Subgroups — C₇×#61380 #13238596

Order 1792.

1734 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3390	C₂	1	2	yes	maximal, complemented
4	C₇×#3389	C₂	1	2	yes	maximal, complemented
5	C₇×#3388	C₂	1	2	yes	maximal, complemented
6	C₇×#3388	C₂	1	2	yes	maximal, complemented
7	C₇×#3387	C₂	1	2	yes	maximal, complemented
8	C₇×#3386	C₂	1	2	yes	maximal, complemented
9	C₇×#3385	C₂	1	2	yes	maximal, complemented
10	C₇×#3384	C₂	1	2	yes	maximal, complemented
11	C₇×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3163	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#501	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3084	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3084	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3080	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2961	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2952	C₂	1	1	yes	maximal, characteristic
22	C₇×#2951	C₂	1	1	yes	maximal, characteristic
23	C₇×#2943	C₂	1	1	yes	maximal, characteristic
24	C₂×C₇×#135	C₂²	1	1	yes	characteristic
25	C₇×Q₈²	C₂²	1	2	yes	—
26	C₇×#557	C₂²	1	2	yes	—
27	C₇×#557	C₂²	1	2	yes	—
28	C₇×#557	C₂²	1	2	yes	—
29	C₇×#554	—	2	2	no	—
30	C₇×#554	—	2	2	no	—
31	C₇×#554	—	2	2	no	—
32	C₇×#554	C₂²	1	2	yes	—
33	C₇×#554	C₂²	1	2	yes	—
34	C₇×#554	C₂²	1	2	yes	—
35	C₇×D₄×Q₈	—	2	2	no	—
36	C₇×D₄×Q₈	C₂²	1	2	yes	—
37	C₇×#544	—	2	1	no	—
38	C₇×#544	—	2	1	no	—
39	C₇×#544	—	2	1	no	—
40	C₇×#544	—	2	1	no	—
41	C₇×#544	C₂²	1	1	yes	characteristic
42	C₇×#544	C₂²	1	1	yes	characteristic
43	C₇×#544	C₂²	1	1	yes	characteristic
44	C₇×#544	C₂²	1	1	yes	characteristic
45	C₇×#533	—	2	1	no	—
46	C₇×#533	—	2	1	no	—
47	C₇×#533	C₂²	1	1	yes	characteristic
48	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
49	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
50	C₂×C₇×#125	—	2	1	no	—
51	C₂×C₇×#125	C₂²	1	1	yes	characteristic
52	C₇×#520	C₂²	1	1	yes	characteristic
53	C₇×#520	C₂²	1	1	yes	characteristic
54	C₇×#520	C₂²	1	1	yes	characteristic
55	C₇×#520	C₂²	1	1	yes	characteristic
56	C₄×C₇×#41	C₂²	1	1	yes	characteristic
57	C₄×C₇×#41	C₂²	1	1	yes	characteristic
58	C₇×#501	C₂²	1	2	yes	—
59	C₇×#501	C₂²	1	2	yes	—
60	C₇×#501	C₂²	1	2	yes	—
61	C₇×#501	C₂²	1	2	yes	—
62	C₇×#501	C₂²	1	2	yes	—
63	C₇×#501	C₂²	1	2	yes	—
64	C₇×#501	C₂²	1	2	yes	—
65	C₇×#501	C₂²	1	2	yes	—
66	C₇×#500	C₂²	1	2	yes	—
67	C₇×#499	C₂²	1	2	yes	—
68	C₇×#499	C₂²	1	2	yes	—
69	C₇×#498	C₂²	1	2	yes	—
70	C₇×#479	C₂²	1	2	yes	—
71	C₇×#479	C₂²	1	2	yes	—
72	C₇×#479	C₂²	1	2	yes	—
73	C₇×#479	C₂²	1	2	yes	—
74	C₇×#479	C₂²	1	2	yes	—
75	C₇×#479	C₂²	1	2	yes	—
76	C₇×#478	C₂²	1	2	yes	—
77	C₇×#478	C₂²	1	2	yes	—
78	C₇×#478	C₂²	1	2	yes	—
79	C₇×#478	C₂²	1	2	yes	—
80	C₇×#478	C₂²	1	2	yes	—
81	C₇×#478	C₂²	1	2	yes	—
82	C₇×#477	C₂²	1	2	yes	—
83	C₇×#477	C₂²	1	2	yes	—
84	C₇×#477	C₂²	1	2	yes	—
85	C₇×#476	C₂²	1	2	yes	—
86	C₇×#476	C₂²	1	2	yes	—
87	C₇×#476	C₂²	1	2	yes	—
88	C₇×#475	C₂²	1	2	yes	—
89	C₇×#475	C₂²	1	2	yes	—
90	C₇×#475	C₂²	1	2	yes	—
91	C₇×#474	C₂²	1	2	yes	—
92	C₇×#474	C₂²	1	2	yes	—
93	C₇×#474	C₂²	1	2	yes	—
94	C₇×#446	C₂²	1	2	yes	—
95	C₇×#446	C₂²	1	2	yes	—
96	C₇×#446	C₂²	1	2	yes	—
97	C₇×#446	C₂²	1	2	yes	—
98	C₇×#442	C₂²	1	1	yes	characteristic
99	C₇×#442	C₂²	1	1	yes	characteristic
100	C₇×#442	C₂²	1	2	yes	—
101	C₇×#441	C₂²	1	1	yes	characteristic
102	C₇×#441	C₂²	1	1	yes	characteristic
103	C₇×#441	C₂²	1	2	yes	—
104	C₇×#440	C₂²	1	1	yes	characteristic
105	C₇×#440	C₂²	1	1	yes	characteristic
106	C₇×#440	C₂²	1	1	yes	characteristic
107	C₇×#440	C₂²	1	1	yes	characteristic
108	C₇×#440	C₂²	1	2	yes	—
109	C₇×#440	C₂²	1	2	yes	—
110	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
111	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
112	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
113	C₄×C₇×D₈	C₂²	1	2	yes	—
114	C₇×#428	C₂²	1	1	yes	characteristic
115	C₇×#428	C₂²	1	1	yes	characteristic
116	C₇×#428	C₂²	1	1	yes	characteristic
117	C₇×#428	C₂²	1	1	yes	characteristic
118	C₇×#427	C₂²	1	1	yes	characteristic
119	C₂×C₇×#107	C₂²	1	1	yes	characteristic
120	C₂×C₇×#107	C₂²	1	1	yes	characteristic
121	C₂×C₇×#106	C₂²	1	1	yes	characteristic
122	C₂×C₇×#106	C₂²	1	1	yes	characteristic
123	C₇×#424	C₂²	1	1	yes	characteristic
124	C₇×#424	C₂²	1	1	yes	characteristic
125	C₇×#423	C₂²	1	1	yes	characteristic
126	C₇×#417	C₂²	1	1	yes	characteristic
127	C₇×#417	C₂²	1	1	yes	characteristic
