Subgroups — #13324331

Order 1792.

630 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11740579	C₂	1	1	yes	maximal, characteristic
2	#11740571	C₂	1	1	yes	maximal, characteristic, complemented
3	#11736770	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1494	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728548	C₂	1	1	yes	maximal, characteristic, complemented
6	#11727490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₈×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#11725979	C₂	1	1	yes	maximal, characteristic, complemented
9	#11725978	C₂	1	1	yes	maximal, characteristic, complemented
10	#11725967	C₂	1	1	yes	maximal, characteristic, complemented
11	#11725966	C₂	1	1	yes	maximal, characteristic, complemented
12	#11725915	C₂	1	1	yes	maximal, characteristic, complemented
13	#11725914	C₂	1	1	yes	maximal, characteristic, complemented
14	#11725903	C₂	1	1	yes	maximal, characteristic, complemented
15	#11725902	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#529	C₂²	1	1	yes	characteristic
17	#90170	C₂²	1	1	yes	characteristic
18	C₇×#432	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
20	#89840	C₄	1	1	yes	characteristic
21	#89836	C₄	1	1	yes	characteristic
22	#89831	C₄	1	1	yes	characteristic
23	#89828	C₄	1	1	yes	characteristic
24	#89823	C₄	1	1	yes	characteristic
25	#89820	C₄	1	1	yes	characteristic
26	#89813	C₄	1	1	yes	characteristic
27	#89810	C₄	1	1	yes	characteristic
28	C₄×#1144	C₂²	1	1	yes	characteristic
29	C₄×#1143	C₂²	1	1	yes	characteristic
30	#89796	C₂²	1	1	yes	characteristic
31	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
32	C₄×#1142	C₂²	1	1	yes	characteristic
33	C₄×#1141	C₂²	1	1	yes	characteristic
34	#89784	C₂²	1	1	yes	characteristic
35	#89783	—	2	1	no	—
36	D₄×C₇⋊C₈	—	2	1	no	—
37	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
38	#89772	—	2	1	no	—
39	#89769	—	2	1	no	—
40	#89698	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
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	C₈×C₇⋊C₈	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	#17959	—	7	1	no	maximal, Sylow
68	C₂²×C₇×C₈	—	2	1	no	—
69	C₇×#126	—	2	1	no	—
70	C₇×#125	C₂×C₄	1	1	yes	characteristic
71	C₇×#124	C₂×C₄	1	1	yes	characteristic
72	C₇×#123	—	2	1	no	—
73	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
74	C₇×#121	C₂×C₄	1	1	yes	characteristic
75	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
76	C₄×C₇×D₄	—	2	1	no	—
77	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
78	C₇×#117	—	2	1	no	—
79	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
80	C₂×#1144	C₂×C₄	1	1	yes	characteristic
81	C₂×#1143	C₂×C₄	1	1	yes	characteristic
82	C₂×#1142	C₂×C₄	1	1	yes	characteristic
83	C₂×#1141	C₂×C₄	1	1	yes	characteristic
84	#6493	C₂×C₄	1	1	yes	characteristic
85	#6492	—	2	1	no	—
86	C₄×C₂²⋊D₇	—	2	1	no	—
87	#6487	C₂×C₄	1	1	yes	characteristic
88	C₂×#1136	—	2	1	no	—
89	C₂²×C₇⋊C₈	—	2	1	no	—
90	C₂²×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
91	C₂²×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₂²×C₇⋊C₈	D₄	1	1	yes	characteristic
93	C₂²×C₇⋊C₈	D₄	1	1	yes	characteristic
