Subgroups — C₇×#61155 #13238371

Order 1792.

2572 conjugacy classes of subgroups.

The subgroup lattice has 992 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×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3325	C₂	1	2	yes	maximal, complemented
4	C₇×#3324	C₂	1	2	yes	maximal, complemented
5	C₇×#3318	C₂	1	4	yes	maximal, complemented
6	C₇×#3310	C₂	1	4	yes	maximal, complemented
7	C₇×#3295	C₂	1	2	yes	maximal, complemented
8	C₇×#3294	C₂	1	2	yes	maximal, complemented
9	C₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3094	C₂	1	2	yes	maximal, complemented
11	C₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3055	C₂	1	2	yes	maximal, complemented
13	C₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3003	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×#418	C₂	1	2	yes	maximal, complemented
18	C₂³×C₇×D₄	—	2	1	no	—
19	C₂³×C₇×D₄	C₂²	1	2	yes	—
20	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
21	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂²×C₇×M₁₆	C₂²	1	2	yes	complemented
23	C₇×#556	C₂²	1	1	yes	characteristic, complemented
24	C₇×#555	C₂²	1	1	yes	characteristic, complemented
25	C₇×#554	C₂²	1	1	yes	characteristic, complemented
26	C₇×#553	C₂²	1	2	yes	complemented
27	C₇×#552	—	2	1	no	—
28	C₇×#552	C₂²	1	2	yes	complemented
29	C₇×#551	—	2	2	no	—
30	C₇×#547	C₂²	1	1	yes	characteristic, complemented
31	C₇×#546	—	2	1	no	—
32	C₇×D₄²	—	2	1	no	—
33	C₇×D₄²	—	2	1	no	—
34	C₇×D₄²	—	2	2	no	—
35	C₇×D₄²	C₂²	1	2	yes	—
36	C₇×D₄²	C₂²	1	4	yes	—
37	C₇×D₄²	C₂²	1	2	yes	—
38	C₇×#533	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₇×#127	C₂²	1	1	yes	characteristic
40	C₇×#529	—	2	2	no	—
41	C₇×#529	—	2	1	no	—
42	C₇×#525	C₂²	1	2	yes	complemented
43	C₂×C₇×#121	—	2	1	no	—
44	C₂×C₇×#121	C₂²	1	2	yes	—
45	C₂×C₇×#120	—	2	2	no	—
46	C₄×C₇×#41	—	2	1	no	—
47	C₄×C₇×#41	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₇×#117	C₂²	1	2	yes	complemented
51	C₇×#490	C₂²	1	4	yes	complemented
52	C₇×#486	C₂²	1	2	yes	complemented
53	C₇×#486	C₂²	1	2	yes	complemented
54	C₇×#482	C₂²	1	4	yes	complemented
55	C₇×#482	C₂²	1	4	yes	complemented
56	C₇×#481	C₂²	1	4	yes	complemented
57	C₇×#480	C₂²	1	4	yes	complemented
58	C₇×#478	C₂²	1	4	yes	complemented
59	C₇×#476	C₂²	1	2	yes	complemented
60	C₇×#474	C₂²	1	2	yes	complemented
61	C₇×#469	C₂²	1	4	yes	complemented
62	C₇×#468	C₂²	1	4	yes	complemented
63	C₇×#466	C₂²	1	4	yes	complemented
64	C₇×#465	C₂²	1	4	yes	complemented
65	C₇×#460	C₂²	1	2	yes	complemented
66	C₇×#460	C₂²	1	2	yes	complemented
67	C₇×#459	C₂²	1	2	yes	complemented
68	C₇×#459	C₂²	1	2	yes	complemented
69	C₇×#450	C₂²	1	4	yes	complemented
70	C₇×#450	C₂²	1	4	yes	complemented
71	C₇×#447	C₂²	1	4	yes	complemented
72	C₇×#447	C₂²	1	4	yes	complemented
73	C₇×#442	C₂²	1	2	yes	complemented
74	C₇×#440	C₂²	1	2	yes	complemented
75	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
76	C₄×C₇×D₈	C₂²	1	2	yes	complemented
77	C₇×#436	C₂²	1	2	yes	complemented
78	C₇×#435	C₂²	1	4	yes	complemented
79	C₇×C₈×D₄	C₂²	1	2	yes	complemented
80	C₇×#428	C₂²	1	1	yes	characteristic, complemented
81	C₇×#428	C₂²	1	2	yes	complemented
82	C₇×#423	C₂²	1	1	yes	characteristic, complemented
83	C₇×#418	C₂²	1	1	yes	characteristic
84	C₇×#418	C₂²	1	2	yes	—
85	C₇×#418	C₂²	1	4	yes	complemented
86	C₇×#418	C₂²	1	4	yes	complemented
87	C₇×#418	C₂²	1	2	yes	complemented
88	C₇×#418	C₂²	1	2	yes	complemented
89	C₇×#418	C₂²	1	2	yes	complemented
90	C₇×#417	C₂²	1	1	yes	characteristic, complemented
91	C₂×C₇×#102	C₂²	1	4	yes	complemented
92	C₂×C₇×#102	C₂²	1	4	yes	complemented
93	C₇×#407	C₂²	1	2	yes	complemented
94	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
95	#61155	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁵×C₇	—	2	2	no	—
97	C₂×C₇×#41	—	2	1	no	—
98	C₂×C₇×#41	C₂³	1	1	yes	characteristic
99	C₂²×C₇×D₄	—	2	8	no	—
100	C₂²×C₇×D₄	—	2	2	no	—
101	C₂²×C₇×D₄	—	2	4	no	—
102	C₂²×C₇×D₄	—	2	2	no	—
103	C₂²×C₇×D₄	—	2	2	no	—
104	C₂²×C₇×D₄	—	2	1	no	—
105	C₂²×C₇×D₄	—	2	2	no	—
106	C₂²×C₇×D₄	—	2	2	no	—
107	C₂²×C₇×D₄	—	2	2	no	—
108	C₂²×C₇×D₄	—	2	1	no	—
109	C₂²×C₇×D₄	—	4	4	no	—
110	C₂²×C₇×D₄	—	4	8	no	—
111	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
112	C₂²×C₇×D₄	C₂³	1	2	yes	—
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	C₂³	1	2	yes	—
118	C₇×AGL(1,ℤ/8)	—	2	4	no	—
119	C₇×AGL(1,ℤ/8)	—	4	4	no	—
120	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
121	C₂×C₇×SD₁₆	C₂³	1	4	yes	complemented
122	C₂×C₇×D₈	C₂³	1	2	yes	—
123	C₂×C₇×D₈	C₂³	1	4	yes	complemented
124	C₂×C₇×M₁₆	—	4	4	no	—
125	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
126	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
