Subgroups — C₇×#61170 #13238386

Order 1792.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3321	C₂	1	2	yes	maximal, complemented
4	C₇×#3317	C₂	1	2	yes	maximal, complemented
5	C₇×#3313	C₂	1	2	yes	maximal, complemented
6	C₇×#3309	C₂	1	2	yes	maximal, complemented
7	C₇×#3305	C₂	1	2	yes	maximal, complemented
8	C₇×#3304	C₂	1	2	yes	maximal, complemented
9	C₇×#3301	C₂	1	2	yes	maximal, complemented
10	C₇×#3300	C₂	1	2	yes	maximal, complemented
11	C₇×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3093	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3050	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3045	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3005	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₇×#416	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
26	C₂×C₇×#137	C₂²	1	1	yes	characteristic
27	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₇×#135	C₂²	1	1	yes	characteristic
29	C₂×C₇×#131	C₂²	1	1	yes	characteristic
30	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
31	C₇×#556	—	2	1	no	—
32	C₇×#556	C₂²	1	2	yes	complemented
33	C₇×#555	—	2	1	no	—
34	C₇×#555	C₂²	1	2	yes	complemented
35	C₇×#553	—	2	1	no	—
36	C₇×#553	C₂²	1	2	yes	complemented
37	C₇×#552	—	2	1	no	—
38	C₇×#552	C₂²	1	2	yes	complemented
39	C₇×#550	—	2	1	no	—
40	C₇×#550	—	2	1	no	—
41	C₇×#550	C₂²	1	2	yes	—
42	C₇×#550	C₂²	1	2	yes	—
43	C₇×#548	—	2	1	no	—
44	C₇×#548	—	2	1	no	—
45	C₇×#548	C₂²	1	2	yes	—
46	C₇×#548	C₂²	1	2	yes	—
47	C₇×#544	C₂²	1	1	yes	characteristic
48	C₇×#538	—	2	2	no	—
49	C₇×#537	C₂²	1	1	yes	characteristic
50	C₇×#535	—	2	2	no	—
51	C₇×#535	C₂²	1	1	yes	characteristic
52	C₇×#535	C₂²	1	1	yes	characteristic
53	C₇×#529	—	2	2	no	—
54	C₇×#525	—	2	2	no	—
55	C₇×#525	C₂²	1	1	yes	characteristic
56	C₇×#525	C₂²	1	1	yes	characteristic
57	C₇×#525	C₂²	1	1	yes	characteristic
58	C₇×#520	C₂²	1	1	yes	characteristic
59	C₇×#520	C₂²	1	1	yes	characteristic
60	C₇×#519	C₂²	1	1	yes	characteristic
61	C₂×C₇×#117	C₂²	1	1	yes	characteristic
62	C₇×#490	C₂²	1	2	yes	complemented
63	C₇×#489	C₂²	1	2	yes	complemented
64	C₇×#488	C₂²	1	2	yes	complemented
65	C₇×#486	C₂²	1	2	yes	complemented
66	C₇×#485	C₂²	1	2	yes	complemented
67	C₇×#485	C₂²	1	2	yes	complemented
68	C₇×#482	C₂²	1	2	yes	complemented
69	C₇×#482	C₂²	1	2	yes	complemented
70	C₇×#482	C₂²	1	2	yes	complemented
71	C₇×#482	C₂²	1	2	yes	complemented
72	C₇×#481	C₂²	1	2	yes	complemented
73	C₇×#480	C₂²	1	2	yes	complemented
74	C₇×#479	C₂²	1	2	yes	complemented
75	C₇×#479	C₂²	1	2	yes	complemented
76	C₇×#477	C₂²	1	2	yes	complemented
77	C₇×#475	C₂²	1	2	yes	complemented
78	C₇×#469	C₂²	1	2	yes	complemented
79	C₇×#468	C₂²	1	2	yes	complemented
80	C₇×#467	C₂²	1	1	yes	characteristic, complemented
81	C₇×#467	C₂²	1	1	yes	characteristic, complemented
82	C₇×#466	C₂²	1	2	yes	complemented
83	C₇×#466	C₂²	1	1	yes	characteristic, complemented
84	C₇×#466	C₂²	1	1	yes	characteristic, complemented
85	C₇×#465	C₂²	1	2	yes	complemented
86	C₇×#465	C₂²	1	1	yes	characteristic, complemented
87	C₇×#465	C₂²	1	1	yes	characteristic, complemented
88	C₇×#465	C₂²	1	1	yes	characteristic, complemented
89	C₇×#465	C₂²	1	1	yes	characteristic, complemented
90	C₇×#464	C₂²	1	2	yes	complemented
91	C₇×#463	C₂²	1	2	yes	complemented
92	C₇×#460	C₂²	1	2	yes	complemented
93	C₇×#459	C₂²	1	2	yes	complemented
94	C₇×#452	C₂²	1	2	yes	—
95	C₇×#452	C₂²	1	2	yes	—
96	C₇×#452	C₂²	1	2	yes	complemented
97	C₇×#451	C₂²	1	2	yes	complemented
98	C₇×#449	C₂²	1	2	yes	—
99	C₇×#449	C₂²	1	2	yes	—
100	C₇×#449	C₂²	1	2	yes	complemented
101	C₇×#448	C₂²	1	2	yes	complemented
102	C₇×#441	C₂²	1	2	yes	complemented
103	C₇×#440	C₂²	1	2	yes	complemented
104	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
105	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
106	C₇×#435	C₂²	1	2	yes	complemented
107	C₇×#435	C₂²	1	2	yes	complemented
108	C₇×C₈×D₄	C₂²	1	2	yes	complemented
109	C₇×C₈×D₄	C₂²	1	2	yes	complemented
110	C₇×#428	C₂²	1	1	yes	characteristic
111	C₇×#428	C₂²	1	1	yes	characteristic
112	C₇×#427	C₂²	1	1	yes	characteristic
113	C₇×#424	C₂²	1	1	yes	characteristic
114	C₇×#419	C₂²	1	1	yes	characteristic
115	C₇×#419	C₂²	1	2	yes	complemented
116	C₇×#418	C₂²	1	1	yes	characteristic
117	C₇×#417	C₂²	1	1	yes	characteristic
118	C₇×#417	C₂²	1	1	yes	characteristic
119	C₇×#417	C₂²	1	2	yes	complemented
120	C₇×#416	C₂²	1	1	yes	characteristic
121	C₇×#416	C₂²	1	2	yes	—
122	C₇×#416	C₂²	1	2	yes	—
123	C₇×#416	C₂²	1	1	yes	characteristic
124	C₇×#416	C₂²	1	2	yes	—
125	C₇×#416	C₂²	1	2	yes	—
126	C₇×#416	C₂²	1	2	yes	complemented
127	C₂×C₇×#103	C₂²	1	1	yes	characteristic
128	C₂×C₇×#103	C₂²	1	1	yes	characteristic
129	C₂×C₇×#103	C₂²	1	2	yes	complemented
130	C₂×C₇×#102	C₂²	1	1	yes	characteristic
131	C₂×C₇×#102	C₂²	1	1	yes	characteristic
132	C₇×#408	C₂²	1	1	yes	characteristic
133	C₇×#407	C₂²	1	1	yes	characteristic
134	C₇×#405	C₂²	1	1	yes	characteristic
135	#61170	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₇×2₋¹⁺⁴	—	2	4	no	—
137	C₇×2₋¹⁺⁴	—	4	2	no	—
138	C₂×C₇×#41	—	2	2	no	—
139	C₂×C₇×#41	—	2	1	no	—
140	C₂×C₇×#41	—	2	1	no	—
141	C₂×C₇×#41	—	2	1	no	—
142	C₂×C₇×#41	—	2	4	no	—
143	C₂×C₇×#41	—	4	2	no	—
144	C₂×C₇×#41	C₂³	1	1	yes	characteristic
145	C₂×C₇×#41	C₂³	1	1	yes	characteristic
