Subgroups — #26219800

Order 12032.

906 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689170	C₂	1	2	yes	maximal
2	C₂×#15689145	C₂	1	1	yes	maximal, characteristic
3	#423×D₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄×M₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic
5	#20244164	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244163	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244162	C₂	1	2	yes	maximal, complemented
8	#20244161	C₂	1	1	yes	maximal, characteristic, complemented
9	#20244160	C₂	1	2	yes	maximal, complemented
10	#20243113	C₂	1	2	yes	maximal
11	C₄₇×#1950	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	2	yes	—
13	C₂×M₁₆×D₄₇	C₂²	1	2	yes	—
14	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
15	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
17	#15689170	—	2	8	no	—
18	C₂×#13093960	C₂²	1	2	yes	—
19	C₂×#13093959	C₂²	1	2	yes	—
20	C₂×#13093959	C₂²	1	2	yes	—
21	#15689147	C₂²	1	1	yes	characteristic
22	#15689146	C₂²	1	2	yes	—
23	#15689145	—	2	1	no	—
24	#15689145	—	2	1	no	—
25	#15689145	C₄	1	2	yes	—
26	#15689145	C₄	1	2	yes	—
27	#15689145	C₄	1	2	yes	—
28	#15689145	C₄	1	2	yes	—
29	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
30	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
31	C₄⋊C₈×D₄₇	—	2	1	no	—
32	C₄⋊C₈×D₄₇	—	2	1	no	—
33	C₄×#10625329	C₂²	1	1	yes	characteristic
34	#15689075	—	2	1	no	—
35	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
36	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
37	C₄×#10625324	—	2	1	no	—
38	#97×D₄₇	—	2	1	no	—
39	C₄×C₈×D₄₇	—	2	1	no	—
40	#15688888	C₂²	1	2	yes	—
41	#15688887	C₂²	1	2	yes	—
42	#15688887	C₂²	1	2	yes	—
43	C₂×#108×C₄₇	C₂²	1	2	yes	—
44	C₄₇×#423	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
47	C₄₇×#341	C₂²	1	2	yes	—
48	C₂²×C₄×D₄₇	Q₈	1	1	yes	characteristic
49	C₂²×C₄×D₄₇	Q₈	1	1	yes	characteristic
50	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
51	C₂×#10625329	C₂³	1	2	yes	—
52	C₂×#10625329	C₂³	1	1	yes	characteristic
53	C₂×#10625329	C₂³	1	1	yes	characteristic
54	C₂×#10625324	—	2	1	no	—
55	C₂×#10625324	—	2	1	no	—
56	C₂×#10625324	—	2	4	no	—
57	C₂×#10625324	—	2	4	no	—
58	C₂×#10625324	—	2	2	no	—
59	C₂×#10625324	C₂×C₄	1	4	yes	—
60	C₂×#10625324	C₂×C₄	1	4	yes	—
61	M₁₆×D₄₇	—	2	2	no	—
62	M₁₆×D₄₇	—	2	2	no	—
63	M₁₆×D₄₇	—	2	4	no	—
64	M₁₆×D₄₇	—	2	4	no	—
65	M₁₆×D₄₇	D₄	1	4	yes	—
66	M₁₆×D₄₇	Q₈	1	4	yes	—
67	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
68	C₂×C₈×D₄₇	—	2	1	no	—
69	C₂×C₈×D₄₇	—	2	1	no	—
70	C₂×C₈×D₄₇	—	2	2	no	—
71	C₂×C₄×Dic₄₇	Q₈	1	1	yes	characteristic
72	C₂×C₄×Dic₄₇	Q₈	1	1	yes	characteristic
73	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
74	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
75	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
