Subgroups — C₂×C₇×#3268 #13238242

Order 1792.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 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×#550	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3268	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×#464	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#449	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#449	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
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×SD₁₆	C₂²	1	1	yes	characteristic
27	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
31	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
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×#550	—	2	4	no	—
37	C₇×#550	C₂²	1	8	yes	complemented
38	C₇×#546	—	2	4	no	—
39	C₇×#546	C₂²	1	8	yes	complemented
40	C₂×C₇×#127	—	2	1	no	—
41	C₂×C₇×#127	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₇×#124	C₂²	1	1	yes	characteristic
43	C₂×C₇×#123	—	2	1	no	—
44	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₇×#121	—	2	1	no	—
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×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄×C₇×D₄	—	2	1	no	—
54	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
56	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
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×#464	C₂²	1	8	yes	complemented
61	C₇×#459	C₂²	1	8	yes	complemented
62	C₇×#452	C₂²	1	8	yes	complemented
63	C₇×#449	C₂²	1	8	yes	complemented
64	C₇×#449	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
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
77	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
79	C₂×#3268	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×D₄	—	2	4	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	1	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	1	no	—
105	C₂²×C₇×D₄	—	2	1	no	—
106	C₂²×C₇×D₄	—	4	2	no	—
107	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
108	C₂²×C₇×D₄	C₂³	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	4	yes	—
112	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₇	—	2	1	no	—
114	C₂³×C₄×C₇	—	2	1	no	—
115	C₂³×C₄×C₇	—	2	1	no	—
116	C₂³×C₄×C₇	—	2	1	no	—
117	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
119	C₇×AGL(1,ℤ/8)	—	2	32	no	—
120	C₇×#135	—	2	32	no	—
121	C₂×C₇×Q₁₆	—	2	4	no	—
122	C₂×C₇×Q₁₆	C₂³	1	4	yes	complemented
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	D₄	1	8	yes	complemented
127	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
128	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
129	C₂×C₇×SD₁₆	C₂³	1	4	yes	complemented
130	C₂×C₇×SD₁₆	C₂³	1	4	yes	complemented
131	C₂×C₇×D₈	—	2	4	no	—
132	C₂×C₇×D₈	—	2	4	no	—
133	C₂×C₇×D₈	—	2	4	no	—
134	C₂×C₇×D₈	—	4	2	no	—
135	C₂×C₇×D₈	C₂³	1	4	yes	—
136	C₂×C₇×D₈	C₂³	1	4	yes	—
137	C₂×C₇×D₈	C₂³	1	4	yes	—
138	C₂×C₇×D₈	C₂³	1	4	yes	—
139	C₂×C₇×M₁₆	—	2	4	no	—
140	C₂×C₇×M₁₆	C₂³	1	4	yes	—
141	C₂²×C₇×C₈	—	2	4	no	—
142	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
143	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
144	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
145	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
146	C₂²×C₇×C₈	C₂³	1	4	yes	complemented
147	C₇×#127	—	2	8	no	—
148	C₇×#127	—	2	2	no	—
149	C₇×#127	C₂³	1	4	yes	complemented
150	C₇×#124	—	2	2	no	—
151	C₇×#124	C₂³	1	4	yes	—
152	C₇×#123	—	2	8	no	—
153	C₇×C₂²⋊Q₈	—	2	2	no	—
