Subgroups — #11743876

Order 896.

1032 conjugacy classes of subgroups.

The subgroup lattice has 982 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	#90403	C₂	1	1	yes	maximal, characteristic, complemented
3	#90401	C₂	1	1	yes	maximal, characteristic, complemented
4	#90401	C₂	1	1	yes	maximal, characteristic, complemented
5	#90393	C₂	1	1	yes	maximal, characteristic, complemented
6	#90368	C₂	1	1	yes	maximal, characteristic, complemented
7	#90360	C₂	1	1	yes	maximal, characteristic, complemented
8	#90358	C₂	1	1	yes	maximal, characteristic, complemented
9	#90358	C₂	1	1	yes	maximal, characteristic, complemented
10	#90353	C₂	1	1	yes	maximal, characteristic, complemented
11	#90349	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	#90337	C₂	1	1	yes	maximal, characteristic, complemented
15	#90325	C₂	1	1	yes	maximal, characteristic, complemented
16	#90323	C₂	1	1	yes	maximal, characteristic, complemented
17	#90319	C₂	1	1	yes	maximal, characteristic, complemented
18	#90284	C₂	1	1	yes	maximal, characteristic, complemented
19	#90282	C₂	1	1	yes	maximal, characteristic, complemented
20	#90252	C₂	1	1	yes	maximal, characteristic, complemented
21	#90251	C₂	1	1	yes	maximal, characteristic, complemented
22	#90243	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×Dic₁₄	C₂	1	1	yes	maximal, characteristic, complemented
24	#90225	C₂	1	1	yes	maximal, characteristic, complemented
25	#90224	C₂	1	1	yes	maximal, characteristic, complemented
26	#90218	C₂	1	1	yes	maximal, characteristic, complemented
27	#90208	C₂	1	1	yes	maximal, characteristic, complemented
28	#90186	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#6448	C₂	1	1	yes	maximal, characteristic, complemented
30	#90181	C₂	1	1	yes	maximal, characteristic, complemented
31	#90174	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×C₂²⋊D₇	C₂²	1	1	yes	characteristic
33	C₂×Q₈×D₇	C₂²	1	1	yes	characteristic, complemented
34	C₂×#1159	C₂²	1	1	yes	characteristic
35	C₂×#1157	C₂²	1	1	yes	characteristic
36	C₂²×Dic₁₄	C₂²	1	1	yes	characteristic
37	C₂²×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
38	C₇×#126	C₂²	1	1	yes	characteristic, complemented
39	C₇×#126	C₂²	1	1	yes	characteristic, complemented
40	C₇×#124	C₂²	1	1	yes	characteristic, complemented
41	C₇×#123	C₂²	1	1	yes	characteristic
42	C₇×#123	C₂²	1	1	yes	characteristic, complemented
43	C₇×#123	C₂²	1	1	yes	characteristic, complemented
44	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₇×#120	C₂²	1	1	yes	characteristic
47	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
48	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
49	C₇×#117	C₂²	1	1	yes	characteristic
50	C₇×#117	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
52	C₂×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
53	#6516	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
56	#6509	C₂²	1	1	yes	characteristic, complemented
57	#6509	C₂²	1	1	yes	characteristic, complemented
58	#6507	C₂²	1	1	yes	characteristic, complemented
59	#6502	C₂²	1	1	yes	characteristic
60	#6502	C₂²	1	1	yes	characteristic
61	#6502	C₂²	1	1	yes	characteristic
62	#6502	C₂²	1	1	yes	characteristic, complemented
63	#6501	C₂²	1	1	yes	characteristic
64	#6501	C₂²	1	1	yes	characteristic, complemented
65	#6500	C₂²	1	1	yes	characteristic
66	#6499	C₂²	1	1	yes	characteristic, complemented
67	#6498	C₂²	1	1	yes	characteristic, complemented
68	D₄×Dic₇	C₂²	1	1	yes	characteristic
69	D₄×Dic₇	C₂²	1	1	yes	characteristic
70	#6493	C₂²	1	1	yes	characteristic
71	#6493	C₂²	1	1	yes	characteristic, complemented
72	#6492	C₂²	1	1	yes	characteristic
73	#6492	C₂²	1	1	yes	characteristic
74	#6492	C₂²	1	1	yes	characteristic, complemented
75	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
77	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
78	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
79	#6489	C₂²	1	1	yes	characteristic
80	#6487	C₂²	1	1	yes	characteristic
81	#6487	C₂²	1	1	yes	characteristic, complemented
