Subgroups — C₇×#34468 #13211684

Order 1792.

3220 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₄²	C₂	1	1	yes	maximal, characteristic
2	C₇×#2380	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2377	C₂	1	2	yes	maximal, complemented
4	C₇×#2375	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2364	C₂	1	2	yes	maximal, complemented
6	C₇×#2358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2358	C₂	1	2	yes	maximal, complemented
8	C₇×#2353	C₂	1	2	yes	maximal, complemented
9	C₇×D₄×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₇×D₄×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₇×#2333	C₂	1	2	yes	maximal, complemented
12	C₇×#2328	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2325	C₂	1	2	yes	maximal, complemented
14	C₇×#2321	C₂	1	2	yes	maximal, complemented
15	C₇×#2321	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2318	C₂	1	2	yes	maximal, complemented
17	C₇×#2308	C₂	1	2	yes	maximal, complemented
18	C₄×C₇×#120	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₇×#386	C₂	1	2	yes	maximal, complemented
20	C₂³×C₇×D₄	C₂²	1	2	yes	—
21	C₂³×C₇×D₄	C₂²	1	2	yes	—
22	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
23	C₇×D₄²	C₄	1	16	yes	complemented
24	C₂×C₇×#127	C₂²	1	1	yes	characteristic
25	C₂×C₇×#121	C₂²	1	2	yes	—
26	C₂×C₇×#121	C₂²	1	2	yes	—
27	C₂×C₇×#120	C₂²	1	1	yes	characteristic
28	C₂×C₇×#120	C₂²	1	2	yes	—
29	C₂×C₇×#120	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
31	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
33	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
34	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
35	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
36	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
38	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
39	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
40	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
41	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₇×#390	C₂²	1	1	yes	characteristic, complemented
43	C₇×#390	C₂²	1	2	yes	complemented
44	C₇×#390	C₂²	1	2	yes	complemented
45	C₇×#390	C₂²	1	1	yes	characteristic, complemented
46	C₇×#390	C₂²	1	2	yes	complemented
47	C₇×#390	C₂²	1	2	yes	complemented
48	C₇×#388	C₂²	1	2	yes	complemented
49	C₇×#388	C₂²	1	2	yes	complemented
50	C₇×#388	C₂²	1	2	yes	complemented
51	C₇×#388	C₂²	1	2	yes	complemented
52	C₇×#388	C₂²	1	2	yes	complemented
53	C₇×#388	C₂²	1	2	yes	complemented
54	C₇×#388	C₂²	1	2	yes	complemented
55	C₇×#388	C₂²	1	2	yes	complemented
56	C₇×#387	C₂²	1	2	yes	complemented
57	C₇×#387	C₂²	1	2	yes	complemented
58	C₇×#387	C₂²	1	2	yes	complemented
59	C₇×#387	C₂²	1	2	yes	complemented
60	C₇×#386	C₂²	1	2	yes	—
61	C₇×#386	C₂²	1	2	yes	—
62	C₇×#386	C₂²	1	2	yes	—
63	C₇×#386	C₂²	1	2	yes	—
64	C₇×#386	C₂²	1	2	yes	complemented
65	C₇×#386	C₂²	1	2	yes	complemented
66	C₇×#386	C₂²	1	2	yes	complemented
67	C₇×#386	C₂²	1	2	yes	complemented
68	C₇×#386	C₂²	1	2	yes	complemented
69	C₇×#386	C₂²	1	2	yes	complemented
70	C₇×#386	C₂²	1	2	yes	complemented
71	C₇×#386	C₂²	1	1	yes	characteristic, complemented
72	C₇×#386	C₂²	1	2	yes	complemented
73	C₇×#386	C₂²	1	2	yes	complemented
74	C₇×#386	C₂²	1	2	yes	complemented
75	C₇×#386	C₂²	1	2	yes	complemented
76	C₇×#386	C₂²	1	2	yes	complemented
77	C₇×#386	C₂²	1	2	yes	complemented
78	C₇×#386	C₂²	1	1	yes	characteristic, complemented
79	C₇×#386	C₂²	1	2	yes	complemented
80	C₇×#386	C₂²	1	2	yes	complemented
81	C₇×#386	C₂²	1	2	yes	complemented
82	C₇×#386	C₂²	1	2	yes	complemented
83	C₇×#385	C₂²	1	2	yes	complemented
84	C₇×#385	C₂²	1	1	yes	characteristic, complemented
85	C₇×#385	C₂²	1	2	yes	complemented
86	C₇×#385	C₂²	1	1	yes	characteristic, complemented
87	C₇×#385	C₂²	1	2	yes	complemented
88	C₇×#383	C₂²	1	2	yes	complemented
89	C₇×#382	C₂²	1	1	yes	characteristic, complemented
90	C₇×#381	C₂²	1	2	yes	complemented
91	C₇×#381	C₂²	1	2	yes	complemented
92	C₇×#380	C₂²	1	2	yes	complemented
93	C₇×#380	C₂²	1	2	yes	complemented
94	C₇×#379	C₂²	1	1	yes	characteristic, complemented
95	C₇×#379	C₂²	1	1	yes	characteristic, complemented
96	C₇×#379	C₂²	1	2	yes	complemented
97	C₇×#379	C₂²	1	2	yes	complemented
98	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
100	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
101	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
102	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
104	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
105	C₇×#376	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₇×#95	C₂²	1	2	yes	complemented
107	C₂×C₇×#95	C₂²	1	2	yes	complemented
108	#34468	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁵×C₇	C₂³	1	1	yes	characteristic
