Subgroups — C₄₇×#29408 #26069106

Order 12032.

952 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#121×C₄₇	C₂	1	2	yes	maximal, complemented
2	C₄₇×#2075	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2033	C₂	1	2	yes	maximal, complemented
4	C₄₇×#1999	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1925	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1918	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1879	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1862	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1817	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×#121×C₄₇	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₄₇	—	2	2	no	—
13	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#107×C₄₇	C₂²	1	2	yes	—
16	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#102×C₄₇	C₂²	1	2	yes	—
18	C₂×#102×C₄₇	C₂²	1	2	yes	—
19	C₂×#102×C₄₇	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#390	C₂²	1	2	yes	—
23	C₄₇×#389	C₂²	1	2	yes	—
24	C₄₇×#388	—	2	2	no	—
25	C₄₇×#386	—	2	2	no	—
26	C₄₇×#380	C₂²	1	2	yes	—
27	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
28	C₄×C₂²⋊C₄×C₄₇	—	2	2	no	—
29	C₄₇×#340	C₂²	1	2	yes	—
30	C₄₇×#340	C₂²	1	2	yes	—
31	C₄₇×#340	C₂²	1	1	yes	characteristic
32	C₄₇×#340	C₂²	1	1	yes	characteristic
33	C₄₇×#336	C₂²	1	2	yes	—
34	C₄₇×#336	C₂²	1	2	yes	—
35	C₂²×D₄×C₄₇	—	2	2	no	—
36	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₇	—	2	2	no	—
38	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂×D₈×C₄₇	—	2	4	no	—
42	C₂×D₈×C₄₇	—	4	1	no	—
43	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
45	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
46	#121×C₄₇	—	2	4	no	—
47	#121×C₄₇	—	2	4	no	—
48	C₄×D₄×C₄₇	—	4	2	no	—
49	C₄×D₄×C₄₇	—	4	2	no	—
50	C₄×D₄×C₄₇	—	4	8	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
60	C₂×C₄²×C₄₇	—	2	2	no	—
61	C₂×C₄²×C₄₇	—	4	1	no	—
62	C₂×C₄²×C₄₇	—	4	1	no	—
63	C₂×C₄²×C₄₇	D₄	1	2	yes	—
64	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
65	#107×C₄₇	—	2	4	no	—
66	#107×C₄₇	—	4	1	no	—
67	#102×C₄₇	—	2	4	no	—
68	#102×C₄₇	—	2	4	no	—
69	#102×C₄₇	—	4	2	no	—
70	C₂²⋊C₈×C₄₇	—	4	1	no	—
71	C₂²⋊C₈×C₄₇	—	4	1	no	—
72	#95×C₄₇	—	2	2	no	—
73	#95×C₄₇	—	2	2	no	—
74	#95×C₄₇	—	2	2	no	—
75	C₂⁴×C₄₇	—	2	2	no	—
76	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₂×D₄×C₄₇	—	2	8	no	—
78	C₂×D₄×C₄₇	—	2	2	no	—
79	C₂×D₄×C₄₇	—	2	2	no	—
80	C₂×D₄×C₄₇	—	2	2	no	—
81	C₂×D₄×C₄₇	—	2	2	no	—
82	C₂×D₄×C₄₇	—	2	2	no	—
83	C₂×D₄×C₄₇	—	4	4	no	—
84	C₂×D₄×C₄₇	—	4	4	no	—
85	C₂×D₄×C₄₇	#41	1	4	yes	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	1	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	4	1	no	—
94	C₂²×C₄×C₄₇	—	4	1	no	—
95	C₂²×C₄×C₄₇	—	4	1	no	—
96	C₂²×C₄×C₄₇	—	4	2	no	—
97	C₂²×C₄×C₄₇	—	4	4	no	—
98	C₂²×C₄×C₄₇	—	4	4	no	—
99	C₂²×C₄×C₄₇	—	4	4	no	—
100	C₂²×C₄×C₄₇	D₈	1	4	yes	complemented
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	D₈×C₄₇	—	4	4	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	1	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	2	2	no	—
116	C₄⋊C₄×C₄₇	—	2	2	no	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄⋊C₄×C₄₇	—	4	4	no	—
119	C₄⋊C₄×C₄₇	#41	1	4	yes	—
120	C₂²⋊C₄×C₄₇	—	2	8	no	—
121	C₂²⋊C₄×C₄₇	—	4	4	no	—
122	C₂²⋊C₄×C₄₇	—	4	4	no	—
123	C₂²⋊C₄×C₄₇	—	4	4	no	—
124	C₂²⋊C₄×C₄₇	—	4	4	no	—
125	C₄²×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	—	4	2	no	—
128	C₄²×C₄₇	—	4	4	no	—
129	C₂³×C₄₇	—	2	2	no	—
130	C₂³×C₄₇	—	2	1	no	—
131	C₂³×C₄₇	—	2	2	no	—