128	C₇×#417	C₂²	1	1	yes	characteristic
129	C₇×#417	C₂²	1	1	yes	characteristic
130	C₇×#416	C₂²	1	1	yes	characteristic
131	C₇×#416	C₂²	1	1	yes	characteristic
132	C₇×#405	C₂²	1	1	yes	characteristic
133	C₇×#405	C₂²	1	1	yes	characteristic
134	C₂×C₇×#97	C₂²	1	1	yes	characteristic
135	#61380	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	C₂³	1	1	yes	characteristic
137	C₂×C₇×#41	C₂³	1	1	yes	characteristic
138	C₂²×C₇×Q₈	—	2	2	no	—
139	C₂²×C₇×Q₈	—	2	1	no	—
140	C₇×#135	Q₈	1	8	yes	complemented
141	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
142	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
143	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
145	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
147	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
148	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
149	C₇×C₄⋊Q₈	—	2	2	no	—
150	C₇×C₄⋊Q₈	—	2	2	no	—
151	C₇×C₄⋊Q₈	—	2	2	no	—
152	C₇×C₄⋊Q₈	—	2	1	no	—
153	C₇×C₄⋊Q₈	—	2	1	no	—
154	C₇×C₄⋊Q₈	—	2	2	no	—
155	C₇×C₄⋊Q₈	—	2	1	no	—
156	C₇×C₄⋊Q₈	—	2	1	no	—
157	C₇×C₄⋊Q₈	—	2	2	no	—
158	C₇×C₄⋊Q₈	—	2	2	no	—
159	C₇×C₄⋊Q₈	—	2	1	no	—
160	C₇×C₄⋊Q₈	—	2	1	no	—
161	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
162	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
163	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
168	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
169	C₇×#125	—	2	1	no	—
170	C₇×#125	—	2	1	no	—
171	C₇×#125	—	2	2	no	—
172	C₇×#125	—	2	2	no	—
173	C₇×#125	—	2	1	no	—
174	C₇×#125	—	2	1	no	—
175	C₇×#125	—	2	2	no	—
176	C₇×#125	—	2	2	no	—
177	C₇×#125	—	2	2	no	—
178	C₇×#125	—	2	2	no	—
179	C₇×#125	—	2	1	no	—
180	C₇×#125	—	2	1	no	—
181	C₇×#125	D₄	1	1	yes	characteristic
182	C₇×#125	D₄	1	1	yes	characteristic
183	C₇×#125	C₂³	1	2	yes	—
184	C₇×#125	C₂³	1	2	yes	—
185	C₇×#125	C₂³	1	2	yes	—
186	C₇×#125	C₂³	1	2	yes	—
187	C₇×#125	C₂³	1	2	yes	—
188	C₇×#125	C₂³	1	2	yes	—
189	C₇×C₂²⋊Q₈	—	2	2	no	—
190	C₇×C₂²⋊Q₈	—	2	2	no	—
191	C₇×C₂²⋊Q₈	—	2	2	no	—
192	C₇×C₂²⋊Q₈	—	2	2	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	—	2	2	no	—
202	C₇×C₂²⋊Q₈	—	2	2	no	—
203	C₇×C₂²⋊Q₈	—	2	2	no	—
204	C₇×C₂²⋊Q₈	—	2	2	no	—
205	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
206	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
207	C₄×C₇×Q₈	—	2	2	no	—
208	C₄×C₇×Q₈	—	2	2	no	—
209	C₄×C₇×Q₈	—	2	2	no	—
210	C₄×C₇×Q₈	—	2	2	no	—
211	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
212	C₄×C₇×Q₈	C₂³	1	2	yes	—
213	C₄×C₇×Q₈	C₂³	1	2	yes	—
214	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
215	C₄×C₇×Q₈	C₂³	1	2	yes	—
216	C₄×C₇×Q₈	C₂³	1	2	yes	—
217	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
218	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
219	C₄×C₇×Q₈	C₂³	1	2	yes	—
220	C₄×C₇×Q₈	C₂³	1	2	yes	—
221	C₄×C₇×D₄	—	2	1	no	—
222	C₄×C₇×D₄	—	2	1	no	—
223	C₄×C₇×D₄	—	2	1	no	—
224	C₄×C₇×D₄	—	2	1	no	—
225	C₄×C₇×D₄	—	2	2	no	—
226	C₄×C₇×D₄	—	2	2	no	—
227	C₄×C₇×D₄	—	2	2	no	—
228	C₄×C₇×D₄	—	2	2	no	—
229	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
230	C₄×C₇×D₄	C₂³	1	2	yes	—
231	C₄×C₇×D₄	C₂³	1	2	yes	—
232	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
233	C₄×C₇×D₄	C₂³	1	2	yes	—
234	C₄×C₇×D₄	C₂³	1	2	yes	—
235	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
236	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
237	C₇×#117	—	2	1	no	—
238	C₇×#117	—	2	1	no	—
239	C₇×#117	—	2	1	no	—
240	C₇×#117	—	2	1	no	—
241	C₇×#117	—	2	1	no	—
242	C₇×#117	—	2	1	no	—
243	C₇×#117	C₂³	1	1	yes	characteristic
244	C₇×#117	C₂³	1	1	yes	characteristic
245	C₇×#117	C₂³	1	1	yes	characteristic
246	C₇×#117	C₂³	1	1	yes	characteristic
247	C₂×C₇×C₄⋊C₄	—	2	1	no	—
248	C₂×C₇×C₄⋊C₄	—	2	1	no	—
249	C₂×C₇×C₄⋊C₄	—	2	1	no	—
250	C₂×C₇×C₄⋊C₄	—	2	1	no	—
251	C₂×C₇×C₄⋊C₄	—	2	1	no	—
252	C₂×C₇×C₄⋊C₄	—	2	1	no	—
253	C₂×C₇×C₄⋊C₄	—	2	1	no	—
254	C₂×C₇×C₄⋊C₄	—	2	2	no	—
255	C₂×C₇×C₄⋊C₄	—	2	2	no	—
256	C₂×C₇×C₄⋊C₄	—	2	2	no	—
257	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₄²×C₇	—	2	1	no	—
262	C₂×C₄²×C₇	—	2	1	no	—
263	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
264	C₇×#107	C₂³	1	2	yes	—
265	C₇×#107	C₂³	1	2	yes	—
266	C₇×#107	C₂³	1	2	yes	—
267	C₇×#107	C₂³	1	2	yes	—
268	C₇×#107	C₂³	1	2	yes	—
269	C₇×#107	C₂³	1	2	yes	—
270	C₇×#107	C₂³	1	1	yes	characteristic
271	C₇×#107	C₂³	1	2	yes	—
272	C₇×#107	C₂³	1	1	yes	characteristic
273	C₇×#107	C₂³	1	2	yes	—
