Subgroups — C₂×C₄₇×#1885 #26060646

Order 12032.

1966 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#518	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#419	C₂	1	2	yes	maximal, complemented
4	C₂²×#100×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1885	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₇×#339	C₂	1	2	yes	maximal, complemented
7	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
10	C₂×#124×C₄₇	—	2	4	no	—
11	C₂×#124×C₄₇	—	2	2	no	—
12	C₂×#124×C₄₇	C₄	1	8	yes	complemented
13	C₂×#124×C₄₇	C₂²	1	4	yes	—
14	C₄₇×#518	—	2	2	no	—
15	C₄₇×#518	—	2	4	no	—
16	C₄₇×#518	C₂²	1	4	yes	—
17	C₂×C₄×D₄×C₄₇	—	2	4	no	—
18	C₂×#117×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₄₇	—	2	2	no	—
20	C₂²×C₂²⋊C₄×C₄₇	—	2	2	no	—
21	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#419	—	2	4	no	—
23	C₄₇×#419	C₂²	1	8	yes	complemented
24	C₂×#103×C₄₇	—	2	4	no	—
25	C₂×#100×C₄₇	—	2	4	no	—
26	C₂×#100×C₄₇	C₂²	1	4	yes	—
27	C₄₇×#339	C₂²	1	8	yes	complemented
28	C₂⁵×C₄₇	D₄	1	2	yes	—
29	C₂²×Q₈×C₄₇	—	2	2	no	—
30	C₂²×Q₈×C₄₇	—	2	1	no	—
31	C₂²×Q₈×C₄₇	—	2	2	no	—
32	C₂²×Q₈×C₄₇	—	2	2	no	—
33	C₂²×Q₈×C₄₇	—	2	4	no	—
34	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
35	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
36	C₂²×D₄×C₄₇	—	2	2	no	—
37	C₂²×D₄×C₄₇	—	2	2	no	—
38	C₂²×D₄×C₄₇	—	2	4	no	—
39	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
40	C₂²×D₄×C₄₇	D₄	1	2	yes	—
41	C₂²×D₄×C₄₇	D₄	1	4	yes	—
42	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₇	—	2	1	no	—
44	C₂³×C₄×C₄₇	—	2	1	no	—
45	C₂³×C₄×C₄₇	—	2	4	no	—
46	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₄₇	—	2	2	no	—
48	C₂×M₁₆×C₄₇	—	2	4	no	—
49	C₂×M₁₆×C₄₇	—	2	4	no	—
50	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
51	C₂²×C₈×C₄₇	—	2	2	no	—
52	#124×C₄₇	—	2	16	no	—
53	#124×C₄₇	—	2	8	no	—
54	#124×C₄₇	C₂×C₄	1	16	yes	complemented
55	C₄×D₄×C₄₇	—	2	16	no	—
56	C₄×D₄×C₄₇	—	2	16	no	—
57	#117×C₄₇	—	2	2	no	—
58	#117×C₄₇	—	2	2	no	—
59	#117×C₄₇	D₄	1	4	yes	—
60	#117×C₄₇	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
62	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
64	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
68	C₂×C₄²×C₄₇	—	2	1	no	—
69	C₂×C₄²×C₄₇	—	2	2	no	—
70	C₂×C₄²×C₄₇	—	2	2	no	—
71	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	complemented
72	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
73	#103×C₄₇	—	2	16	no	—
74	#100×C₄₇	—	2	8	no	—
75	C₂⁴×C₄₇	—	2	2	no	—
76	C₂⁴×C₄₇	—	2	2	no	—
77	C₂⁴×C₄₇	—	2	4	no	—
78	C₂⁴×C₄₇	—	4	8	no	—
79	C₂⁴×C₄₇	C₂²⋊C₄	1	8	yes	—
80	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
82	C₂×Q₈×C₄₇	—	2	4	no	—
83	C₂×Q₈×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	—	2	8	no	—
85	C₂×Q₈×C₄₇	—	2	8	no	—
86	C₂×Q₈×C₄₇	—	2	4	no	—
87	C₂×Q₈×C₄₇	—	2	4	no	—
88	C₂×Q₈×C₄₇	—	4	2	no	—
89	C₂×Q₈×C₄₇	—	4	4	no	—
90	C₂×Q₈×C₄₇	—	4	4	no	—
91	C₂×Q₈×C₄₇	—	4	2	no	—
92	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	complemented
93	C₂×D₄×C₄₇	—	2	8	no	—
94	C₂×D₄×C₄₇	—	2	8	no	—
95	C₂×D₄×C₄₇	—	2	4	no	—
96	C₂×D₄×C₄₇	—	2	8	no	—
97	C₂×D₄×C₄₇	—	2	8	no	—
98	C₂×D₄×C₄₇	—	2	4	no	—
99	C₂×D₄×C₄₇	—	2	4	no	—
100	C₂×D₄×C₄₇	—	2	4	no	—
101	C₂×D₄×C₄₇	C₂²⋊C₄	1	8	yes	—
102	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
103	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₄₇	—	2	4	no	—
105	C₂²×C₄×C₄₇	—	2	4	no	—
