	2	2	no	—
390	C₇×C₂²⋊C₄	—	2	2	no	—
391	C₇×C₂²⋊C₄	—	2	2	no	—
392	C₇×C₂²⋊C₄	—	2	2	no	—
393	C₇×C₂²⋊C₄	—	2	1	no	—
394	C₇×C₂²⋊C₄	—	2	1	no	—
395	C₇×C₂²⋊C₄	—	2	1	no	—
396	C₇×C₂²⋊C₄	—	2	2	no	—
397	C₇×C₂²⋊C₄	—	2	2	no	—
398	C₇×C₂²⋊C₄	—	2	2	no	—
399	C₇×C₂²⋊C₄	—	2	1	no	—
400	C₇×C₂²⋊C₄	—	2	2	no	—
401	C₇×C₂²⋊C₄	—	2	2	no	—
402	C₇×C₂²⋊C₄	—	2	2	no	—
403	C₇×C₂²⋊C₄	—	2	2	no	—
404	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
405	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
406	C₄²×C₇	—	2	1	no	—
407	C₄²×C₇	—	2	2	no	—
408	C₄²×C₇	—	2	2	no	—
409	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
410	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
411	C₄²×C₇	C₂⁴	1	2	yes	—
412	C₄²×C₇	C₂⁴	1	2	yes	—
413	C₄²×C₇	C₂⁴	1	1	yes	characteristic
414	C₄²×C₇	C₂⁴	1	1	yes	characteristic
415	#562	—	2	2	no	—
416	#559	C₂²×C₇	1	1	yes	characteristic, complemented
417	#559	C₂²×C₇	1	2	yes	complemented
418	#557	C₂²×C₇	1	1	yes	characteristic, complemented
419	#554	—	2	1	no	—
420	#554	—	2	2	no	—
421	#554	C₂²×C₇	1	2	yes	—
422	#554	C₂²×C₇	1	2	yes	—
423	#554	C₂²×C₇	1	2	yes	—
424	#554	C₂²×C₇	1	2	yes	complemented
425	#550	C₂²×C₇	1	1	yes	characteristic, complemented
426	D₄×Q₈	—	2	1	no	—
427	D₄×Q₈	C₂²×C₇	1	2	yes	—
428	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
429	#548	—	2	1	no	—
430	#547	—	2	1	no	—
431	#544	C₂²×C₇	1	2	yes	—
432	#543	—	2	1	no	—
433	#543	—	2	1	no	—
434	#542	—	2	1	no	—
435	#542	C₂²×C₇	1	2	yes	—
436	#540	C₂²×C₇	1	2	yes	—
437	#539	—	2	2	no	—
438	#536	—	2	1	no	—
439	#533	C₂²×C₇	1	1	yes	characteristic
440	#533	C₂²×C₇	1	1	yes	characteristic
441	#532	C₂²×C₇	1	1	yes	characteristic
442	#529	C₂²×C₇	1	1	yes	characteristic
443	C₂×C₂²⋊Q₈	—	2	2	no	—
444	#518	C₂²×C₇	1	2	yes	—
445	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
446	#501	C₂²×C₇	1	1	yes	characteristic, complemented
447	#501	C₂²×C₇	1	2	yes	complemented
448	#501	C₂²×C₇	1	2	yes	complemented
449	#501	C₂²×C₇	1	2	yes	complemented
450	#501	C₂²×C₇	1	1	yes	characteristic, complemented
451	#499	C₂²×C₇	1	2	yes	complemented
452	#498	C₂²×C₇	1	2	yes	complemented
453	#490	C₂²×C₇	1	2	yes	complemented
454	#490	C₂²×C₇	1	2	yes	complemented
455	#489	C₂²×C₇	1	1	yes	characteristic, complemented
456	#489	C₂²×C₇	1	2	yes	complemented
457	#489	C₂²×C₇	1	1	yes	characteristic, complemented
458	#488	C₂²×C₇	1	2	yes	complemented
459	#486	C₂²×C₇	1	2	yes	complemented
460	#485	C₂²×C₇	1	2	yes	—
461	#483	C₂²×C₇	1	1	yes	characteristic
462	#482	C₂²×C₇	1	2	yes	—
463	#482	C₂²×C₇	1	2	yes	—
464	#482	C₂²×C₇	1	2	yes	—
465	#481	C₂²×C₇	1	2	yes	—
466	#480	C₂²×C₇	1	1	yes	characteristic
467	#479	C₂²×C₇	1	2	yes	complemented
468	#479	C₂²×C₇	1	2	yes	complemented
469	#478	C₂²×C₇	1	2	yes	—
470	#478	C₂²×C₇	1	2	yes	—
471	#478	C₂²×C₇	1	2	yes	—
472	#478	C₂²×C₇	1	2	yes	complemented
473	#478	C₂²×C₇	1	2	yes	complemented
474	#478	C₂²×C₇	1	2	yes	complemented
