Subgroups — C₂×C₇×#3264 #13238238

Order 1792.

3366 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#546	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3264	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₇×#496	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#469	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#465	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#463	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#450	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#447	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#447	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#442	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₇×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂³×C₇×D₄	—	2	1	no	—
19	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
20	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₇×AGL(1,ℤ/8)	—	2	8	no	—
23	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
24	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₇×D₈	—	2	8	no	—
28	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
29	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
30	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₇×D₈	C₂²	1	8	yes	complemented
35	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
37	C₇×#546	—	2	4	no	—
38	C₇×#546	C₂²	1	8	yes	complemented
39	C₇×D₄²	—	2	4	no	—
40	C₇×D₄²	C₂²	1	8	yes	complemented
41	C₂×C₇×#127	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₇×#123	—	2	1	no	—
44	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₇×#121	—	2	1	no	—
46	C₂×C₇×#121	—	2	1	no	—
47	C₂×C₇×#121	C₂²	1	1	yes	characteristic
48	C₂×C₇×#121	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₇×#121	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₇×#120	—	2	1	no	—
51	C₂×C₇×#120	—	2	1	no	—
52	C₂×C₇×#120	—	2	1	no	—
53	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
56	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
57	C₇×#496	C₂²	1	8	yes	complemented
58	C₇×#469	C₂²	1	8	yes	complemented
59	C₇×#465	C₂²	1	8	yes	complemented
60	C₇×#463	C₂²	1	8	yes	complemented
61	C₇×#459	C₂²	1	8	yes	complemented
62	C₇×#450	C₂²	1	8	yes	complemented
63	C₇×#449	C₂²	1	8	yes	complemented
64	C₇×#447	C₂²	1	8	yes	complemented
65	C₇×#447	C₂²	1	8	yes	complemented
66	C₇×#442	C₂²	1	8	yes	complemented
67	C₇×#435	C₂²	1	8	yes	complemented
68	C₂×C₇×#106	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
79	C₂×#3264	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂⁵×C₇	—	2	1	no	—
81	C₂⁵×C₇	—	2	1	no	—
82	C₂⁵×C₇	—	2	1	no	—
83	C₂×C₇×#41	—	2	2	no	—
84	C₂×C₇×#41	—	2	4	no	—
85	C₂×C₇×#41	—	4	2	no	—
86	C₂×C₇×#41	C₂³	1	4	yes	complemented
87	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
88	C₂²×C₇×D₄	—	2	4	no	—
89	C₂²×C₇×D₄	—	2	4	no	—
90	C₂²×C₇×D₄	—	2	4	no	—
91	C₂²×C₇×D₄	—	2	1	no	—
92	C₂²×C₇×D₄	—	2	1	no	—
93	C₂²×C₇×D₄	—	2	1	no	—
94	C₂²×C₇×D₄	—	2	1	no	—
95	C₂²×C₇×D₄	—	2	8	no	—
96	C₂²×C₇×D₄	—	2	1	no	—
97	C₂²×C₇×D₄	—	2	1	no	—
98	C₂²×C₇×D₄	—	2	2	no	—
99	C₂²×C₇×D₄	—	2	1	no	—
100	C₂²×C₇×D₄	—	2	1	no	—
101	C₂²×C₇×D₄	—	2	2	no	—
102	C₂²×C₇×D₄	—	2	2	no	—
103	C₂²×C₇×D₄	—	2	1	no	—
104	C₂²×C₇×D₄	—	4	2	no	—
105	C₂²×C₇×D₄	—	4	2	no	—
106	C₂²×C₇×D₄	—	4	2	no	—
107	C₂²×C₇×D₄	—	4	8	no	—
108	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
109	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
110	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
111	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
112	C₂²×C₇×D₄	C₂³	1	4	yes	—
113	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
114	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
115	C₂²×C₇×D₄	C₂³	1	4	yes	complemented
116	C₂²×C₇×D₄	C₂³	1	4	yes	complemented
117	C₂³×C₄×C₇	—	2	1	no	—
118	C₂³×C₄×C₇	—	2	1	no	—
119	C₂³×C₄×C₇	—	2	1	no	—
120	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
122	C₇×AGL(1,ℤ/8)	—	2	32	no	—
123	C₂×C₇×SD₁₆	—	2	4	no	—
124	C₂×C₇×SD₁₆	—	2	4	no	—
125	C₂×C₇×SD₁₆	—	4	2	no	—
126	C₂×C₇×SD₁₆	C₂³	1	4	yes	complemented
127	C₂×C₇×SD₁₆	C₂³	1	4	yes	complemented
128	C₂×C₇×SD₁₆	C₂³	1	4	yes	complemented
129	C₂×C₇×D₈	—	2	4	no	—
130	C₂×C₇×D₈	—	2	4	no	—
131	C₂×C₇×D₈	—	2	4	no	—
132	C₂×C₇×D₈	—	2	32	no	—
133	C₂×C₇×D₈	—	2	4	no	—
134	C₂×C₇×D₈	—	4	2	no	—
135	C₂×C₇×D₈	D₄	1	8	yes	complemented
136	C₂×C₇×D₈	C₂³	1	4	yes	—
