Subgroups — C₂×C₇×#3267 #13238241

Order 1792.

2914 conjugacy classes of subgroups.

The subgroup lattice has 916 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	C₂²×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3267	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₇×#497	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#470	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×#461	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#452	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#450	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
18	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
19	C₂²×C₇×#41	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₇×AGL(1,ℤ/8)	—	2	8	no	—
22	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
23	C₂×C₇×#135	—	2	8	no	—
24	C₂×C₇×#135	C₂²	1	8	yes	complemented
25	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
29	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
30	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
31	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
33	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
34	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
35	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
36	C₇×#547	—	2	4	no	—
37	C₇×#547	C₂²	1	8	yes	complemented
38	C₇×#546	—	2	4	no	—
39	C₇×#546	C₂²	1	8	yes	complemented
40	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₇×#124	C₂²	1	1	yes	characteristic
42	C₂×C₇×#123	—	2	1	no	—
43	C₂×C₇×#123	—	2	1	no	—
44	C₂×C₇×#123	—	2	1	no	—
45	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₇×#121	—	2	1	no	—
49	C₂×C₇×#121	—	2	1	no	—
50	C₂×C₇×#121	C₂²	1	1	yes	characteristic
51	C₂×C₇×#120	—	2	1	no	—
52	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
56	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
57	C₇×#497	C₂²	1	8	yes	complemented
58	C₇×#470	C₂²	1	8	yes	complemented
59	C₇×#465	C₂²	1	8	yes	complemented
60	C₇×#463	C₂²	1	8	yes	complemented
61	C₇×#461	C₂²	1	8	yes	complemented
62	C₇×#452	C₂²	1	8	yes	complemented
63	C₇×#452	C₂²	1	8	yes	complemented
64	C₇×#450	C₂²	1	8	yes	complemented
65	C₇×#449	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×#103	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₇×#102	C₂²	1	1	yes	characteristic
74	C₂×C₇×#102	C₂²	1	1	yes	characteristic
75	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
77	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
79	C₂×#3267	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂⁵×C₇	—	2	1	no	—
81	C₂×C₇×#41	—	2	2	no	—
82	C₂×C₇×#41	—	2	2	no	—
83	C₂×C₇×#41	—	2	2	no	—
84	C₂×C₇×#41	—	2	4	no	—
85	C₂×C₇×#41	—	2	4	no	—
86	C₂×C₇×#41	—	2	4	no	—
87	C₂×C₇×#41	—	4	2	no	—
88	C₂×C₇×#41	—	4	2	no	—
89	C₂×C₇×#41	—	4	2	no	—
90	C₂×C₇×#41	C₂³	1	4	yes	—
91	C₂×C₇×#41	C₂³	1	4	yes	—
92	C₂×C₇×#41	C₂³	1	4	yes	complemented
93	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
94	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
95	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
96	C₂²×C₇×D₄	—	2	4	no	—
97	C₂²×C₇×D₄	—	2	1	no	—
98	C₂²×C₇×D₄	—	2	1	no	—
99	C₂²×C₇×D₄	—	2	1	no	—
100	C₂²×C₇×D₄	—	2	1	no	—
101	C₂²×C₇×D₄	—	2	1	no	—
102	C₂²×C₇×D₄	—	2	2	no	—
103	C₂²×C₇×D₄	—	4	2	no	—
104	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
105	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
106	C₂²×C₇×D₄	C₂³	1	4	yes	—
107	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
108	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₇	—	2	1	no	—
110	C₂³×C₄×C₇	—	2	1	no	—
111	C₂³×C₄×C₇	—	2	1	no	—
112	C₂³×C₄×C₇	—	2	1	no	—
113	C₂³×C₄×C₇	—	2	1	no	—
114	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
116	C₇×AGL(1,ℤ/8)	—	2	32	no	—
117	C₇×#135	—	2	32	no	—
118	C₂×C₇×Q₁₆	—	2	4	no	—
