Subgroups — C₄₇×#29809 #26069507

Order 12032.

966 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2850	C₂	1	2	yes	maximal, complemented
4	C₄₇×#2056	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2055	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2054	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#2001	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#2000	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1999	C₂	1	1	yes	maximal, characteristic
10	C₄₇×#1958	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1835	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×D₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#124×C₄₇	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
17	C₂×#121×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#495	—	2	4	no	—
20	C₄₇×#431	—	2	4	no	—
21	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×#103×C₄₇	C₂²	1	2	yes	—
24	C₂×#103×C₄₇	C₂²	1	2	yes	—
25	C₂×#102×C₄₇	C₂²	1	2	yes	—
26	C₂×#102×C₄₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#391	C₂²	1	2	yes	—
32	C₄₇×#390	C₂²	1	2	yes	—
33	C₄₇×#388	—	2	2	no	—
34	C₄₇×#388	—	2	2	no	—
35	C₄₇×#386	—	2	2	no	—
36	C₄₇×#386	—	2	2	no	—
37	C₄₇×#382	C₂²	1	2	yes	—
38	C₄₇×#340	C₂²	1	1	yes	characteristic
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₄₇×#340	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
42	C₂²×D₄×C₄₇	—	2	2	no	—
43	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
44	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₄₇	—	2	2	no	—
48	C₂×Q₁₆×C₄₇	—	4	2	no	—
49	C₂×SD₁₆×C₄₇	—	2	4	no	—
50	C₂×SD₁₆×C₄₇	—	4	2	no	—
51	C₂×SD₁₆×C₄₇	—	4	2	no	—
52	C₂×D₈×C₄₇	—	2	2	no	—
53	C₂×D₈×C₄₇	—	4	2	no	—
54	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
58	#124×C₄₇	—	2	4	no	—
59	#124×C₄₇	—	2	4	no	—
60	C₂²⋊Q₈×C₄₇	—	4	2	no	—
61	C₂²⋊Q₈×C₄₇	—	4	2	no	—
62	#121×C₄₇	—	4	2	no	—
63	#121×C₄₇	—	4	2	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₇	—	2	2	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	2	no	—
75	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₄₇	—	2	2	no	—
80	C₄⋊C₈×C₄₇	—	2	2	no	—
81	#103×C₄₇	—	4	2	no	—
82	#103×C₄₇	—	4	2	no	—
83	#102×C₄₇	—	4	2	no	—
84	#102×C₄₇	—	4	2	no	—
85	C₂²⋊C₈×C₄₇	—	2	2	no	—
86	C₂²⋊C₈×C₄₇	—	2	2	no	—
87	C₄×C₈×C₄₇	—	2	2	no	—
88	C₄×C₈×C₄₇	D₄	1	4	yes	complemented
89	#95×C₄₇	—	2	2	no	—
90	#95×C₄₇	—	2	2	no	—
91	#95×C₄₇	—	2	2	no	—
92	#95×C₄₇	—	2	2	no	—
93	C₂⁴×C₄₇	—	2	2	no	—
94	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	—	2	2	no	—
99	C₂×Q₈×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	2	2	no	—
104	C₂×D₄×C₄₇	—	2	2	no	—
105	C₂×D₄×C₄₇	—	2	2	no	—
106	C₂×D₄×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	—	4	4	no	—
108	C₂×D₄×C₄₇	—	4	4	no	—
109	C₂×D₄×C₄₇	—	4	4	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	1	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	2	no	—
121	C₂²×C₄×C₄₇	—	4	2	no	—
122	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
128	Q₁₆×C₄₇	—	4	4	no	—
129	SD₁₆×C₄₇	—	4	8	no	—
130	D₈×C₄₇	—	4	4	no	—
