Subgroups — C₂×C₄₇×#2013 #26063117

Order 12032.

2254 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×SD₁₆×C₄₇	C₂	1	2	yes	maximal
2	C₂²×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#103×C₄₇	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₇×#390	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#2013	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×Q₈×C₄₇	C₂²	1	2	yes	—
8	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂²×SD₁₆×C₄₇	—	2	8	no	—
10	C₂²×SD₁₆×C₄₇	—	2	8	no	—
11	C₂²×SD₁₆×C₄₇	—	2	8	no	—
12	C₂²×SD₁₆×C₄₇	C₂²	1	8	yes	—
13	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₄₇	—	2	8	no	—
15	C₂×C₄⋊Q₈×C₄₇	—	2	2	no	—
16	C₂×C₄⋊Q₈×C₄₇	C₂²	1	4	yes	complemented
17	C₂²×C₄⋊C₄×C₄₇	—	2	2	no	—
18	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₄₇	—	2	2	no	—
20	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#103×C₄₇	—	2	8	no	—
22	C₂×#103×C₄₇	C₂²	1	8	yes	complemented
23	C₄₇×#390	—	2	2	no	—
24	C₄₇×#390	C₂²	1	4	yes	—
25	C₄₇×#336	C₂²	1	4	yes	complemented
26	C₂⁵×C₄₇	—	2	1	no	—
27	C₂²×Q₈×C₄₇	—	2	4	no	—
28	C₂²×Q₈×C₄₇	—	2	2	no	—
29	C₂²×Q₈×C₄₇	—	2	4	no	—
30	C₂²×Q₈×C₄₇	—	2	4	no	—
31	C₂²×Q₈×C₄₇	—	2	4	no	—
32	C₂²×Q₈×C₄₇	—	2	4	no	—
33	C₂²×Q₈×C₄₇	D₄	1	8	yes	—
34	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
35	C₂²×D₄×C₄₇	—	2	4	no	—
36	C₂²×D₄×C₄₇	—	2	4	no	—
37	C₂²×D₄×C₄₇	—	2	1	no	—
38	C₂²×D₄×C₄₇	—	2	2	no	—
39	C₂²×D₄×C₄₇	D₄	1	4	yes	—
40	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₇	—	2	2	no	—
42	C₂³×C₄×C₄₇	—	2	1	no	—
43	C₂³×C₄×C₄₇	D₄	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂×SD₁₆×C₄₇	—	2	64	no	—
46	C₂×SD₁₆×C₄₇	—	2	16	no	—
47	C₂×SD₁₆×C₄₇	—	2	16	no	—
48	C₂×SD₁₆×C₄₇	—	2	16	no	—
49	C₂²×C₈×C₄₇	—	2	4	no	—
50	C₂²×C₈×C₄₇	—	2	4	no	—
51	C₂²×C₈×C₄₇	D₄	1	8	yes	—
52	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
53	C₄⋊Q₈×C₄₇	—	2	16	no	—
54	C₄⋊Q₈×C₄₇	—	2	16	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	16	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
61	C₂×C₂²⋊C₄×C₄₇	—	4	8	no	—
62	C₂×C₄²×C₄₇	—	2	4	no	—
63	C₂×C₄²×C₄₇	D₄	1	2	yes	—
64	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
65	#103×C₄₇	—	2	16	no	—
66	C₂⁴×C₄₇	—	2	4	no	—
67	C₂⁴×C₄₇	—	2	2	no	—
68	C₂⁴×C₄₇	—	4	2	no	—
69	C₂⁴×C₄₇	—	4	2	no	—
70	C₂⁴×C₄₇	—	4	4	no	—
71	C₂⁴×C₄₇	—	4	4	no	—
72	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
73	C₂×Q₈×C₄₇	—	2	8	no	—
74	C₂×Q₈×C₄₇	—	2	4	no	—
75	C₂×Q₈×C₄₇	—	2	16	no	—
