Subgroups — C₄₇×#18712 #26058410

Order 12032.

1084 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3247	C₂	1	2	yes	maximal, complemented
3	C₄₇×#3151	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1631	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1630	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1629	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1621	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1620	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1619	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₇×#331	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1483	C₂	1	2	yes	maximal, complemented
12	C₂×AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
13	C₄₇×#560	—	2	2	no	—
14	C₄₇×#559	C₂²	1	1	yes	characteristic
15	C₄₇×#550	C₂²	1	2	yes	—
16	C₄₇×#546	—	2	2	no	—
17	D₄²×C₄₇	—	2	2	no	—
18	D₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#540	—	2	2	no	—
20	C₄₇×#535	—	2	2	no	—
21	C₄₇×#534	—	2	2	no	—
22	C₄₇×#532	C₂²	1	1	yes	characteristic, complemented
23	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#529	C₂²	1	2	yes	—
25	C₄₇×#496	—	2	2	no	—
26	C₄₇×#493	C₂²	1	1	yes	characteristic
27	C₄₇×#493	C₂²	1	1	yes	characteristic, complemented
28	C₄₇×#492	C₂²	1	1	yes	characteristic
29	C₄₇×#492	C₂²	1	1	yes	characteristic, complemented
30	C₄₇×#478	—	2	2	no	—
31	C₄₇×#477	C₂²	1	2	yes	complemented
32	C₄₇×#476	C₂²	1	2	yes	complemented
33	C₄₇×#466	—	2	2	no	—
34	C₄₇×#465	—	2	2	no	—
35	C₄₇×#463	—	2	2	no	—
36	C₄₇×#460	C₂²	1	2	yes	complemented
37	C₄₇×#459	C₂²	1	2	yes	complemented
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	complemented
39	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
40	C₄₇×#331	C₂²	1	1	yes	characteristic
41	C₄₇×#331	C₂²	1	1	yes	characteristic
42	C₄₇×#331	C₂²	1	2	yes	complemented
43	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
44	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
45	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
46	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
47	C₂×#41×C₄₇	—	2	2	no	—
48	C₂×#41×C₄₇	—	2	1	no	—
49	C₂²×D₄×C₄₇	—	2	2	no	—
50	C₂²×D₄×C₄₇	—	2	2	no	—
51	C₂²×D₄×C₄₇	—	2	2	no	—
52	C₂²×D₄×C₄₇	D₄	1	2	yes	—
53	AGL(1,ℤ/8)×C₄₇	—	4	8	no	—
54	C₂×SD₁₆×C₄₇	—	2	2	no	—
55	C₂×SD₁₆×C₄₇	—	2	2	no	—
56	C₂×SD₁₆×C₄₇	—	2	2	no	—
57	C₂×D₈×C₄₇	—	2	2	no	—
58	C₂×D₈×C₄₇	—	2	2	no	—
59	C₂×D₈×C₄₇	—	2	2	no	—
60	C₂×M₁₆×C₄₇	—	2	1	no	—
61	C₂²×C₈×C₄₇	—	2	2	no	—
62	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
63	#127×C₄₇	—	2	2	no	—
64	#127×C₄₇	—	2	2	no	—
65	#127×C₄₇	D₄	1	2	yes	—
