Subgroups — C₇×#36747 #13213963

Order 1792.

2146 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2848	C₂	1	2	yes	maximal, complemented
2	C₇×#2804	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2784	C₂	1	2	yes	maximal, complemented
4	C₇×#2780	C₂	1	2	yes	maximal, complemented
5	C₇×#2780	C₂	1	2	yes	maximal, complemented
6	C₇×#2748	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2748	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2732	C₂	1	2	yes	maximal, complemented
9	C₇×#2692	C₂	1	2	yes	maximal, complemented
10	C₇×#2692	C₂	1	2	yes	maximal, complemented
11	C₇×#2683	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2626	C₂	1	2	yes	maximal, complemented
13	C₇×#2438	C₂	1	2	yes	maximal, complemented
14	C₇×#2438	C₂	1	2	yes	maximal, complemented
15	C₇×#2437	C₂	1	2	yes	maximal, complemented
16	C₇×#2437	C₂	1	2	yes	maximal, complemented
17	C₇×#2309	C₂	1	1	yes	maximal, characteristic
18	C₇×#2308	C₂	1	1	yes	maximal, characteristic
19	C₂×C₇×#386	C₂	1	1	yes	maximal, characteristic
20	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
25	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₇×#117	C₂²	1	1	yes	characteristic
29	C₂×C₇×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₇×#400	C₂²	1	2	yes	complemented
35	C₇×#400	C₂²	1	2	yes	complemented
36	C₇×#399	C₂²	1	2	yes	complemented
37	C₇×#399	C₂²	1	2	yes	complemented
38	C₇×#399	C₂²	1	2	yes	complemented
39	C₇×#399	C₂²	1	2	yes	complemented
40	C₇×#398	C₂²	1	2	yes	complemented
41	C₇×#398	C₂²	1	2	yes	complemented
42	C₇×#398	C₂²	1	2	yes	complemented
43	C₇×#398	C₂²	1	2	yes	complemented
44	C₇×#396	C₂²	1	2	yes	complemented
45	C₇×#396	C₂²	1	2	yes	complemented
46	C₇×#396	C₂²	1	2	yes	complemented
47	C₇×#396	C₂²	1	2	yes	complemented
48	C₇×#396	C₂²	1	2	yes	complemented
49	C₇×#396	C₂²	1	2	yes	complemented
50	C₇×#396	C₂²	1	2	yes	complemented
51	C₇×#396	C₂²	1	2	yes	complemented
52	C₇×#395	C₂²	1	2	yes	complemented
53	C₇×#395	C₂²	1	2	yes	complemented
54	C₇×#393	C₂²	1	2	yes	complemented
55	C₇×#393	C₂²	1	2	yes	complemented
56	C₇×#393	C₂²	1	2	yes	complemented
57	C₇×#393	C₂²	1	2	yes	complemented
58	C₇×#391	C₂²	1	2	yes	complemented
59	C₇×#391	C₂²	1	2	yes	complemented
60	C₇×#390	C₂²	1	1	yes	characteristic
61	C₇×#390	C₂²	1	1	yes	characteristic
62	C₇×#390	C₂²	1	2	yes	—
63	C₇×#390	C₂²	1	2	yes	—
64	C₇×#390	C₂²	1	1	yes	characteristic
65	C₇×#390	C₂²	1	1	yes	characteristic
66	C₇×#389	C₂²	1	2	yes	complemented
67	C₇×#389	C₂²	1	2	yes	complemented
68	C₇×#387	C₂²	1	2	yes	complemented
69	C₇×#387	C₂²	1	2	yes	complemented
70	C₇×#387	C₂²	1	2	yes	complemented
71	C₇×#387	C₂²	1	2	yes	complemented
72	C₇×#386	C₂²	1	1	yes	characteristic
73	C₇×#386	C₂²	1	1	yes	characteristic
74	C₇×#386	C₂²	1	1	yes	characteristic
75	C₇×#386	C₂²	1	2	yes	—
76	C₇×#386	C₂²	1	2	yes	—
77	C₇×#386	C₂²	1	2	yes	—
78	C₇×#386	C₂²	1	1	yes	characteristic
79	C₇×#386	C₂²	1	2	yes	—
80	C₇×#386	C₂²	1	1	yes	characteristic
81	C₇×#386	C₂²	1	1	yes	characteristic
82	C₇×#386	C₂²	1	1	yes	characteristic
83	C₇×#386	C₂²	1	1	yes	characteristic
84	C₇×#385	C₂²	1	2	yes	—
85	C₇×#385	C₂²	1	2	yes	—
86	C₇×#385	C₂²	1	2	yes	—
87	C₇×#385	C₂²	1	2	yes	—
88	C₇×#385	C₂²	1	2	yes	complemented
89	C₇×#385	C₂²	1	2	yes	complemented
90	C₇×#385	C₂²	1	2	yes	complemented
91	C₇×#385	C₂²	1	2	yes	complemented
92	C₇×#385	C₂²	1	2	yes	complemented
93	C₇×#385	C₂²	1	2	yes	complemented
94	C₇×#385	C₂²	1	2	yes	complemented
95	C₇×#385	C₂²	1	2	yes	complemented
96	C₇×#381	C₂²	1	2	yes	—
