Subgroups — #26369384

Order 12032.

600 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	#405×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#20245194	C₂	1	2	yes	maximal, complemented
3	#20245194	C₂	1	2	yes	maximal, complemented
4	#20245190	C₂	1	2	yes	maximal, complemented
5	#20245186	C₂	1	2	yes	maximal, complemented
6	#20245147	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244998	C₂	1	1	yes	maximal, characteristic
8	C₂×(C₂×D₄₇)⋊C₁₆	C₂	1	1	yes	maximal, characteristic
9	#20244987	C₂	1	1	yes	maximal, characteristic, complemented
10	#20244984	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2151	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₄₇	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	#117×D₄₇	C₄	1	1	yes	characteristic
15	C₂×#13093964	C₂²	1	1	yes	characteristic
16	C₂²×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
17	#15689081	C₄	1	1	yes	characteristic
18	#15689080	C₄	1	2	yes	—
19	#15689079	C₄	1	1	yes	characteristic
20	#15689078	C₂²	1	1	yes	characteristic
21	#15689077	C₂²	1	2	yes	—
22	#97×D₄₇	C₄	1	2	yes	—
23	C₄×C₈×D₄₇	C₂²	1	2	yes	—
24	C₄⋊(C₄₇⋊C₁₆)	C₂²	1	2	yes	complemented
25	C₄⋊(C₄₇⋊C₁₆)	C₂²	1	2	yes	complemented
26	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic
27	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic
28	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic
29	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic
30	(C₂×D₄₇)⋊C₁₆	C₂²	1	2	yes	—
31	(C₂×D₄₇)⋊C₁₆	C₂²	1	2	yes	—
32	#15688898	C₂²	1	2	yes	complemented
33	#15688898	C₂²	1	2	yes	complemented
34	C₁₆×Dic₄₇	C₂²	1	2	yes	complemented
35	C₁₆×Dic₄₇	C₂²	1	2	yes	complemented
36	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic
37	C₂²×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#405	C₂²	1	1	yes	characteristic
39	C₄₇×C₄⋊C₁₆	C₂²	1	2	yes	complemented
40	C₄₇×C₄⋊C₁₆	C₂²	1	2	yes	complemented
41	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
43	C₂×#10625324	C₂×C₄	1	2	yes	—
44	M₁₆×D₄₇	—	2	4	no	—
45	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₄₇	—	2	2	no	—
47	C₂×C₈×D₄₇	—	2	2	no	—
48	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
49	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
52	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
53	#13093983	C₂×C₄	1	1	yes	characteristic
54	#13093982	C₈	1	1	yes	characteristic
55	#13093982	C₈	1	1	yes	characteristic
56	#13093981	C₂×C₄	1	2	yes	—
57	#13093980	C₈	1	2	yes	—
58	C₄⋊C₄×D₄₇	C₈	1	1	yes	characteristic
59	C₄⋊C₄×D₄₇	C₈	1	1	yes	characteristic
60	C₂²⋊C₄×D₄₇	C₈	1	2	yes	—
61	C₄²×D₄₇	C₂×C₄	1	2	yes	—
62	#13093964	—	2	2	no	—