66	#127×C₄₇	C₂³	1	1	yes	characteristic
67	#127×C₄₇	C₂³	1	1	yes	characteristic
68	#127×C₄₇	C₂³	1	1	yes	characteristic
69	#126×C₄₇	—	2	2	no	—
70	#125×C₄₇	D₄	1	2	yes	—
71	#124×C₄₇	—	2	2	no	—
72	#124×C₄₇	—	2	1	no	—
73	#124×C₄₇	D₄	1	2	yes	—
74	#123×C₄₇	—	2	2	no	—
75	#123×C₄₇	—	2	4	no	—
76	#123×C₄₇	—	2	2	no	—
77	#123×C₄₇	—	2	2	no	—
78	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
79	#121×C₄₇	—	2	4	no	—
80	#121×C₄₇	—	2	4	no	—
81	#121×C₄₇	—	2	4	no	—
82	#121×C₄₇	—	2	4	no	—
83	#121×C₄₇	—	2	2	no	—
84	#121×C₄₇	—	2	2	no	—
85	#121×C₄₇	—	2	2	no	—
86	#121×C₄₇	D₄	1	2	yes	—
87	#120×C₄₇	—	2	2	no	—
88	#120×C₄₇	—	2	4	no	—
89	#120×C₄₇	—	2	4	no	—
90	#120×C₄₇	—	2	2	no	—
91	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
92	C₄×D₄×C₄₇	—	2	2	no	—
93	C₄×D₄×C₄₇	—	2	2	no	—
94	C₄×D₄×C₄₇	—	2	2	no	—
95	C₄×D₄×C₄₇	—	2	2	no	—
96	C₄×D₄×C₄₇	C₂³	1	2	yes	—
97	#117×C₄₇	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
99	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
100	#107×C₄₇	—	2	2	no	—
101	#106×C₄₇	—	2	2	no	—
102	C₄⋊C₈×C₄₇	—	2	2	no	—
103	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
104	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
105	#103×C₄₇	—	2	2	no	—
106	#102×C₄₇	—	2	2	no	—
107	#102×C₄₇	—	2	2	no	—
108	#102×C₄₇	—	2	2	no	—
109	#97×C₄₇	—	2	1	no	—
110	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
112	C₂⁴×C₄₇	—	2	2	no	—
113	C₂⁴×C₄₇	—	2	2	no	—
114	#41×C₄₇	—	4	4	no	—
115	#41×C₄₇	—	8	2	no	—
116	#41×C₄₇	—	8	2	no	—
117	C₂×Q₈×C₄₇	—	2	1	no	—
118	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₄₇	—	2	2	no	—
120	C₂×D₄×C₄₇	—	2	4	no	—
121	C₂×D₄×C₄₇	—	2	4	no	—
122	C₂×D₄×C₄₇	—	2	4	no	—
123	C₂×D₄×C₄₇	—	2	2	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	2	no	—
128	C₂×D₄×C₄₇	—	2	1	no	—
129	C₂×D₄×C₄₇	—	4	4	no	—
130	C₂×D₄×C₄₇	—	4	1	no	—
131	C₂×D₄×C₄₇	—	8	2	no	—
132	C₂×D₄×C₄₇	—	8	2	no	—
133	C₂×D₄×C₄₇	—	8	2	no	—
134	C₂×D₄×C₄₇	—	8	2	no	—
135	C₂×D₄×C₄₇	—	8	4	no	—
136	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
137	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₄₇	—	2	4	no	—
140	C₂²×C₄×C₄₇	—	2	2	no	—
141	C₂²×C₄×C₄₇	—	2	2	no	—
142	C₂²×C₄×C₄₇	—	4	1	no	—
143	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
145	SD₁₆×C₄₇	—	4	4	no	—
146	SD₁₆×C₄₇	—	4	4	no	—
147	SD₁₆×C₄₇	—	8	2	no	—
148	D₈×C₄₇	—	4	4	no	—
149	D₈×C₄₇	—	4	4	no	—
150	D₈×C₄₇	—	8	2	no	—
151	M₁₆×C₄₇	—	2	4	no	—
152	C₂×C₈×C₄₇	—	2	1	no	—
153	C₂×C₈×C₄₇	—	2	1	no	—
154	C₂×C₈×C₄₇	—	2	2	no	—
155	C₂×C₈×C₄₇	—	2	2	no	—
156	C₂×C₈×C₄₇	—	8	2	no	—
157	C₄⋊C₄×C₄₇	—	2	2	no	—
158	C₄⋊C₄×C₄₇	—	2	2	no	—
159	C₄⋊C₄×C₄₇	—	2	2	no	—
160	C₄⋊C₄×C₄₇	—	2	2	no	—
