Subgroups — #13324697

Order 1792.

680 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11737405	C₂	1	1	yes	maximal, characteristic, complemented
2	#11737096	C₂	1	1	yes	maximal, characteristic
3	#11736985	C₂	1	1	yes	maximal, characteristic
4	C₇×#1590	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728707	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728650	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728618	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726286	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726273	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	D₇×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
13	#11725915	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#1132	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×#1131	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₇×M₁₆	—	2	1	no	—
17	#90269	C₂²	1	1	yes	characteristic
18	C₄×D₄×D₇	C₂²	1	1	yes	characteristic
19	C₇×#446	C₂²	1	1	yes	characteristic, complemented
20	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
21	C₇×#436	C₂²	1	1	yes	characteristic
22	#89941	C₄	1	1	yes	characteristic
23	#89934	C₄	1	1	yes	characteristic
24	#89899	—	2	1	no	—
25	C₄×#1143	C₂²	1	1	yes	characteristic
26	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
27	C₄×#1142	C₂²	1	1	yes	characteristic
28	#89784	C₂²	1	1	yes	characteristic
29	#89642	C₄	1	1	yes	characteristic
30	#89634	C₄	1	1	yes	characteristic
31	#89611	—	2	1	no	—
32	#89609	C₂²	1	1	yes	characteristic
33	#89606	C₂²	1	1	yes	characteristic
34	D₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	#89603	—	2	1	no	—
36	#89603	C₂²	1	1	yes	characteristic, complemented
37	#89590	C₄	1	1	yes	characteristic
38	#89577	C₄	1	1	yes	characteristic
39	#89548	C₄	1	1	yes	characteristic
40	#89533	C₄	1	1	yes	characteristic
41	#89500	—	2	1	no	—
42	#89498	—	2	1	no	—
43	#89480	—	2	1	no	—
44	#89473	—	2	1	no	—
45	C₄×#1132	C₂²	1	1	yes	characteristic
46	C₄×#1131	C₂²	1	1	yes	characteristic
47	C₈×D₂₈	C₂²	1	1	yes	characteristic
48	#89457	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
50	C₈×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
51	C₇×#334	C₂²	1	1	yes	characteristic, complemented
52	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₇×C₈²	C₂²	1	1	yes	characteristic, complemented
55	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
56	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
57	#89279	C₂²	1	1	yes	characteristic, complemented
58	#89278	C₂²	1	1	yes	characteristic
59	#89275	C₂²	1	1	yes	characteristic, complemented
60	#89275	C₂²	1	1	yes	characteristic, complemented
61	#89254	C₂²	1	1	yes	characteristic
62	#89252	C₂²	1	1	yes	characteristic, complemented
63	#89251	C₂²	1	1	yes	characteristic, complemented
64	#89250	C₂²	1	1	yes	characteristic, complemented
65	#89249	C₂²	1	1	yes	characteristic, complemented
66	C₈×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
67	#17995	—	7	1	no	maximal, Sylow