82	#6487	C₂²	1	1	yes	characteristic, complemented
83	#6487	C₂²	1	1	yes	characteristic, complemented
84	#6487	C₂²	1	1	yes	characteristic, complemented
85	#6487	C₂²	1	1	yes	characteristic, complemented
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	#6461	C₂²	1	1	yes	characteristic, complemented
91	#6461	C₂²	1	1	yes	characteristic, complemented
92	#6460	C₂²	1	1	yes	characteristic, complemented
93	#6460	C₂²	1	1	yes	characteristic, complemented
94	#6460	C₂²	1	1	yes	characteristic, complemented
95	#6460	C₂²	1	1	yes	characteristic, complemented
96	#6459	C₂²	1	1	yes	characteristic, complemented
97	#6459	C₂²	1	1	yes	characteristic, complemented
98	#6459	C₂²	1	1	yes	characteristic, complemented
99	#6459	C₂²	1	1	yes	characteristic, complemented
100	#6459	C₂²	1	1	yes	characteristic, complemented
101	#6459	C₂²	1	1	yes	characteristic, complemented
102	#6459	C₂²	1	1	yes	characteristic, complemented
103	#6457	C₂²	1	1	yes	characteristic, complemented
104	#6457	C₂²	1	1	yes	characteristic, complemented
105	#6457	C₂²	1	1	yes	characteristic, complemented
106	#6455	C₂²	1	1	yes	characteristic, complemented
107	#6455	C₂²	1	1	yes	characteristic, complemented
108	#6453	C₂²	1	1	yes	characteristic, complemented
109	#6453	C₂²	1	1	yes	characteristic, complemented
110	#6452	C₂²	1	1	yes	characteristic, complemented
111	#6451	C₂²	1	1	yes	characteristic, complemented
112	#6451	C₂²	1	1	yes	characteristic, complemented
113	#6451	C₂²	1	1	yes	characteristic, complemented
114	#6451	C₂²	1	1	yes	characteristic, complemented
115	#6451	C₂²	1	1	yes	characteristic, complemented
116	#6451	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, complemented
121	#6449	C₂²	1	1	yes	characteristic, complemented
122	#6448	C₂²	1	1	yes	characteristic
123	#6448	C₂²	1	1	yes	characteristic
124	#6448	C₂²	1	1	yes	characteristic
125	#6448	C₂²	1	1	yes	characteristic
126	#6448	C₂²	1	1	yes	characteristic
127	#6448	C₂²	1	1	yes	characteristic
128	#6448	C₂²	1	1	yes	characteristic
129	#6448	C₂²	1	1	yes	characteristic
130	#6448	C₂²	1	1	yes	characteristic
131	#6448	C₂²	1	1	yes	characteristic
132	#6448	C₂²	1	1	yes	characteristic, complemented
133	#6448	C₂²	1	1	yes	characteristic, complemented
134	#6448	C₂²	1	1	yes	characteristic, complemented
135	#6448	C₂²	1	1	yes	characteristic, complemented
136	#6448	C₂²	1	1	yes	characteristic, complemented
137	#6447	C₂²	1	1	yes	characteristic
138	#6447	C₂²	1	1	yes	characteristic
139	#6447	C₂²	1	1	yes	characteristic, complemented
140	#6446	C₂²	1	1	yes	characteristic
141	#6446	C₂²	1	1	yes	characteristic
142	#6446	C₂²	1	1	yes	characteristic, complemented
143	#6446	C₂²	1	1	yes	characteristic, complemented
144	#6446	C₂²	1	1	yes	characteristic, complemented
145	#6445	C₂²	1	1	yes	characteristic
146	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
147	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
148	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
149	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
150	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
151	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
152	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
153	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
154	#6442	C₂²	1	1	yes	characteristic, complemented
155	#6442	C₂²	1	1	yes	characteristic, complemented
156	#6442	C₂²	1	1	yes	characteristic, complemented
157	#6442	C₂²	1	1	yes	characteristic, complemented
158	#6442	C₂²	1	1	yes	characteristic, complemented
159	#6441	C₂²	1	1	yes	characteristic
160	#6441	C₂²	1	1	yes	characteristic
161	#6441	C₂²	1	1	yes	characteristic
162	#6441	C₂²	1	1	yes	characteristic
163	#6441	C₂²	1	1	yes	characteristic
164	#6441	C₂²	1	1	yes	characteristic
165	#6441	C₂²	1	1	yes	characteristic
166	#6441	C₂²	1	1	yes	characteristic, complemented
167	#6441	C₂²	1	1	yes	characteristic, complemented
168	#6441	C₂²	1	1	yes	characteristic, complemented
169	#6441	C₂²	1	1	yes	characteristic, complemented
170	#6441	C₂²	1	1	yes	characteristic, complemented
