Subgroups — #13323747

Order 1792.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11739973	C₂	1	1	yes	maximal, characteristic
2	#41×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#11736770	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1488	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728550	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728514	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728496	C₂	1	1	yes	maximal, characteristic, complemented
8	#11725977	C₂	1	1	yes	maximal, characteristic, complemented
9	#11725975	C₂	1	1	yes	maximal, characteristic, complemented
10	#11725969	C₂	1	1	yes	maximal, characteristic, complemented
11	#11725968	C₂	1	1	yes	maximal, characteristic, complemented
12	#11725911	C₂	1	1	yes	maximal, characteristic, complemented
13	#11725910	C₂	1	1	yes	maximal, characteristic, complemented
14	#11725905	C₂	1	1	yes	maximal, characteristic, complemented
15	#11725904	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₇×#41	C₂²	1	1	yes	characteristic
17	#90170	C₂²	1	1	yes	characteristic
18	C₇×#432	C₂²	1	1	yes	characteristic
19	C₇×#431	C₂²	1	1	yes	characteristic
20	#90011	C₄	1	1	yes	characteristic
21	#90010	C₄	1	1	yes	characteristic
22	C₄×#1144	C₂²	1	1	yes	characteristic
23	#89800	C₄	1	1	yes	characteristic
24	C₄×#1143	C₂²	1	1	yes	characteristic
25	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
26	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
27	#89794	C₄	1	1	yes	characteristic
28	C₄×#1142	C₂²	1	1	yes	characteristic
29	#89788	C₄	1	1	yes	characteristic
30	C₄×#1141	C₂²	1	1	yes	characteristic
31	D₄×C₇⋊C₈	—	2	1	no	—
32	D₄×C₇⋊C₈	—	2	1	no	—
33	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
34	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
35	#89781	C₄	1	1	yes	characteristic
36	#89775	C₄	1	1	yes	characteristic
37	#89768	C₄	1	1	yes	characteristic
38	#89697	—	2	1	no	—
39	#89697	C₂²	1	1	yes	characteristic
40	#89697	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇⋊C₈	—	2	1	no	—
42	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
43	#89610	C₂²	1	1	yes	characteristic
44	#89606	C₂²	1	1	yes	characteristic
45	#89603	C₂²	1	1	yes	characteristic
46	#89602	C₂²	1	1	yes	characteristic
47	#89502	—	2	1	no	—
48	(C₂²⋊D₇)⋊C₈	—	2	1	no	—
49	#89481	—	2	1	no	—
50	#89480	—	2	1	no	—
51	C₇×Q₈⋊C₈	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×D₄⋊C₈	C₂²	1	1	yes	characteristic
55	#89275	C₂²	1	1	yes	characteristic
56	#89275	C₂²	1	1	yes	characteristic
57	#89274	C₂²	1	1	yes	characteristic
58	#89274	C₂²	1	1	yes	characteristic
59	#89254	C₂²	1	1	yes	characteristic
60	#89254	C₂²	1	1	yes	characteristic
61	#89251	C₂²	1	1	yes	characteristic
62	#89251	C₂²	1	1	yes	characteristic
63	#89250	C₂²	1	1	yes	characteristic
64	#89250	C₂²	1	1	yes	characteristic
65	#89249	C₂²	1	1	yes	characteristic
66	#89249	C₂²	1	1	yes	characteristic
67	#17909	—	7	1	no	maximal, Sylow
68	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
