Subgroups — #26220422

Order 12032.

838 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689181	C₂	1	2	yes	maximal, complemented
2	#20245853	C₂	1	1	yes	maximal, characteristic
3	#20244183	C₂	1	1	yes	maximal, characteristic
4	#20244106	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244104	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244004	C₂	1	2	yes	maximal, complemented
7	#20243998	C₂	1	2	yes	maximal, complemented
8	C₄⋊C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243156	C₂	1	2	yes	maximal, complemented
10	C₄×#13093934	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1954	C₂	1	1	yes	maximal, characteristic
12	C₂×#13093983	C₂²	1	2	yes	—
13	#15689181	—	2	8	no	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
16	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
17	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
19	C₂×#13093934	C₂²	1	1	yes	characteristic
20	C₂×#13093934	C₂²	1	1	yes	characteristic
21	C₂×#13093934	C₂²	1	1	yes	characteristic
22	C₂×#13093934	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
25	#15689026	C₄	1	1	yes	characteristic
26	#15689026	C₄	1	1	yes	characteristic
27	#15689022	C₄	1	1	yes	characteristic
28	#15689022	C₄	1	1	yes	characteristic
29	#15689016	C₄	1	2	yes	—
30	#15689016	C₄	1	2	yes	—
31	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
32	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
33	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
40	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	#13093983	—	2	4	no	—
46	#13093983	—	2	4	no	—
47	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
51	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
61	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
62	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
63	Dic₄₇⋊C₈	—	2	4	no	—
64	Dic₄₇⋊C₈	—	2	4	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
67	#13093934	—	2	2	no	—
68	#13093934	—	2	2	no	—
69	#13093934	—	2	2	no	—
70	#13093934	D₄	1	4	yes	complemented
71	C₄×C₄₇⋊C₈	—	2	2	no	—
72	C₈×Dic₄₇	—	2	4	no	—
73	C₄₇⋊#95	C₂×C₄	1	2	yes	—
74	C₄₇⋊#95	C₂×C₄	1	2	yes	—
75	C₄₇⋊#95	C₂×C₄	1	2	yes	—
76	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
78	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₄×D₄×C₄₇	—	2	2	no	—
82	C₄×D₄×C₄₇	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
85	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₄₇	—	2	2	no	—
87	C₂²⋊C₈×C₄₇	—	2	4	no	—
88	C₂²⋊C₈×C₄₇	—	2	4	no	—
89	C₄×C₈×C₄₇	—	2	2	no	—
90	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
91	C₂×D₄×C₄₇	—	2	2	no	—
92	C₂×D₄×C₄₇	—	2	2	no	—
93	C₂×D₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
104	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
107	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
108	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₄₇	—	2	1	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₂×C₈×C₄₇	—	2	1	no	—
114	C₂×C₈×C₄₇	—	2	2	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₄₇	#41	1	2	yes	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₂²⋊C₄×C₄₇	—	2	4	no	—
121	C₄²×C₄₇	#41	1	2	yes	—
122	C₄²×C₄₇	#41	1	2	yes	—
123	C₂²⋊Dic₄₇	—	2	4	no	—
124	C₂²⋊Dic₄₇	—	2	4	no	—
