Subgroups — #26222788

Order 12032.

1054 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689361	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20245926	C₂	1	2	yes	maximal
5	#20244121	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244067	C₂	1	2	yes	maximal, complemented
7	#20243808	C₂	1	2	yes	maximal
8	#20243414	C₂	1	1	yes	maximal, characteristic
9	#107×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#103×Dic₄₇	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1969	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	C₂×#13094000	C₂²	1	2	yes	—
15	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
16	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
17	#15689361	C₄	1	8	yes	complemented
18	Q₁₆×Dic₄₇	—	2	4	no	—
19	C₂×#13093958	C₂²	1	1	yes	characteristic
20	C₂×#13093958	C₂²	1	1	yes	characteristic
21	C₂×#13093948	C₂²	1	2	yes	—
22	C₂×#13093948	C₂²	1	2	yes	—
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
26	C₄×C₈×D₄₇	—	2	4	no	—
27	#15689021	C₂²	1	2	yes	—
28	#15689010	—	2	2	no	—
29	#15688997	—	2	2	no	—
30	#15688980	C₂²	1	2	yes	—
31	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
32	#15688974	—	2	2	no	—
33	#15688970	—	2	2	no	—
34	#15688886	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	#15688885	C₂²	1	2	yes	—
37	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#103×C₄₇	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#391	C₂²	1	2	yes	—
42	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
43	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂×C₈×D₄₇	—	2	2	no	—
48	C₂×C₈×D₄₇	—	2	2	no	—
49	C₂×C₈×D₄₇	—	2	2	no	—
50	C₂×C₈×D₄₇	—	2	2	no	—
51	C₂×C₈×D₄₇	—	2	2	no	—
52	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
53	#13094000	—	2	4	no	—
54	#13094000	C₂×C₄	1	8	yes	—
55	Q₈×Dic₄₇	—	2	4	no	—
56	Q₈×Dic₄₇	—	2	4	no	—
57	C₂×C₄⋊Dic₄₇	—	2	2	no	—
58	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
59	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
60	C₂×Dic₄₇⋊C₄	—	2	2	no	—
61	C₂×Dic₄₇⋊C₄	—	2	2	no	—
62	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
63	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
64	C₂×C₄×Dic₄₇	—	2	2	no	—
65	C₂×C₄×Dic₄₇	—	2	2	no	—
66	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
67	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
68	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
69	C₄²×D₄₇	—	2	2	no	—
70	C₄²×D₄₇	—	2	2	no	—
71	#13093958	—	2	2	no	—
72	#13093958	C₂×C₄	1	4	yes	complemented
73	#13093948	—	2	4	no	—
74	#13093948	C₂×C₄	1	8	yes	complemented
75	C₄×C₄₇⋊C₈	—	2	2	no	—
76	C₈×Dic₄₇	—	2	2	no	—
77	C₈×Dic₄₇	D₄	1	4	yes	—
78	C₄₇⋊#95	—	2	2	no	—
79	C₄₇⋊#95	—	2	2	no	—
80	C₄₇⋊#95	—	2	2	no	—
81	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
82	C₂×Q₁₆×C₄₇	—	2	2	no	—
83	C₂×Q₁₆×C₄₇	—	2	2	no	—
84	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
