Subgroups — C₇×#60872 #13238088

Order 1792.

1682 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#544	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3244	C₂	1	4	yes	maximal, complemented
4	C₇×#3242	C₂	1	4	yes	maximal, complemented
5	C₇×#3238	C₂	1	2	yes	maximal, complemented
6	C₇×#3236	C₂	1	2	yes	maximal, complemented
7	C₇×#3232	C₂	1	2	yes	maximal, complemented
8	C₇×#3229	C₂	1	2	yes	maximal, complemented
9	C₇×#3163	C₂	1	2	yes	maximal, complemented
10	C₇×#3137	C₂	1	2	yes	maximal, complemented
11	C₇×#3095	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3092	C₂	1	1	yes	maximal, characteristic
13	C₇×#3091	C₂	1	1	yes	maximal, characteristic
14	C₂×C₇×#483	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3084	C₂	1	2	yes	maximal, complemented
16	C₇×#3082	C₂	1	2	yes	maximal, complemented
17	C₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#556	—	2	1	no	—
19	C₇×#554	—	2	1	no	—
20	C₇×#552	—	2	2	no	—
21	C₇×#552	—	2	1	no	—
22	C₇×#552	—	2	1	no	—
23	C₇×#551	—	2	2	no	—
24	C₇×#544	—	2	2	no	—
25	C₇×#544	—	2	1	no	—
26	C₇×#544	—	2	1	no	—
27	C₇×#544	C₂²	1	1	yes	characteristic
28	C₇×#544	C₂²	1	2	yes	—
29	C₇×#544	C₂²	1	4	yes	—
30	C₇×#544	C₂²	1	2	yes	—
31	C₇×#542	C₂²	1	2	yes	—
32	C₇×#541	C₂²	1	2	yes	—
33	C₇×#536	C₂²	1	1	yes	characteristic
34	C₇×#533	C₂²	1	2	yes	—
35	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
36	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
37	C₇×#529	C₂²	1	2	yes	—
38	C₂×C₇×#125	—	2	1	no	—
39	C₂×C₇×#125	C₂²	1	2	yes	—
40	C₇×#525	C₂²	1	1	yes	characteristic
41	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
42	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₇×#520	C₂²	1	1	yes	characteristic
44	C₇×#519	C₂²	1	1	yes	characteristic
45	C₂×C₇×#117	C₂²	1	1	yes	characteristic
46	C₂×C₇×#117	C₂²	1	1	yes	characteristic
47	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₇×#501	C₂²	1	4	yes	complemented
49	C₇×#501	C₂²	1	4	yes	complemented
50	C₇×#499	C₂²	1	4	yes	complemented
51	C₇×#498	C₂²	1	4	yes	complemented
52	C₇×#491	C₂²	1	4	yes	complemented
53	C₇×#489	C₂²	1	4	yes	complemented
54	C₇×#488	C₂²	1	4	yes	complemented
55	C₇×#487	C₂²	1	4	yes	complemented
56	C₇×#485	C₂²	1	2	yes	—
57	C₇×#485	C₂²	1	4	yes	—
58	C₇×#484	C₂²	1	2	yes	—
59	C₇×#484	C₂²	1	1	yes	characteristic
60	C₇×#484	C₂²	1	2	yes	—
61	C₇×#483	C₂²	1	1	yes	characteristic
62	C₇×#483	C₂²	1	2	yes	—
63	C₇×#483	C₂²	1	2	yes	—
64	C₇×#483	C₂²	1	2	yes	—
65	C₇×#483	C₂²	1	2	yes	—
66	C₇×#483	C₂²	1	4	yes	—
67	C₇×#482	C₂²	1	2	yes	—
68	C₇×#481	C₂²	1	1	yes	characteristic
69	C₇×#481	C₂²	1	2	yes	—
70	C₇×#480	C₂²	1	2	yes	—
71	C₇×#480	C₂²	1	1	yes	characteristic
72	C₇×#479	C₂²	1	4	yes	complemented
73	C₇×#479	C₂²	1	4	yes	complemented
74	C₇×#479	C₂²	1	4	yes	complemented
75	C₇×#478	C₂²	1	4	yes	complemented
76	C₇×#477	C₂²	1	4	yes	complemented
77	C₇×#476	C₂²	1	4	yes	complemented
78	C₇×#475	C₂²	1	4	yes	complemented
79	C₇×#475	C₂²	1	4	yes	complemented
80	C₇×#433	C₂²	1	4	yes	—
81	C₇×#432	C₂²	1	2	yes	—
82	C₇×#431	C₂²	1	2	yes	—
83	C₇×#428	C₂²	1	2	yes	—
84	C₇×#428	C₂²	1	2	yes	—
85	C₇×#427	C₂²	1	2	yes	—
86	C₂×C₇×#106	C₂²	1	2	yes	—
87	C₇×#424	C₂²	1	2	yes	—
