Subgroups — #27088588

Order 12032.

2036 conjugacy classes of subgroups.

The subgroup lattice has 750 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	#20254586	C₂	1	4	yes	maximal, complemented
3	#20254578	C₂	1	4	yes	maximal, complemented
4	#20254524	C₂	1	4	yes	maximal, complemented
5	#20254516	C₂	1	2	yes	maximal, complemented
6	#20254509	C₂	1	2	yes	maximal, complemented
7	#20253935	C₂	1	2	yes	maximal, complemented
8	#20253764	C₂	1	2	yes	maximal, complemented
9	#20253328	C₂	1	4	yes	maximal, complemented
10	#20253181	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	—	2	1	no	—
14	#15689673	—	2	1	no	—
15	#15689673	—	2	1	no	—
16	#15689673	—	2	1	no	—
17	#15689673	—	2	1	no	—
18	#15689673	C₂²	1	2	yes	—
19	#15689673	C₂²	1	2	yes	—
20	#15689673	C₂²	1	2	yes	—
21	#15689673	C₂²	1	2	yes	—
22	C₂×#13094024	C₂²	1	1	yes	characteristic
23	C₂×#13094021	C₂²	1	1	yes	characteristic
24	C₂×#13094012	—	2	1	no	—
25	C₂×#13093998	—	2	1	no	—
26	C₂×#13093998	C₂²	1	2	yes	—
27	C₂×C₄×D₁₈₈	—	2	1	no	—
28	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
29	#15689533	C₂²	1	8	yes	complemented
30	#15689526	C₂²	1	4	yes	complemented
31	#15689519	C₂²	1	4	yes	complemented
32	#15689489	C₂²	1	8	yes	complemented
33	#15689471	C₂²	1	4	yes	complemented
34	#15689471	C₂²	1	4	yes	complemented
35	#15689447	C₂²	1	16	yes	complemented
36	#15689441	C₂²	1	8	yes	complemented
37	#15689436	C₂²	1	8	yes	complemented
38	#15689420	C₂²	1	16	yes	complemented
39	#15689410	C₂²	1	8	yes	complemented
40	#15689400	C₂²	1	8	yes	complemented
41	#15689180	C₂²	1	2	yes	complemented
42	#15689180	C₂²	1	2	yes	complemented
43	#15689176	C₂²	1	2	yes	complemented
44	#15689176	C₂²	1	2	yes	complemented
45	#15689166	C₂²	1	8	yes	—
46	#15689147	C₂²	1	2	yes	—
47	#15689127	C₂²	1	8	yes	—
48	#15689087	C₂²	1	2	yes	—
49	C₄×#10625329	C₂²	1	2	yes	—
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	C₂²	1	2	yes	complemented
61	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
62	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
63	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
64	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
65	C₂×#117×C₄₇	C₂²	1	2	yes	—
66	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
67	C₂×#10625350	—	2	2	no	—
68	C₂×#10625350	—	2	2	no	—
69	C₂×#10625350	—	2	2	no	—
70	C₂×#10625350	—	2	2	no	—
71	C₂×#10625350	—	4	8	no	—
72	C₂²×Dic₉₄	—	2	1	no	—
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	C₂×#10625329	C₂³	1	4	yes	—
79	#13094024	—	2	1	no	—
80	#13094024	—	2	1	no	—
81	#13094024	C₂³	1	2	yes	—
82	#13094024	C₂³	1	2	yes	—
83	#13094021	—	2	1	no	—
84	#13094021	—	2	1	no	—
85	#13094021	C₂³	1	2	yes	—
86	#13094021	C₂³	1	2	yes	—
87	#13094012	—	2	2	no	—
88	#13094012	—	2	2	no	—
89	#13094012	—	2	2	no	—
90	#13094012	—	2	2	no	—
91	#13093998	—	2	2	no	—
92	#13093998	—	2	2	no	—
93	#13093998	—	2	2	no	—
94	#13093998	—	2	2	no	—
95	#13093998	—	2	2	no	—
96	#13093998	—	2	2	no	—
97	#13093998	C₂³	1	4	yes	—
98	#13093998	C₂³	1	4	yes	—
99	C₄×D₁₈₈	—	2	2	no	—
100	C₄×D₁₈₈	—	2	2	no	—
101	C₄×D₁₈₈	—	2	2	no	—
102	C₄×D₁₈₈	—	2	2	no	—
103	C₄×D₁₈₈	—	2	2	no	—
104	C₄×D₁₈₈	—	2	2	no	—
105	C₄×D₁₈₈	C₂³	1	4	yes	—
106	C₄×D₁₈₈	C₂³	1	4	yes	—
107	C₂×C₄⋊Dic₄₇	—	2	1	no	—
108	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
