Subgroups — C₂×C₇×#3265 #13238239

Order 1792.

3226 conjugacy classes of subgroups.

The subgroup lattice has 956 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×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#548	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3265	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₇×#496	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#468	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#450	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#447	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#440	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×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₇×D₄	—	2	1	no	—
20	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
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	—	2	8	no	—
25	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
27	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₇×SD₁₆	C₂²	1	8	yes	complemented
32	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
33	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
37	C₇×#548	—	2	4	no	—
38	C₇×#548	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
42	C₂×C₇×#124	—	2	1	no	—
43	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
45	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₇×#121	—	2	1	no	—
47	C₂×C₇×#121	—	2	1	no	—
48	C₂×C₇×#121	C₂²	1	1	yes	characteristic
49	C₂×C₇×#121	C₂²	1	1	yes	characteristic
50	C₂×C₇×#121	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₇×#120	—	2	1	no	—
52	C₂×C₇×#120	—	2	1	no	—
53	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₄×C₇×D₄	—	2	1	no	—
55	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
57	C₇×#496	C₂²	1	8	yes	complemented
58	C₇×#468	C₂²	1	8	yes	complemented
59	C₇×#466	C₂²	1	8	yes	complemented
60	C₇×#463	C₂²	1	8	yes	complemented
61	C₇×#460	C₂²	1	8	yes	complemented
62	C₇×#450	C₂²	1	8	yes	complemented
63	C₇×#449	C₂²	1	8	yes	complemented
64	C₇×#448	C₂²	1	8	yes	complemented
65	C₇×#447	C₂²	1	8	yes	complemented
66	C₇×#440	C₂²	1	8	yes	complemented
67	C₇×#435	C₂²	1	8	yes	complemented
68	C₂×C₇×#107	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×#102	C₂²	1	1	yes	characteristic
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×#3265	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂⁵×C₇	—	2	1	no	—
81	C₂⁵×C₇	—	2	1	no	—
82	C₂×C₇×#41	—	2	2	no	—
83	C₂×C₇×#41	—	2	4	no	—
84	C₂×C₇×#41	—	4	2	no	—
85	C₂×C₇×#41	C₂³	1	4	yes	complemented
86	C₂²×C₇×Q₈	—	2	1	no	—
87	C₂²×C₇×Q₈	—	2	2	no	—
88	C₂²×C₇×Q₈	—	2	4	no	—
89	C₂²×C₇×Q₈	—	4	2	no	—
90	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
91	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
92	C₂²×C₇×Q₈	C₂³	1	4	yes	complemented
93	C₂²×C₇×D₄	—	2	4	no	—
94	C₂²×C₇×D₄	—	2	4	no	—
95	C₂²×C₇×D₄	—	2	1	no	—
96	C₂²×C₇×D₄	—	2	1	no	—
97	C₂²×C₇×D₄	—	2	1	no	—
98	C₂²×C₇×D₄	—	2	1	no	—
99	C₂²×C₇×D₄	—	2	8	no	—
100	C₂²×C₇×D₄	—	2	1	no	—
101	C₂²×C₇×D₄	—	2	1	no	—
102	C₂²×C₇×D₄	—	2	1	no	—
103	C₂²×C₇×D₄	—	2	2	no	—
104	C₂²×C₇×D₄	—	2	2	no	—
105	C₂²×C₇×D₄	—	2	1	no	—
106	C₂²×C₇×D₄	—	4	2	no	—
107	C₂²×C₇×D₄	—	4	2	no	—
108	C₂²×C₇×D₄	—	4	8	no	—
109	C₂²×C₇×D₄	D₄	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	1	yes	characteristic
113	C₂²×C₇×D₄	C₂³	1	4	yes	—
114	C₂²×C₇×D₄	C₂³	1	4	yes	—
115	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₇	—	2	1	no	—
117	C₂³×C₄×C₇	—	2	1	no	—
118	C₂³×C₄×C₇	—	2	1	no	—
119	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
121	C₇×AGL(1,ℤ/8)	—	2	32	no	—
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	32	no	—
126	C₂×C₇×SD₁₆	—	2	4	no	—
127	C₂×C₇×SD₁₆	—	4	2	no	—
128	C₂×C₇×SD₁₆	D₄	1	8	yes	complemented
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×SD₁₆	C₂³	1	4	yes	complemented
133	C₂×C₇×SD₁₆	C₂³	1	4	yes	complemented
134	C₂×C₇×SD₁₆	C₂³	1	4	yes	complemented