137	C₂×C₇×D₈	C₂³	1	4	yes	—
138	C₂×C₇×D₈	C₂³	1	4	yes	complemented
139	C₂×C₇×D₈	C₂³	1	4	yes	complemented
140	C₂×C₇×D₈	C₂³	1	4	yes	complemented
141	C₂×C₇×D₈	C₂³	1	4	yes	complemented
142	C₂×C₇×M₁₆	—	2	4	no	—
143	C₂×C₇×M₁₆	C₂³	1	4	yes	complemented
144	C₂²×C₇×C₈	—	2	4	no	—
145	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
146	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
147	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
148	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
149	C₂²×C₇×C₈	C₂³	1	4	yes	complemented
150	C₇×#127	—	2	2	no	—
151	C₇×#127	C₂³	1	4	yes	complemented
152	C₇×#124	—	2	2	no	—
153	C₇×#124	C₂³	1	4	yes	complemented
154	C₇×#123	—	2	8	no	—
155	C₇×C₂²⋊Q₈	—	2	2	no	—
156	C₇×C₂²⋊Q₈	C₂³	1	4	yes	complemented
157	C₇×#121	—	2	2	no	—
158	C₇×#121	—	2	2	no	—
159	C₇×#121	—	2	2	no	—
160	C₇×#121	—	2	8	no	—
161	C₇×#121	—	2	8	no	—
162	C₇×#121	C₂³	1	4	yes	—
163	C₇×#121	C₂³	1	4	yes	complemented
164	C₇×#121	C₂³	1	4	yes	complemented
165	C₇×#120	—	2	8	no	—
166	C₇×#120	—	2	8	no	—
167	C₇×#120	—	2	8	no	—
168	C₄×C₇×D₄	—	2	2	no	—
169	C₄×C₇×D₄	—	2	2	no	—
170	C₄×C₇×D₄	D₄	1	4	yes	—
171	C₄×C₇×D₄	C₂³	1	4	yes	—
172	C₄×C₇×D₄	C₂³	1	4	yes	complemented
173	C₄×C₇×D₄	C₂³	1	4	yes	complemented
174	C₂×C₇×C₄⋊C₄	—	2	1	no	—
175	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
176	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
179	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
180	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
181	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
184	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
185	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
186	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
187	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
188	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
190	C₇×#106	C₂³	1	4	yes	complemented
191	C₇×C₄⋊C₈	C₂³	1	4	yes	complemented
192	C₇×#103	C₂³	1	4	yes	complemented
193	C₇×#102	C₂³	1	4	yes	complemented
194	C₇×#102	C₂³	1	4	yes	complemented
195	C₇×#102	C₂³	1	4	yes	complemented
196	C₇×#102	C₂³	1	4	yes	complemented
197	C₇×#102	C₂³	1	4	yes	complemented
198	C₇×C₂²⋊C₈	C₂³	1	4	yes	complemented
199	C₇×C₂²⋊C₈	C₂³	1	4	yes	complemented
200	C₇×#97	C₂³	1	4	yes	complemented
201	C₂²×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic, complemented
202	C₂³×D₈	C₂×C₇	1	1	yes	characteristic, complemented
203	C₂×#546	C₂×C₇	1	1	yes	characteristic, complemented
204	C₂×D₄²	C₂×C₇	1	1	yes	characteristic, complemented
205	#3264	C₂×C₇	1	16	yes	direct product factor
206	C₂×#496	C₂×C₇	1	1	yes	characteristic, complemented
207	C₂×#469	C₂×C₇	1	1	yes	characteristic, complemented
208	C₂×#465	C₂×C₇	1	1	yes	characteristic, complemented
209	C₂×#463	C₂×C₇	1	1	yes	characteristic, complemented
210	C₂×#459	C₂×C₇	1	1	yes	characteristic, complemented
211	C₂×#449	C₂×C₇	1	1	yes	characteristic, complemented
212	C₂×#450	C₂×C₇	1	1	yes	characteristic, complemented
213	C₂×#447	C₂×C₇	1	1	yes	characteristic, complemented
214	C₂×#447	C₂×C₇	1	1	yes	characteristic, complemented
215	C₂×#442	C₂×C₇	1	1	yes	characteristic, complemented
216	C₂×#435	C₂×C₇	1	1	yes	characteristic, complemented
217	C₂⁴×C₇	—	2	1	no	—
218	C₂⁴×C₇	—	2	1	no	—
219	C₂⁴×C₇	—	2	1	no	—
220	C₂⁴×C₇	—	2	1	no	—
221	C₂⁴×C₇	—	2	1	no	—
222	C₂⁴×C₇	—	2	4	no	—
223	C₂⁴×C₇	—	2	4	no	—
224	C₂⁴×C₇	—	2	4	no	—
225	C₂⁴×C₇	—	4	4	no	—
226	C₂⁴×C₇	—	4	4	no	—
227	C₂⁴×C₇	—	4	4	no	—
228	C₂⁴×C₇	—	4	4	no	—
229	C₂⁴×C₇	—	4	4	no	—
230	C₂⁴×C₇	—	4	4	no	—
231	C₂⁴×C₇	—	8	2	no	—
232	C₂⁴×C₇	—	8	2	no	—
233	C₂⁴×C₇	—	8	2	no	—
234	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
235	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
236	C₇×#41	—	2	8	no	—
237	C₇×#41	—	4	4	no	—
238	C₇×#41	—	4	8	no	—
239	C₂×C₇×Q₈	—	2	1	no	—
240	C₂×C₇×Q₈	—	2	2	no	—
241	C₂×C₇×Q₈	—	2	2	no	—
242	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
243	C₂×C₇×D₄	—	2	4	no	—
244	C₂×C₇×D₄	—	2	8	no	—
245	C₂×C₇×D₄	—	2	8	no	—
246	C₂×C₇×D₄	—	2	8	no	—
247	C₂×C₇×D₄	—	2	4	no	—
248	C₂×C₇×D₄	—	2	4	no	—
249	C₂×C₇×D₄	—	2	4	no	—
250	C₂×C₇×D₄	—	2	4	no	—
251	C₂×C₇×D₄	—	2	1	no	—
252	C₂×C₇×D₄	—	2	1	no	—
253	C₂×C₇×D₄	—	2	2	no	—
254	C₂×C₇×D₄	—	2	2	no	—
255	C₂×C₇×D₄	—	2	2	no	—
256	C₂×C₇×D₄	—	2	4	no	—
257	C₂×C₇×D₄	—	2	4	no	—
258	C₂×C₇×D₄	—	2	4	no	—
259	C₂×C₇×D₄	—	2	1	no	—