119	C₂×C₇×Q₁₆	—	4	2	no	—
120	C₂×C₇×Q₁₆	C₂³	1	4	yes	complemented
121	C₂×C₇×Q₁₆	C₂³	1	4	yes	complemented
122	C₂×C₇×SD₁₆	—	2	4	no	—
123	C₂×C₇×SD₁₆	—	2	4	no	—
124	C₂×C₇×SD₁₆	—	2	4	no	—
125	C₂×C₇×SD₁₆	—	2	4	no	—
126	C₂×C₇×SD₁₆	—	4	2	no	—
127	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
128	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
129	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
130	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
131	C₂×C₇×SD₁₆	C₂³	1	4	yes	complemented
132	C₂×C₇×D₈	—	2	4	no	—
133	C₂×C₇×D₈	D₄	1	8	yes	complemented
134	C₂×C₇×D₈	C₂³	1	4	yes	—
135	C₂×C₇×D₈	C₂³	1	4	yes	—
136	C₂×C₇×M₁₆	—	2	4	no	—
137	C₂×C₇×M₁₆	C₂³	1	4	yes	—
138	C₂²×C₇×C₈	—	2	4	no	—
139	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
140	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
141	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
142	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
143	C₂²×C₇×C₈	C₂³	1	4	yes	complemented
144	C₇×C₄⋊Q₈	—	2	2	no	—
145	C₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
146	C₇×#124	—	2	2	no	—
147	C₇×#124	C₂³	1	4	yes	—
148	C₇×#123	—	2	8	no	—
149	C₇×#123	—	2	8	no	—
150	C₇×#123	—	2	8	no	—
151	C₇×C₂²⋊Q₈	—	2	2	no	—
152	C₇×C₂²⋊Q₈	—	2	2	no	—
153	C₇×C₂²⋊Q₈	—	2	2	no	—
154	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
155	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
156	C₇×C₂²⋊Q₈	C₂³	1	4	yes	complemented
157	C₇×#121	—	2	8	no	—
158	C₇×#121	—	2	2	no	—
159	C₇×#121	—	2	8	no	—
160	C₇×#121	C₂³	1	4	yes	—
161	C₇×#120	—	2	8	no	—
162	C₄×C₇×D₄	—	2	2	no	—
163	C₄×C₇×D₄	—	2	2	no	—
164	C₄×C₇×D₄	D₄	1	4	yes	—
165	C₄×C₇×D₄	C₂³	1	4	yes	—
166	C₄×C₇×D₄	C₂³	1	4	yes	—
167	C₄×C₇×D₄	C₂³	1	4	yes	complemented
168	C₂×C₇×C₄⋊C₄	—	2	1	no	—
169	C₂×C₇×C₄⋊C₄	—	2	1	no	—
170	C₂×C₇×C₄⋊C₄	—	2	1	no	—
171	C₂×C₇×C₄⋊C₄	—	2	1	no	—
172	C₂×C₇×C₄⋊C₄	—	2	1	no	—
173	C₂×C₇×C₄⋊C₄	—	2	8	no	—
174	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
175	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
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	8	no	—
186	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
187	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
189	C₇×#106	C₂³	1	4	yes	complemented
190	C₇×C₄⋊C₈	C₂³	1	4	yes	complemented
191	C₇×#103	C₂³	1	4	yes	complemented
192	C₇×#103	C₂³	1	4	yes	complemented
193	C₇×#103	C₂³	1	4	yes	complemented
194	C₇×#102	C₂³	1	4	yes	—
195	C₇×#102	C₂³	1	4	yes	—
196	C₇×#102	C₂³	1	4	yes	complemented
197	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
198	C₇×C₂²⋊C₈	C₂³	1	4	yes	complemented
199	C₇×#97	C₂³	1	4	yes	complemented
200	C₂²×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic, complemented
201	C₂²×#135	C₂×C₇	1	1	yes	characteristic, complemented
202	C₂×#547	C₂×C₇	1	1	yes	characteristic, complemented
203	C₂×#546	C₂×C₇	1	1	yes	characteristic, complemented
204	#3267	C₂×C₇	1	16	yes	direct product factor
205	C₂×#497	C₂×C₇	1	1	yes	characteristic, complemented
206	C₂×#470	C₂×C₇	1	1	yes	characteristic, complemented
207	C₂×#465	C₂×C₇	1	1	yes	characteristic, complemented
208	C₂×#463	C₂×C₇	1	1	yes	characteristic, complemented
209	C₂×#461	C₂×C₇	1	1	yes	characteristic, complemented
210	C₂×#452	C₂×C₇	1	1	yes	characteristic, complemented
211	C₂×#452	C₂×C₇	1	1	yes	characteristic, complemented
212	C₂×#449	C₂×C₇	1	1	yes	characteristic, complemented
213	C₂×#450	C₂×C₇	1	1	yes	characteristic, complemented
214	C₂×#442	C₂×C₇	1	1	yes	characteristic, complemented
215	C₂×#435	C₂×C₇	1	1	yes	characteristic, complemented
216	C₂⁴×C₇	—	2	1	no	—
217	C₂⁴×C₇	—	2	1	no	—
218	C₂⁴×C₇	—	2	1	no	—
219	C₂⁴×C₇	—	2	4	no	—
220	C₂⁴×C₇	—	4	4	no	—
221	C₂⁴×C₇	—	4	4	no	—
222	C₂⁴×C₇	—	8	2	no	—
223	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
224	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
