Subgroups — C₇×#61216 #13238432

Order 1792.

2060 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3327	C₂	1	2	yes	maximal, complemented
4	C₇×#3326	C₂	1	2	yes	maximal, complemented
5	C₇×#3323	C₂	1	2	yes	maximal, complemented
6	C₇×#3322	C₂	1	2	yes	maximal, complemented
7	C₇×#3301	C₂	1	2	yes	maximal, complemented
8	C₇×#3300	C₂	1	2	yes	maximal, complemented
9	C₇×#3297	C₂	1	2	yes	maximal, complemented
10	C₇×#3296	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#488	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3080	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3062	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3040	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3012	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
26	C₂×C₇×#137	C₂²	1	1	yes	characteristic, complemented
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	C₂×C₇×#131	C₂²	1	1	yes	characteristic, complemented
31	C₇×#553	—	2	2	no	—
32	C₇×#553	—	2	2	no	—
33	C₇×#553	C₂²	1	2	yes	complemented
34	C₇×#553	C₂²	1	2	yes	complemented
35	C₇×#552	C₂²	1	2	yes	complemented
36	C₇×#552	C₂²	1	2	yes	complemented
37	C₇×#548	C₂²	1	2	yes	—
38	C₇×#548	C₂²	1	2	yes	—
39	C₇×#546	—	2	2	no	—
40	C₇×#546	—	2	2	no	—
41	C₇×#546	C₂²	1	2	yes	—
42	C₇×#546	C₂²	1	2	yes	—
43	C₇×#541	—	2	1	no	—
44	C₇×#540	—	2	1	no	—
45	C₇×#537	C₂²	1	1	yes	characteristic
46	C₇×#537	C₂²	1	1	yes	characteristic, complemented
47	C₇×#536	—	2	1	no	—
48	C₇×#536	C₂²	1	1	yes	characteristic
49	C₇×#535	—	2	1	no	—
50	C₇×#535	C₂²	1	1	yes	characteristic
51	C₇×#532	—	2	1	no	—
52	C₇×#532	C₂²	1	1	yes	characteristic
53	C₇×#529	—	2	1	no	—
54	C₇×#529	—	2	1	no	—
55	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₇×#124	—	2	1	no	—
57	C₂×C₇×#124	C₂²	1	1	yes	characteristic
58	C₇×#520	C₂²	1	1	yes	characteristic
59	C₇×#520	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₇×#41	C₂²	1	1	yes	characteristic
61	C₄×C₇×#41	C₂²	1	1	yes	characteristic, complemented
62	C₇×#488	C₂²	1	2	yes	complemented
63	C₇×#488	C₂²	1	2	yes	complemented
64	C₇×#488	C₂²	1	2	yes	complemented
65	C₇×#488	C₂²	1	2	yes	complemented
66	C₇×#485	C₂²	1	2	yes	complemented
67	C₇×#485	C₂²	1	2	yes	complemented
68	C₇×#484	C₂²	1	2	yes	complemented
69	C₇×#483	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×#478	C₂²	1	2	yes	complemented
77	C₇×#478	C₂²	1	2	yes	complemented
78	C₇×#470	C₂²	1	2	yes	complemented
79	C₇×#469	C₂²	1	2	yes	complemented
80	C₇×#468	C₂²	1	2	yes	complemented
81	C₇×#468	C₂²	1	2	yes	complemented
82	C₇×#467	C₂²	1	2	yes	complemented
83	C₇×#466	C₂²	1	2	yes	complemented
84	C₇×#465	C₂²	1	2	yes	complemented
85	C₇×#465	C₂²	1	2	yes	complemented
86	C₇×#464	C₂²	1	2	yes	complemented
87	C₇×#464	C₂²	1	2	yes	complemented
88	C₇×#463	C₂²	1	2	yes	complemented
89	C₇×#463	C₂²	1	2	yes	complemented
90	C₇×#452	C₂²	1	2	yes	—
91	C₇×#452	C₂²	1	2	yes	complemented
92	C₇×#451	C₂²	1	2	yes	complemented
93	C₇×#450	C₂²	1	2	yes	—
94	C₇×#449	C₂²	1	2	yes	—
95	C₇×#449	C₂²	1	2	yes	complemented
96	C₇×#448	C₂²	1	2	yes	complemented
97	C₇×#447	C₂²	1	2	yes	—
98	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
106	C₇×#436	C₂²	1	2	yes	complemented
107	C₇×#436	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, complemented
111	C₇×#428	C₂²	1	1	yes	characteristic, complemented
112	C₇×#427	C₂²	1	1	yes	characteristic, complemented
113	C₇×#423	C₂²	1	1	yes	characteristic, complemented
114	C₇×#419	C₂²	1	1	yes	characteristic, complemented
115	C₇×#419	C₂²	1	2	yes	complemented
116	C₇×#418	C₂²	1	1	yes	characteristic
117	C₇×#418	C₂²	1	2	yes	—
118	C₇×#417	C₂²	1	1	yes	characteristic
119	C₇×#417	C₂²	1	1	yes	characteristic
120	C₇×#417	C₂²	1	2	yes	—
121	C₇×#417	C₂²	1	2	yes	complemented
122	C₇×#416	C₂²	1	1	yes	characteristic
123	C₇×#416	C₂²	1	2	yes	—
124	C₇×#416	C₂²	1	1	yes	characteristic, complemented
125	C₇×#416	C₂²	1	2	yes	complemented
126	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₇×#103	C₂²	1	2	yes	complemented
128	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₇×#102	C₂²	1	1	yes	characteristic
130	C₂×C₇×#102	C₂²	1	2	yes	—
131	C₂×C₇×#102	C₂²	1	1	yes	characteristic
132	C₇×#408	C₂²	1	1	yes	characteristic
133	C₇×#408	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
135	#61216	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	C₇×H(5,𝔽₂)	—	2	4	no	—
139	C₇×H(5,𝔽₂)	—	4	2	no	—
140	C₂×C₇×#41	—	2	1	no	—
141	C₂×C₇×#41	—	2	1	no	—
142	C₂×C₇×#41	—	2	2	no	—
143	C₂×C₇×#41	C₂³	1	1	yes	characteristic
144	C₂×C₇×#41	C₂³	1	2	yes	—
145	C₂×C₇×#41	C₂³	1	2	yes	—
146	C₂×C₇×#41	C₂³	1	1	yes	characteristic
147	C₂×C₇×#41	C₂³	1	1	yes	characteristic
148	C₂×C₇×#41	C₂³	1	1	yes	characteristic
149	C₂²×C₇×Q₈	—	2	1	no	—
150	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
151	C₂²×C₇×Q₈	C₂³	1	2	yes	—
152	C₂²×C₇×D₄	—	2	1	no	—
153	C₂²×C₇×D₄	—	2	2	no	—
154	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
155	C₂²×C₇×D₄	C₂³	1	2	yes	—
156	C₇×#137	—	4	2	no	—
157	C₇×AGL(1,ℤ/8)	—	4	2	no	—
158	C₇×#135	—	2	4	no	—
159	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
160	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