146	C₂×C₇×#41	C₂³	1	2	yes	—
147	C₂×C₇×#41	C₂³	1	2	yes	—
148	C₂×C₇×#41	C₂³	1	2	yes	—
149	C₂×C₇×#41	C₂³	1	1	yes	characteristic
150	C₂²×C₇×Q₈	—	2	1	no	—
151	C₂²×C₇×Q₈	C₂³	1	2	yes	—
152	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₇×D₄	—	2	1	no	—
154	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₇	—	2	1	no	—
156	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
157	C₇×#137	—	2	4	no	—
158	C₇×AGL(1,ℤ/8)	—	4	2	no	—
159	C₇×#135	—	4	2	no	—
160	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
161	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
162	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
163	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
166	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
167	C₂×C₇×D₈	C₂³	1	2	yes	—
168	C₇×#131	—	4	2	no	—
169	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
170	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
171	C₂×C₇×M₁₆	C₂³	1	2	yes	—
172	C₂²×C₇×C₈	—	4	2	no	—
173	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
174	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
175	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
176	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
177	C₂²×C₇×C₈	C₂³	1	2	yes	—
178	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
179	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
180	C₇×C₄⋊Q₈	—	2	1	no	—
181	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
182	C₇×#127	—	2	2	no	—
183	C₇×#127	—	2	2	no	—
184	C₇×#127	—	2	1	no	—
185	C₇×#127	C₂³	1	2	yes	—
186	C₇×#126	—	2	2	no	—
187	C₇×#126	—	2	2	no	—
188	C₇×#126	—	2	2	no	—
189	C₇×#126	—	2	2	no	—
190	C₇×#125	—	2	2	no	—
191	C₇×#125	—	2	1	no	—
192	C₇×#125	C₂³	1	2	yes	—
193	C₇×#124	—	2	1	no	—
194	C₇×#124	—	2	2	no	—
195	C₇×#124	—	2	2	no	—
196	C₇×#124	—	2	2	no	—
197	C₇×#124	—	2	2	no	—
198	C₇×#124	—	2	2	no	—
199	C₇×#124	C₂³	1	2	yes	—
200	C₇×#123	—	2	2	no	—
201	C₇×#123	—	2	1	no	—
202	C₇×#123	—	2	1	no	—
203	C₇×#123	—	2	2	no	—
204	C₇×#123	D₄	1	2	yes	—
205	C₇×C₂²⋊Q₈	—	2	1	no	—
206	C₇×C₂²⋊Q₈	—	2	2	no	—
207	C₇×C₂²⋊Q₈	—	2	2	no	—
208	C₇×C₂²⋊Q₈	—	2	2	no	—
209	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
211	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₇×#121	—	2	2	no	—
217	C₇×#121	—	2	2	no	—
218	C₇×#121	—	2	2	no	—
219	C₇×#121	—	2	1	no	—
220	C₇×#121	—	2	2	no	—
221	C₇×#121	—	2	2	no	—
222	C₇×#121	—	2	1	no	—
223	C₇×#121	—	2	1	no	—
224	C₇×#121	—	2	2	no	—
225	C₇×#121	—	2	2	no	—
226	C₇×#121	—	2	2	no	—
227	C₇×#121	—	2	2	no	—
228	C₇×#121	D₄	1	1	yes	characteristic
229	C₇×#121	D₄	1	1	yes	characteristic
230	C₇×#121	C₂³	1	2	yes	—
231	C₇×#121	C₂³	1	2	yes	—
232	C₇×#121	C₂³	1	1	yes	characteristic
233	C₇×#121	C₂³	1	1	yes	characteristic
234	C₇×#121	C₂³	1	1	yes	characteristic
235	C₇×#121	C₂³	1	1	yes	characteristic
236	C₇×#121	C₂³	1	2	yes	—
237	C₇×#120	—	2	1	no	—
238	C₇×#120	—	2	1	no	—
239	C₇×#120	—	2	2	no	—
240	C₇×#120	—	2	2	no	—
241	C₇×#120	D₄	1	2	yes	—
242	C₄×C₇×Q₈	—	2	1	no	—
243	C₄×C₇×Q₈	—	2	1	no	—
244	C₄×C₇×Q₈	—	2	1	no	—
245	C₄×C₇×Q₈	—	2	2	no	—
246	C₄×C₇×Q₈	C₂³	1	2	yes	—
247	C₄×C₇×Q₈	C₂³	1	2	yes	—
248	C₄×C₇×Q₈	C₂³	1	2	yes	—
249	C₄×C₇×D₄	—	2	2	no	—
250	C₄×C₇×D₄	—	2	1	no	—
251	C₄×C₇×D₄	—	2	1	no	—
252	C₄×C₇×D₄	—	2	1	no	—
253	C₄×C₇×D₄	—	2	1	no	—
254	C₄×C₇×D₄	—	2	1	no	—
255	C₄×C₇×D₄	—	2	2	no	—
256	C₄×C₇×D₄	—	2	2	no	—
257	C₄×C₇×D₄	—	2	2	no	—
258	C₄×C₇×D₄	—	2	2	no	—
259	C₄×C₇×D₄	—	2	2	no	—
260	C₄×C₇×D₄	—	2	2	no	—
261	C₄×C₇×D₄	C₂³	1	2	yes	—
262	C₄×C₇×D₄	C₂³	1	2	yes	—
263	C₄×C₇×D₄	C₂³	1	2	yes	—
264	C₇×#117	—	2	1	no	—
265	C₇×#117	—	2	1	no	—
266	C₇×#117	—	2	1	no	—
267	C₇×#117	—	2	2	no	—
268	C₇×#117	—	2	2	no	—
269	C₇×#117	—	2	2	no	—
270	C₇×#117	C₂³	1	2	yes	—
271	C₇×#117	C₂³	1	2	yes	—
272	C₇×#117	C₂³	1	2	yes	—
273	C₇×#117	C₂³	1	1	yes	characteristic
274	C₇×#117	C₂³	1	1	yes	characteristic
275	C₇×#117	C₂³	1	1	yes	characteristic
276	C₂×C₇×C₄⋊C₄	—	2	1	no	—
277	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
278	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₄²×C₇	—	2	1	no	—
282	C₇×#107	C₂³	1	1	yes	characteristic
283	C₇×#107	C₂³	1	1	yes	characteristic
284	C₇×#107	C₂³	1	2	yes	—
285	C₇×#107	C₂³	1	2	yes	—
286	C₇×#106	C₂³	1	2	yes	—
287	C₇×#106	C₂³	1	1	yes	characteristic
288	C₇×#106	C₂³	1	1	yes	characteristic
289	C₇×#106	C₂³	1	2	yes	—
290	C₇×C₄⋊C₈	C₂³	1	2	yes	—
291	C₇×C₄⋊C₈	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	1	yes	characteristic
293	C₇×#103	C₂³	1	1	yes	characteristic
294	C₇×#103	C₂³	1	1	yes	characteristic
295	C₇×#103	C₂³	1	1	yes	characteristic
296	C₇×#103	C₂³	1	2	yes	—
297	C₇×#103	C₂³	1	2	yes	—
298	C₇×#103	C₂³	1	2	yes	—
299	C₇×#103	C₂³	1	2	yes	—
300	C₇×#103	C₂³	1	2	yes	—
301	C₇×#103	C₂³	1	2	yes	—
302	C₇×#103	C₂³	1	2	yes	—
303	C₇×#103	C₂³	1	2	yes	—
304	C₇×#102	C₂³	1	1	yes	characteristic
305	C₇×#102	C₂³	1	1	yes	characteristic
306	C₇×#102	C₂³	1	1	yes	characteristic
307	C₇×#102	C₂³	1	2	yes	—
308	C₇×#102	C₂³	1	1	yes	characteristic
309	C₇×#102	C₂³	1	2	yes	—
310	C₇×#102	C₂³	1	2	yes	—
311	C₇×#102	C₂³	1	2	yes	—
312	C₇×#102	C₂³	1	2	yes	—
313	C₇×#102	C₂³	1	2	yes	—
314	C₇×#102	C₂³	1	2	yes	—
315	C₇×#102	C₂³	1	2	yes	—
316	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
320	C₇×#97	C₂³	1	2	yes	—
321	C₄×C₇×C₈	C₂³	1	2	yes	—
