Subgroups — #11743861

Order 896.

1022 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#551	C₂	1	1	yes	maximal, characteristic, complemented
2	#90399	C₂	1	1	yes	maximal, characteristic, complemented
3	#90393	C₂	1	1	yes	maximal, characteristic, complemented
4	#90392	C₂	1	1	yes	maximal, characteristic, complemented
5	#90392	C₂	1	1	yes	maximal, characteristic, complemented
6	#90362	C₂	1	1	yes	maximal, characteristic, complemented
7	#90360	C₂	1	1	yes	maximal, characteristic, complemented
8	#90353	C₂	1	1	yes	maximal, characteristic, complemented
9	#90341	C₂	1	1	yes	maximal, characteristic, complemented
10	#90341	C₂	1	1	yes	maximal, characteristic, complemented
11	#90341	C₂	1	1	yes	maximal, characteristic, complemented
12	#90340	C₂	1	1	yes	maximal, characteristic, complemented
13	#90339	C₂	1	1	yes	maximal, characteristic, complemented
14	#90333	C₂	1	1	yes	maximal, characteristic, complemented
15	#90327	C₂	1	1	yes	maximal, characteristic, complemented
16	#90314	C₂	1	1	yes	maximal, characteristic, complemented
17	#90313	C₂	1	1	yes	maximal, characteristic, complemented
18	#90278	C₂	1	1	yes	maximal, characteristic, complemented
19	#90277	C₂	1	1	yes	maximal, characteristic
20	#90237	C₂	1	1	yes	maximal, characteristic, complemented
21	#90232	C₂	1	1	yes	maximal, characteristic, complemented
22	#90230	C₂	1	1	yes	maximal, characteristic, complemented
23	#90229	C₂	1	1	yes	maximal, characteristic, complemented
24	#90222	C₂	1	1	yes	maximal, characteristic, complemented
25	#90222	C₂	1	1	yes	maximal, characteristic, complemented
26	#90208	C₂	1	1	yes	maximal, characteristic, complemented
27	#90207	C₂	1	1	yes	maximal, characteristic, complemented
28	#90186	C₂	1	1	yes	maximal, characteristic, complemented
29	#90186	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#6441	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#6440	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂³×Dic₇	C₂²	1	1	yes	characteristic
33	C₂×#1159	C₂²	1	1	yes	characteristic
34	C₂²×Dic₁₄	C₂²	1	1	yes	characteristic
35	C₇×#126	C₂²	1	1	yes	characteristic
36	C₇×#126	C₂²	1	1	yes	characteristic
37	C₇×#124	C₂²	1	1	yes	characteristic
38	C₇×#123	C₂²	1	1	yes	characteristic
39	C₇×#123	C₂²	1	1	yes	characteristic
40	C₇×#123	C₂²	1	1	yes	characteristic
41	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₇×#120	C₂²	1	1	yes	characteristic
44	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
45	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
46	C₇×#117	C₂²	1	1	yes	characteristic
47	C₇×#117	C₂²	1	1	yes	characteristic
48	C₂×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	#6516	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
53	#6509	C₂²	1	1	yes	characteristic, complemented
54	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
55	#6507	C₂²	1	1	yes	characteristic, complemented
56	#6507	C₂²	1	1	yes	characteristic, complemented
57	#6502	C₂²	1	1	yes	characteristic
58	#6502	C₂²	1	1	yes	characteristic
59	#6499	C₂²	1	1	yes	characteristic
60	#6498	C₂²	1	1	yes	characteristic
61	#6498	C₂²	1	1	yes	characteristic
62	#6498	C₂²	1	1	yes	characteristic
63	#6498	C₂²	1	1	yes	characteristic
64	D₄×Dic₇	C₂²	1	1	yes	characteristic
65	D₄×Dic₇	C₂²	1	1	yes	characteristic
66	D₄×Dic₇	C₂²	1	1	yes	characteristic
67	D₄×Dic₇	C₂²	1	1	yes	characteristic
68	#6492	C₂²	1	1	yes	characteristic
69	#6492	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
73	#6489	C₂²	1	1	yes	characteristic
74	#6489	C₂²	1	1	yes	characteristic
75	#6489	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
77	#6487	C₂²	1	1	yes	characteristic
78	#6487	C₂²	1	1	yes	characteristic
79	#6487	C₂²	1	1	yes	characteristic, complemented
80	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
81	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
82	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
83	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
84	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic
86	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic
87	#6461	C₂²	1	1	yes	characteristic, complemented
88	#6461	C₂²	1	1	yes	characteristic, complemented
89	#6461	C₂²	1	1	yes	characteristic, complemented
90	#6459	C₂²	1	1	yes	characteristic, complemented
91	#6459	C₂²	1	1	yes	characteristic, complemented
92	#6459	C₂²	1	1	yes	characteristic, complemented