85	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	#107×C₄₇	—	2	2	no	—
90	#103×C₄₇	—	2	4	no	—
91	C₄×C₈×C₄₇	—	2	2	no	—
92	#95×C₄₇	—	2	2	no	—
93	#95×C₄₇	—	2	2	no	—
94	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	—	2	2	no	—
99	C₂×Q₈×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₂²×Dic₄₇	—	2	2	no	—
107	C₂²×Dic₄₇	—	2	2	no	—
108	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₄₇	—	2	2	no	—
112	C₂×C₄×D₄₇	—	2	2	no	—
113	C₂×C₄×D₄₇	—	2	1	no	—
114	C₂×C₄×D₄₇	—	2	1	no	—
115	C₂×C₄×D₄₇	—	2	1	no	—
116	C₂×C₄×D₄₇	—	2	1	no	—
117	C₂×C₄×D₄₇	—	2	2	no	—
118	C₂×C₄×D₄₇	—	2	2	no	—
119	C₂×C₄×D₄₇	—	2	2	no	—
120	C₂×C₄×D₄₇	Q₁₆	1	4	yes	complemented
121	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
122	C₂×C₄×D₄₇	#41	1	2	yes	—
123	Q₁₆×C₄₇	—	2	8	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	2	1	no	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₄₇	#41	1	2	yes	—
129	C₂×C₈×C₄₇	#41	1	2	yes	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄⋊C₄×C₄₇	—	2	2	no	—
132	C₄²×C₄₇	—	2	1	no	—
133	C₄²×C₄₇	—	2	1	no	—
134	(C₂×D₄₇)⋊C₄	—	2	8	no	—
135	(C₂×D₄₇)⋊C₄	—	4	4	no	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	2	2	no	—
139	C₄⋊Dic₄₇	—	4	4	no	—
140	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
141	Dic₄₇⋊C₄	—	2	8	no	—
142	Dic₄₇⋊C₄	—	4	4	no	—
143	C₄×Dic₄₇	—	2	2	no	—
144	C₄×Dic₄₇	—	2	2	no	—
145	C₄×Dic₄₇	—	4	4	no	—
146	C₄×Dic₄₇	—	4	4	no	—
147	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
148	C₄×Dic₄₇	#41	1	2	yes	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
154	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
155	C₈×D₄₇	—	2	8	no	—
156	C₈×D₄₇	—	2	8	no	—
157	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
158	C₂²×D₄₇	—	2	1	no	—
159	C₂²×D₄₇	—	2	1	no	—
160	C₂²×D₄₇	—	2	1	no	—
161	C₂²×D₄₇	—	2	1	no	—
162	C₂²×D₄₇	C₄×D₄	1	2	yes	—
163	C₂²×D₄₇	C₂×Q₁₆	1	2	yes	—
164	C₂²×D₄₇	#135	1	2	yes	—
165	Q₈×C₄₇	—	2	4	no	—
166	Q₈×C₄₇	—	2	4	no	—
167	Q₈×C₄₇	—	4	2	no	—
168	Q₈×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
180	C₂×C₄×C₄₇	#135	1	2	yes	—
181	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
187	C₂×Dic₄₇	—	2	1	no	—
188	C₂×Dic₄₇	—	2	1	no	—
189	C₂×Dic₄₇	—	2	1	no	—
190	C₂×Dic₄₇	—	2	1	no	—
191	C₂×Dic₄₇	—	2	4	no	—
192	C₂×Dic₄₇	—	4	2	no	—
193	C₂×Dic₄₇	—	4	2	no	—
194	C₂×Dic₄₇	—	4	2	no	—
195	C₂×Dic₄₇	—	4	2	no	—
196	C₂×Dic₄₇	—	4	2	no	—
197	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
198	C₂×Dic₄₇	#121	1	2	yes	—
199	C₂×Dic₄₇	#121	1	2	yes	—
200	C₂×Dic₄₇	C₂×Q₁₆	1	2	yes	—
201	C₂×Dic₄₇	#135	1	2	yes	—
202	C₄×D₄₇	—	2	8	no	—
203	C₄×D₄₇	—	2	2	no	—
204	C₄×D₄₇	—	2	2	no	—
205	C₄×D₄₇	—	2	2	no	—
206	C₄×D₄₇	—	2	2	no	—
207	C₄×D₄₇	—	2	8	no	—
208	C₈×C₄₇	—	2	2	no	—
209	C₈×C₄₇	C₄×D₄	1	4	yes	—
210	C₄₇⋊C₈	—	2	2	no	—
211	C₄₇⋊C₈	—	2	2	no	—
212	C₄×#467	—	47	1	no	maximal, Sylow
213	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
214	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