135	C₂×C₇×D₈	—	2	4	no	—
136	C₂×C₇×D₈	—	2	4	no	—
137	C₂×C₇×D₈	—	4	2	no	—
138	C₂×C₇×D₈	C₂³	1	4	yes	—
139	C₂×C₇×D₈	C₂³	1	4	yes	complemented
140	C₂×C₇×D₈	C₂³	1	4	yes	complemented
141	C₂×C₇×M₁₆	—	2	4	no	—
142	C₂×C₇×M₁₆	C₂³	1	4	yes	complemented
143	C₂²×C₇×C₈	—	2	4	no	—
144	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
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	4	yes	complemented
149	C₇×#127	—	2	2	no	—
150	C₇×#127	C₂³	1	4	yes	—
151	C₇×#124	—	2	8	no	—
152	C₇×#124	—	2	2	no	—
153	C₇×#124	C₂³	1	4	yes	complemented
154	C₇×C₂²⋊Q₈	—	2	2	no	—
155	C₇×C₂²⋊Q₈	—	2	8	no	—
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	2	no	—
160	C₇×#121	—	2	2	no	—
161	C₇×#121	—	2	8	no	—
162	C₇×#121	C₂³	1	4	yes	—
163	C₇×#121	C₂³	1	4	yes	—
164	C₇×#121	C₂³	1	4	yes	complemented
165	C₇×#120	—	2	8	no	—
166	C₇×#120	—	2	8	no	—
167	C₄×C₇×Q₈	—	2	2	no	—
168	C₄×C₇×Q₈	C₂³	1	4	yes	complemented
169	C₄×C₇×D₄	—	2	8	no	—
170	C₄×C₇×D₄	—	2	2	no	—
171	C₄×C₇×D₄	D₄	1	4	yes	—
172	C₄×C₇×D₄	C₂³	1	4	yes	—
173	C₄×C₇×D₄	C₂³	1	4	yes	—
174	C₂×C₇×C₄⋊C₄	—	2	1	no	—
175	C₂×C₇×C₄⋊C₄	—	2	1	no	—
176	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
177	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
187	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₇	—	2	1	no	—
189	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
190	C₇×#107	C₂³	1	4	yes	complemented
191	C₇×C₄⋊C₈	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	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×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
203	C₂×#548	C₂×C₇	1	1	yes	characteristic, complemented
204	C₂×D₄²	C₂×C₇	1	1	yes	characteristic, complemented
205	#3265	C₂×C₇	1	16	yes	direct product factor
206	C₂×#496	C₂×C₇	1	1	yes	characteristic, complemented
207	C₂×#468	C₂×C₇	1	1	yes	characteristic, complemented
208	C₂×#466	C₂×C₇	1	1	yes	characteristic, complemented
209	C₂×#460	C₂×C₇	1	1	yes	characteristic, complemented
210	C₂×#463	C₂×C₇	1	1	yes	characteristic, complemented
211	C₂×#449	C₂×C₇	1	1	yes	characteristic, complemented
212	C₂×#448	C₂×C₇	1	1	yes	characteristic, complemented
213	C₂×#450	C₂×C₇	1	1	yes	characteristic, complemented
214	C₂×#447	C₂×C₇	1	1	yes	characteristic, complemented
215	C₂×#440	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	4	no	—
222	C₂⁴×C₇	—	2	4	no	—
223	C₂⁴×C₇	—	4	4	no	—
224	C₂⁴×C₇	—	4	4	no	—
225	C₂⁴×C₇	—	4	4	no	—
226	C₂⁴×C₇	—	4	4	no	—
227	C₂⁴×C₇	—	8	2	no	—
228	C₂⁴×C₇	—	8	2	no	—
229	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
230	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
231	C₇×#41	—	2	8	no	—
232	C₇×#41	—	4	4	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	4	no	—
237	C₂×C₇×Q₈	—	2	2	no	—
238	C₂×C₇×Q₈	—	2	8	no	—
239	C₂×C₇×Q₈	—	2	2	no	—
240	C₂×C₇×Q₈	—	2	2	no	—
241	C₂×C₇×Q₈	—	4	4	no	—
242	C₂×C₇×Q₈	—	4	4	no	—
243	C₂×C₇×Q₈	—	4	8	no	—
244	C₂×C₇×Q₈	C₂×D₄	1	4	yes	complemented
245	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
246	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
247	C₂×C₇×D₄	—	2	4	no	—
248	C₂×C₇×D₄	—	2	8	no	—
249	C₂×C₇×D₄	—	2	8	no	—
250	C₂×C₇×D₄	—	2	4	no	—
251	C₂×C₇×D₄	—	2	4	no	—
252	C₂×C₇×D₄	—	2	4	no	—
253	C₂×C₇×D₄	—	2	4	no	—
254	C₂×C₇×D₄	—	2	1	no	—
255	C₂×C₇×D₄	—	2	2	no	—
256	C₂×C₇×D₄	—	2	2	no	—
257	C₂×C₇×D₄	—	2	2	no	—
258	C₂×C₇×D₄	—	2	4	no	—
259	C₂×C₇×D₄	—	2	4	no	—
260	C₂×C₇×D₄	—	2	1	no	—
261	C₂×C₇×D₄	—	2	1	no	—
262	C₂×C₇×D₄	—	2	1	no	—
263	C₂×C₇×D₄	—	2	4	no	—
264	C₂×C₇×D₄	—	2	4	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	8	no	—
272	C₂×C₇×D₄	—	4	8	no	—
273	C₂×C₇×D₄	—	4	4	no	—
274	C₂×C₇×D₄	—	4	4	no	—
275	C₂×C₇×D₄	—	4	4	no	—
276	C₂×C₇×D₄	—	4	4	no	—
277	C₂×C₇×D₄	—	4	32	no	—
278	C₂×C₇×D₄	—	4	4	no	—
279	C₂×C₇×D₄	—	4	4	no	—
280	C₂×C₇×D₄	—	4	4	no	—
281	C₂×C₇×D₄	—	8	2	no	—
282	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
