Subgroups — C₄₇×#20023 #26059721

Order 12032.

774 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3294	C₂	1	2	yes	maximal, complemented
2	C₄₇×#3272	C₂	1	2	yes	maximal, complemented
3	C₄₇×#1715	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1701	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1665	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1654	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1619	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1619	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1586	C₂	1	2	yes	maximal, complemented
10	C₂×AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
11	C₄₇×#547	C₂²	1	2	yes	—
12	D₄²×C₄₇	C₂²	1	1	yes	characteristic, complemented
13	D₄²×C₄₇	C₂²	1	1	yes	characteristic, complemented
14	C₄₇×#498	C₂²	1	1	yes	characteristic, complemented
15	C₄₇×#493	C₂²	1	1	yes	characteristic
16	C₄₇×#492	C₂²	1	2	yes	complemented
17	C₄₇×#486	C₂²	1	2	yes	complemented
18	C₄₇×#480	—	2	2	no	—
19	C₄₇×#474	C₂²	1	2	yes	complemented
20	C₄₇×#468	—	2	2	no	—
21	C₄₇×#466	—	2	2	no	—
22	C₄₇×#461	C₂²	1	2	yes	complemented
23	C₄₇×#459	C₂²	1	2	yes	—
24	C₄₇×#459	C₂²	1	2	yes	—
25	C₄₇×#450	—	2	2	no	—
26	C₄₇×#449	—	2	2	no	—
27	C₄₇×#447	—	2	2	no	—
28	C₄×D₈×C₄₇	C₂²	1	2	yes	—
29	C₄₇×#436	C₂²	1	2	yes	complemented
30	C₈×D₄×C₄₇	C₂²	1	2	yes	complemented
31	C₂×#102×C₄₇	—	2	2	no	—
32	C₄₇×#334	C₂²	1	2	yes	complemented
33	C₄₇×#332	C₂²	1	2	yes	complemented
34	C₄₇×#331	C₂²	1	1	yes	characteristic, complemented
35	C₄₇×#331	C₂²	1	1	yes	characteristic, complemented
36	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
37	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
38	C₄₇×#322	C₂²	1	1	yes	characteristic, complemented
39	C₂×#41×C₄₇	—	2	2	no	—
40	C₂²×D₄×C₄₇	—	2	2	no	—
41	C₂²×D₄×C₄₇	—	2	2	no	—
42	AGL(1,ℤ/8)×C₄₇	—	4	8	no	—
43	C₂×SD₁₆×C₄₇	—	2	2	no	—
44	C₂×SD₁₆×C₄₇	—	2	2	no	—
45	C₂×SD₁₆×C₄₇	—	2	2	no	—
46	C₂×D₈×C₄₇	—	2	2	no	—
47	C₂×D₈×C₄₇	—	2	2	no	—
48	C₂×D₈×C₄₇	—	4	1	no	—
49	C₂×D₈×C₄₇	D₄	1	2	yes	—
50	C₂×M₁₆×C₄₇	—	2	2	no	—
51	C₂²×C₈×C₄₇	—	2	2	no	—
52	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
53	#127×C₄₇	C₂³	1	1	yes	characteristic
54	#127×C₄₇	C₂³	1	1	yes	characteristic
55	#123×C₄₇	—	4	2	no	—
56	C₂²⋊Q₈×C₄₇	—	2	2	no	—
57	#121×C₄₇	—	2	2	no	—
58	#121×C₄₇	—	2	2	no	—
59	#121×C₄₇	—	2	2	no	—
60	#120×C₄₇	—	4	1	no	—
61	#120×C₄₇	—	4	1	no	—
62	C₄×D₄×C₄₇	C₂³	1	2	yes	—
63	C₄×D₄×C₄₇	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
65	#107×C₄₇	—	2	2	no	—
66	#107×C₄₇	D₄	1	2	yes	—
67	#106×C₄₇	—	4	1	no	—
68	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
69	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
70	#103×C₄₇	—	2	2	no	—
71	#102×C₄₇	—	2	2	no	—
72	#102×C₄₇	—	2	2	no	—
73	#102×C₄₇	—	2	2	no	—
74	#102×C₄₇	—	2	2	no	—
75	#102×C₄₇	—	2	2	no	—
76	#102×C₄₇	D₄	1	2	yes	—
77	#102×C₄₇	D₄	1	2	yes	—
78	C₂²⋊C₈×C₄₇	—	2	2	no	—
79	C₂²⋊C₈×C₄₇	—	2	2	no	—
80	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₄₇	C₂³	1	2	yes	—
82	C₂⁴×C₄₇	—	4	1	no	—
83	C₂⁴×C₄₇	—	4	1	no	—
84	#41×C₄₇	—	4	4	no	—
85	#41×C₄₇	—	8	2	no	—