132	C₂³×C₄₇	—	2	1	no	—
133	C₂³×C₄₇	—	2	4	no	—
134	C₂³×C₄₇	—	4	2	no	—
135	C₂³×C₄₇	—	4	2	no	—
136	C₂³×C₄₇	—	4	2	no	—
137	C₂³×C₄₇	—	4	2	no	—
138	C₂³×C₄₇	—	4	2	no	—
139	C₂³×C₄₇	—	4	2	no	—
140	C₂³×C₄₇	C₂×D₈	1	2	yes	—
141	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
142	D₄×C₄₇	—	2	4	no	—
143	D₄×C₄₇	—	2	4	no	—
144	D₄×C₄₇	—	4	16	no	—
145	D₄×C₄₇	—	4	2	no	—
146	D₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	4	4	no	—
156	C₂×C₄×C₄₇	—	4	4	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	1	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	1	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	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	—	8	8	no	—
169	C₂×C₄×C₄₇	C₂×D₈	1	4	yes	—
170	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
171	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
172	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
174	C₈×C₄₇	—	4	1	no	—
175	C₈×C₄₇	—	4	2	no	—
176	C₈×C₄₇	—	4	1	no	—
177	#29408	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂²×C₄₇	—	2	4	no	—
179	C₂²×C₄₇	—	2	2	no	—
180	C₂²×C₄₇	—	4	2	no	—
181	C₂²×C₄₇	—	4	1	no	—
182	C₂²×C₄₇	—	4	1	no	—
183	C₂²×C₄₇	—	4	4	no	—
184	C₂²×C₄₇	—	4	4	no	—
185	C₂²×C₄₇	—	4	4	no	—
186	C₂²×C₄₇	—	8	2	no	—
187	C₂²×C₄₇	—	8	2	no	—
188	C₂²×C₄₇	—	8	2	no	—
189	C₂²×C₄₇	—	8	2	no	—
190	C₂²×C₄₇	#525	1	2	yes	—
191	C₂²×C₄₇	#534	1	1	yes	characteristic
192	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
193	C₂²×C₄₇	#575	1	2	yes	—
194	C₂²×C₄₇	#575	1	1	yes	characteristic
195	C₄×C₄₇	—	2	4	no	—
196	C₄×C₄₇	—	4	4	no	—
197	C₄×C₄₇	—	4	1	no	—
198	C₄×C₄₇	—	4	2	no	—
199	C₄×C₄₇	—	8	2	no	—
200	C₄×C₄₇	—	8	2	no	—
201	C₄×C₄₇	#551	1	1	yes	characteristic
202	C₄×C₄₇	#553	1	2	yes	—
203	C₄×C₄₇	#559	1	1	yes	characteristic
204	C₄×#121	C₂×C₄₇	1	2	yes	complemented
205	#2075	C₂×C₄₇	1	1	yes	characteristic, complemented
206	#2033	C₂×C₄₇	1	2	yes	complemented
207	#1999	C₂×C₄₇	1	1	yes	characteristic
208	#1925	C₂×C₄₇	1	2	yes	complemented
209	#1918	C₂×C₄₇	1	2	yes	complemented
210	#1879	C₂×C₄₇	1	2	yes	complemented
211	#1862	C₂×C₄₇	1	2	yes	complemented
212	#1817	C₂×C₄₇	1	1	yes	characteristic, complemented
213	C₂×C₄₇	—	4	2	no	—
214	C₂×C₄₇	—	8	4	no	—
215	C₂×C₄₇	#2600	1	1	yes	characteristic
216	C₂×C₄₇	#3100	1	2	yes	—
217	C₂×C₄₇	#3111	1	2	yes	—
218	C₂×C₄₇	#3186	1	1	yes	characteristic
219	C₂×C₄₇	#3197	1	1	yes	characteristic
220	C₂²×D₈	C₂²×C₄₇	1	1	yes	characteristic
221	C₂×#121	C₂²×C₄₇	1	2	yes	—
222	C₂×C₄×D₄	—	2	2	no	—
223	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
224	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
225	C₂×#107	C₂²×C₄₇	1	2	yes	—
226	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic
227	C₂×#102	C₂²×C₄₇	1	2	yes	—
228	C₂×#102	C₂²×C₄₇	1	2	yes	—
229	C₂×#102	C₂²×C₄₇	1	2	yes	—
230	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
231	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
232	#390	C₂²×C₄₇	1	2	yes	—
233	#389	C₂²×C₄₇	1	2	yes	—
234	#388	—	2	2	no	—
235	#386	—	2	2	no	—
236	#380	C₂²×C₄₇	1	2	yes	—
237	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
238	C₄×C₂²⋊C₄	—	2	2	no	—
239	#340	C₂²×C₄₇	1	2	yes	—
240	#340	C₂²×C₄₇	1	1	yes	characteristic
241	#340	C₂²×C₄₇	1	2	yes	—
242	#340	C₂²×C₄₇	1	1	yes	characteristic
243	#336	C₂²×C₄₇	1	2	yes	—
244	#336	C₂²×C₄₇	1	2	yes	—
245	C₄₇	#29408	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
248	C₂³×C₄	—	2	2	no	—
249	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
