Subgroups — #11743324

Order 896.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	#90525	C₂	1	1	yes	maximal, characteristic, complemented
3	#90522	C₂	1	1	yes	maximal, characteristic, complemented
4	#90520	C₂	1	1	yes	maximal, characteristic, complemented
5	#90515	C₂	1	1	yes	maximal, characteristic, complemented
6	#90422	C₂	1	1	yes	maximal, characteristic, complemented
7	#90415	C₂	1	1	yes	maximal, characteristic, complemented
8	#90410	C₂	1	1	yes	maximal, characteristic, complemented
9	#90406	C₂	1	1	yes	maximal, characteristic, complemented
10	#90372	C₂	1	1	yes	maximal, characteristic, complemented
11	#90368	C₂	1	1	yes	maximal, characteristic, complemented
12	#90367	C₂	1	1	yes	maximal, characteristic, complemented
13	#90362	C₂	1	1	yes	maximal, characteristic, complemented
14	#90312	C₂	1	2	yes	maximal, complemented
15	#90311	C₂	1	2	yes	maximal, complemented
16	#90306	C₂	1	2	yes	maximal, complemented
17	#90304	C₂	1	2	yes	maximal, complemented
18	#90255	C₂	1	2	yes	maximal, complemented
19	#90251	C₂	1	2	yes	maximal, complemented
20	#90247	C₂	1	2	yes	maximal, complemented
21	#90231	C₂	1	2	yes	maximal, complemented
22	#90170	C₂	1	1	yes	maximal, characteristic, complemented
23	#90170	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#41	C₂²	1	1	yes	characteristic
25	C₂×C₇×#41	C₂²	1	1	yes	characteristic, complemented
26	C₂×#1161	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×#1159	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
30	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₇×#127	C₂²	1	1	yes	characteristic
32	C₇×#124	C₂²	1	1	yes	characteristic
33	C₇×#124	C₂²	1	1	yes	characteristic, complemented
34	C₇×#121	C₂²	1	2	yes	complemented
35	C₇×#121	C₂²	1	2	yes	complemented
36	C₄×C₇×D₄	C₂²	1	2	yes	complemented
37	C₄×C₇×D₄	C₂²	1	2	yes	complemented
38	C₂×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
39	#6510	C₂²	1	1	yes	characteristic
40	#6509	C₂²	1	1	yes	characteristic
41	#6509	C₂²	1	1	yes	characteristic
42	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
44	#6507	C₂²	1	1	yes	characteristic, complemented
45	#6503	C₂²	1	1	yes	characteristic
46	#6503	C₂²	1	2	yes	complemented
47	#6502	C₂²	1	2	yes	—
48	#6502	C₂²	1	2	yes	—
49	#6502	C₂²	1	2	yes	—
50	#6502	C₂²	1	2	yes	—
51	#6502	C₂²	1	2	yes	complemented
52	#6502	C₂²	1	2	yes	complemented
53	#6501	C₂²	1	1	yes	characteristic
54	#6501	C₂²	1	1	yes	characteristic, complemented
55	#6501	C₂²	1	2	yes	complemented
56	#6501	C₂²	1	2	yes	complemented
57	#6500	C₂²	1	2	yes	—
58	#6500	C₂²	1	2	yes	—
