Subgroups — #13324316

Order 1792.

682 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11737403	C₂	1	1	yes	maximal, characteristic, complemented
2	#11737107	C₂	1	1	yes	maximal, characteristic
3	#11736983	C₂	1	1	yes	maximal, characteristic
4	C₇×#1590	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728704	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₁₆×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728620	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726283	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726270	C₂	1	1	yes	maximal, characteristic, complemented
10	#11725994	C₂	1	1	yes	maximal, characteristic, complemented
11	#11725966	C₂	1	1	yes	maximal, characteristic, complemented
12	#11725930	C₂	1	1	yes	maximal, characteristic
13	#11725903	C₂	1	1	yes	maximal, characteristic, complemented
14	#11725809	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈²×D₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#6470	—	2	1	no	—
17	#90269	C₂²	1	1	yes	characteristic
18	#90239	C₂²	1	1	yes	characteristic
19	C₇×#446	C₂²	1	1	yes	characteristic
20	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
21	C₇×#436	C₂²	1	1	yes	characteristic
22	#89947	C₄	1	1	yes	characteristic
23	#89943	C₄	1	1	yes	characteristic
24	#89900	—	2	1	no	—
25	C₄×#1143	C₂²	1	1	yes	characteristic
26	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₄×#1142	C₂²	1	1	yes	characteristic
28	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
29	#89636	C₄	1	1	yes	characteristic
30	#89627	C₄	1	1	yes	characteristic
31	#89611	—	2	1	no	—
32	#89609	C₂²	1	1	yes	characteristic
33	#89609	C₂²	1	1	yes	characteristic
34	#89606	C₂²	1	1	yes	characteristic
35	#89602	—	2	1	no	—
36	#89602	C₂²	1	1	yes	characteristic
37	#89579	C₄	1	1	yes	characteristic
38	#89564	C₄	1	1	yes	characteristic
39	#89550	C₄	1	1	yes	characteristic
40	#89532	C₄	1	1	yes	characteristic
41	#89499	—	2	1	no	—
42	(C₂²⋊D₇)⋊C₈	—	2	1	no	—
43	#89480	—	2	1	no	—
44	#89473	—	2	1	no	—
45	C₄×#1132	C₂²	1	1	yes	characteristic
46	#89460	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
48	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
50	#89451	C₂²	1	1	yes	characteristic
51	C₇×#334	C₂²	1	1	yes	characteristic
52	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
53	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₇×C₈²	C₂²	1	1	yes	characteristic
55	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
56	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
57	#89279	C₂²	1	1	yes	characteristic
58	#89278	C₂²	1	1	yes	characteristic
59	#89275	C₂²	1	1	yes	characteristic
60	#89275	C₂²	1	1	yes	characteristic
