Subgroups — D₄₇×#2178 #26369674

Order 12032.

662 conjugacy classes of subgroups.

The subgroup lattice has 422 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	#20245270	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245269	C₂	1	1	yes	maximal, characteristic, complemented
5	#20245268	C₂	1	1	yes	maximal, characteristic, complemented
6	#20245267	C₂	1	2	yes	maximal, complemented
7	#20245266	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	C₄×C₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2178	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	C₄×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
38	C₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
39	C₁₆×Dic₄₇	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	C₄×C₁₆×C₄₇	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	1	yes	characteristic
140	C₈×D₄₇	D₈	1	1	yes	characteristic
141	C₈×D₄₇	D₈	1	1	yes	characteristic
142	C₈×D₄₇	D₈	1	1	yes	characteristic
143	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₈×D₄₇	#41	1	1	yes	characteristic
146	C₈×D₄₇	#41	1	1	yes	characteristic
147	C₁₆×C₄₇	—	2	1	no	—
148	C₁₆×C₄₇	C₂²×C₄	1	1	yes	characteristic
149	C₁₆×C₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₄₇⋊C₁₆	—	2	1	no	—
151	C₄₇⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
152	C₄₇⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
153	C₂²×D₄₇	—	4	2	no	—
154	C₂²×D₄₇	#135	1	1	yes	characteristic
155	Q₈×C₄₇	—	2	2	no	—
156	D₄×C₄₇	—	2	2	no	—
157	D₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂²⋊D₄₇	—	4	2	no	—
162	C₂²⋊D₄₇	—	4	2	no	—
163	C₂²⋊D₄₇	—	4	2	no	—
164	C₂×Dic₄₇	—	2	1	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	#135	1	1	yes	characteristic
167	D₁₈₈	—	2	2	no	—
168	D₁₈₈	—	4	2	no	—
169	C₄×D₄₇	—	2	4	no	—
170	C₄×D₄₇	—	4	2	no	—
171	C₄×D₄₇	—	4	2	no	—
172	C₄×D₄₇	—	4	2	no	—
173	C₄×D₄₇	C₄×D₄	1	1	yes	characteristic
174	C₄×D₄₇	C₄×D₄	1	1	yes	characteristic
175	C₄×D₄₇	C₂×D₈	1	1	yes	characteristic
176	C₄×D₄₇	C₂×D₈	1	1	yes	characteristic
177	Dic₉₄	—	2	2	no	—
178	Dic₉₄	—	4	2	no	—
179	C₈×C₄₇	—	4	2	no	—
180	C₈×C₄₇	C₂×D₈	1	1	yes	characteristic
181	C₈×C₄₇	C₂×D₈	1	1	yes	characteristic
182	C₈×C₄₇	C₂³×C₄	1	1	yes	characteristic
183	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₄₇⋊C₈	—	4	2	no	—
185	C₄₇⋊C₈	C₄×D₄	1	1	yes	characteristic
186	C₄₇⋊C₈	C₄×D₄	1	1	yes	characteristic
187	C₄₇⋊C₈	C₂×D₈	1	1	yes	characteristic
188	C₄₇⋊C₈	C₂×D₈	1	1	yes	characteristic
189	C₂×#2178	—	47	1	no	maximal, Sylow
190	C₂²×C₄₇	—	4	2	no	—
191	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
192	C₂×D₄₇	—	2	2	no	—
193	C₂×D₄₇	—	4	2	no	—
194	C₂×D₄₇	—	8	4	no	—
195	C₂×D₄₇	C₄×D₈	1	1	yes	characteristic
196	C₂×D₄₇	C₄×D₈	1	1	yes	characteristic
197	C₄×C₄₇	—	2	2	no	—
198	C₄×C₄₇	—	4	2	no	—
199	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
200	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
201	Dic₄₇	—	2	2	no	—
202	Dic₄₇	—	4	2	no	—