86	C₂×Q₈×C₄₇	—	2	2	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	2	1	no	—
90	C₂×D₄×C₄₇	—	2	1	no	—
91	C₂×D₄×C₄₇	—	4	2	no	—
92	C₂×D₄×C₄₇	—	4	2	no	—
93	C₂×D₄×C₄₇	—	4	4	no	—
94	C₂×D₄×C₄₇	—	4	4	no	—
95	C₂×D₄×C₄₇	—	4	2	no	—
96	C₂×D₄×C₄₇	—	8	2	no	—
97	C₂×D₄×C₄₇	—	8	2	no	—
98	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
99	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	4	2	no	—
103	SD₁₆×C₄₇	—	4	4	no	—
104	SD₁₆×C₄₇	—	4	4	no	—
105	SD₁₆×C₄₇	—	8	2	no	—
106	D₈×C₄₇	—	2	4	no	—
107	D₈×C₄₇	—	4	4	no	—
108	D₈×C₄₇	—	8	2	no	—
109	D₈×C₄₇	—	8	2	no	—
110	M₁₆×C₄₇	—	4	4	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	—	8	2	no	—
115	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	4	2	no	—
120	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
121	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
122	C₂²⋊C₄×C₄₇	—	2	2	no	—
123	C₂²⋊C₄×C₄₇	—	2	2	no	—
124	C₂²⋊C₄×C₄₇	—	4	1	no	—
125	C₂²⋊C₄×C₄₇	—	4	1	no	—
126	C₂²⋊C₄×C₄₇	—	4	2	no	—
127	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	—	2	2	no	—
130	C₂³×C₄₇	—	4	1	no	—
131	C₂³×C₄₇	—	4	1	no	—
132	C₂³×C₄₇	—	8	4	no	—
133	C₂³×C₄₇	—	8	4	no	—
134	C₂³×C₄₇	—	16	1	no	—
135	C₂³×C₄₇	—	16	1	no	—
136	Q₈×C₄₇	—	4	2	no	—
137	Q₈×C₄₇	—	4	2	no	—
138	D₄×C₄₇	—	2	2	no	—
139	D₄×C₄₇	—	2	2	no	—
140	D₄×C₄₇	—	2	2	no	—
141	D₄×C₄₇	—	4	2	no	—
142	D₄×C₄₇	—	4	2	no	—
143	D₄×C₄₇	—	4	2	no	—
144	D₄×C₄₇	—	4	2	no	—
145	D₄×C₄₇	—	8	1	no	—
146	D₄×C₄₇	—	8	1	no	—
147	D₄×C₄₇	—	8	4	no	—
148	D₄×C₄₇	—	8	4	no	—
149	D₄×C₄₇	—	8	4	no	—
150	D₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	complemented
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	8	4	no	—
159	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
160	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
161	C₈×C₄₇	—	2	2	no	—
162	C₈×C₄₇	—	2	2	no	—
163	C₈×C₄₇	—	2	2	no	—
164	C₈×C₄₇	—	4	2	no	—
165	C₈×C₄₇	—	4	2	no	—
166	#20023	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂²×C₄₇	—	2	4	no	—
168	C₂²×C₄₇	—	4	2	no	—
169	C₂²×C₄₇	—	4	2	no	—
170	C₂²×C₄₇	—	4	2	no	—
171	C₂²×C₄₇	—	4	2	no	—
172	C₂²×C₄₇	—	4	2	no	—
173	C₂²×C₄₇	—	8	2	no	—
174	C₂²×C₄₇	—	8	2	no	—
175	C₂²×C₄₇	—	8	1	no	—
176	C₂²×C₄₇	—	8	1	no	—
177	C₂²×C₄₇	—	16	4	no	—
178	C₂²×C₄₇	—	16	4	no	—
179	C₂²×C₄₇	D₄²	1	1	yes	characteristic
180	C₄×C₄₇	—	2	1	no	—
181	C₄×C₄₇	—	4	2	no	—
182	C₄×C₄₇	—	4	2	no	—
183	C₄×C₄₇	—	8	2	no	—
184	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
185	C₄×C₄₇	#576	1	2	yes	—
186	#3294	C₂×C₄₇	1	2	yes	complemented
187	#3272	C₂×C₄₇	1	2	yes	complemented
188	#1715	C₂×C₄₇	1	1	yes	characteristic, complemented
189	#1701	C₂×C₄₇	1	2	yes	complemented
190	#1665	C₂×C₄₇	1	2	yes	complemented
191	#1654	C₂×C₄₇	1	2	yes	complemented
192	#1619	C₂×C₄₇	1	1	yes	characteristic, complemented
193	#1619	C₂×C₄₇	1	1	yes	characteristic, complemented
194	#1586	C₂×C₄₇	1	2	yes	complemented
195	C₂×C₄₇	—	4	4	no	—
196	C₂×C₄₇	—	8	2	no	—
197	C₂×C₄₇	—	16	1	no	—
198	C₂×C₄₇	—	16	1	no	—
199	C₂×C₄₇	#3264	1	2	yes	—
200	C₂×C₄₇	#3291	1	1	yes	characteristic
201	C₂×AGL(1,ℤ/8)	—	2	2	no	—
202	#547	C₂²×C₄₇	1	2	yes	—
203	D₄²	C₂²×C₄₇	1	1	yes	characteristic, complemented