59	#6500	C₂²	1	2	yes	—
60	#6499	C₂²	1	1	yes	characteristic
61	#6499	C₂²	1	2	yes	complemented
62	#6498	C₂²	1	2	yes	complemented
63	#6498	C₂²	1	2	yes	complemented
64	#6498	C₂²	1	2	yes	complemented
65	D₄×Dic₇	C₂²	1	1	yes	characteristic
66	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
67	#6493	C₂²	1	1	yes	characteristic
68	#6493	C₂²	1	1	yes	characteristic
69	#6493	C₂²	1	2	yes	complemented
70	#6492	C₂²	1	1	yes	characteristic
71	#6492	C₂²	1	2	yes	—
72	#6492	C₂²	1	2	yes	—
73	#6492	C₂²	1	1	yes	characteristic, complemented
74	#6492	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
78	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
79	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
80	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
81	#6487	C₂²	1	1	yes	characteristic, complemented
82	#6487	C₂²	1	1	yes	characteristic, complemented
83	#6487	C₂²	1	2	yes	complemented
84	C₂×Dic₇⋊C₄	C₂²	1	2	yes	complemented
85	#6461	C₂²	1	2	yes	—
86	#6461	C₂²	1	2	yes	—
87	#6459	C₂²	1	2	yes	complemented
88	#6459	C₂²	1	2	yes	complemented
89	#6457	C₂²	1	2	yes	complemented
90	#6457	C₂²	1	2	yes	complemented
91	#6452	C₂²	1	2	yes	complemented
92	#6452	C₂²	1	2	yes	complemented
93	#6449	C₂²	1	2	yes	complemented
94	#6448	C₂²	1	2	yes	—
95	#6448	C₂²	1	2	yes	complemented
96	#6447	C₂²	1	2	yes	—
97	#6447	C₂²	1	2	yes	—
98	#6446	C₂²	1	2	yes	—
99	#6446	C₂²	1	2	yes	complemented
100	#6445	C₂²	1	2	yes	—
101	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
102	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
103	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
104	#6442	C₂²	1	2	yes	complemented
105	#6442	C₂²	1	2	yes	complemented
106	#6441	C₂²	1	2	yes	complemented
107	#6441	C₂²	1	2	yes	complemented
108	#6440	C₂²	1	2	yes	complemented
109	#6439	C₂²	1	1	yes	characteristic
110	#6439	C₂²	1	1	yes	characteristic, complemented
111	#6439	C₂²	1	2	yes	complemented
112	#6438	C₂²	1	1	yes	characteristic
113	#6438	C₂²	1	1	yes	characteristic
114	C₄×D₂₈	C₂²	1	1	yes	characteristic
115	C₄×D₂₈	C₂²	1	1	yes	characteristic
116	#6435	C₂²	1	1	yes	characteristic
117	#6435	C₂²	1	1	yes	characteristic, complemented
118	#6435	C₂²	1	2	yes	complemented
119	#6433	C₂²	1	1	yes	characteristic, complemented
120	#6433	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
123	#3562	—	7	1	no	maximal, Sylow
124	C₂³×D₇	C₂³	1	2	yes	—
125	C₇×#41	—	4	2	no	—
126	C₇×#41	—	4	2	no	—
127	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
128	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
