Subgroups — #26369477

Order 12032.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252080	C₂	1	1	yes	maximal, characteristic
3	#20245218	C₂	1	2	yes	maximal, complemented
4	#20245213	C₂	1	2	yes	maximal, complemented
5	#20245211	C₂	1	2	yes	maximal, complemented
6	C₁₆×C₂²⋊D₄₇	C₂	1	2	yes	maximal, complemented
7	#20245146	C₂	1	1	yes	maximal, characteristic, complemented
8	#20245002	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×(C₂×D₄₇)⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#20244987	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#504	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
13	#15689630	C₄	1	1	yes	characteristic
14	C₂×#13093964	C₂²	1	1	yes	characteristic
15	C₂×#13093963	C₂²	1	2	yes	—
16	M₃₂×D₄₇	—	2	4	no	—
17	C₂²×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×D₄₇	C₂²	1	2	yes	—
19	#15689192	C₄	1	2	yes	—
20	#15689192	C₄	1	2	yes	—
21	C₈×C₂²⋊D₄₇	C₂²	1	2	yes	—
22	C₈×C₂²⋊D₄₇	C₂²	1	2	yes	—
23	#15689151	C₄	1	1	yes	characteristic
24	#15689090	C₄	1	1	yes	characteristic
25	#15689086	C₄	1	1	yes	characteristic
26	#15689078	C₂²	1	1	yes	characteristic
27	Dic₄₇⋊C₁₆	C₂²	1	2	yes	complemented
28	Dic₄₇⋊C₁₆	C₂²	1	2	yes	complemented
29	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	2	yes	complemented
30	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	2	yes	complemented
31	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic
32	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic
33	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic
34	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic
35	#15688898	C₂²	1	2	yes	complemented
36	C₁₆×Dic₄₇	C₂²	1	2	yes	complemented
37	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#504	—	2	4	no	—
39	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×M₃₂×C₄₇	C₂²	1	2	yes	complemented
41	C₂²×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
42	C₂²×C₁₆×C₄₇	C₂²	1	2	yes	complemented
43	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₄₇	—	2	2	no	—
47	C₂×C₈×D₄₇	—	2	2	no	—
48	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
51	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
52	#13094005	C₈	1	2	yes	—
53	#13094000	C₈	1	1	yes	characteristic
54	#13094000	C₈	1	1	yes	characteristic
55	#13093995	C₈	1	1	yes	characteristic
56	#13093995	C₈	1	1	yes	characteristic
57	#13093992	C₈	1	2	yes	—
58	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
59	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
60	#13093983	C₂×C₄	1	1	yes	characteristic
61	#13093964	—	2	2	no	—
62	#13093963	—	2	4	no	—
63	C₂×C₄₇⋊C₁₆	—	2	2	no	—
64	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
65	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
67	C₁₆×D₄₇	—	2	4	no	—
68	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