475	#478	C₂²×C₇	1	2	yes	complemented
476	#476	C₂²×C₇	1	2	yes	—
477	#476	C₂²×C₇	1	2	yes	—
478	#476	C₂²×C₇	1	2	yes	complemented
479	#476	C₂²×C₇	1	2	yes	complemented
480	#476	C₂²×C₇	1	2	yes	complemented
481	#475	C₂²×C₇	1	2	yes	complemented
482	#474	C₂²×C₇	1	2	yes	—
483	#474	C₂²×C₇	1	2	yes	complemented
484	#474	C₂²×C₇	1	2	yes	complemented
485	#463	C₂²×C₇	1	2	yes	—
486	#463	C₂²×C₇	1	2	yes	—
487	#463	C₂²×C₇	1	2	yes	—
488	#459	C₂²×C₇	1	2	yes	—
489	#459	C₂²×C₇	1	2	yes	—
490	#459	C₂²×C₇	1	2	yes	—
491	#450	C₂²×C₇	1	1	yes	characteristic
492	#447	C₂²×C₇	1	2	yes	—
493	#447	C₂²×C₇	1	1	yes	characteristic
494	#446	C₂²×C₇	1	2	yes	complemented
495	#446	C₂²×C₇	1	2	yes	complemented
496	#446	C₂²×C₇	1	2	yes	complemented
497	#446	C₂²×C₇	1	2	yes	complemented
498	#442	C₂²×C₇	1	2	yes	—
499	#442	C₂²×C₇	1	2	yes	—
500	#442	C₂²×C₇	1	2	yes	—
501	#442	C₂²×C₇	1	2	yes	—
502	#442	C₂²×C₇	1	2	yes	—
503	#442	C₂²×C₇	1	2	yes	—
504	#440	C₂²×C₇	1	2	yes	—
505	#440	C₂²×C₇	1	2	yes	—
506	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
507	C₄×D₈	C₂²×C₇	1	2	yes	—
508	C₄×D₈	C₂²×C₇	1	2	yes	—
509	C₄×D₈	C₂²×C₇	1	2	yes	—
510	#433	C₂²×C₇	1	2	yes	—
511	#433	C₂²×C₇	1	2	yes	—
512	#432	C₂²×C₇	1	1	yes	characteristic
513	#432	C₂²×C₇	1	1	yes	characteristic
514	C₂³×C₇	—	2	4	no	—
515	C₂³×C₇	—	2	2	no	—
516	C₂³×C₇	—	2	1	no	—
517	C₂³×C₇	—	2	2	no	—
518	C₂³×C₇	—	8	1	no	—
519	C₂³×C₇	—	8	1	no	—
520	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
521	C₇×Q₈	—	2	2	no	—
522	C₇×Q₈	—	4	2	no	—
523	C₇×Q₈	—	4	1	no	—
524	C₇×Q₈	—	4	1	no	—
525	C₇×Q₈	—	4	2	no	—
526	C₇×Q₈	—	4	2	no	—
527	C₇×Q₈	—	8	1	no	—
528	C₇×Q₈	—	8	2	no	—
529	C₇×Q₈	—	8	2	no	—
530	C₇×Q₈	—	8	2	no	—
531	C₇×D₄	—	2	4	no	—
532	C₇×D₄	—	2	2	no	—
533	C₇×D₄	—	2	2	no	—
534	C₇×D₄	—	2	2	no	—
535	C₇×D₄	—	2	2	no	—
536	C₇×D₄	—	4	2	no	—
537	C₇×D₄	—	8	1	no	—
538	C₇×D₄	—	8	2	no	—
539	C₇×D₄	—	8	2	no	—
540	C₇×D₄	—	8	1	no	—
541	C₇×D₄	—	8	2	no	—
542	C₇×D₄	2₋¹⁺⁴	1	4	yes	—
543	C₂×C₄×C₇	—	2	2	no	—
544	C₂×C₄×C₇	—	2	1	no	—
545	C₂×C₄×C₇	—	2	1	no	—
546	C₂×C₄×C₇	—	2	2	no	—
547	C₂×C₄×C₇	—	2	2	no	—
548	C₂×C₄×C₇	—	2	2	no	—
549	C₂×C₄×C₇	—	2	1	no	—
550	C₂×C₄×C₇	—	2	2	no	—
551	C₂×C₄×C₇	—	4	1	no	—
552	C₂×C₄×C₇	—	4	1	no	—
553	C₂×C₄×C₇	—	4	4	no	—
554	C₂×C₄×C₇	—	4	2	no	—
555	C₂×C₄×C₇	—	8	2	no	—
556	C₂×C₄×C₇	—	8	2	no	—
557	C₂×C₄×C₇	—	8	2	no	—
558	C₂×C₄×C₇	—	8	2	no	—
559	C₂×C₄×C₇	—	8	2	no	—
560	C₂×C₄×C₇	—	8	2	no	—
561	C₂×C₄×C₇	—	8	2	no	—
562	C₂×C₄×C₇	—	8	2	no	—
563	C₂×C₄×C₇	—	8	2	no	—
564	C₂×C₄×C₇	—	8	1	no	—
565	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
568	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
572	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
573	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
574	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
575	C₇×C₈	—	2	2	no	—
576	C₇×C₈	—	2	2	no	—
577	C₇×C₈	—	2	2	no	—
578	C₇×C₈	—	2	2	no	—
579	C₂×#41	—	2	1	no	—
