Subgroups — C₄₇×#24748 #26064446

Order 12032.

976 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#461	C₂	1	2	yes	maximal
2	C₂×C₄₇×#461	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#440	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2349	C₂	1	1	yes	maximal, characteristic
6	C₄₇×#2068	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2043	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1960	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1877	C₂	1	2	yes	maximal
11	C₄₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#461	—	2	8	no	—
20	C₄₇×#461	—	2	4	no	—
21	C₄₇×#440	—	2	4	no	—
22	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
25	C₂×#103×C₄₇	C₂²	1	2	yes	—
26	C₂×#103×C₄₇	C₂²	1	2	yes	—
27	C₂×#103×C₄₇	C₂²	1	2	yes	—
28	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#103×C₄₇	C₂²	1	2	yes	—
30	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#398	—	2	1	no	—
33	C₄₇×#398	—	2	1	no	—
34	C₄₇×#391	C₂²	1	2	yes	—
35	C₄₇×#389	—	2	2	no	—
36	C₄₇×#389	C₂²	1	2	yes	—
37	C₄₇×#385	—	2	2	no	—
38	C₄₇×#382	C₂²	1	1	yes	characteristic
39	C₄₇×#380	—	2	1	no	—
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#95×C₄₇	—	2	1	no	—
42	C₄₇×#340	C₂²	1	2	yes	—
43	C₄₇×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
45	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	—	2	1	no	—
48	C₂³×C₄×C₄₇	—	2	2	no	—
49	C₂×SD₁₆×C₄₇	—	2	2	no	—
50	C₂×SD₁₆×C₄₇	—	2	2	no	—
51	C₂×SD₁₆×C₄₇	—	2	4	no	—
52	C₂×SD₁₆×C₄₇	—	2	4	no	—
53	C₂×SD₁₆×C₄₇	—	2	4	no	—
54	C₂×SD₁₆×C₄₇	D₄	1	4	yes	—
55	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
56	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₄₇	—	2	4	no	—
59	C₄⋊Q₈×C₄₇	—	2	2	no	—
60	C₄⋊Q₈×C₄₇	—	2	2	no	—
61	C₄⋊Q₈×C₄₇	—	4	2	no	—
62	C₄×Q₈×C₄₇	—	2	2	no	—
63	C₄×Q₈×C₄₇	—	2	2	no	—
64	C₄×D₄×C₄₇	—	2	4	no	—
65	C₄×D₄×C₄₇	—	2	2	no	—
66	C₄×D₄×C₄₇	—	4	2	no	—
67	C₄×D₄×C₄₇	D₄	1	4	yes	—
68	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
74	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
80	C₂×C₄²×C₄₇	—	2	1	no	—
81	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
82	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
83	#107×C₄₇	—	2	2	no	—
84	C₄⋊C₈×C₄₇	—	2	4	no	—
85	C₄⋊C₈×C₄₇	—	2	2	no	—
86	#103×C₄₇	—	2	4	no	—
87	#103×C₄₇	—	2	4	no	—
88	#103×C₄₇	—	2	4	no	—
89	#103×C₄₇	—	2	2	no	—
90	#103×C₄₇	—	4	2	no	—
91	#102×C₄₇	—	2	2	no	—
92	#97×C₄₇	—	2	2	no	—
93	#95×C₄₇	—	2	1	no	—
94	#95×C₄₇	—	2	2	no	—
95	#95×C₄₇	—	2	1	no	—
96	#95×C₄₇	—	2	2	no	—
97	#95×C₄₇	—	2	2	no	—
98	#95×C₄₇	D₄	1	1	yes	characteristic
99	#95×C₄₇	D₄	1	1	yes	characteristic
100	C₂⁴×C₄₇	—	2	1	no	—
101	C₂×Q₈×C₄₇	—	2	1	no	—
102	C₂×Q₈×C₄₇	—	2	1	no	—
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	2	2	no	—
105	C₂×Q₈×C₄₇	—	2	1	no	—
106	C₂×Q₈×C₄₇	—	2	1	no	—
107	C₂×Q₈×C₄₇	—	2	2	no	—
108	C₂×Q₈×C₄₇	—	2	2	no	—
109	C₂×Q₈×C₄₇	—	2	2	no	—
110	C₂×Q₈×C₄₇	—	2	1	no	—
111	C₂×Q₈×C₄₇	—	2	2	no	—
112	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
113	C₂×D₄×C₄₇	—	2	1	no	—
114	C₂×D₄×C₄₇	—	2	1	no	—
115	C₂×D₄×C₄₇	—	2	1	no	—
116	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
