Subgroups — C₇×#61324 #13238540

Order 1792.

1878 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×Q₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3375	C₂	1	2	yes	maximal, complemented
4	C₇×#3373	C₂	1	2	yes	maximal, complemented
5	C₇×#3371	C₂	1	4	yes	maximal, complemented
6	C₇×#3370	C₂	1	4	yes	maximal, complemented
7	C₇×#3365	C₂	1	2	yes	maximal, complemented
8	C₇×#3361	C₂	1	2	yes	maximal, complemented
9	C₇×#3140	C₂	1	2	yes	maximal, complemented
10	C₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3077	C₂	1	2	yes	maximal, complemented
13	C₇×#3040	C₂	1	2	yes	maximal, complemented
14	C₇×#3038	C₂	1	1	yes	maximal, characteristic
15	C₇×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₇×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×#137	C₂²	1	1	yes	characteristic
19	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₇×#559	—	2	1	no	—
21	C₇×#559	—	2	2	no	—
22	C₇×#559	—	2	1	no	—
23	C₇×#559	C₂²	1	2	yes	—
24	C₇×#559	C₂²	1	4	yes	—
25	C₇×#559	C₂²	1	2	yes	—
26	C₇×Q₈²	C₂²	1	1	yes	characteristic, complemented
27	C₇×#557	C₂²	1	1	yes	characteristic, complemented
28	C₇×#557	C₂²	1	2	yes	complemented
29	C₇×#554	—	2	1	no	—
30	C₇×#554	—	2	2	no	—
31	C₇×#554	C₂²	1	1	yes	characteristic, complemented
32	C₇×#554	C₂²	1	2	yes	complemented
33	C₇×D₄×Q₈	—	2	1	no	—
34	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₇×#533	—	2	2	no	—
36	C₇×#533	—	2	1	no	—
37	C₇×#533	C₂²	1	2	yes	—
38	C₇×#533	C₂²	1	1	yes	characteristic
39	C₂×C₇×#127	C₂²	1	1	yes	characteristic
40	C₂×C₇×#124	—	2	1	no	—
41	C₂×C₇×#124	C₂²	1	2	yes	—
42	C₂×C₇×#123	—	2	2	no	—
43	C₄×C₇×#41	C₂²	1	2	yes	—
44	C₄×C₇×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×Q₈	—	2	1	no	—
46	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₇×D₄	—	2	1	no	—
49	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
50	C₇×#490	C₂²	1	4	yes	—
51	C₇×#489	C₂²	1	4	yes	complemented
52	C₇×#489	C₂²	1	4	yes	complemented
53	C₇×#488	C₂²	1	4	yes	complemented
54	C₇×#488	C₂²	1	4	yes	complemented
55	C₇×#486	C₂²	1	2	yes	—
56	C₇×#486	C₂²	1	2	yes	—
57	C₇×#479	C₂²	1	4	yes	complemented
58	C₇×#478	C₂²	1	4	yes	complemented
59	C₇×#478	C₂²	1	4	yes	complemented
60	C₇×#477	C₂²	1	2	yes	complemented
61	C₇×#476	C₂²	1	4	yes	complemented
62	C₇×#475	C₂²	1	2	yes	complemented
63	C₇×#474	C₂²	1	4	yes	complemented
64	C₇×#464	C₂²	1	4	yes	complemented
65	C₇×#464	C₂²	1	4	yes	complemented
66	C₇×#463	C₂²	1	4	yes	complemented
67	C₇×#463	C₂²	1	4	yes	complemented
68	C₇×#460	C₂²	1	2	yes	—
69	C₇×#460	C₂²	1	2	yes	—
70	C₇×#459	C₂²	1	2	yes	—
71	C₇×#459	C₂²	1	2	yes	—
72	C₇×#446	C₂²	1	4	yes	complemented
73	C₇×#446	C₂²	1	2	yes	complemented
74	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
75	C₇×#442	C₂²	1	4	yes	complemented
76	C₇×#441	C₂²	1	2	yes	complemented
77	C₇×#440	C₂²	1	4	yes	complemented
78	C₇×#440	C₂²	1	2	yes	complemented
79	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
80	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
81	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
82	C₄×C₇×D₈	C₂²	1	4	yes	complemented
83	C₇×#428	C₂²	1	2	yes	—
84	C₇×#428	C₂²	1	1	yes	characteristic
85	C₇×#423	C₂²	1	1	yes	characteristic
86	C₇×#423	C₂²	1	2	yes	—
87	C₇×#419	C₂²	1	1	yes	characteristic
88	C₇×#419	C₂²	1	2	yes	—
89	C₇×#418	C₂²	1	2	yes	—
90	C₇×#418	C₂²	1	2	yes	—
91	C₇×#418	C₂²	1	2	yes	—
92	C₇×#417	C₂²	1	1	yes	characteristic
93	C₄×C₇×M₁₆	C₂²	1	2	yes	—
94	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
95	#61324	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₇×#41	C₂³	1	1	yes	characteristic
97	C₂²×C₇×Q₈	—	2	1	no	—
