Subgroups — C₄₇×#20952 #26060650

Order 12032.

1818 conjugacy classes of subgroups.

The subgroup lattice has 540 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×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2896	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₇×#413	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1888	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1887	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1886	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1885	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₇×#339	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
11	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
13	C₄₇×#532	—	2	4	no	—
14	C₄₇×#532	C₄	1	8	yes	complemented
15	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#121×C₄₇	—	2	2	no	—
20	C₄₇×#520	—	2	4	no	—
21	C₄₇×#519	C₂²	1	2	yes	—
22	C₄₇×#518	—	2	2	no	—
23	C₄₇×#518	C₂²	1	2	yes	—
24	C₄×#41×C₄₇	—	2	4	no	—
25	C₂×C₄×D₄×C₄₇	—	2	2	no	—
26	C₂×#117×C₄₇	—	2	2	no	—
27	C₂×#117×C₄₇	C₂²	1	2	yes	—
28	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#419	C₂²	1	4	yes	—
30	C₄₇×#418	C₂²	1	4	yes	—
31	C₄₇×#417	—	2	4	no	—
32	C₄₇×#416	—	2	4	no	—
33	C₄₇×#413	—	2	4	no	—
34	C₂×#101×C₄₇	C₂²	1	2	yes	—
35	C₂×#100×C₄₇	C₂²	1	2	yes	—
36	C₄₇×#339	C₂²	1	4	yes	—
37	C₄₇×#339	C₂²	1	4	yes	—
38	C₂×#41×C₄₇	—	2	2	no	—
39	C₂×#41×C₄₇	—	2	2	no	—
40	C₂×#41×C₄₇	—	2	2	no	—
41	C₂×#41×C₄₇	—	2	4	no	—
42	C₂×#41×C₄₇	—	2	2	no	—
43	C₂×#41×C₄₇	—	2	2	no	—
44	C₂×#41×C₄₇	—	2	4	no	—
45	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
46	C₂×#41×C₄₇	C₂×C₄	1	4	yes	complemented
47	C₂×#41×C₄₇	D₄	1	4	yes	—
48	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₄₇	—	2	2	no	—
51	C₂²×D₄×C₄₇	—	2	1	no	—
52	C₂²×D₄×C₄₇	D₄	1	2	yes	—
53	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	—	2	1	no	—
56	C₂³×C₄×C₄₇	—	2	1	no	—
57	C₂³×C₄×C₄₇	D₄	1	2	yes	—
58	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₄₇	—	2	2	no	—
60	C₂×M₁₆×C₄₇	—	2	4	no	—
61	C₂×M₁₆×C₄₇	—	2	4	no	—
62	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
63	C₂²×C₈×C₄₇	—	2	2	no	—
64	C₄⋊Q₈×C₄₇	—	2	2	no	—
65	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
66	#127×C₄₇	—	2	2	no	—
67	#127×C₄₇	C₂×C₄	1	4	yes	complemented
68	#124×C₄₇	—	2	2	no	—
69	#124×C₄₇	—	2	2	no	—
70	#124×C₄₇	C₂×C₄	1	4	yes	complemented
71	#124×C₄₇	C₂×C₄	1	4	yes	complemented
72	#121×C₄₇	—	2	16	no	—
73	C₄×Q₈×C₄₇	—	2	8	no	—
74	C₄×D₄×C₄₇	—	2	16	no	—
75	C₄×D₄×C₄₇	—	2	16	no	—
76	C₄×D₄×C₄₇	—	2	8	no	—
77	#117×C₄₇	—	2	4	no	—
78	#117×C₄₇	—	2	4	no	—
79	#117×C₄₇	—	2	2	no	—
80	#117×C₄₇	—	2	4	no	—
81	#117×C₄₇	—	2	2	no	—
82	#117×C₄₇	D₄	1	4	yes	complemented
83	#117×C₄₇	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
85	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
86	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	complemented
