Subgroups — C₇×#61367 #13238583

Order 1792.

1826 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3389	C₂	1	4	yes	maximal, complemented
4	C₇×#3388	C₂	1	4	yes	maximal, complemented
5	C₇×#3385	C₂	1	2	yes	maximal, complemented
6	C₇×#3384	C₂	1	2	yes	maximal, complemented
7	C₇×#3381	C₂	1	2	yes	maximal, complemented
8	C₇×#3380	C₂	1	2	yes	maximal, complemented
9	C₇×#3166	C₂	1	2	yes	maximal, complemented
10	C₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3080	C₂	1	2	yes	maximal, complemented
12	C₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3077	C₂	1	2	yes	maximal, complemented
15	C₇×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
17	C₄×C₇×AGL(1,ℤ/8)	C₂	1	2	yes	maximal
18	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₇×Q₈²	C₂²	1	1	yes	characteristic, complemented
20	C₇×#557	C₂²	1	1	yes	characteristic, complemented
21	C₇×#557	C₂²	1	2	yes	complemented
22	C₇×#554	—	2	1	no	—
23	C₇×#554	—	2	2	no	—
24	C₇×#554	—	2	1	no	—
25	C₇×#554	—	2	1	no	—
26	C₇×#554	—	2	2	no	—
27	C₇×#554	C₂²	1	2	yes	—
28	C₇×#554	C₂²	1	2	yes	—
29	C₇×#554	C₂²	1	4	yes	—
30	C₇×#554	C₂²	1	1	yes	characteristic, complemented
31	C₇×#554	C₂²	1	2	yes	complemented
32	C₇×D₄×Q₈	—	2	1	no	—
33	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₇×#533	—	2	2	no	—
35	C₇×#533	—	2	1	no	—
36	C₇×#533	C₂²	1	1	yes	characteristic
37	C₇×#533	C₂²	1	2	yes	—
38	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₇×#125	C₂²	1	2	yes	—
40	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
41	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
42	C₄×C₇×#41	C₂²	1	1	yes	characteristic
43	C₄×C₇×#41	C₂²	1	2	yes	—
44	C₂×C₄×C₇×Q₈	—	2	1	no	—
45	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
47	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
48	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
49	C₇×#501	C₂²	1	4	yes	complemented
50	C₇×#501	C₂²	1	4	yes	complemented
51	C₇×#501	C₂²	1	4	yes	complemented
52	C₇×#500	C₂²	1	2	yes	complemented
53	C₇×#499	C₂²	1	4	yes	complemented
54	C₇×#499	C₂²	1	4	yes	complemented
55	C₇×#498	C₂²	1	2	yes	complemented
56	C₇×#479	C₂²	1	4	yes	complemented
57	C₇×#479	C₂²	1	4	yes	complemented
58	C₇×#478	C₂²	1	4	yes	—
59	C₇×#478	C₂²	1	4	yes	—
60	C₇×#478	C₂²	1	4	yes	—
61	C₇×#478	C₂²	1	4	yes	complemented
62	C₇×#478	C₂²	1	4	yes	complemented
63	C₇×#477	C₂²	1	2	yes	complemented
64	C₇×#476	C₂²	1	2	yes	—
65	C₇×#476	C₂²	1	4	yes	—
66	C₇×#476	C₂²	1	2	yes	complemented
67	C₇×#475	C₂²	1	2	yes	complemented
68	C₇×#474	C₂²	1	2	yes	—
69	C₇×#474	C₂²	1	4	yes	—
70	C₇×#474	C₂²	1	2	yes	complemented
71	C₇×#446	C₂²	1	2	yes	complemented
72	C₇×#446	C₂²	1	4	yes	complemented
73	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
74	C₇×#442	C₂²	1	4	yes	—
75	C₇×#442	C₂²	1	2	yes	—
76	C₇×#440	C₂²	1	4	yes	—
77	C₇×#440	C₂²	1	2	yes	—
78	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
79	C₄×C₇×SD₁₆	C₂²	1	4	yes	—
80	C₄×C₇×D₈	C₂²	1	2	yes	—
81	C₄×C₇×D₈	C₂²	1	4	yes	—
82	C₇×#428	C₂²	1	2	yes	—
83	C₇×#428	C₂²	1	2	yes	—
84	C₇×#428	C₂²	1	1	yes	characteristic
85	C₇×#428	C₂²	1	2	yes	—
86	C₇×#428	C₂²	1	2	yes	—
87	C₇×#423	C₂²	1	1	yes	characteristic
88	C₇×#423	C₂²	1	2	yes	—
89	C₇×#418	C₂²	1	1	yes	characteristic
90	C₇×#418	C₂²	1	2	yes	—
91	C₇×#417	C₂²	1	2	yes	—
92	C₇×#417	C₂²	1	1	yes	characteristic
93	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
94	C₄×C₇×M₁₆	C₂²	1	2	yes	—
95	#61367	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₇×#41	C₂³	1	1	yes	characteristic
97	C₂²×C₇×Q₈	—	2	1	no	—
