Subgroups — #13322904

Order 1792.

692 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇×#431	C₂	1	1	yes	maximal, characteristic
2	C₂×#89609	C₂	1	1	yes	maximal, characteristic
3	#11735962	C₂	1	1	yes	maximal, characteristic
4	C₇×#1565	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728500	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728174	C₂	1	1	yes	maximal, characteristic, complemented
7	#11727604	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726329	C₂	1	2	yes	maximal, complemented
9	#11726326	C₂	1	2	yes	maximal, complemented
10	#11726289	C₂	1	2	yes	maximal, complemented
11	#11726286	C₂	1	2	yes	maximal, complemented
12	C₂²×#1131	—	2	1	no	—
13	C₂×C₄²×D₇	C₂²	1	1	yes	characteristic
14	C₇×#431	C₂²	1	1	yes	characteristic
15	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
17	#89898	C₄	1	1	yes	characteristic
18	#89898	C₄	1	1	yes	characteristic
19	#89890	C₄	1	1	yes	characteristic
20	#89890	C₄	1	1	yes	characteristic
21	C₂×Dic₇⋊C₈	—	2	1	no	—
22	#89697	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
24	C₄×#1136	C₂²	1	1	yes	characteristic
25	#89609	—	2	1	no	—
26	#89609	—	2	1	no	—
27	#89609	C₂²	1	2	yes	—
28	#89609	C₂²	1	2	yes	—
29	#89605	C₂²	1	1	yes	characteristic
30	#89605	C₂²	1	1	yes	characteristic
31	D₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	D₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	D₇×C₂²⋊C₈	—	2	1	no	—
34	#89490	—	2	1	no	—
35	#89477	C₄	1	2	yes	—
36	#89477	C₄	1	2	yes	—
37	#89457	—	2	1	no	—
38	#89457	C₂²	1	2	yes	—
39	#89457	C₂²	1	2	yes	—
40	C₄×C₈×D₇	—	2	1	no	—
41	C₇×#335	C₂²	1	2	yes	complemented
42	C₇×#334	C₂²	1	2	yes	complemented
43	#89275	C₂²	1	2	yes	complemented
44	#89275	C₂²	1	2	yes	complemented
45	#89274	C₂²	1	2	yes	complemented
46	#89274	C₂²	1	2	yes	complemented
47	#89253	C₂²	1	2	yes	complemented
48	#89252	C₂²	1	2	yes	complemented
49	#17809	—	7	1	no	maximal, Sylow
50	C₂²×C₄×D₇	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄×D₇	D₄	1	1	yes	characteristic
52	C₂²×C₄×D₇	Q₈	1	1	yes	characteristic
53	C₂×C₇×M₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₇×M₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₇×C₈	—	2	1	no	—
56	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₇	D₄	1	1	yes	characteristic
59	C₂×C₄×Dic₇	Q₈	1	1	yes	characteristic
60	C₂×#1136	C₂×C₄	1	1	yes	characteristic
61	C₂×#1136	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₇⋊C₈	—	2	1	no	—
63	C₂×#1131	—	2	2	no	—
64	C₂×#1131	—	2	2	no	—
65	C₂×#1131	—	4	4	no	—
66	C₂×C₈×D₇	—	2	1	no	—
67	C₂×C₈×D₇	—	2	1	no	—
