Subgroups — C₇×#61873 #13239089

Order 1792.

1666 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3389	C₂	1	2	yes	maximal, complemented
4	C₇×#3388	C₂	1	2	yes	maximal, complemented
5	C₇×#3386	C₂	1	2	yes	maximal, complemented
6	C₇×#3385	C₂	1	2	yes	maximal, complemented
7	C₇×#3376	C₂	1	2	yes	maximal, complemented
8	C₇×#3376	C₂	1	2	yes	maximal, complemented
9	C₇×#3372	C₂	1	2	yes	maximal, complemented
10	C₇×#3367	C₂	1	2	yes	maximal, complemented
11	C₇×#3243	C₂	1	2	yes	maximal, complemented
12	C₇×#3242	C₂	1	2	yes	maximal, complemented
13	C₇×#3240	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3237	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3123	C₂	1	2	yes	maximal, complemented
16	C₇×#3118	C₂	1	2	yes	maximal
17	C₇×#3114	C₂	1	1	yes	maximal, characteristic
18	C₇×#3110	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#563	—	2	2	no	—
21	C₇×Q₈²	C₂²	1	1	yes	characteristic, complemented
22	C₇×#557	C₂²	1	1	yes	characteristic, complemented
23	C₇×#557	C₂²	1	2	yes	complemented
24	C₇×#556	—	2	1	no	—
25	C₇×#556	C₂²	1	2	yes	complemented
26	C₇×#556	C₂²	1	1	yes	characteristic, complemented
27	C₇×#554	—	2	1	no	—
28	C₇×#554	—	2	2	no	—
29	C₇×#554	C₂²	1	2	yes	—
30	C₇×#554	C₂²	1	2	yes	—
31	C₇×#554	C₂²	1	2	yes	—
32	C₇×#554	C₂²	1	1	yes	characteristic, complemented
33	C₇×#552	—	2	1	no	—
34	C₇×D₄×Q₈	—	2	1	no	—
35	C₇×D₄×Q₈	C₂²	1	2	yes	—
36	C₇×#544	—	2	1	no	—
37	C₇×#544	C₂²	1	2	yes	—
38	C₇×#543	—	2	1	no	—
39	C₇×#543	—	2	1	no	—
40	C₇×#542	C₂²	1	2	yes	—
41	C₇×#541	—	2	1	no	—
42	C₇×#541	—	2	2	no	—
43	C₇×#541	C₂²	1	2	yes	—
44	C₇×#533	C₂²	1	1	yes	characteristic
45	C₇×#533	C₂²	1	1	yes	characteristic
46	C₇×#533	C₂²	1	1	yes	characteristic
47	C₇×#529	C₂²	1	1	yes	characteristic
48	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
49	C₇×#518	C₂²	1	2	yes	—
50	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
51	C₇×#501	C₂²	1	2	yes	complemented
52	C₇×#501	C₂²	1	1	yes	characteristic, complemented
53	C₇×#501	C₂²	1	1	yes	characteristic, complemented
54	C₇×#501	C₂²	1	2	yes	complemented
55	C₇×#501	C₂²	1	2	yes	complemented
56	C₇×#500	C₂²	1	2	yes	complemented
57	C₇×#499	C₂²	1	2	yes	complemented
58	C₇×#491	C₂²	1	2	yes	complemented
59	C₇×#491	C₂²	1	2	yes	complemented
60	C₇×#489	C₂²	1	1	yes	characteristic, complemented
61	C₇×#489	C₂²	1	1	yes	characteristic, complemented
62	C₇×#489	C₂²	1	2	yes	complemented
63	C₇×#488	C₂²	1	2	yes	complemented
64	C₇×#487	C₂²	1	2	yes	complemented
65	C₇×#485	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	1	yes	characteristic
70	C₇×#482	C₂²	1	2	yes	—
71	C₇×#480	C₂²	1	1	yes	characteristic
72	C₇×#479	C₂²	1	2	yes	complemented
73	C₇×#479	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	—
77	C₇×#478	C₂²	1	2	yes	—
78	C₇×#478	C₂²	1	2	yes	—
79	C₇×#478	C₂²	1	2	yes	complemented
80	C₇×#478	C₂²	1	2	yes	complemented
81	C₇×#477	C₂²	1	2	yes	complemented
82	C₇×#477	C₂²	1	2	yes	complemented
83	C₇×#477	C₂²	1	2	yes	complemented
84	C₇×#476	C₂²	1	2	yes	—
85	C₇×#475	C₂²	1	2	yes	complemented
86	C₇×#475	C₂²	1	2	yes	complemented
87	C₇×#474	C₂²	1	2	yes	—
88	C₇×#474	C₂²	1	2	yes	—
89	C₇×#474	C₂²	1	2	yes	complemented
90	C₇×#463	C₂²	1	2	yes	—
91	C₇×#463	C₂²	1	2	yes	—
92	C₇×#463	C₂²	1	2	yes	—
93	C₇×#461	C₂²	1	2	yes	—
94	C₇×#461	C₂²	1	2	yes	—
95	C₇×#461	C₂²	1	2	yes	—
96	C₇×#450	C₂²	1	2	yes	—
97	C₇×#450	C₂²	1	1	yes	characteristic
98	C₇×#447	C₂²	1	1	yes	characteristic
99	C₇×#446	C₂²	1	2	yes	complemented
100	C₇×#446	C₂²	1	2	yes	complemented
101	C₇×#446	C₂²	1	2	yes	complemented
102	C₇×#446	C₂²	1	2	yes	complemented
103	C₇×#442	C₂²	1	2	yes	—
104	C₇×#442	C₂²	1	2	yes	—
105	C₇×#440	C₂²	1	2	yes	—
106	C₇×#440	C₂²	1	2	yes	—
107	C₇×#440	C₂²	1	2	yes	—
108	C₇×#440	C₂²	1	2	yes	—
109	C₇×#440	C₂²	1	2	yes	—
110	C₇×#440	C₂²	1	2	yes	—
111	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
112	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
113	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
114	C₄×C₇×D₈	C₂²	1	2	yes	—
115	C₇×#433	C₂²	1	2	yes	—
116	C₇×#433	C₂²	1	2	yes	—
117	C₇×#432	C₂²	1	1	yes	characteristic