129	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
130	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
131	C₂×C₇×D₄	C₂³	1	2	yes	—
132	C₂×C₇×D₄	C₂³	1	2	yes	—
133	C₂×C₇×D₄	C₂³	1	2	yes	—
134	C₂×C₇×D₄	C₂³	1	2	yes	—
135	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₇	C₂³	1	2	yes	—
137	C₂²×C₄×C₇	C₂³	1	2	yes	—
138	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
149	C₂²×Dic₇	C₂³	1	2	yes	—
150	C₂²×Dic₇	C₂³	1	2	yes	—
151	C₂²×Dic₇	C₂³	1	2	yes	—
152	#1161	—	4	2	no	—
153	Q₈×D₇	—	4	2	no	—
154	#1159	—	4	2	no	—
155	D₄×D₇	—	4	2	no	—
156	C₂×D₂₈	C₂³	1	1	yes	characteristic
157	C₂×D₂₈	C₂³	1	1	yes	characteristic
158	C₂×D₂₈	C₂³	1	2	yes	—
159	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₇	C₂³	1	2	yes	—
162	C₂×C₄×D₇	C₂³	1	2	yes	—
163	C₂×C₄×D₇	C₂³	1	2	yes	—
164	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
165	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
166	C₂×Dic₁₄	C₂³	1	2	yes	—
167	C₇×C₄⋊C₄	C₂³	1	2	yes	—
168	C₇×C₄⋊C₄	C₂³	1	2	yes	—
169	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₄²×C₇	C₂³	1	1	yes	characteristic
174	C₄²×C₇	C₂³	1	1	yes	characteristic
175	C₄²×C₇	C₂³	1	1	yes	characteristic
176	C₄²×C₇	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₇	C₂³	1	2	yes	—
178	C₂²⋊Dic₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₇	C₂³	1	2	yes	—
182	C₂²⋊Dic₇	C₂³	1	2	yes	—
183	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₇	C₂³	1	2	yes	—
186	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
202	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₇	C₂³	1	2	yes	—
207	C₄⋊Dic₇	C₂³	1	2	yes	—
208	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
209	Dic₇⋊C₄	C₂³	1	2	yes	—
210	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₇⋊C₄	C₂³	1	2	yes	—
213	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₇⋊C₄	C₂³	1	2	yes	—
216	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
217	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
219	Dic₇⋊C₄	C₂³	1	2	yes	—
220	Dic₇⋊C₄	C₂³	1	2	yes	—
221	Dic₇⋊C₄	C₂³	1	2	yes	—
222	Dic₇⋊C₄	C₂³	1	2	yes	—
223	Dic₇⋊C₄	C₂³	1	2	yes	—
224	C₄×Dic₇	C₂³	1	1	yes	characteristic
225	C₄×Dic₇	C₂³	1	2	yes	—
226	C₄×Dic₇	C₂³	1	1	yes	characteristic
227	C₄×Dic₇	C₂³	1	2	yes	—
228	C₄×Dic₇	C₂³	1	2	yes	—
229	#562	—	7	2	no	—
230	#560	—	7	2	no	—
231	#559	—	7	1	no	—
232	#556	—	7	1	no	—
233	#553	—	7	2	no	—
234	#551	—	7	2	no	—
235	#550	—	7	1	no	—
236	#548	—	7	1	no	—
237	#548	—	7	1	no	—
238	#547	—	7	1	no	—
239	#546	—	7	1	no	—
240	#546	—	7	1	no	—
241	#541	—	7	1	no	—
242	#540	—	7	1	no	—
243	#540	—	7	2	no	—
244	#539	—	7	2	no	—
