Subgroups — C₇×#61252 #13238468

Order 1792.

2088 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3354	C₂	1	2	yes	maximal, complemented
4	C₇×#3353	C₂	1	2	yes	maximal, complemented
5	C₇×#3345	C₂	1	4	yes	maximal, complemented
6	C₇×#3343	C₂	1	4	yes	maximal, complemented
7	C₇×#3335	C₂	1	2	yes	maximal, complemented
8	C₇×#3334	C₂	1	2	yes	maximal, complemented
9	C₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3094	C₂	1	2	yes	maximal, complemented
11	C₇×#3092	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×#3055	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#428	C₂	1	2	yes	maximal, complemented
18	C₂²×C₇×#41	—	2	1	no	—
19	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
21	C₇×#556	C₂²	1	1	yes	characteristic, complemented
22	C₇×#555	C₂²	1	1	yes	characteristic, complemented
23	C₇×#554	C₂²	1	1	yes	characteristic, complemented
24	C₇×#553	C₂²	1	2	yes	complemented
25	C₇×#552	—	2	1	no	—
26	C₇×#552	C₂²	1	2	yes	complemented
27	C₇×#551	—	2	2	no	—
28	C₇×#547	—	2	1	no	—
29	C₇×#547	—	2	2	no	—
30	C₇×#547	—	2	1	no	—
31	C₇×#547	C₂²	1	2	yes	—
32	C₇×#547	C₂²	1	4	yes	—
33	C₇×#547	C₂²	1	2	yes	—
34	C₇×#547	C₂²	1	1	yes	characteristic, complemented
35	C₇×#546	—	2	1	no	—
36	C₇×#533	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
38	C₇×#529	—	2	2	no	—
39	C₇×#529	—	2	1	no	—
40	C₇×#525	C₂²	1	2	yes	—
41	C₂×C₇×#123	—	2	2	no	—
42	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
43	C₂×C₇×#121	C₂²	1	2	yes	—
44	C₄×C₇×#41	—	2	1	no	—
45	C₄×C₇×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₇×#117	C₂²	1	2	yes	—
49	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
50	C₇×#501	C₂²	1	4	yes	complemented
51	C₇×#500	C₂²	1	2	yes	complemented
52	C₇×#498	C₂²	1	2	yes	complemented
53	C₇×#484	C₂²	1	4	yes	complemented
54	C₇×#483	C₂²	1	4	yes	complemented
55	C₇×#482	C₂²	1	4	yes	complemented
56	C₇×#482	C₂²	1	4	yes	complemented
57	C₇×#481	C₂²	1	4	yes	complemented
58	C₇×#481	C₂²	1	4	yes	complemented
59	C₇×#480	C₂²	1	4	yes	complemented
60	C₇×#480	C₂²	1	4	yes	complemented
61	C₇×#478	C₂²	1	4	yes	complemented
62	C₇×#477	C₂²	1	2	yes	complemented
63	C₇×#476	C₂²	1	2	yes	complemented
64	C₇×#476	C₂²	1	2	yes	complemented
65	C₇×#475	C₂²	1	2	yes	complemented
66	C₇×#474	C₂²	1	2	yes	complemented
67	C₇×#474	C₂²	1	2	yes	complemented
68	C₇×#469	C₂²	1	4	yes	complemented
69	C₇×#468	C₂²	1	4	yes	complemented
70	C₇×#466	C₂²	1	4	yes	complemented
71	C₇×#465	C₂²	1	4	yes	complemented
72	C₇×#442	C₂²	1	2	yes	complemented
73	C₇×#440	C₂²	1	2	yes	complemented
74	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
75	C₄×C₇×D₈	C₂²	1	2	yes	complemented
76	C₇×#436	C₂²	1	2	yes	complemented
77	C₇×#435	C₂²	1	4	yes	complemented
78	C₇×C₈×D₄	C₂²	1	2	yes	complemented
79	C₇×#428	C₂²	1	2	yes	—
80	C₇×#428	C₂²	1	2	yes	—
81	C₇×#428	C₂²	1	1	yes	characteristic
82	C₇×#428	C₂²	1	2	yes	—
83	C₇×#428	C₂²	1	2	yes	—
84	C₇×#428	C₂²	1	4	yes	complemented
85	C₇×#428	C₂²	1	4	yes	complemented
86	C₂×C₇×#107	C₂²	1	4	yes	complemented
87	C₂×C₇×#106	C₂²	1	4	yes	complemented
88	C₇×#423	C₂²	1	1	yes	characteristic
89	C₇×#418	C₂²	1	1	yes	characteristic
90	C₇×#418	C₂²	1	2	yes	—
91	C₇×#417	C₂²	1	1	yes	characteristic
92	C₇×#417	C₂²	1	2	yes	—
93	C₇×#407	C₂²	1	2	yes	—
94	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
95	#61252	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₇×#41	—	2	4	no	—
97	C₂×C₇×#41	—	2	2	no	—
98	C₂×C₇×#41	—	2	2	no	—
99	C₂×C₇×#41	—	2	1	no	—
100	C₂×C₇×#41	—	4	8	no	—
101	C₂×C₇×#41	C₂³	1	1	yes	characteristic
102	C₂²×C₇×Q₈	—	2	1	no	—
103	C₂²×C₇×D₄	—	2	2	no	—
104	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
105	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₇	—	2	2	no	—
107	C₂³×C₄×C₇	—	2	1	no	—
108	C₂³×C₄×C₇	C₂³	1	2	yes	—
109	C₇×AGL(1,ℤ/8)	—	2	4	no	—
