Subgroups — C₄₇×#19269 #26058967

Order 12032.

716 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3115	C₂	1	2	yes	maximal, complemented
3	C₈×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1670	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1669	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1668	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1667	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1666	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1665	C₂	1	2	yes	maximal, complemented
10	C₄₇×#1568	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1553	C₂	1	2	yes	maximal, complemented
12	C₂×#135×C₄₇	—	2	1	no	—
13	C₂×#135×C₄₇	—	2	1	no	—
14	C₄₇×#532	C₂²	1	2	yes	—
15	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#495	—	2	1	no	—
17	C₄₇×#495	—	2	1	no	—
18	C₄₇×#494	C₂²	1	1	yes	characteristic
19	C₄₇×#493	C₂²	1	1	yes	characteristic
20	C₄₇×#492	C₂²	1	2	yes	—
21	C₄₇×#482	—	2	2	no	—
22	C₄₇×#475	C₂²	1	2	yes	—
23	C₄₇×#474	C₂²	1	2	yes	—
24	C₄₇×#460	C₂²	1	2	yes	—
25	C₄₇×#459	C₂²	1	2	yes	—
26	C₄₇×#449	—	2	2	no	—
27	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#442	—	2	2	no	—
30	C₄₇×#440	—	2	2	no	—
31	C₈×D₄×C₄₇	—	2	1	no	—
32	C₈×D₄×C₄₇	—	2	1	no	—
33	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
34	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#432	C₂²	1	2	yes	—
36	C₄₇×#431	—	2	1	no	—
37	C₄₇×#431	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₇	—	2	1	no	—
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#335	C₂²	1	1	yes	characteristic
41	C₄₇×#335	C₂²	1	1	yes	characteristic
42	C₄₇×#334	C₂²	1	2	yes	—
43	C₄₇×#332	C₂²	1	2	yes	—
44	C₄₇×#332	C₂²	1	2	yes	—
45	C₄₇×#331	C₂²	1	2	yes	—
46	C₄₇×#331	C₂²	1	2	yes	—
47	C₂×#41×C₄₇	—	2	2	no	—
48	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
49	#135×C₄₇	—	4	4	no	—
50	#135×C₄₇	—	4	4	no	—
51	C₂×Q₁₆×C₄₇	—	2	1	no	—
52	C₂×Q₁₆×C₄₇	—	2	1	no	—
53	C₂×SD₁₆×C₄₇	—	2	2	no	—
54	C₂×SD₁₆×C₄₇	—	2	2	no	—
55	C₂×SD₁₆×C₄₇	—	2	2	no	—
56	C₂×D₈×C₄₇	—	2	2	no	—
57	C₂×D₈×C₄₇	—	2	1	no	—
58	C₂×D₈×C₄₇	—	2	1	no	—
59	C₂²×C₈×C₄₇	—	2	1	no	—
60	C₂²×C₈×C₄₇	—	2	1	no	—
61	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
63	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
64	#127×C₄₇	C₂³	1	2	yes	—
65	#124×C₄₇	—	2	2	no	—
66	#121×C₄₇	—	2	2	no	—
67	#121×C₄₇	—	2	2	no	—
68	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
69	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
70	C₄×D₄×C₄₇	—	2	1	no	—
71	C₄×D₄×C₄₇	—	2	1	no	—
72	C₄×D₄×C₄₇	—	2	2	no	—
73	C₄×D₄×C₄₇	—	2	2	no	—
74	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
75	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
76	#117×C₄₇	—	2	1	no	—
77	#117×C₄₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	—	2	1	no	—
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	#107×C₄₇	—	2	2	no	—
81	#106×C₄₇	—	2	2	no	—
82	C₄⋊C₈×C₄₇	—	2	1	no	—
83	C₄⋊C₈×C₄₇	—	2	1	no	—
84	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
85	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
86	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
88	#103×C₄₇	—	2	2	no	—
89	#102×C₄₇	—	2	2	no	—
90	#102×C₄₇	—	2	2	no	—
91	#102×C₄₇	—	2	2	no	—
92	C₂²⋊C₈×C₄₇	—	2	2	no	—
93	C₂²⋊C₈×C₄₇	—	2	1	no	—
94	C₂²⋊C₈×C₄₇	—	2	1	no	—
95	C₂²⋊C₈×C₄₇	—	2	1	no	—
96	#97×C₄₇	—	2	2	no	—
97	C₄×C₈×C₄₇	—	2	1	no	—
98	C₄×C₈×C₄₇	—	2	1	no	—
99	C₄×C₈×C₄₇	—	2	1	no	—
100	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