580	C₂×#41	—	2	1	no	—
581	C₂²×Q₈	—	2	2	no	—
582	C₂²×Q₈	—	2	1	no	—
583	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
584	C₂³×C₄	—	2	1	no	—
585	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
586	C₂×D₈	C₂³×C₇	1	2	yes	—
587	C₂×D₈	C₂³×C₇	1	2	yes	—
588	C₂×D₈	C₂³×C₇	1	2	yes	—
589	C₄⋊Q₈	—	2	1	no	—
590	C₄⋊Q₈	—	2	2	no	—
591	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
592	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
593	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
594	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
595	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
596	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
597	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
598	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
599	#127	C₂³×C₇	1	1	yes	characteristic
600	#127	C₂³×C₇	1	2	yes	—
601	#126	—	2	2	no	—
602	#126	—	2	1	no	—
603	#125	—	2	2	no	—
604	#125	—	2	2	no	—
605	#125	C₇×D₄	1	2	yes	—
606	#125	C₂³×C₇	1	1	yes	characteristic
607	#125	C₂³×C₇	1	2	yes	—
608	#125	C₂³×C₇	1	2	yes	—
609	#125	C₂³×C₇	1	2	yes	—
610	#125	C₂³×C₇	1	2	yes	—
611	#124	—	2	1	no	—
612	#124	—	2	2	no	—
613	#124	—	2	2	no	—
614	#124	—	2	1	no	—
615	#124	C₂³×C₇	1	1	yes	characteristic
616	#124	C₂³×C₇	1	2	yes	—
617	#123	—	2	1	no	—
618	#123	—	2	2	no	—
619	#123	—	2	2	no	—
620	#123	—	2	2	no	—
621	#123	—	2	2	no	—
622	#123	—	2	2	no	—
623	#123	—	2	2	no	—
624	C₂²⋊Q₈	—	2	2	no	—
625	C₂²⋊Q₈	—	2	2	no	—
626	C₂²⋊Q₈	—	2	2	no	—
627	C₂²⋊Q₈	—	2	2	no	—
628	C₂²⋊Q₈	—	2	1	no	—
629	C₂²⋊Q₈	—	2	1	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	—	2	1	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	—	2	2	no	—
646	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
647	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
648	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
649	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
650	#121	—	2	1	no	—
651	#121	—	2	2	no	—
652	#121	—	2	1	no	—
653	#121	—	2	2	no	—
654	#121	—	2	2	no	—
655	#121	C₂³×C₇	1	1	yes	characteristic
656	#121	C₂³×C₇	1	2	yes	—
657	C₄×Q₈	—	2	1	no	—
658	C₄×Q₈	—	2	1	no	—
659	C₄×Q₈	—	2	1	no	—
660	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
661	C₄×Q₈	C₂³×C₇	1	2	yes	—
662	C₄×Q₈	C₂³×C₇	1	2	yes	—
663	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
664	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
665	C₄×D₄	—	2	1	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	1	no	—
670	C₄×D₄	—	2	1	no	—
671	C₄×D₄	—	2	1	no	—
672	C₄×D₄	—	2	1	no	—
673	C₄×D₄	C₂³×C₇	1	2	yes	—
674	C₄×D₄	C₂³×C₇	1	2	yes	—
675	C₄×D₄	C₂³×C₇	1	2	yes	—
676	C₄×D₄	C₂³×C₇	1	2	yes	—
677	C₄×D₄	C₂³×C₇	1	2	yes	—
678	C₄×D₄	C₂³×C₇	1	2	yes	—
679	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
680	C₄×D₄	C₂³×C₇	1	2	yes	—
681	C₄×D₄	C₂³×C₇	1	2	yes	—
682	C₄×D₄	C₂³×C₇	1	2	yes	—
683	C₄×D₄	C₂³×C₇	1	2	yes	—
