Subgroups — C₄₇×#18912 #26058610

Order 12032.

1218 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3205	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3205	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1627	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1621	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1540	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×2₋¹⁺⁴×C₄₇	—	2	1	no	—
11	C₂²×SD₁₆×C₄₇	—	2	1	no	—
12	C₄₇×#550	—	2	1	no	—
13	C₄₇×#550	C₂²	1	2	yes	complemented
14	D₄×Q₈×C₄₇	—	2	1	no	—
15	D₄×Q₈×C₄₇	C₂²	1	2	yes	complemented
16	C₄₇×#548	—	2	2	no	—
17	C₄₇×#548	—	2	2	no	—
18	C₄₇×#537	—	2	2	no	—
19	C₄₇×#537	—	2	1	no	—
20	C₄₇×#532	—	2	2	no	—
21	C₄₇×#532	C₂²	1	1	yes	characteristic
22	C₄₇×#532	C₂²	1	1	yes	characteristic
23	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₄₇×#493	—	2	1	no	—
26	C₄₇×#493	C₂²	1	2	yes	—
27	C₄₇×#486	—	2	1	no	—
28	C₄₇×#486	C₂²	1	2	yes	—
29	C₄₇×#460	—	2	2	no	—
30	C₄₇×#460	C₂²	1	4	yes	—
31	C₄₇×#459	—	2	2	no	—
32	C₄₇×#459	C₂²	1	4	yes	—
33	C₄₇×#447	—	2	2	no	—
34	C₄₇×#447	—	2	2	no	—
35	C₄₇×#431	C₂²	1	1	yes	characteristic
36	C₄₇×#431	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#102×C₄₇	—	2	1	no	—
39	C₄₇×#332	C₂²	1	2	yes	complemented
40	C₄₇×#331	C₂²	1	2	yes	complemented
41	C₄₇×Q₈⋊C₈	C₂²	1	4	yes	complemented
42	C₄₇×D₄⋊C₈	C₂²	1	4	yes	complemented
43	2₋¹⁺⁴×C₄₇	—	4	4	no	—
44	2₋¹⁺⁴×C₄₇	—	4	4	no	—
45	C₂×#41×C₄₇	—	2	4	no	—
46	C₂×#41×C₄₇	—	2	2	no	—
47	C₂×#41×C₄₇	—	2	2	no	—
48	C₂×#41×C₄₇	—	2	1	no	—
49	C₂×#41×C₄₇	—	2	1	no	—
50	C₂²×Q₈×C₄₇	—	2	2	no	—
51	C₂²×Q₈×C₄₇	—	2	2	no	—
52	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
53	C₂²×D₄×C₄₇	—	2	1	no	—
54	C₂²×D₄×C₄₇	—	2	1	no	—
55	C₂²×D₄×C₄₇	—	2	1	no	—
56	C₂×SD₁₆×C₄₇	—	2	4	no	—
57	C₂×SD₁₆×C₄₇	—	4	4	no	—
58	C₂×D₈×C₄₇	—	2	4	no	—
59	C₂×D₈×C₄₇	—	2	4	no	—
60	C₂²×C₈×C₄₇	—	2	1	no	—
61	C₄⋊Q₈×C₄₇	—	2	2	no	—
62	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
63	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
64	#127×C₄₇	—	2	2	no	—
65	#127×C₄₇	—	2	1	no	—
66	#127×C₄₇	—	2	1	no	—
67	#127×C₄₇	—	2	1	no	—
68	#127×C₄₇	D₄	1	1	yes	characteristic
69	#127×C₄₇	C₂³	1	2	yes	—
70	#127×C₄₇	C₂³	1	1	yes	characteristic
71	#124×C₄₇	—	2	4	no	—
72	#124×C₄₇	—	2	1	no	—
73	#124×C₄₇	—	2	1	no	—
74	C₂²⋊Q₈×C₄₇	—	2	2	no	—
75	C₂²⋊Q₈×C₄₇	—	2	4	no	—
76	C₂²⋊Q₈×C₄₇	—	2	2	no	—
77	C₂²⋊Q₈×C₄₇	—	2	4	no	—
78	#121×C₄₇	—	2	4	no	—
79	#121×C₄₇	—	2	2	no	—
80	#121×C₄₇	—	2	4	no	—
81	#121×C₄₇	—	2	4	no	—
82	#121×C₄₇	—	2	1	no	—
83	#121×C₄₇	—	2	1	no	—
84	#121×C₄₇	—	2	2	no	—
85	#121×C₄₇	D₄	1	2	yes	—