260	C₂×C₇×D₄	—	2	1	no	—
261	C₂×C₇×D₄	—	2	1	no	—
262	C₂×C₇×D₄	—	2	4	no	—
263	C₂×C₇×D₄	—	2	4	no	—
264	C₂×C₇×D₄	—	2	2	no	—
265	C₂×C₇×D₄	—	2	2	no	—
266	C₂×C₇×D₄	—	2	2	no	—
267	C₂×C₇×D₄	—	2	2	no	—
268	C₂×C₇×D₄	—	2	2	no	—
269	C₂×C₇×D₄	—	4	4	no	—
270	C₂×C₇×D₄	—	4	4	no	—
271	C₂×C₇×D₄	—	4	4	no	—
272	C₂×C₇×D₄	—	4	8	no	—
273	C₂×C₇×D₄	—	4	8	no	—
274	C₂×C₇×D₄	—	4	8	no	—
275	C₂×C₇×D₄	—	4	4	no	—
276	C₂×C₇×D₄	—	4	4	no	—
277	C₂×C₇×D₄	—	4	4	no	—
278	C₂×C₇×D₄	—	4	4	no	—
279	C₂×C₇×D₄	—	4	32	no	—
280	C₂×C₇×D₄	—	4	4	no	—
281	C₂×C₇×D₄	—	4	4	no	—
282	C₂×C₇×D₄	—	4	4	no	—
283	C₂×C₇×D₄	—	8	2	no	—
284	C₂×C₇×D₄	—	8	2	no	—
285	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
286	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
287	C₂×C₇×D₄	C₂×D₄	1	4	yes	complemented
288	C₂×C₇×D₄	C₂⁴	1	2	yes	—
289	C₂×C₇×D₄	C₂⁴	1	2	yes	—
290	C₂×C₇×D₄	C₂⁴	1	2	yes	—
291	C₂×C₇×D₄	C₂⁴	1	2	yes	—
292	C₂×C₇×D₄	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₇	—	2	2	no	—
294	C₂²×C₄×C₇	—	2	2	no	—
295	C₂²×C₄×C₇	—	2	2	no	—
296	C₂²×C₄×C₇	—	2	2	no	—
297	C₂²×C₄×C₇	—	2	1	no	—
298	C₂²×C₄×C₇	—	2	1	no	—
299	C₂²×C₄×C₇	—	2	1	no	—
300	C₂²×C₄×C₇	—	2	4	no	—
301	C₂²×C₄×C₇	—	2	4	no	—
302	C₂²×C₄×C₇	—	2	4	no	—
303	C₂²×C₄×C₇	—	4	4	no	—
304	C₂²×C₄×C₇	—	4	4	no	—
305	C₂²×C₄×C₇	—	8	2	no	—
306	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
307	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
308	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
315	C₇×SD₁₆	—	2	8	no	—
316	C₇×SD₁₆	—	2	8	no	—
317	C₇×SD₁₆	—	4	4	no	—
318	C₇×D₈	—	2	8	no	—
319	C₇×D₈	—	2	8	no	—
320	C₇×D₈	—	2	8	no	—
321	C₇×D₈	—	2	8	no	—
322	C₇×D₈	—	4	4	no	—
323	C₇×D₈	C₂×D₄	1	16	yes	complemented
324	C₇×M₁₆	—	2	8	no	—
325	C₂×C₇×C₈	—	2	2	no	—
326	C₂×C₇×C₈	—	2	2	no	—
327	C₂×C₇×C₈	—	2	2	no	—
328	C₂×C₇×C₈	—	2	8	no	—
329	C₂×C₇×C₈	C₂×D₄	1	4	yes	complemented
330	C₂×C₇×C₈	C₂⁴	1	2	yes	—
331	C₂×C₇×C₈	C₂⁴	1	2	yes	—
332	C₂×C₇×C₈	C₂⁴	1	2	yes	—
333	C₂×C₇×C₈	C₂⁴	1	2	yes	—
334	C₇×C₄⋊C₄	—	2	4	no	—
335	C₇×C₄⋊C₄	—	2	1	no	—
336	C₇×C₄⋊C₄	—	2	1	no	—
337	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
338	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
339	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
340	C₇×C₂²⋊C₄	—	2	4	no	—
341	C₇×C₂²⋊C₄	—	2	4	no	—
342	C₇×C₂²⋊C₄	—	2	4	no	—
343	C₇×C₂²⋊C₄	—	2	4	no	—
344	C₇×C₂²⋊C₄	—	2	4	no	—
345	C₇×C₂²⋊C₄	—	2	4	no	—
346	C₇×C₂²⋊C₄	—	2	4	no	—
347	C₇×C₂²⋊C₄	—	2	4	no	—
348	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
349	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
350	C₄²×C₇	C₂×D₄	1	2	yes	—
351	C₄²×C₇	C₂⁴	1	2	yes	—
352	C₂²×#41	C₂²×C₇	1	1	yes	characteristic, complemented
353	C₂³×D₄	—	2	1	no	—
354	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
355	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
356	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
357	C₂×AGL(1,ℤ/8)	—	2	8	no	—
358	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	8	yes	complemented
359	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
360	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
361	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
362	C₂²×D₈	—	2	8	no	—
363	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
364	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
365	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
366	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
367	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
368	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
369	C₂²×D₈	C₂²×C₇	1	8	yes	complemented
370	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
371	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
372	#546	—	2	4	no	—
373	#546	C₂²×C₇	1	8	yes	complemented
374	D₄²	—	2	4	no	—
375	D₄²	C₂²×C₇	1	8	yes	complemented
376	C₂×#127	C₂²×C₇	1	1	yes	characteristic, complemented
377	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
378	C₂×#123	—	2	1	no	—
379	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
380	C₂×#121	—	2	1	no	—
381	C₂×#121	—	2	1	no	—
382	C₂×#121	C₂²×C₇	1	1	yes	characteristic
383	C₂×#121	C₂²×C₇	1	1	yes	characteristic, complemented
384	C₂×#121	C₂²×C₇	1	1	yes	characteristic, complemented
385	C₂×#120	—	2	1	no	—
386	C₂×#120	—	2	1	no	—
387	C₂×#120	—	2	1	no	—
388	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