97	C₇×#380	C₂²	1	2	yes	—
98	C₇×#380	C₂²	1	2	yes	—
99	C₇×#380	C₂²	1	2	yes	complemented
100	C₇×#380	C₂²	1	2	yes	complemented
101	C₇×#380	C₂²	1	2	yes	complemented
102	C₇×#380	C₂²	1	2	yes	complemented
103	C₇×#379	C₂²	1	2	yes	—
104	C₇×#379	C₂²	1	2	yes	—
105	C₇×#379	C₂²	1	2	yes	—
106	C₂×C₇×#95	C₂²	1	2	yes	—
107	#36747	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁵×C₇	C₂³	1	1	yes	characteristic
109	C₂⁵×C₇	C₂³	1	1	yes	characteristic
110	C₂²×C₇×Q₈	C₂³	1	2	yes	—
111	C₂²×C₇×Q₈	C₂³	1	2	yes	—
112	C₂²×C₇×D₄	—	4	2	no	—
113	C₂²×C₇×D₄	—	4	2	no	—
114	C₂²×C₇×D₄	Q₈	1	8	yes	complemented
115	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
116	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
117	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
118	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₇	—	4	4	no	—
120	C₂³×C₄×C₇	—	4	2	no	—
121	C₂³×C₄×C₇	C₂³	1	2	yes	—
122	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₇	C₂³	1	2	yes	—
125	C₂³×C₄×C₇	C₂³	1	2	yes	—
126	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₇	C₂³	1	2	yes	—
128	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
130	C₇×C₂²⋊Q₈	—	4	4	no	—
131	C₇×C₂²⋊Q₈	—	4	4	no	—
132	C₇×C₂²⋊Q₈	—	4	4	no	—
133	C₇×C₂²⋊Q₈	—	4	4	no	—
134	C₇×C₂²⋊Q₈	—	4	4	no	—
135	C₇×C₂²⋊Q₈	—	4	4	no	—
136	C₇×#117	—	4	2	no	—
137	C₇×#117	—	4	2	no	—
138	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
160	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
161	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
162	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
163	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₇	C₂³	1	2	yes	—
191	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
192	C₇×#95	C₂³	1	2	yes	—
193	C₇×#95	C₂³	1	2	yes	—
194	C₇×#95	C₂³	1	2	yes	—
195	C₇×#95	C₂³	1	2	yes	—
196	C₇×#95	C₂³	1	2	yes	—
197	C₇×#95	C₂³	1	2	yes	—
198	C₇×#95	C₂³	1	2	yes	—
199	C₇×#95	C₂³	1	2	yes	—
200	C₇×#95	C₂³	1	2	yes	—
201	C₇×#95	C₂³	1	2	yes	—
202	C₇×#95	C₂³	1	2	yes	—
203	C₇×#95	C₂³	1	2	yes	—
204	C₇×#95	C₂³	1	2	yes	—
205	C₇×#95	C₂³	1	2	yes	—
206	C₇×#95	C₂³	1	2	yes	—
207	C₇×#95	C₂³	1	2	yes	—
208	C₇×#95	C₂³	1	2	yes	—
209	C₇×#95	C₂³	1	2	yes	—
210	C₇×#95	C₂³	1	2	yes	—
211	C₇×#95	C₂³	1	2	yes	—
212	#2848	C₂×C₇	1	2	yes	complemented
213	#2804	C₂×C₇	1	1	yes	characteristic, complemented
214	#2784	C₂×C₇	1	2	yes	complemented
215	#2780	C₂×C₇	1	2	yes	complemented
216	#2780	C₂×C₇	1	2	yes	complemented
217	#2748	C₂×C₇	1	1	yes	characteristic, complemented
218	#2748	C₂×C₇	1	1	yes	characteristic, complemented
219	#2732	C₂×C₇	1	2	yes	complemented
220	#2692	C₂×C₇	1	2	yes	complemented
221	#2692	C₂×C₇	1	2	yes	complemented
222	#2683	C₂×C₇	1	1	yes	characteristic, complemented
223	#2626	C₂×C₇	1	2	yes	complemented
224	#2438	C₂×C₇	1	2	yes	complemented
225	#2438	C₂×C₇	1	2	yes	complemented
226	#2437	C₂×C₇	1	2	yes	complemented
227	#2437	C₂×C₇	1	2	yes	complemented
228	#2309	C₂×C₇	1	1	yes	characteristic
229	#2308	C₂×C₇	1	1	yes	characteristic
230	C₂×#386	C₂×C₇	1	1	yes	characteristic
231	C₂⁴×C₇	—	2	2	no	—
232	C₂⁴×C₇	—	2	2	no	—
233	C₂⁴×C₇	—	2	2	no	—
234	C₂⁴×C₇	—	2	2	no	—
235	C₂⁴×C₇	—	4	2	no	—
236	C₂⁴×C₇	—	4	2	no	—
237	C₂⁴×C₇	—	4	2	no	—
238	C₂⁴×C₇	—	4	2	no	—
239	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
240	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
241	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
242	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