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	2	yes	—
278	C₇×#106	C₂³	1	2	yes	—
279	C₇×#106	C₂³	1	2	yes	—
280	C₇×#106	C₂³	1	1	yes	characteristic
281	C₇×#106	C₂³	1	2	yes	—
282	C₇×#106	C₂³	1	1	yes	characteristic
283	C₇×#106	C₂³	1	2	yes	—
284	C₇×C₄⋊C₈	C₂³	1	2	yes	—
285	C₇×C₄⋊C₈	C₂³	1	2	yes	—
286	C₇×C₄⋊C₈	C₂³	1	2	yes	—
287	C₇×C₄⋊C₈	C₂³	1	2	yes	—
288	C₇×C₄⋊C₈	C₂³	1	2	yes	—
289	C₇×C₄⋊C₈	C₂³	1	2	yes	—
290	C₇×#103	C₂³	1	1	yes	characteristic
291	C₇×#103	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	1	yes	characteristic
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	1	yes	characteristic
296	C₇×#103	C₂³	1	2	yes	—
297	C₇×#103	C₂³	1	1	yes	characteristic
298	C₇×#102	C₂³	1	1	yes	characteristic
299	C₇×#102	C₂³	1	2	yes	—
300	C₇×#102	C₂³	1	1	yes	characteristic
301	C₇×#102	C₂³	1	2	yes	—
302	C₇×#102	C₂³	1	2	yes	—
303	C₇×#102	C₂³	1	1	yes	characteristic
304	C₇×#102	C₂³	1	2	yes	—
305	C₇×#102	C₂³	1	1	yes	characteristic
306	C₇×#97	C₂³	1	1	yes	characteristic
307	C₇×#97	C₂³	1	1	yes	characteristic
308	C₇×#97	C₂³	1	1	yes	characteristic
309	C₇×#97	C₂³	1	1	yes	characteristic
310	C₇×#97	C₂³	1	2	yes	—
311	C₇×#97	C₂³	1	2	yes	—
312	C₄×C₇×C₈	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	2	yes	—
314	#3504	C₂×C₇	1	1	yes	characteristic, complemented
315	#3503	C₂×C₇	1	1	yes	characteristic, complemented
316	#3390	C₂×C₇	1	2	yes	complemented
317	#3389	C₂×C₇	1	2	yes	complemented
318	#3388	C₂×C₇	1	2	yes	complemented
319	#3388	C₂×C₇	1	2	yes	complemented
320	#3387	C₂×C₇	1	2	yes	complemented
321	#3386	C₂×C₇	1	2	yes	complemented
322	#3385	C₂×C₇	1	2	yes	complemented
323	#3384	C₂×C₇	1	2	yes	complemented
324	#3164	C₂×C₇	1	1	yes	characteristic, complemented
325	#3163	C₂×C₇	1	1	yes	characteristic, complemented
326	C₂×#501	C₂×C₇	1	1	yes	characteristic, complemented
327	#3084	C₂×C₇	1	1	yes	characteristic, complemented
328	#3084	C₂×C₇	1	1	yes	characteristic, complemented
329	#3083	C₂×C₇	1	1	yes	characteristic, complemented
330	#3083	C₂×C₇	1	1	yes	characteristic, complemented
331	#3080	C₂×C₇	1	1	yes	characteristic, complemented
332	#3079	C₂×C₇	1	1	yes	characteristic, complemented
333	#2961	C₂×C₇	1	1	yes	characteristic, complemented
334	#2952	C₂×C₇	1	1	yes	characteristic
335	#2951	C₂×C₇	1	1	yes	characteristic
336	#2943	C₂×C₇	1	1	yes	characteristic
337	C₇×#41	—	2	2	no	—
338	C₇×#41	—	2	2	no	—
339	C₇×#41	C₂×Q₈	1	4	yes	—
340	C₇×#41	C₂×Q₈	1	4	yes	complemented
341	C₂×C₇×Q₈	—	2	2	no	—
342	C₂×C₇×Q₈	—	2	2	no	—
343	C₂×C₇×Q₈	—	2	2	no	—
344	C₂×C₇×Q₈	—	2	2	no	—
345	C₂×C₇×Q₈	—	2	2	no	—
346	C₂×C₇×Q₈	—	2	2	no	—
347	C₂×C₇×Q₈	—	8	2	no	—
348	C₂×C₇×Q₈	—	8	4	no	—
349	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
350	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
351	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
352	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
353	C₂×C₇×D₄	—	2	1	no	—
354	C₂×C₇×D₄	—	2	1	no	—
355	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
356	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₇	—	2	1	no	—
358	C₂²×C₄×C₇	—	2	1	no	—
359	C₂²×C₄×C₇	—	2	1	no	—
360	C₂²×C₄×C₇	—	2	1	no	—
361	C₂²×C₄×C₇	—	2	1	no	—
362	C₂²×C₄×C₇	—	2	1	no	—
363	C₂²×C₄×C₇	—	2	1	no	—
364	C₂²×C₄×C₇	—	2	1	no	—
365	C₂²×C₄×C₇	—	2	1	no	—
366	C₂²×C₄×C₇	—	2	1	no	—
367	C₂²×C₄×C₇	—	2	2	no	—
368	C₂²×C₄×C₇	—	2	2	no	—
369	C₂²×C₄×C₇	—	2	2	no	—
370	C₂²×C₄×C₇	—	2	2	no	—
371	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
372	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
374	C₇×Q₁₆	C₂×Q₈	1	4	yes	complemented
375	C₇×SD₁₆	C₂×Q₈	1	4	yes	complemented
376	C₇×SD₁₆	C₂×Q₈	1	4	yes	complemented
377	C₇×D₈	C₂×Q₈	1	4	yes	complemented
378	C₇×M₁₆	—	2	2	no	—
379	C₇×M₁₆	—	2	2	no	—
380	C₂×C₇×C₈	—	2	2	no	—
381	C₂×C₇×C₈	C₂×Q₈	1	4	yes	complemented
382	C₂×C₇×C₈	C₂⁴	1	2	yes	—
383	C₂×C₇×C₈	C₂⁴	1	2	yes	—
384	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
385	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
386	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
387	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
388	C₇×C₄⋊C₄	—	2	2	no	—
389	C₇×C₄⋊C₄	—	2	2	no	—
390	C₇×C₄⋊C₄	—	2	2	no	—
391	C₇×C₄⋊C₄	—	2	1	no	—
392	C₇×C₄⋊C₄	—	2	1	no	—
393	C₇×C₄⋊C₄	—	2	1	no	—
394	C₇×C₄⋊C₄	—	2	1	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	2	no	—
402	C₇×C₄⋊C₄	—	2	2	no	—
403	C₇×C₄⋊C₄	—	2	2	no	—
