Subgroups — #27087765

Order 12032.

2164 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	C₂×#15689673	C₂	1	1	yes	maximal, characteristic
2	#20254395	C₂	1	4	yes	maximal, complemented
3	#20254387	C₂	1	4	yes	maximal, complemented
4	#20254340	C₂	1	4	yes	maximal, complemented
5	#20254333	C₂	1	2	yes	maximal, complemented
6	#20254326	C₂	1	2	yes	maximal, complemented
7	#20253845	C₂	1	2	yes	maximal, complemented
8	#20253784	C₂	1	2	yes	maximal, complemented
9	#20252860	C₂	1	4	yes	maximal, complemented
10	#20252646	C₂	1	4	yes	maximal, complemented
11	#20252021	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#10625350	C₂²	1	2	yes	—
14	C₂×#13094055	C₂²	1	8	yes	complemented
15	#15689673	—	2	1	no	—
16	#15689673	—	2	1	no	—
17	#15689673	—	2	1	no	—
18	#15689673	—	2	1	no	—
19	#15689673	C₂²	1	2	yes	—
20	#15689673	C₂²	1	2	yes	—
21	#15689673	C₂²	1	2	yes	—
22	#15689673	C₂²	1	2	yes	—
23	C₂×#13094024	C₂²	1	1	yes	characteristic
24	C₂×#13094021	C₂²	1	1	yes	characteristic
25	C₂×#13094012	C₂²	1	2	yes	—
26	C₂×#13093998	—	2	1	no	—
27	C₂×#13093998	—	2	1	no	—
28	C₂×C₄×D₁₈₈	—	2	1	no	—
29	C₂×C₄×D₁₈₈	—	2	1	no	—
30	#15689515	C₂²	1	8	yes	complemented
31	#15689502	C₂²	1	4	yes	complemented
32	#15689497	C₂²	1	4	yes	complemented
33	#15689485	C₂²	1	8	yes	complemented
34	#15689475	C₂²	1	4	yes	complemented
35	#15689471	C₂²	1	4	yes	complemented
36	#15689345	C₂²	1	16	yes	complemented
37	#15689333	C₂²	1	8	yes	complemented
38	#15689323	C₂²	1	8	yes	complemented
39	#15689283	C₂²	1	16	yes	complemented
40	#15689278	C₂²	1	8	yes	—
41	#15689273	C₂²	1	8	yes	—
42	#15689180	C₂²	1	2	yes	—
43	#15689180	C₂²	1	2	yes	complemented
44	#15689176	C₂²	1	2	yes	—
45	#15689176	C₂²	1	2	yes	complemented
46	#15689147	C₂²	1	2	yes	complemented
47	#15689122	C₂²	1	8	yes	complemented
48	#15689087	C₂²	1	2	yes	—
49	C₄×#10625329	C₂²	1	2	yes	complemented
50	C₄₇×#533	—	2	1	no	—
51	C₄₇×#533	—	2	1	no	—
52	C₄₇×#533	—	2	1	no	—
53	C₄₇×#533	—	2	1	no	—
54	C₄₇×#533	C₂²	1	2	yes	—
55	C₄₇×#533	C₂²	1	2	yes	—
56	C₄₇×#533	C₂²	1	2	yes	complemented
57	C₄₇×#533	C₂²	1	2	yes	complemented
58	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
60	C₂×#125×C₄₇	—	2	1	no	—
61	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
62	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
63	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
64	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	complemented
65	C₂×#117×C₄₇	—	2	1	no	—
66	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
67	C₂×#10625350	—	2	2	no	—
68	C₂×#10625350	—	2	2	no	—
69	C₂×#10625350	—	4	8	no	—
70	C₂×#10625350	C₂³	1	4	yes	—
71	C₂×#10625350	C₂³	1	4	yes	—
72	C₂²×Dic₉₄	C₂³	1	2	yes	—
73	C₂²×D₁₈₈	—	2	1	no	—
74	C₂²×D₁₈₈	—	2	1	no	—
75	C₂²×D₁₈₈	C₂³	1	2	yes	—
76	C₂²×C₂²⋊D₄₇	—	2	2	no	—
77	C₂²×C₄×D₄₇	—	2	2	no	—
78	#13094055	—	4	16	no	—
79	C₂×#10625337	C₂³	1	16	yes	—
80	C₂×#10625336	C₂³	1	16	yes	—
81	C₂×#10625329	C₂³	1	4	yes	—
82	#13094024	—	2	1	no	—
83	#13094024	—	2	1	no	—
