Subgroups — C₄₇×#8341 #26048039

Order 12032.

1082 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#1797	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#1797	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×#332	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#331	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₄₇	—	2	1	no	—
7	C₄₇×#532	—	2	4	no	—
8	C₄₇×#532	—	2	4	no	—
9	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×#124×C₄₇	—	2	1	no	—
12	C₂×#121×C₄₇	—	2	1	no	—
13	C₂×#121×C₄₇	C₄	1	2	yes	—
14	C₂×C₄×D₄×C₄₇	—	2	1	no	—
15	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	—
16	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
20	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
21	C₄₇×#336	—	2	1	no	—
22	C₄₇×#336	—	2	1	no	—
23	C₄₇×#332	—	2	4	no	—
24	C₄₇×#331	—	2	4	no	—
25	C₂×#41×C₄₇	—	2	8	no	—
26	C₂×#41×C₄₇	—	4	4	no	—
27	C₂×#41×C₄₇	—	4	2	no	—
28	C₂×#41×C₄₇	—	4	2	no	—
29	C₂²×Q₈×C₄₇	—	2	1	no	—
30	C₂²×D₄×C₄₇	—	2	2	no	—
31	C₂²×D₄×C₄₇	—	2	1	no	—
32	C₂²×D₄×C₄₇	—	2	1	no	—
33	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₄₇	—	2	2	no	—
35	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₄₇	—	2	2	no	—
39	C₂²×C₈×C₄₇	—	2	2	no	—
40	C₄⋊Q₈×C₄₇	—	2	2	no	—
41	C₄⋊Q₈×C₄₇	D₄	1	4	yes	—
42	#127×C₄₇	—	2	2	no	—
43	#127×C₄₇	D₄	1	4	yes	—
44	#124×C₄₇	—	2	8	no	—
45	#121×C₄₇	—	2	8	no	—
46	#121×C₄₇	—	2	4	no	—
47	#121×C₄₇	—	2	4	no	—
48	C₄×D₄×C₄₇	—	2	8	no	—
49	C₄×D₄×C₄₇	—	2	4	no	—
50	C₄×D₄×C₄₇	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
55	C₂×C₄²×C₄₇	—	2	2	no	—
56	C₂×C₄²×C₄₇	—	2	2	no	—
57	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₄₇	—	2	2	no	—
62	C₄⋊C₈×C₄₇	—	2	2	no	—
63	C₄⋊C₈×C₄₇	—	2	2	no	—
64	C₄⋊C₈×C₄₇	—	2	2	no	—
65	C₂²⋊C₈×C₄₇	—	4	2	no	—
66	C₂²⋊C₈×C₄₇	—	4	2	no	—
67	C₂⁴×C₄₇	—	2	2	no	—
68	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
69	#41×C₄₇	—	4	16	no	—
70	#41×C₄₇	—	4	16	no	—
71	C₂×Q₈×C₄₇	—	2	4	no	—
72	C₂×Q₈×C₄₇	—	4	1	no	—
73	C₂×Q₈×C₄₇	—	4	1	no	—
74	C₂×Q₈×C₄₇	—	4	2	no	—
75	C₂×D₄×C₄₇	—	2	8	no	—
76	C₂×D₄×C₄₇	—	2	2	no	—
77	C₂×D₄×C₄₇	—	2	4	no	—
78	C₂×D₄×C₄₇	—	2	4	no	—
79	C₂×D₄×C₄₇	—	4	2	no	—
80	C₂×D₄×C₄₇	—	4	2	no	—
81	C₂×D₄×C₄₇	—	4	4	no	—
82	C₂×D₄×C₄₇	—	4	4	no	—
83	C₂×D₄×C₄₇	—	4	1	no	—
84	C₂×D₄×C₄₇	—	4	1	no	—
85	C₂×D₄×C₄₇	—	4	2	no	—
86	C₂×D₄×C₄₇	—	4	1	no	—
87	C₂×D₄×C₄₇	—	4	2	no	—
88	C₂×D₄×C₄₇	—	4	1	no	—
89	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	8	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	1	no	—
95	C₂²×C₄×C₄₇	—	2	1	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	4	1	no	—
101	C₂²×C₄×C₄₇	—	4	1	no	—
102	C₂²×C₄×C₄₇	—	4	4	no	—
103	C₂²×C₄×C₄₇	—	4	4	no	—
104	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	D₈	1	2	yes	—
108	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₄₇	—	4	2	no	—
