Subgroups — C₇×#60701 #13237917

Order 1792.

1976 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3185	C₂	1	2	yes	maximal, complemented
4	C₇×#3182	C₂	1	2	yes	maximal, complemented
5	C₇×#3181	C₂	1	4	yes	maximal, complemented
6	C₇×#3172	C₂	1	4	yes	maximal, complemented
7	C₇×#3170	C₂	1	2	yes	maximal, complemented
8	C₇×#3167	C₂	1	2	yes	maximal, complemented
9	C₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3152	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3139	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3056	C₂	1	4	yes	maximal, complemented
14	C₄×C₇×#137	C₂	1	4	yes	maximal, complemented
15	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#137	C₂²	1	4	yes	—
17	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
18	C₇×#533	—	2	1	no	—
19	C₇×#533	—	2	1	no	—
20	C₇×#533	—	2	1	no	—
21	C₇×#533	—	2	1	no	—
22	C₇×#533	C₂²	1	2	yes	—
23	C₇×#533	C₂²	1	1	yes	characteristic
24	C₇×#533	C₂²	1	2	yes	—
25	C₇×#533	C₂²	1	2	yes	—
26	C₇×#533	C₂²	1	2	yes	—
27	C₇×#533	C₂²	1	1	yes	characteristic
28	C₇×#533	C₂²	1	1	yes	characteristic
29	C₇×#532	C₂²	1	1	yes	characteristic
30	C₇×#532	C₂²	1	1	yes	characteristic
31	C₇×#532	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₇×#529	—	2	1	no	—
35	C₇×#529	—	2	1	no	—
36	C₇×#529	—	2	1	no	—
37	C₇×#529	—	2	1	no	—
38	C₇×#529	C₂²	1	2	yes	—
39	C₇×#529	C₂²	1	2	yes	—
40	C₂×C₇×#125	—	2	1	no	—
41	C₇×#525	—	2	1	no	—
42	C₇×#525	—	2	1	no	—
43	C₇×#525	C₂²	1	2	yes	—
44	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
45	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
46	C₄×C₇×#41	—	2	1	no	—
47	C₄×C₇×#41	—	2	1	no	—
48	C₄×C₇×#41	C₂²	1	2	yes	—
49	C₂×C₄×C₇×Q₈	—	2	1	no	—
50	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
51	C₂×C₇×#117	—	2	1	no	—
52	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
53	C₇×#501	C₂²	1	4	yes	complemented
54	C₇×#500	C₂²	1	2	yes	complemented
55	C₇×#498	C₂²	1	2	yes	complemented
56	C₇×#497	C₂²	1	4	yes	complemented
57	C₇×#494	C₂²	1	2	yes	complemented
58	C₇×#492	C₂²	1	2	yes	complemented
59	C₇×#491	C₂²	1	4	yes	complemented
60	C₇×#489	C₂²	1	4	yes	complemented
61	C₇×#487	C₂²	1	2	yes	complemented
62	C₇×#487	C₂²	1	2	yes	complemented
63	C₇×#487	C₂²	1	2	yes	complemented
64	C₇×#486	C₂²	1	2	yes	complemented
65	C₇×#470	C₂²	1	8	yes	—
66	C₇×#468	C₂²	1	8	yes	—
67	C₇×#467	C₂²	1	8	yes	—
68	C₇×#465	C₂²	1	8	yes	—
69	C₇×#441	C₂²	1	8	yes	complemented
70	C₇×#440	C₂²	1	8	yes	complemented
71	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
72	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
73	C₇×#428	C₂²	1	4	yes	—
74	C₇×#419	C₂²	1	4	yes	—
75	C₇×#417	C₂²	1	4	yes	—
76	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
77	C₄×C₇×M₁₆	C₂²	1	2	yes	—
78	C₄×C₇×M₁₆	C₂²	1	2	yes	—
79	C₄×C₇×M₁₆	C₂²	1	2	yes	—
80	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
81	C₂×C₇×#97	C₂²	1	2	yes	—
82	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
83	#60701	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂×C₇×#41	—	2	1	no	—
85	C₂×C₇×#41	—	2	1	no	—
86	C₂×C₇×#41	C₂³	1	2	yes	—
87	C₂²×C₇×Q₈	—	2	1	no	—
88	C₂²×C₇×Q₈	C₂³	1	2	yes	—
89	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