84	#13094024	C₂³	1	2	yes	—
85	#13094024	C₂³	1	2	yes	—
86	#13094021	—	2	1	no	—
87	#13094021	—	2	1	no	—
88	#13094021	C₂³	1	2	yes	—
89	#13094021	C₂³	1	2	yes	—
90	#13094012	—	2	2	no	—
91	#13094012	—	2	2	no	—
92	#13094012	C₂³	1	4	yes	—
93	#13094012	C₂³	1	4	yes	—
94	#13093998	—	2	2	no	—
95	#13093998	—	2	2	no	—
96	#13093998	—	2	2	no	—
97	#13093998	—	2	2	no	—
98	#13093998	—	2	2	no	—
99	#13093998	—	2	2	no	—
100	#13093998	—	2	2	no	—
101	#13093998	—	2	2	no	—
102	C₄×D₁₈₈	—	2	2	no	—
103	C₄×D₁₈₈	—	2	2	no	—
104	C₄×D₁₈₈	—	2	2	no	—
105	C₄×D₁₈₈	—	2	2	no	—
106	C₄×D₁₈₈	—	2	2	no	—
107	C₄×D₁₈₈	—	2	2	no	—
108	C₄×D₁₈₈	—	2	2	no	—
109	C₄×D₁₈₈	—	2	2	no	—
110	C₂×C₄⋊Dic₄₇	—	2	1	no	—
111	C₂×C₄⋊Dic₄₇	—	2	1	no	—
112	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
113	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
114	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
115	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
116	#13093947	C₂³	1	16	yes	—
117	#13093944	C₂³	1	16	yes	—
118	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
119	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
120	#13093935	C₂³	1	4	yes	—
121	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
122	C₂²×Q₈×C₄₇	—	2	1	no	—
123	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
124	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
125	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
126	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
127	C₄⋊Q₈×C₄₇	—	2	1	no	—
128	C₄⋊Q₈×C₄₇	—	2	1	no	—
129	C₄⋊Q₈×C₄₇	—	2	1	no	—
130	C₄⋊Q₈×C₄₇	—	2	1	no	—
131	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
132	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
135	#125×C₄₇	—	2	2	no	—
136	#125×C₄₇	—	2	2	no	—
137	#125×C₄₇	—	2	2	no	—
138	#125×C₄₇	—	2	2	no	—
139	C₂²⋊Q₈×C₄₇	—	2	2	no	—
140	C₂²⋊Q₈×C₄₇	—	2	2	no	—
141	C₂²⋊Q₈×C₄₇	—	2	2	no	—
142	C₂²⋊Q₈×C₄₇	—	2	2	no	—
143	C₂²⋊Q₈×C₄₇	—	2	2	no	—
144	C₂²⋊Q₈×C₄₇	—	2	2	no	—
145	C₂²⋊Q₈×C₄₇	C₂³	1	4	yes	—
146	C₂²⋊Q₈×C₄₇	C₂³	1	4	yes	—
147	C₄×Q₈×C₄₇	—	2	2	no	—
148	C₄×Q₈×C₄₇	—	2	2	no	—
149	C₄×Q₈×C₄₇	—	2	2	no	—
150	C₄×Q₈×C₄₇	—	2	2	no	—
151	C₄×Q₈×C₄₇	—	2	2	no	—
152	C₄×Q₈×C₄₇	—	2	2	no	—
153	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
154	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
155	#117×C₄₇	—	2	2	no	—
156	#117×C₄₇	—	2	2	no	—
157	#117×C₄₇	—	2	2	no	—
158	#117×C₄₇	—	2	2	no	—
159	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
160	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
161	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
162	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
163	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
164	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
166	C₂×C₄²×C₄₇	—	2	2	no	—
167	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
168	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
169	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
