Subgroups — #27098759

Order 12032.

1900 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257351	C₂	1	2	yes	maximal, complemented
2	#20256401	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256182	C₂	1	2	yes	maximal, complemented
5	#20255819	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255811	C₂	1	2	yes	maximal, complemented
7	#20255620	C₂	1	2	yes	maximal, complemented
8	#20255546	C₂	1	4	yes	maximal, complemented
9	#20255075	C₂	1	2	yes	maximal, complemented
10	D₄×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
11	#20254027	C₂	1	2	yes	maximal, complemented
12	#20253967	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253574	C₂	1	4	yes	maximal, complemented
14	#20253540	C₂	1	2	yes	maximal, complemented
15	#20252241	C₂	1	2	yes	maximal, complemented
16	C₄×#13094046	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13094046	C₂²	1	1	yes	characteristic
19	C₂²×D₃₇₆	C₂²	1	2	yes	—
20	#15689858	C₂²	1	2	yes	complemented
21	#15689843	C₂²	1	2	yes	—
22	#15689838	C₂²	1	4	yes	complemented
23	#15689798	—	2	4	no	—
24	Q₈×D₁₈₈	C₂²	1	2	yes	complemented
25	#15689783	—	2	2	no	—
26	#15689770	—	2	2	no	—
27	#15689769	C₂²	1	4	yes	complemented
28	D₄×D₁₈₈	C₂²	1	2	yes	—
29	#15689744	C₂²	1	4	yes	complemented
30	#15689709	—	2	4	no	—
31	#15689673	C₂²	1	2	yes	complemented
32	#15689658	—	2	2	no	—
33	#124×D₄₇	—	2	2	no	—
34	#15689597	C₂²	1	4	yes	complemented
35	C₄×#10625350	C₂²	1	2	yes	complemented
36	#15689528	C₂²	1	1	yes	characteristic, complemented
37	#15689528	C₂²	1	2	yes	complemented
38	#15689507	C₂²	1	2	yes	complemented
39	#15689500	C₂²	1	1	yes	characteristic
40	#15689483	C₂²	1	4	yes	complemented
41	#15689470	C₂²	1	2	yes	complemented
42	#15689465	C₂²	1	4	yes	complemented
43	#15689448	C₂²	1	4	yes	complemented
44	#15689448	C₂²	1	4	yes	complemented
45	#15689414	C₂²	1	4	yes	complemented
46	#15689409	C₂²	1	2	yes	complemented
47	#15689404	C₂²	1	4	yes	complemented
48	#15689404	C₂²	1	2	yes	complemented
49	#15689369	C₂²	1	4	yes	complemented
50	#15689364	C₂²	1	2	yes	complemented
51	#15689359	C₂²	1	2	yes	—
52	#15689359	C₂²	1	2	yes	complemented
53	#15689359	C₂²	1	2	yes	complemented
54	#15689339	C₂²	1	4	yes	complemented
55	#15689339	C₂²	1	4	yes	complemented
56	#15689324	C₂²	1	2	yes	complemented
57	#15689319	C₂²	1	2	yes	—
58	#15689276	C₂²	1	4	yes	complemented
59	#15689270	C₂²	1	4	yes	complemented
60	#15689259	C₂²	1	4	yes	—
61	#15689236	C₂²	1	4	yes	complemented
62	#15689236	C₂²	1	4	yes	complemented
63	#15689225	C₂²	1	4	yes	complemented
64	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic, complemented
65	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic, complemented
66	C₄×#10625325	C₂²	1	2	yes	complemented
67	C₄×#10625325	C₂²	1	2	yes	complemented
68	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
69	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
70	C₄×D₃₇₆	C₂²	1	2	yes	—
71	C₄×D₃₇₆	C₂²	1	2	yes	complemented
72	C₄×D₃₇₆	C₂²	1	2	yes	complemented
73	C₄×D₃₇₆	C₂²	1	2	yes	complemented
74	#15689161	C₂²	1	1	yes	characteristic, complemented
75	#15689161	C₂²	1	2	yes	complemented
76	#15689129	C₂²	1	4	yes	complemented
77	#15689120	C₂²	1	2	yes	complemented