215	C₂²×C₄₇	#532	1	1	yes	characteristic
216	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
217	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
218	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
219	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
220	C₂×D₄₇	—	2	2	no	—
221	C₂×D₄₇	—	2	2	no	—
222	C₂×D₄₇	—	2	2	no	—
223	C₂×D₄₇	—	2	2	no	—
224	C₂×D₄₇	—	2	2	no	—
225	C₂×D₄₇	—	2	2	no	—
226	C₂×D₄₇	C₄×Q₁₆	1	4	yes	complemented
227	C₄×C₄₇	—	2	2	no	—
228	C₄×C₄₇	—	2	2	no	—
229	C₄×C₄₇	—	4	4	no	—
230	C₄×C₄₇	—	8	2	no	—
231	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
232	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
233	C₄×C₄₇	#525	1	1	yes	characteristic
234	C₄×C₄₇	#529	1	1	yes	characteristic
235	Dic₄₇	—	2	2	no	—
236	Dic₄₇	—	2	2	no	—
237	Dic₄₇	—	4	4	no	—
238	Dic₄₇	—	8	2	no	—
239	Dic₄₇	#467	1	4	yes	complemented
240	C₂×#467	—	47	1	no	—
241	C₂×C₄×Q₁₆	—	47	1	no	—
242	C₂²×C₄×C₈	—	47	1	no	—
243	C₄×C₂²⋊Q₈	—	47	2	no	—
244	#1969	D₄₇	1	1	yes	characteristic, complemented
245	#1942	—	47	1	no	—
246	#1933	—	47	2	no	—
247	#1892	—	47	2	no	—
248	#1808	—	47	1	no	—
249	C₄×#107	—	47	1	no	—
250	C₄×#103	—	47	2	no	—
251	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
252	C₂×C₄₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
253	C₂×C₄₇	C₄×#135	1	1	yes	characteristic
254	C₂×C₄₇	C₂×#467	1	1	yes	characteristic
255	C₂×C₄₇	#3050	1	1	yes	characteristic
256	C₂×C₄₇	#3168	1	1	yes	characteristic
257	C₂×C₄₇	#3170	1	1	yes	characteristic
258	D₄₇	—	2	4	no	—
259	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
260	C₂³×C₈	—	47	1	no	—
261	C₂³×C₈	—	47	1	no	—
262	C₂×C₂²⋊Q₈	—	47	2	no	—
263	C₂×C₄×Q₈	—	47	2	no	—
264	C₂²×C₄²	—	47	1	no	—
265	#467	—	47	8	no	—
266	C₄×Q₁₆	—	94	4	no	—
267	C₂×#107	—	47	1	no	—
268	C₂×#107	—	47	1	no	—
269	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
270	C₂×#103	—	47	2	no	—
271	C₂×#103	—	47	2	no	—
272	C₂×#103	C₂×D₄₇	1	2	yes	—
273	C₂×C₄×C₈	—	47	1	no	—
274	C₂×C₄×C₈	—	47	1	no	—
275	C₂×C₄×C₈	—	47	1	no	—
276	C₂×C₄×C₈	—	94	4	no	—
277	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
278	#391	C₂×D₄₇	1	2	yes	—
279	#389	—	47	2	no	—
280	#387	—	94	2	no	—
281	#385	—	94	2	no	—
282	#380	—	47	2	no	—
283	C₄×C₄⋊C₄	—	47	2	no	—
284	C₄×C₄⋊C₄	—	94	2	no	—
285	C₄×C₂²⋊C₄	—	94	2	no	—
286	#340	—	47	2	no	—
287	#340	—	47	2	no	—
288	#340	—	47	2	no	—
289	C₄₇	C₄×#467	1	1	yes	characteristic, complemented, Sylow
290	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
291	C₂³×C₄	—	47	1	no	—
292	C₂³×C₄	—	47	1	no	—
293	C₂³×C₄	—	47	1	no	—
294	C₂×Q₁₆	—	2	2	no	—
295	C₂×Q₁₆	—	2	2	no	—
296	C₂×Q₁₆	C₄×D₄₇	1	4	yes	complemented
297	C₂²×C₈	—	47	1	no	—
298	C₂²×C₈	—	47	1	no	—
299	C₂²×C₈	—	47	4	no	—
300	C₂²×C₈	—	94	2	no	—
301	C₂²×C₈	—	94	2	no	—
302	C₂²×C₈	—	94	2	no	—
303	C₂²×C₈	—	94	2	no	—
304	C₂²×C₈	—	94	2	no	—
305	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