404	C₇×C₄⋊C₄	—	2	2	no	—
405	C₇×C₄⋊C₄	—	2	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	—	2	1	no	—
410	C₇×C₄⋊C₄	—	2	1	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	2	no	—
415	C₇×C₄⋊C₄	—	2	2	no	—
416	C₇×C₄⋊C₄	—	2	2	no	—
417	C₇×C₄⋊C₄	—	2	2	no	—
418	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
419	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
420	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
421	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
422	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
423	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
424	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
425	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
426	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
427	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
428	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
429	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
430	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
431	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
432	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
433	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
434	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
435	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
436	C₇×C₂²⋊C₄	—	2	1	no	—
437	C₇×C₂²⋊C₄	—	2	1	no	—
438	C₇×C₂²⋊C₄	—	2	1	no	—
439	C₇×C₂²⋊C₄	—	2	1	no	—
440	C₇×C₂²⋊C₄	—	2	1	no	—
441	C₇×C₂²⋊C₄	—	2	1	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	C₂×D₄	1	2	yes	—
447	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
448	C₄²×C₇	—	2	1	no	—
449	C₄²×C₇	—	2	1	no	—
450	C₄²×C₇	—	2	1	no	—
451	C₄²×C₇	—	2	1	no	—
452	C₄²×C₇	—	2	1	no	—
453	C₄²×C₇	—	2	1	no	—
454	C₄²×C₇	—	2	2	no	—
455	C₄²×C₇	—	2	2	no	—
456	C₄²×C₇	—	2	2	no	—
457	C₄²×C₇	—	2	2	no	—
458	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
460	C₄²×C₇	C₂⁴	1	2	yes	—
461	C₄²×C₇	C₂⁴	1	2	yes	—
462	C₄²×C₇	C₂⁴	1	1	yes	characteristic
463	C₄²×C₇	C₂⁴	1	1	yes	characteristic
464	C₂×#135	C₂²×C₇	1	1	yes	characteristic
465	Q₈²	C₂²×C₇	1	2	yes	—
466	#557	C₂²×C₇	1	2	yes	—
467	#557	C₂²×C₇	1	2	yes	—
468	#557	C₂²×C₇	1	2	yes	—
469	#554	—	2	2	no	—
470	#554	—	2	2	no	—
471	#554	—	2	2	no	—
472	#554	C₂²×C₇	1	2	yes	—
473	#554	C₂²×C₇	1	2	yes	—
474	#554	C₂²×C₇	1	2	yes	—
475	D₄×Q₈	—	2	2	no	—
476	D₄×Q₈	C₂²×C₇	1	2	yes	—
477	#544	—	2	1	no	—
478	#544	—	2	1	no	—
479	#544	—	2	1	no	—
480	#544	—	2	1	no	—
481	#544	C₂²×C₇	1	1	yes	characteristic
482	#544	C₂²×C₇	1	1	yes	characteristic
483	#544	C₂²×C₇	1	1	yes	characteristic
484	#544	C₂²×C₇	1	1	yes	characteristic
485	#533	—	2	1	no	—
486	#533	—	2	1	no	—
487	#533	C₂²×C₇	1	1	yes	characteristic
488	C₂×C₄⋊Q₈	—	2	1	no	—
489	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
490	C₂×#125	—	2	1	no	—
491	C₂×#125	C₂²×C₇	1	1	yes	characteristic
492	#520	C₂²×C₇	1	1	yes	characteristic
493	#520	C₂²×C₇	1	1	yes	characteristic
494	#520	C₂²×C₇	1	1	yes	characteristic
495	#520	C₂²×C₇	1	1	yes	characteristic
496	C₄×#41	C₂²×C₇	1	1	yes	characteristic
497	C₄×#41	C₂²×C₇	1	1	yes	characteristic
498	#501	C₂²×C₇	1	2	yes	—
499	#501	C₂²×C₇	1	2	yes	—
500	#501	C₂²×C₇	1	2	yes	—
501	#501	C₂²×C₇	1	2	yes	—
502	#501	C₂²×C₇	1	2	yes	—
503	#501	C₂²×C₇	1	2	yes	—
504	#501	C₂²×C₇	1	2	yes	—
505	#501	C₂²×C₇	1	2	yes	—
506	#500	C₂²×C₇	1	2	yes	—
507	#499	C₂²×C₇	1	2	yes	—
508	#499	C₂²×C₇	1	2	yes	—
509	#498	C₂²×C₇	1	2	yes	—
510	#479	C₂²×C₇	1	2	yes	—
511	#479	C₂²×C₇	1	2	yes	—
512	#479	C₂²×C₇	1	2	yes	—
513	#479	C₂²×C₇	1	2	yes	—
514	#479	C₂²×C₇	1	2	yes	—
515	#479	C₂²×C₇	1	2	yes	—
516	#478	C₂²×C₇	1	2	yes	—
517	#478	C₂²×C₇	1	2	yes	—
518	#478	C₂²×C₇	1	2	yes	—
519	#478	C₂²×C₇	1	2	yes	—
520	#478	C₂²×C₇	1	2	yes	—
521	#478	C₂²×C₇	1	2	yes	—
522	#477	C₂²×C₇	1	2	yes	—
523	#477	C₂²×C₇	1	2	yes	—
524	#477	C₂²×C₇	1	2	yes	—
525	#476	C₂²×C₇	1	2	yes	—
526	#476	C₂²×C₇	1	2	yes	—
527	#476	C₂²×C₇	1	2	yes	—
528	#475	C₂²×C₇	1	2	yes	—
529	#475	C₂²×C₇	1	2	yes	—
530	#475	C₂²×C₇	1	2	yes	—
531	#474	C₂²×C₇	1	2	yes	—
532	#474	C₂²×C₇	1	2	yes	—
533	#474	C₂²×C₇	1	2	yes	—
534	#446	C₂²×C₇	1	2	yes	—
535	#446	C₂²×C₇	1	2	yes	—
536	#446	C₂²×C₇	1	2	yes	—
537	#446	C₂²×C₇	1	2	yes	—
538	#442	C₂²×C₇	1	1	yes	characteristic
539	#442	C₂²×C₇	1	2	yes	—
540	#442	C₂²×C₇	1	1	yes	characteristic
541	#441	C₂²×C₇	1	1	yes	characteristic
542	#441	C₂²×C₇	1	2	yes	—