76	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
77	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
78	C₄²×D₄₇	D₄	1	1	yes	characteristic
79	C₄²×D₄₇	D₄	1	1	yes	characteristic
80	C₄²×D₄₇	D₄	1	1	yes	characteristic
81	C₄²×D₄₇	D₄	1	1	yes	characteristic
82	#13093960	—	2	4	no	—
83	#13093959	—	2	4	no	—
84	#13093959	—	2	4	no	—
85	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
86	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
87	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
88	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
89	Dic₄₇⋊C₈	—	2	2	no	—
90	Dic₄₇⋊C₈	—	2	2	no	—
91	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
92	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
93	#13093935	—	2	1	no	—
94	#13093934	—	2	1	no	—
95	#13093934	—	2	1	no	—
96	C₄×C₄₇⋊C₈	—	2	1	no	—
97	C₈×Dic₄₇	—	2	1	no	—
98	C₈×Dic₄₇	—	2	1	no	—
99	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
100	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
103	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
104	#108×C₄₇	—	2	4	no	—
105	C₄⋊C₈×C₄₇	—	2	1	no	—
106	C₄⋊C₈×C₄₇	—	2	1	no	—
107	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
108	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
109	#97×C₄₇	—	2	1	no	—
110	C₄×C₈×C₄₇	—	2	1	no	—
111	C₂³×D₄₇	C₂×Q₈	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
115	C₂²×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
116	C₂²×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
117	C₂²×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
118	C₂×C₄×D₄₇	—	4	2	no	—
119	C₂×C₄×D₄₇	—	4	2	no	—
120	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
131	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
134	C₂×C₄×D₄₇	#41	1	2	yes	—
135	C₂×C₄×D₄₇	#41	1	2	yes	—
136	M₁₆×C₄₇	—	2	1	no	—
137	M₁₆×C₄₇	—	2	1	no	—
138	M₁₆×C₄₇	—	2	2	no	—
139	M₁₆×C₄₇	—	2	2	no	—
140	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
141	M₁₆×C₄₇	C₂×Q₈	1	2	yes	—
142	C₂×C₈×C₄₇	—	2	2	no	—
143	C₂×C₈×C₄₇	—	2	1	no	—
144	C₂×C₈×C₄₇	—	2	1	no	—
145	C₂×C₈×C₄₇	—	2	2	no	—
146	C₂×C₈×C₄₇	—	2	2	no	—
147	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
148	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
152	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
153	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
154	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
155	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
156	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
157	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
158	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
159	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
160	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