61	#89254	C₂²	1	1	yes	characteristic
62	#89252	C₂²	1	1	yes	characteristic
63	#89251	C₂²	1	1	yes	characteristic
64	C₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
65	C₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
66	C₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
67	#17957	—	7	1	no	maximal, Sylow
68	C₂×#1157	—	2	1	no	—
69	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₇×M₁₆	—	2	1	no	—
71	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
72	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
73	#6509	C₂×C₄	1	1	yes	characteristic
74	#6507	C₂×C₄	1	1	yes	characteristic
75	C₂×#1143	C₂×C₄	1	1	yes	characteristic
76	#6503	C₂×C₄	1	1	yes	characteristic
77	#6501	C₂×C₄	1	1	yes	characteristic
78	C₂×#1142	C₂×C₄	1	1	yes	characteristic
79	C₄×C₂²⋊D₇	—	2	1	no	—
80	C₂²×C₇⋊C₈	—	2	1	no	—
81	#6470	—	4	4	no	—
82	C₂×#1132	C₂×C₄	1	1	yes	characteristic
83	C₂×#1131	—	2	1	no	—
84	C₂×#1131	—	2	1	no	—
85	C₂×#1131	—	2	1	no	—
86	C₂×C₈×D₇	—	2	1	no	—
87	C₂×C₈×D₇	—	2	1	no	—
88	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
89	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₈×D₇	D₄	1	1	yes	characteristic
91	C₂×C₈×D₇	D₄	1	1	yes	characteristic
92	#6460	C₂×C₄	1	1	yes	characteristic
93	#6459	—	2	1	no	—
94	#6458	C₂×C₄	1	1	yes	characteristic
95	#6452	—	2	1	no	—
96	#6451	C₂×C₄	1	1	yes	characteristic
97	#6451	C₂×C₄	1	1	yes	characteristic
98	#6448	—	2	1	no	—
99	#6447	—	2	1	no	—
100	C₄×D₂₈	C₂³	1	1	yes	characteristic
101	#6435	—	2	1	no	—
102	C₄²×D₇	C₂³	1	1	yes	characteristic
103	C₄×Dic₁₄	—	2	1	no	—
104	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
105	C₇×#106	C₂×C₄	1	1	yes	characteristic
106	C₇×C₄⋊C₈	—	2	1	no	—
107	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
108	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
109	C₇×#103	C₂×C₄	1	1	yes	characteristic
110	C₇×#102	C₂×C₄	1	1	yes	characteristic
111	C₇×C₂²⋊C₈	—	2	1	no	—
112	C₇×#97	—	2	1	no	—
113	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
114	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
115	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
116	#6409	C₂×C₄	1	1	yes	characteristic
117	#6406	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
119	#6395	C₂×C₄	1	1	yes	characteristic
120	(C₂×D₇)⋊C₈	—	2	1	no	—
121	(C₂×D₇)⋊C₈	—	2	1	no	—
122	#6391	C₂×C₄	1	1	yes	characteristic
123	#6390	C₂×C₄	1	1	yes	characteristic
124	#6389	—	2	1	no	—
125	Dic₇⋊C₈	—	2	1	no	—
126	Dic₇⋊C₈	—	2	1	no	—
127	Dic₇⋊C₈	—	2	1	no	—
128	Dic₇⋊C₈	—	2	1	no	—
129	C₈×Dic₇	—	2	1	no	—
130	C₈×Dic₇	—	2	1	no	—
131	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
132	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
