Subgroups — #343×Dic₄₇ #26121482

Order 12032.

994 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×Dic₄₇	C₂	1	2	yes	maximal
2	C₂×C₄⋊C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688892	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688891	C₂	1	2	yes	maximal
5	C₂×C₄₇×#343	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
8	C₂²×C₄×Dic₄₇	C₄	1	2	yes	—
9	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
10	M₁₆×Dic₄₇	—	2	4	no	—
11	M₁₆×Dic₄₇	C₄	1	8	yes	complemented
12	C₂×#13093934	—	2	2	no	—
13	C₂×C₈×Dic₄₇	—	2	2	no	—
14	C₄⋊C₄×Dic₄₇	—	2	2	no	—
15	C₄⋊C₄×Dic₄₇	—	2	2	no	—
16	C₂×C₄₇⋊#95	C₄	1	2	yes	—
17	#15688892	C₄	1	4	yes	complemented
18	#15688891	C₄	1	8	yes	complemented
19	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
21	C₄₇×#343	C₄	1	4	yes	complemented
22	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
23	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
24	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	C₂×C₄	1	4	yes	—
29	C₂×#10625329	C₂×C₄	1	4	yes	—
30	C₂×#10625329	C₂×C₄	1	4	yes	—
31	C₂²×C₄₇⋊C₈	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	2	no	—
33	C₂×C₄⋊Dic₄₇	—	2	1	no	—
34	C₂×C₄⋊Dic₄₇	—	2	1	no	—
35	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
36	C₂×C₄×Dic₄₇	—	2	2	no	—
37	C₂×C₄×Dic₄₇	—	2	2	no	—
38	C₂×C₄×Dic₄₇	—	4	4	no	—
39	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
40	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
41	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
42	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
43	C₂×C₄×Dic₄₇	Q₈	1	2	yes	—
44	#13093934	—	2	8	no	—
45	C₈×Dic₄₇	—	2	8	no	—
46	C₄₇⋊#95	—	2	4	no	—
47	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
48	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₄₇	—	2	2	no	—
50	C₂×M₁₆×C₄₇	—	2	2	no	—
51	C₂×M₁₆×C₄₇	—	2	2	no	—
52	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
53	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
54	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
55	C₂²×C₈×C₄₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
60	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₄₇	—	2	2	no	—
62	C₂²×C₄×C₄₇	—	2	2	no	—
63	C₂²×C₄×C₄₇	—	4	2	no	—
64	C₂²×C₄×C₄₇	—	4	2	no	—
65	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
66	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
67	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
69	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
72	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	#41	1	2	yes	—
74	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
76	C₂²×Dic₄₇	—	2	2	no	—
77	C₂²×Dic₄₇	—	2	2	no	—
78	C₂²×Dic₄₇	—	2	2	no	—
79	C₂²×Dic₄₇	—	2	2	no	—
80	C₂²×Dic₄₇	—	4	1	no	—
81	C₂²×Dic₄₇	—	4	1	no	—
82	C₂²×Dic₄₇	—	4	2	no	—
83	C₂²×Dic₄₇	—	4	2	no	—
84	C₂²×Dic₄₇	C₄²	1	2	yes	—
85	C₂²×Dic₄₇	C₄²	1	4	yes	—
86	C₂²×Dic₄₇	C₄²	1	2	yes	—
87	C₂²×Dic₄₇	C₂²⋊C₄	1	2	yes	—
88	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×Dic₄₇	C₄⋊C₄	1	2	yes	—
91	C₂²×Dic₄₇	C₄⋊C₄	1	2	yes	—
92	M₁₆×C₄₇	—	2	4	no	—
93	M₁₆×C₄₇	—	2	4	no	—
94	M₁₆×C₄₇	—	2	4	no	—
95	M₁₆×C₄₇	C₄²	1	8	yes	complemented
96	C₂×C₈×C₄₇	—	2	4	no	—
97	C₂×C₈×C₄₇	—	2	4	no	—
98	C₂×C₈×C₄₇	—	2	4	no	—
99	C₄⋊C₄×C₄₇	—	2	4	no	—
100	C₄⋊C₄×C₄₇	—	2	4	no	—
101	C₄⋊Dic₄₇	—	2	4	no	—
102	C₄⋊Dic₄₇	—	2	4	no	—
103	C₄×Dic₄₇	—	4	4	no	—
104	C₄×Dic₄₇	—	4	4	no	—
105	C₄×Dic₄₇	C₂²⋊C₄	1	4	yes	—
106	C₄×Dic₄₇	C₂²⋊C₄	1	4	yes	—
107	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