78	C₄₇×#529	C₂²	1	1	yes	characteristic
79	C₄₇×#446	C₂²	1	1	yes	characteristic, complemented
80	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
81	C₄₇×#436	C₂²	1	1	yes	characteristic
82	C₄₇×#435	C₂²	1	2	yes	complemented
83	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
84	C₈×D₄×C₄₇	C₂²	1	2	yes	complemented
85	C₄₇×#433	C₂²	1	2	yes	complemented
86	C₄₇×#432	C₂²	1	1	yes	characteristic, complemented
87	C₄₇×#405	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
89	C₂×#10625350	—	2	2	no	—
90	C₂×#10625350	C₂³	1	2	yes	—
91	C₂×Q₈×D₄₇	—	2	2	no	—
92	C₂²×D₁₈₈	C₂³	1	4	yes	—
93	C₂×D₄×D₄₇	—	2	2	no	—
94	#13094046	—	2	4	no	—
95	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic
96	C₂×#10625325	C₂³	1	2	yes	—
97	C₂×#10625325	C₂³	1	4	yes	—
98	C₂×D₃₇₆	—	2	8	no	—
99	C₂×D₃₇₆	C₂³	1	4	yes	—
100	C₂×D₃₇₆	C₂³	1	2	yes	—
101	C₂×D₃₇₆	C₂³	1	2	yes	—
102	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
103	#13094024	C₂³	1	4	yes	—
104	#13094024	C₂³	1	2	yes	—
105	#13094021	C₂³	1	2	yes	—
106	#13094019	—	2	4	no	—
107	#13094017	—	2	4	no	—
108	#13094013	—	2	2	no	—
109	#13094012	—	2	2	no	—
110	#13094012	C₂³	1	4	yes	—
111	#13094011	—	2	2	no	—
112	#13094010	—	2	4	no	—
113	#13094010	—	2	4	no	—
114	#13094010	—	2	4	no	—
115	#13094009	—	2	4	no	—
116	#13094009	—	2	4	no	—
117	#13094006	—	2	4	no	—
118	#13094004	—	2	2	no	—
119	#13094004	—	2	4	no	—
120	#13094003	C₂³	1	4	yes	—
121	#13094002	—	2	4	no	—
122	#13093999	—	2	2	no	—
123	#13093998	—	2	2	no	—
124	#13093998	C₂³	1	4	yes	—
125	#13093998	C₂³	1	4	yes	—
126	#13093997	—	2	4	no	—
127	#13093995	—	2	4	no	—
128	#13093994	—	2	4	no	—
129	#13093992	—	2	4	no	—
130	C₄×Dic₉₄	C₂³	1	2	yes	—
131	C₄×Dic₉₄	C₂³	1	2	yes	—
132	#13093989	—	2	2	no	—
133	C₄×D₁₈₈	—	2	2	no	—
134	C₄×D₁₈₈	C₂³	1	4	yes	—
135	C₄×D₁₈₈	C₂³	1	2	yes	—
136	C₄×D₁₈₈	C₂³	1	4	yes	—
137	C₄×D₁₈₈	C₂³	1	4	yes	—
138	C₄×D₁₈₈	C₂³	1	2	yes	—
139	#13093986	—	2	2	no	—
140	#13093986	—	2	4	no	—
141	#13093986	—	2	4	no	—
142	C₄×C₂²⋊D₄₇	—	2	2	no	—
143	C₄×C₂²⋊D₄₇	—	2	2	no	—
144	#13093983	C₂³	1	2	yes	—
145	#13093983	C₂³	1	4	yes	—
146	#13093982	—	2	4	no	—
147	#13093981	—	2	2	no	—
148	C₂²⋊C₄×D₄₇	—	2	4	no	—
149	C₂²⋊C₄×D₄₇	—	2	4	no	—
150	C₂²⋊C₄×D₄₇	—	2	4	no	—
151	C₄²×D₄₇	—	2	2	no	—
152	#13093958	C₂³	1	1	yes	characteristic
153	#13093958	C₂³	1	1	yes	characteristic
154	#13093958	C₂³	1	4	yes	—
155	#13093958	C₂³	1	2	yes	—
156	#13093958	C₂³	1	2	yes	—
157	#13093956	C₂³	1	4	yes	—
158	#13093956	C₂³	1	2	yes	—
159	#13093949	C₂³	1	2	yes	—
160	#13093949	C₂³	1	2	yes	—
161	#13093949	C₂³	1	4	yes	—
162	#13093946	C₂³	1	4	yes	—
163	#13093946	C₂³	1	4	yes	—
164	#13093946	C₂³	1	2	yes	—
165	#13093946	C₂³	1	4	yes	—
166	#13093946	C₂³	1	4	yes	—
167	#13093946	C₂³	1	2	yes	—
168	#13093946	C₂³	1	4	yes	—
169	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
170	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
171	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
172	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
173	#126×C₄₇	D₄	1	2	yes	—
174	#125×C₄₇	D₄	1	1	yes	characteristic
175	#124×C₄₇	D₄	1	1	yes	characteristic
176	#123×C₄₇	D₄	1	2	yes	—
177	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
