Subgroups — C₄₇×#29803 #26069501

Order 12032.

954 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	C₂×C₄₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2657	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2320	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2042	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2041	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2015	C₂	1	2	yes	maximal, complemented
8	C₄₇×#2014	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1982	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1832	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#127×C₄₇	C₂²	1	2	yes	—
17	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₇	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#464	—	2	4	no	—
21	C₄₇×#460	—	2	4	no	—
22	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#103×C₄₇	C₂²	1	2	yes	—
26	C₂×#102×C₄₇	C₂²	1	2	yes	—
27	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#102×C₄₇	C₂²	1	2	yes	—
29	C₂×#102×C₄₇	C₂²	1	2	yes	—
30	C₂×#102×C₄₇	C₂²	1	2	yes	—
31	C₄₇×#392	—	2	1	no	—
32	C₄₇×#392	—	2	1	no	—
33	C₄₇×#392	—	2	2	no	—
34	C₄₇×#391	C₂²	1	2	yes	—
35	C₄₇×#389	C₂²	1	2	yes	—
36	C₄₇×#387	—	2	2	no	—
37	C₄₇×#383	—	2	1	no	—
38	C₄₇×#382	—	2	1	no	—
39	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#376	C₂²	1	1	yes	characteristic
41	C₄₇×#336	C₂²	1	2	yes	—
42	C₄₇×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₇	—	2	2	no	—
46	C₂²×D₄×C₄₇	—	2	2	no	—
47	C₂²×D₄×C₄₇	—	2	1	no	—
48	C₂²×D₄×C₄₇	—	2	1	no	—
49	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
51	C₂×Q₁₆×C₄₇	—	2	2	no	—
52	C₂×Q₁₆×C₄₇	—	4	2	no	—
53	C₂×SD₁₆×C₄₇	—	2	4	no	—
54	C₂×SD₁₆×C₄₇	—	2	2	no	—
55	C₂×SD₁₆×C₄₇	—	4	2	no	—
56	C₂×SD₁₆×C₄₇	—	4	2	no	—
57	C₂×SD₁₆×C₄₇	—	4	2	no	—
58	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
60	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
61	#127×C₄₇	—	2	2	no	—
62	#127×C₄₇	—	2	2	no	—
63	#127×C₄₇	—	4	2	no	—
64	#127×C₄₇	—	4	2	no	—
65	#124×C₄₇	—	2	2	no	—
66	#124×C₄₇	—	2	2	no	—
67	#124×C₄₇	—	4	2	no	—
68	#124×C₄₇	—	4	2	no	—
69	C₄×Q₈×C₄₇	—	2	2	no	—
70	C₄×Q₈×C₄₇	D₄	1	4	yes	complemented
71	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
79	C₂×C₄²×C₄₇	—	2	1	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	C₄⋊C₈×C₄₇	—	2	2	no	—
84	C₄⋊C₈×C₄₇	—	2	2	no	—
85	#103×C₄₇	—	2	2	no	—
86	#103×C₄₇	—	4	2	no	—
87	#102×C₄₇	—	2	4	no	—
88	#102×C₄₇	—	2	2	no	—
89	#102×C₄₇	—	4	2	no	—
90	#102×C₄₇	—	4	2	no	—
91	#102×C₄₇	—	4	2	no	—
92	#95×C₄₇	—	2	1	no	—
93	#95×C₄₇	—	2	2	no	—
94	#95×C₄₇	—	2	2	no	—
95	#95×C₄₇	—	2	2	no	—
96	#95×C₄₇	D₄	1	1	yes	characteristic
97	#95×C₄₇	D₄	1	1	yes	characteristic
98	#95×C₄₇	D₄	1	2	yes	—
99	C₂⁴×C₄₇	—	2	1	no	—