113	C₂×C₈×C₄₇	—	4	2	no	—
114	C₂×C₈×C₄₇	—	4	2	no	—
115	C₂×C₈×C₄₇	—	4	2	no	—
116	C₂×C₈×C₄₇	—	4	2	no	—
117	C₂×C₈×C₄₇	—	4	2	no	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	4	no	—
120	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
121	C₂²⋊C₄×C₄₇	—	2	8	no	—
122	C₂²⋊C₄×C₄₇	—	2	8	no	—
123	C₄²×C₄₇	—	2	1	no	—
124	C₄²×C₄₇	—	2	1	no	—
125	C₄²×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	C₂×D₄	1	2	yes	—
128	C₄²×C₄₇	C₂×D₄	1	2	yes	—
129	C₂³×C₄₇	—	2	1	no	—
130	C₂³×C₄₇	—	2	1	no	—
131	C₂³×C₄₇	—	2	1	no	—
132	C₂³×C₄₇	—	2	1	no	—
133	C₂³×C₄₇	—	2	1	no	—
134	C₂³×C₄₇	—	2	1	no	—
135	C₂³×C₄₇	—	2	4	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	—	4	2	no	—
141	C₂³×C₄₇	—	4	2	no	—
142	C₂³×C₄₇	#102	1	2	yes	—
143	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	Q₈×C₄₇	—	4	4	no	—
145	Q₈×C₄₇	—	4	4	no	—
146	D₄×C₄₇	—	4	4	no	—
147	D₄×C₄₇	—	4	4	no	—
148	D₄×C₄₇	—	4	16	no	—
149	D₄×C₄₇	—	4	4	no	—
150	D₄×C₄₇	—	4	4	no	—
151	D₄×C₄₇	—	4	4	no	—
152	D₄×C₄₇	—	4	4	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	1	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	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	4	16	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	#102	1	2	yes	—
174	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	#120	1	2	yes	—
177	C₂×C₄×C₄₇	#120	1	2	yes	—
178	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
180	C₂×C₄×C₄₇	#135	1	2	yes	—
181	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
182	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
184	C₈×C₄₇	—	8	2	no	—
185	C₈×C₄₇	—	8	2	no	—
186	#8341	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	—	2	2	no	—
189	C₂²×C₄₇	—	2	2	no	—
190	C₂²×C₄₇	—	4	1	no	—
191	C₂²×C₄₇	—	4	1	no	—
192	C₂²×C₄₇	—	4	1	no	—
193	C₂²×C₄₇	—	4	1	no	—
194	C₂²×C₄₇	—	4	4	no	—
195	C₂²×C₄₇	—	4	4	no	—
196	C₂²×C₄₇	—	4	4	no	—
197	C₂²×C₄₇	—	8	2	no	—
198	C₂²×C₄₇	—	8	2	no	—
199	C₂²×C₄₇	—	8	2	no	—
200	C₂²×C₄₇	—	8	2	no	—
201	C₂²×C₄₇	#379	1	1	yes	characteristic
202	C₂²×C₄₇	#413	1	1	yes	characteristic
203	C₂²×C₄₇	#413	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
205	C₂²×C₄₇	#416	1	1	yes	characteristic
206	C₂²×C₄₇	#417	1	1	yes	characteristic
207	C₂²×C₄₇	#418	1	1	yes	characteristic
208	C₄×C₄₇	—	2	1	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	2	2	no	—
211	C₄×C₄₇	—	4	1	no	—
212	C₄×C₄₇	—	4	4	no	—
213	C₄×C₄₇	—	4	1	no	—
214	C₄×C₄₇	#447	1	2	yes	—
215	C₄×C₄₇	#449	1	2	yes	—
216	C₄×C₄₇	#450	1	2	yes	—
217	C₄×C₄₇	#452	1	2	yes	—
218	C₂×#532	C₂×C₄₇	1	1	yes	characteristic
219	#1797	C₂×C₄₇	1	1	yes	characteristic, complemented
220	#1797	C₂×C₄₇	1	1	yes	characteristic, complemented
221	C₂×#332	C₂×C₄₇	1	2	yes	complemented
222	C₂×#331	C₂×C₄₇	1	2	yes	complemented
223	C₂×C₄₇	—	4	2	no	—
224	C₂×C₄₇	—	8	4	no	—