322	#3493	C₂×C₇	1	1	yes	characteristic, complemented
323	#3487	C₂×C₇	1	1	yes	characteristic, complemented
324	#3321	C₂×C₇	1	2	yes	complemented
325	#3317	C₂×C₇	1	2	yes	complemented
326	#3313	C₂×C₇	1	2	yes	complemented
327	#3309	C₂×C₇	1	2	yes	complemented
328	#3305	C₂×C₇	1	2	yes	complemented
329	#3304	C₂×C₇	1	2	yes	complemented
330	#3301	C₂×C₇	1	2	yes	complemented
331	#3300	C₂×C₇	1	2	yes	complemented
332	#3136	C₂×C₇	1	1	yes	characteristic, complemented
333	#3096	C₂×C₇	1	1	yes	characteristic, complemented
334	#3093	C₂×C₇	1	1	yes	characteristic, complemented
335	#3082	C₂×C₇	1	1	yes	characteristic, complemented
336	#3062	C₂×C₇	1	1	yes	characteristic, complemented
337	#3050	C₂×C₇	1	1	yes	characteristic, complemented
338	#3045	C₂×C₇	1	1	yes	characteristic, complemented
339	#3013	C₂×C₇	1	1	yes	characteristic, complemented
340	#3005	C₂×C₇	1	1	yes	characteristic, complemented
341	#2947	C₂×C₇	1	1	yes	characteristic, complemented
342	#2929	C₂×C₇	1	1	yes	characteristic, complemented
343	#2898	C₂×C₇	1	1	yes	characteristic, complemented
344	C₂×#416	C₂×C₇	1	1	yes	characteristic, complemented
345	C₂⁴×C₇	—	2	1	no	—
346	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
347	C₇×#41	—	2	2	no	—
348	C₇×#41	—	2	2	no	—
349	C₇×#41	—	2	4	no	—
350	C₇×#41	—	2	4	no	—
351	C₇×#41	—	2	4	no	—
352	C₇×#41	—	2	2	no	—
353	C₇×#41	—	2	2	no	—
354	C₇×#41	—	2	2	no	—
355	C₇×#41	—	2	2	no	—
356	C₇×#41	—	4	2	no	—
357	C₇×#41	—	4	2	no	—
358	C₇×#41	—	4	2	no	—
359	C₇×#41	—	4	8	no	—
360	C₇×#41	—	4	4	no	—
361	C₇×#41	—	4	4	no	—
362	C₇×#41	—	4	4	no	—
363	C₂×C₇×Q₈	—	2	1	no	—
364	C₂×C₇×Q₈	—	2	2	no	—
365	C₂×C₇×Q₈	—	2	2	no	—
366	C₂×C₇×Q₈	—	2	2	no	—
367	C₂×C₇×Q₈	—	2	4	no	—
368	C₂×C₇×Q₈	—	4	2	no	—
369	C₂×C₇×Q₈	—	4	4	no	—
370	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
371	C₂×C₇×Q₈	#41	1	4	yes	—
372	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
373	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
374	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
375	C₂×C₇×D₄	—	2	1	no	—
376	C₂×C₇×D₄	—	2	1	no	—
377	C₂×C₇×D₄	—	2	2	no	—
378	C₂×C₇×D₄	—	2	2	no	—
379	C₂×C₇×D₄	—	2	2	no	—
380	C₂×C₇×D₄	—	2	1	no	—
381	C₂×C₇×D₄	—	2	1	no	—
382	C₂×C₇×D₄	—	2	2	no	—
383	C₂×C₇×D₄	—	2	2	no	—
384	C₂×C₇×D₄	—	2	1	no	—
385	C₂×C₇×D₄	—	2	1	no	—
386	C₂×C₇×D₄	—	2	2	no	—
387	C₂×C₇×D₄	—	2	1	no	—
388	C₂×C₇×D₄	—	2	2	no	—
389	C₂×C₇×D₄	—	2	2	no	—
390	C₂×C₇×D₄	—	2	2	no	—
391	C₂×C₇×D₄	—	2	2	no	—
392	C₂×C₇×D₄	—	4	4	no	—
393	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
394	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
395	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
396	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
397	C₂×C₇×D₄	C₂⁴	1	2	yes	—
398	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
399	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₇	—	2	1	no	—
401	C₂²×C₄×C₇	—	2	2	no	—
402	C₂²×C₄×C₇	—	2	2	no	—
403	C₂²×C₄×C₇	—	2	2	no	—
404	C₂²×C₄×C₇	—	2	1	no	—
405	C₂²×C₄×C₇	—	2	1	no	—
406	C₂²×C₄×C₇	—	2	2	no	—
407	C₂²×C₄×C₇	—	2	1	no	—
408	C₂²×C₄×C₇	—	2	2	no	—
409	C₂²×C₄×C₇	—	2	1	no	—
410	C₂²×C₄×C₇	—	2	2	no	—
411	C₂²×C₄×C₇	—	2	2	no	—
412	C₂²×C₄×C₇	—	2	2	no	—
413	C₂²×C₄×C₇	—	4	4	no	—
414	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
415	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
416	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
417	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
418	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
421	C₇×Q₁₆	—	2	4	no	—
422	C₇×Q₁₆	—	4	1	no	—
423	C₇×SD₁₆	—	2	4	no	—
424	C₇×SD₁₆	—	4	1	no	—
425	C₇×SD₁₆	—	4	1	no	—
426	C₇×SD₁₆	—	4	2	no	—
427	C₇×D₈	—	4	1	no	—
428	C₇×D₈	—	4	2	no	—
429	C₇×M₁₆	—	2	2	no	—
430	C₇×M₁₆	—	2	2	no	—
431	C₇×M₁₆	—	4	2	no	—
432	C₂×C₇×C₈	—	2	2	no	—
433	C₂×C₇×C₈	—	2	2	no	—
434	C₂×C₇×C₈	—	4	1	no	—
435	C₂×C₇×C₈	—	4	1	no	—
436	C₂×C₇×C₈	—	4	1	no	—
437	C₂×C₇×C₈	—	4	1	no	—
438	C₂×C₇×C₈	—	4	2	no	—
439	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
440	C₂×C₇×C₈	C₂⁴	1	2	yes	—
441	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
442	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
443	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
444	C₂×C₇×C₈	C₂⁴	1	2	yes	—
445	C₇×C₄⋊C₄	—	2	1	no	—
446	C₇×C₄⋊C₄	—	2	2	no	—
447	C₇×C₄⋊C₄	—	2	1	no	—
448	C₇×C₄⋊C₄	—	2	2	no	—
449	C₇×C₄⋊C₄	—	2	1	no	—
450	C₇×C₄⋊C₄	—	2	2	no	—
451	C₇×C₄⋊C₄	—	2	2	no	—
452	C₇×C₄⋊C₄	—	2	2	no	—
453	C₇×C₄⋊C₄	—	2	2	no	—
454	C₇×C₄⋊C₄	—	2	1	no	—
455	C₇×C₄⋊C₄	—	2	1	no	—
456	C₇×C₄⋊C₄	—	2	1	no	—
457	C₇×C₄⋊C₄	—	2	2	no	—
458	C₇×C₄⋊C₄	—	2	2	no	—
459	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
460	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
461	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
462	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
463	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
464	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
465	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
466	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
467	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
468	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
469	C₇×C₂²⋊C₄	—	2	2	no	—
470	C₇×C₂²⋊C₄	—	2	2	no	—
471	C₇×C₂²⋊C₄	—	2	1	no	—
472	C₇×C₂²⋊C₄	—	2	2	no	—