161	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
162	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
163	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
164	#10625329	—	2	1	no	—
165	#10625329	—	2	1	no	—
166	#10625329	—	2	2	no	—
167	#10625329	—	2	2	no	—
168	#10625329	C₂×D₄	1	2	yes	—
169	#10625329	C₂×Q₈	1	2	yes	—
170	C₂×C₄₇⋊C₈	—	2	1	no	—
171	C₂×C₄₇⋊C₈	—	2	1	no	—
172	C₂×C₄₇⋊C₈	—	2	2	no	—
173	C₂×C₄₇⋊C₈	—	2	2	no	—
174	C₂×C₄₇⋊C₈	—	2	2	no	—
175	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
176	#10625324	—	2	8	no	—
177	#10625324	—	2	8	no	—
178	#10625324	—	2	4	no	—
179	#10625324	—	2	4	no	—
180	#10625324	—	4	4	no	—
181	C₈×D₄₇	—	2	4	no	—
182	C₈×D₄₇	—	2	4	no	—
183	C₈×D₄₇	—	4	4	no	—
184	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
185	C₂²×D₄₇	—	4	1	no	—
186	C₂²×D₄₇	—	4	1	no	—
187	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂²×D₄₇	#125	1	2	yes	—
190	C₂²×D₄₇	C₄⋊Q₈	1	2	yes	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	4	1	no	—
193	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
201	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
203	C₂×Dic₄₇	—	2	2	no	—
204	C₂×Dic₄₇	—	4	1	no	—
205	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂×Dic₄₇	#125	1	2	yes	—
212	C₂×Dic₄₇	C₄⋊Q₈	1	2	yes	—
213	C₄×D₄₇	—	2	2	no	—
214	C₄×D₄₇	—	2	2	no	—
215	C₄×D₄₇	—	2	2	no	—
216	C₄×D₄₇	—	2	2	no	—
217	C₄×D₄₇	—	4	1	no	—
218	C₄×D₄₇	—	4	1	no	—
219	C₄×D₄₇	—	4	1	no	—
220	C₄×D₄₇	—	4	1	no	—
221	C₄×D₄₇	C₄×D₄	1	2	yes	—
222	C₄×D₄₇	C₄×D₄	1	2	yes	—
223	C₄×D₄₇	C₄×Q₈	1	2	yes	—
224	C₄×D₄₇	C₄×Q₈	1	2	yes	—
225	C₄×D₄₇	#121	1	2	yes	—
226	C₄×D₄₇	#121	1	2	yes	—
227	C₄×D₄₇	C₂²⋊Q₈	1	2	yes	—
228	C₄×D₄₇	C₂²⋊Q₈	1	2	yes	—
229	C₈×C₄₇	—	2	4	no	—
230	C₈×C₄₇	—	2	2	no	—
231	C₈×C₄₇	—	2	2	no	—
232	C₈×C₄₇	—	4	2	no	—
233	C₄₇⋊C₈	—	2	4	no	—
234	C₄₇⋊C₈	—	2	2	no	—
235	C₄₇⋊C₈	—	2	2	no	—
236	C₄₇⋊C₈	—	4	2	no	—
237	#21177	—	47	1	no	maximal, Sylow
238	C₂²×C₄₇	—	2	1	no	—
239	C₂²×C₄₇	—	2	1	no	—
240	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
241	C₂²×C₄₇	C₂×#125	1	1	yes	characteristic
242	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
243	C₂×D₄₇	—	2	1	no	—
244	C₂×D₄₇	—	2	1	no	—
245	C₂×D₄₇	—	2	1	no	—
246	C₂×D₄₇	—	2	1	no	—
247	C₂×D₄₇	—	4	2	no	—
248	C₂×D₄₇	—	4	2	no	—
249	C₂×D₄₇	#389	1	2	yes	—
250	C₂×D₄₇	#389	1	2	yes	—
251	C₄×C₄₇	—	2	1	no	—
252	C₄×C₄₇	—	2	1	no	—
253	C₄×C₄₇	—	2	1	no	—
254	C₄×C₄₇	#430	1	2	yes	complemented
255	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
256	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
257	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
258	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
259	Dic₄₇	—	2	1	no	—
260	Dic₄₇	—	2	1	no	—
261	Dic₄₇	—	2	1	no	—
262	Dic₄₇	#389	1	2	yes	—
263	Dic₄₇	#389	1	2	yes	—
264	Dic₄₇	#430	1	2	yes	complemented
