Subgroups — D₄₇×#2221 #26370831

Order 12032.

678 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#504×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#472×D₄₇	C₂	1	2	yes	maximal, complemented
4	#20245509	C₂	1	1	yes	maximal, characteristic, complemented
5	#20245508	C₂	1	1	yes	maximal, characteristic, complemented
6	#20245507	C₂	1	2	yes	maximal, complemented
7	#20245506	C₂	1	2	yes	maximal, complemented
8	#20245505	C₂	1	1	yes	maximal, characteristic, complemented
9	#368×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#361×D₄₇	C₂	1	2	yes	maximal, complemented
11	C₄₇×#2221	C₂	1	1	yes	maximal, characteristic, complemented
12	AGL(1,ℤ/8)×D₄₇	—	2	2	no	—
13	C₂×D₈×D₄₇	C₂²	1	2	yes	—
14	#131×D₄₇	C₂²	1	1	yes	characteristic
15	C₂×D₇₅₂	C₂²	1	1	yes	characteristic, complemented
16	C₂×#13093965	C₂²	1	2	yes	complemented
17	D₁₆×D₄₇	—	2	1	no	—
18	D₁₆×D₄₇	—	2	1	no	—
19	D₁₆×D₄₇	—	2	1	no	—
20	D₁₆×D₄₇	—	2	1	no	—
21	#15689541	—	2	1	no	—
22	#15689541	C₂²	1	1	yes	characteristic, complemented
23	#15689540	C₂²	1	1	yes	characteristic, complemented
24	#15689539	—	2	1	no	—
25	#15689539	C₂²	1	1	yes	characteristic, complemented
26	M₃₂×D₄₇	—	2	1	no	—
27	M₃₂×D₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₁₆×D₄₇	—	2	1	no	—
29	C₂×C₁₆×D₄₇	C₂²	1	1	yes	characteristic
30	#15689394	C₂²	1	2	yes	complemented
31	#15689393	C₂²	1	2	yes	complemented
32	#15689392	—	2	2	no	—
33	#15689391	—	2	2	no	—
34	#15689390	C₂²	1	2	yes	complemented
35	#108×D₄₇	C₂²	1	2	yes	—
36	#100×D₄₇	—	2	2	no	—
37	#15688953	C₂²	1	1	yes	characteristic, complemented
38	#15688952	C₂²	1	2	yes	complemented
39	#15688937	C₂²	1	2	yes	complemented
40	#15688936	C₂²	1	2	yes	complemented
41	#15688935	C₂²	1	2	yes	complemented
42	C₂×D₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
43	C₄₇×#504	C₂²	1	1	yes	characteristic, complemented
44	C₄₇×#472	C₂²	1	2	yes	complemented
45	C₄₇×#368	C₂²	1	1	yes	characteristic, complemented
46	C₄₇×#361	C₂²	1	2	yes	complemented
47	#41×D₄₇	D₄	1	1	yes	characteristic
48	C₂×D₄×D₄₇	—	2	2	no	—
49	#13094052	—	2	2	no	—
50	#13094051	—	4	2	no	—
51	#13094050	—	2	2	no	—
52	#13094049	—	2	2	no	—
53	#13094048	—	4	2	no	—
54	SD₁₆×D₄₇	—	4	2	no	—
55	C₂×D₃₇₆	C₂³	1	2	yes	—
56	C₂×#10625334	—	2	2	no	—
57	D₈×D₄₇	—	2	2	no	—
58	D₈×D₄₇	—	2	2	no	—
59	D₈×D₄₇	—	2	2	no	—
60	D₈×D₄₇	—	2	2	no	—
61	D₈×D₄₇	—	4	2	no	—
62	#13094032	—	2	1	no	—
63	#13094032	D₄	1	1	yes	characteristic
64	#13094031	D₄	1	1	yes	characteristic
65	#13094030	—	2	1	no	—
66	#13094030	C₂³	1	1	yes	characteristic
67	M₁₆×D₄₇	—	2	1	no	—