68	C₄²×D₇	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₇	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₇	D₄	1	1	yes	characteristic
71	C₄²×D₇	D₄	1	1	yes	characteristic
72	C₄²×D₇	Q₈	1	1	yes	characteristic
73	C₄²×D₇	Q₈	1	1	yes	characteristic
74	C₄²×D₇	C₂³	1	1	yes	characteristic
75	C₄²×D₇	C₂³	1	1	yes	characteristic
76	C₇×C₄⋊C₈	—	2	1	no	—
77	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₇×C₄⋊C₈	C₂³	1	2	yes	—
80	C₇×C₂²⋊C₈	—	2	1	no	—
81	C₇×#97	C₂×C₄	1	2	yes	—
82	C₄×C₇×C₈	—	2	1	no	—
83	C₄×C₇×C₈	C₂³	1	2	yes	—
84	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
85	(C₂×D₇)⋊C₈	—	2	1	no	—
86	(C₂×D₇)⋊C₈	—	2	1	no	—
87	(C₂×D₇)⋊C₈	C₂×C₄	1	2	yes	—
88	(C₂×D₇)⋊C₈	C₂×C₄	1	2	yes	—
89	(C₂×D₇)⋊C₈	C₂×C₄	1	2	yes	—
90	(C₂×D₇)⋊C₈	C₂×C₄	1	2	yes	—
91	Dic₇⋊C₈	—	2	1	no	—
92	Dic₇⋊C₈	—	2	1	no	—
93	Dic₇⋊C₈	—	2	2	no	—
94	Dic₇⋊C₈	—	2	2	no	—
95	Dic₇⋊C₈	C₂×C₄	1	2	yes	—
96	Dic₇⋊C₈	C₂×C₄	1	2	yes	—
97	Dic₇⋊C₈	C₂×C₄	1	2	yes	—
98	Dic₇⋊C₈	C₂×C₄	1	2	yes	—
99	C₈×Dic₇	—	2	1	no	—
100	C₈×Dic₇	—	2	1	no	—
101	C₄⋊(C₇⋊C₈)	—	2	1	no	—
102	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
103	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
104	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
105	#6377	C₂×C₄	1	2	yes	—
106	C₄×C₇⋊C₈	—	2	1	no	—
107	C₄×C₇⋊C₈	C₂³	1	2	yes	—
108	#2920	—	7	1	no	—
109	C₂×#431	—	7	1	no	—
110	C₂×#423	—	7	1	no	—
111	#1574	—	7	2	no	—
112	#1574	—	7	2	no	—
113	#1571	—	7	2	no	—
114	#1570	—	7	2	no	—
115	#1565	—	7	1	no	—
116	#1565	—	7	1	no	—
117	#1565	—	7	1	no	—
118	#1565	D₇	1	1	yes	characteristic, complemented
119	C₂³×D₇	C₄⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
123	C₂²×Dic₇	C₄⋊C₄	1	1	yes	characteristic
124	C₂²×Dic₇	C₄⋊C₄	1	1	yes	characteristic
125	C₂²×Dic₇	C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×D₇	—	2	2	no	—
127	C₂×C₄×D₇	—	2	2	no	—
128	C₂×C₄×D₇	—	2	2	no	—
129	C₂×C₄×D₇	—	2	2	no	—
130	C₂×C₄×D₇	—	4	2	no	—
131	C₂×C₄×D₇	C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×D₇	C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×D₇	C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×D₇	C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×D₇	C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×D₇	C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
140	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₄×D₇	C₂×Q₈	1	1	yes	characteristic
142	C₂×C₄×D₇	C₂×Q₈	1	1	yes	characteristic
143	C₇×M₁₆	—	2	2	no	—
144	C₇×M₁₆	—	2	2	no	—
145	C₂×C₇×C₈	—	2	1	no	—
146	C₂×C₇×C₈	—	2	1	no	—
147	C₂×C₇×C₈	—	2	2	no	—
148	C₂×C₇×C₈	—	4	2	no	—
149	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