170	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
171	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
172	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
173	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
179	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
180	C₂³×D₄₇	—	2	2	no	—
181	C₂×Q₈×C₄₇	—	2	2	no	—
182	C₂×Q₈×C₄₇	—	2	2	no	—
183	C₂×Q₈×C₄₇	—	2	2	no	—
184	C₂×Q₈×C₄₇	—	2	8	no	—
185	C₂×Q₈×C₄₇	—	4	4	no	—
186	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₄₇	—	2	4	no	—
188	C₂²×C₄×C₄₇	—	2	4	no	—
189	C₂²×C₄×C₄₇	—	2	2	no	—
190	C₂²×C₄×C₄₇	—	2	2	no	—
191	C₂²×C₄×C₄₇	—	4	2	no	—
192	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
210	C₂×C₂²⋊D₄₇	—	2	4	no	—
211	C₂×C₂²⋊D₄₇	—	2	4	no	—
212	C₂×C₂²⋊D₄₇	—	4	8	no	—
213	C₂²×Dic₄₇	—	2	2	no	—
214	#10625350	—	2	16	no	—
215	#10625350	—	4	8	no	—
216	#10625350	—	4	8	no	—
217	#10625350	—	4	8	no	—
218	C₂×D₁₈₈	—	2	2	no	—
219	C₂×D₁₈₈	—	2	2	no	—
220	C₂×D₁₈₈	—	2	2	no	—
221	C₂×D₁₈₈	—	2	2	no	—
222	C₂×D₁₈₈	—	2	2	no	—
223	C₂×D₁₈₈	—	4	4	no	—
224	C₂×D₁₈₈	—	4	4	no	—
225	C₂×D₁₈₈	—	4	4	no	—
226	C₂×D₁₈₈	C₂⁴	1	4	yes	—
227	C₂×C₄×D₄₇	—	2	4	no	—
228	C₂×C₄×D₄₇	—	2	4	no	—
229	C₂×C₄×D₄₇	—	4	8	no	—
230	C₂×Dic₉₄	—	2	2	no	—
231	C₂×Dic₉₄	—	4	4	no	—
232	C₂×Dic₉₄	C₂⁴	1	4	yes	—
233	C₄⋊C₄×C₄₇	—	2	2	no	—
234	C₄⋊C₄×C₄₇	—	2	2	no	—
235	C₄⋊C₄×C₄₇	—	2	2	no	—
236	C₄⋊C₄×C₄₇	—	2	2	no	—
237	C₄⋊C₄×C₄₇	—	2	2	no	—
238	C₄⋊C₄×C₄₇	—	2	2	no	—
239	C₄⋊C₄×C₄₇	—	2	4	no	—
240	C₄⋊C₄×C₄₇	—	2	4	no	—
241	C₄⋊C₄×C₄₇	—	2	4	no	—
242	C₄⋊C₄×C₄₇	—	2	4	no	—
243	C₄⋊C₄×C₄₇	—	2	2	no	—
244	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
245	C₂²⋊C₄×C₄₇	—	2	4	no	—
246	C₂²⋊C₄×C₄₇	—	2	4	no	—
247	C₄²×C₄₇	—	2	4	no	—
248	C₄²×C₄₇	—	2	4	no	—
249	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
250	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
251	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
252	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
253	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
254	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
255	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
256	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
257	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
258	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
259	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
260	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
261	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
262	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
263	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
264	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
265	#10625337	—	4	16	no	—
266	#10625336	—	4	16	no	—
267	(C₂×D₄₇)⋊C₄	—	2	4	no	—
268	(C₂×D₄₇)⋊C₄	—	2	4	no	—
269	(C₂×D₄₇)⋊C₄	—	2	4	no	—
270	(C₂×D₄₇)⋊C₄	—	2	4	no	—
271	C₄⋊Dic₄₇	—	2	2	no	—
272	C₄⋊Dic₄₇	—	2	2	no	—
273	C₄⋊Dic₄₇	—	2	2	no	—
274	C₄⋊Dic₄₇	—	2	2	no	—
275	#10625329	—	2	8	no	—
276	C₂×C₄₇⋊C₈	C₂⁴	1	8	yes	—