225	C₇×#41	—	2	8	no	—
226	C₇×#41	—	2	8	no	—
227	C₇×#41	—	2	8	no	—
228	C₇×#41	—	4	4	no	—
229	C₇×#41	—	4	4	no	—
230	C₇×#41	—	4	4	no	—
231	C₇×#41	—	4	8	no	—
232	C₇×#41	—	4	8	no	—
233	C₇×#41	—	4	8	no	—
234	C₂×C₇×Q₈	—	2	1	no	—
235	C₂×C₇×Q₈	—	2	1	no	—
236	C₂×C₇×Q₈	—	2	1	no	—
237	C₂×C₇×Q₈	—	2	2	no	—
238	C₂×C₇×Q₈	—	2	2	no	—
239	C₂×C₇×Q₈	—	2	2	no	—
240	C₂×C₇×Q₈	—	2	2	no	—
241	C₂×C₇×Q₈	—	2	2	no	—
242	C₂×C₇×Q₈	—	2	2	no	—
243	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
244	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
245	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
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	4	no	—
255	C₂×C₇×D₄	—	2	1	no	—
256	C₂×C₇×D₄	—	2	2	no	—
257	C₂×C₇×D₄	—	2	2	no	—
258	C₂×C₇×D₄	—	2	2	no	—
259	C₂×C₇×D₄	—	4	4	no	—
260	C₂×C₇×D₄	—	4	8	no	—
261	C₂×C₇×D₄	—	4	2	no	—
262	C₂×C₇×D₄	—	4	4	no	—
263	C₂×C₇×D₄	—	4	4	no	—
264	C₂×C₇×D₄	—	4	4	no	—
265	C₂×C₇×D₄	—	4	4	no	—
266	C₂×C₇×D₄	—	8	2	no	—
267	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
268	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
269	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
270	C₂×C₇×D₄	C₂⁴	1	2	yes	—
271	C₂×C₇×D₄	C₂⁴	1	2	yes	—
272	C₂×C₇×D₄	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₇	—	2	2	no	—
274	C₂²×C₄×C₇	—	2	2	no	—
275	C₂²×C₄×C₇	—	2	2	no	—
276	C₂²×C₄×C₇	—	2	2	no	—
277	C₂²×C₄×C₇	—	2	1	no	—
278	C₂²×C₄×C₇	—	2	1	no	—
279	C₂²×C₄×C₇	—	2	1	no	—
280	C₂²×C₄×C₇	—	2	1	no	—
281	C₂²×C₄×C₇	—	2	1	no	—
282	C₂²×C₄×C₇	—	2	4	no	—
283	C₂²×C₄×C₇	—	2	4	no	—
284	C₂²×C₄×C₇	—	2	4	no	—
285	C₂²×C₄×C₇	—	2	4	no	—
286	C₂²×C₄×C₇	—	2	4	no	—
287	C₂²×C₄×C₇	—	4	4	no	—
288	C₂²×C₄×C₇	—	4	4	no	—
289	C₂²×C₄×C₇	—	4	4	no	—
290	C₂²×C₄×C₇	—	4	4	no	—
291	C₂²×C₄×C₇	—	8	2	no	—
292	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
293	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
294	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
301	C₇×Q₁₆	—	2	8	no	—
302	C₇×Q₁₆	—	4	4	no	—
303	C₇×SD₁₆	—	2	8	no	—
304	C₇×SD₁₆	—	2	8	no	—
305	C₇×SD₁₆	—	2	8	no	—
306	C₇×SD₁₆	—	2	8	no	—
307	C₇×SD₁₆	—	4	4	no	—
308	C₇×D₈	—	2	8	no	—
309	C₇×D₈	C₂×D₄	1	16	yes	complemented
310	C₇×M₁₆	—	2	8	no	—
311	C₂×C₇×C₈	—	2	2	no	—
312	C₂×C₇×C₈	—	2	2	no	—
313	C₂×C₇×C₈	—	2	2	no	—
314	C₂×C₇×C₈	—	2	8	no	—
315	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
316	C₂×C₇×C₈	C₂⁴	1	2	yes	—
317	C₂×C₇×C₈	C₂⁴	1	2	yes	—
318	C₂×C₇×C₈	C₂⁴	1	2	yes	—
319	C₂×C₇×C₈	C₂⁴	1	2	yes	—
320	C₇×C₄⋊C₄	—	2	4	no	—
321	C₇×C₄⋊C₄	—	2	4	no	—
322	C₇×C₄⋊C₄	—	2	4	no	—
323	C₇×C₄⋊C₄	—	2	4	no	—
324	C₇×C₄⋊C₄	—	2	4	no	—
325	C₇×C₄⋊C₄	—	2	1	no	—
326	C₇×C₄⋊C₄	—	2	1	no	—
327	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
328	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
329	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
330	C₇×C₂²⋊C₄	—	2	4	no	—
331	C₇×C₂²⋊C₄	—	2	4	no	—
332	C₇×C₂²⋊C₄	—	2	4	no	—
333	C₇×C₂²⋊C₄	—	2	4	no	—
334	C₇×C₂²⋊C₄	—	2	4	no	—
335	C₇×C₂²⋊C₄	—	2	4	no	—
336	C₇×C₂²⋊C₄	—	2	4	no	—
337	C₇×C₂²⋊C₄	—	2	4	no	—
338	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
339	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
340	C₄²×C₇	C₂×D₄	1	2	yes	—
341	C₄²×C₇	C₂⁴	1	2	yes	—
342	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
343	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
344	C₂²×#41	C₂²×C₇	1	1	yes	characteristic, complemented
345	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
346	C₂×AGL(1,ℤ/8)	—	2	8	no	—
347	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	8	yes	complemented
348	C₂×#135	—	2	8	no	—
349	C₂×#135	C₂²×C₇	1	8	yes	complemented
350	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
351	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
352	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