150	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
151	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₇	C₂×Q₈	1	1	yes	characteristic
154	C₄²×C₇	C₂⁴	1	1	yes	characteristic
155	C₄×Dic₇	C₄⋊C₄	1	1	yes	characteristic
156	C₄×Dic₇	C₄⋊C₄	1	1	yes	characteristic
157	C₄×Dic₇	C₄⋊C₄	1	1	yes	characteristic
158	C₄×Dic₇	C₄⋊C₄	1	1	yes	characteristic
159	C₄×Dic₇	C₄⋊C₄	1	1	yes	characteristic
160	C₄×Dic₇	C₄⋊C₄	1	1	yes	characteristic
161	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
162	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
163	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
164	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
165	C₄×Dic₇	C₂×Q₈	1	1	yes	characteristic
166	C₄×Dic₇	C₂×Q₈	1	1	yes	characteristic
167	#1136	—	2	2	no	—
168	#1136	—	2	2	no	—
169	C₂×C₇⋊C₈	—	2	1	no	—
170	C₂×C₇⋊C₈	—	2	1	no	—
171	C₂×C₇⋊C₈	—	2	2	no	—
172	C₂×C₇⋊C₈	—	4	2	no	—
173	C₂×C₇⋊C₈	C₂²×C₄	1	2	yes	—
174	C₂×C₇⋊C₈	C₂²×C₄	1	2	yes	—
175	#1131	—	4	4	no	—
176	#1131	—	4	4	no	—
177	C₈×D₇	—	4	2	no	—
178	C₈×D₇	—	4	2	no	—
179	C₂²×M₁₆	—	14	1	no	—
180	C₂²×C₄²	—	7	1	no	—
181	#432	—	7	2	no	—
182	#432	—	7	2	no	—
183	#431	—	7	2	no	—
184	#431	—	7	2	no	—
185	#431	—	7	1	no	—
186	#431	—	7	1	no	—
187	#431	—	7	1	no	—
188	#431	—	14	1	no	—
189	#431	—	14	1	no	—
190	#431	C₂×D₇	1	1	yes	characteristic
191	#423	—	7	1	no	—
192	#423	—	7	1	no	—
193	#423	—	7	2	no	—
194	#423	—	7	2	no	—
195	#423	—	14	1	no	—
196	#423	—	14	1	no	—
197	C₂×C₄⋊C₈	—	7	1	no	—
198	C₂×C₄⋊C₈	—	7	1	no	—
199	C₂×C₄⋊C₈	—	7	1	no	—
200	C₂×C₄⋊C₈	—	14	1	no	—
201	C₂×C₄⋊C₈	C₂×D₇	1	1	yes	characteristic
202	#407	—	7	1	no	—
203	#407	—	7	1	no	—
204	C₂×C₂²⋊C₈	—	14	1	no	—
205	C₄×M₁₆	—	7	1	no	—
206	C₄×M₁₆	C₂×D₇	1	1	yes	characteristic
207	C₂×C₄×C₈	—	14	1	no	—
208	#335	—	7	2	no	—
209	#335	—	7	2	no	—
210	#335	—	7	2	no	—
211	#335	C₂×D₇	1	2	yes	complemented
212	#334	—	7	2	no	—
213	#334	—	7	2	no	—
214	#334	—	7	2	no	—
215	#334	C₂×D₇	1	2	yes	complemented
216	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
217	C₂²×D₇	—	2	2	no	—
218	C₂²×D₇	—	2	2	no	—
219	C₂²×D₇	—	4	1	no	—
220	C₂²×D₇	C₂×C₄⋊C₄	1	1	yes	characteristic
221	C₂²×D₇	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₇	—	2	1	no	—
223	C₂×C₄×C₇	—	2	1	no	—
224	C₂×C₄×C₇	—	4	1	no	—
225	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₇	#131	1	2	yes	—
229	C₂×C₄×C₇	#131	1	2	yes	—
230	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
233	C₂×Dic₇	—	2	2	no	—
234	C₂×Dic₇	—	2	2	no	—
235	C₂×Dic₇	—	2	2	no	—
236	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
237	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
