Subgroups — C₇×#61457 #13238673

Order 1792.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3482	C₂	1	1	yes	maximal, characteristic
2	C₇×Q₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3369	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3344	C₂	1	2	yes	maximal, complemented
8	C₇×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3316	C₂	1	2	yes	maximal, complemented
10	C₇×#3312	C₂	1	2	yes	maximal, complemented
11	C₇×#3299	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3298	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×D₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3270	C₂	1	2	yes	maximal, complemented
15	C₇×#3185	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3181	C₂	1	2	yes	maximal, complemented
17	C₇×#3117	C₂	1	2	yes	maximal, complemented
18	C₇×#3116	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#3113	C₂	1	2	yes	maximal, complemented
21	C₇×#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₇×#441	C₂	1	2	yes	maximal, complemented
24	C₂×C₇×#137	C₂²	1	1	yes	characteristic
25	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
26	C₇×Q₈²	C₂²	1	1	yes	characteristic
27	C₇×#557	—	2	1	no	—
28	C₇×#557	C₂²	1	1	yes	characteristic
29	C₇×#557	C₂²	1	1	yes	characteristic
30	C₇×#556	—	2	1	no	—
31	C₇×#556	C₂²	1	1	yes	characteristic
32	C₇×#554	—	2	1	no	—
33	C₇×#554	—	2	2	no	—
34	C₇×#554	C₂²	1	1	yes	characteristic
35	C₇×#554	C₂²	1	2	yes	—
36	C₇×#552	—	2	2	no	—
37	C₇×#552	C₂²	1	2	yes	—
38	C₇×D₄×Q₈	C₂²	1	2	yes	—
39	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
40	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
41	C₇×#548	C₂²	1	2	yes	—
42	C₇×#547	—	2	1	no	—
43	C₇×#547	C₂²	1	1	yes	characteristic
44	C₇×#533	—	2	1	no	—
45	C₇×#533	—	2	2	no	—
46	C₇×#533	—	2	1	no	—
47	C₇×#533	C₂²	1	2	yes	—
48	C₇×#533	C₂²	1	1	yes	characteristic
49	C₇×#533	C₂²	1	1	yes	characteristic
50	C₇×#529	—	2	2	no	—
51	C₇×#529	C₂²	1	2	yes	—
52	C₄×C₇×#41	—	2	1	no	—
53	C₄×C₇×#41	—	2	1	no	—
54	C₄×C₇×#41	C₂²	1	1	yes	characteristic
55	C₄×C₇×#41	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
57	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
58	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
59	C₇×#501	C₂²	1	2	yes	—
60	C₇×#498	C₂²	1	1	yes	characteristic
61	C₇×#497	C₂²	1	2	yes	—
62	C₇×#494	C₂²	1	1	yes	characteristic
63	C₇×#491	C₂²	1	2	yes	—
64	C₇×#489	C₂²	1	2	yes	—
65	C₇×#487	C₂²	1	1	yes	characteristic
66	C₇×#487	C₂²	1	1	yes	characteristic
67	C₇×#485	C₂²	1	2	yes	—
68	C₇×#484	C₂²	1	2	yes	—
69	C₇×#483	C₂²	1	2	yes	—
70	C₇×#483	C₂²	1	2	yes	—
71	C₇×#483	C₂²	1	2	yes	—
72	C₇×#481	C₂²	1	2	yes	—
73	C₇×#479	C₂²	1	2	yes	—
74	C₇×#479	C₂²	1	2	yes	—
75	C₇×#477	C₂²	1	1	yes	characteristic
76	C₇×#476	C₂²	1	1	yes	characteristic
77	C₇×#475	C₂²	1	1	yes	characteristic
78	C₇×#475	C₂²	1	2	yes	—
79	C₇×#475	C₂²	1	1	yes	characteristic
80	C₇×#475	C₂²	1	2	yes	—
81	C₇×#470	C₂²	1	2	yes	—
82	C₇×#470	C₂²	1	2	yes	—
83	C₇×#467	C₂²	1	2	yes	—
84	C₇×#467	C₂²	1	2	yes	—
85	C₇×#465	C₂²	1	2	yes	—
86	C₇×#465	C₂²	1	2	yes	—
87	C₇×#464	C₂²	1	2	yes	—
88	C₇×#464	C₂²	1	2	yes	—
89	C₇×#462	C₂²	1	2	yes	—
90	C₇×#462	C₂²	1	1	yes	characteristic
91	C₇×#462	C₂²	1	1	yes	characteristic
92	C₇×#462	C₂²	1	1	yes	characteristic
93	C₇×#462	C₂²	1	2	yes	—
94	C₇×#461	C₂²	1	1	yes	characteristic
95	C₇×#452	C₂²	1	2	yes	—
96	C₇×#451	C₂²	1	2	yes	—
97	C₇×#451	C₂²	1	2	yes	—
98	C₇×#451	C₂²	1	2	yes	—
99	C₇×#451	C₂²	1	2	yes	—
100	C₇×#448	C₂²	1	2	yes	—
101	C₇×#446	C₂²	1	1	yes	characteristic
102	C₇×#446	C₂²	1	1	yes	characteristic
103	C₇×#441	C₂²	1	2	yes	—
104	C₇×#441	C₂²	1	2	yes	—
105	C₇×#441	C₂²	1	2	yes	—
106	C₇×#441	C₂²	1	1	yes	characteristic
107	C₇×#441	C₂²	1	2	yes	—
108	C₇×#441	C₂²	1	2	yes	—
109	C₇×#441	C₂²	1	2	yes	—
110	C₇×#441	C₂²	1	2	yes	—
111	C₇×#441	C₂²	1	2	yes	—
112	C₇×#441	C₂²	1	2	yes	—
113	C₇×#441	C₂²	1	1	yes	characteristic
114	C₇×#440	C₂²	1	1	yes	characteristic
115	C₇×#440	C₂²	1	2	yes	—
116	C₇×#440	C₂²	1	1	yes	characteristic
117	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
118	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
119	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
121	C₇×#435	C₂²	1	2	yes	—
122	C₇×#435	C₂²	1	2	yes	—
123	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
124	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
125	C₇×#432	C₂²	1	1	yes	characteristic
126	C₇×#432	C₂²	1	2	yes	—
127	C₇×#428	C₂²	1	1	yes	characteristic
128	C₂×C₇×#106	C₂²	1	2	yes	—