109	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
110	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
111	#13093957	C₂³	1	16	yes	—
112	#13093955	C₂³	1	16	yes	—
113	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
114	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
115	#13093944	C₂³	1	16	yes	—
116	#13093944	C₂³	1	16	yes	—
117	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
118	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
119	#13093935	C₂³	1	4	yes	—
120	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
121	C₂²×Q₈×C₄₇	—	2	1	no	—
122	C₂²×Q₈×C₄₇	—	2	1	no	—
123	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
124	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
125	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
126	C₄⋊Q₈×C₄₇	—	2	1	no	—
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	C₂³	1	2	yes	—
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	#125×C₄₇	—	2	2	no	—
135	#125×C₄₇	—	2	2	no	—
136	#125×C₄₇	C₂³	1	4	yes	—
137	#125×C₄₇	C₂³	1	4	yes	—
138	C₂²⋊Q₈×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	—	2	2	no	—
146	C₄×Q₈×C₄₇	—	2	2	no	—
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	—	2	2	no	—
154	#117×C₄₇	—	2	2	no	—
155	#117×C₄₇	—	2	2	no	—
156	#117×C₄₇	C₂³	1	4	yes	—
157	#117×C₄₇	C₂³	1	4	yes	—
158	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
159	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
160	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
161	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
162	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
165	C₂×C₄²×C₄₇	—	2	2	no	—
166	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
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	C₂³	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	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
179	C₂³×D₄₇	—	2	2	no	—
180	C₂×Q₈×C₄₇	—	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	—	4	4	no	—
185	C₂×Q₈×C₄₇	—	4	4	no	—
186	C₂²×C₄×C₄₇	—	2	4	no	—
187	C₂²×C₄×C₄₇	—	2	4	no	—
188	C₂²×C₄×C₄₇	—	2	2	no	—
189	C₂²×C₄×C₄₇	—	2	2	no	—
190	C₂²×C₄×C₄₇	—	4	2	no	—
191	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
209	C₂×C₂²⋊D₄₇	—	2	4	no	—
210	C₂×C₂²⋊D₄₇	—	2	4	no	—
211	C₂×C₂²⋊D₄₇	—	4	8	no	—
212	C₂²×Dic₄₇	—	2	2	no	—
213	#10625350	—	4	8	no	—
214	#10625350	—	4	8	no	—
215	#10625350	—	4	8	no	—
216	#10625350	—	4	8	no	—
217	C₂×D₁₈₈	—	2	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	C₂⁴	1	4	yes	—
226	C₂×C₄×D₄₇	—	2	4	no	—
227	C₂×C₄×D₄₇	—	2	4	no	—
228	C₂×C₄×D₄₇	—	4	8	no	—
229	C₂×Dic₉₄	—	2	2	no	—
230	C₂×Dic₉₄	—	2	2	no	—
231	C₂×Dic₉₄	—	4	4	no	—
232	C₄⋊C₄×C₄₇	—	2	4	no	—
233	C₄⋊C₄×C₄₇	—	2	4	no	—
234	C₄⋊C₄×C₄₇	—	2	4	no	—
235	C₄⋊C₄×C₄₇	—	2	4	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	2	no	—
240	C₄⋊C₄×C₄₇	—	2	2	no	—
241	C₄⋊C₄×C₄₇	—	2	2	no	—
242	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
243	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
244	C₂²⋊C₄×C₄₇	—	2	4	no	—
245	C₂²⋊C₄×C₄₇	—	2	4	no	—
246	C₄²×C₄₇	—	2	4	no	—
247	C₄²×C₄₇	—	2	4	no	—
248	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	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	(C₂×D₄₇)⋊C₄	—	2	4	no	—
265	(C₂×D₄₇)⋊C₄	—	2	4	no	—
