Subgroups — C₇×#62036 #13239252

Order 1792.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3329	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3328	C₂	1	2	yes	maximal, complemented
9	C₇×#3313	C₂	1	2	yes	maximal, complemented
10	C₇×#3303	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×D₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3277	C₂	1	2	yes	maximal, complemented
13	C₇×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3270	C₂	1	2	yes	maximal, complemented
15	C₇×#3258	C₂	1	2	yes	maximal, complemented
16	C₇×#3252	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3225	C₂	1	2	yes	maximal, complemented
18	C₇×#3209	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3127	C₂	1	2	yes	maximal, complemented
20	C₇×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3044	C₂	1	2	yes	maximal, complemented
22	C₇×#3039	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#137	C₂²	1	2	yes	—
25	C₂×C₇×#137	C₂²	1	2	yes	—
26	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
27	C₇×#563	—	2	2	no	—
28	C₇×Q₈²	C₂²	1	1	yes	characteristic
29	C₇×#557	C₂²	1	1	yes	characteristic
30	C₇×#556	—	2	2	no	—
31	C₇×#556	—	2	1	no	—
32	C₇×#556	C₂²	1	1	yes	characteristic
33	C₇×#556	C₂²	1	1	yes	characteristic
34	C₇×#556	C₂²	1	2	yes	—
35	C₇×#555	—	2	1	no	—
36	C₇×#555	C₂²	1	1	yes	characteristic
37	C₇×#554	—	2	1	no	—
38	C₇×#553	—	2	1	no	—
39	C₇×D₄×Q₈	C₂²	1	2	yes	—
40	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
41	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
42	C₇×#548	C₂²	1	2	yes	—
43	C₇×#548	C₂²	1	2	yes	—
44	C₇×#547	C₂²	1	1	yes	characteristic
45	C₇×#544	—	2	1	no	—
46	C₇×#542	—	2	1	no	—
47	C₇×#542	—	2	2	no	—
48	C₇×#542	C₂²	1	2	yes	—
49	C₇×#541	C₂²	1	2	yes	—
50	C₇×#539	—	2	2	no	—
51	C₇×#536	C₂²	1	2	yes	—
52	C₇×#533	—	2	1	no	—
53	C₇×#533	C₂²	1	1	yes	characteristic
54	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
55	C₇×#529	—	2	1	no	—
56	C₇×#529	C₂²	1	1	yes	characteristic
57	C₇×#529	C₂²	1	1	yes	characteristic
58	C₇×#519	C₂²	1	2	yes	—
59	C₄×C₇×#41	C₂²	1	1	yes	characteristic
60	C₇×#497	C₂²	1	2	yes	—
61	C₇×#495	C₂²	1	2	yes	—
62	C₇×#494	C₂²	1	1	yes	characteristic
63	C₇×#494	C₂²	1	1	yes	characteristic
64	C₇×#489	C₂²	1	2	yes	—
65	C₇×#487	C₂²	1	1	yes	characteristic
66	C₇×#487	C₂²	1	1	yes	characteristic
67	C₇×#487	C₂²	1	2	yes	—
68	C₇×#485	C₂²	1	2	yes	—
69	C₇×#485	C₂²	1	2	yes	—
70	C₇×#485	C₂²	1	1	yes	characteristic
71	C₇×#482	C₂²	1	1	yes	characteristic
72	C₇×#479	C₂²	1	2	yes	—
73	C₇×#479	C₂²	1	1	yes	characteristic
74	C₇×#478	C₂²	1	1	yes	characteristic
75	C₇×#477	C₂²	1	1	yes	characteristic
76	C₇×#477	C₂²	1	2	yes	—
77	C₇×#476	C₂²	1	1	yes	characteristic
78	C₇×#475	C₂²	1	2	yes	—
79	C₇×#470	C₂²	1	2	yes	—
80	C₇×#470	C₂²	1	2	yes	—
81	C₇×#468	C₂²	1	2	yes	—
82	C₇×#468	C₂²	1	2	yes	—
83	C₇×#467	C₂²	1	2	yes	—
84	C₇×#465	C₂²	1	2	yes	—
85	C₇×#464	C₂²	1	2	yes	—
86	C₇×#464	C₂²	1	2	yes	—
87	C₇×#464	C₂²	1	2	yes	—
88	C₇×#464	C₂²	1	2	yes	—
89	C₇×#464	C₂²	1	1	yes	characteristic
90	C₇×#464	C₂²	1	2	yes	—
91	C₇×#463	C₂²	1	1	yes	characteristic
92	C₇×#462	C₂²	1	2	yes	—
93	C₇×#462	C₂²	1	2	yes	—
94	C₇×#462	C₂²	1	1	yes	characteristic
95	C₇×#462	C₂²	1	2	yes	—
96	C₇×#462	C₂²	1	1	yes	characteristic
97	C₇×#462	C₂²	1	1	yes	characteristic
98	C₇×#462	C₂²	1	2	yes	—
99	C₇×#462	C₂²	1	2	yes	—
100	C₇×#461	C₂²	1	2	yes	—
101	C₇×#461	C₂²	1	1	yes	characteristic
102	C₇×#461	C₂²	1	1	yes	characteristic
103	C₇×#461	C₂²	1	1	yes	characteristic
104	C₇×#452	C₂²	1	2	yes	—
105	C₇×#452	C₂²	1	1	yes	characteristic
106	C₇×#451	C₂²	1	2	yes	—
107	C₇×#451	C₂²	1	2	yes	—
108	C₇×#451	C₂²	1	2	yes	—
109	C₇×#451	C₂²	1	2	yes	—
110	C₇×#451	C₂²	1	2	yes	—
111	C₇×#449	C₂²	1	2	yes	—
112	C₇×#449	C₂²	1	1	yes	characteristic
113	C₇×#448	C₂²	1	2	yes	—
114	C₇×#446	C₂²	1	1	yes	characteristic
115	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
116	C₇×#441	C₂²	1	2	yes	—
117	C₇×#441	C₂²	1	2	yes	—
118	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
119	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
121	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
122	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
123	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