110	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
111	C₂×C₇×D₈	C₂³	1	2	yes	—
112	C₂×C₇×M₁₆	—	2	8	no	—
113	C₂×C₇×M₁₆	C₂³	1	4	yes	—
114	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
115	C₂×C₇×M₁₆	C₂³	1	2	yes	—
116	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
117	C₂²×C₇×C₈	C₂³	1	4	yes	—
118	C₇×C₄⋊Q₈	—	2	1	no	—
119	C₇×C₄⋊Q₈	—	2	1	no	—
120	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
124	C₇×#126	—	2	2	no	—
125	C₇×#126	—	2	2	no	—
126	C₇×#126	—	2	2	no	—
127	C₇×#125	—	2	2	no	—
128	C₇×#125	—	2	1	no	—
129	C₇×#125	C₂³	1	2	yes	—
130	C₇×#124	—	2	1	no	—
131	C₇×#124	—	2	2	no	—
132	C₇×#123	—	2	2	no	—
133	C₇×#123	—	2	2	no	—
134	C₇×#123	—	2	4	no	—
135	C₇×#123	—	2	4	no	—
136	C₇×#123	—	2	4	no	—
137	C₇×#123	—	2	4	no	—
138	C₇×#123	—	2	2	no	—
139	C₇×#123	—	2	2	no	—
140	C₇×C₂²⋊Q₈	—	2	1	no	—
141	C₇×C₂²⋊Q₈	—	2	1	no	—
142	C₇×C₂²⋊Q₈	—	2	2	no	—
143	C₇×C₂²⋊Q₈	—	2	2	no	—
144	C₇×C₂²⋊Q₈	—	2	4	no	—
145	C₇×C₂²⋊Q₈	—	2	1	no	—
146	C₇×C₂²⋊Q₈	—	2	2	no	—
147	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₇×#121	—	2	2	no	—
150	C₇×#121	—	2	1	no	—
151	C₇×#121	—	2	2	no	—
152	C₇×#121	—	2	2	no	—
153	C₇×#121	C₂³	1	2	yes	—
154	C₇×#121	C₂³	1	4	yes	—
155	C₇×#121	C₂³	1	4	yes	—
156	C₇×#121	C₂³	1	2	yes	—
157	C₇×#120	—	2	2	no	—
158	C₄×C₇×Q₈	—	2	1	no	—
159	C₄×C₇×Q₈	—	2	1	no	—
160	C₄×C₇×Q₈	—	2	1	no	—
161	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
162	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
163	C₄×C₇×D₄	—	2	1	no	—
164	C₄×C₇×D₄	—	2	2	no	—
165	C₄×C₇×D₄	—	2	1	no	—
166	C₄×C₇×D₄	—	2	1	no	—
167	C₄×C₇×D₄	—	2	2	no	—
168	C₄×C₇×D₄	—	2	2	no	—
169	C₄×C₇×D₄	—	2	1	no	—
170	C₄×C₇×D₄	—	2	1	no	—
171	C₄×C₇×D₄	D₄	1	1	yes	characteristic
172	C₄×C₇×D₄	D₄	1	1	yes	characteristic
173	C₄×C₇×D₄	D₄	1	2	yes	—
174	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
175	C₄×C₇×D₄	C₂³	1	2	yes	—
176	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
177	C₄×C₇×D₄	C₂³	1	2	yes	—
178	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
179	C₄×C₇×D₄	C₂³	1	2	yes	—
180	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
181	C₇×#117	—	2	2	no	—
182	C₇×#117	—	2	2	no	—
183	C₇×#117	—	2	1	no	—
184	C₇×#117	—	2	2	no	—
185	C₇×#117	—	2	1	no	—
186	C₇×#117	C₂³	1	2	yes	—
187	C₇×#117	C₂³	1	2	yes	—
188	C₇×#117	C₂³	1	1	yes	characteristic
189	C₇×#117	C₂³	1	2	yes	—
190	C₂×C₇×C₄⋊C₄	—	2	2	no	—
191	C₂×C₇×C₄⋊C₄	—	2	2	no	—
192	C₂×C₇×C₄⋊C₄	—	2	2	no	—
193	C₂×C₇×C₄⋊C₄	—	2	1	no	—
194	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
195	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
197	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
199	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
202	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
203	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
204	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
205	C₂×C₄²×C₇	—	2	2	no	—
206	C₂×C₄²×C₇	—	2	1	no	—
207	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
208	C₇×#107	C₂³	1	4	yes	—
209	C₇×#107	C₂³	1	4	yes	—
210	C₇×#107	C₂³	1	4	yes	—
211	C₇×#107	C₂³	1	4	yes	—
212	C₇×#107	C₂³	1	2	yes	—
213	C₇×#106	C₂³	1	4	yes	—
214	C₇×#106	C₂³	1	4	yes	—
215	C₇×#106	C₂³	1	4	yes	—
216	C₇×#106	C₂³	1	4	yes	—
217	C₇×#106	C₂³	1	2	yes	—
218	C₇×C₄⋊C₈	C₂³	1	2	yes	—
219	C₇×C₄⋊C₈	C₂³	1	2	yes	—
220	C₇×#103	C₂³	1	4	yes	—
221	C₇×#103	C₂³	1	2	yes	—
222	C₇×#102	C₂³	1	4	yes	—
223	C₇×#102	C₂³	1	4	yes	—
224	C₇×#102	C₂³	1	4	yes	—
225	C₇×#102	C₂³	1	2	yes	—
226	C₇×#102	C₂³	1	2	yes	—
227	C₇×#102	C₂³	1	2	yes	—
228	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₇×#97	C₂³	1	2	yes	—
231	C₄×C₇×C₈	C₂³	1	2	yes	—
232	#3475	C₂×C₇	1	1	yes	characteristic, complemented
233	C₂×#547	C₂×C₇	1	1	yes	characteristic, complemented
234	#3354	C₂×C₇	1	2	yes	complemented
235	#3353	C₂×C₇	1	2	yes	complemented