110	C₂⁵×C₇	C₂³	1	2	yes	—
111	C₂⁵×C₇	C₂³	1	1	yes	characteristic
112	C₂²×C₇×D₄	—	4	4	no	—
113	C₂²×C₇×D₄	—	4	4	no	—
114	C₂²×C₇×D₄	—	4	4	no	—
115	C₂²×C₇×D₄	—	4	4	no	—
116	C₂²×C₇×D₄	C₂×C₄	1	16	yes	complemented
117	C₂²×C₇×D₄	C₂×C₄	1	16	yes	complemented
118	C₂²×C₇×D₄	C₂³	1	2	yes	—
119	C₂²×C₇×D₄	C₂³	1	2	yes	—
120	C₂²×C₇×D₄	C₂³	1	2	yes	—
121	C₂²×C₇×D₄	C₂³	1	2	yes	—
122	C₂²×C₇×D₄	C₂³	1	2	yes	—
123	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
124	C₂²×C₇×D₄	C₂³	1	2	yes	—
125	C₂²×C₇×D₄	C₂³	1	2	yes	—
126	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₇	—	4	2	no	—
128	C₂³×C₄×C₇	—	4	4	no	—
129	C₂³×C₄×C₇	C₂³	1	2	yes	—
130	C₂³×C₄×C₇	C₂³	1	2	yes	—
131	C₂³×C₄×C₇	C₂³	1	2	yes	—
132	C₂³×C₄×C₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₇	C₂³	1	2	yes	—
140	C₂³×C₄×C₇	C₂³	1	2	yes	—
141	C₇×#127	C₂×C₄	1	8	yes	complemented
142	C₇×#121	C₂×C₄	1	16	yes	complemented
143	C₇×#121	C₂×C₄	1	16	yes	complemented
144	C₇×#120	C₂×C₄	1	8	yes	complemented
145	C₇×#120	C₂×C₄	1	16	yes	complemented
146	C₇×#120	C₂×C₄	1	8	yes	complemented
147	C₄×C₇×D₄	—	4	2	no	—
148	C₄×C₇×D₄	—	4	2	no	—
149	C₄×C₇×D₄	—	4	4	no	—
150	C₄×C₇×D₄	—	4	4	no	—
151	C₄×C₇×D₄	—	4	4	no	—
152	C₄×C₇×D₄	—	4	4	no	—
153	C₄×C₇×D₄	C₂×C₄	1	16	yes	complemented
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	1	yes	characteristic
159	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
162	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
163	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
164	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
165	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
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×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
185	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₇	C₂³	1	2	yes	—
200	C₂×C₄²×C₇	C₂³	1	2	yes	—
201	C₂×C₄²×C₇	C₂³	1	2	yes	—
202	C₂×C₄²×C₇	C₂³	1	2	yes	—
203	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
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	C₇×#95	C₂³	1	2	yes	—
215	C₇×#95	C₂³	1	2	yes	—
216	C₇×#95	C₂³	1	2	yes	—
217	C₇×#95	C₂³	1	2	yes	—
218	C₇×#95	C₂³	1	2	yes	—
219	C₇×#95	C₂³	1	2	yes	—
220	C₇×#95	C₂³	1	2	yes	—
221	C₇×#95	C₂³	1	2	yes	—
222	C₂×D₄²	C₂×C₇	1	1	yes	characteristic
223	#2380	C₂×C₇	1	1	yes	characteristic, complemented
224	#2377	C₂×C₇	1	2	yes	complemented
225	#2375	C₂×C₇	1	1	yes	characteristic, complemented
226	#2364	C₂×C₇	1	2	yes	complemented
227	#2358	C₂×C₇	1	2	yes	complemented
228	#2358	C₂×C₇	1	1	yes	characteristic, complemented
229	#2353	C₂×C₇	1	2	yes	complemented
230	D₄×C₂²⋊C₄	C₂×C₇	1	2	yes	complemented
231	D₄×C₂²⋊C₄	C₂×C₇	1	2	yes	complemented
232	#2333	C₂×C₇	1	2	yes	complemented
233	#2328	C₂×C₇	1	1	yes	characteristic, complemented
234	#2325	C₂×C₇	1	2	yes	complemented
235	#2321	C₂×C₇	1	2	yes	complemented
236	#2321	C₂×C₇	1	1	yes	characteristic, complemented
237	#2318	C₂×C₇	1	2	yes	complemented
238	#2308	C₂×C₇	1	2	yes	complemented
239	C₄×#120	C₂×C₇	1	1	yes	characteristic, complemented
240	C₂×#386	C₂×C₇	1	2	yes	complemented
241	C₂⁴×C₇	—	2	4	no	—
242	C₂⁴×C₇	—	2	4	no	—
243	C₂⁴×C₇	—	2	4	no	—
244	C₂⁴×C₇	—	2	4	no	—
245	C₂⁴×C₇	—	4	1	no	—
246	C₂⁴×C₇	—	4	1	no	—
247	C₂⁴×C₇	—	4	2	no	—
248	C₂⁴×C₇	—	4	1	no	—
249	C₂⁴×C₇	—	4	2	no	—
250	C₂⁴×C₇	—	4	2	no	—
251	C₂⁴×C₇	—	4	2	no	—
252	C₂⁴×C₇	—	4	2	no	—
253	C₂⁴×C₇	—	4	2	no	—
254	C₂⁴×C₇	—	4	1	no	—
255	C₂⁴×C₇	C₂²×C₄	1	4	yes	—
256	C₂⁴×C₇	C₂²×C₄	1	8	yes	—
257	C₂⁴×C₇	C₂²×C₄	1	4	yes	complemented
258	C₂⁴×C₇	C₂⁴	1	2	yes	—
259	C₂⁴×C₇	C₂⁴	1	2	yes	—
260	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
261	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
262	C₂⁴×C₇	C₂⁴	1	2	yes	—
263	C₂×C₇×D₄	—	2	4	no	—
264	C₂×C₇×D₄	—	2	4	no	—
265	C₂×C₇×D₄	—	2	4	no	—
266	C₂×C₇×D₄	—	2	4	no	—
267	C₂×C₇×D₄	—	2	4	no	—
268	C₂×C₇×D₄	—	2	4	no	—
269	C₂×C₇×D₄	—	4	1	no	—
270	C₂×C₇×D₄	—	4	1	no	—
271	C₂×C₇×D₄	—	4	2	no	—
272	C₂×C₇×D₄	—	4	2	no	—
273	C₂×C₇×D₄	—	4	2	no	—
274	C₂×C₇×D₄	—	4	2	no	—
275	C₂×C₇×D₄	—	4	2	no	—
276	C₂×C₇×D₄	—	4	2	no	—
277	C₂×C₇×D₄	—	4	2	no	—
278	C₂×C₇×D₄	—	4	2	no	—
279	C₂×C₇×D₄	—	4	1	no	—
280	C₂×C₇×D₄	—	4	1	no	—
281	C₂×C₇×D₄	—	4	32	no	—
282	C₂×C₇×D₄	—	4	32	no	—
283	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
284	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
285	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
286	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
287	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
288	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
289	C₂×C₇×D₄	C₂²×C₄	1	4	yes	complemented
290	C₂×C₇×D₄	C₂²×C₄	1	8	yes	complemented