277	C₂³×C₄₇	—	2	2	no	—
278	C₂³×C₄₇	—	2	2	no	—
279	C₂³×C₄₇	—	4	1	no	—
280	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
281	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
282	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
283	C₂²×D₄₇	—	2	4	no	—
284	C₂²×D₄₇	—	4	4	no	—
285	C₂²×D₄₇	—	4	4	no	—
286	C₂²×D₄₇	—	4	4	no	—
287	Q₈×C₄₇	—	2	8	no	—
288	Q₈×C₄₇	—	4	4	no	—
289	Q₈×C₄₇	—	4	4	no	—
290	Q₈×C₄₇	—	4	4	no	—
291	C₂×C₄×C₄₇	—	2	2	no	—
292	C₂×C₄×C₄₇	—	2	2	no	—
293	C₂×C₄×C₄₇	—	2	2	no	—
294	C₂×C₄×C₄₇	—	2	2	no	—
295	C₂×C₄×C₄₇	—	2	2	no	—
296	C₂×C₄×C₄₇	—	2	2	no	—
297	C₂×C₄×C₄₇	—	2	2	no	—
298	C₂×C₄×C₄₇	—	2	2	no	—
299	C₂×C₄×C₄₇	—	2	2	no	—
300	C₂×C₄×C₄₇	—	2	2	no	—
301	C₂×C₄×C₄₇	—	2	2	no	—
302	C₂×C₄×C₄₇	—	2	2	no	—
303	C₂×C₄×C₄₇	—	2	2	no	—
304	C₂×C₄×C₄₇	—	2	4	no	—
305	C₂×C₄×C₄₇	—	2	4	no	—
306	C₂×C₄×C₄₇	—	4	1	no	—
307	C₂×C₄×C₄₇	—	4	1	no	—
308	C₂×C₄×C₄₇	—	4	1	no	—
309	C₂×C₄×C₄₇	—	4	4	no	—
310	C₂×C₄×C₄₇	—	4	4	no	—
311	C₂×C₄×C₄₇	#137	1	4	yes	complemented
312	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
324	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
325	C₂²⋊D₄₇	—	4	8	no	—
326	C₂²⋊D₄₇	—	4	8	no	—
327	C₂×Dic₄₇	—	2	4	no	—
328	C₂×Dic₄₇	—	4	4	no	—
329	D₁₈₈	—	2	8	no	—
330	D₁₈₈	—	4	4	no	—
331	D₁₈₈	—	4	4	no	—
332	D₁₈₈	—	4	4	no	—
333	D₁₈₈	—	4	4	no	—
334	D₁₈₈	—	4	4	no	—
335	C₄×D₄₇	—	4	8	no	—
336	C₄×D₄₇	—	4	8	no	—
337	Dic₉₄	—	2	8	no	—
338	Dic₉₄	—	4	4	no	—
339	C₄₇⋊C₈	—	2	8	no	—
340	#60804	—	47	1	no	maximal, Sylow
341	C₂²×C₄₇	—	2	1	no	—
342	C₂²×C₄₇	—	2	1	no	—
343	C₂²×C₄₇	—	2	1	no	—
344	C₂²×C₄₇	—	2	1	no	—
345	C₂²×C₄₇	—	2	1	no	—
346	C₂²×C₄₇	—	2	1	no	—
347	C₂²×C₄₇	—	2	1	no	—
348	C₂²×C₄₇	—	4	4	no	—
349	C₂²×C₄₇	#535	1	2	yes	—
350	C₂²×C₄₇	C₂×#137	1	2	yes	—
351	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
352	C₂×D₄₇	—	4	4	no	—
353	C₂×D₄₇	—	4	4	no	—
354	C₂×D₄₇	—	4	4	no	—
355	C₂×D₄₇	—	8	8	no	—
356	C₄×C₄₇	—	2	1	no	—
357	C₄×C₄₇	—	2	1	no	—
358	C₄×C₄₇	—	2	1	no	—
359	C₄×C₄₇	—	2	1	no	—
360	C₄×C₄₇	—	2	1	no	—
361	C₄×C₄₇	—	2	1	no	—
362	C₄×C₄₇	—	2	1	no	—
363	C₄×C₄₇	—	4	4	no	—
364	C₄×C₄₇	—	4	4	no	—
365	C₄×C₄₇	#535	1	2	yes	—
366	C₄×C₄₇	C₂×#137	1	2	yes	—
367	C₄×C₄₇	C₂×#137	1	2	yes	—
368	C₄×C₄₇	#575	1	2	yes	—
369	C₄×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
370	Dic₄₇	—	4	4	no	—
371	C₂×#533	D₄₇	1	1	yes	characteristic, complemented
372	C₂×#532	—	47	1	no	—
373	#3216	—	47	4	no	—
374	#3215	—	47	4	no	—
375	#3210	—	47	4	no	—
376	#3209	—	47	2	no	—
377	#3208	—	47	2	no	—
378	#3152	—	47	2	no	—
379	#3141	—	47	2	no	—
380	#3037	—	47	4	no	—
381	#3007	—	47	4	no	—
382	#2920	—	47	1	no	—
383	C₂×C₄₇	—	2	2	no	—
384	C₂×C₄₇	—	2	2	no	—
385	C₂×C₄₇	—	4	1	no	—
386	C₂×C₄₇	C₂×#535	1	1	yes	characteristic
387	C₂×C₄₇	C₂²×#137	1	1	yes	characteristic
388	C₂×C₄₇	C₂×#575	1	1	yes	characteristic
389	D₄₇	—	8	4	no	—
390	C₂²×#41	—	47	2	no	—
391	C₂×#137	—	47	8	no	—
392	#533	—	2	1	no	—
393	#533	—	2	1	no	—
394	#533	—	2	1	no	—
395	#533	—	2	1	no	—
396	#533	C₂×D₄₇	1	2	yes	—
