Subgroups — C₇×#61866 #13239082

Order 1792.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3555	C₂	1	1	yes	maximal, characteristic
2	C₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3390	C₂	1	2	yes	maximal, complemented
4	C₇×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3385	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3383	C₂	1	2	yes	maximal, complemented
7	C₇×Q₈×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3381	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3377	C₂	1	2	yes	maximal, complemented
10	C₇×#3374	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3369	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3364	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3364	C₂	1	2	yes	maximal, complemented
14	C₇×#3363	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3243	C₂	1	2	yes	maximal
16	C₇×#3242	C₂	1	2	yes	maximal, complemented
17	C₇×#3233	C₂	1	1	yes	maximal, characteristic
18	C₇×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3127	C₂	1	2	yes	maximal, complemented
20	C₇×#3121	C₂	1	2	yes	maximal
21	C₇×#3108	C₂	1	1	yes	maximal, characteristic
22	C₇×#3104	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	C₇×#563	—	2	2	no	—
25	C₇×Q₈²	—	2	1	no	—
26	C₇×Q₈²	C₂²	1	1	yes	characteristic
27	C₇×Q₈²	C₂²	1	1	yes	characteristic
28	C₇×Q₈²	C₂²	1	1	yes	characteristic
29	C₇×#557	—	2	1	no	—
30	C₇×#557	—	2	2	no	—
31	C₇×#557	C₂²	1	1	yes	characteristic
32	C₇×#557	C₂²	1	1	yes	characteristic
33	C₇×#557	C₂²	1	2	yes	—
34	C₇×#557	C₂²	1	1	yes	characteristic
35	C₇×#557	C₂²	1	2	yes	—
36	C₇×#557	C₂²	1	2	yes	—
37	C₇×#556	—	2	1	no	—
38	C₇×#556	C₂²	1	1	yes	characteristic
39	C₇×#556	C₂²	1	2	yes	—
40	C₇×#554	C₂²	1	1	yes	characteristic
41	C₇×#552	—	2	1	no	—
42	C₇×#544	—	2	1	no	—
43	C₇×#544	—	2	2	no	—
44	C₇×#544	C₂²	1	2	yes	—
45	C₇×#542	C₂²	1	2	yes	—
46	C₇×#541	—	2	1	no	—
47	C₇×#541	—	2	2	no	—
48	C₇×#541	C₂²	1	2	yes	—
49	C₇×#533	—	2	1	no	—
50	C₇×#533	—	2	1	no	—
51	C₇×#533	C₂²	1	1	yes	characteristic
52	C₇×#533	C₂²	1	1	yes	characteristic
53	C₇×#533	C₂²	1	1	yes	characteristic
54	C₇×#529	C₂²	1	1	yes	characteristic
55	C₇×#519	C₂²	1	2	yes	—
56	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
57	C₇×#501	C₂²	1	2	yes	—
58	C₇×#501	C₂²	1	2	yes	—
59	C₇×#500	C₂²	1	1	yes	characteristic
60	C₇×#500	C₂²	1	2	yes	—
61	C₇×#499	C₂²	1	2	yes	—
62	C₇×#499	C₂²	1	2	yes	—
63	C₇×#498	C₂²	1	1	yes	characteristic
64	C₇×#491	C₂²	1	2	yes	—
65	C₇×#489	C₂²	1	2	yes	—
66	C₇×#488	C₂²	1	2	yes	—
67	C₇×#488	C₂²	1	2	yes	—
68	C₇×#487	C₂²	1	1	yes	characteristic
69	C₇×#487	C₂²	1	1	yes	characteristic
70	C₇×#487	C₂²	1	2	yes	—
71	C₇×#485	C₂²	1	2	yes	—
72	C₇×#485	C₂²	1	2	yes	—
73	C₇×#485	C₂²	1	2	yes	—
74	C₇×#484	C₂²	1	2	yes	—
75	C₇×#483	C₂²	1	1	yes	characteristic
76	C₇×#482	C₂²	1	2	yes	—
77	C₇×#480	C₂²	1	1	yes	characteristic
78	C₇×#479	C₂²	1	2	yes	—
79	C₇×#479	C₂²	1	2	yes	—
80	C₇×#479	C₂²	1	2	yes	—
81	C₇×#479	C₂²	1	2	yes	—
82	C₇×#479	C₂²	1	2	yes	—
83	C₇×#479	C₂²	1	1	yes	characteristic
84	C₇×#479	C₂²	1	1	yes	characteristic
85	C₇×#479	C₂²	1	2	yes	—
86	C₇×#479	C₂²	1	2	yes	—
87	C₇×#478	C₂²	1	2	yes	—
88	C₇×#477	C₂²	1	1	yes	characteristic
89	C₇×#477	C₂²	1	2	yes	—
90	C₇×#477	C₂²	1	2	yes	—
91	C₇×#477	C₂²	1	1	yes	characteristic
92	C₇×#477	C₂²	1	1	yes	characteristic
93	C₇×#477	C₂²	1	2	yes	—
94	C₇×#476	C₂²	1	1	yes	characteristic
95	C₇×#475	C₂²	1	1	yes	characteristic
96	C₇×#475	C₂²	1	2	yes	—
97	C₇×#475	C₂²	1	2	yes	—
98	C₇×#474	C₂²	1	1	yes	characteristic
99	C₇×#474	C₂²	1	2	yes	—
100	C₇×#464	C₂²	1	1	yes	characteristic
101	C₇×#464	C₂²	1	1	yes	characteristic
102	C₇×#464	C₂²	1	2	yes	—
103	C₇×#464	C₂²	1	2	yes	—
104	C₇×#462	C₂²	1	1	yes	characteristic
105	C₇×#462	C₂²	1	1	yes	characteristic
106	C₇×#462	C₂²	1	2	yes	—
107	C₇×#462	C₂²	1	2	yes	—
108	C₇×#451	C₂²	1	2	yes	—
109	C₇×#451	C₂²	1	1	yes	characteristic
110	C₇×#448	C₂²	1	1	yes	characteristic
111	C₇×#446	C₂²	1	1	yes	characteristic
112	C₇×#446	C₂²	1	1	yes	characteristic
113	C₇×#446	C₂²	1	2	yes	—
114	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
115	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
116	C₇×C₈×Q₈	C₂²	1	2	yes	—
117	C₇×#441	C₂²	1	2	yes	—
118	C₇×#441	C₂²	1	2	yes	—
119	C₇×#441	C₂²	1	2	yes	—
120	C₇×#440	C₂²	1	2	yes	—