127	C₂×C₇×M₁₆	C₂³	1	2	yes	—
128	C₂×C₇×M₁₆	C₂³	1	4	yes	complemented
129	C₂²×C₇×C₈	C₂³	1	4	yes	complemented
130	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
131	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
132	C₇×#127	—	2	1	no	—
133	C₇×#127	—	2	1	no	—
134	C₇×#127	C₂³	1	2	yes	—
135	C₇×#127	C₂³	1	2	yes	—
136	C₇×#126	—	2	2	no	—
137	C₇×#126	—	2	2	no	—
138	C₇×#126	—	2	2	no	—
139	C₇×#125	—	2	2	no	—
140	C₇×#125	—	2	1	no	—
141	C₇×#125	C₂³	1	2	yes	complemented
142	C₇×#124	—	2	1	no	—
143	C₇×#124	—	2	2	no	—
144	C₇×#123	—	2	2	no	—
145	C₇×#123	—	2	2	no	—
146	C₇×#123	—	2	2	no	—
147	C₇×#123	—	2	2	no	—
148	C₇×C₂²⋊Q₈	—	2	1	no	—
149	C₇×C₂²⋊Q₈	—	2	1	no	—
150	C₇×C₂²⋊Q₈	—	2	1	no	—
151	C₇×C₂²⋊Q₈	—	2	2	no	—
152	C₇×C₂²⋊Q₈	C₂³	1	2	yes	complemented
153	C₇×C₂²⋊Q₈	C₂³	1	2	yes	complemented
154	C₇×#121	—	2	2	no	—
155	C₇×#121	—	2	1	no	—
156	C₇×#121	—	2	2	no	—
157	C₇×#121	—	2	2	no	—
158	C₇×#121	—	2	2	no	—
159	C₇×#121	—	2	2	no	—
160	C₇×#121	—	2	4	no	—
161	C₇×#121	C₂³	1	4	yes	—
162	C₇×#121	C₂³	1	4	yes	—
163	C₇×#121	C₂³	1	2	yes	complemented
164	C₇×#121	C₂³	1	2	yes	complemented
165	C₇×#120	—	2	2	no	—
166	C₇×#120	—	2	4	no	—
167	C₇×#120	—	2	4	no	—
168	C₇×#120	—	2	4	no	—
169	C₇×#120	—	2	4	no	—
170	C₄×C₇×Q₈	—	2	1	no	—
171	C₄×C₇×Q₈	—	2	1	no	—
172	C₄×C₇×Q₈	—	2	1	no	—
173	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic, complemented
174	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic, complemented
175	C₄×C₇×D₄	—	2	1	no	—
176	C₄×C₇×D₄	—	2	2	no	—
177	C₄×C₇×D₄	—	2	1	no	—
178	C₄×C₇×D₄	—	2	1	no	—
179	C₄×C₇×D₄	—	2	2	no	—
180	C₄×C₇×D₄	—	2	2	no	—
181	C₄×C₇×D₄	—	2	1	no	—
182	C₄×C₇×D₄	—	2	1	no	—
183	C₄×C₇×D₄	D₄	1	1	yes	characteristic
184	C₄×C₇×D₄	D₄	1	1	yes	characteristic
185	C₄×C₇×D₄	D₄	1	2	yes	—
186	C₄×C₇×D₄	C₂³	1	2	yes	—
187	C₄×C₇×D₄	C₂³	1	2	yes	—
188	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
189	C₄×C₇×D₄	C₂³	1	2	yes	—
190	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
191	C₄×C₇×D₄	C₂³	1	1	yes	characteristic, complemented
192	C₄×C₇×D₄	C₂³	1	1	yes	characteristic, complemented
193	C₇×#117	—	2	2	no	—
194	C₇×#117	—	2	2	no	—
195	C₇×#117	—	2	1	no	—
196	C₇×#117	—	2	2	no	—
197	C₇×#117	—	2	1	no	—
198	C₇×#117	C₂³	1	1	yes	characteristic
199	C₇×#117	C₂³	1	2	yes	—
200	C₇×#117	C₂³	1	2	yes	complemented
201	C₇×#117	C₂³	1	2	yes	complemented
202	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
203	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	complemented
205	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	complemented
206	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
207	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
208	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
209	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
210	C₂×C₄²×C₇	—	2	2	no	—
211	C₂×C₄²×C₇	—	2	1	no	—
212	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
213	C₇×#107	C₂³	1	4	yes	complemented
214	C₇×#107	C₂³	1	2	yes	complemented
215	C₇×#106	C₂³	1	4	yes	complemented
216	C₇×#106	C₂³	1	2	yes	complemented
217	C₇×C₄⋊C₈	C₂³	1	2	yes	complemented
218	C₇×C₄⋊C₈	C₂³	1	2	yes	complemented
219	C₇×#103	C₂³	1	2	yes	complemented
220	C₇×#102	C₂³	1	4	yes	—
221	C₇×#102	C₂³	1	4	yes	—
222	C₇×#102	C₂³	1	2	yes	—
223	C₇×#102	C₂³	1	2	yes	—
224	C₇×#102	C₂³	1	2	yes	complemented
225	C₇×#102	C₂³	1	4	yes	complemented
226	C₇×#102	C₂³	1	4	yes	complemented
227	C₇×#102	C₂³	1	4	yes	complemented
228	C₇×#102	C₂³	1	4	yes	complemented
229	C₇×#102	C₂³	1	4	yes	complemented
230	C₇×#102	C₂³	1	4	yes	complemented
231	C₇×C₂²⋊C₈	C₂³	1	4	yes	complemented
232	C₇×C₂²⋊C₈	C₂³	1	4	yes	complemented
233	C₇×#97	C₂³	1	2	yes	complemented
234	C₄×C₇×C₈	C₂³	1	2	yes	complemented
235	#3475	C₂×C₇	1	1	yes	characteristic, complemented
236	C₂×D₄²	C₂×C₇	1	1	yes	characteristic, complemented
237	#3325	C₂×C₇	1	2	yes	complemented
238	#3324	C₂×C₇	1	2	yes	complemented
239	#3318	C₂×C₇	1	4	yes	complemented
240	#3310	C₂×C₇	1	4	yes	complemented
241	#3295	C₂×C₇	1	2	yes	complemented
242	#3294	C₂×C₇	1	2	yes	complemented
243	#3138	C₂×C₇	1	1	yes	characteristic, complemented
244	#3094	C₂×C₇	1	2	yes	complemented
245	#3077	C₂×C₇	1	1	yes	characteristic, complemented
246	#3055	C₂×C₇	1	2	yes	complemented
247	#3038	C₂×C₇	1	1	yes	characteristic, complemented
248	#3003	C₂×C₇	1	2	yes	complemented
249	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic, complemented
250	D₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
251	C₂×#418	C₂×C₇	1	2	yes	complemented
252	C₂⁴×C₇	—	2	1	no	—
253	C₂⁴×C₇	—	2	2	no	—
254	C₂⁴×C₇	—	2	4	no	—
255	C₂⁴×C₇	—	2	4	no	—
256	C₂⁴×C₇	—	4	8	no	—
257	C₂⁴×C₇	—	4	8	no	—
258	C₂⁴×C₇	—	8	4	no	—