291	C₂×C₇×D₄	C₂²×C₄	1	8	yes	complemented
292	C₂²×C₄×C₇	—	2	4	no	—
293	C₂²×C₄×C₇	—	2	4	no	—
294	C₂²×C₄×C₇	—	2	4	no	—
295	C₂²×C₄×C₇	—	2	4	no	—
296	C₂²×C₄×C₇	—	2	4	no	—
297	C₂²×C₄×C₇	—	2	2	no	—
298	C₂²×C₄×C₇	—	2	2	no	—
299	C₂²×C₄×C₇	—	4	2	no	—
300	C₂²×C₄×C₇	—	4	2	no	—
301	C₂²×C₄×C₇	—	4	1	no	—
302	C₂²×C₄×C₇	—	4	2	no	—
303	C₂²×C₄×C₇	—	4	2	no	—
304	C₂²×C₄×C₇	—	4	2	no	—
305	C₂²×C₄×C₇	—	4	2	no	—
306	C₂²×C₄×C₇	—	4	2	no	—
307	C₂²×C₄×C₇	—	4	2	no	—
308	C₂²×C₄×C₇	—	4	2	no	—
309	C₂²×C₄×C₇	—	4	2	no	—
310	C₂²×C₄×C₇	—	4	2	no	—
311	C₂²×C₄×C₇	—	4	1	no	—
312	C₂²×C₄×C₇	—	4	2	no	—
313	C₂²×C₄×C₇	—	4	2	no	—
314	C₂²×C₄×C₇	—	4	2	no	—
315	C₂²×C₄×C₇	—	4	2	no	—
316	C₂²×C₄×C₇	—	4	2	no	—
317	C₂²×C₄×C₇	—	4	2	no	—
318	C₂²×C₄×C₇	—	4	2	no	—
319	C₂²×C₄×C₇	—	4	2	no	—
320	C₂²×C₄×C₇	—	4	2	no	—
321	C₂²×C₄×C₇	—	4	2	no	—
322	C₂²×C₄×C₇	—	4	16	no	—
323	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
324	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	complemented
325	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
339	C₇×C₄⋊C₄	—	4	1	no	—
340	C₇×C₄⋊C₄	—	4	1	no	—
341	C₇×C₄⋊C₄	—	4	2	no	—
342	C₇×C₄⋊C₄	—	4	2	no	—
343	C₇×C₄⋊C₄	—	4	2	no	—
344	C₇×C₄⋊C₄	—	4	2	no	—
345	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	complemented
346	C₇×C₂²⋊C₄	—	2	4	no	—
347	C₇×C₂²⋊C₄	—	2	4	no	—
348	C₇×C₂²⋊C₄	—	2	4	no	—
349	C₇×C₂²⋊C₄	—	2	4	no	—
350	C₇×C₂²⋊C₄	—	2	4	no	—
351	C₇×C₂²⋊C₄	—	2	4	no	—
352	C₇×C₂²⋊C₄	—	4	2	no	—
353	C₇×C₂²⋊C₄	—	4	2	no	—
354	C₇×C₂²⋊C₄	—	4	2	no	—
355	C₇×C₂²⋊C₄	—	4	2	no	—
356	C₇×C₂²⋊C₄	—	4	2	no	—
357	C₇×C₂²⋊C₄	—	4	2	no	—
358	C₇×C₂²⋊C₄	—	4	2	no	—
359	C₇×C₂²⋊C₄	—	4	2	no	—
360	C₇×C₂²⋊C₄	—	4	2	no	—
361	C₇×C₂²⋊C₄	—	4	2	no	—
362	C₇×C₂²⋊C₄	—	4	2	no	—
363	C₇×C₂²⋊C₄	—	4	2	no	—
364	C₇×C₂²⋊C₄	—	4	1	no	—
365	C₇×C₂²⋊C₄	—	4	1	no	—
366	C₇×C₂²⋊C₄	—	4	1	no	—
367	C₇×C₂²⋊C₄	—	4	1	no	—
368	C₇×C₂²⋊C₄	—	4	2	no	—
369	C₇×C₂²⋊C₄	—	4	2	no	—
370	C₇×C₂²⋊C₄	—	4	2	no	—
371	C₇×C₂²⋊C₄	—	4	2	no	—
372	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
373	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
374	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
375	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
376	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	complemented
377	C₄²×C₇	—	2	2	no	—
378	C₄²×C₇	—	4	1	no	—
379	C₄²×C₇	—	4	2	no	—
380	C₄²×C₇	—	4	2	no	—
381	C₄²×C₇	—	4	2	no	—
382	C₄²×C₇	—	4	2	no	—
383	C₄²×C₇	C₂²×C₄	1	4	yes	complemented
384	C₂³×D₄	C₂²×C₇	1	2	yes	—
385	C₂³×D₄	C₂²×C₇	1	2	yes	—
386	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic, complemented
387	D₄²	C₄×C₇	1	16	yes	complemented
388	C₂×#127	C₂²×C₇	1	1	yes	characteristic
389	C₂×#121	C₂²×C₇	1	2	yes	—
390	C₂×#121	C₂²×C₇	1	2	yes	—
391	C₂×#120	C₂²×C₇	1	2	yes	—
392	C₂×#120	C₂²×C₇	1	1	yes	characteristic
393	C₂×#120	C₂²×C₇	1	1	yes	characteristic
394	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
395	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
396	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
397	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
398	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
399	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
400	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
401	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
402	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
403	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
404	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
405	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
406	#390	C₂²×C₇	1	1	yes	characteristic, complemented
407	#390	C₂²×C₇	1	2	yes	complemented
408	#390	C₂²×C₇	1	2	yes	complemented
409	#390	C₂²×C₇	1	1	yes	characteristic, complemented
410	#390	C₂²×C₇	1	2	yes	complemented
411	#390	C₂²×C₇	1	2	yes	complemented
412	#388	C₂²×C₇	1	2	yes	complemented
413	#388	C₂²×C₇	1	2	yes	complemented
414	#388	C₂²×C₇	1	2	yes	complemented
415	#388	C₂²×C₇	1	2	yes	complemented
416	#388	C₂²×C₇	1	2	yes	complemented
417	#388	C₂²×C₇	1	2	yes	complemented
418	#388	C₂²×C₇	1	2	yes	complemented
419	#388	C₂²×C₇	1	2	yes	complemented
420	#387	C₂²×C₇	1	2	yes	complemented
421	#387	C₂²×C₇	1	2	yes	complemented
422	#387	C₂²×C₇	1	2	yes	complemented
423	#387	C₂²×C₇	1	2	yes	complemented
424	#386	C₂²×C₇	1	2	yes	—
425	#386	C₂²×C₇	1	2	yes	—
426	#386	C₂²×C₇	1	2	yes	—
427	#386	C₂²×C₇	1	2	yes	—
428	#386	C₂²×C₇	1	2	yes	complemented
429	#386	C₂²×C₇	1	2	yes	complemented
430	#386	C₂²×C₇	1	2	yes	complemented
431	#386	C₂²×C₇	1	2	yes	complemented
432	#386	C₂²×C₇	1	2	yes	complemented
433	#386	C₂²×C₇	1	2	yes	complemented
434	#386	C₂²×C₇	1	2	yes	complemented
435	#386	C₂²×C₇	1	2	yes	complemented
436	#386	C₂²×C₇	1	2	yes	complemented