121	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
122	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
123	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
124	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
125	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
126	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
127	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
128	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
129	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
130	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
131	C₇×#433	C₂²	1	2	yes	—
132	C₇×#433	C₂²	1	2	yes	—
133	C₇×#431	C₂²	1	1	yes	characteristic
134	C₇×#431	C₂²	1	1	yes	characteristic
135	#61866	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
137	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
138	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
139	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
140	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
141	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
142	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
143	C₇×C₄⋊Q₈	—	2	1	no	—
144	C₇×C₄⋊Q₈	—	2	1	no	—
145	C₇×C₄⋊Q₈	—	2	2	no	—
146	C₇×C₄⋊Q₈	—	2	2	no	—
147	C₇×C₄⋊Q₈	—	2	2	no	—
148	C₇×C₄⋊Q₈	—	2	1	no	—
149	C₇×C₄⋊Q₈	—	2	1	no	—
150	C₇×C₄⋊Q₈	—	2	2	no	—
151	C₇×C₄⋊Q₈	—	2	1	no	—
152	C₇×C₄⋊Q₈	—	2	2	no	—
153	C₇×C₄⋊Q₈	—	2	2	no	—
154	C₇×C₄⋊Q₈	—	2	2	no	—
155	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
156	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
157	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₇×#126	—	2	2	no	—
166	C₇×#126	—	2	2	no	—
167	C₇×#126	—	2	2	no	—
168	C₇×#126	—	2	2	no	—
169	C₇×#126	—	2	2	no	—
170	C₇×#126	—	2	2	no	—
171	C₇×#126	—	2	1	no	—
172	C₇×#125	—	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	2	no	—
181	C₇×#125	—	2	2	no	—
182	C₇×#125	—	2	2	no	—
183	C₇×#125	—	2	2	no	—
184	C₇×#125	—	2	2	no	—
185	C₇×#125	—	2	1	no	—
186	C₇×#125	D₄	1	2	yes	—
187	C₇×#125	C₂³	1	2	yes	—
188	C₇×#125	C₂³	1	2	yes	—
189	C₇×#125	C₂³	1	2	yes	—
190	C₇×#125	C₂³	1	1	yes	characteristic
191	C₇×#125	C₂³	1	2	yes	—
192	C₇×#124	—	2	2	no	—
193	C₇×#124	C₂³	1	1	yes	characteristic
194	C₇×#124	C₂³	1	2	yes	—
195	C₇×#123	—	2	1	no	—
196	C₇×#123	—	2	2	no	—
197	C₇×C₂²⋊Q₈	—	2	1	no	—
198	C₇×C₂²⋊Q₈	—	2	1	no	—
199	C₇×C₂²⋊Q₈	—	2	2	no	—
200	C₇×C₂²⋊Q₈	—	2	1	no	—
201	C₇×C₂²⋊Q₈	—	2	1	no	—
202	C₇×C₂²⋊Q₈	—	2	1	no	—
203	C₇×C₂²⋊Q₈	—	2	2	no	—
204	C₇×C₂²⋊Q₈	—	2	2	no	—
205	C₇×C₂²⋊Q₈	—	2	2	no	—
206	C₇×C₂²⋊Q₈	—	2	2	no	—
207	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
210	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₇×#121	C₂³	1	1	yes	characteristic
213	C₄×C₇×Q₈	—	2	1	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	2	no	—
218	C₄×C₇×Q₈	—	2	2	no	—
219	C₄×C₇×Q₈	—	2	2	no	—
220	C₄×C₇×Q₈	—	2	2	no	—
221	C₄×C₇×Q₈	—	2	1	no	—
222	C₄×C₇×Q₈	—	2	1	no	—
223	C₄×C₇×Q₈	—	2	2	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	—	2	1	no	—
228	C₄×C₇×Q₈	—	2	1	no	—
229	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
230	C₄×C₇×Q₈	C₂³	1	2	yes	—
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	1	yes	characteristic
235	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
236	C₄×C₇×Q₈	C₂³	1	2	yes	—
237	C₄×C₇×Q₈	C₂³	1	2	yes	—
238	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
239	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
240	C₄×C₇×Q₈	C₂³	1	2	yes	—
241	C₄×C₇×Q₈	C₂³	1	2	yes	—
242	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
243	C₄×C₇×Q₈	C₂³	1	2	yes	—
244	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
245	C₄×C₇×D₄	—	2	1	no	—
246	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
247	C₄×C₇×D₄	C₂³	1	2	yes	—
248	C₇×#117	—	2	1	no	—
249	C₇×#117	—	2	2	no	—
250	C₇×#117	—	2	1	no	—
251	C₇×#117	—	2	2	no	—
252	C₇×#117	—	2	2	no	—
253	C₇×#117	—	2	1	no	—
254	C₇×#117	C₂³	1	2	yes	—
255	C₇×#117	C₂³	1	2	yes	—
256	C₂×C₇×C₄⋊C₄	—	2	1	no	—
257	C₂×C₇×C₄⋊C₄	—	2	1	no	—
258	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₇	—	2	1	no	—
260	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
261	C₇×#107	C₂³	1	2	yes	—
262	C₇×#107	C₂³	1	2	yes	—
263	C₇×#107	C₂³	1	2	yes	—
264	C₇×#107	C₂³	1	2	yes	—
265	C₇×#107	C₂³	1	2	yes	—
266	C₇×#107	C₂³	1	1	yes	characteristic