238	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
239	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
240	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
241	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₄×D₇	—	2	2	no	—
243	C₄×D₇	—	2	1	no	—
244	C₄×D₇	—	2	1	no	—
245	C₄×D₇	—	2	1	no	—
246	C₄×D₇	—	2	1	no	—
247	C₄×D₇	—	2	1	no	—
248	C₄×D₇	—	2	1	no	—
249	C₄×D₇	—	2	2	no	—
250	C₄×D₇	—	2	2	no	—
251	C₄×D₇	—	2	2	no	—
252	C₄×D₇	—	2	2	no	—
253	C₄×D₇	—	2	2	no	—
254	C₄×D₇	—	4	1	no	—
255	C₄×D₇	—	4	1	no	—
256	C₄×D₇	AGL(1,ℤ/8)	1	2	yes	—
257	C₄×D₇	#137	1	2	yes	—
258	C₇×C₈	—	2	2	no	—
259	C₇×C₈	—	2	2	no	—
260	C₇×C₈	—	4	1	no	—
261	C₇×C₈	—	4	2	no	—
262	C₇×C₈	—	4	1	no	—
263	C₇⋊C₈	—	2	2	no	—
264	C₇⋊C₈	—	2	2	no	—
265	C₇⋊C₈	—	4	1	no	—
266	C₇⋊C₈	—	4	2	no	—
267	C₇⋊C₈	—	4	1	no	—
268	C₂³×C₄	—	7	1	no	—
269	C₂³×C₄	—	7	1	no	—
270	C₂³×C₄	—	7	1	no	—
271	C₂×M₁₆	—	7	1	no	—
272	C₂×M₁₆	—	7	1	no	—
273	C₂×M₁₆	—	14	2	no	—
274	C₂×M₁₆	—	14	2	no	—
275	C₂×M₁₆	—	28	4	no	—
276	C₂×M₁₆	C₄×D₇	1	1	yes	characteristic
277	C₂×M₁₆	C₄×D₇	1	1	yes	characteristic
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	14	1	no	—
280	C₂²×C₈	—	14	1	no	—
281	C₂²×C₈	—	14	1	no	—
282	C₂×C₄²	—	7	1	no	—
283	C₂×C₄²	—	7	1	no	—
284	C₂×C₄²	—	7	1	no	—
285	C₂×C₄²	—	7	1	no	—
286	C₂×C₄²	—	7	1	no	—
287	C₂×C₄²	—	7	1	no	—
288	C₂×C₄²	—	7	1	no	—
289	C₂×C₄²	—	7	1	no	—
290	C₂×C₄²	—	7	1	no	—
291	C₂×C₄²	—	7	1	no	—
292	C₂×C₄²	—	7	1	no	—
293	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	7	2	no	—
296	C₄⋊C₈	—	7	2	no	—
297	C₄⋊C₈	—	7	2	no	—
298	C₄⋊C₈	—	7	2	no	—
299	C₄⋊C₈	—	7	1	no	—
300	C₄⋊C₈	—	7	2	no	—
301	C₄⋊C₈	—	7	1	no	—
302	C₄⋊C₈	—	14	1	no	—
303	C₄⋊C₈	—	14	1	no	—
304	C₄⋊C₈	—	14	2	no	—
305	C₄⋊C₈	—	14	2	no	—
306	C₄⋊C₈	—	14	1	no	—
307	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
308	C₄⋊C₈	C₂²×D₇	1	2	yes	—
309	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	—	7	2	no	—
312	C₂²⋊C₈	—	7	2	no	—
313	C₂²⋊C₈	—	7	2	no	—
314	C₂²⋊C₈	—	7	2	no	—
315	C₂²⋊C₈	—	14	1	no	—
316	C₂²⋊C₈	—	14	1	no	—
317	C₂²⋊C₈	—	14	1	no	—
318	#97	—	7	2	no	—
319	#97	C₄×D₇	1	2	yes	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	—	7	2	no	—
322	C₄×C₈	—	14	1	no	—
323	C₄×C₈	—	14	1	no	—
324	C₄×C₈	—	14	1	no	—
325	C₄×C₈	C₂²×D₇	1	2	yes	—
326	C₂²×C₇	—	2	1	no	—
327	C₂²×C₇	—	2	1	no	—
328	C₂²×C₇	#424	1	2	yes	—
329	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
330	C₂×D₇	—	2	1	no	—
331	C₂×D₇	—	2	1	no	—
332	C₂×D₇	—	2	1	no	—
333	C₂×D₇	—	2	1	no	—
334	C₂×D₇	—	2	1	no	—
335	C₂×D₇	—	4	4	no	—
336	C₂×D₇	#428	1	2	yes	—
337	C₄×C₇	—	2	1	no	—
338	C₄×C₇	—	2	1	no	—