437	#386	C₂²×C₇	1	1	yes	characteristic, complemented
438	#386	C₂²×C₇	1	2	yes	complemented
439	#386	C₂²×C₇	1	2	yes	complemented
440	#386	C₂²×C₇	1	2	yes	complemented
441	#386	C₂²×C₇	1	2	yes	complemented
442	#386	C₂²×C₇	1	2	yes	complemented
443	#386	C₂²×C₇	1	2	yes	complemented
444	#386	C₂²×C₇	1	2	yes	complemented
445	#386	C₂²×C₇	1	1	yes	characteristic, complemented
446	#386	C₂²×C₇	1	2	yes	complemented
447	#385	C₂²×C₇	1	2	yes	complemented
448	#385	C₂²×C₇	1	2	yes	complemented
449	#385	C₂²×C₇	1	1	yes	characteristic, complemented
450	#385	C₂²×C₇	1	2	yes	complemented
451	#385	C₂²×C₇	1	1	yes	characteristic, complemented
452	#383	C₂²×C₇	1	2	yes	complemented
453	#382	C₂²×C₇	1	1	yes	characteristic, complemented
454	#381	C₂²×C₇	1	2	yes	complemented
455	#381	C₂²×C₇	1	2	yes	complemented
456	#380	C₂²×C₇	1	2	yes	complemented
457	#380	C₂²×C₇	1	2	yes	complemented
458	#379	C₂²×C₇	1	1	yes	characteristic, complemented
459	#379	C₂²×C₇	1	2	yes	complemented
460	#379	C₂²×C₇	1	2	yes	complemented
461	#379	C₂²×C₇	1	1	yes	characteristic, complemented
462	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
463	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
464	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
465	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
466	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
467	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
468	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
469	#376	C₂²×C₇	1	1	yes	characteristic, complemented
470	C₂×#95	C₂²×C₇	1	2	yes	complemented
471	C₂×#95	C₂²×C₇	1	2	yes	complemented
472	C₂³×C₇	—	2	2	no	—
473	C₂³×C₇	—	2	2	no	—
474	C₂³×C₇	—	2	2	no	—
475	C₂³×C₇	—	2	2	no	—
476	C₂³×C₇	—	2	16	no	—
477	C₂³×C₇	—	2	2	no	—
478	C₂³×C₇	—	2	2	no	—
479	C₂³×C₇	—	2	2	no	—
480	C₂³×C₇	—	2	2	no	—
481	C₂³×C₇	—	2	2	no	—
482	C₂³×C₇	—	2	2	no	—
483	C₂³×C₇	—	2	1	no	—
484	C₂³×C₇	—	2	1	no	—
485	C₂³×C₇	—	2	2	no	—
486	C₂³×C₇	—	2	2	no	—
487	C₂³×C₇	—	2	2	no	—
488	C₂³×C₇	—	2	2	no	—
489	C₂³×C₇	—	2	2	no	—
490	C₂³×C₇	—	2	2	no	—
491	C₂³×C₇	—	2	2	no	—
492	C₂³×C₇	—	2	2	no	—
493	C₂³×C₇	—	2	1	no	—
494	C₂³×C₇	—	2	1	no	—
495	C₂³×C₇	—	2	2	no	—
496	C₂³×C₇	—	2	2	no	—
497	C₂³×C₇	—	2	16	no	—
498	C₂³×C₇	—	4	4	no	—
499	C₂³×C₇	—	4	8	no	—
500	C₂³×C₇	—	4	8	no	—
501	C₂³×C₇	—	4	8	no	—
502	C₂³×C₇	—	4	4	no	—
503	C₂³×C₇	—	4	4	no	—
504	C₂³×C₇	—	4	8	no	—
505	C₂³×C₇	—	4	4	no	—
506	C₂³×C₇	—	8	4	no	—
507	C₂³×C₇	—	8	4	no	—
508	C₂³×C₇	—	8	4	no	—
509	C₂³×C₇	—	8	4	no	—
510	C₂³×C₇	—	8	2	no	—
511	C₂³×C₇	—	8	4	no	—
512	C₂³×C₇	—	8	2	no	—
513	C₂³×C₇	C₂³×C₄	1	2	yes	—
514	C₂³×C₇	C₂³×C₄	1	4	yes	—
515	C₂³×C₇	C₂³×C₄	1	2	yes	—
516	C₂³×C₇	C₂³×C₄	1	4	yes	—
517	C₂³×C₇	C₂³×C₄	1	4	yes	—
518	C₂³×C₇	H(5,𝔽₂)	1	4	yes	—
519	C₂³×C₇	H(5,𝔽₂)	1	4	yes	—
520	C₂³×C₇	C₂⁵	1	1	yes	characteristic
521	C₇×D₄	—	2	16	no	—
522	C₇×D₄	—	2	16	no	—
523	C₇×D₄	—	2	16	no	—
524	C₇×D₄	—	4	8	no	—
525	C₇×D₄	—	4	8	no	—
526	C₇×D₄	—	4	8	no	—
527	C₇×D₄	—	4	8	no	—
528	C₇×D₄	—	4	4	no	—
529	C₇×D₄	—	4	4	no	—
530	C₂×C₄×C₇	—	2	1	no	—
531	C₂×C₄×C₇	—	2	2	no	—
532	C₂×C₄×C₇	—	2	2	no	—
533	C₂×C₄×C₇	—	2	2	no	—
534	C₂×C₄×C₇	—	2	2	no	—
535	C₂×C₄×C₇	—	2	2	no	—
536	C₂×C₄×C₇	—	2	2	no	—
537	C₂×C₄×C₇	—	2	2	no	—
538	C₂×C₄×C₇	—	2	1	no	—
539	C₂×C₄×C₇	—	2	1	no	—
540	C₂×C₄×C₇	—	2	2	no	—
541	C₂×C₄×C₇	—	2	2	no	—
542	C₂×C₄×C₇	—	2	2	no	—
543	C₂×C₄×C₇	—	2	2	no	—
544	C₂×C₄×C₇	—	2	2	no	—
545	C₂×C₄×C₇	—	2	2	no	—
546	C₂×C₄×C₇	—	2	2	no	—
547	C₂×C₄×C₇	—	2	2	no	—
548	C₂×C₄×C₇	—	2	2	no	—
549	C₂×C₄×C₇	—	2	2	no	—
550	C₂×C₄×C₇	—	2	2	no	—
551	C₂×C₄×C₇	—	2	2	no	—
552	C₂×C₄×C₇	—	2	2	no	—
553	C₂×C₄×C₇	—	2	1	no	—
554	C₂×C₄×C₇	—	2	2	no	—
555	C₂×C₄×C₇	—	2	2	no	—
556	C₂×C₄×C₇	—	2	2	no	—
557	C₂×C₄×C₇	—	2	2	no	—
558	C₂×C₄×C₇	—	2	2	no	—
559	C₂×C₄×C₇	—	2	1	no	—
560	C₂×C₄×C₇	—	2	2	no	—
561	C₂×C₄×C₇	—	2	2	no	—
562	C₂×C₄×C₇	—	2	2	no	—
563	C₂×C₄×C₇	—	4	8	no	—
564	C₂×C₄×C₇	—	4	8	no	—
565	C₂×C₄×C₇	—	4	8	no	—
566	C₂×C₄×C₇	—	4	4	no	—
567	C₂×C₄×C₇	—	4	8	no	—
568	C₂×C₄×C₇	—	4	4	no	—
569	C₂×C₄×C₇	—	8	2	no	—
570	C₂×C₄×C₇	—	8	4	no	—
571	C₂×C₄×C₇	—	8	4	no	—
572	C₂×C₄×C₇	—	8	4	no	—
573	C₂×C₄×C₇	—	8	4	no	—
574	C₂×C₄×C₇	—	8	2	no	—
575	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
576	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
577	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
578	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
579	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
580	C₂⁵	C₂³×C₇	1	1	yes	characteristic
581	C₂⁵	C₂³×C₇	1	2	yes	—
582	C₂⁵	C₂³×C₇	1	1	yes	characteristic
583	C₂²×D₄	—	4	4	no	—
584	C₂²×D₄	—	4	4	no	—
585	C₂²×D₄	—	4	4	no	—
586	C₂²×D₄	—	4	4	no	—
587	C₂²×D₄	C₂×C₄×C₇	1	16	yes	complemented
588	C₂²×D₄	C₂×C₄×C₇	1	16	yes	complemented