129	C₇×#419	C₂²	1	1	yes	characteristic
130	C₇×#417	C₂²	1	1	yes	characteristic
131	C₂×C₇×#103	C₂²	1	2	yes	—
132	C₂×C₇×#103	C₂²	1	2	yes	—
133	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
134	C₂×C₇×#97	C₂²	1	2	yes	—
135	#61457	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	1	no	—
137	C₂×C₇×#41	D₄	1	1	yes	characteristic
138	C₂×C₇×#41	C₂³	1	1	yes	characteristic
139	C₂²×C₇×Q₈	C₂³	1	2	yes	—
140	C₂²×C₇×Q₈	C₂³	1	2	yes	—
141	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
142	C₇×#137	—	2	4	no	—
143	C₂×C₇×Q₁₆	—	2	8	no	—
144	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
145	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
146	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
147	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
149	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
150	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
151	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
152	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
155	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
156	C₂²×C₇×C₈	C₂³	1	2	yes	—
157	C₂²×C₇×C₈	C₂³	1	2	yes	—
158	C₇×C₄⋊Q₈	—	2	1	no	—
159	C₇×C₄⋊Q₈	—	2	1	no	—
160	C₇×C₄⋊Q₈	—	2	2	no	—
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	C₂³	1	1	yes	characteristic
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×#126	—	2	2	no	—
171	C₇×#126	—	2	2	no	—
172	C₇×#126	—	2	2	no	—
173	C₇×#125	—	2	2	no	—
174	C₇×#125	—	2	2	no	—
175	C₇×#125	—	2	1	no	—
176	C₇×#125	—	2	2	no	—
177	C₇×#125	—	2	2	no	—
178	C₇×#125	—	2	1	no	—
179	C₇×#125	—	2	1	no	—
180	C₇×#125	—	2	1	no	—
181	C₇×#125	—	2	2	no	—
182	C₇×#125	C₂³	1	2	yes	—
183	C₇×#124	—	2	2	no	—
184	C₇×#124	C₂³	1	2	yes	—
185	C₇×#123	—	2	2	no	—
186	C₇×#123	—	2	2	no	—
187	C₇×#123	—	2	2	no	—
188	C₇×C₂²⋊Q₈	—	2	1	no	—
189	C₇×C₂²⋊Q₈	—	2	1	no	—
190	C₇×C₂²⋊Q₈	—	2	2	no	—
191	C₇×C₂²⋊Q₈	—	2	1	no	—
192	C₇×C₂²⋊Q₈	—	2	1	no	—
193	C₇×C₂²⋊Q₈	—	2	2	no	—
194	C₇×C₂²⋊Q₈	—	2	2	no	—
195	C₇×C₂²⋊Q₈	—	2	2	no	—
196	C₇×C₂²⋊Q₈	—	2	2	no	—
197	C₇×C₂²⋊Q₈	—	2	2	no	—
198	C₇×C₂²⋊Q₈	—	2	2	no	—
199	C₇×C₂²⋊Q₈	—	2	2	no	—
200	C₇×C₂²⋊Q₈	—	2	2	no	—
201	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₇×#121	—	2	2	no	—
207	C₇×#121	C₂³	1	2	yes	—
208	C₄×C₇×Q₈	—	2	1	no	—
209	C₄×C₇×Q₈	—	2	1	no	—
210	C₄×C₇×Q₈	—	2	1	no	—
211	C₄×C₇×Q₈	—	2	2	no	—
212	C₄×C₇×Q₈	—	2	1	no	—
213	C₄×C₇×Q₈	—	2	2	no	—
214	C₄×C₇×Q₈	—	2	2	no	—
215	C₄×C₇×Q₈	—	2	1	no	—
216	C₄×C₇×Q₈	—	2	2	no	—
217	C₄×C₇×Q₈	—	2	1	no	—
218	C₄×C₇×Q₈	—	2	1	no	—
219	C₄×C₇×Q₈	—	2	2	no	—
220	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
221	C₄×C₇×Q₈	C₂³	1	2	yes	—
222	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
223	C₄×C₇×Q₈	C₂³	1	2	yes	—
224	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
225	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
226	C₄×C₇×Q₈	C₂³	1	2	yes	—
227	C₄×C₇×Q₈	C₂³	1	2	yes	—
228	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
233	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
234	C₄×C₇×D₄	—	2	1	no	—
235	C₄×C₇×D₄	—	2	2	no	—
236	C₄×C₇×D₄	—	2	1	no	—
237	C₄×C₇×D₄	—	2	2	no	—
238	C₄×C₇×D₄	—	2	1	no	—
239	C₄×C₇×D₄	—	2	2	no	—
240	C₄×C₇×D₄	—	2	1	no	—
241	C₄×C₇×D₄	—	2	1	no	—
242	C₄×C₇×D₄	—	2	2	no	—
243	C₄×C₇×D₄	D₄	1	1	yes	characteristic
244	C₄×C₇×D₄	D₄	1	2	yes	—
245	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
246	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
247	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
248	C₄×C₇×D₄	C₂³	1	2	yes	—
249	C₇×#117	—	2	2	no	—
250	C₇×#117	—	2	1	no	—
251	C₇×#117	—	2	1	no	—
252	C₇×#117	—	2	1	no	—
253	C₇×#117	—	2	2	no	—
254	C₇×#117	—	2	1	no	—
255	C₇×#117	—	2	2	no	—
256	C₇×#117	D₄	1	2	yes	—
257	C₇×#117	D₄	1	1	yes	characteristic
258	C₇×#117	C₂³	1	1	yes	characteristic
259	C₂×C₇×C₄⋊C₄	—	2	2	no	—
260	C₂×C₇×C₄⋊C₄	—	2	2	no	—
261	C₂×C₇×C₄⋊C₄	—	2	1	no	—
262	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
263	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₄²×C₇	—	2	2	no	—
266	C₂×C₄²×C₇	—	2	2	no	—
267	C₂×C₄²×C₇	—	2	1	no	—
268	C₂×C₄²×C₇	—	2	1	no	—
269	C₂×C₄²×C₇	C₂³	1	2	yes	—
270	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
271	C₇×#107	C₂³	1	1	yes	characteristic
272	C₇×#107	C₂³	1	2	yes	—
273	C₇×#107	C₂³	1	1	yes	characteristic
274	C₇×#106	C₂³	1	2	yes	—
275	C₇×#106	C₂³	1	2	yes	—
276	C₇×#106	C₂³	1	2	yes	—
277	C₇×#106	C₂³	1	1	yes	characteristic
278	C₇×#106	C₂³	1	2	yes	—
279	C₇×#106	C₂³	1	2	yes	—
