Subgroups — C₄₇×#24681 #26064379

Order 12032.

822 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#474	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2568	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2354	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#2073	C₂	1	2	yes	maximal
6	C₄₇×#2055	C₂	1	2	yes	maximal
7	C₄₇×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1949	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1928	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₇	—	2	1	no	—
17	C₄₇×#474	—	2	4	no	—
18	C₄×SD₁₆×C₄₇	—	2	4	no	—
19	C₂×#107×C₄₇	C₂²	1	2	yes	—
20	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
23	C₂×#103×C₄₇	C₂²	1	2	yes	—
24	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#102×C₄₇	C₂²	1	2	yes	—
26	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₄₇×#400	—	2	2	no	—
29	C₄₇×#391	—	2	1	no	—
30	C₄₇×#391	—	2	1	no	—
31	C₄₇×#391	C₂²	1	2	yes	—
32	C₄₇×#390	C₂²	1	2	yes	—
33	C₄₇×#388	—	2	2	no	—
34	C₄₇×#384	C₂²	1	1	yes	characteristic
35	C₄₇×#382	C₂²	1	2	yes	—
36	C₄₇×#380	—	2	1	no	—
37	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₄₇×#340	C₂²	1	2	yes	—
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₄₇×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₇	—	2	1	no	—
44	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	—	2	1	no	—
47	C₂×SD₁₆×C₄₇	—	2	2	no	—
48	C₂×SD₁₆×C₄₇	—	2	2	no	—
49	C₂×SD₁₆×C₄₇	—	2	2	no	—
50	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
52	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
53	C₄⋊Q₈×C₄₇	—	2	2	no	—
54	C₄⋊Q₈×C₄₇	—	2	2	no	—
55	C₄×Q₈×C₄₇	—	2	2	no	—
56	C₄×Q₈×C₄₇	—	2	2	no	—
57	C₄×D₄×C₄₇	—	2	2	no	—
58	C₄×D₄×C₄₇	D₄	1	4	yes	—
59	#117×C₄₇	—	4	4	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
73	C₂×C₄²×C₄₇	—	2	2	no	—
74	C₂×C₄²×C₄₇	—	2	1	no	—
75	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	#107×C₄₇	—	2	4	no	—
78	#106×C₄₇	—	2	2	no	—
79	C₄⋊C₈×C₄₇	—	2	4	no	—
80	C₄⋊C₈×C₄₇	—	2	2	no	—
81	#103×C₄₇	—	2	4	no	—
82	#103×C₄₇	—	2	2	no	—
83	#102×C₄₇	—	2	4	no	—
84	#102×C₄₇	—	2	2	no	—
85	C₄×C₈×C₄₇	—	2	2	no	—
86	#95×C₄₇	—	2	2	no	—
87	#95×C₄₇	—	2	2	no	—
88	#95×C₄₇	—	2	2	no	—
89	#95×C₄₇	—	2	2	no	—
90	#95×C₄₇	—	2	2	no	—
91	#95×C₄₇	D₄	1	2	yes	—
92	C₂⁴×C₄₇	—	2	1	no	—
93	C₂×Q₈×C₄₇	—	2	1	no	—
94	C₂×Q₈×C₄₇	—	2	1	no	—
95	C₂×Q₈×C₄₇	—	2	1	no	—
96	C₂×Q₈×C₄₇	—	2	1	no	—
97	C₂×Q₈×C₄₇	—	2	1	no	—
98	C₂×Q₈×C₄₇	—	4	2	no	—
99	C₂×Q₈×C₄₇	—	4	2	no	—
100	C₂×Q₈×C₄₇	—	4	2	no	—
101	C₂×Q₈×C₄₇	#41	1	2	yes	—
102	C₂×D₄×C₄₇	—	2	1	no	—
103	C₂×D₄×C₄₇	—	2	1	no	—
104	C₂×D₄×C₄₇	—	2	1	no	—
105	C₂×D₄×C₄₇	—	2	1	no	—
106	C₂×D₄×C₄₇	—	2	1	no	—
107	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	—	2	1	no	—
109	C₂²×C₄×C₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	—	2	4	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	4	2	no	—
115	C₂²×C₄×C₄₇	—	4	2	no	—
116	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
121	SD₁₆×C₄₇	—	2	8	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₂×C₈×C₄₇	—	2	1	no	—
