Subgroups — C₇×#62032 #13239248

Order 1792.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3329	C₂	1	2	yes	maximal, complemented
8	C₇×#3328	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3321	C₂	1	2	yes	maximal, complemented
10	C₇×#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3275	C₂	1	2	yes	maximal, complemented
13	C₇×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3266	C₂	1	2	yes	maximal, complemented
15	C₇×#3258	C₂	1	2	yes	maximal, complemented
16	C₇×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3225	C₂	1	2	yes	maximal, complemented
18	C₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3123	C₂	1	2	yes	maximal, complemented
20	C₇×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3042	C₂	1	2	yes	maximal, complemented
22	C₇×#3039	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#137	C₂²	1	2	yes	—
25	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
27	C₇×#563	—	2	2	no	—
28	C₇×#559	C₂²	1	1	yes	characteristic
29	C₇×#557	C₂²	1	1	yes	characteristic, complemented
30	C₇×#556	C₂²	1	1	yes	characteristic
31	C₇×#556	C₂²	1	1	yes	characteristic, complemented
32	C₇×#555	C₂²	1	2	yes	—
33	C₇×#554	—	2	1	no	—
34	C₇×#553	—	2	1	no	—
35	C₇×#551	—	2	2	no	—
36	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
37	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
38	C₇×D₄×Q₈	C₂²	1	2	yes	complemented
39	C₇×#548	—	2	1	no	—
40	C₇×#548	C₂²	1	2	yes	complemented
41	C₇×#547	C₂²	1	1	yes	characteristic
42	C₇×#546	—	2	1	no	—
43	C₇×#546	C₂²	1	2	yes	—
44	C₇×D₄²	C₂²	1	1	yes	characteristic
45	C₇×#544	—	2	1	no	—
46	C₇×#542	—	2	1	no	—
47	C₇×#542	C₂²	1	2	yes	—
48	C₇×#541	C₂²	1	2	yes	complemented
49	C₇×#539	—	2	2	no	—
50	C₇×#538	—	2	2	no	—
51	C₇×#536	C₂²	1	2	yes	complemented
52	C₇×#532	C₂²	1	1	yes	characteristic
53	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₇×#529	—	2	1	no	—
55	C₇×#529	C₂²	1	1	yes	characteristic
56	C₇×#529	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₇×#124	—	2	1	no	—
58	C₇×#518	C₂²	1	2	yes	—
59	C₄×C₇×#41	C₂²	1	1	yes	characteristic
60	C₇×#497	C₂²	1	2	yes	complemented
61	C₇×#495	C₂²	1	2	yes	complemented
62	C₇×#492	C₂²	1	1	yes	characteristic
63	C₇×#492	C₂²	1	1	yes	characteristic
64	C₇×#489	C₂²	1	2	yes	complemented
65	C₇×#487	C₂²	1	1	yes	characteristic, complemented
66	C₇×#487	C₂²	1	1	yes	characteristic, complemented
67	C₇×#487	C₂²	1	2	yes	complemented
68	C₇×#485	C₂²	1	2	yes	complemented
69	C₇×#485	C₂²	1	2	yes	complemented
70	C₇×#485	C₂²	1	1	yes	characteristic, complemented
71	C₇×#482	C₂²	1	1	yes	characteristic, complemented
72	C₇×#479	C₂²	1	1	yes	characteristic, complemented
73	C₇×#478	C₂²	1	1	yes	characteristic
74	C₇×#478	C₂²	1	2	yes	complemented
75	C₇×#477	C₂²	1	2	yes	complemented
76	C₇×#475	C₂²	1	1	yes	characteristic, complemented
77	C₇×#475	C₂²	1	2	yes	complemented
78	C₇×#474	C₂²	1	1	yes	characteristic, complemented
79	C₇×#470	C₂²	1	2	yes	complemented
80	C₇×#469	C₂²	1	2	yes	complemented
81	C₇×#468	C₂²	1	2	yes	—
82	C₇×#468	C₂²	1	2	yes	complemented
83	C₇×#467	C₂²	1	2	yes	complemented
84	C₇×#465	C₂²	1	2	yes	—
85	C₇×#464	C₂²	1	1	yes	characteristic, complemented
86	C₇×#464	C₂²	1	2	yes	complemented
87	C₇×#464	C₂²	1	2	yes	complemented
88	C₇×#463	C₂²	1	2	yes	—
89	C₇×#463	C₂²	1	1	yes	characteristic
90	C₇×#463	C₂²	1	2	yes	complemented
91	C₇×#463	C₂²	1	2	yes	complemented
92	C₇×#462	C₂²	1	2	yes	complemented
93	C₇×#462	C₂²	1	1	yes	characteristic, complemented
94	C₇×#462	C₂²	1	1	yes	characteristic, complemented
95	C₇×#461	C₂²	1	2	yes	—
96	C₇×#461	C₂²	1	1	yes	characteristic
97	C₇×#461	C₂²	1	1	yes	characteristic
98	C₇×#461	C₂²	1	2	yes	—
99	C₇×#461	C₂²	1	2	yes	complemented
100	C₇×#461	C₂²	1	2	yes	complemented
101	C₇×#461	C₂²	1	2	yes	complemented
102	C₇×#460	C₂²	1	1	yes	characteristic
103	C₇×#459	C₂²	1	1	yes	characteristic
104	C₇×#452	C₂²	1	1	yes	characteristic
105	C₇×#452	C₂²	1	2	yes	complemented
106	C₇×#451	C₂²	1	2	yes	complemented
107	C₇×#450	C₂²	1	2	yes	—
108	C₇×#450	C₂²	1	2	yes	—
109	C₇×#449	C₂²	1	2	yes	—
110	C₇×#449	C₂²	1	1	yes	characteristic
111	C₇×#448	C₂²	1	2	yes	—
112	C₇×#448	C₂²	1	2	yes	complemented
113	C₇×#448	C₂²	1	2	yes	complemented
114	C₇×#446	C₂²	1	1	yes	characteristic, complemented
115	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
116	C₇×#440	C₂²	1	2	yes	—
117	C₇×#440	C₂²	1	2	yes	complemented
118	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
120	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
121	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
123	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
124	C₇×#436	C₂²	1	1	yes	characteristic
125	C₇×#436	C₂²	1	2	yes	complemented
126	C₇×#435	C₂²	1	2	yes	complemented
127	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