93	#6455	C₂²	1	1	yes	characteristic, complemented
94	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
95	#6453	C₂²	1	1	yes	characteristic, complemented
96	#6453	C₂²	1	1	yes	characteristic, complemented
97	#6453	C₂²	1	1	yes	characteristic, complemented
98	#6453	C₂²	1	1	yes	characteristic, complemented
99	#6452	C₂²	1	1	yes	characteristic, complemented
100	#6452	C₂²	1	1	yes	characteristic, complemented
101	#6452	C₂²	1	1	yes	characteristic, complemented
102	#6452	C₂²	1	1	yes	characteristic, complemented
103	#6452	C₂²	1	1	yes	characteristic, complemented
104	#6452	C₂²	1	1	yes	characteristic, complemented
105	#6452	C₂²	1	1	yes	characteristic, complemented
106	#6452	C₂²	1	1	yes	characteristic, complemented
107	#6452	C₂²	1	1	yes	characteristic, complemented
108	#6452	C₂²	1	1	yes	characteristic, complemented
109	#6451	C₂²	1	1	yes	characteristic, complemented
110	#6451	C₂²	1	1	yes	characteristic, complemented
111	#6451	C₂²	1	1	yes	characteristic, complemented
112	#6451	C₂²	1	1	yes	characteristic, complemented
113	#6450	C₂²	1	1	yes	characteristic, complemented
114	#6450	C₂²	1	1	yes	characteristic, complemented
115	#6450	C₂²	1	1	yes	characteristic, complemented
116	#6450	C₂²	1	1	yes	characteristic, complemented
117	#6450	C₂²	1	1	yes	characteristic, complemented
118	#6450	C₂²	1	1	yes	characteristic, complemented
119	#6449	C₂²	1	1	yes	characteristic
120	#6449	C₂²	1	1	yes	characteristic
121	#6449	C₂²	1	1	yes	characteristic
122	#6448	C₂²	1	1	yes	characteristic
123	#6448	C₂²	1	1	yes	characteristic
124	#6448	C₂²	1	1	yes	characteristic, complemented
125	#6448	C₂²	1	1	yes	characteristic, complemented
126	#6446	C₂²	1	1	yes	characteristic
127	#6446	C₂²	1	1	yes	characteristic
128	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
129	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
130	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
131	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
132	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
133	#6442	C₂²	1	1	yes	characteristic
134	#6442	C₂²	1	1	yes	characteristic
135	#6442	C₂²	1	1	yes	characteristic
136	#6442	C₂²	1	1	yes	characteristic
137	#6442	C₂²	1	1	yes	characteristic
138	#6442	C₂²	1	1	yes	characteristic
139	#6442	C₂²	1	1	yes	characteristic, complemented
140	#6442	C₂²	1	1	yes	characteristic, complemented
141	#6442	C₂²	1	1	yes	characteristic, complemented
142	#6442	C₂²	1	1	yes	characteristic, complemented
143	#6441	C₂²	1	1	yes	characteristic
144	#6441	C₂²	1	1	yes	characteristic
145	#6441	C₂²	1	1	yes	characteristic
146	#6441	C₂²	1	1	yes	characteristic
147	#6441	C₂²	1	1	yes	characteristic
148	#6441	C₂²	1	1	yes	characteristic
149	#6441	C₂²	1	1	yes	characteristic
150	#6441	C₂²	1	1	yes	characteristic
151	#6441	C₂²	1	1	yes	characteristic
152	#6441	C₂²	1	1	yes	characteristic
153	#6441	C₂²	1	1	yes	characteristic
154	#6441	C₂²	1	1	yes	characteristic
155	#6441	C₂²	1	1	yes	characteristic
156	#6441	C₂²	1	1	yes	characteristic
157	#6441	C₂²	1	1	yes	characteristic, complemented
158	#6441	C₂²	1	1	yes	characteristic, complemented
159	#6441	C₂²	1	1	yes	characteristic, complemented
160	#6440	C₂²	1	1	yes	characteristic
161	#6440	C₂²	1	1	yes	characteristic
162	#6440	C₂²	1	1	yes	characteristic
163	#6440	C₂²	1	1	yes	characteristic
164	#6440	C₂²	1	1	yes	characteristic
165	#6440	C₂²	1	1	yes	characteristic
166	#6440	C₂²	1	1	yes	characteristic
167	#6440	C₂²	1	1	yes	characteristic
168	#6440	C₂²	1	1	yes	characteristic
169	#6440	C₂²	1	1	yes	characteristic
170	#6440	C₂²	1	1	yes	characteristic
171	#6440	C₂²	1	1	yes	characteristic
172	#6440	C₂²	1	1	yes	characteristic
173	#6440	C₂²	1	1	yes	characteristic, complemented
174	#6440	C₂²	1	1	yes	characteristic, complemented
175	#6439	C₂²	1	1	yes	characteristic, complemented
176	#6435	C₂²	1	1	yes	characteristic, complemented
177	#6435	C₂²	1	1	yes	characteristic, complemented
178	#6433	C₂²	1	1	yes	characteristic, complemented
179	#6433	C₂²	1	1	yes	characteristic, complemented
180	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
181	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
182	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
183	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
184	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
185	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