124	C₇×#436	C₂²	1	1	yes	characteristic
125	C₇×#436	C₂²	1	2	yes	—
126	C₇×#435	C₂²	1	2	yes	—
127	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
128	C₇×#433	C₂²	1	2	yes	—
129	C₇×#431	C₂²	1	1	yes	characteristic
130	C₇×#424	C₂²	1	2	yes	—
131	C₇×#423	C₂²	1	1	yes	characteristic
132	C₇×#419	C₂²	1	2	yes	—
133	C₇×#419	C₂²	1	2	yes	—
134	C₇×#416	C₂²	1	2	yes	—
135	#62036	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	C₂³	1	1	yes	characteristic
137	C₂×C₇×#41	C₂³	1	2	yes	—
138	C₂²×C₇×Q₈	C₂³	1	2	yes	—
139	C₂²×C₇×Q₈	C₂³	1	2	yes	—
140	C₂²×C₇×Q₈	C₂³	1	2	yes	—
141	C₇×#137	—	4	4	no	—
142	C₇×#137	—	4	4	no	—
143	C₂×C₇×Q₁₆	—	4	4	no	—
144	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
146	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
147	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
149	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
150	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
151	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
152	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
155	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
156	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
157	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
158	C₂×C₇×M₁₆	C₂³	1	2	yes	—
159	C₂×C₇×M₁₆	C₂³	1	2	yes	—
160	C₂²×C₇×C₈	C₂³	1	2	yes	—
161	C₇×C₄⋊Q₈	—	2	1	no	—
162	C₇×C₄⋊Q₈	—	2	1	no	—
163	C₇×C₄⋊Q₈	—	2	2	no	—
164	C₇×C₄⋊Q₈	—	2	1	no	—
165	C₇×C₄⋊Q₈	—	2	2	no	—
166	C₇×C₄⋊Q₈	—	2	1	no	—
167	C₇×C₄⋊Q₈	—	2	1	no	—
168	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
173	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
174	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
175	C₇×#126	—	2	2	no	—
176	C₇×#126	—	2	2	no	—
177	C₇×#126	—	2	2	no	—
178	C₇×#126	—	2	2	no	—
179	C₇×#126	—	2	2	no	—
180	C₇×#126	—	2	2	no	—
181	C₇×#126	—	2	2	no	—
182	C₇×#126	—	2	1	no	—
183	C₇×#126	D₄	1	2	yes	—
184	C₇×#125	—	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	D₄	1	1	yes	characteristic
190	C₇×#125	C₂³	1	1	yes	characteristic
191	C₇×#124	—	2	2	no	—
192	C₇×#124	—	2	2	no	—
193	C₇×#124	—	2	2	no	—
194	C₇×#124	—	2	2	no	—
195	C₇×#124	—	2	2	no	—
196	C₇×#124	D₄	1	1	yes	characteristic
197	C₇×#124	C₂³	1	2	yes	—
198	C₇×#124	C₂³	1	2	yes	—
199	C₇×#124	C₂³	1	1	yes	characteristic
200	C₇×#123	—	2	1	no	—
201	C₇×#123	—	2	2	no	—
202	C₇×#123	—	2	2	no	—
203	C₇×#123	—	2	2	no	—
204	C₇×#123	—	2	2	no	—
205	C₇×#123	D₄	1	2	yes	—
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	—	2	2	no	—
214	C₇×C₂²⋊Q₈	—	2	2	no	—
215	C₇×C₂²⋊Q₈	—	2	2	no	—
216	C₇×C₂²⋊Q₈	—	2	2	no	—
217	C₇×C₂²⋊Q₈	—	2	2	no	—
218	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
219	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₇×#121	—	2	1	no	—
225	C₇×#121	—	2	2	no	—
226	C₇×#121	—	2	1	no	—
227	C₇×#121	—	2	2	no	—
228	C₇×#121	D₄	1	1	yes	characteristic
229	C₇×#121	C₂³	1	1	yes	characteristic
230	C₇×#121	C₂³	1	2	yes	—
231	C₄×C₇×Q₈	—	2	1	no	—
232	C₄×C₇×Q₈	—	2	1	no	—
233	C₄×C₇×Q₈	—	2	2	no	—
234	C₄×C₇×Q₈	—	2	2	no	—
235	C₄×C₇×Q₈	—	2	2	no	—
236	C₄×C₇×Q₈	—	2	1	no	—
237	C₄×C₇×Q₈	C₂³	1	2	yes	—
238	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
239	C₄×C₇×Q₈	C₂³	1	2	yes	—
240	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
241	C₄×C₇×Q₈	C₂³	1	2	yes	—
242	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
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×D₄	—	2	1	no	—
247	C₄×C₇×D₄	—	2	2	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	—	2	1	no	—
252	C₄×C₇×D₄	—	2	2	no	—
253	C₄×C₇×D₄	—	2	2	no	—
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	1	yes	characteristic
258	C₄×C₇×D₄	C₂³	1	2	yes	—
259	C₇×#117	—	2	1	no	—
260	C₇×#117	—	2	1	no	—
261	C₇×#117	—	2	1	no	—
262	C₇×#117	—	2	1	no	—
263	C₇×#117	—	2	2	no	—
264	C₇×#117	—	2	2	no	—
265	C₇×#117	—	2	1	no	—
266	C₇×#117	—	2	1	no	—
267	C₇×#117	C₂³	1	1	yes	characteristic
268	C₇×#117	C₂³	1	2	yes	—
269	C₇×#117	C₂³	1	2	yes	—
270	C₂×C₇×C₄⋊C₄	—	2	1	no	—
271	C₂×C₇×C₄⋊C₄	—	2	1	no	—
272	C₂×C₇×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄²×C₇	—	2	1	no	—
274	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
275	C₇×#107	C₂³	1	1	yes	characteristic
276	C₇×#107	C₂³	1	2	yes	—