128	C₇×#433	C₂²	1	2	yes	complemented
129	C₇×#431	C₂²	1	1	yes	characteristic, complemented
130	C₇×#424	C₂²	1	2	yes	complemented
131	C₇×#423	C₂²	1	1	yes	characteristic, complemented
132	C₇×#419	C₂²	1	2	yes	complemented
133	C₇×#419	C₂²	1	2	yes	complemented
134	C₇×#416	C₂²	1	2	yes	complemented
135	#62032	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	1	no	—
137	C₂×C₇×#41	C₂³	1	1	yes	characteristic
138	C₂×C₇×#41	C₂³	1	2	yes	—
139	C₂²×C₇×Q₈	—	2	1	no	—
140	C₂²×C₇×Q₈	C₂³	1	2	yes	—
141	C₂²×C₇×Q₈	C₂³	1	2	yes	—
142	C₂²×C₇×D₄	—	2	1	no	—
143	C₂²×C₇×D₄	C₂³	1	2	yes	—
144	C₇×#137	—	4	4	no	—
145	C₇×AGL(1,ℤ/8)	—	4	4	no	—
146	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
147	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₇×SD₁₆	—	4	4	no	—
150	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
151	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
155	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
157	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
158	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
159	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
160	C₂×C₇×D₈	C₂³	1	2	yes	—
161	C₂×C₇×M₁₆	C₂³	1	2	yes	—
162	C₂×C₇×M₁₆	C₂³	1	2	yes	—
163	C₂²×C₇×C₈	C₂³	1	2	yes	—
164	C₇×C₄⋊Q₈	—	2	1	no	—
165	C₇×C₄⋊Q₈	—	2	2	no	—
166	C₇×C₄⋊Q₈	—	2	1	no	—
167	C₇×C₄⋊Q₈	—	2	1	no	—
168	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
172	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
173	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
174	C₇×#127	C₂³	1	1	yes	characteristic
175	C₇×#126	—	2	2	no	—
176	C₇×#126	—	2	2	no	—
177	C₇×#126	—	2	2	no	—
178	C₇×#126	—	2	2	no	—
179	C₇×#126	—	2	2	no	—
180	C₇×#126	—	2	1	no	—
181	C₇×#126	D₄	1	2	yes	—
182	C₇×#125	—	2	2	no	—
183	C₇×#125	—	2	2	no	—
184	C₇×#125	—	2	2	no	—
185	C₇×#125	—	2	1	no	—
186	C₇×#125	D₄	1	1	yes	characteristic
187	C₇×#125	C₂³	1	1	yes	characteristic
188	C₇×#124	—	2	1	no	—
189	C₇×#124	—	2	1	no	—
190	C₇×#124	—	2	2	no	—
191	C₇×#124	—	2	2	no	—
192	C₇×#124	—	2	2	no	—
193	C₇×#124	—	2	2	no	—
194	C₇×#124	—	2	1	no	—
195	C₇×#124	D₄	1	1	yes	characteristic
196	C₇×#124	C₂³	1	2	yes	—
197	C₇×#124	C₂³	1	2	yes	—
198	C₇×#124	C₂³	1	1	yes	characteristic
199	C₇×#123	—	2	1	no	—
200	C₇×#123	—	2	2	no	—
201	C₇×#123	—	2	2	no	—
202	C₇×#123	—	2	2	no	—
203	C₇×#123	—	2	2	no	—
204	C₇×#123	—	2	2	no	—
205	C₇×#123	—	2	2	no	—
206	C₇×#123	D₄	1	2	yes	—
207	C₇×C₂²⋊Q₈	—	2	1	no	—
208	C₇×C₂²⋊Q₈	—	2	1	no	—
209	C₇×C₂²⋊Q₈	—	2	2	no	—
210	C₇×C₂²⋊Q₈	—	2	2	no	—
211	C₇×C₂²⋊Q₈	—	2	2	no	—
212	C₇×C₂²⋊Q₈	—	2	2	no	—
213	C₇×C₂²⋊Q₈	—	2	2	no	—
214	C₇×C₂²⋊Q₈	—	2	2	no	—
215	C₇×C₂²⋊Q₈	—	2	2	no	—
216	C₇×C₂²⋊Q₈	—	2	2	no	—
217	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
218	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₇×#121	—	2	2	no	—
223	C₇×#121	—	2	2	no	—
224	C₇×#121	—	2	1	no	—
225	C₇×#121	—	2	1	no	—
226	C₇×#121	—	2	1	no	—
227	C₇×#121	—	2	2	no	—
228	C₇×#121	D₄	1	1	yes	characteristic
229	C₇×#121	C₂³	1	2	yes	—
230	C₇×#121	C₂³	1	2	yes	—
231	C₇×#121	C₂³	1	1	yes	characteristic
232	C₇×#120	—	2	2	no	—
233	C₇×#120	—	2	2	no	—
234	C₄×C₇×Q₈	—	2	1	no	—
235	C₄×C₇×Q₈	—	2	1	no	—
236	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
237	C₄×C₇×Q₈	C₂³	1	2	yes	—
238	C₄×C₇×Q₈	C₂³	1	2	yes	—
239	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
240	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
241	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
242	C₄×C₇×D₄	—	2	2	no	—
243	C₄×C₇×D₄	—	2	1	no	—
244	C₄×C₇×D₄	—	2	1	no	—
245	C₄×C₇×D₄	—	2	1	no	—
246	C₄×C₇×D₄	—	2	1	no	—
247	C₄×C₇×D₄	—	2	2	no	—
248	C₄×C₇×D₄	—	2	2	no	—
249	C₄×C₇×D₄	—	2	1	no	—
250	C₄×C₇×D₄	—	2	2	no	—
251	C₄×C₇×D₄	—	2	1	no	—
252	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
253	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
254	C₄×C₇×D₄	C₂³	1	2	yes	—
255	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
256	C₄×C₇×D₄	C₂³	1	2	yes	—
257	C₄×C₇×D₄	C₂³	1	2	yes	—
258	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
259	C₄×C₇×D₄	C₂³	1	2	yes	—
260	C₇×#117	—	2	2	no	—
261	C₇×#117	—	2	1	no	—
262	C₇×#117	—	2	1	no	—
263	C₇×#117	—	2	1	no	—
264	C₇×#117	C₂³	1	1	yes	characteristic
265	C₇×#117	C₂³	1	2	yes	—
266	C₇×#117	C₂³	1	2	yes	—
267	C₂×C₇×C₄⋊C₄	—	2	1	no	—
268	C₂×C₇×C₄⋊C₄	—	2	1	no	—
269	C₂×C₇×C₄⋊C₄	—	2	1	no	—
270	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₄²×C₇	—	2	1	no	—
274	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
275	C₇×#107	C₂³	1	2	yes	—
276	C₇×#107	C₂³	1	1	yes	characteristic
277	C₇×#107	C₂³	1	1	yes	characteristic
278	C₇×#106	C₂³	1	2	yes	—
279	C₇×#106	C₂³	1	1	yes	characteristic
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₇×C₄⋊C₈	C₂³	1	2	yes	—
287	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₇×#103	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