187	#3495	—	7	1	no	maximal, Sylow
188	C₂⁴×C₇	C₂³	1	1	yes	characteristic
189	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
190	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
191	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
192	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
202	C₂²×Dic₇	—	2	4	no	—
203	C₂²×Dic₇	C₂³	1	1	yes	characteristic
204	C₂²×Dic₇	C₂³	1	1	yes	characteristic
205	C₂²×Dic₇	C₂³	1	1	yes	characteristic
206	C₂²×Dic₇	C₂³	1	1	yes	characteristic
207	C₂²×Dic₇	C₂³	1	1	yes	characteristic
208	C₂²×Dic₇	C₂³	1	1	yes	characteristic
209	C₂²×Dic₇	C₂³	1	1	yes	characteristic
210	C₂²×Dic₇	C₂³	1	1	yes	characteristic
211	C₂²×Dic₇	C₂³	1	1	yes	characteristic
212	C₂²×Dic₇	C₂³	1	1	yes	characteristic
213	C₂²×Dic₇	C₂³	1	1	yes	characteristic
214	C₂²×Dic₇	C₂³	1	1	yes	characteristic
215	#1159	—	2	4	no	—
216	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
217	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
219	C₂×Dic₁₄	—	2	4	no	—
220	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
221	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
222	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
223	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
224	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
225	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
226	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
227	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
228	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
231	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
232	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
237	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
238	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
239	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
240	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
241	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
242	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
244	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
245	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
246	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
247	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
248	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
249	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
250	C₄²×C₇	C₂³	1	1	yes	characteristic
251	C₄²×C₇	C₂³	1	1	yes	characteristic
252	C₄²×C₇	C₂³	1	1	yes	characteristic
253	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
254	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
255	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
256	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
257	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
258	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
259	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
260	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
261	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
262	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
269	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
270	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
271	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
272	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
273	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
274	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
275	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
276	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
277	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
278	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
279	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
280	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
281	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
282	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
283	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
284	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
285	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
286	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
287	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
288	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
289	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
290	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