203	Dic₄₇	C₄×D₈	1	1	yes	characteristic
204	Dic₄₇	C₄×D₈	1	1	yes	characteristic
205	C₂×#508	—	47	1	no	—
206	C₂×#443	—	47	2	no	—
207	#2178	—	47	1	no	—
208	#2178	—	47	2	no	—
209	#2178	—	47	1	no	—
210	#2178	—	47	2	no	—
211	#2178	—	47	1	no	—
212	#2178	D₄₇	1	1	yes	characteristic, direct product factor
213	C₂×#368	—	47	1	no	—
214	C₂×#359	—	47	2	no	—
215	C₂×C₄×C₁₆	—	47	1	no	—
216	C₂×C₄₇	—	2	1	no	—
217	C₂×C₄₇	—	8	2	no	—
218	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
219	D₄₇	—	2	1	no	—
220	D₄₇	—	8	2	no	—
221	D₄₇	#2178	1	2	yes	direct product factor
222	C₂×#135	—	47	2	no	—
223	C₂×#131	—	94	2	no	—
224	#508	—	47	2	no	—
225	#508	—	47	1	no	—
226	#508	—	47	2	no	—
227	#508	—	47	1	no	—
228	#508	—	47	1	no	—
229	#508	C₂×D₄₇	1	1	yes	characteristic
230	C₂×Q₃₂	—	47	1	no	—
231	C₂×SD₃₂	—	47	2	no	—
232	C₂×D₁₆	—	47	1	no	—
233	C₂²×C₁₆	—	47	1	no	—
234	C₂²×C₁₆	—	47	1	no	—
235	#443	—	47	2	no	—
236	#443	—	47	2	no	—
237	#443	—	47	2	no	—
238	#443	—	94	2	no	—
239	#443	—	94	2	no	—
240	#443	C₂×D₄₇	1	2	yes	complemented
241	C₂×#108	—	47	2	no	—
242	C₂×#104	—	94	2	no	—
243	C₂×C₄×C₈	—	47	1	no	—
244	#368	—	47	1	no	—
245	#368	—	47	2	no	—
246	#368	C₂×D₄₇	1	1	yes	characteristic, complemented
247	#359	—	47	2	no	—
248	#359	—	47	2	no	—
249	#359	—	47	2	no	—
250	#359	C₂×D₄₇	1	2	yes	complemented
251	C₄×C₁₆	—	47	1	no	—
252	C₄×C₁₆	—	47	1	no	—
253	C₄×C₁₆	—	47	1	no	—
254	C₄×C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
255	C₄₇	C₂×#2178	1	1	yes	characteristic, complemented, Sylow
256	C₂×#41	—	94	2	no	—
257	#135	—	47	2	no	—
258	#135	—	47	2	no	—
259	#135	—	47	2	no	—
260	#135	—	94	2	no	—
261	#135	—	94	2	no	—
262	#135	C₂²×D₄₇	1	2	yes	—
263	C₂×Q₁₆	—	47	2	no	—
264	C₂×SD₁₆	—	94	2	no	—
265	C₂×D₈	—	47	2	no	—
266	#131	—	2	2	no	—
267	#131	—	94	2	no	—
268	#131	—	94	2	no	—
269	#131	—	94	2	no	—
270	#131	—	188	2	no	—
271	#131	—	188	2	no	—
272	C₂×M₁₆	—	94	2	no	—
273	C₂×M₁₆	—	188	2	no	—
274	C₂²×C₈	—	47	1	no	—
275	C₂²×C₈	—	47	1	no	—
276	C₂²×C₈	—	188	2	no	—
277	C₂×C₄²	—	47	1	no	—
278	Q₃₂	—	47	2	no	—
279	Q₃₂	—	47	1	no	—
280	Q₃₂	C₄×D₄₇	1	1	yes	characteristic, complemented
281	SD₃₂	—	47	2	no	—
282	SD₃₂	—	47	2	no	—
283	SD₃₂	—	47	2	no	—
284	SD₃₂	C₄×D₄₇	1	2	yes	complemented
285	D₁₆	—	47	2	no	—
286	D₁₆	—	47	1	no	—
287	D₁₆	C₄×D₄₇	1	1	yes	characteristic, complemented
288	C₂×C₁₆	—	47	1	no	—
289	C₂×C₁₆	—	47	1	no	—
290	C₂×C₁₆	—	47	1	no	—
291	C₂×C₁₆	—	47	1	no	—
292	C₂×C₁₆	—	47	1	no	—
293	C₂×C₁₆	—	47	1	no	—
294	C₂×C₁₆	—	94	1	no	—
295	C₂×C₁₆	—	94	1	no	—
296	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
297	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
298	#108	—	47	2	no	—
299	#108	—	94	2	no	—
300	#108	C₂²×D₄₇	1	2	yes	—
301	#104	—	2	2	no	—
302	#104	—	94	2	no	—
303	#104	—	94	2	no	—
304	#104	—	94	2	no	—
305	C₄×C₈	—	47	1	no	—
306	C₄×C₈	—	47	1	no	—
307	C₄×C₈	—	47	1	no	—
308	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
309	#41	—	2	2	no	—
310	#41	—	94	2	no	—