265	C₂×#430	—	47	2	no	—
266	C₂×#423	—	47	1	no	—
267	C₂×#423	—	47	1	no	—
268	C₂×C₄×M₁₆	—	47	1	no	—
269	#1950	—	47	2	no	—
270	#1950	—	47	1	no	—
271	#1950	—	47	1	no	—
272	#1950	—	47	1	no	—
273	#1950	—	47	2	no	—
274	#1950	D₄₇	1	1	yes	characteristic, complemented
275	#1738	—	47	2	no	—
276	C₂×C₄₇	—	2	1	no	—
277	C₂×C₄₇	—	2	1	no	—
278	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
279	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
280	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
281	D₄₇	—	2	2	no	—
282	D₄₇	—	2	2	no	—
283	C₂²×M₁₆	—	47	2	no	—
284	C₂²×M₁₆	—	47	1	no	—
285	C₂²×M₁₆	—	47	1	no	—
286	C₂²×M₁₆	—	47	2	no	—
287	C₂²×C₄²	—	47	1	no	—
288	#430	—	94	8	no	—
289	C₂×#108	—	47	2	no	—
290	C₂×#108	—	47	2	no	—
291	C₂×#108	—	47	2	no	—
292	C₂×#108	C₂×D₄₇	1	2	yes	—
293	#423	—	47	2	no	—
294	#423	—	47	2	no	—
295	#423	—	47	2	no	—
296	#423	—	47	2	no	—
297	#423	—	47	2	no	—
298	#423	—	47	1	no	—
299	#423	—	94	1	no	—
300	#423	—	94	1	no	—
301	#423	C₂×D₄₇	1	1	yes	characteristic
302	C₂×C₄⋊C₈	—	47	2	no	—
303	C₂×C₄⋊C₈	—	47	1	no	—
304	C₂×C₄⋊C₈	—	94	1	no	—
305	C₂×C₄⋊C₈	—	94	1	no	—
306	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
307	C₄×M₁₆	—	47	1	no	—
308	C₄×M₁₆	—	47	1	no	—
309	C₄×M₁₆	—	47	1	no	—
310	C₄×M₁₆	—	94	1	no	—
311	C₄×M₁₆	—	94	1	no	—
312	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
313	C₂×#97	—	94	1	no	—
314	C₂×C₄×C₈	—	94	1	no	—
315	#341	—	47	2	no	—
316	#341	—	47	2	no	—
317	#341	—	47	2	no	—
318	#341	C₂×D₄₇	1	2	yes	—
319	C₄₇	#21177	1	1	yes	characteristic, complemented, Sylow
320	C₂³×C₄	—	47	1	no	—
321	C₂³×C₄	—	47	1	no	—
322	C₂³×C₄	—	47	1	no	—
323	C₂×M₁₆	—	47	4	no	—
324	C₂×M₁₆	—	47	4	no	—
325	C₂×M₁₆	—	47	1	no	—
326	C₂×M₁₆	—	47	1	no	—
327	C₂×M₁₆	—	47	4	no	—
328	C₂×M₁₆	—	47	4	no	—
329	C₂×M₁₆	—	47	2	no	—
330	C₂×M₁₆	—	94	4	no	—
331	C₂×M₁₆	—	94	1	no	—
332	C₂×M₁₆	—	94	1	no	—
333	C₂×M₁₆	—	94	4	no	—
334	C₂×M₁₆	—	94	2	no	—
335	C₂×M₁₆	—	94	2	no	—
336	C₂×M₁₆	—	94	2	no	—
337	C₂×M₁₆	—	94	4	no	—
338	C₂×M₁₆	—	94	4	no	—
339	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
340	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
341	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
342	C₂²×C₈	—	47	2	no	—
343	C₂²×C₈	—	94	1	no	—
344	C₂²×C₈	—	94	1	no	—
345	C₂²×C₈	—	94	2	no	—
346	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
347	C₂×C₄²	—	47	1	no	—
348	C₂×C₄²	—	47	1	no	—
349	C₂×C₄²	—	47	1	no	—
350	C₂×C₄²	—	47	1	no	—
351	C₂×C₄²	—	47	1	no	—
352	C₂×C₄²	—	47	1	no	—
353	C₂×C₄²	—	47	1	no	—
354	C₂×C₄²	—	47	1	no	—
355	C₂×C₄²	—	47	1	no	—
356	C₂×C₄²	—	47	1	no	—
357	C₂×C₄²	—	47	1	no	—
358	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
359	#108	—	2	4	no	—
360	#108	—	94	4	no	—
361	#108	—	94	4	no	—
362	#108	—	94	4	no	—
363	C₄⋊C₈	—	2	1	no	—
364	C₄⋊C₈	—	2	1	no	—
