Subgroups — C₄₇×#33865 #26073563

Order 12032.

580 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3334	C₂	1	1	yes	maximal, characteristic
2	D₄×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2241	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2235	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2225	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#2217	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#2185	C₂	1	2	yes	maximal, complemented
9	C₄×SD₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#358	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₁₆×C₄₇	C₂²	1	2	yes	—
13	D₄×Q₈×C₄₇	—	2	1	no	—
14	C₄₇×#547	—	2	1	no	—
15	C₂×SD₃₂×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×SD₃₂×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₁₆×C₄₇	C₂²	1	2	yes	—
18	C₄₇×#500	C₂²	1	1	yes	characteristic
19	C₄₇×#494	C₂²	1	1	yes	characteristic
20	C₄₇×#480	—	2	2	no	—
21	C₄₇×#474	—	2	1	no	—
22	C₄₇×#467	C₂²	1	2	yes	—
23	C₄₇×#466	C₂²	1	2	yes	—
24	C₄₇×#462	—	2	1	no	—
25	C₄₇×#451	—	2	2	no	—
26	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
27	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#107×C₄₇	C₂²	1	2	yes	—
30	C₄₇×#367	C₂²	1	1	yes	characteristic
31	C₄₇×#367	C₂²	1	2	yes	—
32	C₄₇×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
33	C₄₇×#358	C₂²	1	1	yes	characteristic
34	C₄₇×#358	C₂²	1	2	yes	—
35	C₄₇×#358	C₂²	1	2	yes	—
36	C₄₇×#358	C₂²	1	2	yes	—
37	C₄₇×#358	C₂²	1	2	yes	—
38	C₄₇×#357	C₂²	1	1	yes	characteristic
39	C₄₇×C₂²⋊C₁₆	C₂²	1	2	yes	—
40	C₄×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#41×C₄₇	—	4	1	no	—
42	C₂²×Q₈×C₄₇	—	2	2	no	—
43	C₂×Q₁₆×C₄₇	—	2	4	no	—
44	C₂×Q₁₆×C₄₇	—	2	2	no	—
45	C₂×Q₁₆×C₄₇	—	2	1	no	—
46	C₂×Q₁₆×C₄₇	—	4	2	no	—
47	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
48	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
49	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₄₇	—	2	1	no	—
52	C₄⋊Q₈×C₄₇	—	2	1	no	—
53	C₄⋊Q₈×C₄₇	—	4	1	no	—
54	#123×C₄₇	—	4	2	no	—
55	C₂²⋊Q₈×C₄₇	—	2	2	no	—
56	C₂²⋊Q₈×C₄₇	—	4	1	no	—
57	C₂²⋊Q₈×C₄₇	—	4	2	no	—
58	#121×C₄₇	—	2	2	no	—
59	C₄×Q₈×C₄₇	—	2	1	no	—
60	C₄×D₄×C₄₇	—	2	1	no	—
61	C₄×D₄×C₄₇	—	4	1	no	—
62	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
64	SD₃₂×C₄₇	—	2	2	no	—
65	SD₃₂×C₄₇	—	4	2	no	—
66	C₂×C₁₆×C₄₇	—	4	2	no	—
67	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×C₁₆×C₄₇	C₂³	1	2	yes	—