161	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
162	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
163	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
165	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
166	C₂×C₇×D₈	C₂³	1	2	yes	—
167	C₇×#131	—	4	2	no	—
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	C₂×C₇×M₁₆	C₂³	1	2	yes	—
173	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
174	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
175	C₂²×C₇×C₈	C₂³	1	2	yes	—
176	C₂²×C₇×C₈	C₂³	1	2	yes	—
177	C₇×C₄⋊Q₈	—	2	1	no	—
178	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
179	C₇×#127	—	2	1	no	—
180	C₇×#127	D₄	1	1	yes	characteristic
181	C₇×#126	—	2	2	no	—
182	C₇×#126	—	2	2	no	—
183	C₇×#126	—	2	2	no	—
184	C₇×#126	—	2	2	no	—
185	C₇×#125	—	2	2	no	—
186	C₇×#125	—	2	2	no	—
187	C₇×#125	—	2	1	no	—
188	C₇×#125	—	2	1	no	—
189	C₇×#125	C₂³	1	2	yes	—
190	C₇×#125	C₂³	1	2	yes	—
191	C₇×#124	—	2	1	no	—
192	C₇×#124	—	2	1	no	—
193	C₇×#124	—	2	2	no	—
194	C₇×#124	—	2	2	no	—
195	C₇×#124	—	2	1	no	—
196	C₇×#124	—	2	1	no	—
197	C₇×#124	D₄	1	1	yes	characteristic
198	C₇×#124	D₄	1	1	yes	characteristic
199	C₇×#124	C₂³	1	2	yes	—
200	C₇×#124	C₂³	1	2	yes	—
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	—	2	2	no	—
207	C₇×#123	—	2	2	no	—
208	C₇×C₂²⋊Q₈	—	2	1	no	—
209	C₇×C₂²⋊Q₈	—	2	1	no	—
210	C₇×C₂²⋊Q₈	—	2	2	no	—
211	C₇×C₂²⋊Q₈	—	2	2	no	—
212	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₇×#121	—	2	1	no	—
217	C₇×#121	—	2	1	no	—
218	C₇×#121	—	2	2	no	—
219	C₇×#121	—	2	2	no	—
220	C₇×#121	—	2	2	no	—
221	C₇×#121	—	2	2	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	D₄	1	2	yes	—
227	C₇×#121	D₄	1	2	yes	—
228	C₇×#121	C₂³	1	2	yes	—
229	C₇×#121	C₂³	1	2	yes	—
230	C₇×#121	C₂³	1	2	yes	—
231	C₇×#121	C₂³	1	2	yes	—
232	C₇×#120	—	2	2	no	—
233	C₇×#120	—	2	2	no	—
234	C₇×#120	—	2	2	no	—
235	C₄×C₇×Q₈	—	2	1	no	—
236	C₄×C₇×Q₈	—	2	1	no	—
237	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
238	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
239	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
240	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
241	C₄×C₇×D₄	—	2	1	no	—
242	C₄×C₇×D₄	—	2	2	no	—
243	C₄×C₇×D₄	—	2	1	no	—
244	C₄×C₇×D₄	—	2	2	no	—
245	C₄×C₇×D₄	—	2	1	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	2	no	—
250	C₄×C₇×D₄	—	2	2	no	—
251	C₄×C₇×D₄	—	2	2	no	—
252	C₄×C₇×D₄	—	2	2	no	—
253	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
254	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
255	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
256	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
257	C₄×C₇×D₄	C₂³	1	2	yes	—
258	C₄×C₇×D₄	C₂³	1	2	yes	—
259	C₇×#117	—	2	2	no	—
260	C₇×#117	—	2	2	no	—
261	C₇×#117	—	2	1	no	—
262	C₇×#117	—	2	1	no	—
263	C₇×#117	C₂³	1	2	yes	—
264	C₇×#117	C₂³	1	2	yes	—
265	C₇×#117	C₂³	1	1	yes	characteristic
266	C₇×#117	C₂³	1	1	yes	characteristic
267	C₂×C₇×C₄⋊C₄	—	2	1	no	—
268	C₂×C₇×C₄⋊C₄	—	2	1	no	—
269	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
270	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
271	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²×C₇	—	2	1	no	—
278	C₂×C₄²×C₇	—	2	1	no	—
279	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
280	C₇×#107	C₂³	1	2	yes	—
281	C₇×#107	C₂³	1	2	yes	—
282	C₇×#107	C₂³	1	1	yes	characteristic
283	C₇×#107	C₂³	1	1	yes	characteristic
284	C₇×#106	C₂³	1	2	yes	—
285	C₇×#106	C₂³	1	2	yes	—
286	C₇×#106	C₂³	1	1	yes	characteristic
287	C₇×#106	C₂³	1	1	yes	characteristic
288	C₇×C₄⋊C₈	C₂³	1	2	yes	—
289	C₇×C₄⋊C₈	C₂³	1	2	yes	—
290	C₇×#103	C₂³	1	1	yes	characteristic
291	C₇×#103	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	1	yes	characteristic
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	2	yes	—
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×#103	C₂³	1	1	yes	characteristic
302	C₇×#102	C₂³	1	1	yes	characteristic
303	C₇×#102	C₂³	1	2	yes	—
304	C₇×#102	C₂³	1	1	yes	characteristic
305	C₇×#102	C₂³	1	2	yes	—
306	C₇×#102	C₂³	1	2	yes	—
307	C₇×#102	C₂³	1	2	yes	—
308	C₇×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
313	C₇×#102	C₂³	1	1	yes	characteristic
314	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
319	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
320	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
321	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
322	#3512	C₂×C₇	1	1	yes	characteristic, complemented
323	#3500	C₂×C₇	1	1	yes	characteristic, complemented
324	#3327	C₂×C₇	1	2	yes	complemented
325	#3326	C₂×C₇	1	2	yes	complemented
326	#3323	C₂×C₇	1	2	yes	complemented
327	#3322	C₂×C₇	1	2	yes	complemented
328	#3301	C₂×C₇	1	2	yes	complemented
329	#3300	C₂×C₇	1	2	yes	complemented
330	#3297	C₂×C₇	1	2	yes	complemented
331	#3296	C₂×C₇	1	2	yes	complemented
332	C₂×#488	C₂×C₇	1	1	yes	characteristic, complemented
333	#3097	C₂×C₇	1	1	yes	characteristic, complemented
334	#3096	C₂×C₇	1	1	yes	characteristic, complemented
335	#3080	C₂×C₇	1	1	yes	characteristic, complemented
336	#3063	C₂×C₇	1	1	yes	characteristic, complemented