291	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
292	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
293	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
294	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
295	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
296	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
297	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
298	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
299	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
300	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
301	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
302	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
303	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
304	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
305	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
306	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
307	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
308	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
309	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
310	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
311	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
312	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
313	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
314	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
315	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
316	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
317	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
318	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
319	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
320	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
321	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
322	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
323	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
324	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
325	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
326	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
327	C₄×Dic₇	C₂³	1	1	yes	characteristic
328	C₄×Dic₇	C₂³	1	1	yes	characteristic
329	C₄×Dic₇	C₂³	1	1	yes	characteristic
330	C₄×Dic₇	C₂³	1	1	yes	characteristic
331	C₄×Dic₇	C₂³	1	1	yes	characteristic
332	C₄×Dic₇	C₂³	1	1	yes	characteristic
333	C₄×Dic₇	C₂³	1	1	yes	characteristic
334	C₄×Dic₇	C₂³	1	1	yes	characteristic
335	C₄×Dic₇	C₂³	1	1	yes	characteristic
336	C₄×Dic₇	C₂³	1	1	yes	characteristic
337	C₄×Dic₇	C₂³	1	1	yes	characteristic
338	C₄×Dic₇	C₂³	1	1	yes	characteristic
339	C₄×Dic₇	C₂³	1	1	yes	characteristic
340	C₄×Dic₇	C₂³	1	1	yes	characteristic
341	C₄×Dic₇	C₂³	1	1	yes	characteristic
342	C₄×Dic₇	C₂³	1	1	yes	characteristic
343	C₄×Dic₇	C₂³	1	1	yes	characteristic
344	C₄×Dic₇	C₂³	1	1	yes	characteristic
345	C₄×Dic₇	C₂³	1	1	yes	characteristic
346	#556	—	7	1	no	—
347	#556	—	7	1	no	—
348	#554	—	7	1	no	—
349	#554	—	7	1	no	—
350	#552	—	7	1	no	—
351	#552	—	7	1	no	—
352	#552	—	7	1	no	—
353	#552	—	7	1	no	—
354	#552	—	7	1	no	—
355	#552	—	7	1	no	—
356	#552	—	7	1	no	—
357	#552	—	7	1	no	—
358	#551	—	7	1	no	—
359	#551	—	7	1	no	—
360	#551	—	7	1	no	—
361	#551	D₇	1	1	yes	characteristic, complemented
362	#544	—	7	1	no	—
363	#542	—	7	1	no	—
364	#542	—	7	1	no	—
365	#541	—	7	1	no	—
366	#541	—	7	1	no	—
367	#536	—	7	1	no	—
368	#533	—	7	1	no	—
369	#533	—	7	1	no	—
370	#529	—	7	1	no	—
371	#529	—	7	1	no	—
372	#525	—	7	1	no	—
373	C₂×C₂²⋊Q₈	—	7	1	no	—
374	#520	—	7	1	no	—
375	#519	—	7	1	no	—
376	C₂×#117	—	7	1	no	—
377	C₂³×C₇	—	2	2	no	—
378	C₂³×C₇	—	2	2	no	—
379	C₂³×C₇	—	4	1	no	—
380	C₂³×C₇	C₂⁴	1	1	yes	characteristic
381	C₂³×C₇	C₂⁴	1	1	yes	characteristic
382	C₂³×C₇	C₂⁴	1	1	yes	characteristic
383	C₂³×C₇	C₂⁴	1	1	yes	characteristic
384	C₂²×D₇	C₂⁴	1	1	yes	characteristic
385	C₇×Q₈	—	4	1	no	—
386	C₇×D₄	—	2	2	no	—
387	C₇×D₄	—	2	2	no	—
388	C₇×D₄	—	4	1	no	—
389	C₂×C₄×C₇	—	2	2	no	—
390	C₂×C₄×C₇	—	2	2	no	—
391	C₂×C₄×C₇	—	4	1	no	—
392	C₂×C₄×C₇	—	4	1	no	—
393	C₂×C₄×C₇	—	4	1	no	—
394	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
395	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
396	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
397	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
398	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