280	C₇×#106	C₂³	1	1	yes	characteristic
281	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₇×C₄⋊C₈	C₂³	1	2	yes	—
284	C₇×C₄⋊C₈	C₂³	1	2	yes	—
285	C₇×#103	C₂³	1	1	yes	characteristic
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	2	yes	—
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#103	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	1	yes	characteristic
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	2	yes	—
296	C₇×#103	C₂³	1	1	yes	characteristic
297	C₇×#103	C₂³	1	1	yes	characteristic
298	C₇×#103	C₂³	1	2	yes	—
299	C₇×#103	C₂³	1	2	yes	—
300	C₇×#103	C₂³	1	1	yes	characteristic
301	C₇×#103	C₂³	1	1	yes	characteristic
302	C₇×#102	C₂³	1	2	yes	—
303	C₇×#102	C₂³	1	1	yes	characteristic
304	C₇×#102	C₂³	1	1	yes	characteristic
305	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₇×#97	C₂³	1	2	yes	—
309	C₇×#97	C₂³	1	2	yes	—
310	C₇×#97	C₂³	1	1	yes	characteristic
311	C₇×#97	C₂³	1	2	yes	—
312	C₇×#97	C₂³	1	1	yes	characteristic
313	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
315	#3482	C₂×C₇	1	1	yes	characteristic
316	Q₈×#41	C₂×C₇	1	1	yes	characteristic, complemented
317	#3398	C₂×C₇	1	1	yes	characteristic, complemented
318	#3387	C₂×C₇	1	1	yes	characteristic, complemented
319	#3374	C₂×C₇	1	1	yes	characteristic, complemented
320	#3369	C₂×C₇	1	1	yes	characteristic, complemented
321	#3344	C₂×C₇	1	2	yes	complemented
322	#3335	C₂×C₇	1	1	yes	characteristic, complemented
323	#3316	C₂×C₇	1	2	yes	complemented
324	#3312	C₂×C₇	1	2	yes	complemented
325	#3299	C₂×C₇	1	1	yes	characteristic, complemented
326	#3298	C₂×C₇	1	1	yes	characteristic, complemented
327	D₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
328	#3270	C₂×C₇	1	2	yes	complemented
329	#3185	C₂×C₇	1	1	yes	characteristic, complemented
330	#3181	C₂×C₇	1	2	yes	complemented
331	#3117	C₂×C₇	1	2	yes	complemented
332	#3116	C₂×C₇	1	1	yes	characteristic, complemented
333	#3113	C₂×C₇	1	2	yes	complemented
334	#3113	C₂×C₇	1	1	yes	characteristic, complemented
335	#2970	C₂×C₇	1	1	yes	characteristic, complemented
336	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
337	C₂×#441	C₂×C₇	1	2	yes	complemented
338	C₇×#41	—	2	4	no	—
339	C₇×#41	—	2	2	no	—
340	C₇×#41	—	4	1	no	—
341	C₇×#41	—	4	4	no	—
342	C₂×C₇×Q₈	—	2	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	2	no	—
347	C₂×C₇×Q₈	—	2	1	no	—
348	C₂×C₇×Q₈	—	2	4	no	—
349	C₂×C₇×Q₈	—	2	4	no	—
350	C₂×C₇×Q₈	—	2	2	no	—
351	C₂×C₇×Q₈	—	4	2	no	—
352	C₂×C₇×Q₈	—	4	2	no	—
353	C₂×C₇×Q₈	—	4	1	no	—
354	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
355	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
356	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
357	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
358	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
359	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
360	C₂×C₇×D₄	—	2	1	no	—
361	C₂×C₇×D₄	—	2	2	no	—
362	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
363	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
364	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₇	—	2	2	no	—
366	C₂²×C₄×C₇	—	2	2	no	—
367	C₂²×C₄×C₇	—	2	1	no	—
368	C₂²×C₄×C₇	—	2	2	no	—
369	C₂²×C₄×C₇	—	2	1	no	—
370	C₂²×C₄×C₇	—	2	2	no	—
371	C₂²×C₄×C₇	—	2	1	no	—
372	C₂²×C₄×C₇	—	2	1	no	—
373	C₂²×C₄×C₇	—	2	1	no	—
374	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
375	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
377	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
379	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
380	C₇×Q₁₆	—	2	4	no	—
381	C₇×Q₁₆	—	2	4	no	—
382	C₇×Q₁₆	—	2	2	no	—
383	C₇×Q₁₆	—	2	4	no	—
384	C₇×Q₁₆	—	4	2	no	—
385	C₇×Q₁₆	—	4	2	no	—
386	C₇×Q₁₆	#41	1	4	yes	complemented
387	C₇×SD₁₆	—	2	2	no	—
388	C₇×SD₁₆	—	2	2	no	—
389	C₇×SD₁₆	—	4	2	no	—
390	C₇×M₁₆	—	2	2	no	—
391	C₇×M₁₆	—	4	1	no	—
392	C₂×C₇×C₈	—	2	4	no	—
393	C₂×C₇×C₈	—	4	2	no	—
394	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
395	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
396	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
397	C₂×C₇×C₈	C₂⁴	1	2	yes	—
398	C₂×C₇×C₈	C₂⁴	1	2	yes	—
399	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
400	C₇×C₄⋊C₄	—	2	1	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	1	no	—
405	C₇×C₄⋊C₄	—	2	2	no	—
406	C₇×C₄⋊C₄	—	2	1	no	—
407	C₇×C₄⋊C₄	—	2	2	no	—
408	C₇×C₄⋊C₄	—	2	1	no	—
409	C₇×C₄⋊C₄	—	2	2	no	—
410	C₇×C₄⋊C₄	—	2	2	no	—
411	C₇×C₄⋊C₄	—	2	1	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	2	no	—