178	#121×C₄₇	D₄	1	1	yes	characteristic
179	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₄₇	C₂³	1	2	yes	—
182	#117×C₄₇	C₂³	1	2	yes	—
183	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
184	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
185	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
186	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
187	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
188	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
191	#97×C₄₇	C₂³	1	2	yes	—
192	#97×C₄₇	C₂³	1	2	yes	—
193	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₄₇	C₂³	1	2	yes	—
196	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
198	C₂³×D₄₇	—	2	4	no	—
199	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
200	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
201	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
206	C₂×C₂²⋊D₄₇	—	2	2	no	—
207	C₂×C₂²⋊D₄₇	—	2	4	no	—
208	C₂×C₂²⋊D₄₇	—	2	4	no	—
209	Q₈×D₄₇	—	8	4	no	—
210	D₄×D₄₇	—	8	4	no	—
211	#10625350	—	2	4	no	—
212	#10625350	—	4	2	no	—
213	#10625350	—	8	4	no	—
214	C₂×D₁₈₈	—	2	8	no	—
215	C₂×D₁₈₈	—	2	4	no	—
216	C₂×D₁₈₈	—	2	2	no	—
217	C₂×D₁₈₈	—	2	2	no	—
218	C₂×D₁₈₈	—	4	4	no	—
219	C₂×D₁₈₈	C₂⁴	1	4	yes	—
220	C₂×D₁₈₈	C₂⁴	1	2	yes	—
221	C₂×C₄×D₄₇	—	2	2	no	—
222	C₂×C₄×D₄₇	—	2	2	no	—
223	C₂×C₄×D₄₇	—	2	2	no	—
224	C₂×C₄×D₄₇	—	2	4	no	—
225	C₂×C₄×D₄₇	—	2	4	no	—
226	C₂×C₄×D₄₇	—	2	4	no	—
227	C₂×Dic₉₄	—	2	2	no	—
228	C₂×Dic₉₄	—	2	4	no	—
229	C₂×Dic₉₄	C₂⁴	1	2	yes	—
230	M₁₆×C₄₇	—	4	2	no	—
231	C₂×C₈×C₄₇	—	2	4	no	—
232	C₂×C₈×C₄₇	—	2	2	no	—
233	C₂×C₈×C₄₇	—	4	1	no	—
234	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
235	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
236	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
237	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
238	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
239	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
240	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
241	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
242	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
243	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
244	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
245	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
246	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
247	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
248	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
249	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
250	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
251	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
252	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
253	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
254	C₄²×C₄₇	C₂⁴	1	2	yes	—
255	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
256	C₂²⋊Dic₄₇	—	2	4	no	—
257	C₂²⋊Dic₄₇	—	2	4	no	—
258	C₂²⋊Dic₄₇	—	2	2	no	—
259	(C₂×D₄₇)⋊C₄	—	2	2	no	—
260	(C₂×D₄₇)⋊C₄	—	2	4	no	—
261	(C₂×D₄₇)⋊C₄	—	2	4	no	—
262	(C₂×D₄₇)⋊C₄	—	2	4	no	—
263	(C₂×D₄₇)⋊C₄	—	2	4	no	—
264	(C₂×D₄₇)⋊C₄	—	2	4	no	—
265	(C₂×D₄₇)⋊C₄	—	2	2	no	—
266	(C₂×D₄₇)⋊C₄	—	2	4	no	—