69	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
70	#107×C₄₇	—	2	2	no	—
71	#107×C₄₇	—	2	1	no	—
72	#107×C₄₇	C₂³	1	2	yes	—
73	#107×C₄₇	C₂³	1	1	yes	characteristic
74	#107×C₄₇	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
76	#103×C₄₇	—	2	1	no	—
77	#103×C₄₇	—	2	2	no	—
78	#102×C₄₇	—	2	2	no	—
79	#102×C₄₇	—	2	1	no	—
80	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
81	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	#41×C₄₇	—	8	4	no	—
83	C₂×Q₈×C₄₇	—	2	1	no	—
84	C₂×Q₈×C₄₇	—	2	2	no	—
85	C₂×Q₈×C₄₇	—	4	4	no	—
86	C₂×Q₈×C₄₇	—	4	1	no	—
87	C₂×Q₈×C₄₇	—	4	2	no	—
88	C₂×Q₈×C₄₇	—	8	2	no	—
89	C₂×D₄×C₄₇	—	2	1	no	—
90	C₂×D₄×C₄₇	—	4	2	no	—
91	C₂×D₄×C₄₇	D₈	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	—	4	2	no	—
93	C₂²×C₄×C₄₇	—	4	2	no	—
94	C₂²×C₄×C₄₇	—	4	1	no	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
96	Q₁₆×C₄₇	—	2	2	no	—
97	Q₁₆×C₄₇	—	2	1	no	—
98	Q₁₆×C₄₇	—	2	2	no	—
99	Q₁₆×C₄₇	—	4	4	no	—
100	Q₁₆×C₄₇	—	8	1	no	—
101	Q₁₆×C₄₇	#41	1	2	yes	complemented
102	D₈×C₄₇	—	2	1	no	—
103	D₈×C₄₇	—	2	1	no	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₄⋊C₄×C₄₇	—	2	1	no	—
110	C₄⋊C₄×C₄₇	—	2	1	no	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	4	2	no	—
113	C₄⋊C₄×C₄₇	—	4	1	no	—
114	C₄⋊C₄×C₄₇	—	4	1	no	—
115	C₄⋊C₄×C₄₇	—	4	2	no	—
116	C₄⋊C₄×C₄₇	—	4	1	no	—
117	C₄⋊C₄×C₄₇	—	4	1	no	—
118	C₄⋊C₄×C₄₇	D₈	1	1	yes	characteristic
119	C₂²⋊C₄×C₄₇	—	4	2	no	—
120	C₂²⋊C₄×C₄₇	—	4	1	no	—
121	C₂²⋊C₄×C₄₇	—	4	2	no	—
122	C₂²⋊C₄×C₄₇	D₈	1	2	yes	—
123	C₄²×C₄₇	—	4	1	no	—
124	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₁₆×C₄₇	—	2	1	no	—
126	C₁₆×C₄₇	—	2	1	no	—
127	C₁₆×C₄₇	—	2	2	no	—
128	C₂³×C₄₇	—	4	1	no	—
129	C₂³×C₄₇	C₂×D₈	1	2	yes	—
130	Q₈×C₄₇	—	2	2	no	—
131	Q₈×C₄₇	—	4	1	no	—
132	Q₈×C₄₇	—	4	2	no	—
133	Q₈×C₄₇	—	4	2	no	—
134	Q₈×C₄₇	—	8	4	no	—
135	Q₈×C₄₇	—	8	2	no	—
136	D₄×C₄₇	—	4	1	no	—
137	D₄×C₄₇	—	4	1	no	—
138	D₄×C₄₇	—	8	4	no	—
139	D₄×C₄₇	SD₃₂	1	4	yes	complemented
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	4	1	no	—
143	C₂×C₄×C₄₇	—	4	1	no	—
144	C₂×C₄×C₄₇	—	4	1	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	8	4	no	—
148	C₂×C₄×C₄₇	—	8	4	no	—
149	C₂×C₄×C₄₇	—	8	2	no	—
150	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
152	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	C₈×C₄₇	—	2	2	no	—
155	C₈×C₄₇	—	2	1	no	—