108	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
109	#10625329	—	2	4	no	—
110	#10625329	—	2	4	no	—
111	#10625329	—	2	4	no	—
112	#10625329	C₄²	1	8	yes	complemented
113	C₂×C₄₇⋊C₈	—	2	4	no	—
114	C₂×C₄₇⋊C₈	—	2	4	no	—
115	C₂×C₄₇⋊C₈	—	2	4	no	—
116	C₂³×C₄₇	—	2	1	no	—
117	C₂³×C₄₇	—	2	1	no	—
118	C₂³×C₄₇	—	2	1	no	—
119	C₂³×C₄₇	—	2	1	no	—
120	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
121	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
122	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
123	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂³×C₄₇	#117	1	1	yes	characteristic
126	C₂³×C₄₇	#117	1	1	yes	characteristic
127	C₂×C₄×C₄₇	—	2	4	no	—
128	C₂×C₄×C₄₇	—	4	4	no	—
129	C₂×C₄×C₄₇	—	4	2	no	—
130	C₂×C₄×C₄₇	—	4	2	no	—
131	C₂×C₄×C₄₇	—	4	4	no	—
132	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
133	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
134	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
135	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
136	C₂×C₄×C₄₇	#117	1	2	yes	—
137	C₂×C₄×C₄₇	#117	1	2	yes	—
138	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
139	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
140	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
141	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
143	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
145	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
147	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
148	C₂×Dic₄₇	—	2	1	no	—
149	C₂×Dic₄₇	—	2	1	no	—
150	C₂×Dic₄₇	—	2	2	no	—
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	2	4	no	—
153	C₂×Dic₄₇	—	2	4	no	—
154	C₂×Dic₄₇	—	2	4	no	—
155	C₂×Dic₄₇	—	4	2	no	—
156	C₂×Dic₄₇	—	4	2	no	—
157	C₂×Dic₄₇	—	4	4	no	—
158	C₂×Dic₄₇	—	4	2	no	—
159	C₂×Dic₄₇	—	4	2	no	—
160	C₂×Dic₄₇	—	4	4	no	—
161	C₂×Dic₄₇	#95	1	2	yes	—
162	C₂×Dic₄₇	#95	1	4	yes	—
163	C₂×Dic₄₇	#95	1	2	yes	—
164	C₂×Dic₄₇	#100	1	2	yes	—
165	C₂×Dic₄₇	#101	1	2	yes	—
166	C₈×C₄₇	—	2	8	no	—
167	C₄₇⋊C₈	—	2	8	no	—
168	C₄×#343	—	47	1	no	maximal, Sylow
169	C₂²×C₄₇	—	2	1	no	—
170	C₂²×C₄₇	—	2	1	no	—
171	C₂²×C₄₇	—	2	1	no	—
172	C₂²×C₄₇	—	2	1	no	—
173	C₂²×C₄₇	—	2	1	no	—
174	C₂²×C₄₇	—	2	1	no	—
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	—	2	1	no	—
177	C₂²×C₄₇	—	2	1	no	—
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	2	1	no	—
181	C₂²×C₄₇	C₄³	1	1	yes	characteristic
182	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
183	C₂²×C₄₇	#376	1	1	yes	characteristic
184	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
186	C₂²×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
187	C₂²×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
189	C₂²×C₄₇	C₂×#101	1	1	yes	characteristic
190	C₂²×C₄₇	#413	1	1	yes	characteristic
191	C₂²×C₄₇	#413	1	1	yes	characteristic
192	C₄×C₄₇	—	4	4	no	—
193	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
194	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
195	C₄×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
196	C₄×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
197	Dic₄₇	—	2	2	no	—
198	Dic₄₇	—	2	4	no	—
199	Dic₄₇	—	4	4	no	—
200	Dic₄₇	#343	1	4	yes	direct product factor
201	C₂×C₄×M₁₆	—	47	2	no	—
202	C₂×C₄×C₄⋊C₄	—	47	1	no	—
203	C₂×#343	—	47	2	no	—
204	C₂×#343	—	47	1	no	—
205	C₂×#343	D₄₇	1	1	yes	characteristic
206	C₂×C₄₇	—	2	1	no	—
207	C₂×C₄₇	—	2	1	no	—
208	C₂×C₄₇	—	2	1	no	—
209	C₂×C₄₇	—	2	1	no	—