337	#3062	C₂×C₇	1	1	yes	characteristic, complemented
338	#3040	C₂×C₇	1	1	yes	characteristic, complemented
339	#3013	C₂×C₇	1	1	yes	characteristic, complemented
340	#3012	C₂×C₇	1	1	yes	characteristic, complemented
341	C₄×#135	C₂×C₇	1	1	yes	characteristic, complemented
342	#2931	C₂×C₇	1	1	yes	characteristic, complemented
343	#2898	C₂×C₇	1	1	yes	characteristic, complemented
344	#2897	C₂×C₇	1	1	yes	characteristic, complemented
345	C₂⁴×C₇	—	2	2	no	—
346	C₂⁴×C₇	—	2	1	no	—
347	C₇×#41	—	2	2	no	—
348	C₇×#41	—	2	2	no	—
349	C₇×#41	—	2	2	no	—
350	C₇×#41	—	2	2	no	—
351	C₇×#41	—	2	2	no	—
352	C₇×#41	—	2	4	no	—
353	C₇×#41	—	2	4	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	4	no	—
359	C₇×#41	—	4	4	no	—
360	C₇×#41	—	4	8	no	—
361	C₇×#41	#41	1	4	yes	—
362	C₂×C₇×Q₈	—	2	2	no	—
363	C₂×C₇×Q₈	—	2	1	no	—
364	C₂×C₇×Q₈	—	2	4	no	—
365	C₂×C₇×Q₈	—	2	2	no	—
366	C₂×C₇×Q₈	—	2	2	no	—
367	C₂×C₇×Q₈	—	4	2	no	—
368	C₂×C₇×Q₈	—	4	4	no	—
369	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
370	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
371	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
372	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
373	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
374	C₂×C₇×D₄	—	2	1	no	—
375	C₂×C₇×D₄	—	2	4	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	2	no	—
381	C₂×C₇×D₄	—	2	2	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	2	no	—
386	C₂×C₇×D₄	—	2	2	no	—
387	C₂×C₇×D₄	—	4	2	no	—
388	C₂×C₇×D₄	—	4	4	no	—
389	C₂×C₇×D₄	—	4	8	no	—
390	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
391	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
392	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
393	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
394	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
395	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
396	C₂×C₇×D₄	C₂⁴	1	2	yes	—
397	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
398	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₇	—	2	1	no	—
400	C₂²×C₄×C₇	—	2	1	no	—
401	C₂²×C₄×C₇	—	2	2	no	—
402	C₂²×C₄×C₇	—	2	1	no	—
403	C₂²×C₄×C₇	—	2	1	no	—
404	C₂²×C₄×C₇	—	2	2	no	—
405	C₂²×C₄×C₇	—	2	2	no	—
406	C₂²×C₄×C₇	—	2	1	no	—
407	C₂²×C₄×C₇	—	2	2	no	—
408	C₂²×C₄×C₇	—	2	2	no	—
409	C₂²×C₄×C₇	—	2	1	no	—
410	C₂²×C₄×C₇	—	2	1	no	—
411	C₂²×C₄×C₇	—	2	1	no	—
412	C₂²×C₄×C₇	—	2	1	no	—
413	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
414	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
415	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
416	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
417	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
418	C₇×Q₁₆	—	2	2	no	—
419	C₇×Q₁₆	—	4	2	no	—
420	C₇×SD₁₆	—	2	2	no	—
421	C₇×SD₁₆	—	2	2	no	—
422	C₇×SD₁₆	—	4	2	no	—
423	C₇×SD₁₆	—	4	2	no	—
424	C₇×D₈	—	2	2	no	—
425	C₇×D₈	—	4	2	no	—
426	C₇×M₁₆	—	2	2	no	—
427	C₇×M₁₆	—	2	2	no	—
428	C₇×M₁₆	—	4	2	no	—
429	C₇×M₁₆	—	4	2	no	—
430	C₂×C₇×C₈	—	2	2	no	—
431	C₂×C₇×C₈	—	2	2	no	—
432	C₂×C₇×C₈	—	4	2	no	—
433	C₂×C₇×C₈	—	4	2	no	—
434	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
435	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
436	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
437	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
438	C₂×C₇×C₈	C₂⁴	1	2	yes	—
439	C₂×C₇×C₈	C₂⁴	1	2	yes	—
440	C₇×C₄⋊C₄	—	2	2	no	—
441	C₇×C₄⋊C₄	—	2	2	no	—
442	C₇×C₄⋊C₄	—	2	2	no	—
443	C₇×C₄⋊C₄	—	2	2	no	—
444	C₇×C₄⋊C₄	—	2	1	no	—
445	C₇×C₄⋊C₄	—	2	1	no	—
446	C₇×C₄⋊C₄	—	2	2	no	—
447	C₇×C₄⋊C₄	—	2	2	no	—
448	C₇×C₄⋊C₄	—	2	1	no	—
449	C₇×C₄⋊C₄	—	2	1	no	—
450	C₇×C₄⋊C₄	—	2	1	no	—
451	C₇×C₄⋊C₄	—	2	1	no	—
452	C₇×C₄⋊C₄	—	2	2	no	—
453	C₇×C₄⋊C₄	—	2	2	no	—
454	C₇×C₄⋊C₄	—	2	2	no	—
455	C₇×C₄⋊C₄	—	2	2	no	—
456	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
457	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
458	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
459	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
460	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
461	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
462	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
463	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
464	C₇×C₂²⋊C₄	—	2	2	no	—
465	C₇×C₂²⋊C₄	—	2	2	no	—
466	C₇×C₂²⋊C₄	—	2	2	no	—
467	C₇×C₂²⋊C₄	—	2	2	no	—
468	C₇×C₂²⋊C₄	—	2	1	no	—
469	C₇×C₂²⋊C₄	—	2	1	no	—
470	C₇×C₂²⋊C₄	—	2	2	no	—
471	C₇×C₂²⋊C₄	—	2	2	no	—
472	C₇×C₂²⋊C₄	—	2	2	no	—
473	C₇×C₂²⋊C₄	—	2	2	no	—
474	C₇×C₂²⋊C₄	—	2	2	no	—
475	C₇×C₂²⋊C₄	—	2	2	no	—
476	C₇×C₂²⋊C₄	—	2	2	no	—
477	C₇×C₂²⋊C₄	—	2	2	no	—
478	C₇×C₂²⋊C₄	—	2	1	no	—
479	C₇×C₂²⋊C₄	—	2	1	no	—
480	C₇×C₂²⋊C₄	—	2	1	no	—
481	C₇×C₂²⋊C₄	—	2	1	no	—
482	C₇×C₂²⋊C₄	—	2	2	no	—
483	C₇×C₂²⋊C₄	—	2	2	no	—
484	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
485	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
486	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
487	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
488	C₄²×C₇	—	2	1	no	—
489	C₄²×C₇	—	2	1	no	—
490	C₄²×C₇	—	2	1	no	—
491	C₄²×C₇	—	2	1	no	—
492	C₄²×C₇	—	2	1	no	—