301	C₇×#102	C₂³	1	2	yes	—
302	C₇×#102	C₂³	1	2	yes	—
303	C₇×#102	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	1	yes	characteristic
308	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₇×#97	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
315	C₄×C₇×C₈	C₂³	1	2	yes	—
316	#3552	C₂×C₇	1	1	yes	characteristic, complemented
317	#3514	C₂×C₇	1	1	yes	characteristic, complemented
318	#3400	C₂×C₇	1	1	yes	characteristic, complemented
319	#3394	C₂×C₇	1	1	yes	characteristic, complemented
320	#3367	C₂×C₇	1	1	yes	characteristic, complemented
321	#3359	C₂×C₇	1	1	yes	characteristic, complemented
322	#3329	C₂×C₇	1	2	yes	complemented
323	#3328	C₂×C₇	1	1	yes	characteristic, complemented
324	#3321	C₂×C₇	1	2	yes	complemented
325	#3302	C₂×C₇	1	1	yes	characteristic, complemented
326	D₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
327	#3275	C₂×C₇	1	2	yes	complemented
328	#3272	C₂×C₇	1	1	yes	characteristic, complemented
329	#3266	C₂×C₇	1	2	yes	complemented
330	#3258	C₂×C₇	1	2	yes	complemented
331	#3251	C₂×C₇	1	1	yes	characteristic, complemented
332	#3225	C₂×C₇	1	2	yes	complemented
333	#3206	C₂×C₇	1	1	yes	characteristic, complemented
334	#3123	C₂×C₇	1	2	yes	complemented
335	#3102	C₂×C₇	1	1	yes	characteristic, complemented
336	#3042	C₂×C₇	1	2	yes	complemented
337	#3039	C₂×C₇	1	1	yes	characteristic, complemented
338	#2993	C₂×C₇	1	1	yes	characteristic, complemented
339	C₂⁴×C₇	—	2	2	no	—
340	C₇×#41	—	2	2	no	—
341	C₇×#41	—	4	1	no	—
342	C₇×#41	—	4	2	no	—
343	C₇×#41	—	4	2	no	—
344	C₇×#41	—	8	2	no	—
345	C₂×C₇×Q₈	—	2	1	no	—
346	C₂×C₇×Q₈	—	2	2	no	—
347	C₂×C₇×Q₈	—	2	2	no	—
348	C₂×C₇×Q₈	—	2	2	no	—
349	C₂×C₇×Q₈	—	4	2	no	—
350	C₂×C₇×Q₈	—	4	2	no	—
351	C₂×C₇×Q₈	—	4	2	no	—
352	C₂×C₇×Q₈	—	4	2	no	—
353	C₂×C₇×Q₈	—	8	2	no	—
354	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
355	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
356	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
357	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
358	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
359	C₂×C₇×D₄	—	2	4	no	—
360	C₂×C₇×D₄	—	2	1	no	—
361	C₂×C₇×D₄	—	2	1	no	—
362	C₂×C₇×D₄	—	2	2	no	—
363	C₂×C₇×D₄	—	2	2	no	—
364	C₂×C₇×D₄	—	2	2	no	—
365	C₂×C₇×D₄	—	2	2	no	—
366	C₂×C₇×D₄	—	2	1	no	—
367	C₂×C₇×D₄	—	2	1	no	—
368	C₂×C₇×D₄	—	4	2	no	—
369	C₂×C₇×D₄	—	8	2	no	—
370	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
371	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
372	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
373	C₂×C₇×D₄	C₂⁴	1	2	yes	—
374	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₇	—	2	2	no	—
376	C₂²×C₄×C₇	—	2	2	no	—
377	C₂²×C₄×C₇	—	2	1	no	—
378	C₂²×C₄×C₇	—	2	1	no	—
379	C₂²×C₄×C₇	—	2	1	no	—
380	C₂²×C₄×C₇	—	2	1	no	—
381	C₂²×C₄×C₇	—	2	2	no	—
382	C₂²×C₄×C₇	—	2	2	no	—
383	C₂²×C₄×C₇	—	2	2	no	—
384	C₂²×C₄×C₇	—	2	2	no	—
385	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
389	C₇×Q₁₆	—	4	1	no	—
390	C₇×Q₁₆	—	4	2	no	—
391	C₇×Q₁₆	—	4	2	no	—
392	C₇×SD₁₆	—	2	2	no	—
393	C₇×SD₁₆	—	2	4	no	—
394	C₇×SD₁₆	—	2	4	no	—
395	C₇×SD₁₆	—	4	2	no	—
396	C₇×SD₁₆	—	4	2	no	—
397	C₇×SD₁₆	—	4	2	no	—
398	C₇×SD₁₆	—	4	1	no	—
399	C₇×SD₁₆	—	4	2	no	—
400	C₇×SD₁₆	—	4	2	no	—
401	C₇×D₈	—	2	2	no	—
402	C₇×D₈	—	4	2	no	—
403	C₇×M₁₆	—	4	2	no	—
404	C₇×M₁₆	—	4	2	no	—
405	C₂×C₇×C₈	—	4	2	no	—
406	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
407	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
408	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
409	C₂×C₇×C₈	C₂⁴	1	2	yes	—
410	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
411	C₂×C₇×C₈	C₂⁴	1	2	yes	—
412	C₇×C₄⋊C₄	—	2	1	no	—
413	C₇×C₄⋊C₄	—	2	1	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	2	no	—
418	C₇×C₄⋊C₄	—	2	1	no	—
419	C₇×C₄⋊C₄	—	2	1	no	—
420	C₇×C₄⋊C₄	—	2	1	no	—
421	C₇×C₄⋊C₄	—	2	2	no	—
422	C₇×C₄⋊C₄	—	2	1	no	—
423	C₇×C₄⋊C₄	—	2	1	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	—	2	2	no	—
432	C₇×C₄⋊C₄	—	2	1	no	—
433	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
434	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
435	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
436	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
437	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
438	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
439	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
440	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
441	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
442	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
443	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	1	no	—
448	C₇×C₂²⋊C₄	—	2	2	no	—
449	C₇×C₂²⋊C₄	—	2	2	no	—
450	C₇×C₂²⋊C₄	—	2	1	no	—
451	C₇×C₂²⋊C₄	—	2	2	no	—
452	C₇×C₂²⋊C₄	—	2	2	no	—
453	C₇×C₂²⋊C₄	—	2	2	no	—