171	#6441	C₂²	1	1	yes	characteristic, complemented
172	#6441	C₂²	1	1	yes	characteristic, complemented
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	#6439	C₂²	1	1	yes	characteristic, complemented
177	#6438	C₂²	1	1	yes	characteristic, complemented
178	#6438	C₂²	1	1	yes	characteristic, complemented
179	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
180	#6435	C₂²	1	1	yes	characteristic, complemented
181	#6432	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	#3561	—	7	1	no	maximal, Sylow
188	C₂⁴×C₇	C₂³	1	1	yes	characteristic
189	C₂³×D₇	C₂³	1	1	yes	characteristic
190	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
191	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
192	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
193	C₂×C₇×D₄	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	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊D₇	—	4	2	no	—
200	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₇	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	C₂²×Dic₇	C₂³	1	1	yes	characteristic
216	C₂²×Dic₇	C₂³	1	1	yes	characteristic
217	Q₈×D₇	—	4	2	no	—
218	#1159	—	4	2	no	—
219	#1157	—	4	2	no	—
220	C₂×D₂₈	C₂³	1	1	yes	characteristic
221	C₂×D₂₈	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
229	C₂×Dic₁₄	—	4	2	no	—
230	C₂×Dic₁₄	—	4	2	no	—
231	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
232	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
233	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
234	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
235	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
236	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
237	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
238	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
239	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
240	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
241	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
242	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
243	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
249	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
252	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
253	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
254	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
255	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
256	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
257	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
258	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
259	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
260	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
261	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
263	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
264	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₄²×C₇	C₂³	1	1	yes	characteristic
266	C₄²×C₇	C₂³	1	1	yes	characteristic
267	C₄²×C₇	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
282	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
303	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
304	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
305	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
306	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
307	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
308	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
309	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
310	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
311	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
312	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
313	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
314	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
315	C₄⋊Dic₇	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	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
328	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
329	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