473	C₇×C₂²⋊C₄	—	2	1	no	—
474	C₇×C₂²⋊C₄	—	2	2	no	—
475	C₇×C₂²⋊C₄	—	2	1	no	—
476	C₇×C₂²⋊C₄	—	2	1	no	—
477	C₇×C₂²⋊C₄	—	2	1	no	—
478	C₇×C₂²⋊C₄	—	2	1	no	—
479	C₇×C₂²⋊C₄	—	2	1	no	—
480	C₇×C₂²⋊C₄	—	2	2	no	—
481	C₇×C₂²⋊C₄	—	2	2	no	—
482	C₇×C₂²⋊C₄	—	2	1	no	—
483	C₇×C₂²⋊C₄	—	2	1	no	—
484	C₇×C₂²⋊C₄	—	2	1	no	—
485	C₇×C₂²⋊C₄	—	2	2	no	—
486	C₇×C₂²⋊C₄	—	2	2	no	—
487	C₇×C₂²⋊C₄	—	2	2	no	—
488	C₇×C₂²⋊C₄	—	2	2	no	—
489	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
490	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
491	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
492	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
493	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
494	C₄²×C₇	—	2	2	no	—
495	C₄²×C₇	—	2	2	no	—
496	C₄²×C₇	—	2	2	no	—
497	C₄²×C₇	—	2	2	no	—
498	C₄²×C₇	—	2	2	no	—
499	C₄²×C₇	—	2	2	no	—
500	C₄²×C₇	—	2	1	no	—
501	C₄²×C₇	—	2	1	no	—
502	C₄²×C₇	C₂⁴	1	2	yes	—
503	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
504	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
505	C₂×#137	C₂²×C₇	1	1	yes	characteristic
506	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
507	C₂×#135	C₂²×C₇	1	1	yes	characteristic
508	C₂×#131	C₂²×C₇	1	1	yes	characteristic
509	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
510	#556	—	2	1	no	—
511	#556	C₂²×C₇	1	2	yes	complemented
512	#555	—	2	1	no	—
513	#555	C₂²×C₇	1	2	yes	complemented
514	#553	—	2	1	no	—
515	#553	C₂²×C₇	1	2	yes	complemented
516	#552	—	2	1	no	—
517	#552	C₂²×C₇	1	2	yes	complemented
518	#550	—	2	1	no	—
519	#550	—	2	1	no	—
520	#550	C₂²×C₇	1	2	yes	—
521	#550	C₂²×C₇	1	2	yes	—
522	#548	—	2	1	no	—
523	#548	—	2	1	no	—
524	#548	C₂²×C₇	1	2	yes	—
525	#548	C₂²×C₇	1	2	yes	—
526	#544	C₂²×C₇	1	1	yes	characteristic
527	#538	—	2	2	no	—
528	#537	C₂²×C₇	1	1	yes	characteristic
529	#535	—	2	2	no	—
530	#535	C₂²×C₇	1	1	yes	characteristic
531	#535	C₂²×C₇	1	1	yes	characteristic
532	#529	—	2	2	no	—
533	#525	—	2	2	no	—
534	#525	C₂²×C₇	1	1	yes	characteristic
535	#525	C₂²×C₇	1	1	yes	characteristic
536	#525	C₂²×C₇	1	1	yes	characteristic
537	#520	C₂²×C₇	1	1	yes	characteristic
538	#520	C₂²×C₇	1	1	yes	characteristic
539	#519	C₂²×C₇	1	1	yes	characteristic
540	C₂×#117	C₂²×C₇	1	1	yes	characteristic
541	#490	C₂²×C₇	1	2	yes	complemented
542	#489	C₂²×C₇	1	2	yes	complemented
543	#488	C₂²×C₇	1	2	yes	complemented
544	#486	C₂²×C₇	1	2	yes	complemented
545	#485	C₂²×C₇	1	2	yes	complemented
546	#485	C₂²×C₇	1	2	yes	complemented
547	#482	C₂²×C₇	1	2	yes	complemented
548	#482	C₂²×C₇	1	2	yes	complemented
549	#482	C₂²×C₇	1	2	yes	complemented
550	#482	C₂²×C₇	1	2	yes	complemented
551	#481	C₂²×C₇	1	2	yes	complemented
552	#480	C₂²×C₇	1	2	yes	complemented
553	#479	C₂²×C₇	1	2	yes	complemented
554	#479	C₂²×C₇	1	2	yes	complemented
555	#477	C₂²×C₇	1	2	yes	complemented
556	#475	C₂²×C₇	1	2	yes	complemented
557	#469	C₂²×C₇	1	2	yes	complemented
558	#468	C₂²×C₇	1	2	yes	complemented
559	#467	C₂²×C₇	1	1	yes	characteristic, complemented
560	#467	C₂²×C₇	1	1	yes	characteristic, complemented
561	#466	C₂²×C₇	1	2	yes	complemented
562	#466	C₂²×C₇	1	1	yes	characteristic, complemented
563	#466	C₂²×C₇	1	1	yes	characteristic, complemented
564	#465	C₂²×C₇	1	2	yes	complemented
565	#465	C₂²×C₇	1	1	yes	characteristic, complemented
566	#465	C₂²×C₇	1	1	yes	characteristic, complemented
567	#465	C₂²×C₇	1	1	yes	characteristic, complemented
568	#465	C₂²×C₇	1	1	yes	characteristic, complemented
569	#464	C₂²×C₇	1	2	yes	complemented
570	#463	C₂²×C₇	1	2	yes	complemented
571	#460	C₂²×C₇	1	2	yes	complemented
572	#459	C₂²×C₇	1	2	yes	complemented
573	#452	C₂²×C₇	1	2	yes	—
574	#452	C₂²×C₇	1	2	yes	—
575	#452	C₂²×C₇	1	2	yes	complemented
576	#451	C₂²×C₇	1	2	yes	complemented
577	#449	C₂²×C₇	1	2	yes	—
578	#449	C₂²×C₇	1	2	yes	—
579	#449	C₂²×C₇	1	2	yes	complemented
580	#448	C₂²×C₇	1	2	yes	complemented
581	#441	C₂²×C₇	1	2	yes	complemented
582	#440	C₂²×C₇	1	2	yes	complemented
583	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
584	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
585	#435	C₂²×C₇	1	2	yes	complemented
586	#435	C₂²×C₇	1	2	yes	complemented
587	C₈×D₄	C₂²×C₇	1	2	yes	complemented
588	C₈×D₄	C₂²×C₇	1	2	yes	complemented
589	#428	C₂²×C₇	1	1	yes	characteristic
590	#428	C₂²×C₇	1	1	yes	characteristic
591	#427	C₂²×C₇	1	1	yes	characteristic
592	#424	C₂²×C₇	1	1	yes	characteristic
593	#419	C₂²×C₇	1	1	yes	characteristic
594	#419	C₂²×C₇	1	2	yes	complemented
595	#418	C₂²×C₇	1	1	yes	characteristic
596	#417	C₂²×C₇	1	1	yes	characteristic
597	#417	C₂²×C₇	1	1	yes	characteristic
598	#417	C₂²×C₇	1	2	yes	complemented
599	#416	C₂²×C₇	1	1	yes	characteristic
600	#416	C₂²×C₇	1	2	yes	—
601	#416	C₂²×C₇	1	2	yes	—
602	#416	C₂²×C₇	1	2	yes	—
603	#416	C₂²×C₇	1	2	yes	—
604	#416	C₂²×C₇	1	1	yes	characteristic
605	#416	C₂²×C₇	1	2	yes	complemented
606	C₂×#103	C₂²×C₇	1	1	yes	characteristic
607	C₂×#103	C₂²×C₇	1	1	yes	characteristic
608	C₂×#103	C₂²×C₇	1	2	yes	complemented
609	C₂×#102	C₂²×C₇	1	1	yes	characteristic
610	C₂×#102	C₂²×C₇	1	1	yes	characteristic
611	#408	C₂²×C₇	1	1	yes	characteristic
612	#407	C₂²×C₇	1	1	yes	characteristic
613	#405	C₂²×C₇	1	1	yes	characteristic
614	C₂³×C₇	—	2	2	no	—
615	C₂³×C₇	—	2	1	no	—
616	C₂³×C₇	—	2	2	no	—
617	C₂³×C₇	—	2	1	no	—