118	C₂×D₄×C₄₇	#41	1	2	yes	—
119	C₂²×C₄×C₄₇	—	2	1	no	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	4	no	—
122	C₂²×C₄×C₄₇	—	2	1	no	—
123	C₂²×C₄×C₄₇	—	2	2	no	—
124	C₂²×C₄×C₄₇	—	2	2	no	—
125	C₂²×C₄×C₄₇	—	4	4	no	—
126	C₂²×C₄×C₄₇	—	4	4	no	—
127	C₂²×C₄×C₄₇	—	8	2	no	—
128	C₂²×C₄×C₄₇	—	8	2	no	—
129	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
134	SD₁₆×C₄₇	—	2	8	no	—
135	SD₁₆×C₄₇	—	4	8	no	—
136	C₂×C₈×C₄₇	—	2	1	no	—
137	C₂×C₈×C₄₇	—	2	1	no	—
138	C₂×C₈×C₄₇	—	2	2	no	—
139	C₂×C₈×C₄₇	—	2	2	no	—
140	C₂×C₈×C₄₇	—	2	1	no	—
141	C₂×C₈×C₄₇	—	2	2	no	—
142	C₂×C₈×C₄₇	—	2	1	no	—
143	C₂×C₈×C₄₇	—	2	1	no	—
144	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
145	C₄⋊C₄×C₄₇	—	2	4	no	—
146	C₄⋊C₄×C₄₇	—	2	1	no	—
147	C₄⋊C₄×C₄₇	—	2	2	no	—
148	C₄⋊C₄×C₄₇	—	2	1	no	—
149	C₄⋊C₄×C₄₇	—	2	1	no	—
150	C₄⋊C₄×C₄₇	—	2	2	no	—
151	C₄⋊C₄×C₄₇	—	4	4	no	—
152	C₄⋊C₄×C₄₇	—	4	4	no	—
153	C₄⋊C₄×C₄₇	—	4	2	no	—
154	C₄⋊C₄×C₄₇	—	4	2	no	—
155	C₄⋊C₄×C₄₇	—	4	2	no	—
156	C₄⋊C₄×C₄₇	—	8	2	no	—
157	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
158	C₂²⋊C₄×C₄₇	—	2	4	no	—
159	C₂²⋊C₄×C₄₇	—	4	4	no	—
160	C₄²×C₄₇	—	2	2	no	—
161	C₄²×C₄₇	—	2	2	no	—
162	C₄²×C₄₇	—	4	2	no	—
163	C₄²×C₄₇	C₂×D₄	1	2	yes	—
164	C₄²×C₄₇	#41	1	2	yes	—
165	C₂³×C₄₇	—	2	2	no	—
166	C₂³×C₄₇	—	2	2	no	—
167	C₂³×C₄₇	—	2	2	no	—
168	C₂³×C₄₇	—	4	2	no	—
169	C₂³×C₄₇	—	4	2	no	—
170	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₄₇	—	2	2	no	—
172	Q₈×C₄₇	—	2	2	no	—
173	Q₈×C₄₇	—	4	1	no	—
174	Q₈×C₄₇	—	4	1	no	—
175	Q₈×C₄₇	—	4	2	no	—
176	Q₈×C₄₇	—	4	2	no	—
177	Q₈×C₄₇	—	4	2	no	—
178	Q₈×C₄₇	—	4	2	no	—
179	D₄×C₄₇	—	2	2	no	—
180	D₄×C₄₇	—	2	2	no	—
181	D₄×C₄₇	—	2	2	no	—
182	D₄×C₄₇	#121	1	4	yes	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	2	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	2	2	no	—
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	4	1	no	—
193	C₂×C₄×C₄₇	—	4	1	no	—
194	C₂×C₄×C₄₇	—	4	2	no	—
195	C₂×C₄×C₄₇	—	4	1	no	—
196	C₂×C₄×C₄₇	—	4	2	no	—
197	C₂×C₄×C₄₇	—	4	2	no	—
198	C₂×C₄×C₄₇	—	4	2	no	—
199	C₂×C₄×C₄₇	—	4	2	no	—
200	C₂×C₄×C₄₇	—	4	2	no	—
201	C₂×C₄×C₄₇	—	4	2	no	—
202	C₂×C₄×C₄₇	—	4	2	no	—
203	C₂×C₄×C₄₇	—	8	4	no	—
204	C₂×C₄×C₄₇	—	8	8	no	—
205	C₂×C₄×C₄₇	#121	1	2	yes	—
206	C₂×C₄×C₄₇	#121	1	2	yes	—
207	C₂×C₄×C₄₇	#137	1	4	yes	—
208	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
214	C₈×C₄₇	—	2	2	no	—
215	C₈×C₄₇	—	4	2	no	—
216	C₈×C₄₇	—	4	1	no	—
217	#24748	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂²×C₄₇	—	2	4	no	—
219	C₂²×C₄₇	—	4	4	no	—
220	C₂²×C₄₇	—	4	4	no	—
221	C₂²×C₄₇	—	4	2	no	—
222	C₂²×C₄₇	—	4	2	no	—
223	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
224	C₂²×C₄₇	D₄²	1	1	yes	characteristic
225	C₂²×C₄₇	#548	1	1	yes	characteristic
226	C₂²×C₄₇	C₂×#137	1	2	yes	—
227	C₂²×C₄₇	#577	1	2	yes	—
228	C₄×C₄₇	—	2	4	no	—
229	C₄×C₄₇	—	2	2	no	—
230	C₄×C₄₇	—	2	2	no	—
231	C₄×C₄₇	—	4	2	no	—
232	C₄×C₄₇	—	4	2	no	—
233	C₄×C₄₇	—	4	2	no	—
234	C₄×C₄₇	—	8	2	no	—
235	C₄×C₄₇	—	8	2	no	—
236	C₄×C₄₇	—	8	1	no	—
237	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
238	C₄×C₄₇	#537	1	1	yes	characteristic
239	C₄×C₄₇	#547	1	1	yes	characteristic