98	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
99	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
100	C₂²×C₇×D₄	—	2	1	no	—
101	C₂²×C₇×D₄	—	2	1	no	—
102	C₂²×C₇×D₄	C₂³	1	2	yes	—
103	C₂³×C₄×C₇	—	2	2	no	—
104	C₇×#137	—	2	4	no	—
105	C₇×AGL(1,ℤ/8)	—	2	8	no	—
106	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
107	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
108	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
109	C₂×C₇×D₈	C₂³	1	4	yes	—
110	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
111	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
112	C₂×C₇×M₁₆	C₂³	1	2	yes	—
113	C₇×C₄⋊Q₈	—	2	1	no	—
114	C₇×C₄⋊Q₈	—	2	2	no	—
115	C₇×C₄⋊Q₈	—	2	1	no	—
116	C₇×C₄⋊Q₈	—	2	2	no	—
117	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₇×#127	—	2	1	no	—
122	C₇×#127	—	2	1	no	—
123	C₇×#127	C₂³	1	2	yes	—
124	C₇×#127	C₂³	1	2	yes	—
125	C₇×#125	—	2	2	no	—
126	C₇×#125	—	2	2	no	—
127	C₇×#125	—	2	2	no	—
128	C₇×#125	C₂³	1	2	yes	—
129	C₇×#125	C₂³	1	2	yes	—
130	C₇×#125	C₂³	1	2	yes	—
131	C₇×#124	—	2	2	no	—
132	C₇×#124	—	2	2	no	—
133	C₇×#124	—	2	4	no	—
134	C₇×#124	—	2	2	no	—
135	C₇×#124	—	2	2	no	—
136	C₇×#124	C₂³	1	4	yes	—
137	C₇×#124	C₂³	1	4	yes	—
138	C₇×#123	—	2	4	no	—
139	C₇×#123	—	2	4	no	—
140	C₇×#123	—	2	4	no	—
141	C₇×#123	—	2	4	no	—
142	C₇×C₂²⋊Q₈	—	2	1	no	—
143	C₇×C₂²⋊Q₈	—	2	2	no	—
144	C₇×C₂²⋊Q₈	—	2	1	no	—
145	C₇×C₂²⋊Q₈	—	2	2	no	—
146	C₇×C₂²⋊Q₈	—	2	2	no	—
147	C₇×C₂²⋊Q₈	—	2	1	no	—
148	C₇×C₂²⋊Q₈	—	2	1	no	—
149	C₇×C₂²⋊Q₈	—	2	2	no	—
150	C₇×C₂²⋊Q₈	—	2	2	no	—
151	C₇×C₂²⋊Q₈	—	2	2	no	—
152	C₇×C₂²⋊Q₈	—	2	2	no	—
153	C₄×C₇×Q₈	—	2	1	no	—
154	C₄×C₇×Q₈	—	2	1	no	—
155	C₄×C₇×Q₈	—	2	2	no	—
156	C₄×C₇×Q₈	—	2	2	no	—
157	C₄×C₇×Q₈	—	2	1	no	—
158	C₄×C₇×Q₈	—	2	1	no	—
159	C₄×C₇×Q₈	—	2	1	no	—
160	C₄×C₇×Q₈	—	2	2	no	—
161	C₄×C₇×Q₈	—	2	1	no	—
162	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
163	C₄×C₇×Q₈	D₄	1	2	yes	—
164	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
165	C₄×C₇×Q₈	C₂³	1	2	yes	—
166	C₄×C₇×Q₈	C₂³	1	2	yes	—
167	C₄×C₇×Q₈	C₂³	1	2	yes	—
168	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
169	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
170	C₄×C₇×Q₈	C₂³	1	2	yes	—
171	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
172	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
173	C₄×C₇×Q₈	C₂³	1	2	yes	—
174	C₄×C₇×D₄	—	2	1	no	—
175	C₄×C₇×D₄	—	2	2	no	—
176	C₄×C₇×D₄	—	2	2	no	—
177	C₄×C₇×D₄	—	2	1	no	—
178	C₄×C₇×D₄	—	2	2	no	—
179	C₄×C₇×D₄	—	2	4	no	—
180	C₄×C₇×D₄	—	2	2	no	—
181	C₄×C₇×D₄	—	2	2	no	—
182	C₄×C₇×D₄	—	2	2	no	—
183	C₄×C₇×D₄	C₂³	1	4	yes	—
184	C₄×C₇×D₄	C₂³	1	4	yes	—
185	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
186	C₄×C₇×D₄	C₂³	1	2	yes	—
187	C₄×C₇×D₄	C₂³	1	2	yes	—
188	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
189	C₇×#117	—	2	2	no	—
190	C₇×#117	—	2	1	no	—
191	C₇×#117	C₂³	1	2	yes	—
192	C₇×#117	C₂³	1	1	yes	characteristic
193	C₂×C₇×C₄⋊C₄	—	2	1	no	—
194	C₂×C₇×C₄⋊C₄	—	2	1	no	—
195	C₂×C₇×C₄⋊C₄	—	2	2	no	—
196	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
197	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
198	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
202	C₂×C₄²×C₇	—	2	1	no	—
203	C₂×C₄²×C₇	—	2	2	no	—
204	C₂×C₄²×C₇	—	2	1	no	—
205	C₂×C₄²×C₇	C₂³	1	2	yes	—
206	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
207	C₇×#107	C₂³	1	2	yes	—
208	C₇×#107	C₂³	1	4	yes	—
209	C₇×#106	C₂³	1	4	yes	—
210	C₇×#106	C₂³	1	2	yes	—
211	C₇×C₄⋊C₈	C₂³	1	4	yes	—
212	C₇×C₄⋊C₈	C₂³	1	2	yes	—
213	C₇×C₄⋊C₈	C₂³	1	4	yes	—
214	C₇×C₄⋊C₈	C₂³	1	2	yes	—
215	C₇×#103	C₂³	1	4	yes	—
216	C₇×#103	C₂³	1	4	yes	—