493	C₄²×C₇	—	2	1	no	—
494	C₄²×C₇	—	2	2	no	—
495	C₄²×C₇	—	2	2	no	—
496	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
497	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
498	C₄²×C₇	C₂⁴	1	1	yes	characteristic
499	C₄²×C₇	C₂⁴	1	1	yes	characteristic
500	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
501	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
502	C₂×#137	C₂²×C₇	1	1	yes	characteristic, complemented
503	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
504	C₂×#135	C₂²×C₇	1	1	yes	characteristic
505	C₂×#131	C₂²×C₇	1	1	yes	characteristic
506	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
507	#553	—	2	2	no	—
508	#553	—	2	2	no	—
509	#553	C₂²×C₇	1	2	yes	complemented
510	#553	C₂²×C₇	1	2	yes	complemented
511	#552	C₂²×C₇	1	2	yes	complemented
512	#552	C₂²×C₇	1	2	yes	complemented
513	#548	C₂²×C₇	1	2	yes	—
514	#548	C₂²×C₇	1	2	yes	—
515	#546	—	2	2	no	—
516	#546	—	2	2	no	—
517	#546	C₂²×C₇	1	2	yes	—
518	#546	C₂²×C₇	1	2	yes	—
519	#541	—	2	1	no	—
520	#540	—	2	1	no	—
521	#537	C₂²×C₇	1	1	yes	characteristic
522	#537	C₂²×C₇	1	1	yes	characteristic, complemented
523	#536	—	2	1	no	—
524	#536	C₂²×C₇	1	1	yes	characteristic
525	#535	—	2	1	no	—
526	#535	C₂²×C₇	1	1	yes	characteristic
527	#532	—	2	1	no	—
528	#532	C₂²×C₇	1	1	yes	characteristic
529	#529	—	2	1	no	—
530	#529	—	2	1	no	—
531	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
532	C₂×#124	—	2	1	no	—
533	C₂×#124	C₂²×C₇	1	1	yes	characteristic
534	#520	C₂²×C₇	1	1	yes	characteristic
535	#520	C₂²×C₇	1	1	yes	characteristic, complemented
536	C₄×#41	C₂²×C₇	1	1	yes	characteristic
537	C₄×#41	C₂²×C₇	1	1	yes	characteristic, complemented
538	#488	C₂²×C₇	1	2	yes	complemented
539	#488	C₂²×C₇	1	2	yes	complemented
540	#488	C₂²×C₇	1	2	yes	complemented
541	#488	C₂²×C₇	1	2	yes	complemented
542	#485	C₂²×C₇	1	2	yes	complemented
543	#485	C₂²×C₇	1	2	yes	complemented
544	#484	C₂²×C₇	1	2	yes	complemented
545	#483	C₂²×C₇	1	2	yes	complemented
546	#482	C₂²×C₇	1	2	yes	complemented
547	#482	C₂²×C₇	1	2	yes	complemented
548	#481	C₂²×C₇	1	2	yes	complemented
549	#480	C₂²×C₇	1	2	yes	complemented
550	#479	C₂²×C₇	1	2	yes	complemented
551	#479	C₂²×C₇	1	2	yes	complemented
552	#478	C₂²×C₇	1	2	yes	complemented
553	#478	C₂²×C₇	1	2	yes	complemented
554	#470	C₂²×C₇	1	2	yes	complemented
555	#469	C₂²×C₇	1	2	yes	complemented
556	#468	C₂²×C₇	1	2	yes	complemented
557	#468	C₂²×C₇	1	2	yes	complemented
558	#467	C₂²×C₇	1	2	yes	complemented
559	#466	C₂²×C₇	1	2	yes	complemented
560	#465	C₂²×C₇	1	2	yes	complemented
561	#465	C₂²×C₇	1	2	yes	complemented
562	#464	C₂²×C₇	1	2	yes	complemented
563	#464	C₂²×C₇	1	2	yes	complemented
564	#463	C₂²×C₇	1	2	yes	complemented
565	#463	C₂²×C₇	1	2	yes	complemented
566	#452	C₂²×C₇	1	2	yes	—
567	#452	C₂²×C₇	1	2	yes	complemented
568	#451	C₂²×C₇	1	2	yes	complemented
569	#450	C₂²×C₇	1	2	yes	—
570	#449	C₂²×C₇	1	2	yes	—
571	#449	C₂²×C₇	1	2	yes	complemented
572	#448	C₂²×C₇	1	2	yes	complemented
573	#447	C₂²×C₇	1	2	yes	—
574	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
575	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
576	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
577	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
578	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
579	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
580	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
581	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
582	#436	C₂²×C₇	1	2	yes	complemented
583	#436	C₂²×C₇	1	2	yes	complemented
584	C₈×D₄	C₂²×C₇	1	2	yes	complemented
585	C₈×D₄	C₂²×C₇	1	2	yes	complemented
586	#428	C₂²×C₇	1	1	yes	characteristic, complemented
587	#428	C₂²×C₇	1	1	yes	characteristic, complemented
588	#427	C₂²×C₇	1	1	yes	characteristic, complemented
589	#423	C₂²×C₇	1	1	yes	characteristic, complemented
590	#419	C₂²×C₇	1	1	yes	characteristic, complemented
591	#419	C₂²×C₇	1	2	yes	complemented
592	#418	C₂²×C₇	1	1	yes	characteristic
593	#418	C₂²×C₇	1	2	yes	—
594	#417	C₂²×C₇	1	1	yes	characteristic
595	#417	C₂²×C₇	1	1	yes	characteristic
596	#417	C₂²×C₇	1	2	yes	—
597	#417	C₂²×C₇	1	2	yes	complemented
598	#416	C₂²×C₇	1	1	yes	characteristic
599	#416	C₂²×C₇	1	2	yes	—
600	#416	C₂²×C₇	1	2	yes	complemented
601	#416	C₂²×C₇	1	1	yes	characteristic, complemented
602	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
603	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
604	C₂×#103	C₂²×C₇	1	2	yes	complemented
605	C₂×#102	C₂²×C₇	1	1	yes	characteristic
606	C₂×#102	C₂²×C₇	1	1	yes	characteristic
607	C₂×#102	C₂²×C₇	1	2	yes	—
608	#408	C₂²×C₇	1	1	yes	characteristic
609	#408	C₂²×C₇	1	1	yes	characteristic, complemented
610	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
611	C₂³×C₇	—	2	1	no	—
612	C₂³×C₇	—	2	1	no	—
613	C₂³×C₇	—	2	2	no	—
614	C₂³×C₇	—	4	4	no	—
615	C₂³×C₇	—	4	2	no	—
616	C₂³×C₇	—	8	1	no	—
617	C₂³×C₇	—	8	1	no	—
618	C₂³×C₇	—	8	2	no	—
619	C₂³×C₇	—	8	2	no	—
620	C₂³×C₇	C₂²×D₄	1	2	yes	—
621	C₂³×C₇	C₂²×D₄	1	2	yes	—
622	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
623	C₇×Q₈	—	2	2	no	—
624	C₇×Q₈	—	2	2	no	—