210	C₂×C₄₇	C₄×#95	1	1	yes	characteristic
211	C₂×C₄₇	C₂×#343	1	1	yes	characteristic
212	C₂×C₄₇	#1742	1	1	yes	characteristic
213	C₂×C₄₇	C₄×#100	1	1	yes	characteristic
214	C₂×C₄₇	C₄×#100	1	1	yes	characteristic
215	C₂×C₄₇	C₄×#101	1	1	yes	characteristic
216	C₂×C₄₇	C₄×#101	1	1	yes	characteristic
217	C₂²×M₁₆	—	47	2	no	—
218	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
219	C₂²×C₄⋊C₄	—	47	1	no	—
220	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
221	C₂²×C₄²	—	47	1	no	—
222	C₂²×C₄²	—	47	2	no	—
223	C₄×M₁₆	—	47	8	no	—
224	C₄×M₁₆	—	94	4	no	—
225	C₂×#97	—	94	2	no	—
226	C₂×C₄×C₈	—	94	2	no	—
227	C₄×C₄⋊C₄	—	94	2	no	—
228	C₄×C₄⋊C₄	—	94	2	no	—
229	C₂×#95	—	47	2	no	—
230	#343	—	47	8	no	—
231	#343	—	47	4	no	—
232	#343	Dic₄₇	1	4	yes	direct product factor
233	C₄₇	C₄×#343	1	1	yes	characteristic, complemented, Sylow
234	C₂³×C₄	—	47	1	no	—
235	C₂³×C₄	—	47	1	no	—
236	C₂³×C₄	—	47	2	no	—
237	C₂³×C₄	C₄×D₄₇	1	2	yes	—
238	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	—	2	2	no	—
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	—	47	4	no	—
243	C₂×M₁₆	—	47	4	no	—
244	C₂×M₁₆	—	47	4	no	—
245	C₂×M₁₆	—	94	2	no	—
246	C₂×M₁₆	—	94	2	no	—
247	C₂×M₁₆	—	94	2	no	—
248	C₂×M₁₆	C₄×D₄₇	1	4	yes	—
249	C₂×M₁₆	C₄×D₄₇	1	4	yes	—
250	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	94	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	47	4	no	—
256	C₂×C₄⋊C₄	—	94	2	no	—
257	C₂×C₄⋊C₄	—	94	1	no	—
258	C₂×C₄⋊C₄	—	94	1	no	—
259	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
260	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
261	C₂×C₄²	—	47	4	no	—
262	C₂×C₄²	—	47	2	no	—
263	C₂×C₄²	—	47	2	no	—
264	C₂×C₄²	—	47	2	no	—
265	C₂×C₄²	—	47	2	no	—
266	C₂×C₄²	—	94	2	no	—
267	C₂×C₄²	—	94	2	no	—
268	C₂×C₄²	—	188	4	no	—
269	#97	—	94	8	no	—
270	C₄×C₈	—	94	8	no	—
271	#95	—	94	4	no	—
272	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	47	1	no	—
278	C₂²×C₄	—	47	2	no	—
279	C₂²×C₄	—	47	2	no	—
280	C₂²×C₄	—	47	1	no	—
281	C₂²×C₄	—	47	2	no	—
282	C₂²×C₄	—	47	2	no	—
283	C₂²×C₄	—	47	2	no	—
284	C₂²×C₄	—	47	4	no	—
285	C₂²×C₄	—	94	2	no	—
286	C₂²×C₄	—	94	2	no	—
287	C₂²×C₄	—	94	2	no	—
288	C₂²×C₄	—	94	2	no	—
289	C₂²×C₄	—	188	1	no	—
290	C₂²×C₄	—	188	1	no	—
291	C₂²×C₄	—	188	2	no	—
292	C₂²×C₄	—	188	2	no	—
293	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
294	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
296	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
297	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
298	C₂²×C₄	D₄×D₄₇	1	2	yes	—
299	C₂²×C₄	#10625352	1	1	yes	characteristic
300	C₂²×C₄	#10625352	1	2	yes	—
301	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
302	C₂²×C₄	#10625354	1	1	yes	characteristic
303	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
304	M₁₆	—	2	4	no	—
305	M₁₆	—	2	4	no	—
306	M₁₆	—	2	4	no	—
307	M₁₆	—	47	8	no	—
308	M₁₆	—	94	4	no	—
309	M₁₆	—	94	4	no	—
310	M₁₆	—	94	4	no	—
311	M₁₆	C₄×Dic₄₇	1	8	yes	complemented
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	94	4	no	—
316	C₂×C₈	—	94	4	no	—
317	C₂×C₈	—	94	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	94	4	no	—
321	C₄⋊C₄	—	94	4	no	—
322	C₄²	—	47	4	no	—
323	C₄²	—	47	4	no	—
324	C₄²	—	47	4	no	—
325	C₄²	—	47	4	no	—
326	C₄²	—	188	4	no	—
327	C₄²	—	188	4	no	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	C₄²×D₄₇	1	1	yes	characteristic
333	C₂³	C₄²×D₄₇	1	1	yes	characteristic
334	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