454	C₇×C₂²⋊C₄	—	2	2	no	—
455	C₇×C₂²⋊C₄	—	2	2	no	—
456	C₇×C₂²⋊C₄	—	2	1	no	—
457	C₇×C₂²⋊C₄	—	2	2	no	—
458	C₇×C₂²⋊C₄	—	2	2	no	—
459	C₇×C₂²⋊C₄	—	2	1	no	—
460	C₇×C₂²⋊C₄	—	2	1	no	—
461	C₇×C₂²⋊C₄	—	2	2	no	—
462	C₇×C₂²⋊C₄	—	2	1	no	—
463	C₇×C₂²⋊C₄	—	2	2	no	—
464	C₇×C₂²⋊C₄	—	2	1	no	—
465	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
466	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
467	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
468	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
469	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
470	C₄²×C₇	—	2	1	no	—
471	C₄²×C₇	—	2	1	no	—
472	C₄²×C₇	—	2	1	no	—
473	C₄²×C₇	—	2	2	no	—
474	C₄²×C₇	—	2	1	no	—
475	C₄²×C₇	—	2	2	no	—
476	C₄²×C₇	—	2	2	no	—
477	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
478	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
479	C₄²×C₇	C₂⁴	1	1	yes	characteristic
480	C₄²×C₇	C₂⁴	1	2	yes	—
481	C₄²×C₇	C₂⁴	1	1	yes	characteristic
482	C₂×#137	C₂²×C₇	1	2	yes	—
483	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
484	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
485	#563	—	2	2	no	—
486	#559	C₂²×C₇	1	1	yes	characteristic
487	#557	C₂²×C₇	1	1	yes	characteristic, complemented
488	#556	C₂²×C₇	1	1	yes	characteristic
489	#556	C₂²×C₇	1	1	yes	characteristic, complemented
490	#555	C₂²×C₇	1	2	yes	—
491	#554	—	2	1	no	—
492	#553	—	2	1	no	—
493	#551	—	2	2	no	—
494	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
495	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
496	D₄×Q₈	C₂²×C₇	1	2	yes	complemented
497	#548	—	2	1	no	—
498	#548	C₂²×C₇	1	2	yes	complemented
499	#547	C₂²×C₇	1	1	yes	characteristic
500	#546	—	2	1	no	—
501	#546	C₂²×C₇	1	2	yes	—
502	D₄²	C₂²×C₇	1	1	yes	characteristic
503	#544	—	2	1	no	—
504	#542	—	2	1	no	—
505	#542	C₂²×C₇	1	2	yes	—
506	#541	C₂²×C₇	1	2	yes	complemented
507	#539	—	2	2	no	—
508	#538	—	2	2	no	—
509	#536	C₂²×C₇	1	2	yes	complemented
510	#532	C₂²×C₇	1	1	yes	characteristic
511	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
512	#529	—	2	1	no	—
513	#529	C₂²×C₇	1	1	yes	characteristic
514	#529	C₂²×C₇	1	1	yes	characteristic, complemented
515	C₂×#124	—	2	1	no	—
516	#518	C₂²×C₇	1	2	yes	—
517	C₄×#41	C₂²×C₇	1	1	yes	characteristic
518	#497	C₂²×C₇	1	2	yes	complemented
519	#495	C₂²×C₇	1	2	yes	complemented
520	#492	C₂²×C₇	1	1	yes	characteristic
521	#492	C₂²×C₇	1	1	yes	characteristic
522	#489	C₂²×C₇	1	2	yes	complemented
523	#487	C₂²×C₇	1	1	yes	characteristic, complemented
524	#487	C₂²×C₇	1	2	yes	complemented
525	#487	C₂²×C₇	1	1	yes	characteristic, complemented
526	#485	C₂²×C₇	1	2	yes	complemented
527	#485	C₂²×C₇	1	1	yes	characteristic, complemented
528	#485	C₂²×C₇	1	2	yes	complemented
529	#482	C₂²×C₇	1	1	yes	characteristic, complemented
530	#479	C₂²×C₇	1	1	yes	characteristic, complemented
531	#478	C₂²×C₇	1	1	yes	characteristic
532	#478	C₂²×C₇	1	2	yes	complemented
533	#477	C₂²×C₇	1	2	yes	complemented
534	#475	C₂²×C₇	1	1	yes	characteristic, complemented
535	#475	C₂²×C₇	1	2	yes	complemented
536	#474	C₂²×C₇	1	1	yes	characteristic, complemented
537	#470	C₂²×C₇	1	2	yes	complemented
538	#469	C₂²×C₇	1	2	yes	complemented
539	#468	C₂²×C₇	1	2	yes	—
540	#468	C₂²×C₇	1	2	yes	complemented
541	#467	C₂²×C₇	1	2	yes	complemented
542	#465	C₂²×C₇	1	2	yes	—
543	#464	C₂²×C₇	1	1	yes	characteristic, complemented
544	#464	C₂²×C₇	1	2	yes	complemented
545	#464	C₂²×C₇	1	2	yes	complemented
546	#463	C₂²×C₇	1	1	yes	characteristic
547	#463	C₂²×C₇	1	2	yes	—
548	#463	C₂²×C₇	1	2	yes	complemented
549	#463	C₂²×C₇	1	2	yes	complemented
550	#462	C₂²×C₇	1	1	yes	characteristic, complemented
551	#462	C₂²×C₇	1	1	yes	characteristic, complemented
552	#462	C₂²×C₇	1	2	yes	complemented
553	#461	C₂²×C₇	1	2	yes	—
554	#461	C₂²×C₇	1	1	yes	characteristic
555	#461	C₂²×C₇	1	1	yes	characteristic
556	#461	C₂²×C₇	1	2	yes	—
557	#461	C₂²×C₇	1	2	yes	complemented
558	#461	C₂²×C₇	1	2	yes	complemented
559	#461	C₂²×C₇	1	2	yes	complemented
560	#460	C₂²×C₇	1	1	yes	characteristic
561	#459	C₂²×C₇	1	1	yes	characteristic
562	#452	C₂²×C₇	1	1	yes	characteristic
563	#452	C₂²×C₇	1	2	yes	complemented
564	#451	C₂²×C₇	1	2	yes	complemented
565	#450	C₂²×C₇	1	2	yes	—
566	#450	C₂²×C₇	1	2	yes	—
567	#449	C₂²×C₇	1	1	yes	characteristic
568	#449	C₂²×C₇	1	2	yes	—
569	#448	C₂²×C₇	1	2	yes	—
570	#448	C₂²×C₇	1	2	yes	complemented
571	#448	C₂²×C₇	1	2	yes	complemented
572	#446	C₂²×C₇	1	1	yes	characteristic, complemented
573	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
574	#440	C₂²×C₇	1	2	yes	—
575	#440	C₂²×C₇	1	2	yes	complemented
576	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
577	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
578	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
579	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