94	C₂×#1131	—	2	1	no	—
95	C₂×C₈×D₇	—	2	1	no	—
96	#6439	—	2	1	no	—
97	#6438	C₂×C₄	1	1	yes	characteristic
98	C₄×D₂₈	C₂³	1	1	yes	characteristic
99	#6435	—	2	1	no	—
100	#6433	C₂×C₄	1	1	yes	characteristic
101	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
102	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
103	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₇×C₂²⋊C₈	—	2	1	no	—
105	C₇×#97	—	2	1	no	—
106	C₄×C₇×C₈	—	2	1	no	—
107	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
108	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
109	#6409	C₂×C₄	1	1	yes	characteristic
110	#6409	C₂×C₄	1	1	yes	characteristic
111	#6406	C₂×C₄	1	1	yes	characteristic
112	#6406	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
114	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
115	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
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)	C₂³	1	1	yes	characteristic
133	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
134	#6377	—	2	1	no	—
135	#6377	—	2	1	no	—
136	C₄×C₇⋊C₈	—	2	1	no	—
137	C₄×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
138	C₄×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
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	#3168	—	7	1	no	—
146	#2966	—	7	1	no	—
147	#2966	—	7	1	no	—
148	#1591	—	7	1	no	—
149	#1590	—	7	1	no	—
150	#1590	—	7	1	no	—
151	#1589	—	7	1	no	—
152	C₈×Q₁₆	—	7	1	no	—
153	C₈×SD₁₆	—	7	1	no	—
154	C₈×SD₁₆	—	7	1	no	—
155	C₈×D₈	—	7	1	no	—
156	#1568	—	7	1	no	—
157	#1494	—	7	1	no	—
158	#1494	D₇	1	1	yes	characteristic, complemented
159	C₂×C₈²	—	7	1	no	—
160	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₇×D₄	—	2	1	no	—
162	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₇	—	2	1	no	—
164	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	#41	1	1	yes	characteristic
167	C₂×C₂²⋊D₇	—	2	1	no	—
168	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₇	—	2	1	no	—
170	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₇×C₈	—	2	4	no	—
172	C₂×C₇×C₈	—	2	1	no	—
173	C₂×C₇×C₈	—	2	1	no	—
174	C₂×C₇×C₈	—	2	1	no	—
175	C₂×C₇×C₈	—	2	1	no	—
176	C₇×C₄⋊C₄	—	2	1	no	—
177	C₇×C₄⋊C₄	—	2	1	no	—
178	C₇×C₄⋊C₄	—	2	1	no	—
179	C₇×C₄⋊C₄	—	2	1	no	—
180	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
181	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
182	C₇×C₂²⋊C₄	—	2	1	no	—
183	C₇×C₂²⋊C₄	—	2	1	no	—
184	C₇×C₂²⋊C₄	—	2	1	no	—
185	C₇×C₂²⋊C₄	—	2	1	no	—
186	C₇×C₂²⋊C₄	—	2	1	no	—
187	C₄²×C₇	—	2	1	no	—
188	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
189	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₇	#41	1	1	yes	characteristic
191	C₄²×C₇	C₂⁴	1	1	yes	characteristic
192	C₂²⋊Dic₇	—	2	1	no	—
193	#1144	—	2	2	no	—
194	#1143	—	2	2	no	—
195	#1142	—	2	2	no	—
196	#1141	—	2	2	no	—
197	(C₂×D₇)⋊C₄	—	2	1	no	—
198	(C₂×D₇)⋊C₄	—	2	1	no	—
199	(C₂×D₇)⋊C₄	—	2	1	no	—
200	(C₂×D₇)⋊C₄	—	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	C₄×Dic₇	—	2	1	no	—
208	#1136	—	4	2	no	—
209	C₂×C₇⋊C₈	—	2	2	no	—
210	C₂×C₇⋊C₈	—	2	2	no	—
211	C₂×C₇⋊C₈	—	2	2	no	—
212	C₂×C₇⋊C₈	—	2	2	no	—