98	C₂²×C₇×Q₈	—	2	1	no	—
99	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
100	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₇	—	2	1	no	—
102	C₂³×C₄×C₇	—	2	2	no	—
103	C₇×AGL(1,ℤ/8)	Q₈	1	8	yes	complemented
104	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
105	C₂×C₇×D₈	C₂³	1	2	yes	—
106	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
107	C₂×C₇×M₁₆	C₂³	1	2	yes	—
108	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
109	C₇×C₄⋊Q₈	—	2	1	no	—
110	C₇×C₄⋊Q₈	—	2	2	no	—
111	C₇×C₄⋊Q₈	—	2	1	no	—
112	C₇×C₄⋊Q₈	—	2	2	no	—
113	C₇×C₄⋊Q₈	—	2	1	no	—
114	C₇×C₄⋊Q₈	—	2	1	no	—
115	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₇×#125	—	2	2	no	—
122	C₇×#125	—	2	2	no	—
123	C₇×#125	—	2	2	no	—
124	C₇×#125	—	2	2	no	—
125	C₇×#125	—	2	2	no	—
126	C₇×#125	C₂³	1	2	yes	—
127	C₇×#125	C₂³	1	2	yes	—
128	C₇×#125	C₂³	1	2	yes	—
129	C₇×#125	C₂³	1	4	yes	—
130	C₇×#125	C₂³	1	4	yes	—
131	C₇×C₂²⋊Q₈	—	2	2	no	—
132	C₇×C₂²⋊Q₈	—	2	2	no	—
133	C₇×C₂²⋊Q₈	—	2	4	no	—
134	C₇×C₂²⋊Q₈	—	2	1	no	—
135	C₇×C₂²⋊Q₈	—	2	2	no	—
136	C₇×C₂²⋊Q₈	—	2	1	no	—
137	C₇×C₂²⋊Q₈	—	2	2	no	—
138	C₇×C₂²⋊Q₈	—	2	1	no	—
139	C₇×C₂²⋊Q₈	—	2	2	no	—
140	C₇×C₂²⋊Q₈	—	2	4	no	—
141	C₇×C₂²⋊Q₈	—	2	4	no	—
142	C₇×C₂²⋊Q₈	—	2	4	no	—
143	C₇×C₂²⋊Q₈	—	2	4	no	—
144	C₇×C₂²⋊Q₈	—	2	1	no	—
145	C₇×C₂²⋊Q₈	—	2	2	no	—
146	C₇×C₂²⋊Q₈	—	2	2	no	—
147	C₇×C₂²⋊Q₈	—	2	2	no	—
148	C₇×C₂²⋊Q₈	—	2	2	no	—
149	C₄×C₇×Q₈	—	2	1	no	—
150	C₄×C₇×Q₈	—	2	1	no	—
151	C₄×C₇×Q₈	—	2	2	no	—
152	C₄×C₇×Q₈	—	2	2	no	—
153	C₄×C₇×Q₈	—	2	1	no	—
154	C₄×C₇×Q₈	—	2	2	no	—
155	C₄×C₇×Q₈	—	2	1	no	—
156	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
157	C₄×C₇×Q₈	D₄	1	2	yes	—
158	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
159	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
160	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
161	C₄×C₇×Q₈	C₂³	1	2	yes	—
162	C₄×C₇×Q₈	C₂³	1	2	yes	—
163	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
164	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
165	C₄×C₇×Q₈	C₂³	1	2	yes	—
166	C₄×C₇×D₄	—	2	1	no	—
167	C₄×C₇×D₄	—	2	2	no	—
168	C₄×C₇×D₄	—	2	1	no	—
169	C₄×C₇×D₄	—	2	2	no	—
170	C₄×C₇×D₄	—	2	2	no	—
171	C₄×C₇×D₄	—	2	1	no	—
172	C₄×C₇×D₄	—	2	2	no	—
173	C₄×C₇×D₄	—	2	1	no	—
174	C₄×C₇×D₄	C₂³	1	2	yes	—
175	C₄×C₇×D₄	C₂³	1	4	yes	—
176	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
177	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
178	C₄×C₇×D₄	C₂³	1	4	yes	—
179	C₄×C₇×D₄	C₂³	1	2	yes	—
180	C₄×C₇×D₄	C₂³	1	2	yes	—
181	C₄×C₇×D₄	C₂³	1	2	yes	—
182	C₇×#117	—	2	2	no	—
183	C₇×#117	—	2	1	no	—
184	C₇×#117	C₂³	1	1	yes	characteristic
185	C₇×#117	C₂³	1	2	yes	—
186	C₂×C₇×C₄⋊C₄	—	2	2	no	—
187	C₂×C₇×C₄⋊C₄	—	2	1	no	—
188	C₂×C₇×C₄⋊C₄	—	2	2	no	—
189	C₂×C₇×C₄⋊C₄	—	2	2	no	—
190	C₂×C₇×C₄⋊C₄	—	2	4	no	—
191	C₂×C₇×C₄⋊C₄	—	2	2	no	—
192	C₂×C₇×C₄⋊C₄	—	2	1	no	—
193	C₂×C₇×C₄⋊C₄	—	2	2	no	—
194	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
195	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
196	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
199	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₄²×C₇	—	2	2	no	—
201	C₂×C₄²×C₇	—	2	1	no	—
202	C₂×C₄²×C₇	C₂³	1	2	yes	—
203	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
204	C₇×#107	C₂³	1	4	yes	—
205	C₇×#107	C₂³	1	4	yes	—
206	C₇×#107	C₂³	1	4	yes	—
207	C₇×#107	C₂³	1	2	yes	—
208	C₇×#107	C₂³	1	4	yes	—
209	C₇×#106	C₂³	1	4	yes	—
210	C₇×#106	C₂³	1	4	yes	—
211	C₇×#106	C₂³	1	4	yes	—
212	C₇×#106	C₂³	1	4	yes	—
213	C₇×#106	C₂³	1	2	yes	—
214	C₇×C₄⋊C₈	C₂³	1	2	yes	—