580	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
581	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
582	#436	C₂²×C₇	1	1	yes	characteristic
583	#436	C₂²×C₇	1	2	yes	complemented
584	#435	C₂²×C₇	1	2	yes	complemented
585	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
586	#433	C₂²×C₇	1	2	yes	complemented
587	#431	C₂²×C₇	1	1	yes	characteristic, complemented
588	#424	C₂²×C₇	1	2	yes	complemented
589	#423	C₂²×C₇	1	1	yes	characteristic, complemented
590	#419	C₂²×C₇	1	2	yes	complemented
591	#419	C₂²×C₇	1	2	yes	complemented
592	#416	C₂²×C₇	1	2	yes	complemented
593	C₂³×C₇	—	2	1	no	—
594	C₂³×C₇	—	2	1	no	—
595	C₂³×C₇	—	2	2	no	—
596	C₂³×C₇	—	4	4	no	—
597	C₂³×C₇	—	8	2	no	—
598	C₂³×C₇	—	8	2	no	—
599	C₂³×C₇	C₂²×D₄	1	2	yes	—
600	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
601	C₇×Q₈	—	2	2	no	—
602	C₇×Q₈	—	2	1	no	—
603	C₇×Q₈	—	2	2	no	—
604	C₇×Q₈	—	2	2	no	—
605	C₇×Q₈	—	2	1	no	—
606	C₇×Q₈	—	2	1	no	—
607	C₇×Q₈	—	2	2	no	—
608	C₇×Q₈	—	2	2	no	—
609	C₇×Q₈	—	2	1	no	—
610	C₇×Q₈	—	4	2	no	—
611	C₇×Q₈	—	8	2	no	—
612	C₇×Q₈	—	8	2	no	—
613	C₇×Q₈	—	8	2	no	—
614	C₇×D₄	—	2	2	no	—
615	C₇×D₄	—	2	1	no	—
616	C₇×D₄	—	2	2	no	—
617	C₇×D₄	—	2	1	no	—
618	C₇×D₄	—	2	2	no	—
619	C₇×D₄	—	2	1	no	—
620	C₇×D₄	—	4	2	no	—
621	C₇×D₄	—	4	4	no	—
622	C₇×D₄	—	4	2	no	—
623	C₇×D₄	—	4	2	no	—
624	C₇×D₄	—	4	2	no	—
625	C₇×D₄	—	8	1	no	—
626	C₇×D₄	—	8	2	no	—
627	C₇×D₄	—	8	2	no	—
628	C₇×D₄	—	8	2	no	—
629	C₇×D₄	H(5,𝔽₂)	1	2	yes	—
630	C₂×C₄×C₇	—	2	2	no	—
631	C₂×C₄×C₇	—	2	2	no	—
632	C₂×C₄×C₇	—	2	1	no	—
633	C₂×C₄×C₇	—	2	2	no	—
634	C₂×C₄×C₇	—	2	1	no	—
635	C₂×C₄×C₇	—	2	1	no	—
636	C₂×C₄×C₇	—	2	1	no	—
637	C₂×C₄×C₇	—	2	1	no	—
638	C₂×C₄×C₇	—	2	1	no	—
639	C₂×C₄×C₇	—	2	1	no	—
640	C₂×C₄×C₇	—	2	2	no	—
641	C₂×C₄×C₇	—	2	1	no	—
642	C₂×C₄×C₇	—	2	2	no	—
643	C₂×C₄×C₇	—	2	2	no	—
644	C₂×C₄×C₇	—	4	1	no	—
645	C₂×C₄×C₇	—	4	2	no	—
646	C₂×C₄×C₇	—	4	2	no	—
647	C₂×C₄×C₇	—	4	2	no	—
648	C₂×C₄×C₇	—	8	1	no	—
649	C₂×C₄×C₇	—	8	2	no	—
650	C₂×C₄×C₇	—	8	2	no	—
651	C₂×C₄×C₇	—	8	2	no	—
652	C₂×C₄×C₇	—	8	2	no	—
653	C₂×C₄×C₇	—	8	2	no	—
654	C₂×C₄×C₇	—	8	2	no	—
655	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
656	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
657	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
658	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
659	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
660	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
661	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
662	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
663	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
664	C₇×C₈	—	2	1	no	—
665	C₇×C₈	—	2	2	no	—
666	C₇×C₈	—	2	1	no	—
667	C₇×C₈	—	2	2	no	—
668	C₇×C₈	—	2	1	no	—
669	C₇×C₈	—	2	1	no	—
670	C₂×#41	—	2	1	no	—
671	C₂×#41	C₂³×C₇	1	1	yes	characteristic
672	C₂×#41	C₂³×C₇	1	2	yes	—
673	C₂²×Q₈	—	2	1	no	—
674	C₂²×Q₈	C₂³×C₇	1	2	yes	—
675	C₂²×Q₈	C₂³×C₇	1	2	yes	—
676	C₂²×D₄	—	2	1	no	—
677	C₂²×D₄	C₂³×C₇	1	2	yes	—
678	#137	—	4	4	no	—
679	AGL(1,ℤ/8)	—	4	4	no	—
680	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
681	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
682	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
683	C₂×SD₁₆	—	4	4	no	—
684	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
685	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
686	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
689	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
690	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
691	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
692	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
693	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
694	C₂×D₈	C₂³×C₇	1	2	yes	—
695	C₂×M₁₆	C₂³×C₇	1	2	yes	—
696	C₂×M₁₆	C₂³×C₇	1	2	yes	—
697	C₂²×C₈	C₂³×C₇	1	2	yes	—
698	C₄⋊Q₈	—	2	1	no	—
699	C₄⋊Q₈	—	2	2	no	—
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	—	2	1	no	—
702	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
703	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
706	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
708	#127	C₂³×C₇	1	1	yes	characteristic
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	1	no	—
715	#126	C₇×D₄	1	2	yes	—
716	#125	—	2	2	no	—
717	#125	—	2	2	no	—
718	#125	—	2	2	no	—
719	#125	—	2	1	no	—
720	#125	C₇×D₄	1	1	yes	characteristic
721	#125	C₂³×C₇	1	1	yes	characteristic
722	#124	—	2	1	no	—
723	#124	—	2	1	no	—
724	#124	—	2	2	no	—
725	#124	—	2	2	no	—
726	#124	—	2	2	no	—
727	#124	—	2	2	no	—
728	#124	—	2	1	no	—
729	#124	C₇×D₄	1	1	yes	characteristic
730	#124	C₂³×C₇	1	1	yes	characteristic
731	#124	C₂³×C₇	1	2	yes	—
732	#124	C₂³×C₇	1	2	yes	—
733	#123	—	2	1	no	—
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	C₇×D₄	1	2	yes	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