100	C₂⁴×C₄₇	—	2	2	no	—
101	C₂×Q₈×C₄₇	—	2	1	no	—
102	C₂×Q₈×C₄₇	—	2	1	no	—
103	C₂×Q₈×C₄₇	—	2	1	no	—
104	C₂×Q₈×C₄₇	—	2	2	no	—
105	C₂×Q₈×C₄₇	—	2	2	no	—
106	C₂×Q₈×C₄₇	—	2	2	no	—
107	C₂×Q₈×C₄₇	—	2	2	no	—
108	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₄₇	—	2	1	no	—
110	C₂×D₄×C₄₇	—	2	2	no	—
111	C₂×D₄×C₄₇	—	2	1	no	—
112	C₂×D₄×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	—	2	2	no	—
114	C₂×D₄×C₄₇	—	2	2	no	—
115	C₂×D₄×C₄₇	—	2	2	no	—
116	C₂×D₄×C₄₇	—	2	2	no	—
117	C₂×D₄×C₄₇	—	2	2	no	—
118	C₂×D₄×C₄₇	—	2	2	no	—
119	C₂×D₄×C₄₇	—	4	4	no	—
120	C₂×D₄×C₄₇	—	4	4	no	—
121	C₂×D₄×C₄₇	—	4	2	no	—
122	C₂×D₄×C₄₇	—	4	2	no	—
123	C₂×D₄×C₄₇	—	8	1	no	—
124	C₂×D₄×C₄₇	—	8	2	no	—
125	C₂×D₄×C₄₇	—	8	1	no	—
126	C₂×D₄×C₄₇	—	8	2	no	—
127	C₂×D₄×C₄₇	—	8	2	no	—
128	C₂×D₄×C₄₇	—	8	2	no	—
129	C₂×D₄×C₄₇	—	8	2	no	—
130	C₂²×C₄×C₄₇	—	2	1	no	—
131	C₂²×C₄×C₄₇	—	2	1	no	—
132	C₂²×C₄×C₄₇	—	2	2	no	—
133	C₂²×C₄×C₄₇	—	2	1	no	—
134	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
139	Q₁₆×C₄₇	—	4	4	no	—
140	SD₁₆×C₄₇	—	4	8	no	—
141	SD₁₆×C₄₇	—	4	4	no	—
142	C₂×C₈×C₄₇	—	2	1	no	—
143	C₂×C₈×C₄₇	—	2	2	no	—
144	C₂×C₈×C₄₇	—	2	1	no	—
145	C₂×C₈×C₄₇	—	2	2	no	—
146	C₂×C₈×C₄₇	—	2	2	no	—
147	C₂×C₈×C₄₇	—	2	2	no	—
148	C₂×C₈×C₄₇	—	2	2	no	—
149	C₄⋊C₄×C₄₇	—	2	4	no	—
150	C₄⋊C₄×C₄₇	—	2	1	no	—
151	C₄⋊C₄×C₄₇	—	2	2	no	—
152	C₄⋊C₄×C₄₇	—	2	2	no	—
153	C₄⋊C₄×C₄₇	—	8	2	no	—
154	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
155	C₂²⋊C₄×C₄₇	—	4	4	no	—
156	C₂²⋊C₄×C₄₇	—	4	4	no	—
157	C₂²⋊C₄×C₄₇	—	4	2	no	—
158	C₂²⋊C₄×C₄₇	—	4	2	no	—
159	C₄²×C₄₇	—	2	4	no	—
160	C₄²×C₄₇	—	2	2	no	—
161	C₄²×C₄₇	—	2	2	no	—
162	C₄²×C₄₇	—	8	1	no	—
163	C₄²×C₄₇	C₂×D₄	1	2	yes	—
164	C₄²×C₄₇	#41	1	2	yes	—
165	C₂³×C₄₇	—	4	1	no	—
166	C₂³×C₄₇	—	4	2	no	—
167	C₂³×C₄₇	—	4	2	no	—
168	C₂³×C₄₇	—	4	2	no	—
169	C₂³×C₄₇	—	4	2	no	—
170	C₂³×C₄₇	—	4	1	no	—
171	C₂³×C₄₇	—	4	2	no	—
172	C₂³×C₄₇	—	4	1	no	—
173	C₂³×C₄₇	—	4	2	no	—
174	C₂³×C₄₇	—	4	2	no	—
175	C₂³×C₄₇	—	4	2	no	—
176	C₂³×C₄₇	—	4	2	no	—
177	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
178	Q₈×C₄₇	—	2	2	no	—
179	Q₈×C₄₇	—	2	2	no	—
180	Q₈×C₄₇	—	4	2	no	—
181	Q₈×C₄₇	—	4	1	no	—
182	Q₈×C₄₇	—	4	1	no	—
183	Q₈×C₄₇	—	4	2	no	—
184	D₄×C₄₇	—	4	1	no	—
185	D₄×C₄₇	—	4	2	no	—
186	D₄×C₄₇	—	4	1	no	—
187	D₄×C₄₇	—	4	2	no	—
188	D₄×C₄₇	—	4	2	no	—
189	D₄×C₄₇	—	4	2	no	—
190	D₄×C₄₇	—	4	2	no	—
191	D₄×C₄₇	—	8	4	no	—
192	D₄×C₄₇	—	8	4	no	—
193	D₄×C₄₇	—	8	8	no	—
194	D₄×C₄₇	—	8	8	no	—
195	C₂×C₄×C₄₇	—	2	1	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	1	no	—
198	C₂×C₄×C₄₇	—	2	2	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	—	2	2	no	—
202	C₂×C₄×C₄₇	—	2	2	no	—
203	C₂×C₄×C₄₇	—	2	2	no	—
204	C₂×C₄×C₄₇	—	2	2	no	—
205	C₂×C₄×C₄₇	—	2	2	no	—
206	C₂×C₄×C₄₇	—	4	2	no	—