106	C₂²×C₄×C₄₇	—	2	4	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	16	no	—
110	C₂²×C₄×C₄₇	—	4	4	no	—
111	C₂²×C₄×C₄₇	—	4	1	no	—
112	C₂²×C₄×C₄₇	—	4	1	no	—
113	C₂²×C₄×C₄₇	—	4	2	no	—
114	C₂²×C₄×C₄₇	—	8	8	no	—
115	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₇	#41	1	4	yes	—
121	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
122	M₁₆×C₄₇	—	2	4	no	—
123	M₁₆×C₄₇	—	2	4	no	—
124	M₁₆×C₄₇	—	4	4	no	—
125	C₂×C₈×C₄₇	—	2	4	no	—
126	C₂×C₈×C₄₇	—	4	4	no	—
127	C₄⋊C₄×C₄₇	—	2	4	no	—
128	C₄⋊C₄×C₄₇	C₂×D₄	1	8	yes	—
129	C₂²⋊C₄×C₄₇	—	2	16	no	—
130	C₂²⋊C₄×C₄₇	—	2	32	no	—
131	C₂²⋊C₄×C₄₇	—	2	4	no	—
132	C₂²⋊C₄×C₄₇	—	2	4	no	—
133	C₄²×C₄₇	—	2	4	no	—
134	C₄²×C₄₇	—	2	4	no	—
135	C₄²×C₄₇	—	2	2	no	—
136	C₄²×C₄₇	—	2	4	no	—
137	C₄²×C₄₇	C₂²×C₄	1	4	yes	complemented
138	C₂³×C₄₇	—	2	4	no	—
139	C₂³×C₄₇	—	2	4	no	—
140	C₂³×C₄₇	—	2	8	no	—
141	C₂³×C₄₇	—	2	4	no	—
142	C₂³×C₄₇	—	2	8	no	—
143	C₂³×C₄₇	—	4	16	no	—
144	C₂³×C₄₇	—	4	8	no	—
145	C₂³×C₄₇	—	4	8	no	—
146	C₂³×C₄₇	—	8	8	no	—
147	C₂³×C₄₇	—	8	4	no	—
148	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂³×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
150	C₂³×C₄₇	#120	1	1	yes	characteristic
151	C₂³×C₄₇	#120	1	1	yes	characteristic
152	C₂³×C₄₇	#123	1	2	yes	—
153	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	Q₈×C₄₇	—	2	8	no	—
155	Q₈×C₄₇	—	4	4	no	—
156	Q₈×C₄₇	—	4	8	no	—
157	D₄×C₄₇	—	2	8	no	—
158	D₄×C₄₇	—	2	8	no	—
159	D₄×C₄₇	—	2	16	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	2	8	no	—
163	C₂×C₄×C₄₇	—	4	8	no	—
164	C₂×C₄×C₄₇	—	4	4	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	4	no	—
168	C₂×C₄×C₄₇	—	4	4	no	—
169	C₂×C₄×C₄₇	—	4	8	no	—
170	C₂×C₄×C₄₇	—	8	16	no	—
171	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
173	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
174	C₂×C₄×C₄₇	#120	1	2	yes	—
175	C₂×C₄×C₄₇	#121	1	4	yes	—
176	C₂×C₄×C₄₇	#121	1	4	yes	—
177	C₂×C₄×C₄₇	#123	1	2	yes	—
178	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
180	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
182	C₈×C₄₇	—	4	4	no	—
183	C₂×#1885	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₄₇	—	2	4	no	—
185	C₂²×C₄₇	—	2	4	no	—
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	—	2	8	no	—
189	C₂²×C₄₇	—	4	8	no	—
190	C₂²×C₄₇	—	4	16	no	—
191	C₂²×C₄₇	—	4	8	no	—
192	C₂²×C₄₇	—	8	4	no	—
193	C₂²×C₄₇	—	8	8	no	—
194	C₂²×C₄₇	#386	1	2	yes	—
195	C₂²×C₄₇	#386	1	2	yes	—
196	C₂²×C₄₇	#455	1	4	yes	—
197	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
198	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
199	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
200	C₄×C₄₇	—	4	4	no	—
201	C₄×C₄₇	—	4	8	no	—
202	C₄×C₄₇	—	4	4	no	—
203	C₄×C₄₇	#386	1	4	yes	—
204	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
205	C₄×C₄₇	C₂×#121	1	2	yes	—
206	C₂²×#124	C₂×C₄₇	1	1	yes	characteristic
207	C₂×#518	C₂×C₄₇	1	1	yes	characteristic
208	C₂×#419	C₂×C₄₇	1	2	yes	complemented
209	C₂²×#100	C₂×C₄₇	1	1	yes	characteristic
210	#1885	C₂×C₄₇	1	8	yes	direct product factor
211	C₂×#339	C₂×C₄₇	1	2	yes	complemented
212	C₂×C₄₇	—	2	1	no	—
213	C₂×C₄₇	—	2	1	no	—
214	C₂×C₄₇	—	2	2	no	—
215	C₂×C₄₇	—	4	8	no	—
216	C₂×C₄₇	#1885	1	4	yes	direct product factor
217	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
218	C₂×C₄₇	C₂×#455	1	2	yes	—
219	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