283	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
284	C₂×C₇×D₄	C₂⁴	1	2	yes	—
285	C₂×C₇×D₄	C₂⁴	1	2	yes	—
286	C₂×C₇×D₄	C₂⁴	1	2	yes	—
287	C₂×C₇×D₄	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₇	—	2	1	no	—
289	C₂²×C₄×C₇	—	2	2	no	—
290	C₂²×C₄×C₇	—	2	2	no	—
291	C₂²×C₄×C₇	—	2	2	no	—
292	C₂²×C₄×C₇	—	2	2	no	—
293	C₂²×C₄×C₇	—	2	4	no	—
294	C₂²×C₄×C₇	—	2	1	no	—
295	C₂²×C₄×C₇	—	2	1	no	—
296	C₂²×C₄×C₇	—	2	1	no	—
297	C₂²×C₄×C₇	—	2	4	no	—
298	C₂²×C₄×C₇	—	2	4	no	—
299	C₂²×C₄×C₇	—	4	4	no	—
300	C₂²×C₄×C₇	—	4	4	no	—
301	C₂²×C₄×C₇	—	4	4	no	—
302	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
303	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
304	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
311	C₇×SD₁₆	—	2	8	no	—
312	C₇×SD₁₆	—	2	8	no	—
313	C₇×SD₁₆	—	2	8	no	—
314	C₇×SD₁₆	—	2	8	no	—
315	C₇×SD₁₆	—	4	4	no	—
316	C₇×SD₁₆	C₂×D₄	1	16	yes	complemented
317	C₇×D₈	—	2	8	no	—
318	C₇×D₈	—	2	8	no	—
319	C₇×D₈	—	4	4	no	—
320	C₇×M₁₆	—	2	8	no	—
321	C₂×C₇×C₈	—	2	2	no	—
322	C₂×C₇×C₈	—	2	2	no	—
323	C₂×C₇×C₈	—	2	2	no	—
324	C₂×C₇×C₈	—	2	8	no	—
325	C₂×C₇×C₈	C₂×D₄	1	4	yes	complemented
326	C₂×C₇×C₈	C₂⁴	1	2	yes	—
327	C₂×C₇×C₈	C₂⁴	1	2	yes	—
328	C₂×C₇×C₈	C₂⁴	1	2	yes	—
329	C₂×C₇×C₈	C₂⁴	1	2	yes	—
330	C₇×C₄⋊C₄	—	2	4	no	—
331	C₇×C₄⋊C₄	—	2	4	no	—
332	C₇×C₄⋊C₄	—	2	1	no	—
333	C₇×C₄⋊C₄	—	2	1	no	—
334	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
335	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
336	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
337	C₇×C₂²⋊C₄	—	2	4	no	—
338	C₇×C₂²⋊C₄	—	2	4	no	—
339	C₇×C₂²⋊C₄	—	2	4	no	—
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	C₂×D₄	1	4	yes	—
345	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
346	C₄²×C₇	—	2	4	no	—
347	C₄²×C₇	C₂×D₄	1	2	yes	—
348	C₄²×C₇	C₂⁴	1	2	yes	—
349	C₂²×#41	C₂²×C₇	1	1	yes	characteristic, complemented
350	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
351	C₂³×D₄	—	2	1	no	—
352	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
353	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
354	C₂×AGL(1,ℤ/8)	—	2	8	no	—
355	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	8	yes	complemented
356	C₂²×SD₁₆	—	2	8	no	—
357	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
358	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
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×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
363	C₂²×SD₁₆	C₂²×C₇	1	8	yes	complemented
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×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
368	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
369	#548	—	2	4	no	—
370	#548	C₂²×C₇	1	8	yes	complemented
371	D₄²	—	2	4	no	—
372	D₄²	C₂²×C₇	1	8	yes	complemented
373	C₂×#127	C₂²×C₇	1	1	yes	characteristic
374	C₂×#124	—	2	1	no	—
375	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
376	C₂×C₂²⋊Q₈	—	2	1	no	—
377	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
378	C₂×#121	—	2	1	no	—
379	C₂×#121	—	2	1	no	—
380	C₂×#121	C₂²×C₇	1	1	yes	characteristic
381	C₂×#121	C₂²×C₇	1	1	yes	characteristic
382	C₂×#121	C₂²×C₇	1	1	yes	characteristic, complemented
383	C₂×#120	—	2	1	no	—
384	C₂×#120	—	2	1	no	—
385	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
386	C₂×C₄×D₄	—	2	1	no	—
387	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
388	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
389	#496	C₂²×C₇	1	8	yes	complemented
390	#468	C₂²×C₇	1	8	yes	complemented
391	#466	C₂²×C₇	1	8	yes	complemented
392	#463	C₂²×C₇	1	8	yes	complemented
393	#460	C₂²×C₇	1	8	yes	complemented
394	#450	C₂²×C₇	1	8	yes	complemented
395	#449	C₂²×C₇	1	8	yes	complemented
396	#448	C₂²×C₇	1	8	yes	complemented
397	#447	C₂²×C₇	1	8	yes	complemented
398	#440	C₂²×C₇	1	8	yes	complemented
399	#435	C₂²×C₇	1	8	yes	complemented
400	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
