Subgroups — C₄₇×#29115 #26068813

Order 12032.

954 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#2629	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#2309	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2071	C₂	1	2	yes	maximal, complemented
4	C₄₇×#2025	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1936	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1934	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1825	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1786	C₂	1	2	yes	maximal
9	C₄₇×#1750	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic, complemented
12	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#102×C₄₇	C₂²	1	2	yes	—
15	C₂×#102×C₄₇	C₂²	1	2	yes	—
16	C₂×#102×C₄₇	C₂²	1	2	yes	—
17	C₂×#102×C₄₇	C₂²	1	2	yes	—
18	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
19	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
21	C₄₇×#398	—	2	2	no	—
22	C₄₇×#396	—	2	2	no	—
23	C₄₇×#390	—	2	2	no	—
24	C₄₇×#390	C₂²	1	2	yes	—
25	C₄₇×#390	C₂²	1	2	yes	—
26	C₄₇×#389	C₂²	1	2	yes	complemented
27	C₄₇×#384	C₂²	1	1	yes	characteristic, complemented
28	C₄₇×#380	C₂²	1	2	yes	—
29	C₄₇×#379	—	2	2	no	—
30	C₄₇×#340	C₂²	1	2	yes	complemented
31	C₄₇×#340	C₂²	1	2	yes	complemented
32	C₄₇×#340	C₂²	1	2	yes	complemented
33	C₄₇×#340	C₂²	1	2	yes	complemented
34	C₄₇×#336	C₂²	1	2	yes	complemented
35	C₂⁵×C₄₇	—	2	1	no	—
36	C₂²×D₄×C₄₇	—	2	4	no	—
37	C₂²×D₄×C₄₇	—	2	1	no	—
38	C₂²×D₄×C₄₇	—	2	4	no	—
39	C₂²×D₄×C₄₇	—	4	1	no	—
40	C₂²×D₄×C₄₇	—	4	1	no	—
41	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
42	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
44	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
45	#125×C₄₇	—	4	1	no	—
46	#125×C₄₇	—	4	1	no	—
47	#117×C₄₇	—	2	4	no	—
48	#117×C₄₇	—	4	1	no	—
49	#117×C₄₇	—	4	1	no	—
50	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
64	C₂×C₄²×C₄₇	—	2	1	no	—
65	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
67	#102×C₄₇	—	2	4	no	—
68	#102×C₄₇	—	2	4	no	—
69	#102×C₄₇	—	4	2	no	—
70	#102×C₄₇	—	4	2	no	—
71	C₂²⋊C₈×C₄₇	—	2	4	no	—
72	#97×C₄₇	—	4	1	no	—
73	C₄×C₈×C₄₇	—	4	1	no	—
74	#95×C₄₇	—	2	2	no	—
75	#95×C₄₇	—	2	2	no	—
76	C₂⁴×C₄₇	—	2	4	no	—
77	C₂⁴×C₄₇	—	2	2	no	—
78	C₂⁴×C₄₇	—	4	2	no	—
79	C₂⁴×C₄₇	—	4	2	no	—
80	C₂⁴×C₄₇	—	8	2	no	—
81	C₂⁴×C₄₇	—	8	2	no	—
82	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂×D₄×C₄₇	—	2	4	no	—
84	C₂×D₄×C₄₇	—	2	2	no	—
85	C₂×D₄×C₄₇	—	2	2	no	—
86	C₂×D₄×C₄₇	—	2	2	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	4	8	no	—
90	C₂×D₄×C₄₇	—	4	8	no	—
91	C₂×D₄×C₄₇	—	4	2	no	—
92	C₂×D₄×C₄₇	—	4	2	no	—
93	C₂×D₄×C₄₇	#41	1	4	yes	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	1	no	—
96	C₂²×C₄×C₄₇	—	2	1	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	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	#41	1	4	yes	—
