Subgroups — C₇×#61204 #13238420

Order 1792.

2032 conjugacy classes of subgroups.

The subgroup lattice has 1226 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×#3497	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×#3320	C₂	1	2	yes	maximal, complemented
6	C₇×#3317	C₂	1	2	yes	maximal, complemented
7	C₇×#3312	C₂	1	2	yes	maximal, complemented
8	C₇×#3309	C₂	1	2	yes	maximal, complemented
9	C₇×#3301	C₂	1	2	yes	maximal, complemented
10	C₇×#3300	C₂	1	2	yes	maximal, complemented
11	C₇×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#479	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3061	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3060	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
26	C₂×C₇×#137	C₂²	1	1	yes	characteristic
27	C₂×C₇×#135	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
31	C₇×#553	—	2	2	no	—
32	C₇×#553	—	2	2	no	—
33	C₇×#553	C₂²	1	2	yes	—
34	C₇×#553	C₂²	1	2	yes	—
35	C₇×#552	C₂²	1	2	yes	—
36	C₇×#552	C₂²	1	2	yes	—
37	C₇×#550	—	2	1	no	—
38	C₇×#550	C₂²	1	2	yes	—
39	C₇×D₄×Q₈	—	2	1	no	—
40	C₇×D₄×Q₈	C₂²	1	2	yes	—
41	C₇×#548	—	2	1	no	—
42	C₇×#548	—	2	1	no	—
43	C₇×#548	C₂²	1	2	yes	—
44	C₇×#548	C₂²	1	2	yes	—
45	C₇×#541	—	2	1	no	—
46	C₇×#540	—	2	1	no	—
47	C₇×#537	—	2	2	no	—
48	C₇×#537	C₂²	1	1	yes	characteristic
49	C₇×#537	C₂²	1	1	yes	characteristic
50	C₇×#537	C₂²	1	1	yes	characteristic
51	C₇×#537	C₂²	1	1	yes	characteristic
52	C₇×#532	—	2	2	no	—
53	C₇×#532	C₂²	1	1	yes	characteristic
54	C₇×#532	C₂²	1	1	yes	characteristic
55	C₇×#529	—	2	1	no	—
56	C₇×#529	—	2	1	no	—
57	C₂×C₇×#125	C₂²	1	1	yes	characteristic
58	C₇×#520	C₂²	1	1	yes	characteristic
59	C₇×#520	C₂²	1	1	yes	characteristic
60	C₄×C₇×#41	C₂²	1	1	yes	characteristic
61	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
62	C₇×#491	C₂²	1	2	yes	—
63	C₇×#490	C₂²	1	2	yes	—
64	C₇×#488	C₂²	1	2	yes	—
65	C₇×#488	C₂²	1	2	yes	—
66	C₇×#485	C₂²	1	2	yes	—
67	C₇×#485	C₂²	1	2	yes	—
68	C₇×#484	C₂²	1	2	yes	—
69	C₇×#483	C₂²	1	2	yes	—
70	C₇×#482	C₂²	1	2	yes	—
71	C₇×#482	C₂²	1	2	yes	—
72	C₇×#481	C₂²	1	2	yes	—
73	C₇×#480	C₂²	1	2	yes	—
74	C₇×#479	C₂²	1	2	yes	—
75	C₇×#479	C₂²	1	2	yes	—
76	C₇×#479	C₂²	1	2	yes	—
77	C₇×#479	C₂²	1	2	yes	—
78	C₇×#470	C₂²	1	2	yes	—
79	C₇×#469	C₂²	1	2	yes	—
80	C₇×#468	C₂²	1	2	yes	—
81	C₇×#468	C₂²	1	2	yes	—
82	C₇×#467	C₂²	1	2	yes	—
83	C₇×#466	C₂²	1	2	yes	—
84	C₇×#465	C₂²	1	2	yes	—
85	C₇×#465	C₂²	1	2	yes	—
86	C₇×#464	C₂²	1	1	yes	characteristic
87	C₇×#464	C₂²	1	1	yes	characteristic
88	C₇×#463	C₂²	1	1	yes	characteristic
89	C₇×#463	C₂²	1	1	yes	characteristic
90	C₇×#462	C₂²	1	1	yes	characteristic
91	C₇×#461	C₂²	1	1	yes	characteristic
92	C₇×#460	C₂²	1	1	yes	characteristic
93	C₇×#459	C₂²	1	1	yes	characteristic
94	C₇×#452	C₂²	1	2	yes	—
95	C₇×#452	C₂²	1	2	yes	—
96	C₇×#451	C₂²	1	2	yes	—
97	C₇×#451	C₂²	1	2	yes	—
98	C₇×#449	C₂²	1	2	yes	—
99	C₇×#449	C₂²	1	2	yes	—
100	C₇×#448	C₂²	1	2	yes	—
101	C₇×#448	C₂²	1	2	yes	—
102	C₇×#441	C₂²	1	2	yes	—
103	C₇×#440	C₂²	1	2	yes	—
104	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
105	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
106	C₇×#436	C₂²	1	2	yes	—
107	C₇×#435	C₂²	1	2	yes	—
108	C₇×#435	C₂²	1	2	yes	—
109	C₇×C₈×D₄	C₂²	1	2	yes	—
110	C₇×#428	C₂²	1	1	yes	characteristic
111	C₂×C₇×#107	C₂²	1	1	yes	characteristic
112	C₂×C₇×#106	C₂²	1	1	yes	characteristic
113	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
114	C₇×#419	C₂²	1	1	yes	characteristic
115	C₇×#419	C₂²	1	2	yes	—
116	C₇×#419	C₂²	1	2	yes	—
117	C₇×#417	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
122	C₇×#417	C₂²	1	1	yes	characteristic
123	C₇×#417	C₂²	1	2	yes	—
124	C₇×#416	C₂²	1	1	yes	characteristic
125	C₇×#416	C₂²	1	1	yes	characteristic
126	C₇×#416	C₂²	1	2	yes	—
127	C₇×#416	C₂²	1	2	yes	—
128	C₂×C₇×#103	C₂²	1	1	yes	characteristic
129	C₂×C₇×#103	C₂²	1	1	yes	characteristic
130	C₂×C₇×#103	C₂²	1	2	yes	—
131	C₂×C₇×#103	C₂²	1	2	yes	—
132	C₇×#408	C₂²	1	1	yes	characteristic
133	C₇×#408	C₂²	1	1	yes	characteristic
134	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
135	#61204	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₇×2₋¹⁺⁴	—	2	4	no	—
137	C₇×2₋¹⁺⁴	—	2	4	no	—
138	C₇×2₋¹⁺⁴	—	4	2	no	—
139	C₇×2₋¹⁺⁴	—	4	2	no	—
140	C₂×C₇×#41	—	2	2	no	—
141	C₂×C₇×#41	—	2	2	no	—
142	C₂×C₇×#41	—	2	1	no	—
143	C₂×C₇×#41	—	2	1	no	—
144	C₂×C₇×#41	C₂³	1	1	yes	characteristic