131	C₂×C₈×C₄₇	—	2	2	no	—
132	C₂×C₈×C₄₇	—	2	2	no	—
133	C₂×C₈×C₄₇	—	2	1	no	—
134	C₂×C₈×C₄₇	—	2	1	no	—
135	C₂×C₈×C₄₇	—	2	2	no	—
136	C₂×C₈×C₄₇	—	2	2	no	—
137	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₄₇	—	2	2	no	—
140	C₄⋊C₄×C₄₇	—	2	2	no	—
141	C₄⋊C₄×C₄₇	—	2	2	no	—
142	C₄⋊C₄×C₄₇	—	2	2	no	—
143	C₄⋊C₄×C₄₇	—	4	4	no	—
144	C₂²⋊C₄×C₄₇	—	4	4	no	—
145	C₂²⋊C₄×C₄₇	—	4	4	no	—
146	C₂²⋊C₄×C₄₇	—	4	4	no	—
147	C₂²⋊C₄×C₄₇	—	4	4	no	—
148	C₂²⋊C₄×C₄₇	—	4	4	no	—
149	C₂²⋊C₄×C₄₇	—	4	4	no	—
150	C₄²×C₄₇	—	2	2	no	—
151	C₄²×C₄₇	—	2	2	no	—
152	C₄²×C₄₇	—	2	1	no	—
153	C₄²×C₄₇	—	2	1	no	—
154	C₄²×C₄₇	C₂×D₄	1	2	yes	—
155	C₄²×C₄₇	#41	1	2	yes	—
156	C₂³×C₄₇	—	2	1	no	—
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	—	2	1	no	—
159	C₂³×C₄₇	—	2	2	no	—
160	C₂³×C₄₇	—	4	2	no	—
161	C₂³×C₄₇	—	4	2	no	—
162	C₂³×C₄₇	—	4	2	no	—
163	C₂³×C₄₇	—	4	2	no	—
164	C₂³×C₄₇	—	4	2	no	—
165	C₂³×C₄₇	—	4	2	no	—
166	C₂³×C₄₇	—	4	2	no	—
167	C₂³×C₄₇	#135	1	2	yes	—
168	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₄₇	—	4	2	no	—
170	Q₈×C₄₇	—	4	2	no	—
171	Q₈×C₄₇	—	4	2	no	—
172	Q₈×C₄₇	—	4	2	no	—
173	D₄×C₄₇	—	4	2	no	—
174	D₄×C₄₇	—	4	2	no	—
175	D₄×C₄₇	—	4	2	no	—
176	D₄×C₄₇	—	4	2	no	—
177	D₄×C₄₇	—	8	8	no	—
178	C₂×C₄×C₄₇	—	2	8	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	2	no	—
184	C₂×C₄×C₄₇	—	2	1	no	—
185	C₂×C₄×C₄₇	—	2	1	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	2	2	no	—
188	C₂×C₄×C₄₇	—	4	4	no	—
189	C₂×C₄×C₄₇	—	4	1	no	—
190	C₂×C₄×C₄₇	—	4	1	no	—
191	C₂×C₄×C₄₇	—	4	2	no	—
192	C₂×C₄×C₄₇	—	4	2	no	—
193	C₂×C₄×C₄₇	—	4	2	no	—
194	C₂×C₄×C₄₇	—	4	2	no	—
195	C₂×C₄×C₄₇	—	4	2	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	#121	1	2	yes	—
202	C₂×C₄×C₄₇	#121	1	2	yes	—
203	C₂×C₄×C₄₇	#135	1	2	yes	—
204	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
207	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
208	C₈×C₄₇	—	2	2	no	—
209	C₈×C₄₇	—	2	2	no	—
210	C₈×C₄₇	—	4	1	no	—
211	C₈×C₄₇	—	4	1	no	—
212	#29809	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂²×C₄₇	—	2	4	no	—
214	C₂²×C₄₇	—	2	2	no	—
215	C₂²×C₄₇	—	4	1	no	—
216	C₂²×C₄₇	—	4	2	no	—
217	C₂²×C₄₇	—	4	1	no	—
218	C₂²×C₄₇	—	8	2	no	—
219	C₂²×C₄₇	—	8	2	no	—
220	C₂²×C₄₇	—	8	2	no	—
221	C₂²×C₄₇	—	8	2	no	—
222	C₂²×C₄₇	—	8	2	no	—
223	C₂²×C₄₇	—	8	2	no	—
224	C₂²×C₄₇	—	8	2	no	—
225	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
226	C₂²×C₄₇	#535	1	2	yes	—
227	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
228	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
229	C₂²×C₄₇	#575	1	2	yes	—
230	C₄×C₄₇	—	2	2	no	—
231	C₄×C₄₇	—	2	2	no	—
232	C₄×C₄₇	—	2	2	no	—
233	C₄×C₄₇	—	4	1	no	—
234	C₄×C₄₇	—	4	1	no	—
235	C₄×C₄₇	—	8	2	no	—
236	C₄×C₄₇	—	8	2	no	—
237	C₄×C₄₇	—	8	2	no	—
238	C₄×C₄₇	#535	1	1	yes	characteristic
239	C₄×C₄₇	#535	1	1	yes	characteristic
240	C₄×C₄₇	#540	1	2	yes	—
241	C₂×#495	C₂×C₄₇	1	1	yes	characteristic, complemented
242	C₂×#431	C₂×C₄₇	1	1	yes	characteristic, complemented
243	#2850	C₂×C₄₇	1	2	yes	complemented
244	#2056	C₂×C₄₇	1	1	yes	characteristic, complemented