101	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
102	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
104	#41×C₄₇	—	2	2	no	—
105	#41×C₄₇	—	2	2	no	—
106	#41×C₄₇	—	4	4	no	—
107	#41×C₄₇	—	4	4	no	—
108	C₂×Q₈×C₄₇	—	2	2	no	—
109	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂×D₄×C₄₇	—	2	1	no	—
111	C₂×D₄×C₄₇	—	2	2	no	—
112	C₂×D₄×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	—	2	2	no	—
114	C₂×D₄×C₄₇	—	4	2	no	—
115	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	—	2	1	no	—
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	—	2	1	no	—
119	C₂²×C₄×C₄₇	—	4	2	no	—
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
123	Q₁₆×C₄₇	—	4	2	no	—
124	Q₁₆×C₄₇	—	4	2	no	—
125	SD₁₆×C₄₇	—	4	4	no	—
126	SD₁₆×C₄₇	—	4	4	no	—
127	SD₁₆×C₄₇	—	4	4	no	—
128	D₈×C₄₇	—	4	2	no	—
129	D₈×C₄₇	—	4	4	no	—
130	D₈×C₄₇	—	4	2	no	—
131	C₂×C₈×C₄₇	—	2	2	no	—
132	C₂×C₈×C₄₇	—	2	2	no	—
133	C₂×C₈×C₄₇	—	2	2	no	—
134	C₂×C₈×C₄₇	—	2	1	no	—
135	C₂×C₈×C₄₇	—	2	1	no	—
136	C₂×C₈×C₄₇	—	2	2	no	—
137	C₂×C₈×C₄₇	—	4	2	no	—
138	C₂×C₈×C₄₇	—	4	2	no	—
139	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
143	C₄⋊C₄×C₄₇	—	2	1	no	—
144	C₄⋊C₄×C₄₇	—	2	1	no	—
145	C₄⋊C₄×C₄₇	—	2	2	no	—
146	C₄⋊C₄×C₄₇	—	2	2	no	—
147	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
148	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₂²⋊C₄×C₄₇	—	2	1	no	—
150	C₂²⋊C₄×C₄₇	—	2	1	no	—
151	C₂²⋊C₄×C₄₇	—	2	1	no	—
152	C₂²⋊C₄×C₄₇	—	4	2	no	—
153	C₂²⋊C₄×C₄₇	—	4	2	no	—
154	C₄²×C₄₇	—	2	1	no	—
155	C₄²×C₄₇	—	2	1	no	—
156	C₄²×C₄₇	—	2	1	no	—
157	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₄₇	#41	1	1	yes	characteristic
160	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
161	C₂³×C₄₇	—	2	1	no	—
162	C₂³×C₄₇	—	4	2	no	—
163	C₂³×C₄₇	#121	1	1	yes	characteristic
164	Q₈×C₄₇	—	2	1	no	—
165	Q₈×C₄₇	—	4	2	no	—
166	Q₈×C₄₇	—	4	2	no	—
167	Q₈×C₄₇	#135	1	2	yes	complemented
168	D₄×C₄₇	—	2	4	no	—
169	D₄×C₄₇	—	2	1	no	—
170	D₄×C₄₇	—	4	2	no	—
171	D₄×C₄₇	—	4	2	no	—
172	D₄×C₄₇	—	4	2	no	—
173	D₄×C₄₇	—	4	2	no	—
174	D₄×C₄₇	—	8	2	no	—
175	D₄×C₄₇	—	8	4	no	—
176	D₄×C₄₇	#135	1	2	yes	complemented
177	C₂×C₄×C₄₇	—	2	4	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	1	no	—
182	C₂×C₄×C₄₇	—	2	1	no	—
183	C₂×C₄×C₄₇	—	2	1	no	—
184	C₂×C₄×C₄₇	—	2	1	no	—
185	C₂×C₄×C₄₇	—	4	1	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	4	1	no	—
188	C₂×C₄×C₄₇	—	4	1	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	—	8	4	no	—
191	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
192	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
193	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
197	C₈×C₄₇	—	2	1	no	—
198	C₈×C₄₇	—	2	1	no	—
199	C₈×C₄₇	—	4	2	no	—
200	C₈×C₄₇	—	4	2	no	—
201	C₈×C₄₇	—	4	1	no	—
202	C₈×C₄₇	—	4	1	no	—
203	C₈×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
204	C₈×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
205	#19269	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂²×C₄₇	—	2	1	no	—
207	C₂²×C₄₇	—	2	1	no	—
208	C₂²×C₄₇	—	2	2	no	—
209	C₂²×C₄₇	—	2	1	no	—
210	C₂²×C₄₇	—	4	1	no	—
211	C₂²×C₄₇	—	4	1	no	—
212	C₂²×C₄₇	—	8	2	no	—
213	C₂²×C₄₇	—	8	2	no	—
214	C₂²×C₄₇	—	8	2	no	—
215	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
216	C₄×C₄₇	—	2	1	no	—
217	C₄×C₄₇	—	2	1	no	—
218	C₄×C₄₇	—	2	2	no	—
219	C₄×C₄₇	—	2	1	no	—
220	C₄×C₄₇	—	2	1	no	—
221	C₄×C₄₇	—	4	1	no	—
222	C₄×C₄₇	—	4	1	no	—
223	C₄×C₄₇	—	8	2	no	—
224	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
225	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