306	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
307	C₂²⋊Q₈	—	47	8	no	—
308	C₂²⋊Q₈	—	94	4	no	—
309	C₄×Q₈	—	94	4	no	—
310	C₄×Q₈	—	94	4	no	—
311	C₂×C₄⋊C₄	—	47	2	no	—
312	C₂×C₄⋊C₄	—	47	2	no	—
313	C₂×C₄⋊C₄	—	94	2	no	—
314	C₂×C₄⋊C₄	—	94	2	no	—
315	C₂×C₄⋊C₄	—	94	2	no	—
316	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
317	C₂×C₂²⋊C₄	—	94	2	no	—
318	C₂×C₂²⋊C₄	—	94	2	no	—
319	C₂×C₄²	—	47	1	no	—
320	C₂×C₄²	—	47	1	no	—
321	C₂×C₄²	—	47	1	no	—
322	C₂×C₄²	—	94	2	no	—
323	C₂×C₄²	—	94	2	no	—
324	C₂×C₄²	—	94	2	no	—
325	C₂×C₄²	—	94	2	no	—
326	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
327	#107	—	2	2	no	—
328	#107	—	47	4	no	—
329	#107	—	94	2	no	—
330	#103	—	2	4	no	—
331	#103	—	47	8	no	—
332	#103	—	94	4	no	—
333	C₄×C₈	—	2	2	no	—
334	C₄×C₈	—	47	4	no	—
335	C₄×C₈	—	94	2	no	—
336	C₄×C₈	—	94	2	no	—
337	#95	—	2	2	no	—
338	#95	—	2	2	no	—
339	#95	—	94	2	no	—
340	#95	—	94	2	no	—
341	#95	—	94	2	no	—
342	C₂⁴	—	47	1	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	47	1	no	—
352	C₂²×C₄	—	47	1	no	—
353	C₂²×C₄	—	47	1	no	—
354	C₂²×C₄	—	47	4	no	—
355	C₂²×C₄	—	47	2	no	—
356	C₂²×C₄	—	47	2	no	—
357	C₂²×C₄	—	94	2	no	—
358	C₂²×C₄	—	94	2	no	—
359	C₂²×C₄	—	94	2	no	—
360	C₂²×C₄	—	94	2	no	—
361	C₂²×C₄	—	94	2	no	—
362	C₂²×C₄	—	94	1	no	—
363	C₂²×C₄	—	94	1	no	—
364	C₂²×C₄	—	94	1	no	—
365	C₂²×C₄	—	94	1	no	—
366	C₂²×C₄	—	94	2	no	—
367	C₂²×C₄	—	94	2	no	—
368	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
369	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
370	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
371	Q₁₆	—	2	8	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	47	2	no	—
375	C₂×C₈	—	47	2	no	—
376	C₂×C₈	—	94	8	no	—
377	C₂×C₈	—	94	1	no	—
378	C₂×C₈	—	94	1	no	—
379	C₂×C₈	—	94	1	no	—
380	C₂×C₈	—	94	1	no	—
381	C₂×C₈	—	94	8	no	—
382	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
383	C₂×C₈	D₄×D₄₇	1	2	yes	—
384	C₂×C₈	#10625352	1	2	yes	—
385	C₂×C₈	#10625352	1	2	yes	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	47	4	no	—
389	C₄⋊C₄	—	94	8	no	—
390	C₄⋊C₄	—	94	2	no	—
391	C₄⋊C₄	—	94	2	no	—
392	C₄⋊C₄	—	94	2	no	—
393	C₄⋊C₄	—	188	4	no	—
394	C₄⋊C₄	—	188	4	no	—
395	C₂²⋊C₄	—	94	8	no	—
396	C₂²⋊C₄	—	188	4	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	47	2	no	—
400	C₄²	—	47	2	no	—
401	C₄²	—	94	2	no	—
402	C₄²	—	94	2	no	—
403	C₄²	—	188	4	no	—
404	C₄²	—	188	4	no	—
405	C₂³	—	47	2	no	—
406	C₂³	—	47	2	no	—
407	C₂³	—	47	2	no	—
408	C₂³	—	94	1	no	—
409	C₂³	—	94	1	no	—
410	C₂³	—	94	1	no	—
411	C₂³	—	94	1	no	—
412	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
413	Q₈	—	2	4	no	—
414	Q₈	—	2	4	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	4	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	47	2	no	—
428	C₂×C₄	—	47	2	no	—
429	C₂×C₄	—	47	2	no	—
430	C₂×C₄	—	47	2	no	—
431	C₂×C₄	—	47	2	no	—
432	C₂×C₄	—	94	8	no	—
433	C₂×C₄	—	94	8	no	—
434	C₂×C₄	—	94	1	no	—
435	C₂×C₄	—	94	1	no	—