68	M₁₆×D₄₇	—	2	2	no	—
69	M₁₆×D₄₇	D₄	1	1	yes	characteristic
70	C₂×C₈×D₄₇	—	2	1	no	—
71	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
72	D₇₅₂	—	2	1	no	—
73	D₇₅₂	—	2	1	no	—
74	#13093965	—	2	2	no	—
75	#13093965	—	2	2	no	—
76	#13093964	—	2	1	no	—
77	#13093964	C₂³	1	1	yes	characteristic
78	#13093963	—	2	1	no	—
79	#13093963	—	2	1	no	—
80	#13093963	—	2	1	no	—
81	C₂×C₄₇⋊C₁₆	—	2	1	no	—
82	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
83	C₁₆×D₄₇	—	2	1	no	—
84	C₁₆×D₄₇	—	2	1	no	—
85	C₁₆×D₄₇	—	2	1	no	—
86	C₁₆×D₄₇	D₄	1	1	yes	characteristic
87	C₁₆×D₄₇	D₄	1	1	yes	characteristic
88	C₁₆×D₄₇	D₄	1	1	yes	characteristic
89	C₁₆×D₄₇	D₄	1	1	yes	characteristic
90	#13093960	C₂³	1	2	yes	—
91	#13093959	—	2	2	no	—
92	#13093941	—	2	2	no	—
93	#13093940	—	2	2	no	—
94	#13093940	—	2	2	no	—
95	AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
96	C₂×D₈×C₄₇	C₂³	1	2	yes	—
97	#131×C₄₇	C₂³	1	1	yes	characteristic
98	D₁₆×C₄₇	—	2	1	no	—
99	D₁₆×C₄₇	—	2	1	no	—
100	M₃₂×C₄₇	—	2	1	no	—
101	M₃₂×C₄₇	C₂³	1	1	yes	characteristic
102	C₂×C₁₆×C₄₇	—	2	1	no	—
103	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
104	#108×C₄₇	C₂³	1	2	yes	—
105	#100×C₄₇	—	2	2	no	—
106	C₂³×D₄₇	—	4	2	no	—
107	#41×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂×D₄×C₄₇	—	2	2	no	—
109	C₂×C₂²⋊D₄₇	—	4	2	no	—
110	#10625354	D₈	1	1	yes	characteristic
111	Q₈×D₄₇	D₈	1	1	yes	characteristic
112	#10625352	—	2	1	no	—
113	#10625352	D₈	1	1	yes	characteristic
114	D₄×D₄₇	—	2	1	no	—
115	D₄×D₄₇	—	4	2	no	—
116	D₄×D₄₇	—	4	2	no	—
117	D₄×D₄₇	—	4	2	no	—
118	D₄×D₄₇	—	4	2	no	—
119	D₄×D₄₇	D₈	1	1	yes	characteristic
120	#10625350	—	2	1	no	—
121	#10625350	C₂×D₄	1	1	yes	characteristic
122	C₂×D₁₈₈	—	2	2	no	—
123	C₂×C₄×D₄₇	—	2	1	no	—
124	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
125	SD₁₆×C₄₇	—	4	2	no	—
126	D₈×C₄₇	—	2	2	no	—
127	D₈×C₄₇	—	2	2	no	—
128	D₈×C₄₇	—	4	2	no	—
129	M₁₆×C₄₇	—	2	1	no	—
130	M₁₆×C₄₇	—	2	2	no	—
131	M₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₄₇	—	2	1	no	—
133	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
134	#10625336	—	4	2	no	—
135	#10625335	—	4	2	no	—
136	#10625334	—	4	2	no	—
137	#10625334	—	4	2	no	—
138	#10625334	—	4	2	no	—
139	#10625334	—	4	2	no	—
140	#10625329	—	2	1	no	—
141	#10625329	—	2	2	no	—
142	#10625329	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄₇⋊C₈	—	2	1	no	—
144	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
145	D₃₇₆	—	2	2	no	—
146	D₃₇₆	—	2	2	no	—
147	D₃₇₆	—	4	2	no	—
148	#10625325	—	4	2	no	—
149	#10625324	—	2	1	no	—
150	#10625324	—	2	1	no	—