129	C₂×C₈×C₄₇	—	2	1	no	—
130	C₂×C₈×C₄₇	#41	1	2	yes	—
131	C₄⋊C₄×C₄₇	—	2	2	no	—
132	C₄⋊C₄×C₄₇	—	2	2	no	—
133	C₄⋊C₄×C₄₇	—	2	1	no	—
134	C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₄⋊C₄×C₄₇	—	2	2	no	—
136	C₄⋊C₄×C₄₇	—	2	2	no	—
137	C₄⋊C₄×C₄₇	—	2	1	no	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	—	2	2	no	—
140	C₄⋊C₄×C₄₇	—	4	2	no	—
141	C₄⋊C₄×C₄₇	—	4	2	no	—
142	C₄⋊C₄×C₄₇	—	4	2	no	—
143	C₄⋊C₄×C₄₇	—	8	1	no	—
144	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
145	C₂²⋊C₄×C₄₇	—	2	4	no	—
146	C₂²⋊C₄×C₄₇	—	4	4	no	—
147	C₂²⋊C₄×C₄₇	—	8	2	no	—
148	C₄²×C₄₇	—	2	2	no	—
149	C₄²×C₄₇	—	2	2	no	—
150	C₄²×C₄₇	—	4	4	no	—
151	C₄²×C₄₇	—	4	2	no	—
152	C₄²×C₄₇	C₂×D₄	1	2	yes	—
153	C₄²×C₄₇	#41	1	2	yes	—
154	C₂³×C₄₇	—	2	2	no	—
155	C₂³×C₄₇	—	4	1	no	—
156	C₂³×C₄₇	—	4	1	no	—
157	C₂³×C₄₇	—	4	1	no	—
158	C₂³×C₄₇	—	4	1	no	—
159	C₂³×C₄₇	—	4	1	no	—
160	C₂³×C₄₇	—	4	1	no	—
161	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₄₇	—	2	2	no	—
163	Q₈×C₄₇	—	2	2	no	—
164	Q₈×C₄₇	—	4	1	no	—
165	Q₈×C₄₇	—	4	1	no	—
166	Q₈×C₄₇	—	8	4	no	—
167	D₄×C₄₇	—	2	2	no	—
168	D₄×C₄₇	—	2	2	no	—
169	D₄×C₄₇	—	4	1	no	—
170	D₄×C₄₇	—	4	1	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	—	4	1	no	—
183	C₂×C₄×C₄₇	—	4	1	no	—
184	C₂×C₄×C₄₇	—	4	1	no	—
185	C₂×C₄×C₄₇	—	4	8	no	—
186	C₂×C₄×C₄₇	—	4	1	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	—	4	2	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	—	4	2	no	—
191	C₂×C₄×C₄₇	—	4	2	no	—
192	C₂×C₄×C₄₇	—	4	2	no	—
193	C₂×C₄×C₄₇	—	4	1	no	—
194	C₂×C₄×C₄₇	—	4	1	no	—
195	C₂×C₄×C₄₇	#121	1	2	yes	—
196	C₂×C₄×C₄₇	#121	1	2	yes	—
197	C₂×C₄×C₄₇	#135	1	2	yes	—
198	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
199	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
204	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
205	C₈×C₄₇	—	2	2	no	—
206	C₈×C₄₇	—	4	2	no	—
207	C₈×C₄₇	—	4	1	no	—
208	#24681	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂²×C₄₇	—	4	2	no	—
210	C₂²×C₄₇	—	4	2	no	—
211	C₂²×C₄₇	—	4	2	no	—
212	C₂²×C₄₇	—	8	1	no	—
213	C₂²×C₄₇	—	8	1	no	—
214	C₂²×C₄₇	—	8	1	no	—
215	C₂²×C₄₇	—	8	1	no	—
216	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
217	C₂²×C₄₇	#547	1	1	yes	characteristic
218	C₂²×C₄₇	#548	1	1	yes	characteristic
219	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
220	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₂²×C₄₇	#577	1	1	yes	characteristic
222	C₂²×C₄₇	#578	1	1	yes	characteristic
223	C₄×C₄₇	—	2	2	no	—
224	C₄×C₄₇	—	4	2	no	—
225	C₄×C₄₇	—	4	2	no	—
226	C₄×C₄₇	—	4	2	no	—
227	C₄×C₄₇	—	4	2	no	—
228	C₄×C₄₇	—	8	2	no	—
229	C₄×C₄₇	—	8	2	no	—
230	C₄×C₄₇	—	8	1	no	—
231	C₄×C₄₇	#463	1	4	yes	—
232	C₄×C₄₇	#525	1	1	yes	characteristic
233	C₄×C₄₇	#536	1	1	yes	characteristic
234	C₄×C₄₇	#552	1	1	yes	characteristic
235	C₄×C₄₇	#556	1	1	yes	characteristic
236	C₂×#474	C₂×C₄₇	1	1	yes	characteristic
237	C₂×C₄×SD₁₆	C₂×C₄₇	1	1	yes	characteristic
238	#2568	C₂×C₄₇	1	1	yes	characteristic, complemented
239	#2354	C₂×C₄₇	1	1	yes	characteristic
240	#2073	C₂×C₄₇	1	2	yes	—