240	C₄×C₄₇	#553	1	1	yes	characteristic
241	C₂×#461	C₂×C₄₇	1	2	yes	—
242	C₂×#461	C₂×C₄₇	1	1	yes	characteristic
243	C₂×#440	C₂×C₄₇	1	1	yes	characteristic
244	#2546	C₂×C₄₇	1	1	yes	characteristic, complemented
245	#2349	C₂×C₄₇	1	1	yes	characteristic
246	#2068	C₂×C₄₇	1	2	yes	complemented
247	#2043	C₂×C₄₇	1	2	yes	complemented
248	#1960	C₂×C₄₇	1	1	yes	characteristic, complemented
249	#1940	C₂×C₄₇	1	1	yes	characteristic, complemented
250	#1877	C₂×C₄₇	1	2	yes	—
251	#1805	C₂×C₄₇	1	1	yes	characteristic, complemented
252	C₂×C₄₇	—	4	4	no	—
253	C₂×C₄₇	#2416	1	1	yes	characteristic
254	C₂×C₄₇	#3039	1	1	yes	characteristic
255	C₂×C₄₇	#3042	1	1	yes	characteristic
256	C₂×C₄₇	#3266	1	2	yes	—
257	C₂×C₄₇	#3372	1	2	yes	—
258	C₂²×SD₁₆	C₂²×C₄₇	1	2	yes	—
259	C₂²×SD₁₆	C₂²×C₄₇	1	1	yes	characteristic
260	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
261	C₂×C₄⋊Q₈	C₂²×C₄₇	1	2	yes	—
262	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
264	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
265	#461	—	2	8	no	—
266	#461	—	2	4	no	—
267	#440	—	2	4	no	—
268	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
271	C₂×#103	C₂²×C₄₇	1	2	yes	—
272	C₂×#103	C₂²×C₄₇	1	2	yes	—
273	C₂×#103	C₂²×C₄₇	1	2	yes	—
274	C₂×#103	C₂²×C₄₇	1	1	yes	characteristic
275	C₂×#103	C₂²×C₄₇	1	2	yes	—
276	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
277	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
278	#398	—	2	1	no	—
279	#398	—	2	1	no	—
280	#391	C₂²×C₄₇	1	2	yes	—
281	#389	—	2	2	no	—
282	#389	C₂²×C₄₇	1	2	yes	—
283	#385	—	2	2	no	—
284	#382	C₂²×C₄₇	1	1	yes	characteristic
285	#380	—	2	1	no	—
286	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
287	C₂×#95	—	2	1	no	—
288	#340	C₂²×C₄₇	1	2	yes	—
289	#336	C₂²×C₄₇	1	2	yes	—
290	C₄₇	#24748	1	1	yes	characteristic, direct product factor, Sylow
291	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
292	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
293	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
294	C₂³×C₄	—	2	1	no	—
295	C₂³×C₄	—	2	2	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×SD₁₆	—	2	2	no	—
298	C₂×SD₁₆	—	2	4	no	—
299	C₂×SD₁₆	—	2	4	no	—
300	C₂×SD₁₆	—	2	4	no	—
301	C₂×SD₁₆	D₄×C₄₇	1	4	yes	—
302	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
303	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
305	C₄⋊Q₈	—	2	4	no	—
306	C₄⋊Q₈	—	2	2	no	—
307	C₄⋊Q₈	—	2	2	no	—
308	C₄⋊Q₈	—	4	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×D₄	—	2	4	no	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	—	4	2	no	—
314	C₄×D₄	D₄×C₄₇	1	4	yes	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
329	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
330	#107	—	2	2	no	—
331	C₄⋊C₈	—	2	4	no	—
332	C₄⋊C₈	—	2	2	no	—
333	#103	—	2	4	no	—
334	#103	—	2	4	no	—
335	#103	—	2	2	no	—
336	#103	—	2	4	no	—
337	#103	—	4	2	no	—
338	#102	—	2	2	no	—
339	#97	—	2	2	no	—
340	#95	—	2	1	no	—
341	#95	—	2	2	no	—
342	#95	—	2	1	no	—
343	#95	—	2	2	no	—
344	#95	—	2	2	no	—
345	#95	D₄×C₄₇	1	1	yes	characteristic
346	#95	D₄×C₄₇	1	1	yes	characteristic
347	C₂⁴	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
