Subgroups — C₇×#62041 #13239257

Order 1792.

1896 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3333	C₂	1	2	yes	maximal, complemented
8	C₇×#3330	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3314	C₂	1	2	yes	maximal, complemented
10	C₇×#3294	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3273	C₂	1	2	yes	maximal, complemented
13	C₇×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3268	C₂	1	2	yes	maximal, complemented
15	C₇×#3262	C₂	1	2	yes	maximal, complemented
16	C₇×#3254	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3224	C₂	1	2	yes	maximal, complemented
18	C₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3124	C₂	1	2	yes	maximal, complemented
20	C₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3045	C₂	1	2	yes	maximal, complemented
22	C₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
26	C₂×C₇×#135	C₂²	1	2	yes	complemented
27	C₇×#560	—	2	2	no	—
28	C₇×#556	C₂²	1	1	yes	characteristic, complemented
29	C₇×#556	C₂²	1	1	yes	characteristic, complemented
30	C₇×#554	C₂²	1	2	yes	complemented
31	C₇×#553	—	2	1	no	—
32	C₇×#552	—	2	1	no	—
33	C₇×#551	—	2	2	no	—
34	C₇×#550	C₂²	1	2	yes	—
35	C₇×#550	C₂²	1	1	yes	characteristic, complemented
36	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₇×#548	—	2	1	no	—
38	C₇×#547	C₂²	1	1	yes	characteristic
39	C₇×#547	C₂²	1	1	yes	characteristic
40	C₇×#547	C₂²	1	1	yes	characteristic, complemented
41	C₇×#546	—	2	1	no	—
42	C₇×#546	C₂²	1	2	yes	—
43	C₇×#546	C₂²	1	2	yes	complemented
44	C₇×D₄²	C₂²	1	1	yes	characteristic, complemented
45	C₇×#542	C₂²	1	2	yes	complemented
46	C₇×#542	C₂²	1	2	yes	complemented
47	C₇×#539	—	2	2	no	—
48	C₇×#538	—	2	2	no	—
49	C₇×#537	—	2	1	no	—
50	C₇×#535	—	2	1	no	—
51	C₇×#535	C₂²	1	2	yes	complemented
52	C₇×#533	C₂²	1	1	yes	characteristic, complemented
53	C₇×#532	C₂²	1	1	yes	characteristic
54	C₇×#532	C₂²	1	1	yes	characteristic
55	C₇×#529	C₂²	1	1	yes	characteristic
56	C₇×#525	—	2	1	no	—
57	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
58	C₇×#520	C₂²	1	2	yes	complemented
59	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
60	C₇×#496	C₂²	1	2	yes	complemented
61	C₇×#495	C₂²	1	2	yes	—
62	C₇×#494	C₂²	1	1	yes	characteristic, complemented
63	C₇×#492	C₂²	1	1	yes	characteristic, complemented
64	C₇×#489	C₂²	1	2	yes	complemented
65	C₇×#487	C₂²	1	1	yes	characteristic, complemented
66	C₇×#486	C₂²	1	1	yes	characteristic, complemented
67	C₇×#486	C₂²	1	2	yes	complemented
68	C₇×#484	C₂²	1	2	yes	complemented
69	C₇×#480	C₂²	1	1	yes	characteristic
70	C₇×#480	C₂²	1	2	yes	complemented
71	C₇×#480	C₂²	1	1	yes	characteristic, complemented
72	C₇×#477	C₂²	1	2	yes	complemented
73	C₇×#477	C₂²	1	2	yes	complemented
74	C₇×#474	C₂²	1	1	yes	characteristic, complemented
75	C₇×#474	C₂²	1	1	yes	characteristic, complemented
76	C₇×#474	C₂²	1	1	yes	characteristic, complemented
77	C₇×#474	C₂²	1	2	yes	complemented
78	C₇×#474	C₂²	1	1	yes	characteristic, complemented
79	C₇×#468	C₂²	1	2	yes	—
80	C₇×#468	C₂²	1	2	yes	complemented
81	C₇×#468	C₂²	1	2	yes	complemented
82	C₇×#468	C₂²	1	2	yes	complemented
83	C₇×#467	C₂²	1	2	yes	complemented
84	C₇×#466	C₂²	1	2	yes	—
85	C₇×#464	C₂²	1	2	yes	complemented
86	C₇×#464	C₂²	1	2	yes	complemented
87	C₇×#464	C₂²	1	2	yes	complemented
88	C₇×#464	C₂²	1	2	yes	complemented
89	C₇×#463	C₂²	1	2	yes	—
90	C₇×#463	C₂²	1	2	yes	complemented
91	C₇×#463	C₂²	1	2	yes	complemented
92	C₇×#463	C₂²	1	2	yes	complemented
93	C₇×#461	C₂²	1	1	yes	characteristic, complemented
94	C₇×#461	C₂²	1	1	yes	characteristic, complemented
95	C₇×#461	C₂²	1	1	yes	characteristic, complemented
96	C₇×#461	C₂²	1	1	yes	characteristic, complemented
97	C₇×#460	C₂²	1	2	yes	complemented
98	C₇×#460	C₂²	1	2	yes	complemented
99	C₇×#459	C₂²	1	1	yes	characteristic
100	C₇×#459	C₂²	1	1	yes	characteristic
101	C₇×#459	C₂²	1	1	yes	characteristic
102	C₇×#459	C₂²	1	1	yes	characteristic
103	C₇×#459	C₂²	1	2	yes	complemented
104	C₇×#452	C₂²	1	2	yes	complemented
105	C₇×#452	C₂²	1	2	yes	complemented
106	C₇×#452	C₂²	1	2	yes	complemented
107	C₇×#452	C₂²	1	2	yes	complemented
108	C₇×#450	C₂²	1	2	yes	complemented
109	C₇×#449	C₂²	1	2	yes	—
110	C₇×#449	C₂²	1	2	yes	complemented
111	C₇×#447	C₂²	1	2	yes	—
112	C₇×#447	C₂²	1	1	yes	characteristic
113	C₇×#447	C₂²	1	1	yes	characteristic, 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	complemented
117	C₇×#440	C₂²	1	2	yes	complemented
118	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
119	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
120	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
121	C₄×C₇×D₈	C₂²	1	2	yes	complemented
122	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
124	C₇×#436	C₂²	1	1	yes	characteristic, complemented
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, complemented
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×#417	C₂²	1	2	yes	complemented
133	C₇×#417	C₂²	1	2	yes	complemented
134	C₂×C₇×#102	C₂²	1	2	yes	complemented
135	#62041	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	1	no	—
137	C₂×C₇×#41	—	2	1	no	—
138	C₂×C₇×#41	—	2	1	no	—
139	C₂×C₇×#41	C₂³	1	2	yes	—