416	C₇×C₄⋊C₄	—	2	2	no	—
417	C₇×C₄⋊C₄	—	2	1	no	—
418	C₇×C₄⋊C₄	—	2	2	no	—
419	C₇×C₄⋊C₄	—	2	1	no	—
420	C₇×C₄⋊C₄	—	2	2	no	—
421	C₇×C₄⋊C₄	—	2	1	no	—
422	C₇×C₄⋊C₄	—	2	1	no	—
423	C₇×C₄⋊C₄	—	2	2	no	—
424	C₇×C₄⋊C₄	—	2	1	no	—
425	C₇×C₄⋊C₄	—	2	2	no	—
426	C₇×C₄⋊C₄	—	2	2	no	—
427	C₇×C₄⋊C₄	—	2	1	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	C₂×D₄	1	1	yes	characteristic
432	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
433	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
434	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
435	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
436	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
437	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
438	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
439	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
440	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
441	C₇×C₂²⋊C₄	—	2	2	no	—
442	C₇×C₂²⋊C₄	—	2	2	no	—
443	C₇×C₂²⋊C₄	—	2	2	no	—
444	C₇×C₂²⋊C₄	—	2	2	no	—
445	C₇×C₂²⋊C₄	—	2	2	no	—
446	C₇×C₂²⋊C₄	—	2	1	no	—
447	C₇×C₂²⋊C₄	—	2	2	no	—
448	C₇×C₂²⋊C₄	—	2	1	no	—
449	C₇×C₂²⋊C₄	—	2	1	no	—
450	C₇×C₂²⋊C₄	—	2	2	no	—
451	C₇×C₂²⋊C₄	—	2	2	no	—
452	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
453	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
454	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
455	C₄²×C₇	—	2	1	no	—
456	C₄²×C₇	—	2	1	no	—
457	C₄²×C₇	—	2	1	no	—
458	C₄²×C₇	—	2	2	no	—
459	C₄²×C₇	—	2	2	no	—
460	C₄²×C₇	—	2	1	no	—
461	C₄²×C₇	—	2	2	no	—
462	C₄²×C₇	—	2	1	no	—
463	C₄²×C₇	—	2	2	no	—
464	C₄²×C₇	—	2	2	no	—
465	C₄²×C₇	—	2	1	no	—
466	C₄²×C₇	—	2	2	no	—
467	C₄²×C₇	—	2	1	no	—
468	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
469	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
470	C₄²×C₇	C₂×D₄	1	2	yes	—
471	C₄²×C₇	C₂×D₄	1	2	yes	—
472	C₄²×C₇	C₂⁴	1	1	yes	characteristic
473	C₄²×C₇	C₂⁴	1	1	yes	characteristic
474	C₄²×C₇	C₂⁴	1	2	yes	—
475	C₂×#137	C₂²×C₇	1	1	yes	characteristic
476	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
477	Q₈²	C₂²×C₇	1	1	yes	characteristic
478	#557	—	2	1	no	—
479	#557	C₂²×C₇	1	1	yes	characteristic
480	#557	C₂²×C₇	1	1	yes	characteristic
481	#556	—	2	1	no	—
482	#556	C₂²×C₇	1	1	yes	characteristic
483	#554	—	2	1	no	—
484	#554	—	2	2	no	—
485	#554	C₂²×C₇	1	1	yes	characteristic
486	#554	C₂²×C₇	1	2	yes	—
487	#552	—	2	2	no	—
488	#552	C₂²×C₇	1	2	yes	—
489	D₄×Q₈	C₂²×C₇	1	2	yes	—
490	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
491	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
492	#548	C₂²×C₇	1	2	yes	—
493	#547	—	2	1	no	—
494	#547	C₂²×C₇	1	1	yes	characteristic
495	#533	—	2	1	no	—
496	#533	—	2	2	no	—
497	#533	—	2	1	no	—
498	#533	C₂²×C₇	1	2	yes	—
499	#533	C₂²×C₇	1	1	yes	characteristic
500	#533	C₂²×C₇	1	1	yes	characteristic
501	#529	—	2	2	no	—
502	#529	C₂²×C₇	1	2	yes	—
503	C₄×#41	—	2	1	no	—
504	C₄×#41	—	2	1	no	—
505	C₄×#41	C₂²×C₇	1	1	yes	characteristic
506	C₄×#41	C₂²×C₇	1	1	yes	characteristic
507	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
508	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
509	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
510	#501	C₂²×C₇	1	2	yes	—
511	#498	C₂²×C₇	1	1	yes	characteristic
512	#497	C₂²×C₇	1	2	yes	—
513	#494	C₂²×C₇	1	1	yes	characteristic
514	#491	C₂²×C₇	1	2	yes	—
515	#489	C₂²×C₇	1	2	yes	—
516	#487	C₂²×C₇	1	1	yes	characteristic
517	#487	C₂²×C₇	1	1	yes	characteristic
518	#485	C₂²×C₇	1	2	yes	—
519	#484	C₂²×C₇	1	2	yes	—
520	#483	C₂²×C₇	1	2	yes	—
521	#483	C₂²×C₇	1	2	yes	—
522	#483	C₂²×C₇	1	2	yes	—
523	#481	C₂²×C₇	1	2	yes	—
524	#479	C₂²×C₇	1	2	yes	—
525	#479	C₂²×C₇	1	2	yes	—
526	#477	C₂²×C₇	1	1	yes	characteristic
527	#476	C₂²×C₇	1	1	yes	characteristic
528	#475	C₂²×C₇	1	1	yes	characteristic
529	#475	C₂²×C₇	1	2	yes	—
530	#475	C₂²×C₇	1	1	yes	characteristic
531	#475	C₂²×C₇	1	2	yes	—
532	#470	C₂²×C₇	1	2	yes	—
533	#470	C₂²×C₇	1	2	yes	—
534	#467	C₂²×C₇	1	2	yes	—
535	#467	C₂²×C₇	1	2	yes	—
536	#465	C₂²×C₇	1	2	yes	—
537	#465	C₂²×C₇	1	2	yes	—
538	#464	C₂²×C₇	1	2	yes	—
539	#464	C₂²×C₇	1	2	yes	—
540	#462	C₂²×C₇	1	1	yes	characteristic
541	#462	C₂²×C₇	1	2	yes	—
542	#462	C₂²×C₇	1	1	yes	characteristic
543	#462	C₂²×C₇	1	2	yes	—
544	#462	C₂²×C₇	1	1	yes	characteristic
545	#461	C₂²×C₇	1	1	yes	characteristic
546	#452	C₂²×C₇	1	2	yes	—
547	#451	C₂²×C₇	1	2	yes	—
548	#451	C₂²×C₇	1	2	yes	—
549	#451	C₂²×C₇	1	2	yes	—
