Subgroups — D₄₇×#1706 #26203917

Order 12032.

1046 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#493×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#492×D₄₇	C₂	1	2	yes	maximal, complemented
4	#486×D₄₇	C₂	1	2	yes	maximal, complemented
5	#20242981	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242980	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242979	C₂	1	2	yes	maximal, complemented
8	#20242978	C₂	1	2	yes	maximal, complemented
9	#20242977	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈²×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1706	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×SD₁₆×D₄₇	—	2	4	no	—
13	C₂×D₈×D₄₇	—	2	2	no	—
14	C₄⋊Q₈×D₄₇	C₂²	1	2	yes	—
15	#127×D₄₇	C₂²	1	2	yes	—
16	#15689528	C₂²	1	1	yes	characteristic, complemented
17	#15689527	—	2	2	no	—
18	#15689526	C₂²	1	2	yes	complemented
19	#15689500	C₂²	1	1	yes	characteristic
20	#15689499	C₂²	1	2	yes	—
21	#15689498	—	2	2	no	—
22	#15689497	C₂²	1	2	yes	complemented
23	#15689496	C₂²	1	2	yes	complemented
24	#15689495	C₂²	1	2	yes	complemented
25	#15689494	—	2	4	no	—
26	#15689471	C₂²	1	2	yes	complemented
27	#15689470	C₂²	1	2	yes	complemented
28	#15689469	C₂²	1	2	yes	complemented
29	#15689468	—	2	4	no	—
30	#107×D₄₇	—	2	2	no	—
31	#102×D₄₇	—	2	4	no	—
32	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
35	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
36	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
37	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	C₄₇×#500	C₂²	1	1	yes	characteristic, complemented
39	C₄₇×#493	C₂²	1	1	yes	characteristic
40	C₄₇×#492	C₂²	1	2	yes	complemented
41	C₄₇×#486	C₂²	1	2	yes	complemented
42	C₈²×C₄₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×Q₈×D₄₇	—	2	2	no	—
44	C₂×D₄×D₄₇	—	2	2	no	—
45	C₂×D₄×D₄₇	—	2	2	no	—
46	C₂×D₄×D₄₇	—	2	2	no	—
47	C₂×#10625325	—	2	4	no	—
48	C₂×#10625335	—	2	4	no	—
49	C₂×#10625336	—	2	4	no	—
50	SD₁₆×D₄₇	—	4	16	no	—
51	C₂×D₃₇₆	—	2	2	no	—
52	C₂×#10625334	—	2	4	no	—
53	D₈×D₄₇	—	4	8	no	—
54	C₂×C₈×D₄₇	D₄	1	2	yes	—
55	C₂×C₈×D₄₇	D₄	1	2	yes	—
56	C₂×C₈×D₄₇	D₄	1	2	yes	—
57	#13094024	C₂³	1	2	yes	—
58	#13094023	—	2	2	no	—
59	#13094023	—	2	2	no	—
60	#13094022	—	2	2	no	—
61	#13094021	C₂³	1	2	yes	—
62	#13094020	—	2	2	no	—
63	#13094020	—	2	2	no	—
64	#13094020	—	2	2	no	—
65	C₄⋊C₄×D₄₇	—	2	2	no	—
66	C₄⋊C₄×D₄₇	—	2	2	no	—
67	C₄²×D₄₇	C₂³	1	1	yes	characteristic
68	#13093958	—	2	2	no	—
69	#13093957	—	2	4	no	—
70	#13093946	—	2	4	no	—
71	#13093945	—	2	4	no	—
72	#13093944	—	2	4	no	—