684	#117	—	2	1	no	—
685	#117	C₂³×C₇	1	2	yes	—
686	#117	C₂³×C₇	1	2	yes	—
687	C₂×C₄⋊C₄	—	2	2	no	—
688	C₂×C₄⋊C₄	—	2	2	no	—
689	C₂×C₄⋊C₄	—	2	2	no	—
690	C₂×C₄⋊C₄	—	2	2	no	—
691	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
692	C₂×C₂²⋊C₄	—	2	1	no	—
693	C₂×C₂²⋊C₄	—	2	2	no	—
694	C₂×C₂²⋊C₄	—	2	2	no	—
695	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
696	#107	C₂³×C₇	1	2	yes	—
697	#107	C₂³×C₇	1	2	yes	—
698	#107	C₂³×C₇	1	2	yes	—
699	#107	C₂³×C₇	1	2	yes	—
700	#107	C₂³×C₇	1	2	yes	—
701	#106	C₂³×C₇	1	2	yes	—
702	#106	C₂³×C₇	1	2	yes	—
703	#106	C₂³×C₇	1	2	yes	—
704	#106	C₂³×C₇	1	2	yes	—
705	#106	C₂³×C₇	1	2	yes	—
706	#106	C₂³×C₇	1	2	yes	—
707	#106	C₂³×C₇	1	2	yes	—
708	C₄⋊C₈	C₂³×C₇	1	2	yes	—
709	C₄⋊C₈	C₂³×C₇	1	2	yes	—
710	C₄⋊C₈	C₂³×C₇	1	2	yes	—
711	C₄⋊C₈	C₂³×C₇	1	2	yes	—
712	C₄⋊C₈	C₂³×C₇	1	2	yes	—
713	C₄⋊C₈	C₂³×C₇	1	2	yes	—
714	#103	C₂³×C₇	1	2	yes	—
715	#103	C₂³×C₇	1	2	yes	—
716	#103	C₂³×C₇	1	2	yes	—
717	#102	C₂³×C₇	1	2	yes	—
718	#102	C₂³×C₇	1	2	yes	—
719	#102	C₂³×C₇	1	2	yes	—
720	#102	C₂³×C₇	1	2	yes	—
721	#102	C₂³×C₇	1	2	yes	—
722	#102	C₂³×C₇	1	2	yes	—
723	#102	C₂³×C₇	1	2	yes	—
724	#102	C₂³×C₇	1	2	yes	—
725	#102	C₂³×C₇	1	2	yes	—
726	#102	C₂³×C₇	1	2	yes	—
727	#102	C₂³×C₇	1	2	yes	—
728	#102	C₂³×C₇	1	2	yes	—
729	#102	C₂³×C₇	1	2	yes	—
730	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
731	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
732	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
733	#97	C₂³×C₇	1	2	yes	—
734	#97	C₂³×C₇	1	1	yes	characteristic
735	#97	C₂³×C₇	1	1	yes	characteristic
736	#97	C₂³×C₇	1	2	yes	—
737	#97	C₂³×C₇	1	2	yes	—
738	C₄×C₈	C₂³×C₇	1	2	yes	—
739	C₄×C₈	C₂³×C₇	1	2	yes	—
740	C₂²×C₇	—	2	1	no	—
741	C₂²×C₇	—	2	1	no	—
742	C₂²×C₇	—	2	1	no	—
743	C₂²×C₇	—	2	4	no	—
744	C₂²×C₇	—	4	2	no	—
745	C₂²×C₇	—	4	2	no	—
746	C₂²×C₇	—	4	1	no	—
747	C₂²×C₇	—	4	2	no	—
748	C₂²×C₇	—	4	2	no	—
749	C₂²×C₇	—	4	1	no	—
750	C₂²×C₇	—	4	1	no	—
751	C₂²×C₇	—	4	2	no	—
752	C₂²×C₇	—	8	4	no	—
753	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
754	C₄×C₇	—	2	1	no	—
755	C₄×C₇	—	2	1	no	—
756	C₄×C₇	—	2	1	no	—
757	C₄×C₇	—	2	1	no	—
758	C₄×C₇	—	2	2	no	—
759	C₄×C₇	—	2	2	no	—
760	C₄×C₇	—	2	2	no	—
761	C₄×C₇	—	2	2	no	—
762	C₄×C₇	—	2	1	no	—
763	C₄×C₇	—	4	1	no	—
764	C₄×C₇	—	4	2	no	—
765	C₄×C₇	—	4	1	no	—
766	C₄×C₇	—	4	2	no	—
767	C₄×C₇	—	4	2	no	—
768	C₄×C₇	—	4	2	no	—
769	C₄×C₇	—	4	1	no	—
770	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
771	C₂⁴	—	2	1	no	—
772	#41	—	8	2	no	—
773	#41	—	8	2	no	—
774	C₂×Q₈	—	2	1	no	—
775	C₂×Q₈	—	2	1	no	—
776	C₂×Q₈	—	2	1	no	—
777	C₂×Q₈	—	2	2	no	—
778	C₂×Q₈	—	2	2	no	—
779	C₂×Q₈	—	2	2	no	—
780	C₂×Q₈	—	8	4	no	—
781	C₂×Q₈	—	8	2	no	—
782	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
783	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
784	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
785	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