90	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
91	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
92	C₇×#137	—	2	16	no	—
93	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
94	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
95	C₂×C₇×M₁₆	—	2	8	no	—
96	C₂×C₇×M₁₆	C₂³	1	4	yes	—
97	C₂×C₇×M₁₆	C₂³	1	2	yes	—
98	C₂×C₇×M₁₆	C₂³	1	2	yes	—
99	C₂²×C₇×C₈	C₂³	1	4	yes	—
100	C₇×C₄⋊Q₈	—	2	1	no	—
101	C₇×C₄⋊Q₈	—	2	1	no	—
102	C₇×C₄⋊Q₈	—	2	1	no	—
103	C₇×C₄⋊Q₈	—	2	1	no	—
104	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
105	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
106	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
109	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₇×#127	C₂³	1	1	yes	characteristic
112	C₇×#126	—	2	2	no	—
113	C₇×#126	—	2	2	no	—
114	C₇×#125	—	2	2	no	—
115	C₇×#125	—	2	2	no	—
116	C₇×#125	—	2	2	no	—
117	C₇×#125	—	2	2	no	—
118	C₇×#125	—	2	1	no	—
119	C₇×#125	—	2	1	no	—
120	C₇×#125	C₂³	1	2	yes	—
121	C₇×#124	—	2	1	no	—
122	C₇×#124	—	2	1	no	—
123	C₇×#124	C₂³	1	2	yes	—
124	C₇×#123	—	2	2	no	—
125	C₇×#123	—	2	2	no	—
126	C₇×#123	—	2	2	no	—
127	C₇×C₂²⋊Q₈	—	2	2	no	—
128	C₇×C₂²⋊Q₈	—	2	2	no	—
129	C₇×C₂²⋊Q₈	—	2	2	no	—
130	C₇×C₂²⋊Q₈	—	2	2	no	—
131	C₇×C₂²⋊Q₈	—	2	2	no	—
132	C₇×C₂²⋊Q₈	—	2	2	no	—
133	C₇×C₂²⋊Q₈	—	2	1	no	—
134	C₇×C₂²⋊Q₈	—	2	1	no	—
135	C₇×C₂²⋊Q₈	—	2	1	no	—
136	C₇×C₂²⋊Q₈	—	2	1	no	—
137	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
138	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
140	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
141	C₇×#121	—	2	1	no	—
142	C₇×#121	—	2	1	no	—
143	C₇×#121	—	2	1	no	—
144	C₇×#121	—	2	1	no	—
145	C₇×#121	C₂³	1	2	yes	—
146	C₇×#121	C₂³	1	2	yes	—
147	C₇×#120	—	2	2	no	—
148	C₄×C₇×Q₈	—	2	2	no	—
149	C₄×C₇×Q₈	—	2	2	no	—
150	C₄×C₇×Q₈	—	2	2	no	—
151	C₄×C₇×Q₈	—	2	2	no	—
152	C₄×C₇×Q₈	—	2	2	no	—
153	C₄×C₇×Q₈	—	2	2	no	—
154	C₄×C₇×Q₈	—	2	1	no	—
155	C₄×C₇×Q₈	—	2	1	no	—
156	C₄×C₇×Q₈	—	2	1	no	—
157	C₄×C₇×Q₈	—	2	1	no	—
158	C₄×C₇×Q₈	C₂³	1	4	yes	—
159	C₄×C₇×Q₈	C₂³	1	4	yes	—
160	C₄×C₇×Q₈	C₂³	1	2	yes	—
161	C₄×C₇×Q₈	C₂³	1	2	yes	—
162	C₄×C₇×D₄	—	2	2	no	—
163	C₄×C₇×D₄	—	2	2	no	—
164	C₄×C₇×D₄	—	2	2	no	—
165	C₄×C₇×D₄	—	2	2	no	—
166	C₄×C₇×D₄	—	2	2	no	—
167	C₄×C₇×D₄	—	2	2	no	—
168	C₄×C₇×D₄	—	2	1	no	—
169	C₄×C₇×D₄	—	2	1	no	—
170	C₄×C₇×D₄	—	2	1	no	—
171	C₄×C₇×D₄	—	2	1	no	—
172	C₄×C₇×D₄	C₂³	1	2	yes	—
173	C₄×C₇×D₄	C₂³	1	2	yes	—
174	C₇×#117	—	2	2	no	—
175	C₇×#117	—	2	2	no	—
176	C₇×#117	—	2	2	no	—
177	C₇×#117	—	2	2	no	—
178	C₇×#117	—	2	1	no	—
179	C₇×#117	—	2	1	no	—
180	C₇×#117	—	2	2	no	—
181	C₇×#117	—	2	2	no	—
182	C₇×#117	—	2	2	no	—
183	C₇×#117	C₂³	1	2	yes	—
184	C₂×C₇×C₄⋊C₄	—	2	1	no	—
185	C₂×C₇×C₄⋊C₄	—	2	1	no	—
186	C₂×C₇×C₄⋊C₄	—	2	1	no	—
187	C₂×C₇×C₄⋊C₄	—	2	2	no	—
188	C₂×C₇×C₄⋊C₄	—	2	2	no	—
189	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
191	C₂×C₄²×C₇	—	2	2	no	—
192	C₂×C₄²×C₇	—	2	2	no	—
193	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
194	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
195	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
196	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
197	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
