Subgroups — D₄₇×#2179 #26369680

Order 12032.

654 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#508×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#443×D₄₇	C₂	1	2	yes	maximal, complemented
3	#20245275	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245274	C₂	1	1	yes	maximal, characteristic, complemented
5	#20245273	C₂	1	1	yes	maximal, characteristic, complemented
6	#20245272	C₂	1	2	yes	maximal, complemented
7	#20245271	C₂	1	2	yes	maximal, complemented
8	#368×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#359×D₄₇	C₂	1	2	yes	maximal, complemented
10	#346×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2179	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₄₇	C₂²	1	2	yes	—
13	#131×D₄₇	—	2	2	no	—
14	#15689556	C₄	1	1	yes	characteristic, complemented
15	#15689555	C₂²	1	1	yes	characteristic
16	#15689554	C₄	1	2	yes	complemented
17	#15689553	C₂²	1	2	yes	—
18	#15689552	C₄	1	1	yes	characteristic, complemented
19	Q₃₂×D₄₇	C₄	1	1	yes	characteristic, complemented
20	SD₃₂×D₄₇	C₄	1	2	yes	complemented
21	D₁₆×D₄₇	C₄	1	1	yes	characteristic, complemented
22	C₂×C₁₆×D₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₄₇	C₂²	1	1	yes	characteristic
24	#15689241	C₂²	1	2	yes	complemented
25	#15689240	C₂²	1	2	yes	complemented
26	#15689239	C₂²	1	2	yes	complemented
27	#15689238	—	2	2	no	—
28	#15689237	—	2	2	no	—
29	#108×D₄₇	C₂²	1	2	yes	—
30	#104×D₄₇	—	2	2	no	—
31	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
32	#15688953	C₂²	1	1	yes	characteristic, complemented
33	#15688952	C₂²	1	2	yes	complemented
34	#15688931	C₂²	1	2	yes	complemented
35	#15688930	C₂²	1	2	yes	complemented
36	#15688929	C₂²	1	2	yes	complemented
37	#15688899	C₂²	1	1	yes	characteristic, complemented
38	#15688898	C₂²	1	1	yes	characteristic, complemented
39	#15688898	C₂²	1	1	yes	characteristic, complemented
40	C₄₇×#508	C₂²	1	1	yes	characteristic
41	C₄₇×#443	C₂²	1	2	yes	complemented
42	C₄₇×#368	C₂²	1	1	yes	characteristic, complemented
43	C₄₇×#359	C₂²	1	2	yes	complemented
44	C₄₇×#346	C₂²	1	1	yes	characteristic, complemented
45	#41×D₄₇	—	2	2	no	—
46	#13094047	C₂×C₄	1	2	yes	—
47	#13094046	C₂³	1	2	yes	—
48	#13094045	—	2	2	no	—
49	#13094044	—	2	2	no	—
50	#13094043	C₂×C₄	1	2	yes	—
51	Q₁₆×D₄₇	C₂×C₄	1	2	yes	—
52	SD₁₆×D₄₇	—	2	2	no	—
53	D₈×D₄₇	C₂×C₄	1	2	yes	—
54	#13094032	—	2	2	no	—
55	#13094032	—	4	2	no	—
56	#13094031	—	2	2	no	—
57	#13094030	—	2	2	no	—
58	#13094030	—	4	2	no	—
59	M₁₆×D₄₇	—	2	2	no	—
60	M₁₆×D₄₇	—	4	2	no	—
61	C₂×C₈×D₄₇	—	4	2	no	—
62	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
63	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
64	C₄²×D₄₇	D₄	1	1	yes	characteristic
65	Dic₃₇₆	C₂×C₄	1	1	yes	characteristic, complemented
66	#13093970	C₂×C₄	1	2	yes	complemented
67	#13093969	C₂×C₄	1	2	yes	complemented
68	#13093968	C₂×C₄	1	2	yes	complemented
69	#13093967	C₂×C₄	1	2	yes	complemented
70	D₇₅₂	C₂×C₄	1	1	yes	characteristic, complemented