618	C₂³×C₇	—	4	1	no	—
619	C₂³×C₇	—	4	1	no	—
620	C₂³×C₇	—	4	2	no	—
621	C₂³×C₇	—	8	1	no	—
622	C₂³×C₇	—	8	1	no	—
623	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
624	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
625	C₂³×C₇	C₂²×D₄	1	2	yes	—
626	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
627	C₇×Q₈	—	2	4	no	—
628	C₇×Q₈	—	2	2	no	—
629	C₇×Q₈	—	2	2	no	—
630	C₇×Q₈	—	2	1	no	—
631	C₇×Q₈	—	2	1	no	—
632	C₇×Q₈	—	2	1	no	—
633	C₇×Q₈	—	2	1	no	—
634	C₇×Q₈	—	4	4	no	—
635	C₇×Q₈	—	8	2	no	—
636	C₇×Q₈	C₂×#41	1	4	yes	—
637	C₇×D₄	—	2	4	no	—
638	C₇×D₄	—	2	2	no	—
639	C₇×D₄	—	2	1	no	—
640	C₇×D₄	—	2	2	no	—
641	C₇×D₄	—	2	1	no	—
642	C₇×D₄	—	2	1	no	—
643	C₇×D₄	—	2	2	no	—
644	C₇×D₄	—	2	1	no	—
645	C₇×D₄	—	4	2	no	—
646	C₇×D₄	—	4	2	no	—
647	C₇×D₄	—	4	4	no	—
648	C₇×D₄	—	4	4	no	—
649	C₇×D₄	—	4	4	no	—
650	C₇×D₄	—	4	2	no	—
651	C₇×D₄	—	4	2	no	—
652	C₇×D₄	—	4	2	no	—
653	C₇×D₄	—	8	2	no	—
654	C₇×D₄	—	8	2	no	—
655	C₇×D₄	—	8	1	no	—
656	C₇×D₄	—	8	2	no	—
657	C₇×D₄	—	8	2	no	—
658	C₇×D₄	—	8	2	no	—
659	C₇×D₄	—	8	1	no	—
660	C₇×D₄	—	8	1	no	—
661	C₇×D₄	—	8	1	no	—
662	C₂×C₄×C₇	—	2	2	no	—
663	C₂×C₄×C₇	—	2	4	no	—
664	C₂×C₄×C₇	—	2	2	no	—
665	C₂×C₄×C₇	—	2	2	no	—
666	C₂×C₄×C₇	—	2	2	no	—
667	C₂×C₄×C₇	—	2	1	no	—
668	C₂×C₄×C₇	—	2	1	no	—
669	C₂×C₄×C₇	—	2	2	no	—
670	C₂×C₄×C₇	—	2	1	no	—
671	C₂×C₄×C₇	—	2	1	no	—
672	C₂×C₄×C₇	—	2	2	no	—
673	C₂×C₄×C₇	—	2	2	no	—
674	C₂×C₄×C₇	—	2	1	no	—
675	C₂×C₄×C₇	—	2	1	no	—
676	C₂×C₄×C₇	—	2	1	no	—
677	C₂×C₄×C₇	—	2	1	no	—
678	C₂×C₄×C₇	—	2	2	no	—
679	C₂×C₄×C₇	—	2	1	no	—
680	C₂×C₄×C₇	—	2	1	no	—
681	C₂×C₄×C₇	—	4	4	no	—
682	C₂×C₄×C₇	—	4	4	no	—
683	C₂×C₄×C₇	—	4	4	no	—
684	C₂×C₄×C₇	—	4	4	no	—
685	C₂×C₄×C₇	—	4	2	no	—
686	C₂×C₄×C₇	—	4	2	no	—
687	C₂×C₄×C₇	—	8	2	no	—
688	C₂×C₄×C₇	—	8	1	no	—
689	C₂×C₄×C₇	—	8	2	no	—
690	C₂×C₄×C₇	—	8	1	no	—
691	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
692	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
693	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
694	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
695	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
696	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
697	C₂×C₄×C₇	C₂×#41	1	2	yes	—
698	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
699	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
700	C₇×C₈	—	2	2	no	—
701	C₇×C₈	—	2	1	no	—
702	C₇×C₈	—	2	1	no	—
703	C₇×C₈	—	2	1	no	—
704	C₇×C₈	—	2	1	no	—
705	C₇×C₈	—	2	2	no	—
706	2₋¹⁺⁴	—	2	4	no	—
707	2₋¹⁺⁴	—	4	2	no	—
708	C₂×#41	—	2	2	no	—
709	C₂×#41	—	2	1	no	—
710	C₂×#41	—	2	1	no	—
711	C₂×#41	—	2	1	no	—
712	C₂×#41	—	2	4	no	—
713	C₂×#41	—	4	2	no	—
714	C₂×#41	C₂³×C₇	1	1	yes	characteristic
715	C₂×#41	C₂³×C₇	1	1	yes	characteristic
716	C₂×#41	C₂³×C₇	1	2	yes	—
717	C₂×#41	C₂³×C₇	1	2	yes	—
718	C₂×#41	C₂³×C₇	1	2	yes	—
719	C₂×#41	C₂³×C₇	1	1	yes	characteristic
720	C₂²×Q₈	—	2	1	no	—
721	C₂²×Q₈	C₂³×C₇	1	2	yes	—
722	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
723	C₂²×D₄	—	2	1	no	—
724	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
725	C₂³×C₄	—	2	1	no	—
726	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
727	#137	—	2	4	no	—
728	AGL(1,ℤ/8)	—	4	2	no	—
729	#135	—	4	2	no	—
730	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
731	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
732	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
734	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
735	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
736	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
737	C₂×D₈	C₂³×C₇	1	2	yes	—
738	#131	—	4	2	no	—
739	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
740	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
741	C₂×M₁₆	C₂³×C₇	1	2	yes	—
742	C₂²×C₈	—	4	2	no	—
743	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
744	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
745	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
746	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
747	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
748	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
749	C₂²×C₈	C₂³×C₇	1	2	yes	—
750	C₄⋊Q₈	—	2	1	no	—
751	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
752	#127	—	2	2	no	—
753	#127	—	2	2	no	—
754	#127	—	2	1	no	—
755	#127	C₂³×C₇	1	2	yes	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#125	—	2	2	no	—
761	#125	—	2	1	no	—
762	#125	C₂³×C₇	1	2	yes	—
763	#124	—	2	1	no	—
764	#124	—	2	2	no	—
765	#124	—	2	2	no	—
766	#124	—	2	2	no	—
767	#124	—	2	2	no	—
768	#124	—	2	2	no	—
769	#124	C₂³×C₇	1	2	yes	—
770	#123	—	2	2	no	—
771	#123	—	2	1	no	—
772	#123	—	2	1	no	—
773	#123	—	2	2	no	—
774	#123	C₇×D₄	1	2	yes	—
775	C₂²⋊Q₈	—	2	1	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
780	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
781	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
782	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
784	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	—	2	1	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	C₇×D₄	1	1	yes	characteristic
799	#121	C₇×D₄	1	1	yes	characteristic
800	#121	C₂³×C₇	1	1	yes	characteristic
801	#121	C₂³×C₇	1	1	yes	characteristic
802	#121	C₂³×C₇	1	1	yes	characteristic