436	C₂×C₄	—	94	1	no	—
437	C₂×C₄	—	94	1	no	—
438	C₂×C₄	—	94	2	no	—
439	C₂×C₄	—	94	2	no	—
440	C₂×C₄	—	94	2	no	—
441	C₂×C₄	—	94	2	no	—
442	C₂×C₄	—	94	4	no	—
443	C₂×C₄	—	188	2	no	—
444	C₂×C₄	—	188	2	no	—
445	C₂×C₄	—	188	2	no	—
446	C₂×C₄	—	188	2	no	—
447	C₂×C₄	—	188	2	no	—
448	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
449	C₂×C₄	#13094047	1	2	yes	—
450	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
451	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
452	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
453	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
454	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
455	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
456	C₈	—	2	2	no	—
457	C₈	—	94	2	no	—
458	C₈	—	94	2	no	—
459	C₈	(C₂²⋊D₄₇)⋊C₄	1	4	yes	—
460	C₂²	—	47	4	no	—
461	C₂²	—	94	2	no	—
462	C₂²	—	94	2	no	—
463	C₂²	—	94	2	no	—
464	C₂²	—	94	2	no	—
465	C₂²	—	94	2	no	—
466	C₂²	—	94	2	no	—
467	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
468	C₂²	#121×D₄₇	1	1	yes	characteristic
469	C₂²	#15689671	1	1	yes	characteristic
470	C₂²	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
471	C₂²	#135×D₄₇	1	1	yes	characteristic
472	C₂²	#135×D₄₇	1	1	yes	characteristic
473	C₂²	C₂×#13094047	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	4	4	no	—
477	C₄	—	8	2	no	—
478	C₄	—	47	4	no	—
479	C₄	—	94	2	no	—
480	C₄	—	94	2	no	—
481	C₄	—	376	2	no	—
482	C₄	—	188	4	no	—
483	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
484	C₄	C₄×#10625352	1	1	yes	characteristic
485	C₄	#15689633	1	1	yes	characteristic
486	C₄	#15689652	1	1	yes	characteristic
487	C₂	—	94	4	no	—
488	C₂	#20245904	1	1	yes	characteristic
489	C₂	C₄×Q₁₆×D₄₇	1	1	yes	characteristic
490	C₂	C₄×#13094047	1	1	yes	characteristic
491	C₂	#467×D₄₇	1	1	yes	characteristic
492	C₂	#20252971	1	1	yes	characteristic
493	C₂	#20253955	1	1	yes	characteristic
494	C₂	#20253972	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1969	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1969	D₄₇
hypocenter	C₄₇	C₄×#467
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1969

Complements

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

N	H ≅ G/N	type
2. C₂×Q₁₆×Dic₄₇	C₂	semidirect
5. #20244121	C₂	semidirect
6. #20244067	C₂	semidirect
9. #107×Dic₄₇	C₂	semidirect
10. #103×Dic₄₇	C₂	semidirect
11. C₄₇×#1969	C₂	semidirect
17. #15689361	C₄	semidirect
72. #13093958	C₂×C₄	semidirect
74. #13093948	C₂×C₄	semidirect
84. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
120. C₂×C₄×D₄₇	Q₁₆	semidirect
226. C₂×D₄₇	C₄×Q₁₆	semidirect
239. Dic₄₇	#467	semidirect
244. #1969	D₄₇	semidirect
289. C₄₇	C₄×#467	semidirect
296. C₂×Q₁₆	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689361	2
C₂×Q₁₆×Dic₄₇	2
C₂×C₄×C₈×D₄₇	2
#20245926	2
#20244121	2
#20244067	2
#20243808	2
#20243414	2
#107×Dic₄₇	2
#103×Dic₄₇	2
C₄₇×#1969	2
C₄×#467	47