397	#533	C₂×D₄₇	1	2	yes	—
398	#533	C₂×D₄₇	1	2	yes	complemented
399	#533	C₂×D₄₇	1	2	yes	complemented
400	#532	—	47	2	no	—
401	#532	—	47	2	no	—
402	#532	—	47	2	no	—
403	#532	—	47	2	no	—
404	#532	—	94	1	no	—
405	#532	—	94	1	no	—
406	#532	—	94	1	no	—
407	#532	—	94	1	no	—
408	C₂×C₄⋊Q₈	—	47	1	no	—
409	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
410	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
411	C₂×#127	—	47	1	no	—
412	C₂×#125	—	2	1	no	—
413	C₂×#124	—	47	2	no	—
414	C₂×C₂²⋊Q₈	—	2	1	no	—
415	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
416	C₂×#121	—	94	1	no	—
417	C₂×#121	—	94	1	no	—
418	C₂×C₄×Q₈	—	2	1	no	—
419	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	complemented
420	C₂×C₄×D₄	—	94	1	no	—
421	C₂×C₄×D₄	—	94	1	no	—
422	C₂×#117	—	2	1	no	—
423	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
424	#497	—	47	8	no	—
425	#494	—	47	4	no	—
426	#492	—	47	4	no	—
427	#489	—	47	8	no	—
428	#487	—	47	4	no	—
429	#486	—	47	4	no	—
430	#464	—	47	16	no	—
431	#462	—	47	8	no	—
432	#460	—	47	8	no	—
433	#452	—	47	16	no	—
434	#451	—	47	8	no	—
435	#450	—	47	8	no	—
436	#432	—	47	2	no	—
437	#432	—	47	2	no	—
438	#431	—	47	2	no	—
439	#431	—	47	2	no	—
440	#423	—	47	2	no	—
441	#417	—	47	8	no	—
442	#407	—	47	2	no	—
443	C₄×M₁₆	—	47	2	no	—
444	C₄₇	#60804	1	1	yes	characteristic, complemented, Sylow
445	C₂×#41	—	47	4	no	—
446	C₂×#41	—	47	4	no	—
447	C₂×#41	—	94	2	no	—
448	C₂×#41	—	94	2	no	—
449	C₂×#41	—	188	8	no	—
450	C₂²×Q₈	—	2	1	no	—
451	C₂²×Q₈	—	47	2	no	—
452	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
453	C₂²×D₄	—	47	2	no	—
454	C₂²×D₄	—	94	2	no	—
455	C₂²×D₄	—	94	1	no	—
456	C₂²×D₄	—	94	1	no	—
457	C₂³×C₄	—	94	2	no	—
458	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
459	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
460	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
461	#137	—	188	16	no	—
462	C₂×Q₁₆	—	47	16	no	—
463	C₂×SD₁₆	—	47	16	no	—
464	C₂×M₁₆	—	47	4	no	—
465	C₄⋊Q₈	—	2	1	no	—
466	C₄⋊Q₈	—	2	1	no	—
467	C₄⋊Q₈	—	2	1	no	—
468	C₄⋊Q₈	—	2	1	no	—
469	C₄⋊Q₈	—	47	2	no	—
470	C₄⋊Q₈	—	47	2	no	—
471	C₄⋊Q₈	—	94	1	no	—
472	C₄⋊Q₈	—	94	1	no	—
473	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
474	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
475	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
476	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
477	#127	—	47	2	no	—
478	#127	—	47	2	no	—
479	#127	—	94	1	no	—
480	#127	—	94	1	no	—
481	#125	—	2	2	no	—
482	#125	—	2	2	no	—
483	#125	—	2	2	no	—
484	#125	—	2	2	no	—
485	#124	—	47	4	no	—
486	#124	—	47	4	no	—
487	#124	—	94	2	no	—
488	#124	—	94	2	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	—	2	2	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	C₂²×D₄₇	1	4	yes	—
496	C₂²⋊Q₈	C₂²×D₄₇	1	4	yes	—
497	#121	—	94	2	no	—
498	#121	—	94	2	no	—
499	#121	—	94	2	no	—
500	#121	—	94	2	no	—
501	#121	—	94	2	no	—
502	#121	—	94	2	no	—
503	#121	—	94	2	no	—
504	#121	—	94	2	no	—