266	(C₂×D₄₇)⋊C₄	—	2	4	no	—
267	(C₂×D₄₇)⋊C₄	—	2	4	no	—
268	C₄⋊Dic₄₇	—	2	2	no	—
269	C₄⋊Dic₄₇	—	2	2	no	—
270	C₄⋊Dic₄₇	—	2	2	no	—
271	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
272	#10625329	—	2	8	no	—
273	C₂×C₄₇⋊C₈	C₂⁴	1	8	yes	—
274	C₂³×C₄₇	—	2	2	no	—
275	C₂³×C₄₇	—	2	2	no	—
276	C₂³×C₄₇	—	4	1	no	—
277	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
278	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
279	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
280	C₂²×D₄₇	—	2	4	no	—
281	C₂²×D₄₇	—	4	4	no	—
282	C₂²×D₄₇	—	4	4	no	—
283	C₂²×D₄₇	—	4	4	no	—
284	Q₈×C₄₇	—	4	4	no	—
285	Q₈×C₄₇	—	4	4	no	—
286	Q₈×C₄₇	—	4	4	no	—
287	Q₈×C₄₇	—	4	4	no	—
288	C₂×C₄×C₄₇	—	2	2	no	—
289	C₂×C₄×C₄₇	—	2	2	no	—
290	C₂×C₄×C₄₇	—	2	2	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	4	no	—
302	C₂×C₄×C₄₇	—	2	4	no	—
303	C₂×C₄×C₄₇	—	4	1	no	—
304	C₂×C₄×C₄₇	—	4	1	no	—
305	C₂×C₄×C₄₇	—	4	1	no	—
306	C₂×C₄×C₄₇	—	4	4	no	—
307	C₂×C₄×C₄₇	—	4	4	no	—
308	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
309	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
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	2₋¹⁺⁴	1	4	yes	—
321	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
322	C₂²⋊D₄₇	—	4	8	no	—
323	C₂²⋊D₄₇	—	4	8	no	—
324	C₂×Dic₄₇	—	2	4	no	—
325	C₂×Dic₄₇	—	4	4	no	—
326	D₁₈₈	—	2	8	no	—
327	D₁₈₈	—	4	4	no	—
328	D₁₈₈	—	4	4	no	—
329	D₁₈₈	—	4	4	no	—
330	D₁₈₈	—	4	4	no	—
331	D₁₈₈	—	4	4	no	—
332	C₄×D₄₇	—	4	8	no	—
333	C₄×D₄₇	—	4	8	no	—
334	Dic₉₄	—	4	4	no	—
335	Dic₉₄	—	4	4	no	—
336	C₄₇⋊C₈	—	2	8	no	—
337	#60864	—	47	1	no	maximal, Sylow
338	C₂²×C₄₇	—	2	1	no	—
339	C₂²×C₄₇	—	2	1	no	—
340	C₂²×C₄₇	—	2	1	no	—
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	—	4	4	no	—
346	C₂²×C₄₇	#536	1	2	yes	—
347	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
348	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
349	C₂×D₄₇	—	4	4	no	—
350	C₂×D₄₇	—	4	4	no	—
351	C₂×D₄₇	—	4	4	no	—
352	C₂×D₄₇	—	8	8	no	—
353	C₄×C₄₇	—	2	1	no	—
354	C₄×C₄₇	—	2	1	no	—
355	C₄×C₄₇	—	2	1	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	—	4	4	no	—
361	C₄×C₄₇	—	4	4	no	—
362	C₄×C₄₇	#536	1	2	yes	—
363	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
364	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
365	C₄×C₄₇	#575	1	2	yes	—
366	C₄×C₄₇	C₂×2₋¹⁺⁴	1	2	yes	—
367	Dic₄₇	—	4	4	no	—
368	C₂×#533	D₄₇	1	1	yes	characteristic, complemented
369	C₂×#532	—	47	1	no	—
370	#3235	—	47	4	no	—
371	#3234	—	47	4	no	—
372	#3228	—	47	4	no	—
373	#3227	—	47	2	no	—
374	#3226	—	47	2	no	—
375	#3165	—	47	2	no	—
376	#3138	—	47	2	no	—
377	#3094	—	47	4	no	—
378	#3077	—	47	4	no	—
379	#2920	—	47	1	no	—
380	C₂×C₄₇	—	2	2	no	—
381	C₂×C₄₇	—	2	2	no	—
382	C₂×C₄₇	—	4	1	no	—
383	C₂×C₄₇	C₂×#536	1	1	yes	characteristic
384	C₂×C₄₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
385	C₂×C₄₇	C₂×#575	1	1	yes	characteristic
386	D₄₇	—	8	4	no	—
387	C₂²×#41	—	94	1	no	—
388	#533	—	2	1	no	—
389	#533	—	2	1	no	—
390	#533	—	2	1	no	—
391	#533	—	2	1	no	—
392	#533	C₂×D₄₇	1	2	yes	—
393	#533	C₂×D₄₇	1	2	yes	—
394	#533	C₂×D₄₇	1	2	yes	complemented
395	#533	C₂×D₄₇	1	2	yes	complemented
396	#532	—	47	2	no	—
397	#532	—	47	2	no	—
398	#532	—	47	2	no	—
399	#532	—	47	2	no	—
400	#532	—	94	1	no	—
401	#532	—	94	1	no	—
402	#532	—	94	1	no	—
403	#532	—	94	1	no	—
