Subgroups — C₄₇×#29732 #26069430

Order 12032.

1278 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2847	C₂	1	2	yes	maximal, complemented
4	C₄₇×#2076	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2034	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1999	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1893	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1807	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
11	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×#121×C₄₇	C₂²	1	2	yes	—
14	C₂×#121×C₄₇	C₂²	1	4	yes	—
15	C₂×#120×C₄₇	—	2	2	no	—
16	C₄₇×#466	—	2	4	no	—
17	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic, complemented
18	C₂×#106×C₄₇	C₂²	1	2	yes	complemented
19	C₂×#102×C₄₇	C₂²	1	2	yes	complemented
20	C₂×#102×C₄₇	C₂²	1	4	yes	complemented
21	C₂×C₂²⋊C₈×C₄₇	—	2	4	no	—
22	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
24	C₄₇×#386	—	2	4	no	—
25	C₄₇×#386	—	2	2	no	—
26	C₄₇×#380	C₂²	1	4	yes	—
27	C₄₇×#380	C₂²	1	2	yes	—
28	C₄₇×#340	C₂²	1	4	yes	complemented
29	C₄₇×#340	C₂²	1	2	yes	complemented
30	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
31	C₂²×D₄×C₄₇	—	2	4	no	—
32	C₂²×D₄×C₄₇	—	2	2	no	—
33	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
34	C₂³×C₄×C₄₇	—	2	2	no	—
35	C₂³×C₄×C₄₇	—	2	2	no	—
36	C₂³×C₄×C₄₇	—	4	2	no	—
37	C₂³×C₄×C₄₇	—	4	2	no	—
38	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	D₄	1	2	yes	—
40	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂×D₈×C₄₇	—	2	2	no	—
43	C₂×D₈×C₄₇	—	4	2	no	—
44	C₂²×C₈×C₄₇	—	2	2	no	—
45	C₂²×C₈×C₄₇	—	4	2	no	—
46	C₂²×C₈×C₄₇	—	4	2	no	—
47	C₂²×C₈×C₄₇	D₄	1	4	yes	complemented
48	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
51	#121×C₄₇	—	2	4	no	—
52	#121×C₄₇	—	2	4	no	—
53	#121×C₄₇	—	4	4	no	—
54	#121×C₄₇	—	4	4	no	—
55	#120×C₄₇	—	4	8	no	—
56	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
57	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
62	#107×C₄₇	—	2	2	no	—
63	#106×C₄₇	—	4	2	no	—
64	#102×C₄₇	—	2	4	no	—
65	#102×C₄₇	—	4	4	no	—
66	C₂²⋊C₈×C₄₇	—	2	4	no	—
67	C₂²⋊C₈×C₄₇	—	2	4	no	—
68	#95×C₄₇	—	2	4	no	—
69	#95×C₄₇	—	2	2	no	—
70	C₂⁴×C₄₇	—	2	2	no	—
71	C₂⁴×C₄₇	—	2	4	no	—
72	C₂⁴×C₄₇	—	2	4	no	—
73	C₂⁴×C₄₇	—	2	2	no	—
74	C₂⁴×C₄₇	—	4	2	no	—
75	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
76	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₂×D₄×C₄₇	—	2	2	no	—
78	C₂×D₄×C₄₇	—	2	2	no	—
79	C₂×D₄×C₄₇	—	2	4	no	—
80	C₂×D₄×C₄₇	—	2	4	no	—
81	C₂×D₄×C₄₇	—	4	8	no	—
82	C₂×D₄×C₄₇	—	4	8	no	—
83	C₂×D₄×C₄₇	—	4	4	no	—
84	C₂×D₄×C₄₇	—	4	8	no	—
85	C₂×D₄×C₄₇	—	4	4	no	—
86	C₂×D₄×C₄₇	—	4	4	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	4	4	no	—
98	C₂²×C₄×C₄₇	—	4	2	no	—
99	C₂²×C₄×C₄₇	—	4	4	no	—
100	C₂²×C₄×C₄₇	—	4	4	no	—
101	C₂²×C₄×C₄₇	—	4	8	no	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	#41	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
107	D₈×C₄₇	—	4	4	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	4	no	—