145	C₂×C₇×#41	C₂³	1	1	yes	characteristic
146	C₂×C₇×#41	C₂³	1	1	yes	characteristic
147	C₂×C₇×#41	C₂³	1	2	yes	—
148	C₂×C₇×#41	C₂³	1	2	yes	—
149	C₂×C₇×#41	C₂³	1	1	yes	characteristic
150	C₂×C₇×#41	C₂³	1	1	yes	characteristic
151	C₂²×C₇×Q₈	—	2	1	no	—
152	C₂²×C₇×Q₈	—	2	1	no	—
153	C₂²×C₇×Q₈	C₂³	1	2	yes	—
154	C₂²×C₇×Q₈	C₂³	1	2	yes	—
155	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
156	C₇×#137	—	2	4	no	—
157	C₇×#135	—	4	2	no	—
158	C₇×#135	—	4	2	no	—
159	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
160	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
161	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
162	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
163	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
164	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
166	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
167	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
168	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
169	C₇×#131	—	4	2	no	—
170	C₇×#131	—	4	2	no	—
171	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
172	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
173	C₂×C₇×M₁₆	C₂³	1	2	yes	—
174	C₂×C₇×M₁₆	C₂³	1	2	yes	—
175	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
176	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
177	C₂²×C₇×C₈	C₂³	1	2	yes	—
178	C₂²×C₇×C₈	C₂³	1	2	yes	—
179	C₇×C₄⋊Q₈	—	2	2	no	—
180	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
181	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
182	C₇×#127	—	2	2	no	—
183	C₇×#127	D₄	1	1	yes	characteristic
184	C₇×#127	C₂³	1	1	yes	characteristic
185	C₇×#126	—	2	2	no	—
186	C₇×#126	—	2	2	no	—
187	C₇×#126	—	2	2	no	—
188	C₇×#126	—	2	2	no	—
189	C₇×#125	—	2	2	no	—
190	C₇×#125	—	2	2	no	—
191	C₇×#125	—	2	1	no	—
192	C₇×#125	—	2	1	no	—
193	C₇×#125	C₂³	1	2	yes	—
194	C₇×#125	C₂³	1	2	yes	—
195	C₇×#124	—	2	2	no	—
196	C₇×#124	—	2	2	no	—
197	C₇×#124	D₄	1	1	yes	characteristic
198	C₇×#124	D₄	1	1	yes	characteristic
199	C₇×#124	C₂³	1	1	yes	characteristic
200	C₇×#124	C₂³	1	1	yes	characteristic
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×C₂²⋊Q₈	—	2	1	no	—
206	C₇×C₂²⋊Q₈	—	2	1	no	—
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	C₂³	1	2	yes	—
214	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
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	2	no	—
222	C₇×#121	—	2	2	no	—
223	C₇×#121	—	2	1	no	—
224	C₇×#121	—	2	1	no	—
225	C₇×#121	—	2	2	no	—
226	C₇×#121	—	2	2	no	—
227	C₇×#121	—	2	2	no	—
228	C₇×#121	—	2	2	no	—
229	C₇×#121	—	2	1	no	—
230	C₇×#121	—	2	1	no	—
231	C₇×#121	—	2	2	no	—
232	C₇×#121	—	2	2	no	—
233	C₇×#121	D₄	1	2	yes	—
234	C₇×#121	D₄	1	2	yes	—
235	C₇×#121	C₂³	1	2	yes	—
236	C₇×#121	C₂³	1	2	yes	—
237	C₇×#121	C₂³	1	2	yes	—
238	C₇×#121	C₂³	1	2	yes	—
239	C₄×C₇×Q₈	—	2	1	no	—
240	C₄×C₇×Q₈	—	2	1	no	—
241	C₄×C₇×Q₈	—	2	1	no	—
242	C₄×C₇×Q₈	—	2	1	no	—
243	C₄×C₇×Q₈	C₂³	1	2	yes	—
244	C₄×C₇×Q₈	C₂³	1	2	yes	—
245	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
246	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
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	1	no	—
253	C₄×C₇×D₄	—	2	1	no	—
254	C₄×C₇×D₄	—	2	2	no	—
255	C₄×C₇×D₄	—	2	2	no	—
256	C₄×C₇×D₄	—	2	2	no	—
257	C₄×C₇×D₄	—	2	2	no	—
258	C₄×C₇×D₄	—	2	2	no	—
259	C₄×C₇×D₄	—	2	1	no	—
260	C₄×C₇×D₄	—	2	1	no	—
261	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
262	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
263	C₄×C₇×D₄	C₂³	1	2	yes	—
264	C₄×C₇×D₄	C₂³	1	2	yes	—
265	C₇×#117	—	2	2	no	—
266	C₇×#117	—	2	2	no	—
267	C₇×#117	—	2	1	no	—
268	C₇×#117	C₂³	1	2	yes	—
269	C₇×#117	C₂³	1	2	yes	—
270	C₇×#117	C₂³	1	1	yes	characteristic
271	C₂×C₇×C₄⋊C₄	—	2	1	no	—
272	C₂×C₇×C₄⋊C₄	—	2	1	no	—
273	C₂×C₇×C₄⋊C₄	—	2	1	no	—
274	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
275	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
276	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
278	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×C₄²×C₇	—	2	1	no	—
280	C₂×C₄²×C₇	—	2	1	no	—
281	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
282	C₇×#107	C₂³	1	2	yes	—
283	C₇×#107	C₂³	1	2	yes	—
284	C₇×#107	C₂³	1	2	yes	—
285	C₇×#106	C₂³	1	2	yes	—
286	C₇×#106	C₂³	1	2	yes	—
287	C₇×#106	C₂³	1	2	yes	—
288	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