118	C₇×#432	C₂²	1	1	yes	characteristic
119	#61873	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂²×C₇×Q₈	—	2	2	no	—
121	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₇	—	2	1	no	—
123	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
124	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
125	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
126	C₂×C₇×D₈	C₂³	1	2	yes	—
127	C₇×C₄⋊Q₈	—	2	2	no	—
128	C₇×C₄⋊Q₈	—	2	2	no	—
129	C₇×C₄⋊Q₈	—	2	1	no	—
130	C₇×C₄⋊Q₈	—	2	2	no	—
131	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
132	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
133	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
134	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
135	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
136	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₇×#126	—	2	2	no	—
142	C₇×#126	—	2	2	no	—
143	C₇×#126	—	2	2	no	—
144	C₇×#126	—	2	2	no	—
145	C₇×#126	—	2	2	no	—
146	C₇×#126	—	2	2	no	—
147	C₇×#126	—	2	1	no	—
148	C₇×#125	—	2	2	no	—
149	C₇×#125	—	2	2	no	—
150	C₇×#125	—	2	2	no	—
151	C₇×#125	—	2	2	no	—
152	C₇×#125	—	2	2	no	—
153	C₇×#125	—	2	1	no	—
154	C₇×#125	—	2	2	no	—
155	C₇×#125	—	2	1	no	—
156	C₇×#125	D₄	1	2	yes	—
157	C₇×#125	C₂³	1	2	yes	—
158	C₇×#125	C₂³	1	1	yes	characteristic
159	C₇×#125	C₂³	1	2	yes	—
160	C₇×#125	C₂³	1	2	yes	—
161	C₇×#125	C₂³	1	2	yes	—
162	C₇×#124	—	2	2	no	—
163	C₇×#124	C₂³	1	2	yes	—
164	C₇×#124	C₂³	1	1	yes	characteristic
165	C₇×#123	—	2	1	no	—
166	C₇×#123	—	2	2	no	—
167	C₇×C₂²⋊Q₈	—	2	2	no	—
168	C₇×C₂²⋊Q₈	—	2	1	no	—
169	C₇×C₂²⋊Q₈	—	2	1	no	—
170	C₇×C₂²⋊Q₈	—	2	2	no	—
171	C₇×C₂²⋊Q₈	—	2	2	no	—
172	C₇×C₂²⋊Q₈	—	2	2	no	—
173	C₇×C₂²⋊Q₈	—	2	1	no	—
174	C₇×C₂²⋊Q₈	—	2	1	no	—
175	C₇×C₂²⋊Q₈	—	2	1	no	—
176	C₇×C₂²⋊Q₈	—	2	2	no	—
177	C₇×C₂²⋊Q₈	—	2	2	no	—
178	C₇×C₂²⋊Q₈	—	2	2	no	—
179	C₇×C₂²⋊Q₈	—	2	2	no	—
180	C₇×C₂²⋊Q₈	—	2	2	no	—
181	C₇×C₂²⋊Q₈	—	2	2	no	—
182	C₇×C₂²⋊Q₈	—	2	2	no	—
183	C₇×C₂²⋊Q₈	—	2	2	no	—
184	C₇×C₂²⋊Q₈	—	2	2	no	—
185	C₇×C₂²⋊Q₈	—	2	2	no	—
186	C₇×C₂²⋊Q₈	—	2	2	no	—
187	C₇×C₂²⋊Q₈	—	2	2	no	—
188	C₇×C₂²⋊Q₈	—	2	2	no	—
189	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
190	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
191	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
192	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
193	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₇×#121	C₂³	1	1	yes	characteristic
195	C₄×C₇×Q₈	—	2	1	no	—
196	C₄×C₇×Q₈	—	2	1	no	—
197	C₄×C₇×Q₈	—	2	2	no	—
198	C₄×C₇×Q₈	—	2	1	no	—
199	C₄×C₇×Q₈	—	2	1	no	—
200	C₄×C₇×Q₈	—	2	1	no	—
201	C₄×C₇×Q₈	C₂³	1	2	yes	—
202	C₄×C₇×Q₈	C₂³	1	2	yes	—
203	C₄×C₇×Q₈	C₂³	1	2	yes	—
204	C₄×C₇×Q₈	C₂³	1	2	yes	—
205	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
206	C₄×C₇×Q₈	C₂³	1	2	yes	—
207	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
208	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
209	C₄×C₇×D₄	—	2	1	no	—
210	C₄×C₇×D₄	—	2	2	no	—
211	C₄×C₇×D₄	—	2	2	no	—
212	C₄×C₇×D₄	—	2	1	no	—
213	C₄×C₇×D₄	—	2	1	no	—
214	C₄×C₇×D₄	C₂³	1	2	yes	—
215	C₄×C₇×D₄	C₂³	1	2	yes	—
216	C₄×C₇×D₄	C₂³	1	2	yes	—
217	C₄×C₇×D₄	C₂³	1	2	yes	—
218	C₄×C₇×D₄	C₂³	1	2	yes	—
219	C₄×C₇×D₄	C₂³	1	2	yes	—
220	C₄×C₇×D₄	C₂³	1	2	yes	—
221	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
222	C₇×#117	—	2	1	no	—
223	C₇×#117	—	2	2	no	—
224	C₇×#117	—	2	1	no	—
225	C₇×#117	—	2	1	no	—
226	C₇×#117	C₂³	1	2	yes	—
227	C₇×#117	C₂³	1	2	yes	—
228	C₂×C₇×C₄⋊C₄	—	2	2	no	—
229	C₂×C₇×C₄⋊C₄	—	2	2	no	—
230	C₂×C₇×C₄⋊C₄	—	2	2	no	—
231	C₂×C₇×C₄⋊C₄	—	2	1	no	—
232	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
234	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
237	C₇×#107	C₂³	1	2	yes	—
238	C₇×#107	C₂³	1	2	yes	—
239	C₇×#107	C₂³	1	2	yes	—
240	C₇×#107	C₂³	1	2	yes	—
241	C₇×#107	C₂³	1	2	yes	—
242	C₇×#107	C₂³	1	2	yes	—
243	C₇×#107	C₂³	1	2	yes	—
244	C₇×#106	C₂³	1	2	yes	—
245	C₇×#106	C₂³	1	2	yes	—
246	C₇×#106	C₂³	1	2	yes	—
247	C₇×#106	C₂³	1	2	yes	—
248	C₇×#106	C₂³	1	2	yes	—
249	C₇×C₄⋊C₈	C₂³	1	2	yes	—
250	C₇×C₄⋊C₈	C₂³	1	2	yes	—
251	C₇×C₄⋊C₈	C₂³	1	2	yes	—