803	#121	C₂³×C₇	1	1	yes	characteristic
804	#121	C₂³×C₇	1	2	yes	—
805	#121	C₂³×C₇	1	2	yes	—
806	#121	C₂³×C₇	1	2	yes	—
807	#120	—	2	1	no	—
808	#120	—	2	1	no	—
809	#120	—	2	2	no	—
810	#120	—	2	2	no	—
811	#120	C₇×D₄	1	2	yes	—
812	C₄×Q₈	—	2	1	no	—
813	C₄×Q₈	—	2	1	no	—
814	C₄×Q₈	—	2	1	no	—
815	C₄×Q₈	—	2	2	no	—
816	C₄×Q₈	C₂³×C₇	1	2	yes	—
817	C₄×Q₈	C₂³×C₇	1	2	yes	—
818	C₄×Q₈	C₂³×C₇	1	2	yes	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	C₂³×C₇	1	2	yes	—
832	C₄×D₄	C₂³×C₇	1	2	yes	—
833	C₄×D₄	C₂³×C₇	1	2	yes	—
834	#117	—	2	1	no	—
835	#117	—	2	1	no	—
836	#117	—	2	1	no	—
837	#117	—	2	2	no	—
838	#117	—	2	2	no	—
839	#117	—	2	2	no	—
840	#117	C₂³×C₇	1	2	yes	—
841	#117	C₂³×C₇	1	2	yes	—
842	#117	C₂³×C₇	1	1	yes	characteristic
843	#117	C₂³×C₇	1	1	yes	characteristic
844	#117	C₂³×C₇	1	2	yes	—
845	#117	C₂³×C₇	1	1	yes	characteristic
846	C₂×C₄⋊C₄	—	2	1	no	—
847	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
848	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
849	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
850	C₂×C₂²⋊C₄	—	2	1	no	—
851	C₂×C₄²	—	2	1	no	—
852	#107	C₂³×C₇	1	1	yes	characteristic
853	#107	C₂³×C₇	1	1	yes	characteristic
854	#107	C₂³×C₇	1	2	yes	—
855	#107	C₂³×C₇	1	2	yes	—
856	#106	C₂³×C₇	1	1	yes	characteristic
857	#106	C₂³×C₇	1	1	yes	characteristic
858	#106	C₂³×C₇	1	2	yes	—
859	#106	C₂³×C₇	1	2	yes	—
860	C₄⋊C₈	C₂³×C₇	1	2	yes	—
861	C₄⋊C₈	C₂³×C₇	1	2	yes	—
862	#103	C₂³×C₇	1	2	yes	—
863	#103	C₂³×C₇	1	2	yes	—
864	#103	C₂³×C₇	1	2	yes	—
865	#103	C₂³×C₇	1	2	yes	—
866	#103	C₂³×C₇	1	1	yes	characteristic
867	#103	C₂³×C₇	1	2	yes	—
868	#103	C₂³×C₇	1	2	yes	—
869	#103	C₂³×C₇	1	1	yes	characteristic
870	#103	C₂³×C₇	1	1	yes	characteristic
871	#103	C₂³×C₇	1	1	yes	characteristic
872	#103	C₂³×C₇	1	2	yes	—
873	#103	C₂³×C₇	1	2	yes	—
874	#102	C₂³×C₇	1	2	yes	—
875	#102	C₂³×C₇	1	2	yes	—
876	#102	C₂³×C₇	1	2	yes	—
877	#102	C₂³×C₇	1	2	yes	—
878	#102	C₂³×C₇	1	1	yes	characteristic
879	#102	C₂³×C₇	1	1	yes	characteristic
880	#102	C₂³×C₇	1	1	yes	characteristic
881	#102	C₂³×C₇	1	1	yes	characteristic
882	#102	C₂³×C₇	1	2	yes	—
883	#102	C₂³×C₇	1	2	yes	—
884	#102	C₂³×C₇	1	2	yes	—
885	#102	C₂³×C₇	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
890	#97	C₂³×C₇	1	2	yes	—
891	C₄×C₈	C₂³×C₇	1	2	yes	—
892	C₂²×C₇	—	2	1	no	—
893	C₂²×C₇	—	2	1	no	—
894	C₂²×C₇	—	2	2	no	—
895	C₂²×C₇	—	2	1	no	—
896	C₂²×C₇	—	2	1	no	—
897	C₂²×C₇	—	2	2	no	—
898	C₂²×C₇	—	2	1	no	—
899	C₂²×C₇	—	2	1	no	—
900	C₂²×C₇	—	2	1	no	—
901	C₂²×C₇	—	2	1	no	—
902	C₂²×C₇	—	2	2	no	—
903	C₂²×C₇	—	4	4	no	—
904	C₂²×C₇	—	4	1	no	—
905	C₂²×C₇	—	4	1	no	—
906	C₂²×C₇	—	4	1	no	—
907	C₂²×C₇	—	4	1	no	—
908	C₂²×C₇	—	4	2	no	—
909	C₂²×C₇	—	4	2	no	—
910	C₂²×C₇	—	4	1	no	—
911	C₂²×C₇	—	4	2	no	—
912	C₂²×C₇	—	4	1	no	—
913	C₂²×C₇	—	8	4	no	—
914	C₂²×C₇	#546	1	2	yes	—
915	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
916	C₄×C₇	—	2	2	no	—
917	C₄×C₇	—	2	2	no	—
918	C₄×C₇	—	2	1	no	—
919	C₄×C₇	—	2	1	no	—
920	C₄×C₇	—	2	4	no	—
921	C₄×C₇	—	2	2	no	—
922	C₄×C₇	—	4	2	no	—
923	C₄×C₇	—	4	1	no	—
924	C₄×C₇	—	4	2	no	—
925	C₄×C₇	—	4	1	no	—
926	C₄×C₇	—	4	1	no	—
927	C₄×C₇	—	4	1	no	—
928	C₄×C₇	—	4	1	no	—
929	C₄×C₇	—	4	1	no	—
930	C₄×C₇	#546	1	2	yes	—
931	C₄×C₇	C₂²×#41	1	1	yes	characteristic
932	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
933	C₂⁴	—	2	1	no	—
934	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
935	#41	—	2	2	no	—
936	#41	—	2	2	no	—
937	#41	—	2	4	no	—
938	#41	—	2	4	no	—
939	#41	—	2	4	no	—
940	#41	—	2	2	no	—
941	#41	—	2	2	no	—
942	#41	—	2	2	no	—
943	#41	—	2	2	no	—
944	#41	—	4	2	no	—
945	#41	—	4	2	no	—
946	#41	—	4	2	no	—
947	#41	—	4	8	no	—
948	#41	—	4	4	no	—
949	#41	—	4	4	no	—
950	#41	—	4	4	no	—
951	C₂×Q₈	—	2	1	no	—
952	C₂×Q₈	—	2	2	no	—
953	C₂×Q₈	—	2	2	no	—
954	C₂×Q₈	—	2	2	no	—
955	C₂×Q₈	—	2	4	no	—
956	C₂×Q₈	—	4	2	no	—
957	C₂×Q₈	—	4	4	no	—
958	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
959	C₂×Q₈	C₇×#41	1	4	yes	—
960	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
961	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
962	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
963	C₂×D₄	—	2	1	no	—
964	C₂×D₄	—	2	1	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	2	1	no	—
969	C₂×D₄	—	2	1	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	1	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	1	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	2	no	—
980	C₂×D₄	—	4	4	no	—
981	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
982	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
983	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
984	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
985	C₂×D₄	C₂⁴×C₇	1	2	yes	—
986	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
987	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
988	C₂²×C₄	—	2	1	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	1	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	—	4	4	no	—
1002	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1003	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1004	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1005	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