289	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
290	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
292	C₇×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
300	C₇×#103	C₂³	1	2	yes	—
301	C₇×#103	C₂³	1	1	yes	characteristic
302	C₇×#103	C₂³	1	2	yes	—
303	C₇×#103	C₂³	1	1	yes	characteristic
304	C₇×#103	C₂³	1	1	yes	characteristic
305	C₇×#103	C₂³	1	2	yes	—
306	C₇×#103	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	1	yes	characteristic
311	C₇×#102	C₂³	1	2	yes	—
312	C₇×#102	C₂³	1	1	yes	characteristic
313	C₇×#102	C₂³	1	2	yes	—
314	C₇×#102	C₂³	1	1	yes	characteristic
315	C₇×#102	C₂³	1	1	yes	characteristic
316	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
320	C₇×#97	C₂³	1	2	yes	—
321	C₄×C₇×C₈	C₂³	1	2	yes	—
322	#3512	C₂×C₇	1	1	yes	characteristic, complemented
323	#3497	C₂×C₇	1	1	yes	characteristic, complemented
324	#3327	C₂×C₇	1	2	yes	complemented
325	#3326	C₂×C₇	1	2	yes	complemented
326	#3320	C₂×C₇	1	2	yes	complemented
327	#3317	C₂×C₇	1	2	yes	complemented
328	#3312	C₂×C₇	1	2	yes	complemented
329	#3309	C₂×C₇	1	2	yes	complemented
330	#3301	C₂×C₇	1	2	yes	complemented
331	#3300	C₂×C₇	1	2	yes	complemented
332	#3142	C₂×C₇	1	1	yes	characteristic, complemented
333	#3099	C₂×C₇	1	1	yes	characteristic, complemented
334	#3098	C₂×C₇	1	1	yes	characteristic, complemented
335	C₂×#479	C₂×C₇	1	1	yes	characteristic, complemented
336	#3061	C₂×C₇	1	1	yes	characteristic, complemented
337	#3060	C₂×C₇	1	1	yes	characteristic, complemented
338	#3035	C₂×C₇	1	1	yes	characteristic, complemented
339	#3013	C₂×C₇	1	1	yes	characteristic, complemented
340	#3013	C₂×C₇	1	1	yes	characteristic, complemented
341	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
342	#2935	C₂×C₇	1	1	yes	characteristic, complemented
343	#2898	C₂×C₇	1	1	yes	characteristic, complemented
344	#2898	C₂×C₇	1	1	yes	characteristic, complemented
345	C₇×#41	—	2	2	no	—
346	C₇×#41	—	2	2	no	—
347	C₇×#41	—	2	2	no	—
348	C₇×#41	—	2	2	no	—
349	C₇×#41	—	2	4	no	—
350	C₇×#41	—	2	4	no	—
351	C₇×#41	—	2	2	no	—
352	C₇×#41	—	2	2	no	—
353	C₇×#41	—	2	2	no	—
354	C₇×#41	—	2	2	no	—
355	C₇×#41	—	2	2	no	—
356	C₇×#41	—	2	2	no	—
357	C₇×#41	—	4	2	no	—
358	C₇×#41	—	4	2	no	—
359	C₇×#41	—	4	8	no	—
360	C₇×#41	—	4	8	no	—
361	C₇×#41	—	4	4	no	—
362	C₇×#41	—	4	4	no	—
363	C₂×C₇×Q₈	—	2	1	no	—
364	C₂×C₇×Q₈	—	2	2	no	—
365	C₂×C₇×Q₈	—	2	2	no	—
366	C₂×C₇×Q₈	—	2	2	no	—
367	C₂×C₇×Q₈	—	2	4	no	—
368	C₂×C₇×Q₈	—	2	4	no	—
369	C₂×C₇×Q₈	—	4	2	no	—
370	C₂×C₇×Q₈	—	4	2	no	—
371	C₂×C₇×Q₈	—	4	4	no	—
372	C₂×C₇×Q₈	—	4	4	no	—
373	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
374	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
375	C₂×C₇×Q₈	#41	1	4	yes	—
376	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
377	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
378	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
379	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
380	C₂×C₇×D₄	—	2	1	no	—
381	C₂×C₇×D₄	—	2	1	no	—
382	C₂×C₇×D₄	—	2	1	no	—
383	C₂×C₇×D₄	—	2	2	no	—
384	C₂×C₇×D₄	—	2	2	no	—
385	C₂×C₇×D₄	—	2	2	no	—
386	C₂×C₇×D₄	—	2	2	no	—
387	C₂×C₇×D₄	—	2	2	no	—
388	C₂×C₇×D₄	—	2	2	no	—
389	C₂×C₇×D₄	—	2	1	no	—
390	C₂×C₇×D₄	—	2	1	no	—
391	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
392	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
393	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
394	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
395	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
396	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
397	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
398	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
399	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₇	—	2	1	no	—
401	C₂²×C₄×C₇	—	2	2	no	—
402	C₂²×C₄×C₇	—	2	2	no	—
403	C₂²×C₄×C₇	—	2	1	no	—
404	C₂²×C₄×C₇	—	2	1	no	—
405	C₂²×C₄×C₇	—	2	1	no	—
406	C₂²×C₄×C₇	—	2	2	no	—
407	C₂²×C₄×C₇	—	2	2	no	—
408	C₂²×C₄×C₇	—	2	1	no	—
409	C₂²×C₄×C₇	—	2	2	no	—
410	C₂²×C₄×C₇	—	2	2	no	—
411	C₂²×C₄×C₇	—	2	1	no	—
412	C₂²×C₄×C₇	—	2	1	no	—
413	C₂²×C₄×C₇	—	2	1	no	—
414	C₂²×C₄×C₇	—	2	1	no	—
415	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
416	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
417	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
418	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