252	C₇×C₄⋊C₈	C₂³	1	2	yes	—
253	C₇×C₄⋊C₈	C₂³	1	2	yes	—
254	C₇×C₄⋊C₈	C₂³	1	2	yes	—
255	C₇×#103	C₂³	1	2	yes	—
256	C₇×#103	C₂³	1	2	yes	—
257	C₇×#103	C₂³	1	2	yes	—
258	C₇×#103	C₂³	1	2	yes	—
259	C₇×#103	C₂³	1	2	yes	—
260	C₇×#103	C₂³	1	2	yes	—
261	C₇×#103	C₂³	1	2	yes	—
262	C₇×#103	C₂³	1	2	yes	—
263	C₇×#103	C₂³	1	2	yes	—
264	C₇×#102	C₂³	1	2	yes	—
265	C₇×#102	C₂³	1	2	yes	—
266	C₇×#102	C₂³	1	2	yes	—
267	C₇×#102	C₂³	1	2	yes	—
268	C₇×#102	C₂³	1	2	yes	—
269	C₇×#102	C₂³	1	2	yes	—
270	C₇×#102	C₂³	1	2	yes	—
271	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₇×#97	C₂³	1	1	yes	characteristic
275	C₇×#97	C₂³	1	1	yes	characteristic
276	C₇×#97	C₂³	1	2	yes	—
277	C₇×#97	C₂³	1	2	yes	—
278	C₇×#97	C₂³	1	2	yes	—
279	C₄×C₇×C₈	C₂³	1	2	yes	—
280	C₄×C₇×C₈	C₂³	1	2	yes	—
281	#3555	C₂×C₇	1	1	yes	characteristic, complemented
282	#3501	C₂×C₇	1	1	yes	characteristic, complemented
283	#3389	C₂×C₇	1	2	yes	complemented
284	#3388	C₂×C₇	1	2	yes	complemented
285	#3386	C₂×C₇	1	2	yes	complemented
286	#3385	C₂×C₇	1	2	yes	complemented
287	#3376	C₂×C₇	1	2	yes	complemented
288	#3376	C₂×C₇	1	2	yes	complemented
289	#3372	C₂×C₇	1	2	yes	complemented
290	#3367	C₂×C₇	1	2	yes	complemented
291	#3243	C₂×C₇	1	2	yes	complemented
292	#3242	C₂×C₇	1	2	yes	complemented
293	#3240	C₂×C₇	1	1	yes	characteristic, complemented
294	#3237	C₂×C₇	1	1	yes	characteristic, complemented
295	#3123	C₂×C₇	1	2	yes	complemented
296	#3118	C₂×C₇	1	2	yes	—
297	#3114	C₂×C₇	1	1	yes	characteristic
298	#3110	C₂×C₇	1	1	yes	characteristic, complemented
299	#2987	C₂×C₇	1	1	yes	characteristic, complemented
300	C₂⁴×C₇	—	2	1	no	—
301	C₂×C₇×Q₈	—	2	1	no	—
302	C₂×C₇×Q₈	—	2	1	no	—
303	C₂×C₇×Q₈	—	2	1	no	—
304	C₂×C₇×Q₈	—	2	2	no	—
305	C₂×C₇×Q₈	—	2	2	no	—
306	C₂×C₇×Q₈	—	2	2	no	—
307	C₂×C₇×Q₈	—	8	4	no	—
308	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
309	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
310	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
311	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
312	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
313	C₂×C₇×D₄	—	2	4	no	—
314	C₂×C₇×D₄	—	2	1	no	—
315	C₂×C₇×D₄	—	2	1	no	—
316	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
317	C₂×C₇×D₄	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₇	—	2	1	no	—
319	C₂²×C₄×C₇	—	2	1	no	—
320	C₂²×C₄×C₇	—	2	2	no	—
321	C₂²×C₄×C₇	—	2	2	no	—
322	C₂²×C₄×C₇	—	2	2	no	—
323	C₂²×C₄×C₇	—	2	2	no	—
324	C₂²×C₄×C₇	—	2	2	no	—
325	C₂²×C₄×C₇	—	2	2	no	—
326	C₂²×C₄×C₇	—	2	2	no	—
327	C₂²×C₄×C₇	—	8	2	no	—
328	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
331	C₇×SD₁₆	—	2	4	no	—
332	C₇×SD₁₆	—	2	4	no	—
333	C₇×SD₁₆	—	2	4	no	—
334	C₇×D₈	—	2	4	no	—
335	C₂×C₇×C₈	C₂⁴	1	2	yes	—
336	C₂×C₇×C₈	C₂⁴	1	2	yes	—
337	C₂×C₇×C₈	C₂⁴	1	2	yes	—
338	C₂×C₇×C₈	C₂⁴	1	2	yes	—
339	C₇×C₄⋊C₄	—	2	2	no	—
340	C₇×C₄⋊C₄	—	2	1	no	—
341	C₇×C₄⋊C₄	—	2	1	no	—
342	C₇×C₄⋊C₄	—	2	2	no	—
343	C₇×C₄⋊C₄	—	2	2	no	—
344	C₇×C₄⋊C₄	—	2	2	no	—
345	C₇×C₄⋊C₄	—	2	2	no	—
346	C₇×C₄⋊C₄	—	2	2	no	—
347	C₇×C₄⋊C₄	—	2	2	no	—
348	C₇×C₄⋊C₄	—	2	2	no	—
349	C₇×C₄⋊C₄	—	2	1	no	—
350	C₇×C₄⋊C₄	—	2	1	no	—
351	C₇×C₄⋊C₄	—	2	2	no	—
352	C₇×C₄⋊C₄	—	2	1	no	—
353	C₇×C₄⋊C₄	—	2	1	no	—
354	C₇×C₄⋊C₄	—	2	1	no	—
355	C₇×C₄⋊C₄	—	2	2	no	—
356	C₇×C₄⋊C₄	—	2	1	no	—
357	C₇×C₄⋊C₄	—	2	2	no	—
358	C₇×C₄⋊C₄	—	2	2	no	—
359	C₇×C₄⋊C₄	—	2	1	no	—
360	C₇×C₄⋊C₄	—	2	2	no	—
361	C₇×C₄⋊C₄	—	2	2	no	—
362	C₇×C₄⋊C₄	—	2	2	no	—
363	C₇×C₄⋊C₄	—	2	2	no	—
364	C₇×C₄⋊C₄	—	2	2	no	—
365	C₇×C₄⋊C₄	—	2	2	no	—
366	C₇×C₄⋊C₄	—	2	1	no	—
367	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
368	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
369	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
370	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
371	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
372	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
373	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
374	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
375	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
376	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