217	C₇×#103	C₂³	1	2	yes	—
218	C₇×#103	C₂³	1	2	yes	—
219	C₇×#103	C₂³	1	2	yes	—
220	C₇×#102	C₂³	1	4	yes	—
221	C₇×#102	C₂³	1	4	yes	—
222	C₇×#102	C₂³	1	4	yes	—
223	C₇×#102	C₂³	1	4	yes	—
224	C₇×#102	C₂³	1	4	yes	—
225	C₇×#102	C₂³	1	4	yes	—
226	C₇×#102	C₂³	1	2	yes	—
227	C₇×#97	C₂³	1	4	yes	—
228	C₇×#97	C₂³	1	2	yes	—
229	C₄×C₇×C₈	C₂³	1	2	yes	—
230	C₄×C₇×C₈	C₂³	1	4	yes	—
231	C₂×#559	C₂×C₇	1	1	yes	characteristic, complemented
232	Q₈×#41	C₂×C₇	1	1	yes	characteristic, complemented
233	#3375	C₂×C₇	1	2	yes	complemented
234	#3373	C₂×C₇	1	2	yes	complemented
235	#3371	C₂×C₇	1	4	yes	complemented
236	#3370	C₂×C₇	1	4	yes	complemented
237	#3365	C₂×C₇	1	2	yes	complemented
238	#3361	C₂×C₇	1	2	yes	complemented
239	#3140	C₂×C₇	1	2	yes	complemented
240	#3138	C₂×C₇	1	1	yes	characteristic, complemented
241	#3078	C₂×C₇	1	1	yes	characteristic, complemented
242	#3077	C₂×C₇	1	2	yes	complemented
243	#3040	C₂×C₇	1	2	yes	complemented
244	#3038	C₂×C₇	1	1	yes	characteristic
245	Q₈×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
246	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
247	C₄×AGL(1,ℤ/8)	C₂×C₇	1	2	yes	complemented
248	C₂⁴×C₇	—	2	2	no	—
249	C₇×#41	—	2	2	no	—
250	C₇×#41	#41	1	4	yes	—
251	C₂×C₇×Q₈	—	2	2	no	—
252	C₂×C₇×Q₈	—	2	1	no	—
253	C₂×C₇×Q₈	—	2	1	no	—
254	C₂×C₇×Q₈	—	2	2	no	—
255	C₂×C₇×Q₈	—	2	1	no	—
256	C₂×C₇×Q₈	—	2	2	no	—
257	C₂×C₇×Q₈	—	2	2	no	—
258	C₂×C₇×Q₈	—	4	2	no	—
259	C₂×C₇×Q₈	—	4	4	no	—
260	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
261	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
262	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
263	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
264	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
265	C₂×C₇×D₄	—	2	1	no	—
266	C₂×C₇×D₄	—	2	2	no	—
267	C₂×C₇×D₄	—	2	2	no	—
268	C₂×C₇×D₄	—	2	2	no	—
269	C₂×C₇×D₄	—	2	2	no	—
270	C₂×C₇×D₄	—	2	2	no	—
271	C₂×C₇×D₄	—	2	4	no	—
272	C₂×C₇×D₄	—	2	4	no	—
273	C₂×C₇×D₄	—	4	4	no	—
274	C₂×C₇×D₄	—	8	2	no	—
275	C₂×C₇×D₄	C₂⁴	1	4	yes	—
276	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₇	—	2	1	no	—
278	C₂²×C₄×C₇	—	2	1	no	—
279	C₂²×C₄×C₇	—	2	1	no	—
280	C₂²×C₄×C₇	—	2	2	no	—
281	C₂²×C₄×C₇	—	2	1	no	—
282	C₂²×C₄×C₇	—	2	2	no	—
283	C₂²×C₄×C₇	—	2	1	no	—
284	C₂²×C₄×C₇	—	2	4	no	—
285	C₂²×C₄×C₇	—	2	4	no	—
286	C₂²×C₄×C₇	—	8	4	no	—
287	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
289	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
290	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
292	C₇×Q₁₆	—	2	4	no	—
293	C₇×SD₁₆	—	2	8	no	—
294	C₇×SD₁₆	—	2	4	no	—
295	C₇×D₈	—	2	8	no	—
296	C₇×M₁₆	—	2	4	no	—
297	C₇×M₁₆	—	2	2	no	—
298	C₇×M₁₆	—	2	2	no	—
299	C₂×C₇×C₈	C₂⁴	1	2	yes	—
300	C₂×C₇×C₈	C₂⁴	1	2	yes	—
301	C₂×C₇×C₈	C₂⁴	1	4	yes	—
302	C₇×C₄⋊C₄	—	2	2	no	—
303	C₇×C₄⋊C₄	—	2	2	no	—
304	C₇×C₄⋊C₄	—	2	2	no	—
305	C₇×C₄⋊C₄	—	2	2	no	—
306	C₇×C₄⋊C₄	—	2	1	no	—
307	C₇×C₄⋊C₄	—	2	2	no	—
308	C₇×C₄⋊C₄	—	2	2	no	—
309	C₇×C₄⋊C₄	—	2	1	no	—
310	C₇×C₄⋊C₄	—	2	1	no	—
311	C₇×C₄⋊C₄	—	2	2	no	—
312	C₇×C₄⋊C₄	—	2	2	no	—
313	C₇×C₄⋊C₄	—	2	1	no	—
314	C₇×C₄⋊C₄	—	2	2	no	—
315	C₇×C₄⋊C₄	—	2	1	no	—
316	C₇×C₄⋊C₄	—	2	2	no	—
317	C₇×C₄⋊C₄	—	2	2	no	—
318	C₇×C₄⋊C₄	—	2	2	no	—
319	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
320	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
321	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
322	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
323	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
324	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
325	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