236	#3345	C₂×C₇	1	4	yes	complemented
237	#3343	C₂×C₇	1	4	yes	complemented
238	#3335	C₂×C₇	1	2	yes	complemented
239	#3334	C₂×C₇	1	2	yes	complemented
240	#3165	C₂×C₇	1	1	yes	characteristic, complemented
241	#3094	C₂×C₇	1	2	yes	complemented
242	#3092	C₂×C₇	1	2	yes	complemented
243	#3079	C₂×C₇	1	1	yes	characteristic, complemented
244	#3077	C₂×C₇	1	1	yes	characteristic, complemented
245	#3055	C₂×C₇	1	2	yes	complemented
246	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic, complemented
247	D₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
248	C₂×#428	C₂×C₇	1	2	yes	complemented
249	C₂⁴×C₇	—	2	1	no	—
250	C₂⁴×C₇	C₂×D₄	1	2	yes	—
251	C₇×#41	—	2	2	no	—
252	C₇×#41	—	2	2	no	—
253	C₇×#41	—	4	16	no	—
254	C₇×#41	—	4	8	no	—
255	C₇×#41	—	4	4	no	—
256	C₇×#41	—	4	8	no	—
257	C₂×C₇×Q₈	—	2	1	no	—
258	C₂×C₇×Q₈	—	2	2	no	—
259	C₂×C₇×Q₈	—	2	2	no	—
260	C₂×C₇×Q₈	—	2	1	no	—
261	C₂×C₇×Q₈	—	4	4	no	—
262	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
263	C₂×C₇×D₄	—	2	4	no	—
264	C₂×C₇×D₄	—	2	1	no	—
265	C₂×C₇×D₄	—	2	2	no	—
266	C₂×C₇×D₄	—	2	4	no	—
267	C₂×C₇×D₄	—	2	4	no	—
268	C₂×C₇×D₄	—	2	2	no	—
269	C₂×C₇×D₄	—	2	1	no	—
270	C₂×C₇×D₄	—	2	2	no	—
271	C₂×C₇×D₄	—	2	2	no	—
272	C₂×C₇×D₄	—	4	8	no	—
273	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
274	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
275	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
276	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
277	C₂×C₇×D₄	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₇	—	2	4	no	—
279	C₂²×C₄×C₇	—	2	4	no	—
280	C₂²×C₄×C₇	—	2	2	no	—
281	C₂²×C₄×C₇	—	2	1	no	—
282	C₂²×C₄×C₇	—	2	2	no	—
283	C₂²×C₄×C₇	—	2	4	no	—
284	C₂²×C₄×C₇	—	2	4	no	—
285	C₂²×C₄×C₇	—	2	2	no	—
286	C₂²×C₄×C₇	—	2	1	no	—
287	C₂²×C₄×C₇	—	2	1	no	—
288	C₂²×C₄×C₇	—	2	2	no	—
289	C₂²×C₄×C₇	—	2	2	no	—
290	C₂²×C₄×C₇	—	2	1	no	—
291	C₂²×C₄×C₇	—	4	4	no	—
292	C₂²×C₄×C₇	—	4	8	no	—
293	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
294	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
296	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
297	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
301	C₇×SD₁₆	—	2	4	no	—
302	C₇×D₈	—	2	4	no	—
303	C₇×M₁₆	—	2	4	no	—
304	C₇×M₁₆	—	2	2	no	—
305	C₇×M₁₆	—	2	8	no	—
306	C₇×M₁₆	#41	1	4	yes	complemented
307	C₂×C₇×C₈	—	2	8	no	—
308	C₂×C₇×C₈	C₂⁴	1	2	yes	—
309	C₂×C₇×C₈	C₂⁴	1	4	yes	—
310	C₂×C₇×C₈	C₂⁴	1	2	yes	—
311	C₇×C₄⋊C₄	—	2	1	no	—
312	C₇×C₄⋊C₄	—	2	2	no	—
313	C₇×C₄⋊C₄	—	2	4	no	—
314	C₇×C₄⋊C₄	—	2	4	no	—
315	C₇×C₄⋊C₄	—	2	2	no	—
316	C₇×C₄⋊C₄	—	2	2	no	—
317	C₇×C₄⋊C₄	—	2	2	no	—
318	C₇×C₄⋊C₄	—	2	2	no	—
319	C₇×C₄⋊C₄	—	2	1	no	—
320	C₇×C₄⋊C₄	—	2	2	no	—
321	C₇×C₄⋊C₄	—	2	2	no	—
322	C₇×C₄⋊C₄	—	2	1	no	—
323	C₇×C₄⋊C₄	—	2	1	no	—
324	C₇×C₄⋊C₄	—	2	2	no	—
325	C₇×C₄⋊C₄	—	2	2	no	—
326	C₇×C₄⋊C₄	—	2	1	no	—
327	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
328	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
329	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
330	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
331	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
332	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
333	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
334	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
335	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
336	C₇×C₂²⋊C₄	—	2	1	no	—
337	C₇×C₂²⋊C₄	—	2	2	no	—
338	C₇×C₂²⋊C₄	—	2	2	no	—
339	C₇×C₂²⋊C₄	—	2	2	no	—
340	C₇×C₂²⋊C₄	—	2	2	no	—
341	C₇×C₂²⋊C₄	—	2	2	no	—
342	C₇×C₂²⋊C₄	—	2	2	no	—
343	C₇×C₂²⋊C₄	—	2	2	no	—
344	C₇×C₂²⋊C₄	—	2	4	no	—
345	C₇×C₂²⋊C₄	—	2	4	no	—
346	C₇×C₂²⋊C₄	—	2	2	no	—
347	C₇×C₂²⋊C₄	—	2	1	no	—
348	C₇×C₂²⋊C₄	—	2	1	no	—
349	C₇×C₂²⋊C₄	—	2	2	no	—
350	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