505	C₄×Q₈	—	2	2	no	—
506	C₄×Q₈	—	2	2	no	—
507	C₄×Q₈	—	2	2	no	—
508	C₄×Q₈	—	2	2	no	—
509	C₄×Q₈	—	2	2	no	—
510	C₄×Q₈	—	2	2	no	—
511	C₄×Q₈	C₂²×D₄₇	1	4	yes	—
512	C₄×Q₈	C₂²×D₄₇	1	4	yes	—
513	C₄×D₄	—	94	2	no	—
514	C₄×D₄	—	94	2	no	—
515	C₄×D₄	—	94	2	no	—
516	C₄×D₄	—	94	2	no	—
517	C₄×D₄	—	94	2	no	—
518	C₄×D₄	—	94	2	no	—
519	C₄×D₄	—	94	2	no	—
520	C₄×D₄	—	94	2	no	—
521	#117	—	2	2	no	—
522	#117	—	2	2	no	—
523	#117	—	2	2	no	—
524	#117	—	2	2	no	—
525	C₂×C₄⋊C₄	—	2	1	no	—
526	C₂×C₄⋊C₄	—	2	1	no	—
527	C₂×C₄⋊C₄	—	2	1	no	—
528	C₂×C₄⋊C₄	—	2	2	no	—
529	C₂×C₄⋊C₄	—	2	2	no	—
530	C₂×C₄⋊C₄	—	94	1	no	—
531	C₂×C₄⋊C₄	—	94	1	no	—
532	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
533	C₂×C₂²⋊C₄	—	2	2	no	—
534	C₂×C₂²⋊C₄	—	94	2	no	—
535	C₂×C₂²⋊C₄	—	94	2	no	—
536	C₂×C₄²	—	2	2	no	—
537	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
538	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
539	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
540	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
541	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
542	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
543	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
544	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
545	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
546	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
547	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
548	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
549	C₄⋊C₈	—	47	4	no	—
550	C₄⋊C₈	—	47	4	no	—
551	#103	—	47	16	no	—
552	#102	—	47	16	no	—
553	C₂²⋊C₈	—	47	4	no	—
554	C₂²⋊C₈	—	47	4	no	—
555	#97	—	47	4	no	—
556	C₄×C₈	—	47	4	no	—
557	C₂⁴	—	94	2	no	—
558	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
559	#41	—	94	16	no	—
560	#41	—	188	8	no	—
561	#41	—	188	8	no	—
562	#41	—	188	8	no	—
563	C₂×Q₈	—	2	2	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	2	8	no	—
567	C₂×Q₈	—	4	4	no	—
568	C₂×Q₈	—	47	4	no	—
569	C₂×Q₈	—	94	2	no	—
570	C₂×Q₈	—	188	4	no	—
571	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
572	C₂×D₄	—	47	4	no	—
573	C₂×D₄	—	94	4	no	—
574	C₂×D₄	—	94	4	no	—
575	C₂×D₄	—	94	2	no	—
576	C₂×D₄	—	94	2	no	—
577	C₂×D₄	—	94	2	no	—
578	C₂×D₄	—	94	2	no	—
579	C₂×D₄	—	94	2	no	—
580	C₂×D₄	—	188	4	no	—
581	C₂×D₄	—	188	4	no	—
582	C₂×D₄	—	188	8	no	—
583	C₂×D₄	—	188	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	—	94	2	no	—
590	C₂²×C₄	—	94	4	no	—
591	C₂²×C₄	—	94	4	no	—
592	C₂²×C₄	—	188	8	no	—
593	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
594	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
595	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
596	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
597	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
598	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
599	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
600	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
