Subgroups — C₄₇×#9147 #26048845

Order 12032.

1348 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#2847	C₂	1	1	yes	maximal, characteristic
2	C₂²×#95×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#1779	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×#327	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1294	C₂	1	2	yes	maximal, complemented
6	C₂⁴×C₄×C₄₇	—	2	1	no	—
7	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
8	C₂×#121×C₄₇	C₄	1	2	yes	complemented
9	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×#120×C₄₇	—	2	1	no	—
11	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
12	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
13	C₄₇×#386	—	2	2	no	—
14	C₄₇×#386	—	2	1	no	—
15	C₄₇×#380	C₄	1	2	yes	complemented
16	C₄₇×#380	C₂²	1	1	yes	characteristic
17	C₂×#95×C₄₇	—	2	4	no	—
18	C₂×#95×C₄₇	—	2	1	no	—
19	C₂×#95×C₄₇	C₂²	1	2	yes	—
20	C₄₇×#327	—	2	4	no	—
21	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
22	C₂²×D₄×C₄₇	—	2	2	no	—
23	C₂²×D₄×C₄₇	—	2	1	no	—
24	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
25	C₂³×C₄×C₄₇	—	2	8	no	—
26	C₂³×C₄×C₄₇	—	2	4	no	—
27	C₂³×C₄×C₄₇	—	2	2	no	—
28	C₂³×C₄×C₄₇	—	2	2	no	—
29	C₂³×C₄×C₄₇	—	2	2	no	—
30	C₂³×C₄×C₄₇	—	4	4	no	—
31	C₂³×C₄×C₄₇	—	4	4	no	—
32	C₂³×C₄×C₄₇	—	4	2	no	—
33	C₂³×C₄×C₄₇	—	4	2	no	—
34	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₄₇	D₄	1	2	yes	—
36	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₄₇	—	2	2	no	—
39	#121×C₄₇	—	2	2	no	—
40	#121×C₄₇	—	2	2	no	—
41	#121×C₄₇	—	4	4	no	—
42	#120×C₄₇	—	4	2	no	—
43	#120×C₄₇	—	4	2	no	—
44	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
45	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	complemented
46	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
47	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
48	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
49	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
50	C₂²⋊C₈×C₄₇	—	2	2	no	—
51	C₂²⋊C₈×C₄₇	—	2	2	no	—
52	C₂²⋊C₈×C₄₇	—	4	4	no	—
53	#95×C₄₇	—	2	4	no	—
54	#95×C₄₇	—	2	2	no	—
55	#95×C₄₇	—	2	2	no	—
56	#95×C₄₇	—	2	1	no	—
57	#95×C₄₇	D₄	1	4	yes	complemented
58	C₂⁴×C₄₇	—	2	4	no	—
59	C₂⁴×C₄₇	—	2	4	no	—
60	C₂⁴×C₄₇	—	2	1	no	—
61	C₂⁴×C₄₇	—	2	1	no	—
62	C₂⁴×C₄₇	—	2	1	no	—
63	C₂⁴×C₄₇	—	2	1	no	—
64	C₂⁴×C₄₇	—	2	1	no	—
65	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
66	C₂⁴×C₄₇	D₈	1	2	yes	—
67	C₂⁴×C₄₇	SD₁₆	1	2	yes	—
68	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
69	C₂×D₄×C₄₇	—	2	2	no	—
70	C₂×D₄×C₄₇	—	4	2	no	—
71	C₂×D₄×C₄₇	—	4	4	no	—
72	C₂×D₄×C₄₇	—	4	4	no	—
73	C₂×D₄×C₄₇	—	4	4	no	—
74	C₂×D₄×C₄₇	—	4	1	no	—
75	C₂×D₄×C₄₇	—	4	1	no	—
76	C₂×D₄×C₄₇	—	4	1	no	—
77	C₂×D₄×C₄₇	—	4	1	no	—
78	C₂×D₄×C₄₇	—	4	1	no	—
79	C₂×D₄×C₄₇	—	4	1	no	—
80	C₂²×C₄×C₄₇	—	2	16	no	—
81	C₂²×C₄×C₄₇	—	2	8	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	1	no	—
86	C₂²×C₄×C₄₇	—	2	1	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	4	2	no	—
92	C₂²×C₄×C₄₇	—	4	2	no	—
93	C₂²×C₄×C₄₇	—	4	2	no	—
94	C₂²×C₄×C₄₇	—	4	2	no	—
95	C₂²×C₄×C₄₇	—	4	8	no	—
96	C₂²×C₄×C₄₇	—	4	8	no	—
97	C₂²×C₄×C₄₇	—	4	8	no	—
98	C₂²×C₄×C₄₇	—	4	16	no	—
99	C₂²×C₄×C₄₇	—	4	16	no	—
