Subgroups — C₇×#34433 #13211649

Order 1792.

2234 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#543	C₂	1	1	yes	maximal, characteristic
2	C₇×#2378	C₂	1	2	yes	maximal, complemented
3	C₇×#2378	C₂	1	2	yes	maximal, complemented
4	C₇×#2368	C₂	1	2	yes	maximal, complemented
5	C₇×#2362	C₂	1	2	yes	maximal, complemented
6	C₇×#2362	C₂	1	2	yes	maximal, complemented
7	C₇×#2360	C₂	1	2	yes	maximal, complemented
8	C₇×#2342	C₂	1	2	yes	maximal
9	C₇×#2342	C₂	1	2	yes	maximal
10	C₇×#2332	C₂	1	2	yes	maximal, complemented
11	C₇×#2332	C₂	1	2	yes	maximal, complemented
12	C₇×#2329	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2329	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2323	C₂	1	2	yes	maximal, complemented
15	C₇×#2323	C₂	1	2	yes	maximal, complemented
16	C₇×#2312	C₂	1	1	yes	maximal, characteristic
17	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₇×#388	C₂	1	1	yes	maximal, characteristic
20	C₇×#543	C₄	1	16	yes	complemented
21	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
31	C₂×C₇×#117	C₂²	1	2	yes	—
32	C₂×C₇×#117	C₂²	1	2	yes	—
33	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
39	C₇×#391	C₂²	1	1	yes	characteristic, complemented
40	C₇×#391	C₂²	1	1	yes	characteristic, complemented
41	C₇×#391	C₂²	1	2	yes	complemented
42	C₇×#391	C₂²	1	2	yes	complemented
43	C₇×#391	C₂²	1	2	yes	complemented
44	C₇×#391	C₂²	1	2	yes	complemented
45	C₇×#391	C₂²	1	2	yes	complemented
46	C₇×#389	C₂²	1	1	yes	characteristic, complemented
47	C₇×#389	C₂²	1	1	yes	characteristic, complemented
48	C₇×#389	C₂²	1	2	yes	complemented
49	C₇×#389	C₂²	1	2	yes	complemented
50	C₇×#389	C₂²	1	2	yes	complemented
51	C₇×#389	C₂²	1	2	yes	complemented
52	C₇×#389	C₂²	1	2	yes	complemented
53	C₇×#388	C₂²	1	2	yes	—
54	C₇×#388	C₂²	1	2	yes	—
55	C₇×#388	C₂²	1	2	yes	—
56	C₇×#388	C₂²	1	2	yes	—
57	C₇×#388	C₂²	1	2	yes	—
58	C₇×#388	C₂²	1	2	yes	—
59	C₇×#388	C₂²	1	2	yes	—
60	C₇×#388	C₂²	1	2	yes	—
61	C₇×#388	C₂²	1	2	yes	—
62	C₇×#388	C₂²	1	2	yes	—
63	C₇×#388	C₂²	1	2	yes	—
64	C₇×#388	C₂²	1	2	yes	—
65	C₇×#388	C₂²	1	2	yes	—
66	C₇×#388	C₂²	1	2	yes	—
67	C₇×#388	C₂²	1	2	yes	—
68	C₇×#388	C₂²	1	2	yes	—
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×#387	C₂²	1	2	yes	complemented
73	C₇×#387	C₂²	1	2	yes	complemented
74	C₇×#387	C₂²	1	2	yes	complemented
75	C₇×#387	C₂²	1	2	yes	complemented
76	C₇×#387	C₂²	1	2	yes	complemented
77	C₇×#387	C₂²	1	2	yes	complemented
78	C₇×#387	C₂²	1	2	yes	complemented
79	C₇×#387	C₂²	1	2	yes	complemented
80	C₇×#387	C₂²	1	2	yes	complemented
81	C₇×#385	C₂²	1	2	yes	—
82	C₇×#385	C₂²	1	2	yes	—
83	C₇×#385	C₂²	1	2	yes	—
84	C₇×#385	C₂²	1	2	yes	—
85	C₇×#381	C₂²	1	2	yes	—
86	C₇×#381	C₂²	1	2	yes	—
87	C₇×#380	C₂²	1	1	yes	characteristic
88	C₇×#380	C₂²	1	1	yes	characteristic
89	C₇×#380	C₂²	1	2	yes	—
90	C₇×#380	C₂²	1	2	yes	—
91	C₇×#379	C₂²	1	2	yes	—
92	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
93	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
96	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
97	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
98	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
99	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₂×C₇×#95	C₂²	1	1	yes	characteristic
107	C₂×C₇×#95	C₂²	1	1	yes	characteristic
108	#34433	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁵×C₇	C₂³	1	1	yes	characteristic