311	#41	—	94	2	no	—
312	#41	—	94	2	no	—
313	#41	—	188	2	no	—
314	#41	—	188	2	no	—
315	C₂×Q₈	—	94	2	no	—
316	C₂×D₄	—	94	2	no	—
317	C₂×D₄	—	188	2	no	—
318	C₂²×C₄	—	47	1	no	—
319	C₂²×C₄	—	94	1	no	—
320	C₂²×C₄	—	188	2	no	—
321	Q₁₆	—	47	2	no	—
322	Q₁₆	—	94	2	no	—
323	Q₁₆	C₂×C₄×D₄₇	1	2	yes	—
324	SD₁₆	—	2	2	no	—
325	SD₁₆	—	94	2	no	—
326	SD₁₆	—	94	2	no	—
327	SD₁₆	—	94	2	no	—
328	D₈	—	47	2	no	—
329	D₈	—	94	2	no	—
330	D₈	C₂×C₄×D₄₇	1	2	yes	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	4	2	no	—
333	M₁₆	—	94	2	no	—
334	M₁₆	—	188	2	no	—
335	M₁₆	—	188	2	no	—
336	M₁₆	—	188	2	no	—
337	M₁₆	—	188	2	no	—
338	C₂×C₈	—	4	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	—	47	1	no	—
344	C₂×C₈	—	47	1	no	—
345	C₂×C₈	—	47	1	no	—
346	C₂×C₈	—	47	1	no	—
347	C₂×C₈	—	47	1	no	—
348	C₂×C₈	—	47	1	no	—
349	C₂×C₈	—	188	2	no	—
350	C₂×C₈	—	188	2	no	—
351	C₂×C₈	—	188	2	no	—
352	C₂×C₈	—	188	2	no	—
353	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
354	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
355	C₄²	—	47	1	no	—
356	C₄²	—	94	1	no	—
357	C₄²	D₄×D₄₇	1	1	yes	characteristic
358	C₁₆	—	2	1	no	—
359	C₁₆	—	47	1	no	—
360	C₁₆	—	47	1	no	—
361	C₁₆	—	94	1	no	—
362	C₁₆	C₂×C₄×D₄₇	1	1	yes	characteristic
363	C₁₆	C₂×C₄×D₄₇	1	1	yes	characteristic
364	C₂³	—	47	1	no	—
365	C₂³	—	188	2	no	—
366	Q₈	—	2	2	no	—
367	Q₈	—	94	2	no	—
368	Q₈	—	188	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	94	2	no	—
372	D₄	—	188	2	no	—
373	D₄	—	188	2	no	—
374	D₄	—	188	2	no	—
375	D₄	—	188	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	47	1	no	—
379	C₂×C₄	—	47	1	no	—
380	C₂×C₄	—	47	1	no	—
381	C₂×C₄	—	47	1	no	—
382	C₂×C₄	—	47	1	no	—
383	C₂×C₄	—	94	4	no	—
384	C₂×C₄	—	94	1	no	—
385	C₂×C₄	—	188	2	no	—
386	C₂×C₄	—	188	2	no	—
387	C₂×C₄	—	188	2	no	—
388	C₂×C₄	—	188	2	no	—
389	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
390	C₈	—	4	2	no	—
391	C₈	—	47	1	no	—
392	C₈	—	47	1	no	—
393	C₈	—	47	1	no	—
394	C₈	—	47	1	no	—
395	C₈	—	188	2	no	—
396	C₈	D₈×D₄₇	1	1	yes	characteristic
397	C₈	D₈×D₄₇	1	1	yes	characteristic
398	C₈	C₂²×C₄×D₄₇	1	1	yes	characteristic
399	C₈	#41×D₄₇	1	1	yes	characteristic
400	C₂²	—	4	2	no	—
401	C₂²	—	47	1	no	—
402	C₂²	—	47	1	no	—
403	C₂²	—	94	2	no	—
404	C₂²	—	376	4	no	—
405	C₂²	—	188	2	no	—
406	C₂²	#135×D₄₇	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	47	1	no	—
410	C₄	—	47	1	no	—
411	C₄	—	94	2	no	—
412	C₄	—	188	2	no	—
413	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
414	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	8	2	no	—
417	C₂	—	47	2	no	—
418	C₂	—	94	1	no	—
419	C₂	—	376	2	no	—
420	C₂	C₄×D₈×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₈×D₄₇
commutator	C₈×C₄₇	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₄₇×#2178	C₂
socle	C₂×C₄₇	C₂×C₄×D₈
prime radical	#508×D₄₇	C₂
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	#2178	D₄₇
hypocenter	C₄₇	C₂×#2178
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #2178