140	C₂×C₇×#41	C₂³	1	2	yes	—
141	C₂×C₇×#41	C₂³	1	2	yes	—
142	C₂²×C₇×Q₈	—	2	1	no	—
143	C₂²×C₇×D₄	—	2	1	no	—
144	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
145	C₂²×C₇×D₄	C₂³	1	2	yes	—
146	C₂³×C₄×C₇	—	2	1	no	—
147	C₇×AGL(1,ℤ/8)	—	4	4	no	—
148	C₇×AGL(1,ℤ/8)	—	4	4	no	—
149	C₇×#135	—	4	4	no	—
150	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
151	C₂×C₇×Q₁₆	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×D₈	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×D₈	C₂³	1	2	yes	—
162	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
163	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
164	C₂×C₇×M₁₆	C₂³	1	2	yes	—
165	C₂×C₇×M₁₆	C₂³	1	2	yes	—
166	C₂²×C₇×C₈	C₂³	1	2	yes	—
167	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
172	C₇×#127	—	2	2	no	—
173	C₇×#127	C₂³	1	1	yes	characteristic
174	C₇×#127	C₂³	1	2	yes	—
175	C₇×#127	C₂³	1	1	yes	characteristic
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	D₄	1	2	yes	—
181	C₇×#125	—	2	2	no	—
182	C₇×#125	—	2	1	no	—
183	C₇×#125	D₄	1	1	yes	characteristic
184	C₇×#124	—	2	2	no	—
185	C₇×#124	—	2	2	no	—
186	C₇×#124	—	2	1	no	—
187	C₇×#124	D₄	1	1	yes	characteristic
188	C₇×#124	C₂³	1	2	yes	—
189	C₇×#124	C₂³	1	2	yes	—
190	C₇×#124	C₂³	1	2	yes	—
191	C₇×#123	—	2	2	no	—
192	C₇×#123	—	2	2	no	—
193	C₇×#123	—	2	2	no	—
194	C₇×#123	—	2	2	no	—
195	C₇×#123	—	2	2	no	—
196	C₇×#123	—	2	2	no	—
197	C₇×#123	—	2	2	no	—
198	C₇×#123	D₄	1	2	yes	—
199	C₇×C₂²⋊Q₈	—	2	1	no	—
200	C₇×C₂²⋊Q₈	—	2	1	no	—
201	C₇×C₂²⋊Q₈	—	2	1	no	—
202	C₇×C₂²⋊Q₈	—	2	2	no	—
203	C₇×C₂²⋊Q₈	—	2	1	no	—
204	C₇×C₂²⋊Q₈	—	2	1	no	—
205	C₇×C₂²⋊Q₈	—	2	2	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	C₂³	1	2	yes	—
211	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₇×#121	—	2	1	no	—
214	C₇×#121	—	2	1	no	—
215	C₇×#121	—	2	1	no	—
216	C₇×#121	—	2	1	no	—
217	C₇×#121	—	2	1	no	—
218	C₇×#121	—	2	1	no	—
219	C₇×#121	—	2	2	no	—
220	C₇×#121	—	2	2	no	—
221	C₇×#121	—	2	1	no	—
222	C₇×#121	—	2	2	no	—
223	C₇×#121	—	2	2	no	—
224	C₇×#121	—	2	2	no	—
225	C₇×#121	—	2	2	no	—
226	C₇×#121	—	2	2	no	—
227	C₇×#121	D₄	1	1	yes	characteristic
228	C₇×#121	C₂³	1	2	yes	—
229	C₇×#121	C₂³	1	2	yes	—
230	C₇×#121	C₂³	1	1	yes	characteristic
231	C₇×#121	C₂³	1	1	yes	characteristic
232	C₇×#120	—	2	2	no	—
233	C₇×#120	—	2	2	no	—
234	C₇×#120	—	2	2	no	—
235	C₇×#120	—	2	2	no	—
236	C₇×#120	—	2	2	no	—
237	C₄×C₇×Q₈	—	2	1	no	—
238	C₄×C₇×Q₈	C₂³	1	2	yes	—
239	C₄×C₇×Q₈	C₂³	1	2	yes	—
240	C₄×C₇×Q₈	C₂³	1	2	yes	—
241	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
242	C₄×C₇×D₄	—	2	2	no	—
243	C₄×C₇×D₄	—	2	2	no	—
244	C₄×C₇×D₄	—	2	2	no	—
245	C₄×C₇×D₄	—	2	2	no	—
246	C₄×C₇×D₄	—	2	1	no	—
247	C₄×C₇×D₄	—	2	1	no	—
248	C₄×C₇×D₄	—	2	1	no	—
249	C₄×C₇×D₄	—	2	1	no	—
250	C₄×C₇×D₄	—	2	1	no	—
251	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
252	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
253	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
254	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
255	C₄×C₇×D₄	C₂³	1	2	yes	—
256	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
257	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
258	C₄×C₇×D₄	C₂³	1	2	yes	—
259	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
260	C₄×C₇×D₄	C₂³	1	2	yes	—
261	C₇×#117	—	2	1	no	—
262	C₇×#117	—	2	2	no	—
263	C₇×#117	—	2	1	no	—
264	C₇×#117	—	2	1	no	—
265	C₇×#117	C₂³	1	2	yes	—
266	C₂×C₇×C₄⋊C₄	—	2	2	no	—
267	C₂×C₇×C₄⋊C₄	—	2	1	no	—
268	C₂×C₇×C₄⋊C₄	—	2	1	no	—
269	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
271	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₇×C₂²⋊C₄	—	2	2	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	2	yes	—
278	C₇×#107	C₂³	1	1	yes	characteristic
279	C₇×#107	C₂³	1	1	yes	characteristic
280	C₇×#107	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	1	yes	characteristic
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	2	yes	—
288	C₇×#103	C₂³	1	2	yes	—
289	C₇×#103	C₂³	1	2	yes	—
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#103	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	2	yes	—
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#102	C₂³	1	1	yes	characteristic
295	C₇×#102	C₂³	1	2	yes	—
296	C₇×#102	C₂³	1	2	yes	—
297	C₇×#102	C₂³	1	1	yes	characteristic
298	C₇×#102	C₂³	1	2	yes	—
299	C₇×#102	C₂³	1	2	yes	—
300	C₇×#102	C₂³	1	1	yes	characteristic
301	C₇×#102	C₂³	1	1	yes	characteristic
302	C₇×#102	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	2	yes	—
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	2	yes	—
315	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
316	#3546	C₂×C₇	1	1	yes	characteristic, complemented
317	#3520	C₂×C₇	1	1	yes	characteristic, complemented
318	#3397	C₂×C₇	1	1	yes	characteristic, complemented
319	#3393	C₂×C₇	1	1	yes	characteristic, complemented
320	#3367	C₂×C₇	1	1	yes	characteristic, complemented
321	#3358	C₂×C₇	1	1	yes	characteristic, complemented
322	#3333	C₂×C₇	1	2	yes	complemented
323	#3330	C₂×C₇	1	1	yes	characteristic, complemented
324	#3314	C₂×C₇	1	2	yes	complemented
325	#3294	C₂×C₇	1	1	yes	characteristic, complemented