215	C₇×C₄⋊C₈	C₂³	1	4	yes	—
216	C₇×C₄⋊C₈	C₂³	1	2	yes	—
217	C₇×C₄⋊C₈	C₂³	1	4	yes	—
218	C₇×#103	C₂³	1	4	yes	—
219	C₇×#103	C₂³	1	2	yes	—
220	C₇×#102	C₂³	1	2	yes	—
221	C₇×#102	C₂³	1	4	yes	—
222	C₇×#102	C₂³	1	4	yes	—
223	C₇×#102	C₂³	1	4	yes	—
224	C₇×#102	C₂³	1	2	yes	—
225	C₇×#102	C₂³	1	2	yes	—
226	C₇×#97	C₂³	1	2	yes	—
227	C₇×#97	C₂³	1	4	yes	—
228	C₄×C₇×C₈	C₂³	1	2	yes	—
229	C₄×C₇×C₈	C₂³	1	4	yes	—
230	Q₈×#41	C₂×C₇	1	1	yes	characteristic, complemented
231	C₂×#554	C₂×C₇	1	1	yes	characteristic, complemented
232	#3389	C₂×C₇	1	4	yes	complemented
233	#3388	C₂×C₇	1	4	yes	complemented
234	#3385	C₂×C₇	1	2	yes	complemented
235	#3384	C₂×C₇	1	2	yes	complemented
236	#3381	C₂×C₇	1	2	yes	complemented
237	#3380	C₂×C₇	1	2	yes	complemented
238	#3166	C₂×C₇	1	2	yes	complemented
239	#3165	C₂×C₇	1	1	yes	characteristic, complemented
240	#3080	C₂×C₇	1	2	yes	complemented
241	#3079	C₂×C₇	1	1	yes	characteristic, complemented
242	#3077	C₂×C₇	1	1	yes	characteristic, complemented
243	#3077	C₂×C₇	1	2	yes	complemented
244	Q₈×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
245	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic
246	C₄×AGL(1,ℤ/8)	C₂×C₇	1	2	yes	—
247	C₂⁴×C₇	—	2	1	no	—
248	C₇×#41	—	2	2	no	—
249	C₇×#41	C₂×Q₈	1	4	yes	—
250	C₂×C₇×Q₈	—	2	2	no	—
251	C₂×C₇×Q₈	—	2	1	no	—
252	C₂×C₇×Q₈	—	2	1	no	—
253	C₂×C₇×Q₈	—	2	2	no	—
254	C₂×C₇×Q₈	—	2	2	no	—
255	C₂×C₇×Q₈	—	2	2	no	—
256	C₂×C₇×Q₈	—	4	2	no	—
257	C₂×C₇×Q₈	—	4	4	no	—
258	C₂×C₇×Q₈	—	8	2	no	—
259	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
260	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
261	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
262	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
263	C₂×C₇×D₄	—	2	1	no	—
264	C₂×C₇×D₄	—	2	1	no	—
265	C₂×C₇×D₄	—	2	2	no	—
266	C₂×C₇×D₄	C₂×Q₈	1	4	yes	complemented
267	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
268	C₂×C₇×D₄	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₇	—	2	1	no	—
270	C₂²×C₄×C₇	—	2	1	no	—
271	C₂²×C₄×C₇	—	2	2	no	—
272	C₂²×C₄×C₇	—	2	2	no	—
273	C₂²×C₄×C₇	—	2	1	no	—
274	C₂²×C₄×C₇	—	2	2	no	—
275	C₂²×C₄×C₇	—	2	2	no	—
276	C₂²×C₄×C₇	—	2	1	no	—
277	C₂²×C₄×C₇	—	2	2	no	—
278	C₂²×C₄×C₇	—	2	4	no	—
279	C₂²×C₄×C₇	—	2	4	no	—
280	C₂²×C₄×C₇	—	4	4	no	—
281	C₂²×C₄×C₇	—	8	4	no	—
282	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
287	C₇×SD₁₆	C₂×Q₈	1	8	yes	complemented
288	C₇×D₈	C₂×Q₈	1	8	yes	complemented
289	C₇×M₁₆	—	2	2	no	—
290	C₇×M₁₆	—	2	4	no	—
291	C₇×M₁₆	C₂×Q₈	1	4	yes	complemented
292	C₂×C₇×C₈	C₂⁴	1	2	yes	—
293	C₂×C₇×C₈	C₂⁴	1	4	yes	—
294	C₂×C₇×C₈	C₂⁴	1	2	yes	—
295	C₇×C₄⋊C₄	—	2	4	no	—
296	C₇×C₄⋊C₄	—	2	4	no	—
297	C₇×C₄⋊C₄	—	2	2	no	—
298	C₇×C₄⋊C₄	—	2	2	no	—
299	C₇×C₄⋊C₄	—	2	2	no	—
300	C₇×C₄⋊C₄	—	2	2	no	—
301	C₇×C₄⋊C₄	—	2	2	no	—
302	C₇×C₄⋊C₄	—	2	2	no	—
303	C₇×C₄⋊C₄	—	2	1	no	—
304	C₇×C₄⋊C₄	—	2	4	no	—
305	C₇×C₄⋊C₄	—	2	4	no	—
306	C₇×C₄⋊C₄	—	2	1	no	—
307	C₇×C₄⋊C₄	—	2	2	no	—
308	C₇×C₄⋊C₄	—	2	2	no	—
309	C₇×C₄⋊C₄	—	2	1	no	—
310	C₇×C₄⋊C₄	—	2	1	no	—
311	C₇×C₄⋊C₄	—	2	2	no	—
312	C₇×C₄⋊C₄	—	2	1	no	—
313	C₇×C₄⋊C₄	—	2	2	no	—
314	C₇×C₄⋊C₄	—	2	2	no	—
315	C₇×C₄⋊C₄	—	2	2	no	—
316	C₇×C₄⋊C₄	—	2	2	no	—
317	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
318	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
319	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
320	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
321	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
322	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
323	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