550	#451	C₂²×C₇	1	2	yes	—
551	#448	C₂²×C₇	1	2	yes	—
552	#446	C₂²×C₇	1	1	yes	characteristic
553	#446	C₂²×C₇	1	1	yes	characteristic
554	#441	C₂²×C₇	1	2	yes	—
555	#441	C₂²×C₇	1	2	yes	—
556	#441	C₂²×C₇	1	1	yes	characteristic
557	#441	C₂²×C₇	1	2	yes	—
558	#441	C₂²×C₇	1	2	yes	—
559	#441	C₂²×C₇	1	2	yes	—
560	#441	C₂²×C₇	1	2	yes	—
561	#441	C₂²×C₇	1	2	yes	—
562	#441	C₂²×C₇	1	2	yes	—
563	#441	C₂²×C₇	1	2	yes	—
564	#441	C₂²×C₇	1	1	yes	characteristic
565	#440	C₂²×C₇	1	2	yes	—
566	#440	C₂²×C₇	1	1	yes	characteristic
567	#440	C₂²×C₇	1	1	yes	characteristic
568	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
569	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
570	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
571	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
572	#435	C₂²×C₇	1	2	yes	—
573	#435	C₂²×C₇	1	2	yes	—
574	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
575	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
576	#432	C₂²×C₇	1	1	yes	characteristic
577	#432	C₂²×C₇	1	2	yes	—
578	#428	C₂²×C₇	1	1	yes	characteristic
579	C₂×#106	C₂²×C₇	1	2	yes	—
580	#419	C₂²×C₇	1	1	yes	characteristic
581	#417	C₂²×C₇	1	1	yes	characteristic
582	C₂×#103	C₂²×C₇	1	2	yes	—
583	C₂×#103	C₂²×C₇	1	2	yes	—
584	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
585	C₂×#97	C₂²×C₇	1	2	yes	—
586	C₂³×C₇	—	2	1	no	—
587	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
588	C₂³×C₇	C₂²×D₄	1	2	yes	—
589	C₇×Q₈	—	2	2	no	—
590	C₇×Q₈	—	2	1	no	—
591	C₇×Q₈	—	2	1	no	—
592	C₇×Q₈	—	2	1	no	—
593	C₇×Q₈	—	2	2	no	—
594	C₇×Q₈	—	2	2	no	—
595	C₇×Q₈	—	2	2	no	—
596	C₇×Q₈	—	2	2	no	—
597	C₇×Q₈	—	2	1	no	—
598	C₇×Q₈	—	4	2	no	—
599	C₇×Q₈	—	4	4	no	—
600	C₇×Q₈	—	4	4	no	—
601	C₇×Q₈	—	4	2	no	—
602	C₇×Q₈	—	8	2	no	—
603	C₇×Q₈	—	8	1	no	—
604	C₇×Q₈	C₂×#41	1	2	yes	—
605	C₇×Q₈	C₂×#41	1	2	yes	—
606	C₇×D₄	—	2	4	no	—
607	C₇×D₄	—	2	1	no	—
608	C₇×D₄	—	2	1	no	—
609	C₇×D₄	—	4	2	no	—
610	C₇×D₄	—	4	4	no	—
611	C₇×D₄	#137	1	4	yes	complemented
612	C₂×C₄×C₇	—	2	4	no	—
613	C₂×C₄×C₇	—	2	1	no	—
614	C₂×C₄×C₇	—	2	1	no	—
615	C₂×C₄×C₇	—	2	2	no	—
616	C₂×C₄×C₇	—	2	2	no	—
617	C₂×C₄×C₇	—	2	1	no	—
618	C₂×C₄×C₇	—	2	2	no	—
619	C₂×C₄×C₇	—	2	1	no	—
620	C₂×C₄×C₇	—	2	1	no	—
621	C₂×C₄×C₇	—	2	1	no	—
622	C₂×C₄×C₇	—	2	1	no	—
623	C₂×C₄×C₇	—	2	2	no	—
624	C₂×C₄×C₇	—	2	1	no	—
625	C₂×C₄×C₇	—	2	2	no	—
626	C₂×C₄×C₇	—	2	2	no	—
627	C₂×C₄×C₇	—	2	2	no	—
628	C₂×C₄×C₇	—	2	1	no	—
629	C₂×C₄×C₇	—	4	2	no	—
630	C₂×C₄×C₇	—	4	1	no	—
631	C₂×C₄×C₇	—	4	2	no	—
632	C₂×C₄×C₇	—	4	4	no	—
633	C₂×C₄×C₇	—	4	4	no	—
634	C₂×C₄×C₇	—	4	2	no	—
635	C₂×C₄×C₇	—	4	2	no	—
636	C₂×C₄×C₇	—	4	4	no	—
637	C₂×C₄×C₇	—	4	2	no	—
638	C₂×C₄×C₇	—	8	2	no	—
639	C₂×C₄×C₇	—	8	1	no	—
640	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
641	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
642	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
643	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
644	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
645	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
646	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
647	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
648	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
649	C₇×C₈	—	2	2	no	—
650	C₇×C₈	—	2	1	no	—
651	C₇×C₈	—	2	1	no	—
652	C₇×C₈	—	2	2	no	—
653	C₇×C₈	—	2	1	no	—
654	C₇×C₈	C₂×#41	1	2	yes	—
655	C₂×#41	—	2	1	no	—
656	C₂×#41	C₇×D₄	1	1	yes	characteristic
657	C₂×#41	C₂³×C₇	1	1	yes	characteristic
658	C₂²×Q₈	C₂³×C₇	1	2	yes	—
659	C₂²×Q₈	C₂³×C₇	1	2	yes	—
660	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
661	#137	—	2	4	no	—
662	C₂×Q₁₆	—	2	8	no	—
663	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
664	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
665	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
666	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
667	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
668	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
669	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
670	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
671	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
672	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
673	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
674	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
675	C₂²×C₈	C₂³×C₇	1	2	yes	—
676	C₂²×C₈	C₂³×C₇	1	2	yes	—
677	C₄⋊Q₈	—	2	1	no	—
678	C₄⋊Q₈	—	2	1	no	—
679	C₄⋊Q₈	—	2	2	no	—
680	C₄⋊Q₈	—	2	1	no	—