786	C₂×D₄	—	2	4	no	—
787	C₂×D₄	—	2	1	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	1	no	—
790	C₂×D₄	—	2	1	no	—
791	C₂×D₄	—	2	1	no	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	C₂⁴×C₇	1	2	yes	—
795	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
796	C₂×D₄	C₂⁴×C₇	1	2	yes	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	1	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	8	2	no	—
810	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
811	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
813	SD₁₆	—	2	4	no	—
814	D₈	—	2	4	no	—
815	D₈	—	2	4	no	—
816	D₈	—	2	4	no	—
817	C₂×C₈	C₂⁴×C₇	1	2	yes	—
818	C₂×C₈	C₂⁴×C₇	1	2	yes	—
819	C₂×C₈	C₂⁴×C₇	1	2	yes	—
820	C₂×C₈	C₂⁴×C₇	1	2	yes	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	1	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	1	no	—
833	C₄⋊C₄	—	2	1	no	—
834	C₄⋊C₄	—	2	1	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	1	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	1	no	—
841	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
842	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
843	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
844	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
845	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
846	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
847	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
848	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
849	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
850	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
851	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
852	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
853	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
854	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
855	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	1	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	1	no	—
865	C₂²⋊C₄	—	2	1	no	—
866	C₂²⋊C₄	—	2	1	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	1	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
876	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
877	C₄²	—	2	1	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
881	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
882	C₄²	C₂⁴×C₇	1	2	yes	—
883	C₄²	C₂⁴×C₇	1	2	yes	—
884	C₄²	C₂⁴×C₇	1	1	yes	characteristic
885	C₄²	C₂⁴×C₇	1	1	yes	characteristic
886	C₂×C₇	—	4	1	no	—
887	C₂×C₇	—	4	4	no	—
888	C₂×C₇	—	8	1	no	—
889	C₂×C₇	—	8	2	no	—
890	C₂×C₇	#3486	1	1	yes	characteristic
891	C₂×C₇	#3585	1	1	yes	characteristic
892	C₂×C₇	#3585	1	1	yes	characteristic
893	C₂³	—	2	4	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	8	1	no	—
898	C₂³	—	8	1	no	—
899	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
900	Q₈	—	2	2	no	—
901	Q₈	—	4	2	no	—
902	Q₈	—	4	1	no	—