326	#3283	C₂×C₇	1	1	yes	characteristic, complemented
327	#3273	C₂×C₇	1	2	yes	complemented
328	#3272	C₂×C₇	1	1	yes	characteristic, complemented
329	#3268	C₂×C₇	1	2	yes	complemented
330	#3262	C₂×C₇	1	2	yes	complemented
331	#3254	C₂×C₇	1	1	yes	characteristic, complemented
332	#3224	C₂×C₇	1	2	yes	complemented
333	#3210	C₂×C₇	1	1	yes	characteristic, complemented
334	#3124	C₂×C₇	1	2	yes	complemented
335	#3100	C₂×C₇	1	1	yes	characteristic, complemented
336	#3045	C₂×C₇	1	2	yes	complemented
337	#3036	C₂×C₇	1	1	yes	characteristic, complemented
338	#2993	C₂×C₇	1	1	yes	characteristic, complemented
339	C₂⁴×C₇	—	2	1	no	—
340	C₂⁴×C₇	—	2	2	no	—
341	C₇×#41	—	2	4	no	—
342	C₇×#41	—	4	2	no	—
343	C₇×#41	—	4	2	no	—
344	C₇×#41	—	4	2	no	—
345	C₇×#41	—	4	2	no	—
346	C₇×#41	—	4	2	no	—
347	C₇×#41	—	8	2	no	—
348	C₇×#41	—	8	2	no	—
349	C₇×#41	—	8	2	no	—
350	C₂×C₇×Q₈	—	2	1	no	—
351	C₂×C₇×Q₈	—	2	2	no	—
352	C₂×C₇×Q₈	—	2	1	no	—
353	C₂×C₇×Q₈	—	8	2	no	—
354	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
355	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
356	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
357	C₂×C₇×D₄	—	2	2	no	—
358	C₂×C₇×D₄	—	2	2	no	—
359	C₂×C₇×D₄	—	2	1	no	—
360	C₂×C₇×D₄	—	2	2	no	—
361	C₂×C₇×D₄	—	2	2	no	—
362	C₂×C₇×D₄	—	2	2	no	—
363	C₂×C₇×D₄	—	2	2	no	—
364	C₂×C₇×D₄	—	2	1	no	—
365	C₂×C₇×D₄	—	2	1	no	—
366	C₂×C₇×D₄	—	2	1	no	—
367	C₂×C₇×D₄	—	2	1	no	—
368	C₂×C₇×D₄	—	2	1	no	—
369	C₂×C₇×D₄	—	2	2	no	—
370	C₂×C₇×D₄	—	2	1	no	—
371	C₂×C₇×D₄	—	2	2	no	—
372	C₂×C₇×D₄	—	2	2	no	—
373	C₂×C₇×D₄	—	4	1	no	—
374	C₂×C₇×D₄	—	4	2	no	—
375	C₂×C₇×D₄	—	4	2	no	—
376	C₂×C₇×D₄	—	8	2	no	—
377	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
378	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
379	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
380	C₂×C₇×D₄	C₂⁴	1	2	yes	—
381	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
382	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
383	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₇	—	2	1	no	—
385	C₂²×C₄×C₇	—	2	2	no	—
386	C₂²×C₄×C₇	—	2	2	no	—
387	C₂²×C₄×C₇	—	2	1	no	—
388	C₂²×C₄×C₇	—	2	1	no	—
389	C₂²×C₄×C₇	—	2	1	no	—
390	C₂²×C₄×C₇	—	2	1	no	—
391	C₂²×C₄×C₇	—	2	2	no	—
392	C₂²×C₄×C₇	—	2	2	no	—
393	C₂²×C₄×C₇	—	2	2	no	—
394	C₂²×C₄×C₇	—	2	1	no	—
395	C₂²×C₄×C₇	—	2	2	no	—
396	C₂²×C₄×C₇	—	2	1	no	—
397	C₂²×C₄×C₇	—	8	2	no	—
398	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
402	C₇×Q₁₆	—	4	2	no	—
403	C₇×Q₁₆	—	4	2	no	—
404	C₇×SD₁₆	—	2	4	no	—
405	C₇×SD₁₆	—	4	2	no	—
406	C₇×SD₁₆	—	4	2	no	—
407	C₇×SD₁₆	—	4	2	no	—
408	C₇×SD₁₆	—	4	2	no	—
409	C₇×SD₁₆	—	4	2	no	—
410	C₇×D₈	—	2	2	no	—
411	C₇×D₈	—	2	4	no	—
412	C₇×D₈	—	2	2	no	—
413	C₇×D₈	—	4	1	no	—
414	C₇×D₈	—	4	1	no	—
415	C₇×D₈	—	4	2	no	—
416	C₇×M₁₆	—	4	2	no	—
417	C₇×M₁₆	—	4	2	no	—
418	C₂×C₇×C₈	—	4	2	no	—
419	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
420	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
421	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
422	C₂×C₇×C₈	C₂⁴	1	2	yes	—
423	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
424	C₂×C₇×C₈	C₂⁴	1	2	yes	—
425	C₇×C₄⋊C₄	—	2	2	no	—
426	C₇×C₄⋊C₄	—	2	1	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	—	2	1	no	—
434	C₇×C₄⋊C₄	—	2	1	no	—
435	C₇×C₄⋊C₄	—	2	1	no	—
436	C₇×C₄⋊C₄	—	2	1	no	—
437	C₇×C₄⋊C₄	—	2	2	no	—
438	C₇×C₄⋊C₄	—	2	2	no	—
439	C₇×C₄⋊C₄	—	2	2	no	—
440	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
441	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
442	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
443	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
444	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
445	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
446	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
447	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
448	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
449	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
450	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	1	no	—
455	C₇×C₂²⋊C₄	—	2	1	no	—
456	C₇×C₂²⋊C₄	—	2	1	no	—
457	C₇×C₂²⋊C₄	—	2	1	no	—
458	C₇×C₂²⋊C₄	—	2	1	no	—
459	C₇×C₂²⋊C₄	—	2	2	no	—
460	C₇×C₂²⋊C₄	—	2	2	no	—
461	C₇×C₂²⋊C₄	—	2	2	no	—
462	C₇×C₂²⋊C₄	—	2	2	no	—
463	C₇×C₂²⋊C₄	—	2	2	no	—
464	C₇×C₂²⋊C₄	—	2	2	no	—
465	C₇×C₂²⋊C₄	—	2	1	no	—
466	C₇×C₂²⋊C₄	—	2	2	no	—
467	C₇×C₂²⋊C₄	—	2	2	no	—
468	C₇×C₂²⋊C₄	—	2	2	no	—
469	C₇×C₂²⋊C₄	—	2	1	no	—
470	C₇×C₂²⋊C₄	—	2	2	no	—
471	C₇×C₂²⋊C₄	—	2	1	no	—
472	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
473	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
474	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
475	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
476	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
477	C₄²×C₇	—	2	2	no	—
478	C₄²×C₇	—	2	2	no	—
479	C₄²×C₇	—	2	2	no	—
480	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
481	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
482	C₄²×C₇	C₂⁴	1	1	yes	characteristic
483	C₄²×C₇	C₂⁴	1	2	yes	—
484	C₄²×C₇	C₂⁴	1	1	yes	characteristic
485	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