419	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
420	C₇×Q₁₆	—	2	4	no	—
421	C₇×Q₁₆	—	4	1	no	—
422	C₇×Q₁₆	—	4	1	no	—
423	C₇×SD₁₆	—	2	4	no	—
424	C₇×SD₁₆	—	4	1	no	—
425	C₇×SD₁₆	—	4	1	no	—
426	C₇×SD₁₆	—	4	1	no	—
427	C₇×SD₁₆	—	4	1	no	—
428	C₇×D₈	—	4	1	no	—
429	C₇×D₈	—	4	1	no	—
430	C₇×M₁₆	—	2	2	no	—
431	C₇×M₁₆	—	2	2	no	—
432	C₇×M₁₆	—	4	2	no	—
433	C₇×M₁₆	—	4	2	no	—
434	C₂×C₇×C₈	—	2	2	no	—
435	C₂×C₇×C₈	—	2	2	no	—
436	C₂×C₇×C₈	—	4	2	no	—
437	C₂×C₇×C₈	—	4	2	no	—
438	C₂×C₇×C₈	C₂⁴	1	2	yes	—
439	C₂×C₇×C₈	C₂⁴	1	2	yes	—
440	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
441	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
442	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
443	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
444	C₇×C₄⋊C₄	—	2	2	no	—
445	C₇×C₄⋊C₄	—	2	2	no	—
446	C₇×C₄⋊C₄	—	2	2	no	—
447	C₇×C₄⋊C₄	—	2	2	no	—
448	C₇×C₄⋊C₄	—	2	2	no	—
449	C₇×C₄⋊C₄	—	2	2	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	1	no	—
455	C₇×C₄⋊C₄	—	2	1	no	—
456	C₇×C₄⋊C₄	—	2	1	no	—
457	C₇×C₄⋊C₄	—	2	2	no	—
458	C₇×C₄⋊C₄	—	2	2	no	—
459	C₇×C₄⋊C₄	—	2	1	no	—
460	C₇×C₄⋊C₄	—	2	1	no	—
461	C₇×C₄⋊C₄	—	2	2	no	—
462	C₇×C₄⋊C₄	—	2	2	no	—
463	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
464	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
465	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
466	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
467	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
468	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
469	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
470	C₇×C₂²⋊C₄	—	2	2	no	—
471	C₇×C₂²⋊C₄	—	2	2	no	—
472	C₇×C₂²⋊C₄	—	2	1	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	1	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	1	no	—
483	C₇×C₂²⋊C₄	—	2	2	no	—
484	C₇×C₂²⋊C₄	—	2	2	no	—
485	C₇×C₂²⋊C₄	—	2	2	no	—
486	C₇×C₂²⋊C₄	—	2	2	no	—
487	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
488	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
489	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
490	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
497	C₄²×C₇	—	2	2	no	—
498	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
499	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
500	C₄²×C₇	C₂⁴	1	1	yes	characteristic
501	C₄²×C₇	C₂⁴	1	1	yes	characteristic
502	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
503	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
504	C₂×#137	C₂²×C₇	1	1	yes	characteristic
505	C₂×#135	C₂²×C₇	1	1	yes	characteristic
506	C₂×#135	C₂²×C₇	1	1	yes	characteristic
507	C₂×#131	C₂²×C₇	1	1	yes	characteristic
508	C₂×#131	C₂²×C₇	1	1	yes	characteristic
509	#553	—	2	2	no	—
510	#553	—	2	2	no	—
511	#553	C₂²×C₇	1	2	yes	—
512	#553	C₂²×C₇	1	2	yes	—
513	#552	C₂²×C₇	1	2	yes	—
514	#552	C₂²×C₇	1	2	yes	—
515	#550	—	2	1	no	—
516	#550	C₂²×C₇	1	2	yes	—
517	D₄×Q₈	—	2	1	no	—
518	D₄×Q₈	C₂²×C₇	1	2	yes	—
519	#548	—	2	1	no	—
520	#548	—	2	1	no	—
521	#548	C₂²×C₇	1	2	yes	—
522	#548	C₂²×C₇	1	2	yes	—
523	#541	—	2	1	no	—
524	#540	—	2	1	no	—
525	#537	—	2	2	no	—
526	#537	C₂²×C₇	1	1	yes	characteristic
527	#537	C₂²×C₇	1	1	yes	characteristic
528	#537	C₂²×C₇	1	1	yes	characteristic
529	#537	C₂²×C₇	1	1	yes	characteristic
530	#532	—	2	2	no	—
531	#532	C₂²×C₇	1	1	yes	characteristic
532	#532	C₂²×C₇	1	1	yes	characteristic
533	#529	—	2	1	no	—
534	#529	—	2	1	no	—
535	C₂×#125	C₂²×C₇	1	1	yes	characteristic
536	#520	C₂²×C₇	1	1	yes	characteristic
537	#520	C₂²×C₇	1	1	yes	characteristic
538	C₄×#41	C₂²×C₇	1	1	yes	characteristic
539	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
540	#491	C₂²×C₇	1	2	yes	—
541	#490	C₂²×C₇	1	2	yes	—
542	#488	C₂²×C₇	1	2	yes	—
543	#488	C₂²×C₇	1	2	yes	—
544	#485	C₂²×C₇	1	2	yes	—
545	#485	C₂²×C₇	1	2	yes	—
546	#484	C₂²×C₇	1	2	yes	—
547	#483	C₂²×C₇	1	2	yes	—
548	#482	C₂²×C₇	1	2	yes	—
549	#482	C₂²×C₇	1	2	yes	—
550	#481	C₂²×C₇	1	2	yes	—
551	#480	C₂²×C₇	1	2	yes	—
552	#479	C₂²×C₇	1	2	yes	—
553	#479	C₂²×C₇	1	2	yes	—
554	#479	C₂²×C₇	1	2	yes	—
555	#479	C₂²×C₇	1	2	yes	—
556	#470	C₂²×C₇	1	2	yes	—
557	#469	C₂²×C₇	1	2	yes	—
558	#468	C₂²×C₇	1	2	yes	—
559	#468	C₂²×C₇	1	2	yes	—
560	#467	C₂²×C₇	1	2	yes	—
561	#466	C₂²×C₇	1	2	yes	—
562	#465	C₂²×C₇	1	2	yes	—
563	#465	C₂²×C₇	1	2	yes	—
564	#464	C₂²×C₇	1	1	yes	characteristic
565	#464	C₂²×C₇	1	1	yes	characteristic