389	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
390	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
391	C₂²×C₂²⋊C₄	—	2	1	no	—
392	#496	C₂²×C₇	1	8	yes	complemented
393	#469	C₂²×C₇	1	8	yes	complemented
394	#465	C₂²×C₇	1	8	yes	complemented
395	#463	C₂²×C₇	1	8	yes	complemented
396	#459	C₂²×C₇	1	8	yes	complemented
397	#450	C₂²×C₇	1	8	yes	complemented
398	#449	C₂²×C₇	1	8	yes	complemented
399	#447	C₂²×C₇	1	8	yes	complemented
400	#447	C₂²×C₇	1	8	yes	complemented
401	#442	C₂²×C₇	1	8	yes	complemented
402	#435	C₂²×C₇	1	8	yes	complemented
403	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
404	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
405	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
406	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
407	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
408	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
409	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
410	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
411	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
412	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
413	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
414	C₂³×C₇	—	2	2	no	—
415	C₂³×C₇	—	2	2	no	—
416	C₂³×C₇	—	2	2	no	—
417	C₂³×C₇	—	2	4	no	—
418	C₂³×C₇	—	2	4	no	—
419	C₂³×C₇	—	2	2	no	—
420	C₂³×C₇	—	2	2	no	—
421	C₂³×C₇	—	2	2	no	—
422	C₂³×C₇	—	2	2	no	—
423	C₂³×C₇	—	2	2	no	—
424	C₂³×C₇	—	2	2	no	—
425	C₂³×C₇	—	2	2	no	—
426	C₂³×C₇	—	4	8	no	—
427	C₂³×C₇	—	4	8	no	—
428	C₂³×C₇	—	4	8	no	—
429	C₂³×C₇	—	4	8	no	—
430	C₂³×C₇	—	4	2	no	—
431	C₂³×C₇	—	4	2	no	—
432	C₂³×C₇	—	4	2	no	—
433	C₂³×C₇	—	4	2	no	—
434	C₂³×C₇	—	4	2	no	—
435	C₂³×C₇	—	4	2	no	—
436	C₂³×C₇	—	4	2	no	—
437	C₂³×C₇	—	4	2	no	—
438	C₂³×C₇	—	4	2	no	—
439	C₂³×C₇	—	4	2	no	—
440	C₂³×C₇	—	4	8	no	—
441	C₂³×C₇	—	4	8	no	—
442	C₂³×C₇	—	4	2	no	—
443	C₂³×C₇	—	4	2	no	—
444	C₂³×C₇	—	4	2	no	—
445	C₂³×C₇	—	8	4	no	—
446	C₂³×C₇	—	8	4	no	—
447	C₂³×C₇	—	8	4	no	—
448	C₂³×C₇	—	8	16	no	—
449	C₂³×C₇	—	8	16	no	—
450	C₂³×C₇	—	8	16	no	—
451	C₂³×C₇	AGL(1,ℤ/8)	1	4	yes	complemented
452	C₂³×C₇	C₂²×D₄	1	2	yes	—
453	C₂³×C₇	C₂²×D₄	1	2	yes	—
454	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
455	C₇×Q₈	—	2	2	no	—
456	C₇×Q₈	—	2	2	no	—
457	C₇×Q₈	—	4	2	no	—
458	C₇×D₄	—	2	8	no	—
459	C₇×D₄	—	2	4	no	—
460	C₇×D₄	—	2	4	no	—
461	C₇×D₄	—	2	2	no	—
462	C₇×D₄	—	2	2	no	—
463	C₇×D₄	—	2	2	no	—
464	C₇×D₄	—	2	2	no	—
465	C₇×D₄	—	2	2	no	—
466	C₇×D₄	—	2	2	no	—
467	C₇×D₄	—	2	2	no	—
468	C₇×D₄	—	2	2	no	—
469	C₇×D₄	—	4	8	no	—
470	C₇×D₄	—	4	8	no	—
471	C₇×D₄	—	4	8	no	—
472	C₇×D₄	—	4	8	no	—
473	C₇×D₄	—	4	8	no	—
474	C₇×D₄	—	4	8	no	—
475	C₇×D₄	—	4	8	no	—
476	C₇×D₄	—	4	2	no	—
477	C₇×D₄	—	4	2	no	—
478	C₇×D₄	—	4	2	no	—
479	C₇×D₄	—	8	4	no	—
480	C₇×D₄	—	8	4	no	—
481	C₇×D₄	C₂²×D₄	1	4	yes	—
482	C₇×D₄	C₂²×D₄	1	4	yes	complemented
483	C₂×C₄×C₇	—	2	2	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	4	no	—
488	C₂×C₄×C₇	—	2	4	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	—	4	8	no	—
497	C₂×C₄×C₇	—	4	8	no	—
498	C₂×C₄×C₇	—	4	2	no	—
499	C₂×C₄×C₇	—	4	2	no	—
500	C₂×C₄×C₇	—	4	2	no	—
501	C₂×C₄×C₇	—	8	4	no	—
502	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
509	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
510	C₇×C₈	—	2	2	no	—
511	C₇×C₈	—	2	2	no	—
512	C₇×C₈	—	2	2	no	—
513	C₇×C₈	C₂²×D₄	1	4	yes	complemented
514	C₂⁵	—	2	1	no	—
515	C₂⁵	—	2	1	no	—
516	C₂⁵	—	2	1	no	—
517	C₂×#41	—	2	2	no	—
518	C₂×#41	—	2	4	no	—
519	C₂×#41	—	4	2	no	—
520	C₂×#41	C₂³×C₇	1	4	yes	complemented
521	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
522	C₂²×D₄	—	2	4	no	—
523	C₂²×D₄	—	2	4	no	—
524	C₂²×D₄	—	2	4	no	—
525	C₂²×D₄	—	2	1	no	—
526	C₂²×D₄	—	2	1	no	—
527	C₂²×D₄	—	2	1	no	—
528	C₂²×D₄	—	2	1	no	—
529	C₂²×D₄	—	2	8	no	—
530	C₂²×D₄	—	2	1	no	—
531	C₂²×D₄	—	2	1	no	—
532	C₂²×D₄	—	2	1	no	—
533	C₂²×D₄	—	2	1	no	—
534	C₂²×D₄	—	2	2	no	—
535	C₂²×D₄	—	2	2	no	—
536	C₂²×D₄	—	2	2	no	—
537	C₂²×D₄	—	2	1	no	—
538	C₂²×D₄	—	4	2	no	—
539	C₂²×D₄	—	4	2	no	—
540	C₂²×D₄	—	4	2	no	—
541	C₂²×D₄	—	4	8	no	—
542	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
544	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
545	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
546	C₂²×D₄	C₂³×C₇	1	4	yes	—
547	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