486	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	complemented
487	C₂×#135	C₂²×C₇	1	2	yes	complemented
488	#560	—	2	2	no	—
489	#556	C₂²×C₇	1	1	yes	characteristic, complemented
490	#556	C₂²×C₇	1	1	yes	characteristic, complemented
491	#554	C₂²×C₇	1	2	yes	complemented
492	#553	—	2	1	no	—
493	#552	—	2	1	no	—
494	#551	—	2	2	no	—
495	#550	C₂²×C₇	1	2	yes	—
496	#550	C₂²×C₇	1	1	yes	characteristic, complemented
497	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
498	#548	—	2	1	no	—
499	#547	C₂²×C₇	1	1	yes	characteristic
500	#547	C₂²×C₇	1	1	yes	characteristic
501	#547	C₂²×C₇	1	1	yes	characteristic, complemented
502	#546	—	2	1	no	—
503	#546	C₂²×C₇	1	2	yes	—
504	#546	C₂²×C₇	1	2	yes	complemented
505	D₄²	C₂²×C₇	1	1	yes	characteristic, complemented
506	#542	C₂²×C₇	1	2	yes	complemented
507	#542	C₂²×C₇	1	2	yes	complemented
508	#539	—	2	2	no	—
509	#538	—	2	2	no	—
510	#537	—	2	1	no	—
511	#535	—	2	1	no	—
512	#535	C₂²×C₇	1	2	yes	complemented
513	#533	C₂²×C₇	1	1	yes	characteristic, complemented
514	#532	C₂²×C₇	1	1	yes	characteristic
515	#532	C₂²×C₇	1	1	yes	characteristic
516	#529	C₂²×C₇	1	1	yes	characteristic
517	#525	—	2	1	no	—
518	C₂×C₂²⋊Q₈	—	2	1	no	—
519	#520	C₂²×C₇	1	2	yes	complemented
520	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
521	#496	C₂²×C₇	1	2	yes	complemented
522	#495	C₂²×C₇	1	2	yes	—
523	#494	C₂²×C₇	1	1	yes	characteristic, complemented
524	#492	C₂²×C₇	1	1	yes	characteristic, complemented
525	#489	C₂²×C₇	1	2	yes	complemented
526	#487	C₂²×C₇	1	1	yes	characteristic, complemented
527	#486	C₂²×C₇	1	2	yes	complemented
528	#486	C₂²×C₇	1	1	yes	characteristic, complemented
529	#484	C₂²×C₇	1	2	yes	complemented
530	#480	C₂²×C₇	1	1	yes	characteristic
531	#480	C₂²×C₇	1	1	yes	characteristic, complemented
532	#480	C₂²×C₇	1	2	yes	complemented
533	#477	C₂²×C₇	1	2	yes	complemented
534	#477	C₂²×C₇	1	2	yes	complemented
535	#474	C₂²×C₇	1	1	yes	characteristic, complemented
536	#474	C₂²×C₇	1	1	yes	characteristic, complemented
537	#474	C₂²×C₇	1	1	yes	characteristic, complemented
538	#474	C₂²×C₇	1	2	yes	complemented
539	#474	C₂²×C₇	1	1	yes	characteristic, complemented
540	#468	C₂²×C₇	1	2	yes	—
541	#468	C₂²×C₇	1	2	yes	complemented
542	#468	C₂²×C₇	1	2	yes	complemented
543	#468	C₂²×C₇	1	2	yes	complemented
544	#467	C₂²×C₇	1	2	yes	complemented
545	#466	C₂²×C₇	1	2	yes	—
546	#464	C₂²×C₇	1	2	yes	complemented
547	#464	C₂²×C₇	1	2	yes	complemented
548	#464	C₂²×C₇	1	2	yes	complemented
549	#464	C₂²×C₇	1	2	yes	complemented
550	#463	C₂²×C₇	1	2	yes	—
551	#463	C₂²×C₇	1	2	yes	complemented
552	#463	C₂²×C₇	1	2	yes	complemented
553	#463	C₂²×C₇	1	2	yes	complemented
554	#461	C₂²×C₇	1	1	yes	characteristic, complemented
555	#461	C₂²×C₇	1	1	yes	characteristic, complemented
556	#461	C₂²×C₇	1	1	yes	characteristic, complemented
557	#461	C₂²×C₇	1	1	yes	characteristic, complemented
558	#460	C₂²×C₇	1	2	yes	complemented
559	#460	C₂²×C₇	1	2	yes	complemented
560	#459	C₂²×C₇	1	1	yes	characteristic
561	#459	C₂²×C₇	1	1	yes	characteristic
562	#459	C₂²×C₇	1	1	yes	characteristic
563	#459	C₂²×C₇	1	1	yes	characteristic
564	#459	C₂²×C₇	1	2	yes	complemented
565	#452	C₂²×C₇	1	2	yes	complemented
566	#452	C₂²×C₇	1	2	yes	complemented
567	#452	C₂²×C₇	1	2	yes	complemented
568	#452	C₂²×C₇	1	2	yes	complemented
569	#450	C₂²×C₇	1	2	yes	complemented
570	#449	C₂²×C₇	1	2	yes	—
571	#449	C₂²×C₇	1	2	yes	complemented
572	#447	C₂²×C₇	1	1	yes	characteristic
573	#447	C₂²×C₇	1	2	yes	—
574	#447	C₂²×C₇	1	1	yes	characteristic, complemented
575	#446	C₂²×C₇	1	1	yes	characteristic, complemented
576	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
577	#440	C₂²×C₇	1	2	yes	complemented
578	#440	C₂²×C₇	1	2	yes	complemented
579	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
580	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
581	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
582	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
583	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
584	C₄×D₈	C₂²×C₇	1	2	yes	complemented
585	#436	C₂²×C₇	1	1	yes	characteristic, complemented
586	#436	C₂²×C₇	1	2	yes	complemented
587	#435	C₂²×C₇	1	2	yes	complemented
588	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
589	#433	C₂²×C₇	1	2	yes	complemented
590	#431	C₂²×C₇	1	1	yes	characteristic, complemented
591	#424	C₂²×C₇	1	2	yes	complemented
592	#423	C₂²×C₇	1	1	yes	characteristic, complemented
593	#417	C₂²×C₇	1	2	yes	complemented
594	#417	C₂²×C₇	1	2	yes	complemented
595	C₂×#102	C₂²×C₇	1	2	yes	complemented
596	C₂³×C₇	—	2	1	no	—
597	C₂³×C₇	—	2	1	no	—
598	C₂³×C₇	—	2	1	no	—
599	C₂³×C₇	—	2	2	no	—
600	C₂³×C₇	—	2	1	no	—
601	C₂³×C₇	—	4	2	no	—
602	C₂³×C₇	—	4	2	no	—
603	C₂³×C₇	—	8	1	no	—
604	C₂³×C₇	—	8	2	no	—
605	C₂³×C₇	—	8	2	no	—
606	C₂³×C₇	—	8	2	no	—
607	C₂³×C₇	C₂²×D₄	1	2	yes	—
608	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
609	C₇×Q₈	—	2	2	no	—
610	C₇×Q₈	—	2	2	no	—
611	C₇×Q₈	—	2	2	no	—
612	C₇×Q₈	—	2	2	no	—
613	C₇×Q₈	—	2	2	no	—
614	C₇×Q₈	—	4	2	no	—
615	C₇×Q₈	—	8	2	no	—
616	C₇×Q₈	—	8	1	no	—
617	C₇×D₄	—	2	2	no	—
618	C₇×D₄	—	2	2	no	—