351	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
352	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
353	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
354	C₄²×C₇	—	2	1	no	—
355	C₄²×C₇	—	2	2	no	—
356	C₄²×C₇	—	2	1	no	—
357	C₄²×C₇	—	2	2	no	—
358	C₄²×C₇	—	2	2	no	—
359	C₄²×C₇	—	2	1	no	—
360	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
361	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
362	C₄²×C₇	C₂⁴	1	1	yes	characteristic
363	C₄²×C₇	C₂⁴	1	1	yes	characteristic
364	C₂²×#41	—	2	1	no	—
365	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
366	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
367	#556	C₂²×C₇	1	1	yes	characteristic, complemented
368	#555	C₂²×C₇	1	1	yes	characteristic, complemented
369	#554	C₂²×C₇	1	1	yes	characteristic, complemented
370	#553	C₂²×C₇	1	2	yes	complemented
371	#552	—	2	1	no	—
372	#552	C₂²×C₇	1	2	yes	complemented
373	#551	—	2	2	no	—
374	#547	—	2	1	no	—
375	#547	—	2	2	no	—
376	#547	—	2	1	no	—
377	#547	C₂²×C₇	1	2	yes	—
378	#547	C₂²×C₇	1	4	yes	—
379	#547	C₂²×C₇	1	2	yes	—
380	#547	C₂²×C₇	1	1	yes	characteristic, complemented
381	#546	—	2	1	no	—
382	#533	C₂²×C₇	1	1	yes	characteristic
383	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
384	#529	—	2	2	no	—
385	#529	—	2	1	no	—
386	#525	C₂²×C₇	1	2	yes	—
387	C₂×#123	—	2	2	no	—
388	C₂×C₂²⋊Q₈	—	2	1	no	—
389	C₂×#121	C₂²×C₇	1	2	yes	—
390	C₄×#41	—	2	1	no	—
391	C₄×#41	C₂²×C₇	1	1	yes	characteristic
392	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
393	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
394	C₂×#117	C₂²×C₇	1	2	yes	—
395	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
396	#501	C₂²×C₇	1	4	yes	complemented
397	#500	C₂²×C₇	1	2	yes	complemented
398	#498	C₂²×C₇	1	2	yes	complemented
399	#484	C₂²×C₇	1	4	yes	complemented
400	#483	C₂²×C₇	1	4	yes	complemented
401	#482	C₂²×C₇	1	4	yes	complemented
402	#482	C₂²×C₇	1	4	yes	complemented
403	#481	C₂²×C₇	1	4	yes	complemented
404	#481	C₂²×C₇	1	4	yes	complemented
405	#480	C₂²×C₇	1	4	yes	complemented
406	#480	C₂²×C₇	1	4	yes	complemented
407	#478	C₂²×C₇	1	4	yes	complemented
408	#477	C₂²×C₇	1	2	yes	complemented
409	#476	C₂²×C₇	1	2	yes	complemented
410	#476	C₂²×C₇	1	2	yes	complemented
411	#475	C₂²×C₇	1	2	yes	complemented
412	#474	C₂²×C₇	1	2	yes	complemented
413	#474	C₂²×C₇	1	2	yes	complemented
414	#469	C₂²×C₇	1	4	yes	complemented
415	#468	C₂²×C₇	1	4	yes	complemented
416	#466	C₂²×C₇	1	4	yes	complemented
417	#465	C₂²×C₇	1	4	yes	complemented
418	#442	C₂²×C₇	1	2	yes	complemented
419	#440	C₂²×C₇	1	2	yes	complemented
420	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
421	C₄×D₈	C₂²×C₇	1	2	yes	complemented
422	#436	C₂²×C₇	1	2	yes	complemented
423	#435	C₂²×C₇	1	4	yes	complemented
424	C₈×D₄	C₂²×C₇	1	2	yes	complemented
425	#428	C₂²×C₇	1	2	yes	—
426	#428	C₂²×C₇	1	2	yes	—
427	#428	C₂²×C₇	1	2	yes	—
428	#428	C₂²×C₇	1	2	yes	—
429	#428	C₂²×C₇	1	1	yes	characteristic
430	#428	C₂²×C₇	1	4	yes	complemented
431	#428	C₂²×C₇	1	4	yes	complemented
432	C₂×#107	C₂²×C₇	1	4	yes	complemented
433	C₂×#106	C₂²×C₇	1	4	yes	complemented
434	#423	C₂²×C₇	1	1	yes	characteristic
435	#418	C₂²×C₇	1	2	yes	—
436	#418	C₂²×C₇	1	1	yes	characteristic
437	#417	C₂²×C₇	1	2	yes	—
438	#417	C₂²×C₇	1	1	yes	characteristic
439	#407	C₂²×C₇	1	2	yes	—
440	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
441	C₂³×C₇	—	2	4	no	—
442	C₂³×C₇	—	2	4	no	—
443	C₂³×C₇	—	2	1	no	—
444	C₂³×C₇	—	2	2	no	—
445	C₂³×C₇	—	4	2	no	—
446	C₂³×C₇	—	4	2	no	—
447	C₂³×C₇	—	4	2	no	—
448	C₂³×C₇	—	4	2	no	—
449	C₂³×C₇	C₂²×D₄	1	2	yes	—
450	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
451	C₂³×C₇	C₂²×D₄	1	2	yes	—
452	C₇×Q₈	—	2	1	no	—
453	C₇×Q₈	—	2	1	no	—
454	C₇×Q₈	—	4	4	no	—
455	C₇×Q₈	—	4	4	no	—
456	C₇×Q₈	—	4	2	no	—
457	C₇×Q₈	—	8	1	no	—