267	(C₂×D₄₇)⋊C₄	—	2	4	no	—
268	C₄⋊Dic₄₇	—	2	4	no	—
269	C₄⋊Dic₄₇	—	2	2	no	—
270	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
271	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
272	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
273	Dic₄₇⋊C₄	—	2	2	no	—
274	Dic₄₇⋊C₄	—	2	2	no	—
275	Dic₄₇⋊C₄	—	2	4	no	—
276	C₄×Dic₄₇	—	2	2	no	—
277	C₄×Dic₄₇	—	2	2	no	—
278	C₄×Dic₄₇	—	2	2	no	—
279	C₄×Dic₄₇	—	2	4	no	—
280	Dic₁₈₈	—	2	2	no	—
281	D₃₇₆	—	2	8	no	—
282	D₃₇₆	—	2	4	no	—
283	D₃₇₆	—	4	2	no	—
284	D₃₇₆	#41	1	4	yes	complemented
285	#10625325	—	2	4	no	—
286	#10625325	—	4	4	no	—
287	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
288	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
289	C₂²×D₄₇	—	2	2	no	—
290	C₂²×D₄₇	—	2	4	no	—
291	C₂²×D₄₇	—	4	8	no	—
292	C₂²×D₄₇	—	8	4	no	—
293	C₂²×D₄₇	—	8	4	no	—
294	Q₈×C₄₇	—	2	2	no	—
295	D₄×C₄₇	—	2	2	no	—
296	D₄×C₄₇	—	4	2	no	—
297	C₂×C₄×C₄₇	—	2	2	no	—
298	C₂×C₄×C₄₇	—	2	2	no	—
299	C₂×C₄×C₄₇	—	2	1	no	—
300	C₂×C₄×C₄₇	—	2	1	no	—
301	C₂×C₄×C₄₇	—	2	2	no	—
302	C₂×C₄×C₄₇	—	4	1	no	—
303	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
312	C₂²⋊D₄₇	—	4	4	no	—
313	C₂²⋊D₄₇	—	8	4	no	—
314	C₂²⋊D₄₇	—	8	4	no	—
315	C₂×Dic₄₇	—	2	2	no	—
316	C₂×Dic₄₇	—	2	2	no	—
317	C₂×Dic₄₇	—	2	2	no	—
318	C₂×Dic₄₇	—	2	4	no	—
319	D₁₈₈	—	2	4	no	—
320	D₁₈₈	—	2	2	no	—
321	D₁₈₈	—	2	4	no	—
322	D₁₈₈	—	4	8	no	—
323	D₁₈₈	—	4	4	no	—
324	D₁₈₈	—	8	2	no	—
325	D₁₈₈	C₂×#41	1	4	yes	—
326	C₄×D₄₇	—	4	4	no	—
327	C₄×D₄₇	—	4	4	no	—
328	C₄×D₄₇	—	8	2	no	—
329	C₄×D₄₇	—	8	4	no	—
330	C₄×D₄₇	—	8	4	no	—
331	C₄×D₄₇	—	8	4	no	—
332	Dic₉₄	—	2	2	no	—
333	Dic₉₄	—	2	2	no	—
334	Dic₉₄	—	4	4	no	—
335	Dic₉₄	—	8	4	no	—
336	C₈×C₄₇	—	2	1	no	—
337	C₈×C₄₇	—	2	2	no	—
338	C₈×C₄₇	—	2	2	no	—
339	C₈×C₄₇	—	2	1	no	—
340	C₈×C₄₇	—	2	1	no	—
341	C₈×C₄₇	C₂×#41	1	2	yes	—
342	#61475	—	47	1	no	maximal, Sylow
343	C₂²×C₄₇	—	2	1	no	—
344	C₂²×C₄₇	—	2	2	no	—
345	C₂²×C₄₇	—	2	1	no	—
346	C₂²×C₄₇	—	2	2	no	—
347	C₂²×C₄₇	—	2	1	no	—
348	C₂²×C₄₇	—	2	2	no	—
349	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
350	C₂×D₄₇	—	2	4	no	—
351	C₂×D₄₇	—	4	2	no	—
352	C₂×D₄₇	—	4	2	no	—
353	C₂×D₄₇	—	4	4	no	—
354	C₂×D₄₇	—	4	4	no	—
355	C₂×D₄₇	—	4	4	no	—
356	C₂×D₄₇	—	16	8	no	—
357	C₄×C₄₇	—	2	1	no	—
358	C₄×C₄₇	—	2	2	no	—
359	C₄×C₄₇	—	2	1	no	—
360	C₄×C₄₇	—	2	1	no	—
361	C₄×C₄₇	—	2	2	no	—
362	C₄×C₄₇	—	2	2	no	—
363	C₄×C₄₇	—	2	1	no	—
364	C₄×C₄₇	#576	1	2	yes	—
365	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
366	C₄×C₄₇	#585	1	1	yes	characteristic
367	Dic₄₇	—	4	2	no	—
368	Dic₄₇	—	4	2	no	—
369	Dic₄₇	—	4	4	no	—
370	Dic₄₇	—	4	2	no	—
371	#3514	—	47	2	no	—
372	#3396	—	47	1	no	—
373	Q₈×D₈	—	47	1	no	—
374	#3373	—	47	2	no	—
375	#3342	—	47	1	no	—
376	#3341	—	47	2	no	—
377	#3324	—	47	2	no	—
378	#3319	—	47	4	no	—
379	#3280	—	47	2	no	—
380	D₄×D₈	—	47	1	no	—
381	#3175	—	47	2	no	—
382	#3169	—	47	1	no	—
383	#3118	—	47	4	no	—
384	#3115	—	47	2	no	—
385	#2966	D₄₇	1	1	yes	characteristic, complemented
386	#2948	—	47	2	no	—
387	C₄×#135	—	47	1	no	—
388	C₂×C₄₇	—	4	2	no	—
389	C₂×C₄₇	—	4	1	no	—
390	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
391	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
392	C₂×C₄₇	#3584	1	1	yes	characteristic