76	C₂×Q₈×C₄₇	—	2	16	no	—
77	C₂×Q₈×C₄₇	—	2	4	no	—
78	C₂×Q₈×C₄₇	—	2	4	no	—
79	C₂×Q₈×C₄₇	—	2	4	no	—
80	C₂×Q₈×C₄₇	—	2	4	no	—
81	C₂×Q₈×C₄₇	—	4	8	no	—
82	C₂×Q₈×C₄₇	—	4	4	no	—
83	C₂×Q₈×C₄₇	—	4	8	no	—
84	C₂×Q₈×C₄₇	—	4	4	no	—
85	C₂×Q₈×C₄₇	C₂×D₄	1	8	yes	—
86	C₂×D₄×C₄₇	—	2	16	no	—
87	C₂×D₄×C₄₇	—	2	4	no	—
88	C₂×D₄×C₄₇	—	2	4	no	—
89	C₂×D₄×C₄₇	—	2	4	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	—	4	2	no	—
92	C₂×D₄×C₄₇	—	4	8	no	—
93	C₂×D₄×C₄₇	—	4	2	no	—
94	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	2	8	no	—
98	C₂²×C₄×C₄₇	—	2	4	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	4	4	no	—
101	C₂²×C₄×C₄₇	—	4	4	no	—
102	C₂²×C₄×C₄₇	—	4	2	no	—
103	C₂²×C₄×C₄₇	—	4	4	no	—
104	C₂²×C₄×C₄₇	SD₁₆	1	8	yes	complemented
105	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₄₇	#41	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
112	SD₁₆×C₄₇	—	2	64	no	—
113	C₂×C₈×C₄₇	—	2	16	no	—
114	C₂×C₈×C₄₇	—	2	4	no	—
115	C₂×C₈×C₄₇	—	2	4	no	—
116	C₂×C₈×C₄₇	C₂×D₄	1	8	yes	—
117	C₄⋊C₄×C₄₇	—	2	32	no	—
118	C₄⋊C₄×C₄₇	—	2	4	no	—
119	C₄⋊C₄×C₄₇	—	4	2	no	—
120	C₂²⋊C₄×C₄₇	—	4	16	no	—
121	C₄²×C₄₇	—	2	4	no	—
122	C₄²×C₄₇	—	2	4	no	—
123	C₂³×C₄₇	—	2	4	no	—
124	C₂³×C₄₇	—	4	2	no	—
125	C₂³×C₄₇	—	4	2	no	—
126	C₂³×C₄₇	—	4	4	no	—
127	C₂³×C₄₇	—	4	4	no	—
128	C₂³×C₄₇	—	4	8	no	—
129	C₂³×C₄₇	—	4	16	no	—
130	C₂³×C₄₇	—	8	8	no	—
131	C₂³×C₄₇	—	8	4	no	—
132	C₂³×C₄₇	—	8	4	no	—
133	C₂³×C₄₇	#120	1	2	yes	—
134	C₂³×C₄₇	#121	1	2	yes	—
135	C₂³×C₄₇	#127	1	2	yes	—
136	C₂³×C₄₇	C₂×SD₁₆	1	4	yes	—
137	C₂³×C₄₇	#137	1	4	yes	—
138	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₄₇	—	2	8	no	—
140	Q₈×C₄₇	—	2	8	no	—
141	Q₈×C₄₇	—	4	4	no	—
142	Q₈×C₄₇	—	4	4	no	—
143	Q₈×C₄₇	—	4	16	no	—
144	D₄×C₄₇	—	2	8	no	—
145	D₄×C₄₇	—	4	4	no	—
146	D₄×C₄₇	—	4	8	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	16	no	—
150	C₂×C₄×C₄₇	—	2	8	no	—
151	C₂×C₄×C₄₇	—	4	4	no	—
152	C₂×C₄×C₄₇	—	4	4	no	—
153	C₂×C₄×C₄₇	—	4	16	no	—
154	C₂×C₄×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	—	4	4	no	—
156	C₂×C₄×C₄₇	—	8	4	no	—
157	C₂×C₄×C₄₇	#120	1	8	yes	—
158	C₂×C₄×C₄₇	#120	1	2	yes	—
159	C₂×C₄×C₄₇	#121	1	8	yes	—
160	C₂×C₄×C₄₇	#121	1	2	yes	—
161	C₂×C₄×C₄₇	#127	1	2	yes	—
162	C₂×C₄×C₄₇	C₂×SD₁₆	1	8	yes	complemented
163	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
166	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
167	C₈×C₄₇	—	2	8	no	—
168	C₂×#2013	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂²×C₄₇	—	4	4	no	—