68	C₂×D₄×D₇	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₇	—	2	1	no	—
70	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₇×M₁₆	—	2	1	no	—
72	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
73	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
74	#6509	C₂×C₄	1	1	yes	characteristic
75	#6507	C₂×C₄	1	1	yes	characteristic
76	C₂×#1143	C₂×C₄	1	1	yes	characteristic
77	D₄×Dic₇	C₂×C₄	1	1	yes	characteristic
78	C₂×#1142	C₂×C₄	1	1	yes	characteristic
79	C₄×C₂²⋊D₇	—	2	1	no	—
80	C₂×#1136	—	2	1	no	—
81	D₇×M₁₆	—	4	4	no	—
82	C₂×#1132	C₂×C₄	1	1	yes	characteristic
83	C₂×#1131	—	2	1	no	—
84	C₂×#1131	D₄	1	1	yes	characteristic
85	C₂×#1131	D₄	1	1	yes	characteristic
86	C₂×C₈×D₇	—	2	1	no	—
87	C₂×C₈×D₇	—	2	1	no	—
88	C₂×C₈×D₇	—	2	1	no	—
89	C₂×C₈×D₇	—	2	1	no	—
90	#6460	C₂×C₄	1	1	yes	characteristic
91	#6459	—	2	1	no	—
92	#6456	C₂×C₄	1	1	yes	characteristic
93	D₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
94	#6452	—	2	1	no	—
95	#6451	C₂×C₄	1	1	yes	characteristic
96	(C₂²⋊D₇)⋊C₄	—	2	1	no	—
97	D₇×C₂²⋊C₄	—	2	1	no	—
98	C₄×D₂₈	C₂³	1	1	yes	characteristic
99	#6435	—	2	1	no	—
100	C₄²×D₇	C₂³	1	1	yes	characteristic
101	C₄×Dic₁₄	—	2	1	no	—
102	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
103	C₇×#106	C₂×C₄	1	1	yes	characteristic
104	C₇×C₄⋊C₈	—	2	1	no	—
105	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
106	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
107	C₇×#103	C₂×C₄	1	1	yes	characteristic
108	C₇×#102	C₂×C₄	1	1	yes	characteristic
109	C₇×C₂²⋊C₈	—	2	1	no	—
110	C₇×#97	—	2	1	no	—
111	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
112	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
113	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
114	#6409	C₂×C₄	1	1	yes	characteristic
115	#6406	C₂×C₄	1	1	yes	characteristic
116	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
117	#6395	C₂×C₄	1	1	yes	characteristic
118	(C₂×D₇)⋊C₈	—	2	1	no	—
119	(C₂×D₇)⋊C₈	—	2	1	no	—
120	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
121	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
122	#6391	C₂×C₄	1	1	yes	characteristic
123	#6390	C₂×C₄	1	1	yes	characteristic
124	#6389	—	2	1	no	—
125	#6389	D₄	1	1	yes	characteristic
126	#6389	D₄	1	1	yes	characteristic
127	Dic₇⋊C₈	—	2	1	no	—
128	Dic₇⋊C₈	—	2	1	no	—
129	Dic₇⋊C₈	—	2	1	no	—
130	Dic₇⋊C₈	—	2	1	no	—
131	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
132	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
133	C₈×Dic₇	—	2	1	no	—
134	C₈×Dic₇	—	2	1	no	—
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	#3101	—	7	1	no	—
147	#2962	—	7	1	no	—
148	D₄×M₁₆	—	7	1	no	—
149	#1590	—	7	1	no	—
150	#1590	D₇	1	1	yes	characteristic, complemented
151	#1583	—	7	1	no	—
152	#1583	—	7	1	no	—
153	#1582	—	7	1	no	—
154	#1582	—	7	1	no	—
155	C₈×SD₁₆	—	7	1	no	—
156	C₈×SD₁₆	—	7	1	no	—
157	#1570	—	7	1	no	—
158	#1493	—	7	1	no	—
159	C₂×D₄⋊C₈	—	7	1	no	—
160	C₈×M₁₆	—	7	1	no	—
161	C₂³×D₇	—	2	1	no	—
162	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	—	2	1	no	—
165	C₂×C₂²⋊D₇	—	2	1	no	—
166	C₂²×Dic₇	—	2	1	no	—