267	C₇×#107	C₂³	1	2	yes	—
268	C₇×#107	C₂³	1	1	yes	characteristic
269	C₇×#106	C₂³	1	2	yes	—
270	C₇×#106	C₂³	1	1	yes	characteristic
271	C₇×#106	C₂³	1	2	yes	—
272	C₇×#106	C₂³	1	2	yes	—
273	C₇×#106	C₂³	1	2	yes	—
274	C₇×#106	C₂³	1	1	yes	characteristic
275	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₇×C₄⋊C₈	C₂³	1	2	yes	—
277	C₇×C₄⋊C₈	C₂³	1	2	yes	—
278	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₇×C₄⋊C₈	C₂³	1	2	yes	—
280	C₇×C₄⋊C₈	C₂³	1	2	yes	—
281	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₇×#103	C₂³	1	1	yes	characteristic
284	C₇×#103	C₂³	1	2	yes	—
285	C₇×#103	C₂³	1	2	yes	—
286	C₇×#103	C₂³	1	2	yes	—
287	C₇×#103	C₂³	1	2	yes	—
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	2	yes	—
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	1	yes	characteristic
295	C₇×#103	C₂³	1	1	yes	characteristic
296	C₇×#103	C₂³	1	1	yes	characteristic
297	C₇×#103	C₂³	1	2	yes	—
298	C₇×#103	C₂³	1	2	yes	—
299	C₇×#102	C₂³	1	1	yes	characteristic
300	C₇×#102	C₂³	1	2	yes	—
301	C₇×#102	C₂³	1	2	yes	—
302	C₇×#102	C₂³	1	1	yes	characteristic
303	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₇×#97	C₂³	1	2	yes	—
307	C₇×#97	C₂³	1	2	yes	—
308	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
309	C₄×C₇×C₈	C₂³	1	2	yes	—
310	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
311	C₄×C₇×C₈	C₂³	1	2	yes	—
312	C₄×C₇×C₈	C₂³	1	2	yes	—
313	#3555	C₂×C₇	1	1	yes	characteristic
314	#3502	C₂×C₇	1	1	yes	characteristic, complemented
315	#3390	C₂×C₇	1	2	yes	complemented
316	#3387	C₂×C₇	1	1	yes	characteristic, complemented
317	#3385	C₂×C₇	1	1	yes	characteristic, complemented
318	#3383	C₂×C₇	1	2	yes	complemented
319	Q₈×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
320	#3381	C₂×C₇	1	1	yes	characteristic, complemented
321	#3377	C₂×C₇	1	2	yes	complemented
322	#3374	C₂×C₇	1	1	yes	characteristic, complemented
323	#3369	C₂×C₇	1	1	yes	characteristic, complemented
324	#3364	C₂×C₇	1	1	yes	characteristic, complemented
325	#3364	C₂×C₇	1	2	yes	complemented
326	#3363	C₂×C₇	1	1	yes	characteristic, complemented
327	#3243	C₂×C₇	1	2	yes	—
328	#3242	C₂×C₇	1	2	yes	complemented
329	#3233	C₂×C₇	1	1	yes	characteristic
330	#3231	C₂×C₇	1	1	yes	characteristic, complemented
331	#3127	C₂×C₇	1	2	yes	complemented
332	#3121	C₂×C₇	1	2	yes	—
333	#3108	C₂×C₇	1	1	yes	characteristic
334	#3104	C₂×C₇	1	1	yes	characteristic, complemented
335	#2986	C₂×C₇	1	1	yes	characteristic, complemented
336	C₂×C₇×Q₈	—	2	2	no	—
337	C₂×C₇×Q₈	—	2	2	no	—
338	C₂×C₇×Q₈	—	2	1	no	—
339	C₂×C₇×Q₈	—	2	1	no	—
340	C₂×C₇×Q₈	—	2	1	no	—
341	C₂×C₇×Q₈	—	2	2	no	—
342	C₂×C₇×Q₈	—	2	1	no	—
343	C₂×C₇×Q₈	—	2	2	no	—
344	C₂×C₇×Q₈	—	2	2	no	—
345	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
346	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
347	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
348	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
349	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
350	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
351	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
352	C₂×C₇×D₄	—	2	1	no	—
353	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₇	—	2	1	no	—
355	C₂²×C₄×C₇	—	2	1	no	—
356	C₂²×C₄×C₇	—	2	1	no	—
357	C₂²×C₄×C₇	—	2	2	no	—
358	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
361	C₇×Q₁₆	—	2	4	no	—
362	C₇×Q₁₆	—	2	2	no	—
363	C₇×Q₁₆	—	2	4	no	—
364	C₇×Q₁₆	—	2	2	no	—
365	C₇×SD₁₆	—	2	2	no	—
366	C₇×SD₁₆	—	2	2	no	—
367	C₂×C₇×C₈	C₂⁴	1	2	yes	—
368	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
369	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
370	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
371	C₂×C₇×C₈	C₂⁴	1	2	yes	—
372	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
373	C₇×C₄⋊C₄	—	2	1	no	—
374	C₇×C₄⋊C₄	—	2	1	no	—
375	C₇×C₄⋊C₄	—	2	1	no	—
376	C₇×C₄⋊C₄	—	2	1	no	—
377	C₇×C₄⋊C₄	—	2	1	no	—
378	C₇×C₄⋊C₄	—	2	2	no	—
379	C₇×C₄⋊C₄	—	2	1	no	—
380	C₇×C₄⋊C₄	—	2	1	no	—
381	C₇×C₄⋊C₄	—	2	2	no	—
382	C₇×C₄⋊C₄	—	2	2	no	—
383	C₇×C₄⋊C₄	—	2	2	no	—
384	C₇×C₄⋊C₄	—	2	2	no	—
385	C₇×C₄⋊C₄	—	2	2	no	—
386	C₇×C₄⋊C₄	—	2	1	no	—
387	C₇×C₄⋊C₄	—	2	1	no	—
388	C₇×C₄⋊C₄	—	2	1	no	—
389	C₇×C₄⋊C₄	—	2	2	no	—
390	C₇×C₄⋊C₄	—	2	1	no	—
391	C₇×C₄⋊C₄	—	2	2	no	—
392	C₇×C₄⋊C₄	—	2	2	no	—