458	C₇×D₄	—	2	4	no	—
459	C₇×D₄	—	2	2	no	—
460	C₇×D₄	—	2	1	no	—
461	C₇×D₄	—	2	2	no	—
462	C₇×D₄	—	2	2	no	—
463	C₇×D₄	—	2	1	no	—
464	C₇×D₄	—	4	8	no	—
465	C₇×D₄	—	4	2	no	—
466	C₇×D₄	—	4	8	no	—
467	C₇×D₄	—	4	4	no	—
468	C₇×D₄	—	4	2	no	—
469	C₇×D₄	—	8	2	no	—
470	C₇×D₄	AGL(1,ℤ/8)	1	4	yes	complemented
471	C₂×C₄×C₇	—	2	4	no	—
472	C₂×C₄×C₇	—	2	4	no	—
473	C₂×C₄×C₇	—	2	4	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	—	2	1	no	—
480	C₂×C₄×C₇	—	2	1	no	—
481	C₂×C₄×C₇	—	2	1	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	4	no	—
486	C₂×C₄×C₇	—	4	1	no	—
487	C₂×C₄×C₇	—	4	4	no	—
488	C₂×C₄×C₇	—	4	2	no	—
489	C₂×C₄×C₇	—	4	4	no	—
490	C₂×C₄×C₇	—	4	8	no	—
491	C₂×C₄×C₇	—	4	8	no	—
492	C₂×C₄×C₇	—	4	4	no	—
493	C₂×C₄×C₇	—	4	2	no	—
494	C₂×C₄×C₇	—	4	4	no	—
495	C₂×C₄×C₇	—	4	2	no	—
496	C₂×C₄×C₇	—	8	1	no	—
497	C₂×C₄×C₇	—	8	2	no	—
498	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₇	C₂×#41	1	2	yes	—
506	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
507	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
508	C₇×C₈	—	2	4	no	—
509	C₇×C₈	—	2	2	no	—
510	C₇×C₈	C₂×#41	1	4	yes	complemented
511	C₂×#41	—	2	1	no	—
512	C₂×#41	—	2	4	no	—
513	C₂×#41	—	2	2	no	—
514	C₂×#41	—	2	2	no	—
515	C₂×#41	—	4	8	no	—
516	C₂×#41	C₂³×C₇	1	1	yes	characteristic
517	C₂²×Q₈	—	2	1	no	—
518	C₂²×D₄	—	2	2	no	—
519	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
520	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
521	C₂³×C₄	—	2	2	no	—
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	C₂³×C₇	1	2	yes	—
524	AGL(1,ℤ/8)	—	2	4	no	—
525	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
526	C₂×D₈	C₂³×C₇	1	2	yes	—
527	C₂×M₁₆	—	2	8	no	—
528	C₂×M₁₆	C₂³×C₇	1	2	yes	—
529	C₂×M₁₆	C₂³×C₇	1	4	yes	—
530	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
531	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
532	C₂²×C₈	C₂³×C₇	1	4	yes	—
533	C₄⋊Q₈	—	2	1	no	—
534	C₄⋊Q₈	—	2	1	no	—
535	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
536	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
537	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
538	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
539	#126	—	2	2	no	—
540	#126	—	2	2	no	—
541	#126	—	2	2	no	—
542	#125	—	2	2	no	—
543	#125	—	2	1	no	—
544	#125	C₂³×C₇	1	2	yes	—
545	#124	—	2	1	no	—
546	#124	—	2	2	no	—
547	#123	—	2	2	no	—
548	#123	—	2	2	no	—
549	#123	—	2	4	no	—
550	#123	—	2	4	no	—
551	#123	—	2	4	no	—
552	#123	—	2	4	no	—
553	#123	—	2	2	no	—
554	#123	—	2	2	no	—
555	C₂²⋊Q₈	—	2	1	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	4	no	—
560	C₂²⋊Q₈	—	2	1	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
563	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
564	#121	—	2	2	no	—
565	#121	—	2	1	no	—
566	#121	—	2	2	no	—
567	#121	—	2	2	no	—
568	#121	C₂³×C₇	1	4	yes	—
569	#121	C₂³×C₇	1	4	yes	—
570	#121	C₂³×C₇	1	2	yes	—
571	#121	C₂³×C₇	1	2	yes	—
572	#120	—	2	2	no	—
573	C₄×Q₈	—	2	1	no	—
574	C₄×Q₈	—	2	1	no	—
575	C₄×Q₈	—	2	1	no	—
576	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
577	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	1	no	—
585	C₄×D₄	—	2	1	no	—
586	C₄×D₄	C₇×D₄	1	1	yes	characteristic
587	C₄×D₄	C₇×D₄	1	1	yes	characteristic
588	C₄×D₄	C₇×D₄	1	2	yes	—
589	C₄×D₄	C₂³×C₇	1	2	yes	—
590	C₄×D₄	C₂³×C₇	1	2	yes	—
591	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
592	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
593	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
594	C₄×D₄	C₂³×C₇	1	2	yes	—
595	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
596	#117	—	2	2	no	—
597	#117	—	2	2	no	—
598	#117	—	2	1	no	—
599	#117	—	2	2	no	—
600	#117	—	2	1	no	—
601	#117	C₂³×C₇	1	1	yes	characteristic
602	#117	C₂³×C₇	1	2	yes	—
603	#117	C₂³×C₇	1	2	yes	—
604	#117	C₂³×C₇	1	2	yes	—