543	#441	C₂²×C₇	1	1	yes	characteristic
544	#440	C₂²×C₇	1	1	yes	characteristic
545	#440	C₂²×C₇	1	2	yes	—
546	#440	C₂²×C₇	1	1	yes	characteristic
547	#440	C₂²×C₇	1	2	yes	—
548	#440	C₂²×C₇	1	1	yes	characteristic
549	#440	C₂²×C₇	1	1	yes	characteristic
550	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
551	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
552	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
553	C₄×D₈	C₂²×C₇	1	2	yes	—
554	#428	C₂²×C₇	1	1	yes	characteristic
555	#428	C₂²×C₇	1	1	yes	characteristic
556	#428	C₂²×C₇	1	1	yes	characteristic
557	#428	C₂²×C₇	1	1	yes	characteristic
558	#427	C₂²×C₇	1	1	yes	characteristic
559	C₂×#107	C₂²×C₇	1	1	yes	characteristic
560	C₂×#107	C₂²×C₇	1	1	yes	characteristic
561	C₂×#106	C₂²×C₇	1	1	yes	characteristic
562	C₂×#106	C₂²×C₇	1	1	yes	characteristic
563	#424	C₂²×C₇	1	1	yes	characteristic
564	#424	C₂²×C₇	1	1	yes	characteristic
565	#423	C₂²×C₇	1	1	yes	characteristic
566	#417	C₂²×C₇	1	1	yes	characteristic
567	#417	C₂²×C₇	1	1	yes	characteristic
568	#417	C₂²×C₇	1	1	yes	characteristic
569	#417	C₂²×C₇	1	1	yes	characteristic
570	#416	C₂²×C₇	1	1	yes	characteristic
571	#416	C₂²×C₇	1	1	yes	characteristic
572	#405	C₂²×C₇	1	1	yes	characteristic
573	#405	C₂²×C₇	1	1	yes	characteristic
574	C₂×#97	C₂²×C₇	1	1	yes	characteristic
575	C₂³×C₇	—	2	1	no	—
576	C₂³×C₇	—	2	1	no	—
577	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
578	C₇×Q₈	—	2	1	no	—
579	C₇×Q₈	—	2	1	no	—
580	C₇×Q₈	—	4	2	no	—
581	C₇×Q₈	—	4	2	no	—
582	C₇×Q₈	—	4	4	no	—
583	C₇×Q₈	—	8	2	no	—
584	C₇×Q₈	—	8	2	no	—
585	C₇×Q₈	—	8	2	no	—
586	C₇×Q₈	—	8	2	no	—
587	C₇×Q₈	—	8	2	no	—
588	C₇×Q₈	C₂²×Q₈	1	2	yes	—
589	C₇×Q₈	C₂²×Q₈	1	2	yes	—
590	C₇×D₄	—	2	4	no	—
591	C₇×D₄	—	2	4	no	—
592	C₇×D₄	—	2	1	no	—
593	C₇×D₄	—	2	1	no	—
594	C₇×D₄	C₂²×Q₈	1	2	yes	—
595	C₇×D₄	C₂²×Q₈	1	2	yes	—
596	C₂×C₄×C₇	—	2	1	no	—
597	C₂×C₄×C₇	—	2	1	no	—
598	C₂×C₄×C₇	—	2	4	no	—
599	C₂×C₄×C₇	—	2	4	no	—
600	C₂×C₄×C₇	—	2	1	no	—
601	C₂×C₄×C₇	—	2	1	no	—
602	C₂×C₄×C₇	—	2	1	no	—
603	C₂×C₄×C₇	—	2	1	no	—
604	C₂×C₄×C₇	—	2	2	no	—
605	C₂×C₄×C₇	—	2	2	no	—
606	C₂×C₄×C₇	—	2	2	no	—
607	C₂×C₄×C₇	—	2	2	no	—
608	C₂×C₄×C₇	—	4	1	no	—
609	C₂×C₄×C₇	—	4	1	no	—
610	C₂×C₄×C₇	—	4	2	no	—
611	C₂×C₄×C₇	—	4	2	no	—
612	C₂×C₄×C₇	—	8	1	no	—
613	C₂×C₄×C₇	—	8	2	no	—
614	C₂×C₄×C₇	—	8	1	no	—
615	C₂×C₄×C₇	—	8	2	no	—
616	C₂×C₄×C₇	—	8	2	no	—
617	C₂×C₄×C₇	—	8	2	no	—
618	C₂×C₄×C₇	—	8	1	no	—
619	C₂×C₄×C₇	—	8	1	no	—
620	C₂×C₄×C₇	—	8	1	no	—
621	C₂×C₄×C₇	—	8	1	no	—
622	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
623	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
624	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
625	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
626	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
627	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
628	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
629	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
630	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
631	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
632	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
633	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
634	C₇×C₈	—	2	1	no	—
635	C₇×C₈	—	2	1	no	—
636	C₇×C₈	—	2	2	no	—
637	C₇×C₈	—	2	2	no	—
638	C₇×C₈	C₂²×Q₈	1	2	yes	—
639	C₇×C₈	C₂²×Q₈	1	2	yes	—
640	C₂×#41	C₂³×C₇	1	1	yes	characteristic
641	C₂×#41	C₂³×C₇	1	1	yes	characteristic
642	C₂²×Q₈	—	2	2	no	—
643	C₂²×Q₈	—	2	1	no	—
644	#135	C₇×Q₈	1	8	yes	complemented
645	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
646	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
647	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
648	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
649	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
650	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
651	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
652	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
653	C₄⋊Q₈	—	2	2	no	—
654	C₄⋊Q₈	—	2	2	no	—
655	C₄⋊Q₈	—	2	2	no	—
656	C₄⋊Q₈	—	2	1	no	—
657	C₄⋊Q₈	—	2	1	no	—
658	C₄⋊Q₈	—	2	2	no	—
659	C₄⋊Q₈	—	2	1	no	—
660	C₄⋊Q₈	—	2	1	no	—
661	C₄⋊Q₈	—	2	2	no	—
662	C₄⋊Q₈	—	2	2	no	—
663	C₄⋊Q₈	—	2	1	no	—
664	C₄⋊Q₈	—	2	1	no	—
665	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
666	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