241	#2055	C₂×C₄₇	1	2	yes	—
242	#1990	C₂×C₄₇	1	1	yes	characteristic, complemented
243	#1949	C₂×C₄₇	1	2	yes	complemented
244	#1939	C₂×C₄₇	1	1	yes	characteristic, complemented
245	#1928	C₂×C₄₇	1	2	yes	complemented
246	#1803	C₂×C₄₇	1	1	yes	characteristic, complemented
247	C₂×C₄₇	—	8	2	no	—
248	C₂×C₄₇	#2415	1	1	yes	characteristic
249	C₂×C₄₇	C₂×#463	1	1	yes	characteristic
250	C₂×C₄₇	#3046	1	1	yes	characteristic
251	C₂×C₄₇	#3340	1	1	yes	characteristic
252	C₂×C₄₇	#3353	1	1	yes	characteristic
253	C₂×C₄₇	#3364	1	1	yes	characteristic
254	C₂×C₄₇	#3368	1	1	yes	characteristic
255	C₂²×SD₁₆	C₂²×C₄₇	1	1	yes	characteristic
256	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
257	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
258	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
259	C₂×#117	—	2	1	no	—
260	#474	—	2	4	no	—
261	C₄×SD₁₆	—	2	4	no	—
262	C₂×#107	C₂²×C₄₇	1	2	yes	—
263	C₂×#106	C₂²×C₄₇	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
265	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
266	C₂×#103	C₂²×C₄₇	1	2	yes	—
267	C₂×#103	C₂²×C₄₇	1	1	yes	characteristic
268	C₂×#102	C₂²×C₄₇	1	2	yes	—
269	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
270	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
271	#400	—	2	2	no	—
272	#391	—	2	1	no	—
273	#391	—	2	1	no	—
274	#391	C₂²×C₄₇	1	2	yes	—
275	#390	C₂²×C₄₇	1	2	yes	—
276	#388	—	2	2	no	—
277	#384	C₂²×C₄₇	1	1	yes	characteristic
278	#382	C₂²×C₄₇	1	2	yes	—
279	#380	—	2	1	no	—
280	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
281	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
282	#340	C₂²×C₄₇	1	2	yes	—
283	#340	C₂²×C₄₇	1	2	yes	—
284	#340	C₂²×C₄₇	1	2	yes	—
285	#336	C₂²×C₄₇	1	2	yes	—
286	C₄₇	#24681	1	1	yes	characteristic, direct product factor, Sylow
287	C₂²×Q₈	—	2	1	no	—
288	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
289	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
290	C₂³×C₄	—	2	1	no	—
291	C₂×SD₁₆	—	2	2	no	—
292	C₂×SD₁₆	—	2	2	no	—
293	C₂×SD₁₆	—	2	2	no	—
294	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
296	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
297	C₄⋊Q₈	—	2	2	no	—
298	C₄⋊Q₈	—	2	2	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	D₄×C₄₇	1	4	yes	—
303	#117	—	4	4	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
309	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
320	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
321	#107	—	2	4	no	—
322	#106	—	2	2	no	—
323	C₄⋊C₈	—	2	4	no	—
324	C₄⋊C₈	—	2	2	no	—
325	#103	—	2	4	no	—
326	#103	—	2	2	no	—
327	#102	—	2	2	no	—
328	#102	—	2	4	no	—
329	C₄×C₈	—	2	2	no	—
330	#95	—	2	2	no	—
331	#95	—	2	2	no	—
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	D₄×C₄₇	1	2	yes	—
336	C₂⁴	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	4	2	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×Q₈	—	4	2	no	—
345	C₂×Q₈	#41×C₄₇	1	2	yes	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
365	SD₁₆	—	2	8	no	—