69	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
70	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
71	C₄×C₇×D₄	—	2	1	no	—
72	C₄×C₇×D₄	—	2	1	no	—
73	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
74	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
75	C₇×#117	—	2	1	no	—
76	C₇×#117	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₇	—	2	1	no	—
78	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
79	C₂×#1144	C₂×C₄	1	1	yes	characteristic
80	C₂×#1143	C₂×C₄	1	1	yes	characteristic
81	C₂×#1142	C₂×C₄	1	1	yes	characteristic
82	C₂×#1141	C₂×C₄	1	1	yes	characteristic
83	#6493	C₂×C₄	1	1	yes	characteristic
84	#6492	—	2	1	no	—
85	C₄×C₂²⋊D₇	—	2	1	no	—
86	#6487	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₇⋊C₈	—	2	1	no	—
88	C₂²×C₇⋊C₈	—	2	1	no	—
89	C₂²×C₇⋊C₈	D₄	1	1	yes	characteristic
90	C₂²×C₇⋊C₈	D₄	1	1	yes	characteristic
91	C₂×#1131	—	2	1	no	—
92	C₂×C₈×D₇	—	2	1	no	—
93	#6439	—	2	1	no	—
94	#6438	C₂×C₄	1	1	yes	characteristic
95	C₄×D₂₈	C₂³	1	1	yes	characteristic
96	#6435	—	2	1	no	—
97	#6433	C₂×C₄	1	1	yes	characteristic
98	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
99	C₇×C₄⋊C₈	—	2	1	no	—
100	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
101	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
102	C₇×C₂²⋊C₈	—	2	1	no	—
103	C₇×C₂²⋊C₈	—	2	1	no	—
104	C₇×#97	—	2	1	no	—
105	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
106	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
107	#6409	C₂×C₄	1	1	yes	characteristic
108	#6409	C₂×C₄	1	1	yes	characteristic
109	#6406	C₂×C₄	1	1	yes	characteristic
110	#6406	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
112	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
113	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
114	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
115	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
116	(C₂×D₇)⋊C₈	—	2	1	no	—
117	(C₂×D₇)⋊C₈	—	2	1	no	—
118	#6389	—	2	1	no	—
119	Dic₇⋊C₈	—	2	1	no	—
120	Dic₇⋊C₈	—	2	1	no	—
121	C₈×Dic₇	—	2	1	no	—
122	#6384	C₂×C₄	1	1	yes	characteristic
123	#6384	C₂×C₄	1	1	yes	characteristic
124	#6383	C₂×C₄	1	1	yes	characteristic
125	#6383	C₂×C₄	1	1	yes	characteristic
126	#6382	C₂×C₄	1	1	yes	characteristic
127	#6382	C₂×C₄	1	1	yes	characteristic
128	#6381	C₂×C₄	1	1	yes	characteristic
129	#6381	C₂×C₄	1	1	yes	characteristic
130	C₄⋊(C₇⋊C₈)	—	2	1	no	—
131	C₄⋊(C₇⋊C₈)	—	2	1	no	—
132	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
133	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
134	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
135	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
136	C₄×C₇⋊C₈	—	2	1	no	—
137	C₄×C₇⋊C₈	—	2	1	no	—
138	C₄×C₇⋊C₈	—	2	1	no	—
139	C₄×C₇⋊C₈	D₄	1	1	yes	characteristic
140	C₄×C₇⋊C₈	D₄	1	1	yes	characteristic
141	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
142	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
143	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