667	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
668	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
669	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
670	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
671	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
672	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
673	#125	—	2	1	no	—
674	#125	—	2	1	no	—
675	#125	—	2	2	no	—
676	#125	—	2	2	no	—
677	#125	—	2	1	no	—
678	#125	—	2	1	no	—
679	#125	—	2	2	no	—
680	#125	—	2	2	no	—
681	#125	—	2	2	no	—
682	#125	—	2	2	no	—
683	#125	—	2	1	no	—
684	#125	—	2	1	no	—
685	#125	C₇×D₄	1	1	yes	characteristic
686	#125	C₇×D₄	1	1	yes	characteristic
687	#125	C₂³×C₇	1	2	yes	—
688	#125	C₂³×C₇	1	2	yes	—
689	#125	C₂³×C₇	1	2	yes	—
690	#125	C₂³×C₇	1	2	yes	—
691	#125	C₂³×C₇	1	2	yes	—
692	#125	C₂³×C₇	1	2	yes	—
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	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	—	2	2	no	—
703	C₂²⋊Q₈	—	2	2	no	—
704	C₂²⋊Q₈	—	2	2	no	—
705	C₂²⋊Q₈	—	2	2	no	—
706	C₂²⋊Q₈	—	2	2	no	—
707	C₂²⋊Q₈	—	2	2	no	—
708	C₂²⋊Q₈	—	2	2	no	—
709	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
710	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
711	C₄×Q₈	—	2	2	no	—
712	C₄×Q₈	—	2	2	no	—
713	C₄×Q₈	—	2	2	no	—
714	C₄×Q₈	—	2	2	no	—
715	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
716	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
717	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
718	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
719	C₄×Q₈	C₂³×C₇	1	2	yes	—
720	C₄×Q₈	C₂³×C₇	1	2	yes	—
721	C₄×Q₈	C₂³×C₇	1	2	yes	—
722	C₄×Q₈	C₂³×C₇	1	2	yes	—
723	C₄×Q₈	C₂³×C₇	1	2	yes	—
724	C₄×Q₈	C₂³×C₇	1	2	yes	—
725	C₄×D₄	—	2	1	no	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	1	no	—
729	C₄×D₄	—	2	2	no	—
730	C₄×D₄	—	2	2	no	—
731	C₄×D₄	—	2	2	no	—
732	C₄×D₄	—	2	2	no	—
733	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
734	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
735	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
736	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
737	C₄×D₄	C₂³×C₇	1	2	yes	—
738	C₄×D₄	C₂³×C₇	1	2	yes	—
739	C₄×D₄	C₂³×C₇	1	2	yes	—
740	C₄×D₄	C₂³×C₇	1	2	yes	—
741	#117	—	2	1	no	—
742	#117	—	2	1	no	—
743	#117	—	2	1	no	—
744	#117	—	2	1	no	—
745	#117	—	2	1	no	—
746	#117	—	2	1	no	—
747	#117	C₂³×C₇	1	1	yes	characteristic
748	#117	C₂³×C₇	1	1	yes	characteristic
749	#117	C₂³×C₇	1	1	yes	characteristic
750	#117	C₂³×C₇	1	1	yes	characteristic
751	C₂×C₄⋊C₄	—	2	1	no	—
752	C₂×C₄⋊C₄	—	2	1	no	—
753	C₂×C₄⋊C₄	—	2	1	no	—
754	C₂×C₄⋊C₄	—	2	1	no	—
755	C₂×C₄⋊C₄	—	2	1	no	—
756	C₂×C₄⋊C₄	—	2	1	no	—
757	C₂×C₄⋊C₄	—	2	1	no	—
758	C₂×C₄⋊C₄	—	2	2	no	—
759	C₂×C₄⋊C₄	—	2	2	no	—
760	C₂×C₄⋊C₄	—	2	2	no	—
761	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
762	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
763	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
764	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
765	C₂×C₄²	—	2	1	no	—
766	C₂×C₄²	—	2	1	no	—
767	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
768	#107	C₂³×C₇	1	2	yes	—
769	#107	C₂³×C₇	1	2	yes	—
770	#107	C₂³×C₇	1	2	yes	—
771	#107	C₂³×C₇	1	2	yes	—
772	#107	C₂³×C₇	1	1	yes	characteristic
773	#107	C₂³×C₇	1	1	yes	characteristic
774	#107	C₂³×C₇	1	2	yes	—
775	#107	C₂³×C₇	1	2	yes	—
776	#107	C₂³×C₇	1	2	yes	—
777	#107	C₂³×C₇	1	2	yes	—
778	#106	C₂³×C₇	1	2	yes	—
779	#106	C₂³×C₇	1	2	yes	—
780	#106	C₂³×C₇	1	2	yes	—
781	#106	C₂³×C₇	1	2	yes	—
782	#106	C₂³×C₇	1	1	yes	characteristic
783	#106	C₂³×C₇	1	1	yes	characteristic
784	#106	C₂³×C₇	1	2	yes	—
785	#106	C₂³×C₇	1	2	yes	—
786	#106	C₂³×C₇	1	2	yes	—
787	#106	C₂³×C₇	1	2	yes	—
788	C₄⋊C₈	C₂³×C₇	1	2	yes	—
789	C₄⋊C₈	C₂³×C₇	1	2	yes	—
790	C₄⋊C₈	C₂³×C₇	1	2	yes	—
791	C₄⋊C₈	C₂³×C₇	1	2	yes	—
792	C₄⋊C₈	C₂³×C₇	1	2	yes	—
793	C₄⋊C₈	C₂³×C₇	1	2	yes	—
794	#103	C₂³×C₇	1	1	yes	characteristic
795	#103	C₂³×C₇	1	1	yes	characteristic
796	#103	C₂³×C₇	1	1	yes	characteristic
797	#103	C₂³×C₇	1	1	yes	characteristic
798	#103	C₂³×C₇	1	2	yes	—
799	#103	C₂³×C₇	1	2	yes	—
800	#103	C₂³×C₇	1	2	yes	—
801	#103	C₂³×C₇	1	2	yes	—
802	#102	C₂³×C₇	1	1	yes	characteristic
803	#102	C₂³×C₇	1	1	yes	characteristic
804	#102	C₂³×C₇	1	1	yes	characteristic
805	#102	C₂³×C₇	1	1	yes	characteristic
806	#102	C₂³×C₇	1	2	yes	—
807	#102	C₂³×C₇	1	2	yes	—
808	#102	C₂³×C₇	1	2	yes	—