401	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
402	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
403	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
404	C₂×#102	C₂²×C₇	1	1	yes	characteristic
405	C₂×#102	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×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
409	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
410	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
411	C₂³×C₇	—	2	2	no	—
412	C₂³×C₇	—	2	2	no	—
413	C₂³×C₇	—	2	2	no	—
414	C₂³×C₇	—	2	4	no	—
415	C₂³×C₇	—	2	2	no	—
416	C₂³×C₇	—	2	2	no	—
417	C₂³×C₇	—	2	2	no	—
418	C₂³×C₇	—	2	2	no	—
419	C₂³×C₇	—	2	2	no	—
420	C₂³×C₇	—	2	2	no	—
421	C₂³×C₇	—	4	8	no	—
422	C₂³×C₇	—	4	8	no	—
423	C₂³×C₇	—	4	8	no	—
424	C₂³×C₇	—	4	2	no	—
425	C₂³×C₇	—	4	2	no	—
426	C₂³×C₇	—	4	2	no	—
427	C₂³×C₇	—	4	2	no	—
428	C₂³×C₇	—	4	2	no	—
429	C₂³×C₇	—	4	2	no	—
430	C₂³×C₇	—	4	2	no	—
431	C₂³×C₇	—	4	2	no	—
432	C₂³×C₇	—	4	8	no	—
433	C₂³×C₇	—	4	2	no	—
434	C₂³×C₇	—	4	2	no	—
435	C₂³×C₇	—	4	2	no	—
436	C₂³×C₇	—	8	4	no	—
437	C₂³×C₇	—	8	4	no	—
438	C₂³×C₇	—	8	16	no	—
439	C₂³×C₇	—	8	16	no	—
440	C₂³×C₇	AGL(1,ℤ/8)	1	4	yes	complemented
441	C₂³×C₇	C₂²×D₄	1	2	yes	—
442	C₂³×C₇	C₂²×D₄	1	2	yes	—
443	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
444	C₇×Q₈	—	2	4	no	—
445	C₇×Q₈	—	2	2	no	—
446	C₇×Q₈	—	2	2	no	—
447	C₇×Q₈	—	2	2	no	—
448	C₇×Q₈	—	4	8	no	—
449	C₇×Q₈	—	4	2	no	—
450	C₇×Q₈	C₂²×D₄	1	4	yes	complemented
451	C₇×D₄	—	2	8	no	—
452	C₇×D₄	—	2	4	no	—
453	C₇×D₄	—	2	2	no	—
454	C₇×D₄	—	2	2	no	—
455	C₇×D₄	—	2	2	no	—
456	C₇×D₄	—	2	2	no	—
457	C₇×D₄	—	2	2	no	—
458	C₇×D₄	—	2	2	no	—
459	C₇×D₄	—	2	2	no	—
460	C₇×D₄	—	4	8	no	—
461	C₇×D₄	—	4	8	no	—
462	C₇×D₄	—	4	8	no	—
463	C₇×D₄	—	4	8	no	—
464	C₇×D₄	—	4	8	no	—
465	C₇×D₄	—	4	8	no	—
466	C₇×D₄	—	4	8	no	—
467	C₇×D₄	—	4	2	no	—
468	C₇×D₄	—	4	2	no	—
469	C₇×D₄	—	4	2	no	—
470	C₇×D₄	—	8	4	no	—
471	C₇×D₄	C₂²×D₄	1	4	yes	—
472	C₂×C₄×C₇	—	2	2	no	—
473	C₂×C₄×C₇	—	2	2	no	—
474	C₂×C₄×C₇	—	2	4	no	—
475	C₂×C₄×C₇	—	2	2	no	—
476	C₂×C₄×C₇	—	2	2	no	—
477	C₂×C₄×C₇	—	2	2	no	—
478	C₂×C₄×C₇	—	2	4	no	—
479	C₂×C₄×C₇	—	2	4	no	—
480	C₂×C₄×C₇	—	2	2	no	—
481	C₂×C₄×C₇	—	2	2	no	—
482	C₂×C₄×C₇	—	2	2	no	—
483	C₂×C₄×C₇	—	2	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	—	4	8	no	—
488	C₂×C₄×C₇	—	4	8	no	—
489	C₂×C₄×C₇	—	4	8	no	—
490	C₂×C₄×C₇	—	4	2	no	—
491	C₂×C₄×C₇	—	4	2	no	—
492	C₂×C₄×C₇	—	4	2	no	—
493	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
500	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
501	C₇×C₈	—	2	2	no	—
502	C₇×C₈	—	2	2	no	—
503	C₇×C₈	—	2	2	no	—
504	C₇×C₈	C₂²×D₄	1	4	yes	complemented
505	C₂⁵	—	2	1	no	—
506	C₂⁵	—	2	1	no	—
507	C₂×#41	—	2	2	no	—
508	C₂×#41	—	2	4	no	—
509	C₂×#41	—	4	2	no	—
510	C₂×#41	C₂³×C₇	1	4	yes	complemented
511	C₂²×Q₈	—	2	1	no	—
512	C₂²×Q₈	—	2	2	no	—
513	C₂²×Q₈	—	2	4	no	—
514	C₂²×Q₈	—	4	2	no	—
515	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
516	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
517	C₂²×Q₈	C₂³×C₇	1	4	yes	complemented
518	C₂²×D₄	—	2	4	no	—
519	C₂²×D₄	—	2	4	no	—
520	C₂²×D₄	—	2	1	no	—
521	C₂²×D₄	—	2	1	no	—
522	C₂²×D₄	—	2	1	no	—
523	C₂²×D₄	—	2	1	no	—
524	C₂²×D₄	—	2	8	no	—
525	C₂²×D₄	—	2	1	no	—
526	C₂²×D₄	—	2	1	no	—
527	C₂²×D₄	—	2	1	no	—
528	C₂²×D₄	—	2	2	no	—
529	C₂²×D₄	—	2	2	no	—
530	C₂²×D₄	—	2	1	no	—
531	C₂²×D₄	—	4	2	no	—
532	C₂²×D₄	—	4	2	no	—
533	C₂²×D₄	—	4	8	no	—
534	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
535	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
536	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
537	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
538	C₂²×D₄	C₂³×C₇	1	4	yes	—
539	C₂²×D₄	C₂³×C₇	1	4	yes	—
540	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
541	C₂³×C₄	—	2	1	no	—
542	C₂³×C₄	—	2	1	no	—
543	C₂³×C₄	—	2	1	no	—