213	C₂×C₇⋊C₈	—	2	1	no	—
214	C₂×C₇⋊C₈	—	2	1	no	—
215	C₂×C₇⋊C₈	—	4	2	no	—
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	C₂²×C₄	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	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
224	#1131	—	4	2	no	—
225	C₈×D₇	—	4	2	no	—
226	#529	—	7	1	no	—
227	#529	C₂×D₇	1	1	yes	characteristic
228	#499	—	7	1	no	—
229	#495	—	7	1	no	—
230	#488	—	7	1	no	—
231	#488	—	7	1	no	—
232	#467	—	7	1	no	—
233	#466	—	7	1	no	—
234	#465	—	7	1	no	—
235	#465	—	7	1	no	—
236	#446	—	7	1	no	—
237	#446	—	7	1	no	—
238	C₈×Q₈	—	7	1	no	—
239	C₈×Q₈	—	7	1	no	—
240	C₄×Q₁₆	—	7	1	no	—
241	C₄×SD₁₆	—	7	1	no	—
242	C₄×SD₁₆	—	7	1	no	—
243	C₄×D₈	—	7	1	no	—
244	#436	—	7	1	no	—
245	#436	—	7	1	no	—
246	#435	—	14	1	no	—
247	#435	—	14	1	no	—
248	C₈×D₄	—	7	1	no	—
249	C₈×D₄	—	7	1	no	—
250	C₈×D₄	—	14	1	no	—
251	C₈×D₄	—	14	1	no	—
252	#433	—	14	1	no	—
253	#433	—	14	1	no	—
254	#432	—	7	1	no	—
255	#432	C₂×D₇	1	1	yes	characteristic
256	#405	—	14	1	no	—
257	#405	—	14	1	no	—
258	C₂×C₄×C₈	—	7	1	no	—
259	C₂×C₄×C₈	—	7	1	no	—
260	C₂×C₄×C₈	C₂×D₇	1	1	yes	characteristic
261	#335	—	7	1	no	—
262	#335	—	7	1	no	—
263	#334	—	7	1	no	—
264	#334	—	7	1	no	—
265	Q₈⋊C₈	—	7	1	no	—
266	Q₈⋊C₈	—	7	1	no	—
267	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic
268	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic
269	D₄⋊C₈	—	7	1	no	—
270	D₄⋊C₈	—	7	1	no	—
271	D₄⋊C₈	C₂×D₇	1	1	yes	characteristic
272	D₄⋊C₈	C₂×D₇	1	1	yes	characteristic
273	C₈²	—	7	1	no	—
274	C₈²	—	7	1	no	—
275	C₈²	—	7	1	no	—
276	C₈²	—	7	1	no	—
277	C₂³×C₇	—	2	1	no	—
278	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
279	C₂²×D₇	—	2	1	no	—
280	C₇×Q₈	—	2	1	no	—
281	C₇×Q₈	—	2	1	no	—
282	C₇×D₄	—	2	1	no	—
283	C₇×D₄	—	2	1	no	—
284	C₇×D₄	—	4	2	no	—
285	C₂×C₄×C₇	—	2	2	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	—	2	1	no	—
293	C₂×C₄×C₇	—	4	1	no	—
294	C₂×C₄×C₇	—	4	1	no	—
295	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
296	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
297	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
298	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
299	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
301	C₂²⋊D₇	—	4	2	no	—
302	C₂×Dic₇	—	2	1	no	—
303	C₂×Dic₇	—	2	1	no	—
304	C₂×Dic₇	—	2	1	no	—
305	D₂₈	—	2	1	no	—
306	D₂₈	—	2	1	no	—
307	C₄×D₇	—	4	1	no	—
308	C₄×D₇	—	4	1	no	—
309	Dic₁₄	—	2	1	no	—
310	Dic₁₄	—	2	1	no	—
311	C₇×C₈	—	2	2	no	—
312	C₇×C₈	—	2	2	no	—
313	C₇×C₈	—	4	1	no	—
314	C₇×C₈	—	4	1	no	—
315	C₇⋊C₈	—	2	1	no	—
316	C₇⋊C₈	—	2	1	no	—
317	C₇⋊C₈	—	2	1	no	—
318	C₇⋊C₈	—	2	1	no	—
319	C₇⋊C₈	—	4	1	no	—
320	C₇⋊C₈	—	4	1	no	—
321	C₇⋊C₈	#131	1	2	yes	—
322	C₇⋊C₈	#131	1	2	yes	—
323	C₇⋊C₈	#135	1	2	yes	—
324	C₇⋊C₈	#135	1	2	yes	—
325	C₂×Q₁₆	—	7	1	no	—
326	C₂×SD₁₆	—	7	1	no	—
327	C₂×SD₁₆	—	7	1	no	—
328	C₂×D₈	—	7	1	no	—
329	C₂×M₁₆	—	14	1	no	—
330	C₂×M₁₆	—	14	1	no	—
331	C₂²×C₈	—	2	1	no	—
332	C₂²×C₈	—	7	1	no	—
333	C₂²×C₈	—	7	1	no	—
334	C₂²×C₈	—	7	1	no	—
335	C₂²×C₈	—	7	1	no	—
336	C₂²×C₈	—	14	1	no	—
337	C₂²×C₈	—	14	1	no	—
338	#126	—	2	1	no	—
339	#126	—	14	1	no	—
340	#125	—	7	1	no	—