87	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
91	C₂×C₄²×C₄₇	—	2	4	no	—
92	C₂×C₄²×C₄₇	—	2	1	no	—
93	C₂×C₄²×C₄₇	—	2	2	no	—
94	C₂×C₄²×C₄₇	—	2	2	no	—
95	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	complemented
96	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	#103×C₄₇	—	2	8	no	—
99	#102×C₄₇	—	2	8	no	—
100	#101×C₄₇	—	2	4	no	—
101	#100×C₄₇	—	2	4	no	—
102	C₂⁴×C₄₇	—	2	1	no	—
103	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
104	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
105	#41×C₄₇	—	2	8	no	—
106	#41×C₄₇	—	2	8	no	—
107	#41×C₄₇	—	2	8	no	—
108	#41×C₄₇	—	2	8	no	—
109	#41×C₄₇	—	2	8	no	—
110	#41×C₄₇	—	2	8	no	—
111	#41×C₄₇	—	4	4	no	—
112	#41×C₄₇	—	4	4	no	—
113	C₂×Q₈×C₄₇	—	2	2	no	—
114	C₂×Q₈×C₄₇	—	2	1	no	—
115	C₂×Q₈×C₄₇	—	2	2	no	—
116	C₂×Q₈×C₄₇	—	2	2	no	—
117	C₂×Q₈×C₄₇	—	2	2	no	—
118	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
119	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
120	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₄₇	—	2	4	no	—
122	C₂×D₄×C₄₇	—	2	4	no	—
123	C₂×D₄×C₄₇	—	2	8	no	—
124	C₂×D₄×C₄₇	—	2	4	no	—
125	C₂×D₄×C₄₇	—	2	2	no	—
126	C₂×D₄×C₄₇	—	2	2	no	—
127	C₂×D₄×C₄₇	—	2	1	no	—
128	C₂×D₄×C₄₇	—	2	2	no	—
129	C₂×D₄×C₄₇	—	2	2	no	—
130	C₂×D₄×C₄₇	—	4	8	no	—
131	C₂×D₄×C₄₇	—	4	2	no	—
132	C₂×D₄×C₄₇	—	4	2	no	—
133	C₂×D₄×C₄₇	C₂²⋊C₄	1	8	yes	—
134	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
135	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
136	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₄₇	—	2	1	no	—
138	C₂²×C₄×C₄₇	—	2	2	no	—
139	C₂²×C₄×C₄₇	—	2	2	no	—
140	C₂²×C₄×C₄₇	—	2	4	no	—
141	C₂²×C₄×C₄₇	—	2	4	no	—
142	C₂²×C₄×C₄₇	—	2	1	no	—
143	C₂²×C₄×C₄₇	—	2	1	no	—
144	C₂²×C₄×C₄₇	—	2	8	no	—
145	C₂²×C₄×C₄₇	—	2	4	no	—
146	C₂²×C₄×C₄₇	—	2	4	no	—
147	C₂²×C₄×C₄₇	—	4	4	no	—
148	C₂²×C₄×C₄₇	—	4	1	no	—
149	C₂²×C₄×C₄₇	—	4	1	no	—
150	C₂²×C₄×C₄₇	—	4	2	no	—
151	C₂²×C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
152	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
153	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₄₇	#41	1	4	yes	—
159	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
160	M₁₆×C₄₇	—	2	4	no	—
161	M₁₆×C₄₇	—	2	4	no	—
162	M₁₆×C₄₇	—	4	4	no	—
163	C₂×C₈×C₄₇	—	2	4	no	—
164	C₂×C₈×C₄₇	—	4	4	no	—
165	C₄⋊C₄×C₄₇	—	2	8	no	—
166	C₄⋊C₄×C₄₇	—	2	8	no	—
167	C₄⋊C₄×C₄₇	—	2	4	no	—
168	C₄⋊C₄×C₄₇	C₂×D₄	1	8	yes	—
169	C₂²⋊C₄×C₄₇	—	2	8	no	—
170	C₂²⋊C₄×C₄₇	—	2	8	no	—
171	C₂²⋊C₄×C₄₇	—	2	4	no	—
172	C₂²⋊C₄×C₄₇	—	2	4	no	—
173	C₂²⋊C₄×C₄₇	—	2	8	no	—
174	C₄²×C₄₇	—	2	8	no	—
175	C₄²×C₄₇	—	2	4	no	—
176	C₄²×C₄₇	—	2	4	no	—
177	C₄²×C₄₇	—	2	1	no	—
178	C₄²×C₄₇	—	2	1	no	—
179	C₄²×C₄₇	—	2	4	no	—
180	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
181	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
182	C₂³×C₄₇	—	2	2	no	—