809	#102	C₂³×C₇	1	2	yes	—
810	#97	C₂³×C₇	1	1	yes	characteristic
811	#97	C₂³×C₇	1	1	yes	characteristic
812	#97	C₂³×C₇	1	1	yes	characteristic
813	#97	C₂³×C₇	1	1	yes	characteristic
814	#97	C₂³×C₇	1	2	yes	—
815	#97	C₂³×C₇	1	2	yes	—
816	C₄×C₈	C₂³×C₇	1	2	yes	—
817	C₄×C₈	C₂³×C₇	1	2	yes	—
818	C₂²×C₇	—	2	1	no	—
819	C₂²×C₇	—	2	1	no	—
820	C₂²×C₇	—	2	2	no	—
821	C₂²×C₇	—	2	2	no	—
822	C₂²×C₇	—	4	1	no	—
823	C₂²×C₇	—	4	1	no	—
824	C₂²×C₇	—	4	1	no	—
825	C₂²×C₇	—	4	1	no	—
826	C₂²×C₇	D₄×Q₈	1	2	yes	—
827	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
828	C₄×C₇	—	2	1	no	—
829	C₄×C₇	—	2	1	no	—
830	C₄×C₇	—	2	2	no	—
831	C₄×C₇	—	2	2	no	—
832	C₄×C₇	—	2	1	no	—
833	C₄×C₇	—	2	1	no	—
834	C₄×C₇	—	2	2	no	—
835	C₄×C₇	—	2	2	no	—
836	C₄×C₇	—	2	2	no	—
837	C₄×C₇	—	2	2	no	—
838	C₄×C₇	—	4	1	no	—
839	C₄×C₇	—	4	2	no	—
840	C₄×C₇	—	4	2	no	—
841	C₄×C₇	—	4	2	no	—
842	C₄×C₇	—	4	1	no	—
843	C₄×C₇	—	4	1	no	—
844	C₄×C₇	—	4	2	no	—
845	C₄×C₇	—	4	1	no	—
846	C₄×C₇	D₄×Q₈	1	2	yes	—
847	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
848	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
849	#41	—	2	2	no	—
850	#41	—	2	2	no	—
851	#41	C₂×C₇×Q₈	1	4	yes	—
852	#41	C₂×C₇×Q₈	1	4	yes	complemented
853	C₂×Q₈	—	2	2	no	—
854	C₂×Q₈	—	2	2	no	—
855	C₂×Q₈	—	2	2	no	—
856	C₂×Q₈	—	2	2	no	—
857	C₂×Q₈	—	2	2	no	—
858	C₂×Q₈	—	2	2	no	—
859	C₂×Q₈	—	8	2	no	—
860	C₂×Q₈	—	8	4	no	—
861	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
862	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
863	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
864	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
865	C₂×D₄	—	2	1	no	—
866	C₂×D₄	—	2	1	no	—
867	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
868	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
884	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
886	Q₁₆	C₂×C₇×Q₈	1	4	yes	complemented
887	SD₁₆	C₂×C₇×Q₈	1	4	yes	complemented
888	SD₁₆	C₂×C₇×Q₈	1	4	yes	complemented
889	D₈	C₂×C₇×Q₈	1	4	yes	complemented
890	M₁₆	—	2	2	no	—
891	M₁₆	—	2	2	no	—
892	C₂×C₈	—	2	2	no	—
893	C₂×C₈	C₂×C₇×Q₈	1	4	yes	complemented
894	C₂×C₈	C₂⁴×C₇	1	2	yes	—
895	C₂×C₈	C₂⁴×C₇	1	2	yes	—
896	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
897	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
898	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
899	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
931	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
932	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
933	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
934	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
935	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
936	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
937	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
938	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
939	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
940	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
941	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
942	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
943	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
944	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
945	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
946	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
948	C₂²⋊C₄	—	2	1	no	—
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	1	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
959	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
960	C₄²	—	2	1	no	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	1	no	—
963	C₄²	—	2	1	no	—
964	C₄²	—	2	1	no	—
965	C₄²	—	2	1	no	—
966	C₄²	—	2	2	no	—
967	C₄²	—	2	2	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	2	2	no	—
970	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
971	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
972	C₄²	C₂⁴×C₇	1	2	yes	—
973	C₄²	C₂⁴×C₇	1	2	yes	—
974	C₄²	C₂⁴×C₇	1	1	yes	characteristic
975	C₄²	C₂⁴×C₇	1	1	yes	characteristic
976	C₂×C₇	—	2	2	no	—
977	C₂×C₇	—	4	2	no	—
978	C₂×C₇	—	4	2	no	—
979	C₂×C₇	C₂×D₄×Q₈	1	1	yes	characteristic
980	C₂×C₇	#3585	1	1	yes	characteristic
981	C₂×C₇	#3586	1	1	yes	characteristic
982	C₂³	—	2	1	no	—
983	C₂³	—	2	1	no	—
984	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
985	Q₈	—	2	1	no	—
986	Q₈	—	2	1	no	—
987	Q₈	—	4	2	no	—