151	#10625324	—	2	1	no	—
152	#10625324	—	4	2	no	—
153	C₈×D₄₇	—	2	1	no	—
154	C₈×D₄₇	—	2	1	no	—
155	C₈×D₄₇	—	2	1	no	—
156	C₈×D₄₇	—	4	2	no	—
157	C₈×D₄₇	C₂×D₄	1	1	yes	characteristic
158	C₈×D₄₇	C₂×D₄	1	1	yes	characteristic
159	C₈×D₄₇	#41	1	1	yes	characteristic
160	C₈×D₄₇	#41	1	1	yes	characteristic
161	C₁₆×C₄₇	—	2	1	no	—
162	C₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
163	C₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
164	C₄₇⋊C₁₆	—	2	1	no	—
165	C₄₇⋊C₁₆	C₂×D₄	1	1	yes	characteristic
166	C₄₇⋊C₁₆	C₂×D₄	1	1	yes	characteristic
167	C₂³×C₄₇	—	4	2	no	—
168	C₂²×D₄₇	—	2	1	no	—
169	C₂²×D₄₇	—	4	2	no	—
170	C₂²×D₄₇	—	8	2	no	—
171	C₂²×D₄₇	—	8	2	no	—
172	C₂²×D₄₇	—	16	4	no	—
173	C₂²×D₄₇	#135	1	1	yes	characteristic
174	Q₈×C₄₇	C₂×D₈	1	1	yes	characteristic
175	D₄×C₄₇	—	2	1	no	—
176	D₄×C₄₇	—	4	2	no	—
177	D₄×C₄₇	—	4	2	no	—
178	D₄×C₄₇	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
181	C₂²⋊D₄₇	—	2	1	no	—
182	C₂²⋊D₄₇	—	2	1	no	—
183	C₂²⋊D₄₇	—	2	1	no	—
184	C₂²⋊D₄₇	—	8	2	no	—
185	C₂²⋊D₄₇	—	8	2	no	—
186	C₂×Dic₄₇	—	2	1	no	—
187	C₂×Dic₄₇	#135	1	1	yes	characteristic
188	D₁₈₈	—	2	1	no	—
189	D₁₈₈	—	4	2	no	—
190	D₁₈₈	—	4	2	no	—
191	D₁₈₈	C₂×D₈	1	1	yes	characteristic
192	C₄×D₄₇	—	2	1	no	—
193	C₄×D₄₇	—	2	1	no	—
194	C₄×D₄₇	—	2	1	no	—
195	C₄×D₄₇	#121	1	1	yes	characteristic
196	C₄×D₄₇	#121	1	1	yes	characteristic
197	C₄×D₄₇	C₂×D₈	1	1	yes	characteristic
198	C₄×D₄₇	C₂×D₈	1	1	yes	characteristic
199	Dic₉₄	—	2	1	no	—
200	Dic₉₄	C₂×D₈	1	1	yes	characteristic
201	C₈×C₄₇	—	2	1	no	—
202	C₈×C₄₇	—	4	2	no	—
203	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
204	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
205	C₄₇⋊C₈	—	2	1	no	—
206	C₄₇⋊C₈	—	4	2	no	—
207	C₄₇⋊C₈	#121	1	1	yes	characteristic
208	C₄₇⋊C₈	#121	1	1	yes	characteristic
209	C₂×#2221	—	47	1	no	maximal, Sylow
210	C₂²×C₄₇	—	2	1	no	—
211	C₂²×C₄₇	—	8	2	no	—
212	C₂²×C₄₇	—	16	2	no	—
213	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
214	C₂×D₄₇	—	2	2	no	—
215	C₂×D₄₇	—	2	1	no	—
216	C₂×D₄₇	—	4	2	no	—
217	C₂×D₄₇	—	8	2	no	—
218	C₂×D₄₇	—	16	4	no	—
219	C₂×D₄₇	—	16	4	no	—
220	C₂×D₄₇	—	16	2	no	—
221	C₂×D₄₇	#466	1	1	yes	characteristic
222	C₂×D₄₇	#466	1	1	yes	characteristic
223	C₄×C₄₇	—	2	1	no	—
224	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
225	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
226	Dic₄₇	—	2	1	no	—
227	Dic₄₇	#466	1	1	yes	characteristic
228	Dic₄₇	#466	1	1	yes	characteristic
229	C₂²×D₁₆	—	47	1	no	—
230	C₂×#504	—	47	1	no	—
231	C₂×#472	—	47	2	no	—
232	#2221	—	47	1	no	—