404	C₂×C₄⋊Q₈	—	47	1	no	—
405	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
406	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
407	C₂×#127	—	47	1	no	—
408	C₂×#125	C₂×D₄₇	1	2	yes	complemented
409	C₂×#124	—	94	1	no	—
410	C₂×C₂²⋊Q₈	—	2	1	no	—
411	C₂×C₂²⋊Q₈	—	2	1	no	—
412	C₂×#121	—	47	2	no	—
413	C₂×#121	—	94	1	no	—
414	C₂×C₄×Q₈	—	2	1	no	—
415	C₂×C₄×Q₈	—	2	1	no	—
416	C₂×C₄×D₄	—	47	2	no	—
417	C₂×C₄×D₄	—	94	1	no	—
418	C₂×#117	C₂×D₄₇	1	2	yes	—
419	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
420	#501	—	47	8	no	—
421	#500	—	47	4	no	—
422	#498	—	47	4	no	—
423	#490	—	47	8	no	—
424	#486	—	47	4	no	—
425	#486	—	47	4	no	—
426	#482	—	47	16	no	—
427	#481	—	47	8	no	—
428	#480	—	47	8	no	—
429	#478	—	47	16	no	—
430	#476	—	47	8	no	—
431	#474	—	47	8	no	—
432	#432	—	47	2	no	—
433	#432	—	47	2	no	—
434	#431	—	47	2	no	—
435	#431	—	47	2	no	—
436	#428	—	47	8	no	—
437	#423	—	47	2	no	—
438	#418	—	47	8	no	—
439	#407	—	47	2	no	—
440	C₄×M₁₆	—	47	2	no	—
441	C₄₇	#60864	1	1	yes	characteristic, complemented, Sylow
442	C₂×#41	—	94	2	no	—
443	C₂×#41	—	94	2	no	—
444	C₂×#41	—	94	2	no	—
445	C₂×#41	—	94	2	no	—
446	C₂×#41	—	188	8	no	—
447	C₂²×Q₈	—	2	1	no	—
448	C₂²×Q₈	—	2	1	no	—
449	C₂²×Q₈	—	94	1	no	—
450	C₂²×D₄	—	47	2	no	—
451	C₂²×D₄	—	94	2	no	—
452	C₂²×D₄	—	94	1	no	—
453	C₂²×D₄	—	94	1	no	—
454	C₂³×C₄	—	94	2	no	—
455	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
456	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
457	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
458	C₂×M₁₆	—	47	4	no	—
459	C₄⋊Q₈	—	2	1	no	—
460	C₄⋊Q₈	—	2	1	no	—
461	C₄⋊Q₈	—	2	1	no	—
462	C₄⋊Q₈	—	2	1	no	—
463	C₄⋊Q₈	—	47	2	no	—
464	C₄⋊Q₈	—	47	2	no	—
465	C₄⋊Q₈	—	94	1	no	—
466	C₄⋊Q₈	—	94	1	no	—
467	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
468	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
469	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
470	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
471	#127	—	47	2	no	—
472	#127	—	47	2	no	—
473	#127	—	94	1	no	—
474	#127	—	94	1	no	—
475	#125	—	2	2	no	—
476	#125	—	2	2	no	—
477	#125	C₂²×D₄₇	1	4	yes	—
478	#125	C₂²×D₄₇	1	4	yes	—
479	#124	—	94	2	no	—
480	#124	—	94	2	no	—
481	#124	—	94	2	no	—
482	#124	—	94	2	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	#121	—	47	4	no	—
492	#121	—	47	4	no	—
493	#121	—	94	2	no	—
494	#121	—	94	2	no	—
495	#121	—	94	2	no	—
496	#121	—	94	2	no	—
497	#121	—	94	2	no	—
498	#121	—	94	2	no	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	—	2	2	no	—
501	C₄×Q₈	—	2	2	no	—
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	—	2	2	no	—
504	C₄×Q₈	—	2	2	no	—
505	C₄×Q₈	—	2	2	no	—
506	C₄×Q₈	—	2	2	no	—
507	C₄×D₄	—	47	4	no	—
508	C₄×D₄	—	47	4	no	—
509	C₄×D₄	—	94	2	no	—
510	C₄×D₄	—	94	2	no	—
511	C₄×D₄	—	94	2	no	—
512	C₄×D₄	—	94	2	no	—
513	C₄×D₄	—	94	2	no	—
514	C₄×D₄	—	94	2	no	—
515	#117	—	2	2	no	—
516	#117	—	2	2	no	—
517	#117	C₂²×D₄₇	1	4	yes	—
518	#117	C₂²×D₄₇	1	4	yes	—
519	C₂×C₄⋊C₄	—	2	2	no	—
520	C₂×C₄⋊C₄	—	2	2	no	—
521	C₂×C₄⋊C₄	—	2	1	no	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	—	47	2	no	—
524	C₂×C₄⋊C₄	—	94	1	no	—
525	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
526	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
527	C₂×C₂²⋊C₄	—	2	2	no	—