220	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
221	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
222	C₂×#124	—	2	4	no	—
223	C₂×#124	—	2	2	no	—
224	C₂×#124	C₄×C₄₇	1	8	yes	complemented
225	C₂×#124	C₂²×C₄₇	1	4	yes	—
226	#518	—	2	2	no	—
227	#518	—	2	4	no	—
228	#518	C₂²×C₄₇	1	4	yes	—
229	C₂×C₄×D₄	—	2	4	no	—
230	C₂×#117	C₂²×C₄₇	1	2	yes	—
231	C₂²×C₂²⋊C₄	—	2	2	no	—
232	C₂²×C₂²⋊C₄	—	2	2	no	—
233	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
234	#419	—	2	4	no	—
235	#419	C₂²×C₄₇	1	8	yes	complemented
236	C₂×#103	—	2	4	no	—
237	C₂×#100	—	2	4	no	—
238	C₂×#100	C₂²×C₄₇	1	4	yes	—
239	#339	C₂²×C₄₇	1	8	yes	complemented
240	C₄₇	C₂×#1885	1	1	yes	characteristic, direct product factor, Sylow
241	C₂⁵	D₄×C₄₇	1	2	yes	—
242	C₂²×Q₈	—	2	2	no	—
243	C₂²×Q₈	—	2	1	no	—
244	C₂²×Q₈	—	2	2	no	—
245	C₂²×Q₈	—	2	2	no	—
246	C₂²×Q₈	—	2	4	no	—
247	C₂²×Q₈	C₂×C₄×C₄₇	1	4	yes	complemented
248	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
249	C₂²×D₄	—	2	2	no	—
250	C₂²×D₄	—	2	2	no	—
251	C₂²×D₄	—	2	4	no	—
252	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	—
253	C₂²×D₄	D₄×C₄₇	1	2	yes	—
254	C₂²×D₄	D₄×C₄₇	1	4	yes	—
255	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
256	C₂³×C₄	—	2	1	no	—
257	C₂³×C₄	—	2	1	no	—
258	C₂³×C₄	—	2	4	no	—
259	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	4	no	—
262	C₂×M₁₆	—	2	4	no	—
263	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
264	C₂²×C₈	—	2	2	no	—
265	#124	—	2	16	no	—
266	#124	—	2	8	no	—
267	#124	C₂×C₄×C₄₇	1	16	yes	complemented
268	C₄×D₄	—	2	16	no	—
269	C₄×D₄	—	2	16	no	—
270	#117	—	2	2	no	—
271	#117	—	2	2	no	—
272	#117	D₄×C₄₇	1	4	yes	—
273	#117	C₂³×C₄₇	1	4	yes	—
274	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	—
275	C₂×C₂²⋊C₄	—	2	4	no	—
276	C₂×C₂²⋊C₄	—	2	8	no	—
277	C₂×C₂²⋊C₄	—	2	16	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	8	no	—
280	C₂×C₂²⋊C₄	—	2	8	no	—
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	complemented
285	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
286	#103	—	2	16	no	—
287	#100	—	2	8	no	—
288	C₂⁴	—	2	2	no	—
289	C₂⁴	—	2	2	no	—
290	C₂⁴	—	2	4	no	—
291	C₂⁴	—	4	8	no	—
292	C₂⁴	C₂²⋊C₄×C₄₇	1	8	yes	—
293	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
294	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	8	no	—
298	C₂×Q₈	—	2	8	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×Q₈	—	4	4	no	—
303	C₂×Q₈	—	4	4	no	—
304	C₂×Q₈	—	4	2	no	—
305	C₂×Q₈	C₂²×C₄×C₄₇	1	4	yes	complemented
306	C₂×D₄	—	2	8	no	—
307	C₂×D₄	—	2	8	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	8	no	—
310	C₂×D₄	—	2	8	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	C₂²⋊C₄×C₄₇	1	8	yes	—
315	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
316	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	16	no	—
323	C₂²×C₄	—	4	4	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	8	8	no	—
328	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
333	C₂²×C₄	#41×C₄₇	1	4	yes	—
334	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
335	M₁₆	—	2	4	no	—
336	M₁₆	—	2	4	no	—
337	M₁₆	—	4	4	no	—
338	C₂×C₈	—	2	4	no	—
339	C₂×C₈	—	4	4	no	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	C₂×D₄×C₄₇	1	8	yes	—
342	C₂²⋊C₄	—	2	16	no	—
343	C₂²⋊C₄	—	2	32	no	—
344	C₂²⋊C₄	—	2	4	no	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₄²	—	2	4	no	—