161	C₄⋊C₄×C₄₇	—	2	2	no	—
162	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
164	C₂²⋊C₄×C₄₇	—	2	2	no	—
165	C₂²⋊C₄×C₄₇	—	2	2	no	—
166	C₂²⋊C₄×C₄₇	—	2	4	no	—
167	C₂²⋊C₄×C₄₇	—	2	4	no	—
168	C₂²⋊C₄×C₄₇	—	2	2	no	—
169	C₂²⋊C₄×C₄₇	—	2	2	no	—
170	C₂²⋊C₄×C₄₇	—	2	2	no	—
171	C₂²⋊C₄×C₄₇	—	2	2	no	—
172	C₂²⋊C₄×C₄₇	—	2	2	no	—
173	C₂²⋊C₄×C₄₇	—	4	2	no	—
174	C₄²×C₄₇	—	2	2	no	—
175	C₄²×C₄₇	C₂×D₄	1	2	yes	—
176	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
178	C₂³×C₄₇	—	2	2	no	—
179	C₂³×C₄₇	—	2	2	no	—
180	C₂³×C₄₇	—	2	2	no	—
181	C₂³×C₄₇	—	4	4	no	—
182	C₂³×C₄₇	—	4	1	no	—
183	C₂³×C₄₇	—	8	4	no	—
184	C₂³×C₄₇	—	8	4	no	—
185	C₂³×C₄₇	—	8	2	no	—
186	C₂³×C₄₇	#120	1	1	yes	characteristic
187	Q₈×C₄₇	—	2	2	no	—
188	Q₈×C₄₇	—	2	2	no	—
189	Q₈×C₄₇	—	4	2	no	—
190	D₄×C₄₇	—	2	2	no	—
191	D₄×C₄₇	—	2	2	no	—
192	D₄×C₄₇	—	4	2	no	—
193	D₄×C₄₇	—	4	2	no	—
194	D₄×C₄₇	—	4	2	no	—
195	D₄×C₄₇	—	4	4	no	—
196	D₄×C₄₇	—	4	2	no	—
197	D₄×C₄₇	—	4	2	no	—
198	D₄×C₄₇	—	4	2	no	—
199	D₄×C₄₇	—	4	2	no	—
200	D₄×C₄₇	—	4	2	no	—
201	D₄×C₄₇	—	4	2	no	—
202	D₄×C₄₇	—	8	2	no	—
203	D₄×C₄₇	—	8	4	no	—
204	D₄×C₄₇	—	8	4	no	—
205	D₄×C₄₇	—	8	4	no	—
206	D₄×C₄₇	—	8	4	no	—
207	D₄×C₄₇	—	8	2	no	—
208	C₂×C₄×C₄₇	—	2	2	no	—
209	C₂×C₄×C₄₇	—	2	2	no	—
210	C₂×C₄×C₄₇	—	2	2	no	—
211	C₂×C₄×C₄₇	—	2	2	no	—
212	C₂×C₄×C₄₇	—	2	2	no	—
213	C₂×C₄×C₄₇	—	2	2	no	—
214	C₂×C₄×C₄₇	—	4	2	no	—
215	C₂×C₄×C₄₇	—	4	2	no	—
216	C₂×C₄×C₄₇	—	4	1	no	—
217	C₂×C₄×C₄₇	—	8	2	no	—
218	C₂×C₄×C₄₇	—	8	2	no	—
219	C₂×C₄×C₄₇	—	8	4	no	—
220	C₂×C₄×C₄₇	#120	1	2	yes	—
221	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
222	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
224	C₈×C₄₇	—	2	2	no	—
225	C₈×C₄₇	—	2	2	no	—
226	C₈×C₄₇	—	4	2	no	—
227	C₈×C₄₇	—	4	2	no	—
228	#18712	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂²×C₄₇	—	2	2	no	—
230	C₂²×C₄₇	—	4	2	no	—
231	C₂²×C₄₇	—	4	4	no	—
232	C₂²×C₄₇	—	4	2	no	—
233	C₂²×C₄₇	—	4	4	no	—
234	C₂²×C₄₇	—	4	2	no	—
235	C₂²×C₄₇	—	4	2	no	—
236	C₂²×C₄₇	—	4	2	no	—
237	C₂²×C₄₇	—	8	2	no	—
238	C₂²×C₄₇	—	8	1	no	—
239	C₂²×C₄₇	—	16	4	no	—
240	C₂²×C₄₇	—	16	4	no	—
241	C₂²×C₄₇	#453	1	2	yes	—
242	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
243	C₄×C₄₇	—	2	2	no	—
244	C₄×C₄₇	—	2	1	no	—
245	C₄×C₄₇	—	2	1	no	—
246	C₄×C₄₇	—	4	2	no	—
247	C₄×C₄₇	—	4	2	no	—
248	C₄×C₄₇	—	4	2	no	—
249	C₄×C₄₇	—	8	1	no	—
250	C₄×C₄₇	#576	1	2	yes	—
251	C₄×C₄₇	#577	1	2	yes	—
252	#3543	C₂×C₄₇	1	1	yes	characteristic, complemented
253	#3247	C₂×C₄₇	1	2	yes	complemented
254	#3151	C₂×C₄₇	1	1	yes	characteristic, complemented
255	#1631	C₂×C₄₇	1	2	yes	complemented
256	#1630	C₂×C₄₇	1	1	yes	characteristic, complemented