86	#121×C₄₇	D₄	1	2	yes	—
87	C₄×Q₈×C₄₇	—	2	1	no	—
88	C₄×Q₈×C₄₇	—	2	1	no	—
89	C₄×Q₈×C₄₇	D₄	1	2	yes	—
90	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
91	C₄×D₄×C₄₇	—	2	4	no	—
92	C₄×D₄×C₄₇	—	2	2	no	—
93	C₄×D₄×C₄₇	—	2	2	no	—
94	C₄×D₄×C₄₇	—	2	1	no	—
95	C₄×D₄×C₄₇	—	2	1	no	—
96	C₄×D₄×C₄₇	D₄	1	2	yes	—
97	C₄×D₄×C₄₇	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
99	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₇	—	2	1	no	—
101	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₄₇	—	2	1	no	—
103	C₄⋊C₈×C₄₇	—	2	1	no	—
104	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
105	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
106	#102×C₄₇	—	2	4	no	—
107	#102×C₄₇	—	2	4	no	—
108	#102×C₄₇	—	2	4	no	—
109	C₂²⋊C₈×C₄₇	—	2	1	no	—
110	C₂²⋊C₈×C₄₇	—	2	1	no	—
111	C₄×C₈×C₄₇	—	2	1	no	—
112	C₄×C₈×C₄₇	C₂³	1	2	yes	—
113	C₂⁴×C₄₇	—	4	1	no	—
114	#41×C₄₇	—	4	16	no	—
115	#41×C₄₇	—	4	4	no	—
116	#41×C₄₇	—	4	8	no	—
117	#41×C₄₇	—	4	4	no	—
118	#41×C₄₇	—	4	2	no	—
119	#41×C₄₇	—	4	2	no	—
120	#41×C₄₇	—	4	2	no	—
121	#41×C₄₇	—	4	2	no	—
122	C₂×Q₈×C₄₇	—	2	4	no	—
123	C₂×Q₈×C₄₇	—	2	1	no	—
124	C₂×Q₈×C₄₇	—	2	1	no	—
125	C₂×Q₈×C₄₇	—	2	2	no	—
126	C₂×Q₈×C₄₇	—	2	1	no	—
127	C₂×Q₈×C₄₇	—	4	4	no	—
128	C₂×Q₈×C₄₇	—	4	8	no	—
129	C₂×Q₈×C₄₇	—	4	4	no	—
130	C₂×Q₈×C₄₇	D₈	1	4	yes	complemented
131	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
132	C₂×D₄×C₄₇	—	2	4	no	—
133	C₂×D₄×C₄₇	—	2	2	no	—
134	C₂×D₄×C₄₇	—	2	2	no	—
135	C₂×D₄×C₄₇	—	2	4	no	—
136	C₂×D₄×C₄₇	—	2	1	no	—
137	C₂×D₄×C₄₇	—	2	1	no	—
138	C₂×D₄×C₄₇	—	2	1	no	—
139	C₂×D₄×C₄₇	—	2	1	no	—
140	C₂×D₄×C₄₇	—	2	2	no	—
141	C₂×D₄×C₄₇	—	2	2	no	—
142	C₂×D₄×C₄₇	—	2	2	no	—
143	C₂×D₄×C₄₇	—	4	1	no	—
144	C₂×D₄×C₄₇	—	4	1	no	—
145	C₂×D₄×C₄₇	—	4	1	no	—
146	C₂×D₄×C₄₇	—	4	2	no	—
147	C₂×D₄×C₄₇	—	4	2	no	—
148	C₂×D₄×C₄₇	—	8	2	no	—
149	C₂×D₄×C₄₇	—	8	2	no	—
150	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
151	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₄₇	—	2	1	no	—
153	C₂²×C₄×C₄₇	—	2	4	no	—
154	C₂²×C₄×C₄₇	—	2	4	no	—
155	C₂²×C₄×C₄₇	—	2	1	no	—
156	C₂²×C₄×C₄₇	—	2	2	no	—
157	C₂²×C₄×C₄₇	—	2	2	no	—
158	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
161	SD₁₆×C₄₇	—	4	8	no	—
162	D₈×C₄₇	—	8	4	no	—
163	D₈×C₄₇	—	8	4	no	—
164	C₂×C₈×C₄₇	—	2	2	no	—
165	C₂×C₈×C₄₇	—	2	2	no	—
166	C₂×C₈×C₄₇	—	2	2	no	—
167	C₂×C₈×C₄₇	—	4	2	no	—
168	C₄⋊C₄×C₄₇	—	2	4	no	—
169	C₄⋊C₄×C₄₇	—	2	2	no	—
170	C₄⋊C₄×C₄₇	—	2	1	no	—
171	C₄⋊C₄×C₄₇	—	2	1	no	—
172	C₄⋊C₄×C₄₇	—	2	2	no	—
173	C₄⋊C₄×C₄₇	—	2	1	no	—
174	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
175	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