341	#125	C₄×D₇	1	1	yes	characteristic
342	#124	—	7	1	no	—
343	#124	C₄×D₇	1	1	yes	characteristic
344	#123	—	2	1	no	—
345	#123	—	14	1	no	—
346	C₂²⋊Q₈	—	7	1	no	—
347	C₂²⋊Q₈	C₄×D₇	1	1	yes	characteristic
348	#121	—	7	1	no	—
349	#121	C₄×D₇	1	1	yes	characteristic
350	C₄×Q₈	—	7	1	no	—
351	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
352	C₄×D₄	—	2	1	no	—
353	C₄×D₄	—	7	1	no	—
354	C₄×D₄	—	14	1	no	—
355	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
356	#117	—	2	1	no	—
357	#117	—	14	1	no	—
358	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
359	#107	—	7	1	no	—
360	#107	—	7	1	no	—
361	#106	—	7	1	no	—
362	#106	—	7	1	no	—
363	C₄⋊C₈	—	7	1	no	—
364	C₄⋊C₈	—	7	1	no	—
365	C₄⋊C₈	—	14	1	no	—
366	C₄⋊C₈	—	14	1	no	—
367	C₄⋊C₈	—	14	1	no	—
368	C₄⋊C₈	—	14	1	no	—
369	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
370	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
371	#103	—	7	1	no	—
372	#103	—	7	1	no	—
373	#103	—	7	1	no	—
374	#103	—	7	1	no	—
375	#102	—	7	1	no	—
376	#102	—	7	1	no	—
377	#102	—	7	1	no	—
378	#102	—	7	1	no	—
379	C₂²⋊C₈	—	2	1	no	—
380	C₂²⋊C₈	—	14	1	no	—
381	C₂²⋊C₈	—	14	1	no	—
382	C₂²⋊C₈	—	14	1	no	—
383	C₂²⋊C₈	—	14	1	no	—
384	C₂²⋊C₈	—	14	1	no	—
385	#97	—	2	1	no	—
386	#97	—	14	1	no	—
387	#97	—	14	1	no	—
388	#97	—	14	1	no	—
389	C₄×C₈	—	2	1	no	—
390	C₄×C₈	—	7	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	—	7	1	no	—
398	C₄×C₈	—	14	1	no	—
399	C₄×C₈	—	14	1	no	—
400	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
401	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
402	C₂²×C₇	—	2	1	no	—
403	C₂²×C₇	—	2	1	no	—
404	C₂²×C₇	—	4	1	no	—
405	C₂²×C₇	—	4	1	no	—
406	C₂²×C₇	—	4	1	no	—
407	C₂²×C₇	#443	1	2	yes	—
408	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
409	C₂×D₇	—	4	1	no	—
410	C₂×D₇	—	4	1	no	—
411	C₂×D₇	—	4	1	no	—
412	C₄×C₇	—	2	1	no	—
413	C₄×C₇	—	2	1	no	—
414	C₄×C₇	—	2	1	no	—
415	C₄×C₇	—	2	1	no	—
416	C₄×C₇	—	4	1	no	—
417	C₄×C₇	—	4	1	no	—
418	C₄×C₇	—	4	1	no	—
419	C₄×C₇	C₂×#131	1	1	yes	characteristic
420	C₄×C₇	C₂×#131	1	1	yes	characteristic
421	C₄×C₇	C₂×#135	1	1	yes	characteristic
422	C₄×C₇	C₂×#135	1	1	yes	characteristic
423	Dic₇	—	4	1	no	—
424	Dic₇	—	4	1	no	—
425	Dic₇	—	4	1	no	—
426	C₂×Q₈	—	7	1	no	—
427	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	7	1	no	—
430	C₂×D₄	—	14	1	no	—
431	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	14	1	no	—
434	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
435	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
436	C₂²×C₄	#1159	1	1	yes	characteristic
437	Q₁₆	—	14	2	no	—
438	SD₁₆	—	14	2	no	—
439	SD₁₆	—	14	2	no	—
440	D₈	—	14	2	no	—
441	M₁₆	—	28	2	no	—
442	M₁₆	—	28	2	no	—
443	C₂×C₈	—	2	4	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	7	1	no	—
449	C₂×C₈	—	7	1	no	—
450	C₂×C₈	—	7	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	—	14	2	no	—
457	C₂×C₈	—	14	2	no	—
458	C₂×C₈	—	14	2	no	—
459	C₂×C₈	—	14	2	no	—
460	C₂×C₈	—	14	1	no	—
461	C₂×C₈	—	14	1	no	—
462	C₂×C₈	—	28	2	no	—
463	C₂×C₈	—	28	2	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	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	—	2	1	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	14	1	no	—