245	#2055	C₂×C₄₇	1	2	yes	complemented
246	#2054	C₂×C₄₇	1	1	yes	characteristic, complemented
247	#2001	C₂×C₄₇	1	1	yes	characteristic, complemented
248	#2000	C₂×C₄₇	1	2	yes	complemented
249	#1999	C₂×C₄₇	1	1	yes	characteristic
250	#1958	C₂×C₄₇	1	2	yes	complemented
251	#1835	C₂×C₄₇	1	1	yes	characteristic, complemented
252	C₂×C₄₇	—	4	2	no	—
253	C₂×C₄₇	—	16	2	no	—
254	C₂×C₄₇	#2619	1	1	yes	characteristic
255	C₂×C₄₇	#3050	1	1	yes	characteristic
256	C₂×C₄₇	#3054	1	1	yes	characteristic
257	C₂×C₄₇	#3211	1	2	yes	—
258	C₂×C₄₇	#3212	1	2	yes	—
259	C₂²×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
260	C₂²×SD₁₆	C₂²×C₄₇	1	2	yes	—
261	C₂²×D₈	C₂²×C₄₇	1	1	yes	characteristic
262	C₂×#124	C₂²×C₄₇	1	2	yes	—
263	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
264	C₂×#121	C₂²×C₄₇	1	2	yes	—
265	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
266	#495	—	2	4	no	—
267	#431	—	2	4	no	—
268	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
270	C₂×#103	C₂²×C₄₇	1	2	yes	—
271	C₂×#103	C₂²×C₄₇	1	2	yes	—
272	C₂×#102	C₂²×C₄₇	1	2	yes	—
273	C₂×#102	C₂²×C₄₇	1	2	yes	—
274	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
275	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
277	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
278	#391	C₂²×C₄₇	1	2	yes	—
279	#390	C₂²×C₄₇	1	2	yes	—
280	#388	—	2	2	no	—
281	#388	—	2	2	no	—
282	#386	—	2	2	no	—
283	#386	—	2	2	no	—
284	#382	C₂²×C₄₇	1	2	yes	—
285	#340	C₂²×C₄₇	1	1	yes	characteristic
286	#340	C₂²×C₄₇	1	2	yes	—
287	#340	C₂²×C₄₇	1	1	yes	characteristic
288	C₄₇	#29809	1	1	yes	characteristic, direct product factor, Sylow
289	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
290	C₂²×D₄	—	2	2	no	—
291	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
292	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
293	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
295	C₂×Q₁₆	—	2	2	no	—
296	C₂×Q₁₆	—	4	2	no	—
297	C₂×SD₁₆	—	2	4	no	—
298	C₂×SD₁₆	—	4	2	no	—
299	C₂×SD₁₆	—	4	2	no	—
300	C₂×D₈	—	2	2	no	—
301	C₂×D₈	—	4	2	no	—
302	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
306	#124	—	2	4	no	—
307	#124	—	2	4	no	—
308	C₂²⋊Q₈	—	4	2	no	—
309	C₂²⋊Q₈	—	4	2	no	—
310	#121	—	4	2	no	—
311	#121	—	4	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	—	2	2	no	—
323	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
324	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
327	C₄⋊C₈	—	2	2	no	—
328	C₄⋊C₈	—	2	2	no	—
329	#103	—	4	2	no	—
330	#103	—	4	2	no	—
331	#102	—	4	2	no	—
332	#102	—	4	2	no	—
333	C₂²⋊C₈	—	2	2	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	C₄×C₈	—	2	2	no	—
336	C₄×C₈	D₄×C₄₇	1	4	yes	complemented
337	#95	—	2	2	no	—
338	#95	—	2	2	no	—
339	#95	—	2	2	no	—
340	#95	—	2	2	no	—
341	C₂⁴	—	2	2	no	—
342	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	4	4	no	—
356	C₂×D₄	—	4	4	no	—
357	C₂×D₄	—	4	4	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
375	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
376	Q₁₆	—	4	4	no	—
377	SD₁₆	—	4	8	no	—