324	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
325	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
326	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
327	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
328	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
329	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
330	C₇×C₂²⋊C₄	—	2	1	no	—
331	C₇×C₂²⋊C₄	—	2	2	no	—
332	C₇×C₂²⋊C₄	—	2	2	no	—
333	C₇×C₂²⋊C₄	—	2	2	no	—
334	C₇×C₂²⋊C₄	—	2	4	no	—
335	C₇×C₂²⋊C₄	—	2	4	no	—
336	C₇×C₂²⋊C₄	—	2	2	no	—
337	C₇×C₂²⋊C₄	—	2	1	no	—
338	C₇×C₂²⋊C₄	—	2	1	no	—
339	C₇×C₂²⋊C₄	—	2	2	no	—
340	C₄²×C₇	—	2	2	no	—
341	C₄²×C₇	—	2	1	no	—
342	C₄²×C₇	—	2	1	no	—
343	C₄²×C₇	—	2	2	no	—
344	C₄²×C₇	—	2	2	no	—
345	C₄²×C₇	—	2	1	no	—
346	C₄²×C₇	C₂×D₄	1	2	yes	—
347	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₇	C₂×D₄	1	2	yes	—
349	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
350	C₄²×C₇	C₂⁴	1	2	yes	—
351	C₄²×C₇	C₂⁴	1	1	yes	characteristic
352	C₄²×C₇	C₂⁴	1	2	yes	—
353	C₄²×C₇	C₂⁴	1	1	yes	characteristic
354	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
355	Q₈²	C₂²×C₇	1	1	yes	characteristic, complemented
356	#557	C₂²×C₇	1	1	yes	characteristic, complemented
357	#557	C₂²×C₇	1	2	yes	complemented
358	#554	—	2	1	no	—
359	#554	—	2	2	no	—
360	#554	—	2	1	no	—
361	#554	—	2	1	no	—
362	#554	—	2	2	no	—
363	#554	C₂²×C₇	1	2	yes	—
364	#554	C₂²×C₇	1	2	yes	—
365	#554	C₂²×C₇	1	4	yes	—
366	#554	C₂²×C₇	1	1	yes	characteristic, complemented
367	#554	C₂²×C₇	1	2	yes	complemented
368	D₄×Q₈	—	2	1	no	—
369	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
370	#533	—	2	2	no	—
371	#533	—	2	1	no	—
372	#533	C₂²×C₇	1	1	yes	characteristic
373	#533	C₂²×C₇	1	2	yes	—
374	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
375	C₂×#125	C₂²×C₇	1	2	yes	—
376	C₂×C₂²⋊Q₈	—	2	1	no	—
377	C₂×C₂²⋊Q₈	—	2	2	no	—
378	C₄×#41	C₂²×C₇	1	1	yes	characteristic
379	C₄×#41	C₂²×C₇	1	2	yes	—
380	C₂×C₄×Q₈	—	2	1	no	—
381	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
382	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
383	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
384	C₂²×C₄⋊C₄	—	2	1	no	—
385	#501	C₂²×C₇	1	4	yes	complemented
386	#501	C₂²×C₇	1	4	yes	complemented
387	#501	C₂²×C₇	1	4	yes	complemented
388	#500	C₂²×C₇	1	2	yes	complemented
389	#499	C₂²×C₇	1	4	yes	complemented
390	#499	C₂²×C₇	1	4	yes	complemented
391	#498	C₂²×C₇	1	2	yes	complemented
392	#479	C₂²×C₇	1	4	yes	complemented
393	#479	C₂²×C₇	1	4	yes	complemented
394	#478	C₂²×C₇	1	4	yes	—
395	#478	C₂²×C₇	1	4	yes	—
396	#478	C₂²×C₇	1	4	yes	—
397	#478	C₂²×C₇	1	4	yes	complemented
398	#478	C₂²×C₇	1	4	yes	complemented
399	#477	C₂²×C₇	1	2	yes	complemented
400	#476	C₂²×C₇	1	2	yes	—
401	#476	C₂²×C₇	1	4	yes	—
402	#476	C₂²×C₇	1	2	yes	complemented
403	#475	C₂²×C₇	1	2	yes	complemented
404	#474	C₂²×C₇	1	2	yes	—
405	#474	C₂²×C₇	1	4	yes	—
406	#474	C₂²×C₇	1	2	yes	complemented
407	#446	C₂²×C₇	1	2	yes	complemented
408	#446	C₂²×C₇	1	4	yes	complemented
409	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
410	#442	C₂²×C₇	1	4	yes	—
411	#442	C₂²×C₇	1	2	yes	—
412	#440	C₂²×C₇	1	4	yes	—
413	#440	C₂²×C₇	1	2	yes	—
414	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
415	C₄×SD₁₆	C₂²×C₇	1	4	yes	—
416	C₄×D₈	C₂²×C₇	1	2	yes	—
417	C₄×D₈	C₂²×C₇	1	4	yes	—
418	#428	C₂²×C₇	1	2	yes	—
419	#428	C₂²×C₇	1	2	yes	—
420	#428	C₂²×C₇	1	2	yes	—
421	#428	C₂²×C₇	1	2	yes	—
422	#428	C₂²×C₇	1	1	yes	characteristic
423	#423	C₂²×C₇	1	1	yes	characteristic