544	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
546	AGL(1,ℤ/8)	—	2	32	no	—
547	C₂×SD₁₆	—	2	4	no	—
548	C₂×SD₁₆	—	2	4	no	—
549	C₂×SD₁₆	—	2	4	no	—
550	C₂×SD₁₆	—	2	32	no	—
551	C₂×SD₁₆	—	2	4	no	—
552	C₂×SD₁₆	—	4	2	no	—
553	C₂×SD₁₆	C₇×D₄	1	8	yes	complemented
554	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
555	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
556	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
557	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
558	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
559	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
560	C₂×D₈	—	2	4	no	—
561	C₂×D₈	—	2	4	no	—
562	C₂×D₈	—	4	2	no	—
563	C₂×D₈	C₂³×C₇	1	4	yes	—
564	C₂×D₈	C₂³×C₇	1	4	yes	complemented
565	C₂×D₈	C₂³×C₇	1	4	yes	complemented
566	C₂×M₁₆	—	2	4	no	—
567	C₂×M₁₆	C₂³×C₇	1	4	yes	complemented
568	C₂²×C₈	—	2	4	no	—
569	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
570	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
571	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
572	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
573	C₂²×C₈	C₂³×C₇	1	4	yes	complemented
574	#127	—	2	2	no	—
575	#127	C₂³×C₇	1	4	yes	—
576	#124	—	2	8	no	—
577	#124	—	2	2	no	—
578	#124	C₂³×C₇	1	4	yes	complemented
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	8	no	—
581	C₂²⋊Q₈	C₂³×C₇	1	4	yes	complemented
582	#121	—	2	8	no	—
583	#121	—	2	2	no	—
584	#121	—	2	2	no	—
585	#121	—	2	2	no	—
586	#121	—	2	8	no	—
587	#121	C₂³×C₇	1	4	yes	—
588	#121	C₂³×C₇	1	4	yes	—
589	#121	C₂³×C₇	1	4	yes	complemented
590	#120	—	2	8	no	—
591	#120	—	2	8	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	C₂³×C₇	1	4	yes	complemented
594	C₄×D₄	—	2	8	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	C₇×D₄	1	4	yes	—
597	C₄×D₄	C₂³×C₇	1	4	yes	—
598	C₄×D₄	C₂³×C₇	1	4	yes	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
613	C₂×C₄²	—	2	1	no	—
614	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
615	#107	C₂³×C₇	1	4	yes	complemented
616	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
617	#103	C₂³×C₇	1	4	yes	complemented
618	#103	C₂³×C₇	1	4	yes	complemented
619	#102	C₂³×C₇	1	4	yes	—
620	#102	C₂³×C₇	1	4	yes	complemented
621	#102	C₂³×C₇	1	4	yes	complemented
622	#102	C₂³×C₇	1	4	yes	complemented
623	C₂²⋊C₈	C₂³×C₇	1	4	yes	complemented
624	C₂²⋊C₈	C₂³×C₇	1	4	yes	complemented
625	#97	C₂³×C₇	1	4	yes	complemented
626	C₂²×C₇	—	2	2	no	—
627	C₂²×C₇	—	2	8	no	—
628	C₂²×C₇	—	2	2	no	—
629	C₂²×C₇	—	2	2	no	—
630	C₂²×C₇	—	2	4	no	—
631	C₂²×C₇	—	2	2	no	—
632	C₂²×C₇	—	2	2	no	—
633	C₂²×C₇	—	4	4	no	—
634	C₂²×C₇	—	4	8	no	—
635	C₂²×C₇	—	4	2	no	—
636	C₂²×C₇	—	4	2	no	—
637	C₂²×C₇	—	4	2	no	—
638	C₂²×C₇	—	4	2	no	—
639	C₂²×C₇	—	4	2	no	—
640	C₂²×C₇	—	4	2	no	—
641	C₂²×C₇	—	4	2	no	—
642	C₂²×C₇	—	4	2	no	—
643	C₂²×C₇	—	4	2	no	—
644	C₂²×C₇	—	4	2	no	—
645	C₂²×C₇	—	4	2	no	—
646	C₂²×C₇	—	8	16	no	—
647	C₂²×C₇	—	8	16	no	—
648	C₂²×C₇	—	8	4	no	—
649	C₂²×C₇	—	8	4	no	—
650	C₂²×C₇	—	8	4	no	—
651	C₂²×C₇	D₄²	1	2	yes	—
652	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
653	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	complemented
654	C₂²×C₇	#577	1	2	yes	—
655	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
656	C₄×C₇	—	2	2	no	—
657	C₄×C₇	—	2	2	no	—
658	C₄×C₇	—	2	4	no	—
659	C₄×C₇	—	2	2	no	—
660	C₄×C₇	—	2	2	no	—
661	C₄×C₇	—	4	2	no	—
662	C₄×C₇	—	4	2	no	—
663	C₄×C₇	—	4	2	no	—
664	C₄×C₇	D₄²	1	2	yes	—
665	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
666	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
667	C₂⁴	—	2	1	no	—
668	C₂⁴	—	2	1	no	—
669	C₂⁴	—	2	1	no	—
670	C₂⁴	—	2	1	no	—
671	C₂⁴	—	2	4	no	—
672	C₂⁴	—	2	4	no	—
673	C₂⁴	—	4	4	no	—
674	C₂⁴	—	4	4	no	—
675	C₂⁴	—	4	4	no	—
676	C₂⁴	—	4	4	no	—
677	C₂⁴	—	8	2	no	—
678	C₂⁴	—	8	2	no	—
679	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