377	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
378	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
379	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
380	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
381	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
382	C₇×C₂²⋊C₄	—	2	2	no	—
383	C₇×C₂²⋊C₄	—	2	2	no	—
384	C₇×C₂²⋊C₄	—	2	1	no	—
385	C₇×C₂²⋊C₄	—	2	2	no	—
386	C₇×C₂²⋊C₄	—	2	2	no	—
387	C₇×C₂²⋊C₄	—	2	2	no	—
388	C₇×C₂²⋊C₄	—	2	2	no	—
389	C₇×C₂²⋊C₄	—	2	2	no	—
390	C₇×C₂²⋊C₄	—	2	2	no	—
391	C₇×C₂²⋊C₄	—	2	1	no	—
392	C₇×C₂²⋊C₄	—	2	1	no	—
393	C₇×C₂²⋊C₄	—	2	1	no	—
394	C₇×C₂²⋊C₄	—	2	2	no	—
395	C₇×C₂²⋊C₄	—	2	2	no	—
396	C₇×C₂²⋊C₄	—	2	1	no	—
397	C₇×C₂²⋊C₄	—	2	2	no	—
398	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
399	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
400	C₄²×C₇	—	2	2	no	—
401	C₄²×C₇	—	2	1	no	—
402	C₄²×C₇	—	2	2	no	—
403	C₄²×C₇	—	2	2	no	—
404	C₄²×C₇	—	2	2	no	—
405	C₄²×C₇	—	2	2	no	—
406	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
407	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
408	C₄²×C₇	C₂⁴	1	2	yes	—
409	C₄²×C₇	C₂⁴	1	2	yes	—
410	C₄²×C₇	C₂⁴	1	1	yes	characteristic
411	C₄²×C₇	C₂⁴	1	1	yes	characteristic
412	#563	—	2	2	no	—
413	Q₈²	C₂²×C₇	1	1	yes	characteristic, complemented
414	#557	C₂²×C₇	1	1	yes	characteristic, complemented
415	#557	C₂²×C₇	1	2	yes	complemented
416	#556	—	2	1	no	—
417	#556	C₂²×C₇	1	2	yes	complemented
418	#556	C₂²×C₇	1	1	yes	characteristic, complemented
419	#554	—	2	1	no	—
420	#554	—	2	2	no	—
421	#554	C₂²×C₇	1	2	yes	—
422	#554	C₂²×C₇	1	2	yes	—
423	#554	C₂²×C₇	1	2	yes	—
424	#554	C₂²×C₇	1	1	yes	characteristic, complemented
425	#552	—	2	1	no	—
426	D₄×Q₈	—	2	1	no	—
427	D₄×Q₈	C₂²×C₇	1	2	yes	—
428	#544	—	2	1	no	—
429	#544	C₂²×C₇	1	2	yes	—
430	#543	—	2	1	no	—
431	#543	—	2	1	no	—
432	#542	C₂²×C₇	1	2	yes	—
433	#541	—	2	1	no	—
434	#541	—	2	2	no	—
435	#541	C₂²×C₇	1	2	yes	—
436	#533	C₂²×C₇	1	1	yes	characteristic
437	#533	C₂²×C₇	1	1	yes	characteristic
438	#533	C₂²×C₇	1	1	yes	characteristic
439	#529	C₂²×C₇	1	1	yes	characteristic
440	C₂×C₂²⋊Q₈	—	2	2	no	—
441	#518	C₂²×C₇	1	2	yes	—
442	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
443	#501	C₂²×C₇	1	2	yes	complemented
444	#501	C₂²×C₇	1	2	yes	complemented
445	#501	C₂²×C₇	1	1	yes	characteristic, complemented
446	#501	C₂²×C₇	1	2	yes	complemented
447	#501	C₂²×C₇	1	1	yes	characteristic, complemented
448	#500	C₂²×C₇	1	2	yes	complemented
449	#499	C₂²×C₇	1	2	yes	complemented
450	#491	C₂²×C₇	1	2	yes	complemented
451	#491	C₂²×C₇	1	2	yes	complemented
452	#489	C₂²×C₇	1	1	yes	characteristic, complemented
453	#489	C₂²×C₇	1	2	yes	complemented
454	#489	C₂²×C₇	1	1	yes	characteristic, complemented
455	#488	C₂²×C₇	1	2	yes	complemented
456	#487	C₂²×C₇	1	2	yes	complemented
457	#485	C₂²×C₇	1	2	yes	—
458	#485	C₂²×C₇	1	2	yes	—
459	#485	C₂²×C₇	1	2	yes	—
460	#484	C₂²×C₇	1	2	yes	—
461	#483	C₂²×C₇	1	1	yes	characteristic
462	#482	C₂²×C₇	1	2	yes	—
463	#480	C₂²×C₇	1	1	yes	characteristic
464	#479	C₂²×C₇	1	2	yes	complemented
465	#479	C₂²×C₇	1	2	yes	complemented
466	#479	C₂²×C₇	1	2	yes	complemented
467	#479	C₂²×C₇	1	2	yes	complemented
468	#478	C₂²×C₇	1	2	yes	—
469	#478	C₂²×C₇	1	2	yes	—
470	#478	C₂²×C₇	1	2	yes	—
471	#478	C₂²×C₇	1	2	yes	complemented
472	#478	C₂²×C₇	1	2	yes	complemented
473	#477	C₂²×C₇	1	2	yes	complemented
474	#477	C₂²×C₇	1	2	yes	complemented
475	#477	C₂²×C₇	1	2	yes	complemented
476	#476	C₂²×C₇	1	2	yes	—
477	#475	C₂²×C₇	1	2	yes	complemented
478	#475	C₂²×C₇	1	2	yes	complemented
479	#474	C₂²×C₇	1	2	yes	—
480	#474	C₂²×C₇	1	2	yes	—
481	#474	C₂²×C₇	1	2	yes	complemented
482	#463	C₂²×C₇	1	2	yes	—
483	#463	C₂²×C₇	1	2	yes	—
484	#463	C₂²×C₇	1	2	yes	—
485	#461	C₂²×C₇	1	2	yes	—
486	#461	C₂²×C₇	1	2	yes	—
487	#461	C₂²×C₇	1	2	yes	—
488	#450	C₂²×C₇	1	2	yes	—
489	#450	C₂²×C₇	1	1	yes	characteristic
490	#447	C₂²×C₇	1	1	yes	characteristic
491	#446	C₂²×C₇	1	2	yes	complemented
492	#446	C₂²×C₇	1	2	yes	complemented
493	#446	C₂²×C₇	1	2	yes	complemented
494	#446	C₂²×C₇	1	2	yes	complemented