125	C₂²⋊Dic₄₇	—	4	2	no	—
126	C₂²⋊Dic₄₇	—	4	2	no	—
127	C₄⋊Dic₄₇	—	2	2	no	—
128	C₄⋊Dic₄₇	—	2	2	no	—
129	C₄⋊Dic₄₇	—	2	4	no	—
130	C₄⋊Dic₄₇	—	2	4	no	—
131	C₄×Dic₄₇	—	2	2	no	—
132	C₄×Dic₄₇	—	2	2	no	—
133	C₄×Dic₄₇	—	2	2	no	—
134	C₄×Dic₄₇	—	2	1	no	—
135	C₄×Dic₄₇	—	2	1	no	—
136	C₄×Dic₄₇	—	2	2	no	—
137	C₄×Dic₄₇	—	4	1	no	—
138	C₄×Dic₄₇	—	4	1	no	—
139	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
140	C₄×Dic₄₇	#41	1	2	yes	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	—	2	1	no	—
143	C₂×C₄₇⋊C₈	—	2	1	no	—
144	C₂×C₄₇⋊C₈	—	2	1	no	—
145	C₂×C₄₇⋊C₈	—	2	2	no	—
146	C₂×C₄₇⋊C₈	—	2	2	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
149	C₂×C₄₇⋊C₈	#41	1	2	yes	—
150	C₂³×C₄₇	—	2	2	no	—
151	C₂³×C₄₇	—	2	2	no	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	—	2	2	no	—
154	C₂³×C₄₇	—	2	2	no	—
155	C₂³×C₄₇	—	2	2	no	—
156	C₂³×C₄₇	—	2	2	no	—
157	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
158	D₄×C₄₇	—	4	4	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	#117	1	2	yes	—
169	C₂×C₄×C₄₇	#117	1	2	yes	—
170	C₂×C₄×C₄₇	#131	1	2	yes	—
171	C₂×C₄×C₄₇	#131	1	2	yes	—
172	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
178	C₂×Dic₄₇	—	2	1	no	—
179	C₂×Dic₄₇	—	2	1	no	—
180	C₂×Dic₄₇	—	2	1	no	—
181	C₂×Dic₄₇	—	2	1	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	2	2	no	—
184	C₂×Dic₄₇	—	2	1	no	—
185	C₂×Dic₄₇	—	2	1	no	—
186	C₂×Dic₄₇	—	2	1	no	—
187	C₂×Dic₄₇	—	2	1	no	—
188	C₂×Dic₄₇	—	2	2	no	—
189	C₂×Dic₄₇	—	2	2	no	—
190	C₂×Dic₄₇	—	2	1	no	—
191	C₂×Dic₄₇	—	2	1	no	—
192	C₂×Dic₄₇	—	2	2	no	—
193	C₂×Dic₄₇	—	2	2	no	—
194	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
195	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
196	C₈×C₄₇	—	2	2	no	—
197	C₈×C₄₇	—	2	2	no	—
198	C₈×C₄₇	—	4	2	no	—
199	C₄₇⋊C₈	—	2	2	no	—
200	C₄₇⋊C₈	—	2	2	no	—
201	C₄₇⋊C₈	—	4	2	no	—
202	#21268	—	47	1	no	maximal, Sylow
203	C₂²×C₄₇	—	4	2	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	—	4	2	no	—
206	C₂²×C₄₇	—	4	2	no	—
207	C₂²×C₄₇	—	4	2	no	—
208	C₂²×C₄₇	—	4	2	no	—
209	C₂²×C₄₇	—	4	2	no	—
210	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
211	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
212	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
213	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
214	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
215	C₂²×C₄₇	#568	1	1	yes	characteristic
216	C₂²×C₄₇	#568	1	1	yes	characteristic
217	C₄×C₄₇	—	2	2	no	—
218	C₄×C₄₇	—	4	2	no	—
219	C₄×C₄₇	#433	1	4	yes	complemented
220	C₄×C₄₇	#529	1	1	yes	characteristic
221	C₄×C₄₇	#529	1	1	yes	characteristic
222	C₄×C₄₇	#532	1	1	yes	characteristic
223	C₄×C₄₇	#532	1	1	yes	characteristic
224	Dic₄₇	—	2	2	no	—
225	Dic₄₇	—	2	2	no	—
226	Dic₄₇	—	4	2	no	—
227	Dic₄₇	—	4	2	no	—
228	Dic₄₇	—	4	1	no	—
229	Dic₄₇	—	4	1	no	—
230	C₂×#433	—	47	2	no	—
231	#2293	—	47	1	no	—
232	#1954	—	47	1	no	—
233	#1954	D₄₇	1	1	yes	characteristic
234	#1939	—	47	1	no	—
235	#1939	—	47	1	no	—
236	#1924	—	47	2	no	—
237	#1924	—	47	2	no	—
238	C₄×C₄⋊C₈	—	47	1	no	—
239	#1750	—	47	2	no	—
240	C₄×#97	—	47	1	no	—
241	C₂×C₄₇	—	8	2	no	—
242	C₂×C₄₇	#2293	1	1	yes	characteristic
243	C₂×C₄₇	C₂×#433	1	1	yes	characteristic
244	C₂×C₄₇	#2923	1	1	yes	characteristic
245	C₂×C₄₇	#2935	1	1	yes	characteristic