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₄₇	—	2	2	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	2	no	—
111	C₄⋊C₄×C₄₇	—	2	4	no	—
112	C₄⋊C₄×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	—	4	2	no	—
117	C₄⋊C₄×C₄₇	—	4	4	no	—
118	C₄⋊C₄×C₄₇	—	8	2	no	—
119	C₄⋊C₄×C₄₇	—	8	2	no	—
120	C₂²⋊C₄×C₄₇	—	4	2	no	—
121	C₂²⋊C₄×C₄₇	—	4	2	no	—
122	C₂²⋊C₄×C₄₇	—	8	2	no	—
123	C₂²⋊C₄×C₄₇	—	8	2	no	—
124	C₂²⋊C₄×C₄₇	—	8	2	no	—
125	C₂²⋊C₄×C₄₇	—	8	2	no	—
126	C₂²⋊C₄×C₄₇	—	8	2	no	—
127	C₄²×C₄₇	—	2	1	no	—
128	C₄²×C₄₇	—	2	1	no	—
129	C₄²×C₄₇	—	2	1	no	—
130	C₄²×C₄₇	—	2	1	no	—
131	C₄²×C₄₇	—	4	2	no	—
132	C₂³×C₄₇	—	2	1	no	—
133	C₂³×C₄₇	—	2	1	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	2	no	—
136	C₂³×C₄₇	—	2	4	no	—
137	C₂³×C₄₇	—	4	8	no	—
138	C₂³×C₄₇	—	4	2	no	—
139	C₂³×C₄₇	—	4	2	no	—
140	C₂³×C₄₇	—	4	2	no	—
141	C₂³×C₄₇	—	4	2	no	—
142	C₂³×C₄₇	—	4	2	no	—
143	C₂³×C₄₇	—	4	2	no	—
144	C₂³×C₄₇	—	8	8	no	—
145	C₂³×C₄₇	—	8	4	no	—
146	C₂³×C₄₇	—	8	4	no	—
147	C₂³×C₄₇	—	8	8	no	—
148	C₂³×C₄₇	#124	1	2	yes	—
149	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	D₄×C₄₇	—	2	4	no	—
151	D₄×C₄₇	—	2	4	no	—
152	D₄×C₄₇	—	4	8	no	—
153	D₄×C₄₇	—	4	2	no	—
154	D₄×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	2	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	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	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	—	4	2	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	#124	1	2	yes	—
175	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
176	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
177	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
179	C₈×C₄₇	—	4	2	no	—
180	C₈×C₄₇	—	4	2	no	—
181	#29115	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂²×C₄₇	—	2	2	no	—
183	C₂²×C₄₇	—	2	4	no	—
184	C₂²×C₄₇	—	4	1	no	—
185	C₂²×C₄₇	—	4	1	no	—
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	—	4	4	no	—
188	C₂²×C₄₇	—	4	4	no	—
189	C₂²×C₄₇	—	4	4	no	—
190	C₂²×C₄₇	—	8	16	no	—
191	C₂²×C₄₇	—	8	2	no	—
192	C₂²×C₄₇	—	8	2	no	—
193	C₂²×C₄₇	—	8	2	no	—
194	C₂²×C₄₇	—	8	2	no	—
195	C₂²×C₄₇	#525	1	1	yes	characteristic
196	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
197	C₂²×C₄₇	#534	1	1	yes	characteristic
198	C₂²×C₄₇	#576	1	2	yes	—
199	C₂²×C₄₇	#577	1	2	yes	—
200	C₄×C₄₇	—	2	2	no	—
201	C₄×C₄₇	—	4	2	no	—
202	C₄×C₄₇	—	4	2	no	—
203	C₄×C₄₇	—	8	2	no	—
204	C₄×C₄₇	—	8	2	no	—
205	C₄×C₄₇	—	8	2	no	—
206	C₄×C₄₇	#551	1	2	yes	—
207	C₄×C₄₇	#551	1	2	yes	—
208	#2629	C₂×C₄₇	1	1	yes	characteristic, complemented
209	#2309	C₂×C₄₇	1	1	yes	characteristic
210	#2071	C₂×C₄₇	1	2	yes	complemented
211	#2025	C₂×C₄₇	1	2	yes	complemented
212	#1936	C₂×C₄₇	1	2	yes	complemented
213	#1934	C₂×C₄₇	1	2	yes	complemented