133	C₈×Dic₇	D₄	1	1	yes	characteristic
134	C₈×Dic₇	D₄	1	1	yes	characteristic
135	#6384	C₂×C₄	1	1	yes	characteristic
136	#6383	C₂×C₄	1	1	yes	characteristic
137	#6382	C₂×C₄	1	1	yes	characteristic
138	#6382	C₂×C₄	1	1	yes	characteristic
139	C₄⋊(C₇⋊C₈)	—	2	1	no	—
140	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
141	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
142	C₄×C₇⋊C₈	—	2	1	no	—
143	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
144	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
145	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
146	#3167	—	7	1	no	—
147	#2960	—	7	1	no	—
148	#2931	—	7	1	no	—
149	#1590	—	7	1	no	—
150	#1590	—	7	1	no	—
151	#1590	—	7	1	no	—
152	#1590	D₇	1	1	yes	characteristic, complemented
153	C₈×SD₁₆	—	7	1	no	—
154	C₈×SD₁₆	—	7	1	no	—
155	C₈×SD₁₆	—	7	1	no	—
156	C₈×SD₁₆	—	7	1	no	—
157	#1566	—	7	1	no	—
158	#1493	—	7	1	no	—
159	#1492	—	7	1	no	—
160	C₂×C₈²	—	7	1	no	—
161	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₇	—	2	1	no	—
164	C₂×C₂²⋊D₇	—	2	1	no	—
165	C₂×C₂²⋊D₇	—	2	1	no	—
166	C₂×C₂²⋊D₇	—	2	1	no	—
167	#1157	—	4	2	no	—
168	#1157	—	4	2	no	—
169	C₂×D₂₈	—	2	1	no	—
170	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄×D₇	—	2	1	no	—
172	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
174	C₂×C₄×D₇	#41	1	1	yes	characteristic
175	C₂×Dic₁₄	—	2	1	no	—
176	C₂×Dic₁₄	—	2	1	no	—
177	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
178	C₇×SD₁₆	—	2	2	no	—
179	C₇×M₁₆	—	4	2	no	—
180	C₂×C₇×C₈	—	2	1	no	—
181	C₂×C₇×C₈	—	2	1	no	—
182	C₂×C₇×C₈	—	2	1	no	—
183	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
186	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
187	C₇×C₄⋊C₄	—	2	1	no	—
188	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
189	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
190	C₇×C₂²⋊C₄	—	2	1	no	—
191	C₄²×C₇	—	2	1	no	—
192	C₄²×C₇	C₂⁴	1	1	yes	characteristic
193	C₂²⋊Dic₇	—	2	1	no	—
194	#1143	—	2	2	no	—
195	#1142	—	2	2	no	—
196	(C₂×D₇)⋊C₄	—	2	1	no	—
197	(C₂×D₇)⋊C₄	—	2	1	no	—
198	(C₂×D₇)⋊C₄	—	2	1	no	—
199	(C₂×D₇)⋊C₄	—	2	1	no	—
200	C₄⋊Dic₇	—	2	1	no	—
201	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
202	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
203	Dic₇⋊C₄	—	2	1	no	—
204	Dic₇⋊C₄	—	2	1	no	—
205	Dic₇⋊C₄	—	2	1	no	—
206	Dic₇⋊C₄	—	2	1	no	—
207	Dic₇⋊C₄	—	2	1	no	—
208	Dic₇⋊C₄	—	2	1	no	—
209	C₄×Dic₇	—	2	1	no	—
210	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
211	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
212	C₄×Dic₇	#41	1	1	yes	characteristic
213	C₂×C₇⋊C₈	—	2	1	no	—
214	C₂×C₇⋊C₈	—	2	1	no	—
215	C₂×C₇⋊C₈	—	2	1	no	—
216	C₂×C₇⋊C₈	—	4	2	no	—