110	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
111	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
112	C₂²×C₇×Q₈	C₂³	1	2	yes	—
113	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₇	C₂³	1	2	yes	—
121	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
122	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
123	C₇×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
124	C₇×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
125	C₇×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
126	C₇×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
127	C₇×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
128	C₄×C₇×Q₈	—	4	2	no	—
129	C₄×C₇×Q₈	—	4	2	no	—
130	C₄×C₇×Q₈	—	4	4	no	—
131	C₇×#117	—	4	4	no	—
132	C₇×#117	—	4	4	no	—
133	C₂×C₇×C₄⋊C₄	—	4	2	no	—
134	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
142	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
147	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	4	2	no	—
156	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
157	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	16	yes	—
158	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	8	yes	—
159	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
172	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₄²×C₇	—	4	2	no	—
176	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₇	C₂³	1	2	yes	—
179	C₂×C₄²×C₇	C₂³	1	2	yes	—
180	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₇	C₂³	1	2	yes	—
183	C₂×C₄²×C₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₇	C₂³	1	2	yes	—
185	C₂×C₄²×C₇	C₂³	1	2	yes	—
186	C₂×C₄²×C₇	C₂³	1	2	yes	—
187	C₂×C₄²×C₇	C₂³	1	2	yes	—
188	C₂×C₄²×C₇	C₂³	1	2	yes	—
189	C₂×C₄²×C₇	C₂³	1	2	yes	—
190	C₇×#95	C₂³	1	2	yes	—
191	C₇×#95	C₂³	1	2	yes	—
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	C₇×#95	C₂³	1	2	yes	—
213	C₇×#95	C₂³	1	2	yes	—
214	C₂×#543	C₂×C₇	1	1	yes	characteristic
215	#2378	C₂×C₇	1	2	yes	complemented
216	#2378	C₂×C₇	1	2	yes	complemented
217	#2368	C₂×C₇	1	2	yes	complemented
218	#2362	C₂×C₇	1	2	yes	complemented
219	#2362	C₂×C₇	1	2	yes	complemented
220	#2360	C₂×C₇	1	2	yes	complemented
221	#2342	C₂×C₇	1	2	yes	—
222	#2342	C₂×C₇	1	2	yes	—
223	#2332	C₂×C₇	1	2	yes	complemented
224	#2332	C₂×C₇	1	2	yes	complemented
225	#2329	C₂×C₇	1	1	yes	characteristic, complemented
226	#2329	C₂×C₇	1	1	yes	characteristic, complemented
227	#2323	C₂×C₇	1	2	yes	complemented
228	#2323	C₂×C₇	1	2	yes	complemented
229	#2312	C₂×C₇	1	1	yes	characteristic
230	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
231	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
232	C₂×#388	C₂×C₇	1	1	yes	characteristic
233	C₂⁴×C₇	—	2	2	no	—
234	C₂⁴×C₇	—	2	2	no	—
235	C₂⁴×C₇	—	4	1	no	—
236	C₂⁴×C₇	—	4	1	no	—
237	C₂⁴×C₇	—	4	1	no	—
238	C₂⁴×C₇	—	4	1	no	—
239	C₂⁴×C₇	C₂²×C₄	1	4	yes	—
240	C₂⁴×C₇	C₂⁴	1	2	yes	—
241	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
242	C₂×C₇×Q₈	—	4	1	no	—
243	C₂×C₇×Q₈	—	4	1	no	—
244	C₂×C₇×Q₈	—	4	2	no	—
245	C₂×C₇×Q₈	—	4	2	no	—
246	C₂×C₇×Q₈	—	4	1	no	—
247	C₂×C₇×Q₈	—	4	1	no	—
248	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
249	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
250	C₂×C₇×Q₈	C₂²×C₄	1	8	yes	—
251	C₂²×C₄×C₇	—	2	2	no	—
252	C₂²×C₄×C₇	—	2	2	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	—	4	1	no	—
258	C₂²×C₄×C₇	—	4	1	no	—
259	C₂²×C₄×C₇	—	4	1	no	—