330	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
331	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
332	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
333	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
334	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
335	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
336	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
337	Dic₇⋊C₄	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	C₄×Dic₇	C₂³	1	1	yes	characteristic
347	C₄×Dic₇	C₂³	1	1	yes	characteristic
348	C₄×Dic₇	C₂³	1	1	yes	characteristic
349	#563	—	7	1	no	—
350	#563	—	7	1	no	—
351	#562	—	7	1	no	—
352	#562	—	7	1	no	—
353	#556	—	7	1	no	—
354	#556	—	7	1	no	—
355	#551	—	7	1	no	—
356	#551	—	7	1	no	—
357	#551	—	7	1	no	—
358	#551	D₇	1	1	yes	characteristic, complemented
359	D₄×Q₈	—	7	1	no	—
360	D₄×Q₈	—	7	1	no	—
361	#548	—	7	1	no	—
362	#548	—	7	1	no	—
363	#546	—	7	1	no	—
364	#546	—	7	1	no	—
365	#543	—	7	1	no	—
366	#543	—	7	1	no	—
367	#542	—	7	1	no	—
368	#542	—	7	1	no	—
369	#542	—	7	1	no	—
370	#542	—	7	1	no	—
371	#542	—	7	1	no	—
372	#542	—	7	1	no	—
373	#538	—	7	1	no	—
374	#538	—	7	1	no	—
375	#536	—	7	1	no	—
376	#536	—	7	1	no	—
377	#533	—	7	1	no	—
378	#529	—	7	1	no	—
379	C₂×#124	—	7	1	no	—
380	C₂³×C₇	—	2	2	no	—
381	C₂³×C₇	—	4	1	no	—
382	C₂³×C₇	—	4	1	no	—
383	C₂³×C₇	C₂⁴	1	1	yes	characteristic
384	C₂³×C₇	C₂⁴	1	1	yes	characteristic
385	C₂³×C₇	C₂⁴	1	1	yes	characteristic
386	C₂³×C₇	C₂⁴	1	1	yes	characteristic
387	C₂²×D₇	—	2	2	no	—
388	C₂²×D₇	—	4	1	no	—
389	C₂²×D₇	—	4	1	no	—
390	C₂²×D₇	C₂⁴	1	1	yes	characteristic
391	C₂²×D₇	C₂⁴	1	1	yes	characteristic
392	C₂²×D₇	C₂⁴	1	1	yes	characteristic
393	C₇×Q₈	—	4	1	no	—
394	C₇×D₄	—	2	2	no	—
395	C₇×D₄	—	4	1	no	—
396	C₇×D₄	—	4	1	no	—
397	C₂×C₄×C₇	—	2	2	no	—
398	C₂×C₄×C₇	—	4	1	no	—
399	C₂×C₄×C₇	—	4	1	no	—
400	C₂×C₄×C₇	—	4	1	no	—
401	C₂×C₄×C₇	—	4	1	no	—
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	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
406	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
407	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
408	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
409	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
410	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
411	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
412	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
413	C₂²⋊D₇	—	2	2	no	—
414	C₂²⋊D₇	—	2	2	no	—
415	C₂²⋊D₇	—	2	2	no	—
416	C₂²⋊D₇	—	4	1	no	—
417	C₂²⋊D₇	—	4	1	no	—
418	C₂²⋊D₇	—	4	1	no	—
419	C₂²⋊D₇	—	4	1	no	—
420	C₂²⋊D₇	—	4	1	no	—
421	C₂²⋊D₇	—	4	1	no	—
422	C₂²⋊D₇	—	4	1	no	—
423	C₂×Dic₇	—	2	2	no	—
424	C₂×Dic₇	—	2	2	no	—
425	C₂×Dic₇	—	4	1	no	—
426	C₂×Dic₇	—	4	1	no	—
427	C₂×Dic₇	—	4	1	no	—
428	C₂×Dic₇	—	4	1	no	—
429	C₂×Dic₇	—	4	1	no	—
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	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
437	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
438	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
439	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
440	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
441	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
442	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
443	D₂₈	—	4	1	no	—
444	D₂₈	—	4	1	no	—
445	C₄×D₇	—	2	2	no	—
446	C₄×D₇	—	4	1	no	—
447	C₄×D₇	—	4	1	no	—
448	C₄×D₇	—	4	1	no	—
449	C₄×D₇	—	4	1	no	—
450	C₄×D₇	—	4	1	no	—
451	C₄×D₇	—	4	1	no	—
452	Dic₁₄	—	2	2	no	—
453	Dic₁₄	—	2	2	no	—
454	Dic₁₄	—	2	2	no	—
455	Dic₁₄	—	2	2	no	—
456	Dic₁₄	—	4	1	no	—
457	Dic₁₄	—	4	1	no	—
458	Dic₁₄	—	4	1	no	—
459	Dic₁₄	—	4	1	no	—
460	Dic₁₄	—	4	1	no	—
461	Dic₁₄	—	4	1	no	—
462	Dic₁₄	—	4	1	no	—
463	Dic₁₄	—	4	1	no	—
464	C₂×#41	—	7	1	no	—
465	C₂×#41	—	7	1	no	—
466	C₂²×Q₈	—	7	1	no	—
467	C₂²×Q₈	—	7	1	no	—
468	C₂²×Q₈	—	7	1	no	—
469	C₂²×D₄	—	7	1	no	—
470	C₄⋊Q₈	—	7	1	no	—
471	C₄⋊Q₈	—	7	1	no	—
472	C₄⋊Q₈	—	7	1	no	—
473	C₄⋊Q₈	—	7	1	no	—
474	C₄⋊Q₈	—	7	1	no	—
475	C₄⋊Q₈	—	7	1	no	—
476	C₄⋊Q₈	—	7	1	no	—
477	C₄⋊Q₈	—	7	1	no	—