243	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
244	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
245	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₇×Q₈	—	2	4	no	—
247	C₂×C₇×Q₈	—	4	2	no	—
248	C₂×C₇×Q₈	—	4	2	no	—
249	C₂×C₇×Q₈	—	4	2	no	—
250	C₂×C₇×Q₈	—	4	2	no	—
251	C₂×C₇×Q₈	—	4	2	no	—
252	C₂×C₇×D₄	—	4	16	no	—
253	C₂×C₇×D₄	—	4	1	no	—
254	C₂×C₇×D₄	—	4	1	no	—
255	C₂×C₇×D₄	—	4	1	no	—
256	C₂×C₇×D₄	—	4	1	no	—
257	C₂×C₇×D₄	—	4	1	no	—
258	C₂×C₇×D₄	—	4	1	no	—
259	C₂×C₇×D₄	—	4	1	no	—
260	C₂×C₇×D₄	—	4	1	no	—
261	C₂×C₇×D₄	C₂×Q₈	1	4	yes	—
262	C₂×C₇×D₄	C₂×Q₈	1	4	yes	—
263	C₂×C₇×D₄	C₂×Q₈	1	4	yes	—
264	C₂×C₇×D₄	C₂×Q₈	1	4	yes	—
265	C₂²×C₄×C₇	—	2	2	no	—
266	C₂²×C₄×C₇	—	2	2	no	—
267	C₂²×C₄×C₇	—	2	4	no	—
268	C₂²×C₄×C₇	—	2	4	no	—
269	C₂²×C₄×C₇	—	2	4	no	—
270	C₂²×C₄×C₇	—	2	4	no	—
271	C₂²×C₄×C₇	—	2	4	no	—
272	C₂²×C₄×C₇	—	4	1	no	—
273	C₂²×C₄×C₇	—	4	2	no	—
274	C₂²×C₄×C₇	—	4	2	no	—
275	C₂²×C₄×C₇	—	4	2	no	—
276	C₂²×C₄×C₇	—	4	2	no	—
277	C₂²×C₄×C₇	—	4	1	no	—
278	C₂²×C₄×C₇	—	4	1	no	—
279	C₂²×C₄×C₇	—	4	2	no	—
280	C₂²×C₄×C₇	—	4	2	no	—
281	C₂²×C₄×C₇	—	4	1	no	—
282	C₂²×C₄×C₇	—	4	2	no	—
283	C₂²×C₄×C₇	—	4	2	no	—
284	C₂²×C₄×C₇	—	4	2	no	—
285	C₂²×C₄×C₇	—	4	2	no	—
286	C₂²×C₄×C₇	—	4	2	no	—
287	C₂²×C₄×C₇	—	4	16	no	—
288	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
289	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
303	C₇×C₄⋊C₄	—	2	4	no	—
304	C₇×C₄⋊C₄	—	2	4	no	—
305	C₇×C₄⋊C₄	—	2	4	no	—
306	C₇×C₄⋊C₄	—	4	2	no	—
307	C₇×C₄⋊C₄	—	4	2	no	—
308	C₇×C₄⋊C₄	—	4	2	no	—
309	C₇×C₄⋊C₄	—	4	1	no	—
310	C₇×C₄⋊C₄	—	4	2	no	—
311	C₇×C₄⋊C₄	—	4	1	no	—
312	C₇×C₄⋊C₄	—	4	2	no	—
313	C₇×C₄⋊C₄	—	4	2	no	—
314	C₇×C₄⋊C₄	—	4	2	no	—
315	C₇×C₄⋊C₄	—	4	2	no	—
316	C₇×C₄⋊C₄	—	4	2	no	—
317	C₇×C₄⋊C₄	—	4	2	no	—
318	C₇×C₄⋊C₄	—	4	2	no	—
319	C₇×C₄⋊C₄	—	4	2	no	—
320	C₇×C₄⋊C₄	—	4	2	no	—
321	C₇×C₄⋊C₄	—	4	2	no	—
322	C₇×C₄⋊C₄	—	4	2	no	—
323	C₇×C₄⋊C₄	—	4	2	no	—
324	C₇×C₂²⋊C₄	—	2	4	no	—
325	C₇×C₂²⋊C₄	—	2	4	no	—
326	C₇×C₂²⋊C₄	—	2	4	no	—
327	C₇×C₂²⋊C₄	—	2	4	no	—
328	C₇×C₂²⋊C₄	—	2	4	no	—
329	C₇×C₂²⋊C₄	—	2	4	no	—
330	C₇×C₂²⋊C₄	—	4	1	no	—
331	C₇×C₂²⋊C₄	—	4	2	no	—
332	C₇×C₂²⋊C₄	—	4	2	no	—
333	C₇×C₂²⋊C₄	—	4	1	no	—
334	C₇×C₂²⋊C₄	—	4	2	no	—
335	C₇×C₂²⋊C₄	—	4	1	no	—
336	C₇×C₂²⋊C₄	—	4	2	no	—
337	C₇×C₂²⋊C₄	—	4	1	no	—
338	C₇×C₂²⋊C₄	—	4	2	no	—
339	C₇×C₂²⋊C₄	—	4	2	no	—
340	C₇×C₂²⋊C₄	—	4	2	no	—
341	C₇×C₂²⋊C₄	—	4	2	no	—
342	C₇×C₂²⋊C₄	—	4	2	no	—
343	C₇×C₂²⋊C₄	—	4	2	no	—
344	C₇×C₂²⋊C₄	—	4	2	no	—
345	C₇×C₂²⋊C₄	—	4	2	no	—
346	C₇×C₂²⋊C₄	—	4	2	no	—
347	C₇×C₂²⋊C₄	—	4	2	no	—
348	C₇×C₂²⋊C₄	—	4	2	no	—
349	C₇×C₂²⋊C₄	—	4	2	no	—
350	C₄²×C₇	—	4	1	no	—
351	C₄²×C₇	—	4	2	no	—
352	C₄²×C₇	—	4	1	no	—
353	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
354	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
355	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
356	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
357	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
358	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
359	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
360	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
361	C₂×#117	C₂²×C₇	1	1	yes	characteristic
362	C₂×#117	C₂²×C₇	1	1	yes	characteristic
363	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
364	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
365	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
366	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
367	#400	C₂²×C₇	1	2	yes	complemented