1006	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1007	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1008	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1009	Q₁₆	—	2	4	no	—
1010	Q₁₆	—	4	1	no	—
1011	SD₁₆	—	2	4	no	—
1012	SD₁₆	—	4	1	no	—
1013	SD₁₆	—	4	1	no	—
1014	SD₁₆	—	4	2	no	—
1015	D₈	—	4	1	no	—
1016	D₈	—	4	2	no	—
1017	M₁₆	—	2	2	no	—
1018	M₁₆	—	2	2	no	—
1019	M₁₆	—	4	2	no	—
1020	C₂×C₈	—	2	2	no	—
1021	C₂×C₈	—	2	2	no	—
1022	C₂×C₈	—	4	1	no	—
1023	C₂×C₈	—	4	1	no	—
1024	C₂×C₈	—	4	1	no	—
1025	C₂×C₈	—	4	1	no	—
1026	C₂×C₈	—	4	2	no	—
1027	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1028	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1029	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1030	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1031	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1032	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1048	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1049	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1050	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1051	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1052	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1053	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1054	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1055	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1056	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	1	no	—
1067	C₂²⋊C₄	—	2	1	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1078	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1079	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1080	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1081	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1082	C₄²	—	2	2	no	—
1083	C₄²	—	2	2	no	—
1084	C₄²	—	2	2	no	—
1085	C₄²	—	2	2	no	—
1086	C₄²	—	2	2	no	—
1087	C₄²	—	2	2	no	—
1088	C₄²	—	2	1	no	—
1089	C₄²	—	2	1	no	—
1090	C₄²	C₂⁴×C₇	1	2	yes	—
1091	C₂×C₇	—	2	2	no	—
1092	C₂×C₇	—	4	2	no	—
1093	C₂×C₇	—	4	1	no	—
1094	C₂×C₇	—	4	1	no	—
1095	C₂×C₇	—	8	1	no	—
1096	C₂×C₇	—	8	1	no	—
1097	C₂×C₇	—	8	2	no	—
1098	C₂×C₇	C₂×#546	1	1	yes	characteristic
1099	C₂×C₇	#3584	1	1	yes	characteristic
1100	C₂×C₇	#3584	1	1	yes	characteristic
1101	C₂³	—	2	2	no	—
1102	C₂³	—	2	1	no	—
1103	C₂³	—	2	2	no	—
1104	C₂³	—	2	1	no	—
1105	C₂³	—	4	1	no	—
1106	C₂³	—	4	1	no	—
1107	C₂³	—	4	2	no	—
1108	C₂³	—	8	1	no	—
1109	C₂³	—	8	1	no	—
1110	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1111	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1112	C₂³	C₂²×C₇×D₄	1	2	yes	—
1113	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1114	Q₈	—	2	2	no	—
1115	Q₈	—	2	4	no	—
1116	Q₈	—	2	2	no	—
1117	Q₈	—	2	1	no	—
1118	Q₈	—	2	1	no	—
1119	Q₈	—	2	1	no	—
1120	Q₈	—	2	1	no	—
1121	Q₈	—	4	4	no	—
1122	Q₈	—	8	2	no	—
1123	Q₈	C₂×C₇×#41	1	4	yes	—
1124	D₄	—	2	4	no	—
1125	D₄	—	2	1	no	—
1126	D₄	—	2	2	no	—
1127	D₄	—	2	1	no	—
1128	D₄	—	2	1	no	—
1129	D₄	—	2	2	no	—
1130	D₄	—	2	1	no	—
1131	D₄	—	2	2	no	—
1132	D₄	—	4	2	no	—
1133	D₄	—	4	2	no	—
1134	D₄	—	4	4	no	—
1135	D₄	—	4	4	no	—
1136	D₄	—	4	4	no	—
1137	D₄	—	4	2	no	—
1138	D₄	—	4	2	no	—
1139	D₄	—	4	2	no	—
1140	D₄	—	8	2	no	—
1141	D₄	—	8	2	no	—
1142	D₄	—	8	1	no	—
1143	D₄	—	8	2	no	—
1144	D₄	—	8	2	no	—
1145	D₄	—	8	2	no	—
1146	D₄	—	8	1	no	—
1147	D₄	—	8	1	no	—
1148	D₄	—	8	1	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	4	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	2	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	2	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	4	4	no	—
1169	C₂×C₄	—	4	4	no	—
1170	C₂×C₄	—	4	4	no	—
1171	C₂×C₄	—	4	4	no	—
1172	C₂×C₄	—	4	2	no	—
1173	C₂×C₄	—	4	2	no	—
1174	C₂×C₄	—	8	2	no	—
1175	C₂×C₄	—	8	1	no	—
1176	C₂×C₄	—	8	2	no	—
1177	C₂×C₄	—	8	1	no	—
1178	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1179	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1180	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1181	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1182	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1183	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1184	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1185	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1186	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1187	C₈	—	2	2	no	—
1188	C₈	—	2	1	no	—
1189	C₈	—	2	1	no	—
1190	C₈	—	2	1	no	—
1191	C₈	—	2	1	no	—
1192	C₈	—	2	2	no	—
1193	C₇	#61170	1	1	yes	characteristic, direct product factor, Sylow
1194	C₂²	—	2	1	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	2	no	—
1197	C₂²	—	2	1	no	—
1198	C₂²	—	2	1	no	—
1199	C₂²	—	2	2	no	—
1200	C₂²	—	2	1	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	2	1	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	4	4	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	2	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	1	no	—
1213	C₂²	—	4	2	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	8	4	no	—
1216	C₂²	C₇×#546	1	2	yes	—
1217	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1218	C₄	—	2	2	no	—
1219	C₄	—	2	2	no	—
1220	C₄	—	2	1	no	—
1221	C₄	—	2	1	no	—
1222	C₄	—	2	4	no	—
1223	C₄	—	2	2	no	—
1224	C₄	—	4	2	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	2	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	1	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	C₇×#546	1	2	yes	—