478	#126	—	7	1	no	—
479	#126	—	7	1	no	—
480	#126	—	7	1	no	—
481	#126	—	7	1	no	—
482	#126	—	7	1	no	—
483	#126	—	7	1	no	—
484	#126	—	7	1	no	—
485	#126	—	7	1	no	—
486	#126	—	7	1	no	—
487	#126	—	7	1	no	—
488	#126	—	7	1	no	—
489	#126	—	7	1	no	—
490	#126	C₂×D₇	1	1	yes	characteristic, complemented
491	#126	C₂×D₇	1	1	yes	characteristic, complemented
492	#125	—	7	1	no	—
493	#125	—	7	1	no	—
494	#125	—	7	1	no	—
495	#124	—	7	1	no	—
496	#124	—	7	1	no	—
497	#124	—	7	1	no	—
498	#124	—	7	1	no	—
499	#124	—	7	1	no	—
500	#124	—	7	1	no	—
501	#124	—	7	1	no	—
502	#124	—	7	1	no	—
503	#124	—	7	1	no	—
504	#124	—	7	1	no	—
505	#124	—	7	1	no	—
506	#124	—	7	1	no	—
507	#124	—	7	1	no	—
508	#124	—	7	1	no	—
509	#124	—	7	1	no	—
510	#124	—	7	1	no	—
511	#124	—	7	1	no	—
512	#124	—	7	1	no	—
513	#124	C₂×D₇	1	1	yes	characteristic, complemented
514	#123	—	7	1	no	—
515	#123	—	7	1	no	—
516	#123	—	7	1	no	—
517	#123	—	7	1	no	—
518	#123	—	7	1	no	—
519	#123	—	7	1	no	—
520	#123	—	7	1	no	—
521	#123	—	7	1	no	—
522	#123	—	7	1	no	—
523	#123	—	7	1	no	—
524	#123	—	7	1	no	—
525	#123	—	7	1	no	—
526	#123	—	7	1	no	—
527	#123	—	7	1	no	—
528	#123	—	7	1	no	—
529	#123	C₂×D₇	1	1	yes	characteristic
530	#123	C₂×D₇	1	1	yes	characteristic, complemented
531	#123	C₂×D₇	1	1	yes	characteristic, complemented
532	C₂²⋊Q₈	—	7	1	no	—
533	C₂²⋊Q₈	—	7	1	no	—
534	C₂²⋊Q₈	—	7	1	no	—
535	C₂²⋊Q₈	—	7	1	no	—
536	C₂²⋊Q₈	—	7	1	no	—
537	C₂²⋊Q₈	—	7	1	no	—
538	C₂²⋊Q₈	—	7	1	no	—
539	C₂²⋊Q₈	—	7	1	no	—
540	C₂²⋊Q₈	—	7	1	no	—
541	C₂²⋊Q₈	—	7	1	no	—
542	C₂²⋊Q₈	—	7	1	no	—
543	C₂²⋊Q₈	—	7	1	no	—
544	C₂²⋊Q₈	—	7	1	no	—
545	C₂²⋊Q₈	—	7	1	no	—
546	C₂²⋊Q₈	—	7	1	no	—
547	C₂²⋊Q₈	—	7	1	no	—
548	C₂²⋊Q₈	—	7	1	no	—
549	C₂²⋊Q₈	—	7	1	no	—
550	C₂²⋊Q₈	—	7	1	no	—
551	C₂²⋊Q₈	—	7	1	no	—
552	C₂²⋊Q₈	—	7	1	no	—
553	C₂²⋊Q₈	—	7	1	no	—
554	C₂²⋊Q₈	—	7	1	no	—
555	C₂²⋊Q₈	—	7	1	no	—
556	C₂²⋊Q₈	—	7	1	no	—
557	C₂²⋊Q₈	—	7	1	no	—
558	C₂²⋊Q₈	—	7	1	no	—
559	C₂²⋊Q₈	—	7	1	no	—
560	C₂²⋊Q₈	—	7	1	no	—
561	C₂²⋊Q₈	—	7	1	no	—
562	C₂²⋊Q₈	—	7	1	no	—
563	C₂²⋊Q₈	—	7	1	no	—
564	C₂²⋊Q₈	—	7	1	no	—
565	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
566	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
567	#121	—	7	1	no	—
568	#121	—	7	1	no	—
569	#121	—	7	1	no	—
570	#121	—	7	1	no	—
571	#121	—	7	1	no	—
572	#121	—	7	1	no	—
573	#121	—	7	1	no	—
574	#121	—	7	1	no	—
575	#121	—	7	1	no	—
576	#121	—	7	1	no	—
577	#121	—	7	1	no	—
578	#120	—	7	1	no	—
579	#120	—	7	1	no	—
580	#120	—	7	1	no	—
581	#120	C₂×D₇	1	1	yes	characteristic
582	C₄×Q₈	—	7	1	no	—
583	C₄×Q₈	—	7	1	no	—
584	C₄×Q₈	—	7	1	no	—
585	C₄×Q₈	—	7	1	no	—
586	C₄×Q₈	—	7	1	no	—
587	C₄×Q₈	—	7	1	no	—
588	C₄×Q₈	—	7	1	no	—
589	C₄×D₄	—	7	1	no	—
590	C₄×D₄	—	7	1	no	—
591	C₄×D₄	—	7	1	no	—
592	C₄×D₄	—	7	1	no	—
593	C₄×D₄	—	7	1	no	—
594	C₄×D₄	—	7	1	no	—
595	C₄×D₄	—	7	1	no	—
596	C₄×D₄	—	7	1	no	—
597	C₄×D₄	—	7	1	no	—
598	C₄×D₄	—	7	1	no	—
599	C₄×D₄	—	7	1	no	—
600	C₄×D₄	C₂×D₇	1	1	yes	characteristic
601	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
602	#117	—	7	1	no	—
603	#117	—	7	1	no	—
604	#117	—	7	1	no	—
605	#117	—	7	1	no	—
606	#117	—	7	1	no	—
607	#117	—	7	1	no	—
608	#117	C₂×D₇	1	1	yes	characteristic
609	#117	C₂×D₇	1	1	yes	characteristic, complemented
610	C₂×C₂²⋊C₄	—	7	1	no	—
611	C₂×C₂²⋊C₄	—	7	1	no	—
612	C₂×C₂²⋊C₄	—	7	1	no	—
613	C₂×C₂²⋊C₄	—	7	1	no	—
614	C₂×C₂²⋊C₄	—	7	1	no	—
615	C₂×C₂²⋊C₄	—	7	1	no	—
616	C₂×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
618	C₂×C₄²	—	7	1	no	—
619	C₂²×C₇	—	2	1	no	—
620	C₂²×C₇	—	2	1	no	—
621	C₂²×C₇	—	2	1	no	—
622	C₂²×C₇	—	2	1	no	—
623	C₂²×C₇	—	2	1	no	—
624	C₂²×C₇	—	2	1	no	—
625	C₂²×C₇	—	2	1	no	—
626	C₂²×C₇	—	2	1	no	—
627	C₂²×C₇	—	2	1	no	—
628	C₂²×C₇	—	2	1	no	—
629	C₂²×C₇	—	2	1	no	—
630	C₂²×C₇	—	8	2	no	—
631	C₂²×C₇	2₋¹⁺⁴	1	2	yes	—
632	C₂²×C₇	C₂⁵	1	1	yes	characteristic
633	C₂×D₇	—	2	1	no	—
634	C₂×D₇	—	2	1	no	—
635	C₂×D₇	—	2	1	no	—
636	C₂×D₇	—	2	1	no	—
637	C₂×D₇	—	2	1	no	—
638	C₂×D₇	—	2	1	no	—
639	C₂×D₇	—	2	1	no	—
640	C₂×D₇	—	2	1	no	—
641	C₂×D₇	—	2	1	no	—
642	C₂×D₇	—	8	2	no	—
643	C₄×C₇	—	2	1	no	—
644	C₄×C₇	—	2	1	no	—
645	C₄×C₇	—	2	1	no	—