548	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
549	C₂²×D₄	C₂³×C₇	1	4	yes	complemented
550	C₂²×D₄	C₂³×C₇	1	4	yes	complemented
551	C₂³×C₄	—	2	1	no	—
552	C₂³×C₄	—	2	1	no	—
553	C₂³×C₄	—	2	1	no	—
554	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
556	AGL(1,ℤ/8)	—	2	32	no	—
557	C₂×SD₁₆	—	2	4	no	—
558	C₂×SD₁₆	—	2	4	no	—
559	C₂×SD₁₆	—	4	2	no	—
560	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
561	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
562	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
563	C₂×D₈	—	2	4	no	—
564	C₂×D₈	—	2	4	no	—
565	C₂×D₈	—	2	4	no	—
566	C₂×D₈	—	2	32	no	—
567	C₂×D₈	—	2	4	no	—
568	C₂×D₈	—	4	2	no	—
569	C₂×D₈	C₇×D₄	1	8	yes	complemented
570	C₂×D₈	C₂³×C₇	1	4	yes	—
571	C₂×D₈	C₂³×C₇	1	4	yes	—
572	C₂×D₈	C₂³×C₇	1	4	yes	complemented
573	C₂×D₈	C₂³×C₇	1	4	yes	complemented
574	C₂×D₈	C₂³×C₇	1	4	yes	complemented
575	C₂×D₈	C₂³×C₇	1	4	yes	complemented
576	C₂×M₁₆	—	2	4	no	—
577	C₂×M₁₆	C₂³×C₇	1	4	yes	complemented
578	C₂²×C₈	—	2	4	no	—
579	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
580	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
581	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
582	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
583	C₂²×C₈	C₂³×C₇	1	4	yes	complemented
584	#127	—	2	2	no	—
585	#127	C₂³×C₇	1	4	yes	complemented
586	#124	—	2	2	no	—
587	#124	C₂³×C₇	1	4	yes	complemented
588	#123	—	2	8	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	C₂³×C₇	1	4	yes	complemented
591	#121	—	2	2	no	—
592	#121	—	2	2	no	—
593	#121	—	2	2	no	—
594	#121	—	2	8	no	—
595	#121	—	2	8	no	—
596	#121	C₂³×C₇	1	4	yes	—
597	#121	C₂³×C₇	1	4	yes	complemented
598	#121	C₂³×C₇	1	4	yes	complemented
599	#120	—	2	8	no	—
600	#120	—	2	8	no	—
601	#120	—	2	8	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	C₇×D₄	1	4	yes	—
605	C₄×D₄	C₂³×C₇	1	4	yes	—
606	C₄×D₄	C₂³×C₇	1	4	yes	complemented
607	C₄×D₄	C₂³×C₇	1	4	yes	complemented
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	8	no	—
621	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
622	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
624	#106	C₂³×C₇	1	4	yes	complemented
625	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
626	#103	C₂³×C₇	1	4	yes	complemented
627	#102	C₂³×C₇	1	4	yes	complemented
628	#102	C₂³×C₇	1	4	yes	complemented
629	#102	C₂³×C₇	1	4	yes	complemented
630	#102	C₂³×C₇	1	4	yes	complemented
631	#102	C₂³×C₇	1	4	yes	complemented
632	C₂²⋊C₈	C₂³×C₇	1	4	yes	complemented
633	C₂²⋊C₈	C₂³×C₇	1	4	yes	complemented
634	#97	C₂³×C₇	1	4	yes	complemented
635	C₂²×C₇	—	2	2	no	—
636	C₂²×C₇	—	2	8	no	—
637	C₂²×C₇	—	2	2	no	—
638	C₂²×C₇	—	2	2	no	—
639	C₂²×C₇	—	2	4	no	—
640	C₂²×C₇	—	2	4	no	—
641	C₂²×C₇	—	2	2	no	—
642	C₂²×C₇	—	2	2	no	—
643	C₂²×C₇	—	4	4	no	—
644	C₂²×C₇	—	4	8	no	—
645	C₂²×C₇	—	4	8	no	—
646	C₂²×C₇	—	4	2	no	—
647	C₂²×C₇	—	4	2	no	—
648	C₂²×C₇	—	4	2	no	—
649	C₂²×C₇	—	4	2	no	—
650	C₂²×C₇	—	4	2	no	—
651	C₂²×C₇	—	4	2	no	—
652	C₂²×C₇	—	4	2	no	—
653	C₂²×C₇	—	4	2	no	—
654	C₂²×C₇	—	4	2	no	—
655	C₂²×C₇	—	4	2	no	—
656	C₂²×C₇	—	4	2	no	—
657	C₂²×C₇	—	4	2	no	—
658	C₂²×C₇	—	4	2	no	—
659	C₂²×C₇	—	8	16	no	—
660	C₂²×C₇	—	8	16	no	—
661	C₂²×C₇	—	8	16	no	—
662	C₂²×C₇	—	8	4	no	—
663	C₂²×C₇	—	8	4	no	—
664	C₂²×C₇	—	8	4	no	—
665	C₂²×C₇	D₄²	1	2	yes	—
666	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
667	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	complemented
668	C₂²×C₇	#576	1	2	yes	—
669	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
670	C₄×C₇	—	2	2	no	—
671	C₄×C₇	—	2	2	no	—
672	C₄×C₇	—	2	2	no	—
673	C₄×C₇	—	2	2	no	—
674	C₄×C₇	—	4	2	no	—
675	C₄×C₇	—	4	2	no	—
676	C₄×C₇	—	4	2	no	—
677	C₄×C₇	D₄²	1	2	yes	—
678	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
679	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂⁴	—	2	1	no	—
681	C₂⁴	—	2	1	no	—
682	C₂⁴	—	2	1	no	—
683	C₂⁴	—	2	1	no	—
684	C₂⁴	—	2	1	no	—
685	C₂⁴	—	2	4	no	—
686	C₂⁴	—	2	4	no	—
687	C₂⁴	—	2	4	no	—
688	C₂⁴	—	4	4	no	—
689	C₂⁴	—	4	4	no	—
690	C₂⁴	—	4	4	no	—
691	C₂⁴	—	4	4	no	—
692	C₂⁴	—	4	4	no	—
693	C₂⁴	—	4	4	no	—
694	C₂⁴	—	8	2	no	—
695	C₂⁴	—	8	2	no	—
696	C₂⁴	—	8	2	no	—
697	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
698	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
699	#41	—	2	8	no	—
700	#41	—	4	4	no	—
701	#41	—	4	8	no	—
702	C₂×Q₈	—	2	1	no	—