589	C₂²×D₄	C₂³×C₇	1	2	yes	—
590	C₂²×D₄	C₂³×C₇	1	2	yes	—
591	C₂²×D₄	C₂³×C₇	1	2	yes	—
592	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
593	C₂²×D₄	C₂³×C₇	1	2	yes	—
594	C₂²×D₄	C₂³×C₇	1	2	yes	—
595	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
596	C₂²×D₄	C₂³×C₇	1	2	yes	—
597	C₂²×D₄	C₂³×C₇	1	2	yes	—
598	C₂³×C₄	—	4	2	no	—
599	C₂³×C₄	—	4	4	no	—
600	C₂³×C₄	C₂³×C₇	1	2	yes	—
601	C₂³×C₄	C₂³×C₇	1	2	yes	—
602	C₂³×C₄	C₂³×C₇	1	2	yes	—
603	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
604	C₂³×C₄	C₂³×C₇	1	2	yes	—
605	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₇	1	2	yes	—
607	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₇	1	2	yes	—
609	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₇	1	2	yes	—
611	C₂³×C₄	C₂³×C₇	1	2	yes	—
612	#127	C₂×C₄×C₇	1	8	yes	complemented
613	#121	C₂×C₄×C₇	1	16	yes	complemented
614	#121	C₂×C₄×C₇	1	16	yes	complemented
615	#120	C₂×C₄×C₇	1	8	yes	complemented
616	#120	C₂×C₄×C₇	1	16	yes	complemented
617	#120	C₂×C₄×C₇	1	8	yes	complemented
618	C₄×D₄	—	4	2	no	—
619	C₄×D₄	—	4	2	no	—
620	C₄×D₄	—	4	4	no	—
621	C₄×D₄	—	4	4	no	—
622	C₄×D₄	—	4	4	no	—
623	C₄×D₄	—	4	4	no	—
624	C₄×D₄	C₂×C₄×C₇	1	16	yes	complemented
625	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
632	C₂×C₂²⋊C₄	—	4	2	no	—
633	C₂×C₂²⋊C₄	—	4	4	no	—
634	C₂×C₂²⋊C₄	—	4	4	no	—
635	C₂×C₂²⋊C₄	—	4	4	no	—
636	C₂×C₂²⋊C₄	—	4	4	no	—
637	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
662	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
663	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₇	1	2	yes	—
670	C₂×C₄²	C₂³×C₇	1	2	yes	—
671	C₂×C₄²	C₂³×C₇	1	2	yes	—
672	C₂×C₄²	C₂³×C₇	1	2	yes	—
673	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
675	#95	C₂³×C₇	1	2	yes	—
676	#95	C₂³×C₇	1	2	yes	—
677	#95	C₂³×C₇	1	2	yes	—
678	#95	C₂³×C₇	1	2	yes	—
679	#95	C₂³×C₇	1	2	yes	—
680	#95	C₂³×C₇	1	2	yes	—
681	#95	C₂³×C₇	1	2	yes	—
682	#95	C₂³×C₇	1	2	yes	—
683	#95	C₂³×C₇	1	2	yes	—
684	#95	C₂³×C₇	1	2	yes	—
685	#95	C₂³×C₇	1	2	yes	—
686	#95	C₂³×C₇	1	2	yes	—
687	#95	C₂³×C₇	1	2	yes	—
688	#95	C₂³×C₇	1	2	yes	—
689	#95	C₂³×C₇	1	2	yes	—
690	#95	C₂³×C₇	1	2	yes	—
691	#95	C₂³×C₇	1	2	yes	—
692	#95	C₂³×C₇	1	2	yes	—
693	C₂²×C₇	—	2	4	no	—
694	C₂²×C₇	—	2	4	no	—
695	C₂²×C₇	—	2	4	no	—
696	C₂²×C₇	—	2	4	no	—
697	C₂²×C₇	—	2	4	no	—
698	C₂²×C₇	—	2	4	no	—
699	C₂²×C₇	—	2	4	no	—
700	C₂²×C₇	—	2	4	no	—
701	C₂²×C₇	—	2	4	no	—
702	C₂²×C₇	—	2	4	no	—
703	C₂²×C₇	—	2	4	no	—
704	C₂²×C₇	—	2	4	no	—
705	C₂²×C₇	—	2	2	no	—
706	C₂²×C₇	—	2	2	no	—
707	C₂²×C₇	—	2	4	no	—
708	C₂²×C₇	—	2	4	no	—
709	C₂²×C₇	—	4	16	no	—
710	C₂²×C₇	—	4	1	no	—
711	C₂²×C₇	—	4	1	no	—
712	C₂²×C₇	—	4	2	no	—
713	C₂²×C₇	—	4	2	no	—
714	C₂²×C₇	—	4	2	no	—
715	C₂²×C₇	—	4	2	no	—
716	C₂²×C₇	—	4	2	no	—
717	C₂²×C₇	—	4	2	no	—
718	C₂²×C₇	—	4	2	no	—
719	C₂²×C₇	—	4	2	no	—
720	C₂²×C₇	—	4	2	no	—
721	C₂²×C₇	—	4	1	no	—
722	C₂²×C₇	—	4	1	no	—
723	C₂²×C₇	—	4	2	no	—
724	C₂²×C₇	—	8	16	no	—
725	C₂²×C₇	—	8	8	no	—
726	C₂²×C₇	#518	1	8	yes	—
727	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
728	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
729	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
730	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
731	C₂²×C₇	#585	1	1	yes	characteristic
732	C₄×C₇	—	2	4	no	—
733	C₄×C₇	—	2	4	no	—
734	C₄×C₇	—	2	4	no	—
735	C₄×C₇	—	2	2	no	—
736	C₄×C₇	—	2	2	no	—
737	C₄×C₇	—	4	2	no	—
738	C₄×C₇	—	4	1	no	—
739	C₄×C₇	—	4	1	no	—
740	C₄×C₇	—	4	2	no	—
741	C₄×C₇	—	4	2	no	—
742	C₄×C₇	—	4	2	no	—
743	C₄×C₇	—	4	1	no	—
744	C₄×C₇	—	4	2	no	—
745	C₄×C₇	—	4	2	no	—
746	C₂⁴	—	2	4	no	—
747	C₂⁴	—	2	4	no	—
748	C₂⁴	—	2	4	no	—
749	C₂⁴	—	2	4	no	—
750	C₂⁴	—	4	1	no	—
751	C₂⁴	—	4	1	no	—
752	C₂⁴	—	4	2	no	—
753	C₂⁴	—	4	1	no	—
754	C₂⁴	—	4	2	no	—
755	C₂⁴	—	4	2	no	—
756	C₂⁴	—	4	2	no	—
757	C₂⁴	—	4	2	no	—
758	C₂⁴	—	4	2	no	—
759	C₂⁴	—	4	1	no	—
760	C₂⁴	C₂²×C₄×C₇	1	4	yes	—
761	C₂⁴	C₂²×C₄×C₇	1	8	yes	—
762	C₂⁴	C₂²×C₄×C₇	1	4	yes	complemented
763	C₂⁴	C₂⁴×C₇	1	2	yes	—
764	C₂⁴	C₂⁴×C₇	1	2	yes	—
765	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
766	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
767	C₂⁴	C₂⁴×C₇	1	2	yes	—
768	C₂×D₄	—	2	4	no	—
769	C₂×D₄	—	2	4	no	—
770	C₂×D₄	—	2	4	no	—
771	C₂×D₄	—	2	4	no	—
772	C₂×D₄	—	2	4	no	—
773	C₂×D₄	—	2	4	no	—
774	C₂×D₄	—	4	1	no	—
775	C₂×D₄	—	4	1	no	—
776	C₂×D₄	—	4	2	no	—
777	C₂×D₄	—	4	2	no	—
778	C₂×D₄	—	4	2	no	—
779	C₂×D₄	—	4	2	no	—
780	C₂×D₄	—	4	2	no	—
781	C₂×D₄	—	4	2	no	—
782	C₂×D₄	—	4	2	no	—
783	C₂×D₄	—	4	2	no	—
784	C₂×D₄	—	4	1	no	—
785	C₂×D₄	—	4	1	no	—
786	C₂×D₄	—	4	32	no	—
787	C₂×D₄	—	4	32	no	—
788	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
789	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