217	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
220	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
221	#1132	—	2	2	no	—
222	#1131	—	4	2	no	—
223	#1131	—	4	2	no	—
224	#1131	—	4	2	no	—
225	C₈×D₇	—	2	4	no	—
226	C₈×D₇	—	2	2	no	—
227	C₈×D₇	—	2	2	no	—
228	C₈×D₇	—	2	2	no	—
229	C₈×D₇	—	4	2	no	—
230	C₈×D₇	SD₁₆	1	4	yes	complemented
231	C₂×#131	—	14	1	no	—
232	#533	—	7	1	no	—
233	#532	—	7	1	no	—
234	#498	—	7	1	no	—
235	#492	—	7	1	no	—
236	#487	—	7	1	no	—
237	#486	—	7	1	no	—
238	#465	—	7	1	no	—
239	#465	—	7	1	no	—
240	#465	—	7	1	no	—
241	#465	—	7	1	no	—
242	#446	—	7	1	no	—
243	#446	—	14	1	no	—
244	#446	C₂×D₇	1	1	yes	characteristic
245	C₈×Q₈	—	7	1	no	—
246	C₈×Q₈	—	7	1	no	—
247	C₈×Q₈	—	14	1	no	—
248	C₄×SD₁₆	—	7	1	no	—
249	C₄×SD₁₆	—	7	1	no	—
250	C₄×SD₁₆	—	7	1	no	—
251	C₄×SD₁₆	C₂×D₇	1	1	yes	characteristic
252	#436	—	7	1	no	—
253	#436	—	14	1	no	—
254	#436	C₂×D₇	1	1	yes	characteristic
255	C₈×D₄	—	7	1	no	—
256	C₈×D₄	—	7	1	no	—
257	C₈×D₄	—	14	1	no	—
258	#424	—	14	1	no	—
259	#423	—	7	1	no	—
260	#423	—	7	1	no	—
261	#408	—	14	1	no	—
262	#405	—	14	1	no	—
263	C₂×C₄×C₈	—	7	1	no	—
264	C₂×C₄×C₈	—	7	1	no	—
265	C₂×C₄×C₈	—	7	1	no	—
266	#334	—	7	1	no	—
267	#334	—	7	1	no	—
268	#334	—	7	1	no	—
269	#334	C₂×D₇	1	1	yes	characteristic
270	Q₈⋊C₈	—	7	1	no	—
271	Q₈⋊C₈	—	7	1	no	—
272	Q₈⋊C₈	—	7	1	no	—
273	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic
274	D₄⋊C₈	—	7	1	no	—
275	D₄⋊C₈	—	7	1	no	—
276	D₄⋊C₈	—	7	1	no	—
277	D₄⋊C₈	C₂×D₇	1	1	yes	characteristic
278	C₈²	—	7	1	no	—
279	C₈²	—	7	1	no	—
280	C₈²	—	7	1	no	—
281	C₈²	C₂×D₇	1	1	yes	characteristic
282	C₂³×C₇	—	2	1	no	—
283	C₂²×D₇	—	2	1	no	—
284	C₂²×D₇	C₄×D₄	1	1	yes	characteristic
285	C₇×Q₈	—	2	1	no	—
286	C₇×Q₈	—	2	1	no	—
287	C₇×D₄	—	2	1	no	—
288	C₇×D₄	—	2	1	no	—
289	C₂×C₄×C₇	—	2	1	no	—
290	C₂×C₄×C₇	—	2	1	no	—
291	C₂×C₄×C₇	—	2	1	no	—
292	C₂×C₄×C₇	—	4	1	no	—
293	C₂×C₄×C₇	—	4	1	no	—
294	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
295	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
297	C₂²⋊D₇	—	4	2	no	—
298	C₂²⋊D₇	—	4	2	no	—
299	C₂²⋊D₇	—	4	2	no	—
300	C₂×Dic₇	—	2	1	no	—
301	C₂×Dic₇	—	2	1	no	—
302	C₂×Dic₇	—	2	1	no	—
303	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
304	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
305	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
306	D₂₈	—	2	1	no	—
307	D₂₈	—	2	1	no	—
308	D₂₈	—	4	2	no	—
309	C₄×D₇	—	2	1	no	—
310	C₄×D₇	—	2	1	no	—
311	C₄×D₇	—	2	2	no	—
312	C₄×D₇	—	4	1	no	—
313	C₄×D₇	—	4	1	no	—
314	C₄×D₇	C₂×SD₁₆	1	2	yes	—
315	C₄×D₇	#135	1	2	yes	—
316	Dic₁₄	—	2	1	no	—
317	Dic₁₄	—	2	1	no	—
318	Dic₁₄	—	4	2	no	—
319	Dic₁₄	—	4	2	no	—
320	C₇×C₈	—	2	2	no	—
321	C₇×C₈	—	2	1	no	—