625	C₇×Q₈	—	2	1	no	—
626	C₇×Q₈	—	2	1	no	—
627	C₇×Q₈	—	2	2	no	—
628	C₇×Q₈	—	2	1	no	—
629	C₇×Q₈	—	2	2	no	—
630	C₇×Q₈	—	4	4	no	—
631	C₇×Q₈	—	4	2	no	—
632	C₇×Q₈	C₂×#41	1	2	yes	—
633	C₇×D₄	—	2	4	no	—
634	C₇×D₄	—	2	4	no	—
635	C₇×D₄	—	2	4	no	—
636	C₇×D₄	—	2	2	no	—
637	C₇×D₄	—	2	2	no	—
638	C₇×D₄	—	2	1	no	—
639	C₇×D₄	—	2	2	no	—
640	C₇×D₄	—	2	1	no	—
641	C₇×D₄	—	2	1	no	—
642	C₇×D₄	—	2	2	no	—
643	C₇×D₄	—	4	2	no	—
644	C₇×D₄	—	4	2	no	—
645	C₇×D₄	—	4	4	no	—
646	C₇×D₄	—	4	4	no	—
647	C₇×D₄	—	4	4	no	—
648	C₇×D₄	—	4	2	no	—
649	C₇×D₄	—	4	2	no	—
650	C₇×D₄	—	8	2	no	—
651	C₇×D₄	—	8	2	no	—
652	C₇×D₄	—	8	2	no	—
653	C₇×D₄	—	8	2	no	—
654	C₇×D₄	C₂×#41	1	2	yes	—
655	C₂×C₄×C₇	—	2	1	no	—
656	C₂×C₄×C₇	—	2	4	no	—
657	C₂×C₄×C₇	—	2	2	no	—
658	C₂×C₄×C₇	—	2	2	no	—
659	C₂×C₄×C₇	—	2	2	no	—
660	C₂×C₄×C₇	—	2	2	no	—
661	C₂×C₄×C₇	—	2	1	no	—
662	C₂×C₄×C₇	—	2	1	no	—
663	C₂×C₄×C₇	—	2	1	no	—
664	C₂×C₄×C₇	—	2	1	no	—
665	C₂×C₄×C₇	—	2	1	no	—
666	C₂×C₄×C₇	—	2	2	no	—
667	C₂×C₄×C₇	—	2	2	no	—
668	C₂×C₄×C₇	—	2	2	no	—
669	C₂×C₄×C₇	—	4	1	no	—
670	C₂×C₄×C₇	—	4	1	no	—
671	C₂×C₄×C₇	—	4	4	no	—
672	C₂×C₄×C₇	—	4	4	no	—
673	C₂×C₄×C₇	—	4	4	no	—
674	C₂×C₄×C₇	—	4	2	no	—
675	C₂×C₄×C₇	—	4	2	no	—
676	C₂×C₄×C₇	—	8	1	no	—
677	C₂×C₄×C₇	—	8	1	no	—
678	C₂×C₄×C₇	—	8	1	no	—
679	C₂×C₄×C₇	—	8	1	no	—
680	C₂×C₄×C₇	—	8	2	no	—
681	C₂×C₄×C₇	—	8	2	no	—
682	C₂×C₄×C₇	—	8	1	no	—
683	C₂×C₄×C₇	—	8	1	no	—
684	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
685	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
686	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
687	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
688	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
689	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
690	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
691	C₂×C₄×C₇	C₂×#41	1	2	yes	—
692	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
693	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
694	C₇×C₈	—	2	1	no	—
695	C₇×C₈	—	2	1	no	—
696	C₇×C₈	—	2	1	no	—
697	C₇×C₈	—	2	1	no	—
698	C₇×C₈	—	2	2	no	—
699	C₇×C₈	—	2	2	no	—
700	2₋¹⁺⁴	—	2	4	no	—
701	2₋¹⁺⁴	—	4	2	no	—
702	H(5,𝔽₂)	—	2	4	no	—
703	H(5,𝔽₂)	—	4	2	no	—
704	C₂×#41	—	2	1	no	—
705	C₂×#41	—	2	1	no	—
706	C₂×#41	—	2	2	no	—
707	C₂×#41	C₂³×C₇	1	1	yes	characteristic
708	C₂×#41	C₂³×C₇	1	2	yes	—
709	C₂×#41	C₂³×C₇	1	2	yes	—
710	C₂×#41	C₂³×C₇	1	1	yes	characteristic
711	C₂×#41	C₂³×C₇	1	1	yes	characteristic
712	C₂×#41	C₂³×C₇	1	1	yes	characteristic
713	C₂²×Q₈	—	2	1	no	—
714	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
715	C₂²×Q₈	C₂³×C₇	1	2	yes	—
716	C₂²×D₄	—	2	1	no	—
717	C₂²×D₄	—	2	2	no	—
718	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
719	C₂²×D₄	C₂³×C₇	1	2	yes	—
720	#137	—	4	2	no	—
721	AGL(1,ℤ/8)	—	4	2	no	—
722	#135	—	2	4	no	—
723	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
724	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
726	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
727	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
729	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
730	C₂×D₈	C₂³×C₇	1	2	yes	—
731	#131	—	4	2	no	—
732	#131	—	4	2	no	—
733	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
734	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
735	C₂×M₁₆	C₂³×C₇	1	2	yes	—
736	C₂×M₁₆	C₂³×C₇	1	2	yes	—
737	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
738	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
739	C₂²×C₈	C₂³×C₇	1	2	yes	—
740	C₂²×C₈	C₂³×C₇	1	2	yes	—
741	C₄⋊Q₈	—	2	1	no	—
742	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
743	#127	—	2	1	no	—
744	#127	C₇×D₄	1	1	yes	characteristic
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#125	—	2	2	no	—
750	#125	—	2	2	no	—
751	#125	—	2	1	no	—
752	#125	—	2	1	no	—
753	#125	C₂³×C₇	1	2	yes	—
754	#125	C₂³×C₇	1	2	yes	—
755	#124	—	2	1	no	—
756	#124	—	2	1	no	—
757	#124	—	2	2	no	—
758	#124	—	2	2	no	—
759	#124	—	2	1	no	—
760	#124	—	2	1	no	—
761	#124	C₇×D₄	1	1	yes	characteristic
762	#124	C₇×D₄	1	1	yes	characteristic
763	#124	C₂³×C₇	1	2	yes	—
764	#124	C₂³×C₇	1	2	yes	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	—	2	1	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
779	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
780	#121	—	2	1	no	—
781	#121	—	2	1	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	C₇×D₄	1	2	yes	—
791	#121	C₇×D₄	1	2	yes	—
792	#121	C₂³×C₇	1	2	yes	—
793	#121	C₂³×C₇	1	2	yes	—
794	#121	C₂³×C₇	1	2	yes	—
795	#121	C₂³×C₇	1	2	yes	—
796	#120	—	2	2	no	—
797	#120	—	2	2	no	—
798	#120	—	2	2	no	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
803	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
804	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₇	1	2	yes	—
822	C₄×D₄	C₂³×C₇	1	2	yes	—
823	#117	—	2	2	no	—
824	#117	—	2	2	no	—
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	C₂³×C₇	1	1	yes	characteristic
828	#117	C₂³×C₇	1	1	yes	characteristic
829	#117	C₂³×C₇	1	2	yes	—
830	#117	C₂³×C₇	1	2	yes	—
831	C₂×C₄⋊C₄	—	2	1	no	—
832	C₂×C₄⋊C₄	—	2	1	no	—
833	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