Complements

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

N	H ≅ G/N	type
2. #443×D₄₇	C₂	semidirect
3. #20245270	C₂	semidirect
4. #20245269	C₂	semidirect
5. #20245268	C₂	semidirect
6. #20245267	C₂	semidirect
7. #20245266	C₂	semidirect
8. #368×D₄₇	C₂	semidirect
9. #359×D₄₇	C₂	semidirect
10. C₄×C₁₆×D₄₇	C₂	semidirect
11. C₄₇×#2178	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. C₄×C₄₇⋊C₁₆	C₂²	semidirect
38. C₁₆×Dic₄₇	C₂²	semidirect
39. C₁₆×Dic₄₇	C₂²	semidirect
41. C₄₇×#443	C₂²	semidirect
42. C₄₇×#368	C₂²	semidirect
43. C₄₇×#359	C₂²	semidirect
44. C₄×C₁₆×C₄₇	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
212. #2178	D₄₇	direct (N × H)
221. D₄₇	#2178	direct (N × H)
240. #443	C₂×D₄₇	semidirect
246. #368	C₂×D₄₇	semidirect
250. #359	C₂×D₄₇	semidirect
254. C₄×C₁₆	C₂×D₄₇	semidirect
255. C₄₇	C₂×#2178	semidirect
280. Q₃₂	C₄×D₄₇	semidirect
284. SD₃₂	C₄×D₄₇	semidirect
287. 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
#20245270	2
#20245269	2
#20245268	2
#20245267	2
#20245266	2
#368×D₄₇	2
#359×D₄₇	2
C₄×C₁₆×D₄₇	2
C₄₇×#2178	2
C₂×#2178	47

Subgroups — D47×#2178 #26369674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#2178 #26369674