204	D₄²	C₂²×C₄₇	1	1	yes	characteristic, complemented
205	#498	C₂²×C₄₇	1	1	yes	characteristic, complemented
206	#493	C₂²×C₄₇	1	1	yes	characteristic
207	#492	C₂²×C₄₇	1	2	yes	complemented
208	#486	C₂²×C₄₇	1	2	yes	complemented
209	#480	—	2	2	no	—
210	#474	C₂²×C₄₇	1	2	yes	complemented
211	#468	—	2	2	no	—
212	#466	—	2	2	no	—
213	#461	C₂²×C₄₇	1	2	yes	complemented
214	#459	C₂²×C₄₇	1	2	yes	—
215	#459	C₂²×C₄₇	1	2	yes	—
216	#450	—	2	2	no	—
217	#449	—	2	2	no	—
218	#447	—	2	2	no	—
219	C₄×D₈	C₂²×C₄₇	1	2	yes	—
220	#436	C₂²×C₄₇	1	2	yes	complemented
221	C₈×D₄	C₂²×C₄₇	1	2	yes	complemented
222	C₂×#102	—	2	2	no	—
223	#334	C₂²×C₄₇	1	2	yes	complemented
224	#332	C₂²×C₄₇	1	2	yes	complemented
225	#331	C₂²×C₄₇	1	1	yes	characteristic, complemented
226	#331	C₂²×C₄₇	1	1	yes	characteristic, complemented
227	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
228	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
229	#322	C₂²×C₄₇	1	1	yes	characteristic, complemented
230	C₄₇	#20023	1	1	yes	characteristic, direct product factor, Sylow
231	C₂×#41	—	2	2	no	—
232	C₂²×D₄	—	2	2	no	—
233	C₂²×D₄	—	2	2	no	—
234	AGL(1,ℤ/8)	—	4	8	no	—
235	C₂×SD₁₆	—	2	2	no	—
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×SD₁₆	—	2	2	no	—
238	C₂×D₈	—	2	2	no	—
239	C₂×D₈	—	2	2	no	—
240	C₂×D₈	—	4	1	no	—
241	C₂×D₈	D₄×C₄₇	1	2	yes	—
242	C₂×M₁₆	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
245	#127	C₂³×C₄₇	1	1	yes	characteristic
246	#127	C₂³×C₄₇	1	1	yes	characteristic
247	#123	—	4	2	no	—
248	C₂²⋊Q₈	—	2	2	no	—
249	#121	—	2	2	no	—
250	#121	—	2	2	no	—
251	#121	—	2	2	no	—
252	#120	—	4	1	no	—
253	#120	—	4	1	no	—
254	C₄×D₄	C₂³×C₄₇	1	2	yes	—
255	C₄×D₄	C₂³×C₄₇	1	2	yes	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	#107	—	2	2	no	—
258	#107	D₄×C₄₇	1	2	yes	—
259	#106	—	4	1	no	—
260	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
261	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
262	#103	—	2	2	no	—
263	#102	—	2	2	no	—
264	#102	—	2	2	no	—
265	#102	—	2	2	no	—
266	#102	—	2	2	no	—
267	#102	—	2	2	no	—
268	#102	D₄×C₄₇	1	2	yes	—
269	#102	D₄×C₄₇	1	2	yes	—
270	C₂²⋊C₈	—	2	2	no	—
271	C₂²⋊C₈	—	2	2	no	—
272	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₄₇	1	2	yes	—
274	C₂⁴	—	4	1	no	—
275	C₂⁴	—	4	1	no	—
276	#41	—	4	4	no	—
277	#41	—	8	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	4	2	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	4	no	—
286	C₂×D₄	—	4	4	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	8	2	no	—
289	C₂×D₄	—	8	2	no	—
290	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
291	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	SD₁₆	—	4	4	no	—
296	SD₁₆	—	4	4	no	—
297	SD₁₆	—	8	2	no	—
298	D₈	—	2	4	no	—
299	D₈	—	4	4	no	—
300	D₈	—	8	2	no	—
301	D₈	—	8	2	no	—
302	M₁₆	—	4	4	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	8	2	no	—
307	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
308	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
313	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₂²⋊C₄	—	4	1	no	—
318	C₂²⋊C₄	—	4	2	no	—