199	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
205	C₇×#107	C₂³	1	8	yes	—
206	C₇×#106	C₂³	1	8	yes	—
207	C₇×#103	C₂³	1	8	yes	—
208	C₇×#103	C₂³	1	8	yes	—
209	C₇×#103	C₂³	1	8	yes	—
210	C₇×#102	C₂³	1	8	yes	—
211	C₇×#97	C₂³	1	2	yes	—
212	C₇×#97	C₂³	1	2	yes	—
213	C₇×#97	C₂³	1	4	yes	—
214	C₄×C₇×C₈	C₂³	1	2	yes	—
215	C₄×C₇×C₈	C₂³	1	2	yes	—
216	C₄×C₇×C₈	C₂³	1	4	yes	—
217	#3444	C₂×C₇	1	1	yes	characteristic
218	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
219	#3185	C₂×C₇	1	2	yes	complemented
220	#3182	C₂×C₇	1	2	yes	complemented
221	#3181	C₂×C₇	1	4	yes	complemented
222	#3172	C₂×C₇	1	4	yes	complemented
223	#3170	C₂×C₇	1	2	yes	complemented
224	#3167	C₂×C₇	1	2	yes	complemented
225	#3165	C₂×C₇	1	1	yes	characteristic, complemented
226	#3152	C₂×C₇	1	1	yes	characteristic, complemented
227	#3141	C₂×C₇	1	1	yes	characteristic, complemented
228	#3139	C₂×C₇	1	1	yes	characteristic, complemented
229	#3056	C₂×C₇	1	4	yes	complemented
230	C₄×#137	C₂×C₇	1	4	yes	complemented
231	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
232	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
233	C₇×#41	—	2	8	no	—
234	C₇×#41	—	4	4	no	—
235	C₇×#41	—	4	4	no	—
236	C₂×C₇×Q₈	—	2	1	no	—
237	C₂×C₇×Q₈	—	2	1	no	—
238	C₂×C₇×Q₈	—	2	2	no	—
239	C₂×C₇×Q₈	—	2	2	no	—
240	C₂×C₇×Q₈	—	2	2	no	—
241	C₂×C₇×Q₈	—	2	8	no	—
242	C₂×C₇×Q₈	—	4	4	no	—
243	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
244	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
245	C₂×C₇×D₄	—	2	2	no	—
246	C₂×C₇×D₄	—	2	2	no	—
247	C₂×C₇×D₄	—	2	2	no	—
248	C₂×C₇×D₄	—	2	1	no	—
249	C₂×C₇×D₄	—	2	1	no	—
250	C₂×C₇×D₄	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₇	—	2	4	no	—
252	C₂²×C₄×C₇	—	2	4	no	—
253	C₂²×C₄×C₇	—	2	2	no	—
254	C₂²×C₄×C₇	—	2	2	no	—
255	C₂²×C₄×C₇	—	2	2	no	—
256	C₂²×C₄×C₇	—	2	2	no	—
257	C₂²×C₄×C₇	—	2	2	no	—
258	C₂²×C₄×C₇	—	4	2	no	—
259	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
277	C₇×Q₁₆	—	2	16	no	—
278	C₇×SD₁₆	—	2	16	no	—
279	C₇×M₁₆	—	2	4	no	—
280	C₇×M₁₆	—	2	8	no	—
281	C₇×M₁₆	#41	1	8	yes	complemented
282	C₂×C₇×C₈	—	2	8	no	—
283	C₂×C₇×C₈	C₂⁴	1	4	yes	—
284	C₂×C₇×C₈	C₂⁴	1	4	yes	—
285	C₇×C₄⋊C₄	—	2	2	no	—
286	C₇×C₄⋊C₄	—	2	2	no	—
287	C₇×C₄⋊C₄	—	2	2	no	—
288	C₇×C₄⋊C₄	—	2	2	no	—
289	C₇×C₄⋊C₄	—	2	2	no	—
290	C₇×C₄⋊C₄	—	2	2	no	—
291	C₇×C₄⋊C₄	—	2	4	no	—
292	C₇×C₄⋊C₄	—	2	4	no	—
293	C₇×C₄⋊C₄	—	2	4	no	—
294	C₇×C₄⋊C₄	—	2	4	no	—
295	C₇×C₄⋊C₄	—	2	2	no	—
296	C₇×C₄⋊C₄	—	2	1	no	—
297	C₇×C₄⋊C₄	—	2	1	no	—
298	C₇×C₄⋊C₄	—	2	1	no	—
299	C₇×C₄⋊C₄	—	2	1	no	—
300	C₇×C₄⋊C₄	—	2	2	no	—
301	C₇×C₄⋊C₄	—	2	2	no	—
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	C₂⁴	1	4	yes	—
307	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
308	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
309	C₇×C₂²⋊C₄	—	2	4	no	—
310	C₇×C₂²⋊C₄	—	2	4	no	—
311	C₇×C₂²⋊C₄	—	2	2	no	—
312	C₇×C₂²⋊C₄	—	2	2	no	—
313	C₇×C₂²⋊C₄	—	2	2	no	—
314	C₇×C₂²⋊C₄	—	2	2	no	—
315	C₇×C₂²⋊C₄	—	2	2	no	—
316	C₇×C₂²⋊C₄	—	2	2	no	—
317	C₇×C₂²⋊C₄	—	2	2	no	—
318	C₇×C₂²⋊C₄	—	2	2	no	—
319	C₇×C₂²⋊C₄	—	2	2	no	—
320	C₄²×C₇	—	2	2	no	—
321	C₄²×C₇	—	2	4	no	—
322	C₄²×C₇	—	2	2	no	—
323	C₄²×C₇	—	2	2	no	—
324	C₄²×C₇	—	2	4	no	—