170	C₂²×C₄₇	—	4	8	no	—
171	C₂²×C₄₇	—	8	2	no	—
172	C₂²×C₄₇	—	8	2	no	—
173	C₂²×C₄₇	—	8	4	no	—
174	C₂²×C₄₇	—	8	16	no	—
175	C₂²×C₄₇	#392	1	4	yes	—
176	C₂²×C₄₇	#448	1	8	yes	—
177	C₂²×C₄₇	#461	1	8	yes	—
178	C₂²×C₄₇	#492	1	4	yes	—
179	C₂²×C₄₇	#497	1	4	yes	—
180	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
181	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
182	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
183	C₂²×C₄₇	C₂²×SD₁₆	1	2	yes	—
184	C₂²×C₄₇	C₂×#137	1	2	yes	—
185	C₄×C₄₇	—	2	8	no	—
186	C₄×C₄₇	—	4	8	no	—
187	C₄×C₄₇	—	8	2	no	—
188	C₄×C₄₇	#392	1	4	yes	—
189	C₄×C₄₇	C₂×#120	1	2	yes	—
190	C₄×C₄₇	C₂×#121	1	2	yes	—
191	C₂³×SD₁₆	C₂×C₄₇	1	2	yes	—
192	C₂²×C₄⋊Q₈	C₂×C₄₇	1	1	yes	characteristic, complemented
193	C₂²×#103	C₂×C₄₇	1	2	yes	complemented
194	C₂×#390	C₂×C₄₇	1	1	yes	characteristic
195	#2013	C₂×C₄₇	1	8	yes	direct product factor
196	C₂×#336	C₂×C₄₇	1	1	yes	characteristic, complemented
197	C₂×C₄₇	—	8	4	no	—
198	C₂×C₄₇	#2013	1	8	yes	direct product factor
199	C₂×C₄₇	C₂×#392	1	1	yes	characteristic
200	C₂×C₄₇	C₂×#448	1	2	yes	—
201	C₂×C₄₇	C₂×#461	1	2	yes	—
202	C₂×C₄₇	C₂×#492	1	1	yes	characteristic
203	C₂×C₄₇	C₂×#497	1	1	yes	characteristic
204	C₂³×Q₈	C₂²×C₄₇	1	2	yes	—
205	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
206	C₂²×SD₁₆	—	2	8	no	—
207	C₂²×SD₁₆	—	2	8	no	—
208	C₂²×SD₁₆	—	2	8	no	—
209	C₂²×SD₁₆	C₂²×C₄₇	1	8	yes	—
210	C₂³×C₈	C₂²×C₄₇	1	2	yes	—
211	C₂×C₄⋊Q₈	—	2	8	no	—
212	C₂×C₄⋊Q₈	—	2	2	no	—
213	C₂×C₄⋊Q₈	C₂²×C₄₇	1	4	yes	complemented
214	C₂²×C₄⋊C₄	—	2	2	no	—
215	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
216	C₂²×C₂²⋊C₄	—	2	2	no	—
217	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
218	C₂×#103	—	2	8	no	—
219	C₂×#103	C₂²×C₄₇	1	8	yes	complemented
220	#390	—	2	2	no	—
221	#390	C₂²×C₄₇	1	4	yes	—
222	#336	C₂²×C₄₇	1	4	yes	complemented
223	C₄₇	C₂×#2013	1	1	yes	characteristic, direct product factor, Sylow
224	C₂⁵	—	2	1	no	—
225	C₂²×Q₈	—	2	4	no	—
226	C₂²×Q₈	—	2	2	no	—
227	C₂²×Q₈	—	2	4	no	—
228	C₂²×Q₈	—	2	4	no	—
229	C₂²×Q₈	—	2	4	no	—
230	C₂²×Q₈	—	2	4	no	—
231	C₂²×Q₈	D₄×C₄₇	1	8	yes	—
232	C₂²×Q₈	C₂³×C₄₇	1	4	yes	—
233	C₂²×D₄	—	2	4	no	—
234	C₂²×D₄	—	2	4	no	—
235	C₂²×D₄	—	2	1	no	—
236	C₂²×D₄	—	2	2	no	—
237	C₂²×D₄	D₄×C₄₇	1	4	yes	—
238	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
239	C₂³×C₄	—	2	2	no	—
240	C₂³×C₄	—	2	1	no	—
241	C₂³×C₄	D₄×C₄₇	1	2	yes	—
242	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