233	#2221	—	47	1	no	—
234	#2221	—	47	2	no	—
235	#2221	—	47	1	no	—
236	#2221	—	47	2	no	—
237	#2221	D₄₇	1	1	yes	characteristic, direct product factor
238	C₂×#368	—	47	1	no	—
239	C₂×#361	—	47	2	no	—
240	C₂×C₄₇	—	2	1	no	—
241	C₂×C₄₇	—	4	1	no	—
242	C₂×C₄₇	—	16	2	no	—
243	C₂×C₄₇	C₂×#466	1	1	yes	characteristic
244	D₄₇	—	2	1	no	—
245	D₄₇	—	4	1	no	—
246	D₄₇	—	16	2	no	—
247	D₄₇	#2221	1	2	yes	direct product factor
248	C₂×AGL(1,ℤ/8)	—	94	2	no	—
249	C₂²×D₈	—	47	2	no	—
250	C₂×#131	—	47	1	no	—
251	C₂×D₁₆	—	47	2	no	—
252	C₂×D₁₆	—	47	1	no	—
253	C₂×D₁₆	—	94	1	no	—
254	C₂×D₁₆	—	94	1	no	—
255	C₂×D₁₆	—	94	1	no	—
256	C₂×D₁₆	—	94	1	no	—
257	C₂×D₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
258	#504	—	47	1	no	—
259	#504	—	47	1	no	—
260	#504	—	47	1	no	—
261	#504	—	94	1	no	—
262	#504	—	94	1	no	—
263	#504	C₂×D₄₇	1	1	yes	characteristic, complemented
264	C₂×M₃₂	—	47	1	no	—
265	C₂×M₃₂	—	94	1	no	—
266	C₂²×C₁₆	—	47	1	no	—
267	C₂²×C₁₆	—	94	1	no	—
268	#472	—	47	2	no	—
269	#472	—	47	2	no	—
270	#472	—	47	2	no	—
271	#472	—	94	2	no	—
272	#472	—	94	2	no	—
273	#472	C₂×D₄₇	1	2	yes	complemented
274	C₂×#108	—	47	2	no	—
275	C₂×#100	—	94	2	no	—
276	#368	—	47	1	no	—
277	#368	—	47	2	no	—
278	#368	C₂×D₄₇	1	1	yes	characteristic, complemented
279	#361	—	47	2	no	—
280	#361	—	47	2	no	—
281	#361	—	47	2	no	—
282	#361	C₂×D₄₇	1	2	yes	complemented
283	C₄₇	C₂×#2221	1	1	yes	characteristic, complemented, Sylow
284	C₂×#41	—	47	1	no	—
285	C₂²×D₄	—	94	2	no	—
286	AGL(1,ℤ/8)	—	2	2	no	—
287	AGL(1,ℤ/8)	—	94	2	no	—
288	AGL(1,ℤ/8)	—	94	2	no	—
289	AGL(1,ℤ/8)	—	94	2	no	—
290	AGL(1,ℤ/8)	—	188	2	no	—
291	AGL(1,ℤ/8)	—	188	2	no	—
292	C₂×SD₁₆	—	188	2	no	—
293	C₂×D₈	—	47	2	no	—
294	C₂×D₈	—	94	2	no	—
295	C₂×D₈	—	94	2	no	—
296	C₂×D₈	—	94	2	no	—
297	C₂×D₈	—	94	2	no	—
298	C₂×D₈	—	94	2	no	—
299	C₂×D₈	—	188	2	no	—
300	C₂×D₈	C₂²×D₄₇	1	2	yes	—
301	#131	—	47	1	no	—
302	#131	—	47	1	no	—
303	#131	—	47	1	no	—
304	#131	—	94	1	no	—
305	#131	—	94	1	no	—
306	#131	C₂²×D₄₇	1	1	yes	characteristic
307	C₂×M₁₆	—	47	1	no	—
308	C₂×M₁₆	—	94	1	no	—
309	C₂×M₁₆	—	94	2	no	—
310	C₂²×C₈	—	47	1	no	—
311	C₂²×C₈	—	94	1	no	—
312	D₁₆	—	2	1	no	—
313	D₁₆	—	2	1	no	—
314	D₁₆	—	94	2	no	—
315	D₁₆	—	94	2	no	—
316	D₁₆	—	94	1	no	—
317	D₁₆	—	94	1	no	—
318	M₃₂	—	2	1	no	—
319	M₃₂	—	47	1	no	—
320	M₃₂	—	94	1	no	—
321	M₃₂	—	94	1	no	—
322	M₃₂	—	94	1	no	—
323	M₃₂	—	94	1	no	—
324	M₃₂	C₂²×D₄₇	1	1	yes	characteristic
325	C₂×C₁₆	—	2	1	no	—
326	C₂×C₁₆	—	47	1	no	—
327	C₂×C₁₆	—	47	1	no	—
328	C₂×C₁₆	—	47	1	no	—
329	C₂×C₁₆	—	47	1	no	—
330	C₂×C₁₆	—	47	1	no	—