393	D₄₇	—	4	4	no	—
394	D₄₇	—	8	4	no	—
395	C₂×#135	—	47	1	no	—
396	C₂²×D₈	—	47	2	no	—
397	#559	—	47	2	no	—
398	#556	—	47	2	no	—
399	#555	—	47	4	no	—
400	#551	—	94	4	no	—
401	D₄×Q₈	—	47	2	no	—
402	#548	—	94	2	no	—
403	#546	—	47	4	no	—
404	#546	—	94	2	no	—
405	D₄²	—	47	2	no	—
406	#542	—	47	4	no	—
407	#538	—	94	4	no	—
408	#532	—	47	2	no	—
409	#529	—	94	2	no	—
410	#529	C₂×D₄₇	1	1	yes	characteristic
411	C₂×#124	—	94	2	no	—
412	#518	—	47	4	no	—
413	C₄×#41	—	47	2	no	—
414	#500	—	47	2	no	—
415	#500	—	47	1	no	—
416	#495	—	47	2	no	—
417	#493	—	47	1	no	—
418	#489	—	47	4	no	—
419	#486	—	47	2	no	—
420	#485	—	47	4	no	—
421	#482	—	47	4	no	—
422	#482	—	47	4	no	—
423	#476	—	47	4	no	—
424	#475	—	47	2	no	—
425	#474	—	47	2	no	—
426	#474	—	47	4	no	—
427	#468	—	47	4	no	—
428	#467	—	47	2	no	—
429	#466	—	47	2	no	—
430	#466	—	47	2	no	—
431	#466	—	47	2	no	—
432	#463	—	47	4	no	—
433	#463	—	47	4	no	—
434	#460	—	47	2	no	—
435	#459	—	47	2	no	—
436	#450	—	47	4	no	—
437	#449	—	47	4	no	—
438	#447	—	47	4	no	—
439	#446	C₂×D₄₇	1	1	yes	characteristic, complemented
440	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
441	#442	—	47	4	no	—
442	#442	—	47	4	no	—
443	#440	—	47	4	no	—
444	C₄×Q₁₆	—	47	1	no	—
445	C₄×Q₁₆	—	47	1	no	—
446	C₄×SD₁₆	—	47	2	no	—
447	C₄×SD₁₆	—	47	2	no	—
448	C₄×D₈	—	47	2	no	—
449	C₄×D₈	—	47	2	no	—
450	C₄×D₈	—	47	1	no	—
451	C₄×D₈	—	47	2	no	—
452	C₄×D₈	—	47	2	no	—
453	C₄×D₈	—	47	1	no	—
454	#436	C₂×D₄₇	1	1	yes	characteristic
455	#435	C₂×D₄₇	1	2	yes	complemented
456	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic
457	C₈×D₄	C₂×D₄₇	1	2	yes	complemented
458	#433	C₂×D₄₇	1	2	yes	complemented
459	#432	C₂×D₄₇	1	1	yes	characteristic, complemented
460	#427	—	47	1	no	—
461	#427	—	47	2	no	—
462	#418	—	47	4	no	—
463	#416	—	47	2	no	—
464	#405	C₂×D₄₇	1	2	yes	complemented
465	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
466	C₄₇	#61475	1	1	yes	characteristic, complemented, Sylow
467	C₂×#41	—	47	2	no	—
468	C₂×#41	—	94	2	no	—
469	C₂²×Q₈	—	94	2	no	—
470	C₂²×D₄	—	47	4	no	—
471	C₂²×D₄	—	94	2	no	—
472	#135	—	94	4	no	—
473	C₂×Q₁₆	—	47	1	no	—
474	C₂×SD₁₆	—	47	2	no	—
475	C₂×SD₁₆	—	47	4	no	—
476	C₂×D₈	—	47	1	no	—
477	C₂×D₈	—	47	2	no	—
478	C₂×D₈	—	47	4	no	—
479	C₂×D₈	—	47	2	no	—
480	C₂×D₈	—	94	8	no	—
481	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
482	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
483	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
484	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
485	C₄⋊Q₈	—	47	2	no	—
486	C₄⋊Q₈	—	47	4	no	—
487	#127	—	47	2	no	—
488	#126	—	94	4	no	—
489	#126	—	94	4	no	—
490	#126	D₁₈₈	1	2	yes	—
491	#125	D₁₈₈	1	1	yes	characteristic
492	#124	—	47	4	no	—
493	#124	—	94	2	no	—
494	#124	—	94	2	no	—
495	#124	—	94	4	no	—
496	#124	—	94	4	no	—
497	#124	—	94	4	no	—
498	#124	—	94	2	no	—
499	#124	D₁₈₈	1	1	yes	characteristic
500	#123	—	94	4	no	—
501	#123	—	94	4	no	—
502	#123	—	94	4	no	—
503	#123	D₁₈₈	1	2	yes	—
504	C₂²⋊Q₈	—	47	4	no	—
505	C₂²⋊Q₈	—	94	2	no	—
506	C₂²⋊Q₈	—	94	4	no	—
507	C₂²⋊Q₈	—	94	4	no	—
508	C₂²⋊Q₈	D₁₈₈	1	1	yes	characteristic
509	#121	—	47	4	no	—
510	#121	—	47	4	no	—
511	#121	—	94	4	no	—
512	#121	—	94	2	no	—