703	C₂×Q₈	—	2	2	no	—
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
706	C₂×D₄	—	2	4	no	—
707	C₂×D₄	—	2	8	no	—
708	C₂×D₄	—	2	8	no	—
709	C₂×D₄	—	2	8	no	—
710	C₂×D₄	—	2	4	no	—
711	C₂×D₄	—	2	4	no	—
712	C₂×D₄	—	2	4	no	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	1	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	4	no	—
726	C₂×D₄	—	2	4	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	4	4	no	—
733	C₂×D₄	—	4	4	no	—
734	C₂×D₄	—	4	4	no	—
735	C₂×D₄	—	4	8	no	—
736	C₂×D₄	—	4	8	no	—
737	C₂×D₄	—	4	8	no	—
738	C₂×D₄	—	4	4	no	—
739	C₂×D₄	—	4	4	no	—
740	C₂×D₄	—	4	4	no	—
741	C₂×D₄	—	4	4	no	—
742	C₂×D₄	—	4	32	no	—
743	C₂×D₄	—	4	4	no	—
744	C₂×D₄	—	4	4	no	—
745	C₂×D₄	—	4	4	no	—
746	C₂×D₄	—	8	2	no	—
747	C₂×D₄	—	8	2	no	—
748	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
749	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
750	C₂×D₄	C₂×C₇×D₄	1	4	yes	complemented
751	C₂×D₄	C₂⁴×C₇	1	2	yes	—
752	C₂×D₄	C₂⁴×C₇	1	2	yes	—
753	C₂×D₄	C₂⁴×C₇	1	2	yes	—
754	C₂×D₄	C₂⁴×C₇	1	2	yes	—
755	C₂×D₄	C₂⁴×C₇	1	2	yes	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	1	no	—
762	C₂²×C₄	—	2	1	no	—
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	2	4	no	—
765	C₂²×C₄	—	2	4	no	—
766	C₂²×C₄	—	4	4	no	—
767	C₂²×C₄	—	4	4	no	—
768	C₂²×C₄	—	8	2	no	—
769	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
770	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
771	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
772	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
773	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
774	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
778	SD₁₆	—	2	8	no	—
779	SD₁₆	—	2	8	no	—
780	SD₁₆	—	4	4	no	—
781	D₈	—	2	8	no	—
782	D₈	—	2	8	no	—
783	D₈	—	2	8	no	—
784	D₈	—	2	8	no	—
785	D₈	—	4	4	no	—
786	D₈	C₂×C₇×D₄	1	16	yes	complemented
787	M₁₆	—	2	8	no	—
788	C₂×C₈	—	2	2	no	—
789	C₂×C₈	—	2	2	no	—
790	C₂×C₈	—	2	2	no	—
791	C₂×C₈	—	2	8	no	—
792	C₂×C₈	C₂×C₇×D₄	1	4	yes	complemented
793	C₂×C₈	C₂⁴×C₇	1	2	yes	—
794	C₂×C₈	C₂⁴×C₇	1	2	yes	—
795	C₂×C₈	C₂⁴×C₇	1	2	yes	—
796	C₂×C₈	C₂⁴×C₇	1	2	yes	—
797	C₄⋊C₄	—	2	4	no	—
798	C₄⋊C₄	—	2	1	no	—
799	C₄⋊C₄	—	2	1	no	—
800	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
801	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
802	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
812	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
813	C₄²	C₂×C₇×D₄	1	2	yes	—
814	C₄²	C₂⁴×C₇	1	2	yes	—
815	C₂×C₇	—	2	4	no	—
816	C₂×C₇	—	4	2	no	—
817	C₂×C₇	—	4	4	no	—
818	C₂×C₇	—	4	4	no	—
819	C₂×C₇	—	8	2	no	—
820	C₂×C₇	—	8	2	no	—
821	C₂×C₇	—	8	2	no	—
822	C₂×C₇	#3264	1	4	yes	direct product factor
823	C₂×C₇	C₂×D₄²	1	1	yes	characteristic
824	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
825	C₂×C₇	C₂×#576	1	1	yes	characteristic
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	4	no	—
832	C₂³	—	2	4	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	4	8	no	—
839	C₂³	—	4	8	no	—
840	C₂³	—	4	8	no	—
841	C₂³	—	4	8	no	—
842	C₂³	—	4	2	no	—
843	C₂³	—	4	2	no	—
844	C₂³	—	4	2	no	—
845	C₂³	—	4	2	no	—
846	C₂³	—	4	2	no	—
847	C₂³	—	4	2	no	—
848	C₂³	—	4	2	no	—
849	C₂³	—	4	2	no	—
850	C₂³	—	4	2	no	—
851	C₂³	—	4	2	no	—
852	C₂³	—	4	8	no	—
853	C₂³	—	4	8	no	—
854	C₂³	—	4	2	no	—
855	C₂³	—	4	2	no	—
856	C₂³	—	4	2	no	—
857	C₂³	—	8	4	no	—
858	C₂³	—	8	4	no	—
859	C₂³	—	8	4	no	—
860	C₂³	—	8	16	no	—
861	C₂³	—	8	16	no	—
862	C₂³	—	8	16	no	—
863	C₂³	C₇×AGL(1,ℤ/8)	1	4	yes	complemented
864	C₂³	C₂²×C₇×D₄	1	2	yes	—
865	C₂³	C₂²×C₇×D₄	1	2	yes	—
866	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
867	Q₈	—	2	2	no	—
868	Q₈	—	2	2	no	—
869	Q₈	—	4	2	no	—
870	D₄	—	2	8	no	—
871	D₄	—	2	2	no	—
872	D₄	—	2	2	no	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	2	2	no	—
876	D₄	—	2	2	no	—
877	D₄	—	2	2	no	—
878	D₄	—	2	2	no	—
879	D₄	—	2	4	no	—
880	D₄	—	2	4	no	—
881	D₄	—	4	8	no	—
882	D₄	—	4	8	no	—
883	D₄	—	4	8	no	—
884	D₄	—	4	8	no	—
885	D₄	—	4	8	no	—
886	D₄	—	4	8	no	—
887	D₄	—	4	8	no	—
888	D₄	—	4	2	no	—
889	D₄	—	4	2	no	—
890	D₄	—	4	2	no	—
891	D₄	—	8	4	no	—
892	D₄	—	8	4	no	—
893	D₄	C₂²×C₇×D₄	1	4	yes	—
894	D₄	C₂²×C₇×D₄	1	4	yes	complemented
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	4	no	—
904	C₂×C₄	—	2	4	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	4	8	no	—
909	C₂×C₄	—	4	8	no	—
910	C₂×C₄	—	4	2	no	—