88	C₇×#419	C₂²	1	2	yes	—
89	C₇×#417	C₂²	1	2	yes	—
90	C₇×#416	C₂²	1	2	yes	—
91	C₂×C₇×#103	C₂²	1	2	yes	—
92	C₇×#407	C₂²	1	1	yes	characteristic
93	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₇×#405	C₂²	1	2	yes	—
95	#60872	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₇×#41	C₂³	1	1	yes	characteristic
97	C₂²×C₇×Q₈	—	2	2	no	—
98	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₇	—	2	1	no	—
100	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
101	C₂×C₇×M₁₆	C₂³	1	2	yes	—
102	C₂²×C₇×C₈	C₂³	1	2	yes	—
103	C₇×C₄⋊Q₈	—	2	2	no	—
104	C₇×C₄⋊Q₈	—	2	2	no	—
105	C₇×C₄⋊Q₈	—	2	4	no	—
106	C₇×C₄⋊Q₈	—	2	1	no	—
107	C₇×C₄⋊Q₈	—	2	2	no	—
108	C₇×C₄⋊Q₈	—	2	2	no	—
109	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
111	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
112	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₇×#126	—	2	2	no	—
114	C₇×#126	—	2	2	no	—
115	C₇×#126	—	2	2	no	—
116	C₇×#126	—	2	2	no	—
117	C₇×#125	—	2	2	no	—
118	C₇×#125	—	2	4	no	—
119	C₇×#125	—	2	2	no	—
120	C₇×#125	—	2	2	no	—
121	C₇×#125	—	2	2	no	—
122	C₇×#125	—	2	1	no	—
123	C₇×#125	—	2	2	no	—
124	C₇×#125	—	2	2	no	—
125	C₇×#125	—	2	2	no	—
126	C₇×#125	C₂³	1	4	yes	—
127	C₇×#125	C₂³	1	4	yes	—
128	C₇×#125	C₂³	1	2	yes	—
129	C₇×#124	—	2	2	no	—
130	C₇×#124	C₂³	1	2	yes	—
131	C₇×#123	—	2	1	no	—
132	C₇×#123	—	2	2	no	—
133	C₇×#123	—	2	2	no	—
134	C₇×#123	—	2	2	no	—
135	C₇×C₂²⋊Q₈	—	2	1	no	—
136	C₇×C₂²⋊Q₈	—	2	1	no	—
137	C₇×C₂²⋊Q₈	—	2	2	no	—
138	C₇×C₂²⋊Q₈	—	2	1	no	—
139	C₇×C₂²⋊Q₈	—	2	1	no	—
140	C₇×C₂²⋊Q₈	—	2	2	no	—
141	C₇×C₂²⋊Q₈	—	2	4	no	—
142	C₇×C₂²⋊Q₈	—	2	4	no	—
143	C₇×C₂²⋊Q₈	—	2	4	no	—
144	C₇×C₂²⋊Q₈	—	2	4	no	—
145	C₇×C₂²⋊Q₈	—	2	2	no	—
146	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
148	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
150	C₇×#121	C₂³	1	1	yes	characteristic
151	C₇×#121	C₂³	1	1	yes	characteristic
152	C₇×#120	—	2	1	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	C₂³	1	2	yes	—
157	C₄×C₇×Q₈	C₂³	1	2	yes	—
158	C₄×C₇×Q₈	C₂³	1	2	yes	—
159	C₄×C₇×D₄	—	2	1	no	—
160	C₄×C₇×D₄	—	2	1	no	—
161	C₄×C₇×D₄	—	2	2	no	—
162	C₄×C₇×D₄	—	2	2	no	—
163	C₄×C₇×D₄	C₂³	1	2	yes	—
164	C₇×#117	—	2	1	no	—
165	C₇×#117	—	2	1	no	—
166	C₇×#117	—	2	2	no	—
167	C₇×#117	—	2	1	no	—
168	C₇×#117	—	2	2	no	—
169	C₇×#117	—	2	2	no	—
170	C₇×#117	D₄	1	1	yes	characteristic
171	C₇×#117	D₄	1	2	yes	—
172	C₇×#117	D₄	1	1	yes	characteristic
173	C₇×#117	C₂³	1	2	yes	—
174	C₇×#117	C₂³	1	2	yes	—
175	C₇×#117	C₂³	1	1	yes	characteristic
176	C₇×#117	C₂³	1	1	yes	characteristic
177	C₇×#117	C₂³	1	1	yes	characteristic
178	C₇×#117	C₂³	1	2	yes	—
179	C₂×C₇×C₄⋊C₄	—	2	1	no	—
180	C₂×C₇×C₄⋊C₄	—	2	1	no	—
181	C₂×C₇×C₄⋊C₄	—	2	1	no	—
182	C₂×C₇×C₄⋊C₄	—	2	2	no	—
183	C₂×C₇×C₄⋊C₄	—	2	2	no	—
184	C₂×C₇×C₄⋊C₄	—	2	2	no	—
185	C₂×C₇×C₄⋊C₄	—	2	1	no	—
186	C₂×C₇×C₄⋊C₄	—	2	1	no	—
187	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
188	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
189	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
196	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
197	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
198	C₂×C₄²×C₇	—	2	1	no	—
199	C₂×C₄²×C₇	C₂³	1	2	yes	—