681	C₄⋊Q₈	—	2	1	no	—
682	C₄⋊Q₈	—	2	2	no	—
683	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
684	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
685	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
686	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
687	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
688	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
689	#126	—	2	2	no	—
690	#126	—	2	2	no	—
691	#126	—	2	2	no	—
692	#125	—	2	2	no	—
693	#125	—	2	2	no	—
694	#125	—	2	1	no	—
695	#125	—	2	2	no	—
696	#125	—	2	2	no	—
697	#125	—	2	1	no	—
698	#125	—	2	1	no	—
699	#125	—	2	1	no	—
700	#125	—	2	2	no	—
701	#125	C₂³×C₇	1	2	yes	—
702	#124	—	2	2	no	—
703	#124	C₂³×C₇	1	2	yes	—
704	#123	—	2	2	no	—
705	#123	—	2	2	no	—
706	#123	—	2	2	no	—
707	C₂²⋊Q₈	—	2	1	no	—
708	C₂²⋊Q₈	—	2	1	no	—
709	C₂²⋊Q₈	—	2	2	no	—
710	C₂²⋊Q₈	—	2	1	no	—
711	C₂²⋊Q₈	—	2	1	no	—
712	C₂²⋊Q₈	—	2	2	no	—
713	C₂²⋊Q₈	—	2	2	no	—
714	C₂²⋊Q₈	—	2	2	no	—
715	C₂²⋊Q₈	—	2	2	no	—
716	C₂²⋊Q₈	—	2	2	no	—
717	C₂²⋊Q₈	—	2	2	no	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	—	2	2	no	—
720	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
721	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
722	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
723	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
724	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
725	#121	—	2	2	no	—
726	#121	C₂³×C₇	1	2	yes	—
727	C₄×Q₈	—	2	1	no	—
728	C₄×Q₈	—	2	1	no	—
729	C₄×Q₈	—	2	1	no	—
730	C₄×Q₈	—	2	2	no	—
731	C₄×Q₈	—	2	1	no	—
732	C₄×Q₈	—	2	2	no	—
733	C₄×Q₈	—	2	2	no	—
734	C₄×Q₈	—	2	1	no	—
735	C₄×Q₈	—	2	2	no	—
736	C₄×Q₈	—	2	1	no	—
737	C₄×Q₈	—	2	1	no	—
738	C₄×Q₈	—	2	2	no	—
739	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
740	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
741	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
742	C₄×Q₈	C₂³×C₇	1	2	yes	—
743	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
744	C₄×Q₈	C₂³×C₇	1	2	yes	—
745	C₄×Q₈	C₂³×C₇	1	2	yes	—
746	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
747	C₄×Q₈	C₂³×C₇	1	2	yes	—
748	C₄×Q₈	C₂³×C₇	1	2	yes	—
749	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
750	C₄×Q₈	C₂³×C₇	1	2	yes	—
751	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
752	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
753	C₄×D₄	—	2	1	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	1	no	—
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	—	2	1	no	—
758	C₄×D₄	—	2	2	no	—
759	C₄×D₄	—	2	1	no	—
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	2	2	no	—
762	C₄×D₄	C₇×D₄	1	1	yes	characteristic
763	C₄×D₄	C₇×D₄	1	2	yes	—
764	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
765	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
766	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
767	C₄×D₄	C₂³×C₇	1	2	yes	—
768	#117	—	2	2	no	—
769	#117	—	2	1	no	—
770	#117	—	2	1	no	—
771	#117	—	2	1	no	—
772	#117	—	2	2	no	—
773	#117	—	2	1	no	—
774	#117	—	2	2	no	—
775	#117	C₇×D₄	1	2	yes	—
776	#117	C₇×D₄	1	1	yes	characteristic
777	#117	C₂³×C₇	1	1	yes	characteristic
778	C₂×C₄⋊C₄	—	2	2	no	—
779	C₂×C₄⋊C₄	—	2	2	no	—
780	C₂×C₄⋊C₄	—	2	1	no	—
781	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
782	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
783	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
784	C₂×C₄²	—	2	2	no	—
785	C₂×C₄²	—	2	2	no	—
786	C₂×C₄²	—	2	1	no	—
787	C₂×C₄²	—	2	1	no	—
788	C₂×C₄²	C₂³×C₇	1	2	yes	—
789	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
790	#107	C₂³×C₇	1	1	yes	characteristic
791	#107	C₂³×C₇	1	1	yes	characteristic
792	#107	C₂³×C₇	1	2	yes	—
793	#106	C₂³×C₇	1	1	yes	characteristic
794	#106	C₂³×C₇	1	2	yes	—
795	#106	C₂³×C₇	1	2	yes	—
796	#106	C₂³×C₇	1	2	yes	—
797	#106	C₂³×C₇	1	1	yes	characteristic
798	#106	C₂³×C₇	1	2	yes	—
799	#106	C₂³×C₇	1	2	yes	—
800	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
801	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
802	C₄⋊C₈	C₂³×C₇	1	2	yes	—
803	C₄⋊C₈	C₂³×C₇	1	2	yes	—
804	#103	C₂³×C₇	1	1	yes	characteristic
805	#103	C₂³×C₇	1	1	yes	characteristic
806	#103	C₂³×C₇	1	2	yes	—
807	#103	C₂³×C₇	1	2	yes	—
808	#103	C₂³×C₇	1	2	yes	—
809	#103	C₂³×C₇	1	2	yes	—
810	#103	C₂³×C₇	1	2	yes	—
811	#103	C₂³×C₇	1	2	yes	—
812	#103	C₂³×C₇	1	1	yes	characteristic
813	#103	C₂³×C₇	1	1	yes	characteristic
814	#103	C₂³×C₇	1	1	yes	characteristic