144	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
145	#3102	—	7	1	no	—
146	#2966	—	7	1	no	—
147	C₈×#41	—	7	1	no	—
148	#1588	—	7	1	no	—
149	#1587	—	7	1	no	—
150	#1586	—	7	1	no	—
151	#1585	—	7	1	no	—
152	#1580	—	7	1	no	—
153	#1579	—	7	1	no	—
154	SD₁₆⋊C₈	—	7	1	no	—
155	SD₁₆⋊C₈	—	7	1	no	—
156	#1572	—	7	1	no	—
157	#1488	D₇	1	1	yes	characteristic, complemented
158	#1482	—	7	1	no	—
159	#1452	—	7	1	no	—
160	C₇×#41	—	2	2	no	—
161	C₇×#41	—	2	2	no	—
162	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₇×D₄	—	2	1	no	—
164	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	—	2	1	no	—
166	C₂²×C₄×C₇	—	2	1	no	—
167	C₂²×C₄×C₇	—	2	1	no	—
168	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₇	#41	1	1	yes	characteristic
171	C₂×C₂²⋊D₇	—	2	1	no	—
172	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×D₇	—	2	1	no	—
174	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₇×C₈	—	2	1	no	—
176	C₂×C₇×C₈	—	2	1	no	—
177	C₂×C₇×C₈	—	2	1	no	—
178	C₂×C₇×C₈	—	2	1	no	—
179	C₇×C₄⋊C₄	—	2	1	no	—
180	C₇×C₄⋊C₄	—	2	1	no	—
181	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
182	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
183	C₇×C₂²⋊C₄	—	2	1	no	—
184	C₇×C₂²⋊C₄	—	2	1	no	—
185	C₇×C₂²⋊C₄	—	2	1	no	—
186	C₄²×C₇	—	2	1	no	—
187	C₄²×C₇	—	2	1	no	—
188	C₄²×C₇	—	2	1	no	—
189	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
190	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₇	#41	1	1	yes	characteristic
192	C₄²×C₇	C₂⁴	1	1	yes	characteristic
193	C₂²⋊Dic₇	—	2	1	no	—
194	#1144	—	2	2	no	—
195	#1143	—	2	2	no	—
196	#1142	—	2	2	no	—
197	#1141	—	2	2	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	C₂²×C₄	1	1	yes	characteristic
203	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
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	C₄×Dic₇	—	2	1	no	—
209	C₂×C₇⋊C₈	—	2	1	no	—
210	C₂×C₇⋊C₈	—	2	1	no	—
211	C₂×C₇⋊C₈	—	4	1	no	—
212	C₂×C₇⋊C₈	—	4	1	no	—
213	C₂×C₇⋊C₈	—	4	2	no	—
214	C₂×C₇⋊C₈	—	4	2	no	—
215	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
216	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
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	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
222	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
223	#1131	—	4	2	no	—
224	C₈×D₇	—	4	2	no	—
225	#529	—	7	1	no	—
226	C₄×#41	C₂×D₇	1	1	yes	characteristic
227	#485	—	7	1	no	—
228	#482	—	7	1	no	—
229	#479	—	7	1	no	—
230	#478	—	7	1	no	—
231	#464	—	7	1	no	—
232	#463	—	7	1	no	—
233	#452	—	7	1	no	—
234	#449	—	7	1	no	—
235	#446	—	7	1	no	—
236	C₈×Q₈	—	7	1	no	—
237	C₈×Q₈	—	7	1	no	—
238	C₈×Q₈	—	7	1	no	—
239	C₄×Q₁₆	—	7	1	no	—
240	C₄×SD₁₆	—	7	1	no	—
241	C₄×SD₁₆	—	7	1	no	—
242	C₄×D₈	—	7	1	no	—
243	#436	—	7	1	no	—
244	#435	—	14	1	no	—
245	C₈×D₄	—	7	1	no	—
246	C₈×D₄	—	7	1	no	—
247	C₈×D₄	—	7	1	no	—
248	C₈×D₄	—	14	1	no	—
249	C₈×D₄	—	14	1	no	—
250	C₈×D₄	—	14	1	no	—
251	#433	—	14	1	no	—
252	#432	C₂×D₇	1	1	yes	characteristic
253	#431	—	7	1	no	—