200	C₇×#107	C₂³	1	2	yes	—
201	C₇×#107	C₂³	1	4	yes	—
202	C₇×#107	C₂³	1	4	yes	—
203	C₇×#107	C₂³	1	2	yes	—
204	C₇×#106	C₂³	1	2	yes	—
205	C₇×#106	C₂³	1	4	yes	—
206	C₇×#106	C₂³	1	4	yes	—
207	C₇×#106	C₂³	1	4	yes	—
208	C₇×#106	C₂³	1	4	yes	—
209	C₇×#106	C₂³	1	2	yes	—
210	C₇×C₄⋊C₈	C₂³	1	4	yes	—
211	C₇×C₄⋊C₈	C₂³	1	4	yes	—
212	C₇×#103	C₂³	1	2	yes	—
213	C₇×#103	C₂³	1	4	yes	—
214	C₇×#103	C₂³	1	4	yes	—
215	C₇×#103	C₂³	1	4	yes	—
216	C₇×#103	C₂³	1	4	yes	—
217	C₇×#103	C₂³	1	4	yes	—
218	C₇×#103	C₂³	1	2	yes	—
219	C₇×#102	C₂³	1	2	yes	—
220	C₇×#102	C₂³	1	4	yes	—
221	C₇×#102	C₂³	1	2	yes	—
222	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
223	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
224	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₇×#97	C₂³	1	4	yes	—
228	C₄×C₇×C₈	C₂³	1	4	yes	—
229	#3495	C₂×C₇	1	1	yes	characteristic
230	C₂×#544	C₂×C₇	1	1	yes	characteristic, complemented
231	#3244	C₂×C₇	1	4	yes	complemented
232	#3242	C₂×C₇	1	4	yes	complemented
233	#3238	C₂×C₇	1	2	yes	complemented
234	#3236	C₂×C₇	1	2	yes	complemented
235	#3232	C₂×C₇	1	2	yes	complemented
236	#3229	C₂×C₇	1	2	yes	complemented
237	#3163	C₂×C₇	1	2	yes	complemented
238	#3137	C₂×C₇	1	2	yes	complemented
239	#3095	C₂×C₇	1	1	yes	characteristic, complemented
240	#3092	C₂×C₇	1	1	yes	characteristic
241	#3091	C₂×C₇	1	1	yes	characteristic
242	C₂×#483	C₂×C₇	1	1	yes	characteristic, complemented
243	#3084	C₂×C₇	1	2	yes	complemented
244	#3082	C₂×C₇	1	2	yes	complemented
245	#2924	C₂×C₇	1	1	yes	characteristic, complemented
246	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
247	C₇×#41	—	2	4	no	—
248	C₂×C₇×Q₈	—	2	1	no	—
249	C₂×C₇×Q₈	—	2	2	no	—
250	C₂×C₇×Q₈	—	2	4	no	—
251	C₂×C₇×Q₈	—	2	4	no	—
252	C₂×C₇×Q₈	—	2	4	no	—
253	C₂×C₇×Q₈	—	8	4	no	—
254	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
255	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
256	C₂×C₇×D₄	—	2	1	no	—
257	C₂×C₇×D₄	—	2	1	no	—
258	C₂×C₇×D₄	—	2	1	no	—
259	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₇	—	2	4	no	—
261	C₂²×C₄×C₇	—	2	1	no	—
262	C₂²×C₄×C₇	—	2	1	no	—
263	C₂²×C₄×C₇	—	2	1	no	—
264	C₂²×C₄×C₇	—	2	2	no	—
265	C₂²×C₄×C₇	—	2	1	no	—
266	C₂²×C₄×C₇	—	2	2	no	—
267	C₂²×C₄×C₇	—	2	2	no	—
268	C₂²×C₄×C₇	—	2	1	no	—
269	C₂²×C₄×C₇	—	2	2	no	—
270	C₂²×C₄×C₇	—	8	2	no	—
271	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
279	C₇×M₁₆	—	2	4	no	—
280	C₂×C₇×C₈	—	2	4	no	—
281	C₂×C₇×C₈	C₂⁴	1	2	yes	—
282	C₂×C₇×C₈	C₂⁴	1	4	yes	—
283	C₂×C₇×C₈	C₂⁴	1	2	yes	—
284	C₇×C₄⋊C₄	—	2	2	no	—
285	C₇×C₄⋊C₄	—	2	2	no	—
286	C₇×C₄⋊C₄	—	2	2	no	—
287	C₇×C₄⋊C₄	—	2	1	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	4	no	—
296	C₇×C₄⋊C₄	—	2	4	no	—
297	C₇×C₄⋊C₄	—	2	1	no	—
298	C₇×C₄⋊C₄	—	2	1	no	—
299	C₇×C₄⋊C₄	—	2	2	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	1	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	C₂×D₄	1	1	yes	characteristic
309	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
310	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
311	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
312	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
313	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