399	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
400	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
401	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
402	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
403	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
404	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
405	C₂²⋊D₇	—	2	2	no	—
406	C₂²⋊D₇	—	2	2	no	—
407	C₂²⋊D₇	—	2	2	no	—
408	C₂²⋊D₇	—	4	1	no	—
409	C₂×Dic₇	—	2	2	no	—
410	C₂×Dic₇	—	2	2	no	—
411	C₂×Dic₇	—	2	2	no	—
412	C₂×Dic₇	—	2	2	no	—
413	C₂×Dic₇	—	2	2	no	—
414	C₂×Dic₇	—	2	2	no	—
415	C₂×Dic₇	—	2	2	no	—
416	C₂×Dic₇	—	2	2	no	—
417	C₂×Dic₇	—	4	1	no	—
418	C₂×Dic₇	—	4	1	no	—
419	C₂×Dic₇	—	4	1	no	—
420	C₂×Dic₇	#41	1	4	yes	—
421	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
422	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
423	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
424	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
425	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
426	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
427	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
428	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
429	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
430	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
431	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
432	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
433	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
434	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
435	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
436	C₄×D₇	—	2	2	no	—
437	C₄×D₇	—	4	1	no	—
438	C₄×D₇	—	4	1	no	—
439	Dic₁₄	—	2	2	no	—
440	Dic₁₄	—	2	2	no	—
441	Dic₁₄	—	2	2	no	—
442	Dic₁₄	—	2	2	no	—
443	Dic₁₄	—	2	2	no	—
444	Dic₁₄	—	4	1	no	—
445	Dic₁₄	—	4	1	no	—
446	Dic₁₄	—	4	1	no	—
447	C₂×#41	—	7	1	no	—
448	C₂²×Q₈	—	7	1	no	—
449	C₂³×C₄	—	7	1	no	—
450	C₄⋊Q₈	—	7	1	no	—
451	C₄⋊Q₈	—	7	1	no	—
452	C₄⋊Q₈	—	7	1	no	—
453	C₄⋊Q₈	—	7	1	no	—
454	C₄⋊Q₈	—	7	1	no	—
455	C₄⋊Q₈	—	7	1	no	—
456	#126	—	7	1	no	—
457	#126	—	7	1	no	—
458	#126	—	7	1	no	—
459	#126	—	7	1	no	—
460	#126	—	7	1	no	—
461	#126	—	7	1	no	—
462	#126	—	7	1	no	—
463	#126	—	7	1	no	—
464	#126	—	7	1	no	—
465	#126	—	7	1	no	—
466	#126	—	7	1	no	—
467	#126	—	7	1	no	—
468	#126	—	7	1	no	—
469	#126	—	7	1	no	—
470	#126	C₂×D₇	1	1	yes	characteristic
471	#126	C₂×D₇	1	1	yes	characteristic
472	#125	—	7	1	no	—
473	#125	—	7	1	no	—
474	#125	—	7	1	no	—
475	#125	—	7	1	no	—
476	#125	—	7	1	no	—
477	#125	—	7	1	no	—
478	#125	—	7	1	no	—
479	#125	—	7	1	no	—
480	#125	—	7	1	no	—
481	#125	—	7	1	no	—
482	#125	—	7	1	no	—
483	#125	—	7	1	no	—
484	#125	—	7	1	no	—
485	#125	—	7	1	no	—
486	#125	—	7	1	no	—
487	#125	—	7	1	no	—
488	#124	—	7	1	no	—
489	#124	—	7	1	no	—
490	#124	—	7	1	no	—
491	#124	—	7	1	no	—
492	#124	—	7	1	no	—
493	#124	C₂×D₇	1	1	yes	characteristic
494	#123	—	7	1	no	—
495	#123	—	7	1	no	—
496	#123	—	7	1	no	—
497	#123	—	7	1	no	—
498	#123	—	7	1	no	—
499	#123	—	7	1	no	—
500	#123	—	7	1	no	—
501	#123	—	7	1	no	—
502	#123	—	7	1	no	—
503	#123	—	7	1	no	—
504	#123	—	7	1	no	—
505	#123	C₂×D₇	1	1	yes	characteristic
506	#123	C₂×D₇	1	1	yes	characteristic
507	#123	C₂×D₇	1	1	yes	characteristic
508	C₂²⋊Q₈	—	7	1	no	—
509	C₂²⋊Q₈	—	7	1	no	—
510	C₂²⋊Q₈	—	7	1	no	—
511	C₂²⋊Q₈	—	7	1	no	—
512	C₂²⋊Q₈	—	7	1	no	—
513	C₂²⋊Q₈	—	7	1	no	—
514	C₂²⋊Q₈	—	7	1	no	—
515	C₂²⋊Q₈	—	7	1	no	—
516	C₂²⋊Q₈	—	7	1	no	—
517	C₂²⋊Q₈	—	7	1	no	—
518	C₂²⋊Q₈	—	7	1	no	—
519	C₂²⋊Q₈	—	7	1	no	—
520	C₂²⋊Q₈	—	7	1	no	—
521	C₂²⋊Q₈	—	7	1	no	—
522	C₂²⋊Q₈	—	7	1	no	—
523	C₂²⋊Q₈	—	7	1	no	—
524	C₂²⋊Q₈	—	7	1	no	—
525	C₂²⋊Q₈	—	7	1	no	—
526	C₂²⋊Q₈	—	7	1	no	—
527	C₂²⋊Q₈	—	7	1	no	—
528	C₂²⋊Q₈	—	7	1	no	—
529	C₂²⋊Q₈	—	7	1	no	—
530	C₂²⋊Q₈	—	7	1	no	—
531	C₂²⋊Q₈	—	7	1	no	—
532	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
533	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
534	#121	—	7	1	no	—
535	#121	—	7	1	no	—
536	#120	—	7	1	no	—
537	#120	C₂×D₇	1	1	yes	characteristic
538	C₄×Q₈	—	7	1	no	—
539	C₄×Q₈	—	7	1	no	—
540	C₄×Q₈	—	7	1	no	—
541	C₄×Q₈	—	7	1	no	—
542	C₄×Q₈	—	7	1	no	—
543	C₄×Q₈	—	7	1	no	—
544	C₄×Q₈	—	7	1	no	—
545	C₄×Q₈	—	7	1	no	—
546	C₄×Q₈	—	7	1	no	—
547	C₄×Q₈	—	7	1	no	—
548	C₄×Q₈	—	7	1	no	—
549	C₄×Q₈	—	7	1	no	—
550	C₄×Q₈	—	7	1	no	—
551	C₄×Q₈	—	7	1	no	—
552	C₄×D₄	—	7	1	no	—
553	C₄×D₄	—	7	1	no	—
554	C₄×D₄	—	7	1	no	—
555	C₄×D₄	—	7	1	no	—
556	C₄×D₄	—	7	1	no	—