790	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
791	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
792	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
793	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
794	C₂×D₄	C₂²×C₄×C₇	1	4	yes	complemented
795	C₂×D₄	C₂²×C₄×C₇	1	8	yes	complemented
796	C₂×D₄	C₂²×C₄×C₇	1	8	yes	complemented
797	C₂²×C₄	—	2	4	no	—
798	C₂²×C₄	—	2	4	no	—
799	C₂²×C₄	—	2	4	no	—
800	C₂²×C₄	—	2	4	no	—
801	C₂²×C₄	—	2	4	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	4	2	no	—
805	C₂²×C₄	—	4	2	no	—
806	C₂²×C₄	—	4	1	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	1	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	—	4	2	no	—
820	C₂²×C₄	—	4	2	no	—
821	C₂²×C₄	—	4	2	no	—
822	C₂²×C₄	—	4	2	no	—
823	C₂²×C₄	—	4	2	no	—
824	C₂²×C₄	—	4	2	no	—
825	C₂²×C₄	—	4	2	no	—
826	C₂²×C₄	—	4	2	no	—
827	C₂²×C₄	—	4	16	no	—
828	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
829	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	complemented
830	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
831	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
838	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
840	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
844	C₄⋊C₄	—	4	1	no	—
845	C₄⋊C₄	—	4	1	no	—
846	C₄⋊C₄	—	4	2	no	—
847	C₄⋊C₄	—	4	2	no	—
848	C₄⋊C₄	—	4	2	no	—
849	C₄⋊C₄	—	4	2	no	—
850	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	complemented
851	C₂²⋊C₄	—	2	4	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	2	4	no	—
854	C₂²⋊C₄	—	2	4	no	—
855	C₂²⋊C₄	—	2	4	no	—
856	C₂²⋊C₄	—	2	4	no	—
857	C₂²⋊C₄	—	4	2	no	—
858	C₂²⋊C₄	—	4	2	no	—
859	C₂²⋊C₄	—	4	2	no	—
860	C₂²⋊C₄	—	4	2	no	—
861	C₂²⋊C₄	—	4	2	no	—
862	C₂²⋊C₄	—	4	2	no	—
863	C₂²⋊C₄	—	4	2	no	—
864	C₂²⋊C₄	—	4	2	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	—	4	2	no	—
868	C₂²⋊C₄	—	4	1	no	—
869	C₂²⋊C₄	—	4	1	no	—
870	C₂²⋊C₄	—	4	2	no	—
871	C₂²⋊C₄	—	4	2	no	—
872	C₂²⋊C₄	—	4	2	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	1	no	—
876	C₂²⋊C₄	—	4	1	no	—
877	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
878	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
879	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	complemented
880	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	complemented
881	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	complemented
882	C₄²	—	2	2	no	—
883	C₄²	—	4	2	no	—
884	C₄²	—	4	2	no	—
885	C₄²	—	4	2	no	—
886	C₄²	—	4	2	no	—
887	C₄²	—	4	1	no	—
888	C₄²	C₂²×C₄×C₇	1	4	yes	complemented
889	C₂×C₇	—	2	8	no	—
890	C₂×C₇	—	4	2	no	—
891	C₂×C₇	—	4	2	no	—
892	C₂×C₇	—	4	4	no	—
893	C₂×C₇	—	4	4	no	—
894	C₂×C₇	C₂×#518	1	2	yes	—
895	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
896	C₂×C₇	#3532	1	1	yes	characteristic
897	C₂×C₇	#3534	1	2	yes	—
898	C₂×C₇	#3537	1	1	yes	characteristic
899	C₂³	—	2	2	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	2	no	—
912	C₂³	—	2	2	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	2	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	1	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	2	2	no	—
923	C₂³	—	2	16	no	—
924	C₂³	—	2	16	no	—
925	C₂³	—	4	4	no	—
926	C₂³	—	4	8	no	—
927	C₂³	—	4	8	no	—
928	C₂³	—	4	8	no	—
929	C₂³	—	4	4	no	—
930	C₂³	—	4	4	no	—
931	C₂³	—	4	8	no	—
932	C₂³	—	4	4	no	—
933	C₂³	—	8	4	no	—
934	C₂³	—	8	4	no	—
935	C₂³	—	8	4	no	—
936	C₂³	—	8	4	no	—
937	C₂³	—	8	2	no	—
938	C₂³	—	8	4	no	—
939	C₂³	—	8	2	no	—
940	C₂³	C₂³×C₄×C₇	1	2	yes	—
941	C₂³	C₂³×C₄×C₇	1	4	yes	—
942	C₂³	C₂³×C₄×C₇	1	2	yes	—
943	C₂³	C₂³×C₄×C₇	1	4	yes	—
944	C₂³	C₂³×C₄×C₇	1	4	yes	—
945	C₂³	C₇×H(5,𝔽₂)	1	4	yes	—
946	C₂³	C₇×H(5,𝔽₂)	1	4	yes	—
947	C₂³	C₂⁵×C₇	1	1	yes	characteristic
948	D₄	—	2	16	no	—
949	D₄	—	2	16	no	—
950	D₄	—	2	16	no	—
951	D₄	—	4	8	no	—
952	D₄	—	4	8	no	—
953	D₄	—	4	8	no	—
954	D₄	—	4	8	no	—
955	D₄	—	4	4	no	—
956	D₄	—	4	4	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	4	8	no	—
991	C₂×C₄	—	4	8	no	—
992	C₂×C₄	—	4	8	no	—
993	C₂×C₄	—	4	4	no	—
994	C₂×C₄	—	4	8	no	—
995	C₂×C₄	—	4	4	no	—
996	C₂×C₄	—	8	2	no	—
997	C₂×C₄	—	8	4	no	—
998	C₂×C₄	—	8	4	no	—
999	C₂×C₄	—	8	4	no	—
1000	C₂×C₄	—	8	4	no	—
1001	C₂×C₄	—	8	2	no	—
1002	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1003	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
1004	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
1005	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
1006	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1007	C₇	#34468	1	1	yes	characteristic, direct product factor, Sylow
1008	C₂²	—	2	4	no	—
1009	C₂²	—	2	4	no	—
1010	C₂²	—	2	4	no	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	2	4	no	—