277	C₇×#107	C₂³	1	1	yes	characteristic
278	C₇×#106	C₂³	1	1	yes	characteristic
279	C₇×#106	C₂³	1	2	yes	—
280	C₇×#106	C₂³	1	1	yes	characteristic
281	C₇×C₄⋊C₈	C₂³	1	2	yes	—
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	1	yes	characteristic
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×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	1	yes	characteristic
296	C₇×#103	C₂³	1	1	yes	characteristic
297	C₇×#103	C₂³	1	2	yes	—
298	C₇×#103	C₂³	1	1	yes	characteristic
299	C₇×#103	C₂³	1	2	yes	—
300	C₇×#103	C₂³	1	2	yes	—
301	C₇×#103	C₂³	1	1	yes	characteristic
302	C₇×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
307	C₇×#102	C₂³	1	1	yes	characteristic
308	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₇×#97	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
315	C₄×C₇×C₈	C₂³	1	2	yes	—
316	#3552	C₂×C₇	1	1	yes	characteristic, complemented
317	#3518	C₂×C₇	1	1	yes	characteristic, complemented
318	#3398	C₂×C₇	1	1	yes	characteristic, complemented
319	#3393	C₂×C₇	1	1	yes	characteristic, complemented
320	#3369	C₂×C₇	1	1	yes	characteristic, complemented
321	#3363	C₂×C₇	1	1	yes	characteristic, complemented
322	#3329	C₂×C₇	1	1	yes	characteristic, complemented
323	#3328	C₂×C₇	1	2	yes	complemented
324	#3313	C₂×C₇	1	2	yes	complemented
325	#3303	C₂×C₇	1	1	yes	characteristic, complemented
326	D₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
327	#3277	C₂×C₇	1	2	yes	complemented
328	#3276	C₂×C₇	1	1	yes	characteristic, complemented
329	#3270	C₂×C₇	1	2	yes	complemented
330	#3258	C₂×C₇	1	2	yes	complemented
331	#3252	C₂×C₇	1	1	yes	characteristic, complemented
332	#3225	C₂×C₇	1	2	yes	complemented
333	#3209	C₂×C₇	1	1	yes	characteristic, complemented
334	#3127	C₂×C₇	1	2	yes	complemented
335	#3102	C₂×C₇	1	1	yes	characteristic, complemented
336	#3044	C₂×C₇	1	2	yes	complemented
337	#3039	C₂×C₇	1	1	yes	characteristic, complemented
338	#2993	C₂×C₇	1	1	yes	characteristic, complemented
339	C₇×#41	—	2	2	no	—
340	C₇×#41	—	4	1	no	—
341	C₇×#41	—	4	2	no	—
342	C₇×#41	—	4	2	no	—
343	C₂×C₇×Q₈	—	2	2	no	—
344	C₂×C₇×Q₈	—	2	1	no	—
345	C₂×C₇×Q₈	—	2	2	no	—
346	C₂×C₇×Q₈	—	2	2	no	—
347	C₂×C₇×Q₈	—	2	2	no	—
348	C₂×C₇×Q₈	—	2	4	no	—
349	C₂×C₇×Q₈	—	4	2	no	—
350	C₂×C₇×Q₈	—	4	2	no	—
351	C₂×C₇×Q₈	—	4	2	no	—
352	C₂×C₇×Q₈	—	4	2	no	—
353	C₂×C₇×Q₈	—	4	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	1	yes	characteristic
357	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
358	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
359	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
360	C₂×C₇×D₄	—	2	1	no	—
361	C₂×C₇×D₄	—	2	1	no	—
362	C₂×C₇×D₄	—	2	2	no	—
363	C₂×C₇×D₄	—	2	2	no	—
364	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
365	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
366	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
367	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₇	—	2	2	no	—
369	C₂²×C₄×C₇	—	2	2	no	—
370	C₂²×C₄×C₇	—	2	2	no	—
371	C₂²×C₄×C₇	—	2	1	no	—
372	C₂²×C₄×C₇	—	2	1	no	—
373	C₂²×C₄×C₇	—	2	1	no	—
374	C₂²×C₄×C₇	—	2	1	no	—
375	C₂²×C₄×C₇	—	2	2	no	—
376	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
380	C₇×Q₁₆	—	2	2	no	—
381	C₇×Q₁₆	—	2	4	no	—
382	C₇×Q₁₆	—	2	4	no	—
383	C₇×Q₁₆	—	4	2	no	—
384	C₇×Q₁₆	—	4	2	no	—
385	C₇×Q₁₆	—	4	2	no	—
386	C₇×Q₁₆	—	4	2	no	—
387	C₇×Q₁₆	—	4	2	no	—
388	C₇×SD₁₆	—	2	2	no	—
389	C₇×SD₁₆	—	4	1	no	—
390	C₇×SD₁₆	—	4	2	no	—
391	C₇×SD₁₆	—	4	2	no	—
392	C₇×SD₁₆	—	4	2	no	—
393	C₇×D₈	—	4	1	no	—
394	C₇×M₁₆	—	4	2	no	—
395	C₇×M₁₆	—	4	2	no	—
396	C₂×C₇×C₈	—	4	2	no	—
397	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
398	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
399	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
400	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
401	C₂×C₇×C₈	C₂⁴	1	2	yes	—
402	C₂×C₇×C₈	C₂⁴	1	2	yes	—
403	C₇×C₄⋊C₄	—	2	1	no	—
404	C₇×C₄⋊C₄	—	2	1	no	—
405	C₇×C₄⋊C₄	—	2	1	no	—
406	C₇×C₄⋊C₄	—	2	2	no	—
407	C₇×C₄⋊C₄	—	2	2	no	—
408	C₇×C₄⋊C₄	—	2	2	no	—
409	C₇×C₄⋊C₄	—	2	1	no	—
410	C₇×C₄⋊C₄	—	2	1	no	—
411	C₇×C₄⋊C₄	—	2	1	no	—
412	C₇×C₄⋊C₄	—	2	1	no	—
413	C₇×C₄⋊C₄	—	2	1	no	—
414	C₇×C₄⋊C₄	—	2	2	no	—
415	C₇×C₄⋊C₄	—	2	2	no	—