325	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₇	C₂⁴	1	1	yes	characteristic
338	C₄²×C₇	C₂⁴	1	1	yes	characteristic
339	C₄²×C₇	C₂⁴	1	1	yes	characteristic
340	C₄²×C₇	C₂⁴	1	1	yes	characteristic
341	C₂×#137	C₂²×C₇	1	4	yes	—
342	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
343	#533	—	2	1	no	—
344	#533	—	2	1	no	—
345	#533	—	2	1	no	—
346	#533	—	2	1	no	—
347	#533	C₂²×C₇	1	2	yes	—
348	#533	C₂²×C₇	1	1	yes	characteristic
349	#533	C₂²×C₇	1	2	yes	—
350	#533	C₂²×C₇	1	2	yes	—
351	#533	C₂²×C₇	1	2	yes	—
352	#533	C₂²×C₇	1	1	yes	characteristic
353	#533	C₂²×C₇	1	1	yes	characteristic
354	#532	C₂²×C₇	1	1	yes	characteristic
355	#532	C₂²×C₇	1	1	yes	characteristic
356	#532	C₂²×C₇	1	1	yes	characteristic
357	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
358	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
359	#529	—	2	1	no	—
360	#529	—	2	1	no	—
361	#529	—	2	1	no	—
362	#529	—	2	1	no	—
363	#529	C₂²×C₇	1	2	yes	—
364	#529	C₂²×C₇	1	2	yes	—
365	C₂×#125	—	2	1	no	—
366	#525	—	2	1	no	—
367	#525	—	2	1	no	—
368	#525	C₂²×C₇	1	2	yes	—
369	C₂×C₂²⋊Q₈	—	2	1	no	—
370	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
371	C₄×#41	—	2	1	no	—
372	C₄×#41	—	2	1	no	—
373	C₄×#41	C₂²×C₇	1	2	yes	—
374	C₂×C₄×Q₈	—	2	1	no	—
375	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
376	C₂×#117	—	2	1	no	—
377	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
378	#501	C₂²×C₇	1	4	yes	complemented
379	#500	C₂²×C₇	1	2	yes	complemented
380	#498	C₂²×C₇	1	2	yes	complemented
381	#497	C₂²×C₇	1	4	yes	complemented
382	#494	C₂²×C₇	1	2	yes	complemented
383	#492	C₂²×C₇	1	2	yes	complemented
384	#491	C₂²×C₇	1	4	yes	complemented
385	#489	C₂²×C₇	1	4	yes	complemented
386	#487	C₂²×C₇	1	2	yes	complemented
387	#487	C₂²×C₇	1	2	yes	complemented
388	#487	C₂²×C₇	1	2	yes	complemented
389	#486	C₂²×C₇	1	2	yes	complemented
390	#470	C₂²×C₇	1	8	yes	—
391	#468	C₂²×C₇	1	8	yes	—
392	#467	C₂²×C₇	1	8	yes	—
393	#465	C₂²×C₇	1	8	yes	—
394	#441	C₂²×C₇	1	8	yes	complemented
395	#440	C₂²×C₇	1	8	yes	complemented
396	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
397	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
398	#428	C₂²×C₇	1	4	yes	—
399	#419	C₂²×C₇	1	4	yes	—
400	#417	C₂²×C₇	1	4	yes	—
401	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
402	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
403	C₄×M₁₆	C₂²×C₇	1	2	yes	—
404	C₄×M₁₆	C₂²×C₇	1	2	yes	—
405	C₄×M₁₆	C₂²×C₇	1	2	yes	—
406	C₂×#97	C₂²×C₇	1	2	yes	—
407	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
408	C₂³×C₇	—	2	2	no	—
409	C₂³×C₇	—	2	2	no	—
410	C₂³×C₇	—	2	2	no	—
411	C₂³×C₇	—	4	1	no	—
412	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
413	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
414	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
415	C₇×Q₈	—	2	8	no	—
416	C₇×Q₈	—	2	4	no	—
417	C₇×Q₈	—	4	4	no	—
418	C₇×Q₈	—	4	4	no	—
419	C₇×Q₈	—	4	2	no	—
420	C₇×Q₈	—	4	4	no	—
421	C₇×Q₈	—	4	2	no	—
422	C₇×D₄	—	2	4	no	—
423	C₇×D₄	—	4	4	no	—
424	C₇×D₄	—	4	4	no	—
425	C₇×D₄	—	4	4	no	—
426	C₇×D₄	—	4	2	no	—
427	C₇×D₄	—	4	2	no	—
428	C₂×C₄×C₇	—	2	2	no	—
429	C₂×C₄×C₇	—	2	2	no	—
430	C₂×C₄×C₇	—	2	2	no	—
431	C₂×C₄×C₇	—	2	2	no	—
432	C₂×C₄×C₇	—	2	2	no	—
433	C₂×C₄×C₇	—	2	2	no	—