254	#431	—	7	1	no	—
255	#431	—	14	1	no	—
256	#431	C₂×D₇	1	1	yes	characteristic
257	#405	—	14	1	no	—
258	C₂×C₄×C₈	—	7	1	no	—
259	C₂×C₄×C₈	—	14	1	no	—
260	#335	—	7	1	no	—
261	#335	—	7	1	no	—
262	#334	—	7	1	no	—
263	#334	—	7	1	no	—
264	Q₈⋊C₈	—	7	1	no	—
265	Q₈⋊C₈	—	7	1	no	—
266	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic
267	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic
268	D₄⋊C₈	—	7	1	no	—
269	D₄⋊C₈	—	7	1	no	—
270	D₄⋊C₈	C₂×D₇	1	1	yes	characteristic
271	D₄⋊C₈	C₂×D₇	1	1	yes	characteristic
272	#322	—	7	1	no	—
273	#322	—	7	1	no	—
274	#322	—	7	1	no	—
275	#322	—	7	1	no	—
276	C₂³×C₇	—	2	1	no	—
277	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
278	C₂²×D₇	—	2	1	no	—
279	C₇×Q₈	—	2	1	no	—
280	C₇×Q₈	#131	1	2	yes	—
281	C₇×D₄	—	2	4	no	—
282	C₇×D₄	—	2	1	no	—
283	C₇×D₄	#131	1	2	yes	—
284	C₂×C₄×C₇	—	2	4	no	—
285	C₂×C₄×C₇	—	2	1	no	—
286	C₂×C₄×C₇	—	2	1	no	—
287	C₂×C₄×C₇	—	2	1	no	—
288	C₂×C₄×C₇	—	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	2	no	—
294	C₂×C₄×C₇	—	4	1	no	—
295	C₂×C₄×C₇	—	4	1	no	—
296	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
297	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
298	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
299	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
300	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
302	C₂²⋊D₇	—	4	2	no	—
303	C₂×Dic₇	—	2	1	no	—
304	C₂×Dic₇	—	2	1	no	—
305	C₂×Dic₇	—	2	1	no	—
306	D₂₈	—	2	1	no	—
307	D₂₈	—	2	1	no	—
308	C₄×D₇	—	4	1	no	—
309	C₄×D₇	—	4	1	no	—
310	Dic₁₄	—	2	1	no	—
311	Dic₁₄	—	2	1	no	—
312	C₇×C₈	—	4	1	no	—
313	C₇×C₈	—	4	1	no	—
314	C₇×C₈	—	4	1	no	—
315	C₇×C₈	—	4	1	no	—
316	C₇⋊C₈	—	2	1	no	—
317	C₇⋊C₈	—	2	1	no	—
318	C₇⋊C₈	—	2	1	no	—
319	C₇⋊C₈	—	2	1	no	—
320	C₇⋊C₈	—	2	1	no	—
321	C₇⋊C₈	—	2	1	no	—
322	C₇⋊C₈	—	2	1	no	—
323	C₇⋊C₈	—	2	1	no	—
324	C₇⋊C₈	—	4	1	no	—
325	C₇⋊C₈	—	4	1	no	—
326	C₂×#41	C₄×D₇	1	1	yes	characteristic
327	C₂×Q₁₆	—	7	1	no	—
328	C₂×SD₁₆	—	7	1	no	—
329	C₂×SD₁₆	—	7	1	no	—
330	C₂×D₈	—	7	1	no	—
331	C₂×M₁₆	—	14	1	no	—
332	C₂²×C₈	—	7	1	no	—
333	C₂²×C₈	—	7	1	no	—
334	C₂²×C₈	—	14	1	no	—
335	C₂²×C₈	—	14	1	no	—
336	C₂²×C₈	—	14	1	no	—
337	#126	—	14	1	no	—
338	#125	—	7	1	no	—
339	#124	—	7	1	no	—
340	#123	—	14	1	no	—
341	C₂²⋊Q₈	—	7	1	no	—
342	#121	—	7	1	no	—
343	C₄×Q₈	—	7	1	no	—
344	C₄×Q₈	C₄×D₇	1	1	yes	characteristic
345	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	—	2	1	no	—
348	C₄×D₄	—	7	1	no	—
349	C₄×D₄	—	14	1	no	—
350	C₄×D₄	C₄×D₇	1	1	yes	characteristic
351	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
352	#117	—	2	1	no	—
353	#117	—	14	1	no	—
354	#117	C₄×D₇	1	1	yes	characteristic
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
357	#107	—	7	1	no	—
358	#107	—	7	1	no	—
359	#106	—	7	1	no	—
360	#106	—	7	1	no	—
361	C₄⋊C₈	—	2	1	no	—
362	C₄⋊C₈	—	7	1	no	—
363	C₄⋊C₈	—	7	1	no	—
364	C₄⋊C₈	—	7	1	no	—
365	C₄⋊C₈	—	7	1	no	—
366	C₄⋊C₈	—	14	1	no	—
367	C₄⋊C₈	—	14	1	no	—
368	C₄⋊C₈	—	14	1	no	—
369	C₄⋊C₈	—	14	1	no	—
370	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