339	C₄×C₇	—	2	1	no	—
340	C₄×C₇	#424	1	2	yes	—
341	C₄×C₇	C₂×#131	1	1	yes	characteristic
342	C₄×C₇	C₂×#131	1	1	yes	characteristic
343	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
344	C₄×C₇	C₂×#137	1	1	yes	characteristic
345	Dic₇	—	2	1	no	—
346	Dic₇	—	2	1	no	—
347	Dic₇	—	2	1	no	—
348	Dic₇	—	2	1	no	—
349	Dic₇	#428	1	2	yes	—
350	Dic₇	#430	1	2	yes	—
351	C₂⁴	—	7	1	no	—
352	C₂²×C₄	—	7	1	no	—
353	C₂²×C₄	—	7	1	no	—
354	C₂²×C₄	—	7	1	no	—
355	C₂²×C₄	—	7	1	no	—
356	C₂²×C₄	—	7	1	no	—
357	C₂²×C₄	—	7	1	no	—
358	C₂²×C₄	—	7	1	no	—
359	C₂²×C₄	—	7	1	no	—
360	C₂²×C₄	—	7	1	no	—
361	C₂²×C₄	—	7	1	no	—
362	C₂²×C₄	—	7	1	no	—
363	C₂²×C₄	—	7	1	no	—
364	C₂²×C₄	—	7	1	no	—
365	C₂²×C₄	—	7	1	no	—
366	C₂²×C₄	—	7	1	no	—
367	C₂²×C₄	—	14	2	no	—
368	C₂²×C₄	—	14	2	no	—
369	C₂²×C₄	—	14	2	no	—
370	C₂²×C₄	—	14	2	no	—
371	C₂²×C₄	—	28	2	no	—
372	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
373	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
374	C₂²×C₄	Q₈×D₇	1	1	yes	characteristic
375	M₁₆	—	2	2	no	—
376	M₁₆	—	2	2	no	—
377	M₁₆	—	14	2	no	—
378	M₁₆	—	14	2	no	—
379	M₁₆	—	28	4	no	—
380	M₁₆	—	28	4	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	4	2	no	—
385	C₂×C₈	—	7	2	no	—
386	C₂×C₈	—	7	2	no	—
387	C₂×C₈	—	14	1	no	—
388	C₂×C₈	—	14	1	no	—
389	C₂×C₈	—	14	2	no	—
390	C₂×C₈	—	28	2	no	—
391	C₂×C₈	—	28	2	no	—
392	C₂×C₈	—	28	2	no	—
393	C₂×C₈	C₂×C₄×D₇	1	2	yes	—
394	C₂×C₈	C₂×C₄×D₇	1	2	yes	—
395	C₄²	—	7	1	no	—
396	C₄²	—	7	1	no	—
397	C₄²	—	7	1	no	—
398	C₄²	—	7	1	no	—
399	C₄²	—	7	1	no	—
400	C₄²	—	7	1	no	—
401	C₄²	—	7	1	no	—
402	C₄²	—	7	1	no	—
403	C₄²	—	7	1	no	—
404	C₄²	—	7	1	no	—
405	C₄²	—	7	1	no	—
406	C₄²	—	7	1	no	—
407	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
408	C₄²	D₄×D₇	1	1	yes	characteristic
409	C₄²	Q₈×D₇	1	1	yes	characteristic
410	C₄²	C₂³×D₇	1	1	yes	characteristic
411	C₂×C₇	—	2	2	no	—
412	C₂×C₇	C₂×#424	1	1	yes	characteristic
413	C₂×C₇	C₂×#428	1	1	yes	characteristic
414	C₂×C₇	C₂×#430	1	1	yes	characteristic
415	D₇	—	2	2	no	—
416	D₇	—	4	1	no	—
417	C₂³	—	7	1	no	—
418	C₂³	—	7	1	no	—
419	C₂³	—	14	2	no	—
420	C₂³	—	14	2	no	—
421	C₂³	—	28	1	no	—
422	C₂³	D₇×C₄⋊C₄	1	1	yes	characteristic
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	7	1	no	—
427	C₂×C₄	—	7	1	no	—
428	C₂×C₄	—	7	2	no	—
429	C₂×C₄	—	7	2	no	—
430	C₂×C₄	—	7	1	no	—
431	C₂×C₄	—	7	1	no	—
432	C₂×C₄	—	7	1	no	—
433	C₂×C₄	—	7	1	no	—
434	C₂×C₄	—	14	2	no	—
435	C₂×C₄	—	14	2	no	—
436	C₂×C₄	—	14	2	no	—
437	C₂×C₄	—	14	2	no	—
438	C₂×C₄	—	14	2	no	—
439	C₂×C₄	—	14	2	no	—
440	C₂×C₄	—	14	2	no	—
441	C₂×C₄	—	14	2	no	—
442	C₂×C₄	—	14	2	no	—
443	C₂×C₄	—	14	1	no	—