112	C₂×C₈×C₄₇	—	4	4	no	—
113	C₂×C₈×C₄₇	—	4	4	no	—
114	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
116	C₄⋊C₄×C₄₇	—	2	2	no	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄⋊C₄×C₄₇	—	2	4	no	—
119	C₄⋊C₄×C₄₇	—	2	4	no	—
120	C₂²⋊C₄×C₄₇	—	4	8	no	—
121	C₂²⋊C₄×C₄₇	—	4	8	no	—
122	C₂²⋊C₄×C₄₇	—	4	4	no	—
123	C₂²⋊C₄×C₄₇	—	4	4	no	—
124	C₂³×C₄₇	—	2	2	no	—
125	C₂³×C₄₇	—	2	2	no	—
126	C₂³×C₄₇	—	2	8	no	—
127	C₂³×C₄₇	—	2	2	no	—
128	C₂³×C₄₇	—	2	4	no	—
129	C₂³×C₄₇	—	2	2	no	—
130	C₂³×C₄₇	—	2	4	no	—
131	C₂³×C₄₇	—	4	16	no	—
132	C₂³×C₄₇	—	4	4	no	—
133	C₂³×C₄₇	—	4	4	no	—
134	C₂³×C₄₇	—	4	2	no	—
135	C₂³×C₄₇	—	4	4	no	—
136	C₂³×C₄₇	—	4	4	no	—
137	C₂³×C₄₇	—	4	2	no	—
138	C₂³×C₄₇	—	4	2	no	—
139	C₂³×C₄₇	#121	1	2	yes	—
140	C₂³×C₄₇	#135	1	4	yes	—
141	C₂³×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
142	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
143	D₄×C₄₇	—	4	2	no	—
144	D₄×C₄₇	—	4	2	no	—
145	D₄×C₄₇	—	4	4	no	—
146	D₄×C₄₇	—	8	16	no	—
147	D₄×C₄₇	—	8	8	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	4	8	no	—
155	C₂×C₄×C₄₇	—	4	4	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	4	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	4	no	—
161	C₂×C₄×C₄₇	—	4	4	no	—
162	C₂×C₄×C₄₇	—	4	4	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	#121	1	2	yes	—
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
169	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
170	C₈×C₄₇	—	2	2	no	—
171	C₈×C₄₇	—	2	2	no	—
172	C₈×C₄₇	—	4	2	no	—
173	#29732	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₄₇	—	2	2	no	—
175	C₂²×C₄₇	—	2	8	no	—
176	C₂²×C₄₇	—	2	2	no	—
177	C₂²×C₄₇	—	2	8	no	—
178	C₂²×C₄₇	—	2	4	no	—
179	C₂²×C₄₇	—	4	16	no	—
180	C₂²×C₄₇	—	4	2	no	—
181	C₂²×C₄₇	—	4	4	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	—	8	2	no	—
184	C₂²×C₄₇	—	8	4	no	—
185	C₂²×C₄₇	—	8	4	no	—
186	C₂²×C₄₇	—	8	2	no	—
187	C₂²×C₄₇	—	8	2	no	—
188	C₂²×C₄₇	#469	1	4	yes	—
189	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
190	C₂²×C₄₇	#534	1	2	yes	—
191	C₂²×C₄₇	C₂×#135	1	2	yes	—
192	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
193	C₄×C₄₇	—	2	2	no	—
194	C₄×C₄₇	—	4	2	no	—
195	C₄×C₄₇	—	8	4	no	—
196	C₄×C₄₇	—	8	2	no	—
197	C₄×C₄₇	#534	1	1	yes	characteristic
198	C₄×C₄₇	#535	1	1	yes	characteristic
199	C₄×C₄₇	#538	1	2	yes	—
200	C₂×#466	C₂×C₄₇	1	1	yes	characteristic, complemented
201	C₂²×C₂²⋊C₈	C₂×C₄₇	1	1	yes	characteristic, complemented
202	#2847	C₂×C₄₇	1	2	yes	complemented
203	#2076	C₂×C₄₇	1	2	yes	complemented
204	#2034	C₂×C₄₇	1	4	yes	complemented
205	#1999	C₂×C₄₇	1	2	yes	complemented
206	#1893	C₂×C₄₇	1	2	yes	complemented
207	#1807	C₂×C₄₇	1	1	yes	characteristic, complemented
208	C₂×C₄₇	—	2	4	no	—
209	C₂×C₄₇	—	4	4	no	—
210	C₂×C₄₇	—	16	2	no	—
211	C₂×C₄₇	#2617	1	1	yes	characteristic
212	C₂×C₄₇	#3050	1	1	yes	characteristic
213	C₂×C₄₇	C₂×#469	1	1	yes	characteristic
214	C₂×C₄₇	#3188	1	4	yes	—