257	#1629	C₂×C₄₇	1	1	yes	characteristic, complemented
258	#1621	C₂×C₄₇	1	2	yes	complemented
259	#1620	C₂×C₄₇	1	1	yes	characteristic, complemented
260	#1619	C₂×C₄₇	1	1	yes	characteristic, complemented
261	C₂×#331	C₂×C₄₇	1	1	yes	characteristic, complemented
262	#1483	C₂×C₄₇	1	2	yes	complemented
263	C₂×C₄₇	—	2	2	no	—
264	C₂×C₄₇	—	8	2	no	—
265	C₂×C₄₇	—	8	2	no	—
266	C₂×C₄₇	—	8	2	no	—
267	C₂×C₄₇	—	16	1	no	—
268	C₂×C₄₇	#3012	1	2	yes	—
269	C₂×C₄₇	C₂×#453	1	1	yes	characteristic
270	C₂×AGL(1,ℤ/8)	—	2	2	no	—
271	#560	—	2	2	no	—
272	#559	C₂²×C₄₇	1	1	yes	characteristic
273	#550	C₂²×C₄₇	1	2	yes	—
274	#546	—	2	2	no	—
275	D₄²	—	2	2	no	—
276	D₄²	C₂²×C₄₇	1	1	yes	characteristic
277	#540	—	2	2	no	—
278	#535	—	2	2	no	—
279	#534	—	2	2	no	—
280	#532	C₂²×C₄₇	1	1	yes	characteristic, complemented
281	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
282	#529	C₂²×C₄₇	1	2	yes	—
283	#496	—	2	2	no	—
284	#493	C₂²×C₄₇	1	1	yes	characteristic
285	#493	C₂²×C₄₇	1	1	yes	characteristic, complemented
286	#492	C₂²×C₄₇	1	1	yes	characteristic
287	#492	C₂²×C₄₇	1	1	yes	characteristic, complemented
288	#478	—	2	2	no	—
289	#477	C₂²×C₄₇	1	2	yes	complemented
290	#476	C₂²×C₄₇	1	2	yes	complemented
291	#466	—	2	2	no	—
292	#465	—	2	2	no	—
293	#463	—	2	2	no	—
294	#460	C₂²×C₄₇	1	2	yes	complemented
295	#459	C₂²×C₄₇	1	2	yes	complemented
296	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
297	C₄×M₁₆	C₂²×C₄₇	1	1	yes	characteristic, complemented
298	#331	C₂²×C₄₇	1	1	yes	characteristic
299	#331	C₂²×C₄₇	1	1	yes	characteristic
300	#331	C₂²×C₄₇	1	2	yes	complemented
301	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	complemented
302	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	complemented
303	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
304	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
305	C₄₇	#18712	1	1	yes	characteristic, direct product factor, Sylow
306	C₂×#41	—	2	2	no	—
307	C₂×#41	—	2	1	no	—
308	C₂²×D₄	—	2	2	no	—
309	C₂²×D₄	—	2	2	no	—
310	C₂²×D₄	—	2	2	no	—
311	C₂²×D₄	D₄×C₄₇	1	2	yes	—
312	AGL(1,ℤ/8)	—	4	8	no	—
313	C₂×SD₁₆	—	2	2	no	—
314	C₂×SD₁₆	—	2	2	no	—
315	C₂×SD₁₆	—	2	2	no	—
316	C₂×D₈	—	2	2	no	—
317	C₂×D₈	—	2	2	no	—
318	C₂×D₈	—	2	2	no	—
319	C₂×M₁₆	—	2	1	no	—
320	C₂²×C₈	—	2	2	no	—
321	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
322	#127	—	2	2	no	—
323	#127	—	2	2	no	—
324	#127	D₄×C₄₇	1	2	yes	—
325	#127	C₂³×C₄₇	1	1	yes	characteristic
326	#127	C₂³×C₄₇	1	1	yes	characteristic
327	#127	C₂³×C₄₇	1	1	yes	characteristic
328	#126	—	2	2	no	—
329	#125	D₄×C₄₇	1	2	yes	—
330	#124	—	2	2	no	—