495	#442	C₂²×C₇	1	2	yes	—
496	#442	C₂²×C₇	1	2	yes	—
497	#440	C₂²×C₇	1	2	yes	—
498	#440	C₂²×C₇	1	2	yes	—
499	#440	C₂²×C₇	1	2	yes	—
500	#440	C₂²×C₇	1	2	yes	—
501	#440	C₂²×C₇	1	2	yes	—
502	#440	C₂²×C₇	1	2	yes	—
503	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
504	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
505	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
506	C₄×D₈	C₂²×C₇	1	2	yes	—
507	#433	C₂²×C₇	1	2	yes	—
508	#433	C₂²×C₇	1	2	yes	—
509	#432	C₂²×C₇	1	1	yes	characteristic
510	#432	C₂²×C₇	1	1	yes	characteristic
511	C₂³×C₇	—	2	4	no	—
512	C₂³×C₇	—	2	2	no	—
513	C₂³×C₇	—	2	1	no	—
514	C₂³×C₇	—	8	1	no	—
515	C₂³×C₇	—	8	1	no	—
516	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
517	C₇×Q₈	—	2	2	no	—
518	C₇×Q₈	—	2	2	no	—
519	C₇×Q₈	—	2	2	no	—
520	C₇×Q₈	—	4	2	no	—
521	C₇×Q₈	—	4	1	no	—
522	C₇×Q₈	—	4	1	no	—
523	C₇×Q₈	—	4	2	no	—
524	C₇×Q₈	—	8	1	no	—
525	C₇×Q₈	—	8	2	no	—
526	C₇×Q₈	—	8	1	no	—
527	C₇×Q₈	—	8	2	no	—
528	C₇×Q₈	—	8	2	no	—
529	C₇×D₄	—	2	4	no	—
530	C₇×D₄	—	2	2	no	—
531	C₇×D₄	—	2	2	no	—
532	C₇×D₄	—	8	1	no	—
533	C₇×D₄	2₋¹⁺⁴	1	4	yes	—
534	C₂×C₄×C₇	—	2	2	no	—
535	C₂×C₄×C₇	—	2	2	no	—
536	C₂×C₄×C₇	—	2	1	no	—
537	C₂×C₄×C₇	—	2	1	no	—
538	C₂×C₄×C₇	—	2	1	no	—
539	C₂×C₄×C₇	—	2	2	no	—
540	C₂×C₄×C₇	—	2	2	no	—
541	C₂×C₄×C₇	—	2	2	no	—
542	C₂×C₄×C₇	—	2	2	no	—
543	C₂×C₄×C₇	—	4	1	no	—
544	C₂×C₄×C₇	—	4	1	no	—
545	C₂×C₄×C₇	—	4	2	no	—
546	C₂×C₄×C₇	—	4	4	no	—
547	C₂×C₄×C₇	—	8	2	no	—
548	C₂×C₄×C₇	—	8	2	no	—
549	C₂×C₄×C₇	—	8	2	no	—
550	C₂×C₄×C₇	—	8	2	no	—
551	C₂×C₄×C₇	—	8	2	no	—
552	C₂×C₄×C₇	—	8	2	no	—
553	C₂×C₄×C₇	—	8	1	no	—
554	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
558	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
559	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
560	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
563	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
564	C₇×C₈	—	2	2	no	—
565	C₇×C₈	—	2	2	no	—
566	C₇×C₈	—	2	2	no	—
567	C₇×C₈	—	2	2	no	—
568	C₂²×Q₈	—	2	2	no	—
569	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
570	C₂³×C₄	—	2	1	no	—
571	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
572	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
573	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
574	C₂×D₈	C₂³×C₇	1	2	yes	—
575	C₄⋊Q₈	—	2	2	no	—
576	C₄⋊Q₈	—	2	2	no	—
577	C₄⋊Q₈	—	2	1	no	—
578	C₄⋊Q₈	—	2	2	no	—
579	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
580	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
581	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
582	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
583	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
584	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
585	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
586	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
587	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
588	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
589	#126	—	2	2	no	—
590	#126	—	2	2	no	—
591	#126	—	2	2	no	—
592	#126	—	2	2	no	—
593	#126	—	2	2	no	—
594	#126	—	2	2	no	—
595	#126	—	2	1	no	—
596	#125	—	2	2	no	—
597	#125	—	2	2	no	—
598	#125	—	2	2	no	—
599	#125	—	2	2	no	—
600	#125	—	2	2	no	—
601	#125	—	2	1	no	—
602	#125	—	2	2	no	—
603	#125	—	2	1	no	—
604	#125	C₇×D₄	1	2	yes	—
605	#125	C₂³×C₇	1	1	yes	characteristic
606	#125	C₂³×C₇	1	2	yes	—
607	#125	C₂³×C₇	1	2	yes	—
608	#125	C₂³×C₇	1	2	yes	—
609	#125	C₂³×C₇	1	2	yes	—
610	#124	—	2	2	no	—
611	#124	C₂³×C₇	1	1	yes	characteristic
612	#124	C₂³×C₇	1	2	yes	—
613	#123	—	2	1	no	—
614	#123	—	2	2	no	—
615	C₂²⋊Q₈	—	2	2	no	—
616	C₂²⋊Q₈	—	2	1	no	—
617	C₂²⋊Q₈	—	2	1	no	—
618	C₂²⋊Q₈	—	2	2	no	—
619	C₂²⋊Q₈	—	2	2	no	—
620	C₂²⋊Q₈	—	2	2	no	—
621	C₂²⋊Q₈	—	2	1	no	—
622	C₂²⋊Q₈	—	2	1	no	—
623	C₂²⋊Q₈	—	2	1	no	—
624	C₂²⋊Q₈	—	2	2	no	—
625	C₂²⋊Q₈	—	2	2	no	—
626	C₂²⋊Q₈	—	2	2	no	—
627	C₂²⋊Q₈	—	2	2	no	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	—	2	2	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
638	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