646	C₄×C₇	—	2	1	no	—
647	C₄×C₇	—	2	1	no	—
648	C₄×C₇	—	2	1	no	—
649	C₄×C₇	—	2	1	no	—
650	C₄×C₇	—	2	1	no	—
651	C₄×C₇	—	2	1	no	—
652	C₄×C₇	—	2	1	no	—
653	C₄×C₇	—	2	1	no	—
654	Dic₇	—	2	1	no	—
655	Dic₇	—	2	1	no	—
656	Dic₇	—	2	1	no	—
657	Dic₇	—	2	1	no	—
658	Dic₇	—	2	1	no	—
659	Dic₇	—	2	1	no	—
660	Dic₇	—	2	1	no	—
661	Dic₇	—	2	1	no	—
662	Dic₇	—	2	1	no	—
663	Dic₇	—	2	1	no	—
664	Dic₇	—	2	1	no	—
665	Dic₇	—	2	1	no	—
666	Dic₇	H(5,𝔽₂)	1	2	yes	—
667	C₂⁴	—	7	1	no	—
668	C₂⁴	C₂²×D₇	1	1	yes	characteristic
669	#41	—	28	2	no	—
670	#41	—	28	2	no	—
671	C₂×Q₈	—	7	1	no	—
672	C₂×Q₈	—	7	1	no	—
673	C₂×Q₈	—	7	1	no	—
674	C₂×Q₈	—	7	1	no	—
675	C₂×Q₈	—	7	1	no	—
676	C₂×Q₈	—	7	1	no	—
677	C₂×Q₈	—	7	1	no	—
678	C₂×Q₈	—	7	1	no	—
679	C₂×Q₈	—	7	1	no	—
680	C₂×Q₈	—	7	1	no	—
681	C₂×Q₈	—	7	1	no	—
682	C₂×Q₈	—	7	1	no	—
683	C₂×Q₈	—	28	2	no	—
684	C₂×Q₈	—	28	2	no	—
685	C₂×Q₈	—	28	2	no	—
686	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
687	C₂×D₄	—	7	1	no	—
688	C₂×D₄	—	7	1	no	—
689	C₂×D₄	—	7	1	no	—
690	C₂×D₄	—	7	1	no	—
691	C₂×D₄	—	7	1	no	—
692	C₂×D₄	—	7	1	no	—
693	C₂×D₄	—	7	1	no	—
694	C₂×D₄	—	7	1	no	—
695	C₂×D₄	—	7	1	no	—
696	C₂×D₄	—	7	1	no	—
697	C₂×D₄	—	7	1	no	—
698	C₂×D₄	—	7	1	no	—
699	C₂×D₄	—	28	2	no	—
700	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
701	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
702	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
703	C₂²×C₄	—	7	1	no	—
704	C₂²×C₄	—	7	1	no	—
705	C₂²×C₄	—	7	1	no	—
706	C₂²×C₄	—	7	1	no	—
707	C₂²×C₄	—	7	1	no	—
708	C₂²×C₄	—	7	1	no	—
709	C₂²×C₄	—	7	1	no	—
710	C₂²×C₄	—	7	1	no	—
711	C₂²×C₄	—	7	1	no	—
712	C₂²×C₄	—	7	1	no	—
713	C₂²×C₄	—	7	1	no	—
714	C₂²×C₄	—	7	1	no	—
715	C₂²×C₄	—	7	1	no	—
716	C₂²×C₄	—	7	1	no	—
717	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
718	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
719	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
720	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
721	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
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	—	7	1	no	—
736	C₄⋊C₄	—	7	1	no	—
737	C₄⋊C₄	—	7	1	no	—
738	C₄⋊C₄	—	7	1	no	—
739	C₄⋊C₄	—	7	1	no	—
740	C₄⋊C₄	—	7	1	no	—
741	C₄⋊C₄	—	7	1	no	—
742	C₄⋊C₄	—	7	1	no	—
743	C₄⋊C₄	—	7	1	no	—
744	C₄⋊C₄	—	7	1	no	—
745	C₄⋊C₄	—	7	1	no	—
746	C₄⋊C₄	—	7	1	no	—
747	C₄⋊C₄	—	7	1	no	—
748	C₄⋊C₄	—	7	1	no	—
749	C₄⋊C₄	—	7	1	no	—
750	C₄⋊C₄	—	7	1	no	—
751	C₄⋊C₄	—	7	1	no	—
752	C₄⋊C₄	—	7	1	no	—
753	C₄⋊C₄	—	7	1	no	—
754	C₄⋊C₄	—	7	1	no	—
755	C₄⋊C₄	—	7	1	no	—
756	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
757	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
758	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
759	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
760	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
761	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
762	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
763	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
764	C₂²⋊C₄	—	7	1	no	—
765	C₂²⋊C₄	—	7	1	no	—
766	C₂²⋊C₄	—	7	1	no	—
767	C₂²⋊C₄	—	7	1	no	—
768	C₂²⋊C₄	—	7	1	no	—
769	C₂²⋊C₄	—	7	1	no	—
770	C₂²⋊C₄	—	7	1	no	—
771	C₂²⋊C₄	—	7	1	no	—
772	C₂²⋊C₄	—	7	1	no	—
773	C₂²⋊C₄	—	7	1	no	—
774	C₂²⋊C₄	—	7	1	no	—
775	C₂²⋊C₄	—	7	1	no	—
776	C₂²⋊C₄	—	7	1	no	—
777	C₂²⋊C₄	—	7	1	no	—
778	C₂²⋊C₄	—	7	1	no	—
779	C₂²⋊C₄	—	7	1	no	—
780	C₂²⋊C₄	—	7	1	no	—
781	C₂²⋊C₄	—	7	1	no	—
782	C₂²⋊C₄	—	7	1	no	—
783	C₂²⋊C₄	—	7	1	no	—
784	C₂²⋊C₄	—	7	1	no	—
785	C₂²⋊C₄	—	7	1	no	—
786	C₂²⋊C₄	—	7	1	no	—
787	C₂²⋊C₄	—	7	1	no	—
788	C₂²⋊C₄	—	7	1	no	—
789	C₂²⋊C₄	—	7	1	no	—
790	C₂²⋊C₄	—	7	1	no	—
791	C₂²⋊C₄	—	7	1	no	—
792	C₂²⋊C₄	—	7	1	no	—
793	C₂²⋊C₄	—	7	1	no	—
794	C₂²⋊C₄	—	7	1	no	—
795	C₂²⋊C₄	—	7	1	no	—
796	C₂²⋊C₄	—	7	1	no	—
797	C₂²⋊C₄	—	7	1	no	—
798	C₂²⋊C₄	—	7	1	no	—
799	C₂²⋊C₄	—	7	1	no	—
800	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
801	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
802	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
803	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