331	#124	—	2	1	no	—
332	#124	D₄×C₄₇	1	2	yes	—
333	#123	—	2	2	no	—
334	#123	—	2	4	no	—
335	#123	—	2	2	no	—
336	#123	—	2	2	no	—
337	C₂²⋊Q₈	D₄×C₄₇	1	2	yes	—
338	#121	—	2	4	no	—
339	#121	—	2	4	no	—
340	#121	—	2	4	no	—
341	#121	—	2	4	no	—
342	#121	—	2	2	no	—
343	#121	—	2	2	no	—
344	#121	—	2	2	no	—
345	#121	D₄×C₄₇	1	2	yes	—
346	#120	—	2	2	no	—
347	#120	—	2	4	no	—
348	#120	—	2	4	no	—
349	#120	—	2	2	no	—
350	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
351	C₄×D₄	—	2	2	no	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	C₂³×C₄₇	1	2	yes	—
356	#117	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
359	#107	—	2	2	no	—
360	#106	—	2	2	no	—
361	C₄⋊C₈	—	2	2	no	—
362	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
363	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
364	#103	—	2	2	no	—
365	#102	—	2	2	no	—
366	#102	—	2	2	no	—
367	#102	—	2	2	no	—
368	#97	—	2	1	no	—
369	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
370	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
371	C₂⁴	—	2	2	no	—
372	C₂⁴	—	2	2	no	—
373	#41	—	4	4	no	—
374	#41	—	8	2	no	—
375	#41	—	8	2	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	4	4	no	—
389	C₂×D₄	—	4	1	no	—
390	C₂×D₄	—	8	2	no	—
391	C₂×D₄	—	8	2	no	—
392	C₂×D₄	—	8	2	no	—
393	C₂×D₄	—	8	2	no	—
394	C₂×D₄	—	8	4	no	—
395	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
396	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
397	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	4	1	no	—
402	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
403	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
404	SD₁₆	—	4	4	no	—
405	SD₁₆	—	4	4	no	—
406	SD₁₆	—	8	2	no	—
407	D₈	—	4	4	no	—
408	D₈	—	4	4	no	—
409	D₈	—	8	2	no	—
410	M₁₆	—	2	4	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	8	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
422	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	4	2	no	—
433	C₄²	—	2	2	no	—
434	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
435	C₄²	C₂×D₄×C₄₇	1	2	yes	—
436	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	8	4	no	—
443	C₂³	—	8	4	no	—
444	C₂³	—	8	2	no	—
445	C₂³	#120×C₄₇	1	1	yes	characteristic
446	Q₈	—	2	2	no	—
447	Q₈	—	2	2	no	—
448	Q₈	—	4	2	no	—
449	D₄	—	2	2	no	—
450	D₄	—	2	2	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	4	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	8	2	no	—
462	D₄	—	8	4	no	—
463	D₄	—	8	4	no	—
464	D₄	—	8	4	no	—
465	D₄	—	8	4	no	—
466	D₄	—	8	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	8	2	no	—
477	C₂×C₄	—	8	2	no	—
478	C₂×C₄	—	8	4	no	—