154	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
155	C₇×#121	—	2	2	no	—
156	C₇×#121	—	2	2	no	—
157	C₇×#121	—	2	2	no	—
158	C₇×#121	—	2	8	no	—
159	C₇×#121	—	2	8	no	—
160	C₇×#121	—	2	8	no	—
161	C₇×#121	C₂³	1	4	yes	—
162	C₇×#121	C₂³	1	4	yes	—
163	C₇×#121	C₂³	1	4	yes	complemented
164	C₇×#120	—	2	8	no	—
165	C₄×C₇×Q₈	—	2	2	no	—
166	C₄×C₇×Q₈	C₂³	1	4	yes	complemented
167	C₄×C₇×D₄	—	2	8	no	—
168	C₄×C₇×D₄	—	2	2	no	—
169	C₄×C₇×D₄	D₄	1	4	yes	—
170	C₄×C₇×D₄	C₂³	1	4	yes	—
171	C₄×C₇×D₄	C₂³	1	4	yes	—
172	C₂×C₇×C₄⋊C₄	—	2	1	no	—
173	C₂×C₇×C₄⋊C₄	—	2	1	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	8	no	—
185	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
186	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₇	—	2	1	no	—
188	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
189	C₇×#107	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×#102	C₂³	1	4	yes	—
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×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×#550	C₂×C₇	1	1	yes	characteristic, complemented
203	C₂×#546	C₂×C₇	1	1	yes	characteristic, complemented
204	#3268	C₂×C₇	1	16	yes	direct product factor
205	C₂×#496	C₂×C₇	1	1	yes	characteristic, complemented
206	C₂×#468	C₂×C₇	1	1	yes	characteristic, complemented
207	C₂×#466	C₂×C₇	1	1	yes	characteristic, complemented
208	C₂×#464	C₂×C₇	1	1	yes	characteristic, complemented
209	C₂×#459	C₂×C₇	1	1	yes	characteristic, complemented
210	C₂×#452	C₂×C₇	1	1	yes	characteristic, complemented
211	C₂×#449	C₂×C₇	1	1	yes	characteristic, complemented
212	C₂×#449	C₂×C₇	1	1	yes	characteristic, complemented
213	C₂×#447	C₂×C₇	1	1	yes	characteristic, complemented
214	C₂×#440	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	1	no	—
220	C₂⁴×C₇	—	2	4	no	—
221	C₂⁴×C₇	—	4	4	no	—
222	C₂⁴×C₇	—	4	4	no	—
223	C₂⁴×C₇	—	8	2	no	—
224	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
225	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
226	C₇×#41	—	2	8	no	—
227	C₇×#41	—	2	8	no	—
228	C₇×#41	—	2	8	no	—
229	C₇×#41	—	4	4	no	—
230	C₇×#41	—	4	4	no	—
231	C₇×#41	—	4	4	no	—
232	C₇×#41	—	4	8	no	—
233	C₇×#41	—	4	8	no	—
234	C₇×#41	—	4	8	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	C₂×D₄	1	4	yes	—
241	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
242	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
243	C₂×C₇×D₄	—	2	8	no	—
244	C₂×C₇×D₄	—	2	4	no	—
245	C₂×C₇×D₄	—	2	4	no	—
246	C₂×C₇×D₄	—	2	4	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	1	no	—
251	C₂×C₇×D₄	—	2	2	no	—
252	C₂×C₇×D₄	—	2	2	no	—
253	C₂×C₇×D₄	—	2	2	no	—
254	C₂×C₇×D₄	—	2	4	no	—
255	C₂×C₇×D₄	—	2	4	no	—
256	C₂×C₇×D₄	—	2	1	no	—
257	C₂×C₇×D₄	—	2	1	no	—
258	C₂×C₇×D₄	—	2	1	no	—
259	C₂×C₇×D₄	—	2	4	no	—
260	C₂×C₇×D₄	—	2	2	no	—
261	C₂×C₇×D₄	—	2	2	no	—
262	C₂×C₇×D₄	—	2	2	no	—
263	C₂×C₇×D₄	—	2	2	no	—
264	C₂×C₇×D₄	—	4	4	no	—
265	C₂×C₇×D₄	—	4	8	no	—
266	C₂×C₇×D₄	—	4	2	no	—
267	C₂×C₇×D₄	—	4	4	no	—
268	C₂×C₇×D₄	—	4	4	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	—	8	2	no	—
273	C₂×C₇×D₄	—	8	2	no	—
274	C₂×C₇×D₄	—	8	2	no	—
275	C₂×C₇×D₄	—	8	2	no	—
276	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
277	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
278	C₂×C₇×D₄	C₂⁴	1	2	yes	—
279	C₂×C₇×D₄	C₂⁴	1	2	yes	—
280	C₂×C₇×D₄	C₂⁴	1	2	yes	—
281	C₂×C₇×D₄	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₇	—	2	1	no	—
283	C₂²×C₄×C₇	—	2	2	no	—
284	C₂²×C₄×C₇	—	2	2	no	—
285	C₂²×C₄×C₇	—	2	2	no	—