246	C₂×C₄₇	#2935	1	1	yes	characteristic
247	C₂×C₄₇	#2969	1	1	yes	characteristic
248	C₂×C₄₇	#2969	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
250	C₂×#117	—	47	2	no	—
251	#433	—	94	8	no	—
252	C₂×C₄⋊C₈	—	47	2	no	—
253	C₂×C₄⋊C₈	—	47	2	no	—
254	C₂×C₄⋊C₈	—	47	1	no	—
255	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
256	C₂×C₂²⋊C₈	—	47	2	no	—
257	C₂×C₂²⋊C₈	—	47	2	no	—
258	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
259	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
260	C₂×#97	—	47	1	no	—
261	C₂×#97	—	47	1	no	—
262	C₂×#97	—	47	1	no	—
263	C₂×#97	—	47	1	no	—
264	C₂×C₄×C₈	—	47	2	no	—
265	C₂×C₄×C₈	—	47	1	no	—
266	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
267	#390	—	47	1	no	—
268	#390	—	47	1	no	—
269	#389	—	47	1	no	—
270	#389	—	47	1	no	—
271	#388	—	47	2	no	—
272	#388	—	47	2	no	—
273	C₄×C₄⋊C₄	—	47	1	no	—
274	C₄×C₂²⋊C₄	—	47	2	no	—
275	C₄³	—	47	1	no	—
276	#336	—	47	2	no	—
277	#336	—	47	2	no	—
278	#336	—	47	2	no	—
279	C₄₇	#21268	1	1	yes	characteristic, complemented, Sylow
280	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
281	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
282	C₂²×C₈	—	47	1	no	—
283	C₂²×C₈	—	47	1	no	—
284	C₂²×C₈	—	47	2	no	—
285	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
286	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
287	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	#117	—	94	4	no	—
291	#117	—	94	4	no	—
292	C₂×C₄⋊C₄	—	47	2	no	—
293	C₂×C₄⋊C₄	—	47	2	no	—
294	C₂×C₄⋊C₄	—	47	1	no	—
295	C₂×C₄⋊C₄	—	47	1	no	—
296	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	—	47	2	no	—
298	C₂×C₂²⋊C₄	—	47	2	no	—
299	C₂×C₂²⋊C₄	—	47	2	no	—
300	C₂×C₂²⋊C₄	—	47	2	no	—
301	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
302	C₂×C₄²	—	47	1	no	—
303	C₂×C₄²	—	47	1	no	—
304	C₂×C₄²	—	47	1	no	—
305	C₂×C₄²	—	47	2	no	—
306	C₂×C₄²	—	47	1	no	—
307	C₂×C₄²	—	47	1	no	—
308	C₂×C₄²	—	47	1	no	—
309	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
310	C₄⋊C₈	—	2	2	no	—
311	C₄⋊C₈	—	94	4	no	—
312	C₄⋊C₈	—	94	4	no	—
313	C₄⋊C₈	—	94	2	no	—
314	C₂²⋊C₈	—	2	4	no	—
315	C₂²⋊C₈	—	2	4	no	—
316	C₂²⋊C₈	—	94	4	no	—
317	C₂²⋊C₈	—	94	4	no	—
318	#97	—	47	4	no	—
319	#97	—	94	2	no	—
320	#97	—	94	2	no	—
321	#97	—	94	2	no	—
322	C₄×C₈	—	2	2	no	—
323	C₄×C₈	—	94	4	no	—
324	C₄×C₈	—	94	2	no	—
325	#95	—	47	2	no	—
326	#95	—	47	2	no	—
327	#95	—	47	2	no	—
328	C₂⁴	C₂×C₄×D₄₇	1	2	yes	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	47	1	no	—
339	C₂²×C₄	—	47	1	no	—
340	C₂²×C₄	—	47	1	no	—
341	C₂²×C₄	—	47	1	no	—
342	C₂²×C₄	—	47	2	no	—
343	C₂²×C₄	—	47	2	no	—
344	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
345	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
347	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	47	2	no	—
356	C₂×C₈	—	47	2	no	—
357	C₂×C₈	—	94	1	no	—
358	C₂×C₈	—	94	1	no	—
359	C₂×C₈	—	94	1	no	—
360	C₂×C₈	—	94	1	no	—
361	C₂×C₈	—	94	2	no	—
362	C₂×C₈	—	94	2	no	—
363	C₂×C₈	—	94	2	no	—
364	C₂×C₈	D₄×D₄₇	1	2	yes	—
365	C₂×C₈	#10625352	1	2	yes	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	94	4	no	—
368	C₄⋊C₄	—	94	4	no	—
369	C₄⋊C₄	—	94	2	no	—
370	C₄⋊C₄	—	94	2	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	94	4	no	—