260	C₂²×C₄×C₇	—	4	2	no	—
261	C₂²×C₄×C₇	—	4	2	no	—
262	C₂²×C₄×C₇	—	4	1	no	—
263	C₂²×C₄×C₇	—	4	1	no	—
264	C₂²×C₄×C₇	—	4	2	no	—
265	C₂²×C₄×C₇	—	4	2	no	—
266	C₂²×C₄×C₇	—	4	1	no	—
267	C₂²×C₄×C₇	—	4	1	no	—
268	C₂²×C₄×C₇	—	4	1	no	—
269	C₂²×C₄×C₇	—	4	1	no	—
270	C₂²×C₄×C₇	—	4	1	no	—
271	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
272	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
273	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
274	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
275	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	—	4	2	no	—
296	C₇×C₄⋊C₄	—	4	1	no	—
297	C₇×C₄⋊C₄	—	4	2	no	—
298	C₇×C₄⋊C₄	—	4	2	no	—
299	C₇×C₄⋊C₄	—	4	1	no	—
300	C₇×C₄⋊C₄	—	4	2	no	—
301	C₇×C₄⋊C₄	—	4	2	no	—
302	C₇×C₄⋊C₄	—	4	2	no	—
303	C₇×C₄⋊C₄	—	4	1	no	—
304	C₇×C₄⋊C₄	—	4	1	no	—
305	C₇×C₄⋊C₄	—	4	2	no	—
306	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
307	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
308	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
309	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
310	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
311	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
312	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
313	C₇×C₂²⋊C₄	—	2	4	no	—
314	C₇×C₂²⋊C₄	—	2	4	no	—
315	C₇×C₂²⋊C₄	—	2	4	no	—
316	C₇×C₂²⋊C₄	—	2	4	no	—
317	C₇×C₂²⋊C₄	—	4	2	no	—
318	C₇×C₂²⋊C₄	—	4	2	no	—
319	C₇×C₂²⋊C₄	—	4	2	no	—
320	C₇×C₂²⋊C₄	—	4	2	no	—
321	C₇×C₂²⋊C₄	—	4	2	no	—
322	C₇×C₂²⋊C₄	—	4	2	no	—
323	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
324	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
325	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
326	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
327	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
328	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
329	C₄²×C₇	—	2	2	no	—
330	C₄²×C₇	—	2	2	no	—
331	C₄²×C₇	—	2	4	no	—
332	C₄²×C₇	—	2	4	no	—
333	C₄²×C₇	—	4	1	no	—
334	C₄²×C₇	—	4	1	no	—
335	C₄²×C₇	—	4	2	no	—
336	C₄²×C₇	—	4	2	no	—
337	C₄²×C₇	—	4	2	no	—
338	C₄²×C₇	—	4	2	no	—
339	C₄²×C₇	—	4	2	no	—
340	C₄²×C₇	—	4	2	no	—
341	C₄²×C₇	—	4	2	no	—
342	C₄²×C₇	—	4	2	no	—
343	#543	C₄×C₇	1	16	yes	complemented
344	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
345	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
346	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
347	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
348	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
349	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
350	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
351	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
352	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
353	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
354	C₂×#117	C₂²×C₇	1	2	yes	—
355	C₂×#117	C₂²×C₇	1	2	yes	—
356	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
357	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
358	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
359	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
360	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
361	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
362	#391	C₂²×C₇	1	2	yes	complemented
363	#391	C₂²×C₇	1	2	yes	complemented
364	#391	C₂²×C₇	1	2	yes	complemented