167	D₄×D₇	—	2	2	no	—
168	D₄×D₇	—	4	1	no	—
169	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₇	—	2	1	no	—
171	C₂×C₄×D₇	—	2	1	no	—
172	C₂×C₄×D₇	—	2	1	no	—
173	C₂×C₄×D₇	—	4	2	no	—
174	C₂×C₄×D₇	—	4	2	no	—
175	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
177	C₂×C₄×D₇	#41	1	1	yes	characteristic
178	C₂×Dic₁₄	—	2	1	no	—
179	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
180	C₇×SD₁₆	—	4	1	no	—
181	C₇×M₁₆	—	4	2	no	—
182	C₂×C₇×C₈	—	2	1	no	—
183	C₂×C₇×C₈	—	2	1	no	—
184	C₂×C₇×C₈	—	2	1	no	—
185	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
188	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
189	C₇×C₄⋊C₄	—	2	1	no	—
190	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
191	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
192	C₇×C₂²⋊C₄	—	2	1	no	—
193	C₄²×C₇	—	2	1	no	—
194	C₄²×C₇	C₂⁴	1	1	yes	characteristic
195	C₂²⋊Dic₇	—	2	1	no	—
196	#1143	—	2	2	no	—
197	#1142	—	4	1	no	—
198	(C₂×D₇)⋊C₄	—	2	1	no	—
199	(C₂×D₇)⋊C₄	—	2	1	no	—
200	(C₂×D₇)⋊C₄	—	2	1	no	—
201	(C₂×D₇)⋊C₄	—	2	1	no	—
202	C₄⋊Dic₇	—	2	1	no	—
203	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
204	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
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	Dic₇⋊C₄	—	2	1	no	—
210	Dic₇⋊C₄	—	2	1	no	—
211	C₄×Dic₇	—	2	1	no	—
212	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
213	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
214	C₄×Dic₇	#41	1	1	yes	characteristic
215	#1136	—	4	2	no	—
216	C₂×C₇⋊C₈	—	2	1	no	—
217	C₂×C₇⋊C₈	—	2	1	no	—
218	C₂×C₇⋊C₈	—	2	1	no	—
219	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
220	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
221	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
222	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
223	#1132	—	2	2	no	—
224	#1131	—	2	2	no	—
225	#1131	—	4	2	no	—
226	#1131	SD₁₆	1	4	yes	complemented
227	C₈×D₇	—	4	2	no	—
228	C₈×D₇	—	4	2	no	—
229	C₈×D₇	—	4	2	no	—
230	C₈×D₇	—	4	2	no	—
231	C₂²×M₁₆	—	14	1	no	—
232	#533	—	7	1	no	—
233	C₂×C₄×D₄	—	7	1	no	—
234	#483	—	7	1	no	—
235	#483	—	7	1	no	—
236	#476	—	7	1	no	—
237	#476	—	7	1	no	—
238	#461	—	7	1	no	—
239	#461	—	7	1	no	—
240	#450	—	7	1	no	—
241	#450	—	7	1	no	—
242	#446	—	7	1	no	—
243	#446	—	14	1	no	—
244	#446	—	14	1	no	—
245	#446	C₂×D₇	1	1	yes	characteristic, complemented
246	C₈×Q₈	—	7	1	no	—
247	C₈×Q₈	—	7	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	C₂×D₇	1	1	yes	characteristic
254	#435	—	14	1	no	—
255	#435	—	14	1	no	—
256	C₈×D₄	—	7	1	no	—
257	C₈×D₄	—	7	1	no	—
258	#431	—	7	1	no	—
259	#424	—	14	1	no	—
260	#423	—	7	1	no	—
261	C₂×C₄⋊C₈	—	7	1	no	—
262	#407	—	14	1	no	—
263	#405	—	14	1	no	—
264	C₄×M₁₆	—	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, complemented
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, complemented
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	#322	—	7	1	no	—
279	#322	—	7	1	no	—
280	C₈²	—	7	1	no	—
281	C₈²	C₂×D₇	1	1	yes	characteristic, complemented
282	C₂³×C₇	—	2	1	no	—