183	C₂³×C₄₇	—	2	2	no	—
184	C₂³×C₄₇	—	2	2	no	—
185	C₂³×C₄₇	—	4	2	no	—
186	C₂³×C₄₇	—	4	4	no	—
187	C₂³×C₄₇	—	4	4	no	—
188	C₂³×C₄₇	—	4	1	no	—
189	C₂³×C₄₇	—	4	1	no	—
190	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
191	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂³×C₄₇	#120	1	2	yes	—
193	C₂³×C₄₇	#123	1	2	yes	—
194	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₄₇	—	2	4	no	—
196	Q₈×C₄₇	—	2	4	no	—
197	Q₈×C₄₇	—	2	4	no	—
198	Q₈×C₄₇	—	4	2	no	—
199	D₄×C₄₇	—	2	16	no	—
200	D₄×C₄₇	—	2	4	no	—
201	D₄×C₄₇	—	2	4	no	—
202	D₄×C₄₇	—	2	4	no	—
203	D₄×C₄₇	—	4	16	no	—
204	D₄×C₄₇	—	4	8	no	—
205	D₄×C₄₇	—	4	2	no	—
206	C₂×C₄×C₄₇	—	2	4	no	—
207	C₂×C₄×C₄₇	—	2	2	no	—
208	C₂×C₄×C₄₇	—	2	2	no	—
209	C₂×C₄×C₄₇	—	2	2	no	—
210	C₂×C₄×C₄₇	—	2	8	no	—
211	C₂×C₄×C₄₇	—	2	8	no	—
212	C₂×C₄×C₄₇	—	2	2	no	—
213	C₂×C₄×C₄₇	—	2	2	no	—
214	C₂×C₄×C₄₇	—	2	8	no	—
215	C₂×C₄×C₄₇	—	4	8	no	—
216	C₂×C₄×C₄₇	—	4	2	no	—
217	C₂×C₄×C₄₇	—	4	1	no	—
218	C₂×C₄×C₄₇	—	4	1	no	—
219	C₂×C₄×C₄₇	—	4	4	no	—
220	C₂×C₄×C₄₇	—	4	4	no	—
221	C₂×C₄×C₄₇	—	8	4	no	—
222	C₂×C₄×C₄₇	—	8	8	no	—
223	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
224	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
225	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
226	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
227	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
228	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
229	C₂×C₄×C₄₇	#121	1	4	yes	—
230	C₂×C₄×C₄₇	#121	1	4	yes	—
231	C₂×C₄×C₄₇	#123	1	2	yes	—
232	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
236	C₈×C₄₇	—	4	4	no	—
237	#20952	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂²×C₄₇	—	2	2	no	—
239	C₂²×C₄₇	—	2	4	no	—
240	C₂²×C₄₇	—	2	4	no	—
241	C₂²×C₄₇	—	4	2	no	—
242	C₂²×C₄₇	—	4	2	no	—
243	C₂²×C₄₇	—	4	4	no	—
244	C₂²×C₄₇	—	4	4	no	—
245	C₂²×C₄₇	—	4	4	no	—
246	C₂²×C₄₇	—	4	2	no	—
247	C₂²×C₄₇	—	8	2	no	—
248	C₂²×C₄₇	—	8	2	no	—
249	C₂²×C₄₇	—	8	2	no	—
250	C₂²×C₄₇	#386	1	4	yes	—
251	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
253	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
254	C₄×C₄₇	—	2	4	no	—
255	C₄×C₄₇	—	2	4	no	—
256	C₄×C₄₇	—	4	2	no	—
257	C₄×C₄₇	—	4	8	no	—
258	C₄×C₄₇	—	4	2	no	—
259	C₄×C₄₇	#386	1	2	yes	—
260	C₄×C₄₇	#386	1	2	yes	—
261	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
262	C₄×C₄₇	C₂×#121	1	2	yes	—
263	C₂×#532	C₂×C₄₇	1	1	yes	characteristic
264	#3428	C₂×C₄₇	1	1	yes	characteristic, complemented
265	#2896	C₂×C₄₇	1	2	yes	complemented
266	C₂×#413	C₂×C₄₇	1	1	yes	characteristic, complemented
267	#1888	C₂×C₄₇	1	2	yes	complemented
268	#1887	C₂×C₄₇	1	2	yes	complemented
269	#1886	C₂×C₄₇	1	2	yes	complemented
270	#1885	C₂×C₄₇	1	2	yes	complemented
271	C₂×#339	C₂×C₄₇	1	2	yes	complemented
272	C₂×C₄₇	—	2	1	no	—
273	C₂×C₄₇	—	2	1	no	—
274	C₂×C₄₇	—	2	4	no	—
275	C₂×C₄₇	—	4	4	no	—