364	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
365	C₂×D₄	#41×C₄₇	1	2	yes	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	4	4	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	—	8	2	no	—
375	C₂²×C₄	—	8	2	no	—
376	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
380	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
381	SD₁₆	—	2	8	no	—
382	SD₁₆	—	4	8	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	4	4	no	—
399	C₄⋊C₄	—	4	4	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₄⋊C₄	—	4	2	no	—
403	C₄⋊C₄	—	8	2	no	—
404	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	4	4	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	4	2	no	—
410	C₄²	C₂×D₄×C₄₇	1	2	yes	—
411	C₄²	#41×C₄₇	1	2	yes	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	4	1	no	—
421	Q₈	—	4	1	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	4	2	no	—
424	Q₈	—	4	2	no	—
425	Q₈	—	4	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	2	2	no	—
428	D₄	—	2	2	no	—
429	D₄	#121×C₄₇	1	4	yes	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	8	4	no	—
451	C₂×C₄	—	8	8	no	—
452	C₂×C₄	#121×C₄₇	1	2	yes	—
453	C₂×C₄	#121×C₄₇	1	2	yes	—
454	C₂×C₄	#137×C₄₇	1	4	yes	—
455	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
456	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
457	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
458	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
459	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
460	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	4	2	no	—
463	C₈	—	4	1	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	4	no	—
469	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
470	C₂²	D₄²×C₄₇	1	1	yes	characteristic
471	C₂²	C₄₇×#548	1	1	yes	characteristic
472	C₂²	C₂×#137×C₄₇	1	2	yes	—
473	C₂²	C₄₇×#577	1	2	yes	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	4	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	8	1	no	—
481	C₄	—	8	2	no	—
482	C₄	—	8	2	no	—
483	C₄	C₂×#121×C₄₇	1	1	yes	characteristic
484	C₄	C₄₇×#537	1	1	yes	characteristic
485	C₄	C₄₇×#547	1	1	yes	characteristic
486	C₄	C₄₇×#553	1	1	yes	characteristic
487	C₂	—	4	4	no	—
488	C₂	C₄₇×#2416	1	1	yes	characteristic
489	C₂	C₄₇×#3039	1	1	yes	characteristic
490	C₂	C₄₇×#3042	1	1	yes	characteristic
491	C₂	C₄₇×#3266	1	2	yes	—
492	C₂	C₄₇×#3372	1	2	yes	—

	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
4. C₄₇×#2546	C₂	semidirect
6. C₄₇×#2068	C₂	semidirect
7. C₄₇×#2043	C₂	semidirect
8. C₄₇×#1960	C₂	semidirect
9. C₄₇×#1940	C₂	semidirect
11. C₄₇×#1805	C₂	semidirect
217. #24748	C₄₇	direct (N × H)
244. #2546	C₂×C₄₇	semidirect
246. #2068	C₂×C₄₇	semidirect
247. #2043	C₂×C₄₇	semidirect
248. #1960	C₂×C₄₇	semidirect
249. #1940	C₂×C₄₇	semidirect
251. #1805	C₂×C₄₇	semidirect
290. C₄₇	#24748	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×#461	2
C₂×C₄₇×#440	2
C₄₇×#2546	2
C₄₇×#2349	2
C₄₇×#2068	2
C₄₇×#2043	2
C₄₇×#1960	2
C₄₇×#1940	2
C₄₇×#1877	2
C₄₇×#1805	2
#24748	47

Subgroups — C47×#24748 #26064446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#24748 #26064446