326	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
327	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
328	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
329	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
330	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
331	C₇×C₂²⋊C₄	—	2	2	no	—
332	C₇×C₂²⋊C₄	—	2	1	no	—
333	C₇×C₂²⋊C₄	—	2	4	no	—
334	C₇×C₂²⋊C₄	—	2	4	no	—
335	C₇×C₂²⋊C₄	—	2	4	no	—
336	C₇×C₂²⋊C₄	—	2	4	no	—
337	C₇×C₂²⋊C₄	—	2	4	no	—
338	C₇×C₂²⋊C₄	—	2	4	no	—
339	C₇×C₂²⋊C₄	—	2	1	no	—
340	C₇×C₂²⋊C₄	—	2	2	no	—
341	C₇×C₂²⋊C₄	—	2	2	no	—
342	C₇×C₂²⋊C₄	—	2	1	no	—
343	C₄²×C₇	—	2	2	no	—
344	C₄²×C₇	—	2	1	no	—
345	C₄²×C₇	—	2	2	no	—
346	C₄²×C₇	—	2	2	no	—
347	C₄²×C₇	—	2	2	no	—
348	C₄²×C₇	—	2	1	no	—
349	C₄²×C₇	—	2	2	no	—
350	C₄²×C₇	—	2	1	no	—
351	C₄²×C₇	C₂×D₄	1	2	yes	—
352	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
353	C₄²×C₇	C₂×D₄	1	2	yes	—
354	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
355	C₄²×C₇	C₂⁴	1	2	yes	—
356	C₄²×C₇	C₂⁴	1	1	yes	characteristic
357	C₄²×C₇	C₂⁴	1	2	yes	—
358	C₄²×C₇	C₂⁴	1	1	yes	characteristic
359	C₂×#137	C₂²×C₇	1	1	yes	characteristic
360	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
361	#559	—	2	1	no	—
362	#559	—	2	2	no	—
363	#559	—	2	1	no	—
364	#559	C₂²×C₇	1	2	yes	—
365	#559	C₂²×C₇	1	4	yes	—
366	#559	C₂²×C₇	1	2	yes	—
367	Q₈²	C₂²×C₇	1	1	yes	characteristic, complemented
368	#557	C₂²×C₇	1	1	yes	characteristic, complemented
369	#557	C₂²×C₇	1	2	yes	complemented
370	#554	—	2	1	no	—
371	#554	—	2	2	no	—
372	#554	C₂²×C₇	1	1	yes	characteristic, complemented
373	#554	C₂²×C₇	1	2	yes	complemented
374	D₄×Q₈	—	2	1	no	—
375	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
376	#533	—	2	2	no	—
377	#533	—	2	1	no	—
378	#533	C₂²×C₇	1	2	yes	—
379	#533	C₂²×C₇	1	1	yes	characteristic
380	C₂×#127	C₂²×C₇	1	1	yes	characteristic
381	C₂×#124	—	2	1	no	—
382	C₂×#124	C₂²×C₇	1	2	yes	—
383	C₂×#123	—	2	2	no	—
384	C₄×#41	C₂²×C₇	1	2	yes	—
385	C₄×#41	C₂²×C₇	1	1	yes	characteristic
386	C₂×C₄×Q₈	—	2	1	no	—
387	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
388	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
389	C₂×C₄×D₄	—	2	1	no	—
390	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
391	#490	C₂²×C₇	1	4	yes	—
392	#489	C₂²×C₇	1	4	yes	complemented
393	#489	C₂²×C₇	1	4	yes	complemented
394	#488	C₂²×C₇	1	4	yes	complemented
395	#488	C₂²×C₇	1	4	yes	complemented
396	#486	C₂²×C₇	1	2	yes	—
397	#486	C₂²×C₇	1	2	yes	—
398	#479	C₂²×C₇	1	4	yes	complemented
399	#478	C₂²×C₇	1	4	yes	complemented
400	#478	C₂²×C₇	1	4	yes	complemented
401	#477	C₂²×C₇	1	2	yes	complemented
402	#476	C₂²×C₇	1	4	yes	complemented
403	#475	C₂²×C₇	1	2	yes	complemented
404	#474	C₂²×C₇	1	4	yes	complemented
405	#464	C₂²×C₇	1	4	yes	complemented
406	#464	C₂²×C₇	1	4	yes	complemented
407	#463	C₂²×C₇	1	4	yes	complemented
408	#463	C₂²×C₇	1	4	yes	complemented
409	#460	C₂²×C₇	1	2	yes	—
410	#460	C₂²×C₇	1	2	yes	—
411	#459	C₂²×C₇	1	2	yes	—
412	#459	C₂²×C₇	1	2	yes	—
413	#446	C₂²×C₇	1	4	yes	complemented
414	#446	C₂²×C₇	1	2	yes	complemented
415	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
416	#442	C₂²×C₇	1	4	yes	complemented
417	#441	C₂²×C₇	1	2	yes	complemented
418	#440	C₂²×C₇	1	2	yes	complemented
419	#440	C₂²×C₇	1	4	yes	complemented
420	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
421	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
422	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
423	C₄×D₈	C₂²×C₇	1	4	yes	complemented
424	#428	C₂²×C₇	1	1	yes	characteristic
425	#428	C₂²×C₇	1	2	yes	—
426	#423	C₂²×C₇	1	2	yes	—