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	2	yes	—
819	#103	C₂³×C₇	1	2	yes	—
820	#103	C₂³×C₇	1	2	yes	—
821	#102	C₂³×C₇	1	1	yes	characteristic
822	#102	C₂³×C₇	1	1	yes	characteristic
823	#102	C₂³×C₇	1	2	yes	—
824	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
825	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
826	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
827	#97	C₂³×C₇	1	1	yes	characteristic
828	#97	C₂³×C₇	1	2	yes	—
829	#97	C₂³×C₇	1	2	yes	—
830	#97	C₂³×C₇	1	2	yes	—
831	#97	C₂³×C₇	1	1	yes	characteristic
832	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
833	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
834	C₂²×C₇	—	2	2	no	—
835	C₂²×C₇	—	2	2	no	—
836	C₂²×C₇	—	2	1	no	—
837	C₂²×C₇	—	2	1	no	—
838	C₂²×C₇	—	2	1	no	—
839	C₂²×C₇	—	4	1	no	—
840	C₂²×C₇	—	4	1	no	—
841	C₂²×C₇	—	4	1	no	—
842	C₂²×C₇	C₂×#137	1	4	yes	—
843	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
844	C₄×C₇	—	2	1	no	—
845	C₄×C₇	—	2	2	no	—
846	C₄×C₇	—	2	1	no	—
847	C₄×C₇	—	2	1	no	—
848	C₄×C₇	—	2	2	no	—
849	C₄×C₇	—	2	2	no	—
850	C₄×C₇	—	2	2	no	—
851	C₄×C₇	—	2	1	no	—
852	C₄×C₇	—	2	2	no	—
853	C₄×C₇	—	4	1	no	—
854	C₄×C₇	—	4	1	no	—
855	C₄×C₇	—	4	2	no	—
856	C₄×C₇	—	4	1	no	—
857	C₄×C₇	—	4	2	no	—
858	C₄×C₇	—	4	1	no	—
859	C₄×C₇	—	4	2	no	—
860	C₄×C₇	—	4	1	no	—
861	C₄×C₇	—	4	2	no	—
862	C₄×C₇	C₂×#137	1	2	yes	—
863	C₄×C₇	C₂²×#41	1	1	yes	characteristic
864	C₄×C₇	#585	1	1	yes	characteristic
865	#41	—	2	4	no	—
866	#41	—	2	2	no	—
867	#41	—	4	1	no	—
868	#41	—	4	4	no	—
869	C₂×Q₈	—	2	2	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	2	no	—
872	C₂×Q₈	—	2	1	no	—
873	C₂×Q₈	—	2	2	no	—
874	C₂×Q₈	—	2	1	no	—
875	C₂×Q₈	—	2	4	no	—
876	C₂×Q₈	—	2	4	no	—
877	C₂×Q₈	—	2	2	no	—
878	C₂×Q₈	—	4	2	no	—
879	C₂×Q₈	—	4	2	no	—
880	C₂×Q₈	—	4	1	no	—
881	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
882	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
883	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
884	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
885	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
886	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
887	C₂×D₄	—	2	1	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
890	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
891	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
892	C₂²×C₄	—	2	2	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	1	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
902	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
903	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
904	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
905	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
906	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
907	Q₁₆	—	2	4	no	—
908	Q₁₆	—	2	4	no	—
909	Q₁₆	—	2	2	no	—
910	Q₁₆	—	2	4	no	—
911	Q₁₆	—	4	2	no	—
912	Q₁₆	—	4	2	no	—
913	Q₁₆	C₇×#41	1	4	yes	complemented
914	SD₁₆	—	2	2	no	—
915	SD₁₆	—	2	2	no	—
916	SD₁₆	—	4	2	no	—
917	M₁₆	—	2	2	no	—
918	M₁₆	—	4	1	no	—
919	C₂×C₈	—	2	4	no	—
920	C₂×C₈	—	4	2	no	—
921	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
922	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
923	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
924	C₂×C₈	C₂⁴×C₇	1	2	yes	—
925	C₂×C₈	C₂⁴×C₇	1	2	yes	—
926	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	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	1	no	—
945	C₄⋊C₄	—	2	2	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	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
959	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
960	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
961	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
964	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
965	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
980	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
981	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
982	C₄²	—	2	1	no	—
983	C₄²	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	1	no	—
995	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
996	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
997	C₄²	C₂×C₇×D₄	1	2	yes	—
998	C₄²	C₂×C₇×D₄	1	2	yes	—
999	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1000	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1001	C₄²	C₂⁴×C₇	1	2	yes	—
1002	C₂×C₇	—	2	4	no	—
1003	C₂×C₇	—	4	1	no	—
1004	C₂×C₇	—	8	1	no	—