286	C₂²×C₄×C₇	—	2	2	no	—
287	C₂²×C₄×C₇	—	2	1	no	—
288	C₂²×C₄×C₇	—	2	1	no	—
289	C₂²×C₄×C₇	—	2	1	no	—
290	C₂²×C₄×C₇	—	2	4	no	—
291	C₂²×C₄×C₇	—	2	4	no	—
292	C₂²×C₄×C₇	—	2	4	no	—
293	C₂²×C₄×C₇	—	2	4	no	—
294	C₂²×C₄×C₇	—	4	4	no	—
295	C₂²×C₄×C₇	—	4	4	no	—
296	C₂²×C₄×C₇	—	4	4	no	—
297	C₂²×C₄×C₇	—	8	2	no	—
298	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
299	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
300	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
307	C₇×Q₁₆	—	2	8	no	—
308	C₇×SD₁₆	—	2	8	no	—
309	C₇×SD₁₆	—	2	8	no	—
310	C₇×SD₁₆	—	4	4	no	—
311	C₇×SD₁₆	C₂×D₄	1	16	yes	complemented
312	C₇×D₈	—	2	8	no	—
313	C₇×D₈	—	2	8	no	—
314	C₇×D₈	—	2	8	no	—
315	C₇×D₈	—	4	4	no	—
316	C₇×M₁₆	—	2	8	no	—
317	C₂×C₇×C₈	—	2	2	no	—
318	C₂×C₇×C₈	—	2	2	no	—
319	C₂×C₇×C₈	—	2	2	no	—
320	C₂×C₇×C₈	—	2	8	no	—
321	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
322	C₂×C₇×C₈	C₂⁴	1	2	yes	—
323	C₂×C₇×C₈	C₂⁴	1	2	yes	—
324	C₂×C₇×C₈	C₂⁴	1	2	yes	—
325	C₂×C₇×C₈	C₂⁴	1	2	yes	—
326	C₇×C₄⋊C₄	—	2	4	no	—
327	C₇×C₄⋊C₄	—	2	4	no	—
328	C₇×C₄⋊C₄	—	2	1	no	—
329	C₇×C₄⋊C₄	—	2	1	no	—
330	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
331	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
332	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
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	—	2	4	no	—
339	C₇×C₂²⋊C₄	—	2	4	no	—
340	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
341	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
342	C₄²×C₇	—	2	4	no	—
343	C₄²×C₇	C₂×D₄	1	2	yes	—
344	C₄²×C₇	C₂⁴	1	2	yes	—
345	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
346	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
347	C₂²×#41	C₂²×C₇	1	1	yes	characteristic, complemented
348	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
349	C₂×AGL(1,ℤ/8)	—	2	8	no	—
350	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	8	yes	complemented
351	C₂×#135	—	2	8	no	—
352	C₂×#135	C₂²×C₇	1	8	yes	complemented
353	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
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×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
358	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
359	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
360	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
361	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
362	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
363	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
364	#550	—	2	4	no	—
365	#550	C₂²×C₇	1	8	yes	complemented
366	#546	—	2	4	no	—
367	#546	C₂²×C₇	1	8	yes	complemented
368	C₂×#127	—	2	1	no	—
369	C₂×#127	C₂²×C₇	1	1	yes	characteristic, complemented
370	C₂×#124	C₂²×C₇	1	1	yes	characteristic
371	C₂×#123	—	2	1	no	—
372	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
373	C₂×#121	—	2	1	no	—
374	C₂×#121	—	2	1	no	—
375	C₂×#121	—	2	1	no	—
376	C₂×#121	C₂²×C₇	1	1	yes	characteristic
377	C₂×#121	C₂²×C₇	1	1	yes	characteristic
378	C₂×#121	C₂²×C₇	1	1	yes	characteristic, complemented
379	C₂×#120	—	2	1	no	—
380	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
381	C₂×C₄×D₄	—	2	1	no	—
382	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
384	C₂²×C₂²⋊C₄	—	2	1	no	—
385	#496	C₂²×C₇	1	8	yes	complemented
386	#468	C₂²×C₇	1	8	yes	complemented
387	#466	C₂²×C₇	1	8	yes	complemented
388	#464	C₂²×C₇	1	8	yes	complemented
389	#459	C₂²×C₇	1	8	yes	complemented
390	#452	C₂²×C₇	1	8	yes	complemented