424	#423	C₂²×C₇	1	2	yes	—
425	#418	C₂²×C₇	1	2	yes	—
426	#418	C₂²×C₇	1	1	yes	characteristic
427	#417	C₂²×C₇	1	2	yes	—
428	#417	C₂²×C₇	1	1	yes	characteristic
429	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
430	C₄×M₁₆	C₂²×C₇	1	2	yes	—
431	C₂³×C₇	—	2	4	no	—
432	C₂³×C₇	—	2	1	no	—
433	C₂³×C₇	—	2	2	no	—
434	C₂³×C₇	—	4	2	no	—
435	C₂³×C₇	—	4	2	no	—
436	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
437	C₇×Q₈	—	2	2	no	—
438	C₇×Q₈	—	2	2	no	—
439	C₇×Q₈	—	2	1	no	—
440	C₇×Q₈	—	4	2	no	—
441	C₇×Q₈	—	4	4	no	—
442	C₇×Q₈	—	4	2	no	—
443	C₇×Q₈	—	8	2	no	—
444	C₇×Q₈	—	8	1	no	—
445	C₇×Q₈	—	8	2	no	—
446	C₇×Q₈	—	8	2	no	—
447	C₇×Q₈	C₂²×Q₈	1	2	yes	—
448	C₇×D₄	—	2	4	no	—
449	C₇×D₄	—	2	4	no	—
450	C₇×D₄	—	2	2	no	—
451	C₇×D₄	—	2	1	no	—
452	C₇×D₄	C₂²×Q₈	1	2	yes	—
453	C₇×D₄	C₂²×Q₈	1	4	yes	—
454	C₂×C₄×C₇	—	2	1	no	—
455	C₂×C₄×C₇	—	2	4	no	—
456	C₂×C₄×C₇	—	2	2	no	—
457	C₂×C₄×C₇	—	2	2	no	—
458	C₂×C₄×C₇	—	2	1	no	—
459	C₂×C₄×C₇	—	2	2	no	—
460	C₂×C₄×C₇	—	2	1	no	—
461	C₂×C₄×C₇	—	2	2	no	—
462	C₂×C₄×C₇	—	2	4	no	—
463	C₂×C₄×C₇	—	4	2	no	—
464	C₂×C₄×C₇	—	4	2	no	—
465	C₂×C₄×C₇	—	4	1	no	—
466	C₂×C₄×C₇	—	4	4	no	—
467	C₂×C₄×C₇	—	4	4	no	—
468	C₂×C₄×C₇	—	4	2	no	—
469	C₂×C₄×C₇	—	4	4	no	—
470	C₂×C₄×C₇	—	4	4	no	—
471	C₂×C₄×C₇	—	4	2	no	—
472	C₂×C₄×C₇	—	8	2	no	—
473	C₂×C₄×C₇	—	8	1	no	—
474	C₂×C₄×C₇	—	8	4	no	—
475	C₂×C₄×C₇	—	8	4	no	—
476	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
477	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
481	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
486	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
487	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
488	C₇×C₈	—	2	2	no	—
489	C₇×C₈	—	2	4	no	—
490	C₇×C₈	C₂²×Q₈	1	4	yes	—
491	C₂×#41	C₂³×C₇	1	1	yes	characteristic
492	C₂²×Q₈	—	2	1	no	—
493	C₂²×Q₈	—	2	1	no	—
494	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
495	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
496	C₂³×C₄	—	2	1	no	—
497	C₂³×C₄	—	2	2	no	—
498	AGL(1,ℤ/8)	C₇×Q₈	1	8	yes	complemented
499	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
500	C₂×D₈	C₂³×C₇	1	2	yes	—
501	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
502	C₂×M₁₆	C₂³×C₇	1	2	yes	—
503	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
504	C₄⋊Q₈	—	2	1	no	—
505	C₄⋊Q₈	—	2	2	no	—
506	C₄⋊Q₈	—	2	1	no	—
507	C₄⋊Q₈	—	2	2	no	—
508	C₄⋊Q₈	—	2	1	no	—
509	C₄⋊Q₈	—	2	1	no	—
510	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
511	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
512	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
513	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
514	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
515	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
516	#125	—	2	2	no	—
517	#125	—	2	2	no	—
518	#125	—	2	2	no	—
519	#125	—	2	2	no	—
520	#125	—	2	2	no	—
521	#125	C₂³×C₇	1	4	yes	—
522	#125	C₂³×C₇	1	4	yes	—
523	#125	C₂³×C₇	1	2	yes	—
524	#125	C₂³×C₇	1	2	yes	—
525	#125	C₂³×C₇	1	2	yes	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	—	2	1	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	1	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	1	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	4	no	—
536	C₂²⋊Q₈	—	2	4	no	—
537	C₂²⋊Q₈	—	2	4	no	—
538	C₂²⋊Q₈	—	2	4	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	1	no	—
545	C₄×Q₈	—	2	1	no	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	1	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	1	no	—