834	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
835	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
836	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
837	C₂×C₂²⋊C₄	—	2	1	no	—
838	C₂×C₂²⋊C₄	—	2	1	no	—
839	C₂×C₂²⋊C₄	—	2	2	no	—
840	C₂×C₂²⋊C₄	—	2	2	no	—
841	C₂×C₄²	—	2	1	no	—
842	C₂×C₄²	—	2	1	no	—
843	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
844	#107	C₂³×C₇	1	1	yes	characteristic
845	#107	C₂³×C₇	1	1	yes	characteristic
846	#107	C₂³×C₇	1	2	yes	—
847	#107	C₂³×C₇	1	2	yes	—
848	#106	C₂³×C₇	1	1	yes	characteristic
849	#106	C₂³×C₇	1	1	yes	characteristic
850	#106	C₂³×C₇	1	2	yes	—
851	#106	C₂³×C₇	1	2	yes	—
852	C₄⋊C₈	C₂³×C₇	1	2	yes	—
853	C₄⋊C₈	C₂³×C₇	1	2	yes	—
854	#103	C₂³×C₇	1	1	yes	characteristic
855	#103	C₂³×C₇	1	2	yes	—
856	#103	C₂³×C₇	1	2	yes	—
857	#103	C₂³×C₇	1	2	yes	—
858	#103	C₂³×C₇	1	2	yes	—
859	#103	C₂³×C₇	1	2	yes	—
860	#103	C₂³×C₇	1	2	yes	—
861	#103	C₂³×C₇	1	1	yes	characteristic
862	#103	C₂³×C₇	1	2	yes	—
863	#103	C₂³×C₇	1	2	yes	—
864	#103	C₂³×C₇	1	1	yes	characteristic
865	#103	C₂³×C₇	1	1	yes	characteristic
866	#102	C₂³×C₇	1	1	yes	characteristic
867	#102	C₂³×C₇	1	2	yes	—
868	#102	C₂³×C₇	1	2	yes	—
869	#102	C₂³×C₇	1	2	yes	—
870	#102	C₂³×C₇	1	2	yes	—
871	#102	C₂³×C₇	1	2	yes	—
872	#102	C₂³×C₇	1	2	yes	—
873	#102	C₂³×C₇	1	1	yes	characteristic
874	#102	C₂³×C₇	1	2	yes	—
875	#102	C₂³×C₇	1	2	yes	—
876	#102	C₂³×C₇	1	1	yes	characteristic
877	#102	C₂³×C₇	1	1	yes	characteristic
878	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
882	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
885	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
886	C₂²×C₇	—	2	1	no	—
887	C₂²×C₇	—	2	1	no	—
888	C₂²×C₇	—	2	2	no	—
889	C₂²×C₇	—	2	2	no	—
890	C₂²×C₇	—	2	2	no	—
891	C₂²×C₇	—	2	2	no	—
892	C₂²×C₇	—	2	2	no	—
893	C₂²×C₇	—	2	2	no	—
894	C₂²×C₇	—	2	2	no	—
895	C₂²×C₇	—	4	1	no	—
896	C₂²×C₇	—	4	1	no	—
897	C₂²×C₇	—	4	1	no	—
898	C₂²×C₇	—	4	1	no	—
899	C₂²×C₇	—	4	2	no	—
900	C₂²×C₇	—	4	2	no	—
901	C₂²×C₇	—	4	2	no	—
902	C₂²×C₇	—	4	1	no	—
903	C₂²×C₇	—	16	2	no	—
904	C₂²×C₇	—	16	4	no	—
905	C₂²×C₇	#546	1	2	yes	—
906	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
907	C₄×C₇	—	2	1	no	—
908	C₄×C₇	—	2	1	no	—
909	C₄×C₇	—	2	1	no	—
910	C₄×C₇	—	2	1	no	—
911	C₄×C₇	—	2	2	no	—
912	C₄×C₇	—	2	2	no	—
913	C₄×C₇	—	2	2	no	—
914	C₄×C₇	—	4	1	no	—
915	C₄×C₇	—	4	1	no	—
916	C₄×C₇	—	4	2	no	—
917	C₄×C₇	—	4	2	no	—
918	C₄×C₇	—	4	1	no	—
919	C₄×C₇	—	4	1	no	—
920	C₄×C₇	—	4	2	no	—
921	C₄×C₇	—	4	1	no	—
922	C₄×C₇	#546	1	2	yes	—
923	C₄×C₇	C₂²×#41	1	1	yes	characteristic
924	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
925	C₂⁴	—	2	2	no	—
926	C₂⁴	—	2	1	no	—
927	#41	—	2	2	no	—
928	#41	—	2	2	no	—
929	#41	—	2	2	no	—
930	#41	—	2	2	no	—
931	#41	—	2	2	no	—
932	#41	—	2	4	no	—
933	#41	—	2	4	no	—
934	#41	—	2	2	no	—
935	#41	—	2	2	no	—
936	#41	—	4	2	no	—
937	#41	—	4	2	no	—
938	#41	—	4	4	no	—
939	#41	—	4	4	no	—
940	#41	—	4	8	no	—
941	#41	C₇×#41	1	4	yes	—
942	C₂×Q₈	—	2	2	no	—
943	C₂×Q₈	—	2	1	no	—
944	C₂×Q₈	—	2	4	no	—
945	C₂×Q₈	—	2	2	no	—
946	C₂×Q₈	—	2	2	no	—
947	C₂×Q₈	—	4	2	no	—
948	C₂×Q₈	—	4	4	no	—
949	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
950	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
951	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
952	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
953	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
954	C₂×D₄	—	2	1	no	—
955	C₂×D₄	—	2	4	no	—
956	C₂×D₄	—	2	1	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	2	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	1	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	4	2	no	—
968	C₂×D₄	—	4	4	no	—
969	C₂×D₄	—	4	8	no	—
970	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
971	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
972	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
973	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
974	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
975	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
976	C₂×D₄	C₂⁴×C₇	1	2	yes	—
977	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
978	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	1	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	1	no	—
991	C₂²×C₄	—	2	1	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
994	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
995	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
996	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
997	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
998	Q₁₆	—	2	2	no	—
999	Q₁₆	—	4	2	no	—
1000	SD₁₆	—	2	2	no	—
1001	SD₁₆	—	2	2	no	—
1002	SD₁₆	—	4	2	no	—
1003	SD₁₆	—	4	2	no	—
1004	D₈	—	2	2	no	—
1005	D₈	—	4	2	no	—
1006	M₁₆	—	2	2	no	—
1007	M₁₆	—	2	2	no	—
1008	M₁₆	—	4	2	no	—
1009	M₁₆	—	4	2	no	—
1010	C₂×C₈	—	2	2	no	—
1011	C₂×C₈	—	2	2	no	—
1012	C₂×C₈	—	4	2	no	—
1013	C₂×C₈	—	4	2	no	—