314	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
315	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
316	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
317	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
318	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
319	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
320	C₇×C₂²⋊C₄	—	2	2	no	—
321	C₇×C₂²⋊C₄	—	2	2	no	—
322	C₇×C₂²⋊C₄	—	2	2	no	—
323	C₇×C₂²⋊C₄	—	2	2	no	—
324	C₇×C₂²⋊C₄	—	2	1	no	—
325	C₇×C₂²⋊C₄	—	2	1	no	—
326	C₇×C₂²⋊C₄	—	2	1	no	—
327	C₇×C₂²⋊C₄	—	2	1	no	—
328	C₇×C₂²⋊C₄	—	2	2	no	—
329	C₇×C₂²⋊C₄	—	2	2	no	—
330	C₇×C₂²⋊C₄	—	2	1	no	—
331	C₇×C₂²⋊C₄	—	2	2	no	—
332	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
333	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
334	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
335	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
336	C₄²×C₇	—	2	2	no	—
337	C₄²×C₇	—	2	2	no	—
338	C₄²×C₇	—	2	2	no	—
339	C₄²×C₇	—	2	2	no	—
340	C₄²×C₇	—	2	2	no	—
341	C₄²×C₇	—	2	1	no	—
342	C₄²×C₇	C₂×D₄	1	2	yes	—
343	C₄²×C₇	C₂×D₄	1	2	yes	—
344	C₄²×C₇	C₂⁴	1	2	yes	—
345	C₄²×C₇	C₂⁴	1	2	yes	—
346	#556	—	2	1	no	—
347	#554	—	2	1	no	—
348	#552	—	2	2	no	—
349	#552	—	2	1	no	—
350	#552	—	2	1	no	—
351	#551	—	2	2	no	—
352	#544	—	2	2	no	—
353	#544	—	2	1	no	—
354	#544	—	2	1	no	—
355	#544	C₂²×C₇	1	2	yes	—
356	#544	C₂²×C₇	1	2	yes	—
357	#544	C₂²×C₇	1	1	yes	characteristic
358	#544	C₂²×C₇	1	4	yes	—
359	#542	C₂²×C₇	1	2	yes	—
360	#541	C₂²×C₇	1	2	yes	—
361	#536	C₂²×C₇	1	1	yes	characteristic
362	#533	C₂²×C₇	1	2	yes	—
363	C₂×C₄⋊Q₈	—	2	1	no	—
364	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
365	#529	C₂²×C₇	1	2	yes	—
366	C₂×#125	—	2	1	no	—
367	C₂×#125	C₂²×C₇	1	2	yes	—
368	#525	C₂²×C₇	1	1	yes	characteristic
369	C₂×C₂²⋊Q₈	—	2	2	no	—
370	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
371	#520	C₂²×C₇	1	1	yes	characteristic
372	#519	C₂²×C₇	1	1	yes	characteristic
373	C₂×#117	C₂²×C₇	1	1	yes	characteristic
374	C₂×#117	C₂²×C₇	1	1	yes	characteristic
375	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
376	#501	C₂²×C₇	1	4	yes	complemented
377	#501	C₂²×C₇	1	4	yes	complemented
378	#499	C₂²×C₇	1	4	yes	complemented
379	#498	C₂²×C₇	1	4	yes	complemented
380	#491	C₂²×C₇	1	4	yes	complemented
381	#489	C₂²×C₇	1	4	yes	complemented
382	#488	C₂²×C₇	1	4	yes	complemented
383	#487	C₂²×C₇	1	4	yes	complemented
384	#485	C₂²×C₇	1	2	yes	—
385	#485	C₂²×C₇	1	4	yes	—
386	#484	C₂²×C₇	1	1	yes	characteristic
387	#484	C₂²×C₇	1	2	yes	—
388	#484	C₂²×C₇	1	2	yes	—
389	#483	C₂²×C₇	1	2	yes	—
390	#483	C₂²×C₇	1	2	yes	—
391	#483	C₂²×C₇	1	4	yes	—
392	#483	C₂²×C₇	1	1	yes	characteristic
393	#483	C₂²×C₇	1	2	yes	—
394	#483	C₂²×C₇	1	2	yes	—
395	#482	C₂²×C₇	1	2	yes	—
396	#481	C₂²×C₇	1	1	yes	characteristic
397	#481	C₂²×C₇	1	2	yes	—
398	#480	C₂²×C₇	1	1	yes	characteristic
399	#480	C₂²×C₇	1	2	yes	—
400	#479	C₂²×C₇	1	4	yes	complemented
401	#479	C₂²×C₇	1	4	yes	complemented
402	#479	C₂²×C₇	1	4	yes	complemented
403	#478	C₂²×C₇	1	4	yes	complemented
404	#477	C₂²×C₇	1	4	yes	complemented
405	#476	C₂²×C₇	1	4	yes	complemented
406	#475	C₂²×C₇	1	4	yes	complemented