100	C₂²×C₄×C₄₇	—	4	4	no	—
101	C₂²×C₄×C₄₇	—	4	8	no	—
102	C₂²×C₄×C₄₇	—	4	2	no	—
103	C₂²×C₄×C₄₇	—	4	2	no	—
104	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	#41	1	2	yes	—
109	C₂×C₈×C₄₇	—	4	4	no	—
110	C₂×C₈×C₄₇	—	4	2	no	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	4	2	no	—
113	C₂²⋊C₄×C₄₇	—	4	4	no	—
114	C₂²⋊C₄×C₄₇	—	4	4	no	—
115	C₂²⋊C₄×C₄₇	—	4	1	no	—
116	C₂²⋊C₄×C₄₇	—	4	1	no	—
117	C₂²⋊C₄×C₄₇	—	4	2	no	—
118	C₂³×C₄₇	—	2	4	no	—
119	C₂³×C₄₇	—	2	4	no	—
120	C₂³×C₄₇	—	2	8	no	—
121	C₂³×C₄₇	—	2	4	no	—
122	C₂³×C₄₇	—	2	4	no	—
123	C₂³×C₄₇	—	2	8	no	—
124	C₂³×C₄₇	—	2	8	no	—
125	C₂³×C₄₇	—	2	8	no	—
126	C₂³×C₄₇	—	2	2	no	—
127	C₂³×C₄₇	—	2	2	no	—
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	—	2	2	no	—
130	C₂³×C₄₇	—	2	2	no	—
131	C₂³×C₄₇	—	2	2	no	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	2	no	—
136	C₂³×C₄₇	—	4	1	no	—
137	C₂³×C₄₇	—	4	2	no	—
138	C₂³×C₄₇	—	4	1	no	—
139	C₂³×C₄₇	—	4	1	no	—
140	C₂³×C₄₇	—	4	2	no	—
141	C₂³×C₄₇	#99	1	4	yes	—
142	C₂³×C₄₇	#102	1	4	yes	—
143	C₂³×C₄₇	#104	1	4	yes	—
144	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂³×C₄₇	#120	1	1	yes	characteristic
146	C₂³×C₄₇	#123	1	1	yes	characteristic
147	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
148	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
149	C₂³×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂³×C₄₇	#137	1	1	yes	characteristic
151	D₄×C₄₇	—	8	2	no	—
152	D₄×C₄₇	—	8	8	no	—
153	D₄×C₄₇	—	8	1	no	—
154	D₄×C₄₇	—	8	1	no	—
155	D₄×C₄₇	—	8	1	no	—
156	D₄×C₄₇	—	8	1	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	8	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	8	no	—
166	C₂×C₄×C₄₇	—	4	8	no	—
167	C₂×C₄×C₄₇	—	4	32	no	—
168	C₂×C₄×C₄₇	—	4	4	no	—
169	C₂×C₄×C₄₇	—	4	8	no	—
170	C₂×C₄×C₄₇	—	4	8	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	4	no	—
174	C₂×C₄×C₄₇	—	4	1	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	1	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₄₇	#121	1	2	yes	—
182	C₈×C₄₇	—	8	2	no	—
183	#9147	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₄₇	—	2	8	no	—
185	C₂²×C₄₇	—	2	8	no	—
186	C₂²×C₄₇	—	2	8	no	—
187	C₂²×C₄₇	—	2	8	no	—
188	C₂²×C₄₇	—	2	4	no	—
189	C₂²×C₄₇	—	2	1	no	—
190	C₂²×C₄₇	—	2	4	no	—
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	2	4	no	—
194	C₂²×C₄₇	—	2	1	no	—
195	C₂²×C₄₇	—	2	2	no	—
196	C₂²×C₄₇	—	2	4	no	—
197	C₂²×C₄₇	—	2	2	no	—
198	C₂²×C₄₇	—	2	2	no	—
199	C₂²×C₄₇	—	2	4	no	—
200	C₂²×C₄₇	—	2	4	no	—
201	C₂²×C₄₇	—	2	2	no	—
202	C₂²×C₄₇	—	8	1	no	—
203	C₂²×C₄₇	—	8	1	no	—
204	C₂²×C₄₇	—	8	1	no	—
205	C₂²×C₄₇	—	8	2	no	—
206	C₂²×C₄₇	—	8	2	no	—
207	C₂²×C₄₇	#327	1	8	yes	complemented
208	C₂²×C₄₇	#386	1	1	yes	characteristic
209	C₂²×C₄₇	C₂×#99	1	2	yes	—
210	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
211	C₂²×C₄₇	#417	1	1	yes	characteristic
212	C₂²×C₄₇	C₂×#104	1	2	yes	—
213	C₂²×C₄₇	#447	1	1	yes	characteristic
214	C₂²×C₄₇	#448	1	1	yes	characteristic
215	C₂²×C₄₇	#480	1	1	yes	characteristic
216	C₂²×C₄₇	#481	1	1	yes	characteristic
217	C₄×C₄₇	—	2	2	no	—
218	C₄×C₄₇	—	2	2	no	—
219	C₄×C₄₇	—	4	8	no	—
220	C₄×C₄₇	—	4	2	no	—
221	C₄×C₄₇	—	8	1	no	—
222	C₄×C₄₇	—	8	2	no	—