393	C₇×C₄⋊C₄	—	2	1	no	—
394	C₇×C₄⋊C₄	—	2	2	no	—
395	C₇×C₄⋊C₄	—	2	2	no	—
396	C₇×C₄⋊C₄	—	2	2	no	—
397	C₇×C₄⋊C₄	—	2	2	no	—
398	C₇×C₄⋊C₄	—	2	2	no	—
399	C₇×C₄⋊C₄	—	2	2	no	—
400	C₇×C₄⋊C₄	—	2	2	no	—
401	C₇×C₄⋊C₄	—	2	1	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	2	no	—
406	C₇×C₄⋊C₄	—	2	2	no	—
407	C₇×C₄⋊C₄	—	2	2	no	—
408	C₇×C₄⋊C₄	—	2	1	no	—
409	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
410	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
411	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
412	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
413	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
414	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
415	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
416	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
417	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
418	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
419	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
420	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
421	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
422	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
423	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
424	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
425	C₇×C₂²⋊C₄	—	2	2	no	—
426	C₇×C₂²⋊C₄	—	2	2	no	—
427	C₇×C₂²⋊C₄	—	2	1	no	—
428	C₇×C₂²⋊C₄	—	2	1	no	—
429	C₇×C₂²⋊C₄	—	2	1	no	—
430	C₇×C₂²⋊C₄	—	2	1	no	—
431	C₇×C₂²⋊C₄	—	2	2	no	—
432	C₇×C₂²⋊C₄	—	2	2	no	—
433	C₇×C₂²⋊C₄	—	2	1	no	—
434	C₇×C₂²⋊C₄	—	2	2	no	—
435	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
436	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
437	C₄²×C₇	—	2	1	no	—
438	C₄²×C₇	—	2	1	no	—
439	C₄²×C₇	—	2	1	no	—
440	C₄²×C₇	—	2	1	no	—
441	C₄²×C₇	—	2	2	no	—
442	C₄²×C₇	—	2	1	no	—
443	C₄²×C₇	—	2	2	no	—
444	C₄²×C₇	—	2	2	no	—
445	C₄²×C₇	—	2	2	no	—
446	C₄²×C₇	—	2	2	no	—
447	C₄²×C₇	—	2	2	no	—
448	C₄²×C₇	—	2	2	no	—
449	C₄²×C₇	—	2	2	no	—
450	C₄²×C₇	—	2	2	no	—
451	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₇	C₂⁴	1	1	yes	characteristic
454	C₄²×C₇	C₂⁴	1	1	yes	characteristic
455	C₄²×C₇	C₂⁴	1	2	yes	—
456	C₄²×C₇	C₂⁴	1	2	yes	—
457	#563	—	2	2	no	—
458	Q₈²	—	2	1	no	—
459	Q₈²	C₂²×C₇	1	1	yes	characteristic
460	Q₈²	C₂²×C₇	1	1	yes	characteristic
461	Q₈²	C₂²×C₇	1	1	yes	characteristic
462	#557	—	2	1	no	—
463	#557	—	2	2	no	—
464	#557	C₂²×C₇	1	1	yes	characteristic
465	#557	C₂²×C₇	1	1	yes	characteristic
466	#557	C₂²×C₇	1	2	yes	—
467	#557	C₂²×C₇	1	1	yes	characteristic
468	#557	C₂²×C₇	1	2	yes	—
469	#557	C₂²×C₇	1	2	yes	—
470	#556	—	2	1	no	—
471	#556	C₂²×C₇	1	1	yes	characteristic
472	#556	C₂²×C₇	1	2	yes	—
473	#554	C₂²×C₇	1	1	yes	characteristic
474	#552	—	2	1	no	—
475	#544	—	2	1	no	—
476	#544	—	2	2	no	—
477	#544	C₂²×C₇	1	2	yes	—
478	#542	C₂²×C₇	1	2	yes	—
479	#541	—	2	1	no	—
480	#541	—	2	2	no	—
481	#541	C₂²×C₇	1	2	yes	—
482	#533	—	2	1	no	—
483	#533	—	2	1	no	—
484	#533	C₂²×C₇	1	1	yes	characteristic
485	#533	C₂²×C₇	1	1	yes	characteristic
486	#533	C₂²×C₇	1	1	yes	characteristic
487	#529	C₂²×C₇	1	1	yes	characteristic
488	#519	C₂²×C₇	1	2	yes	—
489	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
490	#501	C₂²×C₇	1	2	yes	—
491	#501	C₂²×C₇	1	2	yes	—
492	#500	C₂²×C₇	1	2	yes	—
493	#500	C₂²×C₇	1	1	yes	characteristic
494	#499	C₂²×C₇	1	2	yes	—
495	#499	C₂²×C₇	1	2	yes	—
496	#498	C₂²×C₇	1	1	yes	characteristic
497	#491	C₂²×C₇	1	2	yes	—
498	#489	C₂²×C₇	1	2	yes	—
499	#488	C₂²×C₇	1	2	yes	—
500	#488	C₂²×C₇	1	2	yes	—
501	#487	C₂²×C₇	1	2	yes	—
502	#487	C₂²×C₇	1	1	yes	characteristic
503	#487	C₂²×C₇	1	1	yes	characteristic
504	#485	C₂²×C₇	1	2	yes	—
505	#485	C₂²×C₇	1	2	yes	—
506	#485	C₂²×C₇	1	2	yes	—
507	#484	C₂²×C₇	1	2	yes	—
508	#483	C₂²×C₇	1	1	yes	characteristic
509	#482	C₂²×C₇	1	2	yes	—
510	#480	C₂²×C₇	1	1	yes	characteristic
511	#479	C₂²×C₇	1	1	yes	characteristic
512	#479	C₂²×C₇	1	1	yes	characteristic
513	#479	C₂²×C₇	1	2	yes	—
514	#479	C₂²×C₇	1	2	yes	—
515	#479	C₂²×C₇	1	2	yes	—
516	#479	C₂²×C₇	1	2	yes	—
517	#479	C₂²×C₇	1	2	yes	—
518	#479	C₂²×C₇	1	2	yes	—
519	#479	C₂²×C₇	1	2	yes	—
520	#478	C₂²×C₇	1	2	yes	—
521	#477	C₂²×C₇	1	1	yes	characteristic
522	#477	C₂²×C₇	1	1	yes	characteristic
523	#477	C₂²×C₇	1	1	yes	characteristic
524	#477	C₂²×C₇	1	2	yes	—