322	C₇×C₈	—	2	1	no	—
323	C₇×C₈	—	4	1	no	—
324	C₇×C₈	—	4	1	no	—
325	C₇×C₈	#131	1	2	yes	complemented
326	C₇×C₈	C₂×SD₁₆	1	2	yes	—
327	C₇⋊C₈	—	2	2	no	—
328	C₇⋊C₈	—	2	1	no	—
329	C₇⋊C₈	—	2	1	no	—
330	C₇⋊C₈	—	4	1	no	—
331	C₇⋊C₈	—	4	1	no	—
332	C₇⋊C₈	#131	1	2	yes	complemented
333	C₇⋊C₈	C₂×SD₁₆	1	2	yes	—
334	C₂×#41	—	14	1	no	—
335	C₂×SD₁₆	—	7	1	no	—
336	C₂×SD₁₆	—	7	1	no	—
337	C₂×SD₁₆	—	7	1	no	—
338	C₂×SD₁₆	C₄×D₇	1	1	yes	characteristic
339	#131	—	28	4	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	14	1	no	—
342	C₂×M₁₆	—	14	1	no	—
343	C₂×M₁₆	—	14	1	no	—
344	C₂²×C₈	—	7	1	no	—
345	C₂²×C₈	—	7	1	no	—
346	C₂²×C₈	—	7	1	no	—
347	C₂²×C₈	—	7	1	no	—
348	C₂²×C₈	—	14	1	no	—
349	C₂²×C₈	—	14	1	no	—
350	C₂²×C₈	—	14	1	no	—
351	C₄⋊Q₈	—	7	1	no	—
352	C₄⋊Q₈	—	7	1	no	—
353	C₄⋊Q₈	—	7	1	no	—
354	#127	—	7	1	no	—
355	#125	—	14	1	no	—
356	#124	—	14	1	no	—
357	C₂²⋊Q₈	—	7	1	no	—
358	C₂²⋊Q₈	—	7	1	no	—
359	C₂²⋊Q₈	—	14	1	no	—
360	#121	—	7	1	no	—
361	#121	—	7	1	no	—
362	#121	—	14	1	no	—
363	C₄×Q₈	—	7	1	no	—
364	C₄×Q₈	—	14	1	no	—
365	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
366	C₄×D₄	—	7	1	no	—
367	C₄×D₄	—	14	1	no	—
368	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
369	#117	—	14	1	no	—
370	C₂×C₄²	—	7	1	no	—
371	#106	—	7	1	no	—
372	#106	—	7	1	no	—
373	#106	—	7	1	no	—
374	#106	C₄×D₇	1	1	yes	characteristic
375	C₄⋊C₈	—	2	1	no	—
376	C₄⋊C₈	—	7	1	no	—
377	C₄⋊C₈	—	7	1	no	—
378	C₄⋊C₈	—	14	1	no	—
379	C₄⋊C₈	—	14	1	no	—
380	C₄⋊C₈	—	14	1	no	—
381	C₄⋊C₈	—	14	1	no	—
382	C₄⋊C₈	—	14	1	no	—
383	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
384	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
385	#103	—	7	1	no	—
386	#103	—	7	1	no	—
387	#103	—	7	1	no	—
388	#103	C₄×D₇	1	1	yes	characteristic
389	#102	—	7	1	no	—
390	#102	—	7	1	no	—
391	#102	—	7	1	no	—
392	#102	C₄×D₇	1	1	yes	characteristic
393	C₂²⋊C₈	—	2	1	no	—
394	C₂²⋊C₈	—	14	1	no	—
395	C₂²⋊C₈	—	14	1	no	—
396	C₂²⋊C₈	—	14	1	no	—
397	#97	—	2	1	no	—
398	#97	—	14	1	no	—
399	C₄×C₈	—	7	1	no	—
400	C₄×C₈	—	7	1	no	—
401	C₄×C₈	—	7	1	no	—
402	C₄×C₈	—	7	1	no	—
403	C₄×C₈	—	7	1	no	—
404	C₄×C₈	—	7	1	no	—
405	C₄×C₈	—	7	1	no	—
406	C₄×C₈	—	14	1	no	—
407	C₄×C₈	—	14	1	no	—
408	C₄×C₈	—	14	1	no	—
409	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
410	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
411	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
412	C₂²×C₇	—	4	1	no	—
413	C₂²×C₇	—	4	1	no	—
414	C₂²×C₇	—	4	1	no	—
415	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
416	C₂×D₇	—	2	1	no	—
417	C₂×D₇	—	2	1	no	—
418	C₂×D₇	—	4	1	no	—
419	C₂×D₇	—	4	1	no	—
420	C₂×D₇	—	4	1	no	—
421	C₂×D₇	C₄×SD₁₆	1	2	yes	—
422	C₄×C₇	—	2	1	no	—
423	C₄×C₇	—	4	1	no	—