619	C₇×D₄	—	2	1	no	—
620	C₇×D₄	—	2	1	no	—
621	C₇×D₄	—	2	1	no	—
622	C₇×D₄	—	2	1	no	—
623	C₇×D₄	—	2	1	no	—
624	C₇×D₄	—	2	1	no	—
625	C₇×D₄	—	2	1	no	—
626	C₇×D₄	—	2	2	no	—
627	C₇×D₄	—	4	2	no	—
628	C₇×D₄	—	4	2	no	—
629	C₇×D₄	—	4	4	no	—
630	C₇×D₄	—	4	2	no	—
631	C₇×D₄	—	8	1	no	—
632	C₇×D₄	—	8	1	no	—
633	C₇×D₄	—	8	2	no	—
634	C₇×D₄	—	8	2	no	—
635	C₇×D₄	—	8	1	no	—
636	C₇×D₄	—	8	2	no	—
637	C₇×D₄	—	8	2	no	—
638	C₇×D₄	—	8	2	no	—
639	C₇×D₄	—	8	2	no	—
640	C₇×D₄	—	8	1	no	—
641	C₇×D₄	—	8	1	no	—
642	C₇×D₄	—	8	2	no	—
643	C₇×D₄	H(5,𝔽₂)	1	2	yes	—
644	C₂×C₄×C₇	—	2	2	no	—
645	C₂×C₄×C₇	—	2	2	no	—
646	C₂×C₄×C₇	—	2	1	no	—
647	C₂×C₄×C₇	—	2	2	no	—
648	C₂×C₄×C₇	—	2	1	no	—
649	C₂×C₄×C₇	—	2	2	no	—
650	C₂×C₄×C₇	—	2	1	no	—
651	C₂×C₄×C₇	—	2	1	no	—
652	C₂×C₄×C₇	—	2	2	no	—
653	C₂×C₄×C₇	—	2	2	no	—
654	C₂×C₄×C₇	—	2	1	no	—
655	C₂×C₄×C₇	—	2	1	no	—
656	C₂×C₄×C₇	—	4	1	no	—
657	C₂×C₄×C₇	—	4	4	no	—
658	C₂×C₄×C₇	—	4	2	no	—
659	C₂×C₄×C₇	—	4	2	no	—
660	C₂×C₄×C₇	—	4	2	no	—
661	C₂×C₄×C₇	—	4	2	no	—
662	C₂×C₄×C₇	—	8	1	no	—
663	C₂×C₄×C₇	—	8	1	no	—
664	C₂×C₄×C₇	—	8	2	no	—
665	C₂×C₄×C₇	—	8	2	no	—
666	C₂×C₄×C₇	—	8	2	no	—
667	C₂×C₄×C₇	—	8	2	no	—
668	C₂×C₄×C₇	—	8	1	no	—
669	C₂×C₄×C₇	—	8	2	no	—
670	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
671	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
672	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
673	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
674	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
675	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
676	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
677	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
678	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
679	C₇×C₈	—	2	1	no	—
680	C₇×C₈	—	2	2	no	—
681	C₇×C₈	—	2	2	no	—
682	C₇×C₈	—	2	1	no	—
683	C₇×C₈	—	2	1	no	—
684	C₇×C₈	—	2	1	no	—
685	C₂×#41	—	2	1	no	—
686	C₂×#41	—	2	1	no	—
687	C₂×#41	—	2	1	no	—
688	C₂×#41	C₂³×C₇	1	2	yes	—
689	C₂×#41	C₂³×C₇	1	2	yes	—
690	C₂×#41	C₂³×C₇	1	2	yes	—
691	C₂²×Q₈	—	2	1	no	—
692	C₂²×D₄	—	2	1	no	—
693	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
694	C₂²×D₄	C₂³×C₇	1	2	yes	—
695	C₂³×C₄	—	2	1	no	—
696	AGL(1,ℤ/8)	—	4	4	no	—
697	AGL(1,ℤ/8)	—	4	4	no	—
698	#135	—	4	4	no	—
699	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
700	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
701	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
702	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
703	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
704	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
705	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
706	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
707	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
708	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
709	C₂×D₈	C₂³×C₇	1	2	yes	—
710	C₂×D₈	C₂³×C₇	1	2	yes	—
711	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
712	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
713	C₂×M₁₆	C₂³×C₇	1	2	yes	—
714	C₂×M₁₆	C₂³×C₇	1	2	yes	—
715	C₂²×C₈	C₂³×C₇	1	2	yes	—
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	1	yes	characteristic
720	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
721	#127	—	2	2	no	—
722	#127	C₂³×C₇	1	1	yes	characteristic
723	#127	C₂³×C₇	1	1	yes	characteristic
724	#127	C₂³×C₇	1	2	yes	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#126	C₇×D₄	1	2	yes	—
730	#125	—	2	2	no	—
731	#125	—	2	1	no	—
732	#125	C₇×D₄	1	1	yes	characteristic
733	#124	—	2	2	no	—
734	#124	—	2	2	no	—
735	#124	—	2	1	no	—
736	#124	C₇×D₄	1	1	yes	characteristic
737	#124	C₂³×C₇	1	2	yes	—
738	#124	C₂³×C₇	1	2	yes	—
739	#124	C₂³×C₇	1	2	yes	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	C₇×D₄	1	2	yes	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
762	#121	—	2	1	no	—
763	#121	—	2	1	no	—
764	#121	—	2	1	no	—
765	#121	—	2	1	no	—
766	#121	—	2	1	no	—
767	#121	—	2	1	no	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	—	2	1	no	—
771	#121	—	2	2	no	—
772	#121	—	2	2	no	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	—	2	2	no	—
776	#121	C₇×D₄	1	1	yes	characteristic
777	#121	C₂³×C₇	1	1	yes	characteristic
778	#121	C₂³×C₇	1	1	yes	characteristic
779	#121	C₂³×C₇	1	2	yes	—
780	#121	C₂³×C₇	1	2	yes	—
781	#120	—	2	2	no	—
782	#120	—	2	2	no	—
783	#120	—	2	2	no	—
784	#120	—	2	2	no	—
785	#120	—	2	2	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	C₂³×C₇	1	2	yes	—
788	C₄×Q₈	C₂³×C₇	1	2	yes	—
789	C₄×Q₈	C₂³×C₇	1	2	yes	—
790	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₇	1	2	yes	—
805	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
806	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₇	1	2	yes	—
808	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₇	1	2	yes	—
810	#117	—	2	1	no	—
811	#117	—	2	2	no	—
812	#117	—	2	1	no	—
813	#117	—	2	1	no	—
814	#117	C₂³×C₇	1	2	yes	—
815	C₂×C₄⋊C₄	—	2	2	no	—
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	—	2	1	no	—
818	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
819	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