63	C₂×C₄₇⋊C₁₆	—	2	2	no	—
64	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
67	#13093935	C₂×C₄	1	2	yes	—
68	#13093934	C₂×C₄	1	2	yes	—
69	#13093934	C₂×C₄	1	2	yes	—
70	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
71	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
72	C₈×Dic₄₇	C₂³	1	2	yes	—
73	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
76	M₃₂×C₄₇	—	2	2	no	—
77	C₂×C₁₆×C₄₇	—	2	2	no	—
78	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₁₆×C₄₇	C₂³	1	2	yes	—
81	#97×C₄₇	C₂×C₄	1	2	yes	—
82	C₄×C₈×C₄₇	C₂³	1	2	yes	—
83	C₂³×D₄₇	C₂×C₈	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×Dic₄₇	C₂×C₈	1	1	yes	characteristic
86	C₂×C₄×D₄₇	—	2	2	no	—
87	C₂×C₄×D₄₇	—	2	2	no	—
88	C₂×C₄×D₄₇	C₂×C₈	1	2	yes	—
89	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
90	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
91	C₂×C₄×D₄₇	C₂×C₈	1	2	yes	—
92	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
94	M₁₆×C₄₇	—	2	2	no	—
95	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₄₇	#41	1	2	yes	—
98	C₂×C₈×C₄₇	#41	1	2	yes	—
99	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
100	C₄⋊C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
101	C₄⋊C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
102	C₂²⋊C₄×C₄₇	C₂×C₈	1	2	yes	—
103	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²⋊Dic₄₇	C₂×C₈	1	2	yes	—
105	(C₂×D₄₇)⋊C₄	C₂×C₈	1	2	yes	—
106	(C₂×D₄₇)⋊C₄	C₂×C₈	1	2	yes	—
107	C₄⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
108	C₄⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
109	Dic₄₇⋊C₄	C₂×C₈	1	2	yes	—
110	Dic₄₇⋊C₄	C₂×C₈	1	2	yes	—
111	C₄×Dic₄₇	C₂×C₈	1	2	yes	—
112	C₄×Dic₄₇	C₂×C₈	1	2	yes	—
113	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
114	#10625329	M₁₆	1	4	yes	—
115	C₂×C₄₇⋊C₈	—	2	2	no	—
116	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
119	#10625324	—	2	4	no	—
120	C₈×D₄₇	—	2	2	no	—
121	C₈×D₄₇	—	2	2	no	—
122	C₈×D₄₇	—	2	1	no	—
123	C₈×D₄₇	—	2	1	no	—
124	C₈×D₄₇	—	2	1	no	—
125	C₈×D₄₇	—	2	1	no	—
126	C₈×D₄₇	—	2	4	no	—
127	C₁₆×C₄₇	—	2	1	no	—
128	C₁₆×C₄₇	—	2	1	no	—
129	C₁₆×C₄₇	—	2	2	no	—
130	C₄₇⋊C₁₆	—	2	1	no	—
131	C₄₇⋊C₁₆	—	2	1	no	—
132	C₄₇⋊C₁₆	—	2	2	no	—
133	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
134	C₂²×D₄₇	—	2	2	no	—
135	C₂²×D₄₇	—	2	2	no	—
136	C₂²×D₄₇	—	4	1	no	—
137	C₂²×D₄₇	C₂²×C₈	1	1	yes	characteristic
138	C₂²×D₄₇	C₂²×C₈	1	1	yes	characteristic
139	C₂×C₄×C₄₇	#117	1	2	yes	—
140	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
141	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
142	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