259	C₂⁴×C₇	C₂×D₄	1	2	yes	—
260	C₇×#41	—	2	2	no	—
261	C₇×#41	—	2	2	no	—
262	C₇×#41	—	4	4	no	—
263	C₂×C₇×Q₈	—	2	1	no	—
264	C₂×C₇×Q₈	—	2	1	no	—
265	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
266	C₂×C₇×D₄	—	2	4	no	—
267	C₂×C₇×D₄	—	2	8	no	—
268	C₂×C₇×D₄	—	2	8	no	—
269	C₂×C₇×D₄	—	2	1	no	—
270	C₂×C₇×D₄	—	2	2	no	—
271	C₂×C₇×D₄	—	2	4	no	—
272	C₂×C₇×D₄	—	2	4	no	—
273	C₂×C₇×D₄	—	2	2	no	—
274	C₂×C₇×D₄	—	2	1	no	—
275	C₂×C₇×D₄	—	2	4	no	—
276	C₂×C₇×D₄	—	2	4	no	—
277	C₂×C₇×D₄	—	2	2	no	—
278	C₂×C₇×D₄	—	2	2	no	—
279	C₂×C₇×D₄	—	2	2	no	—
280	C₂×C₇×D₄	—	2	2	no	—
281	C₂×C₇×D₄	—	2	2	no	—
282	C₂×C₇×D₄	—	2	4	no	—
283	C₂×C₇×D₄	—	2	2	no	—
284	C₂×C₇×D₄	—	2	4	no	—
285	C₂×C₇×D₄	—	4	4	no	—
286	C₂×C₇×D₄	—	4	4	no	—
287	C₂×C₇×D₄	—	4	8	no	—
288	C₂×C₇×D₄	—	4	8	no	—
289	C₂×C₇×D₄	—	4	8	no	—
290	C₂×C₇×D₄	—	4	4	no	—
291	C₂×C₇×D₄	—	4	16	no	—
292	C₂×C₇×D₄	—	4	8	no	—
293	C₂×C₇×D₄	—	4	8	no	—
294	C₂×C₇×D₄	—	4	8	no	—
295	C₂×C₇×D₄	—	8	2	no	—
296	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
297	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
298	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
299	C₂×C₇×D₄	#41	1	4	yes	complemented
300	C₂×C₇×D₄	C₂⁴	1	4	yes	—
301	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
302	C₂×C₇×D₄	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₇	—	2	4	no	—
304	C₂²×C₄×C₇	—	2	4	no	—
305	C₂²×C₄×C₇	—	2	2	no	—
306	C₂²×C₄×C₇	—	2	1	no	—
307	C₂²×C₄×C₇	—	2	2	no	—
308	C₂²×C₄×C₇	—	2	1	no	—
309	C₂²×C₄×C₇	—	2	1	no	—
310	C₂²×C₄×C₇	—	2	2	no	—
311	C₂²×C₄×C₇	—	2	2	no	—
312	C₂²×C₄×C₇	—	2	1	no	—
313	C₂²×C₄×C₇	—	4	4	no	—
314	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
315	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
317	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
318	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
322	C₇×SD₁₆	—	2	4	no	—
323	C₇×SD₁₆	—	4	4	no	—
324	C₇×D₈	—	2	4	no	—
325	C₇×D₈	—	4	4	no	—
326	C₇×M₁₆	—	2	2	no	—
327	C₇×M₁₆	—	2	2	no	—
328	C₇×M₁₆	—	2	4	no	—
329	C₇×M₁₆	—	4	4	no	—
330	C₂×C₇×C₈	—	4	4	no	—
331	C₂×C₇×C₈	C₂⁴	1	2	yes	—
332	C₂×C₇×C₈	C₂⁴	1	2	yes	—
333	C₂×C₇×C₈	C₂⁴	1	4	yes	—
334	C₇×C₄⋊C₄	—	2	1	no	—
335	C₇×C₄⋊C₄	—	2	2	no	—
336	C₇×C₄⋊C₄	—	2	2	no	—
337	C₇×C₄⋊C₄	—	2	1	no	—
338	C₇×C₄⋊C₄	—	2	2	no	—
339	C₇×C₄⋊C₄	—	2	2	no	—
340	C₇×C₄⋊C₄	—	2	1	no	—
341	C₇×C₄⋊C₄	—	2	1	no	—
342	C₇×C₄⋊C₄	—	2	2	no	—
343	C₇×C₄⋊C₄	—	2	2	no	—
344	C₇×C₄⋊C₄	—	2	1	no	—
345	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
346	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
347	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
348	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
349	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
350	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
351	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
352	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
353	C₇×C₂²⋊C₄	—	2	1	no	—
354	C₇×C₂²⋊C₄	—	2	2	no	—
355	C₇×C₂²⋊C₄	—	2	2	no	—
356	C₇×C₂²⋊C₄	—	2	2	no	—
357	C₇×C₂²⋊C₄	—	2	2	no	—
358	C₇×C₂²⋊C₄	—	2	2	no	—
359	C₇×C₂²⋊C₄	—	2	2	no	—
360	C₇×C₂²⋊C₄	—	2	2	no	—
361	C₇×C₂²⋊C₄	—	2	4	no	—
362	C₇×C₂²⋊C₄	—	2	4	no	—
363	C₇×C₂²⋊C₄	—	2	2	no	—
364	C₇×C₂²⋊C₄	—	2	1	no	—
365	C₇×C₂²⋊C₄	—	2	1	no	—
366	C₇×C₂²⋊C₄	—	2	2	no	—
367	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
368	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
369	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
370	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
371	C₄²×C₇	—	2	1	no	—
372	C₄²×C₇	—	2	2	no	—
373	C₄²×C₇	—	2	1	no	—
374	C₄²×C₇	—	2	2	no	—
375	C₄²×C₇	—	2	2	no	—
376	C₄²×C₇	—	2	1	no	—
377	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
378	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
379	C₄²×C₇	C₂⁴	1	1	yes	characteristic
380	C₄²×C₇	C₂⁴	1	1	yes	characteristic
381	C₂³×D₄	—	2	1	no	—
382	C₂³×D₄	C₂²×C₇	1	2	yes	—
383	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
384	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	complemented
385	C₂²×M₁₆	C₂²×C₇	1	2	yes	complemented
386	#556	C₂²×C₇	1	1	yes	characteristic, complemented
387	#555	C₂²×C₇	1	1	yes	characteristic, complemented
388	#554	C₂²×C₇	1	1	yes	characteristic, complemented
389	#553	C₂²×C₇	1	2	yes	complemented
390	#552	—	2	1	no	—
391	#552	C₂²×C₇	1	2	yes	complemented
392	#551	—	2	2	no	—
393	#547	C₂²×C₇	1	1	yes	characteristic, complemented
394	#546	—	2	1	no	—
395	D₄²	—	2	1	no	—
396	D₄²	—	2	1	no	—
397	D₄²	—	2	2	no	—
398	D₄²	C₂²×C₇	1	2	yes	—
399	D₄²	C₂²×C₇	1	4	yes	—
400	D₄²	C₂²×C₇	1	2	yes	—
401	#533	C₂²×C₇	1	1	yes	characteristic, complemented
402	C₂×#127	C₂²×C₇	1	1	yes	characteristic
403	#529	—	2	2	no	—