176	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
177	C₂²⋊C₄×C₄₇	—	2	4	no	—
178	C₂²⋊C₄×C₄₇	—	2	4	no	—
179	C₂²⋊C₄×C₄₇	—	2	2	no	—
180	C₂²⋊C₄×C₄₇	—	2	2	no	—
181	C₂²⋊C₄×C₄₇	—	2	2	no	—
182	C₂²⋊C₄×C₄₇	—	2	2	no	—
183	C₄²×C₄₇	—	2	2	no	—
184	C₄²×C₄₇	—	2	2	no	—
185	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
189	C₂³×C₄₇	—	2	2	no	—
190	C₂³×C₄₇	—	2	2	no	—
191	C₂³×C₄₇	—	4	2	no	—
192	C₂³×C₄₇	—	8	2	no	—
193	C₂³×C₄₇	—	8	2	no	—
194	C₂³×C₄₇	—	8	2	no	—
195	C₂³×C₄₇	#120	1	1	yes	characteristic
196	Q₈×C₄₇	—	2	2	no	—
197	Q₈×C₄₇	—	2	4	no	—
198	Q₈×C₄₇	—	4	8	no	—
199	Q₈×C₄₇	—	4	1	no	—
200	Q₈×C₄₇	—	4	1	no	—
201	Q₈×C₄₇	—	4	2	no	—
202	Q₈×C₄₇	C₂×D₈	1	4	yes	—
203	D₄×C₄₇	—	2	4	no	—
204	D₄×C₄₇	—	4	2	no	—
205	D₄×C₄₇	—	4	8	no	—
206	D₄×C₄₇	—	4	4	no	—
207	D₄×C₄₇	—	4	4	no	—
208	D₄×C₄₇	—	4	4	no	—
209	D₄×C₄₇	—	4	1	no	—
210	D₄×C₄₇	—	4	2	no	—
211	D₄×C₄₇	—	4	1	no	—
212	D₄×C₄₇	—	4	2	no	—
213	D₄×C₄₇	—	4	2	no	—
214	D₄×C₄₇	—	4	4	no	—
215	D₄×C₄₇	—	4	2	no	—
216	D₄×C₄₇	—	8	1	no	—
217	D₄×C₄₇	—	8	2	no	—
218	D₄×C₄₇	—	8	2	no	—
219	D₄×C₄₇	—	8	4	no	—
220	D₄×C₄₇	—	8	2	no	—
221	C₂×C₄×C₄₇	—	2	2	no	—
222	C₂×C₄×C₄₇	—	2	4	no	—
223	C₂×C₄×C₄₇	—	2	2	no	—
224	C₂×C₄×C₄₇	—	2	2	no	—
225	C₂×C₄×C₄₇	—	2	2	no	—
226	C₂×C₄×C₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	—	4	1	no	—
228	C₂×C₄×C₄₇	—	4	8	no	—
229	C₂×C₄×C₄₇	—	4	8	no	—
230	C₂×C₄×C₄₇	—	4	2	no	—
231	C₂×C₄×C₄₇	—	4	2	no	—
232	C₂×C₄×C₄₇	—	4	4	no	—
233	C₂×C₄×C₄₇	—	8	1	no	—
234	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
235	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
236	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
238	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
239	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
242	C₈×C₄₇	—	4	2	no	—
243	C₈×C₄₇	—	4	2	no	—
244	C₈×C₄₇	—	4	2	no	—
245	#18912	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
246	C₂²×C₄₇	—	2	1	no	—
247	C₂²×C₄₇	—	2	1	no	—
248	C₂²×C₄₇	—	4	2	no	—
249	C₂²×C₄₇	—	4	2	no	—
250	C₂²×C₄₇	—	4	2	no	—
251	C₂²×C₄₇	—	4	2	no	—
252	C₂²×C₄₇	—	4	2	no	—
253	C₂²×C₄₇	—	4	2	no	—
254	C₂²×C₄₇	—	8	2	no	—
255	C₂²×C₄₇	—	8	2	no	—
256	C₂²×C₄₇	—	8	2	no	—
257	C₂²×C₄₇	—	16	4	no	—
258	C₂²×C₄₇	#447	1	2	yes	—
259	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
260	C₄×C₄₇	—	2	4	no	—
261	C₄×C₄₇	—	2	1	no	—
262	C₄×C₄₇	—	2	1	no	—
263	C₄×C₄₇	—	2	1	no	—
264	C₄×C₄₇	—	4	2	no	—
265	C₄×C₄₇	—	4	2	no	—
266	C₄×C₄₇	—	4	2	no	—
267	C₄×C₄₇	#447	1	2	yes	—
268	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
269	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