225	C₂×C₄₇	#1540	1	1	yes	characteristic
226	C₂×C₄₇	#1547	1	1	yes	characteristic
227	C₂×C₄₇	#1553	1	1	yes	characteristic
228	C₂×C₄₇	#1557	1	1	yes	characteristic
229	C₂×C₄₇	#1785	1	1	yes	characteristic
230	C₂×C₄₇	#1786	1	1	yes	characteristic
231	C₂×C₄₇	#1788	1	1	yes	characteristic
232	C₂²×#41	—	2	1	no	—
233	#532	—	2	4	no	—
234	#532	—	2	4	no	—
235	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
236	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
237	C₂×#124	—	2	1	no	—
238	C₂×#121	—	2	1	no	—
239	C₂×#121	C₄×C₄₇	1	2	yes	—
240	C₂×C₄×D₄	—	2	1	no	—
241	C₂×C₄×D₄	C₄×C₄₇	1	2	yes	—
242	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
244	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
245	C₂×C₂²⋊C₈	—	2	1	no	—
246	C₂×C₂²⋊C₈	—	2	1	no	—
247	#336	—	2	1	no	—
248	#336	—	2	1	no	—
249	#332	—	2	4	no	—
250	#331	—	2	4	no	—
251	C₄₇	#8341	1	1	yes	characteristic, direct product factor, Sylow
252	C₂×#41	—	2	8	no	—
253	C₂×#41	—	4	4	no	—
254	C₂×#41	—	4	2	no	—
255	C₂×#41	—	4	2	no	—
256	C₂²×Q₈	—	2	1	no	—
257	C₂²×D₄	—	2	2	no	—
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
261	C₂³×C₄	—	2	2	no	—
262	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
263	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
264	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
265	C₂²×C₈	—	2	2	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₄⋊Q₈	—	2	2	no	—
268	C₄⋊Q₈	D₄×C₄₇	1	4	yes	—
269	#127	—	2	2	no	—
270	#127	D₄×C₄₇	1	4	yes	—
271	#124	—	2	8	no	—
272	#121	—	2	8	no	—
273	#121	—	2	4	no	—
274	#121	—	2	4	no	—
275	C₄×D₄	—	2	8	no	—
276	C₄×D₄	—	2	4	no	—
277	C₄×D₄	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₄²	—	2	2	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
285	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
286	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
288	C₄⋊C₈	—	2	2	no	—
289	C₄⋊C₈	—	2	2	no	—
290	C₄⋊C₈	—	2	2	no	—
291	C₄⋊C₈	—	2	2	no	—
292	C₂²⋊C₈	—	4	2	no	—
293	C₂²⋊C₈	—	4	2	no	—
294	C₂⁴	—	2	2	no	—
295	C₂⁴	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
296	#41	—	4	16	no	—
297	#41	—	4	16	no	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×Q₈	—	4	1	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×D₄	—	2	8	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	4	no	—
309	C₂×D₄	—	4	4	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	C₂²⋊C₄×C₄₇	1	4	yes	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	4	no	—
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
332	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
333	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
334	C₂²×C₄	D₈×C₄₇	1	2	yes	—
335	C₂²×C₄	SD₁₆×C₄₇	1	2	yes	—
336	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
339	C₂×C₈	—	4	2	no	—
340	C₂×C₈	—	4	2	no	—