903	Q₈	—	4	1	no	—
904	Q₈	—	4	2	no	—
905	Q₈	—	4	2	no	—
906	Q₈	—	8	1	no	—
907	Q₈	—	8	2	no	—
908	Q₈	—	8	2	no	—
909	Q₈	—	8	2	no	—
910	D₄	—	2	4	no	—
911	D₄	—	2	2	no	—
912	D₄	—	2	2	no	—
913	D₄	—	2	2	no	—
914	D₄	—	2	2	no	—
915	D₄	—	4	2	no	—
916	D₄	—	8	1	no	—
917	D₄	—	8	2	no	—
918	D₄	—	8	2	no	—
919	D₄	—	8	1	no	—
920	D₄	—	8	2	no	—
921	D₄	C₇×2₋¹⁺⁴	1	4	yes	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	4	1	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	4	no	—
933	C₂×C₄	—	4	2	no	—
934	C₂×C₄	—	8	2	no	—
935	C₂×C₄	—	8	2	no	—
936	C₂×C₄	—	8	2	no	—
937	C₂×C₄	—	8	2	no	—
938	C₂×C₄	—	8	2	no	—
939	C₂×C₄	—	8	2	no	—
940	C₂×C₄	—	8	2	no	—
941	C₂×C₄	—	8	2	no	—
942	C₂×C₄	—	8	2	no	—
943	C₂×C₄	—	8	1	no	—
944	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
945	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
946	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
947	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
948	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
949	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
950	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
951	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
952	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
953	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
954	C₈	—	2	2	no	—
955	C₈	—	2	2	no	—
956	C₈	—	2	2	no	—
957	C₈	—	2	2	no	—
958	C₇	#61872	1	1	yes	characteristic, direct product factor, Sylow
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	4	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	1	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	8	4	no	—
972	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
973	C₄	—	2	1	no	—
974	C₄	—	2	1	no	—
975	C₄	—	2	1	no	—
976	C₄	—	2	1	no	—
977	C₄	—	2	2	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	2	no	—
980	C₄	—	2	2	no	—
981	C₄	—	2	1	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	1	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	1	no	—
989	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
990	C₂	—	4	1	no	—
991	C₂	—	4	4	no	—
992	C₂	—	8	1	no	—
993	C₂	—	8	2	no	—
994	C₂	C₇×#3486	1	1	yes	characteristic
995	C₂	C₇×#3585	1	1	yes	characteristic
996	C₂	C₇×#3585	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×#3501	C₂	semidirect
3. C₇×#3389	C₂	semidirect
4. C₇×#3388	C₂	semidirect
5. C₇×#3384	C₂	semidirect
6. C₇×#3384	C₂	semidirect
7. C₇×#3373	C₂	semidirect
8. C₇×#3370	C₂	semidirect
9. C₇×#3370	C₂	semidirect
10. C₇×#3366	C₂	semidirect
11. C₇×#3244	C₂	semidirect
12. C₇×#3241	C₂	semidirect
13. C₇×#3240	C₂	semidirect
14. C₇×#3235	C₂	semidirect
15. C₇×#3122	C₂	semidirect
16. C₇×#3118	C₂	semidirect
17. C₇×#3114	C₂	semidirect
18. C₇×#3109	C₂	semidirect
19. C₇×#2987	C₂	semidirect
21. C₇×#559	C₂²	semidirect
22. C₇×#559	C₂²	semidirect
23. C₇×#557	C₂²	semidirect
29. C₇×#554	C₂²	semidirect