331	C₂×C₁₆	—	94	1	no	—
332	C₂×C₁₆	—	94	1	no	—
333	C₂×C₁₆	—	94	1	no	—
334	C₂×C₁₆	—	94	1	no	—
335	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
336	#108	—	47	2	no	—
337	#108	—	94	2	no	—
338	#108	C₂²×D₄₇	1	2	yes	—
339	#100	—	2	2	no	—
340	#100	—	94	2	no	—
341	#100	—	94	2	no	—
342	#100	—	94	2	no	—
343	C₂⁴	—	188	2	no	—
344	#41	—	47	1	no	—
345	#41	—	47	1	no	—
346	#41	—	47	1	no	—
347	#41	—	94	1	no	—
348	#41	—	94	1	no	—
349	#41	D₄×D₄₇	1	1	yes	characteristic
350	C₂×Q₈	—	47	1	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	47	1	no	—
353	C₂×D₄	—	94	1	no	—
354	C₂×D₄	—	94	2	no	—
355	C₂×D₄	—	188	2	no	—
356	C₂×D₄	—	188	2	no	—
357	C₂×D₄	—	188	2	no	—
358	C₂×D₄	—	188	2	no	—
359	C₂×D₄	—	188	2	no	—
360	C₂²×C₄	—	47	1	no	—
361	C₂²×C₄	—	94	1	no	—
362	SD₁₆	—	4	2	no	—
363	SD₁₆	—	188	2	no	—
364	SD₁₆	—	188	2	no	—
365	SD₁₆	—	188	2	no	—
366	D₈	—	2	2	no	—
367	D₈	—	2	2	no	—
368	D₈	—	4	2	no	—
369	D₈	—	94	2	no	—
370	D₈	—	94	2	no	—
371	D₈	—	188	2	no	—
372	D₈	—	188	2	no	—
373	D₈	—	188	2	no	—
374	D₈	—	188	2	no	—
375	D₈	—	188	2	no	—
376	M₁₆	—	2	1	no	—
377	M₁₆	—	2	2	no	—
378	M₁₆	—	47	1	no	—
379	M₁₆	—	94	1	no	—
380	M₁₆	—	94	1	no	—
381	M₁₆	—	94	1	no	—
382	M₁₆	—	94	1	no	—
383	M₁₆	—	94	2	no	—
384	M₁₆	—	188	2	no	—
385	M₁₆	D₄×D₄₇	1	1	yes	characteristic
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	47	1	no	—
388	C₂×C₈	—	47	1	no	—
389	C₂×C₈	—	47	1	no	—
390	C₂×C₈	—	47	1	no	—
391	C₂×C₈	—	47	1	no	—
392	C₂×C₈	—	94	1	no	—
393	C₂×C₈	—	94	1	no	—
394	C₂×C₈	—	94	1	no	—
395	C₂×C₈	—	94	1	no	—
396	C₂×C₈	—	188	2	no	—
397	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
398	C₁₆	—	2	1	no	—
399	C₁₆	—	47	1	no	—
400	C₁₆	—	47	1	no	—
401	C₁₆	—	94	1	no	—
402	C₁₆	D₄×D₄₇	1	1	yes	characteristic
403	C₁₆	D₄×D₄₇	1	1	yes	characteristic
404	C₂³	—	4	2	no	—
405	C₂³	—	47	1	no	—
406	C₂³	—	94	1	no	—
407	C₂³	—	376	2	no	—
408	C₂³	—	376	2	no	—
409	C₂³	—	188	2	no	—
410	C₂³	—	752	4	no	—
411	Q₈	—	47	1	no	—
412	Q₈	—	94	1	no	—
413	Q₈	D₈×D₄₇	1	1	yes	characteristic
414	D₄	—	2	1	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	47	1	no	—
418	D₄	—	94	1	no	—
419	D₄	—	94	1	no	—
420	D₄	—	94	1	no	—
421	D₄	—	94	1	no	—
422	D₄	—	376	2	no	—
423	D₄	—	376	2	no	—
424	D₄	—	188	2	no	—
425	D₄	—	188	2	no	—
426	D₄	D₈×D₄₇	1	1	yes	characteristic
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	47	1	no	—
429	C₂×C₄	—	47	1	no	—
430	C₂×C₄	—	47	1	no	—
431	C₂×C₄	—	47	1	no	—
432	C₂×C₄	—	47	1	no	—
433	C₂×C₄	—	94	1	no	—
434	C₂×C₄	—	94	1	no	—
435	C₂×C₄	—	94	1	no	—
436	C₂×C₄	—	94	1	no	—
437	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