601	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
602	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
603	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
604	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
605	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
606	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
607	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
608	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
609	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
610	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
611	Q₁₆	—	188	16	no	—
612	SD₁₆	—	188	16	no	—
613	M₁₆	—	94	8	no	—
614	C₂×C₈	—	47	8	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	94	2	no	—
627	C₄⋊C₄	—	94	2	no	—
628	C₄⋊C₄	—	94	2	no	—
629	C₄⋊C₄	—	94	2	no	—
630	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	94	4	no	—
634	C₂²⋊C₄	—	94	4	no	—
635	C₂²⋊C₄	—	94	4	no	—
636	C₂²⋊C₄	—	94	4	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	4	no	—
639	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
640	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
641	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
642	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
643	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
644	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
645	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
646	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
647	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
648	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
649	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
650	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
651	C₄²	C₂³×D₄₇	1	1	yes	characteristic
652	C₄²	C₂³×D₄₇	1	1	yes	characteristic
653	C₄²	C₂³×D₄₇	1	1	yes	characteristic
654	C₄²	C₂³×D₄₇	1	1	yes	characteristic
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	94	4	no	—
659	C₂³	—	188	4	no	—
660	C₂³	—	188	4	no	—
661	C₂³	—	188	4	no	—
662	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
663	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
664	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
665	Q₈	—	2	8	no	—
666	Q₈	—	4	4	no	—
667	Q₈	—	4	4	no	—
668	Q₈	—	4	4	no	—
669	Q₈	—	94	8	no	—
670	Q₈	—	188	4	no	—
671	D₄	—	94	8	no	—
672	D₄	—	188	4	no	—
673	D₄	—	188	4	no	—
674	D₄	—	188	8	no	—
675	D₄	—	188	8	no	—
676	D₄	—	188	4	no	—
677	D₄	—	188	4	no	—
678	D₄	—	188	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	94	4	no	—
700	C₂×C₄	—	188	8	no	—
701	C₂×C₄	—	188	4	no	—
702	C₂×C₄	—	188	8	no	—
703	C₂×C₄	#13094055	1	4	yes	complemented
704	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
705	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
706	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
707	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
708	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