365	C₄⋊C₈	—	47	4	no	—
366	C₄⋊C₈	—	47	4	no	—
367	C₄⋊C₈	—	47	2	no	—
368	C₄⋊C₈	—	47	2	no	—
369	C₄⋊C₈	—	94	2	no	—
370	C₄⋊C₈	—	94	2	no	—
371	C₄⋊C₈	—	94	1	no	—
372	C₄⋊C₈	—	94	1	no	—
373	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
374	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
375	#97	—	2	1	no	—
376	#97	—	94	1	no	—
377	#97	—	94	1	no	—
378	#97	—	94	1	no	—
379	C₄×C₈	—	2	1	no	—
380	C₄×C₈	—	94	1	no	—
381	C₄×C₈	—	94	1	no	—
382	C₄×C₈	—	94	1	no	—
383	C₂⁴	—	47	1	no	—
384	C₂²×C₄	—	47	1	no	—
385	C₂²×C₄	—	47	1	no	—
386	C₂²×C₄	—	47	1	no	—
387	C₂²×C₄	—	47	2	no	—
388	C₂²×C₄	—	47	1	no	—
389	C₂²×C₄	—	47	1	no	—
390	C₂²×C₄	—	47	2	no	—
391	C₂²×C₄	—	47	2	no	—
392	C₂²×C₄	—	47	2	no	—
393	C₂²×C₄	—	47	1	no	—
394	C₂²×C₄	—	47	1	no	—
395	C₂²×C₄	—	47	1	no	—
396	C₂²×C₄	—	47	1	no	—
397	C₂²×C₄	—	47	1	no	—
398	C₂²×C₄	—	47	1	no	—
399	C₂²×C₄	—	47	1	no	—
400	C₂²×C₄	—	47	1	no	—
401	C₂²×C₄	—	47	1	no	—
402	C₂²×C₄	—	47	1	no	—
403	C₂²×C₄	—	188	2	no	—
404	C₂²×C₄	—	188	2	no	—
405	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
406	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
407	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
408	M₁₆	—	2	1	no	—
409	M₁₆	—	2	1	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	2	2	no	—
412	M₁₆	—	47	2	no	—
413	M₁₆	—	47	2	no	—
414	M₁₆	—	94	8	no	—
415	M₁₆	—	94	8	no	—
416	M₁₆	—	94	4	no	—
417	M₁₆	—	94	4	no	—
418	M₁₆	—	94	1	no	—
419	M₁₆	—	94	1	no	—
420	M₁₆	—	94	2	no	—
421	M₁₆	—	94	2	no	—
422	M₁₆	—	188	4	no	—
423	M₁₆	D₄×D₄₇	1	2	yes	—
424	M₁₆	Q₈×D₄₇	1	2	yes	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	47	4	no	—
431	C₂×C₈	—	94	4	no	—
432	C₂×C₈	—	94	4	no	—
433	C₂×C₈	—	94	2	no	—
434	C₂×C₈	—	94	1	no	—
435	C₂×C₈	—	94	1	no	—
436	C₂×C₈	—	94	2	no	—
437	C₂×C₈	—	94	2	no	—
438	C₂×C₈	—	188	4	no	—
439	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
440	C₄²	—	47	1	no	—
441	C₄²	—	47	1	no	—
442	C₄²	—	47	1	no	—
443	C₄²	—	47	1	no	—
444	C₄²	—	47	1	no	—
445	C₄²	—	47	1	no	—
446	C₄²	—	47	1	no	—
447	C₄²	—	47	1	no	—
448	C₄²	—	47	1	no	—
449	C₄²	—	47	1	no	—
450	C₄²	—	47	1	no	—
451	C₄²	—	47	1	no	—
452	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
453	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
454	C₄²	D₄×D₄₇	1	1	yes	characteristic
455	C₄²	D₄×D₄₇	1	1	yes	characteristic
456	C₂³	—	47	1	no	—
457	C₂³	—	47	1	no	—
458	C₂³	—	47	2	no	—
459	C₂³	—	47	2	no	—
460	C₂³	—	188	1	no	—
461	C₂³	—	188	1	no	—
462	C₂³	C₂×Q₈×D₄₇	1	1	yes	characteristic
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	47	1	no	—
466	C₂×C₄	—	47	1	no	—
467	C₂×C₄	—	47	1	no	—
468	C₂×C₄	—	47	2	no	—
469	C₂×C₄	—	47	2	no	—
470	C₂×C₄	—	47	2	no	—
471	C₂×C₄	—	47	2	no	—
472	C₂×C₄	—	47	2	no	—
473	C₂×C₄	—	47	2	no	—
474	C₂×C₄	—	47	2	no	—
475	C₂×C₄	—	47	2	no	—
476	C₂×C₄	—	47	2	no	—
477	C₂×C₄	—	47	2	no	—