250	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
252	C₂×D₈	—	2	4	no	—
253	C₂×D₈	—	4	1	no	—
254	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
257	#121	—	2	4	no	—
258	#121	—	2	4	no	—
259	C₄×D₄	—	4	2	no	—
260	C₄×D₄	—	4	2	no	—
261	C₄×D₄	—	4	8	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	—	4	1	no	—
273	C₂×C₄²	—	4	1	no	—
274	C₂×C₄²	D₄×C₄₇	1	2	yes	—
275	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
276	#107	—	2	4	no	—
277	#107	—	4	1	no	—
278	#102	—	2	4	no	—
279	#102	—	2	4	no	—
280	#102	—	4	2	no	—
281	C₂²⋊C₈	—	4	1	no	—
282	C₂²⋊C₈	—	4	1	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	C₂⁴	—	2	2	no	—
287	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
288	C₂×D₄	—	2	8	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	—	4	4	no	—
296	C₂×D₄	#41×C₄₇	1	4	yes	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	4	no	—
309	C₂²×C₄	—	4	4	no	—
310	C₂²×C₄	—	4	4	no	—
311	C₂²×C₄	D₈×C₄₇	1	4	yes	complemented
312	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
316	D₈	—	4	4	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	#41×C₄₇	1	4	yes	—
331	C₂²⋊C₄	—	2	8	no	—
332	C₂²⋊C₄	—	4	4	no	—
333	C₂²⋊C₄	—	4	4	no	—
334	C₂²⋊C₄	—	4	4	no	—
335	C₂²⋊C₄	—	4	4	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	4	2	no	—
339	C₄²	—	4	4	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	C₂×D₈×C₄₇	1	2	yes	—
352	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
353	D₄	—	2	4	no	—
354	D₄	—	2	4	no	—
355	D₄	—	4	16	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	8	8	no	—
380	C₂×C₄	C₂×D₈×C₄₇	1	4	yes	—
381	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
382	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
383	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
384	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
385	C₈	—	4	1	no	—
386	C₈	—	4	2	no	—
387	C₈	—	4	1	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	C₄₇×#525	1	2	yes	—
401	C₂²	C₄₇×#534	1	1	yes	characteristic
402	C₂²	C₂²×D₈×C₄₇	1	1	yes	characteristic
403	C₂²	C₄₇×#575	1	2	yes	—
404	C₂²	C₄₇×#575	1	1	yes	characteristic
405	C₄	—	2	4	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	2	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	2	no	—
411	C₄	C₄₇×#551	1	1	yes	characteristic
412	C₄	C₄₇×#553	1	2	yes	—
413	C₄	C₄₇×#559	1	1	yes	characteristic
414	C₂	—	4	2	no	—
415	C₂	—	8	4	no	—
416	C₂	C₄₇×#2600	1	1	yes	characteristic
417	C₂	C₄₇×#3100	1	2	yes	—
418	C₂	C₄₇×#3111	1	2	yes	—
419	C₂	C₄₇×#3186	1	1	yes	characteristic
420	C₂	C₄₇×#3197	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₄₇×#1999	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×#121×C₄₇	C₂	semidirect
2. C₄₇×#2075	C₂	semidirect
3. C₄₇×#2033	C₂	semidirect
5. C₄₇×#1925	C₂	semidirect
6. C₄₇×#1918	C₂	semidirect
7. C₄₇×#1879	C₂	semidirect
8. C₄₇×#1862	C₂	semidirect
9. C₄₇×#1817	C₂	semidirect
100. C₂²×C₄×C₄₇	D₈	semidirect
177. #29408	C₄₇	direct (N × H)
204. C₄×#121	C₂×C₄₇	semidirect
205. #2075	C₂×C₄₇	semidirect
206. #2033	C₂×C₄₇	semidirect
208. #1925	C₂×C₄₇	semidirect
209. #1918	C₂×C₄₇	semidirect
210. #1879	C₂×C₄₇	semidirect
211. #1862	C₂×C₄₇	semidirect
212. #1817	C₂×C₄₇	semidirect
245. C₄₇	#29408	direct (N × H)
311. C₂²×C₄	D₈×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×#121×C₄₇	2
C₄₇×#2075	2
C₄₇×#2033	2
C₄₇×#1999	2
C₄₇×#1925	2
C₄₇×#1918	2
C₄₇×#1879	2
C₄₇×#1862	2
C₄₇×#1817	2
#29408	47

Subgroups — C47×#29408 #26069106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29408 #26069106