371	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
372	#103	—	7	1	no	—
373	#103	—	7	1	no	—
374	#103	—	7	1	no	—
375	#103	—	7	1	no	—
376	#102	—	7	1	no	—
377	#102	—	7	1	no	—
378	#102	—	7	1	no	—
379	#102	—	7	1	no	—
380	C₂²⋊C₈	—	2	1	no	—
381	C₂²⋊C₈	—	2	1	no	—
382	C₂²⋊C₈	—	7	1	no	—
383	C₂²⋊C₈	—	7	1	no	—
384	C₂²⋊C₈	—	14	1	no	—
385	C₂²⋊C₈	—	14	1	no	—
386	C₂²⋊C₈	—	14	1	no	—
387	C₂²⋊C₈	—	14	1	no	—
388	C₂²⋊C₈	—	14	1	no	—
389	#97	—	2	1	no	—
390	#97	—	14	1	no	—
391	C₄×C₈	—	7	1	no	—
392	C₄×C₈	—	7	1	no	—
393	C₄×C₈	—	7	1	no	—
394	C₄×C₈	—	7	1	no	—
395	C₄×C₈	—	7	1	no	—
396	C₄×C₈	—	7	1	no	—
397	C₄×C₈	—	14	1	no	—
398	C₄×C₈	—	14	1	no	—
399	C₄×C₈	—	14	1	no	—
400	C₄×C₈	—	14	1	no	—
401	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
402	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
403	C₂²×C₇	—	2	1	no	—
404	C₂²×C₇	—	2	2	no	—
405	C₂²×C₇	—	2	1	no	—
406	C₂²×C₇	—	2	1	no	—
407	C₂²×C₇	—	4	1	no	—
408	C₂²×C₇	—	4	1	no	—
409	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
410	C₂×D₇	—	4	1	no	—
411	C₂×D₇	—	4	1	no	—
412	C₂×D₇	—	4	1	no	—
413	C₄×C₇	—	2	1	no	—
414	C₄×C₇	—	2	2	no	—
415	C₄×C₇	—	2	1	no	—
416	C₄×C₇	—	2	1	no	—
417	C₄×C₇	—	2	1	no	—
418	C₄×C₇	—	4	1	no	—
419	C₄×C₇	—	4	1	no	—
420	C₄×C₇	C₂×#131	1	1	yes	characteristic
421	C₄×C₇	C₂×#131	1	1	yes	characteristic
422	C₄×C₇	#575	1	1	yes	characteristic
423	C₄×C₇	#575	1	1	yes	characteristic
424	Dic₇	—	4	1	no	—
425	Dic₇	—	4	1	no	—
426	Dic₇	—	4	1	no	—
427	#41	—	2	2	no	—
428	#41	—	2	2	no	—
429	C₂×Q₈	—	7	1	no	—
430	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	7	1	no	—
433	C₂×D₄	—	14	1	no	—
434	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	14	1	no	—
439	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
440	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
441	C₂²×C₄	#1159	1	1	yes	characteristic
442	Q₁₆	—	14	2	no	—
443	SD₁₆	—	14	2	no	—
444	SD₁₆	—	14	2	no	—
445	D₈	—	14	2	no	—
446	M₁₆	—	28	2	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	7	1	no	—
452	C₂×C₈	—	7	1	no	—
453	C₂×C₈	—	7	1	no	—
454	C₂×C₈	—	7	1	no	—
455	C₂×C₈	—	7	1	no	—
456	C₂×C₈	—	7	1	no	—
457	C₂×C₈	—	7	1	no	—
458	C₂×C₈	—	7	1	no	—
459	C₂×C₈	—	14	1	no	—
460	C₂×C₈	—	14	1	no	—
461	C₂×C₈	—	28	2	no	—
462	C₂×C₈	—	28	1	no	—
463	C₂×C₈	—	28	1	no	—
464	C₂×C₈	—	28	2	no	—
465	C₂×C₈	—	28	2	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	7	1	no	—
469	C₄⋊C₄	—	7	1	no	—
470	C₄⋊C₄	—	14	1	no	—
471	C₄⋊C₄	—	14	1	no	—
472	C₄⋊C₄	—	14	1	no	—
473	C₄⋊C₄	—	14	1	no	—
474	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
475	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	14	1	no	—
480	C₂²⋊C₄	—	14	1	no	—
481	C₂²⋊C₄	—	14	1	no	—
482	C₂²⋊C₄	—	14	1	no	—
483	C₂²⋊C₄	—	14	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	14	1	no	—
488	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
489	C₄²	D₄×D₇	1	1	yes	characteristic
490	C₄²	#1159	1	1	yes	characteristic
491	C₄²	C₂³×D₇	1	1	yes	characteristic
492	C₂×C₇	—	4	1	no	—