214	#1825	C₂×C₄₇	1	2	yes	complemented
215	#1786	C₂×C₄₇	1	2	yes	—
216	#1750	C₂×C₄₇	1	1	yes	characteristic, complemented
217	C₂×C₄₇	—	4	2	no	—
218	C₂×C₄₇	—	8	4	no	—
219	C₂×C₄₇	#2561	1	1	yes	characteristic
220	C₂×C₄₇	#3122	1	1	yes	characteristic
221	C₂×C₄₇	#3123	1	1	yes	characteristic
222	C₂×C₄₇	#3136	1	2	yes	—
223	C₂×C₄₇	#3198	1	2	yes	—
224	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
225	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic, complemented
226	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
227	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
228	C₂×#102	C₂²×C₄₇	1	2	yes	—
229	C₂×#102	C₂²×C₄₇	1	2	yes	—
230	C₂×#102	C₂²×C₄₇	1	2	yes	—
231	C₂×#102	C₂²×C₄₇	1	2	yes	—
232	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
233	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic, complemented
234	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
235	#398	—	2	2	no	—
236	#396	—	2	2	no	—
237	#390	—	2	2	no	—
238	#390	C₂²×C₄₇	1	2	yes	—
239	#390	C₂²×C₄₇	1	2	yes	—
240	#389	C₂²×C₄₇	1	2	yes	complemented
241	#384	C₂²×C₄₇	1	1	yes	characteristic, complemented
242	#380	C₂²×C₄₇	1	2	yes	—
243	#379	—	2	2	no	—
244	#340	C₂²×C₄₇	1	2	yes	complemented
245	#340	C₂²×C₄₇	1	2	yes	complemented
246	#340	C₂²×C₄₇	1	2	yes	complemented
247	#340	C₂²×C₄₇	1	2	yes	complemented
248	#336	C₂²×C₄₇	1	2	yes	complemented
249	C₄₇	#29115	1	1	yes	characteristic, direct product factor, Sylow
250	C₂⁵	—	2	1	no	—
251	C₂²×D₄	—	2	4	no	—
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	—	2	4	no	—
254	C₂²×D₄	—	4	1	no	—
255	C₂²×D₄	—	4	1	no	—
256	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
257	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
259	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
260	#125	—	4	1	no	—
261	#125	—	4	1	no	—
262	#117	—	2	4	no	—
263	#117	—	4	1	no	—
264	#117	—	4	1	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
282	#102	—	2	4	no	—
283	#102	—	2	4	no	—
284	#102	—	4	2	no	—
285	#102	—	4	2	no	—
286	C₂²⋊C₈	—	2	4	no	—
287	#97	—	4	1	no	—
288	C₄×C₈	—	4	1	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	C₂⁴	—	2	4	no	—
292	C₂⁴	—	2	2	no	—
293	C₂⁴	—	4	2	no	—
294	C₂⁴	—	4	2	no	—
295	C₂⁴	—	8	2	no	—
296	C₂⁴	—	8	2	no	—
297	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	8	no	—
305	C₂×D₄	—	4	8	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	#41×C₄₇	1	4	yes	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
318	C₂²×C₄	#41×C₄₇	1	4	yes	—
319	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	4	no	—
333	C₄⋊C₄	—	8	2	no	—
334	C₄⋊C₄	—	8	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	8	2	no	—
338	C₂²⋊C₄	—	8	2	no	—
339	C₂²⋊C₄	—	8	2	no	—
340	C₂²⋊C₄	—	8	2	no	—