245	#538	—	7	2	no	—
246	#538	—	7	2	no	—
247	#536	—	7	1	no	—
248	#535	—	7	1	no	—
249	#532	D₇	1	1	yes	characteristic, complemented
250	#529	—	7	1	no	—
251	#529	—	7	1	no	—
252	C₂³×C₇	C₂⁴	1	2	yes	—
253	C₂³×C₇	C₂⁴	1	1	yes	characteristic
254	C₂³×C₇	C₂⁴	1	2	yes	—
255	C₂²×D₇	—	4	2	no	—
256	C₂²×D₇	—	4	2	no	—
257	C₂²×D₇	—	4	2	no	—
258	C₂²×D₇	C₂⁴	1	1	yes	characteristic
259	C₂²×D₇	C₂⁴	1	2	yes	—
260	C₂²×D₇	C₂⁴	1	1	yes	characteristic
261	C₇×Q₈	—	2	2	no	—
262	C₇×Q₈	—	2	2	no	—
263	C₇×D₄	—	2	2	no	—
264	C₇×D₄	—	2	2	no	—
265	C₇×D₄	—	4	2	no	—
266	C₇×D₄	—	4	2	no	—
267	C₇×D₄	—	4	2	no	—
268	C₇×D₄	—	4	2	no	—
269	C₂×C₄×C₇	—	2	2	no	—
270	C₂×C₄×C₇	—	4	1	no	—
271	C₂×C₄×C₇	—	4	1	no	—
272	C₂×C₄×C₇	—	4	2	no	—
273	C₂×C₄×C₇	—	4	2	no	—
274	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₇	C₂⁴	1	2	yes	—
276	C₂×C₄×C₇	C₂⁴	1	2	yes	—
277	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
282	C₂²⋊D₇	—	4	2	no	—
283	C₂²⋊D₇	—	4	2	no	—
284	C₂²⋊D₇	—	4	2	no	—
285	C₂²⋊D₇	—	4	2	no	—
286	C₂²⋊D₇	—	4	1	no	—
287	C₂²⋊D₇	—	4	2	no	—
288	C₂²⋊D₇	—	4	2	no	—
289	C₂²⋊D₇	—	4	2	no	—
290	C₂²⋊D₇	—	4	1	no	—
291	C₂×Dic₇	—	4	2	no	—
292	C₂×Dic₇	—	4	2	no	—
293	C₂×Dic₇	—	4	2	no	—
294	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
295	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
296	C₂×Dic₇	C₂⁴	1	2	yes	—
297	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
298	C₂×Dic₇	C₂⁴	1	2	yes	—
299	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₇	C₂⁴	1	2	yes	—
301	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
302	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
303	D₂₈	—	2	2	no	—
304	D₂₈	—	4	1	no	—
305	D₂₈	—	4	2	no	—
306	C₄×D₇	—	2	2	no	—
307	C₄×D₇	—	2	2	no	—
308	C₄×D₇	—	4	2	no	—
309	C₄×D₇	—	4	2	no	—
310	C₄×D₇	—	4	2	no	—
311	Dic₁₄	—	2	2	no	—
312	Dic₁₄	—	4	1	no	—
313	Dic₁₄	—	4	2	no	—
314	C₂×#41	—	7	1	no	—
315	C₂×#41	—	7	1	no	—
316	C₂×#41	C₂×D₇	1	1	yes	characteristic
317	C₂×#41	C₂×D₇	1	1	yes	characteristic, complemented
318	C₂²×Q₈	—	7	1	no	—
319	C₂²×D₄	—	7	1	no	—
320	C₄⋊Q₈	—	7	1	no	—
321	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
322	#127	—	7	1	no	—
323	#127	—	7	2	no	—
324	#127	C₂×D₇	1	1	yes	characteristic
325	#126	—	7	2	no	—
326	#126	—	7	2	no	—
327	#126	—	7	2	no	—
328	#126	—	7	2	no	—
329	#126	—	7	2	no	—
330	#126	—	7	1	no	—
331	#126	—	7	1	no	—
332	#125	—	7	2	no	—
333	#125	—	7	2	no	—
334	#125	—	7	1	no	—
335	#125	—	7	1	no	—
336	#124	—	7	1	no	—
337	#124	—	7	1	no	—
338	#124	—	7	2	no	—
339	#124	—	7	2	no	—
340	#124	—	7	2	no	—
341	#124	—	7	1	no	—
342	#124	—	7	1	no	—
343	#124	C₂×D₇	1	1	yes	characteristic