404	#529	—	2	1	no	—
405	#525	C₂²×C₇	1	2	yes	complemented
406	C₂×#121	—	2	1	no	—
407	C₂×#121	C₂²×C₇	1	2	yes	—
408	C₂×#120	—	2	2	no	—
409	C₄×#41	—	2	1	no	—
410	C₄×#41	C₂²×C₇	1	1	yes	characteristic, complemented
411	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
412	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
413	C₂×#117	C₂²×C₇	1	2	yes	complemented
414	#490	C₂²×C₇	1	4	yes	complemented
415	#486	C₂²×C₇	1	2	yes	complemented
416	#486	C₂²×C₇	1	2	yes	complemented
417	#482	C₂²×C₇	1	4	yes	complemented
418	#482	C₂²×C₇	1	4	yes	complemented
419	#481	C₂²×C₇	1	4	yes	complemented
420	#480	C₂²×C₇	1	4	yes	complemented
421	#478	C₂²×C₇	1	4	yes	complemented
422	#476	C₂²×C₇	1	2	yes	complemented
423	#474	C₂²×C₇	1	2	yes	complemented
424	#469	C₂²×C₇	1	4	yes	complemented
425	#468	C₂²×C₇	1	4	yes	complemented
426	#466	C₂²×C₇	1	4	yes	complemented
427	#465	C₂²×C₇	1	4	yes	complemented
428	#460	C₂²×C₇	1	2	yes	complemented
429	#460	C₂²×C₇	1	2	yes	complemented
430	#459	C₂²×C₇	1	2	yes	complemented
431	#459	C₂²×C₇	1	2	yes	complemented
432	#450	C₂²×C₇	1	4	yes	complemented
433	#450	C₂²×C₇	1	4	yes	complemented
434	#447	C₂²×C₇	1	4	yes	complemented
435	#447	C₂²×C₇	1	4	yes	complemented
436	#442	C₂²×C₇	1	2	yes	complemented
437	#440	C₂²×C₇	1	2	yes	complemented
438	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
439	C₄×D₈	C₂²×C₇	1	2	yes	complemented
440	#436	C₂²×C₇	1	2	yes	complemented
441	#435	C₂²×C₇	1	4	yes	complemented
442	C₈×D₄	C₂²×C₇	1	2	yes	complemented
443	#428	C₂²×C₇	1	2	yes	complemented
444	#428	C₂²×C₇	1	1	yes	characteristic, complemented
445	#423	C₂²×C₇	1	1	yes	characteristic, complemented
446	#418	C₂²×C₇	1	2	yes	—
447	#418	C₂²×C₇	1	1	yes	characteristic
448	#418	C₂²×C₇	1	4	yes	complemented
449	#418	C₂²×C₇	1	4	yes	complemented
450	#418	C₂²×C₇	1	2	yes	complemented
451	#418	C₂²×C₇	1	2	yes	complemented
452	#418	C₂²×C₇	1	2	yes	complemented
453	#417	C₂²×C₇	1	1	yes	characteristic, complemented
454	C₂×#102	C₂²×C₇	1	4	yes	complemented
455	C₂×#102	C₂²×C₇	1	4	yes	complemented
456	#407	C₂²×C₇	1	2	yes	complemented
457	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
458	C₂³×C₇	—	2	4	no	—
459	C₂³×C₇	—	2	4	no	—
460	C₂³×C₇	—	2	4	no	—
461	C₂³×C₇	—	2	2	no	—
462	C₂³×C₇	—	2	1	no	—
463	C₂³×C₇	—	2	4	no	—
464	C₂³×C₇	—	4	2	no	—
465	C₂³×C₇	—	4	8	no	—
466	C₂³×C₇	—	4	8	no	—
467	C₂³×C₇	—	4	2	no	—
468	C₂³×C₇	—	4	2	no	—
469	C₂³×C₇	—	4	4	no	—
470	C₂³×C₇	—	4	8	no	—
471	C₂³×C₇	—	4	4	no	—
472	C₂³×C₇	—	4	4	no	—
473	C₂³×C₇	—	4	8	no	—
474	C₂³×C₇	—	8	4	no	—
475	C₂³×C₇	—	8	4	no	—
476	C₂³×C₇	—	8	32	no	—
477	C₂³×C₇	C₂²×D₄	1	2	yes	—
478	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
479	C₂³×C₇	C₂²×D₄	1	2	yes	—
480	C₇×Q₈	—	2	1	no	—
481	C₇×Q₈	—	2	1	no	—
482	C₇×Q₈	—	4	2	no	—
483	C₇×Q₈	—	8	1	no	—
484	C₇×D₄	—	2	4	no	—
485	C₇×D₄	—	2	4	no	—
486	C₇×D₄	—	2	2	no	—
487	C₇×D₄	—	2	1	no	—
488	C₇×D₄	—	2	4	no	—
489	C₇×D₄	—	2	2	no	—
490	C₇×D₄	—	2	1	no	—
491	C₇×D₄	—	2	4	no	—
492	C₇×D₄	—	4	8	no	—
493	C₇×D₄	—	4	8	no	—
494	C₇×D₄	—	4	4	no	—
495	C₇×D₄	—	4	8	no	—
496	C₇×D₄	—	4	2	no	—
497	C₇×D₄	—	4	8	no	—
498	C₇×D₄	—	4	4	no	—
499	C₇×D₄	—	4	4	no	—
500	C₇×D₄	—	4	4	no	—
501	C₇×D₄	—	8	2	no	—
502	C₇×D₄	—	8	2	no	—
503	C₇×D₄	—	8	2	no	—
504	C₇×D₄	AGL(1,ℤ/8)	1	4	yes	complemented
505	C₇×D₄	C₂×#41	1	4	yes	—
506	C₂×C₄×C₇	—	2	4	no	—
507	C₂×C₄×C₇	—	2	4	no	—
508	C₂×C₄×C₇	—	2	4	no	—
509	C₂×C₄×C₇	—	2	2	no	—
510	C₂×C₄×C₇	—	2	2	no	—
511	C₂×C₄×C₇	—	2	2	no	—
512	C₂×C₄×C₇	—	2	2	no	—
513	C₂×C₄×C₇	—	2	2	no	—
514	C₂×C₄×C₇	—	2	1	no	—
515	C₂×C₄×C₇	—	2	1	no	—
516	C₂×C₄×C₇	—	2	1	no	—
517	C₂×C₄×C₇	—	2	2	no	—
518	C₂×C₄×C₇	—	2	2	no	—
519	C₂×C₄×C₇	—	2	2	no	—
520	C₂×C₄×C₇	—	4	1	no	—
521	C₂×C₄×C₇	—	4	4	no	—
522	C₂×C₄×C₇	—	4	2	no	—
523	C₂×C₄×C₇	—	4	4	no	—
524	C₂×C₄×C₇	—	4	2	no	—
525	C₂×C₄×C₇	—	4	4	no	—
526	C₂×C₄×C₇	—	4	2	no	—
527	C₂×C₄×C₇	—	8	1	no	—
528	C₂×C₄×C₇	—	8	2	no	—
529	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₇	C₂×#41	1	2	yes	—
537	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
538	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
539	C₇×C₈	—	2	2	no	—
540	C₇×C₈	—	2	2	no	—
541	C₇×C₈	—	2	4	no	—
542	C₂⁵	—	2	2	no	—
543	C₂×#41	—	2	1	no	—
544	C₂×#41	C₂³×C₇	1	1	yes	characteristic
545	C₂²×D₄	—	2	8	no	—
546	C₂²×D₄	—	2	2	no	—
547	C₂²×D₄	—	2	4	no	—
548	C₂²×D₄	—	2	2	no	—
549	C₂²×D₄	—	2	2	no	—
550	C₂²×D₄	—	2	2	no	—
551	C₂²×D₄	—	2	1	no	—
552	C₂²×D₄	—	2	2	no	—
553	C₂²×D₄	—	2	2	no	—
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	—	4	4	no	—
556	C₂²×D₄	—	4	8	no	—
557	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
558	C₂²×D₄	C₂³×C₇	1	2	yes	—
559	C₂²×D₄	C₂³×C₇	1	4	yes	—
560	C₂²×D₄	C₂³×C₇	1	4	yes	—