479	C₂×C₄	#120×C₄₇	1	2	yes	—
480	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
481	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
483	C₈	—	2	2	no	—
484	C₈	—	2	2	no	—
485	C₈	—	4	2	no	—
486	C₈	—	4	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	1	no	—
497	C₂²	—	16	4	no	—
498	C₂²	—	16	4	no	—
499	C₂²	C₄₇×#453	1	2	yes	—
500	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
501	C₄	—	2	2	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	8	1	no	—
508	C₄	C₄₇×#576	1	2	yes	—
509	C₄	C₄₇×#577	1	2	yes	—
510	C₂	—	2	2	no	—
511	C₂	—	8	2	no	—
512	C₂	—	8	2	no	—
513	C₂	—	8	2	no	—
514	C₂	—	16	1	no	—
515	C₂	C₄₇×#3012	1	2	yes	—
516	C₂	C₂×C₄₇×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#3543	C₂	semidirect
2. C₄₇×#3247	C₂	semidirect
3. C₄₇×#3151	C₂	semidirect
4. C₄₇×#1631	C₂	semidirect
5. C₄₇×#1630	C₂	semidirect
6. C₄₇×#1629	C₂	semidirect
7. C₄₇×#1621	C₂	semidirect
8. C₄₇×#1620	C₂	semidirect
9. C₄₇×#1619	C₂	semidirect
10. C₂×C₄₇×#331	C₂	semidirect
11. C₄₇×#1483	C₂	semidirect
22. C₄₇×#532	C₂²	semidirect
27. C₄₇×#493	C₂²	semidirect
29. C₄₇×#492	C₂²	semidirect
31. C₄₇×#477	C₂²	semidirect
32. C₄₇×#476	C₂²	semidirect
36. C₄₇×#460	C₂²	semidirect
37. C₄₇×#459	C₂²	semidirect
38. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
39. C₄×M₁₆×C₄₇	C₂²	semidirect
42. C₄₇×#331	C₂²	semidirect
43. C₄₇×Q₈⋊C₈	C₂²	semidirect
44. C₄₇×Q₈⋊C₈	C₂²	semidirect
45. C₄₇×D₄⋊C₈	C₂²	semidirect
46. C₄₇×D₄⋊C₈	C₂²	semidirect
228. #18712	C₄₇	direct (N × H)
252. #3543	C₂×C₄₇	semidirect
253. #3247	C₂×C₄₇	semidirect
254. #3151	C₂×C₄₇	semidirect
255. #1631	C₂×C₄₇	semidirect
256. #1630	C₂×C₄₇	semidirect
257. #1629	C₂×C₄₇	semidirect
258. #1621	C₂×C₄₇	semidirect
259. #1620	C₂×C₄₇	semidirect
260. #1619	C₂×C₄₇	semidirect
261. C₂×#331	C₂×C₄₇	semidirect
262. #1483	C₂×C₄₇	semidirect
280. #532	C₂²×C₄₇	semidirect
285. #493	C₂²×C₄₇	semidirect
287. #492	C₂²×C₄₇	semidirect
289. #477	C₂²×C₄₇	semidirect
290. #476	C₂²×C₄₇	semidirect
294. #460	C₂²×C₄₇	semidirect
295. #459	C₂²×C₄₇	semidirect
296. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
297. C₄×M₁₆	C₂²×C₄₇	semidirect
300. #331	C₂²×C₄₇	semidirect
301. Q₈⋊C₈	C₂²×C₄₇	semidirect
302. Q₈⋊C₈	C₂²×C₄₇	semidirect
303. D₄⋊C₈	C₂²×C₄₇	semidirect
304. D₄⋊C₈	C₂²×C₄₇	semidirect
305. C₄₇	#18712	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#3543	2
C₄₇×#3247	2
C₄₇×#3151	2
C₄₇×#1631	2
C₄₇×#1630	2
C₄₇×#1629	2
C₄₇×#1621	2
C₄₇×#1620	2
C₄₇×#1619	2
C₂×C₄₇×#331	2
C₄₇×#1483	2
#18712	47

Subgroups — C47×#18712 #26058410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18712 #26058410