283	C₂²×D₇	—	2	1	no	—
284	C₂²×D₇	—	4	2	no	—
285	C₂²×D₇	—	4	2	no	—
286	C₂²×D₇	—	8	1	no	—
287	C₂²×D₇	C₄×D₄	1	1	yes	characteristic
288	C₇×Q₈	—	2	1	no	—
289	C₇×Q₈	—	2	1	no	—
290	C₇×D₄	—	2	1	no	—
291	C₇×D₄	—	2	1	no	—
292	C₂×C₄×C₇	—	2	1	no	—
293	C₂×C₄×C₇	—	2	1	no	—
294	C₂×C₄×C₇	—	2	1	no	—
295	C₂×C₄×C₇	—	4	1	no	—
296	C₂×C₄×C₇	—	4	1	no	—
297	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
298	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
300	C₂²⋊D₇	—	4	2	no	—
301	C₂×Dic₇	—	2	1	no	—
302	C₂×Dic₇	—	2	1	no	—
303	C₂×Dic₇	—	2	1	no	—
304	C₂×Dic₇	—	4	2	no	—
305	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
306	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
307	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
308	D₂₈	—	2	1	no	—
309	D₂₈	#131	1	2	yes	—
310	C₄×D₇	—	2	1	no	—
311	C₄×D₇	—	2	1	no	—
312	C₄×D₇	—	4	1	no	—
313	C₄×D₇	—	4	2	no	—
314	C₄×D₇	—	4	1	no	—
315	C₄×D₇	—	4	1	no	—
316	C₄×D₇	—	4	2	no	—
317	C₄×D₇	C₂×SD₁₆	1	2	yes	—
318	C₄×D₇	#135	1	2	yes	—
319	Dic₁₄	—	2	1	no	—
320	Dic₁₄	—	2	1	no	—
321	Dic₁₄	—	8	1	no	—
322	C₇×C₈	—	2	2	no	—
323	C₇×C₈	—	2	1	no	—
324	C₇×C₈	—	2	1	no	—
325	C₇×C₈	—	2	1	no	—
326	C₇×C₈	—	4	1	no	—
327	C₇×C₈	—	4	1	no	—
328	C₇×C₈	C₂×SD₁₆	1	2	yes	—
329	C₇⋊C₈	—	2	1	no	—
330	C₇⋊C₈	—	2	1	no	—
331	C₇⋊C₈	—	2	1	no	—
332	C₇⋊C₈	—	4	1	no	—
333	C₇⋊C₈	—	4	1	no	—
334	C₇⋊C₈	—	4	1	no	—
335	C₇⋊C₈	C₂×SD₁₆	1	2	yes	—
336	C₂²×D₄	—	7	1	no	—
337	C₂³×C₄	—	14	1	no	—
338	C₂×SD₁₆	—	7	1	no	—
339	C₂×SD₁₆	—	7	1	no	—
340	C₂×SD₁₆	—	7	1	no	—
341	C₂×SD₁₆	C₄×D₇	1	1	yes	characteristic
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	7	1	no	—
344	C₂×M₁₆	—	7	1	no	—
345	C₂×M₁₆	—	14	1	no	—
346	C₂×M₁₆	—	14	1	no	—
347	C₂×M₁₆	—	28	4	no	—
348	C₂²×C₈	—	14	1	no	—
349	C₂²×C₈	—	14	1	no	—
350	C₂²×C₈	—	14	1	no	—
351	C₂²×C₈	—	14	1	no	—
352	C₄⋊Q₈	—	7	1	no	—
353	C₄⋊Q₈	—	7	1	no	—
354	#125	—	14	1	no	—
355	C₂²⋊Q₈	—	7	1	no	—
356	C₂²⋊Q₈	—	7	1	no	—
357	C₂²⋊Q₈	—	14	1	no	—
358	C₄×Q₈	—	7	1	no	—
359	C₄×Q₈	—	14	1	no	—
360	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
361	C₄×D₄	—	7	1	no	—
362	C₄×D₄	—	7	1	no	—
363	C₄×D₄	—	7	1	no	—
364	C₄×D₄	—	14	1	no	—
365	C₄×D₄	—	14	1	no	—
366	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
367	#117	—	14	1	no	—
368	C₂×C₄⋊C₄	—	7	1	no	—
369	C₂×C₂²⋊C₄	—	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	—	7	1	no	—
379	C₄⋊C₈	—	7	1	no	—
380	C₄⋊C₈	—	14	1	no	—
381	C₄⋊C₈	—	14	1	no	—
382	C₄⋊C₈	—	14	1	no	—
383	C₄⋊C₈	—	14	1	no	—
384	C₄⋊C₈	—	14	1	no	—
385	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
386	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
387	#103	—	7	1	no	—
388	#103	—	7	1	no	—
389	#103	—	7	1	no	—
390	#103	C₄×D₇	1	1	yes	characteristic
391	#102	—	7	1	no	—
392	#102	—	7	1	no	—
393	#102	—	7	1	no	—
394	#102	C₄×D₇	1	1	yes	characteristic
395	C₂²⋊C₈	—	2	1	no	—
396	C₂²⋊C₈	—	7	1	no	—
397	C₂²⋊C₈	—	7	1	no	—
398	C₂²⋊C₈	—	14	1	no	—
399	C₂²⋊C₈	—	14	1	no	—
400	C₂²⋊C₈	—	14	1	no	—
401	#97	—	2	1	no	—
402	#97	—	7	1	no	—
403	#97	—	7	1	no	—
404	#97	—	14	1	no	—
405	C₄×C₈	—	7	1	no	—