353	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
354	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
355	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
356	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
357	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
358	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
359	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
360	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
361	#547	—	2	4	no	—
362	#547	C₂²×C₇	1	8	yes	complemented
363	#546	—	2	4	no	—
364	#546	C₂²×C₇	1	8	yes	complemented
365	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
366	C₂×#124	C₂²×C₇	1	1	yes	characteristic
367	C₂×#123	—	2	1	no	—
368	C₂×#123	—	2	1	no	—
369	C₂×#123	—	2	1	no	—
370	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
371	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
372	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
373	C₂×#121	—	2	1	no	—
374	C₂×#121	—	2	1	no	—
375	C₂×#121	C₂²×C₇	1	1	yes	characteristic
376	C₂×#120	—	2	1	no	—
377	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
378	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
379	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
380	C₂²×C₄⋊C₄	—	2	1	no	—
381	C₂²×C₂²⋊C₄	—	2	1	no	—
382	#497	C₂²×C₇	1	8	yes	complemented
383	#470	C₂²×C₇	1	8	yes	complemented
384	#465	C₂²×C₇	1	8	yes	complemented
385	#463	C₂²×C₇	1	8	yes	complemented
386	#461	C₂²×C₇	1	8	yes	complemented
387	#452	C₂²×C₇	1	8	yes	complemented
388	#452	C₂²×C₇	1	8	yes	complemented
389	#450	C₂²×C₇	1	8	yes	complemented
390	#449	C₂²×C₇	1	8	yes	complemented
391	#442	C₂²×C₇	1	8	yes	complemented
392	#435	C₂²×C₇	1	8	yes	complemented
393	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
394	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
395	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
396	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
397	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
398	C₂×#102	C₂²×C₇	1	1	yes	characteristic
399	C₂×#102	C₂²×C₇	1	1	yes	characteristic
400	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
401	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
402	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
403	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
404	C₂³×C₇	—	2	2	no	—
405	C₂³×C₇	—	2	2	no	—
406	C₂³×C₇	—	2	4	no	—
407	C₂³×C₇	—	2	4	no	—
408	C₂³×C₇	—	2	2	no	—
409	C₂³×C₇	—	2	2	no	—
410	C₂³×C₇	—	2	2	no	—
411	C₂³×C₇	—	2	2	no	—
412	C₂³×C₇	—	2	2	no	—
413	C₂³×C₇	—	2	2	no	—
414	C₂³×C₇	—	2	2	no	—
415	C₂³×C₇	—	4	8	no	—
416	C₂³×C₇	—	4	8	no	—
417	C₂³×C₇	—	4	2	no	—
418	C₂³×C₇	—	4	2	no	—
419	C₂³×C₇	—	4	2	no	—
420	C₂³×C₇	—	4	2	no	—
421	C₂³×C₇	—	4	2	no	—
422	C₂³×C₇	—	4	2	no	—
423	C₂³×C₇	—	4	2	no	—
424	C₂³×C₇	—	8	4	no	—
425	C₂³×C₇	—	8	16	no	—
426	C₂³×C₇	C₂²×D₄	1	2	yes	—
427	C₂³×C₇	C₂²×D₄	1	2	yes	—
428	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
429	C₇×Q₈	—	2	2	no	—
430	C₇×Q₈	—	2	2	no	—
431	C₇×Q₈	—	2	2	no	—
432	C₇×Q₈	—	2	2	no	—
433	C₇×Q₈	—	2	2	no	—
434	C₇×Q₈	—	2	2	no	—
435	C₇×Q₈	—	4	2	no	—
436	C₇×Q₈	—	4	2	no	—
437	C₇×Q₈	—	4	2	no	—
438	C₇×D₄	—	2	4	no	—
439	C₇×D₄	—	2	4	no	—
440	C₇×D₄	—	2	2	no	—
441	C₇×D₄	—	2	2	no	—
442	C₇×D₄	—	2	2	no	—
443	C₇×D₄	—	2	2	no	—
444	C₇×D₄	—	4	4	no	—
445	C₇×D₄	—	4	8	no	—
446	C₇×D₄	—	4	8	no	—
447	C₇×D₄	—	4	8	no	—
448	C₇×D₄	—	4	8	no	—
449	C₇×D₄	—	4	2	no	—
450	C₇×D₄	—	8	4	no	—
451	C₇×D₄	C₂²×D₄	1	4	yes	—
452	C₇×D₄	C₂²×D₄	1	4	yes	—
453	C₂×C₄×C₇	—	2	2	no	—
454	C₂×C₄×C₇	—	2	2	no	—
455	C₂×C₄×C₇	—	2	2	no	—
456	C₂×C₄×C₇	—	2	2	no	—
457	C₂×C₄×C₇	—	2	4	no	—
458	C₂×C₄×C₇	—	2	4	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	2	no	—
465	C₂×C₄×C₇	—	2	2	no	—
466	C₂×C₄×C₇	—	2	2	no	—
467	C₂×C₄×C₇	—	2	2	no	—
468	C₂×C₄×C₇	—	4	8	no	—