416	C₇×C₄⋊C₄	—	2	2	no	—
417	C₇×C₄⋊C₄	—	2	1	no	—
418	C₇×C₄⋊C₄	—	2	1	no	—
419	C₇×C₄⋊C₄	—	2	2	no	—
420	C₇×C₄⋊C₄	—	2	2	no	—
421	C₇×C₄⋊C₄	—	2	2	no	—
422	C₇×C₄⋊C₄	—	2	1	no	—
423	C₇×C₄⋊C₄	—	2	2	no	—
424	C₇×C₄⋊C₄	—	2	1	no	—
425	C₇×C₄⋊C₄	—	2	2	no	—
426	C₇×C₄⋊C₄	—	2	2	no	—
427	C₇×C₄⋊C₄	—	2	2	no	—
428	C₇×C₄⋊C₄	—	2	2	no	—
429	C₇×C₄⋊C₄	—	2	1	no	—
430	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
431	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
432	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
433	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
434	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
435	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
436	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
437	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
438	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
439	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
440	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
441	C₇×C₂²⋊C₄	—	2	2	no	—
442	C₇×C₂²⋊C₄	—	2	2	no	—
443	C₇×C₂²⋊C₄	—	2	1	no	—
444	C₇×C₂²⋊C₄	—	2	1	no	—
445	C₇×C₂²⋊C₄	—	2	2	no	—
446	C₇×C₂²⋊C₄	—	2	2	no	—
447	C₇×C₂²⋊C₄	—	2	2	no	—
448	C₇×C₂²⋊C₄	—	2	1	no	—
449	C₇×C₂²⋊C₄	—	2	1	no	—
450	C₇×C₂²⋊C₄	—	2	2	no	—
451	C₇×C₂²⋊C₄	—	2	2	no	—
452	C₇×C₂²⋊C₄	—	2	1	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	2	no	—
457	C₇×C₂²⋊C₄	—	2	2	no	—
458	C₇×C₂²⋊C₄	—	2	1	no	—
459	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
460	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
461	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
462	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
463	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
464	C₄²×C₇	—	2	1	no	—
465	C₄²×C₇	—	2	1	no	—
466	C₄²×C₇	—	2	1	no	—
467	C₄²×C₇	—	2	2	no	—
468	C₄²×C₇	—	2	2	no	—
469	C₄²×C₇	—	2	2	no	—
470	C₄²×C₇	—	2	1	no	—
471	C₄²×C₇	—	2	2	no	—
472	C₄²×C₇	—	2	2	no	—
473	C₄²×C₇	—	2	2	no	—
474	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
475	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
476	C₄²×C₇	C₂⁴	1	1	yes	characteristic
477	C₄²×C₇	C₂⁴	1	2	yes	—
478	C₄²×C₇	C₂⁴	1	1	yes	characteristic
479	C₂×#137	C₂²×C₇	1	2	yes	—
480	C₂×#137	C₂²×C₇	1	2	yes	—
481	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
482	#563	—	2	2	no	—
483	Q₈²	C₂²×C₇	1	1	yes	characteristic
484	#557	C₂²×C₇	1	1	yes	characteristic
485	#556	—	2	2	no	—
486	#556	—	2	1	no	—
487	#556	C₂²×C₇	1	1	yes	characteristic
488	#556	C₂²×C₇	1	1	yes	characteristic
489	#556	C₂²×C₇	1	2	yes	—
490	#555	—	2	1	no	—
491	#555	C₂²×C₇	1	1	yes	characteristic
492	#554	—	2	1	no	—
493	#553	—	2	1	no	—
494	D₄×Q₈	C₂²×C₇	1	2	yes	—
495	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
496	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
497	#548	C₂²×C₇	1	2	yes	—
498	#548	C₂²×C₇	1	2	yes	—
499	#547	C₂²×C₇	1	1	yes	characteristic
500	#544	—	2	1	no	—
501	#542	—	2	1	no	—
502	#542	—	2	2	no	—
503	#542	C₂²×C₇	1	2	yes	—
504	#541	C₂²×C₇	1	2	yes	—
505	#539	—	2	2	no	—
506	#536	C₂²×C₇	1	2	yes	—
507	#533	—	2	1	no	—
508	#533	C₂²×C₇	1	1	yes	characteristic
509	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
510	#529	—	2	1	no	—
511	#529	C₂²×C₇	1	1	yes	characteristic
512	#529	C₂²×C₇	1	1	yes	characteristic
513	#519	C₂²×C₇	1	2	yes	—
514	C₄×#41	C₂²×C₇	1	1	yes	characteristic
515	#497	C₂²×C₇	1	2	yes	—
516	#495	C₂²×C₇	1	2	yes	—
517	#494	C₂²×C₇	1	1	yes	characteristic
518	#494	C₂²×C₇	1	1	yes	characteristic
519	#489	C₂²×C₇	1	2	yes	—
520	#487	C₂²×C₇	1	2	yes	—
521	#487	C₂²×C₇	1	1	yes	characteristic
522	#487	C₂²×C₇	1	1	yes	characteristic
523	#485	C₂²×C₇	1	1	yes	characteristic
524	#485	C₂²×C₇	1	2	yes	—
525	#485	C₂²×C₇	1	2	yes	—
526	#482	C₂²×C₇	1	1	yes	characteristic
527	#479	C₂²×C₇	1	1	yes	characteristic
528	#479	C₂²×C₇	1	2	yes	—
529	#478	C₂²×C₇	1	1	yes	characteristic
530	#477	C₂²×C₇	1	1	yes	characteristic
531	#477	C₂²×C₇	1	2	yes	—
532	#476	C₂²×C₇	1	1	yes	characteristic
533	#475	C₂²×C₇	1	2	yes	—
534	#470	C₂²×C₇	1	2	yes	—
535	#470	C₂²×C₇	1	2	yes	—
536	#468	C₂²×C₇	1	2	yes	—
537	#468	C₂²×C₇	1	2	yes	—
538	#467	C₂²×C₇	1	2	yes	—
539	#465	C₂²×C₇	1	2	yes	—
540	#464	C₂²×C₇	1	1	yes	characteristic
541	#464	C₂²×C₇	1	2	yes	—