69	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
70	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
71	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
72	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
73	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
74	#13093934	C₂×C₄	1	2	yes	—
75	C₈×Dic₄₇	C₂³	1	2	yes	—
76	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
77	#131×C₄₇	—	2	2	no	—
78	#131×C₄₇	—	2	2	no	—
79	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
81	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	M₃₂×C₄₇	—	2	4	no	—
84	M₃₂×C₄₇	D₄	1	4	yes	complemented
85	C₂×C₁₆×C₄₇	—	2	2	no	—
86	C₂×C₁₆×C₄₇	—	2	4	no	—
87	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₁₆×C₄₇	C₂³	1	2	yes	—
90	C₂³×D₄₇	C₂×C₈	1	1	yes	characteristic
91	#41×C₄₇	—	2	2	no	—
92	#41×C₄₇	—	2	2	no	—
93	C₂×Q₈×C₄₇	C₂×C₈	1	1	yes	characteristic
94	C₂×D₄×C₄₇	C₂×C₈	1	2	yes	—
95	C₂×D₄×C₄₇	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊D₄₇	C₂×C₈	1	2	yes	—
99	C₂×C₂²⋊D₄₇	C₂×C₈	1	2	yes	—
100	C₂²×Dic₄₇	C₂×C₈	1	1	yes	characteristic
101	C₂×C₄×D₄₇	—	2	2	no	—
102	C₂×C₄×D₄₇	—	2	2	no	—
103	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
107	M₁₆×C₄₇	—	2	2	no	—
108	M₁₆×C₄₇	—	2	4	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₄₇	#41	1	2	yes	—
115	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₂²⋊Dic₄₇	C₂×C₈	1	2	yes	—
117	C₂²⋊Dic₄₇	C₂×C₈	1	2	yes	—
118	C₂²⋊Dic₄₇	C₂×C₈	1	2	yes	—
119	(C₂×D₄₇)⋊C₄	C₂×C₈	1	2	yes	—
120	(C₂×D₄₇)⋊C₄	C₂×C₈	1	2	yes	—
121	C₄⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
122	C₄⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
123	Dic₄₇⋊C₄	C₂×C₈	1	2	yes	—
124	Dic₄₇⋊C₄	C₂×C₈	1	2	yes	—
125	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
126	#10625329	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
129	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
131	C₈×D₄₇	—	2	2	no	—
132	C₈×D₄₇	—	2	2	no	—
133	C₈×D₄₇	—	2	1	no	—
134	C₈×D₄₇	—	2	1	no	—
135	C₈×D₄₇	—	2	1	no	—
136	C₈×D₄₇	—	2	1	no	—
137	C₁₆×C₄₇	—	2	1	no	—
138	C₁₆×C₄₇	—	2	1	no	—
139	C₁₆×C₄₇	C₂×D₄	1	4	yes	—
140	C₄₇⋊C₁₆	—	2	2	no	—
141	C₄₇⋊C₁₆	—	2	1	no	—
142	C₄₇⋊C₁₆	—	2	1	no	—
143	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
144	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
145	C₂²×D₄₇	—	2	2	no	—
146	C₂²×D₄₇	—	2	2	no	—
147	C₂²×D₄₇	—	4	1	no	—
148	C₂²×D₄₇	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₄₇	C₂²×C₈	1	1	yes	characteristic
150	Q₈×C₄₇	—	2	2	no	—
151	D₄×C₄₇	—	2	4	no	—
152	D₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
156	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
157	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#131	1	2	yes	—
159	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
160	C₂²⋊D₄₇	—	2	4	no	—