407	#475	C₂²×C₇	1	4	yes	complemented
408	#433	C₂²×C₇	1	4	yes	—
409	#432	C₂²×C₇	1	2	yes	—
410	#431	C₂²×C₇	1	2	yes	—
411	#428	C₂²×C₇	1	2	yes	—
412	#428	C₂²×C₇	1	2	yes	—
413	#427	C₂²×C₇	1	2	yes	—
414	C₂×#106	C₂²×C₇	1	2	yes	—
415	#424	C₂²×C₇	1	2	yes	—
416	#419	C₂²×C₇	1	2	yes	—
417	#417	C₂²×C₇	1	2	yes	—
418	#416	C₂²×C₇	1	2	yes	—
419	C₂×#103	C₂²×C₇	1	2	yes	—
420	#407	C₂²×C₇	1	1	yes	characteristic
421	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
422	#405	C₂²×C₇	1	2	yes	—
423	C₂³×C₇	—	2	2	no	—
424	C₂³×C₇	—	2	2	no	—
425	C₂³×C₇	—	2	1	no	—
426	C₂³×C₇	—	4	1	no	—
427	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
428	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
429	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
430	C₇×Q₈	—	2	4	no	—
431	C₇×Q₈	—	2	2	no	—
432	C₇×Q₈	—	4	2	no	—
433	C₇×Q₈	—	8	2	no	—
434	C₇×Q₈	—	8	4	no	—
435	C₇×Q₈	—	8	4	no	—
436	C₇×D₄	—	2	2	no	—
437	C₇×D₄	—	4	2	no	—
438	C₇×D₄	—	4	2	no	—
439	C₇×D₄	—	8	1	no	—
440	C₂×C₄×C₇	—	2	2	no	—
441	C₂×C₄×C₇	—	2	4	no	—
442	C₂×C₄×C₇	—	2	2	no	—
443	C₂×C₄×C₇	—	2	2	no	—
444	C₂×C₄×C₇	—	2	2	no	—
445	C₂×C₄×C₇	—	2	2	no	—
446	C₂×C₄×C₇	—	2	1	no	—
447	C₂×C₄×C₇	—	2	1	no	—
448	C₂×C₄×C₇	—	2	2	no	—
449	C₂×C₄×C₇	—	2	2	no	—
450	C₂×C₄×C₇	—	2	1	no	—
451	C₂×C₄×C₇	—	2	2	no	—
452	C₂×C₄×C₇	—	2	2	no	—
453	C₂×C₄×C₇	—	2	4	no	—
454	C₂×C₄×C₇	—	4	2	no	—
455	C₂×C₄×C₇	—	4	2	no	—
456	C₂×C₄×C₇	—	4	2	no	—
457	C₂×C₄×C₇	—	4	4	no	—
458	C₂×C₄×C₇	—	4	2	no	—
459	C₂×C₄×C₇	—	4	2	no	—
460	C₂×C₄×C₇	—	8	2	no	—
461	C₂×C₄×C₇	—	8	1	no	—
462	C₂×C₄×C₇	—	8	2	no	—
463	C₂×C₄×C₇	—	8	2	no	—
464	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
467	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
469	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
472	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
473	C₇×C₈	—	2	2	no	—
474	C₇×C₈	—	2	2	no	—
475	C₇×C₈	—	2	4	no	—
476	C₂×#41	C₂³×C₇	1	1	yes	characteristic
477	C₂²×Q₈	—	2	2	no	—
478	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
479	C₂³×C₄	—	2	1	no	—
480	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
481	C₂×M₁₆	C₂³×C₇	1	2	yes	—
482	C₂²×C₈	C₂³×C₇	1	2	yes	—
483	C₄⋊Q₈	—	2	2	no	—
484	C₄⋊Q₈	—	2	2	no	—
485	C₄⋊Q₈	—	2	4	no	—
486	C₄⋊Q₈	—	2	1	no	—
487	C₄⋊Q₈	—	2	2	no	—
488	C₄⋊Q₈	—	2	2	no	—
489	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
490	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
491	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
492	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
493	#126	—	2	2	no	—
494	#126	—	2	2	no	—
495	#126	—	2	2	no	—
496	#126	—	2	2	no	—
497	#125	—	2	2	no	—
498	#125	—	2	4	no	—
499	#125	—	2	2	no	—
500	#125	—	2	2	no	—
501	#125	—	2	2	no	—
502	#125	—	2	1	no	—
503	#125	—	2	2	no	—
504	#125	—	2	2	no	—
505	#125	—	2	2	no	—
506	#125	C₂³×C₇	1	4	yes	—
507	#125	C₂³×C₇	1	4	yes	—
508	#125	C₂³×C₇	1	2	yes	—
509	#124	—	2	2	no	—
510	#124	C₂³×C₇	1	2	yes	—
511	#123	—	2	1	no	—
512	#123	—	2	2	no	—
513	#123	—	2	2	no	—
514	#123	—	2	2	no	—
515	C₂²⋊Q₈	—	2	1	no	—
516	C₂²⋊Q₈	—	2	1	no	—
517	C₂²⋊Q₈	—	2	2	no	—
518	C₂²⋊Q₈	—	2	1	no	—
519	C₂²⋊Q₈	—	2	1	no	—
520	C₂²⋊Q₈	—	2	2	no	—
521	C₂²⋊Q₈	—	2	4	no	—