542	#464	C₂²×C₇	1	2	yes	—
543	#464	C₂²×C₇	1	2	yes	—
544	#464	C₂²×C₇	1	2	yes	—
545	#464	C₂²×C₇	1	2	yes	—
546	#463	C₂²×C₇	1	1	yes	characteristic
547	#462	C₂²×C₇	1	2	yes	—
548	#462	C₂²×C₇	1	2	yes	—
549	#462	C₂²×C₇	1	1	yes	characteristic
550	#462	C₂²×C₇	1	1	yes	characteristic
551	#462	C₂²×C₇	1	2	yes	—
552	#462	C₂²×C₇	1	2	yes	—
553	#462	C₂²×C₇	1	1	yes	characteristic
554	#462	C₂²×C₇	1	2	yes	—
555	#461	C₂²×C₇	1	1	yes	characteristic
556	#461	C₂²×C₇	1	1	yes	characteristic
557	#461	C₂²×C₇	1	1	yes	characteristic
558	#461	C₂²×C₇	1	2	yes	—
559	#452	C₂²×C₇	1	1	yes	characteristic
560	#452	C₂²×C₇	1	2	yes	—
561	#451	C₂²×C₇	1	2	yes	—
562	#451	C₂²×C₇	1	2	yes	—
563	#451	C₂²×C₇	1	2	yes	—
564	#451	C₂²×C₇	1	2	yes	—
565	#451	C₂²×C₇	1	2	yes	—
566	#449	C₂²×C₇	1	1	yes	characteristic
567	#449	C₂²×C₇	1	2	yes	—
568	#448	C₂²×C₇	1	2	yes	—
569	#446	C₂²×C₇	1	1	yes	characteristic
570	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
571	#441	C₂²×C₇	1	2	yes	—
572	#441	C₂²×C₇	1	2	yes	—
573	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
574	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
575	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
576	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
577	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
578	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
579	#436	C₂²×C₇	1	2	yes	—
580	#436	C₂²×C₇	1	1	yes	characteristic
581	#435	C₂²×C₇	1	2	yes	—
582	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
583	#433	C₂²×C₇	1	2	yes	—
584	#431	C₂²×C₇	1	1	yes	characteristic
585	#424	C₂²×C₇	1	2	yes	—
586	#423	C₂²×C₇	1	1	yes	characteristic
587	#419	C₂²×C₇	1	2	yes	—
588	#419	C₂²×C₇	1	2	yes	—
589	#416	C₂²×C₇	1	2	yes	—
590	C₂³×C₇	—	2	1	no	—
591	C₂³×C₇	—	2	1	no	—
592	C₂³×C₇	C₂²×D₄	1	2	yes	—
593	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
594	C₇×Q₈	—	2	2	no	—
595	C₇×Q₈	—	2	1	no	—
596	C₇×Q₈	—	2	2	no	—
597	C₇×Q₈	—	2	2	no	—
598	C₇×Q₈	—	2	2	no	—
599	C₇×Q₈	—	2	1	no	—
600	C₇×Q₈	—	2	1	no	—
601	C₇×Q₈	—	2	2	no	—
602	C₇×Q₈	—	2	2	no	—
603	C₇×Q₈	—	2	2	no	—
604	C₇×Q₈	—	4	4	no	—
605	C₇×Q₈	—	8	1	no	—
606	C₇×Q₈	—	8	2	no	—
607	C₇×Q₈	—	8	2	no	—
608	C₇×Q₈	—	8	2	no	—
609	C₇×Q₈	H(5,𝔽₂)	1	2	yes	—
610	C₇×D₄	—	2	2	no	—
611	C₇×D₄	—	2	1	no	—
612	C₇×D₄	—	2	1	no	—
613	C₇×D₄	—	2	1	no	—
614	C₇×D₄	—	2	1	no	—
615	C₇×D₄	—	4	2	no	—
616	C₇×D₄	—	4	2	no	—
617	C₇×D₄	—	4	2	no	—
618	C₇×D₄	—	8	2	no	—
619	C₇×D₄	—	8	2	no	—
620	C₂×C₄×C₇	—	2	1	no	—
621	C₂×C₄×C₇	—	2	2	no	—
622	C₂×C₄×C₇	—	2	2	no	—
623	C₂×C₄×C₇	—	2	1	no	—
624	C₂×C₄×C₇	—	2	1	no	—
625	C₂×C₄×C₇	—	2	2	no	—
626	C₂×C₄×C₇	—	2	1	no	—
627	C₂×C₄×C₇	—	2	1	no	—
628	C₂×C₄×C₇	—	2	2	no	—
629	C₂×C₄×C₇	—	2	1	no	—
630	C₂×C₄×C₇	—	2	2	no	—
631	C₂×C₄×C₇	—	2	1	no	—
632	C₂×C₄×C₇	—	2	1	no	—
633	C₂×C₄×C₇	—	2	2	no	—
634	C₂×C₄×C₇	—	2	2	no	—
635	C₂×C₄×C₇	—	4	1	no	—
636	C₂×C₄×C₇	—	4	2	no	—
637	C₂×C₄×C₇	—	4	4	no	—
638	C₂×C₄×C₇	—	4	2	no	—
639	C₂×C₄×C₇	—	4	2	no	—
640	C₂×C₄×C₇	—	8	1	no	—
641	C₂×C₄×C₇	—	8	2	no	—
642	C₂×C₄×C₇	—	8	2	no	—
643	C₂×C₄×C₇	—	8	2	no	—
644	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
645	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
646	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
647	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
648	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
649	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
650	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
651	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
652	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
653	C₇×C₈	—	2	1	no	—
654	C₇×C₈	—	2	2	no	—
655	C₇×C₈	—	2	1	no	—
656	C₇×C₈	—	2	2	no	—
657	C₇×C₈	—	2	1	no	—
658	C₇×C₈	—	2	1	no	—
659	C₂×#41	C₂³×C₇	1	1	yes	characteristic
660	C₂×#41	C₂³×C₇	1	2	yes	—
661	C₂²×Q₈	C₂³×C₇	1	2	yes	—
662	C₂²×Q₈	C₂³×C₇	1	2	yes	—
663	C₂²×Q₈	C₂³×C₇	1	2	yes	—
664	#137	—	4	4	no	—
665	#137	—	4	4	no	—
666	C₂×Q₁₆	—	4	4	no	—
667	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
668	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
669	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
670	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
671	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