605	C₂×C₄⋊C₄	—	2	2	no	—
606	C₂×C₄⋊C₄	—	2	2	no	—
607	C₂×C₄⋊C₄	—	2	2	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
613	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
614	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
616	C₂×C₂²⋊C₄	—	2	2	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	2	no	—
619	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
620	C₂×C₄²	—	2	2	no	—
621	C₂×C₄²	—	2	1	no	—
622	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
623	#107	C₂³×C₇	1	2	yes	—
624	#107	C₂³×C₇	1	4	yes	—
625	#107	C₂³×C₇	1	4	yes	—
626	#107	C₂³×C₇	1	4	yes	—
627	#107	C₂³×C₇	1	4	yes	—
628	#106	C₂³×C₇	1	2	yes	—
629	#106	C₂³×C₇	1	4	yes	—
630	#106	C₂³×C₇	1	4	yes	—
631	#106	C₂³×C₇	1	4	yes	—
632	#106	C₂³×C₇	1	4	yes	—
633	C₄⋊C₈	C₂³×C₇	1	2	yes	—
634	C₄⋊C₈	C₂³×C₇	1	2	yes	—
635	#103	C₂³×C₇	1	2	yes	—
636	#103	C₂³×C₇	1	4	yes	—
637	#102	C₂³×C₇	1	2	yes	—
638	#102	C₂³×C₇	1	4	yes	—
639	#102	C₂³×C₇	1	2	yes	—
640	#102	C₂³×C₇	1	2	yes	—
641	#102	C₂³×C₇	1	4	yes	—
642	#102	C₂³×C₇	1	4	yes	—
643	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
644	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
645	#97	C₂³×C₇	1	2	yes	—
646	C₄×C₈	C₂³×C₇	1	2	yes	—
647	C₂²×C₇	—	2	1	no	—
648	C₂²×C₇	—	2	2	no	—
649	C₂²×C₇	—	2	2	no	—
650	C₂²×C₇	—	2	1	no	—
651	C₂²×C₇	—	2	2	no	—
652	C₂²×C₇	—	2	2	no	—
653	C₂²×C₇	—	2	2	no	—
654	C₂²×C₇	—	4	8	no	—
655	C₂²×C₇	—	4	1	no	—
656	C₂²×C₇	—	4	2	no	—
657	C₂²×C₇	—	4	1	no	—
658	C₂²×C₇	—	4	2	no	—
659	C₂²×C₇	—	4	2	no	—
660	C₂²×C₇	—	4	1	no	—
661	C₂²×C₇	—	8	4	no	—
662	C₂²×C₇	#547	1	2	yes	—
663	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
664	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
665	C₄×C₇	—	2	1	no	—
666	C₄×C₇	—	2	1	no	—
667	C₄×C₇	—	2	2	no	—
668	C₄×C₇	—	2	2	no	—
669	C₄×C₇	—	2	1	no	—
670	C₄×C₇	—	4	1	no	—
671	C₄×C₇	—	4	2	no	—
672	C₄×C₇	—	4	1	no	—
673	C₄×C₇	—	4	1	no	—
674	C₄×C₇	—	4	2	no	—
675	C₄×C₇	—	4	4	no	—
676	C₄×C₇	—	4	2	no	—
677	C₄×C₇	#547	1	2	yes	—
678	C₄×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
679	C₄×C₇	C₂²×#41	1	1	yes	characteristic
680	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
681	C₂⁴	—	2	1	no	—
682	C₂⁴	C₂×C₇×D₄	1	2	yes	—
683	#41	—	2	2	no	—
684	#41	—	2	2	no	—
685	#41	—	4	16	no	—
686	#41	—	4	8	no	—
687	#41	—	4	8	no	—
688	#41	—	4	4	no	—
689	C₂×Q₈	—	2	1	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	2	2	no	—
692	C₂×Q₈	—	2	1	no	—
693	C₂×Q₈	—	4	4	no	—
694	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	4	8	no	—
705	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
706	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
707	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
708	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
709	C₂×D₄	C₂⁴×C₇	1	2	yes	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	4	4	no	—
724	C₂²×C₄	—	4	8	no	—
725	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
726	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
727	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
728	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
729	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
733	SD₁₆	—	2	4	no	—
734	D₈	—	2	4	no	—
735	M₁₆	—	2	4	no	—
736	M₁₆	—	2	2	no	—
737	M₁₆	—	2	8	no	—
738	M₁₆	C₇×#41	1	4	yes	complemented
739	C₂×C₈	—	2	8	no	—
740	C₂×C₈	C₂⁴×C₇	1	2	yes	—
741	C₂×C₈	C₂⁴×C₇	1	4	yes	—
742	C₂×C₈	C₂⁴×C₇	1	2	yes	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
760	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
761	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
762	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
763	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
764	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
765	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