344	#124	C₂×D₇	1	1	yes	characteristic, complemented
345	#123	—	7	2	no	—
346	#123	—	7	2	no	—
347	#123	—	7	2	no	—
348	#123	—	7	1	no	—
349	#123	—	7	1	no	—
350	#123	—	7	2	no	—
351	#123	—	7	2	no	—
352	#123	—	7	2	no	—
353	#123	—	7	2	no	—
354	#123	—	7	2	no	—
355	#123	—	7	2	no	—
356	#123	—	7	2	no	—
357	#123	—	7	2	no	—
358	C₂²⋊Q₈	—	7	1	no	—
359	C₂²⋊Q₈	—	7	1	no	—
360	C₂²⋊Q₈	—	7	1	no	—
361	C₂²⋊Q₈	—	7	1	no	—
362	C₂²⋊Q₈	—	7	2	no	—
363	C₂²⋊Q₈	—	7	2	no	—
364	C₂²⋊Q₈	—	7	2	no	—
365	C₂²⋊Q₈	—	7	2	no	—
366	C₂²⋊Q₈	—	7	2	no	—
367	#121	—	7	2	no	—
368	#121	—	7	2	no	—
369	#121	—	7	2	no	—
370	#121	—	7	2	no	—
371	#121	—	7	2	no	—
372	#121	—	7	1	no	—
373	#121	—	7	2	no	—
374	#121	—	7	1	no	—
375	#121	—	7	2	no	—
376	#121	—	7	2	no	—
377	#121	—	7	1	no	—
378	#121	—	7	1	no	—
379	#121	—	7	2	no	—
380	#121	—	7	2	no	—
381	#121	—	7	2	no	—
382	#121	C₂×D₇	1	2	yes	complemented
383	#121	C₂×D₇	1	2	yes	complemented
384	#120	—	7	2	no	—
385	#120	—	7	2	no	—
386	#120	—	7	2	no	—
387	#120	—	7	2	no	—
388	C₄×Q₈	—	7	1	no	—
389	C₄×Q₈	—	7	1	no	—
390	C₄×Q₈	—	7	1	no	—
391	C₄×Q₈	—	7	1	no	—
392	C₄×D₄	—	7	1	no	—
393	C₄×D₄	—	7	1	no	—
394	C₄×D₄	—	7	2	no	—
395	C₄×D₄	—	7	1	no	—
396	C₄×D₄	—	7	1	no	—
397	C₄×D₄	—	7	2	no	—
398	C₄×D₄	—	7	2	no	—
399	C₄×D₄	—	7	2	no	—
400	C₄×D₄	—	7	2	no	—
401	C₄×D₄	—	7	1	no	—
402	C₄×D₄	—	7	1	no	—
403	C₄×D₄	C₂×D₇	1	2	yes	complemented
404	C₄×D₄	C₂×D₇	1	2	yes	complemented
405	#117	—	7	2	no	—
406	#117	—	7	1	no	—
407	#117	—	7	1	no	—
408	#117	—	7	2	no	—
409	C₂×C₄⋊C₄	—	7	2	no	—
410	C₂×C₂²⋊C₄	—	7	2	no	—
411	C₂×C₂²⋊C₄	—	7	2	no	—
412	C₂×C₄²	C₂×D₇	1	1	yes	characteristic, complemented
413	C₂²×C₇	—	2	2	no	—
414	C₂²×C₇	—	2	2	no	—
415	C₂²×C₇	—	2	1	no	—
416	C₂²×C₇	—	2	2	no	—
417	C₂²×C₇	—	2	2	no	—
418	C₂²×C₇	—	2	1	no	—
419	C₂²×C₇	—	2	1	no	—
420	C₂²×C₇	—	2	2	no	—
421	C₂²×C₇	—	2	2	no	—
422	C₂²×C₇	C₂⁵	1	1	yes	characteristic
423	C₂×D₇	—	2	1	no	—
424	C₂×D₇	—	2	1	no	—
425	C₂×D₇	—	2	2	no	—
426	C₂×D₇	—	2	2	no	—
427	C₂×D₇	—	2	1	no	—
428	C₂×D₇	—	2	1	no	—
429	C₂×D₇	—	2	1	no	—
430	C₂×D₇	—	2	2	no	—
431	C₂×D₇	—	2	1	no	—
432	C₂×D₇	—	8	4	no	—
433	C₄×C₇	—	2	2	no	—
434	C₄×C₇	—	2	2	no	—
435	C₄×C₇	—	2	1	no	—
436	C₄×C₇	—	2	1	no	—
437	C₄×C₇	—	2	1	no	—
438	C₄×C₇	—	2	1	no	—
439	C₄×C₇	—	2	1	no	—
440	C₄×C₇	H(5,𝔽₂)	1	2	yes	—
441	Dic₇	—	2	2	no	—
442	Dic₇	—	2	1	no	—
443	Dic₇	—	2	1	no	—
444	Dic₇	—	2	1	no	—
445	Dic₇	—	2	1	no	—
446	Dic₇	—	2	2	no	—
447	Dic₇	—	2	1	no	—
448	Dic₇	—	2	2	no	—
449	Dic₇	—	2	1	no	—
450	C₂⁴	—	7	2	no	—
451	#41	—	4	2	no	—
452	#41	—	4	2	no	—
453	#41	—	28	2	no	—
454	#41	—	28	2	no	—
455	C₂×Q₈	—	7	1	no	—
456	C₂×Q₈	—	7	1	no	—