525	#477	C₂²×C₇	1	2	yes	—
526	#477	C₂²×C₇	1	2	yes	—
527	#476	C₂²×C₇	1	1	yes	characteristic
528	#475	C₂²×C₇	1	2	yes	—
529	#475	C₂²×C₇	1	1	yes	characteristic
530	#475	C₂²×C₇	1	2	yes	—
531	#474	C₂²×C₇	1	1	yes	characteristic
532	#474	C₂²×C₇	1	2	yes	—
533	#464	C₂²×C₇	1	1	yes	characteristic
534	#464	C₂²×C₇	1	1	yes	characteristic
535	#464	C₂²×C₇	1	2	yes	—
536	#464	C₂²×C₇	1	2	yes	—
537	#462	C₂²×C₇	1	1	yes	characteristic
538	#462	C₂²×C₇	1	1	yes	characteristic
539	#462	C₂²×C₇	1	2	yes	—
540	#462	C₂²×C₇	1	2	yes	—
541	#451	C₂²×C₇	1	2	yes	—
542	#451	C₂²×C₇	1	1	yes	characteristic
543	#448	C₂²×C₇	1	1	yes	characteristic
544	#446	C₂²×C₇	1	1	yes	characteristic
545	#446	C₂²×C₇	1	1	yes	characteristic
546	#446	C₂²×C₇	1	2	yes	—
547	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
548	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
549	C₈×Q₈	C₂²×C₇	1	2	yes	—
550	#441	C₂²×C₇	1	2	yes	—
551	#441	C₂²×C₇	1	2	yes	—
552	#441	C₂²×C₇	1	2	yes	—
553	#440	C₂²×C₇	1	2	yes	—
554	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
555	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
556	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
557	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
558	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
559	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
560	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
561	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
562	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
563	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
564	#433	C₂²×C₇	1	2	yes	—
565	#433	C₂²×C₇	1	2	yes	—
566	#431	C₂²×C₇	1	1	yes	characteristic
567	#431	C₂²×C₇	1	1	yes	characteristic
568	C₂³×C₇	—	2	1	no	—
569	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
570	C₇×Q₈	—	2	4	no	—
571	C₇×Q₈	—	2	2	no	—
572	C₇×Q₈	—	2	2	no	—
573	C₇×Q₈	—	2	1	no	—
574	C₇×Q₈	—	2	1	no	—
575	C₇×Q₈	—	2	2	no	—
576	C₇×Q₈	—	2	1	no	—
577	C₇×Q₈	—	2	2	no	—
578	C₇×Q₈	—	2	1	no	—
579	C₇×Q₈	—	4	2	no	—
580	C₇×Q₈	—	4	2	no	—
581	C₇×Q₈	—	8	1	no	—
582	C₇×Q₈	—	8	1	no	—
583	C₇×Q₈	—	8	2	no	—
584	C₇×Q₈	—	8	2	no	—
585	C₇×Q₈	—	8	2	no	—
586	C₇×Q₈	2₋¹⁺⁴	1	2	yes	—
587	C₇×Q₈	2₋¹⁺⁴	1	2	yes	—
588	C₇×D₄	—	2	1	no	—
589	C₇×D₄	—	2	1	no	—
590	C₇×D₄	—	8	1	no	—
591	C₂×C₄×C₇	—	2	4	no	—
592	C₂×C₄×C₇	—	2	1	no	—
593	C₂×C₄×C₇	—	2	1	no	—
594	C₂×C₄×C₇	—	2	2	no	—
595	C₂×C₄×C₇	—	2	1	no	—
596	C₂×C₄×C₇	—	2	1	no	—
597	C₂×C₄×C₇	—	2	2	no	—
598	C₂×C₄×C₇	—	2	1	no	—
599	C₂×C₄×C₇	—	2	2	no	—
600	C₂×C₄×C₇	—	2	1	no	—
601	C₂×C₄×C₇	—	2	2	no	—
602	C₂×C₄×C₇	—	2	1	no	—
603	C₂×C₄×C₇	—	2	2	no	—
604	C₂×C₄×C₇	—	2	1	no	—
605	C₂×C₄×C₇	—	2	1	no	—
606	C₂×C₄×C₇	—	4	1	no	—
607	C₂×C₄×C₇	—	4	2	no	—
608	C₂×C₄×C₇	—	8	2	no	—
609	C₂×C₄×C₇	—	8	1	no	—
610	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
611	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
612	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
613	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
614	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
615	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
616	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
617	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
618	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
619	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
620	C₇×C₈	—	2	1	no	—
621	C₇×C₈	—	2	1	no	—
622	C₇×C₈	—	2	2	no	—
623	C₇×C₈	—	2	1	no	—
624	C₇×C₈	—	2	1	no	—
625	C₇×C₈	—	2	2	no	—
626	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
627	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
628	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
629	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
630	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
631	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
632	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
633	C₄⋊Q₈	—	2	1	no	—
634	C₄⋊Q₈	—	2	1	no	—
635	C₄⋊Q₈	—	2	2	no	—
636	C₄⋊Q₈	—	2	2	no	—
637	C₄⋊Q₈	—	2	2	no	—
638	C₄⋊Q₈	—	2	1	no	—
639	C₄⋊Q₈	—	2	1	no	—
640	C₄⋊Q₈	—	2	2	no	—
641	C₄⋊Q₈	—	2	1	no	—
642	C₄⋊Q₈	—	2	2	no	—
643	C₄⋊Q₈	—	2	2	no	—
644	C₄⋊Q₈	—	2	2	no	—
645	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
646	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