161	C₂²⋊D₄₇	—	4	2	no	—
162	C₂×Dic₄₇	—	2	2	no	—
163	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
164	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
165	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
166	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
167	C₄×D₄₇	—	2	1	no	—
168	C₄×D₄₇	—	2	1	no	—
169	C₄×D₄₇	—	2	1	no	—
170	C₄×D₄₇	—	2	1	no	—
171	C₄×D₄₇	—	2	2	no	—
172	C₄×D₄₇	—	2	2	no	—
173	C₈×C₄₇	—	2	2	no	—
174	C₈×C₄₇	C₄×D₄	1	2	yes	—
175	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
177	C₄₇⋊C₈	—	2	1	no	—
178	C₄₇⋊C₈	—	2	1	no	—
179	C₄₇⋊C₈	—	2	2	no	—
180	#33436	—	47	1	no	maximal, Sylow
181	C₂²×C₄₇	—	2	1	no	—
182	C₂²×C₄₇	—	2	1	no	—
183	C₂²×C₄₇	—	2	2	no	—
184	C₂²×C₄₇	—	2	2	no	—
185	C₂²×C₄₇	—	2	2	no	—
186	C₂²×C₄₇	C₈×D₄	1	2	yes	—
187	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
188	C₂×D₄₇	—	2	1	no	—
189	C₂×D₄₇	—	2	1	no	—
190	C₂×D₄₇	—	2	1	no	—
191	C₂×D₄₇	—	2	1	no	—
192	C₂×D₄₇	—	2	1	no	—
193	C₂×D₄₇	—	4	4	no	—
194	C₂×D₄₇	#504	1	2	yes	complemented
195	C₄×C₄₇	—	2	2	no	—
196	C₄×C₄₇	C₈×D₄	1	2	yes	—
197	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
198	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
199	Dic₄₇	—	2	2	no	—
200	Dic₄₇	—	2	2	no	—
201	Dic₄₇	—	2	1	no	—
202	Dic₄₇	—	2	1	no	—
203	C₂×#504	D₄₇	1	1	yes	characteristic, complemented
204	C₂²×M₃₂	—	47	1	no	—
205	#2929	—	47	1	no	—
206	#2169	—	47	2	no	—
207	#2168	—	47	2	no	—
208	#2168	—	47	2	no	—
209	D₄×C₁₆	—	47	2	no	—
210	#2151	—	47	1	no	—
211	#2113	—	47	1	no	—
212	C₂×C₂²⋊C₁₆	—	47	1	no	—
213	#2108	—	47	1	no	—
214	C₂×C₄₇	—	2	2	no	—
215	C₂×C₄₇	—	4	2	no	—
216	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
217	C₂×C₄₇	C₂×#504	1	1	yes	characteristic
218	C₂×C₄₇	#3407	1	1	yes	characteristic
219	D₄₇	—	2	2	no	—
220	D₄₇	—	4	1	no	—
221	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
222	C₂³×C₈	—	47	1	no	—
223	#525	—	47	1	no	—
224	#504	—	2	4	no	—
225	C₂×M₃₂	—	47	1	no	—
226	C₂×M₃₂	—	47	2	no	—
227	C₂×M₃₂	—	94	4	no	—
228	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic
229	C₂×M₃₂	C₂×D₄₇	1	2	yes	complemented
230	C₂²×C₁₆	—	47	1	no	—
231	C₂²×C₁₆	—	47	2	no	—
232	C₂²×C₁₆	C₂×D₄₇	1	1	yes	characteristic
233	C₂²×C₁₆	C₂×D₄₇	1	2	yes	complemented
234	#435	—	47	2	no	—
235	#435	—	47	2	no	—
236	C₈×D₄	—	47	2	no	—
237	C₈×D₄	—	47	2	no	—
238	#424	—	47	1	no	—
239	#408	—	47	1	no	—
240	#407	—	47	1	no	—
241	#405	—	47	1	no	—
242	C₄⋊C₁₆	—	47	2	no	—
243	C₄⋊C₁₆	—	47	2	no	—
244	C₂²⋊C₁₆	—	47	2	no	—
245	C₂²⋊C₁₆	—	47	2	no	—
246	C₂²⋊C₁₆	—	47	1	no	—
247	C₂²⋊C₁₆	—	47	1	no	—
248	C₂²⋊C₁₆	—	47	1	no	—
249	C₂²⋊C₁₆	—	47	1	no	—
250	#346	—	47	2	no	—
251	C₄×C₁₆	—	47	2	no	—
252	C₄₇	#33436	1	1	yes	characteristic, complemented, Sylow
253	C₂×#41	C₄×D₄₇	1	1	yes	characteristic
254	C₂³×C₄	—	47	1	no	—
255	#131	—	2	2	no	—
256	#131	—	2	2	no	—