156	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
157	C₈×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
158	#33865	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂²×C₄₇	—	2	2	no	—
160	C₂²×C₄₇	—	2	2	no	—
161	C₂²×C₄₇	—	8	1	no	—
162	C₂²×C₄₇	—	8	1	no	—
163	C₂²×C₄₇	—	8	1	no	—
164	C₂²×C₄₇	C₂×SD₃₂	1	4	yes	—
165	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
166	C₄×C₄₇	—	2	1	no	—
167	C₄×C₄₇	—	2	2	no	—
168	C₄×C₄₇	—	4	2	no	—
169	C₄×C₄₇	—	8	1	no	—
170	C₄×C₄₇	—	8	2	no	—
171	C₄×C₄₇	—	8	1	no	—
172	C₄×C₄₇	—	8	2	no	—
173	C₄×C₄₇	C₂×SD₃₂	1	2	yes	—
174	C₄×C₄₇	#546	1	1	yes	characteristic
175	C₄×C₄₇	#577	1	1	yes	characteristic
176	#3334	C₂×C₄₇	1	1	yes	characteristic
177	D₄×Q₁₆	C₂×C₄₇	1	1	yes	characteristic, complemented
178	#2241	C₂×C₄₇	1	1	yes	characteristic, complemented
179	#2235	C₂×C₄₇	1	2	yes	complemented
180	#2225	C₂×C₄₇	1	1	yes	characteristic, complemented
181	#2217	C₂×C₄₇	1	2	yes	complemented
182	#2208	C₂×C₄₇	1	1	yes	characteristic, complemented
183	#2185	C₂×C₄₇	1	2	yes	complemented
184	C₄×SD₃₂	C₂×C₄₇	1	1	yes	characteristic, complemented
185	D₄×C₁₆	C₂×C₄₇	1	1	yes	characteristic, complemented
186	C₂×#358	C₂×C₄₇	1	2	yes	complemented
187	C₂×C₄₇	—	2	4	no	—
188	C₂×C₄₇	—	16	1	no	—
189	C₂×C₄₇	#3294	1	1	yes	characteristic
190	C₂×C₄₇	C₂²×SD₃₂	1	1	yes	characteristic
191	C₂×C₄₇	#3417	1	1	yes	characteristic
192	C₂²×Q₁₆	C₂²×C₄₇	1	2	yes	—
193	D₄×Q₈	—	2	1	no	—
194	#547	—	2	1	no	—
195	C₂×SD₃₂	C₂²×C₄₇	1	1	yes	characteristic
196	C₂×SD₃₂	C₂²×C₄₇	1	2	yes	—
197	C₂²×C₁₆	C₂²×C₄₇	1	2	yes	—
198	#500	C₂²×C₄₇	1	1	yes	characteristic
199	#494	C₂²×C₄₇	1	1	yes	characteristic
200	#480	—	2	2	no	—
201	#474	—	2	1	no	—
202	#467	C₂²×C₄₇	1	2	yes	—
203	#466	C₂²×C₄₇	1	2	yes	—
204	#462	—	2	1	no	—
205	#451	—	2	2	no	—
206	C₄×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
207	C₄×D₈	C₂²×C₄₇	1	1	yes	characteristic
208	C₈×D₄	C₂²×C₄₇	1	1	yes	characteristic
209	C₂×#107	C₂²×C₄₇	1	2	yes	—
210	#367	C₂²×C₄₇	1	1	yes	characteristic
211	#367	C₂²×C₄₇	1	2	yes	—
212	C₄⋊C₁₆	C₂²×C₄₇	1	1	yes	characteristic
213	#358	C₂²×C₄₇	1	1	yes	characteristic
214	#358	C₂²×C₄₇	1	2	yes	—
215	#358	C₂²×C₄₇	1	2	yes	—
216	#358	C₂²×C₄₇	1	2	yes	—
217	#358	C₂²×C₄₇	1	2	yes	—
218	#357	C₂²×C₄₇	1	1	yes	characteristic
219	C₂²⋊C₁₆	C₂²×C₄₇	1	2	yes	—
220	C₄×C₁₆	C₂²×C₄₇	1	1	yes	characteristic
221	C₄₇	#33865	1	1	yes	characteristic, direct product factor, Sylow