30. C₇×#550	C₂²	semidirect
33. C₇×D₄×Q₈	C₂²	semidirect
51. C₇×#501	C₂²	semidirect
52. C₇×#501	C₂²	semidirect
53. C₇×#501	C₂²	semidirect
54. C₇×#501	C₂²	semidirect
55. C₇×#501	C₂²	semidirect
56. C₇×#499	C₂²	semidirect
57. C₇×#498	C₂²	semidirect
58. C₇×#490	C₂²	semidirect
59. C₇×#490	C₂²	semidirect
60. C₇×#489	C₂²	semidirect
61. C₇×#489	C₂²	semidirect
62. C₇×#489	C₂²	semidirect
63. C₇×#488	C₂²	semidirect
64. C₇×#486	C₂²	semidirect
72. C₇×#479	C₂²	semidirect
73. C₇×#479	C₂²	semidirect
77. C₇×#478	C₂²	semidirect
78. C₇×#478	C₂²	semidirect
79. C₇×#478	C₂²	semidirect
80. C₇×#478	C₂²	semidirect
83. C₇×#476	C₂²	semidirect
84. C₇×#476	C₂²	semidirect
85. C₇×#476	C₂²	semidirect
86. C₇×#475	C₂²	semidirect
88. C₇×#474	C₂²	semidirect
89. C₇×#474	C₂²	semidirect
99. C₇×#446	C₂²	semidirect
100. C₇×#446	C₂²	semidirect
101. C₇×#446	C₂²	semidirect
102. C₇×#446	C₂²	semidirect
119. #61872	C₇	direct (N × H)
281. #3554	C₂×C₇	semidirect
282. #3501	C₂×C₇	semidirect
283. #3389	C₂×C₇	semidirect
284. #3388	C₂×C₇	semidirect
285. #3384	C₂×C₇	semidirect
286. #3384	C₂×C₇	semidirect
287. #3373	C₂×C₇	semidirect
288. #3370	C₂×C₇	semidirect
289. #3370	C₂×C₇	semidirect
290. #3366	C₂×C₇	semidirect
291. #3244	C₂×C₇	semidirect
292. #3241	C₂×C₇	semidirect
293. #3240	C₂×C₇	semidirect
294. #3235	C₂×C₇	semidirect
295. #3122	C₂×C₇	semidirect
296. #3118	C₂×C₇	semidirect
297. #3114	C₂×C₇	semidirect
298. #3109	C₂×C₇	semidirect
299. #2987	C₂×C₇	semidirect
416. #559	C₂²×C₇	semidirect
417. #559	C₂²×C₇	semidirect
418. #557	C₂²×C₇	semidirect
424. #554	C₂²×C₇	semidirect
425. #550	C₂²×C₇	semidirect
428. D₄×Q₈	C₂²×C₇	semidirect
446. #501	C₂²×C₇	semidirect
447. #501	C₂²×C₇	semidirect
448. #501	C₂²×C₇	semidirect
449. #501	C₂²×C₇	semidirect
450. #501	C₂²×C₇	semidirect
451. #499	C₂²×C₇	semidirect
452. #498	C₂²×C₇	semidirect
453. #490	C₂²×C₇	semidirect
454. #490	C₂²×C₇	semidirect
455. #489	C₂²×C₇	semidirect
456. #489	C₂²×C₇	semidirect
457. #489	C₂²×C₇	semidirect
458. #488	C₂²×C₇	semidirect
459. #486	C₂²×C₇	semidirect
467. #479	C₂²×C₇	semidirect
468. #479	C₂²×C₇	semidirect
472. #478	C₂²×C₇	semidirect
473. #478	C₂²×C₇	semidirect
474. #478	C₂²×C₇	semidirect
475. #478	C₂²×C₇	semidirect
478. #476	C₂²×C₇	semidirect
479. #476	C₂²×C₇	semidirect
480. #476	C₂²×C₇	semidirect
481. #475	C₂²×C₇	semidirect
483. #474	C₂²×C₇	semidirect
484. #474	C₂²×C₇	semidirect
494. #446	C₂²×C₇	semidirect
495. #446	C₂²×C₇	semidirect
496. #446	C₂²×C₇	semidirect
497. #446	C₂²×C₇	semidirect
958. C₇	#61872	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×#3501	2
C₇×#3389	2
C₇×#3388	2
C₇×#3384	2
C₇×#3373	2
C₇×#3370	2
C₇×#3366	2
C₇×#3244	2
C₇×#3241	2
C₇×#3240	2
C₇×#3235	2
C₇×#3122	2
C₇×#3118	2
C₇×#3114	2
C₇×#3109	2
C₇×#2987	2
#61872	7

Subgroups — C7×#61872 #13239088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61872 #13239088