391	#449	C₂²×C₇	1	8	yes	complemented
392	#449	C₂²×C₇	1	8	yes	complemented
393	#447	C₂²×C₇	1	8	yes	complemented
394	#440	C₂²×C₇	1	8	yes	complemented
395	#435	C₂²×C₇	1	8	yes	complemented
396	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
397	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
398	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
399	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
400	C₂×#102	C₂²×C₇	1	1	yes	characteristic
401	C₂×#102	C₂²×C₇	1	1	yes	characteristic
402	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
403	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
404	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
405	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
406	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
407	C₂³×C₇	—	2	2	no	—
408	C₂³×C₇	—	2	2	no	—
409	C₂³×C₇	—	2	4	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	—	2	2	no	—
416	C₂³×C₇	—	2	2	no	—
417	C₂³×C₇	—	2	2	no	—
418	C₂³×C₇	—	4	8	no	—
419	C₂³×C₇	—	4	8	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	—	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	—	8	4	no	—
432	C₂³×C₇	—	8	16	no	—
433	C₂³×C₇	C₂²×D₄	1	2	yes	—
434	C₂³×C₇	C₂²×D₄	1	2	yes	—
435	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
436	C₇×Q₈	—	2	4	no	—
437	C₇×Q₈	—	2	2	no	—
438	C₇×Q₈	—	2	2	no	—
439	C₇×Q₈	—	2	2	no	—
440	C₇×Q₈	—	4	2	no	—
441	C₇×Q₈	C₂²×D₄	1	4	yes	—
442	C₇×D₄	—	2	4	no	—
443	C₇×D₄	—	2	2	no	—
444	C₇×D₄	—	2	2	no	—
445	C₇×D₄	—	2	2	no	—
446	C₇×D₄	—	2	2	no	—
447	C₇×D₄	—	2	2	no	—
448	C₇×D₄	—	2	2	no	—
449	C₇×D₄	—	2	2	no	—
450	C₇×D₄	—	4	4	no	—
451	C₇×D₄	—	4	8	no	—
452	C₇×D₄	—	4	8	no	—
453	C₇×D₄	—	4	8	no	—
454	C₇×D₄	—	4	8	no	—
455	C₇×D₄	—	4	8	no	—
456	C₇×D₄	—	4	2	no	—
457	C₇×D₄	—	4	2	no	—
458	C₇×D₄	—	4	2	no	—
459	C₇×D₄	—	8	4	no	—
460	C₇×D₄	—	8	4	no	—
461	C₇×D₄	—	8	4	no	—
462	C₇×D₄	—	8	4	no	—
463	C₇×D₄	C₂²×D₄	1	4	yes	—
464	C₂×C₄×C₇	—	2	2	no	—
465	C₂×C₄×C₇	—	2	2	no	—
466	C₂×C₄×C₇	—	2	4	no	—
467	C₂×C₄×C₇	—	2	2	no	—
468	C₂×C₄×C₇	—	2	2	no	—
469	C₂×C₄×C₇	—	2	2	no	—
470	C₂×C₄×C₇	—	2	4	no	—
471	C₂×C₄×C₇	—	2	4	no	—
472	C₂×C₄×C₇	—	2	2	no	—
473	C₂×C₄×C₇	—	2	2	no	—
474	C₂×C₄×C₇	—	2	2	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	2	no	—
479	C₂×C₄×C₇	—	4	8	no	—
480	C₂×C₄×C₇	—	4	8	no	—
481	C₂×C₄×C₇	—	4	8	no	—
482	C₂×C₄×C₇	—	4	2	no	—
483	C₂×C₄×C₇	—	4	2	no	—
484	C₂×C₄×C₇	—	4	2	no	—
485	C₂×C₄×C₇	—	8	4	no	—
486	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
493	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
494	C₇×C₈	—	2	2	no	—
495	C₇×C₈	—	2	2	no	—
496	C₇×C₈	—	2	2	no	—
497	C₇×C₈	C₂²×D₄	1	4	yes	—
498	C₂⁵	—	2	1	no	—
499	C₂×#41	—	2	2	no	—
500	C₂×#41	—	2	2	no	—
501	C₂×#41	—	2	2	no	—
502	C₂×#41	—	2	4	no	—
503	C₂×#41	—	2	4	no	—
504	C₂×#41	—	2	4	no	—
505	C₂×#41	—	4	2	no	—
506	C₂×#41	—	4	2	no	—
507	C₂×#41	—	4	2	no	—
508	C₂×#41	C₂³×C₇	1	4	yes	—
509	C₂×#41	C₂³×C₇	1	4	yes	—
510	C₂×#41	C₂³×C₇	1	4	yes	complemented
511	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
512	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
513	C₂²×D₄	—	2	4	no	—
514	C₂²×D₄	—	2	1	no	—
515	C₂²×D₄	—	2	1	no	—
516	C₂²×D₄	—	2	1	no	—
517	C₂²×D₄	—	2	1	no	—
518	C₂²×D₄	—	2	1	no	—
519	C₂²×D₄	—	2	1	no	—
520	C₂²×D₄	—	2	1	no	—
521	C₂²×D₄	—	2	1	no	—
522	C₂²×D₄	—	2	2	no	—
523	C₂²×D₄	—	2	1	no	—
524	C₂²×D₄	—	4	2	no	—
525	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
526	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