752	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
753	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
754	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
755	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
756	#121	—	2	2	no	—
757	#121	—	2	2	no	—
758	#121	—	2	1	no	—
759	#121	—	2	1	no	—
760	#121	—	2	1	no	—
761	#121	—	2	2	no	—
762	#121	C₇×D₄	1	1	yes	characteristic
763	#121	C₂³×C₇	1	1	yes	characteristic
764	#121	C₂³×C₇	1	2	yes	—
765	#121	C₂³×C₇	1	2	yes	—
766	#120	—	2	2	no	—
767	#120	—	2	2	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	1	no	—
770	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
771	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
772	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₇	1	2	yes	—
774	C₄×Q₈	C₂³×C₇	1	2	yes	—
775	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	1	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	—	2	2	no	—
782	C₄×D₄	—	2	2	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
787	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
788	C₄×D₄	C₂³×C₇	1	2	yes	—
789	C₄×D₄	C₂³×C₇	1	2	yes	—
790	C₄×D₄	C₂³×C₇	1	2	yes	—
791	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
792	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
793	C₄×D₄	C₂³×C₇	1	2	yes	—
794	#117	—	2	2	no	—
795	#117	—	2	1	no	—
796	#117	—	2	1	no	—
797	#117	—	2	1	no	—
798	#117	C₂³×C₇	1	1	yes	characteristic
799	#117	C₂³×C₇	1	2	yes	—
800	#117	C₂³×C₇	1	2	yes	—
801	C₂×C₄⋊C₄	—	2	1	no	—
802	C₂×C₄⋊C₄	—	2	1	no	—
803	C₂×C₄⋊C₄	—	2	1	no	—
804	C₂×C₂²⋊C₄	—	2	2	no	—
805	C₂×C₂²⋊C₄	—	2	2	no	—
806	C₂×C₂²⋊C₄	—	2	2	no	—
807	C₂×C₄²	—	2	1	no	—
808	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
809	#107	C₂³×C₇	1	1	yes	characteristic
810	#107	C₂³×C₇	1	1	yes	characteristic
811	#107	C₂³×C₇	1	2	yes	—
812	#106	C₂³×C₇	1	1	yes	characteristic
813	#106	C₂³×C₇	1	2	yes	—
814	#106	C₂³×C₇	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₇	1	2	yes	—
816	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
817	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₇	1	2	yes	—
820	C₄⋊C₈	C₂³×C₇	1	2	yes	—
821	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
822	#103	C₂³×C₇	1	2	yes	—
823	#103	C₂³×C₇	1	2	yes	—
824	#103	C₂³×C₇	1	2	yes	—
825	#103	C₂³×C₇	1	1	yes	characteristic
826	#103	C₂³×C₇	1	2	yes	—
827	#103	C₂³×C₇	1	2	yes	—
828	#103	C₂³×C₇	1	2	yes	—
829	#103	C₂³×C₇	1	2	yes	—
830	#103	C₂³×C₇	1	1	yes	characteristic
831	#103	C₂³×C₇	1	2	yes	—
832	#103	C₂³×C₇	1	1	yes	characteristic
833	#103	C₂³×C₇	1	1	yes	characteristic
834	#103	C₂³×C₇	1	2	yes	—
835	#102	C₂³×C₇	1	1	yes	characteristic
836	#102	C₂³×C₇	1	2	yes	—
837	#102	C₂³×C₇	1	1	yes	characteristic
838	#102	C₂³×C₇	1	1	yes	characteristic
839	#102	C₂³×C₇	1	1	yes	characteristic
840	#102	C₂³×C₇	1	2	yes	—
841	#102	C₂³×C₇	1	2	yes	—
842	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
843	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
844	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
845	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
846	#97	C₂³×C₇	1	2	yes	—
847	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
848	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
849	C₄×C₈	C₂³×C₇	1	2	yes	—
850	C₂²×C₇	—	2	1	no	—
851	C₂²×C₇	—	2	2	no	—
852	C₂²×C₇	—	2	1	no	—
853	C₂²×C₇	—	2	2	no	—
854	C₂²×C₇	—	2	2	no	—
855	C₂²×C₇	—	2	1	no	—
856	C₂²×C₇	—	2	2	no	—
857	C₂²×C₇	—	4	1	no	—
858	C₂²×C₇	—	4	1	no	—
859	C₂²×C₇	—	4	2	no	—
860	C₂²×C₇	—	4	1	no	—
861	C₂²×C₇	—	4	1	no	—
862	C₂²×C₇	—	4	2	no	—
863	C₂²×C₇	—	4	1	no	—
864	C₂²×C₇	—	4	2	no	—
865	C₂²×C₇	—	16	4	no	—
866	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
867	C₄×C₇	—	2	1	no	—
868	C₄×C₇	—	2	1	no	—
869	C₄×C₇	—	2	2	no	—
870	C₄×C₇	—	2	1	no	—
871	C₄×C₇	—	2	2	no	—
872	C₄×C₇	—	2	1	no	—
873	C₄×C₇	—	2	2	no	—
874	C₄×C₇	—	4	1	no	—
875	C₄×C₇	—	4	1	no	—
876	C₄×C₇	—	4	1	no	—
877	C₄×C₇	—	4	2	no	—
878	C₄×C₇	—	4	1	no	—
879	C₄×C₇	—	4	2	no	—
880	C₄×C₇	—	4	1	no	—
881	C₄×C₇	—	4	1	no	—
882	C₄×C₇	—	4	2	no	—
883	C₄×C₇	#577	1	2	yes	—
884	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
885	C₄×C₇	#585	1	1	yes	characteristic
886	C₂⁴	—	2	2	no	—
887	#41	—	2	2	no	—
888	#41	—	4	1	no	—
889	#41	—	4	2	no	—
890	#41	—	4	2	no	—
891	#41	—	8	2	no	—
892	C₂×Q₈	—	2	1	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	2	no	—
895	C₂×Q₈	—	2	2	no	—
896	C₂×Q₈	—	4	2	no	—
897	C₂×Q₈	—	4	2	no	—
898	C₂×Q₈	—	4	2	no	—
899	C₂×Q₈	—	4	2	no	—
900	C₂×Q₈	—	8	2	no	—
901	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
902	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
903	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
904	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