528	C₂×C₂²⋊C₄	—	94	2	no	—
529	C₂×C₂²⋊C₄	—	94	2	no	—
530	C₂×C₄²	—	2	2	no	—
531	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
532	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
533	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
534	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
535	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
536	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
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	#107	—	47	16	no	—
544	#106	—	47	16	no	—
545	C₄⋊C₈	—	47	4	no	—
546	C₄⋊C₈	—	47	4	no	—
547	#102	—	47	16	no	—
548	#102	—	47	16	no	—
549	C₂²⋊C₈	—	47	4	no	—
550	C₂²⋊C₈	—	47	4	no	—
551	#97	—	47	4	no	—
552	C₄×C₈	—	47	4	no	—
553	C₂⁴	—	94	2	no	—
554	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
555	#41	—	188	8	no	—
556	#41	—	188	8	no	—
557	#41	—	188	8	no	—
558	#41	—	188	8	no	—
559	C₂×Q₈	—	2	2	no	—
560	C₂×Q₈	—	2	2	no	—
561	C₂×Q₈	—	2	2	no	—
562	C₂×Q₈	—	2	2	no	—
563	C₂×Q₈	—	4	4	no	—
564	C₂×Q₈	—	4	4	no	—
565	C₂×Q₈	—	94	2	no	—
566	C₂×Q₈	—	94	2	no	—
567	C₂×Q₈	—	188	4	no	—
568	C₂×D₄	—	47	4	no	—
569	C₂×D₄	—	94	4	no	—
570	C₂×D₄	—	94	4	no	—
571	C₂×D₄	—	94	2	no	—
572	C₂×D₄	—	94	2	no	—
573	C₂×D₄	—	94	2	no	—
574	C₂×D₄	—	94	2	no	—
575	C₂×D₄	—	94	2	no	—
576	C₂×D₄	—	94	8	no	—
577	C₂×D₄	—	188	4	no	—
578	C₂×D₄	—	188	4	no	—
579	C₂×D₄	—	188	8	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	94	2	no	—
586	C₂²×C₄	—	94	4	no	—
587	C₂²×C₄	—	94	4	no	—
588	C₂²×C₄	—	188	8	no	—
589	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
590	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
591	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
592	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
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	C₂³×D₄₇	1	1	yes	characteristic
605	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
606	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
607	M₁₆	—	94	8	no	—
608	C₂×C₈	—	47	8	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	2	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	—	47	4	no	—
620	C₄⋊C₄	—	94	2	no	—
621	C₄⋊C₄	—	94	2	no	—
622	C₄⋊C₄	—	94	2	no	—
623	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
624	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	94	4	no	—
628	C₂²⋊C₄	—	94	4	no	—
629	C₂²⋊C₄	—	94	4	no	—
630	C₂²⋊C₄	—	94	4	no	—
631	C₄²	—	2	4	no	—
632	C₄²	—	2	4	no	—
633	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
634	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
635	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
636	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
637	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
638	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
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	C₂³×D₄₇	1	1	yes	characteristic
646	C₄²	C₂³×D₄₇	1	1	yes	characteristic
647	C₄²	C₂³×D₄₇	1	1	yes	characteristic
648	C₄²	C₂³×D₄₇	1	1	yes	characteristic
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	4	1	no	—
652	C₂³	—	94	4	no	—
653	C₂³	—	188	4	no	—
654	C₂³	—	188	4	no	—
655	C₂³	—	188	4	no	—
656	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
657	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
658	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