71	#13093965	C₂×C₄	1	2	yes	complemented
72	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
74	C₁₆×D₄₇	—	2	1	no	—
75	C₁₆×D₄₇	—	2	1	no	—
76	C₁₆×D₄₇	C₂×C₄	1	1	yes	characteristic
77	C₁₆×D₄₇	C₂×C₄	1	1	yes	characteristic
78	C₁₆×D₄₇	C₂×C₄	1	1	yes	characteristic
79	C₁₆×D₄₇	C₂×C₄	1	1	yes	characteristic
80	#13093960	C₂³	1	2	yes	—
81	#13093959	—	2	2	no	—
82	#13093952	—	2	2	no	—
83	#13093951	—	2	2	no	—
84	#13093950	—	2	2	no	—
85	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
86	C₈×Dic₄₇	D₄	1	1	yes	characteristic
87	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
88	#135×C₄₇	C₂³	1	2	yes	—
89	#131×C₄₇	—	2	2	no	—
90	Q₃₂×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
91	SD₃₂×C₄₇	C₂×C₄	1	2	yes	complemented
92	D₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
93	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
95	#108×C₄₇	C₂³	1	2	yes	—
96	#104×C₄₇	—	2	2	no	—
97	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
98	#41×C₄₇	—	2	2	no	—
99	#10625354	—	2	2	no	—
100	Q₈×D₄₇	—	2	2	no	—
101	#10625352	—	2	2	no	—
102	#10625352	—	4	2	no	—
103	D₄×D₄₇	—	2	2	no	—
104	D₄×D₄₇	—	4	2	no	—
105	#10625350	—	2	2	no	—
106	#10625350	—	4	2	no	—
107	C₂×C₄×D₄₇	—	2	1	no	—
108	C₂×C₄×D₄₇	—	4	2	no	—
109	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
110	Q₁₆×C₄₇	C₂²×C₄	1	2	yes	—
111	SD₁₆×C₄₇	—	2	2	no	—
112	D₈×C₄₇	C₂²×C₄	1	2	yes	—
113	M₁₆×C₄₇	—	2	2	no	—
114	M₁₆×C₄₇	—	4	2	no	—
115	C₂×C₈×C₄₇	—	4	2	no	—
116	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
118	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
119	#10625337	—	2	2	no	—
120	#10625336	—	2	2	no	—
121	#10625335	—	2	2	no	—
122	#10625334	—	2	2	no	—
123	C₄×Dic₄₇	—	2	1	no	—
124	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
125	#10625329	—	2	2	no	—
126	#10625329	—	4	2	no	—
127	C₂×C₄₇⋊C₈	—	4	2	no	—
128	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
130	Dic₁₈₈	C₂²×C₄	1	2	yes	—
131	D₃₇₆	C₂²×C₄	1	2	yes	—
132	#10625325	—	2	2	no	—
133	#10625324	—	4	2	no	—
134	#10625324	—	4	2	no	—
135	#10625324	—	4	2	no	—
136	C₈×D₄₇	—	4	2	no	—
137	C₈×D₄₇	—	4	2	no	—
138	C₈×D₄₇	—	4	2	no	—
139	C₈×D₄₇	D₈	1	2	yes	—
140	C₈×D₄₇	D₈	1	2	yes	—
141	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₈×D₄₇	#41	1	1	yes	characteristic
144	C₈×D₄₇	#41	1	1	yes	characteristic
145	C₁₆×C₄₇	—	2	1	no	—
146	C₁₆×C₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₁₆×C₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₄₇⋊C₁₆	—	2	1	no	—
149	C₄₇⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
150	C₄₇⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
151	C₂²×D₄₇	—	4	2	no	—
152	C₂²×D₄₇	#135	1	1	yes	characteristic
153	Q₈×C₄₇	—	2	2	no	—
154	D₄×C₄₇	—	2	2	no	—
155	D₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
159	C₂²⋊D₄₇	—	4	2	no	—
160	C₂²⋊D₄₇	—	4	2	no	—
161	C₂²⋊D₄₇	—	4	2	no	—
162	C₂×Dic₄₇	—	2	1	no	—
163	C₂×Dic₄₇	—	4	2	no	—
164	C₂×Dic₄₇	#135	1	1	yes	characteristic