207	C₂×C₄×C₄₇	—	4	1	no	—
208	C₂×C₄×C₄₇	—	4	1	no	—
209	C₂×C₄×C₄₇	—	4	1	no	—
210	C₂×C₄×C₄₇	—	4	2	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	—	4	2	no	—
213	C₂×C₄×C₄₇	—	4	2	no	—
214	C₂×C₄×C₄₇	#121	1	2	yes	—
215	C₂×C₄×C₄₇	#121	1	2	yes	—
216	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
219	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
220	C₈×C₄₇	—	4	1	no	—
221	C₈×C₄₇	—	4	2	no	—
222	C₈×C₄₇	—	4	1	no	—
223	#29803	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂²×C₄₇	—	8	1	no	—
225	C₂²×C₄₇	—	8	2	no	—
226	C₂²×C₄₇	—	8	2	no	—
227	C₂²×C₄₇	—	8	2	no	—
228	C₂²×C₄₇	—	8	2	no	—
229	C₂²×C₄₇	—	8	2	no	—
230	C₂²×C₄₇	—	8	2	no	—
231	C₂²×C₄₇	—	8	2	no	—
232	C₂²×C₄₇	—	8	2	no	—
233	C₂²×C₄₇	—	8	1	no	—
234	C₂²×C₄₇	—	8	2	no	—
235	C₂²×C₄₇	—	8	1	no	—
236	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
237	C₂²×C₄₇	#535	1	2	yes	—
238	C₂²×C₄₇	#576	1	1	yes	characteristic
239	C₂²×C₄₇	#577	1	1	yes	characteristic
240	C₂²×C₄₇	#577	1	2	yes	—
241	C₄×C₄₇	—	2	2	no	—
242	C₄×C₄₇	—	2	2	no	—
243	C₄×C₄₇	—	4	2	no	—
244	C₄×C₄₇	—	4	2	no	—
245	C₄×C₄₇	—	4	2	no	—
246	C₄×C₄₇	—	4	2	no	—
247	C₄×C₄₇	—	8	1	no	—
248	C₄×C₄₇	—	8	2	no	—
249	C₄×C₄₇	#535	1	1	yes	characteristic
250	C₄×C₄₇	#535	1	1	yes	characteristic
251	C₄×C₄₇	#540	1	2	yes	—
252	C₂×#464	C₂×C₄₇	1	1	yes	characteristic, complemented
253	C₂×#460	C₂×C₄₇	1	1	yes	characteristic, complemented
254	#2657	C₂×C₄₇	1	1	yes	characteristic
255	#2320	C₂×C₄₇	1	1	yes	characteristic, complemented
256	#2042	C₂×C₄₇	1	2	yes	complemented
257	#2041	C₂×C₄₇	1	2	yes	complemented
258	#2015	C₂×C₄₇	1	2	yes	complemented
259	#2014	C₂×C₄₇	1	2	yes	complemented
260	#1983	C₂×C₄₇	1	1	yes	characteristic, complemented
261	#1982	C₂×C₄₇	1	1	yes	characteristic, complemented
262	#1832	C₂×C₄₇	1	1	yes	characteristic, complemented
263	C₂×C₄₇	—	16	1	no	—
264	C₂×C₄₇	—	16	2	no	—
265	C₂×C₄₇	#2619	1	1	yes	characteristic
266	C₂×C₄₇	#3043	1	1	yes	characteristic
267	C₂×C₄₇	#3045	1	1	yes	characteristic
268	C₂×C₄₇	#3222	1	2	yes	—
269	C₂×C₄₇	#3224	1	2	yes	—
270	C₂²×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
271	C₂²×SD₁₆	C₂²×C₄₇	1	2	yes	—
272	C₂²×SD₁₆	C₂²×C₄₇	1	1	yes	characteristic
273	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
274	C₂×#127	C₂²×C₄₇	1	2	yes	—
275	C₂×#124	C₂²×C₄₇	1	1	yes	characteristic
276	C₂×#124	C₂²×C₄₇	1	2	yes	—
277	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
278	#464	—	2	4	no	—
279	#460	—	2	4	no	—
280	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
282	C₂×#103	C₂²×C₄₇	1	1	yes	characteristic
283	C₂×#103	C₂²×C₄₇	1	2	yes	—
284	C₂×#102	C₂²×C₄₇	1	2	yes	—
285	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
286	C₂×#102	C₂²×C₄₇	1	2	yes	—