469	C₂×C₄×C₇	—	4	8	no	—
470	C₂×C₄×C₇	—	4	8	no	—
471	C₂×C₄×C₇	—	4	8	no	—
472	C₂×C₄×C₇	—	4	2	no	—
473	C₂×C₄×C₇	—	4	2	no	—
474	C₂×C₄×C₇	—	4	2	no	—
475	C₂×C₄×C₇	—	4	2	no	—
476	C₂×C₄×C₇	—	4	2	no	—
477	C₂×C₄×C₇	—	8	4	no	—
478	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
479	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
481	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
482	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
485	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
486	C₇×C₈	—	2	2	no	—
487	C₇×C₈	—	2	2	no	—
488	C₇×C₈	—	2	2	no	—
489	C₇×C₈	C₂²×D₄	1	4	yes	—
490	C₂⁵	—	2	1	no	—
491	C₂×#41	—	2	2	no	—
492	C₂×#41	—	2	2	no	—
493	C₂×#41	—	2	2	no	—
494	C₂×#41	—	2	4	no	—
495	C₂×#41	—	2	4	no	—
496	C₂×#41	—	2	4	no	—
497	C₂×#41	—	4	2	no	—
498	C₂×#41	—	4	2	no	—
499	C₂×#41	—	4	2	no	—
500	C₂×#41	C₂³×C₇	1	4	yes	—
501	C₂×#41	C₂³×C₇	1	4	yes	—
502	C₂×#41	C₂³×C₇	1	4	yes	complemented
503	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
504	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
505	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
506	C₂²×D₄	—	2	4	no	—
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	—	2	1	no	—
510	C₂²×D₄	—	2	1	no	—
511	C₂²×D₄	—	2	1	no	—
512	C₂²×D₄	—	2	2	no	—
513	C₂²×D₄	—	4	2	no	—
514	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
515	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
516	C₂²×D₄	C₂³×C₇	1	4	yes	—
517	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
518	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
519	C₂³×C₄	—	2	1	no	—
520	C₂³×C₄	—	2	1	no	—
521	C₂³×C₄	—	2	1	no	—
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	—	2	1	no	—
524	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
525	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
526	AGL(1,ℤ/8)	—	2	32	no	—
527	#135	—	2	32	no	—
528	C₂×Q₁₆	—	2	4	no	—
529	C₂×Q₁₆	—	4	2	no	—
530	C₂×Q₁₆	C₂³×C₇	1	4	yes	complemented
531	C₂×Q₁₆	C₂³×C₇	1	4	yes	complemented
532	C₂×SD₁₆	—	2	4	no	—
533	C₂×SD₁₆	—	2	4	no	—
534	C₂×SD₁₆	—	2	4	no	—
535	C₂×SD₁₆	—	2	4	no	—
536	C₂×SD₁₆	—	4	2	no	—
537	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
538	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
539	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
540	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
541	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
542	C₂×D₈	—	2	4	no	—
543	C₂×D₈	C₇×D₄	1	8	yes	complemented
544	C₂×D₈	C₂³×C₇	1	4	yes	—
545	C₂×D₈	C₂³×C₇	1	4	yes	—
546	C₂×M₁₆	—	2	4	no	—
547	C₂×M₁₆	C₂³×C₇	1	4	yes	—
548	C₂²×C₈	—	2	4	no	—
549	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
550	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
551	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
552	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
553	C₂²×C₈	C₂³×C₇	1	4	yes	complemented
554	C₄⋊Q₈	—	2	2	no	—
555	C₄⋊Q₈	C₂³×C₇	1	4	yes	complemented
556	#124	—	2	2	no	—
557	#124	C₂³×C₇	1	4	yes	—
558	#123	—	2	8	no	—
559	#123	—	2	8	no	—
560	#123	—	2	8	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
565	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
566	C₂²⋊Q₈	C₂³×C₇	1	4	yes	complemented
567	#121	—	2	8	no	—
568	#121	—	2	2	no	—
569	#121	—	2	8	no	—
570	#121	C₂³×C₇	1	4	yes	—
571	#120	—	2	8	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	C₇×D₄	1	4	yes	—
575	C₄×D₄	C₂³×C₇	1	4	yes	—
576	C₄×D₄	C₂³×C₇	1	4	yes	—
577	C₄×D₄	C₂³×C₇	1	4	yes	complemented
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	8	no	—
584	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	—	2	1	no	—
591	C₂×C₂²⋊C₄	—	2	1	no	—
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₂²⋊C₄	—	2	1	no	—
594	C₂×C₂²⋊C₄	—	2	1	no	—
595	C₂×C₂²⋊C₄	—	2	8	no	—
596	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