905	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
906	C₂×D₄	—	2	4	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	1	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	4	2	no	—
916	C₂×D₄	—	8	2	no	—
917	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
918	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
919	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
920	C₂×D₄	C₂⁴×C₇	1	2	yes	—
921	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
933	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
935	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
936	Q₁₆	—	4	1	no	—
937	Q₁₆	—	4	2	no	—
938	Q₁₆	—	4	2	no	—
939	SD₁₆	—	2	2	no	—
940	SD₁₆	—	2	4	no	—
941	SD₁₆	—	2	4	no	—
942	SD₁₆	—	4	2	no	—
943	SD₁₆	—	4	2	no	—
944	SD₁₆	—	4	2	no	—
945	SD₁₆	—	4	1	no	—
946	SD₁₆	—	4	2	no	—
947	SD₁₆	—	4	2	no	—
948	D₈	—	2	2	no	—
949	D₈	—	4	2	no	—
950	M₁₆	—	4	2	no	—
951	M₁₆	—	4	2	no	—
952	C₂×C₈	—	4	2	no	—
953	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
954	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
955	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
956	C₂×C₈	C₂⁴×C₇	1	2	yes	—
957	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
958	C₂×C₈	C₂⁴×C₇	1	2	yes	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
981	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
982	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
983	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
984	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
985	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
986	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
987	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
989	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	2	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	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1013	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1014	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1015	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1016	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1025	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1026	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1027	C₄²	C₂⁴×C₇	1	2	yes	—
1028	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1029	C₂×C₇	—	4	1	no	—
1030	C₂×C₇	—	4	2	no	—
1031	C₂×C₇	—	4	2	no	—
1032	C₂×C₇	—	8	1	no	—
1033	C₂×C₇	—	8	2	no	—
1034	C₂×C₇	#3488	1	1	yes	characteristic
1035	C₂×C₇	C₂×#577	1	1	yes	characteristic
1036	C₂×C₇	#3586	1	1	yes	characteristic
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	4	4	no	—
1041	C₂³	—	8	2	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	C₂²×C₇×D₄	1	2	yes	—
1044	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	4	2	no	—
1055	Q₈	—	8	2	no	—
1056	Q₈	—	8	2	no	—
1057	Q₈	—	8	2	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	4	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	8	1	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	2	no	—
1073	D₄	C₇×H(5,𝔽₂)	1	2	yes	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	4	1	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	8	1	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1100	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1101	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1102	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1103	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1104	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1105	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1106	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1107	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1108	C₈	—	2	1	no	—
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	2	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	2	1	no	—
1114	C₇	#62032	1	1	yes	characteristic, direct product factor, Sylow
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	16	4	no	—
1131	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	2	no	—
1148	C₄	C₇×#577	1	2	yes	—
1149	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1150	C₄	C₇×#585	1	1	yes	characteristic
1151	C₂	—	4	2	no	—
1152	C₂	—	4	1	no	—
1153	C₂	—	4	2	no	—
1154	C₂	—	8	2	no	—
1155	C₂	—	8	1	no	—
1156	C₂	C₇×#3488	1	1	yes	characteristic
1157	C₂	C₂×C₇×#577	1	1	yes	characteristic
1158	C₂	C₇×#3586	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3552	C₂	semidirect
2. C₇×#3514	C₂	semidirect
3. C₇×#3400	C₂	semidirect
4. C₇×#3394	C₂	semidirect
5. C₇×#3367	C₂	semidirect
6. C₇×#3359	C₂	semidirect
7. C₇×#3329	C₂	semidirect
8. C₇×#3328	C₂	semidirect
9. C₇×#3321	C₂	semidirect
10. C₇×#3302	C₂	semidirect
11. C₇×D₄×SD₁₆	C₂	semidirect
12. C₇×#3275	C₂	semidirect
13. C₇×#3272	C₂	semidirect
14. C₇×#3266	C₂	semidirect