270	C₄×C₄₇	#577	1	2	yes	—
271	#3497	C₂×C₄₇	1	1	yes	characteristic, complemented
272	#3205	C₂×C₄₇	1	1	yes	characteristic, complemented
273	#3205	C₂×C₄₇	1	1	yes	characteristic, complemented
274	C₂×#460	C₂×C₄₇	1	1	yes	characteristic, complemented
275	#1627	C₂×C₄₇	1	4	yes	complemented
276	#1621	C₂×C₄₇	1	4	yes	complemented
277	#1540	C₂×C₄₇	1	1	yes	characteristic, complemented
278	#1480	C₂×C₄₇	1	1	yes	characteristic, complemented
279	#1479	C₂×C₄₇	1	1	yes	characteristic, complemented
280	C₂×C₄₇	—	2	2	no	—
281	C₂×C₄₇	—	8	2	no	—
282	C₂×C₄₇	—	8	2	no	—
283	C₂×C₄₇	—	16	2	no	—
284	C₂×C₄₇	C₂×#447	1	1	yes	characteristic
285	C₂×C₄₇	#3010	1	1	yes	characteristic
286	C₂×C₄₇	#3021	1	1	yes	characteristic
287	C₂×2₋¹⁺⁴	—	2	1	no	—
288	C₂²×SD₁₆	—	2	1	no	—
289	#550	—	2	1	no	—
290	#550	C₂²×C₄₇	1	2	yes	complemented
291	D₄×Q₈	—	2	1	no	—
292	D₄×Q₈	C₂²×C₄₇	1	2	yes	complemented
293	#548	—	2	2	no	—
294	#548	—	2	2	no	—
295	#537	—	2	2	no	—
296	#537	—	2	1	no	—
297	#532	—	2	2	no	—
298	#532	C₂²×C₄₇	1	1	yes	characteristic
299	#532	C₂²×C₄₇	1	1	yes	characteristic
300	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
301	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
302	#493	—	2	1	no	—
303	#493	C₂²×C₄₇	1	2	yes	—
304	#486	—	2	1	no	—
305	#486	C₂²×C₄₇	1	2	yes	—
306	#460	—	2	2	no	—
307	#460	C₂²×C₄₇	1	4	yes	—
308	#459	—	2	2	no	—
309	#459	C₂²×C₄₇	1	4	yes	—
310	#447	—	2	2	no	—
311	#447	—	2	2	no	—
312	#431	C₂²×C₄₇	1	1	yes	characteristic
313	#431	C₂²×C₄₇	1	1	yes	characteristic
314	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
315	C₂×#102	—	2	1	no	—
316	#332	C₂²×C₄₇	1	2	yes	complemented
317	#331	C₂²×C₄₇	1	2	yes	complemented
318	Q₈⋊C₈	C₂²×C₄₇	1	4	yes	complemented
319	D₄⋊C₈	C₂²×C₄₇	1	4	yes	complemented
320	C₄₇	#18912	1	1	yes	characteristic, direct product factor, Sylow
321	2₋¹⁺⁴	—	4	4	no	—
322	2₋¹⁺⁴	—	4	4	no	—
323	C₂×#41	—	2	4	no	—
324	C₂×#41	—	2	2	no	—
325	C₂×#41	—	2	2	no	—
326	C₂×#41	—	2	1	no	—
327	C₂×#41	—	2	1	no	—
328	C₂²×Q₈	—	2	2	no	—
329	C₂²×Q₈	—	2	2	no	—
330	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	—	2	1	no	—
334	C₂×SD₁₆	—	2	4	no	—
335	C₂×SD₁₆	—	4	4	no	—
336	C₂×D₈	—	2	4	no	—
337	C₂×D₈	—	2	4	no	—
338	C₂²×C₈	—	2	1	no	—
339	C₄⋊Q₈	—	2	2	no	—
340	C₄⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
341	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
342	#127	—	2	2	no	—
343	#127	—	2	1	no	—
344	#127	—	2	1	no	—
345	#127	—	2	1	no	—
346	#127	D₄×C₄₇	1	1	yes	characteristic
347	#127	C₂³×C₄₇	1	2	yes	—
348	#127	C₂³×C₄₇	1	1	yes	characteristic
349	#124	—	2	4	no	—
350	#124	—	2	1	no	—