144	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
145	C₂×Dic₄₇	—	2	2	no	—
146	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
147	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
148	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
149	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
150	C₄×D₄₇	—	2	4	no	—
151	C₄×D₄₇	—	2	1	no	—
152	C₄×D₄₇	—	2	1	no	—
153	C₄×D₄₇	—	2	1	no	—
154	C₄×D₄₇	—	2	1	no	—
155	C₄×D₄₇	—	2	2	no	—
156	C₄×D₄₇	—	2	2	no	—
157	C₄×D₄₇	—	4	2	no	—
158	C₈×C₄₇	—	2	2	no	—
159	C₈×C₄₇	#117	1	2	yes	—
160	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₄₇⋊C₈	—	2	1	no	—
163	C₄₇⋊C₈	—	2	1	no	—
164	C₄₇⋊C₈	C₂×M₁₆	1	4	yes	—
165	#33422	—	47	1	no	maximal, Sylow
166	C₂²×C₄₇	—	2	1	no	—
167	C₂²×C₄₇	—	2	1	no	—
168	C₂²×C₄₇	#431	1	2	yes	—
169	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
170	C₂×D₄₇	—	2	1	no	—
171	C₂×D₄₇	—	2	1	no	—
172	C₂×D₄₇	—	2	1	no	—
173	C₂×D₄₇	—	2	1	no	—
174	C₂×D₄₇	—	2	1	no	—
175	C₂×D₄₇	—	4	4	no	—
176	C₂×D₄₇	#504	1	2	yes	—
177	C₄×C₄₇	—	2	2	no	—
178	C₄×C₄₇	—	2	2	no	—
179	C₄×C₄₇	#431	1	2	yes	—
180	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
181	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
182	Dic₄₇	—	2	2	no	—
183	Dic₄₇	—	2	2	no	—
184	Dic₄₇	—	2	1	no	—
185	Dic₄₇	—	2	1	no	—
186	C₂×#405	—	47	1	no	—
187	#2164	—	47	2	no	—
188	#2164	—	47	2	no	—
189	#2163	—	47	2	no	—
190	#2162	—	47	2	no	—
191	#2151	—	47	1	no	—
192	#2151	D₄₇	1	1	yes	characteristic, complemented
193	#2112	—	47	1	no	—
194	C₂×C₂²⋊C₁₆	—	47	1	no	—
195	#2108	—	47	1	no	—
196	#2108	—	47	1	no	—
197	C₂×C₄₇	—	2	2	no	—
198	C₂×C₄₇	C₂×#431	1	1	yes	characteristic
199	C₂×C₄₇	C₂×#504	1	1	yes	characteristic
200	C₂×C₄₇	#3407	1	1	yes	characteristic
201	D₄₇	—	2	2	no	—
202	D₄₇	—	4	1	no	—
203	C₂²×M₁₆	—	47	1	no	—
204	C₂³×C₈	—	47	1	no	—
205	C₂×#117	—	47	1	no	—
206	C₂×M₃₂	—	47	1	no	—
207	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic
208	C₂²×C₁₆	—	47	1	no	—
209	C₂²×C₁₆	C₂×D₄₇	1	1	yes	characteristic
210	#405	—	47	1	no	—
211	#405	—	47	1	no	—
212	#405	—	47	1	no	—
213	#405	—	47	2	no	—
214	#405	—	47	2	no	—
215	#405	C₂×D₄₇	1	1	yes	characteristic
216	C₂×#97	—	47	2	no	—
217	C₂×C₄×C₈	—	47	2	no	—
218	C₄⋊C₁₆	—	47	2	no	—
219	C₄⋊C₁₆	—	47	2	no	—
220	C₄⋊C₁₆	C₂×D₄₇	1	2	yes	complemented
221	C₄⋊C₁₆	C₂×D₄₇	1	2	yes	complemented
222	C₂²⋊C₁₆	—	47	1	no	—
223	C₂²⋊C₁₆	—	47	1	no	—
224	C₂²⋊C₁₆	—	47	1	no	—
225	C₂²⋊C₁₆	—	47	1	no	—
226	C₂²⋊C₁₆	—	47	2	no	—
227	C₂²⋊C₁₆	—	47	2	no	—
228	#346	—	47	2	no	—
229	#346	—	47	2	no	—
230	C₄×C₁₆	—	47	2	no	—
231	C₄×C₁₆	—	47	2	no	—
232	C₄₇	#33422	1	1	yes	characteristic, complemented, Sylow
233	C₂³×C₄	—	47	1	no	—