427	#423	C₂²×C₇	1	1	yes	characteristic
428	#419	C₂²×C₇	1	2	yes	—
429	#419	C₂²×C₇	1	1	yes	characteristic
430	#418	C₂²×C₇	1	2	yes	—
431	#418	C₂²×C₇	1	2	yes	—
432	#418	C₂²×C₇	1	2	yes	—
433	#417	C₂²×C₇	1	1	yes	characteristic
434	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
435	C₄×M₁₆	C₂²×C₇	1	2	yes	—
436	C₂³×C₇	—	2	1	no	—
437	C₂³×C₇	—	2	4	no	—
438	C₂³×C₇	—	4	4	no	—
439	C₂³×C₇	—	4	4	no	—
440	C₂³×C₇	—	4	4	no	—
441	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
442	C₇×Q₈	—	2	2	no	—
443	C₇×Q₈	—	2	2	no	—
444	C₇×Q₈	—	2	1	no	—
445	C₇×Q₈	—	2	2	no	—
446	C₇×Q₈	—	2	2	no	—
447	C₇×Q₈	—	4	2	no	—
448	C₇×Q₈	—	4	4	no	—
449	C₇×Q₈	—	4	2	no	—
450	C₇×Q₈	—	4	2	no	—
451	C₇×Q₈	—	8	2	no	—
452	C₇×Q₈	—	8	1	no	—
453	C₇×Q₈	C₂×#41	1	2	yes	—
454	C₇×D₄	—	2	4	no	—
455	C₇×D₄	—	2	4	no	—
456	C₇×D₄	—	2	1	no	—
457	C₇×D₄	—	2	4	no	—
458	C₇×D₄	—	4	4	no	—
459	C₇×D₄	—	4	4	no	—
460	C₇×D₄	—	4	4	no	—
461	C₇×D₄	—	8	2	no	—
462	C₇×D₄	—	8	2	no	—
463	C₇×D₄	C₂×#41	1	2	yes	—
464	C₂×C₄×C₇	—	2	1	no	—
465	C₂×C₄×C₇	—	2	4	no	—
466	C₂×C₄×C₇	—	2	2	no	—
467	C₂×C₄×C₇	—	2	2	no	—
468	C₂×C₄×C₇	—	2	2	no	—
469	C₂×C₄×C₇	—	2	2	no	—
470	C₂×C₄×C₇	—	2	1	no	—
471	C₂×C₄×C₇	—	2	2	no	—
472	C₂×C₄×C₇	—	2	1	no	—
473	C₂×C₄×C₇	—	4	2	no	—
474	C₂×C₄×C₇	—	4	1	no	—
475	C₂×C₄×C₇	—	4	2	no	—
476	C₂×C₄×C₇	—	4	4	no	—
477	C₂×C₄×C₇	—	4	2	no	—
478	C₂×C₄×C₇	—	4	2	no	—
479	C₂×C₄×C₇	—	4	2	no	—
480	C₂×C₄×C₇	—	8	2	no	—
481	C₂×C₄×C₇	—	8	1	no	—
482	C₂×C₄×C₇	—	8	4	no	—
483	C₂×C₄×C₇	—	8	4	no	—
484	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₇	C₂×#41	1	2	yes	—
494	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
495	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
496	C₇×C₈	—	2	4	no	—
497	C₇×C₈	—	2	2	no	—
498	C₇×C₈	—	2	2	no	—
499	C₂×#41	C₂³×C₇	1	1	yes	characteristic
500	C₂²×Q₈	—	2	1	no	—
501	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
502	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
503	C₂²×D₄	—	2	1	no	—
504	C₂²×D₄	—	2	1	no	—
505	C₂²×D₄	C₂³×C₇	1	2	yes	—
506	C₂³×C₄	—	2	2	no	—
507	#137	—	2	4	no	—
508	AGL(1,ℤ/8)	—	2	8	no	—
509	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
510	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
511	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
512	C₂×D₈	C₂³×C₇	1	4	yes	—
513	C₂×M₁₆	C₂³×C₇	1	2	yes	—
514	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
515	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
516	C₄⋊Q₈	—	2	1	no	—
517	C₄⋊Q₈	—	2	2	no	—
518	C₄⋊Q₈	—	2	1	no	—
519	C₄⋊Q₈	—	2	2	no	—
520	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
521	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
522	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
523	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
524	#127	—	2	1	no	—
525	#127	—	2	1	no	—
526	#127	C₂³×C₇	1	2	yes	—
527	#127	C₂³×C₇	1	2	yes	—
528	#125	—	2	2	no	—
529	#125	—	2	2	no	—
530	#125	—	2	2	no	—
531	#125	C₂³×C₇	1	2	yes	—
532	#125	C₂³×C₇	1	2	yes	—
533	#125	C₂³×C₇	1	2	yes	—
534	#124	—	2	2	no	—
535	#124	—	2	2	no	—
536	#124	—	2	4	no	—
537	#124	—	2	2	no	—
538	#124	—	2	2	no	—
539	#124	C₂³×C₇	1	4	yes	—
540	#124	C₂³×C₇	1	4	yes	—
541	#123	—	2	4	no	—
542	#123	—	2	4	no	—
543	#123	—	2	4	no	—
544	#123	—	2	4	no	—
545	C₂²⋊Q₈	—	2	1	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	—	2	1	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	1	no	—
551	C₂²⋊Q₈	—	2	1	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	—	2	2	no	—
555	C₂²⋊Q₈	—	2	2	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	—	2	1	no	—
558	C₄×Q₈	—	2	2	no	—
559	C₄×Q₈	—	2	2	no	—
560	C₄×Q₈	—	2	1	no	—