287	C₂×#102	C₂²×C₄₇	1	2	yes	—
288	C₂×#102	C₂²×C₄₇	1	2	yes	—
289	#392	—	2	1	no	—
290	#392	—	2	1	no	—
291	#392	—	2	2	no	—
292	#391	C₂²×C₄₇	1	2	yes	—
293	#389	C₂²×C₄₇	1	2	yes	—
294	#387	—	2	2	no	—
295	#383	—	2	1	no	—
296	#382	—	2	1	no	—
297	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
298	#376	C₂²×C₄₇	1	1	yes	characteristic
299	#336	C₂²×C₄₇	1	2	yes	—
300	#336	C₂²×C₄₇	1	2	yes	—
301	C₄₇	#29803	1	1	yes	characteristic, direct product factor, Sylow
302	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
303	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
304	C₂²×D₄	—	2	2	no	—
305	C₂²×D₄	—	2	2	no	—
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
309	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
310	C₂×Q₁₆	—	2	2	no	—
311	C₂×Q₁₆	—	4	2	no	—
312	C₂×SD₁₆	—	2	4	no	—
313	C₂×SD₁₆	—	2	2	no	—
314	C₂×SD₁₆	—	4	2	no	—
315	C₂×SD₁₆	—	4	2	no	—
316	C₂×SD₁₆	—	4	2	no	—
317	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
318	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
320	#127	—	2	2	no	—
321	#127	—	2	2	no	—
322	#127	—	4	2	no	—
323	#127	—	4	2	no	—
324	#124	—	2	2	no	—
325	#124	—	2	2	no	—
326	#124	—	4	2	no	—
327	#124	—	4	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	D₄×C₄₇	1	4	yes	complemented
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₄²	—	2	1	no	—
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
341	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
342	C₄⋊C₈	—	2	2	no	—
343	C₄⋊C₈	—	2	2	no	—
344	#103	—	2	2	no	—
345	#103	—	4	2	no	—
346	#102	—	2	4	no	—
347	#102	—	2	2	no	—
348	#102	—	4	2	no	—
349	#102	—	4	2	no	—
350	#102	—	4	2	no	—
351	#95	—	2	1	no	—
352	#95	—	2	2	no	—
353	#95	—	2	2	no	—
354	#95	—	2	2	no	—
355	#95	D₄×C₄₇	1	1	yes	characteristic
356	#95	D₄×C₄₇	1	1	yes	characteristic
357	#95	D₄×C₄₇	1	2	yes	—
358	C₂⁴	—	2	1	no	—
359	C₂⁴	—	2	2	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	4	4	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	8	1	no	—
383	C₂×D₄	—	8	2	no	—
384	C₂×D₄	—	8	1	no	—
385	C₂×D₄	—	8	2	no	—
386	C₂×D₄	—	8	2	no	—
387	C₂×D₄	—	8	2	no	—
388	C₂×D₄	—	8	2	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
394	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
395	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
398	Q₁₆	—	4	4	no	—
399	SD₁₆	—	4	8	no	—
400	SD₁₆	—	4	4	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	8	2	no	—
413	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
414	C₂²⋊C₄	—	4	4	no	—
415	C₂²⋊C₄	—	4	4	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₄²	—	2	4	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	8	1	no	—
422	C₄²	C₂×D₄×C₄₇	1	2	yes	—