165	D₁₈₈	—	2	2	no	—
166	D₁₈₈	—	4	2	no	—
167	C₄×D₄₇	—	4	2	no	—
168	C₄×D₄₇	—	4	2	no	—
169	C₄×D₄₇	—	4	2	no	—
170	C₄×D₄₇	—	4	2	no	—
171	C₄×D₄₇	C₄×D₄	1	1	yes	characteristic
172	C₄×D₄₇	C₄×D₄	1	1	yes	characteristic
173	C₄×D₄₇	C₂×D₈	1	1	yes	characteristic
174	C₄×D₄₇	C₂×D₈	1	1	yes	characteristic
175	Dic₉₄	—	2	2	no	—
176	Dic₉₄	—	4	2	no	—
177	C₈×C₄₇	—	4	2	no	—
178	C₈×C₄₇	C₂×D₈	1	2	yes	—
179	C₈×C₄₇	C₂³×C₄	1	1	yes	characteristic
180	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₄₇⋊C₈	—	4	2	no	—
182	C₄₇⋊C₈	C₄×D₄	1	1	yes	characteristic
183	C₄₇⋊C₈	C₄×D₄	1	1	yes	characteristic
184	C₄₇⋊C₈	C₂×D₈	1	2	yes	—
185	C₂×#2179	—	47	1	no	maximal, Sylow
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
188	C₂×D₄₇	—	2	2	no	—
189	C₂×D₄₇	—	4	2	no	—
190	C₂×D₄₇	—	8	4	no	—
191	C₂×D₄₇	C₄×D₈	1	1	yes	characteristic
192	C₂×D₄₇	C₄×D₈	1	1	yes	characteristic
193	C₄×C₄₇	—	4	1	no	—
194	C₄×C₄₇	—	4	2	no	—
195	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
196	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
197	Dic₄₇	—	4	1	no	—
198	Dic₄₇	—	4	2	no	—
199	Dic₄₇	C₄×D₈	1	1	yes	characteristic
200	Dic₄₇	C₄×D₈	1	1	yes	characteristic
201	C₂×#508	—	47	1	no	—
202	C₂×#443	—	47	2	no	—
203	#2179	—	47	1	no	—
204	#2179	—	47	2	no	—
205	#2179	—	47	1	no	—
206	#2179	—	47	2	no	—
207	#2179	—	47	1	no	—
208	#2179	D₄₇	1	1	yes	characteristic, direct product factor
209	C₂×#368	—	47	1	no	—
210	C₂×#359	—	47	2	no	—
211	C₂×#346	—	47	1	no	—
212	C₂×C₄₇	—	2	1	no	—
213	C₂×C₄₇	—	8	2	no	—
214	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
215	D₄₇	—	2	1	no	—
216	D₄₇	—	8	2	no	—
217	D₄₇	#2179	1	2	yes	direct product factor
218	C₂×#135	—	47	2	no	—
219	C₂×#131	—	94	2	no	—
220	#508	—	47	2	no	—
221	#508	—	47	1	no	—
222	#508	—	47	2	no	—
223	#508	—	47	1	no	—
224	#508	—	47	1	no	—
225	#508	C₂×D₄₇	1	1	yes	characteristic
226	C₂×Q₃₂	—	47	1	no	—
227	C₂×SD₃₂	—	47	2	no	—
228	C₂×D₁₆	—	47	1	no	—
229	C₂²×C₁₆	—	47	1	no	—
230	C₂²×C₁₆	—	47	1	no	—
231	#443	—	47	2	no	—
232	#443	—	47	2	no	—
233	#443	—	47	2	no	—
234	#443	—	94	2	no	—
235	#443	—	94	2	no	—
236	#443	C₂×D₄₇	1	2	yes	complemented
237	C₂×#108	—	47	2	no	—
238	C₂×#104	—	94	2	no	—
239	C₂×C₄×C₈	—	47	1	no	—
240	#368	—	47	1	no	—
241	#368	—	47	2	no	—
242	#368	C₂×D₄₇	1	1	yes	characteristic, complemented
243	#359	—	47	2	no	—
244	#359	—	47	2	no	—
245	#359	—	47	2	no	—
246	#359	C₂×D₄₇	1	2	yes	complemented
247	#346	—	47	1	no	—
248	#346	—	47	1	no	—
249	#346	—	47	1	no	—
250	#346	C₂×D₄₇	1	1	yes	characteristic, complemented
251	C₄₇	C₂×#2179	1	1	yes	characteristic, complemented, Sylow
252	C₂×#41	—	94	2	no	—
253	#135	—	47	2	no	—
254	#135	—	47	2	no	—
255	#135	—	47	2	no	—
256	#135	—	94	2	no	—
257	#135	—	94	2	no	—
258	#135	C₂²×D₄₇	1	2	yes	—
259	C₂×Q₁₆	—	47	2	no	—
260	C₂×SD₁₆	—	94	2	no	—
261	C₂×D₈	—	47	2	no	—
262	#131	—	2	2	no	—
263	#131	—	94	2	no	—
264	#131	—	94	2	no	—
265	#131	—	94	2	no	—
266	#131	—	188	2	no	—
267	#131	—	188	2	no	—