366	C₂×C₈	—	2	1	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	—	2	2	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	#41×C₄₇	1	2	yes	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
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	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	—	8	1	no	—
388	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₂²⋊C₄	—	8	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	4	4	no	—
395	C₄²	—	4	2	no	—
396	C₄²	C₂×D₄×C₄₇	1	2	yes	—
397	C₄²	#41×C₄₇	1	2	yes	—
398	C₂³	—	2	2	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
406	Q₈	—	2	2	no	—
407	Q₈	—	2	2	no	—
408	Q₈	—	4	1	no	—
409	Q₈	—	4	1	no	—
410	Q₈	—	8	4	no	—
411	D₄	—	2	2	no	—
412	D₄	—	2	2	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	8	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	#121×C₄₇	1	2	yes	—
440	C₂×C₄	#121×C₄₇	1	2	yes	—
441	C₂×C₄	#135×C₄₇	1	2	yes	—
442	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
443	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
445	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
446	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
447	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
448	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
449	C₈	—	2	2	no	—
450	C₈	—	4	2	no	—
451	C₈	—	4	1	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
460	C₂²	C₄₇×#547	1	1	yes	characteristic
461	C₂²	C₄₇×#548	1	1	yes	characteristic
462	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
463	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
464	C₂²	C₄₇×#577	1	1	yes	characteristic
465	C₂²	C₄₇×#578	1	1	yes	characteristic
466	C₄	—	2	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	8	2	no	—
472	C₄	—	8	1	no	—
473	C₄	—	8	2	no	—
474	C₄	C₄₇×#463	1	4	yes	—
475	C₄	C₄₇×#525	1	1	yes	characteristic
476	C₄	C₄₇×#536	1	1	yes	characteristic
477	C₄	C₄₇×#552	1	1	yes	characteristic
478	C₄	C₄₇×#556	1	1	yes	characteristic
479	C₂	—	8	2	no	—
480	C₂	C₄₇×#2415	1	1	yes	characteristic
481	C₂	C₂×C₄₇×#463	1	1	yes	characteristic
482	C₂	C₄₇×#3046	1	1	yes	characteristic
483	C₂	C₄₇×#3340	1	1	yes	characteristic
484	C₂	C₄₇×#3353	1	1	yes	characteristic
485	C₂	C₄₇×#3364	1	1	yes	characteristic
486	C₂	C₄₇×#3368	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₄₇×#2568	C₂	semidirect
7. C₄₇×#1990	C₂	semidirect
8. C₄₇×#1949	C₂	semidirect
9. C₄₇×#1939	C₂	semidirect
10. C₄₇×#1928	C₂	semidirect
11. C₄₇×#1803	C₂	semidirect
208. #24681	C₄₇	direct (N × H)
238. #2568	C₂×C₄₇	semidirect
242. #1990	C₂×C₄₇	semidirect
243. #1949	C₂×C₄₇	semidirect
244. #1939	C₂×C₄₇	semidirect
245. #1928	C₂×C₄₇	semidirect
246. #1803	C₂×C₄₇	semidirect
286. C₄₇	#24681	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#474	2
C₂×C₄×SD₁₆×C₄₇	2
C₄₇×#2568	2
C₄₇×#2354	2
C₄₇×#2073	2
C₄₇×#2055	2
C₄₇×#1990	2
C₄₇×#1949	2
C₄₇×#1939	2
C₄₇×#1928	2
C₄₇×#1803	2
#24681	47

Subgroups — C47×#24681 #26064379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#24681 #26064379