73	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
74	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
75	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
76	C₈×Dic₄₇	D₄	1	2	yes	—
77	C₈×Dic₄₇	D₄	1	2	yes	—
78	C₈×Dic₄₇	D₄	1	2	yes	—
79	C₂×SD₁₆×C₄₇	—	2	4	no	—
80	C₂×D₈×C₄₇	—	2	2	no	—
81	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
82	#127×C₄₇	C₂³	1	2	yes	—
83	#107×C₄₇	—	2	2	no	—
84	#102×C₄₇	—	2	4	no	—
85	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
88	C₂³×D₄₇	—	4	2	no	—
89	C₂×Q₈×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	—	2	2	no	—
92	C₂×D₄×C₄₇	—	2	2	no	—
93	C₂×C₂²⋊D₄₇	—	4	2	no	—
94	C₂×C₂²⋊D₄₇	—	4	2	no	—
95	C₂×C₂²⋊D₄₇	—	4	2	no	—
96	Q₈×D₄₇	—	4	8	no	—
97	D₄×D₄₇	—	4	8	no	—
98	D₄×D₄₇	—	4	8	no	—
99	D₄×D₄₇	—	4	8	no	—
100	C₂×D₁₈₈	—	2	2	no	—
101	C₂×D₁₈₈	—	2	2	no	—
102	C₂×D₁₈₈	—	2	2	no	—
103	C₂×C₄×D₄₇	—	4	2	no	—
104	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂×Dic₉₄	—	2	2	no	—
108	C₂×Dic₉₄	—	4	2	no	—
109	SD₁₆×C₄₇	—	4	8	no	—
110	D₈×C₄₇	—	4	4	no	—
111	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
117	#10625336	—	4	8	no	—
118	#10625335	—	4	8	no	—
119	#10625334	—	4	8	no	—
120	C₄⋊Dic₄₇	—	2	2	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	Dic₄₇⋊C₄	—	4	2	no	—
123	Dic₄₇⋊C₄	—	4	2	no	—
124	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
125	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
126	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
128	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
129	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
130	D₃₇₆	—	4	4	no	—
131	#10625325	—	4	8	no	—
132	C₈×D₄₇	—	2	4	no	—
133	C₈×D₄₇	D₈	1	8	yes	complemented
134	C₈×D₄₇	SD₁₆	1	8	yes	complemented
135	C₂³×C₄₇	—	4	2	no	—
136	C₂²×D₄₇	—	4	2	no	—
137	C₂²×D₄₇	—	8	4	no	—
138	C₂²×D₄₇	—	8	4	no	—
139	C₂²×D₄₇	—	8	4	no	—
140	C₂²×D₄₇	#127	1	1	yes	characteristic
141	Q₈×C₄₇	—	4	4	no	—
142	D₄×C₄₇	—	4	4	no	—
143	D₄×C₄₇	—	4	4	no	—
144	D₄×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
149	C₂²⋊D₄₇	—	8	4	no	—
150	C₂²⋊D₄₇	—	8	4	no	—
151	C₂²⋊D₄₇	—	8	4	no	—
152	C₂×Dic₄₇	—	4	2	no	—
153	C₂×Dic₄₇	#127	1	1	yes	characteristic
154	C₂×Dic₄₇	#127	1	1	yes	characteristic
155	C₂×Dic₄₇	#127	1	1	yes	characteristic
156	D₁₈₈	—	4	4	no	—
157	D₁₈₈	—	4	4	no	—
158	D₁₈₈	—	4	4	no	—
159	C₄×D₄₇	—	8	4	no	—
160	C₄×D₄₇	C₂×D₈	1	4	yes	—
161	C₄×D₄₇	C₂×SD₁₆	1	4	yes	—
162	C₄×D₄₇	#135	1	4	yes	—
163	Dic₉₄	—	4	4	no	—
164	Dic₉₄	—	8	4	no	—
165	C₈×C₄₇	—	2	2	no	—
166	C₈×C₄₇	C₂×D₈	1	4	yes	complemented
167	C₈×C₄₇	C₂×SD₁₆	1	4	yes	complemented