557	C₄×D₄	—	7	1	no	—
558	C₄×D₄	—	7	1	no	—
559	C₄×D₄	—	7	1	no	—
560	C₄×D₄	—	7	1	no	—
561	C₄×D₄	—	7	1	no	—
562	C₄×D₄	—	7	1	no	—
563	C₄×D₄	—	7	1	no	—
564	C₄×D₄	C₂×D₇	1	1	yes	characteristic
565	C₄×D₄	C₂×D₇	1	1	yes	characteristic
566	#117	—	7	1	no	—
567	#117	—	7	1	no	—
568	#117	—	7	1	no	—
569	#117	—	7	1	no	—
570	#117	—	7	1	no	—
571	#117	—	7	1	no	—
572	#117	—	7	1	no	—
573	#117	—	7	1	no	—
574	#117	—	7	1	no	—
575	#117	—	7	1	no	—
576	#117	—	7	1	no	—
577	#117	—	7	1	no	—
578	#117	—	7	1	no	—
579	#117	—	7	1	no	—
580	#117	—	7	1	no	—
581	#117	—	7	1	no	—
582	#117	—	7	1	no	—
583	#117	—	7	1	no	—
584	#117	—	7	1	no	—
585	#117	—	7	1	no	—
586	#117	—	7	1	no	—
587	#117	C₂×D₇	1	1	yes	characteristic
588	#117	C₂×D₇	1	1	yes	characteristic
589	C₂×C₄⋊C₄	—	7	1	no	—
590	C₂×C₄⋊C₄	—	7	1	no	—
591	C₂×C₄⋊C₄	—	7	1	no	—
592	C₂×C₄⋊C₄	—	7	1	no	—
593	C₂×C₄⋊C₄	—	7	1	no	—
594	C₂×C₄⋊C₄	—	7	1	no	—
595	C₂×C₄⋊C₄	—	7	1	no	—
596	C₂×C₂²⋊C₄	—	7	1	no	—
597	C₂×C₂²⋊C₄	—	7	1	no	—
598	C₂×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
600	C₂×C₄²	—	7	1	no	—
601	C₂×C₄²	—	7	1	no	—
602	C₂²×C₇	—	2	1	no	—
603	C₂²×C₇	—	2	1	no	—
604	C₂²×C₇	—	2	1	no	—
605	C₂²×C₇	—	2	1	no	—
606	C₂²×C₇	—	2	1	no	—
607	C₂²×C₇	—	2	1	no	—
608	C₂²×C₇	—	2	1	no	—
609	C₂²×C₇	—	2	1	no	—
610	C₂²×C₇	—	2	1	no	—
611	C₂²×C₇	—	2	1	no	—
612	C₂²×C₇	—	4	4	no	—
613	C₂²×C₇	C₂×#41	1	2	yes	—
614	C₂²×C₇	2₋¹⁺⁴	1	2	yes	—
615	C₂²×C₇	C₂⁵	1	1	yes	characteristic
616	C₂×D₇	—	2	1	no	—
617	C₂×D₇	—	2	1	no	—
618	C₂×D₇	—	2	1	no	—
619	C₄×C₇	—	2	1	no	—
620	C₄×C₇	—	2	1	no	—
621	C₄×C₇	—	2	1	no	—
622	C₄×C₇	—	2	1	no	—
623	C₄×C₇	—	2	1	no	—
624	C₄×C₇	—	2	1	no	—
625	C₄×C₇	—	2	1	no	—
626	C₄×C₇	—	2	1	no	—
627	C₄×C₇	—	2	1	no	—
628	C₄×C₇	—	2	1	no	—
629	C₄×C₇	—	2	1	no	—
630	Dic₇	—	2	1	no	—
631	Dic₇	—	2	1	no	—
632	Dic₇	—	2	1	no	—
633	Dic₇	—	2	1	no	—
634	Dic₇	—	2	1	no	—
635	Dic₇	—	2	1	no	—
636	Dic₇	—	2	1	no	—
637	Dic₇	—	2	1	no	—
638	Dic₇	—	2	1	no	—
639	Dic₇	—	2	1	no	—
640	Dic₇	—	2	1	no	—
641	Dic₇	—	2	1	no	—
642	Dic₇	—	2	1	no	—
643	Dic₇	C₂×#41	1	2	yes	—
644	Dic₇	C₂×#41	1	2	yes	—
645	C₂⁴	C₂²×D₇	1	1	yes	characteristic
646	#41	—	14	4	no	—
647	C₂×Q₈	—	7	1	no	—
648	C₂×Q₈	—	7	1	no	—
649	C₂×Q₈	—	7	1	no	—
650	C₂×Q₈	—	7	1	no	—
651	C₂×Q₈	—	7	1	no	—
652	C₂×Q₈	—	7	1	no	—
653	C₂×Q₈	—	7	1	no	—
654	C₂×Q₈	—	7	1	no	—
655	C₂×Q₈	—	14	4	no	—
656	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
657	C₂×D₄	—	7	1	no	—
658	C₂×D₄	—	7	1	no	—
659	C₂×D₄	—	7	1	no	—
660	C₂×D₄	—	7	1	no	—
661	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
662	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
663	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
664	C₂²×C₄	—	7	1	no	—
665	C₂²×C₄	—	7	1	no	—
666	C₂²×C₄	—	7	1	no	—
667	C₂²×C₄	—	7	1	no	—
668	C₂²×C₄	—	7	1	no	—
669	C₂²×C₄	—	7	1	no	—
670	C₂²×C₄	—	7	1	no	—
671	C₂²×C₄	—	7	1	no	—
672	C₂²×C₄	—	7	1	no	—
673	C₂²×C₄	—	7	1	no	—
674	C₂²×C₄	—	7	1	no	—
675	C₂²×C₄	—	7	1	no	—
676	C₂²×C₄	—	7	1	no	—
677	C₂²×C₄	—	7	1	no	—
678	C₂²×C₄	—	7	1	no	—
679	C₂²×C₄	—	14	4	no	—
680	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
681	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
682	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
683	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
684	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
685	C₄⋊C₄	—	7	1	no	—
686	C₄⋊C₄	—	7	1	no	—
687	C₄⋊C₄	—	7	1	no	—
688	C₄⋊C₄	—	7	1	no	—
689	C₄⋊C₄	—	7	1	no	—
690	C₄⋊C₄	—	7	1	no	—
691	C₄⋊C₄	—	7	1	no	—
692	C₄⋊C₄	—	7	1	no	—
693	C₄⋊C₄	—	7	1	no	—
694	C₄⋊C₄	—	7	1	no	—
695	C₄⋊C₄	—	7	1	no	—
696	C₄⋊C₄	—	7	1	no	—
697	C₄⋊C₄	—	7	1	no	—
698	C₄⋊C₄	—	7	1	no	—
699	C₄⋊C₄	—	7	1	no	—
700	C₄⋊C₄	—	7	1	no	—
701	C₄⋊C₄	—	7	1	no	—
702	C₄⋊C₄	—	7	1	no	—
703	C₄⋊C₄	—	7	1	no	—
704	C₄⋊C₄	—	7	1	no	—
705	C₄⋊C₄	—	7	1	no	—
706	C₄⋊C₄	—	7	1	no	—
707	C₄⋊C₄	—	7	1	no	—
708	C₄⋊C₄	—	7	1	no	—
709	C₄⋊C₄	—	7	1	no	—
710	C₄⋊C₄	—	7	1	no	—
711	C₄⋊C₄	—	7	1	no	—
712	C₄⋊C₄	—	7	1	no	—
713	C₄⋊C₄	—	7	1	no	—
714	C₄⋊C₄	—	7	1	no	—
715	C₄⋊C₄	—	7	1	no	—
716	C₄⋊C₄	—	7	1	no	—
717	C₄⋊C₄	—	7	1	no	—
718	C₄⋊C₄	—	7	1	no	—
719	C₄⋊C₄	—	7	1	no	—
720	C₄⋊C₄	—	7	1	no	—
721	C₄⋊C₄	—	7	1	no	—
722	C₄⋊C₄	—	7	1	no	—
723	C₄⋊C₄	—	7	1	no	—
724	C₄⋊C₄	—	7	1	no	—
725	C₄⋊C₄	—	7	1	no	—
726	C₄⋊C₄	—	7	1	no	—
727	C₄⋊C₄	—	7	1	no	—
728	C₄⋊C₄	—	7	1	no	—
729	C₄⋊C₄	—	7	1	no	—
730	C₄⋊C₄	—	7	1	no	—
731	C₄⋊C₄	—	7	1	no	—
732	C₄⋊C₄	—	7	1	no	—
733	C₄⋊C₄	—	7	1	no	—
734	C₄⋊C₄	—	7	1	no	—