1013	C₂²	—	2	4	no	—
1014	C₂²	—	2	4	no	—
1015	C₂²	—	2	4	no	—
1016	C₂²	—	2	4	no	—
1017	C₂²	—	2	4	no	—
1018	C₂²	—	2	4	no	—
1019	C₂²	—	2	4	no	—
1020	C₂²	—	2	2	no	—
1021	C₂²	—	2	2	no	—
1022	C₂²	—	2	4	no	—
1023	C₂²	—	2	4	no	—
1024	C₂²	—	4	16	no	—
1025	C₂²	—	4	1	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	2	no	—
1028	C₂²	—	4	2	no	—
1029	C₂²	—	4	2	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	—	4	2	no	—
1033	C₂²	—	4	2	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	4	2	no	—
1036	C₂²	—	4	1	no	—
1037	C₂²	—	4	1	no	—
1038	C₂²	—	4	2	no	—
1039	C₂²	—	8	16	no	—
1040	C₂²	—	8	8	no	—
1041	C₂²	C₇×#518	1	8	yes	—
1042	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
1043	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
1044	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
1045	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1046	C₂²	C₇×#585	1	1	yes	characteristic
1047	C₄	—	2	4	no	—
1048	C₄	—	2	4	no	—
1049	C₄	—	2	4	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	2	2	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	2	no	—
1056	C₄	—	4	2	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	1	no	—
1059	C₄	—	4	2	no	—
1060	C₄	—	4	2	no	—
1061	C₂	—	2	8	no	—
1062	C₂	—	4	2	no	—
1063	C₂	—	4	4	no	—
1064	C₂	—	4	2	no	—
1065	C₂	—	4	4	no	—
1066	C₂	C₂×C₇×#518	1	2	yes	—
1067	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1068	C₂	C₇×#3532	1	1	yes	characteristic
1069	C₂	C₇×#3534	1	2	yes	—
1070	C₂	C₇×#3537	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂×C₇×D₄²	C₂
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×#2380	C₂	semidirect
3. C₇×#2377	C₂	semidirect
4. C₇×#2375	C₂	semidirect
5. C₇×#2364	C₂	semidirect
6. C₇×#2358	C₂	semidirect
7. C₇×#2358	C₂	semidirect
8. C₇×#2353	C₂	semidirect
9. C₇×D₄×C₂²⋊C₄	C₂	semidirect
10. C₇×D₄×C₂²⋊C₄	C₂	semidirect
11. C₇×#2333	C₂	semidirect
12. C₇×#2328	C₂	semidirect
13. C₇×#2325	C₂	semidirect
14. C₇×#2321	C₂	semidirect
15. C₇×#2321	C₂	semidirect
16. C₇×#2318	C₂	semidirect
17. C₇×#2308	C₂	semidirect
18. C₄×C₇×#120	C₂	semidirect
19. C₂×C₇×#386	C₂	semidirect
22. C₂⁴×C₄×C₇	C₂²	semidirect
23. C₇×D₄²	C₄	semidirect
31. C₂×C₄×C₇×D₄	C₂²	semidirect
32. C₂×C₄×C₇×D₄	C₂²	semidirect
33. C₂×C₄×C₇×D₄	C₂²	semidirect
34. C₂×C₄×C₇×D₄	C₂²	semidirect
35. C₂×C₄×C₇×D₄	C₂²	semidirect
36. C₂×C₄×C₇×D₄	C₂²	semidirect
37. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
38. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
39. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
40. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
41. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
42. C₇×#390	C₂²	semidirect
43. C₇×#390	C₂²	semidirect
44. C₇×#390	C₂²	semidirect
45. C₇×#390	C₂²	semidirect
46. C₇×#390	C₂²	semidirect
47. C₇×#390	C₂²	semidirect
48. C₇×#388	C₂²	semidirect
49. C₇×#388	C₂²	semidirect
50. C₇×#388	C₂²	semidirect
51. C₇×#388	C₂²	semidirect
52. C₇×#388	C₂²	semidirect
53. C₇×#388	C₂²	semidirect
54. C₇×#388	C₂²	semidirect
55. C₇×#388	C₂²	semidirect
56. C₇×#387	C₂²	semidirect
57. C₇×#387	C₂²	semidirect
58. C₇×#387	C₂²	semidirect
59. C₇×#387	C₂²	semidirect
64. C₇×#386	C₂²	semidirect
65. C₇×#386	C₂²	semidirect
66. C₇×#386	C₂²	semidirect
67. C₇×#386	C₂²	semidirect
68. C₇×#386	C₂²	semidirect
69. C₇×#386	C₂²	semidirect
70. C₇×#386	C₂²	semidirect
71. C₇×#386	C₂²	semidirect
72. C₇×#386	C₂²	semidirect
73. C₇×#386	C₂²	semidirect
74. C₇×#386	C₂²	semidirect
75. C₇×#386	C₂²	semidirect
76. C₇×#386	C₂²	semidirect
77. C₇×#386	C₂²	semidirect
78. C₇×#386	C₂²	semidirect
79. C₇×#386	C₂²	semidirect
80. C₇×#386	C₂²	semidirect
81. C₇×#386	C₂²	semidirect
82. C₇×#386	C₂²	semidirect
83. C₇×#385	C₂²	semidirect
84. C₇×#385	C₂²	semidirect
85. C₇×#385	C₂²	semidirect
86. C₇×#385	C₂²	semidirect
87. C₇×#385	C₂²	semidirect
88. C₇×#383	C₂²	semidirect
89. C₇×#382	C₂²	semidirect
90. C₇×#381	C₂²	semidirect
91. C₇×#381	C₂²	semidirect
92. C₇×#380	C₂²	semidirect
93. C₇×#380	C₂²	semidirect
94. C₇×#379	C₂²	semidirect
95. C₇×#379	C₂²	semidirect
96. C₇×#379	C₂²	semidirect
97. C₇×#379	C₂²	semidirect
98. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
99. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
100. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
101. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
102. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
103. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
104. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
105. C₇×#376	C₂²	semidirect
106. C₂×C₇×#95	C₂²	semidirect
107. C₂×C₇×#95	C₂²	semidirect
108. #34468	C₇	direct (N × H)
116. C₂²×C₇×D₄	C₂×C₄	semidirect