493	C₂×C₇	—	4	2	no	—
494	C₂×C₇	#2929	1	1	yes	characteristic
495	C₂×C₇	#2943	1	1	yes	characteristic
496	C₂×C₇	#2955	1	1	yes	characteristic
497	D₇	—	8	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	14	1	no	—
500	C₂³	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
501	Q₈	—	2	1	no	—
502	Q₈	—	14	1	no	—
503	Q₈	—	14	1	no	—
504	Q₈	#6470	1	2	yes	—
505	D₄	—	2	4	no	—
506	D₄	—	2	1	no	—
507	D₄	—	14	1	no	—
508	D₄	—	14	1	no	—
509	D₄	—	28	2	no	—
510	D₄	#6470	1	2	yes	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	14	1	no	—
524	C₂×C₄	—	14	1	no	—
525	C₂×C₄	—	14	1	no	—
526	C₂×C₄	—	28	1	no	—
527	C₂×C₄	—	28	1	no	—
528	C₂×C₄	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
529	C₂×C₄	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
530	C₂×C₄	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
531	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
532	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
533	C₂×C₄	C₂×#1159	1	1	yes	characteristic
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	14	1	no	—
539	C₈	—	14	1	no	—
540	C₈	—	14	1	no	—
541	C₈	—	14	1	no	—
542	C₈	—	14	1	no	—
543	C₈	—	14	1	no	—
544	C₈	—	14	1	no	—
545	C₈	—	14	1	no	—
546	C₈	—	28	1	no	—
547	C₈	—	28	1	no	—
548	C₇	#17909	1	1	yes	characteristic, complemented, Sylow
549	C₂²	—	2	1	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	28	1	no	—
556	C₂²	—	28	1	no	—
557	C₂²	—	28	1	no	—
558	C₂²	C₂×(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	2	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	28	1	no	—
567	C₄	—	28	1	no	—
568	C₄	—	28	1	no	—
569	C₄	C₂×#6470	1	1	yes	characteristic
570	C₄	C₂×#6470	1	1	yes	characteristic
571	C₄	#90459	1	1	yes	characteristic
572	C₄	#90459	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	4	2	no	—
575	C₂	—	56	1	no	—
576	C₂	#11736071	1	1	yes	characteristic
577	C₂	#11736264	1	1	yes	characteristic
578	C₂	#11736434	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×#1488	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	#90010	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1488	D₇
hypocenter	C₇	#17909
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1488

Complements

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

N	H ≅ G/N	type
2. #41×C₇⋊C₈	C₂	semidirect
3. #11736770	C₂	semidirect
4. C₇×#1488	C₂	semidirect
5. #11728550	C₂	semidirect
6. #11728514	C₂	semidirect
7. #11728496	C₂	semidirect
8. #11725977	C₂	semidirect
9. #11725975	C₂	semidirect
10. #11725969	C₂	semidirect
11. #11725968	C₂	semidirect
12. #11725911	C₂	semidirect
13. #11725910	C₂	semidirect
14. #11725905	C₂	semidirect
15. #11725904	C₂	semidirect
157. #1488	D₇	semidirect
548. C₇	#17909	semidirect

Maximal subgroups

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

subgroup	index
#11739973	2
#41×C₇⋊C₈	2
#11736770	2
C₇×#1488	2
#11728550	2
#11728514	2
#11728496	2
#11725977	2
#11725975	2
#11725969	2
#11725968	2
#11725911	2
#11725910	2
#11725905	2
#11725904	2
#17909	7