215	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
216	C₂²×D₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
217	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
218	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
219	C₂×#121	C₂²×C₄₇	1	2	yes	—
220	C₂×#121	C₂²×C₄₇	1	4	yes	—
221	C₂×#120	—	2	2	no	—
222	#466	—	2	4	no	—
223	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic, complemented
224	C₂×#106	C₂²×C₄₇	1	2	yes	complemented
225	C₂×#102	C₂²×C₄₇	1	2	yes	complemented
226	C₂×#102	C₂²×C₄₇	1	4	yes	complemented
227	C₂×C₂²⋊C₈	—	2	4	no	—
228	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
229	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
230	#386	—	2	2	no	—
231	#386	—	2	4	no	—
232	#380	C₂²×C₄₇	1	2	yes	—
233	#380	C₂²×C₄₇	1	4	yes	—
234	#340	C₂²×C₄₇	1	2	yes	complemented
235	#340	C₂²×C₄₇	1	4	yes	complemented
236	C₄₇	#29732	1	1	yes	characteristic, direct product factor, Sylow
237	C₂⁵	D₄×C₄₇	1	1	yes	characteristic
238	C₂²×D₄	—	2	4	no	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
241	C₂³×C₄	—	2	2	no	—
242	C₂³×C₄	—	2	2	no	—
243	C₂³×C₄	—	4	2	no	—
244	C₂³×C₄	—	4	2	no	—
245	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
246	C₂³×C₄	D₄×C₄₇	1	2	yes	—
247	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
248	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
249	C₂×D₈	—	2	2	no	—
250	C₂×D₈	—	4	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	4	2	no	—
253	C₂²×C₈	—	4	2	no	—
254	C₂²×C₈	D₄×C₄₇	1	4	yes	complemented
255	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
256	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
258	#121	—	2	4	no	—
259	#121	—	2	4	no	—
260	#121	—	4	4	no	—
261	#121	—	4	4	no	—
262	#120	—	4	8	no	—
263	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
264	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	4	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	4	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	#107	—	2	2	no	—
270	#106	—	4	2	no	—
271	#102	—	2	4	no	—
272	#102	—	4	4	no	—
273	C₂²⋊C₈	—	2	4	no	—
274	C₂²⋊C₈	—	2	4	no	—
275	#95	—	2	4	no	—
276	#95	—	2	2	no	—
277	C₂⁴	—	2	2	no	—
278	C₂⁴	—	2	4	no	—
279	C₂⁴	—	2	4	no	—
280	C₂⁴	—	2	2	no	—
281	C₂⁴	—	4	2	no	—
282	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
283	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	4	8	no	—
289	C₂×D₄	—	4	8	no	—
290	C₂×D₄	—	4	4	no	—
291	C₂×D₄	—	4	8	no	—
292	C₂×D₄	—	4	4	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	—	4	8	no	—
309	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
312	C₂²×C₄	#41×C₄₇	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
314	D₈	—	4	4	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	4	4	no	—
320	C₂×C₈	—	4	4	no	—
321	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
322	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	4	8	no	—