680	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
681	#41	—	2	8	no	—
682	#41	—	4	4	no	—
683	#41	—	4	8	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	1	no	—
686	C₂×Q₈	—	2	4	no	—
687	C₂×Q₈	—	2	2	no	—
688	C₂×Q₈	—	2	8	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	4	4	no	—
692	C₂×Q₈	—	4	4	no	—
693	C₂×Q₈	—	4	8	no	—
694	C₂×Q₈	C₂×C₇×D₄	1	4	yes	complemented
695	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
696	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	8	no	—
699	C₂×D₄	—	2	8	no	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	4	no	—
703	C₂×D₄	—	2	4	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	4	no	—
710	C₂×D₄	—	2	1	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	4	4	no	—
720	C₂×D₄	—	4	4	no	—
721	C₂×D₄	—	4	8	no	—
722	C₂×D₄	—	4	8	no	—
723	C₂×D₄	—	4	4	no	—
724	C₂×D₄	—	4	4	no	—
725	C₂×D₄	—	4	4	no	—
726	C₂×D₄	—	4	4	no	—
727	C₂×D₄	—	4	32	no	—
728	C₂×D₄	—	4	4	no	—
729	C₂×D₄	—	4	4	no	—
730	C₂×D₄	—	4	4	no	—
731	C₂×D₄	—	8	2	no	—
732	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
733	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
734	C₂×D₄	C₂⁴×C₇	1	2	yes	—
735	C₂×D₄	C₂⁴×C₇	1	2	yes	—
736	C₂×D₄	C₂⁴×C₇	1	2	yes	—
737	C₂×D₄	C₂⁴×C₇	1	2	yes	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	1	no	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	4	no	—
747	C₂²×C₄	—	2	4	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	4	4	no	—
750	C₂²×C₄	—	4	4	no	—
751	C₂²×C₄	—	4	4	no	—
752	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
753	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
754	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
755	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
756	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
757	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
761	SD₁₆	—	2	8	no	—
762	SD₁₆	—	2	8	no	—
763	SD₁₆	—	2	8	no	—
764	SD₁₆	—	2	8	no	—
765	SD₁₆	—	4	4	no	—
766	SD₁₆	C₂×C₇×D₄	1	16	yes	complemented
767	D₈	—	2	8	no	—
768	D₈	—	2	8	no	—
769	D₈	—	4	4	no	—
770	M₁₆	—	2	8	no	—
771	C₂×C₈	—	2	2	no	—
772	C₂×C₈	—	2	2	no	—
773	C₂×C₈	—	2	2	no	—
774	C₂×C₈	—	2	8	no	—
775	C₂×C₈	C₂×C₇×D₄	1	4	yes	complemented
776	C₂×C₈	C₂⁴×C₇	1	2	yes	—
777	C₂×C₈	C₂⁴×C₇	1	2	yes	—
778	C₂×C₈	C₂⁴×C₇	1	2	yes	—
779	C₂×C₈	C₂⁴×C₇	1	2	yes	—
780	C₄⋊C₄	—	2	4	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
785	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
786	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
795	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
796	C₄²	—	2	4	no	—
797	C₄²	C₂×C₇×D₄	1	2	yes	—
798	C₄²	C₂⁴×C₇	1	2	yes	—
799	C₂×C₇	—	2	4	no	—
800	C₂×C₇	—	4	2	no	—
801	C₂×C₇	—	4	4	no	—
802	C₂×C₇	—	8	2	no	—
803	C₂×C₇	—	8	2	no	—
804	C₂×C₇	—	8	2	no	—
805	C₂×C₇	#3265	1	4	yes	direct product factor
806	C₂×C₇	C₂×D₄²	1	1	yes	characteristic
807	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
808	C₂×C₇	C₂×#577	1	1	yes	characteristic
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	4	8	no	—
820	C₂³	—	4	8	no	—
821	C₂³	—	4	8	no	—
822	C₂³	—	4	2	no	—
823	C₂³	—	4	2	no	—
824	C₂³	—	4	2	no	—
825	C₂³	—	4	2	no	—
826	C₂³	—	4	2	no	—
827	C₂³	—	4	2	no	—
828	C₂³	—	4	2	no	—
829	C₂³	—	4	2	no	—
830	C₂³	—	4	8	no	—
831	C₂³	—	4	2	no	—
832	C₂³	—	4	2	no	—
833	C₂³	—	4	2	no	—
834	C₂³	—	8	4	no	—
835	C₂³	—	8	4	no	—
836	C₂³	—	8	16	no	—
837	C₂³	—	8	16	no	—
838	C₂³	C₇×AGL(1,ℤ/8)	1	4	yes	complemented
839	C₂³	C₂²×C₇×D₄	1	2	yes	—
840	C₂³	C₂²×C₇×D₄	1	2	yes	—
841	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
842	Q₈	—	2	2	no	—
843	Q₈	—	2	4	no	—
844	Q₈	—	2	2	no	—
845	Q₈	—	2	2	no	—
846	Q₈	—	4	8	no	—
847	Q₈	—	4	2	no	—
848	Q₈	C₂²×C₇×D₄	1	4	yes	complemented
849	D₄	—	2	8	no	—
850	D₄	—	2	2	no	—
851	D₄	—	2	2	no	—
852	D₄	—	2	2	no	—
853	D₄	—	2	2	no	—
854	D₄	—	2	2	no	—
855	D₄	—	2	2	no	—
856	D₄	—	2	2	no	—
857	D₄	—	2	4	no	—
858	D₄	—	4	8	no	—