368	#400	C₂²×C₇	1	2	yes	complemented
369	#399	C₂²×C₇	1	2	yes	complemented
370	#399	C₂²×C₇	1	2	yes	complemented
371	#399	C₂²×C₇	1	2	yes	complemented
372	#399	C₂²×C₇	1	2	yes	complemented
373	#398	C₂²×C₇	1	2	yes	complemented
374	#398	C₂²×C₇	1	2	yes	complemented
375	#398	C₂²×C₇	1	2	yes	complemented
376	#398	C₂²×C₇	1	2	yes	complemented
377	#396	C₂²×C₇	1	2	yes	complemented
378	#396	C₂²×C₇	1	2	yes	complemented
379	#396	C₂²×C₇	1	2	yes	complemented
380	#396	C₂²×C₇	1	2	yes	complemented
381	#396	C₂²×C₇	1	2	yes	complemented
382	#396	C₂²×C₇	1	2	yes	complemented
383	#396	C₂²×C₇	1	2	yes	complemented
384	#396	C₂²×C₇	1	2	yes	complemented
385	#395	C₂²×C₇	1	2	yes	complemented
386	#395	C₂²×C₇	1	2	yes	complemented
387	#393	C₂²×C₇	1	2	yes	complemented
388	#393	C₂²×C₇	1	2	yes	complemented
389	#393	C₂²×C₇	1	2	yes	complemented
390	#393	C₂²×C₇	1	2	yes	complemented
391	#391	C₂²×C₇	1	2	yes	complemented
392	#391	C₂²×C₇	1	2	yes	complemented
393	#390	C₂²×C₇	1	1	yes	characteristic
394	#390	C₂²×C₇	1	1	yes	characteristic
395	#390	C₂²×C₇	1	2	yes	—
396	#390	C₂²×C₇	1	2	yes	—
397	#390	C₂²×C₇	1	1	yes	characteristic
398	#390	C₂²×C₇	1	1	yes	characteristic
399	#389	C₂²×C₇	1	2	yes	complemented
400	#389	C₂²×C₇	1	2	yes	complemented
401	#387	C₂²×C₇	1	2	yes	complemented
402	#387	C₂²×C₇	1	2	yes	complemented
403	#387	C₂²×C₇	1	2	yes	complemented
404	#387	C₂²×C₇	1	2	yes	complemented
405	#386	C₂²×C₇	1	1	yes	characteristic
406	#386	C₂²×C₇	1	2	yes	—
407	#386	C₂²×C₇	1	2	yes	—
408	#386	C₂²×C₇	1	1	yes	characteristic
409	#386	C₂²×C₇	1	1	yes	characteristic
410	#386	C₂²×C₇	1	1	yes	characteristic
411	#386	C₂²×C₇	1	1	yes	characteristic
412	#386	C₂²×C₇	1	1	yes	characteristic
413	#386	C₂²×C₇	1	2	yes	—
414	#386	C₂²×C₇	1	2	yes	—
415	#386	C₂²×C₇	1	1	yes	characteristic
416	#386	C₂²×C₇	1	1	yes	characteristic
417	#385	C₂²×C₇	1	2	yes	—
418	#385	C₂²×C₇	1	2	yes	—
419	#385	C₂²×C₇	1	2	yes	—
420	#385	C₂²×C₇	1	2	yes	—
421	#385	C₂²×C₇	1	2	yes	complemented
422	#385	C₂²×C₇	1	2	yes	complemented
423	#385	C₂²×C₇	1	2	yes	complemented
424	#385	C₂²×C₇	1	2	yes	complemented
425	#385	C₂²×C₇	1	2	yes	complemented
426	#385	C₂²×C₇	1	2	yes	complemented
427	#385	C₂²×C₇	1	2	yes	complemented
428	#385	C₂²×C₇	1	2	yes	complemented
429	#381	C₂²×C₇	1	2	yes	—
430	#380	C₂²×C₇	1	2	yes	—
431	#380	C₂²×C₇	1	2	yes	—
432	#380	C₂²×C₇	1	2	yes	complemented
433	#380	C₂²×C₇	1	2	yes	complemented
434	#380	C₂²×C₇	1	2	yes	complemented
435	#380	C₂²×C₇	1	2	yes	complemented
436	#379	C₂²×C₇	1	2	yes	—
437	#379	C₂²×C₇	1	2	yes	—
438	#379	C₂²×C₇	1	2	yes	—
439	C₂×#95	C₂²×C₇	1	2	yes	—
440	C₂³×C₇	—	2	2	no	—
441	C₂³×C₇	—	2	2	no	—
442	C₂³×C₇	—	2	8	no	—
443	C₂³×C₇	—	2	2	no	—
444	C₂³×C₇	—	2	2	no	—
445	C₂³×C₇	—	2	2	no	—
446	C₂³×C₇	—	2	2	no	—
447	C₂³×C₇	—	2	1	no	—
448	C₂³×C₇	—	2	1	no	—
449	C₂³×C₇	—	2	1	no	—
450	C₂³×C₇	—	2	1	no	—
451	C₂³×C₇	—	2	1	no	—
452	C₂³×C₇	—	2	1	no	—
453	C₂³×C₇	—	2	1	no	—
454	C₂³×C₇	—	2	1	no	—
455	C₂³×C₇	—	2	2	no	—
456	C₂³×C₇	—	2	2	no	—
457	C₂³×C₇	—	2	2	no	—
458	C₂³×C₇	—	2	2	no	—
459	C₂³×C₇	—	2	8	no	—
460	C₂³×C₇	—	4	8	no	—
461	C₂³×C₇	—	4	8	no	—
462	C₂³×C₇	—	4	4	no	—
463	C₂³×C₇	—	4	4	no	—
464	C₂³×C₇	—	4	8	no	—
465	C₂³×C₇	—	8	2	no	—
466	C₂³×C₇	—	8	2	no	—
467	C₂³×C₇	—	8	4	no	—
468	C₂³×C₇	C₂²×Q₈	1	2	yes	—
469	C₂³×C₇	C₂²×Q₈	1	2	yes	—
470	C₂³×C₇	C₂²×Q₈	1	2	yes	—
471	C₂³×C₇	C₂²×Q₈	1	2	yes	—
472	C₂³×C₇	C₂²×Q₈	1	2	yes	—
473	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
474	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