820	C₂×C₂²⋊C₄	—	2	1	no	—
821	C₂×C₂²⋊C₄	—	2	2	no	—
822	C₂×C₂²⋊C₄	—	2	2	no	—
823	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
824	#107	C₂³×C₇	1	1	yes	characteristic
825	#107	C₂³×C₇	1	1	yes	characteristic
826	#107	C₂³×C₇	1	1	yes	characteristic
827	#107	C₂³×C₇	1	1	yes	characteristic
828	#107	C₂³×C₇	1	2	yes	—
829	#107	C₂³×C₇	1	2	yes	—
830	C₄⋊C₈	C₂³×C₇	1	2	yes	—
831	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
833	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
834	C₄⋊C₈	C₂³×C₇	1	2	yes	—
835	C₄⋊C₈	C₂³×C₇	1	2	yes	—
836	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
837	#103	C₂³×C₇	1	2	yes	—
838	#103	C₂³×C₇	1	2	yes	—
839	#103	C₂³×C₇	1	2	yes	—
840	#103	C₂³×C₇	1	2	yes	—
841	#103	C₂³×C₇	1	2	yes	—
842	#103	C₂³×C₇	1	2	yes	—
843	#102	C₂³×C₇	1	1	yes	characteristic
844	#102	C₂³×C₇	1	2	yes	—
845	#102	C₂³×C₇	1	2	yes	—
846	#102	C₂³×C₇	1	2	yes	—
847	#102	C₂³×C₇	1	1	yes	characteristic
848	#102	C₂³×C₇	1	2	yes	—
849	#102	C₂³×C₇	1	2	yes	—
850	#102	C₂³×C₇	1	1	yes	characteristic
851	#102	C₂³×C₇	1	1	yes	characteristic
852	#102	C₂³×C₇	1	1	yes	characteristic
853	#102	C₂³×C₇	1	1	yes	characteristic
854	#102	C₂³×C₇	1	2	yes	—
855	#102	C₂³×C₇	1	1	yes	characteristic
856	#102	C₂³×C₇	1	1	yes	characteristic
857	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
858	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
859	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
860	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
861	#97	C₂³×C₇	1	2	yes	—
862	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
863	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
864	C₄×C₈	C₂³×C₇	1	2	yes	—
865	C₂²×C₇	—	2	1	no	—
866	C₂²×C₇	—	2	2	no	—
867	C₂²×C₇	—	2	2	no	—
868	C₂²×C₇	—	2	1	no	—
869	C₂²×C₇	—	2	2	no	—
870	C₂²×C₇	—	2	1	no	—
871	C₂²×C₇	—	2	2	no	—
872	C₂²×C₇	—	4	1	no	—
873	C₂²×C₇	—	4	1	no	—
874	C₂²×C₇	—	4	1	no	—
875	C₂²×C₇	—	4	2	no	—
876	C₂²×C₇	—	4	1	no	—
877	C₂²×C₇	—	4	1	no	—
878	C₂²×C₇	—	4	1	no	—
879	C₂²×C₇	—	4	2	no	—
880	C₂²×C₇	—	4	1	no	—
881	C₂²×C₇	—	4	1	no	—
882	C₂²×C₇	—	4	1	no	—
883	C₂²×C₇	—	4	1	no	—
884	C₂²×C₇	—	4	1	no	—
885	C₂²×C₇	—	4	2	no	—
886	C₂²×C₇	—	8	4	no	—
887	C₂²×C₇	—	16	4	no	—
888	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
889	C₄×C₇	—	2	1	no	—
890	C₄×C₇	—	2	1	no	—
891	C₄×C₇	—	2	2	no	—
892	C₄×C₇	—	2	2	no	—
893	C₄×C₇	—	2	1	no	—
894	C₄×C₇	—	2	1	no	—
895	C₄×C₇	—	2	2	no	—
896	C₄×C₇	—	4	2	no	—
897	C₄×C₇	—	4	2	no	—
898	C₄×C₇	—	4	1	no	—
899	C₄×C₇	—	4	1	no	—
900	C₄×C₇	—	4	1	no	—
901	C₄×C₇	—	4	1	no	—
902	C₄×C₇	—	4	2	no	—
903	C₄×C₇	#576	1	2	yes	—
904	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
905	C₄×C₇	#585	1	1	yes	characteristic
906	C₂⁴	—	2	1	no	—
907	C₂⁴	—	2	2	no	—
908	#41	—	2	4	no	—
909	#41	—	4	2	no	—
910	#41	—	4	2	no	—
911	#41	—	4	2	no	—
912	#41	—	4	2	no	—
913	#41	—	4	2	no	—
914	#41	—	8	2	no	—
915	#41	—	8	2	no	—
916	#41	—	8	2	no	—
917	C₂×Q₈	—	2	1	no	—
918	C₂×Q₈	—	2	2	no	—
919	C₂×Q₈	—	2	1	no	—
920	C₂×Q₈	—	8	2	no	—
921	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
922	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
923	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	1	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	4	1	no	—
941	C₂×D₄	—	4	2	no	—
942	C₂×D₄	—	4	2	no	—
943	C₂×D₄	—	8	2	no	—
944	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
945	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
946	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
947	C₂×D₄	C₂⁴×C₇	1	2	yes	—
948	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
949	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
950	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	1	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	2	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	8	2	no	—
965	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
966	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
967	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
968	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
969	Q₁₆	—	4	2	no	—
970	Q₁₆	—	4	2	no	—
971	SD₁₆	—	2	4	no	—
972	SD₁₆	—	4	2	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	2	no	—
975	SD₁₆	—	4	2	no	—
976	SD₁₆	—	4	2	no	—
977	D₈	—	2	2	no	—
978	D₈	—	2	4	no	—
979	D₈	—	2	2	no	—
980	D₈	—	4	1	no	—
981	D₈	—	4	1	no	—
982	D₈	—	4	2	no	—
983	M₁₆	—	4	2	no	—
984	M₁₆	—	4	2	no	—
985	C₂×C₈	—	4	2	no	—
986	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
988	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
989	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
990	C₂×C₈	C₂⁴×C₇	1	2	yes	—
991	C₂×C₈	C₂⁴×C₇	1	2	yes	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1008	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1009	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1010	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1011	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1012	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1013	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1014	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1016	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1017	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1040	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1041	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1042	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1043	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	2	no	—