672	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
673	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
674	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
675	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
676	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
677	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
678	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
679	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
680	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
681	C₂×M₁₆	C₂³×C₇	1	2	yes	—
682	C₂×M₁₆	C₂³×C₇	1	2	yes	—
683	C₂²×C₈	C₂³×C₇	1	2	yes	—
684	C₄⋊Q₈	—	2	1	no	—
685	C₄⋊Q₈	—	2	1	no	—
686	C₄⋊Q₈	—	2	2	no	—
687	C₄⋊Q₈	—	2	1	no	—
688	C₄⋊Q₈	—	2	2	no	—
689	C₄⋊Q₈	—	2	1	no	—
690	C₄⋊Q₈	—	2	1	no	—
691	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
692	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
693	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
694	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
695	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
696	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
697	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	—	2	2	no	—
701	#126	—	2	2	no	—
702	#126	—	2	2	no	—
703	#126	—	2	2	no	—
704	#126	—	2	2	no	—
705	#126	—	2	1	no	—
706	#126	C₇×D₄	1	2	yes	—
707	#125	—	2	2	no	—
708	#125	—	2	2	no	—
709	#125	—	2	2	no	—
710	#125	—	2	1	no	—
711	#125	—	2	1	no	—
712	#125	C₇×D₄	1	1	yes	characteristic
713	#125	C₂³×C₇	1	1	yes	characteristic
714	#124	—	2	2	no	—
715	#124	—	2	2	no	—
716	#124	—	2	2	no	—
717	#124	—	2	2	no	—
718	#124	—	2	2	no	—
719	#124	C₇×D₄	1	1	yes	characteristic
720	#124	C₂³×C₇	1	1	yes	characteristic
721	#124	C₂³×C₇	1	2	yes	—
722	#124	C₂³×C₇	1	2	yes	—
723	#123	—	2	1	no	—
724	#123	—	2	2	no	—
725	#123	—	2	2	no	—
726	#123	—	2	2	no	—
727	#123	—	2	2	no	—
728	#123	C₇×D₄	1	2	yes	—
729	C₂²⋊Q₈	—	2	1	no	—
730	C₂²⋊Q₈	—	2	1	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
742	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
743	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
744	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
745	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
746	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
747	#121	—	2	1	no	—
748	#121	—	2	2	no	—
749	#121	—	2	1	no	—
750	#121	—	2	2	no	—
751	#121	C₇×D₄	1	1	yes	characteristic
752	#121	C₂³×C₇	1	1	yes	characteristic
753	#121	C₂³×C₇	1	2	yes	—
754	C₄×Q₈	—	2	1	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	2	no	—
757	C₄×Q₈	—	2	2	no	—
758	C₄×Q₈	—	2	2	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
761	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
762	C₄×Q₈	C₂³×C₇	1	2	yes	—
763	C₄×Q₈	C₂³×C₇	1	2	yes	—
764	C₄×Q₈	C₂³×C₇	1	2	yes	—
765	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
766	C₄×Q₈	C₂³×C₇	1	2	yes	—
767	C₄×Q₈	C₂³×C₇	1	2	yes	—
768	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
769	C₄×D₄	—	2	1	no	—
770	C₄×D₄	—	2	2	no	—
771	C₄×D₄	—	2	1	no	—
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	2	1	no	—
774	C₄×D₄	—	2	1	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
778	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
779	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
780	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
781	C₄×D₄	C₂³×C₇	1	2	yes	—
782	#117	—	2	1	no	—
783	#117	—	2	1	no	—
784	#117	—	2	1	no	—
785	#117	—	2	1	no	—
786	#117	—	2	2	no	—
787	#117	—	2	2	no	—
788	#117	—	2	1	no	—
789	#117	—	2	1	no	—
790	#117	C₂³×C₇	1	1	yes	characteristic
791	#117	C₂³×C₇	1	2	yes	—
792	#117	C₂³×C₇	1	2	yes	—
793	C₂×C₄⋊C₄	—	2	1	no	—
794	C₂×C₄⋊C₄	—	2	1	no	—
795	C₂×C₄⋊C₄	—	2	1	no	—
796	C₂×C₄²	—	2	1	no	—
797	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
798	#107	C₂³×C₇	1	1	yes	characteristic
799	#107	C₂³×C₇	1	1	yes	characteristic
800	#107	C₂³×C₇	1	2	yes	—
801	#106	C₂³×C₇	1	1	yes	characteristic
802	#106	C₂³×C₇	1	1	yes	characteristic
803	#106	C₂³×C₇	1	2	yes	—
804	C₄⋊C₈	C₂³×C₇	1	2	yes	—
805	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
806	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
807	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