475	C₂³×C₇	C₂⁵	1	1	yes	characteristic
476	C₇×Q₈	—	8	4	no	—
477	C₇×Q₈	—	8	4	no	—
478	C₇×D₄	—	4	4	no	—
479	C₇×D₄	—	4	4	no	—
480	C₇×D₄	—	4	4	no	—
481	C₇×D₄	—	4	4	no	—
482	C₂×C₄×C₇	—	2	8	no	—
483	C₂×C₄×C₇	—	2	1	no	—
484	C₂×C₄×C₇	—	2	1	no	—
485	C₂×C₄×C₇	—	2	1	no	—
486	C₂×C₄×C₇	—	2	1	no	—
487	C₂×C₄×C₇	—	2	2	no	—
488	C₂×C₄×C₇	—	2	2	no	—
489	C₂×C₄×C₇	—	2	2	no	—
490	C₂×C₄×C₇	—	2	2	no	—
491	C₂×C₄×C₇	—	2	2	no	—
492	C₂×C₄×C₇	—	2	2	no	—
493	C₂×C₄×C₇	—	2	2	no	—
494	C₂×C₄×C₇	—	2	2	no	—
495	C₂×C₄×C₇	—	2	2	no	—
496	C₂×C₄×C₇	—	2	2	no	—
497	C₂×C₄×C₇	—	2	2	no	—
498	C₂×C₄×C₇	—	2	2	no	—
499	C₂×C₄×C₇	—	2	2	no	—
500	C₂×C₄×C₇	—	2	2	no	—
501	C₂×C₄×C₇	—	2	2	no	—
502	C₂×C₄×C₇	—	2	2	no	—
503	C₂×C₄×C₇	—	2	2	no	—
504	C₂×C₄×C₇	—	2	2	no	—
505	C₂×C₄×C₇	—	2	2	no	—
506	C₂×C₄×C₇	—	2	2	no	—
507	C₂×C₄×C₇	—	2	2	no	—
508	C₂×C₄×C₇	—	2	2	no	—
509	C₂×C₄×C₇	—	2	2	no	—
510	C₂×C₄×C₇	—	2	2	no	—
511	C₂×C₄×C₇	—	2	2	no	—
512	C₂×C₄×C₇	—	2	2	no	—
513	C₂×C₄×C₇	—	2	2	no	—
514	C₂×C₄×C₇	—	2	2	no	—
515	C₂×C₄×C₇	—	2	2	no	—
516	C₂×C₄×C₇	—	2	2	no	—
517	C₂×C₄×C₇	—	2	2	no	—
518	C₂×C₄×C₇	—	2	2	no	—
519	C₂×C₄×C₇	—	2	2	no	—
520	C₂×C₄×C₇	—	2	2	no	—
521	C₂×C₄×C₇	—	2	2	no	—
522	C₂×C₄×C₇	—	4	4	no	—
523	C₂×C₄×C₇	—	4	8	no	—
524	C₂×C₄×C₇	—	4	8	no	—
525	C₂×C₄×C₇	—	4	4	no	—
526	C₂×C₄×C₇	—	8	4	no	—
527	C₂×C₄×C₇	—	8	2	no	—
528	C₂×C₄×C₇	—	8	2	no	—
529	C₂×C₄×C₇	—	8	4	no	—
530	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
531	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
532	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
533	C₂⁵	C₂³×C₇	1	1	yes	characteristic
534	C₂⁵	C₂³×C₇	1	1	yes	characteristic
535	C₂²×Q₈	C₂³×C₇	1	2	yes	—
536	C₂²×Q₈	C₂³×C₇	1	2	yes	—
537	C₂²×D₄	—	4	2	no	—
538	C₂²×D₄	—	4	2	no	—
539	C₂²×D₄	C₇×Q₈	1	8	yes	complemented
540	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
541	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
542	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
544	C₂³×C₄	—	4	4	no	—
545	C₂³×C₄	—	4	2	no	—
546	C₂³×C₄	C₂³×C₇	1	2	yes	—
547	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₇	1	2	yes	—
550	C₂³×C₄	C₂³×C₇	1	2	yes	—
551	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₇	1	2	yes	—
553	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
554	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
555	C₂²⋊Q₈	—	4	4	no	—
556	C₂²⋊Q₈	—	4	4	no	—
557	C₂²⋊Q₈	—	4	4	no	—
558	C₂²⋊Q₈	—	4	4	no	—
559	C₂²⋊Q₈	—	4	4	no	—
560	C₂²⋊Q₈	—	4	4	no	—
561	#117	—	4	2	no	—
562	#117	—	4	2	no	—
563	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₇	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	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
584	C₂×C₂²⋊C₄	—	4	4	no	—
585	C₂×C₂²⋊C₄	—	4	2	no	—
586	C₂×C₂²⋊C₄	—	4	2	no	—
587	C₂×C₂²⋊C₄	—	4	2	no	—
588	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
601	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
602	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
614	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₇	1	2	yes	—
616	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
617	#95	C₂³×C₇	1	2	yes	—
618	#95	C₂³×C₇	1	2	yes	—
619	#95	C₂³×C₇	1	2	yes	—
620	#95	C₂³×C₇	1	2	yes	—
621	#95	C₂³×C₇	1	2	yes	—
622	#95	C₂³×C₇	1	2	yes	—
623	#95	C₂³×C₇	1	2	yes	—
624	#95	C₂³×C₇	1	2	yes	—
625	#95	C₂³×C₇	1	2	yes	—
626	#95	C₂³×C₇	1	2	yes	—
627	#95	C₂³×C₇	1	2	yes	—
628	#95	C₂³×C₇	1	2	yes	—
629	#95	C₂³×C₇	1	2	yes	—
630	#95	C₂³×C₇	1	2	yes	—
631	#95	C₂³×C₇	1	2	yes	—
632	#95	C₂³×C₇	1	2	yes	—