423	C₄²	#41×C₄₇	1	2	yes	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	1	no	—
436	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
437	Q₈	—	2	2	no	—
438	Q₈	—	2	2	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	4	1	no	—
441	Q₈	—	4	1	no	—
442	Q₈	—	4	2	no	—
443	D₄	—	4	1	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	1	no	—
446	D₄	—	4	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	8	4	no	—
451	D₄	—	8	4	no	—
452	D₄	—	8	8	no	—
453	D₄	—	8	8	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	#121×C₄₇	1	2	yes	—
474	C₂×C₄	#121×C₄₇	1	2	yes	—
475	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
476	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
477	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
478	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
479	C₈	—	4	2	no	—
480	C₈	—	4	1	no	—
481	C₈	—	4	1	no	—
482	C₂²	—	8	2	no	—
483	C₂²	—	8	1	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	2	no	—
494	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
495	C₂²	C₄₇×#535	1	2	yes	—
496	C₂²	C₄₇×#576	1	1	yes	characteristic
497	C₂²	C₄₇×#577	1	2	yes	—
498	C₂²	C₄₇×#577	1	1	yes	characteristic
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	8	1	no	—
506	C₄	—	8	2	no	—
507	C₄	C₄₇×#535	1	1	yes	characteristic
508	C₄	C₄₇×#535	1	1	yes	characteristic
509	C₄	C₄₇×#540	1	2	yes	—
510	C₂	—	16	2	no	—
511	C₂	—	16	1	no	—
512	C₂	C₄₇×#2619	1	1	yes	characteristic
513	C₂	C₄₇×#3043	1	1	yes	characteristic
514	C₂	C₄₇×#3045	1	1	yes	characteristic
515	C₂	C₄₇×#3222	1	2	yes	—
516	C₂	C₄₇×#3224	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₄₇×#2657	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₄₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×#464	C₂	semidirect
2. C₂×C₄₇×#460	C₂	semidirect
4. C₄₇×#2320	C₂	semidirect
5. C₄₇×#2042	C₂	semidirect
6. C₄₇×#2041	C₂	semidirect
7. C₄₇×#2015	C₂	semidirect
8. C₄₇×#2014	C₂	semidirect
9. C₄₇×#1983	C₂	semidirect
10. C₄₇×#1982	C₂	semidirect
11. C₄₇×#1832	C₂	semidirect
70. C₄×Q₈×C₄₇	D₄	semidirect
223. #29803	C₄₇	direct (N × H)
252. C₂×#464	C₂×C₄₇	semidirect
253. C₂×#460	C₂×C₄₇	semidirect
255. #2320	C₂×C₄₇	semidirect
256. #2042	C₂×C₄₇	semidirect
257. #2041	C₂×C₄₇	semidirect
258. #2015	C₂×C₄₇	semidirect
259. #2014	C₂×C₄₇	semidirect
260. #1983	C₂×C₄₇	semidirect
261. #1982	C₂×C₄₇	semidirect
262. #1832	C₂×C₄₇	semidirect
301. C₄₇	#29803	direct (N × H)
329. C₄×Q₈	D₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#464	2
C₂×C₄₇×#460	2
C₄₇×#2657	2
C₄₇×#2320	2
C₄₇×#2042	2
C₄₇×#2041	2
C₄₇×#2015	2
C₄₇×#2014	2
C₄₇×#1983	2
C₄₇×#1982	2
C₄₇×#1832	2
#29803	47

Subgroups — C47×#29803 #26069501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29803 #26069501