1046	C₄²	—	2	2	no	—
1047	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1048	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1049	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1050	C₄²	C₂⁴×C₇	1	2	yes	—
1051	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1052	C₂×C₇	—	4	1	no	—
1053	C₂×C₇	—	4	2	no	—
1054	C₂×C₇	—	4	2	no	—
1055	C₂×C₇	—	8	1	no	—
1056	C₂×C₇	—	8	1	no	—
1057	C₂×C₇	—	8	2	no	—
1058	C₂×C₇	—	8	1	no	—
1059	C₂×C₇	#3488	1	1	yes	characteristic
1060	C₂×C₇	C₂×#576	1	1	yes	characteristic
1061	C₂×C₇	#3586	1	1	yes	characteristic
1062	C₂³	—	2	1	no	—
1063	C₂³	—	2	1	no	—
1064	C₂³	—	2	1	no	—
1065	C₂³	—	2	2	no	—
1066	C₂³	—	2	1	no	—
1067	C₂³	—	4	2	no	—
1068	C₂³	—	4	2	no	—
1069	C₂³	—	8	1	no	—
1070	C₂³	—	8	2	no	—
1071	C₂³	—	8	2	no	—
1072	C₂³	—	8	2	no	—
1073	C₂³	C₂²×C₇×D₄	1	2	yes	—
1074	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1075	Q₈	—	2	2	no	—
1076	Q₈	—	2	2	no	—
1077	Q₈	—	2	2	no	—
1078	Q₈	—	2	2	no	—
1079	Q₈	—	2	2	no	—
1080	Q₈	—	4	2	no	—
1081	Q₈	—	8	2	no	—
1082	Q₈	—	8	1	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	2	1	no	—
1087	D₄	—	2	1	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	2	1	no	—
1090	D₄	—	2	1	no	—
1091	D₄	—	2	2	no	—
1092	D₄	—	2	2	no	—
1093	D₄	—	4	2	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	4	4	no	—
1096	D₄	—	4	2	no	—
1097	D₄	—	8	1	no	—
1098	D₄	—	8	1	no	—
1099	D₄	—	8	2	no	—
1100	D₄	—	8	2	no	—
1101	D₄	—	8	1	no	—
1102	D₄	—	8	2	no	—
1103	D₄	—	8	2	no	—
1104	D₄	—	8	2	no	—
1105	D₄	—	8	2	no	—
1106	D₄	—	8	1	no	—
1107	D₄	—	8	1	no	—
1108	D₄	—	8	2	no	—
1109	D₄	C₇×H(5,𝔽₂)	1	2	yes	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	4	no	—
1124	C₂×C₄	—	4	2	no	—
1125	C₂×C₄	—	4	2	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	—	4	2	no	—
1128	C₂×C₄	—	8	1	no	—
1129	C₂×C₄	—	8	1	no	—
1130	C₂×C₄	—	8	2	no	—
1131	C₂×C₄	—	8	2	no	—
1132	C₂×C₄	—	8	2	no	—
1133	C₂×C₄	—	8	2	no	—
1134	C₂×C₄	—	8	1	no	—
1135	C₂×C₄	—	8	2	no	—
1136	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1137	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1138	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1139	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1140	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1141	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1142	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1143	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1144	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1145	C₈	—	2	1	no	—
1146	C₈	—	2	2	no	—
1147	C₈	—	2	1	no	—
1148	C₈	—	2	2	no	—
1149	C₈	—	2	1	no	—
1150	C₈	—	2	1	no	—
1151	C₇	#62041	1	1	yes	characteristic, direct product factor, Sylow
1152	C₂²	—	2	1	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	1	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	1	no	—
1158	C₂²	—	2	2	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	1	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	2	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	8	4	no	—
1174	C₂²	—	16	4	no	—
1175	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1176	C₄	—	2	1	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	1	no	—
1179	C₄	—	2	1	no	—
1180	C₄	—	2	2	no	—
1181	C₄	—	2	2	no	—
1182	C₄	—	2	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	2	no	—
1188	C₄	—	4	2	no	—
1189	C₄	—	4	2	no	—
1190	C₄	C₇×#576	1	2	yes	—
1191	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1192	C₄	C₇×#585	1	1	yes	characteristic
1193	C₂	—	4	1	no	—
1194	C₂	—	4	2	no	—
1195	C₂	—	4	2	no	—
1196	C₂	—	8	1	no	—
1197	C₂	—	8	1	no	—
1198	C₂	—	8	2	no	—
1199	C₂	—	8	1	no	—
1200	C₂	C₇×#3488	1	1	yes	characteristic
1201	C₂	C₂×C₇×#576	1	1	yes	characteristic
1202	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×#3546	C₂	semidirect
2. C₇×#3520	C₂	semidirect
3. C₇×#3397	C₂	semidirect
4. C₇×#3393	C₂	semidirect
5. C₇×#3367	C₂	semidirect
6. C₇×#3358	C₂	semidirect
7. C₇×#3333	C₂	semidirect
8. C₇×#3330	C₂	semidirect
9. C₇×#3314	C₂	semidirect
10. C₇×#3294	C₂	semidirect
11. C₇×#3283	C₂	semidirect
12. C₇×#3273	C₂	semidirect
13. C₇×#3272	C₂	semidirect
14. C₇×#3268	C₂	semidirect
15. C₇×#3262	C₂	semidirect
16. C₇×#3254	C₂	semidirect
17. C₇×#3224	C₂	semidirect
18. C₇×#3210	C₂	semidirect
19. C₇×#3124	C₂	semidirect
20. C₇×#3100	C₂	semidirect
21. C₇×#3045	C₂	semidirect
22. C₇×#3036	C₂	semidirect
23. C₇×#2993	C₂	semidirect
25. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₇×#135	C₂²	semidirect
28. C₇×#556	C₂²	semidirect
29. C₇×#556	C₂²	semidirect
30. C₇×#554	C₂²	semidirect
35. C₇×#550	C₂²	semidirect
36. C₇×D₄×Q₈	C₂²	semidirect
40. C₇×#547	C₂²	semidirect
43. C₇×#546	C₂²	semidirect
44. C₇×D₄²	C₂²	semidirect
45. C₇×#542	C₂²	semidirect
46. C₇×#542	C₂²	semidirect
51. C₇×#535	C₂²	semidirect