599	#106	C₂³×C₇	1	4	yes	complemented
600	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
601	#103	C₂³×C₇	1	4	yes	complemented
602	#103	C₂³×C₇	1	4	yes	complemented
603	#103	C₂³×C₇	1	4	yes	complemented
604	#102	C₂³×C₇	1	4	yes	—
605	#102	C₂³×C₇	1	4	yes	—
606	#102	C₂³×C₇	1	4	yes	complemented
607	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
608	C₂²⋊C₈	C₂³×C₇	1	4	yes	complemented
609	#97	C₂³×C₇	1	4	yes	complemented
610	C₂²×C₇	—	2	2	no	—
611	C₂²×C₇	—	2	2	no	—
612	C₂²×C₇	—	2	4	no	—
613	C₂²×C₇	—	2	4	no	—
614	C₂²×C₇	—	2	2	no	—
615	C₂²×C₇	—	2	2	no	—
616	C₂²×C₇	—	2	2	no	—
617	C₂²×C₇	—	2	2	no	—
618	C₂²×C₇	—	4	4	no	—
619	C₂²×C₇	—	4	4	no	—
620	C₂²×C₇	—	4	8	no	—
621	C₂²×C₇	—	4	8	no	—
622	C₂²×C₇	—	4	2	no	—
623	C₂²×C₇	—	4	2	no	—
624	C₂²×C₇	—	4	2	no	—
625	C₂²×C₇	—	4	2	no	—
626	C₂²×C₇	—	4	2	no	—
627	C₂²×C₇	—	4	2	no	—
628	C₂²×C₇	—	4	2	no	—
629	C₂²×C₇	—	8	16	no	—
630	C₂²×C₇	—	8	4	no	—
631	C₂²×C₇	D₄²	1	2	yes	—
632	C₂²×C₇	#575	1	2	yes	—
633	C₂²×C₇	#577	1	2	yes	—
634	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
635	C₄×C₇	—	2	2	no	—
636	C₄×C₇	—	2	2	no	—
637	C₄×C₇	—	2	2	no	—
638	C₄×C₇	—	2	2	no	—
639	C₄×C₇	—	4	2	no	—
640	C₄×C₇	—	4	2	no	—
641	C₄×C₇	—	4	2	no	—
642	C₄×C₇	—	4	2	no	—
643	C₄×C₇	—	4	2	no	—
644	C₄×C₇	D₄²	1	2	yes	—
645	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
646	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
647	C₂⁴	—	2	1	no	—
648	C₂⁴	—	2	1	no	—
649	C₂⁴	—	2	1	no	—
650	C₂⁴	—	2	4	no	—
651	C₂⁴	—	4	4	no	—
652	C₂⁴	—	4	4	no	—
653	C₂⁴	—	8	2	no	—
654	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
655	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
656	#41	—	2	8	no	—
657	#41	—	2	8	no	—
658	#41	—	2	8	no	—
659	#41	—	4	4	no	—
660	#41	—	4	4	no	—
661	#41	—	4	4	no	—
662	#41	—	4	8	no	—
663	#41	—	4	8	no	—
664	#41	—	4	8	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
675	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
676	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
677	C₂×D₄	—	2	8	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	4	4	no	—
691	C₂×D₄	—	4	8	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	4	no	—
694	C₂×D₄	—	4	4	no	—
695	C₂×D₄	—	4	4	no	—
696	C₂×D₄	—	4	4	no	—
697	C₂×D₄	—	8	2	no	—
698	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
699	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
700	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
701	C₂×D₄	C₂⁴×C₇	1	2	yes	—
702	C₂×D₄	C₂⁴×C₇	1	2	yes	—
703	C₂×D₄	C₂⁴×C₇	1	2	yes	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	4	4	no	—
719	C₂²×C₄	—	4	4	no	—
720	C₂²×C₄	—	4	4	no	—
721	C₂²×C₄	—	4	4	no	—
722	C₂²×C₄	—	8	2	no	—
723	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
724	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
725	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
726	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
727	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
728	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
732	Q₁₆	—	2	8	no	—
733	Q₁₆	—	4	4	no	—
734	SD₁₆	—	2	8	no	—
735	SD₁₆	—	2	8	no	—
736	SD₁₆	—	2	8	no	—
737	SD₁₆	—	2	8	no	—
738	SD₁₆	—	4	4	no	—
739	D₈	—	2	8	no	—
740	D₈	C₂×C₇×D₄	1	16	yes	complemented
741	M₁₆	—	2	8	no	—
742	C₂×C₈	—	2	2	no	—
743	C₂×C₈	—	2	2	no	—
744	C₂×C₈	—	2	2	no	—
745	C₂×C₈	—	2	8	no	—
746	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
747	C₂×C₈	C₂⁴×C₇	1	2	yes	—
748	C₂×C₈	C₂⁴×C₇	1	2	yes	—
749	C₂×C₈	C₂⁴×C₇	1	2	yes	—
750	C₂×C₈	C₂⁴×C₇	1	2	yes	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
759	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
760	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
770	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
771	C₄²	C₂×C₇×D₄	1	2	yes	—