168	C₄₇⋊C₈	—	2	2	no	—
169	C₄₇⋊C₈	C₂×D₈	1	4	yes	complemented
170	C₄₇⋊C₈	C₂×SD₁₆	1	4	yes	complemented
171	C₂×#1706	—	47	1	no	maximal, Sylow
172	C₂²×C₄₇	—	8	2	no	—
173	C₂²×C₄₇	—	8	2	no	—
174	C₂²×C₄₇	—	8	2	no	—
175	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
176	C₂×D₄₇	—	8	2	no	—
177	C₂×D₄₇	—	8	2	no	—
178	C₂×D₄₇	—	8	2	no	—
179	C₂×D₄₇	—	16	8	no	—
180	C₂×D₄₇	#492	1	2	yes	—
181	C₂×D₄₇	#493	1	2	yes	—
182	C₂×D₄₇	#495	1	2	yes	—
183	C₄×C₄₇	—	8	2	no	—
184	C₄×C₄₇	C₂²×D₈	1	2	yes	—
185	C₄×C₄₇	C₂²×SD₁₆	1	2	yes	—
186	C₄×C₄₇	C₂×#135	1	2	yes	—
187	Dic₄₇	—	8	2	no	—
188	Dic₄₇	#492	1	2	yes	—
189	Dic₄₇	#493	1	2	yes	—
190	Dic₄₇	#495	1	2	yes	—
191	C₂×#500	—	47	1	no	—
192	C₂×#493	—	47	1	no	—
193	C₂×#492	—	47	2	no	—
194	C₂×#486	—	47	2	no	—
195	#1706	—	47	1	no	—
196	#1706	—	47	1	no	—
197	#1706	—	47	2	no	—
198	#1706	—	47	2	no	—
199	#1706	—	47	1	no	—
200	#1706	D₄₇	1	1	yes	characteristic, direct product factor
201	C₂×C₈²	—	47	1	no	—
202	C₂×C₄₇	—	16	2	no	—
203	C₂×C₄₇	C₂×#492	1	1	yes	characteristic
204	C₂×C₄₇	C₂×#493	1	1	yes	characteristic
205	C₂×C₄₇	C₂×#495	1	1	yes	characteristic
206	D₄₇	—	16	2	no	—
207	D₄₇	#1706	1	4	yes	direct product factor
208	C₂²×SD₁₆	—	94	4	no	—
209	C₂²×D₈	—	94	2	no	—
210	C₂×C₄⋊Q₈	—	47	2	no	—
211	C₂×#127	—	47	2	no	—
212	#500	—	47	2	no	—
213	#500	—	47	1	no	—
214	#500	—	94	2	no	—
215	#500	C₂×D₄₇	1	1	yes	characteristic, complemented
216	#493	—	47	2	no	—
217	#493	—	47	1	no	—
218	#493	—	94	2	no	—
219	#493	C₂×D₄₇	1	1	yes	characteristic
220	#492	—	47	2	no	—
221	#492	—	47	2	no	—
222	#492	—	47	2	no	—
223	#492	—	94	4	no	—
224	#492	C₂×D₄₇	1	2	yes	complemented
225	#486	—	47	2	no	—
226	#486	—	47	2	no	—
227	#486	—	47	2	no	—
228	#486	—	94	4	no	—
229	#486	C₂×D₄₇	1	2	yes	complemented
230	C₂×#107	—	94	2	no	—
231	C₂×#102	—	94	4	no	—
232	C₂×C₄×C₈	—	47	1	no	—
233	C₂×C₄×C₈	—	47	1	no	—
234	C₂×C₄×C₈	—	47	1	no	—
235	C₈²	—	47	1	no	—
236	C₈²	—	47	1	no	—
237	C₈²	—	47	1	no	—
238	C₈²	C₂×D₄₇	1	1	yes	characteristic, complemented
239	C₄₇	C₂×#1706	1	1	yes	characteristic, complemented, Sylow
240	C₂²×Q₈	—	94	2	no	—
241	C₂²×D₄	—	94	2	no	—
242	C₂²×D₄	—	94	2	no	—
243	C₂²×D₄	—	94	2	no	—
244	C₂×SD₁₆	—	2	4	no	—
245	C₂×SD₁₆	—	94	4	no	—
246	C₂×SD₁₆	—	94	4	no	—
247	C₂×SD₁₆	—	94	4	no	—
248	C₂×SD₁₆	—	188	16	no	—
249	C₂×D₈	—	2	2	no	—
250	C₂×D₈	—	94	4	no	—
251	C₂×D₈	—	94	2	no	—
252	C₂×D₈	—	188	8	no	—
253	C₂²×C₈	—	47	2	no	—
254	C₂²×C₈	—	47	2	no	—
255	C₂²×C₈	—	47	2	no	—
256	C₄⋊Q₈	—	47	2	no	—
257	C₄⋊Q₈	—	94	2	no	—
258	C₄⋊Q₈	—	94	2	no	—
259	C₄⋊Q₈	—	94	2	no	—