566	#463	C₂²×C₇	1	1	yes	characteristic
567	#463	C₂²×C₇	1	1	yes	characteristic
568	#462	C₂²×C₇	1	1	yes	characteristic
569	#461	C₂²×C₇	1	1	yes	characteristic
570	#460	C₂²×C₇	1	1	yes	characteristic
571	#459	C₂²×C₇	1	1	yes	characteristic
572	#452	C₂²×C₇	1	2	yes	—
573	#452	C₂²×C₇	1	2	yes	—
574	#451	C₂²×C₇	1	2	yes	—
575	#451	C₂²×C₇	1	2	yes	—
576	#449	C₂²×C₇	1	2	yes	—
577	#449	C₂²×C₇	1	2	yes	—
578	#448	C₂²×C₇	1	2	yes	—
579	#448	C₂²×C₇	1	2	yes	—
580	#441	C₂²×C₇	1	2	yes	—
581	#440	C₂²×C₇	1	2	yes	—
582	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
583	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
584	#436	C₂²×C₇	1	2	yes	—
585	#435	C₂²×C₇	1	2	yes	—
586	#435	C₂²×C₇	1	2	yes	—
587	C₈×D₄	C₂²×C₇	1	2	yes	—
588	#428	C₂²×C₇	1	1	yes	characteristic
589	C₂×#107	C₂²×C₇	1	1	yes	characteristic
590	C₂×#106	C₂²×C₇	1	1	yes	characteristic
591	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
592	#419	C₂²×C₇	1	1	yes	characteristic
593	#419	C₂²×C₇	1	2	yes	—
594	#419	C₂²×C₇	1	2	yes	—
595	#417	C₂²×C₇	1	1	yes	characteristic
596	#417	C₂²×C₇	1	1	yes	characteristic
597	#417	C₂²×C₇	1	1	yes	characteristic
598	#417	C₂²×C₇	1	1	yes	characteristic
599	#417	C₂²×C₇	1	2	yes	—
600	#417	C₂²×C₇	1	2	yes	—
601	#417	C₂²×C₇	1	1	yes	characteristic
602	#416	C₂²×C₇	1	1	yes	characteristic
603	#416	C₂²×C₇	1	1	yes	characteristic
604	#416	C₂²×C₇	1	2	yes	—
605	#416	C₂²×C₇	1	2	yes	—
606	C₂×#103	C₂²×C₇	1	1	yes	characteristic
607	C₂×#103	C₂²×C₇	1	1	yes	characteristic
608	C₂×#103	C₂²×C₇	1	2	yes	—
609	C₂×#103	C₂²×C₇	1	2	yes	—
610	#408	C₂²×C₇	1	1	yes	characteristic
611	#408	C₂²×C₇	1	1	yes	characteristic
612	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
613	C₂³×C₇	—	2	1	no	—
614	C₂³×C₇	—	2	1	no	—
615	C₂³×C₇	—	2	1	no	—
616	C₂³×C₇	C₂²×D₄	1	2	yes	—
617	C₂³×C₇	C₂²×D₄	1	2	yes	—
618	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
619	C₇×Q₈	—	2	4	no	—
620	C₇×Q₈	—	2	2	no	—
621	C₇×Q₈	—	2	2	no	—
622	C₇×Q₈	—	2	2	no	—
623	C₇×Q₈	—	2	1	no	—
624	C₇×Q₈	—	2	1	no	—
625	C₇×Q₈	—	2	1	no	—
626	C₇×Q₈	—	2	1	no	—
627	C₇×Q₈	—	2	1	no	—
628	C₇×Q₈	—	2	1	no	—
629	C₇×Q₈	—	4	4	no	—
630	C₇×Q₈	—	4	4	no	—
631	C₇×Q₈	C₂×#41	1	4	yes	—
632	C₇×D₄	—	2	4	no	—
633	C₇×D₄	—	2	4	no	—
634	C₇×D₄	—	2	2	no	—
635	C₇×D₄	—	2	2	no	—
636	C₇×D₄	—	2	1	no	—
637	C₇×D₄	—	2	1	no	—
638	C₇×D₄	—	2	1	no	—
639	C₇×D₄	—	2	1	no	—
640	C₇×D₄	—	2	1	no	—
641	C₇×D₄	—	2	1	no	—
642	C₇×D₄	—	4	2	no	—
643	C₇×D₄	—	4	2	no	—
644	C₇×D₄	—	4	4	no	—
645	C₇×D₄	—	4	4	no	—
646	C₇×D₄	—	4	2	no	—
647	C₇×D₄	—	4	2	no	—
648	C₇×D₄	—	4	2	no	—
649	C₇×D₄	—	4	2	no	—
650	C₇×D₄	—	8	1	no	—
651	C₇×D₄	—	8	2	no	—
652	C₇×D₄	—	8	2	no	—
653	C₇×D₄	—	8	2	no	—
654	C₇×D₄	—	8	2	no	—
655	C₂×C₄×C₇	—	2	4	no	—
656	C₂×C₄×C₇	—	2	2	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	2	no	—
665	C₂×C₄×C₇	—	2	2	no	—
666	C₂×C₄×C₇	—	2	2	no	—
667	C₂×C₄×C₇	—	2	1	no	—
668	C₂×C₄×C₇	—	2	1	no	—
669	C₂×C₄×C₇	—	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	4	no	—
675	C₂×C₄×C₇	—	4	2	no	—
676	C₂×C₄×C₇	—	4	2	no	—
677	C₂×C₄×C₇	—	4	2	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	1	no	—
682	C₂×C₄×C₇	—	8	1	no	—
683	C₂×C₄×C₇	—	8	2	no	—
684	C₂×C₄×C₇	—	8	1	no	—
685	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
686	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
687	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
688	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
689	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
690	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
691	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
692	C₂×C₄×C₇	C₂×#41	1	2	yes	—
693	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
694	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
695	C₇×C₈	—	2	2	no	—
696	C₇×C₈	—	2	1	no	—
697	C₇×C₈	—	2	1	no	—
698	C₇×C₈	—	2	1	no	—
699	C₇×C₈	—	2	1	no	—
700	C₇×C₈	—	2	2	no	—
701	2₋¹⁺⁴	—	2	4	no	—
702	2₋¹⁺⁴	—	2	4	no	—
703	2₋¹⁺⁴	—	4	2	no	—
704	2₋¹⁺⁴	—	4	2	no	—
705	C₂×#41	—	2	2	no	—
706	C₂×#41	—	2	2	no	—
707	C₂×#41	—	2	1	no	—
708	C₂×#41	—	2	1	no	—
709	C₂×#41	C₂³×C₇	1	1	yes	characteristic
710	C₂×#41	C₂³×C₇	1	1	yes	characteristic
711	C₂×#41	C₂³×C₇	1	1	yes	characteristic
712	C₂×#41	C₂³×C₇	1	2	yes	—
713	C₂×#41	C₂³×C₇	1	2	yes	—
714	C₂×#41	C₂³×C₇	1	1	yes	characteristic
715	C₂×#41	C₂³×C₇	1	1	yes	characteristic
716	C₂²×Q₈	—	2	1	no	—
717	C₂²×Q₈	—	2	1	no	—
718	C₂²×Q₈	C₂³×C₇	1	2	yes	—