639	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
640	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
641	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
642	#121	C₂³×C₇	1	1	yes	characteristic
643	C₄×Q₈	—	2	1	no	—
644	C₄×Q₈	—	2	1	no	—
645	C₄×Q₈	—	2	2	no	—
646	C₄×Q₈	—	2	1	no	—
647	C₄×Q₈	—	2	1	no	—
648	C₄×Q₈	—	2	1	no	—
649	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
650	C₄×Q₈	C₂³×C₇	1	2	yes	—
651	C₄×Q₈	C₂³×C₇	1	2	yes	—
652	C₄×Q₈	C₂³×C₇	1	2	yes	—
653	C₄×Q₈	C₂³×C₇	1	2	yes	—
654	C₄×Q₈	C₂³×C₇	1	2	yes	—
655	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
656	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
657	C₄×D₄	—	2	1	no	—
658	C₄×D₄	—	2	2	no	—
659	C₄×D₄	—	2	2	no	—
660	C₄×D₄	—	2	1	no	—
661	C₄×D₄	—	2	1	no	—
662	C₄×D₄	C₂³×C₇	1	2	yes	—
663	C₄×D₄	C₂³×C₇	1	2	yes	—
664	C₄×D₄	C₂³×C₇	1	2	yes	—
665	C₄×D₄	C₂³×C₇	1	2	yes	—
666	C₄×D₄	C₂³×C₇	1	2	yes	—
667	C₄×D₄	C₂³×C₇	1	2	yes	—
668	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
669	C₄×D₄	C₂³×C₇	1	2	yes	—
670	#117	—	2	1	no	—
671	#117	—	2	2	no	—
672	#117	—	2	1	no	—
673	#117	—	2	1	no	—
674	#117	C₂³×C₇	1	2	yes	—
675	#117	C₂³×C₇	1	2	yes	—
676	C₂×C₄⋊C₄	—	2	2	no	—
677	C₂×C₄⋊C₄	—	2	2	no	—
678	C₂×C₄⋊C₄	—	2	2	no	—
679	C₂×C₄⋊C₄	—	2	1	no	—
680	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	—	2	1	no	—
682	C₂×C₂²⋊C₄	—	2	2	no	—
683	C₂×C₂²⋊C₄	—	2	2	no	—
684	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
685	#107	C₂³×C₇	1	2	yes	—
686	#107	C₂³×C₇	1	2	yes	—
687	#107	C₂³×C₇	1	2	yes	—
688	#107	C₂³×C₇	1	2	yes	—
689	#107	C₂³×C₇	1	2	yes	—
690	#107	C₂³×C₇	1	2	yes	—
691	#107	C₂³×C₇	1	2	yes	—
692	#106	C₂³×C₇	1	2	yes	—
693	#106	C₂³×C₇	1	2	yes	—
694	#106	C₂³×C₇	1	2	yes	—
695	#106	C₂³×C₇	1	2	yes	—
696	#106	C₂³×C₇	1	2	yes	—
697	C₄⋊C₈	C₂³×C₇	1	2	yes	—
698	C₄⋊C₈	C₂³×C₇	1	2	yes	—
699	C₄⋊C₈	C₂³×C₇	1	2	yes	—
700	C₄⋊C₈	C₂³×C₇	1	2	yes	—
701	C₄⋊C₈	C₂³×C₇	1	2	yes	—
702	C₄⋊C₈	C₂³×C₇	1	2	yes	—
703	#103	C₂³×C₇	1	2	yes	—
704	#103	C₂³×C₇	1	2	yes	—
705	#103	C₂³×C₇	1	2	yes	—
706	#103	C₂³×C₇	1	2	yes	—
707	#103	C₂³×C₇	1	2	yes	—
708	#103	C₂³×C₇	1	2	yes	—
709	#103	C₂³×C₇	1	2	yes	—
710	#103	C₂³×C₇	1	2	yes	—
711	#103	C₂³×C₇	1	2	yes	—
712	#102	C₂³×C₇	1	2	yes	—
713	#102	C₂³×C₇	1	2	yes	—
714	#102	C₂³×C₇	1	2	yes	—
715	#102	C₂³×C₇	1	2	yes	—
716	#102	C₂³×C₇	1	2	yes	—
717	#102	C₂³×C₇	1	2	yes	—
718	#102	C₂³×C₇	1	2	yes	—
719	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
720	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
721	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
722	#97	C₂³×C₇	1	1	yes	characteristic
723	#97	C₂³×C₇	1	1	yes	characteristic
724	#97	C₂³×C₇	1	2	yes	—
725	#97	C₂³×C₇	1	2	yes	—
726	#97	C₂³×C₇	1	2	yes	—
727	C₄×C₈	C₂³×C₇	1	2	yes	—
728	C₄×C₈	C₂³×C₇	1	2	yes	—
729	C₂²×C₇	—	2	1	no	—
730	C₂²×C₇	—	2	1	no	—
731	C₂²×C₇	—	2	1	no	—
732	C₂²×C₇	—	2	4	no	—
733	C₂²×C₇	—	4	2	no	—
734	C₂²×C₇	—	4	2	no	—
735	C₂²×C₇	—	4	1	no	—
736	C₂²×C₇	—	4	1	no	—
737	C₂²×C₇	—	4	1	no	—
738	C₂²×C₇	—	8	4	no	—
739	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
740	C₄×C₇	—	2	1	no	—
741	C₄×C₇	—	2	1	no	—
742	C₄×C₇	—	2	2	no	—
743	C₄×C₇	—	2	2	no	—
744	C₄×C₇	—	2	1	no	—
745	C₄×C₇	—	2	1	no	—
746	C₄×C₇	—	2	2	no	—
747	C₄×C₇	—	2	2	no	—
748	C₄×C₇	—	2	1	no	—
749	C₄×C₇	—	4	2	no	—
750	C₄×C₇	—	4	2	no	—
751	C₄×C₇	—	4	2	no	—
752	C₄×C₇	—	4	1	no	—
753	C₄×C₇	—	4	1	no	—
754	C₄×C₇	—	4	2	no	—
755	C₄×C₇	—	4	2	no	—
756	C₄×C₇	—	4	1	no	—
757	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
758	C₂⁴	—	2	1	no	—
759	C₂×Q₈	—	2	1	no	—
760	C₂×Q₈	—	2	1	no	—
761	C₂×Q₈	—	2	1	no	—
762	C₂×Q₈	—	2	2	no	—
763	C₂×Q₈	—	2	2	no	—
764	C₂×Q₈	—	2	2	no	—
765	C₂×Q₈	—	8	4	no	—
766	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
767	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
768	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
769	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
770	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
771	C₂×D₄	—	2	4	no	—
772	C₂×D₄	—	2	1	no	—
773	C₂×D₄	—	2	1	no	—
774	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