561	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
562	C₂³×C₄	—	2	1	no	—
563	C₂³×C₄	C₂³×C₇	1	2	yes	—
564	AGL(1,ℤ/8)	—	2	4	no	—
565	AGL(1,ℤ/8)	—	4	4	no	—
566	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
567	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
568	C₂×D₈	C₂³×C₇	1	2	yes	—
569	C₂×D₈	C₂³×C₇	1	4	yes	complemented
570	C₂×M₁₆	—	4	4	no	—
571	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
572	C₂×M₁₆	C₂³×C₇	1	2	yes	—
573	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
574	C₂×M₁₆	C₂³×C₇	1	4	yes	complemented
575	C₂²×C₈	C₂³×C₇	1	4	yes	complemented
576	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic, complemented
577	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic, complemented
578	#127	—	2	1	no	—
579	#127	—	2	1	no	—
580	#127	C₂³×C₇	1	2	yes	—
581	#127	C₂³×C₇	1	2	yes	—
582	#126	—	2	2	no	—
583	#126	—	2	2	no	—
584	#126	—	2	2	no	—
585	#125	—	2	2	no	—
586	#125	—	2	1	no	—
587	#125	C₂³×C₇	1	2	yes	complemented
588	#124	—	2	1	no	—
589	#124	—	2	2	no	—
590	#123	—	2	2	no	—
591	#123	—	2	2	no	—
592	#123	—	2	2	no	—
593	#123	—	2	2	no	—
594	C₂²⋊Q₈	—	2	1	no	—
595	C₂²⋊Q₈	—	2	1	no	—
596	C₂²⋊Q₈	—	2	1	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	C₂³×C₇	1	2	yes	complemented
599	C₂²⋊Q₈	C₂³×C₇	1	2	yes	complemented
600	#121	—	2	2	no	—
601	#121	—	2	1	no	—
602	#121	—	2	2	no	—
603	#121	—	2	2	no	—
604	#121	—	2	2	no	—
605	#121	—	2	2	no	—
606	#121	—	2	4	no	—
607	#121	C₂³×C₇	1	4	yes	—
608	#121	C₂³×C₇	1	4	yes	—
609	#121	C₂³×C₇	1	2	yes	complemented
610	#121	C₂³×C₇	1	2	yes	complemented
611	#120	—	2	2	no	—
612	#120	—	2	4	no	—
613	#120	—	2	4	no	—
614	#120	—	2	4	no	—
615	#120	—	2	4	no	—
616	C₄×Q₈	—	2	1	no	—
617	C₄×Q₈	—	2	1	no	—
618	C₄×Q₈	—	2	1	no	—
619	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic, complemented
620	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic, complemented
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	C₇×D₄	1	1	yes	characteristic
630	C₄×D₄	C₇×D₄	1	1	yes	characteristic
631	C₄×D₄	C₇×D₄	1	2	yes	—
632	C₄×D₄	C₂³×C₇	1	2	yes	—
633	C₄×D₄	C₂³×C₇	1	2	yes	—
634	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
635	C₄×D₄	C₂³×C₇	1	2	yes	—
636	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
637	C₄×D₄	C₂³×C₇	1	1	yes	characteristic, complemented
638	C₄×D₄	C₂³×C₇	1	1	yes	characteristic, complemented
639	#117	—	2	2	no	—
640	#117	—	2	2	no	—
641	#117	—	2	1	no	—
642	#117	—	2	2	no	—
643	#117	—	2	1	no	—
644	#117	C₂³×C₇	1	1	yes	characteristic
645	#117	C₂³×C₇	1	2	yes	—
646	#117	C₂³×C₇	1	2	yes	complemented
647	#117	C₂³×C₇	1	2	yes	complemented
648	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	complemented
651	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	complemented
652	C₂×C₂²⋊C₄	—	2	2	no	—
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	—	2	2	no	—
655	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
656	C₂×C₄²	—	2	2	no	—
657	C₂×C₄²	—	2	1	no	—
658	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
659	#107	C₂³×C₇	1	2	yes	complemented
660	#107	C₂³×C₇	1	4	yes	complemented
661	#106	C₂³×C₇	1	2	yes	complemented
662	#106	C₂³×C₇	1	4	yes	complemented
663	C₄⋊C₈	C₂³×C₇	1	2	yes	complemented
664	C₄⋊C₈	C₂³×C₇	1	2	yes	complemented
665	#103	C₂³×C₇	1	2	yes	complemented
666	#102	C₂³×C₇	1	2	yes	—
667	#102	C₂³×C₇	1	2	yes	—
668	#102	C₂³×C₇	1	4	yes	—
669	#102	C₂³×C₇	1	4	yes	—
670	#102	C₂³×C₇	1	4	yes	complemented
671	#102	C₂³×C₇	1	4	yes	complemented
672	#102	C₂³×C₇	1	4	yes	complemented
673	#102	C₂³×C₇	1	4	yes	complemented
674	#102	C₂³×C₇	1	2	yes	complemented
675	#102	C₂³×C₇	1	4	yes	complemented
676	#102	C₂³×C₇	1	4	yes	complemented
677	C₂²⋊C₈	C₂³×C₇	1	4	yes	complemented
678	C₂²⋊C₈	C₂³×C₇	1	4	yes	complemented
679	#97	C₂³×C₇	1	2	yes	complemented
680	C₄×C₈	C₂³×C₇	1	2	yes	complemented
681	C₂²×C₇	—	2	1	no	—
682	C₂²×C₇	—	2	2	no	—
683	C₂²×C₇	—	2	2	no	—
684	C₂²×C₇	—	2	1	no	—
685	C₂²×C₇	—	2	2	no	—
686	C₂²×C₇	—	2	2	no	—
687	C₂²×C₇	—	2	4	no	—
688	C₂²×C₇	—	2	2	no	—
689	C₂²×C₇	—	4	8	no	—
690	C₂²×C₇	—	4	8	no	—
691	C₂²×C₇	—	4	2	no	—
692	C₂²×C₇	—	4	2	no	—
693	C₂²×C₇	—	4	1	no	—
694	C₂²×C₇	—	4	4	no	—
695	C₂²×C₇	—	4	1	no	—
696	C₂²×C₇	—	4	4	no	—
697	C₂²×C₇	—	4	1	no	—
698	C₂²×C₇	—	4	4	no	—
699	C₂²×C₇	—	8	16	no	—
700	C₂²×C₇	—	8	8	no	—
701	C₂²×C₇	—	8	16	no	—
702	C₂²×C₇	#546	1	2	yes	—
703	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
704	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
705	C₄×C₇	—	2	1	no	—
706	C₄×C₇	—	2	1	no	—
707	C₄×C₇	—	2	2	no	—
708	C₄×C₇	—	2	2	no	—
709	C₄×C₇	—	2	1	no	—
710	C₄×C₇	—	4	1	no	—
711	C₄×C₇	—	4	2	no	—
712	C₄×C₇	—	4	1	no	—
713	C₄×C₇	—	4	1	no	—
714	C₄×C₇	—	4	2	no	—