522	C₂²⋊Q₈	—	2	4	no	—
523	C₂²⋊Q₈	—	2	4	no	—
524	C₂²⋊Q₈	—	2	4	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
527	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
528	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
529	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
530	#121	C₂³×C₇	1	1	yes	characteristic
531	#121	C₂³×C₇	1	1	yes	characteristic
532	#120	—	2	1	no	—
533	C₄×Q₈	—	2	1	no	—
534	C₄×Q₈	—	2	1	no	—
535	C₄×Q₈	—	2	2	no	—
536	C₄×Q₈	C₂³×C₇	1	2	yes	—
537	C₄×Q₈	C₂³×C₇	1	2	yes	—
538	C₄×Q₈	C₂³×C₇	1	2	yes	—
539	C₄×D₄	—	2	1	no	—
540	C₄×D₄	—	2	1	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	C₂³×C₇	1	2	yes	—
544	#117	—	2	1	no	—
545	#117	—	2	1	no	—
546	#117	—	2	2	no	—
547	#117	—	2	1	no	—
548	#117	—	2	2	no	—
549	#117	—	2	2	no	—
550	#117	C₇×D₄	1	1	yes	characteristic
551	#117	C₇×D₄	1	2	yes	—
552	#117	C₇×D₄	1	1	yes	characteristic
553	#117	C₂³×C₇	1	2	yes	—
554	#117	C₂³×C₇	1	2	yes	—
555	#117	C₂³×C₇	1	1	yes	characteristic
556	#117	C₂³×C₇	1	1	yes	characteristic
557	#117	C₂³×C₇	1	1	yes	characteristic
558	#117	C₂³×C₇	1	2	yes	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	—	2	2	no	—
563	C₂×C₄⋊C₄	—	2	2	no	—
564	C₂×C₄⋊C₄	—	2	2	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
575	C₂×C₂²⋊C₄	—	2	1	no	—
576	C₂×C₂²⋊C₄	—	2	1	no	—
577	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
578	C₂×C₄²	—	2	1	no	—
579	C₂×C₄²	C₂³×C₇	1	2	yes	—
580	#107	C₂³×C₇	1	2	yes	—
581	#107	C₂³×C₇	1	2	yes	—
582	#107	C₂³×C₇	1	4	yes	—
583	#107	C₂³×C₇	1	4	yes	—
584	#106	C₂³×C₇	1	4	yes	—
585	#106	C₂³×C₇	1	4	yes	—
586	#106	C₂³×C₇	1	2	yes	—
587	#106	C₂³×C₇	1	2	yes	—
588	#106	C₂³×C₇	1	4	yes	—
589	#106	C₂³×C₇	1	4	yes	—
590	C₄⋊C₈	C₂³×C₇	1	4	yes	—
591	C₄⋊C₈	C₂³×C₇	1	4	yes	—
592	#103	C₂³×C₇	1	4	yes	—
593	#103	C₂³×C₇	1	4	yes	—
594	#103	C₂³×C₇	1	2	yes	—
595	#103	C₂³×C₇	1	2	yes	—
596	#103	C₂³×C₇	1	4	yes	—
597	#103	C₂³×C₇	1	4	yes	—
598	#103	C₂³×C₇	1	4	yes	—
599	#102	C₂³×C₇	1	2	yes	—
600	#102	C₂³×C₇	1	2	yes	—
601	#102	C₂³×C₇	1	4	yes	—
602	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
603	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
604	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
605	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
606	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
607	#97	C₂³×C₇	1	4	yes	—
608	C₄×C₈	C₂³×C₇	1	4	yes	—
609	C₂²×C₇	—	2	1	no	—
610	C₂²×C₇	—	2	1	no	—
611	C₂²×C₇	—	2	1	no	—
612	C₂²×C₇	—	2	1	no	—
613	C₂²×C₇	—	2	1	no	—
614	C₂²×C₇	—	2	1	no	—
615	C₂²×C₇	—	2	1	no	—
616	C₂²×C₇	—	4	4	no	—
617	C₂²×C₇	—	4	1	no	—
618	C₂²×C₇	—	4	1	no	—
619	C₂²×C₇	—	4	1	no	—
620	C₂²×C₇	#536	1	2	yes	—
621	C₂²×C₇	#577	1	2	yes	—
622	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
623	C₄×C₇	—	2	2	no	—
624	C₄×C₇	—	2	2	no	—
625	C₄×C₇	—	2	1	no	—
626	C₄×C₇	—	2	1	no	—
627	C₄×C₇	—	2	2	no	—
628	C₄×C₇	—	2	2	no	—
629	C₄×C₇	—	4	2	no	—
630	C₄×C₇	—	4	2	no	—
631	C₄×C₇	—	4	1	no	—
632	C₄×C₇	—	4	1	no	—
633	C₄×C₇	—	4	2	no	—
634	C₄×C₇	—	4	4	no	—
635	C₄×C₇	—	4	2	no	—
636	C₄×C₇	—	4	1	no	—
637	C₄×C₇	#536	1	2	yes	—
638	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
639	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