438	C₈	—	2	1	no	—
439	C₈	—	4	2	no	—
440	C₈	—	47	1	no	—
441	C₈	—	47	1	no	—
442	C₈	—	94	1	no	—
443	C₈	—	188	2	no	—
444	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
445	C₈	#41×D₄₇	1	1	yes	characteristic
446	C₂²	—	2	1	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	16	2	no	—
449	C₂²	—	47	1	no	—
450	C₂²	—	47	1	no	—
451	C₂²	—	94	2	no	—
452	C₂²	—	94	1	no	—
453	C₂²	—	376	2	no	—
454	C₂²	—	188	2	no	—
455	C₂²	—	752	2	no	—
456	C₂²	—	752	4	no	—
457	C₂²	—	752	4	no	—
458	C₂²	#135×D₄₇	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	47	1	no	—
461	C₄	—	47	1	no	—
462	C₄	—	94	1	no	—
463	C₄	#121×D₄₇	1	1	yes	characteristic
464	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
465	C₂	—	2	1	no	—
466	C₂	—	4	1	no	—
467	C₂	—	16	2	no	—
468	C₂	—	47	2	no	—
469	C₂	—	94	1	no	—
470	C₂	—	188	1	no	—
471	C₂	—	752	2	no	—
472	C₂	#466×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#466×D₄₇
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₄₇×#2221	C₂
socle	C₂×C₄₇	C₂×#466
hypercenter	#2221	D₄₇
hypocenter	C₄₇	C₂×#2221
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #2221

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₆×D₄₇	C₂	semidirect
2. #504×D₄₇	C₂	semidirect
3. #472×D₄₇	C₂	semidirect
4. #20245509	C₂	semidirect
5. #20245508	C₂	semidirect
6. #20245507	C₂	semidirect
7. #20245506	C₂	semidirect
8. #20245505	C₂	semidirect
9. #368×D₄₇	C₂	semidirect
10. #361×D₄₇	C₂	semidirect
11. C₄₇×#2221	C₂	semidirect
15. C₂×D₇₅₂	C₂²	semidirect
16. C₂×#13093965	C₂²	semidirect
22. #15689541	C₂²	semidirect
23. #15689540	C₂²	semidirect
25. #15689539	C₂²	semidirect
30. #15689394	C₂²	semidirect
31. #15689393	C₂²	semidirect
34. #15689390	C₂²	semidirect
37. #15688953	C₂²	semidirect
38. #15688952	C₂²	semidirect
39. #15688937	C₂²	semidirect
40. #15688936	C₂²	semidirect
41. #15688935	C₂²	semidirect
42. C₂×D₁₆×C₄₇	C₂²	semidirect
43. C₄₇×#504	C₂²	semidirect
44. C₄₇×#472	C₂²	semidirect
45. C₄₇×#368	C₂²	semidirect
46. C₄₇×#361	C₂²	semidirect
237. #2221	D₄₇	direct (N × H)
247. D₄₇	#2221	direct (N × H)
257. C₂×D₁₆	C₂×D₄₇	semidirect
263. #504	C₂×D₄₇	semidirect
273. #472	C₂×D₄₇	semidirect
278. #368	C₂×D₄₇	semidirect
282. #361	C₂×D₄₇	semidirect
283. C₄₇	C₂×#2221	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₆×D₄₇	2
#504×D₄₇	2
#472×D₄₇	2
#20245509	2
#20245508	2
#20245507	2
#20245506	2
#20245505	2
#368×D₄₇	2
#361×D₄₇	2
C₄₇×#2221	2
C₂×#2221	47

Subgroups — D47×#2221 #26370831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#2221 #26370831