257	C₂×M₁₆	—	47	1	no	—
258	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
259	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
260	C₂²×C₈	—	47	1	no	—
261	C₂²×C₈	—	47	1	no	—
262	C₂²×C₈	—	47	1	no	—
263	C₂²×C₈	—	47	1	no	—
264	C₂²×C₈	—	47	1	no	—
265	C₂²×C₈	—	94	2	no	—
266	C₂²×C₈	—	94	2	no	—
267	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
268	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
269	#123	—	47	2	no	—
270	C₂²⋊Q₈	—	47	1	no	—
271	C₂²⋊Q₈	—	47	1	no	—
272	#121	—	47	1	no	—
273	#121	—	47	1	no	—
274	#120	—	47	2	no	—
275	C₄×D₄	—	47	2	no	—
276	C₄×D₄	—	47	2	no	—
277	#117	—	47	1	no	—
278	M₃₂	—	2	4	no	—
279	M₃₂	—	94	2	no	—
280	M₃₂	—	94	4	no	—
281	M₃₂	C₂²⋊D₄₇	1	4	yes	complemented
282	C₂×C₁₆	—	2	2	no	—
283	C₂×C₁₆	—	2	4	no	—
284	C₂×C₁₆	—	47	1	no	—
285	C₂×C₁₆	—	47	1	no	—
286	C₂×C₁₆	—	47	2	no	—
287	C₂×C₁₆	—	94	2	no	—
288	C₂×C₁₆	—	94	4	no	—
289	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
290	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
291	C₂×C₁₆	C₂²×D₄₇	1	2	yes	—
292	C₄⋊C₈	—	47	2	no	—
293	C₄⋊C₈	—	47	2	no	—
294	C₂²⋊C₈	—	47	2	no	—
295	C₂²⋊C₈	—	47	2	no	—
296	C₂²⋊C₈	—	47	2	no	—
297	C₂²⋊C₈	—	47	2	no	—
298	#97	—	47	2	no	—
299	C₄×C₈	—	47	2	no	—
300	C₂⁴	—	47	1	no	—
301	#41	—	2	2	no	—
302	#41	—	2	2	no	—
303	C₂×Q₈	C₈×D₄₇	1	1	yes	characteristic
304	C₂×D₄	—	47	2	no	—
305	C₂×D₄	—	47	2	no	—
306	C₂×D₄	C₈×D₄₇	1	2	yes	—
307	C₂×D₄	C₈×D₄₇	1	1	yes	characteristic
308	C₂²×C₄	—	47	1	no	—
309	C₂²×C₄	—	47	1	no	—
310	C₂²×C₄	—	47	1	no	—
311	C₂²×C₄	—	47	1	no	—
312	C₂²×C₄	—	47	1	no	—
313	C₂²×C₄	—	94	2	no	—
314	C₂²×C₄	—	94	2	no	—
315	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
316	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	4	no	—
319	M₁₆	—	94	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	47	2	no	—
323	C₂×C₈	—	47	1	no	—
324	C₂×C₈	—	47	1	no	—
325	C₂×C₈	—	94	2	no	—
326	C₂×C₈	—	94	2	no	—
327	C₂×C₈	—	94	2	no	—
328	C₂×C₈	—	94	1	no	—
329	C₂×C₈	—	94	1	no	—
330	C₂×C₈	—	94	1	no	—
331	C₂×C₈	—	94	1	no	—
332	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
333	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
334	C₂×C₈	#10625350	1	2	yes	—
335	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
336	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
337	C₄⋊C₄	—	47	2	no	—
338	C₄⋊C₄	—	47	2	no	—
339	C₄⋊C₄	—	47	1	no	—
340	C₄⋊C₄	—	47	1	no	—
341	C₂²⋊C₄	—	47	2	no	—
342	C₂²⋊C₄	—	47	2	no	—
343	C₂²⋊C₄	—	47	2	no	—
344	C₂²⋊C₄	—	47	2	no	—
345	C₂²⋊C₄	—	47	2	no	—
346	C₄²	—	47	2	no	—
347	C₁₆	—	2	1	no	—
348	C₁₆	—	2	1	no	—
349	C₁₆	—	94	2	no	—
350	C₁₆	—	94	1	no	—
351	C₁₆	—	94	1	no	—
352	C₁₆	C₂×C₂²⋊D₄₇	1	4	yes	—
353	C₂³	—	47	1	no	—
354	C₂³	—	47	1	no	—
355	C₂³	—	94	2	no	—
356	C₂³	—	94	2	no	—
357	C₂³	—	188	1	no	—
358	C₂³	C₂×C₈×D₄₇	1	2	yes	—