808	C₄⋊C₈	C₂³×C₇	1	2	yes	—
809	C₄⋊C₈	C₂³×C₇	1	2	yes	—
810	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
811	#103	C₂³×C₇	1	2	yes	—
812	#103	C₂³×C₇	1	2	yes	—
813	#103	C₂³×C₇	1	1	yes	characteristic
814	#103	C₂³×C₇	1	2	yes	—
815	#103	C₂³×C₇	1	2	yes	—
816	#103	C₂³×C₇	1	2	yes	—
817	#103	C₂³×C₇	1	2	yes	—
818	#103	C₂³×C₇	1	2	yes	—
819	#103	C₂³×C₇	1	1	yes	characteristic
820	#103	C₂³×C₇	1	1	yes	characteristic
821	#103	C₂³×C₇	1	2	yes	—
822	#103	C₂³×C₇	1	1	yes	characteristic
823	#103	C₂³×C₇	1	2	yes	—
824	#103	C₂³×C₇	1	2	yes	—
825	#103	C₂³×C₇	1	2	yes	—
826	#102	C₂³×C₇	1	1	yes	characteristic
827	#102	C₂³×C₇	1	2	yes	—
828	#102	C₂³×C₇	1	1	yes	characteristic
829	#102	C₂³×C₇	1	1	yes	characteristic
830	#102	C₂³×C₇	1	1	yes	characteristic
831	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
832	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
833	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
834	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
835	#97	C₂³×C₇	1	2	yes	—
836	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
837	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
838	C₄×C₈	C₂³×C₇	1	2	yes	—
839	C₂²×C₇	—	2	1	no	—
840	C₂²×C₇	—	2	2	no	—
841	C₂²×C₇	—	2	2	no	—
842	C₂²×C₇	—	2	1	no	—
843	C₂²×C₇	—	2	1	no	—
844	C₂²×C₇	—	2	2	no	—
845	C₂²×C₇	—	4	1	no	—
846	C₂²×C₇	—	4	1	no	—
847	C₂²×C₇	—	4	1	no	—
848	C₂²×C₇	—	4	1	no	—
849	C₂²×C₇	—	4	1	no	—
850	C₂²×C₇	—	4	1	no	—
851	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
852	C₄×C₇	—	2	1	no	—
853	C₄×C₇	—	2	1	no	—
854	C₄×C₇	—	2	2	no	—
855	C₄×C₇	—	2	1	no	—
856	C₄×C₇	—	2	2	no	—
857	C₄×C₇	—	2	2	no	—
858	C₄×C₇	—	2	1	no	—
859	C₄×C₇	—	2	2	no	—
860	C₄×C₇	—	4	1	no	—
861	C₄×C₇	—	4	1	no	—
862	C₄×C₇	—	4	2	no	—
863	C₄×C₇	—	4	2	no	—
864	C₄×C₇	—	4	2	no	—
865	C₄×C₇	—	4	2	no	—
866	C₄×C₇	—	4	1	no	—
867	C₄×C₇	—	4	1	no	—
868	C₄×C₇	—	4	1	no	—
869	C₄×C₇	#578	1	2	yes	—
870	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
871	C₄×C₇	#585	1	1	yes	characteristic
872	#41	—	2	2	no	—
873	#41	—	4	1	no	—
874	#41	—	4	2	no	—
875	#41	—	4	2	no	—
876	C₂×Q₈	—	2	2	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	—	2	2	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	2	4	no	—
882	C₂×Q₈	—	4	2	no	—
883	C₂×Q₈	—	4	2	no	—
884	C₂×Q₈	—	4	2	no	—
885	C₂×Q₈	—	4	2	no	—
886	C₂×Q₈	—	4	2	no	—
887	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
888	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
889	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
890	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
891	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
892	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
898	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
899	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
900	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
910	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
913	Q₁₆	—	2	2	no	—
914	Q₁₆	—	2	4	no	—
915	Q₁₆	—	2	4	no	—
916	Q₁₆	—	4	2	no	—
917	Q₁₆	—	4	2	no	—
918	Q₁₆	—	4	2	no	—
919	Q₁₆	—	4	2	no	—
920	Q₁₆	—	4	2	no	—
921	SD₁₆	—	2	2	no	—
922	SD₁₆	—	4	1	no	—
923	SD₁₆	—	4	2	no	—
924	SD₁₆	—	4	2	no	—
925	SD₁₆	—	4	2	no	—
926	D₈	—	4	1	no	—
927	M₁₆	—	4	2	no	—
928	M₁₆	—	4	2	no	—
929	C₂×C₈	—	4	2	no	—
930	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₇	1	2	yes	—
935	C₂×C₈	C₂⁴×C₇	1	2	yes	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
964	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
965	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
966	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
967	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
968	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
993	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
994	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
995	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
996	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1008	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1009	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1010	C₄²	C₂⁴×C₇	1	2	yes	—
1011	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1012	C₂×C₇	—	4	1	no	—