527	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
529	C₂²×D₄	C₂³×C₇	1	4	yes	—
530	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
531	C₂³×C₄	—	2	1	no	—
532	C₂³×C₄	—	2	1	no	—
533	C₂³×C₄	—	2	1	no	—
534	C₂³×C₄	—	2	1	no	—
535	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
537	AGL(1,ℤ/8)	—	2	32	no	—
538	#135	—	2	32	no	—
539	C₂×Q₁₆	—	2	4	no	—
540	C₂×Q₁₆	C₂³×C₇	1	4	yes	complemented
541	C₂×SD₁₆	—	2	4	no	—
542	C₂×SD₁₆	—	2	4	no	—
543	C₂×SD₁₆	—	4	2	no	—
544	C₂×SD₁₆	C₇×D₄	1	8	yes	complemented
545	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
546	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
547	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
548	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
549	C₂×D₈	—	2	4	no	—
550	C₂×D₈	—	2	4	no	—
551	C₂×D₈	—	2	4	no	—
552	C₂×D₈	—	4	2	no	—
553	C₂×D₈	C₂³×C₇	1	4	yes	—
554	C₂×D₈	C₂³×C₇	1	4	yes	—
555	C₂×D₈	C₂³×C₇	1	4	yes	—
556	C₂×D₈	C₂³×C₇	1	4	yes	—
557	C₂×M₁₆	—	2	4	no	—
558	C₂×M₁₆	C₂³×C₇	1	4	yes	—
559	C₂²×C₈	—	2	4	no	—
560	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
561	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
562	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
563	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
564	C₂²×C₈	C₂³×C₇	1	4	yes	complemented
565	#127	—	2	8	no	—
566	#127	—	2	2	no	—
567	#127	C₂³×C₇	1	4	yes	complemented
568	#124	—	2	2	no	—
569	#124	C₂³×C₇	1	4	yes	—
570	#123	—	2	8	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
573	#121	—	2	2	no	—
574	#121	—	2	2	no	—
575	#121	—	2	2	no	—
576	#121	—	2	8	no	—
577	#121	—	2	8	no	—
578	#121	—	2	8	no	—
579	#121	C₂³×C₇	1	4	yes	—
580	#121	C₂³×C₇	1	4	yes	—
581	#121	C₂³×C₇	1	4	yes	complemented
582	#120	—	2	8	no	—
583	C₄×Q₈	—	2	2	no	—
584	C₄×Q₈	C₂³×C₇	1	4	yes	complemented
585	C₄×D₄	—	2	8	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	C₇×D₄	1	4	yes	—
588	C₄×D₄	C₂³×C₇	1	4	yes	—
589	C₄×D₄	C₂³×C₇	1	4	yes	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	—	2	1	no	—
596	C₂×C₂²⋊C₄	—	2	1	no	—
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₂²⋊C₄	—	2	1	no	—
599	C₂×C₂²⋊C₄	—	2	1	no	—
600	C₂×C₂²⋊C₄	—	2	1	no	—
601	C₂×C₂²⋊C₄	—	2	1	no	—
602	C₂×C₂²⋊C₄	—	2	8	no	—
603	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
604	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
605	C₂×C₄²	—	2	1	no	—
606	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
607	#107	C₂³×C₇	1	4	yes	complemented
608	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
609	#103	C₂³×C₇	1	4	yes	complemented
610	#103	C₂³×C₇	1	4	yes	complemented
611	#102	C₂³×C₇	1	4	yes	—
612	#102	C₂³×C₇	1	4	yes	—
613	#102	C₂³×C₇	1	4	yes	complemented
614	#102	C₂³×C₇	1	4	yes	complemented
615	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
616	C₂²⋊C₈	C₂³×C₇	1	4	yes	complemented
617	#97	C₂³×C₇	1	4	yes	complemented
618	C₂²×C₇	—	2	2	no	—
619	C₂²×C₇	—	2	2	no	—
620	C₂²×C₇	—	2	4	no	—
621	C₂²×C₇	—	2	2	no	—
622	C₂²×C₇	—	2	2	no	—
623	C₂²×C₇	—	2	2	no	—
624	C₂²×C₇	—	2	2	no	—
625	C₂²×C₇	—	4	4	no	—
626	C₂²×C₇	—	4	4	no	—
627	C₂²×C₇	—	4	8	no	—
628	C₂²×C₇	—	4	2	no	—
629	C₂²×C₇	—	4	2	no	—
630	C₂²×C₇	—	4	2	no	—
631	C₂²×C₇	—	4	2	no	—
632	C₂²×C₇	—	4	2	no	—
633	C₂²×C₇	—	4	2	no	—
634	C₂²×C₇	—	4	2	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	—	8	16	no	—
640	C₂²×C₇	—	8	4	no	—
641	C₂²×C₇	—	8	4	no	—
642	C₂²×C₇	—	8	4	no	—
643	C₂²×C₇	D₄²	1	2	yes	—
644	C₂²×C₇	#575	1	2	yes	—