117. C₂²×C₇×D₄	C₂×C₄	semidirect
141. C₇×#127	C₂×C₄	semidirect
142. C₇×#121	C₂×C₄	semidirect
143. C₇×#121	C₂×C₄	semidirect
144. C₇×#120	C₂×C₄	semidirect
145. C₇×#120	C₂×C₄	semidirect
146. C₇×#120	C₂×C₄	semidirect
153. C₄×C₇×D₄	C₂×C₄	semidirect
223. #2380	C₂×C₇	semidirect
224. #2377	C₂×C₇	semidirect
225. #2375	C₂×C₇	semidirect
226. #2364	C₂×C₇	semidirect
227. #2358	C₂×C₇	semidirect
228. #2358	C₂×C₇	semidirect
229. #2353	C₂×C₇	semidirect
230. D₄×C₂²⋊C₄	C₂×C₇	semidirect
231. D₄×C₂²⋊C₄	C₂×C₇	semidirect
232. #2333	C₂×C₇	semidirect
233. #2328	C₂×C₇	semidirect
234. #2325	C₂×C₇	semidirect
235. #2321	C₂×C₇	semidirect
236. #2321	C₂×C₇	semidirect
237. #2318	C₂×C₇	semidirect
238. #2308	C₂×C₇	semidirect
239. C₄×#120	C₂×C₇	semidirect
240. C₂×#386	C₂×C₇	semidirect
257. C₂⁴×C₇	C₂²×C₄	semidirect
289. C₂×C₇×D₄	C₂²×C₄	semidirect
290. C₂×C₇×D₄	C₂²×C₄	semidirect
291. C₂×C₇×D₄	C₂²×C₄	semidirect
324. C₂²×C₄×C₇	C₂²×C₄	semidirect
345. C₇×C₄⋊C₄	C₂²×C₄	semidirect
374. C₇×C₂²⋊C₄	C₂²×C₄	semidirect
375. C₇×C₂²⋊C₄	C₂²×C₄	semidirect
376. C₇×C₂²⋊C₄	C₂²×C₄	semidirect
383. C₄²×C₇	C₂²×C₄	semidirect
386. C₂⁴×C₄	C₂²×C₇	semidirect
387. D₄²	C₄×C₇	semidirect
395. C₂×C₄×D₄	C₂²×C₇	semidirect
396. C₂×C₄×D₄	C₂²×C₇	semidirect
397. C₂×C₄×D₄	C₂²×C₇	semidirect
398. C₂×C₄×D₄	C₂²×C₇	semidirect
399. C₂×C₄×D₄	C₂²×C₇	semidirect
400. C₂×C₄×D₄	C₂²×C₇	semidirect
401. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
402. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
403. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
404. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
405. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
406. #390	C₂²×C₇	semidirect
407. #390	C₂²×C₇	semidirect
408. #390	C₂²×C₇	semidirect
409. #390	C₂²×C₇	semidirect
410. #390	C₂²×C₇	semidirect
411. #390	C₂²×C₇	semidirect
412. #388	C₂²×C₇	semidirect
413. #388	C₂²×C₇	semidirect
414. #388	C₂²×C₇	semidirect
415. #388	C₂²×C₇	semidirect
416. #388	C₂²×C₇	semidirect
417. #388	C₂²×C₇	semidirect
418. #388	C₂²×C₇	semidirect
419. #388	C₂²×C₇	semidirect
420. #387	C₂²×C₇	semidirect
421. #387	C₂²×C₇	semidirect
422. #387	C₂²×C₇	semidirect
423. #387	C₂²×C₇	semidirect
428. #386	C₂²×C₇	semidirect
429. #386	C₂²×C₇	semidirect
430. #386	C₂²×C₇	semidirect
431. #386	C₂²×C₇	semidirect
432. #386	C₂²×C₇	semidirect
433. #386	C₂²×C₇	semidirect
434. #386	C₂²×C₇	semidirect
435. #386	C₂²×C₇	semidirect
436. #386	C₂²×C₇	semidirect
437. #386	C₂²×C₇	semidirect
438. #386	C₂²×C₇	semidirect
439. #386	C₂²×C₇	semidirect
440. #386	C₂²×C₇	semidirect
441. #386	C₂²×C₇	semidirect
442. #386	C₂²×C₇	semidirect
443. #386	C₂²×C₇	semidirect
444. #386	C₂²×C₇	semidirect
445. #386	C₂²×C₇	semidirect
446. #386	C₂²×C₇	semidirect
447. #385	C₂²×C₇	semidirect
448. #385	C₂²×C₇	semidirect
449. #385	C₂²×C₇	semidirect
450. #385	C₂²×C₇	semidirect
451. #385	C₂²×C₇	semidirect
452. #383	C₂²×C₇	semidirect
453. #382	C₂²×C₇	semidirect
454. #381	C₂²×C₇	semidirect
455. #381	C₂²×C₇	semidirect
456. #380	C₂²×C₇	semidirect
457. #380	C₂²×C₇	semidirect
458. #379	C₂²×C₇	semidirect
459. #379	C₂²×C₇	semidirect
460. #379	C₂²×C₇	semidirect
461. #379	C₂²×C₇	semidirect
462. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
463. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
464. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
465. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
466. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
467. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
468. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
469. #376	C₂²×C₇	semidirect
470. C₂×#95	C₂²×C₇	semidirect
471. C₂×#95	C₂²×C₇	semidirect
587. C₂²×D₄	C₂×C₄×C₇	semidirect
588. C₂²×D₄	C₂×C₄×C₇	semidirect
612. #127	C₂×C₄×C₇	semidirect
613. #121	C₂×C₄×C₇	semidirect
614. #121	C₂×C₄×C₇	semidirect
615. #120	C₂×C₄×C₇	semidirect
616. #120	C₂×C₄×C₇	semidirect
617. #120	C₂×C₄×C₇	semidirect
624. C₄×D₄	C₂×C₄×C₇	semidirect
762. C₂⁴	C₂²×C₄×C₇	semidirect
794. C₂×D₄	C₂²×C₄×C₇	semidirect
795. C₂×D₄	C₂²×C₄×C₇	semidirect
796. C₂×D₄	C₂²×C₄×C₇	semidirect
829. C₂²×C₄	C₂²×C₄×C₇	semidirect
850. C₄⋊C₄	C₂²×C₄×C₇	semidirect
879. C₂²⋊C₄	C₂²×C₄×C₇	semidirect
880. C₂²⋊C₄	C₂²×C₄×C₇	semidirect
881. C₂²⋊C₄	C₂²×C₄×C₇	semidirect
888. C₄²	C₂²×C₄×C₇	semidirect
1007. C₇	#34468	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×D₄²	2
C₇×#2380	2
C₇×#2377	2
C₇×#2375	2
C₇×#2364	2
C₇×#2358	2
C₇×#2353	2
C₇×D₄×C₂²⋊C₄	2
C₇×#2333	2
C₇×#2328	2
C₇×#2325	2
C₇×#2321	2
C₇×#2318	2
C₇×#2308	2
C₄×C₇×#120	2
C₂×C₇×#386	2
#34468	7

Subgroups — C7×#34468 #13211684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34468 #13211684