222	C₂×#41	—	4	1	no	—
223	C₂²×Q₈	—	2	2	no	—
224	C₂×Q₁₆	—	2	4	no	—
225	C₂×Q₁₆	—	2	2	no	—
226	C₂×Q₁₆	—	2	1	no	—
227	C₂×Q₁₆	—	4	2	no	—
228	C₂×Q₁₆	C₂³×C₄₇	1	2	yes	—
229	C₂×Q₁₆	C₂³×C₄₇	1	1	yes	characteristic
230	C₂×D₈	C₂³×C₄₇	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	—	4	1	no	—
235	#123	—	4	2	no	—
236	C₂²⋊Q₈	—	2	2	no	—
237	C₂²⋊Q₈	—	4	1	no	—
238	C₂²⋊Q₈	—	4	2	no	—
239	#121	—	2	2	no	—
240	C₄×Q₈	—	2	1	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	4	1	no	—
243	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
244	C₂×C₄⋊C₄	—	2	2	no	—
245	SD₃₂	—	2	2	no	—
246	SD₃₂	—	4	2	no	—
247	C₂×C₁₆	—	4	2	no	—
248	C₂×C₁₆	C₂³×C₄₇	1	1	yes	characteristic
249	C₂×C₁₆	C₂³×C₄₇	1	1	yes	characteristic
250	C₂×C₁₆	C₂³×C₄₇	1	2	yes	—
251	#107	—	2	2	no	—
252	#107	—	2	1	no	—
253	#107	C₂³×C₄₇	1	1	yes	characteristic
254	#107	C₂³×C₄₇	1	1	yes	characteristic
255	#107	C₂³×C₄₇	1	2	yes	—
256	C₄⋊C₈	D₄×C₄₇	1	1	yes	characteristic
257	#103	—	2	1	no	—
258	#103	—	2	2	no	—
259	#102	—	2	1	no	—
260	#102	—	2	2	no	—
261	C₂²⋊C₈	D₄×C₄₇	1	2	yes	—
262	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
263	#41	—	8	4	no	—
264	C₂×Q₈	—	2	1	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	4	4	no	—
267	C₂×Q₈	—	4	1	no	—
268	C₂×Q₈	—	4	2	no	—
269	C₂×Q₈	—	8	2	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	D₈×C₄₇	1	1	yes	characteristic
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	1	no	—
276	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
277	Q₁₆	—	2	2	no	—
278	Q₁₆	—	2	1	no	—
279	Q₁₆	—	2	2	no	—
280	Q₁₆	—	4	4	no	—
281	Q₁₆	—	8	1	no	—
282	Q₁₆	#41×C₄₇	1	2	yes	complemented
283	D₈	—	2	1	no	—
284	D₈	—	2	1	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
288	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
289	C₂×C₈	C₂⁴×C₄₇	1	1	yes	characteristic
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	4	2	no	—
294	C₄⋊C₄	—	4	1	no	—
295	C₄⋊C₄	—	4	1	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	—	4	1	no	—
298	C₄⋊C₄	—	4	1	no	—
299	C₄⋊C₄	D₈×C₄₇	1	1	yes	characteristic
300	C₂²⋊C₄	—	4	2	no	—
301	C₂²⋊C₄	—	4	1	no	—
302	C₂²⋊C₄	—	4	2	no	—
303	C₂²⋊C₄	D₈×C₄₇	1	2	yes	—
304	C₄²	—	4	1	no	—
305	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
306	C₁₆	—	2	1	no	—
307	C₁₆	—	2	1	no	—
308	C₁₆	—	2	2	no	—
309	C₂³	—	4	1	no	—
310	C₂³	C₂×D₈×C₄₇	1	2	yes	—
311	Q₈	—	2	2	no	—