513	#121	—	94	2	no	—
514	#121	—	94	4	no	—
515	#121	D₁₈₈	1	1	yes	characteristic
516	#120	—	94	4	no	—
517	#120	—	94	4	no	—
518	C₄×Q₈	—	47	2	no	—
519	C₄×Q₈	—	47	2	no	—
520	C₄×Q₈	—	94	2	no	—
521	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
522	C₄×D₄	—	47	2	no	—
523	C₄×D₄	—	47	2	no	—
524	C₄×D₄	—	47	4	no	—
525	C₄×D₄	—	47	4	no	—
526	C₄×D₄	—	47	4	no	—
527	C₄×D₄	—	94	2	no	—
528	C₄×D₄	—	94	2	no	—
529	C₄×D₄	—	94	4	no	—
530	C₄×D₄	—	94	4	no	—
531	C₄×D₄	—	94	2	no	—
532	C₄×D₄	—	94	2	no	—
533	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
534	C₄×D₄	C₂²×D₄₇	1	2	yes	—
535	#117	—	47	2	no	—
536	#117	—	47	4	no	—
537	#117	—	94	4	no	—
538	#117	—	94	2	no	—
539	#117	C₂²×D₄₇	1	2	yes	—
540	C₂×C₂²⋊C₄	—	94	4	no	—
541	C₂×C₂²⋊C₄	—	94	4	no	—
542	C₂×C₂²⋊C₄	—	94	4	no	—
543	C₂×C₄²	—	94	2	no	—
544	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
545	#107	—	47	1	no	—
546	#107	—	47	2	no	—
547	#107	—	47	1	no	—
548	#107	—	47	2	no	—
549	#107	—	47	4	no	—
550	#106	—	47	2	no	—
551	#106	—	47	4	no	—
552	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
553	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
554	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
555	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
556	#103	—	47	2	no	—
557	#103	—	47	2	no	—
558	#103	—	47	4	no	—
559	#102	—	47	2	no	—
560	#102	—	47	2	no	—
561	#102	—	47	4	no	—
562	#102	—	47	4	no	—
563	#102	—	47	4	no	—
564	#102	—	47	4	no	—
565	#102	—	47	4	no	—
566	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
567	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
568	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
569	#97	C₂²×D₄₇	1	2	yes	—
570	#97	C₂²×D₄₇	1	2	yes	—
571	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
572	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
573	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
574	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
575	C₄×C₈	C₂²×D₄₇	1	2	yes	—
576	C₂⁴	—	94	4	no	—
577	#41	—	94	4	no	—
578	#41	—	376	4	no	—
579	#41	—	188	2	no	—
580	C₂×Q₈	—	47	2	no	—
581	C₂×Q₈	—	94	4	no	—
582	C₂×Q₈	—	94	2	no	—
583	C₂×Q₈	—	376	4	no	—
584	C₂×Q₈	C₂×D₁₈₈	1	1	yes	characteristic
585	C₂×D₄	—	47	2	no	—
586	C₂×D₄	—	47	4	no	—
587	C₂×D₄	—	94	8	no	—
588	C₂×D₄	—	94	4	no	—
589	C₂×D₄	—	94	4	no	—
590	C₂×D₄	—	94	2	no	—
591	C₂×D₄	—	94	2	no	—
592	C₂×D₄	—	94	4	no	—
593	C₂×D₄	—	94	2	no	—
594	C₂×D₄	—	376	4	no	—
595	C₂×D₄	—	188	4	no	—
596	C₂×D₄	C₂×D₁₈₈	1	1	yes	characteristic
597	C₂×D₄	C₂×D₁₈₈	1	2	yes	—
598	C₂²×C₄	—	94	2	no	—
599	C₂²×C₄	—	94	4	no	—
600	C₂²×C₄	—	94	4	no	—
601	C₂²×C₄	—	94	4	no	—
602	C₂²×C₄	—	94	2	no	—
603	C₂²×C₄	—	94	2	no	—
604	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
606	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
607	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
608	Q₁₆	—	94	2	no	—
609	SD₁₆	—	94	4	no	—
610	SD₁₆	—	188	4	no	—
611	D₈	—	47	4	no	—
612	D₈	—	94	8	no	—
613	D₈	—	94	4	no	—
614	D₈	—	188	2	no	—
615	M₁₆	—	4	2	no	—
616	C₂×C₈	—	2	4	no	—
617	C₂×C₈	—	2	2	no	—
618	C₂×C₈	—	4	1	no	—
619	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
620	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