424	C₄×C₇	—	4	1	no	—
425	C₄×C₇	—	4	1	no	—
426	C₄×C₇	C₂×#131	1	1	yes	characteristic
427	C₄×C₇	C₂×#131	1	1	yes	characteristic
428	C₄×C₇	C₂²×SD₁₆	1	1	yes	characteristic
429	C₄×C₇	C₂×#135	1	1	yes	characteristic
430	Dic₇	—	2	1	no	—
431	Dic₇	—	4	1	no	—
432	Dic₇	—	4	1	no	—
433	Dic₇	—	4	1	no	—
434	Dic₇	C₄×SD₁₆	1	2	yes	—
435	Dic₇	#443	1	2	yes	—
436	#41	—	28	2	no	—
437	#41	—	28	2	no	—
438	C₂×Q₈	—	7	1	no	—
439	C₂×Q₈	—	14	1	no	—
440	C₂×Q₈	—	14	1	no	—
441	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
442	C₂×D₄	—	7	1	no	—
443	C₂×D₄	—	14	1	no	—
444	C₂×D₄	—	14	1	no	—
445	C₂×D₄	—	14	1	no	—
446	C₂×D₄	—	14	1	no	—
447	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	7	1	no	—
450	C₂²×C₄	—	7	1	no	—
451	C₂²×C₄	—	7	1	no	—
452	C₂²×C₄	—	14	1	no	—
453	SD₁₆	—	2	2	no	—
454	SD₁₆	—	14	2	no	—
455	SD₁₆	—	14	2	no	—
456	SD₁₆	—	14	2	no	—
457	M₁₆	—	4	2	no	—
458	M₁₆	—	28	2	no	—
459	M₁₆	—	28	2	no	—
460	M₁₆	—	28	2	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	7	1	no	—
465	C₂×C₈	—	7	1	no	—
466	C₂×C₈	—	7	4	no	—
467	C₂×C₈	—	7	1	no	—
468	C₂×C₈	—	7	1	no	—
469	C₂×C₈	—	14	2	no	—
470	C₂×C₈	—	14	2	no	—
471	C₂×C₈	—	14	4	no	—
472	C₂×C₈	—	14	1	no	—
473	C₂×C₈	—	14	2	no	—
474	C₂×C₈	—	14	1	no	—
475	C₂×C₈	—	14	1	no	—
476	C₂×C₈	—	28	2	no	—
477	C₂×C₈	—	28	2	no	—
478	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
479	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
480	C₂×C₈	D₄×D₇	1	1	yes	characteristic
481	C₂×C₈	D₄×D₇	1	1	yes	characteristic
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	7	1	no	—
484	C₄⋊C₄	—	7	1	no	—
485	C₄⋊C₄	—	14	1	no	—
486	C₄⋊C₄	—	14	1	no	—
487	C₄⋊C₄	—	14	1	no	—
488	C₄⋊C₄	—	14	1	no	—
489	C₄⋊C₄	—	14	1	no	—
490	C₄⋊C₄	—	14	1	no	—
491	C₄⋊C₄	—	14	1	no	—
492	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
493	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	14	1	no	—
496	C₂²⋊C₄	—	14	1	no	—
497	C₂²⋊C₄	—	14	1	no	—
498	C₂²⋊C₄	—	14	1	no	—
499	C₂²⋊C₄	—	14	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	7	1	no	—
502	C₄²	—	7	1	no	—
503	C₄²	—	7	1	no	—
504	C₄²	—	14	1	no	—
505	C₄²	C₂³×D₇	1	1	yes	characteristic
506	C₂×C₇	—	8	1	no	—
507	C₂×C₇	#2931	1	1	yes	characteristic
508	C₂×C₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
509	C₂×C₇	C₂×#443	1	1	yes	characteristic
510	D₇	—	2	2	no	—
511	D₇	—	8	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	7	1	no	—
514	C₂³	—	14	1	no	—
515	Q₈	—	2	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	14	1	no	—
518	Q₈	—	14	1	no	—
519	Q₈	—	28	2	no	—
520	Q₈	—	28	2	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	14	1	no	—
524	D₄	—	14	1	no	—
525	D₄	—	28	2	no	—
526	D₄	—	28	2	no	—
527	D₄	—	28	2	no	—