359	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	2	no	—
363	D₄	—	94	4	no	—
364	D₄	—	188	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	47	2	no	—
368	C₂×C₄	—	47	2	no	—
369	C₂×C₄	—	47	1	no	—
370	C₂×C₄	—	47	1	no	—
371	C₂×C₄	—	94	2	no	—
372	C₂×C₄	—	94	1	no	—
373	C₂×C₄	—	94	1	no	—
374	C₂×C₄	—	94	1	no	—
375	C₂×C₄	—	94	1	no	—
376	C₂×C₄	—	94	2	no	—
377	C₂×C₄	—	94	2	no	—
378	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
379	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
380	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
381	C₂×C₄	#13094030	1	2	yes	—
382	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
383	C₈	—	2	2	no	—
384	C₈	—	94	1	no	—
385	C₈	—	94	1	no	—
386	C₈	—	94	2	no	—
387	C₈	C₄×C₂²⋊D₄₇	1	2	yes	—
388	C₈	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
389	C₈	C₂×#10625350	1	1	yes	characteristic
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	47	2	no	—
396	C₂²	—	94	1	no	—
397	C₂²	—	94	1	no	—
398	C₂²	—	94	1	no	—
399	C₂²	—	94	1	no	—
400	C₂²	—	94	1	no	—
401	C₂²	—	188	4	no	—
402	C₂²	C₈×C₂²⋊D₄₇	1	2	yes	—
403	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	94	1	no	—
406	C₄	—	94	1	no	—
407	C₄	—	94	2	no	—
408	C₄	—	94	2	no	—
409	C₄	C₈×C₂²⋊D₄₇	1	2	yes	—
410	C₄	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
411	C₄	C₂×#13094030	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	4	2	no	—
414	C₂	—	94	2	no	—
415	C₂	—	188	1	no	—
416	C₂	C₂×C₈×C₂²⋊D₄₇	1	1	yes	characteristic
417	C₂	#504×D₄₇	1	1	yes	characteristic
418	C₂	#20256489	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂³×C₈
Fitting	C₂×C₄₇×#504	C₂
prime radical	#15689630	C₄
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	C₂×#504	D₄₇
hypocenter	C₄₇	#33436
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#504

Complements

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

N	H ≅ G/N	type
1. C₂×M₃₂×D₄₇	C₂	semidirect
3. #20245218	C₂	semidirect
4. #20245213	C₂	semidirect
5. #20245211	C₂	semidirect
6. C₁₆×C₂²⋊D₄₇	C₂	semidirect
7. #20245146	C₂	semidirect
8. #20245002	C₂	semidirect
9. C₂×(C₂×D₄₇)⋊C₁₆	C₂	semidirect
10. #20244987	C₂	semidirect
11. C₂×C₄₇×#504	C₂	semidirect
27. Dic₄₇⋊C₁₆	C₂²	semidirect
28. Dic₄₇⋊C₁₆	C₂²	semidirect
29. C₂²⋊(C₄₇⋊C₁₆)	C₂²	semidirect
30. C₂²⋊(C₄₇⋊C₁₆)	C₂²	semidirect
35. #15688898	C₂²	semidirect
36. C₁₆×Dic₄₇	C₂²	semidirect
40. C₂×M₃₂×C₄₇	C₂²	semidirect
42. C₂²×C₁₆×C₄₇	C₂²	semidirect
84. M₃₂×C₄₇	D₄	semidirect
194. C₂×D₄₇	#504	semidirect
203. C₂×#504	D₄₇	semidirect
229. C₂×M₃₂	C₂×D₄₇	semidirect
233. C₂²×C₁₆	C₂×D₄₇	semidirect
252. C₄₇	#33436	semidirect
281. M₃₂	C₂²⋊D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₄₇	2
#20252080	2
#20245218	2
#20245213	2
#20245211	2
C₁₆×C₂²⋊D₄₇	2
#20245146	2
#20245002	2
C₂×(C₂×D₄₇)⋊C₁₆	2
#20244987	2
C₂×C₄₇×#504	2
#33436	47