633	#95	C₂³×C₇	1	2	yes	—
634	#95	C₂³×C₇	1	2	yes	—
635	#95	C₂³×C₇	1	2	yes	—
636	#95	C₂³×C₇	1	2	yes	—
637	C₂²×C₇	—	2	4	no	—
638	C₂²×C₇	—	2	2	no	—
639	C₂²×C₇	—	2	2	no	—
640	C₂²×C₇	—	2	4	no	—
641	C₂²×C₇	—	2	2	no	—
642	C₂²×C₇	—	2	2	no	—
643	C₂²×C₇	—	2	2	no	—
644	C₂²×C₇	—	2	2	no	—
645	C₂²×C₇	—	2	4	no	—
646	C₂²×C₇	—	2	4	no	—
647	C₂²×C₇	—	2	4	no	—
648	C₂²×C₇	—	2	4	no	—
649	C₂²×C₇	—	4	16	no	—
650	C₂²×C₇	—	4	1	no	—
651	C₂²×C₇	—	4	1	no	—
652	C₂²×C₇	—	4	1	no	—
653	C₂²×C₇	—	4	1	no	—
654	C₂²×C₇	—	4	1	no	—
655	C₂²×C₇	—	4	1	no	—
656	C₂²×C₇	—	4	1	no	—
657	C₂²×C₇	—	4	1	no	—
658	C₂²×C₇	—	4	2	no	—
659	C₂²×C₇	—	4	2	no	—
660	C₂²×C₇	—	4	2	no	—
661	C₂²×C₇	—	4	2	no	—
662	C₂²×C₇	—	8	8	no	—
663	C₂²×C₇	#543	1	4	yes	—
664	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
665	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
666	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
667	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
668	C₂²×C₇	#585	1	2	yes	—
669	C₄×C₇	—	2	2	no	—
670	C₄×C₇	—	2	2	no	—
671	C₄×C₇	—	2	4	no	—
672	C₄×C₇	—	4	2	no	—
673	C₄×C₇	—	4	2	no	—
674	C₄×C₇	—	4	2	no	—
675	C₄×C₇	—	4	2	no	—
676	C₄×C₇	—	4	2	no	—
677	C₄×C₇	—	4	2	no	—
678	C₄×C₇	—	4	2	no	—
679	C₄×C₇	—	4	2	no	—
680	C₄×C₇	—	4	2	no	—
681	C₄×C₇	—	4	2	no	—
682	C₄×C₇	—	4	2	no	—
683	C₂⁴	—	2	2	no	—
684	C₂⁴	—	2	2	no	—
685	C₂⁴	—	2	2	no	—
686	C₂⁴	—	2	2	no	—
687	C₂⁴	—	4	2	no	—
688	C₂⁴	—	4	2	no	—
689	C₂⁴	—	4	2	no	—
690	C₂⁴	—	4	2	no	—
691	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
692	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
693	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
694	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
695	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
696	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
697	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
698	C₂×Q₈	—	2	4	no	—
699	C₂×Q₈	—	4	2	no	—
700	C₂×Q₈	—	4	2	no	—
701	C₂×Q₈	—	4	2	no	—
702	C₂×Q₈	—	4	2	no	—
703	C₂×Q₈	—	4	2	no	—
704	C₂×D₄	—	4	16	no	—
705	C₂×D₄	—	4	1	no	—
706	C₂×D₄	—	4	1	no	—
707	C₂×D₄	—	4	1	no	—
708	C₂×D₄	—	4	1	no	—
709	C₂×D₄	—	4	1	no	—
710	C₂×D₄	—	4	1	no	—
711	C₂×D₄	—	4	1	no	—
712	C₂×D₄	—	4	1	no	—
713	C₂×D₄	C₂×C₇×Q₈	1	4	yes	—
714	C₂×D₄	C₂×C₇×Q₈	1	4	yes	—
715	C₂×D₄	C₂×C₇×Q₈	1	4	yes	—
716	C₂×D₄	C₂×C₇×Q₈	1	4	yes	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	2	4	no	—
722	C₂²×C₄	—	2	4	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	4	1	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	—	4	2	no	—
729	C₂²×C₄	—	4	1	no	—
730	C₂²×C₄	—	4	1	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	—	4	1	no	—
734	C₂²×C₄	—	4	2	no	—
735	C₂²×C₄	—	4	2	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	—	4	16	no	—
740	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
741	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	4	1	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	1	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	2	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	2	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	4	1	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	1	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	1	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	1	no	—
790	C₂²⋊C₄	—	4	2	no	—
791	C₂²⋊C₄	—	4	2	no	—
792	C₂²⋊C₄	—	4	2	no	—
793	C₂²⋊C₄	—	4	2	no	—
794	C₂²⋊C₄	—	4	2	no	—
795	C₂²⋊C₄	—	4	2	no	—
796	C₂²⋊C₄	—	4	2	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₄²	—	4	1	no	—