804	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
805	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
806	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
807	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
808	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
809	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
810	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
811	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
812	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
813	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
814	C₄²	—	7	1	no	—
815	C₄²	—	7	1	no	—
816	C₄²	—	7	1	no	—
817	C₄²	—	7	1	no	—
818	C₄²	—	7	1	no	—
819	C₄²	—	7	1	no	—
820	C₄²	—	7	1	no	—
821	C₄²	—	7	1	no	—
822	C₄²	—	7	1	no	—
823	C₄²	—	7	1	no	—
824	C₄²	—	7	1	no	—
825	C₄²	C₂²×D₇	1	1	yes	characteristic
826	C₄²	C₂²×D₇	1	1	yes	characteristic
827	C₄²	C₂²×D₇	1	1	yes	characteristic
828	C₂×C₇	—	2	2	no	—
829	C₂×C₇	—	4	1	no	—
830	C₂×C₇	—	4	1	no	—
831	C₂×C₇	—	4	1	no	—
832	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
833	C₂×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
834	C₂×C₇	#585	1	1	yes	characteristic
835	D₇	—	4	1	no	—
836	D₇	—	4	1	no	—
837	D₇	—	4	1	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	4	1	no	—
840	C₂³	—	4	1	no	—
841	C₂³	—	7	1	no	—
842	C₂³	—	7	1	no	—
843	C₂³	—	7	1	no	—
844	C₂³	—	14	2	no	—
845	C₂³	—	28	1	no	—
846	C₂³	—	28	1	no	—
847	C₂³	C₂³×D₇	1	1	yes	characteristic
848	C₂³	C₂³×D₇	1	1	yes	characteristic
849	C₂³	C₂³×D₇	1	1	yes	characteristic
850	C₂³	C₂³×D₇	1	1	yes	characteristic
851	Q₈	—	4	1	no	—
852	Q₈	—	14	2	no	—
853	Q₈	—	14	2	no	—
854	Q₈	—	14	2	no	—
855	Q₈	—	14	2	no	—
856	Q₈	—	28	1	no	—
857	Q₈	—	28	1	no	—
858	Q₈	—	28	1	no	—
859	Q₈	—	28	1	no	—
860	Q₈	—	28	1	no	—
861	Q₈	—	28	1	no	—
862	Q₈	—	28	1	no	—
863	Q₈	—	28	1	no	—
864	D₄	—	2	2	no	—
865	D₄	—	4	1	no	—
866	D₄	—	4	1	no	—
867	D₄	—	14	2	no	—
868	D₄	—	14	2	no	—
869	D₄	—	14	2	no	—
870	D₄	—	28	1	no	—
871	D₄	—	28	1	no	—
872	D₄	—	28	1	no	—
873	D₄	—	28	1	no	—
874	D₄	—	28	1	no	—
875	D₄	—	28	1	no	—
876	D₄	—	28	1	no	—
877	D₄	—	28	1	no	—
878	D₄	—	28	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	—	4	1	no	—
884	C₂×C₄	—	7	1	no	—
885	C₂×C₄	—	7	1	no	—
886	C₂×C₄	—	7	1	no	—
887	C₂×C₄	—	7	1	no	—
888	C₂×C₄	—	7	1	no	—
889	C₂×C₄	—	7	1	no	—
890	C₂×C₄	—	7	1	no	—
891	C₂×C₄	—	7	1	no	—
892	C₂×C₄	—	7	1	no	—
893	C₂×C₄	—	7	1	no	—
894	C₂×C₄	—	7	1	no	—
895	C₂×C₄	—	7	1	no	—
896	C₂×C₄	—	7	1	no	—
897	C₂×C₄	—	14	2	no	—
898	C₂×C₄	—	14	2	no	—
899	C₂×C₄	—	14	2	no	—
900	C₂×C₄	—	28	1	no	—
901	C₂×C₄	—	28	1	no	—
902	C₂×C₄	—	28	1	no	—
903	C₂×C₄	—	28	1	no	—
904	C₂×C₄	—	28	1	no	—
905	C₂×C₄	—	28	1	no	—
906	C₂×C₄	—	28	1	no	—
907	C₂×C₄	—	28	1	no	—
908	C₂×C₄	—	28	1	no	—
909	C₂×C₄	—	28	1	no	—
910	C₂×C₄	—	28	1	no	—
911	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
912	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
920	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
921	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
922	C₇	#3561	1	1	yes	characteristic, complemented, Sylow
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	2	1	no	—
932	C₂²	—	2	1	no	—
933	C₂²	—	2	1	no	—
934	C₂²	—	8	2	no	—
935	C₂²	—	14	1	no	—
936	C₂²	—	14	1	no	—
937	C₂²	—	14	1	no	—
938	C₂²	—	14	1	no	—
939	C₂²	—	14	1	no	—
940	C₂²	—	14	1	no	—
941	C₂²	—	14	1	no	—
942	C₂²	—	14	1	no	—
943	C₂²	—	14	1	no	—
944	C₂²	—	56	2	no	—
945	C₂²	#6554	1	2	yes	—
946	C₂²	C₂⁴×D₇	1	1	yes	characteristic
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	7	2	no	—
959	C₄	—	14	1	no	—
960	C₄	—	14	1	no	—
961	C₄	—	14	1	no	—
962	C₄	—	14	1	no	—
963	C₄	—	14	1	no	—
964	C₄	—	14	1	no	—
965	C₄	—	14	1	no	—
966	C₄	—	14	1	no	—
967	C₄	—	14	1	no	—
968	C₄	—	14	1	no	—
969	C₄	—	14	1	no	—
970	C₄	—	14	1	no	—
971	C₂	—	2	2	no	—
972	C₂	—	4	1	no	—
973	C₂	—	4	1	no	—
974	C₂	—	4	1	no	—
975	C₂	—	28	1	no	—
976	C₂	—	28	1	no	—
977	C₂	—	28	1	no	—
978	C₂	C₂×#6554	1	1	yes	characteristic
979	C₂	#90616	1	1	yes	characteristic
980	C₂	D₇×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#551	C₂