735	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
736	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
737	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
738	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
739	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
740	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
741	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
742	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
743	C₂²⋊C₄	—	7	1	no	—
744	C₂²⋊C₄	—	7	1	no	—
745	C₂²⋊C₄	—	7	1	no	—
746	C₂²⋊C₄	—	7	1	no	—
747	C₂²⋊C₄	—	7	1	no	—
748	C₂²⋊C₄	—	7	1	no	—
749	C₂²⋊C₄	—	7	1	no	—
750	C₂²⋊C₄	—	7	1	no	—
751	C₂²⋊C₄	—	7	1	no	—
752	C₂²⋊C₄	—	7	1	no	—
753	C₂²⋊C₄	—	7	1	no	—
754	C₂²⋊C₄	—	7	1	no	—
755	C₂²⋊C₄	—	7	1	no	—
756	C₂²⋊C₄	—	7	1	no	—
757	C₂²⋊C₄	—	7	1	no	—
758	C₂²⋊C₄	—	7	1	no	—
759	C₂²⋊C₄	—	7	1	no	—
760	C₂²⋊C₄	—	7	1	no	—
761	C₂²⋊C₄	—	7	1	no	—
762	C₂²⋊C₄	—	7	1	no	—
763	C₂²⋊C₄	—	7	1	no	—
764	C₂²⋊C₄	—	7	1	no	—
765	C₂²⋊C₄	—	7	1	no	—
766	C₂²⋊C₄	—	7	1	no	—
767	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
768	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
769	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
770	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
771	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
772	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
773	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
774	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
775	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
776	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
777	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
778	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
779	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
780	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
781	C₄²	—	7	1	no	—
782	C₄²	—	7	1	no	—
783	C₄²	—	7	1	no	—
784	C₄²	—	7	1	no	—
785	C₄²	—	7	1	no	—
786	C₄²	—	7	1	no	—
787	C₄²	—	7	1	no	—
788	C₄²	—	7	1	no	—
789	C₄²	—	7	1	no	—
790	C₄²	—	7	1	no	—
791	C₄²	—	7	1	no	—
792	C₄²	—	7	1	no	—
793	C₄²	—	7	1	no	—
794	C₄²	—	7	1	no	—
795	C₄²	—	7	1	no	—
796	C₄²	—	7	1	no	—
797	C₄²	—	7	1	no	—
798	C₄²	—	7	1	no	—
799	C₄²	—	7	1	no	—
800	C₄²	C₂²×D₇	1	1	yes	characteristic
801	C₄²	C₂²×D₇	1	1	yes	characteristic
802	C₄²	C₂²×D₇	1	1	yes	characteristic
803	C₂×C₇	—	2	2	no	—
804	C₂×C₇	—	2	2	no	—
805	C₂×C₇	—	4	1	no	—
806	C₂×C₇	—	4	1	no	—
807	C₂×C₇	C₂²×#41	1	1	yes	characteristic
808	C₂×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
809	C₂×C₇	#585	1	1	yes	characteristic
810	D₇	—	4	1	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	4	1	no	—
814	C₂³	—	7	1	no	—
815	C₂³	C₂³×D₇	1	1	yes	characteristic
816	C₂³	C₂³×D₇	1	1	yes	characteristic
817	C₂³	C₂³×D₇	1	1	yes	characteristic
818	C₂³	C₂³×D₇	1	1	yes	characteristic
819	Q₈	—	4	1	no	—
820	Q₈	—	14	2	no	—
821	Q₈	—	14	2	no	—
822	Q₈	—	14	2	no	—
823	Q₈	—	14	2	no	—
824	Q₈	—	14	2	no	—
825	Q₈	—	28	1	no	—
826	Q₈	—	28	1	no	—
827	Q₈	—	28	1	no	—
828	D₄	—	2	2	no	—
829	D₄	—	2	2	no	—
830	D₄	—	4	1	no	—
831	D₄	—	14	2	no	—
832	D₄	—	14	2	no	—
833	D₄	—	14	2	no	—
834	D₄	—	28	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	4	1	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	1	no	—
840	C₂×C₄	—	7	4	no	—
841	C₂×C₄	—	7	1	no	—
842	C₂×C₄	—	7	1	no	—
843	C₂×C₄	—	7	1	no	—
844	C₂×C₄	—	7	1	no	—
845	C₂×C₄	—	7	1	no	—
846	C₂×C₄	—	7	1	no	—
847	C₂×C₄	—	7	1	no	—
848	C₂×C₄	—	7	1	no	—
849	C₂×C₄	—	7	1	no	—
850	C₂×C₄	—	7	1	no	—
851	C₂×C₄	—	7	1	no	—
852	C₂×C₄	—	7	1	no	—
853	C₂×C₄	—	7	1	no	—
854	C₂×C₄	—	7	1	no	—
855	C₂×C₄	—	7	1	no	—
856	C₂×C₄	—	14	2	no	—
857	C₂×C₄	—	14	2	no	—
858	C₂×C₄	—	14	2	no	—
859	C₂×C₄	—	14	2	no	—
860	C₂×C₄	—	14	2	no	—
861	C₂×C₄	—	14	2	no	—
862	C₂×C₄	—	14	2	no	—
863	C₂×C₄	—	14	2	no	—
864	C₂×C₄	—	14	2	no	—
865	C₂×C₄	—	28	1	no	—
866	C₂×C₄	—	28	1	no	—
867	C₂×C₄	—	28	1	no	—
868	C₂×C₄	—	28	1	no	—
869	C₂×C₄	—	28	1	no	—
870	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
871	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
872	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
873	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
874	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
875	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
876	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
877	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