378	D₈	—	4	4	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
386	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₂²⋊C₄	—	4	4	no	—
395	C₂²⋊C₄	—	4	4	no	—
396	C₂²⋊C₄	—	4	4	no	—
397	C₂²⋊C₄	—	4	4	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	2	1	no	—
402	C₄²	C₂×D₄×C₄₇	1	2	yes	—
403	C₄²	#41×C₄₇	1	2	yes	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	#135×C₄₇	1	2	yes	—
416	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
417	Q₈	—	4	2	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	4	2	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	2	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	8	8	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	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	#121×C₄₇	1	2	yes	—
450	C₂×C₄	#121×C₄₇	1	2	yes	—
451	C₂×C₄	#135×C₄₇	1	2	yes	—
452	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
454	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
455	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
456	C₈	—	2	2	no	—
457	C₈	—	2	2	no	—
458	C₈	—	4	1	no	—
459	C₈	—	4	1	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	8	2	no	—
468	C₂²	—	8	2	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	2	no	—
471	C₂²	—	8	2	no	—
472	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
473	C₂²	C₄₇×#535	1	2	yes	—
474	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
475	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
476	C₂²	C₄₇×#575	1	2	yes	—
477	C₄	—	2	2	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	4	1	no	—
481	C₄	—	4	1	no	—
482	C₄	—	8	2	no	—
483	C₄	—	8	2	no	—
484	C₄	—	8	2	no	—
485	C₄	C₄₇×#535	1	1	yes	characteristic
486	C₄	C₄₇×#535	1	1	yes	characteristic
487	C₄	C₄₇×#540	1	2	yes	—
488	C₂	—	4	2	no	—
489	C₂	—	16	2	no	—
490	C₂	C₄₇×#2619	1	1	yes	characteristic
491	C₂	C₄₇×#3050	1	1	yes	characteristic
492	C₂	C₄₇×#3054	1	1	yes	characteristic
493	C₂	C₄₇×#3211	1	2	yes	—
494	C₂	C₄₇×#3212	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₄₇×#1999	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×#495	C₂	semidirect
2. C₂×C₄₇×#431	C₂	semidirect
3. C₄₇×#2850	C₂	semidirect
4. C₄₇×#2056	C₂	semidirect
5. C₄₇×#2055	C₂	semidirect
6. C₄₇×#2054	C₂	semidirect
7. C₄₇×#2001	C₂	semidirect
8. C₄₇×#2000	C₂	semidirect
10. C₄₇×#1958	C₂	semidirect
11. C₄₇×#1835	C₂	semidirect
88. C₄×C₈×C₄₇	D₄	semidirect
212. #29809	C₄₇	direct (N × H)
241. C₂×#495	C₂×C₄₇	semidirect
242. C₂×#431	C₂×C₄₇	semidirect
243. #2850	C₂×C₄₇	semidirect
244. #2056	C₂×C₄₇	semidirect
245. #2055	C₂×C₄₇	semidirect
246. #2054	C₂×C₄₇	semidirect
247. #2001	C₂×C₄₇	semidirect
248. #2000	C₂×C₄₇	semidirect
250. #1958	C₂×C₄₇	semidirect
251. #1835	C₂×C₄₇	semidirect
288. C₄₇	#29809	direct (N × H)
336. C₄×C₈	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×#495	2
C₂×C₄₇×#431	2
C₄₇×#2850	2
C₄₇×#2056	2
C₄₇×#2055	2
C₄₇×#2054	2
C₄₇×#2001	2
C₄₇×#2000	2
C₄₇×#1999	2
C₄₇×#1958	2
C₄₇×#1835	2
#29809	47

Subgroups — C47×#29809 #26069507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29809 #26069507