859	D₄	—	4	8	no	—
860	D₄	—	4	8	no	—
861	D₄	—	4	8	no	—
862	D₄	—	4	8	no	—
863	D₄	—	4	8	no	—
864	D₄	—	4	8	no	—
865	D₄	—	4	2	no	—
866	D₄	—	4	2	no	—
867	D₄	—	4	2	no	—
868	D₄	—	8	4	no	—
869	D₄	C₂²×C₇×D₄	1	4	yes	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	4	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	4	no	—
881	C₂×C₄	—	2	4	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	4	8	no	—
886	C₂×C₄	—	4	8	no	—
887	C₂×C₄	—	4	8	no	—
888	C₂×C₄	—	4	2	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	4	2	no	—
891	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
892	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
893	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
894	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
895	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
896	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
897	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
898	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
899	C₈	—	2	2	no	—
900	C₈	—	2	2	no	—
901	C₈	—	2	2	no	—
902	C₈	C₂²×C₇×D₄	1	4	yes	complemented
903	C₇	C₂×#3265	1	1	yes	characteristic, direct product factor, Sylow
904	C₂²	—	2	2	no	—
905	C₂²	—	2	8	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	2	2	no	—
910	C₂²	—	2	4	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	4	no	—
914	C₂²	—	4	8	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	8	16	no	—
925	C₂²	—	8	16	no	—
926	C₂²	—	8	4	no	—
927	C₂²	—	8	4	no	—
928	C₂²	—	8	4	no	—
929	C₂²	C₇×D₄²	1	2	yes	—
930	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
931	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	complemented
932	C₂²	C₇×#577	1	2	yes	—
933	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	2	no	—
938	C₄	—	2	4	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	2	no	—
942	C₄	C₇×D₄²	1	2	yes	—
943	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
944	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
945	C₂	—	2	4	no	—
946	C₂	—	4	2	no	—
947	C₂	—	4	4	no	—
948	C₂	—	8	2	no	—
949	C₂	—	8	2	no	—
950	C₂	—	8	2	no	—
951	C₂	C₇×#3265	1	4	yes	direct product factor
952	C₂	C₂×C₇×D₄²	1	1	yes	characteristic
953	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
954	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. C₂³×C₇×SD₁₆	C₂	semidirect
3. C₂×C₇×#548	C₂	semidirect
4. C₂×C₇×D₄²	C₂	semidirect
5. C₇×#3265	C₂	direct (N × H)
6. C₂×C₇×#496	C₂	semidirect
7. C₂×C₇×#468	C₂	semidirect
8. C₂×C₇×#466	C₂	semidirect
9. C₂×C₇×#460	C₂	semidirect
10. C₂×C₇×#463	C₂	semidirect
11. C₂×C₇×#449	C₂	semidirect
12. C₂×C₇×#448	C₂	semidirect
13. C₂×C₇×#450	C₂	semidirect
14. C₂×C₇×#447	C₂	semidirect
15. C₂×C₇×#440	C₂	semidirect
16. C₂×C₇×#435	C₂	semidirect
17. C₂²×C₇×#41	C₂²	semidirect
18. C₂³×C₇×Q₈	C₂²	semidirect
23. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂²×C₇×SD₁₆	C₂²	semidirect
28. C₂²×C₇×SD₁₆	C₂²	semidirect
29. C₂²×C₇×SD₁₆	C₂²	semidirect
30. C₂²×C₇×SD₁₆	C₂²	semidirect
31. C₂²×C₇×SD₁₆	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×#548	C₂²	semidirect
40. C₇×D₄²	C₂²	semidirect
43. C₂×C₇×#124	C₂²	semidirect
45. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
50. C₂×C₇×#121	C₂²	semidirect
53. C₂×C₄×C₇×Q₈	C₂²	semidirect
57. C₇×#496	C₂²	semidirect
58. C₇×#468	C₂²	semidirect
59. C₇×#466	C₂²	semidirect
60. C₇×#463	C₂²	semidirect
61. C₇×#460	C₂²	semidirect
62. C₇×#450	C₂²	semidirect
63. C₇×#449	C₂²	semidirect
64. C₇×#448	C₂²	semidirect
65. C₇×#447	C₂²	semidirect
66. C₇×#440	C₂²	semidirect
67. C₇×#435	C₂²	semidirect
68. C₂×C₇×#107	C₂²	semidirect
69. C₂×C₇×C₄⋊C₈	C₂²	semidirect
70. C₂×C₇×#103	C₂²	semidirect
71. C₂×C₇×#103	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×#3265	C₇	direct (N × H)
85. C₂×C₇×#41	C₂³	semidirect
92. C₂²×C₇×Q₈	C₂³	semidirect
128. C₂×C₇×SD₁₆	D₄	semidirect