276	C₂×C₄₇	—	8	2	no	—
277	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
278	C₂×C₄₇	#3018	1	2	yes	—
279	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
280	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
281	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
282	#532	—	2	4	no	—
283	#532	C₄×C₄₇	1	8	yes	complemented
284	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
285	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
286	C₂×#124	C₂²×C₄₇	1	1	yes	characteristic
287	C₂×#124	C₂²×C₄₇	1	1	yes	characteristic
288	C₂×#121	—	2	2	no	—
289	#520	—	2	4	no	—
290	#519	C₂²×C₄₇	1	2	yes	—
291	#518	—	2	2	no	—
292	#518	C₂²×C₄₇	1	2	yes	—
293	C₄×#41	—	2	4	no	—
294	C₂×C₄×D₄	—	2	2	no	—
295	C₂×#117	—	2	2	no	—
296	C₂×#117	C₂²×C₄₇	1	2	yes	—
297	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
298	#419	C₂²×C₄₇	1	4	yes	—
299	#418	C₂²×C₄₇	1	4	yes	—
300	#417	—	2	4	no	—
301	#416	—	2	4	no	—
302	#413	—	2	4	no	—
303	C₂×#101	C₂²×C₄₇	1	2	yes	—
304	C₂×#100	C₂²×C₄₇	1	2	yes	—
305	#339	C₂²×C₄₇	1	4	yes	—
306	#339	C₂²×C₄₇	1	4	yes	—
307	C₄₇	#20952	1	1	yes	characteristic, direct product factor, Sylow
308	C₂×#41	—	2	2	no	—
309	C₂×#41	—	2	2	no	—
310	C₂×#41	—	2	2	no	—
311	C₂×#41	—	2	4	no	—
312	C₂×#41	—	2	2	no	—
313	C₂×#41	—	2	2	no	—
314	C₂×#41	—	2	4	no	—
315	C₂×#41	C₂×C₄×C₄₇	1	4	yes	—
316	C₂×#41	C₂×C₄×C₄₇	1	4	yes	complemented
317	C₂×#41	D₄×C₄₇	1	4	yes	—
318	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
319	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	—	2	1	no	—
322	C₂²×D₄	D₄×C₄₇	1	2	yes	—
323	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
324	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
325	C₂³×C₄	—	2	1	no	—
326	C₂³×C₄	—	2	1	no	—
327	C₂³×C₄	D₄×C₄₇	1	2	yes	—
328	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
329	C₂×M₁₆	—	2	2	no	—
330	C₂×M₁₆	—	2	4	no	—
331	C₂×M₁₆	—	2	4	no	—
332	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
333	C₂²×C₈	—	2	2	no	—
334	C₄⋊Q₈	—	2	2	no	—
335	C₄⋊Q₈	C₂×C₄×C₄₇	1	4	yes	complemented
336	#127	—	2	2	no	—
337	#127	C₂×C₄×C₄₇	1	4	yes	complemented
338	#124	—	2	2	no	—
339	#124	—	2	2	no	—
340	#124	C₂×C₄×C₄₇	1	4	yes	complemented
341	#124	C₂×C₄×C₄₇	1	4	yes	complemented
342	#121	—	2	16	no	—
343	C₄×Q₈	—	2	8	no	—
344	C₄×D₄	—	2	16	no	—
345	C₄×D₄	—	2	16	no	—
346	C₄×D₄	—	2	8	no	—
347	#117	—	2	4	no	—
348	#117	—	2	4	no	—
349	#117	—	2	2	no	—
350	#117	—	2	4	no	—
351	#117	—	2	2	no	—
352	#117	D₄×C₄₇	1	4	yes	complemented
353	#117	C₂³×C₄₇	1	4	yes	—
354	C₂×C₄⋊C₄	—	2	4	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	complemented
357	C₂×C₂²⋊C₄	—	2	4	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₄²	—	2	4	no	—
362	C₂×C₄²	—	2	2	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	—	2	2	no	—
365	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	complemented