645	C₂²×C₇	#576	1	2	yes	—
646	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
647	C₄×C₇	—	2	2	no	—
648	C₄×C₇	—	2	2	no	—
649	C₄×C₇	—	2	4	no	—
650	C₄×C₇	—	2	2	no	—
651	C₄×C₇	—	2	2	no	—
652	C₄×C₇	—	4	2	no	—
653	C₄×C₇	—	4	2	no	—
654	C₄×C₇	—	4	2	no	—
655	C₄×C₇	D₄²	1	2	yes	—
656	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
657	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
658	C₂⁴	—	2	1	no	—
659	C₂⁴	—	2	1	no	—
660	C₂⁴	—	2	1	no	—
661	C₂⁴	—	2	1	no	—
662	C₂⁴	—	2	4	no	—
663	C₂⁴	—	4	4	no	—
664	C₂⁴	—	4	4	no	—
665	C₂⁴	—	8	2	no	—
666	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
667	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
668	#41	—	2	8	no	—
669	#41	—	2	8	no	—
670	#41	—	2	8	no	—
671	#41	—	4	4	no	—
672	#41	—	4	4	no	—
673	#41	—	4	4	no	—
674	#41	—	4	8	no	—
675	#41	—	4	8	no	—
676	#41	—	4	8	no	—
677	C₂×Q₈	—	2	1	no	—
678	C₂×Q₈	—	2	1	no	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
683	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
684	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
685	C₂×D₄	—	2	8	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	4	4	no	—
707	C₂×D₄	—	4	8	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	—	4	4	no	—
710	C₂×D₄	—	4	4	no	—
711	C₂×D₄	—	4	4	no	—
712	C₂×D₄	—	4	4	no	—
713	C₂×D₄	—	4	4	no	—
714	C₂×D₄	—	8	2	no	—
715	C₂×D₄	—	8	2	no	—
716	C₂×D₄	—	8	2	no	—
717	C₂×D₄	—	8	2	no	—
718	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
719	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
720	C₂×D₄	C₂⁴×C₇	1	2	yes	—
721	C₂×D₄	C₂⁴×C₇	1	2	yes	—
722	C₂×D₄	C₂⁴×C₇	1	2	yes	—
723	C₂×D₄	C₂⁴×C₇	1	2	yes	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	2	4	no	—
734	C₂²×C₄	—	2	4	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	4	4	no	—
737	C₂²×C₄	—	4	4	no	—
738	C₂²×C₄	—	4	4	no	—
739	C₂²×C₄	—	8	2	no	—
740	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
741	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
742	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
743	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
744	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
745	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
749	Q₁₆	—	2	8	no	—
750	SD₁₆	—	2	8	no	—
751	SD₁₆	—	2	8	no	—
752	SD₁₆	—	4	4	no	—
753	SD₁₆	C₂×C₇×D₄	1	16	yes	complemented
754	D₈	—	2	8	no	—
755	D₈	—	2	8	no	—
756	D₈	—	2	8	no	—
757	D₈	—	4	4	no	—
758	M₁₆	—	2	8	no	—
759	C₂×C₈	—	2	2	no	—
760	C₂×C₈	—	2	2	no	—
761	C₂×C₈	—	2	2	no	—
762	C₂×C₈	—	2	8	no	—
763	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
764	C₂×C₈	C₂⁴×C₇	1	2	yes	—
765	C₂×C₈	C₂⁴×C₇	1	2	yes	—
766	C₂×C₈	C₂⁴×C₇	1	2	yes	—
767	C₂×C₈	C₂⁴×C₇	1	2	yes	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	4	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
773	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
774	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
783	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
784	C₄²	—	2	4	no	—
785	C₄²	C₂×C₇×D₄	1	2	yes	—
786	C₄²	C₂⁴×C₇	1	2	yes	—
787	C₂×C₇	—	4	2	no	—
788	C₂×C₇	—	4	2	no	—
789	C₂×C₇	—	4	4	no	—
790	C₂×C₇	—	8	2	no	—
791	C₂×C₇	—	8	2	no	—
792	C₂×C₇	—	8	2	no	—
793	C₂×C₇	#3268	1	4	yes	direct product factor
794	C₂×C₇	C₂×D₄²	1	1	yes	characteristic
795	C₂×C₇	C₂×#575	1	1	yes	characteristic
796	C₂×C₇	C₂×#576	1	1	yes	characteristic
797	C₂³	—	2	2	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	4	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	4	8	no	—