243	C₂×SD₁₆	—	2	64	no	—
244	C₂×SD₁₆	—	2	16	no	—
245	C₂×SD₁₆	—	2	16	no	—
246	C₂×SD₁₆	—	2	16	no	—
247	C₂²×C₈	—	2	4	no	—
248	C₂²×C₈	—	2	4	no	—
249	C₂²×C₈	D₄×C₄₇	1	8	yes	—
250	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
251	C₄⋊Q₈	—	2	16	no	—
252	C₄⋊Q₈	—	2	16	no	—
253	C₂×C₄⋊C₄	—	2	16	no	—
254	C₂×C₄⋊C₄	—	2	8	no	—
255	C₂×C₄⋊C₄	—	2	4	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	8	no	—
259	C₂×C₂²⋊C₄	—	4	8	no	—
260	C₂×C₄²	—	2	4	no	—
261	C₂×C₄²	D₄×C₄₇	1	2	yes	—
262	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
263	#103	—	2	16	no	—
264	C₂⁴	—	2	4	no	—
265	C₂⁴	—	2	2	no	—
266	C₂⁴	—	4	2	no	—
267	C₂⁴	—	4	2	no	—
268	C₂⁴	—	4	4	no	—
269	C₂⁴	—	4	4	no	—
270	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
271	C₂×Q₈	—	2	8	no	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	2	16	no	—
274	C₂×Q₈	—	2	16	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	—	2	4	no	—
279	C₂×Q₈	—	4	8	no	—
280	C₂×Q₈	—	4	4	no	—
281	C₂×Q₈	—	4	8	no	—
282	C₂×Q₈	—	4	4	no	—
283	C₂×Q₈	C₂×D₄×C₄₇	1	8	yes	—
284	C₂×D₄	—	2	16	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	8	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	8	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	4	no	—
302	C₂²×C₄	SD₁₆×C₄₇	1	8	yes	complemented
303	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
304	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
306	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
308	C₂²×C₄	#41×C₄₇	1	2	yes	—
309	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
310	SD₁₆	—	2	64	no	—
311	C₂×C₈	—	2	16	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	C₂×D₄×C₄₇	1	8	yes	—
315	C₄⋊C₄	—	2	32	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₂²⋊C₄	—	4	16	no	—
319	C₄²	—	2	4	no	—
320	C₄²	—	2	4	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	4	16	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	4	no	—
327	C₂³	—	4	8	no	—
328	C₂³	—	8	4	no	—
329	C₂³	—	8	4	no	—
330	C₂³	—	8	8	no	—
331	C₂³	#120×C₄₇	1	2	yes	—
332	C₂³	#121×C₄₇	1	2	yes	—
333	C₂³	#127×C₄₇	1	2	yes	—
334	C₂³	C₂×SD₁₆×C₄₇	1	4	yes	—
335	C₂³	#137×C₄₇	1	4	yes	—
336	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
337	Q₈	—	2	8	no	—
338	Q₈	—	2	8	no	—
339	Q₈	—	4	4	no	—
340	Q₈	—	4	4	no	—
341	Q₈	—	4	16	no	—
342	D₄	—	2	8	no	—
343	D₄	—	4	4	no	—
344	D₄	—	4	8	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	16	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	16	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	8	4	no	—