328	C₂²⋊C₄	—	4	8	no	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	8	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	4	16	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	4	no	—
343	C₂³	—	4	4	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	#121×C₄₇	1	2	yes	—
347	C₂³	#135×C₄₇	1	4	yes	—
348	C₂³	AGL(1,ℤ/8)×C₄₇	1	4	yes	—
349	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	4	no	—
353	D₄	—	8	16	no	—
354	D₄	—	8	8	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	4	8	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	#121×C₄₇	1	2	yes	—
373	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
374	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
375	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
376	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₈	—	4	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	8	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	8	no	—
385	C₂²	—	4	16	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	4	no	—
393	C₂²	—	8	4	no	—
394	C₂²	C₄₇×#469	1	4	yes	—
395	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
396	C₂²	C₄₇×#534	1	2	yes	—
397	C₂²	C₂×#135×C₄₇	1	2	yes	—
398	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	8	2	no	—
402	C₄	—	8	4	no	—
403	C₄	C₄₇×#534	1	1	yes	characteristic
404	C₄	C₄₇×#535	1	1	yes	characteristic
405	C₄	C₄₇×#538	1	2	yes	—
406	C₂	—	2	4	no	—
407	C₂	—	4	4	no	—
408	C₂	—	16	2	no	—
409	C₂	C₄₇×#2617	1	1	yes	characteristic
410	C₂	C₄₇×#3050	1	1	yes	characteristic
411	C₂	C₂×C₄₇×#469	1	1	yes	characteristic
412	C₂	C₄₇×#3188	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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
1. C₂×C₄₇×#466	C₂	semidirect
2. C₂²×C₂²⋊C₈×C₄₇	C₂	semidirect
3. C₄₇×#2847	C₂	semidirect
4. C₄₇×#2076	C₂	semidirect
5. C₄₇×#2034	C₂	semidirect
6. C₄₇×#1999	C₂	semidirect
7. C₄₇×#1893	C₂	semidirect
8. C₄₇×#1807	C₂	semidirect
10. C₂²×D₈×C₄₇	C₂²	semidirect
17. C₂×#107×C₄₇	C₂²	semidirect
18. C₂×#106×C₄₇	C₂²	semidirect
19. C₂×#102×C₄₇	C₂²	semidirect
20. C₂×#102×C₄₇	C₂²	semidirect
28. C₄₇×#340	C₂²	semidirect
29. C₄₇×#340	C₂²	semidirect
47. C₂²×C₈×C₄₇	D₄	semidirect
173. #29732	C₄₇	direct (N × H)
200. C₂×#466	C₂×C₄₇	semidirect
201. C₂²×C₂²⋊C₈	C₂×C₄₇	semidirect
202. #2847	C₂×C₄₇	semidirect
203. #2076	C₂×C₄₇	semidirect
204. #2034	C₂×C₄₇	semidirect
205. #1999	C₂×C₄₇	semidirect
206. #1893	C₂×C₄₇	semidirect
207. #1807	C₂×C₄₇	semidirect
216. C₂²×D₈	C₂²×C₄₇	semidirect
223. C₂×#107	C₂²×C₄₇	semidirect
224. C₂×#106	C₂²×C₄₇	semidirect
225. C₂×#102	C₂²×C₄₇	semidirect
226. C₂×#102	C₂²×C₄₇	semidirect
234. #340	C₂²×C₄₇	semidirect
235. #340	C₂²×C₄₇	semidirect
236. C₄₇	#29732	direct (N × H)
254. C₂²×C₈	D₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#466	2
C₂²×C₂²⋊C₈×C₄₇	2
C₄₇×#2847	2
C₄₇×#2076	2
C₄₇×#2034	2
C₄₇×#1999	2
C₄₇×#1893	2
C₄₇×#1807	2
#29732	47

Subgroups — C47×#29732 #26069430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29732 #26069430