766	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
767	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
768	C₂²⋊C₄	—	2	1	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	1	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
783	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
784	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
785	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
786	C₄²	—	2	1	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	1	no	—
789	C₄²	—	2	2	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	1	no	—
792	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
793	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
794	C₄²	C₂⁴×C₇	1	1	yes	characteristic
795	C₄²	C₂⁴×C₇	1	1	yes	characteristic
796	C₂×C₇	—	2	2	no	—
797	C₂×C₇	—	2	4	no	—
798	C₂×C₇	—	4	2	no	—
799	C₂×C₇	—	8	1	no	—
800	C₂×C₇	—	8	2	no	—
801	C₂×C₇	C₂×#547	1	1	yes	characteristic
802	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
803	C₂×C₇	#3586	1	1	yes	characteristic
804	C₂³	—	2	4	no	—
805	C₂³	—	2	4	no	—
806	C₂³	—	2	1	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	4	2	no	—
809	C₂³	—	4	2	no	—
810	C₂³	—	4	2	no	—
811	C₂³	—	4	2	no	—
812	C₂³	C₂²×C₇×D₄	1	2	yes	—
813	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
814	C₂³	C₂²×C₇×D₄	1	2	yes	—
815	Q₈	—	2	1	no	—
816	Q₈	—	2	1	no	—
817	Q₈	—	4	4	no	—
818	Q₈	—	4	4	no	—
819	Q₈	—	4	2	no	—
820	Q₈	—	8	1	no	—
821	D₄	—	2	4	no	—
822	D₄	—	2	1	no	—
823	D₄	—	2	2	no	—
824	D₄	—	2	2	no	—
825	D₄	—	2	1	no	—
826	D₄	—	2	2	no	—
827	D₄	—	4	8	no	—
828	D₄	—	4	2	no	—
829	D₄	—	4	8	no	—
830	D₄	—	4	4	no	—
831	D₄	—	4	2	no	—
832	D₄	—	8	2	no	—
833	D₄	C₇×AGL(1,ℤ/8)	1	4	yes	complemented
834	C₂×C₄	—	2	4	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	4	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	4	1	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	4	8	no	—
854	C₂×C₄	—	4	8	no	—
855	C₂×C₄	—	4	4	no	—
856	C₂×C₄	—	4	2	no	—
857	C₂×C₄	—	4	4	no	—
858	C₂×C₄	—	4	2	no	—
859	C₂×C₄	—	8	1	no	—
860	C₂×C₄	—	8	2	no	—
861	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
862	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
863	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
864	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
865	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
866	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
867	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
868	C₂×C₄	C₂×C₇×#41	1	2	yes	—
869	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
870	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
871	C₈	—	2	4	no	—
872	C₈	—	2	2	no	—
873	C₈	C₂×C₇×#41	1	4	yes	complemented
874	C₇	#61252	1	1	yes	characteristic, direct product factor, Sylow
875	C₂²	—	2	1	no	—
876	C₂²	—	2	1	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	4	8	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	1	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	8	4	no	—
890	C₂²	C₇×#547	1	2	yes	—
891	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
892	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
893	C₄	—	2	1	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	4	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	1	no	—
905	C₄	C₇×#547	1	2	yes	—
906	C₄	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
907	C₄	C₂²×C₇×#41	1	1	yes	characteristic
908	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
909	C₂	—	2	2	no	—
910	C₂	—	2	4	no	—
911	C₂	—	4	2	no	—
912	C₂	—	8	2	no	—
913	C₂	—	8	1	no	—
914	C₂	C₂×C₇×#547	1	1	yes	characteristic
915	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
916	C₂	C₇×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₇×#3475	C₂	semidirect
2. C₂×C₇×#547	C₂	semidirect
3. C₇×#3354	C₂	semidirect