719	C₂²×Q₈	C₂³×C₇	1	2	yes	—
720	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
721	#137	—	2	4	no	—
722	#135	—	4	2	no	—
723	#135	—	4	2	no	—
724	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
725	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
726	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
727	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
729	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
730	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
731	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
732	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
733	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
734	#131	—	4	2	no	—
735	#131	—	4	2	no	—
736	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
737	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
738	C₂×M₁₆	C₂³×C₇	1	2	yes	—
739	C₂×M₁₆	C₂³×C₇	1	2	yes	—
740	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
741	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
742	C₂²×C₈	C₂³×C₇	1	2	yes	—
743	C₂²×C₈	C₂³×C₇	1	2	yes	—
744	C₄⋊Q₈	—	2	2	no	—
745	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
746	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
747	#127	—	2	2	no	—
748	#127	C₇×D₄	1	1	yes	characteristic
749	#127	C₂³×C₇	1	1	yes	characteristic
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#125	—	2	2	no	—
755	#125	—	2	2	no	—
756	#125	—	2	1	no	—
757	#125	—	2	1	no	—
758	#125	C₂³×C₇	1	2	yes	—
759	#125	C₂³×C₇	1	2	yes	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	C₇×D₄	1	1	yes	characteristic
763	#124	C₇×D₄	1	1	yes	characteristic
764	#124	C₂³×C₇	1	1	yes	characteristic
765	#124	C₂³×C₇	1	1	yes	characteristic
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
779	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
780	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
781	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
782	#121	—	2	1	no	—
783	#121	—	2	1	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	1	no	—
789	#121	—	2	1	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	2	no	—
793	#121	—	2	2	no	—
794	#121	—	2	1	no	—
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	C₇×D₄	1	2	yes	—
799	#121	C₇×D₄	1	2	yes	—
800	#121	C₂³×C₇	1	2	yes	—
801	#121	C₂³×C₇	1	2	yes	—
802	#121	C₂³×C₇	1	2	yes	—
803	#121	C₂³×C₇	1	2	yes	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	C₂³×C₇	1	2	yes	—
809	C₄×Q₈	C₂³×C₇	1	2	yes	—
810	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₇	1	2	yes	—
829	C₄×D₄	C₂³×C₇	1	2	yes	—
830	#117	—	2	2	no	—
831	#117	—	2	2	no	—
832	#117	—	2	1	no	—
833	#117	C₂³×C₇	1	1	yes	characteristic
834	#117	C₂³×C₇	1	2	yes	—
835	#117	C₂³×C₇	1	2	yes	—
836	C₂×C₄⋊C₄	—	2	1	no	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	—	2	1	no	—
839	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
842	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
843	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
844	C₂×C₄²	—	2	1	no	—
845	C₂×C₄²	—	2	1	no	—
846	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
847	#107	C₂³×C₇	1	2	yes	—
848	#107	C₂³×C₇	1	2	yes	—
849	#107	C₂³×C₇	1	2	yes	—
850	#106	C₂³×C₇	1	2	yes	—
851	#106	C₂³×C₇	1	2	yes	—
852	#106	C₂³×C₇	1	2	yes	—
853	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
856	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
857	#103	C₂³×C₇	1	2	yes	—
858	#103	C₂³×C₇	1	2	yes	—
859	#103	C₂³×C₇	1	1	yes	characteristic
860	#103	C₂³×C₇	1	1	yes	characteristic
861	#103	C₂³×C₇	1	2	yes	—
862	#103	C₂³×C₇	1	2	yes	—
863	#103	C₂³×C₇	1	2	yes	—
864	#103	C₂³×C₇	1	2	yes	—
865	#103	C₂³×C₇	1	2	yes	—
866	#103	C₂³×C₇	1	2	yes	—
867	#103	C₂³×C₇	1	1	yes	characteristic
868	#103	C₂³×C₇	1	1	yes	characteristic
869	#103	C₂³×C₇	1	2	yes	—
870	#103	C₂³×C₇	1	2	yes	—
871	#103	C₂³×C₇	1	2	yes	—
872	#102	C₂³×C₇	1	1	yes	characteristic
873	#102	C₂³×C₇	1	1	yes	characteristic
874	#102	C₂³×C₇	1	1	yes	characteristic
875	#102	C₂³×C₇	1	1	yes	characteristic
876	#102	C₂³×C₇	1	2	yes	—
877	#102	C₂³×C₇	1	2	yes	—
878	#102	C₂³×C₇	1	2	yes	—
879	#102	C₂³×C₇	1	2	yes	—
880	#102	C₂³×C₇	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
885	#97	C₂³×C₇	1	2	yes	—
886	C₄×C₈	C₂³×C₇	1	2	yes	—
887	C₂²×C₇	—	2	1	no	—
888	C₂²×C₇	—	2	1	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	1	no	—