434	C₂×C₄×C₇	—	2	2	no	—
435	C₂×C₄×C₇	—	2	2	no	—
436	C₂×C₄×C₇	—	2	2	no	—
437	C₂×C₄×C₇	—	2	2	no	—
438	C₂×C₄×C₇	—	2	2	no	—
439	C₂×C₄×C₇	—	2	2	no	—
440	C₂×C₄×C₇	—	2	2	no	—
441	C₂×C₄×C₇	—	2	2	no	—
442	C₂×C₄×C₇	—	2	2	no	—
443	C₂×C₄×C₇	—	2	2	no	—
444	C₂×C₄×C₇	—	2	4	no	—
445	C₂×C₄×C₇	—	2	4	no	—
446	C₂×C₄×C₇	—	4	1	no	—
447	C₂×C₄×C₇	—	4	1	no	—
448	C₂×C₄×C₇	—	4	1	no	—
449	C₂×C₄×C₇	—	4	4	no	—
450	C₂×C₄×C₇	—	4	4	no	—
451	C₂×C₄×C₇	—	4	4	no	—
452	C₂×C₄×C₇	—	4	4	no	—
453	C₂×C₄×C₇	—	4	4	no	—
454	C₂×C₄×C₇	#137	1	4	yes	complemented
455	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₇	C₂×#41	1	4	yes	—
467	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
468	C₇×C₈	—	2	4	no	—
469	C₇×C₈	C₂×#41	1	8	yes	—
470	C₂×#41	—	2	1	no	—
471	C₂×#41	—	2	1	no	—
472	C₂×#41	C₂³×C₇	1	2	yes	—
473	C₂²×Q₈	—	2	1	no	—
474	C₂²×Q₈	C₂³×C₇	1	2	yes	—
475	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
476	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
478	#137	—	2	16	no	—
479	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
480	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
481	C₂×M₁₆	—	2	8	no	—
482	C₂×M₁₆	C₂³×C₇	1	2	yes	—
483	C₂×M₁₆	C₂³×C₇	1	4	yes	—
484	C₂×M₁₆	C₂³×C₇	1	2	yes	—
485	C₂²×C₈	C₂³×C₇	1	4	yes	—
486	C₄⋊Q₈	—	2	1	no	—
487	C₄⋊Q₈	—	2	1	no	—
488	C₄⋊Q₈	—	2	1	no	—
489	C₄⋊Q₈	—	2	1	no	—
490	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
491	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
492	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
493	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
494	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
495	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
496	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
497	#127	C₂³×C₇	1	1	yes	characteristic
498	#126	—	2	2	no	—
499	#126	—	2	2	no	—
500	#125	—	2	2	no	—
501	#125	—	2	2	no	—
502	#125	—	2	2	no	—
503	#125	—	2	2	no	—
504	#125	—	2	1	no	—
505	#125	—	2	1	no	—
506	#125	C₂³×C₇	1	2	yes	—
507	#124	—	2	1	no	—
508	#124	—	2	1	no	—
509	#124	C₂³×C₇	1	2	yes	—
510	#123	—	2	2	no	—
511	#123	—	2	2	no	—
512	#123	—	2	2	no	—
513	C₂²⋊Q₈	—	2	2	no	—
514	C₂²⋊Q₈	—	2	2	no	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	—	2	2	no	—
517	C₂²⋊Q₈	—	2	2	no	—
518	C₂²⋊Q₈	—	2	2	no	—
519	C₂²⋊Q₈	—	2	1	no	—
520	C₂²⋊Q₈	—	2	1	no	—
521	C₂²⋊Q₈	—	2	1	no	—
522	C₂²⋊Q₈	—	2	1	no	—
523	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
524	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
525	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
526	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
527	#121	—	2	1	no	—
528	#121	—	2	1	no	—
529	#121	—	2	1	no	—
530	#121	—	2	1	no	—
531	#121	C₂³×C₇	1	2	yes	—
532	#121	C₂³×C₇	1	2	yes	—
533	#120	—	2	2	no	—
534	C₄×Q₈	—	2	2	no	—
535	C₄×Q₈	—	2	2	no	—
536	C₄×Q₈	—	2	2	no	—
537	C₄×Q₈	—	2	2	no	—
538	C₄×Q₈	—	2	2	no	—
539	C₄×Q₈	—	2	2	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	—	2	1	no	—
543	C₄×Q₈	—	2	1	no	—
544	C₄×Q₈	C₂³×C₇	1	4	yes	—
545	C₄×Q₈	C₂³×C₇	1	4	yes	—
546	C₄×Q₈	C₂³×C₇	1	2	yes	—
547	C₄×Q₈	C₂³×C₇	1	2	yes	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	2	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	—	2	1	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	C₂³×C₇	1	2	yes	—