260	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
261	#127	—	47	2	no	—
262	#127	—	94	2	no	—
263	#127	—	94	2	no	—
264	#127	—	94	2	no	—
265	#127	C₂²×D₄₇	1	2	yes	—
266	C₂×C₄⋊C₄	—	94	2	no	—
267	C₂×C₄⋊C₄	—	94	2	no	—
268	C₂×C₄²	—	47	1	no	—
269	#107	—	2	2	no	—
270	#107	—	94	4	no	—
271	#107	—	94	2	no	—
272	#102	—	2	4	no	—
273	#102	—	94	4	no	—
274	#102	—	94	4	no	—
275	#102	—	94	4	no	—
276	C₄×C₈	—	47	2	no	—
277	C₄×C₈	—	47	2	no	—
278	C₄×C₈	—	47	2	no	—
279	C₄×C₈	—	47	1	no	—
280	C₄×C₈	—	47	1	no	—
281	C₄×C₈	—	47	1	no	—
282	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
283	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
284	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
285	C₂⁴	—	188	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	94	2	no	—
288	C₂×Q₈	—	188	2	no	—
289	C₂×Q₈	—	188	8	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	94	2	no	—
294	C₂×D₄	—	94	2	no	—
295	C₂×D₄	—	94	2	no	—
296	C₂×D₄	—	188	8	no	—
297	C₂×D₄	—	188	8	no	—
298	C₂×D₄	—	188	8	no	—
299	C₂×D₄	—	188	2	no	—
300	C₂×D₄	—	188	2	no	—
301	C₂×D₄	—	188	2	no	—
302	C₂²×C₄	—	47	1	no	—
303	C₂²×C₄	—	47	1	no	—
304	C₂²×C₄	—	47	1	no	—
305	C₂²×C₄	—	188	2	no	—
306	SD₁₆	—	4	8	no	—
307	SD₁₆	—	188	8	no	—
308	SD₁₆	—	188	8	no	—
309	SD₁₆	—	188	8	no	—
310	D₈	—	4	4	no	—
311	D₈	—	188	8	no	—
312	D₈	—	188	4	no	—
313	C₂×C₈	—	47	2	no	—
314	C₂×C₈	—	47	2	no	—
315	C₂×C₈	—	47	8	no	—
316	C₂×C₈	—	47	8	no	—
317	C₂×C₈	—	47	2	no	—
318	C₂×C₈	—	94	4	no	—
319	C₂×C₈	D₄×D₄₇	1	2	yes	—
320	C₂×C₈	D₄×D₄₇	1	2	yes	—
321	C₂×C₈	D₄×D₄₇	1	2	yes	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	94	2	no	—
325	C₄⋊C₄	—	94	2	no	—
326	C₄⋊C₄	—	188	2	no	—
327	C₄⋊C₄	—	188	2	no	—
328	C₄²	—	47	1	no	—
329	C₄²	—	47	1	no	—
330	C₄²	—	47	1	no	—
331	C₄²	C₂³×D₄₇	1	1	yes	characteristic
332	C₂³	—	4	2	no	—
333	C₂³	—	47	1	no	—
334	C₂³	—	376	4	no	—
335	C₂³	—	376	4	no	—
336	C₂³	—	376	4	no	—
337	C₂³	—	188	2	no	—
338	Q₈	—	4	4	no	—
339	Q₈	—	376	4	no	—
340	Q₈	—	188	4	no	—
341	D₄	—	4	4	no	—
342	D₄	—	4	4	no	—
343	D₄	—	4	4	no	—
344	D₄	—	376	4	no	—
345	D₄	—	376	4	no	—
346	D₄	—	376	4	no	—
347	D₄	—	188	4	no	—
348	D₄	—	188	4	no	—
349	D₄	—	188	4	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	47	1	no	—
352	C₂×C₄	—	47	1	no	—
353	C₂×C₄	—	47	1	no	—
354	C₂×C₄	—	47	4	no	—
355	C₂×C₄	—	47	4	no	—
356	C₂×C₄	—	47	4	no	—
357	C₂×C₄	—	376	4	no	—
358	C₂×C₄	—	188	2	no	—
359	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
360	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
361	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