366	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
368	#103	—	2	8	no	—
369	#102	—	2	8	no	—
370	#101	—	2	4	no	—
371	#100	—	2	4	no	—
372	C₂⁴	—	2	1	no	—
373	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
374	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
375	#41	—	2	8	no	—
376	#41	—	2	8	no	—
377	#41	—	2	8	no	—
378	#41	—	2	8	no	—
379	#41	—	2	8	no	—
380	#41	—	2	8	no	—
381	#41	—	4	4	no	—
382	#41	—	4	4	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
389	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
390	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	8	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	4	8	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	C₂²⋊C₄×C₄₇	1	8	yes	—
404	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
405	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
406	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	4	4	no	—
418	C₂²×C₄	—	4	1	no	—
419	C₂²×C₄	—	4	1	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	C₂²⋊C₄×C₄₇	1	8	yes	—
422	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
423	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
424	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
426	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
427	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
428	C₂²×C₄	#41×C₄₇	1	4	yes	—
429	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
430	M₁₆	—	2	4	no	—
431	M₁₆	—	2	4	no	—
432	M₁₆	—	4	4	no	—
433	C₂×C₈	—	2	4	no	—
434	C₂×C₈	—	4	4	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	2	8	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	C₂×D₄×C₄₇	1	8	yes	—
439	C₂²⋊C₄	—	2	8	no	—
440	C₂²⋊C₄	—	2	8	no	—
441	C₂²⋊C₄	—	2	4	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	2	8	no	—
444	C₄²	—	2	8	no	—
445	C₄²	—	2	4	no	—
446	C₄²	—	2	4	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	4	no	—
450	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
451	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	4	no	—
457	C₂³	—	4	4	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	1	no	—
460	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
461	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
462	C₂³	#120×C₄₇	1	2	yes	—
463	C₂³	#123×C₄₇	1	2	yes	—
464	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
465	Q₈	—	2	4	no	—
466	Q₈	—	2	4	no	—
467	Q₈	—	2	4	no	—
468	Q₈	—	4	2	no	—
469	D₄	—	2	16	no	—
470	D₄	—	2	4	no	—
471	D₄	—	2	4	no	—
472	D₄	—	2	4	no	—
473	D₄	—	4	16	no	—
474	D₄	—	4	8	no	—
475	D₄	—	4	2	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	8	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	4	8	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	—	4	4	no	—
491	C₂×C₄	—	8	4	no	—
492	C₂×C₄	—	8	8	no	—
493	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