268	C₂×M₁₆	—	94	2	no	—
269	C₂×M₁₆	—	188	2	no	—
270	C₂²×C₈	—	47	1	no	—
271	C₂²×C₈	—	47	1	no	—
272	C₂²×C₈	—	188	2	no	—
273	C₂×C₄²	—	47	1	no	—
274	Q₃₂	—	47	2	no	—
275	Q₃₂	—	47	1	no	—
276	Q₃₂	C₄×D₄₇	1	1	yes	characteristic, complemented
277	SD₃₂	—	47	2	no	—
278	SD₃₂	—	47	2	no	—
279	SD₃₂	—	47	2	no	—
280	SD₃₂	C₄×D₄₇	1	2	yes	complemented
281	D₁₆	—	47	2	no	—
282	D₁₆	—	47	1	no	—
283	D₁₆	C₄×D₄₇	1	1	yes	characteristic, complemented
284	C₂×C₁₆	—	47	1	no	—
285	C₂×C₁₆	—	47	1	no	—
286	C₂×C₁₆	—	47	1	no	—
287	C₂×C₁₆	—	47	1	no	—
288	C₂×C₁₆	—	47	1	no	—
289	C₂×C₁₆	—	47	1	no	—
290	C₂×C₁₆	—	94	1	no	—
291	C₂×C₁₆	—	94	1	no	—
292	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
293	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
294	#108	—	47	2	no	—
295	#108	—	94	2	no	—
296	#108	C₂²×D₄₇	1	2	yes	—
297	#104	—	2	2	no	—
298	#104	—	94	2	no	—
299	#104	—	94	2	no	—
300	#104	—	94	2	no	—
301	C₄×C₈	—	47	1	no	—
302	C₄×C₈	—	47	1	no	—
303	C₄×C₈	—	47	1	no	—
304	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
305	#41	—	2	2	no	—
306	#41	—	94	2	no	—
307	#41	—	94	2	no	—
308	#41	—	94	2	no	—
309	#41	—	188	2	no	—
310	#41	—	188	2	no	—
311	C₂×Q₈	—	94	2	no	—
312	C₂×D₄	—	94	2	no	—
313	C₂×D₄	—	188	2	no	—
314	C₂²×C₄	—	47	1	no	—
315	C₂²×C₄	—	94	1	no	—
316	C₂²×C₄	—	188	2	no	—
317	Q₁₆	—	47	2	no	—
318	Q₁₆	—	94	2	no	—
319	Q₁₆	C₂×C₄×D₄₇	1	2	yes	—
320	SD₁₆	—	2	2	no	—
321	SD₁₆	—	94	2	no	—
322	SD₁₆	—	94	2	no	—
323	SD₁₆	—	94	2	no	—
324	D₈	—	47	2	no	—
325	D₈	—	94	2	no	—
326	D₈	C₂×C₄×D₄₇	1	2	yes	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	4	2	no	—
329	M₁₆	—	94	2	no	—
330	M₁₆	—	188	2	no	—
331	M₁₆	—	188	2	no	—
332	M₁₆	—	188	2	no	—
333	M₁₆	—	188	2	no	—
334	C₂×C₈	—	4	2	no	—
335	C₂×C₈	—	47	1	no	—
336	C₂×C₈	—	47	1	no	—
337	C₂×C₈	—	47	2	no	—
338	C₂×C₈	—	47	2	no	—
339	C₂×C₈	—	47	1	no	—
340	C₂×C₈	—	47	1	no	—
341	C₂×C₈	—	47	1	no	—
342	C₂×C₈	—	47	1	no	—
343	C₂×C₈	—	188	2	no	—
344	C₂×C₈	—	188	2	no	—
345	C₂×C₈	—	188	2	no	—
346	C₂×C₈	—	188	2	no	—
347	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
348	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
349	C₄²	—	47	1	no	—
350	C₄²	—	94	1	no	—
351	C₄²	D₄×D₄₇	1	1	yes	characteristic
352	C₁₆	—	2	1	no	—
353	C₁₆	—	47	1	no	—
354	C₁₆	—	47	1	no	—
355	C₁₆	—	94	1	no	—
356	C₁₆	C₂×C₄×D₄₇	1	1	yes	characteristic
357	C₁₆	C₂×C₄×D₄₇	1	1	yes	characteristic
358	C₂³	—	47	1	no	—
359	C₂³	—	188	2	no	—
360	Q₈	—	2	2	no	—
361	Q₈	—	94	2	no	—
362	Q₈	—	188	2	no	—
363	D₄	—	2	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	94	2	no	—
366	D₄	—	188	2	no	—
367	D₄	—	188	2	no	—
368	D₄	—	188	2	no	—
369	D₄	—	188	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	47	1	no	—
373	C₂×C₄	—	47	1	no	—
374	C₂×C₄	—	47	1	no	—
375	C₂×C₄	—	47	1	no	—
376	C₂×C₄	—	47	1	no	—
377	C₂×C₄	—	94	1	no	—
378	C₂×C₄	—	188	2	no	—
379	C₂×C₄	—	188	2	no	—
380	C₂×C₄	—	188	2	no	—
381	C₂×C₄	—	188	2	no	—
382	C₂×C₄	—	188	2	no	—
383	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