561	C₄×Q₈	—	2	1	no	—
562	C₄×Q₈	—	2	1	no	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	—	2	1	no	—
565	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
566	C₄×Q₈	C₇×D₄	1	2	yes	—
567	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
568	C₄×Q₈	C₂³×C₇	1	2	yes	—
569	C₄×Q₈	C₂³×C₇	1	2	yes	—
570	C₄×Q₈	C₂³×C₇	1	2	yes	—
571	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
572	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
573	C₄×Q₈	C₂³×C₇	1	2	yes	—
574	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
575	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
576	C₄×Q₈	C₂³×C₇	1	2	yes	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	4	no	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	2	no	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	C₂³×C₇	1	4	yes	—
587	C₄×D₄	C₂³×C₇	1	4	yes	—
588	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
589	C₄×D₄	C₂³×C₇	1	2	yes	—
590	C₄×D₄	C₂³×C₇	1	2	yes	—
591	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
592	#117	—	2	2	no	—
593	#117	—	2	1	no	—
594	#117	C₂³×C₇	1	2	yes	—
595	#117	C₂³×C₇	1	1	yes	characteristic
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	2	no	—
599	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
602	C₂×C₂²⋊C₄	—	2	2	no	—
603	C₂×C₂²⋊C₄	—	2	2	no	—
604	C₂×C₂²⋊C₄	—	2	2	no	—
605	C₂×C₄²	—	2	1	no	—
606	C₂×C₄²	—	2	2	no	—
607	C₂×C₄²	—	2	1	no	—
608	C₂×C₄²	C₂³×C₇	1	2	yes	—
609	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
610	#107	C₂³×C₇	1	4	yes	—
611	#107	C₂³×C₇	1	2	yes	—
612	#106	C₂³×C₇	1	2	yes	—
613	#106	C₂³×C₇	1	4	yes	—
614	C₄⋊C₈	C₂³×C₇	1	2	yes	—
615	C₄⋊C₈	C₂³×C₇	1	4	yes	—
616	C₄⋊C₈	C₂³×C₇	1	2	yes	—
617	C₄⋊C₈	C₂³×C₇	1	4	yes	—
618	#103	C₂³×C₇	1	2	yes	—
619	#103	C₂³×C₇	1	2	yes	—
620	#103	C₂³×C₇	1	2	yes	—
621	#103	C₂³×C₇	1	4	yes	—
622	#103	C₂³×C₇	1	4	yes	—
623	#102	C₂³×C₇	1	2	yes	—
624	#102	C₂³×C₇	1	4	yes	—
625	#102	C₂³×C₇	1	4	yes	—
626	#102	C₂³×C₇	1	4	yes	—
627	#102	C₂³×C₇	1	4	yes	—
628	#102	C₂³×C₇	1	4	yes	—
629	#102	C₂³×C₇	1	4	yes	—
630	#97	C₂³×C₇	1	2	yes	—
631	#97	C₂³×C₇	1	4	yes	—
632	C₄×C₈	C₂³×C₇	1	4	yes	—
633	C₄×C₈	C₂³×C₇	1	2	yes	—
634	C₂²×C₇	—	2	1	no	—
635	C₂²×C₇	—	2	1	no	—
636	C₂²×C₇	—	2	2	no	—
637	C₂²×C₇	—	4	1	no	—
638	C₂²×C₇	—	4	1	no	—
639	C₂²×C₇	—	4	4	no	—
640	C₂²×C₇	—	4	4	no	—
641	C₂²×C₇	—	4	4	no	—
642	C₂²×C₇	—	8	8	no	—
643	C₂²×C₇	#548	1	2	yes	—
644	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
645	C₄×C₇	—	2	2	no	—
646	C₄×C₇	—	2	2	no	—
647	C₄×C₇	—	2	1	no	—
648	C₄×C₇	—	2	1	no	—
649	C₄×C₇	—	2	2	no	—
650	C₄×C₇	—	2	1	no	—
651	C₄×C₇	—	2	2	no	—
652	C₄×C₇	—	2	2	no	—
653	C₄×C₇	—	4	2	no	—
654	C₄×C₇	—	4	2	no	—
655	C₄×C₇	—	4	1	no	—
656	C₄×C₇	—	4	2	no	—
657	C₄×C₇	—	4	2	no	—
658	C₄×C₇	—	4	1	no	—
659	C₄×C₇	#548	1	2	yes	—
660	C₄×C₇	#575	1	2	yes	—
661	C₄×C₇	C₂²×#41	1	1	yes	characteristic
662	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
663	C₂⁴	—	2	2	no	—
664	#41	—	2	2	no	—
665	#41	C₇×#41	1	4	yes	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	4	2	no	—
674	C₂×Q₈	—	4	4	no	—
675	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
676	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
677	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
678	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
679	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	4	4	no	—
689	C₂×D₄	—	8	2	no	—
690	C₂×D₄	C₂⁴×C₇	1	4	yes	—
691	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	8	4	no	—
702	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
703	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