341	C₂²⋊C₄	—	8	2	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	4	2	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	4	8	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	8	8	no	—
360	C₂³	—	8	4	no	—
361	C₂³	—	8	4	no	—
362	C₂³	—	8	8	no	—
363	C₂³	#124×C₄₇	1	2	yes	—
364	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
365	D₄	—	2	4	no	—
366	D₄	—	2	4	no	—
367	D₄	—	4	8	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	#124×C₄₇	1	2	yes	—
390	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
391	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
392	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
393	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
394	C₈	—	4	2	no	—
395	C₈	—	4	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	8	16	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	2	no	—
409	C₂²	C₄₇×#525	1	1	yes	characteristic
410	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
411	C₂²	C₄₇×#534	1	1	yes	characteristic
412	C₂²	C₄₇×#576	1	2	yes	—
413	C₂²	C₄₇×#577	1	2	yes	—
414	C₄	—	2	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	8	2	no	—
418	C₄	—	8	2	no	—
419	C₄	—	8	2	no	—
420	C₄	C₄₇×#551	1	2	yes	—
421	C₄	C₄₇×#551	1	2	yes	—
422	C₂	—	4	2	no	—
423	C₂	—	8	4	no	—
424	C₂	C₄₇×#2561	1	1	yes	characteristic
425	C₂	C₄₇×#3122	1	1	yes	characteristic
426	C₂	C₄₇×#3123	1	1	yes	characteristic
427	C₂	C₄₇×#3136	1	2	yes	—
428	C₂	C₄₇×#3198	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×#117×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#2629	C₂	semidirect
3. C₄₇×#2071	C₂	semidirect
4. C₄₇×#2025	C₂	semidirect
5. C₄₇×#1936	C₂	semidirect
6. C₄₇×#1934	C₂	semidirect
7. C₄₇×#1825	C₂	semidirect
9. C₄₇×#1750	C₂	semidirect
11. C₂×#125×C₄₇	C₂²	semidirect
19. C₂×#97×C₄₇	C₂²	semidirect
20. C₂×C₄×C₈×C₄₇	C₂²	semidirect
26. C₄₇×#389	C₂²	semidirect
27. C₄₇×#384	C₂²	semidirect
30. C₄₇×#340	C₂²	semidirect
31. C₄₇×#340	C₂²	semidirect
32. C₄₇×#340	C₂²	semidirect
33. C₄₇×#340	C₂²	semidirect
34. C₄₇×#336	C₂²	semidirect
181. #29115	C₄₇	direct (N × H)
208. #2629	C₂×C₄₇	semidirect
210. #2071	C₂×C₄₇	semidirect
211. #2025	C₂×C₄₇	semidirect
212. #1936	C₂×C₄₇	semidirect
213. #1934	C₂×C₄₇	semidirect
214. #1825	C₂×C₄₇	semidirect
216. #1750	C₂×C₄₇	semidirect
225. C₂×#125	C₂²×C₄₇	semidirect
233. C₂×#97	C₂²×C₄₇	semidirect
234. C₂×C₄×C₈	C₂²×C₄₇	semidirect
240. #389	C₂²×C₄₇	semidirect
241. #384	C₂²×C₄₇	semidirect
244. #340	C₂²×C₄₇	semidirect
245. #340	C₂²×C₄₇	semidirect
246. #340	C₂²×C₄₇	semidirect
247. #340	C₂²×C₄₇	semidirect
248. #336	C₂²×C₄₇	semidirect
249. C₄₇	#29115	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#2629	2
C₄₇×#2309	2
C₄₇×#2071	2
C₄₇×#2025	2
C₄₇×#1936	2
C₄₇×#1934	2
C₄₇×#1825	2
C₄₇×#1786	2
C₄₇×#1750	2
#29115	47

Subgroups — C47×#29115 #26068813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29115 #26068813