621	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
622	C₂×C₈	C₂³×D₄₇	1	2	yes	—
623	C₂×C₈	C₂³×D₄₇	1	2	yes	—
624	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
625	C₄⋊C₄	—	47	2	no	—
626	C₄⋊C₄	—	47	4	no	—
627	C₄⋊C₄	—	47	2	no	—
628	C₄⋊C₄	—	94	2	no	—
629	C₄⋊C₄	—	94	2	no	—
630	C₄⋊C₄	—	94	4	no	—
631	C₄⋊C₄	—	94	4	no	—
632	C₄⋊C₄	—	94	2	no	—
633	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
634	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
635	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
636	C₄⋊C₄	C₂×D₁₈₈	1	1	yes	characteristic
637	C₄⋊C₄	C₂×D₁₈₈	1	1	yes	characteristic
638	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
639	C₂²⋊C₄	—	94	4	no	—
640	C₂²⋊C₄	—	94	4	no	—
641	C₂²⋊C₄	—	94	2	no	—
642	C₂²⋊C₄	—	94	2	no	—
643	C₂²⋊C₄	—	94	4	no	—
644	C₂²⋊C₄	—	94	4	no	—
645	C₂²⋊C₄	—	94	4	no	—
646	C₂²⋊C₄	—	94	4	no	—
647	C₂²⋊C₄	—	94	4	no	—
648	C₂²⋊C₄	—	94	2	no	—
649	C₂²⋊C₄	—	94	4	no	—
650	C₂²⋊C₄	—	94	4	no	—
651	C₂²⋊C₄	C₂×D₁₈₈	1	2	yes	—
652	C₂²⋊C₄	C₂×D₁₈₈	1	2	yes	—
653	C₂²⋊C₄	C₂×D₁₈₈	1	2	yes	—
654	C₂²⋊C₄	C₂×D₁₈₈	1	2	yes	—
655	C₂²⋊C₄	C₂×D₁₈₈	1	2	yes	—
656	C₄²	—	94	2	no	—
657	C₄²	—	94	2	no	—
658	C₄²	—	94	2	no	—
659	C₄²	—	94	4	no	—
660	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
661	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
662	C₄²	C₂³×D₄₇	1	1	yes	characteristic
663	C₄²	C₂³×D₄₇	1	1	yes	characteristic
664	C₄²	C₂³×D₄₇	1	2	yes	—
665	C₂³	—	94	2	no	—
666	C₂³	—	94	4	no	—
667	C₂³	—	376	4	no	—
668	C₂³	—	376	4	no	—
669	C₂³	—	188	8	no	—
670	C₂³	C₂²×D₁₈₈	1	2	yes	—
671	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
672	Q₈	—	2	2	no	—
673	Q₈	—	94	2	no	—
674	Q₈	—	94	2	no	—
675	Q₈	—	376	4	no	—
676	Q₈	—	188	4	no	—
677	D₄	—	2	2	no	—
678	D₄	—	4	2	no	—
679	D₄	—	47	4	no	—
680	D₄	—	94	4	no	—
681	D₄	—	94	2	no	—
682	D₄	—	94	4	no	—
683	D₄	—	376	2	no	—
684	D₄	—	376	4	no	—
685	D₄	—	376	4	no	—
686	D₄	—	188	8	no	—
687	D₄	—	188	4	no	—
688	D₄	—	188	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	94	2	no	—
696	C₂×C₄	—	94	2	no	—
697	C₂×C₄	—	94	2	no	—
698	C₂×C₄	—	94	4	no	—
699	C₂×C₄	—	376	2	no	—
700	C₂×C₄	—	376	4	no	—
701	C₂×C₄	—	376	4	no	—
702	C₂×C₄	—	376	4	no	—
703	C₂×C₄	—	188	4	no	—
704	C₂×C₄	—	188	4	no	—
705	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₁₈₈	1	2	yes	—
708	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₁₈₈	1	2	yes	—
711	C₂×C₄	C₂²×D₁₈₈	1	2	yes	—
712	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
713	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
714	C₈	—	2	2	no	—
715	C₈	—	2	1	no	—
716	C₈	—	2	1	no	—
717	C₈	—	2	1	no	—
718	C₈	—	2	2	no	—
719	C₈	#41×D₄₇	1	2	yes	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	94	4	no	—
727	C₂²	—	188	4	no	—
728	C₂²	—	188	4	no	—
729	C₂²	—	188	4	no	—
730	C₂²	—	188	2	no	—
731	C₂²	—	188	2	no	—
732	C₂²	—	752	8	no	—
733	C₂²	C₂³×D₁₈₈	1	1	yes	characteristic
734	C₄	—	2	1	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	2	no	—
738	C₄	—	2	1	no	—
739	C₄	—	2	1	no	—
740	C₄	—	2	2	no	—
741	C₄	—	188	4	no	—
742	C₄	—	188	2	no	—
743	C₄	—	188	2	no	—
744	C₄	—	188	2	no	—
745	C₄	#15689928	1	2	yes	—
746	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
747	C₄	#15689959	1	1	yes	characteristic