559	C₄×D₄	C₂³×C₇	1	2	yes	—
560	#117	—	2	2	no	—
561	#117	—	2	2	no	—
562	#117	—	2	2	no	—
563	#117	—	2	2	no	—
564	#117	—	2	1	no	—
565	#117	—	2	1	no	—
566	#117	—	2	2	no	—
567	#117	—	2	2	no	—
568	#117	—	2	2	no	—
569	#117	C₂³×C₇	1	2	yes	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	2	no	—
574	C₂×C₄⋊C₄	—	2	2	no	—
575	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
576	C₂×C₂²⋊C₄	—	2	2	no	—
577	C₂×C₄²	—	2	2	no	—
578	C₂×C₄²	—	2	2	no	—
579	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
580	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
581	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
582	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
583	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
584	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
586	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
587	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
588	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
589	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
591	#107	C₂³×C₇	1	8	yes	—
592	#106	C₂³×C₇	1	8	yes	—
593	#103	C₂³×C₇	1	8	yes	—
594	#103	C₂³×C₇	1	8	yes	—
595	#103	C₂³×C₇	1	8	yes	—
596	#102	C₂³×C₇	1	8	yes	—
597	#97	C₂³×C₇	1	4	yes	—
598	#97	C₂³×C₇	1	2	yes	—
599	#97	C₂³×C₇	1	2	yes	—
600	C₄×C₈	C₂³×C₇	1	4	yes	—
601	C₄×C₈	C₂³×C₇	1	2	yes	—
602	C₄×C₈	C₂³×C₇	1	2	yes	—
603	C₂²×C₇	—	2	1	no	—
604	C₂²×C₇	—	2	1	no	—
605	C₂²×C₇	—	2	1	no	—
606	C₂²×C₇	—	2	1	no	—
607	C₂²×C₇	—	2	1	no	—
608	C₂²×C₇	—	2	1	no	—
609	C₂²×C₇	—	2	1	no	—
610	C₂²×C₇	—	4	4	no	—
611	C₂²×C₇	—	4	2	no	—
612	C₂²×C₇	—	4	2	no	—
613	C₂²×C₇	—	4	2	no	—
614	C₂²×C₇	#532	1	2	yes	—
615	C₂²×C₇	C₂×#137	1	2	yes	—
616	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
617	C₄×C₇	—	2	1	no	—
618	C₄×C₇	—	2	1	no	—
619	C₄×C₇	—	2	1	no	—
620	C₄×C₇	—	2	1	no	—
621	C₄×C₇	—	2	1	no	—
622	C₄×C₇	—	2	1	no	—
623	C₄×C₇	—	2	1	no	—
624	C₄×C₇	—	4	2	no	—
625	C₄×C₇	—	4	4	no	—
626	C₄×C₇	—	4	2	no	—
627	C₄×C₇	—	4	2	no	—
628	C₄×C₇	—	4	4	no	—
629	C₄×C₇	#532	1	2	yes	—
630	C₄×C₇	C₂×#137	1	2	yes	—
631	C₄×C₇	C₂×#137	1	2	yes	—
632	C₄×C₇	#575	1	2	yes	—
633	C₄×C₇	C₂²×#41	1	2	yes	—
634	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
635	#41	—	2	8	no	—
636	#41	—	4	4	no	—
637	#41	—	4	4	no	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	2	1	no	—
640	C₂×Q₈	—	2	2	no	—
641	C₂×Q₈	—	2	2	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	2	8	no	—
644	C₂×Q₈	—	4	4	no	—
645	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
646	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	C₂⁴×C₇	1	2	yes	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
662	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
663	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
664	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
665	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
666	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
667	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
668	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
669	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