362	C₈	—	2	2	no	—
363	C₈	—	47	4	no	—
364	C₈	—	47	4	no	—
365	C₈	—	94	2	no	—
366	C₈	D₈×D₄₇	1	4	yes	complemented
367	C₈	SD₁₆×D₄₇	1	4	yes	complemented
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	47	2	no	—
372	C₂²	—	47	2	no	—
373	C₂²	—	47	2	no	—
374	C₂²	—	376	2	no	—
375	C₂²	—	376	2	no	—
376	C₂²	—	376	2	no	—
377	C₂²	—	752	8	no	—
378	C₂²	#127×D₄₇	1	1	yes	characteristic
379	C₄	—	8	2	no	—
380	C₄	—	47	2	no	—
381	C₄	—	47	2	no	—
382	C₄	—	47	2	no	—
383	C₄	—	376	2	no	—
384	C₄	C₂×D₈×D₄₇	1	2	yes	—
385	C₄	C₂×SD₁₆×D₄₇	1	2	yes	—
386	C₄	#135×D₄₇	1	2	yes	—
387	C₂	—	16	2	no	—
388	C₂	—	47	4	no	—
389	C₂	—	752	2	no	—
390	C₂	#492×D₄₇	1	1	yes	characteristic
391	C₂	#493×D₄₇	1	1	yes	characteristic
392	C₂	#495×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#127×D₄₇
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1706	C₂
socle	C₂²×C₄₇	C₂×#127
prime radical	#493×D₄₇	C₂
hypercenter	#1706	D₄₇
hypocenter	C₄₇	C₂×#1706
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1706

Complements

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

N	H ≅ G/N	type
1. #500×D₄₇	C₂	semidirect
3. #492×D₄₇	C₂	semidirect
4. #486×D₄₇	C₂	semidirect
5. #20242981	C₂	semidirect
6. #20242980	C₂	semidirect
7. #20242979	C₂	semidirect
8. #20242978	C₂	semidirect
9. #20242977	C₂	semidirect
10. C₈²×D₄₇	C₂	semidirect
11. C₄₇×#1706	C₂	semidirect
16. #15689528	C₂²	semidirect
18. #15689526	C₂²	semidirect
22. #15689497	C₂²	semidirect
23. #15689496	C₂²	semidirect
24. #15689495	C₂²	semidirect
26. #15689471	C₂²	semidirect
27. #15689470	C₂²	semidirect
28. #15689469	C₂²	semidirect
35. C₈×C₄₇⋊C₈	C₂²	semidirect
36. C₈×C₄₇⋊C₈	C₂²	semidirect
37. C₈×C₄₇⋊C₈	C₂²	semidirect
38. C₄₇×#500	C₂²	semidirect
40. C₄₇×#492	C₂²	semidirect
41. C₄₇×#486	C₂²	semidirect
42. C₈²×C₄₇	C₂²	semidirect
133. C₈×D₄₇	D₈	semidirect
134. C₈×D₄₇	SD₁₆	semidirect
166. C₈×C₄₇	C₂×D₈	semidirect
167. C₈×C₄₇	C₂×SD₁₆	semidirect
169. C₄₇⋊C₈	C₂×D₈	semidirect
170. C₄₇⋊C₈	C₂×SD₁₆	semidirect
200. #1706	D₄₇	direct (N × H)
207. D₄₇	#1706	direct (N × H)
215. #500	C₂×D₄₇	semidirect
224. #492	C₂×D₄₇	semidirect
229. #486	C₂×D₄₇	semidirect
238. C₈²	C₂×D₄₇	semidirect
239. C₄₇	C₂×#1706	semidirect
366. C₈	D₈×D₄₇	semidirect
367. C₈	SD₁₆×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#500×D₄₇	2
#493×D₄₇	2
#492×D₄₇	2
#486×D₄₇	2
#20242981	2
#20242980	2
#20242979	2
#20242978	2
#20242977	2
C₈²×D₄₇	2
C₄₇×#1706	2
C₂×#1706	47

Subgroups — D47×#1706 #26203917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#1706 #26203917