351	#124	—	2	1	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	—	2	4	no	—
354	C₂²⋊Q₈	—	2	2	no	—
355	C₂²⋊Q₈	—	2	4	no	—
356	#121	—	2	4	no	—
357	#121	—	2	2	no	—
358	#121	—	2	4	no	—
359	#121	—	2	4	no	—
360	#121	—	2	1	no	—
361	#121	—	2	1	no	—
362	#121	—	2	2	no	—
363	#121	D₄×C₄₇	1	2	yes	—
364	#121	D₄×C₄₇	1	2	yes	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	D₄×C₄₇	1	2	yes	—
368	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
369	C₄×D₄	—	2	4	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	D₄×C₄₇	1	2	yes	—
375	C₄×D₄	C₂³×C₄₇	1	2	yes	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
383	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
384	#102	—	2	4	no	—
385	#102	—	2	4	no	—
386	#102	—	2	4	no	—
387	C₂²⋊C₈	—	2	1	no	—
388	C₂²⋊C₈	—	2	1	no	—
389	C₄×C₈	—	2	1	no	—
390	C₄×C₈	C₂³×C₄₇	1	2	yes	—
391	C₂⁴	—	4	1	no	—
392	#41	—	4	16	no	—
393	#41	—	4	4	no	—
394	#41	—	4	8	no	—
395	#41	—	4	4	no	—
396	#41	—	4	2	no	—
397	#41	—	4	2	no	—
398	#41	—	4	2	no	—
399	#41	—	4	2	no	—
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	4	4	no	—
406	C₂×Q₈	—	4	8	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	D₈×C₄₇	1	4	yes	complemented
409	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂×D₄	—	4	1	no	—
423	C₂×D₄	—	4	1	no	—
424	C₂×D₄	—	4	2	no	—
425	C₂×D₄	—	4	2	no	—
426	C₂×D₄	—	8	2	no	—
427	C₂×D₄	—	8	2	no	—
428	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
429	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
439	SD₁₆	—	4	8	no	—
440	D₈	—	8	4	no	—
441	D₈	—	8	4	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	4	2	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
453	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
454	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	2	2	no	—
463	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
464	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
465	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
466	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
467	C₂³	—	2	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	8	2	no	—
471	C₂³	—	8	2	no	—
472	C₂³	—	8	2	no	—
473	C₂³	#120×C₄₇	1	1	yes	characteristic
474	Q₈	—	2	2	no	—
475	Q₈	—	2	4	no	—
476	Q₈	—	4	8	no	—
477	Q₈	—	4	1	no	—
478	Q₈	—	4	1	no	—
479	Q₈	—	4	2	no	—
480	Q₈	C₂×D₈×C₄₇	1	4	yes	—
481	D₄	—	2	4	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	8	no	—
484	D₄	—	4	4	no	—
485	D₄	—	4	4	no	—
486	D₄	—	4	4	no	—
487	D₄	—	4	1	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	1	no	—
490	D₄	—	4	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	4	no	—