15. C₇×#3258	C₂	semidirect
16. C₇×#3251	C₂	semidirect
17. C₇×#3225	C₂	semidirect
18. C₇×#3206	C₂	semidirect
19. C₇×#3123	C₂	semidirect
20. C₇×#3102	C₂	semidirect
21. C₇×#3042	C₂	semidirect
22. C₇×#3039	C₂	semidirect
23. C₇×#2993	C₂	semidirect
29. C₇×#557	C₂²	semidirect
31. C₇×#556	C₂²	semidirect
38. C₇×D₄×Q₈	C₂²	semidirect
40. C₇×#548	C₂²	semidirect
48. C₇×#541	C₂²	semidirect
51. C₇×#536	C₂²	semidirect
53. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
56. C₇×#529	C₂²	semidirect
60. C₇×#497	C₂²	semidirect
61. C₇×#495	C₂²	semidirect
64. C₇×#489	C₂²	semidirect
65. C₇×#487	C₂²	semidirect
66. C₇×#487	C₂²	semidirect
67. C₇×#487	C₂²	semidirect
68. C₇×#485	C₂²	semidirect
69. C₇×#485	C₂²	semidirect
70. C₇×#485	C₂²	semidirect
71. C₇×#482	C₂²	semidirect
72. C₇×#479	C₂²	semidirect
74. C₇×#478	C₂²	semidirect
75. C₇×#477	C₂²	semidirect
76. C₇×#475	C₂²	semidirect
77. C₇×#475	C₂²	semidirect
78. C₇×#474	C₂²	semidirect
79. C₇×#470	C₂²	semidirect
80. C₇×#469	C₂²	semidirect
82. C₇×#468	C₂²	semidirect
83. C₇×#467	C₂²	semidirect
85. C₇×#464	C₂²	semidirect
86. C₇×#464	C₂²	semidirect
87. C₇×#464	C₂²	semidirect
90. C₇×#463	C₂²	semidirect
91. C₇×#463	C₂²	semidirect
92. C₇×#462	C₂²	semidirect
93. C₇×#462	C₂²	semidirect
94. C₇×#462	C₂²	semidirect
99. C₇×#461	C₂²	semidirect
100. C₇×#461	C₂²	semidirect
101. C₇×#461	C₂²	semidirect
105. C₇×#452	C₂²	semidirect
106. C₇×#451	C₂²	semidirect
112. C₇×#448	C₂²	semidirect
113. C₇×#448	C₂²	semidirect
114. C₇×#446	C₂²	semidirect
115. C₇×C₈×Q₈	C₂²	semidirect
117. C₇×#440	C₂²	semidirect
118. C₄×C₇×Q₁₆	C₂²	semidirect
121. C₄×C₇×SD₁₆	C₂²	semidirect
122. C₄×C₇×SD₁₆	C₂²	semidirect
125. C₇×#436	C₂²	semidirect
126. C₇×#435	C₂²	semidirect
128. C₇×#433	C₂²	semidirect
129. C₇×#431	C₂²	semidirect
130. C₇×#424	C₂²	semidirect
131. C₇×#423	C₂²	semidirect
132. C₇×#419	C₂²	semidirect
133. C₇×#419	C₂²	semidirect
134. C₇×#416	C₂²	semidirect
135. #62032	C₇	direct (N × H)
316. #3552	C₂×C₇	semidirect
317. #3514	C₂×C₇	semidirect
318. #3400	C₂×C₇	semidirect
319. #3394	C₂×C₇	semidirect
320. #3367	C₂×C₇	semidirect
321. #3359	C₂×C₇	semidirect
322. #3329	C₂×C₇	semidirect
323. #3328	C₂×C₇	semidirect
324. #3321	C₂×C₇	semidirect
325. #3302	C₂×C₇	semidirect
326. D₄×SD₁₆	C₂×C₇	semidirect
327. #3275	C₂×C₇	semidirect
328. #3272	C₂×C₇	semidirect
329. #3266	C₂×C₇	semidirect
330. #3258	C₂×C₇	semidirect
331. #3251	C₂×C₇	semidirect
332. #3225	C₂×C₇	semidirect
333. #3206	C₂×C₇	semidirect
334. #3123	C₂×C₇	semidirect
335. #3102	C₂×C₇	semidirect
336. #3042	C₂×C₇	semidirect
337. #3039	C₂×C₇	semidirect
338. #2993	C₂×C₇	semidirect
487. #557	C₂²×C₇	semidirect
489. #556	C₂²×C₇	semidirect
496. D₄×Q₈	C₂²×C₇	semidirect
498. #548	C₂²×C₇	semidirect
506. #541	C₂²×C₇	semidirect
509. #536	C₂²×C₇	semidirect
511. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
514. #529	C₂²×C₇	semidirect
518. #497	C₂²×C₇	semidirect
519. #495	C₂²×C₇	semidirect
522. #489	C₂²×C₇	semidirect
523. #487	C₂²×C₇	semidirect
524. #487	C₂²×C₇	semidirect
525. #487	C₂²×C₇	semidirect
526. #485	C₂²×C₇	semidirect
527. #485	C₂²×C₇	semidirect
528. #485	C₂²×C₇	semidirect
529. #482	C₂²×C₇	semidirect
530. #479	C₂²×C₇	semidirect
532. #478	C₂²×C₇	semidirect
533. #477	C₂²×C₇	semidirect
534. #475	C₂²×C₇	semidirect
535. #475	C₂²×C₇	semidirect
536. #474	C₂²×C₇	semidirect
537. #470	C₂²×C₇	semidirect
538. #469	C₂²×C₇	semidirect
540. #468	C₂²×C₇	semidirect
541. #467	C₂²×C₇	semidirect
543. #464	C₂²×C₇	semidirect
544. #464	C₂²×C₇	semidirect
545. #464	C₂²×C₇	semidirect
548. #463	C₂²×C₇	semidirect
549. #463	C₂²×C₇	semidirect
550. #462	C₂²×C₇	semidirect
551. #462	C₂²×C₇	semidirect
552. #462	C₂²×C₇	semidirect
557. #461	C₂²×C₇	semidirect
558. #461	C₂²×C₇	semidirect
559. #461	C₂²×C₇	semidirect
563. #452	C₂²×C₇	semidirect
564. #451	C₂²×C₇	semidirect
570. #448	C₂²×C₇	semidirect
571. #448	C₂²×C₇	semidirect
572. #446	C₂²×C₇	semidirect
573. C₈×Q₈	C₂²×C₇	semidirect
575. #440	C₂²×C₇	semidirect
576. C₄×Q₁₆	C₂²×C₇	semidirect
579. C₄×SD₁₆	C₂²×C₇	semidirect
580. C₄×SD₁₆	C₂²×C₇	semidirect
583. #436	C₂²×C₇	semidirect
584. #435	C₂²×C₇	semidirect
586. #433	C₂²×C₇	semidirect
587. #431	C₂²×C₇	semidirect
588. #424	C₂²×C₇	semidirect
589. #423	C₂²×C₇	semidirect
590. #419	C₂²×C₇	semidirect
591. #419	C₂²×C₇	semidirect
592. #416	C₂²×C₇	semidirect
1114. C₇	#62032	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×#3552	2
C₇×#3514	2
C₇×#3400	2
C₇×#3394	2
C₇×#3367	2
C₇×#3359	2
C₇×#3329	2
C₇×#3328	2
C₇×#3321	2
C₇×#3302	2
C₇×D₄×SD₁₆	2
C₇×#3275	2
C₇×#3272	2
C₇×#3266	2
C₇×#3258	2
C₇×#3251	2
C₇×#3225	2
C₇×#3206	2
C₇×#3123	2
C₇×#3102	2
C₇×#3042	2
C₇×#3039	2
C₇×#2993	2
#62032	7

Subgroups — C7×#62032 #13239248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62032 #13239248