551	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
552	C₄×Q₈	C₇×D₄	1	2	yes	—
553	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
554	C₄×Q₈	C₂³×C₇	1	2	yes	—
555	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
556	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
557	C₄×Q₈	C₂³×C₇	1	2	yes	—
558	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
559	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
560	C₄×Q₈	C₂³×C₇	1	2	yes	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	C₂³×C₇	1	2	yes	—
570	C₄×D₄	C₂³×C₇	1	4	yes	—
571	C₄×D₄	C₂³×C₇	1	4	yes	—
572	C₄×D₄	C₂³×C₇	1	2	yes	—
573	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
574	C₄×D₄	C₂³×C₇	1	2	yes	—
575	C₄×D₄	C₂³×C₇	1	2	yes	—
576	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
577	#117	—	2	2	no	—
578	#117	—	2	1	no	—
579	#117	C₂³×C₇	1	1	yes	characteristic
580	#117	C₂³×C₇	1	2	yes	—
581	C₂×C₄⋊C₄	—	2	2	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	2	no	—
584	C₂×C₄⋊C₄	—	2	2	no	—
585	C₂×C₄⋊C₄	—	2	4	no	—
586	C₂×C₄⋊C₄	—	2	2	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	2	no	—
589	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
593	C₂×C₂²⋊C₄	—	2	1	no	—
594	C₂×C₂²⋊C₄	—	2	2	no	—
595	C₂×C₄²	—	2	2	no	—
596	C₂×C₄²	—	2	1	no	—
597	C₂×C₄²	C₂³×C₇	1	2	yes	—
598	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
599	#107	C₂³×C₇	1	2	yes	—
600	#107	C₂³×C₇	1	4	yes	—
601	#107	C₂³×C₇	1	4	yes	—
602	#107	C₂³×C₇	1	4	yes	—
603	#107	C₂³×C₇	1	4	yes	—
604	#106	C₂³×C₇	1	4	yes	—
605	#106	C₂³×C₇	1	2	yes	—
606	#106	C₂³×C₇	1	4	yes	—
607	#106	C₂³×C₇	1	4	yes	—
608	#106	C₂³×C₇	1	4	yes	—
609	C₄⋊C₈	C₂³×C₇	1	2	yes	—
610	C₄⋊C₈	C₂³×C₇	1	4	yes	—
611	C₄⋊C₈	C₂³×C₇	1	4	yes	—
612	C₄⋊C₈	C₂³×C₇	1	2	yes	—
613	#103	C₂³×C₇	1	4	yes	—
614	#103	C₂³×C₇	1	2	yes	—
615	#102	C₂³×C₇	1	4	yes	—
616	#102	C₂³×C₇	1	2	yes	—
617	#102	C₂³×C₇	1	4	yes	—
618	#102	C₂³×C₇	1	2	yes	—
619	#102	C₂³×C₇	1	2	yes	—
620	#102	C₂³×C₇	1	4	yes	—
621	#97	C₂³×C₇	1	2	yes	—
622	#97	C₂³×C₇	1	4	yes	—
623	C₄×C₈	C₂³×C₇	1	2	yes	—
624	C₄×C₈	C₂³×C₇	1	4	yes	—
625	C₂²×C₇	—	2	1	no	—
626	C₂²×C₇	—	2	1	no	—
627	C₂²×C₇	—	2	2	no	—
628	C₂²×C₇	—	2	4	no	—
629	C₂²×C₇	—	4	8	no	—
630	C₂²×C₇	—	4	2	no	—
631	C₂²×C₇	—	4	1	no	—
632	C₂²×C₇	—	4	1	no	—
633	C₂²×C₇	—	4	2	no	—
634	C₂²×C₇	D₄×Q₈	1	2	yes	—
635	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
636	C₄×C₇	—	2	2	no	—
637	C₄×C₇	—	2	2	no	—
638	C₄×C₇	—	2	1	no	—
639	C₄×C₇	—	2	1	no	—
640	C₄×C₇	—	2	2	no	—
641	C₄×C₇	—	2	1	no	—
642	C₄×C₇	—	2	2	no	—
643	C₄×C₇	—	2	2	no	—
644	C₄×C₇	—	4	4	no	—
645	C₄×C₇	—	4	2	no	—
646	C₄×C₇	—	4	1	no	—
647	C₄×C₇	—	4	2	no	—
648	C₄×C₇	—	4	2	no	—
649	C₄×C₇	—	4	1	no	—
650	C₄×C₇	D₄×Q₈	1	2	yes	—
651	C₄×C₇	#575	1	2	yes	—
652	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
653	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
654	C₂⁴	—	2	1	no	—
655	#41	—	2	2	no	—
656	#41	C₂×C₇×Q₈	1	4	yes	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	2	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	—	4	2	no	—
664	C₂×Q₈	—	4	4	no	—
665	C₂×Q₈	—	8	2	no	—
666	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
667	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
668	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
669	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	C₂×C₇×Q₈	1	4	yes	complemented
674	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
675	C₂×D₄	C₂⁴×C₇	1	2	yes	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	4	4	no	—
688	C₂²×C₄	—	8	4	no	—
689	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