670	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
671	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
672	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
673	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
674	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
675	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
679	Q₁₆	—	2	16	no	—
680	SD₁₆	—	2	16	no	—
681	M₁₆	—	2	4	no	—
682	M₁₆	—	2	8	no	—
683	M₁₆	C₇×#41	1	8	yes	complemented
684	C₂×C₈	—	2	8	no	—
685	C₂×C₈	C₂⁴×C₇	1	4	yes	—
686	C₂×C₈	C₂⁴×C₇	1	4	yes	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
709	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
710	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₄²	—	2	2	no	—
723	C₄²	—	2	2	no	—
724	C₄²	—	2	4	no	—
725	C₄²	—	2	4	no	—
726	C₄²	—	2	2	no	—
727	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
728	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
729	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
730	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
731	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
732	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
733	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
734	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
735	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
736	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
737	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
738	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
739	C₄²	C₂⁴×C₇	1	1	yes	characteristic
740	C₄²	C₂⁴×C₇	1	1	yes	characteristic
741	C₄²	C₂⁴×C₇	1	1	yes	characteristic
742	C₄²	C₂⁴×C₇	1	1	yes	characteristic
743	C₂×C₇	—	2	2	no	—
744	C₂×C₇	—	2	2	no	—
745	C₂×C₇	—	4	1	no	—
746	C₂×C₇	—	8	2	no	—
747	C₂×C₇	C₂×#532	1	1	yes	characteristic
748	C₂×C₇	C₂²×#137	1	1	yes	characteristic
749	C₂×C₇	C₂×#575	1	1	yes	characteristic
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	4	1	no	—
754	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
755	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
756	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
757	Q₈	—	2	8	no	—
758	Q₈	—	2	4	no	—
759	Q₈	—	4	4	no	—
760	Q₈	—	4	4	no	—
761	Q₈	—	4	2	no	—
762	Q₈	—	4	4	no	—
763	Q₈	—	4	2	no	—
764	D₄	—	2	4	no	—
765	D₄	—	4	4	no	—
766	D₄	—	4	4	no	—
767	D₄	—	4	4	no	—
768	D₄	—	4	2	no	—
769	D₄	—	4	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	C₇×#137	1	4	yes	complemented
797	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
798	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
799	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
800	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
801	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
802	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
803	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
804	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
805	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
806	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
807	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
808	C₂×C₄	C₂×C₇×#41	1	4	yes	—