659	Q₈	—	4	4	no	—
660	Q₈	—	4	4	no	—
661	Q₈	—	4	4	no	—
662	Q₈	—	4	4	no	—
663	Q₈	—	188	4	no	—
664	Q₈	—	188	4	no	—
665	D₄	—	94	8	no	—
666	D₄	—	188	4	no	—
667	D₄	—	188	4	no	—
668	D₄	—	188	8	no	—
669	D₄	—	188	8	no	—
670	D₄	—	188	4	no	—
671	D₄	—	188	4	no	—
672	D₄	—	188	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	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	4	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	4	no	—
692	C₂×C₄	—	4	4	no	—
693	C₂×C₄	—	94	4	no	—
694	C₂×C₄	—	188	8	no	—
695	C₂×C₄	—	188	4	no	—
696	C₂×C₄	—	188	8	no	—
697	C₂×C₄	#13094049	1	4	yes	—
698	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
699	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
700	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
701	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
702	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
703	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
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	#13094072	1	4	yes	—
710	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
711	C₈	—	94	8	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	4	4	no	—
720	C₂²	—	376	8	no	—
721	C₂²	—	188	4	no	—
722	C₂²	—	188	4	no	—
723	C₂²	—	188	4	no	—
724	C₂²	#15689697	1	2	yes	—
725	C₂²	C₂×#13094049	1	2	yes	—
726	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
727	C₄	—	2	1	no	—
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	1	no	—
734	C₄	—	4	4	no	—
735	C₄	—	4	4	no	—
736	C₄	—	188	4	no	—
737	C₄	#15689697	1	2	yes	—
738	C₄	C₂×#13094049	1	2	yes	—
739	C₄	C₂×#13094049	1	2	yes	—
740	C₄	#15689921	1	2	yes	—
741	C₄	C₂×#13094072	1	2	yes	—
742	C₂	—	2	2	no	—
743	C₂	—	2	2	no	—
744	C₂	—	4	1	no	—
745	C₂	—	376	4	no	—
746	C₂	C₂×#15689697	1	1	yes	characteristic
747	C₂	C₂²×#13094049	1	1	yes	characteristic
748	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	#60864
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. #20254586	C₂	semidirect
3. #20254578	C₂	semidirect
4. #20254524	C₂	semidirect
5. #20254516	C₂	semidirect
6. #20254509	C₂	semidirect
7. #20253935	C₂	semidirect
8. #20253764	C₂	semidirect
9. #20253328	C₂	semidirect
10. #20253181	C₂	semidirect
11. #20252021	C₂	semidirect
12. C₂×C₄₇×#533	C₂	semidirect
29. #15689533	C₂²	semidirect
30. #15689526	C₂²	semidirect
31. #15689519	C₂²	semidirect
32. #15689489	C₂²	semidirect
33. #15689471	C₂²	semidirect
34. #15689471	C₂²	semidirect
35. #15689447	C₂²	semidirect
36. #15689441	C₂²	semidirect
37. #15689436	C₂²	semidirect
38. #15689420	C₂²	semidirect
39. #15689410	C₂²	semidirect
40. #15689400	C₂²	semidirect
41. #15689180	C₂²	semidirect
42. #15689180	C₂²	semidirect
43. #15689176	C₂²	semidirect
44. #15689176	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
60. C₂×#125×C₄₇	C₂²	semidirect
368. C₂×#533	D₄₇	semidirect
394. #533	C₂×D₄₇	semidirect
395. #533	C₂×D₄₇	semidirect
405. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
406. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
408. C₂×#125	C₂×D₄₇	semidirect
441. C₄₇	#60864	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
#20254586	2
#20254578	2
#20254524	2
#20254516	2
#20254509	2
#20253935	2
#20253764	2
#20253328	2
#20253181	2
#20252021	2
C₂×C₄₇×#533	2
#60864	47