406	C₄×C₈	—	7	1	no	—
407	C₄×C₈	—	7	1	no	—
408	C₄×C₈	—	14	1	no	—
409	C₄×C₈	—	14	1	no	—
410	C₄×C₈	—	14	1	no	—
411	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
412	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
413	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
414	C₂²×C₇	—	4	1	no	—
415	C₂²×C₇	—	4	1	no	—
416	C₂²×C₇	—	4	1	no	—
417	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
418	C₂×D₇	—	2	1	no	—
419	C₂×D₇	—	2	1	no	—
420	C₂×D₇	—	2	2	no	—
421	C₂×D₇	—	4	1	no	—
422	C₂×D₇	—	4	1	no	—
423	C₂×D₇	—	8	4	no	—
424	C₂×D₇	C₄×SD₁₆	1	2	yes	—
425	C₄×C₇	—	2	1	no	—
426	C₄×C₇	—	4	1	no	—
427	C₄×C₇	—	4	1	no	—
428	C₄×C₇	—	4	1	no	—
429	C₄×C₇	C₂×#131	1	1	yes	characteristic
430	C₄×C₇	#568	1	1	yes	characteristic
431	C₄×C₇	C₂²×SD₁₆	1	1	yes	characteristic
432	C₄×C₇	C₂×#135	1	1	yes	characteristic
433	Dic₇	—	2	1	no	—
434	Dic₇	—	2	1	no	—
435	Dic₇	—	4	1	no	—
436	Dic₇	—	4	1	no	—
437	Dic₇	—	4	1	no	—
438	Dic₇	C₄×SD₁₆	1	2	yes	—
439	C₂⁴	—	14	1	no	—
440	C₂×Q₈	—	7	1	no	—
441	C₂×Q₈	—	14	1	no	—
442	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
443	C₂×D₄	—	7	1	no	—
444	C₂×D₄	—	14	1	no	—
445	C₂×D₄	—	14	2	no	—
446	C₂×D₄	—	28	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	C₂²×C₄	—	14	1	no	—
454	C₂²×C₄	—	14	1	no	—
455	C₂²×C₄	—	14	1	no	—
456	C₂²×C₄	—	28	2	no	—
457	C₂²×C₄	—	28	2	no	—
458	SD₁₆	—	4	1	no	—
459	SD₁₆	—	14	2	no	—
460	SD₁₆	—	14	2	no	—
461	SD₁₆	—	28	1	no	—
462	M₁₆	—	4	2	no	—
463	M₁₆	—	7	4	no	—
464	M₁₆	—	14	2	no	—
465	M₁₆	—	28	2	no	—
466	M₁₆	—	28	2	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	7	1	no	—
471	C₂×C₈	—	7	1	no	—
472	C₂×C₈	—	7	1	no	—
473	C₂×C₈	—	7	1	no	—
474	C₂×C₈	—	14	1	no	—
475	C₂×C₈	—	14	1	no	—
476	C₂×C₈	—	14	1	no	—
477	C₂×C₈	—	28	2	no	—
478	C₂×C₈	—	28	2	no	—
479	C₂×C₈	—	28	2	no	—
480	C₂×C₈	—	28	2	no	—
481	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
482	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
483	C₂×C₈	D₄×D₇	1	1	yes	characteristic
484	C₂×C₈	D₄×D₇	1	1	yes	characteristic
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	7	1	no	—
487	C₄⋊C₄	—	7	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	—	14	1	no	—
493	C₄⋊C₄	—	14	1	no	—
494	C₄⋊C₄	—	14	1	no	—
495	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
496	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	14	1	no	—
499	C₂²⋊C₄	—	14	1	no	—
500	C₂²⋊C₄	—	14	1	no	—
501	C₂²⋊C₄	—	14	1	no	—
502	C₂²⋊C₄	—	14	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	7	1	no	—
505	C₄²	—	7	1	no	—
506	C₄²	—	7	1	no	—
507	C₄²	—	14	1	no	—
508	C₄²	C₂³×D₇	1	1	yes	characteristic
509	C₂×C₇	—	8	1	no	—
510	C₂×C₇	#2933	1	1	yes	characteristic
511	C₂×C₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
512	C₂×C₇	#2956	1	1	yes	characteristic
513	D₇	—	2	2	no	—
514	D₇	—	4	2	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	7	1	no	—
517	C₂³	—	14	1	no	—
518	C₂³	—	28	2	no	—
519	C₂³	—	28	2	no	—
520	C₂³	—	56	1	no	—
521	Q₈	—	2	1	no	—
522	Q₈	—	2	1	no	—
523	Q₈	—	14	1	no	—
524	Q₈	—	14	1	no	—
525	Q₈	—	56	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	7	2	no	—