772	C₄²	C₂⁴×C₇	1	2	yes	—
773	C₂×C₇	—	4	2	no	—
774	C₂×C₇	—	4	2	no	—
775	C₂×C₇	—	4	4	no	—
776	C₂×C₇	—	4	4	no	—
777	C₂×C₇	—	8	2	no	—
778	C₂×C₇	#3267	1	4	yes	direct product factor
779	C₂×C₇	C₂×D₄²	1	1	yes	characteristic
780	C₂×C₇	C₂×#575	1	1	yes	characteristic
781	C₂×C₇	C₂×#577	1	1	yes	characteristic
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	4	no	—
787	C₂³	—	2	4	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	4	8	no	—
794	C₂³	—	4	8	no	—
795	C₂³	—	4	2	no	—
796	C₂³	—	4	2	no	—
797	C₂³	—	4	2	no	—
798	C₂³	—	4	2	no	—
799	C₂³	—	4	2	no	—
800	C₂³	—	4	2	no	—
801	C₂³	—	4	2	no	—
802	C₂³	—	8	4	no	—
803	C₂³	—	8	16	no	—
804	C₂³	C₂²×C₇×D₄	1	2	yes	—
805	C₂³	C₂²×C₇×D₄	1	2	yes	—
806	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
807	Q₈	—	2	2	no	—
808	Q₈	—	2	2	no	—
809	Q₈	—	2	2	no	—
810	Q₈	—	2	2	no	—
811	Q₈	—	2	2	no	—
812	Q₈	—	2	2	no	—
813	Q₈	—	4	2	no	—
814	Q₈	—	4	2	no	—
815	Q₈	—	4	2	no	—
816	D₄	—	2	2	no	—
817	D₄	—	2	2	no	—
818	D₄	—	2	2	no	—
819	D₄	—	2	2	no	—
820	D₄	—	2	4	no	—
821	D₄	—	2	4	no	—
822	D₄	—	4	4	no	—
823	D₄	—	4	8	no	—
824	D₄	—	4	8	no	—
825	D₄	—	4	8	no	—
826	D₄	—	4	8	no	—
827	D₄	—	4	2	no	—
828	D₄	—	8	4	no	—
829	D₄	C₂²×C₇×D₄	1	4	yes	—
830	D₄	C₂²×C₇×D₄	1	4	yes	—
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	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	4	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	4	8	no	—
847	C₂×C₄	—	4	8	no	—
848	C₂×C₄	—	4	8	no	—
849	C₂×C₄	—	4	8	no	—
850	C₂×C₄	—	4	2	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	2	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	—	4	2	no	—
855	C₂×C₄	—	8	4	no	—
856	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
857	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
858	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
859	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
860	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
861	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
862	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
863	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
864	C₈	—	2	2	no	—
865	C₈	—	2	2	no	—
866	C₈	—	2	2	no	—
867	C₈	C₂²×C₇×D₄	1	4	yes	—
868	C₇	C₂×#3267	1	1	yes	characteristic, direct product factor, Sylow
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	4	no	—
876	C₂²	—	2	4	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	4	no	—
882	C₂²	—	4	4	no	—
883	C₂²	—	4	8	no	—
884	C₂²	—	4	8	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	8	16	no	—
889	C₂²	—	8	4	no	—
890	C₂²	C₇×D₄²	1	2	yes	—
891	C₂²	C₇×#575	1	2	yes	—
892	C₂²	C₇×#577	1	2	yes	—
893	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	C₇×D₄²	1	2	yes	—
904	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
905	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
906	C₂	—	4	2	no	—
907	C₂	—	4	2	no	—
908	C₂	—	4	4	no	—
909	C₂	—	4	4	no	—
910	C₂	—	8	2	no	—
911	C₂	C₇×#3267	1	4	yes	direct product factor
912	C₂	C₂×C₇×D₄²	1	1	yes	characteristic
913	C₂	C₂×C₇×#575	1	1	yes	characteristic
914	C₂	C₂×C₇×#577	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. C₂²×C₇×#135	C₂	semidirect
3. C₂×C₇×#547	C₂	semidirect
4. C₂×C₇×#546	C₂	semidirect
5. C₇×#3267	C₂	direct (N × H)
6. C₂×C₇×#497	C₂	semidirect
7. C₂×C₇×#470	C₂	semidirect
8. C₂×C₇×#465	C₂	semidirect
9. C₂×C₇×#463	C₂	semidirect
10. C₂×C₇×#461	C₂	semidirect
11. C₂×C₇×#452	C₂	semidirect
12. C₂×C₇×#452	C₂	semidirect
13. C₂×C₇×#449	C₂	semidirect
14. C₂×C₇×#450	C₂	semidirect
15. C₂×C₇×#442	C₂	semidirect
16. C₂×C₇×#435	C₂	semidirect
19. C₂²×C₇×#41	C₂²	semidirect
22. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
24. C₂×C₇×#135	C₂²	semidirect
25. C₂²×C₇×Q₁₆	C₂²	semidirect
26. C₂²×C₇×Q₁₆	C₂²	semidirect
31. C₂²×C₇×SD₁₆	C₂²	semidirect
35. C₂³×C₇×C₈	C₂²	semidirect