715	C₄×C₇	—	4	2	no	—
716	C₄×C₇	#546	1	2	yes	—
717	C₄×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
718	C₄×C₇	C₂²×#41	1	1	yes	characteristic
719	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
720	C₂⁴	—	2	1	no	—
721	C₂⁴	—	2	2	no	—
722	C₂⁴	—	2	4	no	—
723	C₂⁴	—	2	4	no	—
724	C₂⁴	—	4	8	no	—
725	C₂⁴	—	4	8	no	—
726	C₂⁴	—	8	4	no	—
727	C₂⁴	C₂×C₇×D₄	1	2	yes	—
728	#41	—	2	2	no	—
729	#41	—	2	2	no	—
730	#41	—	4	4	no	—
731	C₂×Q₈	—	2	1	no	—
732	C₂×Q₈	—	2	1	no	—
733	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	8	no	—
736	C₂×D₄	—	2	8	no	—
737	C₂×D₄	—	2	1	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	1	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	4	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	4	no	—
753	C₂×D₄	—	4	4	no	—
754	C₂×D₄	—	4	4	no	—
755	C₂×D₄	—	4	8	no	—
756	C₂×D₄	—	4	8	no	—
757	C₂×D₄	—	4	8	no	—
758	C₂×D₄	—	4	4	no	—
759	C₂×D₄	—	4	16	no	—
760	C₂×D₄	—	4	8	no	—
761	C₂×D₄	—	4	8	no	—
762	C₂×D₄	—	4	8	no	—
763	C₂×D₄	—	8	2	no	—
764	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
765	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
766	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
767	C₂×D₄	C₇×#41	1	4	yes	complemented
768	C₂×D₄	C₂⁴×C₇	1	4	yes	—
769	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
770	C₂×D₄	C₂⁴×C₇	1	2	yes	—
771	C₂²×C₄	—	2	4	no	—
772	C₂²×C₄	—	2	4	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	1	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	1	no	—
777	C₂²×C₄	—	2	1	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	1	no	—
781	C₂²×C₄	—	4	4	no	—
782	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
783	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
784	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
785	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
786	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
790	SD₁₆	—	2	4	no	—
791	SD₁₆	—	4	4	no	—
792	D₈	—	2	4	no	—
793	D₈	—	4	4	no	—
794	M₁₆	—	2	2	no	—
795	M₁₆	—	2	2	no	—
796	M₁₆	—	2	4	no	—
797	M₁₆	—	4	4	no	—
798	C₂×C₈	—	4	4	no	—
799	C₂×C₈	C₂⁴×C₇	1	2	yes	—
800	C₂×C₈	C₂⁴×C₇	1	2	yes	—
801	C₂×C₈	C₂⁴×C₇	1	4	yes	—
802	C₄⋊C₄	—	2	1	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	1	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	1	no	—
809	C₄⋊C₄	—	2	1	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
814	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
815	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
816	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
817	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
818	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
819	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
820	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
821	C₂²⋊C₄	—	2	1	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	2	4	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	1	no	—
833	C₂²⋊C₄	—	2	1	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
836	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
837	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
838	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
839	C₄²	—	2	1	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	1	no	—
842	C₄²	—	2	2	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	1	no	—
845	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
846	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
847	C₄²	C₂⁴×C₇	1	1	yes	characteristic
848	C₄²	C₂⁴×C₇	1	1	yes	characteristic
849	C₂×C₇	—	2	2	no	—
850	C₂×C₇	—	2	4	no	—
851	C₂×C₇	—	4	2	no	—
852	C₂×C₇	—	4	4	no	—
853	C₂×C₇	—	8	1	no	—
854	C₂×C₇	—	8	4	no	—
855	C₂×C₇	C₂×#546	1	1	yes	characteristic
856	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
857	C₂×C₇	#3585	1	1	yes	characteristic
858	C₂³	—	2	2	no	—
859	C₂³	—	2	4	no	—
860	C₂³	—	2	4	no	—
861	C₂³	—	2	4	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	4	no	—
864	C₂³	—	4	2	no	—
865	C₂³	—	4	8	no	—
866	C₂³	—	4	8	no	—
867	C₂³	—	4	2	no	—
868	C₂³	—	4	2	no	—
869	C₂³	—	4	4	no	—
870	C₂³	—	4	8	no	—
871	C₂³	—	4	4	no	—
872	C₂³	—	4	4	no	—
873	C₂³	—	4	8	no	—
874	C₂³	—	8	4	no	—
875	C₂³	—	8	4	no	—
876	C₂³	—	8	32	no	—
877	C₂³	C₂²×C₇×D₄	1	2	yes	—
878	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
879	C₂³	C₂²×C₇×D₄	1	2	yes	—
880	Q₈	—	2	1	no	—
881	Q₈	—	2	1	no	—
882	Q₈	—	4	2	no	—
883	Q₈	—	8	1	no	—
884	D₄	—	2	4	no	—
885	D₄	—	2	1	no	—
886	D₄	—	2	4	no	—
887	D₄	—	2	2	no	—
888	D₄	—	2	1	no	—
889	D₄	—	2	4	no	—
890	D₄	—	2	4	no	—
891	D₄	—	2	2	no	—
892	D₄	—	4	8	no	—
893	D₄	—	4	8	no	—
894	D₄	—	4	4	no	—
895	D₄	—	4	8	no	—
896	D₄	—	4	2	no	—
897	D₄	—	4	8	no	—