482	C₂²⋊C₄	—	14	1	no	—
483	C₂²⋊C₄	—	14	1	no	—
484	C₂²⋊C₄	—	14	1	no	—
485	C₂²⋊C₄	—	14	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	—	2	2	no	—
493	C₂×C₇	—	8	1	no	—
494	C₂×C₇	#2931	1	1	yes	characteristic
495	C₂×C₇	C₄×#135	1	1	yes	characteristic
496	C₂×C₇	C₂×#443	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	—	2	1	no	—
503	Q₈	—	14	1	no	—
504	Q₈	—	14	1	no	—
505	D₄	—	2	1	no	—
506	D₄	—	2	1	no	—
507	D₄	—	4	2	no	—
508	D₄	—	14	1	no	—
509	D₄	—	14	1	no	—
510	D₄	—	28	2	no	—
511	C₂×C₄	—	2	2	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	1	no	—
521	C₂×C₄	—	14	1	no	—
522	C₂×C₄	—	14	1	no	—
523	C₂×C₄	—	14	1	no	—
524	C₂×C₄	—	28	1	no	—
525	C₂×C₄	—	28	1	no	—
526	C₂×C₄	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
527	C₂×C₄	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
528	C₂×C₄	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
529	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
530	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
531	C₂×C₄	C₂×#1159	1	1	yes	characteristic
532	C₈	—	2	2	no	—
533	C₈	—	2	2	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	7	2	no	—
537	C₈	—	7	2	no	—
538	C₈	—	7	2	no	—
539	C₈	—	7	2	no	—
540	C₈	—	14	1	no	—
541	C₈	—	14	1	no	—
542	C₈	—	14	1	no	—
543	C₈	—	14	1	no	—
544	C₈	—	28	1	no	—
545	C₈	—	28	1	no	—
546	C₇	#17959	1	1	yes	characteristic, complemented, Sylow
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	28	1	no	—
553	C₂²	—	28	1	no	—
554	C₂²	—	28	1	no	—
555	C₂²	#89596	1	2	yes	—
556	C₂²	C₂×(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	28	1	no	—
565	C₄	—	28	1	no	—
566	C₄	—	28	1	no	—
567	C₄	D₇×#131	1	1	yes	characteristic
568	C₄	D₇×#131	1	1	yes	characteristic
569	C₄	D₇×#135	1	1	yes	characteristic
570	C₄	D₇×#135	1	1	yes	characteristic
571	C₂	—	2	2	no	—
572	C₂	—	8	1	no	—
573	C₂	—	56	1	no	—
574	C₂	#11736102	1	1	yes	characteristic
575	C₂	#11736263	1	1	yes	characteristic
576	C₂	C₂×#89596	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×#1494	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	#89810	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1494	D₇
hypocenter	C₇	#17959
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1494

Complements

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

N	H ≅ G/N	type
2. #11740571	C₂	semidirect
3. #11736770	C₂	semidirect
4. C₇×#1494	C₂	semidirect
5. #11728548	C₂	semidirect
6. #11727490	C₂	semidirect
7. C₂×C₈×C₇⋊C₈	C₂	semidirect
8. #11725979	C₂	semidirect
9. #11725978	C₂	semidirect
10. #11725967	C₂	semidirect
11. #11725966	C₂	semidirect
12. #11725915	C₂	semidirect
13. #11725914	C₂	semidirect
14. #11725903	C₂	semidirect
15. #11725902	C₂	semidirect
158. #1494	D₇	semidirect
546. C₇	#17959	semidirect

Maximal subgroups

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

subgroup	index
#11740579	2
#11740571	2
#11736770	2
C₇×#1494	2
#11728548	2
#11727490	2
C₂×C₈×C₇⋊C₈	2
#11725979	2
#11725978	2
#11725967	2
#11725966	2
#11725915	2
#11725914	2
#11725903	2
#11725902	2
#17959	7