988	Q₈	—	4	2	no	—
989	Q₈	—	4	4	no	—
990	Q₈	—	8	2	no	—
991	Q₈	—	8	2	no	—
992	Q₈	—	8	2	no	—
993	Q₈	—	8	2	no	—
994	Q₈	—	8	2	no	—
995	Q₈	C₂²×C₇×Q₈	1	2	yes	—
996	Q₈	C₂²×C₇×Q₈	1	2	yes	—
997	D₄	—	2	4	no	—
998	D₄	—	2	4	no	—
999	D₄	—	2	1	no	—
1000	D₄	—	2	1	no	—
1001	D₄	C₂²×C₇×Q₈	1	2	yes	—
1002	D₄	C₂²×C₇×Q₈	1	2	yes	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	4	no	—
1006	C₂×C₄	—	2	4	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	4	1	no	—
1016	C₂×C₄	—	4	1	no	—
1017	C₂×C₄	—	4	2	no	—
1018	C₂×C₄	—	4	2	no	—
1019	C₂×C₄	—	8	1	no	—
1020	C₂×C₄	—	8	2	no	—
1021	C₂×C₄	—	8	1	no	—
1022	C₂×C₄	—	8	2	no	—
1023	C₂×C₄	—	8	2	no	—
1024	C₂×C₄	—	8	2	no	—
1025	C₂×C₄	—	8	1	no	—
1026	C₂×C₄	—	8	1	no	—
1027	C₂×C₄	—	8	1	no	—
1028	C₂×C₄	—	8	1	no	—
1029	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1030	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1031	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1032	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1033	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1034	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1035	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1036	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1037	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1038	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
1039	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1040	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1041	C₈	—	2	1	no	—
1042	C₈	—	2	1	no	—
1043	C₈	—	2	2	no	—
1044	C₈	—	2	2	no	—
1045	C₈	C₂²×C₇×Q₈	1	2	yes	—
1046	C₈	C₂²×C₇×Q₈	1	2	yes	—
1047	C₇	#61380	1	1	yes	characteristic, direct product factor, Sylow
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	4	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	C₇×D₄×Q₈	1	2	yes	—
1057	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	2	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	2	no	—
1075	C₄	—	4	1	no	—
1076	C₄	C₇×D₄×Q₈	1	2	yes	—
1077	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
1078	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1079	C₂	—	2	2	no	—
1080	C₂	—	4	2	no	—
1081	C₂	—	4	2	no	—
1082	C₂	C₂×C₇×D₄×Q₈	1	1	yes	characteristic
1083	C₂	C₇×#3585	1	1	yes	characteristic
1084	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	C₂×C₇×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3504	C₂	semidirect
2. C₇×#3503	C₂	semidirect
3. C₇×#3390	C₂	semidirect
4. C₇×#3389	C₂	semidirect
5. C₇×#3388	C₂	semidirect
6. C₇×#3388	C₂	semidirect
7. C₇×#3387	C₂	semidirect
8. C₇×#3386	C₂	semidirect
9. C₇×#3385	C₂	semidirect
10. C₇×#3384	C₂	semidirect
11. C₇×#3164	C₂	semidirect
12. C₇×#3163	C₂	semidirect
13. C₂×C₇×#501	C₂	semidirect
14. C₇×#3084	C₂	semidirect
15. C₇×#3084	C₂	semidirect
16. C₇×#3083	C₂	semidirect
17. C₇×#3083	C₂	semidirect
18. C₇×#3080	C₂	semidirect
19. C₇×#3079	C₂	semidirect
20. C₇×#2961	C₂	semidirect
135. #61380	C₇	direct (N × H)
140. C₇×#135	Q₈	semidirect
314. #3504	C₂×C₇	semidirect
315. #3503	C₂×C₇	semidirect
316. #3390	C₂×C₇	semidirect
317. #3389	C₂×C₇	semidirect
318. #3388	C₂×C₇	semidirect
319. #3388	C₂×C₇	semidirect
320. #3387	C₂×C₇	semidirect
321. #3386	C₂×C₇	semidirect
322. #3385	C₂×C₇	semidirect
323. #3384	C₂×C₇	semidirect
324. #3164	C₂×C₇	semidirect
325. #3163	C₂×C₇	semidirect
326. C₂×#501	C₂×C₇	semidirect
327. #3084	C₂×C₇	semidirect
328. #3084	C₂×C₇	semidirect
329. #3083	C₂×C₇	semidirect
330. #3083	C₂×C₇	semidirect
331. #3080	C₂×C₇	semidirect
332. #3079	C₂×C₇	semidirect
333. #2961	C₂×C₇	semidirect
340. C₇×#41	C₂×Q₈	semidirect
374. C₇×Q₁₆	C₂×Q₈	semidirect
375. C₇×SD₁₆	C₂×Q₈	semidirect
376. C₇×SD₁₆	C₂×Q₈	semidirect
377. C₇×D₈	C₂×Q₈	semidirect
381. C₂×C₇×C₈	C₂×Q₈	semidirect
644. #135	C₇×Q₈	semidirect
852. #41	C₂×C₇×Q₈	semidirect
886. Q₁₆	C₂×C₇×Q₈	semidirect
887. SD₁₆	C₂×C₇×Q₈	semidirect
888. SD₁₆	C₂×C₇×Q₈	semidirect
889. D₈	C₂×C₇×Q₈	semidirect
893. C₂×C₈	C₂×C₇×Q₈	semidirect
1047. C₇	#61380	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×#3504	2
C₇×#3503	2
C₇×#3390	2
C₇×#3389	2
C₇×#3388	2
C₇×#3387	2
C₇×#3386	2
C₇×#3385	2
C₇×#3384	2
C₇×#3164	2
C₇×#3163	2
C₂×C₇×#501	2
C₇×#3084	2
C₇×#3083	2
C₇×#3080	2
C₇×#3079	2
C₇×#2961	2
C₇×#2952	2
C₇×#2951	2
C₇×#2943	2
#61380	7

Subgroups — C7×#61380 #13238596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61380 #13238596