647	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
648	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
649	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
650	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
651	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
652	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
653	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
654	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
655	#126	—	2	2	no	—
656	#126	—	2	2	no	—
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	—	2	1	no	—
662	#125	—	2	2	no	—
663	#125	—	2	2	no	—
664	#125	—	2	2	no	—
665	#125	—	2	2	no	—
666	#125	—	2	2	no	—
667	#125	—	2	2	no	—
668	#125	—	2	2	no	—
669	#125	—	2	1	no	—
670	#125	—	2	2	no	—
671	#125	—	2	2	no	—
672	#125	—	2	2	no	—
673	#125	—	2	2	no	—
674	#125	—	2	2	no	—
675	#125	—	2	1	no	—
676	#125	C₇×D₄	1	2	yes	—
677	#125	C₂³×C₇	1	1	yes	characteristic
678	#125	C₂³×C₇	1	2	yes	—
679	#125	C₂³×C₇	1	2	yes	—
680	#125	C₂³×C₇	1	2	yes	—
681	#125	C₂³×C₇	1	2	yes	—
682	#124	—	2	2	no	—
683	#124	C₂³×C₇	1	1	yes	characteristic
684	#124	C₂³×C₇	1	2	yes	—
685	#123	—	2	1	no	—
686	#123	—	2	2	no	—
687	C₂²⋊Q₈	—	2	1	no	—
688	C₂²⋊Q₈	—	2	1	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	1	no	—
691	C₂²⋊Q₈	—	2	1	no	—
692	C₂²⋊Q₈	—	2	1	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
698	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
699	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
700	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
701	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
702	#121	C₂³×C₇	1	1	yes	characteristic
703	C₄×Q₈	—	2	1	no	—
704	C₄×Q₈	—	2	1	no	—
705	C₄×Q₈	—	2	1	no	—
706	C₄×Q₈	—	2	1	no	—
707	C₄×Q₈	—	2	2	no	—
708	C₄×Q₈	—	2	2	no	—
709	C₄×Q₈	—	2	2	no	—
710	C₄×Q₈	—	2	2	no	—
711	C₄×Q₈	—	2	1	no	—
712	C₄×Q₈	—	2	1	no	—
713	C₄×Q₈	—	2	2	no	—
714	C₄×Q₈	—	2	1	no	—
715	C₄×Q₈	—	2	1	no	—
716	C₄×Q₈	—	2	1	no	—
717	C₄×Q₈	—	2	1	no	—
718	C₄×Q₈	—	2	1	no	—
719	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
720	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
721	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
722	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
723	C₄×Q₈	C₂³×C₇	1	2	yes	—
724	C₄×Q₈	C₂³×C₇	1	2	yes	—
725	C₄×Q₈	C₂³×C₇	1	2	yes	—
726	C₄×Q₈	C₂³×C₇	1	2	yes	—
727	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
728	C₄×Q₈	C₂³×C₇	1	2	yes	—
729	C₄×Q₈	C₂³×C₇	1	2	yes	—
730	C₄×Q₈	C₂³×C₇	1	2	yes	—
731	C₄×Q₈	C₂³×C₇	1	2	yes	—
732	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
733	C₄×Q₈	C₂³×C₇	1	2	yes	—
734	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
735	C₄×D₄	—	2	1	no	—
736	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
737	C₄×D₄	C₂³×C₇	1	2	yes	—
738	#117	—	2	1	no	—
739	#117	—	2	2	no	—
740	#117	—	2	1	no	—
741	#117	—	2	2	no	—
742	#117	—	2	2	no	—
743	#117	—	2	1	no	—
744	#117	C₂³×C₇	1	2	yes	—
745	#117	C₂³×C₇	1	2	yes	—
746	C₂×C₄⋊C₄	—	2	1	no	—
747	C₂×C₄⋊C₄	—	2	1	no	—
748	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
749	C₂×C₄²	—	2	1	no	—
750	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
751	#107	C₂³×C₇	1	2	yes	—
752	#107	C₂³×C₇	1	2	yes	—
753	#107	C₂³×C₇	1	2	yes	—
754	#107	C₂³×C₇	1	2	yes	—
755	#107	C₂³×C₇	1	2	yes	—
756	#107	C₂³×C₇	1	1	yes	characteristic
757	#107	C₂³×C₇	1	1	yes	characteristic
758	#107	C₂³×C₇	1	2	yes	—
759	#106	C₂³×C₇	1	1	yes	characteristic
760	#106	C₂³×C₇	1	2	yes	—
761	#106	C₂³×C₇	1	1	yes	characteristic
762	#106	C₂³×C₇	1	2	yes	—
763	#106	C₂³×C₇	1	2	yes	—
764	#106	C₂³×C₇	1	2	yes	—
765	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
766	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
767	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
768	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
769	C₄⋊C₈	C₂³×C₇	1	2	yes	—
770	C₄⋊C₈	C₂³×C₇	1	2	yes	—
771	C₄⋊C₈	C₂³×C₇	1	2	yes	—
772	C₄⋊C₈	C₂³×C₇	1	2	yes	—
773	#103	C₂³×C₇	1	2	yes	—
774	#103	C₂³×C₇	1	1	yes	characteristic
775	#103	C₂³×C₇	1	1	yes	characteristic
776	#103	C₂³×C₇	1	1	yes	characteristic
777	#103	C₂³×C₇	1	2	yes	—
778	#103	C₂³×C₇	1	1	yes	characteristic
779	#103	C₂³×C₇	1	2	yes	—
780	#103	C₂³×C₇	1	2	yes	—
781	#103	C₂³×C₇	1	2	yes	—
782	#103	C₂³×C₇	1	2	yes	—
783	#103	C₂³×C₇	1	2	yes	—