234	C₂×M₁₆	—	47	1	no	—
235	C₂×M₁₆	—	47	2	no	—
236	C₂×M₁₆	—	94	4	no	—
237	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
238	C₂²×C₈	—	47	1	no	—
239	C₂²×C₈	—	47	1	no	—
240	C₂²×C₈	—	47	1	no	—
241	C₂²×C₈	—	47	2	no	—
242	C₂²×C₈	—	47	1	no	—
243	C₂²×C₈	—	47	1	no	—
244	C₂²×C₈	—	94	2	no	—
245	C₂²×C₈	—	94	2	no	—
246	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
247	#117	—	47	1	no	—
248	#117	—	47	1	no	—
249	#117	—	47	1	no	—
250	#117	—	47	2	no	—
251	#117	—	47	2	no	—
252	#117	C₄×D₄₇	1	1	yes	characteristic
253	C₂×C₄⋊C₄	—	47	1	no	—
254	C₂×C₄⋊C₄	—	47	1	no	—
255	C₂×C₂²⋊C₄	—	47	2	no	—
256	C₂×C₄²	—	47	2	no	—
257	M₃₂	—	2	2	no	—
258	M₃₂	—	94	2	no	—
259	C₂×C₁₆	—	2	2	no	—
260	C₂×C₁₆	—	47	1	no	—
261	C₂×C₁₆	—	47	2	no	—
262	C₂×C₁₆	—	47	1	no	—
263	C₂×C₁₆	—	94	2	no	—
264	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
265	C₂×C₁₆	C₂²×D₄₇	1	2	yes	—
266	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
267	#97	—	47	2	no	—
268	#97	—	47	2	no	—
269	#97	—	47	2	no	—
270	#97	C₄×D₄₇	1	2	yes	—
271	C₄×C₈	—	47	2	no	—
272	C₄×C₈	—	47	2	no	—
273	C₄×C₈	—	47	2	no	—
274	C₄×C₈	C₂²×D₄₇	1	2	yes	—
275	C₂⁴	—	47	1	no	—
276	C₂²×C₄	—	47	1	no	—
277	C₂²×C₄	—	47	2	no	—
278	C₂²×C₄	—	47	1	no	—
279	C₂²×C₄	—	47	1	no	—
280	C₂²×C₄	—	47	1	no	—
281	C₂²×C₄	—	47	1	no	—
282	C₂²×C₄	—	47	2	no	—
283	C₂²×C₄	—	94	2	no	—
284	C₂²×C₄	—	94	2	no	—
285	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
286	M₁₆	—	2	2	no	—
287	M₁₆	—	47	4	no	—
288	M₁₆	—	94	4	no	—
289	C₂×C₈	—	47	2	no	—
290	C₂×C₈	—	47	1	no	—
291	C₂×C₈	—	47	1	no	—
292	C₂×C₈	—	94	4	no	—
293	C₂×C₈	—	94	2	no	—
294	C₂×C₈	—	94	2	no	—
295	C₂×C₈	—	94	2	no	—
296	C₂×C₈	—	94	1	no	—
297	C₂×C₈	—	94	1	no	—
298	C₂×C₈	—	94	1	no	—
299	C₂×C₈	—	94	1	no	—
300	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
301	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
302	C₂×C₈	#10625352	1	2	yes	—
303	C₂×C₈	#10625354	1	2	yes	—
304	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
305	C₄⋊C₄	—	47	2	no	—
306	C₄⋊C₄	—	47	2	no	—
307	C₄⋊C₄	—	47	1	no	—
308	C₄⋊C₄	—	47	1	no	—
309	C₄⋊C₄	C₈×D₄₇	1	1	yes	characteristic
310	C₄⋊C₄	C₈×D₄₇	1	1	yes	characteristic
311	C₂²⋊C₄	—	47	2	no	—
312	C₂²⋊C₄	—	47	2	no	—
313	C₂²⋊C₄	—	47	2	no	—
314	C₂²⋊C₄	C₈×D₄₇	1	2	yes	—
315	C₄²	—	47	2	no	—
316	C₄²	—	47	2	no	—
317	C₄²	—	47	2	no	—
318	C₄²	C₂×C₄×D₄₇	1	2	yes	—
319	C₁₆	—	2	1	no	—
320	C₁₆	—	2	1	no	—
321	C₁₆	—	2	2	no	—
322	C₁₆	—	94	1	no	—
323	C₁₆	—	94	1	no	—
324	C₁₆	—	94	2	no	—
325	C₂³	—	47	1	no	—
326	C₂³	—	47	1	no	—
327	C₂³	—	94	2	no	—
328	C₂³	—	94	2	no	—
329	C₂³	—	188	1	no	—
330	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