494	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
495	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
496	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
497	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
498	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
499	C₂×C₄	#121×C₄₇	1	4	yes	—
500	C₂×C₄	#121×C₄₇	1	4	yes	—
501	C₂×C₄	#123×C₄₇	1	2	yes	—
502	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
504	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
505	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
506	C₈	—	4	4	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	8	2	no	—
517	C₂²	—	8	2	no	—
518	C₂²	—	8	2	no	—
519	C₂²	C₄₇×#386	1	4	yes	—
520	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
521	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
522	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
523	C₄	—	2	4	no	—
524	C₄	—	2	4	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	8	no	—
528	C₄	C₄₇×#386	1	2	yes	—
529	C₄	C₄₇×#386	1	2	yes	—
530	C₄	C₂×C₄×D₄×C₄₇	1	2	yes	—
531	C₄	C₂×#121×C₄₇	1	2	yes	—
532	C₂	—	2	1	no	—
533	C₂	—	2	1	no	—
534	C₂	—	2	4	no	—
535	C₂	—	4	4	no	—
536	C₂	—	8	2	no	—
537	C₂	C₂×C₄₇×#386	1	1	yes	characteristic
538	C₂	C₄₇×#3018	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₇	#120
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂²×C₄₇	C₂×#120
prime radical	C₂×C₄₇×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#3428	C₂	semidirect
3. C₄₇×#2896	C₂	semidirect
4. C₂×C₄₇×#413	C₂	semidirect
5. C₄₇×#1888	C₂	semidirect
6. C₄₇×#1887	C₂	semidirect
7. C₄₇×#1886	C₂	semidirect
8. C₄₇×#1885	C₂	semidirect
9. C₂×C₄₇×#339	C₂	semidirect
14. C₄₇×#532	C₄	semidirect
46. C₂×#41×C₄₇	C₂×C₄	semidirect
65. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
67. #127×C₄₇	C₂×C₄	semidirect
70. #124×C₄₇	C₂×C₄	semidirect
71. #124×C₄₇	C₂×C₄	semidirect
82. #117×C₄₇	D₄	semidirect
86. C₂×C₄⋊C₄×C₄₇	D₄	semidirect
95. C₂×C₄²×C₄₇	C₂×C₄	semidirect
237. #20952	C₄₇	direct (N × H)
264. #3428	C₂×C₄₇	semidirect
265. #2896	C₂×C₄₇	semidirect
266. C₂×#413	C₂×C₄₇	semidirect
267. #1888	C₂×C₄₇	semidirect
268. #1887	C₂×C₄₇	semidirect
269. #1886	C₂×C₄₇	semidirect
270. #1885	C₂×C₄₇	semidirect
271. C₂×#339	C₂×C₄₇	semidirect
283. #532	C₄×C₄₇	semidirect
307. C₄₇	#20952	direct (N × H)
316. C₂×#41	C₂×C₄×C₄₇	semidirect
335. C₄⋊Q₈	C₂×C₄×C₄₇	semidirect
337. #127	C₂×C₄×C₄₇	semidirect
340. #124	C₂×C₄×C₄₇	semidirect
341. #124	C₂×C₄×C₄₇	semidirect
352. #117	D₄×C₄₇	semidirect
356. C₂×C₄⋊C₄	D₄×C₄₇	semidirect
365. C₂×C₄²	C₂×C₄×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×#532	2
C₄₇×#3428	2
C₄₇×#2896	2
C₂×C₄₇×#413	2
C₄₇×#1888	2
C₄₇×#1887	2
C₄₇×#1886	2
C₄₇×#1885	2
C₂×C₄₇×#339	2
#20952	47

Subgroups — C47×#20952 #26060650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20952 #26060650