52. C₇×#533	C₂²	semidirect
58. C₇×#520	C₂²	semidirect
59. C₂×C₄×C₇×D₄	C₂²	semidirect
60. C₇×#496	C₂²	semidirect
62. C₇×#494	C₂²	semidirect
63. C₇×#492	C₂²	semidirect
64. C₇×#489	C₂²	semidirect
65. C₇×#487	C₂²	semidirect
66. C₇×#486	C₂²	semidirect
67. C₇×#486	C₂²	semidirect
68. C₇×#484	C₂²	semidirect
70. C₇×#480	C₂²	semidirect
71. C₇×#480	C₂²	semidirect
72. C₇×#477	C₂²	semidirect
73. C₇×#477	C₂²	semidirect
74. C₇×#474	C₂²	semidirect
75. C₇×#474	C₂²	semidirect
76. C₇×#474	C₂²	semidirect
77. C₇×#474	C₂²	semidirect
78. C₇×#474	C₂²	semidirect
80. C₇×#468	C₂²	semidirect
81. C₇×#468	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
88. C₇×#464	C₂²	semidirect
90. C₇×#463	C₂²	semidirect
91. C₇×#463	C₂²	semidirect
92. C₇×#463	C₂²	semidirect
93. C₇×#461	C₂²	semidirect
94. C₇×#461	C₂²	semidirect
95. C₇×#461	C₂²	semidirect
96. C₇×#461	C₂²	semidirect
97. C₇×#460	C₂²	semidirect
98. C₇×#460	C₂²	semidirect
103. C₇×#459	C₂²	semidirect
104. C₇×#452	C₂²	semidirect
105. C₇×#452	C₂²	semidirect
106. C₇×#452	C₂²	semidirect
107. C₇×#452	C₂²	semidirect
108. C₇×#450	C₂²	semidirect
110. C₇×#449	C₂²	semidirect
113. C₇×#447	C₂²	semidirect
114. C₇×#446	C₂²	semidirect
115. C₇×C₈×Q₈	C₂²	semidirect
116. C₇×#440	C₂²	semidirect
117. C₇×#440	C₂²	semidirect
118. C₄×C₇×Q₁₆	C₂²	semidirect
121. C₄×C₇×D₈	C₂²	semidirect
122. C₄×C₇×D₈	C₂²	semidirect
123. C₄×C₇×D₈	C₂²	semidirect
124. C₇×#436	C₂²	semidirect
125. C₇×#436	C₂²	semidirect
126. C₇×#435	C₂²	semidirect
127. C₇×C₈×D₄	C₂²	semidirect
128. C₇×#433	C₂²	semidirect
129. C₇×#431	C₂²	semidirect
130. C₇×#424	C₂²	semidirect
131. C₇×#423	C₂²	semidirect
132. C₇×#417	C₂²	semidirect
133. C₇×#417	C₂²	semidirect
134. C₂×C₇×#102	C₂²	semidirect
135. #62041	C₇	direct (N × H)
316. #3546	C₂×C₇	semidirect
317. #3520	C₂×C₇	semidirect
318. #3397	C₂×C₇	semidirect
319. #3393	C₂×C₇	semidirect
320. #3367	C₂×C₇	semidirect
321. #3358	C₂×C₇	semidirect
322. #3333	C₂×C₇	semidirect
323. #3330	C₂×C₇	semidirect
324. #3314	C₂×C₇	semidirect
325. #3294	C₂×C₇	semidirect
326. #3283	C₂×C₇	semidirect
327. #3273	C₂×C₇	semidirect
328. #3272	C₂×C₇	semidirect
329. #3268	C₂×C₇	semidirect
330. #3262	C₂×C₇	semidirect
331. #3254	C₂×C₇	semidirect
332. #3224	C₂×C₇	semidirect
333. #3210	C₂×C₇	semidirect
334. #3124	C₂×C₇	semidirect
335. #3100	C₂×C₇	semidirect
336. #3045	C₂×C₇	semidirect
337. #3036	C₂×C₇	semidirect
338. #2993	C₂×C₇	semidirect
486. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
487. C₂×#135	C₂²×C₇	semidirect
489. #556	C₂²×C₇	semidirect
490. #556	C₂²×C₇	semidirect
491. #554	C₂²×C₇	semidirect
496. #550	C₂²×C₇	semidirect
497. D₄×Q₈	C₂²×C₇	semidirect
501. #547	C₂²×C₇	semidirect
504. #546	C₂²×C₇	semidirect
505. D₄²	C₂²×C₇	semidirect
506. #542	C₂²×C₇	semidirect
507. #542	C₂²×C₇	semidirect
512. #535	C₂²×C₇	semidirect
513. #533	C₂²×C₇	semidirect
519. #520	C₂²×C₇	semidirect
520. C₂×C₄×D₄	C₂²×C₇	semidirect
521. #496	C₂²×C₇	semidirect
523. #494	C₂²×C₇	semidirect
524. #492	C₂²×C₇	semidirect
525. #489	C₂²×C₇	semidirect
526. #487	C₂²×C₇	semidirect
527. #486	C₂²×C₇	semidirect
528. #486	C₂²×C₇	semidirect
529. #484	C₂²×C₇	semidirect
531. #480	C₂²×C₇	semidirect
532. #480	C₂²×C₇	semidirect
533. #477	C₂²×C₇	semidirect
534. #477	C₂²×C₇	semidirect
535. #474	C₂²×C₇	semidirect
536. #474	C₂²×C₇	semidirect
537. #474	C₂²×C₇	semidirect
538. #474	C₂²×C₇	semidirect
539. #474	C₂²×C₇	semidirect
541. #468	C₂²×C₇	semidirect
542. #468	C₂²×C₇	semidirect
543. #468	C₂²×C₇	semidirect
544. #467	C₂²×C₇	semidirect
546. #464	C₂²×C₇	semidirect
547. #464	C₂²×C₇	semidirect
548. #464	C₂²×C₇	semidirect
549. #464	C₂²×C₇	semidirect
551. #463	C₂²×C₇	semidirect
552. #463	C₂²×C₇	semidirect
553. #463	C₂²×C₇	semidirect
554. #461	C₂²×C₇	semidirect
555. #461	C₂²×C₇	semidirect
556. #461	C₂²×C₇	semidirect
557. #461	C₂²×C₇	semidirect
558. #460	C₂²×C₇	semidirect
559. #460	C₂²×C₇	semidirect
564. #459	C₂²×C₇	semidirect
565. #452	C₂²×C₇	semidirect
566. #452	C₂²×C₇	semidirect
567. #452	C₂²×C₇	semidirect
568. #452	C₂²×C₇	semidirect
569. #450	C₂²×C₇	semidirect
571. #449	C₂²×C₇	semidirect
574. #447	C₂²×C₇	semidirect
575. #446	C₂²×C₇	semidirect
576. C₈×Q₈	C₂²×C₇	semidirect
577. #440	C₂²×C₇	semidirect
578. #440	C₂²×C₇	semidirect
579. C₄×Q₁₆	C₂²×C₇	semidirect
582. C₄×D₈	C₂²×C₇	semidirect
583. C₄×D₈	C₂²×C₇	semidirect
584. C₄×D₈	C₂²×C₇	semidirect
585. #436	C₂²×C₇	semidirect
586. #436	C₂²×C₇	semidirect
587. #435	C₂²×C₇	semidirect
588. C₈×D₄	C₂²×C₇	semidirect
589. #433	C₂²×C₇	semidirect
590. #431	C₂²×C₇	semidirect
591. #424	C₂²×C₇	semidirect
592. #423	C₂²×C₇	semidirect
593. #417	C₂²×C₇	semidirect
594. #417	C₂²×C₇	semidirect
595. C₂×#102	C₂²×C₇	semidirect
1151. C₇	#62041	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×#3546	2
C₇×#3520	2
C₇×#3397	2
C₇×#3393	2
C₇×#3367	2
C₇×#3358	2
C₇×#3333	2
C₇×#3330	2
C₇×#3314	2
C₇×#3294	2
C₇×#3283	2
C₇×#3273	2
C₇×#3272	2
C₇×#3268	2
C₇×#3262	2
C₇×#3254	2
C₇×#3224	2
C₇×#3210	2
C₇×#3124	2
C₇×#3100	2
C₇×#3045	2
C₇×#3036	2
C₇×#2993	2
#62041	7

Subgroups — C7×#62041 #13239257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62041 #13239257