226	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
228	#3147	C₂×C₄₇	1	1	yes	characteristic, complemented
229	#3115	C₂×C₄₇	1	2	yes	complemented
230	C₈×#41	C₂×C₄₇	1	1	yes	characteristic, complemented
231	#1670	C₂×C₄₇	1	1	yes	characteristic, complemented
232	#1669	C₂×C₄₇	1	1	yes	characteristic, complemented
233	#1668	C₂×C₄₇	1	1	yes	characteristic, complemented
234	#1667	C₂×C₄₇	1	1	yes	characteristic, complemented
235	#1666	C₂×C₄₇	1	2	yes	complemented
236	#1665	C₂×C₄₇	1	2	yes	complemented
237	#1568	C₂×C₄₇	1	1	yes	characteristic, complemented
238	#1553	C₂×C₄₇	1	2	yes	complemented
239	C₂×C₄₇	—	4	1	no	—
240	C₂×C₄₇	—	4	2	no	—
241	C₂×C₄₇	—	16	2	no	—
242	C₂×C₄₇	#3038	1	1	yes	characteristic
243	C₂×C₄₇	#3050	1	1	yes	characteristic
244	C₂×C₄₇	#3067	1	1	yes	characteristic
245	C₂×#135	—	2	1	no	—
246	C₂×#135	—	2	1	no	—
247	#532	C₂²×C₄₇	1	2	yes	—
248	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
249	#495	—	2	1	no	—
250	#495	—	2	1	no	—
251	#494	C₂²×C₄₇	1	1	yes	characteristic
252	#493	C₂²×C₄₇	1	1	yes	characteristic
253	#492	C₂²×C₄₇	1	2	yes	—
254	#482	—	2	2	no	—
255	#475	C₂²×C₄₇	1	2	yes	—
256	#474	C₂²×C₄₇	1	2	yes	—
257	#460	C₂²×C₄₇	1	2	yes	—
258	#459	C₂²×C₄₇	1	2	yes	—
259	#449	—	2	2	no	—
260	C₈×Q₈	C₂²×C₄₇	1	1	yes	characteristic
261	C₈×Q₈	C₂²×C₄₇	1	1	yes	characteristic
262	#442	—	2	2	no	—
263	#440	—	2	2	no	—
264	C₈×D₄	—	2	1	no	—
265	C₈×D₄	—	2	1	no	—
266	C₈×D₄	C₂²×C₄₇	1	1	yes	characteristic
267	C₈×D₄	C₂²×C₄₇	1	1	yes	characteristic
268	#432	C₂²×C₄₇	1	2	yes	—
269	#431	—	2	1	no	—
270	#431	C₂²×C₄₇	1	1	yes	characteristic
271	C₂×C₄×C₈	—	2	1	no	—
272	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
273	#335	C₂²×C₄₇	1	1	yes	characteristic
274	#335	C₂²×C₄₇	1	1	yes	characteristic
275	#334	C₂²×C₄₇	1	2	yes	—
276	#332	C₂²×C₄₇	1	2	yes	—
277	#332	C₂²×C₄₇	1	2	yes	—
278	#331	C₂²×C₄₇	1	2	yes	—
279	#331	C₂²×C₄₇	1	2	yes	—
280	C₄₇	#19269	1	1	yes	characteristic, direct product factor, Sylow
281	C₂×#41	—	2	2	no	—
282	C₂×#41	D₄×C₄₇	1	1	yes	characteristic
283	#135	—	4	4	no	—
284	#135	—	4	4	no	—
285	C₂×Q₁₆	—	2	1	no	—
286	C₂×Q₁₆	—	2	1	no	—
287	C₂×SD₁₆	—	2	2	no	—
288	C₂×SD₁₆	—	2	2	no	—
289	C₂×SD₁₆	—	2	2	no	—
290	C₂×D₈	—	2	2	no	—
291	C₂×D₈	—	2	1	no	—
292	C₂×D₈	—	2	1	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	2	1	no	—
295	C₂²×C₈	D₄×C₄₇	1	1	yes	characteristic
296	C₂²×C₈	D₄×C₄₇	1	1	yes	characteristic
297	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
298	#127	C₂³×C₄₇	1	2	yes	—
299	#124	—	2	2	no	—
300	#121	—	2	2	no	—
301	#121	—	2	2	no	—
302	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
303	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
309	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
310	#117	—	2	1	no	—
311	#117	D₄×C₄₇	1	1	yes	characteristic
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
314	#107	—	2	2	no	—
315	#106	—	2	2	no	—
316	C₄⋊C₈	—	2	1	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
319	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
320	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
321	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
322	#103	—	2	2	no	—
323	#102	—	2	2	no	—
324	#102	—	2	2	no	—
325	#102	—	2	2	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	2	2	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	C₂²⋊C₈	—	2	1	no	—
330	#97	—	2	2	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	2	1	no	—
333	C₄×C₈	—	2	1	no	—