809	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
810	C₈	—	2	4	no	—
811	C₈	C₂×C₇×#41	1	8	yes	—
812	C₇	#60701	1	1	yes	characteristic, direct product factor, Sylow
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	4	4	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	C₇×#532	1	2	yes	—
825	C₂²	C₂×C₇×#137	1	2	yes	—
826	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	1	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	4	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	4	no	—
839	C₄	C₇×#532	1	2	yes	—
840	C₄	C₂×C₇×#137	1	2	yes	—
841	C₄	C₂×C₇×#137	1	2	yes	—
842	C₄	C₇×#575	1	2	yes	—
843	C₄	C₂²×C₇×#41	1	2	yes	—
844	C₂	—	2	2	no	—
845	C₂	—	2	2	no	—
846	C₂	—	4	1	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂×C₇×#532	1	1	yes	characteristic
849	C₂	C₂²×C₇×#137	1	1	yes	characteristic
850	C₂	C₂×C₇×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
prime radical	C₇×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#533	C₂	semidirect
3. C₇×#3185	C₂	semidirect
4. C₇×#3182	C₂	semidirect
5. C₇×#3181	C₂	semidirect
6. C₇×#3172	C₂	semidirect
7. C₇×#3170	C₂	semidirect
8. C₇×#3167	C₂	semidirect
9. C₇×#3165	C₂	semidirect
10. C₇×#3152	C₂	semidirect
11. C₇×#3141	C₂	semidirect
12. C₇×#3139	C₂	semidirect
13. C₇×#3056	C₂	semidirect
14. C₄×C₇×#137	C₂	semidirect
15. C₂×C₄×C₇×M₁₆	C₂	semidirect
53. C₇×#501	C₂²	semidirect
54. C₇×#500	C₂²	semidirect
55. C₇×#498	C₂²	semidirect
56. C₇×#497	C₂²	semidirect
57. C₇×#494	C₂²	semidirect
58. C₇×#492	C₂²	semidirect
59. C₇×#491	C₂²	semidirect
60. C₇×#489	C₂²	semidirect
61. C₇×#487	C₂²	semidirect
62. C₇×#487	C₂²	semidirect
63. C₇×#487	C₂²	semidirect
64. C₇×#486	C₂²	semidirect
69. C₇×#441	C₂²	semidirect
70. C₇×#440	C₂²	semidirect
71. C₄×C₇×Q₁₆	C₂²	semidirect
72. C₄×C₇×SD₁₆	C₂²	semidirect
83. #60701	C₇	direct (N × H)
218. C₂×#533	C₂×C₇	semidirect
219. #3185	C₂×C₇	semidirect
220. #3182	C₂×C₇	semidirect
221. #3181	C₂×C₇	semidirect
222. #3172	C₂×C₇	semidirect
223. #3170	C₂×C₇	semidirect
224. #3167	C₂×C₇	semidirect
225. #3165	C₂×C₇	semidirect
226. #3152	C₂×C₇	semidirect
227. #3141	C₂×C₇	semidirect
228. #3139	C₂×C₇	semidirect
229. #3056	C₂×C₇	semidirect
230. C₄×#137	C₂×C₇	semidirect
231. C₂×C₄×M₁₆	C₂×C₇	semidirect
281. C₇×M₁₆	#41	semidirect
378. #501	C₂²×C₇	semidirect
379. #500	C₂²×C₇	semidirect
380. #498	C₂²×C₇	semidirect
381. #497	C₂²×C₇	semidirect
382. #494	C₂²×C₇	semidirect
383. #492	C₂²×C₇	semidirect
384. #491	C₂²×C₇	semidirect
385. #489	C₂²×C₇	semidirect
386. #487	C₂²×C₇	semidirect
387. #487	C₂²×C₇	semidirect
388. #487	C₂²×C₇	semidirect
389. #486	C₂²×C₇	semidirect
394. #441	C₂²×C₇	semidirect
395. #440	C₂²×C₇	semidirect
396. C₄×Q₁₆	C₂²×C₇	semidirect
397. C₄×SD₁₆	C₂²×C₇	semidirect
454. C₂×C₄×C₇	#137	semidirect
683. M₁₆	C₇×#41	semidirect
796. C₂×C₄	C₇×#137	semidirect
812. C₇	#60701	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×#3444	2
C₂×C₇×#533	2
C₇×#3185	2
C₇×#3182	2
C₇×#3181	2
C₇×#3172	2
C₇×#3170	2
C₇×#3167	2
C₇×#3165	2
C₇×#3152	2
C₇×#3141	2
C₇×#3139	2
C₇×#3056	2
C₄×C₇×#137	2
C₂×C₄×C₇×M₁₆	2
#60701	7

Subgroups — C7×#60701 #13237917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60701 #13237917