809	C₂³	—	4	8	no	—
810	C₂³	—	4	2	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	2	no	—
813	C₂³	—	4	2	no	—
814	C₂³	—	4	2	no	—
815	C₂³	—	4	2	no	—
816	C₂³	—	4	2	no	—
817	C₂³	—	4	2	no	—
818	C₂³	—	4	2	no	—
819	C₂³	—	4	2	no	—
820	C₂³	—	4	2	no	—
821	C₂³	—	8	4	no	—
822	C₂³	—	8	16	no	—
823	C₂³	C₂²×C₇×D₄	1	2	yes	—
824	C₂³	C₂²×C₇×D₄	1	2	yes	—
825	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
826	Q₈	—	2	2	no	—
827	Q₈	—	2	4	no	—
828	Q₈	—	2	2	no	—
829	Q₈	—	2	2	no	—
830	Q₈	—	4	2	no	—
831	Q₈	C₂²×C₇×D₄	1	4	yes	—
832	D₄	—	2	2	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	2	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	2	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	4	no	—
840	D₄	—	4	4	no	—
841	D₄	—	4	8	no	—
842	D₄	—	4	8	no	—
843	D₄	—	4	8	no	—
844	D₄	—	4	8	no	—
845	D₄	—	4	8	no	—
846	D₄	—	4	2	no	—
847	D₄	—	4	2	no	—
848	D₄	—	4	2	no	—
849	D₄	—	8	4	no	—
850	D₄	—	8	4	no	—
851	D₄	—	8	4	no	—
852	D₄	—	8	4	no	—
853	D₄	C₂²×C₇×D₄	1	4	yes	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	4	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	4	no	—
865	C₂×C₄	—	2	4	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	4	8	no	—
870	C₂×C₄	—	4	8	no	—
871	C₂×C₄	—	4	8	no	—
872	C₂×C₄	—	4	2	no	—
873	C₂×C₄	—	4	2	no	—
874	C₂×C₄	—	4	2	no	—
875	C₂×C₄	—	8	4	no	—
876	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
877	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
878	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
879	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
880	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
881	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
882	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
883	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
884	C₈	—	2	2	no	—
885	C₈	—	2	2	no	—
886	C₈	—	2	2	no	—
887	C₈	C₂²×C₇×D₄	1	4	yes	—
888	C₇	C₂×#3268	1	1	yes	characteristic, direct product factor, Sylow
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	4	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	4	no	—
899	C₂²	—	4	4	no	—
900	C₂²	—	4	8	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	8	16	no	—
911	C₂²	—	8	4	no	—
912	C₂²	—	8	4	no	—
913	C₂²	—	8	4	no	—
914	C₂²	C₇×D₄²	1	2	yes	—
915	C₂²	C₇×#575	1	2	yes	—
916	C₂²	C₇×#576	1	2	yes	—
917	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	2	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	4	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	C₇×D₄²	1	2	yes	—
927	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
928	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
929	C₂	—	4	2	no	—
930	C₂	—	4	2	no	—
931	C₂	—	4	4	no	—
932	C₂	—	8	2	no	—
933	C₂	—	8	2	no	—
934	C₂	—	8	2	no	—
935	C₂	C₇×#3268	1	4	yes	direct product factor
936	C₂	C₂×C₇×D₄²	1	1	yes	characteristic
937	C₂	C₂×C₇×#575	1	1	yes	characteristic
938	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. C₂²×C₇×#135	C₂	semidirect
3. C₂×C₇×#550	C₂	semidirect
4. C₂×C₇×#546	C₂	semidirect
5. C₇×#3268	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×#464	C₂	semidirect
10. C₂×C₇×#459	C₂	semidirect
11. C₂×C₇×#452	C₂	semidirect
12. C₂×C₇×#449	C₂	semidirect
13. C₂×C₇×#449	C₂	semidirect
14. C₂×C₇×#447	C₂	semidirect
15. C₂×C₇×#440	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
28. C₂²×C₇×SD₁₆	C₂²	semidirect
29. C₂²×C₇×SD₁₆	C₂²	semidirect
35. C₂³×C₇×C₈	C₂²	semidirect
37. C₇×#550	C₂²	semidirect