457	C₂×Q₈	—	7	2	no	—
458	C₂×Q₈	—	28	2	no	—
459	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
460	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
461	C₂×D₄	—	7	1	no	—
462	C₂×D₄	—	7	2	no	—
463	C₂×D₄	—	7	2	no	—
464	C₂×D₄	—	7	2	no	—
465	C₂×D₄	—	7	2	no	—
466	C₂×D₄	—	7	2	no	—
467	C₂×D₄	—	7	1	no	—
468	C₂×D₄	—	7	2	no	—
469	C₂×D₄	—	7	2	no	—
470	C₂×D₄	—	7	1	no	—
471	C₂×D₄	—	7	1	no	—
472	C₂×D₄	—	7	2	no	—
473	C₂×D₄	—	28	2	no	—
474	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
475	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
476	C₂×D₄	C₂²×D₇	1	2	yes	—
477	C₂×D₄	C₂²×D₇	1	2	yes	—
478	C₂×D₄	C₂²×D₇	1	2	yes	—
479	C₂×D₄	C₂²×D₇	1	2	yes	—
480	C₂²×C₄	—	7	2	no	—
481	C₂²×C₄	—	7	2	no	—
482	C₂²×C₄	—	7	2	no	—
483	C₂²×C₄	—	7	1	no	—
484	C₂²×C₄	—	7	1	no	—
485	C₂²×C₄	—	7	2	no	—
486	C₂²×C₄	—	7	2	no	—
487	C₂²×C₄	—	7	2	no	—
488	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
489	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
490	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
491	C₂²×C₄	C₂²×D₇	1	2	yes	—
492	C₂²×C₄	C₂²×D₇	1	2	yes	—
493	C₄⋊C₄	—	7	1	no	—
494	C₄⋊C₄	—	7	2	no	—
495	C₄⋊C₄	—	7	2	no	—
496	C₄⋊C₄	—	7	2	no	—
497	C₄⋊C₄	—	7	1	no	—
498	C₄⋊C₄	—	7	1	no	—
499	C₄⋊C₄	—	7	1	no	—
500	C₄⋊C₄	—	7	2	no	—
501	C₄⋊C₄	—	7	1	no	—
502	C₄⋊C₄	—	7	1	no	—
503	C₄⋊C₄	—	7	2	no	—
504	C₄⋊C₄	—	7	1	no	—
505	C₄⋊C₄	—	7	1	no	—
506	C₄⋊C₄	—	7	2	no	—
507	C₄⋊C₄	—	7	2	no	—
508	C₄⋊C₄	—	7	2	no	—
509	C₄⋊C₄	—	7	1	no	—
510	C₄⋊C₄	—	7	1	no	—
511	C₄⋊C₄	—	7	1	no	—
512	C₄⋊C₄	—	7	2	no	—
513	C₄⋊C₄	—	7	2	no	—
514	C₄⋊C₄	—	7	1	no	—
515	C₄⋊C₄	C₂²×D₇	1	2	yes	—
516	C₄⋊C₄	C₂²×D₇	1	2	yes	—
517	C₂²⋊C₄	—	7	2	no	—
518	C₂²⋊C₄	—	7	2	no	—
519	C₂²⋊C₄	—	7	2	no	—
520	C₂²⋊C₄	—	7	2	no	—
521	C₂²⋊C₄	—	7	1	no	—
522	C₂²⋊C₄	—	7	2	no	—
523	C₂²⋊C₄	—	7	2	no	—
524	C₂²⋊C₄	—	7	1	no	—
525	C₂²⋊C₄	—	7	2	no	—
526	C₂²⋊C₄	—	7	1	no	—
527	C₂²⋊C₄	—	7	1	no	—
528	C₂²⋊C₄	—	7	2	no	—
529	C₂²⋊C₄	—	7	2	no	—
530	C₂²⋊C₄	—	7	2	no	—
531	C₂²⋊C₄	—	7	2	no	—
532	C₂²⋊C₄	—	7	1	no	—
533	C₂²⋊C₄	—	7	1	no	—
534	C₂²⋊C₄	—	7	2	no	—
535	C₂²⋊C₄	—	7	1	no	—
536	C₂²⋊C₄	—	7	1	no	—
537	C₂²⋊C₄	—	7	1	no	—
538	C₂²⋊C₄	—	7	1	no	—
539	C₂²⋊C₄	—	7	2	no	—
540	C₂²⋊C₄	—	7	2	no	—
541	C₂²⋊C₄	—	7	2	no	—
542	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
546	C₄²	—	7	2	no	—
547	C₄²	—	7	1	no	—
548	C₄²	—	7	1	no	—
549	C₄²	—	7	2	no	—
550	C₄²	—	7	2	no	—
551	C₄²	C₂²×D₇	1	1	yes	characteristic
552	C₄²	C₂²×D₇	1	1	yes	characteristic
553	C₄²	C₂²×D₇	1	1	yes	characteristic
554	C₄²	C₂²×D₇	1	1	yes	characteristic
555	C₂×C₇	—	4	2	no	—
556	C₂×C₇	—	4	2	no	—
557	C₂×C₇	—	4	1	no	—