1005	C₂×C₇	D₄×#41	1	1	yes	characteristic
1006	C₂×C₇	C₂²×#137	1	1	yes	characteristic
1007	C₂×C₇	#3586	1	1	yes	characteristic
1008	C₂³	—	2	1	no	—
1009	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1010	C₂³	C₂²×C₇×D₄	1	2	yes	—
1011	Q₈	—	2	1	no	—
1012	Q₈	—	2	1	no	—
1013	Q₈	—	2	2	no	—
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	2	no	—
1016	Q₈	—	2	2	no	—
1017	Q₈	—	2	2	no	—
1018	Q₈	—	2	2	no	—
1019	Q₈	—	2	1	no	—
1020	Q₈	—	4	2	no	—
1021	Q₈	—	4	4	no	—
1022	Q₈	—	4	4	no	—
1023	Q₈	—	4	2	no	—
1024	Q₈	—	8	2	no	—
1025	Q₈	—	8	1	no	—
1026	Q₈	C₂×C₇×#41	1	2	yes	—
1027	Q₈	C₂×C₇×#41	1	2	yes	—
1028	D₄	—	2	4	no	—
1029	D₄	—	2	1	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	4	4	no	—
1033	D₄	C₇×#137	1	4	yes	complemented
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	4	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	4	1	no	—
1053	C₂×C₄	—	4	2	no	—
1054	C₂×C₄	—	4	4	no	—
1055	C₂×C₄	—	4	4	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	4	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	8	2	no	—
1061	C₂×C₄	—	8	1	no	—
1062	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1063	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1064	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1065	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1066	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1067	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1068	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1069	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1070	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1071	C₈	—	2	2	no	—
1072	C₈	—	2	1	no	—
1073	C₈	—	2	1	no	—
1074	C₈	—	2	2	no	—
1075	C₈	—	2	1	no	—
1076	C₈	C₂×C₇×#41	1	2	yes	—
1077	C₇	#61457	1	1	yes	characteristic, direct product factor, Sylow
1078	C₂²	—	2	2	no	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	C₂×C₇×#137	1	4	yes	—
1087	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1088	C₄	—	2	1	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	2	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	2	1	no	—
1094	C₄	—	2	2	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	2	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	2	no	—
1106	C₄	C₂×C₇×#137	1	2	yes	—
1107	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1108	C₄	C₇×#585	1	1	yes	characteristic
1109	C₂	—	2	4	no	—
1110	C₂	—	4	1	no	—
1111	C₂	—	8	1	no	—
1112	C₂	C₇×D₄×#41	1	1	yes	characteristic
1113	C₂	C₂²×C₇×#137	1	1	yes	characteristic
1114	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×#3482	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×Q₈×#41	C₂	semidirect
3. C₇×#3398	C₂	semidirect
4. C₇×#3387	C₂	semidirect
5. C₇×#3374	C₂	semidirect
6. C₇×#3369	C₂	semidirect
7. C₇×#3344	C₂	semidirect
8. C₇×#3335	C₂	semidirect
9. C₇×#3316	C₂	semidirect
10. C₇×#3312	C₂	semidirect
11. C₇×#3299	C₂	semidirect
12. C₇×#3298	C₂	semidirect
13. C₇×D₄×Q₁₆	C₂	semidirect
14. C₇×#3270	C₂	semidirect
15. C₇×#3185	C₂	semidirect
16. C₇×#3181	C₂	semidirect
17. C₇×#3117	C₂	semidirect
18. C₇×#3116	C₂	semidirect
19. C₇×#3113	C₂	semidirect
20. C₇×#3113	C₂	semidirect
21. C₇×#2970	C₂	semidirect
22. C₄×C₇×#137	C₂	semidirect
23. C₂×C₇×#441	C₂	semidirect
135. #61457	C₇	direct (N × H)
316. Q₈×#41	C₂×C₇	semidirect
317. #3398	C₂×C₇	semidirect
318. #3387	C₂×C₇	semidirect
319. #3374	C₂×C₇	semidirect
320. #3369	C₂×C₇	semidirect
321. #3344	C₂×C₇	semidirect
322. #3335	C₂×C₇	semidirect
323. #3316	C₂×C₇	semidirect
324. #3312	C₂×C₇	semidirect
325. #3299	C₂×C₇	semidirect
326. #3298	C₂×C₇	semidirect
327. D₄×Q₁₆	C₂×C₇	semidirect
328. #3270	C₂×C₇	semidirect
329. #3185	C₂×C₇	semidirect
330. #3181	C₂×C₇	semidirect
331. #3117	C₂×C₇	semidirect
332. #3116	C₂×C₇	semidirect
333. #3113	C₂×C₇	semidirect
334. #3113	C₂×C₇	semidirect
335. #2970	C₂×C₇	semidirect
336. C₄×#137	C₂×C₇	semidirect
337. C₂×#441	C₂×C₇	semidirect
386. C₇×Q₁₆	#41	semidirect
611. C₇×D₄	#137	semidirect
913. Q₁₆	C₇×#41	semidirect
1033. D₄	C₇×#137	semidirect
1077. C₇	#61457	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×#3482	2
C₇×Q₈×#41	2
C₇×#3398	2
C₇×#3387	2
C₇×#3374	2
C₇×#3369	2
C₇×#3344	2
C₇×#3335	2
C₇×#3316	2
C₇×#3312	2
C₇×#3299	2
C₇×#3298	2
C₇×D₄×Q₁₆	2
C₇×#3270	2
C₇×#3185	2
C₇×#3181	2
C₇×#3117	2
C₇×#3116	2
C₇×#3113	2
C₇×#2970	2
C₄×C₇×#137	2
C₂×C₇×#441	2
#61457	7

Subgroups — C7×#61457 #13238673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61457 #13238673