365	#391	C₂²×C₇	1	1	yes	characteristic, complemented
366	#391	C₂²×C₇	1	2	yes	complemented
367	#391	C₂²×C₇	1	2	yes	complemented
368	#391	C₂²×C₇	1	1	yes	characteristic, complemented
369	#389	C₂²×C₇	1	2	yes	complemented
370	#389	C₂²×C₇	1	1	yes	characteristic, complemented
371	#389	C₂²×C₇	1	2	yes	complemented
372	#389	C₂²×C₇	1	2	yes	complemented
373	#389	C₂²×C₇	1	2	yes	complemented
374	#389	C₂²×C₇	1	2	yes	complemented
375	#389	C₂²×C₇	1	1	yes	characteristic, complemented
376	#388	C₂²×C₇	1	2	yes	—
377	#388	C₂²×C₇	1	2	yes	—
378	#388	C₂²×C₇	1	2	yes	—
379	#388	C₂²×C₇	1	2	yes	—
380	#388	C₂²×C₇	1	2	yes	—
381	#388	C₂²×C₇	1	2	yes	—
382	#388	C₂²×C₇	1	2	yes	—
383	#388	C₂²×C₇	1	2	yes	—
384	#388	C₂²×C₇	1	2	yes	—
385	#388	C₂²×C₇	1	2	yes	—
386	#388	C₂²×C₇	1	2	yes	—
387	#388	C₂²×C₇	1	2	yes	—
388	#388	C₂²×C₇	1	2	yes	—
389	#388	C₂²×C₇	1	2	yes	—
390	#388	C₂²×C₇	1	2	yes	—
391	#388	C₂²×C₇	1	2	yes	—
392	#387	C₂²×C₇	1	2	yes	complemented
393	#387	C₂²×C₇	1	2	yes	complemented
394	#387	C₂²×C₇	1	2	yes	complemented
395	#387	C₂²×C₇	1	2	yes	complemented
396	#387	C₂²×C₇	1	2	yes	complemented
397	#387	C₂²×C₇	1	2	yes	complemented
398	#387	C₂²×C₇	1	2	yes	complemented
399	#387	C₂²×C₇	1	2	yes	complemented
400	#387	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	#385	C₂²×C₇	1	2	yes	—
405	#385	C₂²×C₇	1	2	yes	—
406	#385	C₂²×C₇	1	2	yes	—
407	#385	C₂²×C₇	1	2	yes	—
408	#381	C₂²×C₇	1	2	yes	—
409	#381	C₂²×C₇	1	2	yes	—
410	#380	C₂²×C₇	1	1	yes	characteristic
411	#380	C₂²×C₇	1	1	yes	characteristic
412	#380	C₂²×C₇	1	2	yes	—
413	#380	C₂²×C₇	1	2	yes	—
414	#379	C₂²×C₇	1	2	yes	—
415	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
416	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
417	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
418	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
419	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
420	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
421	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
422	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
423	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
424	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
425	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
426	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
427	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
428	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
429	C₂×#95	C₂²×C₇	1	1	yes	characteristic
430	C₂×#95	C₂²×C₇	1	1	yes	characteristic
431	C₂³×C₇	—	2	1	no	—
432	C₂³×C₇	—	2	1	no	—
433	C₂³×C₇	—	2	1	no	—
434	C₂³×C₇	—	2	1	no	—
435	C₂³×C₇	—	2	2	no	—
436	C₂³×C₇	—	2	2	no	—
437	C₂³×C₇	—	2	2	no	—
438	C₂³×C₇	—	2	2	no	—
439	C₂³×C₇	—	2	2	no	—
440	C₂³×C₇	—	2	2	no	—
441	C₂³×C₇	—	2	8	no	—
442	C₂³×C₇	—	4	4	no	—
443	C₂³×C₇	—	4	4	no	—
444	C₂³×C₇	—	8	2	no	—
445	C₂³×C₇	—	8	2	no	—
446	C₂³×C₇	—	8	2	no	—
447	C₂³×C₇	—	8	2	no	—
448	C₂³×C₇	C₂³×C₄	1	4	yes	—
449	C₂³×C₇	C₂³×C₄	1	2	yes	—
450	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
451	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
452	C₂³×C₇	C₂⁵	1	1	yes	characteristic
453	C₇×Q₈	—	4	4	no	—
454	C₇×Q₈	—	4	4	no	—
455	C₇×Q₈	—	4	8	no	—
456	C₂×C₄×C₇	—	2	1	no	—
457	C₂×C₄×C₇	—	2	1	no	—
458	C₂×C₄×C₇	—	2	1	no	—
459	C₂×C₄×C₇	—	2	2	no	—
460	C₂×C₄×C₇	—	2	2	no	—
461	C₂×C₄×C₇	—	2	2	no	—
462	C₂×C₄×C₇	—	2	2	no	—
463	C₂×C₄×C₇	—	2	2	no	—
464	C₂×C₄×C₇	—	2	1	no	—