131. C₂×C₇×SD₁₆	C₂³	semidirect
132. C₂×C₇×SD₁₆	C₂³	semidirect
133. C₂×C₇×SD₁₆	C₂³	semidirect
134. C₂×C₇×SD₁₆	C₂³	semidirect
139. C₂×C₇×D₈	C₂³	semidirect
140. C₂×C₇×D₈	C₂³	semidirect
142. C₂×C₇×M₁₆	C₂³	semidirect
148. C₂²×C₇×C₈	C₂³	semidirect
153. C₇×#124	C₂³	semidirect
156. C₇×C₂²⋊Q₈	C₂³	semidirect
164. C₇×#121	C₂³	semidirect
168. C₄×C₇×Q₈	C₂³	semidirect
190. C₇×#107	C₂³	semidirect
191. C₇×C₄⋊C₈	C₂³	semidirect
192. C₇×#103	C₂³	semidirect
193. C₇×#103	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×SD₁₆	C₂×C₇	semidirect
203. C₂×#548	C₂×C₇	semidirect
204. C₂×D₄²	C₂×C₇	semidirect
205. #3265	C₂×C₇	direct (N × H)
206. C₂×#496	C₂×C₇	semidirect
207. C₂×#468	C₂×C₇	semidirect
208. C₂×#466	C₂×C₇	semidirect
209. C₂×#460	C₂×C₇	semidirect
210. C₂×#463	C₂×C₇	semidirect
211. C₂×#449	C₂×C₇	semidirect
212. C₂×#448	C₂×C₇	semidirect
213. C₂×#450	C₂×C₇	semidirect
214. C₂×#447	C₂×C₇	semidirect
215. C₂×#440	C₂×C₇	semidirect
216. C₂×#435	C₂×C₇	semidirect
244. C₂×C₇×Q₈	C₂×D₄	semidirect
316. C₇×SD₁₆	C₂×D₄	semidirect
325. C₂×C₇×C₈	C₂×D₄	semidirect
349. C₂²×#41	C₂²×C₇	semidirect
350. C₂³×Q₈	C₂²×C₇	semidirect
355. 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
362. C₂²×SD₁₆	C₂²×C₇	semidirect
363. C₂²×SD₁₆	C₂²×C₇	semidirect
365. C₂²×D₈	C₂²×C₇	semidirect
366. C₂²×D₈	C₂²×C₇	semidirect
367. C₂²×M₁₆	C₂²×C₇	semidirect
368. C₂³×C₈	C₂²×C₇	semidirect
370. #548	C₂²×C₇	semidirect
372. D₄²	C₂²×C₇	semidirect
375. C₂×#124	C₂²×C₇	semidirect
377. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
382. C₂×#121	C₂²×C₇	semidirect
385. C₂×C₄×Q₈	C₂²×C₇	semidirect
389. #496	C₂²×C₇	semidirect
390. #468	C₂²×C₇	semidirect
391. #466	C₂²×C₇	semidirect
392. #463	C₂²×C₇	semidirect
393. #460	C₂²×C₇	semidirect
394. #450	C₂²×C₇	semidirect
395. #449	C₂²×C₇	semidirect
396. #448	C₂²×C₇	semidirect
397. #447	C₂²×C₇	semidirect
398. #440	C₂²×C₇	semidirect
399. #435	C₂²×C₇	semidirect
400. C₂×#107	C₂²×C₇	semidirect
401. C₂×C₄⋊C₈	C₂²×C₇	semidirect
402. C₂×#103	C₂²×C₇	semidirect
403. C₂×#103	C₂²×C₇	semidirect
405. C₂×#102	C₂²×C₇	semidirect
406. C₂×#102	C₂²×C₇	semidirect
407. C₂×#102	C₂²×C₇	semidirect
408. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
409. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
410. C₂×#97	C₂²×C₇	semidirect
440. C₂³×C₇	AGL(1,ℤ/8)	semidirect
450. C₇×Q₈	C₂²×D₄	semidirect
504. C₇×C₈	C₂²×D₄	semidirect
510. C₂×#41	C₂³×C₇	semidirect
517. C₂²×Q₈	C₂³×C₇	semidirect
553. C₂×SD₁₆	C₇×D₄	semidirect
556. C₂×SD₁₆	C₂³×C₇	semidirect
557. C₂×SD₁₆	C₂³×C₇	semidirect
558. C₂×SD₁₆	C₂³×C₇	semidirect
559. C₂×SD₁₆	C₂³×C₇	semidirect
564. C₂×D₈	C₂³×C₇	semidirect
565. C₂×D₈	C₂³×C₇	semidirect
567. C₂×M₁₆	C₂³×C₇	semidirect
573. C₂²×C₈	C₂³×C₇	semidirect
578. #124	C₂³×C₇	semidirect
581. C₂²⋊Q₈	C₂³×C₇	semidirect
589. #121	C₂³×C₇	semidirect
593. C₄×Q₈	C₂³×C₇	semidirect
615. #107	C₂³×C₇	semidirect
616. C₄⋊C₈	C₂³×C₇	semidirect
617. #103	C₂³×C₇	semidirect
618. #103	C₂³×C₇	semidirect
620. #102	C₂³×C₇	semidirect
621. #102	C₂³×C₇	semidirect
622. #102	C₂³×C₇	semidirect
623. C₂²⋊C₈	C₂³×C₇	semidirect
624. C₂²⋊C₈	C₂³×C₇	semidirect
625. #97	C₂³×C₇	semidirect
653. C₂²×C₇	C₂×AGL(1,ℤ/8)	semidirect
694. C₂×Q₈	C₂×C₇×D₄	semidirect
766. SD₁₆	C₂×C₇×D₄	semidirect
775. C₂×C₈	C₂×C₇×D₄	semidirect
805. C₂×C₇	#3265	direct (N × H)
838. C₂³	C₇×AGL(1,ℤ/8)	semidirect
848. Q₈	C₂²×C₇×D₄	semidirect
902. C₈	C₂²×C₇×D₄	semidirect
903. C₇	C₂×#3265	direct (N × H)
931. C₂²	C₂×C₇×AGL(1,ℤ/8)	semidirect
951. C₂	C₇×#3265	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×SD₁₆	2
C₂×C₇×#548	2
C₂×C₇×D₄²	2
C₇×#3265	2
C₂×C₇×#496	2
C₂×C₇×#468	2
C₂×C₇×#466	2
C₂×C₇×#460	2
C₂×C₇×#463	2
C₂×C₇×#449	2
C₂×C₇×#448	2
C₂×C₇×#450	2
C₂×C₇×#447	2
C₂×C₇×#440	2
C₂×C₇×#435	2
C₂×#3265	7

Subgroups — C2×C7×#3265 #13238239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3265 #13238239