558	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
559	C₂×C₇	#585	1	1	yes	characteristic
560	C₂×C₇	#585	1	1	yes	characteristic
561	D₇	—	4	1	no	—
562	D₇	—	4	2	no	—
563	D₇	—	4	1	no	—
564	C₂³	—	7	1	no	—
565	C₂³	—	7	2	no	—
566	C₂³	—	7	1	no	—
567	C₂³	—	28	2	no	—
568	C₂³	—	28	2	no	—
569	C₂³	—	28	2	no	—
570	C₂³	C₂³×D₇	1	2	yes	—
571	C₂³	C₂³×D₇	1	1	yes	characteristic
572	C₂³	C₂³×D₇	1	2	yes	—
573	Q₈	—	2	2	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	14	2	no	—
576	Q₈	—	28	1	no	—
577	Q₈	—	28	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	14	2	no	—
585	D₄	—	28	1	no	—
586	D₄	—	28	2	no	—
587	D₄	—	28	1	no	—
588	D₄	—	28	2	no	—
589	D₄	—	28	2	no	—
590	D₄	—	28	2	no	—
591	D₄	—	28	1	no	—
592	D₄	—	28	2	no	—
593	D₄	—	28	2	no	—
594	D₄	—	28	2	no	—
595	D₄	—	28	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	7	1	no	—
602	C₂×C₄	—	7	1	no	—
603	C₂×C₄	—	7	2	no	—
604	C₂×C₄	—	7	1	no	—
605	C₂×C₄	—	7	1	no	—
606	C₂×C₄	—	7	2	no	—
607	C₂×C₄	—	7	2	no	—
608	C₂×C₄	—	7	1	no	—
609	C₂×C₄	—	7	1	no	—
610	C₂×C₄	—	14	2	no	—
611	C₂×C₄	—	14	2	no	—
612	C₂×C₄	—	28	2	no	—
613	C₂×C₄	—	28	2	no	—
614	C₂×C₄	—	28	2	no	—
615	C₂×C₄	—	28	2	no	—
616	C₂×C₄	—	28	2	no	—
617	C₂×C₄	—	28	2	no	—
618	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₇	1	2	yes	—
620	C₂×C₄	C₂³×D₇	1	2	yes	—
621	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
626	C₇	#3562	1	1	yes	characteristic, complemented, Sylow
627	C₂²	—	2	1	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	14	1	no	—
637	C₂²	—	14	1	no	—
638	C₂²	—	14	2	no	—
639	C₂²	—	14	2	no	—
640	C₂²	—	14	1	no	—
641	C₂²	—	14	1	no	—
642	C₂²	—	14	2	no	—
643	C₂²	—	14	1	no	—
644	C₂²	—	14	1	no	—
645	C₂²	—	56	4	no	—
646	C₂²	C₂⁴×D₇	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	14	1	no	—
655	C₄	—	14	1	no	—
656	C₄	—	14	2	no	—
657	C₄	—	14	2	no	—
658	C₄	—	14	1	no	—
659	C₄	—	14	1	no	—
660	C₄	—	14	2	no	—
661	C₄	—	14	1	no	—
662	C₄	—	14	1	no	—
663	C₄	#6548	1	2	yes	—
664	C₂	—	4	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	2	no	—
667	C₂	—	28	1	no	—
668	C₂	—	28	2	no	—
669	C₂	—	28	1	no	—
670	C₂	C₂×#6548	1	1	yes	characteristic
671	C₂	#90616	1	1	yes	characteristic
672	C₂	#90616	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#532	C₂
hypercenter	#532	D₇
hypocenter	C₇	#3562
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₇×#532	C₂	semidirect
2. #90525	C₂	semidirect
3. #90522	C₂	semidirect
4. #90520	C₂	semidirect
5. #90515	C₂	semidirect
6. #90422	C₂	semidirect
7. #90415	C₂	semidirect
8. #90410	C₂	semidirect
9. #90406	C₂	semidirect
10. #90372	C₂	semidirect