878	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
879	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
880	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
881	C₇	#3495	1	1	yes	characteristic, complemented, Sylow
882	C₂²	—	2	1	no	—
883	C₂²	—	2	1	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	1	no	—
887	C₂²	—	2	1	no	—
888	C₂²	—	2	1	no	—
889	C₂²	—	2	1	no	—
890	C₂²	—	2	1	no	—
891	C₂²	—	2	1	no	—
892	C₂²	—	4	4	no	—
893	C₂²	—	14	1	no	—
894	C₂²	—	14	1	no	—
895	C₂²	—	14	1	no	—
896	C₂²	D₇×#41	1	2	yes	—
897	C₂²	#6554	1	2	yes	—
898	C₂²	C₂⁴×D₇	1	1	yes	characteristic
899	C₄	—	2	1	no	—
900	C₄	—	2	1	no	—
901	C₄	—	2	1	no	—
902	C₄	—	2	1	no	—
903	C₄	—	2	1	no	—
904	C₄	—	2	1	no	—
905	C₄	—	2	1	no	—
906	C₄	—	2	1	no	—
907	C₄	—	2	1	no	—
908	C₄	—	2	1	no	—
909	C₄	—	2	1	no	—
910	C₄	—	7	2	no	—
911	C₄	—	7	2	no	—
912	C₄	—	14	1	no	—
913	C₄	—	14	1	no	—
914	C₄	—	14	1	no	—
915	C₄	—	14	1	no	—
916	C₄	—	14	1	no	—
917	C₄	—	14	1	no	—
918	C₄	—	14	1	no	—
919	C₄	—	14	1	no	—
920	C₄	—	14	1	no	—
921	C₄	—	14	1	no	—
922	C₄	—	14	1	no	—
923	C₄	—	14	1	no	—
924	C₄	—	14	1	no	—
925	C₂	—	2	2	no	—
926	C₂	—	2	2	no	—
927	C₂	—	4	1	no	—
928	C₂	—	4	1	no	—
929	C₂	—	28	1	no	—
930	C₂	C₂×D₇×#41	1	1	yes	characteristic
931	C₂	C₂×#6554	1	1	yes	characteristic
932	C₂	#90618	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#551	C₂
prime radical	#90277	C₂
hypercenter	#551	D₇
hypocenter	C₇	#3495
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. C₇×#551	C₂	semidirect
2. #90399	C₂	semidirect
3. #90393	C₂	semidirect
4. #90392	C₂	semidirect
5. #90392	C₂	semidirect
6. #90362	C₂	semidirect
7. #90360	C₂	semidirect
8. #90353	C₂	semidirect
9. #90341	C₂	semidirect
10. #90341	C₂	semidirect
11. #90341	C₂	semidirect
12. #90340	C₂	semidirect
13. #90339	C₂	semidirect
14. #90333	C₂	semidirect
15. #90327	C₂	semidirect
16. #90314	C₂	semidirect
17. #90313	C₂	semidirect
18. #90278	C₂	semidirect
20. #90237	C₂	semidirect
21. #90232	C₂	semidirect
22. #90230	C₂	semidirect
23. #90229	C₂	semidirect
24. #90222	C₂	semidirect
25. #90222	C₂	semidirect
26. #90208	C₂	semidirect
27. #90207	C₂	semidirect
28. #90186	C₂	semidirect
29. #90186	C₂	semidirect
30. C₂×#6441	C₂	semidirect
31. C₂×#6440	C₂	semidirect
53. #6509	C₂²	semidirect
54. Q₈×Dic₇	C₂²	semidirect
55. #6507	C₂²	semidirect
56. #6507	C₂²	semidirect
72. C₄×C₂²⋊D₇	C₂²	semidirect
75. #6489	C₂²	semidirect
79. #6487	C₂²	semidirect
84. C₂×Dic₇⋊C₄	C₂²	semidirect
87. #6461	C₂²	semidirect
88. #6461	C₂²	semidirect
89. #6461	C₂²	semidirect
90. #6459	C₂²	semidirect
91. #6459	C₂²	semidirect
92. #6459	C₂²	semidirect
93. #6455	C₂²	semidirect
94. D₇×C₄⋊C₄	C₂²	semidirect
95. #6453	C₂²	semidirect
96. #6453	C₂²	semidirect
97. #6453	C₂²	semidirect
98. #6453	C₂²	semidirect
99. #6452	C₂²	semidirect
100. #6452	C₂²	semidirect
101. #6452	C₂²	semidirect
102. #6452	C₂²	semidirect
103. #6452	C₂²	semidirect
104. #6452	C₂²	semidirect
105. #6452	C₂²	semidirect
106. #6452	C₂²	semidirect
107. #6452	C₂²	semidirect
108. #6452	C₂²	semidirect
109. #6451	C₂²	semidirect
110. #6451	C₂²	semidirect
111. #6451	C₂²	semidirect
112. #6451	C₂²	semidirect
113. #6450	C₂²	semidirect
114. #6450	C₂²	semidirect
115. #6450	C₂²	semidirect
116. #6450	C₂²	semidirect
117. #6450	C₂²	semidirect
118. #6450	C₂²	semidirect
124. #6448	C₂²	semidirect
125. #6448	C₂²	semidirect
132. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
139. #6442	C₂²	semidirect
140. #6442	C₂²	semidirect
141. #6442	C₂²	semidirect
142. #6442	C₂²	semidirect
157. #6441	C₂²	semidirect
158. #6441	C₂²	semidirect
159. #6441	C₂²	semidirect
173. #6440	C₂²	semidirect
174. #6440	C₂²	semidirect
175. #6439	C₂²	semidirect
176. #6435	C₂²	semidirect
177. #6435	C₂²	semidirect
178. #6433	C₂²	semidirect
179. #6433	C₂²	semidirect
180. C₄×Dic₁₄	C₂²	semidirect
181. C₄×Dic₁₄	C₂²	semidirect
182. C₄×Dic₁₄	C₂²	semidirect
183. C₄×Dic₁₄	C₂²	semidirect
184. C₄×Dic₁₄	C₂²	semidirect
185. C₄×Dic₁₄	C₂²	semidirect
186. C₄×Dic₁₄	C₂²	semidirect
361. #551	D₇	semidirect
881. C₇	#3495	semidirect

Maximal subgroups

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

subgroup	index
C₇×#551	2
#90399	2
#90393	2
#90392	2
#90362	2
#90360	2
#90353	2
#90341	2
#90340	2
#90339	2
#90333	2
#90327	2
#90314	2
#90313	2
#90278	2
#90277	2
#90237	2
#90232	2
#90230	2
#90229	2
#90222	2
#90208	2
#90207	2
#90186	2
C₂×#6441	2
C₂×#6440	2
#3495	7