898	D₄	—	4	4	no	—
899	D₄	—	4	4	no	—
900	D₄	—	4	4	no	—
901	D₄	—	8	2	no	—
902	D₄	—	8	2	no	—
903	D₄	—	8	2	no	—
904	D₄	C₇×AGL(1,ℤ/8)	1	4	yes	complemented
905	D₄	C₂×C₇×#41	1	4	yes	—
906	C₂×C₄	—	2	4	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	4	no	—
912	C₂×C₄	—	2	4	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	4	2	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	2	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	2	no	—
927	C₂×C₄	—	8	1	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
930	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
931	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
932	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
933	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
934	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
935	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
936	C₂×C₄	C₂×C₇×#41	1	2	yes	—
937	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
938	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
939	C₈	—	2	2	no	—
940	C₈	—	2	2	no	—
941	C₈	—	2	4	no	—
942	C₇	#61155	1	1	yes	characteristic, direct product factor, Sylow
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	2	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	4	no	—
951	C₂²	—	4	8	no	—
952	C₂²	—	4	8	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	4	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	4	no	—
959	C₂²	—	4	1	no	—
960	C₂²	—	4	4	no	—
961	C₂²	—	8	16	no	—
962	C₂²	—	8	8	no	—
963	C₂²	—	8	16	no	—
964	C₂²	C₇×#546	1	2	yes	—
965	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
966	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
967	C₄	—	2	1	no	—
968	C₄	—	2	1	no	—
969	C₄	—	2	1	no	—
970	C₄	—	2	2	no	—
971	C₄	—	2	2	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	1	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	1	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	1	no	—
978	C₄	C₇×#546	1	2	yes	—
979	C₄	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
980	C₄	C₂²×C₇×#41	1	1	yes	characteristic
981	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
982	C₂	—	2	2	no	—
983	C₂	—	2	4	no	—
984	C₂	—	4	2	no	—
985	C₂	—	4	4	no	—
986	C₂	—	8	4	no	—
987	C₂	—	8	1	no	—
988	C₂	C₂×C₇×#546	1	1	yes	characteristic
989	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
990	C₂	C₇×#3585	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×D₄²	C₂	semidirect
3. C₇×#3325	C₂	semidirect
4. C₇×#3324	C₂	semidirect
5. C₇×#3318	C₂	semidirect
6. C₇×#3310	C₂	semidirect
7. C₇×#3295	C₂	semidirect
8. C₇×#3294	C₂	semidirect
9. C₇×#3138	C₂	semidirect
10. C₇×#3094	C₂	semidirect
11. C₇×#3077	C₂	semidirect
12. C₇×#3055	C₂	semidirect
13. C₇×#3038	C₂	semidirect
14. C₇×#3003	C₂	semidirect
15. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
16. C₇×D₄×M₁₆	C₂	semidirect
17. C₂×C₇×#418	C₂	semidirect
21. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂²×C₇×M₁₆	C₂²	semidirect
23. C₇×#556	C₂²	semidirect
24. C₇×#555	C₂²	semidirect
25. C₇×#554	C₂²	semidirect
26. C₇×#553	C₂²	semidirect
28. C₇×#552	C₂²	semidirect
30. C₇×#547	C₂²	semidirect
38. C₇×#533	C₂²	semidirect
42. C₇×#525	C₂²	semidirect
47. C₄×C₇×#41	C₂²	semidirect
50. C₂×C₇×#117	C₂²	semidirect
51. C₇×#490	C₂²	semidirect
52. C₇×#486	C₂²	semidirect
53. C₇×#486	C₂²	semidirect
54. C₇×#482	C₂²	semidirect
55. C₇×#482	C₂²	semidirect
56. C₇×#481	C₂²	semidirect
57. C₇×#480	C₂²	semidirect
58. C₇×#478	C₂²	semidirect
59. C₇×#476	C₂²	semidirect
60. C₇×#474	C₂²	semidirect
61. C₇×#469	C₂²	semidirect
62. C₇×#468	C₂²	semidirect
63. C₇×#466	C₂²	semidirect
64. C₇×#465	C₂²	semidirect
65. C₇×#460	C₂²	semidirect
66. C₇×#460	C₂²	semidirect
67. C₇×#459	C₂²	semidirect
68. C₇×#459	C₂²	semidirect
69. C₇×#450	C₂²	semidirect
70. C₇×#450	C₂²	semidirect
71. C₇×#447	C₂²	semidirect
72. C₇×#447	C₂²	semidirect
73. C₇×#442	C₂²	semidirect
74. C₇×#440	C₂²	semidirect
75. C₄×C₇×SD₁₆	C₂²	semidirect
76. C₄×C₇×D₈	C₂²	semidirect
77. C₇×#436	C₂²	semidirect
78. C₇×#435	C₂²	semidirect
79. C₇×C₈×D₄	C₂²	semidirect
80. C₇×#428	C₂²	semidirect
81. C₇×#428	C₂²	semidirect
82. C₇×#423	C₂²	semidirect
85. C₇×#418	C₂²	semidirect
86. C₇×#418	C₂²	semidirect
87. C₇×#418	C₂²	semidirect
88. C₇×#418	C₂²	semidirect
89. C₇×#418	C₂²	semidirect
90. C₇×#417	C₂²	semidirect
91. C₂×C₇×#102	C₂²	semidirect
92. C₂×C₇×#102	C₂²	semidirect
93. C₇×#407	C₂²	semidirect
94. C₄×C₇×M₁₆	C₂²	semidirect
95. #61155	C₇	direct (N × H)
121. C₂×C₇×SD₁₆	C₂³	semidirect
123. C₂×C₇×D₈	C₂³	semidirect
128. C₂×C₇×M₁₆	C₂³	semidirect
129. C₂²×C₇×C₈	C₂³	semidirect
130. C₇×C₄⋊Q₈	C₂³	semidirect
131. C₇×C₄⋊Q₈	C₂³	semidirect