493	D₄	—	4	2	no	—
494	D₄	—	8	1	no	—
495	D₄	—	8	2	no	—
496	D₄	—	8	2	no	—
497	D₄	—	8	4	no	—
498	D₄	—	8	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	8	no	—
507	C₂×C₄	—	4	8	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	8	1	no	—
512	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
513	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
514	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
515	C₂×C₄	C₂×D₈×C₄₇	1	2	yes	—
516	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
517	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
520	C₈	—	4	2	no	—
521	C₈	—	4	2	no	—
522	C₈	—	4	2	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	8	2	no	—
532	C₂²	—	8	2	no	—
533	C₂²	—	8	2	no	—
534	C₂²	—	16	4	no	—
535	C₂²	C₄₇×#447	1	2	yes	—
536	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
537	C₄	—	2	4	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	2	no	—
544	C₄	C₄₇×#447	1	2	yes	—
545	C₄	C₂²×D₈×C₄₇	1	1	yes	characteristic
546	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
547	C₄	C₄₇×#577	1	2	yes	—
548	C₂	—	2	2	no	—
549	C₂	—	8	2	no	—
550	C₂	—	8	2	no	—
551	C₂	—	16	2	no	—
552	C₂	C₂×C₄₇×#447	1	1	yes	characteristic
553	C₂	C₄₇×#3010	1	1	yes	characteristic
554	C₂	C₄₇×#3021	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×#3497	C₂	semidirect
2. C₄₇×#3205	C₂	semidirect
3. C₄₇×#3205	C₂	semidirect
4. C₂×C₄₇×#460	C₂	semidirect
5. C₄₇×#1627	C₂	semidirect
6. C₄₇×#1621	C₂	semidirect
7. C₄₇×#1540	C₂	semidirect
8. C₄₇×#1480	C₂	semidirect
9. C₄₇×#1479	C₂	semidirect
13. C₄₇×#550	C₂²	semidirect
15. D₄×Q₈×C₄₇	C₂²	semidirect
39. C₄₇×#332	C₂²	semidirect
40. C₄₇×#331	C₂²	semidirect
41. C₄₇×Q₈⋊C₈	C₂²	semidirect
42. C₄₇×D₄⋊C₈	C₂²	semidirect
130. C₂×Q₈×C₄₇	D₈	semidirect
245. #18912	C₄₇	direct (N × H)
271. #3497	C₂×C₄₇	semidirect
272. #3205	C₂×C₄₇	semidirect
273. #3205	C₂×C₄₇	semidirect
274. C₂×#460	C₂×C₄₇	semidirect
275. #1627	C₂×C₄₇	semidirect
276. #1621	C₂×C₄₇	semidirect
277. #1540	C₂×C₄₇	semidirect
278. #1480	C₂×C₄₇	semidirect
279. #1479	C₂×C₄₇	semidirect
290. #550	C₂²×C₄₇	semidirect
292. D₄×Q₈	C₂²×C₄₇	semidirect
316. #332	C₂²×C₄₇	semidirect
317. #331	C₂²×C₄₇	semidirect
318. Q₈⋊C₈	C₂²×C₄₇	semidirect
319. D₄⋊C₈	C₂²×C₄₇	semidirect
320. C₄₇	#18912	direct (N × H)
408. C₂×Q₈	D₈×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#3497	2
C₄₇×#3205	2
C₂×C₄₇×#460	2
C₄₇×#1627	2
C₄₇×#1621	2
C₄₇×#1540	2
C₄₇×#1480	2
C₄₇×#1479	2
#18912	47

Subgroups — C47×#18912 #26058610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18912 #26058610