911	C₂×C₄	—	4	2	no	—
912	C₂×C₄	—	4	2	no	—
913	C₂×C₄	—	8	4	no	—
914	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
915	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
916	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
917	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
918	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
919	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
920	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
921	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
922	C₈	—	2	2	no	—
923	C₈	—	2	2	no	—
924	C₈	—	2	2	no	—
925	C₈	C₂²×C₇×D₄	1	4	yes	complemented
926	C₇	C₂×#3264	1	1	yes	characteristic, direct product factor, Sylow
927	C₂²	—	2	2	no	—
928	C₂²	—	2	8	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	4	no	—
934	C₂²	—	2	4	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	2	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	4	no	—
940	C₂²	—	4	8	no	—
941	C₂²	—	4	8	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	8	16	no	—
952	C₂²	—	8	16	no	—
953	C₂²	—	8	16	no	—
954	C₂²	—	8	4	no	—
955	C₂²	—	8	4	no	—
956	C₂²	—	8	4	no	—
957	C₂²	C₇×D₄²	1	2	yes	—
958	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
959	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	complemented
960	C₂²	C₇×#576	1	2	yes	—
961	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
962	C₄	—	2	2	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	C₇×D₄²	1	2	yes	—
970	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
971	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
972	C₂	—	2	4	no	—
973	C₂	—	4	2	no	—
974	C₂	—	4	4	no	—
975	C₂	—	4	4	no	—
976	C₂	—	8	2	no	—
977	C₂	—	8	2	no	—
978	C₂	—	8	2	no	—
979	C₂	C₇×#3264	1	4	yes	direct product factor
980	C₂	C₂×C₇×D₄²	1	1	yes	characteristic
981	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
982	C₂	C₂×C₇×#576	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×AGL(1,ℤ/8)	C₂	semidirect
2. C₂³×C₇×D₈	C₂	semidirect
3. C₂×C₇×#546	C₂	semidirect
4. C₂×C₇×D₄²	C₂	semidirect
5. C₇×#3264	C₂	direct (N × H)
6. C₂×C₇×#496	C₂	semidirect
7. C₂×C₇×#469	C₂	semidirect
8. C₂×C₇×#465	C₂	semidirect
9. C₂×C₇×#463	C₂	semidirect
10. C₂×C₇×#459	C₂	semidirect
11. C₂×C₇×#449	C₂	semidirect
12. C₂×C₇×#450	C₂	semidirect
13. C₂×C₇×#447	C₂	semidirect
14. C₂×C₇×#447	C₂	semidirect
15. C₂×C₇×#442	C₂	semidirect
16. C₂×C₇×#435	C₂	semidirect
17. C₂²×C₇×#41	C₂²	semidirect
20. C₂³×C₇×D₄	C₂²	semidirect
21. C₂³×C₇×D₄	C₂²	semidirect
23. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
24. C₂²×C₇×SD₁₆	C₂²	semidirect
25. C₂²×C₇×SD₁₆	C₂²	semidirect
26. C₂²×C₇×SD₁₆	C₂²	semidirect
30. C₂²×C₇×D₈	C₂²	semidirect
31. C₂²×C₇×D₈	C₂²	semidirect
32. C₂²×C₇×D₈	C₂²	semidirect
33. C₂²×C₇×D₈	C₂²	semidirect
34. C₂²×C₇×D₈	C₂²	semidirect
35. C₂²×C₇×M₁₆	C₂²	semidirect
36. C₂³×C₇×C₈	C₂²	semidirect
38. C₇×#546	C₂²	semidirect
40. C₇×D₄²	C₂²	semidirect
41. C₂×C₇×#127	C₂²	semidirect
42. C₂×C₇×#124	C₂²	semidirect
44. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
48. C₂×C₇×#121	C₂²	semidirect
49. C₂×C₇×#121	C₂²	semidirect
54. C₂×C₄×C₇×D₄	C₂²	semidirect
55. C₂×C₄×C₇×D₄	C₂²	semidirect
57. C₇×#496	C₂²	semidirect
58. C₇×#469	C₂²	semidirect
59. C₇×#465	C₂²	semidirect
60. C₇×#463	C₂²	semidirect
61. C₇×#459	C₂²	semidirect
62. C₇×#450	C₂²	semidirect
63. C₇×#449	C₂²	semidirect
64. C₇×#447	C₂²	semidirect
65. C₇×#447	C₂²	semidirect
66. C₇×#442	C₂²	semidirect
67. C₇×#435	C₂²	semidirect
68. C₂×C₇×#106	C₂²	semidirect
69. C₂×C₇×C₄⋊C₈	C₂²	semidirect
70. C₂×C₇×#103	C₂²	semidirect
71. C₂×C₇×#102	C₂²	semidirect
72. C₂×C₇×#102	C₂²	semidirect
73. C₂×C₇×#102	C₂²	semidirect
74. C₂×C₇×#102	C₂²	semidirect
75. C₂×C₇×#102	C₂²	semidirect
76. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
77. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
78. C₂×C₇×#97	C₂²	semidirect
79. C₂×#3264	C₇	direct (N × H)
86. C₂×C₇×#41	C₂³	semidirect
115. C₂²×C₇×D₄	C₂³	semidirect
116. C₂²×C₇×D₄	C₂³	semidirect
126. C₂×C₇×SD₁₆	C₂³	semidirect
127. C₂×C₇×SD₁₆	C₂³	semidirect
128. C₂×C₇×SD₁₆	C₂³	semidirect
135. C₂×C₇×D₈	D₄	semidirect
138. C₂×C₇×D₈	C₂³	semidirect
139. C₂×C₇×D₈	C₂³	semidirect
140. C₂×C₇×D₈	C₂³	semidirect
141. C₂×C₇×D₈	C₂³	semidirect
143. C₂×C₇×M₁₆	C₂³	semidirect
149. C₂²×C₇×C₈	C₂³	semidirect
151. C₇×#127	C₂³	semidirect