900	C₂²×C₇	—	4	1	no	—
901	C₂²×C₇	—	4	1	no	—
902	C₂²×C₇	—	4	1	no	—
903	C₂²×C₇	—	4	1	no	—
904	C₂²×C₇	#546	1	2	yes	—
905	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
906	C₄×C₇	—	2	1	no	—
907	C₄×C₇	—	2	1	no	—
908	C₄×C₇	—	2	1	no	—
909	C₄×C₇	—	2	1	no	—
910	C₄×C₇	—	2	4	no	—
911	C₄×C₇	—	2	2	no	—
912	C₄×C₇	—	2	2	no	—
913	C₄×C₇	—	4	1	no	—
914	C₄×C₇	—	4	2	no	—
915	C₄×C₇	—	4	2	no	—
916	C₄×C₇	—	4	1	no	—
917	C₄×C₇	—	4	2	no	—
918	C₄×C₇	—	4	1	no	—
919	C₄×C₇	—	4	1	no	—
920	C₄×C₇	—	4	1	no	—
921	C₄×C₇	#546	1	2	yes	—
922	C₄×C₇	C₂²×#41	1	1	yes	characteristic
923	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
924	#41	—	2	2	no	—
925	#41	—	2	2	no	—
926	#41	—	2	2	no	—
927	#41	—	2	2	no	—
928	#41	—	2	4	no	—
929	#41	—	2	4	no	—
930	#41	—	2	2	no	—
931	#41	—	2	2	no	—
932	#41	—	2	2	no	—
933	#41	—	2	2	no	—
934	#41	—	2	2	no	—
935	#41	—	2	2	no	—
936	#41	—	4	2	no	—
937	#41	—	4	2	no	—
938	#41	—	4	8	no	—
939	#41	—	4	8	no	—
940	#41	—	4	4	no	—
941	#41	—	4	4	no	—
942	C₂×Q₈	—	2	1	no	—
943	C₂×Q₈	—	2	2	no	—
944	C₂×Q₈	—	2	2	no	—
945	C₂×Q₈	—	2	2	no	—
946	C₂×Q₈	—	2	4	no	—
947	C₂×Q₈	—	2	4	no	—
948	C₂×Q₈	—	4	2	no	—
949	C₂×Q₈	—	4	2	no	—
950	C₂×Q₈	—	4	4	no	—
951	C₂×Q₈	—	4	4	no	—
952	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
953	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
954	C₂×Q₈	C₇×#41	1	4	yes	—
955	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
956	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
957	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
958	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	1	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	2	1	no	—
969	C₂×D₄	—	2	1	no	—
970	C₂×D₄	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	1	yes	characteristic
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	2	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	1	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	1	no	—
991	C₂²×C₄	—	2	1	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
995	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
996	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
997	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
998	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
999	Q₁₆	—	2	4	no	—
1000	Q₁₆	—	4	1	no	—
1001	Q₁₆	—	4	1	no	—
1002	SD₁₆	—	2	4	no	—
1003	SD₁₆	—	4	1	no	—
1004	SD₁₆	—	4	1	no	—
1005	SD₁₆	—	4	1	no	—
1006	SD₁₆	—	4	1	no	—
1007	D₈	—	4	1	no	—
1008	D₈	—	4	1	no	—
1009	M₁₆	—	2	2	no	—
1010	M₁₆	—	2	2	no	—
1011	M₁₆	—	4	2	no	—
1012	M₁₆	—	4	2	no	—
1013	C₂×C₈	—	2	2	no	—
1014	C₂×C₈	—	2	2	no	—
1015	C₂×C₈	—	4	2	no	—
1016	C₂×C₈	—	4	2	no	—
1017	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1018	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1019	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1020	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1021	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1022	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1043	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1044	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1045	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1046	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1047	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1048	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	1	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	1	no	—
1057	C₂²⋊C₄	—	2	1	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	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1067	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1068	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1069	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1070	C₄²	—	2	1	no	—
1071	C₄²	—	2	1	no	—
1072	C₄²	—	2	1	no	—
1073	C₄²	—	2	2	no	—
1074	C₄²	—	2	2	no	—
1075	C₄²	—	2	2	no	—
1076	C₄²	—	2	2	no	—
1077	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1078	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1079	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1080	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1081	C₂×C₇	—	2	2	no	—
1082	C₂×C₇	—	4	2	no	—
1083	C₂×C₇	—	4	2	no	—
1084	C₂×C₇	—	8	1	no	—
1085	C₂×C₇	—	8	1	no	—
1086	C₂×C₇	—	8	1	no	—
1087	C₂×C₇	C₂×#546	1	1	yes	characteristic
1088	C₂×C₇	#3584	1	1	yes	characteristic
1089	C₂×C₇	#3586	1	1	yes	characteristic