341	C₂×C₈	—	4	2	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	—	4	2	no	—
344	C₂×C₈	—	4	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₂²⋊C₄	—	2	8	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	C₂×D₄×C₄₇	1	2	yes	—
355	C₄²	C₂×D₄×C₄₇	1	2	yes	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	#102×C₄₇	1	2	yes	—
370	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
371	Q₈	—	4	4	no	—
372	Q₈	—	4	4	no	—
373	D₄	—	4	4	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	16	no	—
376	D₄	—	4	4	no	—
377	D₄	—	4	4	no	—
378	D₄	—	4	4	no	—
379	D₄	—	4	4	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	16	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	#102×C₄₇	1	2	yes	—
401	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
402	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
403	C₂×C₄	#120×C₄₇	1	2	yes	—
404	C₂×C₄	#120×C₄₇	1	2	yes	—
405	C₂×C₄	C₂×D₈×C₄₇	1	1	yes	characteristic
406	C₂×C₄	C₂×SD₁₆×C₄₇	1	1	yes	characteristic
407	C₂×C₄	#135×C₄₇	1	2	yes	—
408	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
409	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
410	C₂×C₄	#137×C₄₇	1	1	yes	characteristic
411	C₈	—	8	2	no	—
412	C₈	—	8	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	C₄₇×#379	1	1	yes	characteristic
428	C₂²	C₄₇×#413	1	1	yes	characteristic
429	C₂²	C₄₇×#413	1	1	yes	characteristic
430	C₂²	C₂×#102×C₄₇	1	1	yes	characteristic
431	C₂²	C₄₇×#416	1	1	yes	characteristic
432	C₂²	C₄₇×#417	1	1	yes	characteristic
433	C₂²	C₄₇×#418	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	2	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	1	no	—
440	C₄	C₄₇×#447	1	2	yes	—
441	C₄	C₄₇×#449	1	2	yes	—
442	C₄	C₄₇×#450	1	2	yes	—
443	C₄	C₄₇×#452	1	2	yes	—
444	C₂	—	4	2	no	—
445	C₂	—	8	4	no	—
446	C₂	C₄₇×#1540	1	1	yes	characteristic
447	C₂	C₄₇×#1547	1	1	yes	characteristic
448	C₂	C₄₇×#1553	1	1	yes	characteristic
449	C₂	C₄₇×#1557	1	1	yes	characteristic
450	C₂	C₄₇×#1785	1	1	yes	characteristic
451	C₂	C₄₇×#1786	1	1	yes	characteristic
452	C₂	C₄₇×#1788	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₄₇
Frattini, cosocle	C₂×C₄²	C₂³×C₄₇
prime radical	C₂×C₄₇×#532	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ 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
2. C₄₇×#1797	C₂	semidirect
3. C₄₇×#1797	C₂	semidirect
4. C₂×C₄₇×#332	C₂	semidirect
5. C₂×C₄₇×#331	C₂	semidirect
186. #8341	C₄₇	direct (N × H)
219. #1797	C₂×C₄₇	semidirect
220. #1797	C₂×C₄₇	semidirect
221. C₂×#332	C₂×C₄₇	semidirect
222. C₂×#331	C₂×C₄₇	semidirect
251. C₄₇	#8341	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#532	2
C₄₇×#1797	2
C₂×C₄₇×#332	2
C₂×C₄₇×#331	2
#8341	47

Subgroups — C47×#8341 #26048039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#8341 #26048039