355	C₂×C₄	#120×C₄₇	1	8	yes	—
356	C₂×C₄	#120×C₄₇	1	2	yes	—
357	C₂×C₄	#121×C₄₇	1	8	yes	—
358	C₂×C₄	#121×C₄₇	1	2	yes	—
359	C₂×C₄	#127×C₄₇	1	2	yes	—
360	C₂×C₄	C₂×SD₁₆×C₄₇	1	8	yes	complemented
361	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
362	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
363	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
364	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
365	C₈	—	2	8	no	—
366	C₂²	—	4	8	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	8	16	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	4	no	—
372	C₂²	C₄₇×#392	1	4	yes	—
373	C₂²	C₄₇×#448	1	8	yes	—
374	C₂²	C₄₇×#461	1	8	yes	—
375	C₂²	C₄₇×#492	1	4	yes	—
376	C₂²	C₄₇×#497	1	4	yes	—
377	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
378	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
379	C₂²	C₂×#127×C₄₇	1	1	yes	characteristic
380	C₂²	C₂²×SD₁₆×C₄₇	1	2	yes	—
381	C₂²	C₂×#137×C₄₇	1	2	yes	—
382	C₄	—	2	8	no	—
383	C₄	—	4	8	no	—
384	C₄	—	8	2	no	—
385	C₄	C₄₇×#392	1	4	yes	—
386	C₄	C₂×#120×C₄₇	1	2	yes	—
387	C₄	C₂×#121×C₄₇	1	2	yes	—
388	C₂	—	8	4	no	—
389	C₂	C₄₇×#2013	1	8	yes	direct product factor
390	C₂	C₂×C₄₇×#392	1	1	yes	characteristic
391	C₂	C₂×C₄₇×#448	1	2	yes	—
392	C₂	C₂×C₄₇×#461	1	2	yes	—
393	C₂	C₂×C₄₇×#492	1	1	yes	characteristic
394	C₂	C₂×C₄₇×#497	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊Q₈×C₄₇	C₂	semidirect
3. C₂²×#103×C₄₇	C₂	semidirect
5. C₄₇×#2013	C₂	direct (N × H)
6. C₂×C₄₇×#336	C₂	semidirect
16. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
22. C₂×#103×C₄₇	C₂²	semidirect
25. C₄₇×#336	C₂²	semidirect
104. C₂²×C₄×C₄₇	SD₁₆	semidirect
162. C₂×C₄×C₄₇	C₂×SD₁₆	semidirect
168. C₂×#2013	C₄₇	direct (N × H)
192. C₂²×C₄⋊Q₈	C₂×C₄₇	semidirect
193. C₂²×#103	C₂×C₄₇	semidirect
195. #2013	C₂×C₄₇	direct (N × H)
196. C₂×#336	C₂×C₄₇	semidirect
198. C₂×C₄₇	#2013	direct (N × H)
213. C₂×C₄⋊Q₈	C₂²×C₄₇	semidirect
219. C₂×#103	C₂²×C₄₇	semidirect
222. #336	C₂²×C₄₇	semidirect
223. C₄₇	C₂×#2013	direct (N × H)
302. C₂²×C₄	SD₁₆×C₄₇	semidirect
360. C₂×C₄	C₂×SD₁₆×C₄₇	semidirect
389. C₂	C₄₇×#2013	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×SD₁₆×C₄₇	2
C₂²×C₄⋊Q₈×C₄₇	2
C₂²×#103×C₄₇	2
C₂×C₄₇×#390	2
C₄₇×#2013	2
C₂×C₄₇×#336	2
C₂×#2013	47

Subgroups — C2×C47×#2013 #26063117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2013 #26063117