748	C₂	—	4	2	no	—
749	C₂	—	4	1	no	—
750	C₂	—	376	4	no	—
751	C₂	—	188	4	no	—
752	C₂	#41×D₁₈₈	1	1	yes	characteristic
753	C₂	C₂×#15689928	1	1	yes	characteristic
754	C₂	#20258162	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₁₈₈
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#2966	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#2966	D₄₇
hypocenter	C₄₇	#61475
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #529 ◁ #2966

Complements

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

N	H ≅ G/N	type
1. #20257351	C₂	semidirect
2. #20256401	C₂	semidirect
3. Q₈×D₃₇₆	C₂	semidirect
4. #20256182	C₂	semidirect
5. #20255819	C₂	semidirect
6. #20255811	C₂	semidirect
7. #20255620	C₂	semidirect
8. #20255546	C₂	semidirect
9. #20255075	C₂	semidirect
10. D₄×D₃₇₆	C₂	semidirect
11. #20254027	C₂	semidirect
12. #20253967	C₂	semidirect
13. #20253574	C₂	semidirect
14. #20253540	C₂	semidirect
15. #20252241	C₂	semidirect
16. C₄×#13094046	C₂	semidirect
17. C₄₇×#2966	C₂	semidirect
20. #15689858	C₂²	semidirect
22. #15689838	C₂²	semidirect
24. Q₈×D₁₈₈	C₂²	semidirect
27. #15689769	C₂²	semidirect
29. #15689744	C₂²	semidirect
31. #15689673	C₂²	semidirect
34. #15689597	C₂²	semidirect
35. C₄×#10625350	C₂²	semidirect
36. #15689528	C₂²	semidirect
37. #15689528	C₂²	semidirect
38. #15689507	C₂²	semidirect
40. #15689483	C₂²	semidirect
41. #15689470	C₂²	semidirect
42. #15689465	C₂²	semidirect
43. #15689448	C₂²	semidirect
44. #15689448	C₂²	semidirect
45. #15689414	C₂²	semidirect
46. #15689409	C₂²	semidirect
47. #15689404	C₂²	semidirect
48. #15689404	C₂²	semidirect
49. #15689369	C₂²	semidirect
50. #15689364	C₂²	semidirect
52. #15689359	C₂²	semidirect
53. #15689359	C₂²	semidirect
54. #15689339	C₂²	semidirect
55. #15689339	C₂²	semidirect
56. #15689324	C₂²	semidirect
58. #15689276	C₂²	semidirect
59. #15689270	C₂²	semidirect
61. #15689236	C₂²	semidirect
62. #15689236	C₂²	semidirect
63. #15689225	C₂²	semidirect
64. C₄×Dic₁₈₈	C₂²	semidirect
65. C₄×Dic₁₈₈	C₂²	semidirect
66. C₄×#10625325	C₂²	semidirect
67. C₄×#10625325	C₂²	semidirect
71. C₄×D₃₇₆	C₂²	semidirect
72. C₄×D₃₇₆	C₂²	semidirect
73. C₄×D₃₇₆	C₂²	semidirect
74. #15689161	C₂²	semidirect
75. #15689161	C₂²	semidirect
76. #15689129	C₂²	semidirect
77. #15689120	C₂²	semidirect
79. C₄₇×#446	C₂²	semidirect
80. C₈×Q₈×C₄₇	C₂²	semidirect
82. C₄₇×#435	C₂²	semidirect
84. C₈×D₄×C₄₇	C₂²	semidirect
85. C₄₇×#433	C₂²	semidirect
86. C₄₇×#432	C₂²	semidirect
87. C₄₇×#405	C₂²	semidirect
88. C₂×C₄×C₈×C₄₇	C₂²	semidirect
284. D₃₇₆	#41	semidirect
385. #2966	D₄₇	semidirect
439. #446	C₂×D₄₇	semidirect
440. C₈×Q₈	C₂×D₄₇	semidirect
455. #435	C₂×D₄₇	semidirect
457. C₈×D₄	C₂×D₄₇	semidirect
458. #433	C₂×D₄₇	semidirect
459. #432	C₂×D₄₇	semidirect
464. #405	C₂×D₄₇	semidirect
465. C₂×C₄×C₈	C₂×D₄₇	semidirect
466. C₄₇	#61475	semidirect

Maximal subgroups

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

subgroup	index
#20257351	2
#20256401	2
Q₈×D₃₇₆	2
#20256182	2
#20255819	2
#20255811	2
#20255620	2
#20255546	2
#20255075	2
D₄×D₃₇₆	2
#20254027	2
#20253967	2
#20253574	2
#20253540	2
#20252241	2
C₄×#13094046	2
C₄₇×#2966	2
#61475	47