153. C₇×#124	C₂³	semidirect
156. C₇×C₂²⋊Q₈	C₂³	semidirect
163. C₇×#121	C₂³	semidirect
164. C₇×#121	C₂³	semidirect
172. C₄×C₇×D₄	C₂³	semidirect
173. C₄×C₇×D₄	C₂³	semidirect
190. C₇×#106	C₂³	semidirect
191. C₇×C₄⋊C₈	C₂³	semidirect
192. C₇×#103	C₂³	semidirect
193. C₇×#102	C₂³	semidirect
194. C₇×#102	C₂³	semidirect
195. C₇×#102	C₂³	semidirect
196. C₇×#102	C₂³	semidirect
197. C₇×#102	C₂³	semidirect
198. C₇×C₂²⋊C₈	C₂³	semidirect
199. C₇×C₂²⋊C₈	C₂³	semidirect
200. C₇×#97	C₂³	semidirect
201. C₂²×AGL(1,ℤ/8)	C₂×C₇	semidirect
202. C₂³×D₈	C₂×C₇	semidirect
203. C₂×#546	C₂×C₇	semidirect
204. C₂×D₄²	C₂×C₇	semidirect
205. #3264	C₂×C₇	direct (N × H)
206. C₂×#496	C₂×C₇	semidirect
207. C₂×#469	C₂×C₇	semidirect
208. C₂×#465	C₂×C₇	semidirect
209. C₂×#463	C₂×C₇	semidirect
210. C₂×#459	C₂×C₇	semidirect
211. C₂×#449	C₂×C₇	semidirect
212. C₂×#450	C₂×C₇	semidirect
213. C₂×#447	C₂×C₇	semidirect
214. C₂×#447	C₂×C₇	semidirect
215. C₂×#442	C₂×C₇	semidirect
216. C₂×#435	C₂×C₇	semidirect
287. C₂×C₇×D₄	C₂×D₄	semidirect
323. C₇×D₈	C₂×D₄	semidirect
329. C₂×C₇×C₈	C₂×D₄	semidirect
352. C₂²×#41	C₂²×C₇	semidirect
355. C₂³×D₄	C₂²×C₇	semidirect
356. C₂³×D₄	C₂²×C₇	semidirect
358. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
359. C₂²×SD₁₆	C₂²×C₇	semidirect
360. C₂²×SD₁₆	C₂²×C₇	semidirect
361. C₂²×SD₁₆	C₂²×C₇	semidirect
365. C₂²×D₈	C₂²×C₇	semidirect
366. C₂²×D₈	C₂²×C₇	semidirect
367. C₂²×D₈	C₂²×C₇	semidirect
368. C₂²×D₈	C₂²×C₇	semidirect
369. C₂²×D₈	C₂²×C₇	semidirect
370. C₂²×M₁₆	C₂²×C₇	semidirect
371. C₂³×C₈	C₂²×C₇	semidirect
373. #546	C₂²×C₇	semidirect
375. D₄²	C₂²×C₇	semidirect
376. C₂×#127	C₂²×C₇	semidirect
377. C₂×#124	C₂²×C₇	semidirect
379. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
383. C₂×#121	C₂²×C₇	semidirect
384. C₂×#121	C₂²×C₇	semidirect
389. C₂×C₄×D₄	C₂²×C₇	semidirect
390. C₂×C₄×D₄	C₂²×C₇	semidirect
392. #496	C₂²×C₇	semidirect
393. #469	C₂²×C₇	semidirect
394. #465	C₂²×C₇	semidirect
395. #463	C₂²×C₇	semidirect
396. #459	C₂²×C₇	semidirect
397. #450	C₂²×C₇	semidirect
398. #449	C₂²×C₇	semidirect
399. #447	C₂²×C₇	semidirect
400. #447	C₂²×C₇	semidirect
401. #442	C₂²×C₇	semidirect
402. #435	C₂²×C₇	semidirect
403. C₂×#106	C₂²×C₇	semidirect
404. C₂×C₄⋊C₈	C₂²×C₇	semidirect
405. C₂×#103	C₂²×C₇	semidirect
406. C₂×#102	C₂²×C₇	semidirect
407. C₂×#102	C₂²×C₇	semidirect
408. C₂×#102	C₂²×C₇	semidirect
409. C₂×#102	C₂²×C₇	semidirect
410. C₂×#102	C₂²×C₇	semidirect
411. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
412. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
413. C₂×#97	C₂²×C₇	semidirect
451. C₂³×C₇	AGL(1,ℤ/8)	semidirect
482. C₇×D₄	C₂²×D₄	semidirect
513. C₇×C₈	C₂²×D₄	semidirect
520. C₂×#41	C₂³×C₇	semidirect
549. C₂²×D₄	C₂³×C₇	semidirect
550. C₂²×D₄	C₂³×C₇	semidirect
560. C₂×SD₁₆	C₂³×C₇	semidirect
561. C₂×SD₁₆	C₂³×C₇	semidirect
562. C₂×SD₁₆	C₂³×C₇	semidirect
569. C₂×D₈	C₇×D₄	semidirect
572. C₂×D₈	C₂³×C₇	semidirect
573. C₂×D₈	C₂³×C₇	semidirect
574. C₂×D₈	C₂³×C₇	semidirect
575. C₂×D₈	C₂³×C₇	semidirect
577. C₂×M₁₆	C₂³×C₇	semidirect
583. C₂²×C₈	C₂³×C₇	semidirect
585. #127	C₂³×C₇	semidirect
587. #124	C₂³×C₇	semidirect
590. C₂²⋊Q₈	C₂³×C₇	semidirect
597. #121	C₂³×C₇	semidirect
598. #121	C₂³×C₇	semidirect
606. C₄×D₄	C₂³×C₇	semidirect
607. C₄×D₄	C₂³×C₇	semidirect
624. #106	C₂³×C₇	semidirect
625. C₄⋊C₈	C₂³×C₇	semidirect
626. #103	C₂³×C₇	semidirect
627. #102	C₂³×C₇	semidirect
628. #102	C₂³×C₇	semidirect
629. #102	C₂³×C₇	semidirect
630. #102	C₂³×C₇	semidirect
631. #102	C₂³×C₇	semidirect
632. C₂²⋊C₈	C₂³×C₇	semidirect
633. C₂²⋊C₈	C₂³×C₇	semidirect
634. #97	C₂³×C₇	semidirect
667. C₂²×C₇	C₂×AGL(1,ℤ/8)	semidirect
750. C₂×D₄	C₂×C₇×D₄	semidirect
786. D₈	C₂×C₇×D₄	semidirect
792. C₂×C₈	C₂×C₇×D₄	semidirect
822. C₂×C₇	#3264	direct (N × H)
863. C₂³	C₇×AGL(1,ℤ/8)	semidirect
894. D₄	C₂²×C₇×D₄	semidirect
925. C₈	C₂²×C₇×D₄	semidirect
926. C₇	C₂×#3264	direct (N × H)
959. C₂²	C₂×C₇×AGL(1,ℤ/8)	semidirect
979. C₂	C₇×#3264	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₇×AGL(1,ℤ/8)	2
C₂³×C₇×D₈	2
C₂×C₇×#546	2
C₂×C₇×D₄²	2
C₇×#3264	2
C₂×C₇×#496	2
C₂×C₇×#469	2
C₂×C₇×#465	2
C₂×C₇×#463	2
C₂×C₇×#459	2
C₂×C₇×#449	2
C₂×C₇×#450	2
C₂×C₇×#447	2
C₂×C₇×#442	2
C₂×C₇×#435	2
C₂×#3264	7

Subgroups — C2×C7×#3264 #13238238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3264 #13238238