784	#103	C₂³×C₇	1	1	yes	characteristic
785	#103	C₂³×C₇	1	1	yes	characteristic
786	#103	C₂³×C₇	1	2	yes	—
787	#103	C₂³×C₇	1	2	yes	—
788	#103	C₂³×C₇	1	2	yes	—
789	#102	C₂³×C₇	1	1	yes	characteristic
790	#102	C₂³×C₇	1	2	yes	—
791	#102	C₂³×C₇	1	1	yes	characteristic
792	#102	C₂³×C₇	1	2	yes	—
793	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
794	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
795	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
796	#97	C₂³×C₇	1	2	yes	—
797	#97	C₂³×C₇	1	2	yes	—
798	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
799	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
800	C₄×C₈	C₂³×C₇	1	2	yes	—
801	C₄×C₈	C₂³×C₇	1	2	yes	—
802	C₄×C₈	C₂³×C₇	1	2	yes	—
803	C₂²×C₇	—	2	1	no	—
804	C₂²×C₇	—	2	1	no	—
805	C₂²×C₇	—	2	1	no	—
806	C₂²×C₇	—	4	1	no	—
807	C₂²×C₇	—	4	1	no	—
808	C₂²×C₇	—	4	1	no	—
809	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
810	C₄×C₇	—	2	1	no	—
811	C₄×C₇	—	2	1	no	—
812	C₄×C₇	—	2	2	no	—
813	C₄×C₇	—	2	2	no	—
814	C₄×C₇	—	2	2	no	—
815	C₄×C₇	—	2	2	no	—
816	C₄×C₇	—	2	1	no	—
817	C₄×C₇	—	2	1	no	—
818	C₄×C₇	—	2	2	no	—
819	C₄×C₇	—	2	2	no	—
820	C₄×C₇	—	4	2	no	—
821	C₄×C₇	—	4	1	no	—
822	C₄×C₇	—	4	1	no	—
823	C₄×C₇	—	4	1	no	—
824	C₄×C₇	—	4	2	no	—
825	C₄×C₇	—	4	2	no	—
826	C₄×C₇	—	4	1	no	—
827	C₄×C₇	—	4	1	no	—
828	C₄×C₇	—	4	2	no	—
829	C₄×C₇	#578	1	2	yes	—
830	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
831	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
832	C₂×Q₈	—	2	2	no	—
833	C₂×Q₈	—	2	2	no	—
834	C₂×Q₈	—	2	1	no	—
835	C₂×Q₈	—	2	1	no	—
836	C₂×Q₈	—	2	1	no	—
837	C₂×Q₈	—	2	2	no	—
838	C₂×Q₈	—	2	1	no	—
839	C₂×Q₈	—	2	2	no	—
840	C₂×Q₈	—	2	2	no	—
841	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
842	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
843	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
844	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
845	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
846	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
847	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
848	C₂×D₄	—	2	1	no	—
849	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
850	C₂²×C₄	—	2	1	no	—
851	C₂²×C₄	—	2	1	no	—
852	C₂²×C₄	—	2	1	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
855	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
856	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
857	Q₁₆	—	2	4	no	—
858	Q₁₆	—	2	2	no	—
859	Q₁₆	—	2	4	no	—
860	Q₁₆	—	2	2	no	—
861	SD₁₆	—	2	2	no	—
862	SD₁₆	—	2	2	no	—
863	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
864	C₂×C₈	C₂⁴×C₇	1	2	yes	—
865	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
866	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
867	C₂×C₈	C₂⁴×C₇	1	2	yes	—
868	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	—	2	1	no	—
873	C₄⋊C₄	—	2	1	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	1	no	—
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
906	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
907	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
908	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
909	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
910	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
911	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
912	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
913	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
914	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
915	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
916	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
917	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
918	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
919	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
920	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	1	no	—
924	C₂²⋊C₄	—	2	1	no	—
925	C₂²⋊C₄	—	2	1	no	—
926	C₂²⋊C₄	—	2	1	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	1	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
932	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
933	C₄²	—	2	1	no	—
934	C₄²	—	2	1	no	—
935	C₄²	—	2	1	no	—
936	C₄²	—	2	1	no	—
937	C₄²	—	2	2	no	—
938	C₄²	—	2	1	no	—
939	C₄²	—	2	2	no	—