478	C₂×C₄	—	47	1	no	—
479	C₂×C₄	—	47	1	no	—
480	C₂×C₄	—	47	1	no	—
481	C₂×C₄	—	94	2	no	—
482	C₂×C₄	—	94	2	no	—
483	C₂×C₄	—	94	2	no	—
484	C₂×C₄	—	94	2	no	—
485	C₂×C₄	—	94	2	no	—
486	C₂×C₄	—	188	1	no	—
487	C₂×C₄	—	188	1	no	—
488	C₂×C₄	—	188	1	no	—
489	C₂×C₄	—	188	1	no	—
490	C₂×C₄	—	188	1	no	—
491	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
492	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
493	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
494	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
495	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
496	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
497	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
498	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
499	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
500	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
501	C₈	—	2	4	no	—
502	C₈	—	2	2	no	—
503	C₈	—	2	2	no	—
504	C₈	—	4	2	no	—
505	C₈	—	94	4	no	—
506	C₈	—	94	2	no	—
507	C₈	—	94	2	no	—
508	C₈	—	188	2	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	47	2	no	—
512	C₂²	—	47	2	no	—
513	C₂²	—	94	1	no	—
514	C₂²	—	94	1	no	—
515	C₂²	—	94	1	no	—
516	C₂²	—	94	1	no	—
517	C₂²	—	188	2	no	—
518	C₂²	—	188	2	no	—
519	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
520	C₂²	#125×D₄₇	1	1	yes	characteristic
521	C₂²	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	47	2	no	—
526	C₄	—	47	2	no	—
527	C₄	—	47	2	no	—
528	C₄	—	94	1	no	—
529	C₄	—	94	1	no	—
530	C₄	—	94	1	no	—
531	C₄	#15689170	1	2	yes	complemented
532	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
533	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
534	C₄	#121×D₄₇	1	1	yes	characteristic
535	C₄	C₂²⋊Q₈×D₄₇	1	1	yes	characteristic
536	C₂	—	2	1	no	—
537	C₂	—	2	1	no	—
538	C₂	—	94	2	no	—
539	C₂	—	94	2	no	—
540	C₂	#389×D₄₇	1	1	yes	characteristic
541	C₂	#430×D₄₇	1	1	yes	characteristic
542	C₂	C₂×#15689170	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1950	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂³×D₄₇	C₂×Q₈
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1950	D₄₇
hypocenter	C₄₇	#21177
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1950

Complements

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

N	H ≅ G/N	type
5. #20244164	C₂	semidirect
6. #20244163	C₂	semidirect
7. #20244162	C₂	semidirect
8. #20244161	C₂	semidirect
9. #20244160	C₂	semidirect
11. C₄₇×#1950	C₂	semidirect
254. C₄×C₄₇	#430	semidirect
264. Dic₄₇	#430	semidirect
274. #1950	D₄₇	semidirect
319. C₄₇	#21177	semidirect
531. C₄	#15689170	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689170	2
C₂×#15689145	2
#423×D₄₇	2
C₄×M₁₆×D₄₇	2
#20244164	2
#20244163	2
#20244162	2
#20244161	2
#20244160	2
#20243113	2
C₄₇×#1950	2
#21177	47