334	C₄×C₈	D₄×C₄₇	1	1	yes	characteristic
335	C₄×C₈	D₄×C₄₇	1	1	yes	characteristic
336	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
337	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
338	#41	—	2	2	no	—
339	#41	—	2	2	no	—
340	#41	—	4	4	no	—
341	#41	—	4	4	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
356	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
357	Q₁₆	—	4	2	no	—
358	Q₁₆	—	4	2	no	—
359	SD₁₆	—	4	4	no	—
360	SD₁₆	—	4	4	no	—
361	SD₁₆	—	4	4	no	—
362	D₈	—	4	2	no	—
363	D₈	—	4	4	no	—
364	D₈	—	4	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	4	2	no	—
372	C₂×C₈	—	4	2	no	—
373	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
374	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
375	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
376	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
382	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₂²⋊C₄	—	4	2	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
392	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
393	C₄²	#41×C₄₇	1	1	yes	characteristic
394	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
395	C₂³	—	2	1	no	—
396	C₂³	—	4	2	no	—
397	C₂³	#121×C₄₇	1	1	yes	characteristic
398	Q₈	—	2	1	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	#135×C₄₇	1	2	yes	complemented
402	D₄	—	2	4	no	—
403	D₄	—	2	1	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	8	2	no	—
409	D₄	—	8	4	no	—
410	D₄	#135×C₄₇	1	2	yes	complemented
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	8	4	no	—
425	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
426	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
427	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	2	no	—
435	C₈	—	4	1	no	—
436	C₈	—	4	1	no	—
437	C₈	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
438	C₈	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	1	no	—
456	C₄	—	8	2	no	—
457	C₄	C₂×#135×C₄₇	1	1	yes	characteristic
458	C₄	C₂×#135×C₄₇	1	1	yes	characteristic
459	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
460	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
461	C₂	—	4	1	no	—
462	C₂	—	4	2	no	—
463	C₂	—	16	2	no	—
464	C₂	C₄₇×#3038	1	1	yes	characteristic
465	C₂	C₄₇×#3050	1	1	yes	characteristic
466	C₂	C₄₇×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#121
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×#3147	C₂	semidirect
2. C₄₇×#3115	C₂	semidirect
3. C₈×#41×C₄₇	C₂	semidirect
4. C₄₇×#1670	C₂	semidirect
5. C₄₇×#1669	C₂	semidirect
6. C₄₇×#1668	C₂	semidirect
7. C₄₇×#1667	C₂	semidirect
8. C₄₇×#1666	C₂	semidirect
9. C₄₇×#1665	C₂	semidirect
10. C₄₇×#1568	C₂	semidirect
11. C₄₇×#1553	C₂	semidirect
167. Q₈×C₄₇	#135	semidirect
176. D₄×C₄₇	#135	semidirect
205. #19269	C₄₇	direct (N × H)
228. #3147	C₂×C₄₇	semidirect
229. #3115	C₂×C₄₇	semidirect
230. C₈×#41	C₂×C₄₇	semidirect
231. #1670	C₂×C₄₇	semidirect
232. #1669	C₂×C₄₇	semidirect
233. #1668	C₂×C₄₇	semidirect
234. #1667	C₂×C₄₇	semidirect
235. #1666	C₂×C₄₇	semidirect
236. #1665	C₂×C₄₇	semidirect
237. #1568	C₂×C₄₇	semidirect
238. #1553	C₂×C₄₇	semidirect
280. C₄₇	#19269	direct (N × H)
401. Q₈	#135×C₄₇	semidirect
410. D₄	#135×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#3147	2
C₄₇×#3115	2
C₈×#41×C₄₇	2
C₄₇×#1670	2
C₄₇×#1669	2
C₄₇×#1668	2
C₄₇×#1667	2
C₄₇×#1666	2
C₄₇×#1665	2
C₄₇×#1568	2
C₄₇×#1553	2
#19269	47

Subgroups — C47×#19269 #26058967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#19269 #26058967