528	D₄	—	28	2	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	7	1	no	—
535	C₂×C₄	—	7	1	no	—
536	C₂×C₄	—	7	2	no	—
537	C₂×C₄	—	7	2	no	—
538	C₂×C₄	—	7	1	no	—
539	C₂×C₄	—	14	2	no	—
540	C₂×C₄	—	14	1	no	—
541	C₂×C₄	—	14	1	no	—
542	C₂×C₄	—	14	1	no	—
543	C₂×C₄	—	14	1	no	—
544	C₂×C₄	—	14	1	no	—
545	C₂×C₄	—	28	1	no	—
546	C₂×C₄	—	28	1	no	—
547	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
548	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
549	C₂×C₄	D₇×#41	1	1	yes	characteristic
550	C₈	—	2	2	no	—
551	C₈	—	2	1	no	—
552	C₈	—	2	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	7	2	no	—
556	C₈	—	7	2	no	—
557	C₈	—	14	2	no	—
558	C₈	—	14	1	no	—
559	C₈	—	14	1	no	—
560	C₈	—	28	1	no	—
561	C₈	—	28	1	no	—
562	C₈	#6470	1	2	yes	complemented
563	C₈	D₇×SD₁₆	1	2	yes	—
564	C₇	#17957	1	1	yes	characteristic, complemented, Sylow
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	7	2	no	—
569	C₂²	—	14	1	no	—
570	C₂²	—	14	1	no	—
571	C₂²	—	28	1	no	—
572	C₂²	—	28	1	no	—
573	C₂²	—	28	1	no	—
574	C₂²	C₄×D₄×D₇	1	1	yes	characteristic
575	C₄	—	2	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	7	2	no	—
580	C₄	—	7	2	no	—
581	C₄	—	14	1	no	—
582	C₄	—	28	1	no	—
583	C₄	—	28	1	no	—
584	C₄	—	28	1	no	—
585	C₄	C₂×#6470	1	1	yes	characteristic
586	C₄	D₇×#131	1	1	yes	characteristic
587	C₄	C₂×D₇×SD₁₆	1	1	yes	characteristic
588	C₄	D₇×#135	1	1	yes	characteristic
589	C₂	—	8	1	no	—
590	C₂	—	14	2	no	—
591	C₂	—	56	1	no	—
592	C₂	#11736983	1	1	yes	characteristic
593	C₂	C₄×D₇×SD₁₆	1	1	yes	characteristic
594	C₂	D₇×#443	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×#1590	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	#90239	C₂²
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1590	D₇
hypocenter	C₇	#17957
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1590

Complements

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

N	H ≅ G/N	type
1. #11737403	C₂	semidirect
4. C₇×#1590	C₂	semidirect
5. #11728704	C₂	semidirect
6. SD₁₆×C₇⋊C₈	C₂	semidirect
7. #11728620	C₂	semidirect
8. #11726283	C₂	semidirect
9. #11726270	C₂	semidirect
10. #11725994	C₂	semidirect
11. #11725966	C₂	semidirect
13. #11725903	C₂	semidirect
14. #11725809	C₂	semidirect
15. C₈²×D₇	C₂	semidirect
152. #1590	D₇	semidirect
230. C₈×D₇	SD₁₆	semidirect
325. C₇×C₈	#131	semidirect
332. C₇⋊C₈	#131	semidirect
562. C₈	#6470	semidirect
564. C₇	#17957	semidirect

Maximal subgroups

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

subgroup	index
#11737403	2
#11737107	2
#11736983	2
C₇×#1590	2
#11728704	2
SD₁₆×C₇⋊C₈	2
#11728620	2
#11726283	2
#11726270	2
#11725994	2
#11725966	2
#11725930	2
#11725903	2
#11725809	2
C₈²×D₇	2
#17957	7