709	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
710	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
711	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
712	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
713	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
714	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
715	C₂×C₄	#13094070	1	4	yes	—
716	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
717	C₈	—	94	8	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	376	8	no	—
727	C₂²	—	188	4	no	—
728	C₂²	—	188	4	no	—
729	C₂²	—	188	4	no	—
730	C₂²	#15689687	1	2	yes	—
731	C₂²	C₂×#13094055	1	2	yes	—
732	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
733	C₄	—	2	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	1	no	—
739	C₄	—	2	1	no	—
740	C₄	—	4	4	no	—
741	C₄	—	4	4	no	—
742	C₄	—	188	4	no	—
743	C₄	#15689687	1	2	yes	—
744	C₄	C₂×#13094055	1	2	yes	—
745	C₄	C₂×#13094055	1	2	yes	—
746	C₄	#15689921	1	2	yes	—
747	C₄	C₂×#13094070	1	2	yes	—
748	C₂	—	2	2	no	—
749	C₂	—	2	2	no	—
750	C₂	—	4	1	no	—
751	C₂	—	376	4	no	—
752	C₂	C₂×#15689687	1	1	yes	characteristic
753	C₂	C₂²×#13094055	1	1	yes	characteristic
754	C₂	C₂×#15689921	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#533	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂×#15689673	C₂
hypercenter	C₂×#533	D₄₇
hypocenter	C₄₇	#60804
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
2. #20254395	C₂	semidirect
3. #20254387	C₂	semidirect
4. #20254340	C₂	semidirect
5. #20254333	C₂	semidirect
6. #20254326	C₂	semidirect
7. #20253845	C₂	semidirect
8. #20253784	C₂	semidirect
9. #20252860	C₂	semidirect
10. #20252646	C₂	semidirect
11. #20252021	C₂	semidirect
12. C₂×C₄₇×#533	C₂	semidirect
14. C₂×#13094055	C₂²	semidirect
30. #15689515	C₂²	semidirect
31. #15689502	C₂²	semidirect
32. #15689497	C₂²	semidirect
33. #15689485	C₂²	semidirect
34. #15689475	C₂²	semidirect
35. #15689471	C₂²	semidirect
36. #15689345	C₂²	semidirect
37. #15689333	C₂²	semidirect
38. #15689323	C₂²	semidirect
39. #15689283	C₂²	semidirect
43. #15689180	C₂²	semidirect
45. #15689176	C₂²	semidirect
46. #15689147	C₂²	semidirect
47. #15689122	C₂²	semidirect
49. C₄×#10625329	C₂²	semidirect
56. C₄₇×#533	C₂²	semidirect
57. C₄₇×#533	C₂²	semidirect
58. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
59. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
64. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
311. C₂×C₄×C₄₇	#137	semidirect
371. C₂×#533	D₄₇	semidirect
398. #533	C₂×D₄₇	semidirect
399. #533	C₂×D₄₇	semidirect
409. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
410. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
419. C₂×C₄×Q₈	C₂×D₄₇	semidirect
444. C₄₇	#60804	semidirect
703. C₂×C₄	#13094055	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689673	2
#20254395	2
#20254387	2
#20254340	2
#20254333	2
#20254326	2
#20253845	2
#20253784	2
#20252860	2
#20252646	2
#20252021	2
C₂×C₄₇×#533	2
#60804	47