347	C₄²	—	2	4	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	4	no	—
350	C₄²	C₂²×C₄×C₄₇	1	4	yes	complemented
351	C₂³	—	2	4	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	8	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	2	8	no	—
356	C₂³	—	4	16	no	—
357	C₂³	—	4	8	no	—
358	C₂³	—	4	8	no	—
359	C₂³	—	8	8	no	—
360	C₂³	—	8	4	no	—
361	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
362	C₂³	C₂×C₂²⋊C₄×C₄₇	1	8	yes	—
363	C₂³	#120×C₄₇	1	1	yes	characteristic
364	C₂³	#120×C₄₇	1	1	yes	characteristic
365	C₂³	#123×C₄₇	1	2	yes	—
366	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
367	Q₈	—	2	8	no	—
368	Q₈	—	4	4	no	—
369	Q₈	—	4	8	no	—
370	D₄	—	2	8	no	—
371	D₄	—	2	8	no	—
372	D₄	—	2	16	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	4	8	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	8	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	8	16	no	—
384	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
385	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
386	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
387	C₂×C₄	#120×C₄₇	1	2	yes	—
388	C₂×C₄	#121×C₄₇	1	4	yes	—
389	C₂×C₄	#121×C₄₇	1	4	yes	—
390	C₂×C₄	#123×C₄₇	1	2	yes	—
391	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
393	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
394	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
395	C₈	—	4	4	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	8	no	—
401	C₂²	—	4	8	no	—
402	C₂²	—	4	16	no	—
403	C₂²	—	4	8	no	—
404	C₂²	—	8	4	no	—
405	C₂²	—	8	8	no	—
406	C₂²	C₄₇×#386	1	2	yes	—
407	C₂²	C₄₇×#386	1	2	yes	—
408	C₂²	C₄₇×#455	1	4	yes	—
409	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
410	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
411	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
412	C₄	—	4	4	no	—
413	C₄	—	4	4	no	—
414	C₄	—	4	8	no	—
415	C₄	C₄₇×#386	1	4	yes	—
416	C₄	C₂×C₄×D₄×C₄₇	1	2	yes	—
417	C₄	C₂×#121×C₄₇	1	2	yes	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	2	no	—
421	C₂	—	4	8	no	—
422	C₂	C₄₇×#1885	1	4	yes	direct product factor
423	C₂	C₂×C₄₇×#386	1	1	yes	characteristic
424	C₂	C₂×C₄₇×#455	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	#120
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄₇×#419	C₂	semidirect
5. C₄₇×#1885	C₂	direct (N × H)
6. C₂×C₄₇×#339	C₂	semidirect
12. C₂×#124×C₄₇	C₄	semidirect
23. C₄₇×#419	C₂²	semidirect
27. C₄₇×#339	C₂²	semidirect
34. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
54. #124×C₄₇	C₂×C₄	semidirect
71. C₂×C₄²×C₄₇	C₂×C₄	semidirect
92. C₂×Q₈×C₄₇	C₂²×C₄	semidirect
137. C₄²×C₄₇	C₂²×C₄	semidirect
183. C₂×#1885	C₄₇	direct (N × H)
208. C₂×#419	C₂×C₄₇	semidirect
210. #1885	C₂×C₄₇	direct (N × H)
211. C₂×#339	C₂×C₄₇	semidirect
216. C₂×C₄₇	#1885	direct (N × H)
224. C₂×#124	C₄×C₄₇	semidirect
235. #419	C₂²×C₄₇	semidirect
239. #339	C₂²×C₄₇	semidirect
240. C₄₇	C₂×#1885	direct (N × H)
247. C₂²×Q₈	C₂×C₄×C₄₇	semidirect
267. #124	C₂×C₄×C₄₇	semidirect
284. C₂×C₄²	C₂×C₄×C₄₇	semidirect
305. C₂×Q₈	C₂²×C₄×C₄₇	semidirect
350. C₄²	C₂²×C₄×C₄₇	semidirect
422. C₂	C₄₇×#1885	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#124×C₄₇	2
C₂×C₄₇×#518	2
C₂×C₄₇×#419	2
C₂²×#100×C₄₇	2
C₄₇×#1885	2
C₂×C₄₇×#339	2
C₂×#1885	47

Subgroups — C2×C47×#1885 #26060646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#1885 #26060646