529	D₄	—	14	1	no	—
530	D₄	—	28	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	7	1	no	—
537	C₂×C₄	—	7	2	no	—
538	C₂×C₄	—	7	2	no	—
539	C₂×C₄	—	7	1	no	—
540	C₂×C₄	—	7	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	—	14	1	no	—
546	C₂×C₄	—	28	1	no	—
547	C₂×C₄	—	28	2	no	—
548	C₂×C₄	—	28	2	no	—
549	C₂×C₄	—	28	2	no	—
550	C₂×C₄	—	28	1	no	—
551	C₂×C₄	—	28	1	no	—
552	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
553	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
554	C₂×C₄	D₇×#41	1	1	yes	characteristic
555	C₈	—	2	2	no	—
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	7	2	no	—
562	C₈	—	14	1	no	—
563	C₈	—	14	1	no	—
564	C₈	—	14	1	no	—
565	C₈	—	28	1	no	—
566	C₈	—	28	1	no	—
567	C₈	—	28	1	no	—
568	C₈	D₇×SD₁₆	1	2	yes	—
569	C₇	#17995	1	1	yes	characteristic, complemented, Sylow
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	7	2	no	—
574	C₂²	—	14	1	no	—
575	C₂²	—	14	1	no	—
576	C₂²	—	14	2	no	—
577	C₂²	—	28	1	no	—
578	C₂²	—	28	1	no	—
579	C₂²	—	56	4	no	—
580	C₂²	C₄×D₄×D₇	1	1	yes	characteristic
581	C₄	—	2	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	7	2	no	—
586	C₄	—	14	1	no	—
587	C₄	—	14	1	no	—
588	C₄	—	28	1	no	—
589	C₄	—	28	1	no	—
590	C₄	—	28	1	no	—
591	C₄	#90436	1	1	yes	characteristic
592	C₄	D₇×#131	1	1	yes	characteristic
593	C₄	C₂×D₇×SD₁₆	1	1	yes	characteristic
594	C₄	D₇×#135	1	1	yes	characteristic
595	C₂	—	8	1	no	—
596	C₂	—	14	2	no	—
597	C₂	—	28	2	no	—
598	C₂	#11736984	1	1	yes	characteristic
599	C₂	C₄×D₇×SD₁₆	1	1	yes	characteristic
600	C₂	#11737334	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	C₂×D₄×D₇	C₂×C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1590	D₇
hypocenter	C₇	#17995
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. #11737405	C₂	semidirect
4. C₇×#1590	C₂	semidirect
5. #11728707	C₂	semidirect
6. #11728650	C₂	semidirect
7. #11728618	C₂	semidirect
8. #11726286	C₂	semidirect
9. #11726273	C₂	semidirect
10. #11725994	C₂	semidirect
11. #11725966	C₂	semidirect
13. #11725915	C₂	semidirect
14. C₈×#1132	C₂	semidirect
15. C₈×#1131	C₂	semidirect
19. C₇×#446	C₂²	semidirect
26. Q₈×C₇⋊C₈	C₂²	semidirect
36. #89603	C₂²	semidirect
50. C₈×Dic₁₄	C₂²	semidirect
51. C₇×#334	C₂²	semidirect
52. C₇×Q₈⋊C₈	C₂²	semidirect
54. C₇×C₈²	C₂²	semidirect
55. Q₈⋊(C₇⋊C₈)	C₂²	semidirect
57. #89279	C₂²	semidirect
59. #89275	C₂²	semidirect
60. #89275	C₂²	semidirect
62. #89252	C₂²	semidirect
63. #89251	C₂²	semidirect
64. #89250	C₂²	semidirect
65. #89249	C₂²	semidirect
66. C₈×C₇⋊C₈	C₂²	semidirect
150. #1590	D₇	semidirect
226. #1131	SD₁₆	semidirect
245. #446	C₂×D₇	semidirect
269. #334	C₂×D₇	semidirect
273. Q₈⋊C₈	C₂×D₇	semidirect
281. C₈²	C₂×D₇	semidirect
569. C₇	#17995	semidirect

Maximal subgroups

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

subgroup	index
#11737405	2
#11737096	2
#11736985	2
C₇×#1590	2
#11728707	2
#11728650	2
#11728618	2
#11726286	2
#11726273	2
#11725994	2
#11725966	2
D₇×D₄⋊C₈	2
#11725915	2
C₈×#1132	2
C₈×#1131	2
#17995	7