803	C₄²	—	4	2	no	—
804	C₄²	—	4	1	no	—
805	C₂×C₇	—	2	4	no	—
806	C₂×C₇	—	4	2	no	—
807	C₂×C₇	—	4	2	no	—
808	C₂×C₇	—	4	2	no	—
809	C₂×C₇	—	4	2	no	—
810	C₂×C₇	C₂×#543	1	1	yes	characteristic
811	C₂×C₇	#3501	1	2	yes	—
812	C₂×C₇	#3532	1	1	yes	characteristic
813	C₂×C₇	#3533	1	1	yes	characteristic
814	C₂×C₇	#3542	1	2	yes	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	1	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	8	no	—
834	C₂³	—	2	8	no	—
835	C₂³	—	4	8	no	—
836	C₂³	—	4	8	no	—
837	C₂³	—	4	4	no	—
838	C₂³	—	4	4	no	—
839	C₂³	—	4	8	no	—
840	C₂³	—	8	2	no	—
841	C₂³	—	8	2	no	—
842	C₂³	—	8	4	no	—
843	C₂³	C₂²×C₇×Q₈	1	2	yes	—
844	C₂³	C₂²×C₇×Q₈	1	2	yes	—
845	C₂³	C₂²×C₇×Q₈	1	2	yes	—
846	C₂³	C₂²×C₇×Q₈	1	2	yes	—
847	C₂³	C₂²×C₇×Q₈	1	2	yes	—
848	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
849	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
850	C₂³	C₂⁵×C₇	1	1	yes	characteristic
851	Q₈	—	8	4	no	—
852	Q₈	—	8	4	no	—
853	D₄	—	4	4	no	—
854	D₄	—	4	4	no	—
855	D₄	—	4	4	no	—
856	D₄	—	4	4	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	8	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	4	4	no	—
898	C₂×C₄	—	4	8	no	—
899	C₂×C₄	—	4	8	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	8	4	no	—
902	C₂×C₄	—	8	2	no	—
903	C₂×C₄	—	8	2	no	—
904	C₂×C₄	—	8	4	no	—
905	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
906	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
907	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
908	C₇	#36747	1	1	yes	characteristic, direct product factor, Sylow
909	C₂²	—	2	4	no	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	4	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	4	no	—
918	C₂²	—	2	4	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	4	16	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	1	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	1	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	8	8	no	—
935	C₂²	C₇×#543	1	4	yes	—
936	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
937	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
938	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
939	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
940	C₂²	C₇×#585	1	2	yes	—
941	C₄	—	2	2	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	4	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	2	no	—
955	C₂	—	2	4	no	—
956	C₂	—	4	2	no	—
957	C₂	—	4	2	no	—
958	C₂	—	4	2	no	—
959	C₂	—	4	2	no	—
960	C₂	C₂×C₇×#543	1	1	yes	characteristic
961	C₂	C₇×#3501	1	2	yes	—
962	C₂	C₇×#3532	1	1	yes	characteristic
963	C₂	C₇×#3533	1	1	yes	characteristic
964	C₂	C₇×#3542	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₇×#2848	C₂	semidirect
2. C₇×#2804	C₂	semidirect
3. C₇×#2784	C₂	semidirect
4. C₇×#2780	C₂	semidirect
5. C₇×#2780	C₂	semidirect
6. C₇×#2748	C₂	semidirect
7. C₇×#2748	C₂	semidirect
8. C₇×#2732	C₂	semidirect
9. C₇×#2692	C₂	semidirect
10. C₇×#2692	C₂	semidirect
11. C₇×#2683	C₂	semidirect
12. C₇×#2626	C₂	semidirect
13. C₇×#2438	C₂	semidirect
14. C₇×#2438	C₂	semidirect
15. C₇×#2437	C₂	semidirect
16. C₇×#2437	C₂	semidirect
24. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
25. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
27. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
34. C₇×#400	C₂²	semidirect
35. C₇×#400	C₂²	semidirect
36. C₇×#399	C₂²	semidirect
37. C₇×#399	C₂²	semidirect
38. C₇×#399	C₂²	semidirect
39. C₇×#399	C₂²	semidirect