1013	C₂×C₇	—	4	2	no	—
1014	C₂×C₇	—	8	1	no	—
1015	C₂×C₇	—	8	1	no	—
1016	C₂×C₇	#3488	1	1	yes	characteristic
1017	C₂×C₇	C₂×#578	1	1	yes	characteristic
1018	C₂×C₇	#3586	1	1	yes	characteristic
1019	C₂³	—	2	1	no	—
1020	C₂³	—	2	1	no	—
1021	C₂³	C₂²×C₇×D₄	1	2	yes	—
1022	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	2	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	2	2	no	—
1028	Q₈	—	2	1	no	—
1029	Q₈	—	2	1	no	—
1030	Q₈	—	2	2	no	—
1031	Q₈	—	2	2	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	4	4	no	—
1034	Q₈	—	8	1	no	—
1035	Q₈	—	8	2	no	—
1036	Q₈	—	8	2	no	—
1037	Q₈	—	8	2	no	—
1038	Q₈	C₇×H(5,𝔽₂)	1	2	yes	—
1039	D₄	—	2	1	no	—
1040	D₄	—	2	1	no	—
1041	D₄	—	2	1	no	—
1042	D₄	—	2	1	no	—
1043	D₄	—	2	2	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	4	2	no	—
1046	D₄	—	4	2	no	—
1047	D₄	—	8	2	no	—
1048	D₄	—	8	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	4	1	no	—
1065	C₂×C₄	—	4	2	no	—
1066	C₂×C₄	—	4	4	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	8	1	no	—
1070	C₂×C₄	—	8	2	no	—
1071	C₂×C₄	—	8	2	no	—
1072	C₂×C₄	—	8	2	no	—
1073	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1074	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1075	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1076	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1077	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1078	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1079	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1080	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1081	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1082	C₈	—	2	1	no	—
1083	C₈	—	2	2	no	—
1084	C₈	—	2	1	no	—
1085	C₈	—	2	2	no	—
1086	C₈	—	2	1	no	—
1087	C₈	—	2	1	no	—
1088	C₇	#62036	1	1	yes	characteristic, direct product factor, Sylow
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	2	no	—
1094	C₂²	—	2	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1102	C₄	—	2	1	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	2	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	2	no	—
1118	C₄	—	4	1	no	—
1119	C₄	C₇×#578	1	2	yes	—
1120	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1121	C₄	C₇×#585	1	1	yes	characteristic
1122	C₂	—	4	1	no	—
1123	C₂	—	4	2	no	—
1124	C₂	—	8	1	no	—
1125	C₂	—	8	1	no	—
1126	C₂	C₇×#3488	1	1	yes	characteristic
1127	C₂	C₂×C₇×#578	1	1	yes	characteristic
1128	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3552	C₂	semidirect
2. C₇×#3518	C₂	semidirect
3. C₇×#3398	C₂	semidirect
4. C₇×#3393	C₂	semidirect
5. C₇×#3369	C₂	semidirect
6. C₇×#3363	C₂	semidirect
7. C₇×#3329	C₂	semidirect
8. C₇×#3328	C₂	semidirect
9. C₇×#3313	C₂	semidirect
10. C₇×#3303	C₂	semidirect
11. C₇×D₄×Q₁₆	C₂	semidirect
12. C₇×#3277	C₂	semidirect
13. C₇×#3276	C₂	semidirect
14. C₇×#3270	C₂	semidirect
15. C₇×#3258	C₂	semidirect
16. C₇×#3252	C₂	semidirect
17. C₇×#3225	C₂	semidirect
18. C₇×#3209	C₂	semidirect
19. C₇×#3127	C₂	semidirect
20. C₇×#3102	C₂	semidirect
21. C₇×#3044	C₂	semidirect
22. C₇×#3039	C₂	semidirect
23. C₇×#2993	C₂	semidirect
135. #62036	C₇	direct (N × H)
316. #3552	C₂×C₇	semidirect
317. #3518	C₂×C₇	semidirect
318. #3398	C₂×C₇	semidirect
319. #3393	C₂×C₇	semidirect
320. #3369	C₂×C₇	semidirect
321. #3363	C₂×C₇	semidirect
322. #3329	C₂×C₇	semidirect
323. #3328	C₂×C₇	semidirect
324. #3313	C₂×C₇	semidirect
325. #3303	C₂×C₇	semidirect
326. D₄×Q₁₆	C₂×C₇	semidirect
327. #3277	C₂×C₇	semidirect
328. #3276	C₂×C₇	semidirect
329. #3270	C₂×C₇	semidirect
330. #3258	C₂×C₇	semidirect
331. #3252	C₂×C₇	semidirect
332. #3225	C₂×C₇	semidirect
333. #3209	C₂×C₇	semidirect
334. #3127	C₂×C₇	semidirect
335. #3102	C₂×C₇	semidirect
336. #3044	C₂×C₇	semidirect
337. #3039	C₂×C₇	semidirect
338. #2993	C₂×C₇	semidirect
1088. C₇	#62036	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#3552	2
C₇×#3518	2
C₇×#3398	2
C₇×#3393	2
C₇×#3369	2
C₇×#3363	2
C₇×#3329	2
C₇×#3328	2
C₇×#3313	2
C₇×#3303	2
C₇×D₄×Q₁₆	2
C₇×#3277	2
C₇×#3276	2
C₇×#3270	2
C₇×#3258	2
C₇×#3252	2
C₇×#3225	2
C₇×#3209	2
C₇×#3127	2
C₇×#3102	2
C₇×#3044	2
C₇×#3039	2
C₇×#2993	2
#62036	7

Subgroups — C7×#62036 #13239252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62036 #13239252