704	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
705	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
707	Q₁₆	—	2	4	no	—
708	SD₁₆	—	2	8	no	—
709	SD₁₆	—	2	4	no	—
710	D₈	—	2	8	no	—
711	M₁₆	—	2	4	no	—
712	M₁₆	—	2	2	no	—
713	M₁₆	—	2	2	no	—
714	C₂×C₈	C₂⁴×C₇	1	2	yes	—
715	C₂×C₈	C₂⁴×C₇	1	2	yes	—
716	C₂×C₈	C₂⁴×C₇	1	4	yes	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
735	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
736	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
737	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
738	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
739	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
740	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
742	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
743	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
744	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
745	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	1	no	—
766	C₄²	C₂×C₇×D₄	1	2	yes	—
767	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
768	C₄²	C₂×C₇×D₄	1	2	yes	—
769	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
770	C₄²	C₂⁴×C₇	1	2	yes	—
771	C₄²	C₂⁴×C₇	1	1	yes	characteristic
772	C₄²	C₂⁴×C₇	1	2	yes	—
773	C₄²	C₂⁴×C₇	1	1	yes	characteristic
774	C₂×C₇	—	2	2	no	—
775	C₂×C₇	—	4	2	no	—
776	C₂×C₇	—	8	4	no	—
777	C₂×C₇	C₂×#548	1	1	yes	characteristic
778	C₂×C₇	C₂×#575	1	1	yes	characteristic
779	C₂×C₇	#3585	1	1	yes	characteristic
780	C₂³	—	2	1	no	—
781	C₂³	—	2	4	no	—
782	C₂³	—	4	4	no	—
783	C₂³	—	4	4	no	—
784	C₂³	—	4	4	no	—
785	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
786	Q₈	—	2	1	no	—
787	Q₈	—	2	2	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	2	2	no	—
790	Q₈	—	2	2	no	—
791	Q₈	—	4	2	no	—
792	Q₈	—	4	4	no	—
793	Q₈	—	4	2	no	—
794	Q₈	—	4	2	no	—
795	Q₈	—	8	2	no	—
796	Q₈	—	8	1	no	—
797	Q₈	C₂×C₇×#41	1	2	yes	—
798	D₄	—	2	4	no	—
799	D₄	—	2	4	no	—
800	D₄	—	2	1	no	—
801	D₄	—	2	4	no	—
802	D₄	—	4	4	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	4	no	—
805	D₄	—	8	2	no	—
806	D₄	—	8	2	no	—
807	D₄	C₂×C₇×#41	1	2	yes	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	4	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	4	2	no	—
824	C₂×C₄	—	8	2	no	—
825	C₂×C₄	—	8	1	no	—
826	C₂×C₄	—	8	4	no	—
827	C₂×C₄	—	8	4	no	—
828	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
829	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
830	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
831	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
832	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
833	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
834	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
835	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
836	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
837	C₂×C₄	C₂×C₇×#41	1	2	yes	—
838	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
839	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
840	C₈	—	2	4	no	—
841	C₈	—	2	2	no	—
842	C₈	—	2	2	no	—
843	C₇	#61324	1	1	yes	characteristic, direct product factor, Sylow
844	C₂²	—	2	1	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	2	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	4	no	—
850	C₂²	—	4	4	no	—
851	C₂²	—	4	4	no	—
852	C₂²	—	8	8	no	—
853	C₂²	C₇×#548	1	2	yes	—
854	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
855	C₄	—	2	1	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	1	no	—
861	C₄	—	2	1	no	—
862	C₄	—	2	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	2	no	—
869	C₄	C₇×#548	1	2	yes	—