40. C₇×#398	C₂²	semidirect
41. C₇×#398	C₂²	semidirect
42. C₇×#398	C₂²	semidirect
43. C₇×#398	C₂²	semidirect
44. C₇×#396	C₂²	semidirect
45. C₇×#396	C₂²	semidirect
46. C₇×#396	C₂²	semidirect
47. C₇×#396	C₂²	semidirect
48. C₇×#396	C₂²	semidirect
49. C₇×#396	C₂²	semidirect
50. C₇×#396	C₂²	semidirect
51. C₇×#396	C₂²	semidirect
52. C₇×#395	C₂²	semidirect
53. C₇×#395	C₂²	semidirect
54. C₇×#393	C₂²	semidirect
55. C₇×#393	C₂²	semidirect
56. C₇×#393	C₂²	semidirect
57. C₇×#393	C₂²	semidirect
58. C₇×#391	C₂²	semidirect
59. C₇×#391	C₂²	semidirect
66. C₇×#389	C₂²	semidirect
67. C₇×#389	C₂²	semidirect
68. C₇×#387	C₂²	semidirect
69. C₇×#387	C₂²	semidirect
70. C₇×#387	C₂²	semidirect
71. C₇×#387	C₂²	semidirect
88. C₇×#385	C₂²	semidirect
89. C₇×#385	C₂²	semidirect
90. C₇×#385	C₂²	semidirect
91. C₇×#385	C₂²	semidirect
92. C₇×#385	C₂²	semidirect
93. C₇×#385	C₂²	semidirect
94. C₇×#385	C₂²	semidirect
95. C₇×#385	C₂²	semidirect
99. C₇×#380	C₂²	semidirect
100. C₇×#380	C₂²	semidirect
101. C₇×#380	C₂²	semidirect
102. C₇×#380	C₂²	semidirect
107. #36747	C₇	direct (N × H)
114. C₂²×C₇×D₄	Q₈	semidirect
212. #2848	C₂×C₇	semidirect
213. #2804	C₂×C₇	semidirect
214. #2784	C₂×C₇	semidirect
215. #2780	C₂×C₇	semidirect
216. #2780	C₂×C₇	semidirect
217. #2748	C₂×C₇	semidirect
218. #2748	C₂×C₇	semidirect
219. #2732	C₂×C₇	semidirect
220. #2692	C₂×C₇	semidirect
221. #2692	C₂×C₇	semidirect
222. #2683	C₂×C₇	semidirect
223. #2626	C₂×C₇	semidirect
224. #2438	C₂×C₇	semidirect
225. #2438	C₂×C₇	semidirect
226. #2437	C₂×C₇	semidirect
227. #2437	C₂×C₇	semidirect
357. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
358. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
359. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
360. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
367. #400	C₂²×C₇	semidirect
368. #400	C₂²×C₇	semidirect
369. #399	C₂²×C₇	semidirect
370. #399	C₂²×C₇	semidirect
371. #399	C₂²×C₇	semidirect
372. #399	C₂²×C₇	semidirect
373. #398	C₂²×C₇	semidirect
374. #398	C₂²×C₇	semidirect
375. #398	C₂²×C₇	semidirect
376. #398	C₂²×C₇	semidirect
377. #396	C₂²×C₇	semidirect
378. #396	C₂²×C₇	semidirect
379. #396	C₂²×C₇	semidirect
380. #396	C₂²×C₇	semidirect
381. #396	C₂²×C₇	semidirect
382. #396	C₂²×C₇	semidirect
383. #396	C₂²×C₇	semidirect
384. #396	C₂²×C₇	semidirect
385. #395	C₂²×C₇	semidirect
386. #395	C₂²×C₇	semidirect
387. #393	C₂²×C₇	semidirect
388. #393	C₂²×C₇	semidirect
389. #393	C₂²×C₇	semidirect
390. #393	C₂²×C₇	semidirect
391. #391	C₂²×C₇	semidirect
392. #391	C₂²×C₇	semidirect
399. #389	C₂²×C₇	semidirect
400. #389	C₂²×C₇	semidirect
401. #387	C₂²×C₇	semidirect
402. #387	C₂²×C₇	semidirect
403. #387	C₂²×C₇	semidirect
404. #387	C₂²×C₇	semidirect
421. #385	C₂²×C₇	semidirect
422. #385	C₂²×C₇	semidirect
423. #385	C₂²×C₇	semidirect
424. #385	C₂²×C₇	semidirect
425. #385	C₂²×C₇	semidirect
426. #385	C₂²×C₇	semidirect
427. #385	C₂²×C₇	semidirect
428. #385	C₂²×C₇	semidirect
432. #380	C₂²×C₇	semidirect
433. #380	C₂²×C₇	semidirect
434. #380	C₂²×C₇	semidirect
435. #380	C₂²×C₇	semidirect
539. C₂²×D₄	C₇×Q₈	semidirect
908. C₇	#36747	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×#2848	2
C₇×#2804	2
C₇×#2784	2
C₇×#2780	2
C₇×#2748	2
C₇×#2732	2
C₇×#2692	2
C₇×#2683	2
C₇×#2626	2
C₇×#2438	2
C₇×#2437	2
C₇×#2309	2
C₇×#2308	2
C₂×C₇×#386	2
#36747	7

Subgroups — C7×#36747 #13213963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#36747 #13213963