373	C₂²⋊C₄	—	94	4	no	—
374	C₂²⋊C₄	—	188	2	no	—
375	C₂²⋊C₄	—	188	2	no	—
376	C₄²	—	47	2	no	—
377	C₄²	—	47	2	no	—
378	C₄²	—	94	2	no	—
379	C₄²	—	94	2	no	—
380	C₄²	—	94	2	no	—
381	C₄²	—	94	1	no	—
382	C₄²	—	94	2	no	—
383	C₄²	—	94	1	no	—
384	C₄²	—	188	1	no	—
385	C₄²	—	188	1	no	—
386	C₄²	#10625352	1	2	yes	—
387	C₄²	#10625352	1	2	yes	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
396	D₄	—	4	4	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	47	2	no	—
407	C₂×C₄	—	47	2	no	—
408	C₂×C₄	—	94	1	no	—
409	C₂×C₄	—	94	1	no	—
410	C₂×C₄	—	94	1	no	—
411	C₂×C₄	—	94	1	no	—
412	C₂×C₄	—	94	2	no	—
413	C₂×C₄	—	94	2	no	—
414	C₂×C₄	—	94	1	no	—
415	C₂×C₄	—	94	1	no	—
416	C₂×C₄	—	94	1	no	—
417	C₂×C₄	—	94	2	no	—
418	C₂×C₄	—	94	1	no	—
419	C₂×C₄	—	94	2	no	—
420	C₂×C₄	—	94	1	no	—
421	C₂×C₄	—	94	1	no	—
422	C₂×C₄	—	94	2	no	—
423	C₂×C₄	—	94	2	no	—
424	C₂×C₄	#13093980	1	2	yes	—
425	C₂×C₄	#13093980	1	2	yes	—
426	C₂×C₄	#13094030	1	2	yes	—
427	C₂×C₄	#13094032	1	2	yes	—
428	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
429	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
430	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
431	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
432	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
433	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	2	no	—
437	C₈	—	94	2	no	—
438	C₈	—	94	2	no	—
439	C₈	—	188	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	C₂×#13093980	1	1	yes	characteristic
448	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
449	C₂²	C₄×#10625352	1	1	yes	characteristic
450	C₂²	C₂×#13094030	1	1	yes	characteristic
451	C₂²	C₂×#13094032	1	1	yes	characteristic
452	C₂²	#15689888	1	1	yes	characteristic
453	C₂²	#15689888	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	94	2	no	—
457	C₄	—	94	2	no	—
458	C₄	—	188	2	no	—
459	C₄	—	188	2	no	—
460	C₄	—	188	1	no	—
461	C₄	—	188	1	no	—
462	C₄	#15689181	1	4	yes	complemented
463	C₄	#15689652	1	1	yes	characteristic
464	C₄	#15689654	1	1	yes	characteristic
465	C₄	#15689668	1	1	yes	characteristic
466	C₄	#15689671	1	1	yes	characteristic
467	C₂	—	8	2	no	—
468	C₂	#20245850	1	1	yes	characteristic
469	C₂	C₂×#15689181	1	1	yes	characteristic
470	C₂	#20252035	1	1	yes	characteristic
471	C₂	#20252127	1	1	yes	characteristic
472	C₂	#20252133	1	1	yes	characteristic
473	C₂	#20252389	1	1	yes	characteristic
474	C₂	#20252395	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1954	C₂
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1954	D₄₇
hypocenter	C₄₇	#21268
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1954

Complements

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

N	H ≅ G/N	type
1. C₂×#15689181	C₂	semidirect
4. #20244106	C₂	semidirect
5. #20244104	C₂	semidirect
6. #20244004	C₂	semidirect
7. #20243998	C₂	semidirect
8. C₄⋊C₈×Dic₄₇	C₂	semidirect
9. #20243156	C₂	semidirect
10. C₄×#13093934	C₂	semidirect
70. #13093934	D₄	semidirect
219. C₄×C₄₇	#433	semidirect
279. C₄₇	#21268	semidirect
462. C₄	#15689181	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689181	2
#20245853	2
#20244183	2
#20244106	2
#20244104	2
#20244004	2
#20243998	2
C₄⋊C₈×Dic₄₇	2
#20243156	2
C₄×#13093934	2
C₄₇×#1954	2
#21268	47