hypercenter	#551	D₇
hypocenter	C₇	#3561
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. #90403	C₂	semidirect
3. #90401	C₂	semidirect
4. #90401	C₂	semidirect
5. #90393	C₂	semidirect
6. #90368	C₂	semidirect
7. #90360	C₂	semidirect
8. #90358	C₂	semidirect
9. #90358	C₂	semidirect
10. #90353	C₂	semidirect
11. #90349	C₂	semidirect
12. #90340	C₂	semidirect
13. #90339	C₂	semidirect
14. #90337	C₂	semidirect
15. #90325	C₂	semidirect
16. #90323	C₂	semidirect
17. #90319	C₂	semidirect
18. #90284	C₂	semidirect
19. #90282	C₂	semidirect
20. #90252	C₂	semidirect
21. #90251	C₂	semidirect
22. #90243	C₂	semidirect
23. D₄×Dic₁₄	C₂	semidirect
24. #90225	C₂	semidirect
25. #90224	C₂	semidirect
26. #90218	C₂	semidirect
27. #90208	C₂	semidirect
28. #90186	C₂	semidirect
29. C₂×#6448	C₂	semidirect
30. #90181	C₂	semidirect
31. #90174	C₂	semidirect
33. C₂×Q₈×D₇	C₂²	semidirect
37. C₂²×Dic₁₄	C₂²	semidirect
38. C₇×#126	C₂²	semidirect
39. C₇×#126	C₂²	semidirect
40. C₇×#124	C₂²	semidirect
42. C₇×#123	C₂²	semidirect
43. C₇×#123	C₂²	semidirect
45. C₇×C₂²⋊Q₈	C₂²	semidirect
48. C₄×C₇×D₄	C₂²	semidirect
50. C₇×#117	C₂²	semidirect
56. #6509	C₂²	semidirect
57. #6509	C₂²	semidirect
58. #6507	C₂²	semidirect
62. #6502	C₂²	semidirect
64. #6501	C₂²	semidirect
66. #6499	C₂²	semidirect
67. #6498	C₂²	semidirect
71. #6493	C₂²	semidirect
74. #6492	C₂²	semidirect
81. #6487	C₂²	semidirect
82. #6487	C₂²	semidirect
83. #6487	C₂²	semidirect
84. #6487	C₂²	semidirect
85. #6487	C₂²	semidirect
87. #6461	C₂²	semidirect
88. #6461	C₂²	semidirect
89. #6461	C₂²	semidirect
90. #6461	C₂²	semidirect
91. #6461	C₂²	semidirect
92. #6460	C₂²	semidirect
93. #6460	C₂²	semidirect
94. #6460	C₂²	semidirect
95. #6460	C₂²	semidirect
96. #6459	C₂²	semidirect
97. #6459	C₂²	semidirect
98. #6459	C₂²	semidirect
99. #6459	C₂²	semidirect
100. #6459	C₂²	semidirect
101. #6459	C₂²	semidirect
102. #6459	C₂²	semidirect
103. #6457	C₂²	semidirect
104. #6457	C₂²	semidirect
105. #6457	C₂²	semidirect
106. #6455	C₂²	semidirect
107. #6455	C₂²	semidirect
108. #6453	C₂²	semidirect
109. #6453	C₂²	semidirect
110. #6452	C₂²	semidirect
111. #6451	C₂²	semidirect
112. #6451	C₂²	semidirect
113. #6451	C₂²	semidirect
114. #6451	C₂²	semidirect
115. #6451	C₂²	semidirect
116. #6451	C₂²	semidirect
117. #6450	C₂²	semidirect
118. #6450	C₂²	semidirect
120. #6449	C₂²	semidirect
121. #6449	C₂²	semidirect
132. #6448	C₂²	semidirect
133. #6448	C₂²	semidirect
134. #6448	C₂²	semidirect
135. #6448	C₂²	semidirect
136. #6448	C₂²	semidirect
139. #6447	C₂²	semidirect
142. #6446	C₂²	semidirect
143. #6446	C₂²	semidirect
144. #6446	C₂²	semidirect
149. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
150. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
151. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
154. #6442	C₂²	semidirect
155. #6442	C₂²	semidirect
156. #6442	C₂²	semidirect
157. #6442	C₂²	semidirect
158. #6442	C₂²	semidirect
166. #6441	C₂²	semidirect
167. #6441	C₂²	semidirect
168. #6441	C₂²	semidirect
169. #6441	C₂²	semidirect
170. #6441	C₂²	semidirect
171. #6441	C₂²	semidirect
172. #6441	C₂²	semidirect
173. #6440	C₂²	semidirect
174. #6440	C₂²	semidirect
175. #6439	C₂²	semidirect
176. #6439	C₂²	semidirect
177. #6438	C₂²	semidirect
178. #6438	C₂²	semidirect
179. C₄×D₂₈	C₂²	semidirect
180. #6435	C₂²	semidirect
181. #6432	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
358. #551	D₇	semidirect
490. #126	C₂×D₇	semidirect
491. #126	C₂×D₇	semidirect
513. #124	C₂×D₇	semidirect
530. #123	C₂×D₇	semidirect
531. #123	C₂×D₇	semidirect
566. C₂²⋊Q₈	C₂×D₇	semidirect
601. C₄×D₄	C₂×D₇	semidirect
609. #117	C₂×D₇	semidirect
922. C₇	#3561	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
#90403	2
#90401	2
#90393	2
#90368	2
#90360	2
#90358	2
#90353	2
#90349	2
#90340	2
#90339	2
#90337	2
#90325	2
#90323	2
#90319	2
#90284	2
#90282	2
#90252	2
#90251	2
#90243	2
D₄×Dic₁₄	2
#90225	2
#90224	2
#90218	2
#90208	2
#90186	2
C₂×#6448	2
#90181	2
#90174	2
#3561	7