640	#41	—	2	4	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	2	4	no	—
644	C₂×Q₈	—	2	4	no	—
645	C₂×Q₈	—	2	4	no	—
646	C₂×Q₈	—	8	4	no	—
647	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
648	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	8	2	no	—
664	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
665	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
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	2	yes	—
669	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
672	M₁₆	—	2	4	no	—
673	C₂×C₈	—	2	4	no	—
674	C₂×C₈	C₂⁴×C₇	1	2	yes	—
675	C₂×C₈	C₂⁴×C₇	1	4	yes	—
676	C₂×C₈	C₂⁴×C₇	1	2	yes	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
702	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
703	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
704	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
705	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
706	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
707	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
708	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
709	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
710	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
711	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
712	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
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	1	no	—
718	C₂²⋊C₄	—	2	1	no	—
719	C₂²⋊C₄	—	2	1	no	—
720	C₂²⋊C₄	—	2	1	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
726	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
727	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
728	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	2	no	—
734	C₄²	—	2	1	no	—
735	C₄²	C₂×C₇×D₄	1	2	yes	—
736	C₄²	C₂×C₇×D₄	1	2	yes	—
737	C₄²	C₂⁴×C₇	1	2	yes	—
738	C₄²	C₂⁴×C₇	1	2	yes	—
739	C₂×C₇	—	2	2	no	—
740	C₂×C₇	—	2	2	no	—
741	C₂×C₇	—	4	1	no	—
742	C₂×C₇	—	8	1	no	—
743	C₂×C₇	C₂×#536	1	1	yes	characteristic
744	C₂×C₇	C₂×#577	1	1	yes	characteristic
745	C₂×C₇	#3586	1	1	yes	characteristic
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	4	1	no	—
750	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
751	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
752	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
753	Q₈	—	2	4	no	—
754	Q₈	—	2	2	no	—
755	Q₈	—	4	2	no	—
756	Q₈	—	8	2	no	—
757	Q₈	—	8	4	no	—
758	Q₈	—	8	4	no	—
759	D₄	—	2	2	no	—
760	D₄	—	4	2	no	—
761	D₄	—	4	2	no	—
762	D₄	—	8	1	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	4	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	4	2	no	—
778	C₂×C₄	—	4	2	no	—
779	C₂×C₄	—	4	2	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	4	2	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	8	2	no	—
784	C₂×C₄	—	8	1	no	—
785	C₂×C₄	—	8	2	no	—
786	C₂×C₄	—	8	2	no	—
787	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
788	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
789	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
790	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
791	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