465	C₂×C₄×C₇	—	2	1	no	—
466	C₂×C₄×C₇	—	2	1	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	2	no	—
471	C₂×C₄×C₇	—	2	1	no	—
472	C₂×C₄×C₇	—	2	2	no	—
473	C₂×C₄×C₇	—	2	1	no	—
474	C₂×C₄×C₇	—	2	2	no	—
475	C₂×C₄×C₇	—	2	1	no	—
476	C₂×C₄×C₇	—	2	2	no	—
477	C₂×C₄×C₇	—	2	1	no	—
478	C₂×C₄×C₇	—	2	2	no	—
479	C₂×C₄×C₇	—	2	2	no	—
480	C₂×C₄×C₇	—	2	2	no	—
481	C₂×C₄×C₇	—	2	2	no	—
482	C₂×C₄×C₇	—	2	2	no	—
483	C₂×C₄×C₇	—	2	1	no	—
484	C₂×C₄×C₇	—	2	2	no	—
485	C₂×C₄×C₇	—	2	2	no	—
486	C₂×C₄×C₇	—	2	2	no	—
487	C₂×C₄×C₇	—	2	2	no	—
488	C₂×C₄×C₇	—	2	1	no	—
489	C₂×C₄×C₇	—	2	1	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	1	no	—
498	C₂×C₄×C₇	—	4	4	no	—
499	C₂×C₄×C₇	—	4	4	no	—
500	C₂×C₄×C₇	—	4	8	no	—
501	C₂×C₄×C₇	—	4	8	no	—
502	C₂×C₄×C₇	—	4	4	no	—
503	C₂×C₄×C₇	—	4	4	no	—
504	C₂×C₄×C₇	—	8	2	no	—
505	C₂×C₄×C₇	—	8	2	no	—
506	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
507	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
508	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
509	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
510	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
511	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
512	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
513	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
514	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
515	C₂⁵	C₂³×C₇	1	1	yes	characteristic
516	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
517	C₂²×Q₈	C₂³×C₇	1	2	yes	—
518	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
523	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₇	1	2	yes	—
525	C₂³×C₄	C₂³×C₇	1	2	yes	—
526	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
527	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
528	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
529	C₂²⋊Q₈	C₂×C₄×C₇	1	16	yes	—
530	C₂²⋊Q₈	C₂×C₄×C₇	1	16	yes	complemented
531	C₂²⋊Q₈	C₂×C₄×C₇	1	16	yes	complemented
532	C₂²⋊Q₈	C₂×C₄×C₇	1	16	yes	complemented
533	C₂²⋊Q₈	C₂×C₄×C₇	1	16	yes	complemented
534	C₄×Q₈	—	4	2	no	—
535	C₄×Q₈	—	4	2	no	—
536	C₄×Q₈	—	4	4	no	—
537	#117	—	4	4	no	—
538	#117	—	4	4	no	—
539	C₂×C₄⋊C₄	—	4	2	no	—
540	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
561	C₂×C₂²⋊C₄	—	4	2	no	—
562	C₂×C₂²⋊C₄	—	4	2	no	—
563	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	16	yes	—
564	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	8	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
581	C₂×C₄²	—	4	2	no	—
582	C₂×C₄²	C₂³×C₇	1	2	yes	—
583	C₂×C₄²	C₂³×C₇	1	2	yes	—
584	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
586	C₂×C₄²	C₂³×C₇	1	2	yes	—
587	C₂×C₄²	C₂³×C₇	1	2	yes	—
588	C₂×C₄²	C₂³×C₇	1	2	yes	—
589	C₂×C₄²	C₂³×C₇	1	2	yes	—
590	C₂×C₄²	C₂³×C₇	1	2	yes	—
591	C₂×C₄²	C₂³×C₇	1	2	yes	—
592	C₂×C₄²	C₂³×C₇	1	2	yes	—
593	C₂×C₄²	C₂³×C₇	1	2	yes	—
594	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
596	#95	C₂³×C₇	1	2	yes	—
597	#95	C₂³×C₇	1	2	yes	—
598	#95	C₂³×C₇	1	2	yes	—
599	#95	C₂³×C₇	1	2	yes	—
600	#95	C₂³×C₇	1	2	yes	—
601	#95	C₂³×C₇	1	2	yes	—
602	#95	C₂³×C₇	1	2	yes	—
603	#95	C₂³×C₇	1	2	yes	—
604	#95	C₂³×C₇	1	2	yes	—
605	#95	C₂³×C₇	1	2	yes	—
606	#95	C₂³×C₇	1	2	yes	—
607	#95	C₂³×C₇	1	2	yes	—
608	#95	C₂³×C₇	1	2	yes	—
609	#95	C₂³×C₇	1	2	yes	—
610	#95	C₂³×C₇	1	2	yes	—
611	#95	C₂³×C₇	1	2	yes	—
612	#95	C₂³×C₇	1	2	yes	—
613	#95	C₂³×C₇	1	2	yes	—