775	C₂×D₄	C₂⁴×C₇	1	2	yes	—
776	C₂²×C₄	—	2	1	no	—
777	C₂²×C₄	—	2	1	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	8	2	no	—
786	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
787	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
789	SD₁₆	—	2	4	no	—
790	SD₁₆	—	2	4	no	—
791	SD₁₆	—	2	4	no	—
792	D₈	—	2	4	no	—
793	C₂×C₈	C₂⁴×C₇	1	2	yes	—
794	C₂×C₈	C₂⁴×C₇	1	2	yes	—
795	C₂×C₈	C₂⁴×C₇	1	2	yes	—
796	C₂×C₈	C₂⁴×C₇	1	2	yes	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	1	no	—
799	C₄⋊C₄	—	2	1	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	1	no	—
808	C₄⋊C₄	—	2	1	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	1	no	—
825	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
826	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
827	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
828	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
829	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
830	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
831	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
832	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
833	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
834	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
835	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
836	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
837	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
838	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
839	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	1	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	1	no	—
850	C₂²⋊C₄	—	2	1	no	—
851	C₂²⋊C₄	—	2	1	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	1	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
857	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
858	C₄²	—	2	2	no	—
859	C₄²	—	2	1	no	—
860	C₄²	—	2	2	no	—
861	C₄²	—	2	2	no	—
862	C₄²	—	2	2	no	—
863	C₄²	—	2	2	no	—
864	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
865	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
866	C₄²	C₂⁴×C₇	1	2	yes	—
867	C₄²	C₂⁴×C₇	1	2	yes	—
868	C₄²	C₂⁴×C₇	1	1	yes	characteristic
869	C₄²	C₂⁴×C₇	1	1	yes	characteristic
870	C₂×C₇	—	4	1	no	—
871	C₂×C₇	—	4	4	no	—
872	C₂×C₇	—	8	1	no	—
873	C₂×C₇	#3486	1	1	yes	characteristic
874	C₂×C₇	#3585	1	1	yes	characteristic
875	C₂×C₇	#3586	1	1	yes	characteristic
876	C₂³	—	2	4	no	—
877	C₂³	—	2	2	no	—
878	C₂³	—	2	1	no	—
879	C₂³	—	8	1	no	—
880	C₂³	—	8	1	no	—
881	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
882	Q₈	—	2	2	no	—
883	Q₈	—	2	2	no	—
884	Q₈	—	2	2	no	—
885	Q₈	—	4	2	no	—
886	Q₈	—	4	1	no	—
887	Q₈	—	4	1	no	—
888	Q₈	—	4	2	no	—
889	Q₈	—	8	1	no	—
890	Q₈	—	8	2	no	—
891	Q₈	—	8	1	no	—
892	Q₈	—	8	2	no	—
893	Q₈	—	8	2	no	—
894	D₄	—	2	4	no	—
895	D₄	—	2	2	no	—
896	D₄	—	2	2	no	—
897	D₄	—	8	1	no	—
898	D₄	C₇×2₋¹⁺⁴	1	4	yes	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	4	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	4	2	no	—
911	C₂×C₄	—	4	4	no	—
912	C₂×C₄	—	8	2	no	—
913	C₂×C₄	—	8	2	no	—
914	C₂×C₄	—	8	2	no	—
915	C₂×C₄	—	8	2	no	—
916	C₂×C₄	—	8	2	no	—
917	C₂×C₄	—	8	2	no	—
918	C₂×C₄	—	8	1	no	—
919	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
920	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
921	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
922	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
923	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
924	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
925	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
926	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
927	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
928	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
929	C₈	—	2	2	no	—
930	C₈	—	2	2	no	—
931	C₈	—	2	2	no	—
932	C₈	—	2	2	no	—
933	C₇	#61873	1	1	yes	characteristic, direct product factor, Sylow
934	C₂²	—	2	1	no	—
935	C₂²	—	2	1	no	—
936	C₂²	—	2	1	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	8	4	no	—
944	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