11. #90368	C₂	semidirect
12. #90367	C₂	semidirect
13. #90362	C₂	semidirect
14. #90312	C₂	semidirect
15. #90311	C₂	semidirect
16. #90306	C₂	semidirect
17. #90304	C₂	semidirect
18. #90255	C₂	semidirect
19. #90251	C₂	semidirect
20. #90247	C₂	semidirect
21. #90231	C₂	semidirect
22. #90170	C₂	semidirect
23. #90170	C₂	semidirect
25. C₂×C₇×#41	C₂²	semidirect
27. C₂×Q₈×D₇	C₂²	semidirect
30. C₇×C₄⋊Q₈	C₂²	semidirect
33. C₇×#124	C₂²	semidirect
34. C₇×#121	C₂²	semidirect
35. C₇×#121	C₂²	semidirect
36. C₄×C₇×D₄	C₂²	semidirect
37. C₄×C₇×D₄	C₂²	semidirect
38. C₂×C₄²×C₇	C₂²	semidirect
42. Q₈×Dic₇	C₂²	semidirect
43. Q₈×Dic₇	C₂²	semidirect
44. #6507	C₂²	semidirect
46. #6503	C₂²	semidirect
51. #6502	C₂²	semidirect
52. #6502	C₂²	semidirect
54. #6501	C₂²	semidirect
55. #6501	C₂²	semidirect
56. #6501	C₂²	semidirect
61. #6499	C₂²	semidirect
62. #6498	C₂²	semidirect
63. #6498	C₂²	semidirect
64. #6498	C₂²	semidirect
66. D₄×Dic₇	C₂²	semidirect
69. #6493	C₂²	semidirect
73. #6492	C₂²	semidirect
74. #6492	C₂²	semidirect
76. C₄×C₂²⋊D₇	C₂²	semidirect
77. C₄×C₂²⋊D₇	C₂²	semidirect
78. C₄×C₂²⋊D₇	C₂²	semidirect
79. C₄×C₂²⋊D₇	C₂²	semidirect
81. #6487	C₂²	semidirect
82. #6487	C₂²	semidirect
83. #6487	C₂²	semidirect
84. C₂×Dic₇⋊C₄	C₂²	semidirect
87. #6459	C₂²	semidirect
88. #6459	C₂²	semidirect
89. #6457	C₂²	semidirect
90. #6457	C₂²	semidirect
91. #6452	C₂²	semidirect
92. #6452	C₂²	semidirect
93. #6449	C₂²	semidirect
95. #6448	C₂²	semidirect
99. #6446	C₂²	semidirect
101. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
102. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
104. #6442	C₂²	semidirect
105. #6442	C₂²	semidirect
106. #6441	C₂²	semidirect
107. #6441	C₂²	semidirect
108. #6440	C₂²	semidirect
110. #6439	C₂²	semidirect
111. #6439	C₂²	semidirect
117. #6435	C₂²	semidirect
118. #6435	C₂²	semidirect
119. #6433	C₂²	semidirect
120. #6433	C₂²	semidirect
121. C₄×Dic₁₄	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
249. #532	D₇	semidirect
317. C₂×#41	C₂×D₇	semidirect
321. C₄⋊Q₈	C₂×D₇	semidirect
344. #124	C₂×D₇	semidirect
382. #121	C₂×D₇	semidirect
383. #121	C₂×D₇	semidirect
403. C₄×D₄	C₂×D₇	semidirect
404. C₄×D₄	C₂×D₇	semidirect
412. C₂×C₄²	C₂×D₇	semidirect
626. C₇	#3562	semidirect

Maximal subgroups

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

subgroup	index
C₇×#532	2
#90525	2
#90522	2
#90520	2
#90515	2
#90422	2
#90415	2
#90410	2
#90406	2
#90372	2
#90368	2
#90367	2
#90362	2
#90312	2
#90311	2
#90306	2
#90304	2
#90255	2
#90251	2
#90247	2
#90231	2
#90170	2
#3562	7