1233	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1234	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1235	C₂	—	2	2	no	—
1236	C₂	—	4	1	no	—
1237	C₂	—	4	1	no	—
1238	C₂	—	4	2	no	—
1239	C₂	—	8	2	no	—
1240	C₂	—	8	1	no	—
1241	C₂	—	8	1	no	—
1242	C₂	C₂×C₇×#546	1	1	yes	characteristic
1243	C₂	C₇×#3584	1	1	yes	characteristic
1244	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3493	C₂	semidirect
2. C₇×#3487	C₂	semidirect
3. C₇×#3321	C₂	semidirect
4. C₇×#3317	C₂	semidirect
5. C₇×#3313	C₂	semidirect
6. C₇×#3309	C₂	semidirect
7. C₇×#3305	C₂	semidirect
8. C₇×#3304	C₂	semidirect
9. C₇×#3301	C₂	semidirect
10. C₇×#3300	C₂	semidirect
11. C₇×#3136	C₂	semidirect
12. C₇×#3096	C₂	semidirect
13. C₇×#3093	C₂	semidirect
14. C₇×#3082	C₂	semidirect
15. C₇×#3062	C₂	semidirect
16. C₇×#3050	C₂	semidirect
17. C₇×#3045	C₂	semidirect
18. C₇×#3013	C₂	semidirect
19. C₇×#3005	C₂	semidirect
20. C₇×#2947	C₂	semidirect
21. C₇×#2929	C₂	semidirect
22. C₇×#2898	C₂	semidirect
23. C₂×C₇×#416	C₂	semidirect
32. C₇×#556	C₂²	semidirect
34. C₇×#555	C₂²	semidirect
36. C₇×#553	C₂²	semidirect
38. C₇×#552	C₂²	semidirect
62. C₇×#490	C₂²	semidirect
63. C₇×#489	C₂²	semidirect
64. C₇×#488	C₂²	semidirect
65. C₇×#486	C₂²	semidirect
66. C₇×#485	C₂²	semidirect
67. C₇×#485	C₂²	semidirect
68. C₇×#482	C₂²	semidirect
69. C₇×#482	C₂²	semidirect
70. C₇×#482	C₂²	semidirect
71. C₇×#482	C₂²	semidirect
72. C₇×#481	C₂²	semidirect
73. C₇×#480	C₂²	semidirect
74. C₇×#479	C₂²	semidirect
75. C₇×#479	C₂²	semidirect
76. C₇×#477	C₂²	semidirect
77. C₇×#475	C₂²	semidirect
78. C₇×#469	C₂²	semidirect
79. C₇×#468	C₂²	semidirect
80. C₇×#467	C₂²	semidirect
81. C₇×#467	C₂²	semidirect
82. C₇×#466	C₂²	semidirect
83. C₇×#466	C₂²	semidirect
84. C₇×#466	C₂²	semidirect
85. C₇×#465	C₂²	semidirect
86. C₇×#465	C₂²	semidirect
87. C₇×#465	C₂²	semidirect
88. C₇×#465	C₂²	semidirect
89. C₇×#465	C₂²	semidirect
90. C₇×#464	C₂²	semidirect
91. C₇×#463	C₂²	semidirect
92. C₇×#460	C₂²	semidirect
93. C₇×#459	C₂²	semidirect
96. C₇×#452	C₂²	semidirect
97. C₇×#451	C₂²	semidirect
100. C₇×#449	C₂²	semidirect
101. C₇×#448	C₂²	semidirect
102. C₇×#441	C₂²	semidirect
103. C₇×#440	C₂²	semidirect
104. C₄×C₇×Q₁₆	C₂²	semidirect
105. C₄×C₇×SD₁₆	C₂²	semidirect
106. C₇×#435	C₂²	semidirect
107. C₇×#435	C₂²	semidirect
108. C₇×C₈×D₄	C₂²	semidirect
109. C₇×C₈×D₄	C₂²	semidirect
115. C₇×#419	C₂²	semidirect
119. C₇×#417	C₂²	semidirect
126. C₇×#416	C₂²	semidirect
129. C₂×C₇×#103	C₂²	semidirect
135. #61170	C₇	direct (N × H)
322. #3493	C₂×C₇	semidirect
323. #3487	C₂×C₇	semidirect
324. #3321	C₂×C₇	semidirect
325. #3317	C₂×C₇	semidirect
326. #3313	C₂×C₇	semidirect
327. #3309	C₂×C₇	semidirect
328. #3305	C₂×C₇	semidirect
329. #3304	C₂×C₇	semidirect
330. #3301	C₂×C₇	semidirect
331. #3300	C₂×C₇	semidirect
332. #3136	C₂×C₇	semidirect
333. #3096	C₂×C₇	semidirect
334. #3093	C₂×C₇	semidirect
335. #3082	C₂×C₇	semidirect
336. #3062	C₂×C₇	semidirect
337. #3050	C₂×C₇	semidirect
338. #3045	C₂×C₇	semidirect
339. #3013	C₂×C₇	semidirect
340. #3005	C₂×C₇	semidirect
341. #2947	C₂×C₇	semidirect
342. #2929	C₂×C₇	semidirect
343. #2898	C₂×C₇	semidirect
344. C₂×#416	C₂×C₇	semidirect
511. #556	C₂²×C₇	semidirect
513. #555	C₂²×C₇	semidirect
515. #553	C₂²×C₇	semidirect
517. #552	C₂²×C₇	semidirect
541. #490	C₂²×C₇	semidirect
542. #489	C₂²×C₇	semidirect
543. #488	C₂²×C₇	semidirect
544. #486	C₂²×C₇	semidirect
545. #485	C₂²×C₇	semidirect
546. #485	C₂²×C₇	semidirect
547. #482	C₂²×C₇	semidirect
548. #482	C₂²×C₇	semidirect
549. #482	C₂²×C₇	semidirect
550. #482	C₂²×C₇	semidirect
551. #481	C₂²×C₇	semidirect
552. #480	C₂²×C₇	semidirect
553. #479	C₂²×C₇	semidirect
554. #479	C₂²×C₇	semidirect
555. #477	C₂²×C₇	semidirect
556. #475	C₂²×C₇	semidirect
557. #469	C₂²×C₇	semidirect
558. #468	C₂²×C₇	semidirect
559. #467	C₂²×C₇	semidirect
560. #467	C₂²×C₇	semidirect
561. #466	C₂²×C₇	semidirect
562. #466	C₂²×C₇	semidirect
563. #466	C₂²×C₇	semidirect
564. #465	C₂²×C₇	semidirect
565. #465	C₂²×C₇	semidirect
566. #465	C₂²×C₇	semidirect
567. #465	C₂²×C₇	semidirect
568. #465	C₂²×C₇	semidirect
569. #464	C₂²×C₇	semidirect
570. #463	C₂²×C₇	semidirect
571. #460	C₂²×C₇	semidirect
572. #459	C₂²×C₇	semidirect
575. #452	C₂²×C₇	semidirect
576. #451	C₂²×C₇	semidirect
579. #449	C₂²×C₇	semidirect
580. #448	C₂²×C₇	semidirect
581. #441	C₂²×C₇	semidirect
582. #440	C₂²×C₇	semidirect
583. C₄×Q₁₆	C₂²×C₇	semidirect
584. C₄×SD₁₆	C₂²×C₇	semidirect
585. #435	C₂²×C₇	semidirect
586. #435	C₂²×C₇	semidirect
587. C₈×D₄	C₂²×C₇	semidirect
588. C₈×D₄	C₂²×C₇	semidirect
594. #419	C₂²×C₇	semidirect
598. #417	C₂²×C₇	semidirect
605. #416	C₂²×C₇	semidirect
608. C₂×#103	C₂²×C₇	semidirect
1193. C₇	#61170	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×#3493	2
C₇×#3487	2
C₇×#3321	2
C₇×#3317	2
C₇×#3313	2
C₇×#3309	2
C₇×#3305	2
C₇×#3304	2
C₇×#3301	2
C₇×#3300	2
C₇×#3136	2
C₇×#3096	2
C₇×#3093	2
C₇×#3082	2
C₇×#3062	2
C₇×#3050	2
C₇×#3045	2
C₇×#3013	2
C₇×#3005	2
C₇×#2947	2
C₇×#2929	2
C₇×#2898	2
C₂×C₇×#416	2
#61170	7

Subgroups — C7×#61170 #13238386

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61170 #13238386