1090	C₂³	—	2	1	no	—
1091	C₂³	—	2	1	no	—
1092	C₂³	—	2	1	no	—
1093	C₂³	C₂²×C₇×D₄	1	2	yes	—
1094	C₂³	C₂²×C₇×D₄	1	2	yes	—
1095	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1096	Q₈	—	2	2	no	—
1097	Q₈	—	2	4	no	—
1098	Q₈	—	2	2	no	—
1099	Q₈	—	2	2	no	—
1100	Q₈	—	2	1	no	—
1101	Q₈	—	2	1	no	—
1102	Q₈	—	2	1	no	—
1103	Q₈	—	2	1	no	—
1104	Q₈	—	2	1	no	—
1105	Q₈	—	2	1	no	—
1106	Q₈	—	4	4	no	—
1107	Q₈	—	4	4	no	—
1108	Q₈	C₂×C₇×#41	1	4	yes	—
1109	D₄	—	2	4	no	—
1110	D₄	—	2	4	no	—
1111	D₄	—	2	1	no	—
1112	D₄	—	2	1	no	—
1113	D₄	—	2	1	no	—
1114	D₄	—	2	1	no	—
1115	D₄	—	2	1	no	—
1116	D₄	—	2	1	no	—
1117	D₄	—	2	2	no	—
1118	D₄	—	2	2	no	—
1119	D₄	—	4	2	no	—
1120	D₄	—	4	2	no	—
1121	D₄	—	4	4	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	2	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	4	2	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	8	1	no	—
1128	D₄	—	8	2	no	—
1129	D₄	—	8	2	no	—
1130	D₄	—	8	2	no	—
1131	D₄	—	8	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	4	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	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	4	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	—	4	2	no	—
1155	C₂×C₄	—	8	1	no	—
1156	C₂×C₄	—	8	1	no	—
1157	C₂×C₄	—	8	2	no	—
1158	C₂×C₄	—	8	1	no	—
1159	C₂×C₄	—	8	1	no	—
1160	C₂×C₄	—	8	2	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	1	yes	characteristic
1165	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1166	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
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	2	no	—
1173	C₈	—	2	1	no	—
1174	C₈	—	2	1	no	—
1175	C₈	—	2	1	no	—
1176	C₈	—	2	1	no	—
1177	C₈	—	2	2	no	—
1178	C₇	#61204	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	—	4	1	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	C₇×#546	1	2	yes	—
1197	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1198	C₄	—	2	1	no	—
1199	C₄	—	2	1	no	—
1200	C₄	—	2	1	no	—
1201	C₄	—	2	1	no	—
1202	C₄	—	2	4	no	—
1203	C₄	—	2	2	no	—
1204	C₄	—	2	2	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	2	no	—
1207	C₄	—	4	2	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	1	no	—
1213	C₄	C₇×#546	1	2	yes	—
1214	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1215	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1216	C₂	—	2	2	no	—
1217	C₂	—	4	2	no	—
1218	C₂	—	4	2	no	—
1219	C₂	—	8	1	no	—
1220	C₂	—	8	1	no	—
1221	C₂	—	8	1	no	—
1222	C₂	C₂×C₇×#546	1	1	yes	characteristic
1223	C₂	C₇×#3584	1	1	yes	characteristic
1224	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×#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×#3497	C₂	semidirect
3. C₇×#3327	C₂	semidirect
4. C₇×#3326	C₂	semidirect
5. C₇×#3320	C₂	semidirect
6. C₇×#3317	C₂	semidirect
7. C₇×#3312	C₂	semidirect
8. C₇×#3309	C₂	semidirect
9. C₇×#3301	C₂	semidirect
10. C₇×#3300	C₂	semidirect
11. C₇×#3142	C₂	semidirect
12. C₇×#3099	C₂	semidirect
13. C₇×#3098	C₂	semidirect
14. C₂×C₇×#479	C₂	semidirect
15. C₇×#3061	C₂	semidirect
16. C₇×#3060	C₂	semidirect
17. C₇×#3035	C₂	semidirect
18. C₇×#3013	C₂	semidirect
19. C₇×#3013	C₂	semidirect
20. C₄×C₇×#137	C₂	semidirect
21. C₇×#2935	C₂	semidirect
22. C₇×#2898	C₂	semidirect
23. C₇×#2898	C₂	semidirect
135. #61204	C₇	direct (N × H)
322. #3512	C₂×C₇	semidirect
323. #3497	C₂×C₇	semidirect
324. #3327	C₂×C₇	semidirect
325. #3326	C₂×C₇	semidirect
326. #3320	C₂×C₇	semidirect
327. #3317	C₂×C₇	semidirect
328. #3312	C₂×C₇	semidirect
329. #3309	C₂×C₇	semidirect
330. #3301	C₂×C₇	semidirect
331. #3300	C₂×C₇	semidirect
332. #3142	C₂×C₇	semidirect
333. #3099	C₂×C₇	semidirect
334. #3098	C₂×C₇	semidirect
335. C₂×#479	C₂×C₇	semidirect
336. #3061	C₂×C₇	semidirect
337. #3060	C₂×C₇	semidirect
338. #3035	C₂×C₇	semidirect
339. #3013	C₂×C₇	semidirect
340. #3013	C₂×C₇	semidirect
341. C₄×#137	C₂×C₇	semidirect
342. #2935	C₂×C₇	semidirect
343. #2898	C₂×C₇	semidirect
344. #2898	C₂×C₇	semidirect
1178. C₇	#61204	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×#3497	2
C₇×#3327	2
C₇×#3326	2
C₇×#3320	2
C₇×#3317	2
C₇×#3312	2
C₇×#3309	2
C₇×#3301	2
C₇×#3300	2
C₇×#3142	2
C₇×#3099	2
C₇×#3098	2
C₂×C₇×#479	2
C₇×#3061	2
C₇×#3060	2
C₇×#3035	2
C₇×#3013	2
C₄×C₇×#137	2
C₇×#2935	2
C₇×#2898	2
#61204	7

Subgroups — C7×#61204 #13238420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61204 #13238420