4. C₇×#3353	C₂	semidirect
5. C₇×#3345	C₂	semidirect
6. C₇×#3343	C₂	semidirect
7. C₇×#3335	C₂	semidirect
8. C₇×#3334	C₂	semidirect
9. C₇×#3165	C₂	semidirect
10. C₇×#3094	C₂	semidirect
11. C₇×#3092	C₂	semidirect
12. C₇×#3079	C₂	semidirect
13. C₇×#3077	C₂	semidirect
14. C₇×#3055	C₂	semidirect
15. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
16. C₇×D₄×M₁₆	C₂	semidirect
17. C₂×C₇×#428	C₂	semidirect
21. C₇×#556	C₂²	semidirect
22. C₇×#555	C₂²	semidirect
23. C₇×#554	C₂²	semidirect
24. C₇×#553	C₂²	semidirect
26. C₇×#552	C₂²	semidirect
34. C₇×#547	C₂²	semidirect
50. C₇×#501	C₂²	semidirect
51. C₇×#500	C₂²	semidirect
52. C₇×#498	C₂²	semidirect
53. C₇×#484	C₂²	semidirect
54. C₇×#483	C₂²	semidirect
55. C₇×#482	C₂²	semidirect
56. C₇×#482	C₂²	semidirect
57. C₇×#481	C₂²	semidirect
58. C₇×#481	C₂²	semidirect
59. C₇×#480	C₂²	semidirect
60. C₇×#480	C₂²	semidirect
61. C₇×#478	C₂²	semidirect
62. C₇×#477	C₂²	semidirect
63. C₇×#476	C₂²	semidirect
64. C₇×#476	C₂²	semidirect
65. C₇×#475	C₂²	semidirect
66. C₇×#474	C₂²	semidirect
67. C₇×#474	C₂²	semidirect
68. C₇×#469	C₂²	semidirect
69. C₇×#468	C₂²	semidirect
70. C₇×#466	C₂²	semidirect
71. C₇×#465	C₂²	semidirect
72. C₇×#442	C₂²	semidirect
73. C₇×#440	C₂²	semidirect
74. C₄×C₇×SD₁₆	C₂²	semidirect
75. C₄×C₇×D₈	C₂²	semidirect
76. C₇×#436	C₂²	semidirect
77. C₇×#435	C₂²	semidirect
78. C₇×C₈×D₄	C₂²	semidirect
84. C₇×#428	C₂²	semidirect
85. C₇×#428	C₂²	semidirect
86. C₂×C₇×#107	C₂²	semidirect
87. C₂×C₇×#106	C₂²	semidirect
95. #61252	C₇	direct (N × H)
232. #3475	C₂×C₇	semidirect
233. C₂×#547	C₂×C₇	semidirect
234. #3354	C₂×C₇	semidirect
235. #3353	C₂×C₇	semidirect
236. #3345	C₂×C₇	semidirect
237. #3343	C₂×C₇	semidirect
238. #3335	C₂×C₇	semidirect
239. #3334	C₂×C₇	semidirect
240. #3165	C₂×C₇	semidirect
241. #3094	C₂×C₇	semidirect
242. #3092	C₂×C₇	semidirect
243. #3079	C₂×C₇	semidirect
244. #3077	C₂×C₇	semidirect
245. #3055	C₂×C₇	semidirect
246. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
247. D₄×M₁₆	C₂×C₇	semidirect
248. C₂×#428	C₂×C₇	semidirect
306. C₇×M₁₆	#41	semidirect
367. #556	C₂²×C₇	semidirect
368. #555	C₂²×C₇	semidirect
369. #554	C₂²×C₇	semidirect
370. #553	C₂²×C₇	semidirect
372. #552	C₂²×C₇	semidirect
380. #547	C₂²×C₇	semidirect
396. #501	C₂²×C₇	semidirect
397. #500	C₂²×C₇	semidirect
398. #498	C₂²×C₇	semidirect
399. #484	C₂²×C₇	semidirect
400. #483	C₂²×C₇	semidirect
401. #482	C₂²×C₇	semidirect
402. #482	C₂²×C₇	semidirect
403. #481	C₂²×C₇	semidirect
404. #481	C₂²×C₇	semidirect
405. #480	C₂²×C₇	semidirect
406. #480	C₂²×C₇	semidirect
407. #478	C₂²×C₇	semidirect
408. #477	C₂²×C₇	semidirect
409. #476	C₂²×C₇	semidirect
410. #476	C₂²×C₇	semidirect
411. #475	C₂²×C₇	semidirect
412. #474	C₂²×C₇	semidirect
413. #474	C₂²×C₇	semidirect
414. #469	C₂²×C₇	semidirect
415. #468	C₂²×C₇	semidirect
416. #466	C₂²×C₇	semidirect
417. #465	C₂²×C₇	semidirect
418. #442	C₂²×C₇	semidirect
419. #440	C₂²×C₇	semidirect
420. C₄×SD₁₆	C₂²×C₇	semidirect
421. C₄×D₈	C₂²×C₇	semidirect
422. #436	C₂²×C₇	semidirect
423. #435	C₂²×C₇	semidirect
424. C₈×D₄	C₂²×C₇	semidirect
430. #428	C₂²×C₇	semidirect
431. #428	C₂²×C₇	semidirect
432. C₂×#107	C₂²×C₇	semidirect
433. C₂×#106	C₂²×C₇	semidirect
470. C₇×D₄	AGL(1,ℤ/8)	semidirect
510. C₇×C₈	C₂×#41	semidirect
738. M₁₆	C₇×#41	semidirect
833. D₄	C₇×AGL(1,ℤ/8)	semidirect
873. C₈	C₂×C₇×#41	semidirect
874. C₇	#61252	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×#3475	2
C₂×C₇×#547	2
C₇×#3354	2
C₇×#3353	2
C₇×#3345	2
C₇×#3343	2
C₇×#3335	2
C₇×#3334	2
C₇×#3165	2
C₇×#3094	2
C₇×#3092	2
C₇×#3079	2
C₇×#3077	2
C₇×#3055	2
C₄×C₇×AGL(1,ℤ/8)	2
C₇×D₄×M₁₆	2
C₂×C₇×#428	2
#61252	7

Subgroups — C7×#61252 #13238468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61252 #13238468