444	C₂×C₄	—	14	1	no	—
445	C₂×C₄	—	14	1	no	—
446	C₂×C₄	—	14	1	no	—
447	C₂×C₄	—	14	1	no	—
448	C₂×C₄	—	14	1	no	—
449	C₂×C₄	—	28	1	no	—
450	C₂×C₄	—	28	1	no	—
451	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
452	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
453	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
454	C₂×C₄	#6464	1	2	yes	—
455	C₂×C₄	#6470	1	2	yes	—
456	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
457	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
458	C₂×C₄	C₂×Q₈×D₇	1	1	yes	characteristic
459	C₈	—	2	2	no	—
460	C₈	—	2	2	no	—
461	C₈	—	4	2	no	—
462	C₈	—	4	1	no	—
463	C₈	—	4	1	no	—
464	C₈	—	14	2	no	—
465	C₈	—	14	2	no	—
466	C₈	—	28	1	no	—
467	C₈	—	28	2	no	—
468	C₈	—	28	1	no	—
469	C₇	#17809	1	1	yes	characteristic, complemented, Sylow
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	7	2	no	—
473	C₂²	—	14	1	no	—
474	C₂²	—	14	1	no	—
475	C₂²	—	14	1	no	—
476	C₂²	—	14	1	no	—
477	C₂²	—	14	1	no	—
478	C₂²	—	28	4	no	—
479	C₂²	#89611	1	2	yes	—
480	C₂²	C₂×D₇×C₄⋊C₄	1	1	yes	characteristic
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	7	2	no	—
485	C₄	—	7	2	no	—
486	C₄	—	14	1	no	—
487	C₄	—	14	1	no	—
488	C₄	—	14	1	no	—
489	C₄	—	14	1	no	—
490	C₄	#89611	1	2	yes	—
491	C₄	C₂×#6464	1	1	yes	characteristic
492	C₄	C₂×#6470	1	1	yes	characteristic
493	C₄	D₇×AGL(1,ℤ/8)	1	1	yes	characteristic
494	C₄	D₇×#137	1	1	yes	characteristic
495	C₂	—	2	2	no	—
496	C₂	—	14	2	no	—
497	C₂	—	28	1	no	—
498	C₂	C₂×#89611	1	1	yes	characteristic
499	C₂	D₇×#428	1	1	yes	characteristic
500	C₂	D₇×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting	C₇×#1565	C₂
socle	C₂²×C₇	C₂²×C₄⋊C₄
prime radical	C₂³×D₇	C₄⋊C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1565	D₇
hypocenter	C₇	#17809
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
4. C₇×#1565	C₂	semidirect
5. #11728500	C₂	semidirect
6. #11728174	C₂	semidirect
7. #11727604	C₂	semidirect
8. #11726329	C₂	semidirect
9. #11726326	C₂	semidirect
10. #11726289	C₂	semidirect
11. #11726286	C₂	semidirect
41. C₇×#335	C₂²	semidirect
42. C₇×#334	C₂²	semidirect
43. #89275	C₂²	semidirect
44. #89275	C₂²	semidirect
45. #89274	C₂²	semidirect
46. #89274	C₂²	semidirect
47. #89253	C₂²	semidirect
48. #89252	C₂²	semidirect
118. #1565	D₇	semidirect
211. #335	C₂×D₇	semidirect
215. #334	C₂×D₇	semidirect
469. C₇	#17809	semidirect

Maximal subgroups

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

subgroup	index
D₇×#431	2
C₂×#89609	2
#11735962	2
C₇×#1565	2
#11728500	2
#11728174	2
#11727604	2
#11726329	2
#11726326	2
#11726289	2
#11726286	2
#17809	7