37. C₇×#547	C₂²	semidirect
39. C₇×#546	C₂²	semidirect
40. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
47. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
54. C₂×C₄×C₇×D₄	C₂²	semidirect
57. C₇×#497	C₂²	semidirect
58. C₇×#470	C₂²	semidirect
59. C₇×#465	C₂²	semidirect
60. C₇×#463	C₂²	semidirect
61. C₇×#461	C₂²	semidirect
62. C₇×#452	C₂²	semidirect
63. C₇×#452	C₂²	semidirect
64. C₇×#450	C₂²	semidirect
65. C₇×#449	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×#103	C₂²	semidirect
72. C₂×C₇×#103	C₂²	semidirect
75. C₂×C₇×#102	C₂²	semidirect
77. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
78. C₂×C₇×#97	C₂²	semidirect
79. C₂×#3267	C₇	direct (N × H)
92. C₂×C₇×#41	C₂³	semidirect
120. C₂×C₇×Q₁₆	C₂³	semidirect
121. C₂×C₇×Q₁₆	C₂³	semidirect
131. C₂×C₇×SD₁₆	C₂³	semidirect
133. C₂×C₇×D₈	D₄	semidirect
143. C₂²×C₇×C₈	C₂³	semidirect
145. C₇×C₄⋊Q₈	C₂³	semidirect
156. C₇×C₂²⋊Q₈	C₂³	semidirect
167. C₄×C₇×D₄	C₂³	semidirect
189. C₇×#106	C₂³	semidirect
190. C₇×C₄⋊C₈	C₂³	semidirect
191. C₇×#103	C₂³	semidirect
192. C₇×#103	C₂³	semidirect
193. C₇×#103	C₂³	semidirect
196. C₇×#102	C₂³	semidirect
198. C₇×C₂²⋊C₈	C₂³	semidirect
199. C₇×#97	C₂³	semidirect
200. C₂²×AGL(1,ℤ/8)	C₂×C₇	semidirect
201. C₂²×#135	C₂×C₇	semidirect
202. C₂×#547	C₂×C₇	semidirect
203. C₂×#546	C₂×C₇	semidirect
204. #3267	C₂×C₇	direct (N × H)
205. C₂×#497	C₂×C₇	semidirect
206. C₂×#470	C₂×C₇	semidirect
207. C₂×#465	C₂×C₇	semidirect
208. C₂×#463	C₂×C₇	semidirect
209. C₂×#461	C₂×C₇	semidirect
210. C₂×#452	C₂×C₇	semidirect
211. C₂×#452	C₂×C₇	semidirect
212. C₂×#449	C₂×C₇	semidirect
213. C₂×#450	C₂×C₇	semidirect
214. C₂×#442	C₂×C₇	semidirect
215. C₂×#435	C₂×C₇	semidirect
309. C₇×D₈	C₂×D₄	semidirect
344. C₂²×#41	C₂²×C₇	semidirect
347. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
349. C₂×#135	C₂²×C₇	semidirect
350. C₂²×Q₁₆	C₂²×C₇	semidirect
351. C₂²×Q₁₆	C₂²×C₇	semidirect
356. C₂²×SD₁₆	C₂²×C₇	semidirect
360. C₂³×C₈	C₂²×C₇	semidirect
362. #547	C₂²×C₇	semidirect
364. #546	C₂²×C₇	semidirect
365. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
372. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
379. C₂×C₄×D₄	C₂²×C₇	semidirect
382. #497	C₂²×C₇	semidirect
383. #470	C₂²×C₇	semidirect
384. #465	C₂²×C₇	semidirect
385. #463	C₂²×C₇	semidirect
386. #461	C₂²×C₇	semidirect
387. #452	C₂²×C₇	semidirect
388. #452	C₂²×C₇	semidirect
389. #450	C₂²×C₇	semidirect
390. #449	C₂²×C₇	semidirect
391. #442	C₂²×C₇	semidirect
392. #435	C₂²×C₇	semidirect
393. C₂×#106	C₂²×C₇	semidirect
394. C₂×C₄⋊C₈	C₂²×C₇	semidirect
395. C₂×#103	C₂²×C₇	semidirect
396. C₂×#103	C₂²×C₇	semidirect
397. C₂×#103	C₂²×C₇	semidirect
400. C₂×#102	C₂²×C₇	semidirect
402. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
403. C₂×#97	C₂²×C₇	semidirect
502. C₂×#41	C₂³×C₇	semidirect
530. C₂×Q₁₆	C₂³×C₇	semidirect
531. C₂×Q₁₆	C₂³×C₇	semidirect
541. C₂×SD₁₆	C₂³×C₇	semidirect
543. C₂×D₈	C₇×D₄	semidirect
553. C₂²×C₈	C₂³×C₇	semidirect
555. C₄⋊Q₈	C₂³×C₇	semidirect
566. C₂²⋊Q₈	C₂³×C₇	semidirect
577. C₄×D₄	C₂³×C₇	semidirect
599. #106	C₂³×C₇	semidirect
600. C₄⋊C₈	C₂³×C₇	semidirect
601. #103	C₂³×C₇	semidirect
602. #103	C₂³×C₇	semidirect
603. #103	C₂³×C₇	semidirect
606. #102	C₂³×C₇	semidirect
608. C₂²⋊C₈	C₂³×C₇	semidirect
609. #97	C₂³×C₇	semidirect
740. D₈	C₂×C₇×D₄	semidirect
778. C₂×C₇	#3267	direct (N × H)
868. C₇	C₂×#3267	direct (N × H)
911. C₂	C₇×#3267	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
C₂²×C₇×#135	2
C₂×C₇×#547	2
C₂×C₇×#546	2
C₇×#3267	2
C₂×C₇×#497	2
C₂×C₇×#470	2
C₂×C₇×#465	2
C₂×C₇×#463	2
C₂×C₇×#461	2
C₂×C₇×#452	2
C₂×C₇×#449	2
C₂×C₇×#450	2
C₂×C₇×#442	2
C₂×C₇×#435	2
C₂×#3267	7

Subgroups — C2×C7×#3267 #13238241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3267 #13238241