945	C₄	—	2	1	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	2	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	1	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	2	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	1	no	—
958	C₄	—	4	1	no	—
959	C₄	—	4	2	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	1	no	—
962	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
963	C₂	—	4	1	no	—
964	C₂	—	4	4	no	—
965	C₂	—	8	1	no	—
966	C₂	C₇×#3486	1	1	yes	characteristic
967	C₂	C₇×#3585	1	1	yes	characteristic
968	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#447	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3555	C₂	semidirect
2. C₇×#3501	C₂	semidirect
3. C₇×#3389	C₂	semidirect
4. C₇×#3388	C₂	semidirect
5. C₇×#3386	C₂	semidirect
6. C₇×#3385	C₂	semidirect
7. C₇×#3376	C₂	semidirect
8. C₇×#3376	C₂	semidirect
9. C₇×#3372	C₂	semidirect
10. C₇×#3367	C₂	semidirect
11. C₇×#3243	C₂	semidirect
12. C₇×#3242	C₂	semidirect
13. C₇×#3240	C₂	semidirect
14. C₇×#3237	C₂	semidirect
15. C₇×#3123	C₂	semidirect
18. C₇×#3110	C₂	semidirect
19. C₇×#2987	C₂	semidirect
21. C₇×Q₈²	C₂²	semidirect
22. C₇×#557	C₂²	semidirect
23. C₇×#557	C₂²	semidirect
25. C₇×#556	C₂²	semidirect
26. C₇×#556	C₂²	semidirect
32. C₇×#554	C₂²	semidirect
51. C₇×#501	C₂²	semidirect
52. C₇×#501	C₂²	semidirect
53. C₇×#501	C₂²	semidirect
54. C₇×#501	C₂²	semidirect
55. C₇×#501	C₂²	semidirect
56. C₇×#500	C₂²	semidirect
57. C₇×#499	C₂²	semidirect
58. C₇×#491	C₂²	semidirect
59. C₇×#491	C₂²	semidirect
60. C₇×#489	C₂²	semidirect
61. C₇×#489	C₂²	semidirect
62. C₇×#489	C₂²	semidirect
63. C₇×#488	C₂²	semidirect
64. C₇×#487	C₂²	semidirect
72. C₇×#479	C₂²	semidirect
73. C₇×#479	C₂²	semidirect
74. C₇×#479	C₂²	semidirect
75. C₇×#479	C₂²	semidirect
79. C₇×#478	C₂²	semidirect
80. C₇×#478	C₂²	semidirect
81. C₇×#477	C₂²	semidirect
82. C₇×#477	C₂²	semidirect
83. C₇×#477	C₂²	semidirect
85. C₇×#475	C₂²	semidirect
86. C₇×#475	C₂²	semidirect
89. C₇×#474	C₂²	semidirect
99. C₇×#446	C₂²	semidirect
100. C₇×#446	C₂²	semidirect
101. C₇×#446	C₂²	semidirect
102. C₇×#446	C₂²	semidirect
119. #61873	C₇	direct (N × H)
281. #3555	C₂×C₇	semidirect
282. #3501	C₂×C₇	semidirect
283. #3389	C₂×C₇	semidirect
284. #3388	C₂×C₇	semidirect
285. #3386	C₂×C₇	semidirect
286. #3385	C₂×C₇	semidirect
287. #3376	C₂×C₇	semidirect
288. #3376	C₂×C₇	semidirect
289. #3372	C₂×C₇	semidirect
290. #3367	C₂×C₇	semidirect
291. #3243	C₂×C₇	semidirect
292. #3242	C₂×C₇	semidirect
293. #3240	C₂×C₇	semidirect
294. #3237	C₂×C₇	semidirect
295. #3123	C₂×C₇	semidirect
298. #3110	C₂×C₇	semidirect
299. #2987	C₂×C₇	semidirect
413. Q₈²	C₂²×C₇	semidirect
414. #557	C₂²×C₇	semidirect
415. #557	C₂²×C₇	semidirect
417. #556	C₂²×C₇	semidirect
418. #556	C₂²×C₇	semidirect
424. #554	C₂²×C₇	semidirect
443. #501	C₂²×C₇	semidirect
444. #501	C₂²×C₇	semidirect
445. #501	C₂²×C₇	semidirect
446. #501	C₂²×C₇	semidirect
447. #501	C₂²×C₇	semidirect
448. #500	C₂²×C₇	semidirect
449. #499	C₂²×C₇	semidirect
450. #491	C₂²×C₇	semidirect
451. #491	C₂²×C₇	semidirect
452. #489	C₂²×C₇	semidirect
453. #489	C₂²×C₇	semidirect
454. #489	C₂²×C₇	semidirect
455. #488	C₂²×C₇	semidirect
456. #487	C₂²×C₇	semidirect
464. #479	C₂²×C₇	semidirect
465. #479	C₂²×C₇	semidirect
466. #479	C₂²×C₇	semidirect
467. #479	C₂²×C₇	semidirect
471. #478	C₂²×C₇	semidirect
472. #478	C₂²×C₇	semidirect
473. #477	C₂²×C₇	semidirect
474. #477	C₂²×C₇	semidirect
475. #477	C₂²×C₇	semidirect
477. #475	C₂²×C₇	semidirect
478. #475	C₂²×C₇	semidirect
481. #474	C₂²×C₇	semidirect
491. #446	C₂²×C₇	semidirect
492. #446	C₂²×C₇	semidirect
493. #446	C₂²×C₇	semidirect
494. #446	C₂²×C₇	semidirect
933. C₇	#61873	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×#3555	2
C₇×#3501	2
C₇×#3389	2
C₇×#3388	2
C₇×#3386	2
C₇×#3385	2
C₇×#3376	2
C₇×#3372	2
C₇×#3367	2
C₇×#3243	2
C₇×#3242	2
C₇×#3240	2
C₇×#3237	2
C₇×#3123	2
C₇×#3118	2
C₇×#3114	2
C₇×#3110	2
C₇×#2987	2
#61873	7

Subgroups — C7×#61873 #13239089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61873 #13239089