223	#2847	C₂×C₄₇	1	1	yes	characteristic
224	C₂²×#95	C₂×C₄₇	1	1	yes	characteristic, complemented
225	#1779	C₂×C₄₇	1	1	yes	characteristic, complemented
226	C₂×#327	C₂×C₄₇	1	2	yes	complemented
227	#1294	C₂×C₄₇	1	2	yes	complemented
228	C₂×C₄₇	—	2	1	no	—
229	C₂×C₄₇	—	2	8	no	—
230	C₂×C₄₇	—	2	1	no	—
231	C₂×C₄₇	—	2	1	no	—
232	C₂×C₄₇	—	2	1	no	—
233	C₂×C₄₇	—	16	1	no	—
234	C₂×C₄₇	C₂×#327	1	2	yes	—
235	C₂×C₄₇	#1504	1	2	yes	—
236	C₂×C₄₇	#1874	1	1	yes	characteristic
237	C₂×C₄₇	#1896	1	1	yes	characteristic
238	C₂×C₄₇	#1898	1	1	yes	characteristic
239	C₂⁴×C₄	—	2	1	no	—
240	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
241	C₂×#121	C₄×C₄₇	1	2	yes	complemented
242	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
243	C₂×#120	—	2	1	no	—
244	C₂×C₂²⋊C₈	—	2	2	no	—
245	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
246	#386	—	2	1	no	—
247	#386	—	2	2	no	—
248	#380	C₄×C₄₇	1	2	yes	complemented
249	#380	C₂²×C₄₇	1	1	yes	characteristic
250	C₂×#95	—	2	1	no	—
251	C₂×#95	—	2	4	no	—
252	C₂×#95	C₂²×C₄₇	1	2	yes	—
253	#327	—	2	4	no	—
254	C₄₇	#9147	1	1	yes	characteristic, direct product factor, Sylow
255	C₂⁵	D₄×C₄₇	1	1	yes	characteristic
256	C₂²×D₄	—	2	2	no	—
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic, complemented
259	C₂³×C₄	—	2	8	no	—
260	C₂³×C₄	—	2	4	no	—
261	C₂³×C₄	—	2	2	no	—
262	C₂³×C₄	—	2	2	no	—
263	C₂³×C₄	—	2	2	no	—
264	C₂³×C₄	—	4	4	no	—
265	C₂³×C₄	—	4	4	no	—
266	C₂³×C₄	—	4	2	no	—
267	C₂³×C₄	—	4	2	no	—
268	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
269	C₂³×C₄	D₄×C₄₇	1	2	yes	—
270	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
271	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
272	C₂²×C₈	—	2	2	no	—
273	#121	—	2	2	no	—
274	#121	—	2	2	no	—
275	#121	—	4	4	no	—
276	#120	—	4	2	no	—
277	#120	—	4	2	no	—
278	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic, complemented
279	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	complemented
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂²⋊C₈	—	2	2	no	—
285	C₂²⋊C₈	—	2	2	no	—
286	C₂²⋊C₈	—	4	4	no	—
287	#95	—	2	4	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	1	no	—
291	#95	D₄×C₄₇	1	4	yes	complemented
292	C₂⁴	—	2	4	no	—
293	C₂⁴	—	2	1	no	—
294	C₂⁴	—	2	1	no	—
295	C₂⁴	—	2	1	no	—
296	C₂⁴	—	2	1	no	—
297	C₂⁴	—	2	4	no	—
298	C₂⁴	—	2	1	no	—
299	C₂⁴	C₂²⋊C₄×C₄₇	1	2	yes	—
300	C₂⁴	D₈×C₄₇	1	2	yes	—
301	C₂⁴	SD₁₆×C₄₇	1	2	yes	—
302	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	4	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	4	no	—
313	C₂×D₄	—	4	4	no	—
314	C₂²×C₄	—	2	16	no	—
315	C₂²×C₄	—	2	8	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	8	no	—
330	C₂²×C₄	—	4	8	no	—
331	C₂²×C₄	—	4	8	no	—
332	C₂²×C₄	—	4	16	no	—
333	C₂²×C₄	—	4	16	no	—
334	C₂²×C₄	—	4	4	no	—
335	C₂²×C₄	—	4	8	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
339	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
342	C₂²×C₄	#41×C₄₇	1	2	yes	—
343	C₂×C₈	—	4	4	no	—
344	C₂×C₈	—	4	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	4	no	—
348	C₂²⋊C₄	—	4	1	no	—
349	C₂²⋊C₄	—	4	1	no	—
350	C₂²⋊C₄	—	4	4	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	4	no	—