614	#95	C₂³×C₇	1	2	yes	—
615	#95	C₂³×C₇	1	2	yes	—
616	#95	C₂³×C₇	1	2	yes	—
617	#95	C₂³×C₇	1	2	yes	—
618	#95	C₂³×C₇	1	2	yes	—
619	#95	C₂³×C₇	1	2	yes	—
620	C₂²×C₇	—	2	2	no	—
621	C₂²×C₇	—	2	2	no	—
622	C₂²×C₇	—	2	2	no	—
623	C₂²×C₇	—	2	2	no	—
624	C₂²×C₇	—	2	2	no	—
625	C₂²×C₇	—	2	2	no	—
626	C₂²×C₇	—	2	4	no	—
627	C₂²×C₇	—	2	4	no	—
628	C₂²×C₇	—	2	4	no	—
629	C₂²×C₇	—	4	2	no	—
630	C₂²×C₇	—	4	2	no	—
631	C₂²×C₇	—	4	2	no	—
632	C₂²×C₇	—	4	2	no	—
633	C₂²×C₇	—	8	8	no	—
634	C₂²×C₇	#519	1	4	yes	—
635	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
636	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
637	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
638	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
639	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
640	C₂²×C₇	#585	1	1	yes	characteristic
641	C₂²×C₇	#585	1	1	yes	characteristic
642	C₄×C₇	—	2	2	no	—
643	C₄×C₇	—	2	2	no	—
644	C₄×C₇	—	2	4	no	—
645	C₄×C₇	—	2	4	no	—
646	C₄×C₇	—	2	4	no	—
647	C₄×C₇	—	2	4	no	—
648	C₄×C₇	—	2	4	no	—
649	C₄×C₇	—	2	2	no	—
650	C₄×C₇	—	2	2	no	—
651	C₄×C₇	—	4	2	no	—
652	C₄×C₇	—	4	1	no	—
653	C₄×C₇	—	4	2	no	—
654	C₄×C₇	—	4	1	no	—
655	C₄×C₇	—	4	2	no	—
656	C₄×C₇	—	4	2	no	—
657	C₄×C₇	—	4	2	no	—
658	C₄×C₇	—	4	2	no	—
659	C₂⁴	—	2	2	no	—
660	C₂⁴	—	2	2	no	—
661	C₂⁴	—	4	1	no	—
662	C₂⁴	—	4	1	no	—
663	C₂⁴	—	4	1	no	—
664	C₂⁴	—	4	1	no	—
665	C₂⁴	C₂²×C₄×C₇	1	4	yes	—
666	C₂⁴	C₂⁴×C₇	1	2	yes	—
667	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
668	C₂×Q₈	—	4	1	no	—
669	C₂×Q₈	—	4	2	no	—
670	C₂×Q₈	—	4	1	no	—
671	C₂×Q₈	—	4	1	no	—
672	C₂×Q₈	—	4	2	no	—
673	C₂×Q₈	—	4	1	no	—
674	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
675	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
676	C₂×Q₈	C₂²×C₄×C₇	1	8	yes	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	4	1	no	—
684	C₂²×C₄	—	4	1	no	—
685	C₂²×C₄	—	4	1	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	1	no	—
689	C₂²×C₄	—	4	1	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	1	no	—
693	C₂²×C₄	—	4	1	no	—
694	C₂²×C₄	—	4	1	no	—
695	C₂²×C₄	—	4	1	no	—
696	C₂²×C₄	—	4	1	no	—
697	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
698	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
699	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
700	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
701	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	1	no	—
726	C₄⋊C₄	—	4	1	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	1	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	1	no	—
732	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
733	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
734	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
735	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
736	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
737	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
738	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	4	2	no	—
744	C₂²⋊C₄	—	4	2	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
750	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
751	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
752	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
753	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
754	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	4	no	—
758	C₄²	—	2	4	no	—
759	C₄²	—	4	1	no	—