335	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
336	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
337	C₂³	#13093980	1	1	yes	characteristic
338	C₂³	#13093982	1	1	yes	characteristic
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	47	2	no	—
345	C₂×C₄	—	47	2	no	—
346	C₂×C₄	—	47	2	no	—
347	C₂×C₄	—	47	2	no	—
348	C₂×C₄	—	47	4	no	—
349	C₂×C₄	—	94	4	no	—
350	C₂×C₄	—	94	4	no	—
351	C₂×C₄	—	94	1	no	—
352	C₂×C₄	—	94	1	no	—
353	C₂×C₄	—	94	2	no	—
354	C₂×C₄	—	94	2	no	—
355	C₂×C₄	—	94	4	no	—
356	C₂×C₄	—	188	2	no	—
357	C₂×C₄	—	188	2	no	—
358	C₂×C₄	—	188	4	no	—
359	C₂×C₄	—	188	2	no	—
360	C₂×C₄	—	188	2	no	—
361	C₂×C₄	—	188	4	no	—
362	C₂×C₄	C₄²×D₄₇	1	2	yes	—
363	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
364	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
365	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
366	C₂×C₄	#13093980	1	2	yes	—
367	C₂×C₄	#13093982	1	2	yes	—
368	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
369	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
370	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
371	C₂×C₄	#13093986	1	1	yes	characteristic
372	C₂×C₄	#13093986	1	2	yes	—
373	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
374	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
375	C₂×C₄	#13093989	1	1	yes	characteristic
376	C₂×C₄	#13093989	1	2	yes	—
377	C₂×C₄	Q₈×Dic₄₇	1	1	yes	characteristic
378	C₈	—	2	8	no	—
379	C₈	—	94	8	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	C₄²×Dic₄₇	1	1	yes	characteristic
393	C₂²	#95×D₄₇	1	1	yes	characteristic
394	C₂²	#15688968	1	1	yes	characteristic
395	C₂²	#15688970	1	1	yes	characteristic
396	C₂²	C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
397	C₂²	#15688974	1	1	yes	characteristic
398	C₂²	C₄⋊C₄×Dic₄₇	1	1	yes	characteristic
399	C₂²	#100×D₄₇	1	1	yes	characteristic
400	C₂²	#101×D₄₇	1	1	yes	characteristic
401	C₂²	#15689104	1	1	yes	characteristic
402	C₂²	#15689106	1	1	yes	characteristic
403	C₄	—	4	4	no	—
404	C₄	—	47	4	no	—
405	C₄	—	94	2	no	—
406	C₄	—	94	4	no	—
407	C₄	—	188	4	no	—
408	C₄	#15688970	1	2	yes	—
409	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
410	C₄	#15688974	1	2	yes	—
411	C₄	C₄⋊C₄×Dic₄₇	1	2	yes	—
412	C₂	—	2	1	no	—
413	C₂	—	2	1	no	—
414	C₂	—	2	1	no	—
415	C₂	—	2	1	no	—
416	C₂	#95×Dic₄₇	1	1	yes	characteristic
417	C₂	#343×D₄₇	1	1	yes	characteristic
418	C₂	#20243125	1	1	yes	characteristic
419	C₂	#20243179	1	1	yes	characteristic
420	C₂	#100×Dic₄₇	1	1	yes	characteristic
421	C₂	#20243183	1	1	yes	characteristic
422	C₂	#101×Dic₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₄₇
commutator	C₂²×C₄₇	C₄³
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#343	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#343	D₄₇
hypocenter	C₄₇	C₄×#343
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#343

Complements

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

N	H ≅ G/N	type
11. M₁₆×Dic₄₇	C₄	semidirect
17. #15688892	C₄	semidirect
18. #15688891	C₄	semidirect
21. C₄₇×#343	C₄	semidirect
95. M₁₆×C₄₇	C₄²	semidirect
112. #10625329	C₄²	semidirect
200. Dic₄₇	#343	direct (N × H)
232. #343	Dic₄₇	direct (N × H)
233. C₄₇	C₄×#343	semidirect
311. M₁₆	C₄×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×Dic₄₇	2
C₂×C₄⋊C₄×Dic₄₇	2
C₂×#15688892	2
C₂×#15688891	2
C₂×C₄₇×#343	2
C₄×#343	47

Subgroups — #343×Dic47 #26121482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #343×Dic₄₇ #26121482