1014	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1015	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1016	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1017	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1018	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1019	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	—	2	1	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1037	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1038	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1039	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1040	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1041	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1042	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1043	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1065	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1066	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1067	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1068	C₄²	—	2	1	no	—
1069	C₄²	—	2	1	no	—
1070	C₄²	—	2	1	no	—
1071	C₄²	—	2	1	no	—
1072	C₄²	—	2	1	no	—
1073	C₄²	—	2	1	no	—
1074	C₄²	—	2	2	no	—
1075	C₄²	—	2	2	no	—
1076	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1077	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1078	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1079	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1080	C₂×C₇	—	2	2	no	—
1081	C₂×C₇	—	4	2	no	—
1082	C₂×C₇	—	4	2	no	—
1083	C₂×C₇	—	4	2	no	—
1084	C₂×C₇	—	8	1	no	—
1085	C₂×C₇	—	8	2	no	—
1086	C₂×C₇	C₂×#546	1	1	yes	characteristic
1087	C₂×C₇	#3584	1	1	yes	characteristic
1088	C₂×C₇	#3584	1	1	yes	characteristic
1089	C₂³	—	2	1	no	—
1090	C₂³	—	2	1	no	—
1091	C₂³	—	2	2	no	—
1092	C₂³	—	4	4	no	—
1093	C₂³	—	4	2	no	—
1094	C₂³	—	8	1	no	—
1095	C₂³	—	8	1	no	—
1096	C₂³	—	8	2	no	—
1097	C₂³	—	8	2	no	—
1098	C₂³	C₂²×C₇×D₄	1	2	yes	—
1099	C₂³	C₂²×C₇×D₄	1	2	yes	—
1100	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1101	Q₈	—	2	1	no	—
1102	Q₈	—	2	2	no	—
1103	Q₈	—	2	2	no	—
1104	Q₈	—	2	1	no	—
1105	Q₈	—	2	2	no	—
1106	Q₈	—	2	1	no	—
1107	Q₈	—	2	2	no	—
1108	Q₈	—	4	4	no	—
1109	Q₈	—	4	2	no	—
1110	Q₈	C₂×C₇×#41	1	2	yes	—
1111	D₄	—	2	4	no	—
1112	D₄	—	2	4	no	—
1113	D₄	—	2	4	no	—
1114	D₄	—	2	1	no	—
1115	D₄	—	2	2	no	—
1116	D₄	—	2	1	no	—
1117	D₄	—	2	1	no	—
1118	D₄	—	2	2	no	—
1119	D₄	—	2	2	no	—
1120	D₄	—	2	2	no	—
1121	D₄	—	4	2	no	—
1122	D₄	—	4	2	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	4	no	—
1125	D₄	—	4	4	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	8	2	no	—
1129	D₄	—	8	2	no	—
1130	D₄	—	8	2	no	—
1131	D₄	—	8	2	no	—
1132	D₄	C₂×C₇×#41	1	2	yes	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	4	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	4	no	—
1150	C₂×C₄	—	4	4	no	—
1151	C₂×C₄	—	4	4	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	8	1	no	—
1155	C₂×C₄	—	8	1	no	—
1156	C₂×C₄	—	8	1	no	—
1157	C₂×C₄	—	8	1	no	—
1158	C₂×C₄	—	8	2	no	—
1159	C₂×C₄	—	8	2	no	—
1160	C₂×C₄	—	8	1	no	—
1161	C₂×C₄	—	8	1	no	—
1162	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1163	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1164	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1165	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1166	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1167	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1168	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1169	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1170	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1171	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1172	C₈	—	2	1	no	—
1173	C₈	—	2	1	no	—
1174	C₈	—	2	1	no	—
1175	C₈	—	2	1	no	—
1176	C₈	—	2	2	no	—
1177	C₈	—	2	2	no	—
1178	C₇	#61216	1	1	yes	characteristic, direct product factor, Sylow
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	2	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	2	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	16	2	no	—
1197	C₂²	—	16	4	no	—
1198	C₂²	C₇×#546	1	2	yes	—
1199	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1200	C₄	—	2	1	no	—
1201	C₄	—	2	1	no	—
1202	C₄	—	2	1	no	—
1203	C₄	—	2	1	no	—
1204	C₄	—	2	2	no	—
1205	C₄	—	2	2	no	—
1206	C₄	—	2	2	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	2	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	1	no	—
1213	C₄	—	4	2	no	—
1214	C₄	—	4	1	no	—
1215	C₄	C₇×#546	1	2	yes	—
1216	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1217	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1218	C₂	—	2	2	no	—
1219	C₂	—	4	2	no	—
1220	C₂	—	4	2	no	—
1221	C₂	—	4	2	no	—
1222	C₂	—	8	2	no	—
1223	C₂	—	8	1	no	—
1224	C₂	C₂×C₇×#546	1	1	yes	characteristic
1225	C₂	C₇×#3584	1	1	yes	characteristic
1226	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3512	C₂	semidirect
2. C₇×#3500	C₂	semidirect
3. C₇×#3327	C₂	semidirect
4. C₇×#3326	C₂	semidirect
5. C₇×#3323	C₂	semidirect
6. C₇×#3322	C₂	semidirect
7. C₇×#3301	C₂	semidirect
8. C₇×#3300	C₂	semidirect
9. C₇×#3297	C₂	semidirect
10. C₇×#3296	C₂	semidirect
11. C₂×C₇×#488	C₂	semidirect
12. C₇×#3097	C₂	semidirect
13. C₇×#3096	C₂	semidirect
14. C₇×#3080	C₂	semidirect
15. C₇×#3063	C₂	semidirect
16. C₇×#3062	C₂	semidirect
17. C₇×#3040	C₂	semidirect
18. C₇×#3013	C₂	semidirect
19. C₇×#3012	C₂	semidirect