354	C₂³	—	2	8	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	8	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	8	no	—
361	C₂³	—	2	8	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	2	no	—
375	C₂³	#99×C₄₇	1	4	yes	—
376	C₂³	#102×C₄₇	1	4	yes	—
377	C₂³	#104×C₄₇	1	4	yes	—
378	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
379	C₂³	#120×C₄₇	1	1	yes	characteristic
380	C₂³	#123×C₄₇	1	1	yes	characteristic
381	C₂³	C₂×D₈×C₄₇	1	1	yes	characteristic
382	C₂³	C₂×SD₁₆×C₄₇	1	1	yes	characteristic
383	C₂³	AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
384	C₂³	#137×C₄₇	1	1	yes	characteristic
385	D₄	—	8	2	no	—
386	D₄	—	8	1	no	—
387	D₄	—	8	1	no	—
388	D₄	—	8	8	no	—
389	D₄	—	8	1	no	—
390	D₄	—	8	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	8	no	—
400	C₂×C₄	—	4	8	no	—
401	C₂×C₄	—	4	32	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	4	8	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
415	C₂×C₄	#121×C₄₇	1	2	yes	—
416	C₈	—	8	2	no	—
417	C₂²	—	2	8	no	—
418	C₂²	—	2	8	no	—
419	C₂²	—	2	8	no	—
420	C₂²	—	2	8	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	4	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	C₄₇×#327	1	8	yes	complemented
441	C₂²	C₄₇×#386	1	1	yes	characteristic
442	C₂²	C₂×#99×C₄₇	1	2	yes	—
443	C₂²	C₂×#102×C₄₇	1	1	yes	characteristic
444	C₂²	C₄₇×#417	1	1	yes	characteristic
445	C₂²	C₂×#104×C₄₇	1	2	yes	—
446	C₂²	C₄₇×#447	1	1	yes	characteristic
447	C₂²	C₄₇×#448	1	1	yes	characteristic
448	C₂²	C₄₇×#480	1	1	yes	characteristic
449	C₂²	C₄₇×#481	1	1	yes	characteristic
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	4	8	no	—
453	C₄	—	4	2	no	—
454	C₄	—	8	2	no	—
455	C₄	—	8	1	no	—
456	C₂	—	2	1	no	—
457	C₂	—	2	1	no	—
458	C₂	—	2	1	no	—
459	C₂	—	2	8	no	—
460	C₂	—	2	1	no	—
461	C₂	—	16	1	no	—
462	C₂	C₂×C₄₇×#327	1	2	yes	—
463	C₂	C₄₇×#1504	1	2	yes	—
464	C₂	C₄₇×#1874	1	1	yes	characteristic
465	C₂	C₄₇×#1896	1	1	yes	characteristic
466	C₂	C₄₇×#1898	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₄₇
Frattini, cosocle	C₂³×C₄	C₂³×C₄₇
prime radical	C₄₇×#2847	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂⁴×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#95×C₄₇	C₂	semidirect
3. C₄₇×#1779	C₂	semidirect
4. C₂×C₄₇×#327	C₂	semidirect
5. C₄₇×#1294	C₂	semidirect
8. C₂×#121×C₄₇	C₄	semidirect
15. C₄₇×#380	C₄	semidirect
24. C₂²×D₄×C₄₇	C₂×C₄	semidirect
44. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
45. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
57. #95×C₄₇	D₄	semidirect
183. #9147	C₄₇	direct (N × H)
207. C₂²×C₄₇	#327	semidirect
224. C₂²×#95	C₂×C₄₇	semidirect
225. #1779	C₂×C₄₇	semidirect
226. C₂×#327	C₂×C₄₇	semidirect
227. #1294	C₂×C₄₇	semidirect
241. C₂×#121	C₄×C₄₇	semidirect
248. #380	C₄×C₄₇	semidirect
254. C₄₇	#9147	direct (N × H)
258. C₂²×D₄	C₂×C₄×C₄₇	semidirect
278. C₂×C₄⋊C₄	C₂×C₄×C₄₇	semidirect
279. C₂×C₄⋊C₄	C₂×C₄×C₄₇	semidirect
291. #95	D₄×C₄₇	semidirect
440. C₂²	C₄₇×#327	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#2847	2
C₂²×#95×C₄₇	2
C₄₇×#1779	2
C₂×C₄₇×#327	2
C₄₇×#1294	2
#9147	47

Subgroups — C47×#9147 #26048845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#9147 #26048845