690	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
691	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
692	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
694	SD₁₆	C₂×C₇×Q₈	1	8	yes	complemented
695	D₈	C₂×C₇×Q₈	1	8	yes	complemented
696	M₁₆	—	2	2	no	—
697	M₁₆	—	2	4	no	—
698	M₁₆	C₂×C₇×Q₈	1	4	yes	complemented
699	C₂×C₈	C₂⁴×C₇	1	2	yes	—
700	C₂×C₈	C₂⁴×C₇	1	4	yes	—
701	C₂×C₈	C₂⁴×C₇	1	2	yes	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
725	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
726	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
727	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
728	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
729	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
730	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
731	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
732	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
734	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
735	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	1	no	—
749	C₄²	—	2	1	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	2	1	no	—
753	C₄²	C₂×C₇×D₄	1	2	yes	—
754	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
755	C₄²	C₂×C₇×D₄	1	2	yes	—
756	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
757	C₄²	C₂⁴×C₇	1	2	yes	—
758	C₄²	C₂⁴×C₇	1	1	yes	characteristic
759	C₄²	C₂⁴×C₇	1	2	yes	—
760	C₄²	C₂⁴×C₇	1	1	yes	characteristic
761	C₂×C₇	—	2	2	no	—
762	C₂×C₇	—	4	2	no	—
763	C₂×C₇	—	4	4	no	—
764	C₂×C₇	C₂×D₄×Q₈	1	1	yes	characteristic
765	C₂×C₇	C₂×#575	1	1	yes	characteristic
766	C₂×C₇	#3585	1	1	yes	characteristic
767	C₂³	—	2	1	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	4	no	—
770	C₂³	—	4	2	no	—
771	C₂³	—	4	2	no	—
772	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
773	Q₈	—	2	1	no	—
774	Q₈	—	2	2	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	4	2	no	—
777	Q₈	—	4	4	no	—
778	Q₈	—	4	2	no	—
779	Q₈	—	8	2	no	—
780	Q₈	—	8	1	no	—
781	Q₈	—	8	2	no	—
782	Q₈	—	8	2	no	—
783	Q₈	C₂²×C₇×Q₈	1	2	yes	—
784	D₄	—	2	4	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	1	no	—
787	D₄	—	2	4	no	—
788	D₄	C₂²×C₇×Q₈	1	2	yes	—
789	D₄	C₂²×C₇×Q₈	1	4	yes	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	4	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	4	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	—	8	1	no	—
810	C₂×C₄	—	8	4	no	—
811	C₂×C₄	—	8	4	no	—
812	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
813	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
814	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
815	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
816	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
817	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
818	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
819	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
820	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
821	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
822	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
823	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
824	C₈	—	2	2	no	—
825	C₈	—	2	4	no	—
826	C₈	C₂²×C₇×Q₈	1	4	yes	—
827	C₇	#61367	1	1	yes	characteristic, direct product factor, Sylow
828	C₂²	—	2	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	4	8	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	1	no	—
837	C₂²	C₇×D₄×Q₈	1	2	yes	—
838	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