319	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	4	1	no	—
323	C₂³	—	4	1	no	—
324	C₂³	—	8	4	no	—
325	C₂³	—	8	4	no	—
326	C₂³	—	16	1	no	—
327	C₂³	—	16	1	no	—
328	Q₈	—	4	2	no	—
329	Q₈	—	4	2	no	—
330	D₄	—	2	2	no	—
331	D₄	—	2	2	no	—
332	D₄	—	2	2	no	—
333	D₄	—	4	2	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	8	1	no	—
338	D₄	—	8	1	no	—
339	D₄	—	8	4	no	—
340	D₄	—	8	4	no	—
341	D₄	—	8	4	no	—
342	D₄	AGL(1,ℤ/8)×C₄₇	1	4	yes	complemented
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	8	4	no	—
351	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
352	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
353	C₈	—	2	2	no	—
354	C₈	—	2	2	no	—
355	C₈	—	2	2	no	—
356	C₈	—	4	2	no	—
357	C₈	—	4	2	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	8	1	no	—
365	C₂²	—	8	1	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	16	4	no	—
369	C₂²	—	16	4	no	—
370	C₂²	D₄²×C₄₇	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	2	no	—
374	C₄	—	8	2	no	—
375	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	2	yes	—
376	C₄	C₄₇×#576	1	2	yes	—
377	C₂	—	4	4	no	—
378	C₂	—	8	2	no	—
379	C₂	—	16	1	no	—
380	C₂	—	16	1	no	—
381	C₂	C₄₇×#3264	1	2	yes	—
382	C₂	C₄₇×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#3294	C₂	semidirect
2. C₄₇×#3272	C₂	semidirect
3. C₄₇×#1715	C₂	semidirect
4. C₄₇×#1701	C₂	semidirect
5. C₄₇×#1665	C₂	semidirect
6. C₄₇×#1654	C₂	semidirect
7. C₄₇×#1619	C₂	semidirect
8. C₄₇×#1619	C₂	semidirect
9. C₄₇×#1586	C₂	semidirect
12. D₄²×C₄₇	C₂²	semidirect
13. D₄²×C₄₇	C₂²	semidirect
14. C₄₇×#498	C₂²	semidirect
16. C₄₇×#492	C₂²	semidirect
17. C₄₇×#486	C₂²	semidirect
19. C₄₇×#474	C₂²	semidirect
22. C₄₇×#461	C₂²	semidirect
29. C₄₇×#436	C₂²	semidirect
30. C₈×D₄×C₄₇	C₂²	semidirect
32. C₄₇×#334	C₂²	semidirect
33. C₄₇×#332	C₂²	semidirect
34. C₄₇×#331	C₂²	semidirect
35. C₄₇×#331	C₂²	semidirect
36. C₄₇×D₄⋊C₈	C₂²	semidirect
37. C₄₇×D₄⋊C₈	C₂²	semidirect
38. C₄₇×#322	C₂²	semidirect
150. D₄×C₄₇	AGL(1,ℤ/8)	semidirect
166. #20023	C₄₇	direct (N × H)
186. #3294	C₂×C₄₇	semidirect
187. #3272	C₂×C₄₇	semidirect
188. #1715	C₂×C₄₇	semidirect
189. #1701	C₂×C₄₇	semidirect
190. #1665	C₂×C₄₇	semidirect
191. #1654	C₂×C₄₇	semidirect
192. #1619	C₂×C₄₇	semidirect
193. #1619	C₂×C₄₇	semidirect
194. #1586	C₂×C₄₇	semidirect
203. D₄²	C₂²×C₄₇	semidirect
204. D₄²	C₂²×C₄₇	semidirect
205. #498	C₂²×C₄₇	semidirect
207. #492	C₂²×C₄₇	semidirect
208. #486	C₂²×C₄₇	semidirect
210. #474	C₂²×C₄₇	semidirect
213. #461	C₂²×C₄₇	semidirect
220. #436	C₂²×C₄₇	semidirect
221. C₈×D₄	C₂²×C₄₇	semidirect
223. #334	C₂²×C₄₇	semidirect
224. #332	C₂²×C₄₇	semidirect
225. #331	C₂²×C₄₇	semidirect
226. #331	C₂²×C₄₇	semidirect
227. D₄⋊C₈	C₂²×C₄₇	semidirect
228. D₄⋊C₈	C₂²×C₄₇	semidirect
229. #322	C₂²×C₄₇	semidirect
230. C₄₇	#20023	direct (N × H)
342. D₄	AGL(1,ℤ/8)×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#3294	2
C₄₇×#3272	2
C₄₇×#1715	2
C₄₇×#1701	2
C₄₇×#1665	2
C₄₇×#1654	2
C₄₇×#1619	2
C₄₇×#1586	2
#20023	47

Subgroups — C47×#20023 #26059721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20023 #26059721