792	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
793	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
794	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
795	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
796	C₈	—	2	2	no	—
797	C₈	—	2	2	no	—
798	C₈	—	2	4	no	—
799	C₇	#60872	1	1	yes	characteristic, direct product factor, Sylow
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	4	4	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	C₇×#536	1	2	yes	—
812	C₂²	C₇×#577	1	2	yes	—
813	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
814	C₄	—	2	2	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	4	4	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	2	no	—
828	C₄	C₇×#536	1	2	yes	—
829	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
830	C₂	—	2	2	no	—
831	C₂	—	2	2	no	—
832	C₂	—	4	1	no	—
833	C₂	—	8	1	no	—
834	C₂	C₂×C₇×#536	1	1	yes	characteristic
835	C₂	C₂×C₇×#577	1	1	yes	characteristic
836	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×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#544	C₂	semidirect
3. C₇×#3244	C₂	semidirect
4. C₇×#3242	C₂	semidirect
5. C₇×#3238	C₂	semidirect
6. C₇×#3236	C₂	semidirect
7. C₇×#3232	C₂	semidirect
8. C₇×#3229	C₂	semidirect
9. C₇×#3163	C₂	semidirect
10. C₇×#3137	C₂	semidirect
11. C₇×#3095	C₂	semidirect
14. C₂×C₇×#483	C₂	semidirect
15. C₇×#3084	C₂	semidirect
16. C₇×#3082	C₂	semidirect
17. C₇×#2924	C₂	semidirect
48. C₇×#501	C₂²	semidirect
49. C₇×#501	C₂²	semidirect
50. C₇×#499	C₂²	semidirect
51. C₇×#498	C₂²	semidirect
52. C₇×#491	C₂²	semidirect
53. C₇×#489	C₂²	semidirect
54. C₇×#488	C₂²	semidirect
55. C₇×#487	C₂²	semidirect
72. C₇×#479	C₂²	semidirect
73. C₇×#479	C₂²	semidirect
74. C₇×#479	C₂²	semidirect
75. C₇×#478	C₂²	semidirect
76. C₇×#477	C₂²	semidirect
77. C₇×#476	C₂²	semidirect
78. C₇×#475	C₂²	semidirect
79. C₇×#475	C₂²	semidirect
95. #60872	C₇	direct (N × H)
230. C₂×#544	C₂×C₇	semidirect
231. #3244	C₂×C₇	semidirect
232. #3242	C₂×C₇	semidirect
233. #3238	C₂×C₇	semidirect
234. #3236	C₂×C₇	semidirect
235. #3232	C₂×C₇	semidirect
236. #3229	C₂×C₇	semidirect
237. #3163	C₂×C₇	semidirect
238. #3137	C₂×C₇	semidirect
239. #3095	C₂×C₇	semidirect
242. C₂×#483	C₂×C₇	semidirect
243. #3084	C₂×C₇	semidirect
244. #3082	C₂×C₇	semidirect
245. #2924	C₂×C₇	semidirect
376. #501	C₂²×C₇	semidirect
377. #501	C₂²×C₇	semidirect
378. #499	C₂²×C₇	semidirect
379. #498	C₂²×C₇	semidirect
380. #491	C₂²×C₇	semidirect
381. #489	C₂²×C₇	semidirect
382. #488	C₂²×C₇	semidirect
383. #487	C₂²×C₇	semidirect
400. #479	C₂²×C₇	semidirect
401. #479	C₂²×C₇	semidirect
402. #479	C₂²×C₇	semidirect
403. #478	C₂²×C₇	semidirect
404. #477	C₂²×C₇	semidirect
405. #476	C₂²×C₇	semidirect
406. #475	C₂²×C₇	semidirect
407. #475	C₂²×C₇	semidirect
799. C₇	#60872	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×#3495	2
C₂×C₇×#544	2
C₇×#3244	2
C₇×#3242	2
C₇×#3238	2
C₇×#3236	2
C₇×#3232	2
C₇×#3229	2
C₇×#3163	2
C₇×#3137	2
C₇×#3095	2
C₇×#3092	2
C₇×#3091	2
C₂×C₇×#483	2
C₇×#3084	2
C₇×#3082	2
C₇×#2924	2
#60872	7

Subgroups — C7×#60872 #13238088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60872 #13238088