39. C₇×#546	C₂²	semidirect
41. C₂×C₇×#127	C₂²	semidirect
50. C₂×C₇×#121	C₂²	semidirect
52. C₂×C₄×C₇×Q₈	C₂²	semidirect
57. C₇×#496	C₂²	semidirect
58. C₇×#468	C₂²	semidirect
59. C₇×#466	C₂²	semidirect
60. C₇×#464	C₂²	semidirect
61. C₇×#459	C₂²	semidirect
62. C₇×#452	C₂²	semidirect
63. C₇×#449	C₂²	semidirect
64. C₇×#449	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
74. C₂×C₇×#102	C₂²	semidirect
75. C₂×C₇×#102	C₂²	semidirect
77. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
78. C₂×C₇×#97	C₂²	semidirect
79. C₂×#3268	C₇	direct (N × H)
92. C₂×C₇×#41	C₂³	semidirect
122. C₂×C₇×Q₁₆	C₂³	semidirect
126. C₂×C₇×SD₁₆	D₄	semidirect
129. C₂×C₇×SD₁₆	C₂³	semidirect
130. C₂×C₇×SD₁₆	C₂³	semidirect
146. C₂²×C₇×C₈	C₂³	semidirect
149. C₇×#127	C₂³	semidirect
163. C₇×#121	C₂³	semidirect
166. C₄×C₇×Q₈	C₂³	semidirect
189. C₇×#107	C₂³	semidirect
190. C₇×C₄⋊C₈	C₂³	semidirect
191. C₇×#103	C₂³	semidirect
192. C₇×#103	C₂³	semidirect
195. C₇×#102	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×#550	C₂×C₇	semidirect
203. C₂×#546	C₂×C₇	semidirect
204. #3268	C₂×C₇	direct (N × H)
205. C₂×#496	C₂×C₇	semidirect
206. C₂×#468	C₂×C₇	semidirect
207. C₂×#466	C₂×C₇	semidirect
208. C₂×#464	C₂×C₇	semidirect
209. C₂×#459	C₂×C₇	semidirect
210. C₂×#452	C₂×C₇	semidirect
211. C₂×#449	C₂×C₇	semidirect
212. C₂×#449	C₂×C₇	semidirect
213. C₂×#447	C₂×C₇	semidirect
214. C₂×#440	C₂×C₇	semidirect
215. C₂×#435	C₂×C₇	semidirect
311. C₇×SD₁₆	C₂×D₄	semidirect
347. C₂²×#41	C₂²×C₇	semidirect
350. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
352. C₂×#135	C₂²×C₇	semidirect
353. C₂²×Q₁₆	C₂²×C₇	semidirect
356. C₂²×SD₁₆	C₂²×C₇	semidirect
357. C₂²×SD₁₆	C₂²×C₇	semidirect
363. C₂³×C₈	C₂²×C₇	semidirect
365. #550	C₂²×C₇	semidirect
367. #546	C₂²×C₇	semidirect
369. C₂×#127	C₂²×C₇	semidirect
378. C₂×#121	C₂²×C₇	semidirect
380. C₂×C₄×Q₈	C₂²×C₇	semidirect
385. #496	C₂²×C₇	semidirect
386. #468	C₂²×C₇	semidirect
387. #466	C₂²×C₇	semidirect
388. #464	C₂²×C₇	semidirect
389. #459	C₂²×C₇	semidirect
390. #452	C₂²×C₇	semidirect
391. #449	C₂²×C₇	semidirect
392. #449	C₂²×C₇	semidirect
393. #447	C₂²×C₇	semidirect
394. #440	C₂²×C₇	semidirect
395. #435	C₂²×C₇	semidirect
396. C₂×#107	C₂²×C₇	semidirect
397. C₂×C₄⋊C₈	C₂²×C₇	semidirect
398. C₂×#103	C₂²×C₇	semidirect
399. C₂×#103	C₂²×C₇	semidirect
402. C₂×#102	C₂²×C₇	semidirect
403. C₂×#102	C₂²×C₇	semidirect
405. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
406. C₂×#97	C₂²×C₇	semidirect
510. C₂×#41	C₂³×C₇	semidirect
540. C₂×Q₁₆	C₂³×C₇	semidirect
544. C₂×SD₁₆	C₇×D₄	semidirect
547. C₂×SD₁₆	C₂³×C₇	semidirect
548. C₂×SD₁₆	C₂³×C₇	semidirect
564. C₂²×C₈	C₂³×C₇	semidirect
567. #127	C₂³×C₇	semidirect
581. #121	C₂³×C₇	semidirect
584. C₄×Q₈	C₂³×C₇	semidirect
607. #107	C₂³×C₇	semidirect
608. C₄⋊C₈	C₂³×C₇	semidirect
609. #103	C₂³×C₇	semidirect
610. #103	C₂³×C₇	semidirect
613. #102	C₂³×C₇	semidirect
614. #102	C₂³×C₇	semidirect
616. C₂²⋊C₈	C₂³×C₇	semidirect
617. #97	C₂³×C₇	semidirect
753. SD₁₆	C₂×C₇×D₄	semidirect
793. C₂×C₇	#3268	direct (N × H)
888. C₇	C₂×#3268	direct (N × H)
935. C₂	C₇×#3268	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×#550	2
C₂×C₇×#546	2
C₇×#3268	2
C₂×C₇×#496	2
C₂×C₇×#468	2
C₂×C₇×#466	2
C₂×C₇×#464	2
C₂×C₇×#459	2
C₂×C₇×#452	2
C₂×C₇×#449	2
C₂×C₇×#447	2
C₂×C₇×#440	2
C₂×C₇×#435	2
C₂×#3268	7

Subgroups — C2×C7×#3268 #13238242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3268 #13238242