20. C₄×C₇×#135	C₂	semidirect
21. C₇×#2931	C₂	semidirect
22. C₇×#2898	C₂	semidirect
23. C₇×#2897	C₂	semidirect
26. C₂×C₇×#137	C₂²	semidirect
30. C₂×C₇×#131	C₂²	semidirect
33. C₇×#553	C₂²	semidirect
34. C₇×#553	C₂²	semidirect
35. C₇×#552	C₂²	semidirect
36. C₇×#552	C₂²	semidirect
46. C₇×#537	C₂²	semidirect
55. C₂×C₇×#125	C₂²	semidirect
59. C₇×#520	C₂²	semidirect
61. C₄×C₇×#41	C₂²	semidirect
62. C₇×#488	C₂²	semidirect
63. C₇×#488	C₂²	semidirect
64. C₇×#488	C₂²	semidirect
65. C₇×#488	C₂²	semidirect
66. C₇×#485	C₂²	semidirect
67. C₇×#485	C₂²	semidirect
68. C₇×#484	C₂²	semidirect
69. C₇×#483	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×#478	C₂²	semidirect
77. C₇×#478	C₂²	semidirect
78. C₇×#470	C₂²	semidirect
79. C₇×#469	C₂²	semidirect
80. C₇×#468	C₂²	semidirect
81. C₇×#468	C₂²	semidirect
82. C₇×#467	C₂²	semidirect
83. C₇×#466	C₂²	semidirect
84. C₇×#465	C₂²	semidirect
85. C₇×#465	C₂²	semidirect
86. C₇×#464	C₂²	semidirect
87. C₇×#464	C₂²	semidirect
88. C₇×#463	C₂²	semidirect
89. C₇×#463	C₂²	semidirect
91. C₇×#452	C₂²	semidirect
92. C₇×#451	C₂²	semidirect
95. C₇×#449	C₂²	semidirect
96. C₇×#448	C₂²	semidirect
98. C₄×C₇×Q₁₆	C₂²	semidirect
99. C₄×C₇×Q₁₆	C₂²	semidirect
100. C₄×C₇×SD₁₆	C₂²	semidirect
101. C₄×C₇×SD₁₆	C₂²	semidirect
102. C₄×C₇×SD₁₆	C₂²	semidirect
103. C₄×C₇×SD₁₆	C₂²	semidirect
104. C₄×C₇×D₈	C₂²	semidirect
105. C₄×C₇×D₈	C₂²	semidirect
106. C₇×#436	C₂²	semidirect
107. C₇×#436	C₂²	semidirect
108. C₇×C₈×D₄	C₂²	semidirect
109. C₇×C₈×D₄	C₂²	semidirect
110. C₇×#428	C₂²	semidirect
111. C₇×#428	C₂²	semidirect
112. C₇×#427	C₂²	semidirect
113. C₇×#423	C₂²	semidirect
114. C₇×#419	C₂²	semidirect
115. C₇×#419	C₂²	semidirect
121. C₇×#417	C₂²	semidirect
124. C₇×#416	C₂²	semidirect
125. C₇×#416	C₂²	semidirect
126. C₂×C₇×#103	C₂²	semidirect
127. C₂×C₇×#103	C₂²	semidirect
128. C₂×C₇×#103	C₂²	semidirect
133. C₇×#408	C₂²	semidirect
134. C₂×C₄×C₇×C₈	C₂²	semidirect
135. #61216	C₇	direct (N × H)
322. #3512	C₂×C₇	semidirect
323. #3500	C₂×C₇	semidirect
324. #3327	C₂×C₇	semidirect
325. #3326	C₂×C₇	semidirect
326. #3323	C₂×C₇	semidirect
327. #3322	C₂×C₇	semidirect
328. #3301	C₂×C₇	semidirect
329. #3300	C₂×C₇	semidirect
330. #3297	C₂×C₇	semidirect
331. #3296	C₂×C₇	semidirect
332. C₂×#488	C₂×C₇	semidirect
333. #3097	C₂×C₇	semidirect
334. #3096	C₂×C₇	semidirect
335. #3080	C₂×C₇	semidirect
336. #3063	C₂×C₇	semidirect
337. #3062	C₂×C₇	semidirect
338. #3040	C₂×C₇	semidirect
339. #3013	C₂×C₇	semidirect
340. #3012	C₂×C₇	semidirect
341. C₄×#135	C₂×C₇	semidirect
342. #2931	C₂×C₇	semidirect
343. #2898	C₂×C₇	semidirect
344. #2897	C₂×C₇	semidirect
502. C₂×#137	C₂²×C₇	semidirect
506. C₂×#131	C₂²×C₇	semidirect
509. #553	C₂²×C₇	semidirect
510. #553	C₂²×C₇	semidirect
511. #552	C₂²×C₇	semidirect
512. #552	C₂²×C₇	semidirect
522. #537	C₂²×C₇	semidirect
531. C₂×#125	C₂²×C₇	semidirect
535. #520	C₂²×C₇	semidirect
537. C₄×#41	C₂²×C₇	semidirect
538. #488	C₂²×C₇	semidirect
539. #488	C₂²×C₇	semidirect
540. #488	C₂²×C₇	semidirect
541. #488	C₂²×C₇	semidirect
542. #485	C₂²×C₇	semidirect
543. #485	C₂²×C₇	semidirect
544. #484	C₂²×C₇	semidirect
545. #483	C₂²×C₇	semidirect
546. #482	C₂²×C₇	semidirect
547. #482	C₂²×C₇	semidirect
548. #481	C₂²×C₇	semidirect
549. #480	C₂²×C₇	semidirect
550. #479	C₂²×C₇	semidirect
551. #479	C₂²×C₇	semidirect
552. #478	C₂²×C₇	semidirect
553. #478	C₂²×C₇	semidirect
554. #470	C₂²×C₇	semidirect
555. #469	C₂²×C₇	semidirect
556. #468	C₂²×C₇	semidirect
557. #468	C₂²×C₇	semidirect
558. #467	C₂²×C₇	semidirect
559. #466	C₂²×C₇	semidirect
560. #465	C₂²×C₇	semidirect
561. #465	C₂²×C₇	semidirect
562. #464	C₂²×C₇	semidirect
563. #464	C₂²×C₇	semidirect
564. #463	C₂²×C₇	semidirect
565. #463	C₂²×C₇	semidirect
567. #452	C₂²×C₇	semidirect
568. #451	C₂²×C₇	semidirect
571. #449	C₂²×C₇	semidirect
572. #448	C₂²×C₇	semidirect
574. C₄×Q₁₆	C₂²×C₇	semidirect
575. C₄×Q₁₆	C₂²×C₇	semidirect
576. C₄×SD₁₆	C₂²×C₇	semidirect
577. C₄×SD₁₆	C₂²×C₇	semidirect
578. C₄×SD₁₆	C₂²×C₇	semidirect
579. C₄×SD₁₆	C₂²×C₇	semidirect
580. C₄×D₈	C₂²×C₇	semidirect
581. C₄×D₈	C₂²×C₇	semidirect
582. #436	C₂²×C₇	semidirect
583. #436	C₂²×C₇	semidirect
584. C₈×D₄	C₂²×C₇	semidirect
585. C₈×D₄	C₂²×C₇	semidirect
586. #428	C₂²×C₇	semidirect
587. #428	C₂²×C₇	semidirect
588. #427	C₂²×C₇	semidirect
589. #423	C₂²×C₇	semidirect
590. #419	C₂²×C₇	semidirect
591. #419	C₂²×C₇	semidirect
597. #417	C₂²×C₇	semidirect
600. #416	C₂²×C₇	semidirect
601. #416	C₂²×C₇	semidirect
602. C₂×#103	C₂²×C₇	semidirect
603. C₂×#103	C₂²×C₇	semidirect
604. C₂×#103	C₂²×C₇	semidirect
609. #408	C₂²×C₇	semidirect
610. C₂×C₄×C₈	C₂²×C₇	semidirect
1178. C₇	#61216	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×#3512	2
C₇×#3500	2
C₇×#3327	2
C₇×#3326	2
C₇×#3323	2
C₇×#3322	2
C₇×#3301	2
C₇×#3300	2
C₇×#3297	2
C₇×#3296	2
C₂×C₇×#488	2
C₇×#3097	2
C₇×#3096	2
C₇×#3080	2
C₇×#3063	2
C₇×#3062	2
C₇×#3040	2
C₇×#3013	2
C₇×#3012	2
C₄×C₇×#135	2
C₇×#2931	2
C₇×#2898	2
C₇×#2897	2
#61216	7

Subgroups — C7×#61216 #13238432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61216 #13238432