870	C₄	C₇×#575	1	2	yes	—
871	C₄	C₂²×C₇×#41	1	1	yes	characteristic
872	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
873	C₂	—	2	2	no	—
874	C₂	—	4	2	no	—
875	C₂	—	8	4	no	—
876	C₂	C₂×C₇×#548	1	1	yes	characteristic
877	C₂	C₂×C₇×#575	1	1	yes	characteristic
878	C₂	C₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3038	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#559	C₂	semidirect
2. C₇×Q₈×#41	C₂	semidirect
3. C₇×#3375	C₂	semidirect
4. C₇×#3373	C₂	semidirect
5. C₇×#3371	C₂	semidirect
6. C₇×#3370	C₂	semidirect
7. C₇×#3365	C₂	semidirect
8. C₇×#3361	C₂	semidirect
9. C₇×#3140	C₂	semidirect
10. C₇×#3138	C₂	semidirect
11. C₇×#3078	C₂	semidirect
12. C₇×#3077	C₂	semidirect
13. C₇×#3040	C₂	semidirect
15. C₇×Q₈×M₁₆	C₂	semidirect
16. C₄×C₇×#137	C₂	semidirect
17. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
26. C₇×Q₈²	C₂²	semidirect
27. C₇×#557	C₂²	semidirect
28. C₇×#557	C₂²	semidirect
31. C₇×#554	C₂²	semidirect
32. C₇×#554	C₂²	semidirect
34. C₇×D₄×Q₈	C₂²	semidirect
51. C₇×#489	C₂²	semidirect
52. C₇×#489	C₂²	semidirect
53. C₇×#488	C₂²	semidirect
54. C₇×#488	C₂²	semidirect
57. C₇×#479	C₂²	semidirect
58. C₇×#478	C₂²	semidirect
59. C₇×#478	C₂²	semidirect
60. C₇×#477	C₂²	semidirect
61. C₇×#476	C₂²	semidirect
62. C₇×#475	C₂²	semidirect
63. C₇×#474	C₂²	semidirect
64. C₇×#464	C₂²	semidirect
65. C₇×#464	C₂²	semidirect
66. C₇×#463	C₂²	semidirect
67. C₇×#463	C₂²	semidirect
72. C₇×#446	C₂²	semidirect
73. C₇×#446	C₂²	semidirect
74. C₇×C₈×Q₈	C₂²	semidirect
75. C₇×#442	C₂²	semidirect
76. C₇×#441	C₂²	semidirect
77. C₇×#440	C₂²	semidirect
78. C₇×#440	C₂²	semidirect
79. C₄×C₇×Q₁₆	C₂²	semidirect
80. C₄×C₇×SD₁₆	C₂²	semidirect
81. C₄×C₇×SD₁₆	C₂²	semidirect
82. C₄×C₇×D₈	C₂²	semidirect
95. #61324	C₇	direct (N × H)
231. C₂×#559	C₂×C₇	semidirect
232. Q₈×#41	C₂×C₇	semidirect
233. #3375	C₂×C₇	semidirect
234. #3373	C₂×C₇	semidirect
235. #3371	C₂×C₇	semidirect
236. #3370	C₂×C₇	semidirect
237. #3365	C₂×C₇	semidirect
238. #3361	C₂×C₇	semidirect
239. #3140	C₂×C₇	semidirect
240. #3138	C₂×C₇	semidirect
241. #3078	C₂×C₇	semidirect
242. #3077	C₂×C₇	semidirect
243. #3040	C₂×C₇	semidirect
245. Q₈×M₁₆	C₂×C₇	semidirect
246. C₄×#137	C₂×C₇	semidirect
247. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
367. Q₈²	C₂²×C₇	semidirect
368. #557	C₂²×C₇	semidirect
369. #557	C₂²×C₇	semidirect
372. #554	C₂²×C₇	semidirect
373. #554	C₂²×C₇	semidirect
375. D₄×Q₈	C₂²×C₇	semidirect
392. #489	C₂²×C₇	semidirect
393. #489	C₂²×C₇	semidirect
394. #488	C₂²×C₇	semidirect
395. #488	C₂²×C₇	semidirect
398. #479	C₂²×C₇	semidirect
399. #478	C₂²×C₇	semidirect
400. #478	C₂²×C₇	semidirect
401. #477	C₂²×C₇	semidirect
402. #476	C₂²×C₇	semidirect
403. #475	C₂²×C₇	semidirect
404. #474	C₂²×C₇	semidirect
405. #464	C₂²×C₇	semidirect
406. #464	C₂²×C₇	semidirect
407. #463	C₂²×C₇	semidirect
408. #463	C₂²×C₇	semidirect
413. #446	C₂²×C₇	semidirect
414. #446	C₂²×C₇	semidirect
415. C₈×Q₈	C₂²×C₇	semidirect
416. #442	C₂²×C₇	semidirect
417. #441	C₂²×C₇	semidirect
418. #440	C₂²×C₇	semidirect
419. #440	C₂²×C₇	semidirect
420. C₄×Q₁₆	C₂²×C₇	semidirect
421. C₄×SD₁₆	C₂²×C₇	semidirect
422. C₄×SD₁₆	C₂²×C₇	semidirect
423. C₄×D₈	C₂²×C₇	semidirect
843. C₇	#61324	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#559	2
C₇×Q₈×#41	2
C₇×#3375	2
C₇×#3373	2
C₇×#3371	2
C₇×#3370	2
C₇×#3365	2
C₇×#3361	2
C₇×#3140	2
C₇×#3138	2
C₇×#3078	2
C₇×#3077	2
C₇×#3040	2
C₇×#3038	2
C₇×Q₈×M₁₆	2
C₄×C₇×#137	2
C₄×C₇×AGL(1,ℤ/8)	2
#61324	7

Subgroups — C7×#61324 #13238540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61324 #13238540