331	C₂×C₄	—	47	1	no	—
332	C₂×C₄	—	47	2	no	—
333	C₂×C₄	—	47	2	no	—
334	C₂×C₄	—	47	1	no	—
335	C₂×C₄	—	94	4	no	—
336	C₂×C₄	—	94	2	no	—
337	C₂×C₄	—	94	1	no	—
338	C₂×C₄	—	94	1	no	—
339	C₂×C₄	—	94	1	no	—
340	C₂×C₄	—	94	1	no	—
341	C₂×C₄	—	94	2	no	—
342	C₂×C₄	—	94	2	no	—
343	C₂×C₄	—	188	2	no	—
344	C₂×C₄	#13093982	1	2	yes	—
345	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
346	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
347	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
348	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
349	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
350	C₈	—	2	2	no	—
351	C₈	—	47	4	no	—
352	C₈	—	94	1	no	—
353	C₈	—	94	1	no	—
354	C₈	#13093982	1	2	yes	—
355	C₈	C₂×#10625352	1	1	yes	characteristic
356	C₈	C₂×#10625354	1	1	yes	characteristic
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	47	2	no	—
360	C₂²	—	94	1	no	—
361	C₂²	—	94	1	no	—
362	C₂²	—	94	1	no	—
363	C₂²	—	94	1	no	—
364	C₂²	—	94	1	no	—
365	C₂²	—	188	4	no	—
366	C₂²	#15689175	1	2	yes	—
367	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
368	C₄	—	2	2	no	—
369	C₄	—	2	2	no	—
370	C₄	—	94	1	no	—
371	C₄	—	94	1	no	—
372	C₄	—	94	2	no	—
373	C₄	—	94	2	no	—
374	C₄	#15689175	1	2	yes	—
375	C₄	C₂×#13093982	1	1	yes	characteristic
376	C₄	C₂×M₁₆×D₄₇	1	1	yes	characteristic
377	C₂	—	2	2	no	—
378	C₂	—	94	2	no	—
379	C₂	—	188	1	no	—
380	C₂	C₂×#15689175	1	1	yes	characteristic
381	C₂	#504×D₄₇	1	1	yes	characteristic
382	C₂	#20256489	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#2151	C₂
prime radical	C₂³×D₄₇	C₂×C₈
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	#2151	D₄₇
hypocenter	C₄₇	#33422
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ #2151

Complements

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

N	H ≅ G/N	type
2. #20245194	C₂	semidirect
3. #20245194	C₂	semidirect
4. #20245190	C₂	semidirect
5. #20245186	C₂	semidirect
6. #20245147	C₂	semidirect
9. #20244987	C₂	semidirect
10. #20244984	C₂	semidirect
11. C₄₇×#2151	C₂	semidirect
24. C₄⋊(C₄₇⋊C₁₆)	C₂²	semidirect
25. C₄⋊(C₄₇⋊C₁₆)	C₂²	semidirect
32. #15688898	C₂²	semidirect
33. #15688898	C₂²	semidirect
34. C₁₆×Dic₄₇	C₂²	semidirect
35. C₁₆×Dic₄₇	C₂²	semidirect
39. C₄₇×C₄⋊C₁₆	C₂²	semidirect
40. C₄₇×C₄⋊C₁₆	C₂²	semidirect
192. #2151	D₄₇	semidirect
220. C₄⋊C₁₆	C₂×D₄₇	semidirect
221. C₄⋊C₁₆	C₂×D₄₇	semidirect
232. C₄₇	#33422	semidirect

Maximal subgroups

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

subgroup	index
#405×D₄₇	2
#20245194	2
#20245190	2
#20245186	2
#20245147	2
#20244998	2
C₂×(C₂×D₄₇)⋊C₁₆	2
#20244987	2
#20244984	2
C₄₇×#2151	2
#33422	47