760	C₄²	—	4	1	no	—
761	C₄²	—	4	2	no	—
762	C₄²	—	4	2	no	—
763	C₄²	—	4	2	no	—
764	C₄²	—	4	2	no	—
765	C₄²	—	4	2	no	—
766	C₄²	—	4	2	no	—
767	C₄²	—	4	2	no	—
768	C₄²	—	4	2	no	—
769	C₂×C₇	—	2	4	no	—
770	C₂×C₇	—	4	4	no	—
771	C₂×C₇	C₂×#519	1	1	yes	characteristic
772	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
773	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
774	C₂×C₇	#3535	1	1	yes	characteristic
775	C₂×C₇	#3536	1	1	yes	characteristic
776	C₂×C₇	#3561	1	1	yes	characteristic
777	C₂×C₇	#3564	1	1	yes	characteristic
778	C₂³	—	2	1	no	—
779	C₂³	—	2	1	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	8	no	—
789	C₂³	—	4	4	no	—
790	C₂³	—	4	4	no	—
791	C₂³	—	8	2	no	—
792	C₂³	—	8	2	no	—
793	C₂³	—	8	2	no	—
794	C₂³	—	8	2	no	—
795	C₂³	C₂³×C₄×C₇	1	4	yes	—
796	C₂³	C₂³×C₄×C₇	1	2	yes	—
797	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
798	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
799	C₂³	C₂⁵×C₇	1	1	yes	characteristic
800	Q₈	—	4	4	no	—
801	Q₈	—	4	8	no	—
802	Q₈	—	4	4	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	4	4	no	—
846	C₂×C₄	—	4	4	no	—
847	C₂×C₄	—	4	8	no	—
848	C₂×C₄	—	4	8	no	—
849	C₂×C₄	—	4	4	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	8	2	no	—
852	C₂×C₄	—	8	2	no	—
853	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
854	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
855	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
856	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
857	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
858	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
859	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
860	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
861	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
862	C₇	#34433	1	1	yes	characteristic, direct product factor, Sylow
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	8	8	no	—
877	C₂²	C₇×#519	1	4	yes	—
878	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
879	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
880	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
881	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
882	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
883	C₂²	C₇×#585	1	1	yes	characteristic
884	C₂²	C₇×#585	1	1	yes	characteristic
885	C₄	—	2	4	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	4	no	—
890	C₄	—	2	4	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₂	—	2	4	no	—
903	C₂	—	4	4	no	—
904	C₂	C₂×C₇×#519	1	1	yes	characteristic
905	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
906	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
907	C₂	C₇×#3535	1	1	yes	characteristic
908	C₂	C₇×#3536	1	1	yes	characteristic
909	C₂	C₇×#3561	1	1	yes	characteristic
910	C₂	C₇×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂⁵×C₇	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2378	C₂	semidirect
3. C₇×#2378	C₂	semidirect
4. C₇×#2368	C₂	semidirect
5. C₇×#2362	C₂	semidirect
6. C₇×#2362	C₂	semidirect
7. C₇×#2360	C₂	semidirect
10. C₇×#2332	C₂	semidirect
11. C₇×#2332	C₂	semidirect
12. C₇×#2329	C₂	semidirect
13. C₇×#2329	C₂	semidirect
14. C₇×#2323	C₂	semidirect
15. C₇×#2323	C₂	semidirect
17. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
20. C₇×#543	C₄	semidirect
28. C₂×C₄×C₇×Q₈	C₂²	semidirect
29. C₂×C₄×C₇×Q₈	C₂²	semidirect