384	C₈	—	4	2	no	—
385	C₈	—	47	1	no	—
386	C₈	—	47	1	no	—
387	C₈	—	47	2	no	—
388	C₈	—	188	2	no	—
389	C₈	D₈×D₄₇	1	2	yes	—
390	C₈	C₂²×C₄×D₄₇	1	1	yes	characteristic
391	C₈	#41×D₄₇	1	1	yes	characteristic
392	C₂²	—	4	2	no	—
393	C₂²	—	47	1	no	—
394	C₂²	—	47	1	no	—
395	C₂²	—	94	2	no	—
396	C₂²	—	376	4	no	—
397	C₂²	—	188	2	no	—
398	C₂²	#135×D₄₇	1	1	yes	characteristic
399	C₄	—	4	1	no	—
400	C₄	—	4	2	no	—
401	C₄	—	47	1	no	—
402	C₄	—	47	1	no	—
403	C₄	—	188	1	no	—
404	C₄	—	188	2	no	—
405	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
406	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
407	C₂	—	2	1	no	—
408	C₂	—	8	2	no	—
409	C₂	—	47	2	no	—
410	C₂	—	94	1	no	—
411	C₂	—	376	2	no	—
412	C₂	C₄×D₈×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₈×D₄₇
commutator	C₈×C₄₇	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₄₇×#2179	C₂
socle	C₂×C₄₇	C₂×C₄×D₈
prime radical	#508×D₄₇	C₂
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	#2179	D₄₇
hypocenter	C₄₇	C₂×#2179
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #2179

Complements

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

N	H ≅ G/N	type
2. #443×D₄₇	C₂	semidirect
3. #20245275	C₂	semidirect
4. #20245274	C₂	semidirect
5. #20245273	C₂	semidirect
6. #20245272	C₂	semidirect
7. #20245271	C₂	semidirect
8. #368×D₄₇	C₂	semidirect
9. #359×D₄₇	C₂	semidirect
10. #346×D₄₇	C₂	semidirect
11. C₄₇×#2179	C₂	semidirect
14. #15689556	C₄	semidirect
16. #15689554	C₄	semidirect
18. #15689552	C₄	semidirect
19. Q₃₂×D₄₇	C₄	semidirect
20. SD₃₂×D₄₇	C₄	semidirect
21. D₁₆×D₄₇	C₄	semidirect
24. #15689241	C₂²	semidirect
25. #15689240	C₂²	semidirect
26. #15689239	C₂²	semidirect
32. #15688953	C₂²	semidirect
33. #15688952	C₂²	semidirect
34. #15688931	C₂²	semidirect
35. #15688930	C₂²	semidirect
36. #15688929	C₂²	semidirect
37. #15688899	C₂²	semidirect
38. #15688898	C₂²	semidirect
39. #15688898	C₂²	semidirect
41. C₄₇×#443	C₂²	semidirect
42. C₄₇×#368	C₂²	semidirect
43. C₄₇×#359	C₂²	semidirect
44. C₄₇×#346	C₂²	semidirect
65. Dic₃₇₆	C₂×C₄	semidirect
66. #13093970	C₂×C₄	semidirect
67. #13093969	C₂×C₄	semidirect
68. #13093968	C₂×C₄	semidirect
69. #13093967	C₂×C₄	semidirect
70. D₇₅₂	C₂×C₄	semidirect
71. #13093965	C₂×C₄	semidirect
90. Q₃₂×C₄₇	C₂×C₄	semidirect
91. SD₃₂×C₄₇	C₂×C₄	semidirect
92. D₁₆×C₄₇	C₂×C₄	semidirect
208. #2179	D₄₇	direct (N × H)
217. D₄₇	#2179	direct (N × H)
236. #443	C₂×D₄₇	semidirect
242. #368	C₂×D₄₇	semidirect
246. #359	C₂×D₄₇	semidirect
250. #346	C₂×D₄₇	semidirect
251. C₄₇	C₂×#2179	semidirect
276. Q₃₂	C₄×D₄₇	semidirect
280. SD₃₂	C₄×D₄₇	semidirect
283. D₁₆	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#508×D₄₇	2
#443×D₄₇	2
#20245275	2
#20245274	2
#20245273	2
#20245272	2
#20245271	2
#368×D₄₇	2
#359×D₄₇	2
#346×D₄₇	2
C₄₇×#2179	2
C₂×#2179	47

Subgroups — D47×#2179 #26369680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#2179 #26369680