141. C₇×#125	C₂³	semidirect
152. C₇×C₂²⋊Q₈	C₂³	semidirect
153. C₇×C₂²⋊Q₈	C₂³	semidirect
163. C₇×#121	C₂³	semidirect
164. C₇×#121	C₂³	semidirect
173. C₄×C₇×Q₈	C₂³	semidirect
174. C₄×C₇×Q₈	C₂³	semidirect
191. C₄×C₇×D₄	C₂³	semidirect
192. C₄×C₇×D₄	C₂³	semidirect
200. C₇×#117	C₂³	semidirect
201. C₇×#117	C₂³	semidirect
204. C₂×C₇×C₄⋊C₄	C₂³	semidirect
205. C₂×C₇×C₄⋊C₄	C₂³	semidirect
213. C₇×#107	C₂³	semidirect
214. C₇×#107	C₂³	semidirect
215. C₇×#106	C₂³	semidirect
216. C₇×#106	C₂³	semidirect
217. C₇×C₄⋊C₈	C₂³	semidirect
218. C₇×C₄⋊C₈	C₂³	semidirect
219. C₇×#103	C₂³	semidirect
224. C₇×#102	C₂³	semidirect
225. C₇×#102	C₂³	semidirect
226. C₇×#102	C₂³	semidirect
227. C₇×#102	C₂³	semidirect
228. C₇×#102	C₂³	semidirect
229. C₇×#102	C₂³	semidirect
230. C₇×#102	C₂³	semidirect
231. C₇×C₂²⋊C₈	C₂³	semidirect
232. C₇×C₂²⋊C₈	C₂³	semidirect
233. C₇×#97	C₂³	semidirect
234. C₄×C₇×C₈	C₂³	semidirect
235. #3475	C₂×C₇	semidirect
236. C₂×D₄²	C₂×C₇	semidirect
237. #3325	C₂×C₇	semidirect
238. #3324	C₂×C₇	semidirect
239. #3318	C₂×C₇	semidirect
240. #3310	C₂×C₇	semidirect
241. #3295	C₂×C₇	semidirect
242. #3294	C₂×C₇	semidirect
243. #3138	C₂×C₇	semidirect
244. #3094	C₂×C₇	semidirect
245. #3077	C₂×C₇	semidirect
246. #3055	C₂×C₇	semidirect
247. #3038	C₂×C₇	semidirect
248. #3003	C₂×C₇	semidirect
249. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
250. D₄×M₁₆	C₂×C₇	semidirect
251. C₂×#418	C₂×C₇	semidirect
299. C₂×C₇×D₄	#41	semidirect
384. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
385. C₂²×M₁₆	C₂²×C₇	semidirect
386. #556	C₂²×C₇	semidirect
387. #555	C₂²×C₇	semidirect
388. #554	C₂²×C₇	semidirect
389. #553	C₂²×C₇	semidirect
391. #552	C₂²×C₇	semidirect
393. #547	C₂²×C₇	semidirect
401. #533	C₂²×C₇	semidirect
405. #525	C₂²×C₇	semidirect
410. C₄×#41	C₂²×C₇	semidirect
413. C₂×#117	C₂²×C₇	semidirect
414. #490	C₂²×C₇	semidirect
415. #486	C₂²×C₇	semidirect
416. #486	C₂²×C₇	semidirect
417. #482	C₂²×C₇	semidirect
418. #482	C₂²×C₇	semidirect
419. #481	C₂²×C₇	semidirect
420. #480	C₂²×C₇	semidirect
421. #478	C₂²×C₇	semidirect
422. #476	C₂²×C₇	semidirect
423. #474	C₂²×C₇	semidirect
424. #469	C₂²×C₇	semidirect
425. #468	C₂²×C₇	semidirect
426. #466	C₂²×C₇	semidirect
427. #465	C₂²×C₇	semidirect
428. #460	C₂²×C₇	semidirect
429. #460	C₂²×C₇	semidirect
430. #459	C₂²×C₇	semidirect
431. #459	C₂²×C₇	semidirect
432. #450	C₂²×C₇	semidirect
433. #450	C₂²×C₇	semidirect
434. #447	C₂²×C₇	semidirect
435. #447	C₂²×C₇	semidirect
436. #442	C₂²×C₇	semidirect
437. #440	C₂²×C₇	semidirect
438. C₄×SD₁₆	C₂²×C₇	semidirect
439. C₄×D₈	C₂²×C₇	semidirect
440. #436	C₂²×C₇	semidirect
441. #435	C₂²×C₇	semidirect
442. C₈×D₄	C₂²×C₇	semidirect
443. #428	C₂²×C₇	semidirect
444. #428	C₂²×C₇	semidirect
445. #423	C₂²×C₇	semidirect
448. #418	C₂²×C₇	semidirect
449. #418	C₂²×C₇	semidirect
450. #418	C₂²×C₇	semidirect
451. #418	C₂²×C₇	semidirect
452. #418	C₂²×C₇	semidirect
453. #417	C₂²×C₇	semidirect
454. C₂×#102	C₂²×C₇	semidirect
455. C₂×#102	C₂²×C₇	semidirect
456. #407	C₂²×C₇	semidirect
457. C₄×M₁₆	C₂²×C₇	semidirect
504. C₇×D₄	AGL(1,ℤ/8)	semidirect
567. C₂×SD₁₆	C₂³×C₇	semidirect
569. C₂×D₈	C₂³×C₇	semidirect
574. C₂×M₁₆	C₂³×C₇	semidirect
575. C₂²×C₈	C₂³×C₇	semidirect
576. C₄⋊Q₈	C₂³×C₇	semidirect
577. C₄⋊Q₈	C₂³×C₇	semidirect
587. #125	C₂³×C₇	semidirect
598. C₂²⋊Q₈	C₂³×C₇	semidirect
599. C₂²⋊Q₈	C₂³×C₇	semidirect
609. #121	C₂³×C₇	semidirect
610. #121	C₂³×C₇	semidirect
619. C₄×Q₈	C₂³×C₇	semidirect
620. C₄×Q₈	C₂³×C₇	semidirect
637. C₄×D₄	C₂³×C₇	semidirect
638. C₄×D₄	C₂³×C₇	semidirect
646. #117	C₂³×C₇	semidirect
647. #117	C₂³×C₇	semidirect
650. C₂×C₄⋊C₄	C₂³×C₇	semidirect
651. C₂×C₄⋊C₄	C₂³×C₇	semidirect
659. #107	C₂³×C₇	semidirect
660. #107	C₂³×C₇	semidirect
661. #106	C₂³×C₇	semidirect
662. #106	C₂³×C₇	semidirect
663. C₄⋊C₈	C₂³×C₇	semidirect
664. C₄⋊C₈	C₂³×C₇	semidirect
665. #103	C₂³×C₇	semidirect
670. #102	C₂³×C₇	semidirect
671. #102	C₂³×C₇	semidirect
672. #102	C₂³×C₇	semidirect
673. #102	C₂³×C₇	semidirect
674. #102	C₂³×C₇	semidirect
675. #102	C₂³×C₇	semidirect
676. #102	C₂³×C₇	semidirect
677. C₂²⋊C₈	C₂³×C₇	semidirect
678. C₂²⋊C₈	C₂³×C₇	semidirect
679. #97	C₂³×C₇	semidirect
680. C₄×C₈	C₂³×C₇	semidirect
767. C₂×D₄	C₇×#41	semidirect
904. D₄	C₇×AGL(1,ℤ/8)	semidirect
942. C₇	#61155	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×D₄²	2
C₇×#3325	2
C₇×#3324	2
C₇×#3318	2
C₇×#3310	2
C₇×#3295	2
C₇×#3294	2
C₇×#3138	2
C₇×#3094	2
C₇×#3077	2
C₇×#3055	2
C₇×#3038	2
C₇×#3003	2
C₄×C₇×AGL(1,ℤ/8)	2
C₇×D₄×M₁₆	2
C₂×C₇×#418	2
#61155	7

Subgroups — C7×#61155 #13238371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61155 #13238371