30. C₂×C₄×C₇×Q₈	C₂²	semidirect
39. C₇×#391	C₂²	semidirect
40. C₇×#391	C₂²	semidirect
41. C₇×#391	C₂²	semidirect
42. C₇×#391	C₂²	semidirect
43. C₇×#391	C₂²	semidirect
44. C₇×#391	C₂²	semidirect
45. C₇×#391	C₂²	semidirect
46. C₇×#389	C₂²	semidirect
47. C₇×#389	C₂²	semidirect
48. C₇×#389	C₂²	semidirect
49. C₇×#389	C₂²	semidirect
50. C₇×#389	C₂²	semidirect
51. C₇×#389	C₂²	semidirect
52. C₇×#389	C₂²	semidirect
69. C₇×#387	C₂²	semidirect
70. C₇×#387	C₂²	semidirect
71. C₇×#387	C₂²	semidirect
72. C₇×#387	C₂²	semidirect
73. C₇×#387	C₂²	semidirect
74. C₇×#387	C₂²	semidirect
75. C₇×#387	C₂²	semidirect
76. C₇×#387	C₂²	semidirect
77. C₇×#387	C₂²	semidirect
78. C₇×#387	C₂²	semidirect
79. C₇×#387	C₂²	semidirect
80. C₇×#387	C₂²	semidirect
92. C₄×C₇×C₄⋊C₄	C₂²	semidirect
93. C₄×C₇×C₄⋊C₄	C₂²	semidirect
94. C₄×C₇×C₄⋊C₄	C₂²	semidirect
95. C₄×C₇×C₄⋊C₄	C₂²	semidirect
96. C₄×C₇×C₄⋊C₄	C₂²	semidirect
97. C₄×C₇×C₄⋊C₄	C₂²	semidirect
98. C₄×C₇×C₄⋊C₄	C₂²	semidirect
108. #34433	C₇	direct (N × H)
124. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
125. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
126. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
127. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
215. #2378	C₂×C₇	semidirect
216. #2378	C₂×C₇	semidirect
217. #2368	C₂×C₇	semidirect
218. #2362	C₂×C₇	semidirect
219. #2362	C₂×C₇	semidirect
220. #2360	C₂×C₇	semidirect
223. #2332	C₂×C₇	semidirect
224. #2332	C₂×C₇	semidirect
225. #2329	C₂×C₇	semidirect
226. #2329	C₂×C₇	semidirect
227. #2323	C₂×C₇	semidirect
228. #2323	C₂×C₇	semidirect
230. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
231. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
343. #543	C₄×C₇	semidirect
351. C₂×C₄×Q₈	C₂²×C₇	semidirect
352. C₂×C₄×Q₈	C₂²×C₇	semidirect
353. C₂×C₄×Q₈	C₂²×C₇	semidirect
362. #391	C₂²×C₇	semidirect
363. #391	C₂²×C₇	semidirect
364. #391	C₂²×C₇	semidirect
365. #391	C₂²×C₇	semidirect
366. #391	C₂²×C₇	semidirect
367. #391	C₂²×C₇	semidirect
368. #391	C₂²×C₇	semidirect
369. #389	C₂²×C₇	semidirect
370. #389	C₂²×C₇	semidirect
371. #389	C₂²×C₇	semidirect
372. #389	C₂²×C₇	semidirect
373. #389	C₂²×C₇	semidirect
374. #389	C₂²×C₇	semidirect
375. #389	C₂²×C₇	semidirect
392. #387	C₂²×C₇	semidirect
393. #387	C₂²×C₇	semidirect
394. #387	C₂²×C₇	semidirect
395. #387	C₂²×C₇	semidirect
396. #387	C₂²×C₇	semidirect
397. #387	C₂²×C₇	semidirect
398. #387	C₂²×C₇	semidirect
399. #387	C₂²×C₇	semidirect
400. #387	C₂²×C₇	semidirect
401. #387	C₂²×C₇	semidirect
402. #387	C₂²×C₇	semidirect
403. #387	C₂²×C₇	semidirect
415. C₄×C₄⋊C₄	C₂²×C₇	semidirect
416. C₄×C₄⋊C₄	C₂²×C₇	semidirect
417. C₄×C₄⋊C₄	C₂²×C₇	semidirect
418. C₄×C₄⋊C₄	C₂²×C₇	semidirect
419. C₄×C₄⋊C₄	C₂²×C₇	semidirect
420. C₄×C₄⋊C₄	C₂²×C₇	semidirect
421. C₄×C₄⋊C₄	C₂²×C₇	semidirect
530. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
531. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
532. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
533. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
862. C₇	#34433	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×#543	2
C₇×#2378	2
C₇×#2368	2
C₇×#2362	2
C₇×#2360	2
C₇×#2342	2
C₇×#2332	2
C₇×#2329	2
C₇×#2323	2
C₇×#2312	2
C₄×C₇×C₂²⋊Q₈	2
C₂×C₇×#388	2
#34433	7

Subgroups — C7×#34433 #13211649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34433 #13211649