312	Q₈	—	4	1	no	—
313	Q₈	—	4	2	no	—
314	Q₈	—	4	2	no	—
315	Q₈	—	8	4	no	—
316	Q₈	—	8	2	no	—
317	D₄	—	4	1	no	—
318	D₄	—	4	1	no	—
319	D₄	—	8	4	no	—
320	D₄	SD₃₂×C₄₇	1	4	yes	complemented
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	8	4	no	—
329	C₂×C₄	—	8	4	no	—
330	C₂×C₄	—	8	2	no	—
331	C₂×C₄	C₂×D₈×C₄₇	1	1	yes	characteristic
332	C₂×C₄	C₂×D₈×C₄₇	1	2	yes	—
333	C₂×C₄	C₂×D₈×C₄₇	1	1	yes	characteristic
334	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
335	C₈	—	2	2	no	—
336	C₈	—	2	1	no	—
337	C₈	C₂×#41×C₄₇	1	1	yes	characteristic
338	C₈	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	8	1	no	—
342	C₂²	—	8	1	no	—
343	C₂²	—	8	1	no	—
344	C₂²	C₂×SD₃₂×C₄₇	1	4	yes	—
345	C₂²	C₂²×D₈×C₄₇	1	1	yes	characteristic
346	C₄	—	2	2	no	—
347	C₄	—	2	1	no	—
348	C₄	—	4	2	no	—
349	C₄	—	8	2	no	—
350	C₄	—	8	1	no	—
351	C₄	—	8	2	no	—
352	C₄	—	8	1	no	—
353	C₄	C₂×SD₃₂×C₄₇	1	2	yes	—
354	C₄	C₄₇×#546	1	1	yes	characteristic
355	C₄	C₄₇×#577	1	1	yes	characteristic
356	C₂	—	2	4	no	—
357	C₂	—	16	1	no	—
358	C₂	C₄₇×#3294	1	1	yes	characteristic
359	C₂	C₂²×SD₃₂×C₄₇	1	1	yes	characteristic
360	C₂	C₄₇×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₄₇
prime radical	C₄₇×#3334	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₄×D₄×C₄₇ ◁ C₈×D₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×Q₁₆×C₄₇	C₂	semidirect
3. C₄₇×#2241	C₂	semidirect
4. C₄₇×#2235	C₂	semidirect
5. C₄₇×#2225	C₂	semidirect
6. C₄₇×#2217	C₂	semidirect
7. C₄₇×#2208	C₂	semidirect
8. C₄₇×#2185	C₂	semidirect
9. C₄×SD₃₂×C₄₇	C₂	semidirect
10. D₄×C₁₆×C₄₇	C₂	semidirect
11. C₂×C₄₇×#358	C₂	semidirect
101. Q₁₆×C₄₇	#41	semidirect
139. D₄×C₄₇	SD₃₂	semidirect
158. #33865	C₄₇	direct (N × H)
177. D₄×Q₁₆	C₂×C₄₇	semidirect
178. #2241	C₂×C₄₇	semidirect
179. #2235	C₂×C₄₇	semidirect
180. #2225	C₂×C₄₇	semidirect
181. #2217	C₂×C₄₇	semidirect
182. #2208	C₂×C₄₇	semidirect
183. #2185	C₂×C₄₇	semidirect
184. C₄×SD₃₂	C₂×C₄₇	semidirect
185. D₄×C₁₆	C₂×C₄₇	semidirect
186. C₂×#358	C₂×C₄₇	semidirect
221. C₄₇	#33865	direct (N × H)
282. Q₁₆	#41×C₄₇	semidirect
320. D₄	SD₃₂×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#3334	2
D₄×Q₁₆×C₄₇	2
C₄₇×#2241	2
C₄₇×#2235	2
C₄₇×#2225	2
C₄₇×#2217	2
C₄₇×#2208	2
C₄₇×#2185	2
C₄×SD₃₂×C₄₇	2
D₄×C₁₆×C₄₇	2
C₂×C₄₇×#358	2
#33865	47

Subgroups — C47×#33865 #26073563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#33865 #26073563