839	C₄	—	2	1	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	1	no	—
846	C₄	—	2	2	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	4	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	1	no	—
853	C₄	C₇×D₄×Q₈	1	2	yes	—
854	C₄	C₇×#575	1	2	yes	—
855	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
856	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
857	C₂	—	2	2	no	—
858	C₂	—	4	4	no	—
859	C₂	—	4	2	no	—
860	C₂	C₂×C₇×D₄×Q₈	1	1	yes	characteristic
861	C₂	C₂×C₇×#575	1	1	yes	characteristic
862	C₂	C₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×Q₈×#41	C₂	semidirect
2. C₂×C₇×#554	C₂	semidirect
3. C₇×#3389	C₂	semidirect
4. C₇×#3388	C₂	semidirect
5. C₇×#3385	C₂	semidirect
6. C₇×#3384	C₂	semidirect
7. C₇×#3381	C₂	semidirect
8. C₇×#3380	C₂	semidirect
9. C₇×#3166	C₂	semidirect
10. C₇×#3165	C₂	semidirect
11. C₇×#3080	C₂	semidirect
12. C₇×#3079	C₂	semidirect
13. C₇×#3077	C₂	semidirect
14. C₇×#3077	C₂	semidirect
15. C₇×Q₈×M₁₆	C₂	semidirect
19. C₇×Q₈²	C₂²	semidirect
20. C₇×#557	C₂²	semidirect
21. C₇×#557	C₂²	semidirect
30. C₇×#554	C₂²	semidirect
31. C₇×#554	C₂²	semidirect
33. C₇×D₄×Q₈	C₂²	semidirect
49. C₇×#501	C₂²	semidirect
50. C₇×#501	C₂²	semidirect
51. C₇×#501	C₂²	semidirect
52. C₇×#500	C₂²	semidirect
53. C₇×#499	C₂²	semidirect
54. C₇×#499	C₂²	semidirect
55. C₇×#498	C₂²	semidirect
56. C₇×#479	C₂²	semidirect
57. C₇×#479	C₂²	semidirect
61. C₇×#478	C₂²	semidirect
62. C₇×#478	C₂²	semidirect
63. C₇×#477	C₂²	semidirect
66. C₇×#476	C₂²	semidirect
67. C₇×#475	C₂²	semidirect
70. C₇×#474	C₂²	semidirect
71. C₇×#446	C₂²	semidirect
72. C₇×#446	C₂²	semidirect
73. C₇×C₈×Q₈	C₂²	semidirect
95. #61367	C₇	direct (N × H)
103. C₇×AGL(1,ℤ/8)	Q₈	semidirect
230. Q₈×#41	C₂×C₇	semidirect
231. C₂×#554	C₂×C₇	semidirect
232. #3389	C₂×C₇	semidirect
233. #3388	C₂×C₇	semidirect
234. #3385	C₂×C₇	semidirect
235. #3384	C₂×C₇	semidirect
236. #3381	C₂×C₇	semidirect
237. #3380	C₂×C₇	semidirect
238. #3166	C₂×C₇	semidirect
239. #3165	C₂×C₇	semidirect
240. #3080	C₂×C₇	semidirect
241. #3079	C₂×C₇	semidirect
242. #3077	C₂×C₇	semidirect
243. #3077	C₂×C₇	semidirect
244. Q₈×M₁₆	C₂×C₇	semidirect
266. C₂×C₇×D₄	C₂×Q₈	semidirect
287. C₇×SD₁₆	C₂×Q₈	semidirect
288. C₇×D₈	C₂×Q₈	semidirect
291. C₇×M₁₆	C₂×Q₈	semidirect
355. Q₈²	C₂²×C₇	semidirect
356. #557	C₂²×C₇	semidirect
357. #557	C₂²×C₇	semidirect
366. #554	C₂²×C₇	semidirect
367. #554	C₂²×C₇	semidirect
369. D₄×Q₈	C₂²×C₇	semidirect
385. #501	C₂²×C₇	semidirect
386. #501	C₂²×C₇	semidirect
387. #501	C₂²×C₇	semidirect
388. #500	C₂²×C₇	semidirect
389. #499	C₂²×C₇	semidirect
390. #499	C₂²×C₇	semidirect
391. #498	C₂²×C₇	semidirect
392. #479	C₂²×C₇	semidirect
393. #479	C₂²×C₇	semidirect
397. #478	C₂²×C₇	semidirect
398. #478	C₂²×C₇	semidirect
399. #477	C₂²×C₇	semidirect
402. #476	C₂²×C₇	semidirect
403. #475	C₂²×C₇	semidirect
406. #474	C₂²×C₇	semidirect
407. #446	C₂²×C₇	semidirect
408. #446	C₂²×C₇	semidirect
409. C₈×Q₈	C₂²×C₇	semidirect
498. AGL(1,ℤ/8)	C₇×Q₈	semidirect
673. C₂×D₄	C₂×C₇×Q₈	semidirect
694. SD₁₆	C₂×C₇×Q₈	semidirect
695. D₈	C₂×C₇×Q₈	semidirect
698. M₁₆	C₂×C₇×Q₈	semidirect
827. C₇	#61367	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×Q₈×#41	2
C₂×C₇×#554	2
C₇×#3389	2
C₇×#3388	2
C₇×#3385	2
C₇×#3384	2
C₇×#3381	2
C₇×#3380	2
C₇×#3166	2
C₇×#3165	2
C₇×#3080	2
C₇×#3079	2
C₇×#3077	2
C₇×Q₈×M₁₆	2
C₄×C₇×AGL(1,ℤ/8)	2
#61367	7

Subgroups — C7×#61367 #13238583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61367 #13238583