940	C₄²	—	2	2	no	—
941	C₄²	—	2	2	no	—
942	C₄²	—	2	2	no	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	2	2	no	—
946	C₄²	—	2	2	no	—
947	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
948	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
949	C₄²	C₂⁴×C₇	1	1	yes	characteristic
950	C₄²	C₂⁴×C₇	1	1	yes	characteristic
951	C₄²	C₂⁴×C₇	1	2	yes	—
952	C₄²	C₂⁴×C₇	1	2	yes	—
953	C₂×C₇	—	4	1	no	—
954	C₂×C₇	—	8	1	no	—
955	C₂×C₇	#3486	1	1	yes	characteristic
956	C₂×C₇	C₂×#578	1	1	yes	characteristic
957	C₂×C₇	#3584	1	1	yes	characteristic
958	C₂³	—	2	1	no	—
959	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
960	Q₈	—	2	4	no	—
961	Q₈	—	2	1	no	—
962	Q₈	—	2	1	no	—
963	Q₈	—	2	2	no	—
964	Q₈	—	2	2	no	—
965	Q₈	—	2	2	no	—
966	Q₈	—	2	1	no	—
967	Q₈	—	2	2	no	—
968	Q₈	—	2	1	no	—
969	Q₈	—	4	2	no	—
970	Q₈	—	4	2	no	—
971	Q₈	—	8	1	no	—
972	Q₈	—	8	1	no	—
973	Q₈	—	8	2	no	—
974	Q₈	—	8	2	no	—
975	Q₈	—	8	2	no	—
976	Q₈	C₇×2₋¹⁺⁴	1	2	yes	—
977	Q₈	C₇×2₋¹⁺⁴	1	2	yes	—
978	D₄	—	2	1	no	—
979	D₄	—	2	1	no	—
980	D₄	—	8	1	no	—
981	C₂×C₄	—	2	4	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	4	1	no	—
997	C₂×C₄	—	4	2	no	—
998	C₂×C₄	—	8	2	no	—
999	C₂×C₄	—	8	1	no	—
1000	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1001	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1002	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1003	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1004	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1005	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1006	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1007	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1008	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1009	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1010	C₈	—	2	1	no	—
1011	C₈	—	2	1	no	—
1012	C₈	—	2	1	no	—
1013	C₈	—	2	2	no	—
1014	C₈	—	2	1	no	—
1015	C₈	—	2	2	no	—
1016	C₇	#61866	1	1	yes	characteristic, direct product factor, Sylow
1017	C₂²	—	2	1	no	—
1018	C₂²	—	2	1	no	—
1019	C₂²	—	2	1	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1024	C₄	—	2	1	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	1	no	—
1028	C₄	—	2	1	no	—
1029	C₄	—	2	2	no	—
1030	C₄	—	2	2	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	2	1	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	2	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	2	no	—
1041	C₄	—	4	2	no	—
1042	C₄	—	4	1	no	—
1043	C₄	C₇×#578	1	2	yes	—
1044	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1045	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1046	C₂	—	4	1	no	—
1047	C₂	—	8	1	no	—
1048	C₂	C₇×#3486	1	1	yes	characteristic
1049	C₂	C₂×C₇×#578	1	1	yes	characteristic
1050	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#121	C₂³
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×#3390	C₂	semidirect
4. C₇×#3387	C₂	semidirect
5. C₇×#3385	C₂	semidirect
6. C₇×#3383	C₂	semidirect
7. C₇×Q₈×Q₁₆	C₂	semidirect
8. C₇×#3381	C₂	semidirect
9. C₇×#3377	C₂	semidirect
10. C₇×#3374	C₂	semidirect
11. C₇×#3369	C₂	semidirect
12. C₇×#3364	C₂	semidirect
13. C₇×#3364	C₂	semidirect
14. C₇×#3363	C₂	semidirect
16. C₇×#3242	C₂	semidirect
18. C₇×#3231	C₂	semidirect
19. C₇×#3127	C₂	semidirect
22. C₇×#3104	C₂	semidirect
23. C₇×#2986	C₂	semidirect
135. #61866	C₇	direct (N × H)
314. #3502	C₂×C₇	semidirect
315. #3390	C₂×C₇	semidirect
316. #3387	C₂×C₇	semidirect
317. #3385	C₂×C₇	semidirect
318. #3383	C₂×C₇	semidirect
319. Q₈×Q₁₆	C₂×C₇	semidirect
320. #3381	C₂×C₇	semidirect
321. #3377	C₂×C₇	semidirect
322. #3374	C₂×C₇	semidirect
323. #3369	C₂×C₇	semidirect
324. #3364	C₂×C₇	semidirect
325. #3364	C₂×C₇	semidirect
326. #3363	C₂×C₇	semidirect
328. #3242	C₂×C₇	semidirect
330. #3231	C₂×C₇	semidirect
331. #3127	C₂×C₇	semidirect
334. #3104	C₂×C₇	semidirect
335. #2986	C₂×C₇	semidirect
1016. C₇	#61866	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×#3555	2
C₇×#3502	2
C₇×#3390	2
C₇×#3387	2
C₇×#3385	2
C₇×#3383	2
C₇×Q₈×Q₁₆	2
C₇×#3381	2
C₇×#3377	2
C₇×#3374	2
C₇×#3369	2
C₇×#3364	2
C₇×#3363	2
C₇×#3243	2
C₇×#3242	2
C₇×#3233	2
C₇×#3231	2
C₇×#3127	2
C₇×#3121	2
C₇×#3108	2
C₇×#3104	2
C₇×#2986	2
#61866	7

Subgroups — C7×#61866 #13239082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61866 #13239082