Subgroups — C₄₇×#20015 #26059713

Order 12032.

590 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×#3396	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#3395	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3365	C₂	1	2	yes	maximal, complemented
4	C₄₇×#1709	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1682	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1670	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1668	C₂	1	1	yes	maximal, characteristic
8	C₄₇×#1640	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1626	C₂	1	2	yes	maximal, complemented
10	C₈×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#559	C₂²	1	2	yes	—
13	C₄₇×#557	C₂²	1	2	yes	—
14	C₄₇×#495	—	2	1	no	—
15	C₄₇×#494	—	2	1	no	—
16	C₄₇×#494	C₂²	1	1	yes	characteristic
17	C₄₇×#493	C₂²	1	1	yes	characteristic
18	C₄₇×#488	—	2	2	no	—
19	C₄₇×#486	C₂²	1	2	yes	—
20	C₄₇×#486	C₂²	1	2	yes	—
21	C₄₇×#478	—	2	2	no	—
22	C₄₇×#475	C₂²	1	2	yes	—
23	C₄₇×#464	—	2	2	no	—
24	C₄₇×#463	—	2	2	no	—
25	C₄₇×#462	—	2	2	no	—
26	C₄₇×#462	C₂²	1	2	yes	—
27	C₄₇×#460	C₂²	1	2	yes	—
28	C₄₇×#460	C₂²	1	2	yes	—
29	C₈×Q₈×C₄₇	C₂²	1	2	yes	—
30	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₄×Q₁₆×C₄₇	—	2	1	no	—
33	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
34	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
35	C₄×SD₁₆×C₄₇	—	2	2	no	—
36	C₄×D₈×C₄₇	—	2	1	no	—
37	C₄₇×#335	C₂²	1	1	yes	characteristic
38	C₄₇×#335	C₂²	1	1	yes	characteristic
39	C₄₇×#332	C₂²	1	2	yes	—
40	C₄₇×#331	C₂²	1	2	yes	—
41	C₄₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₄₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
44	C₈²×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₄₇	—	2	2	no	—
46	C₂×Q₁₆×C₄₇	—	2	1	no	—
47	C₂×Q₁₆×C₄₇	—	2	1	no	—
48	C₂×Q₁₆×C₄₇	D₄	1	1	yes	characteristic
49	C₂×Q₁₆×C₄₇	D₄	1	1	yes	characteristic
50	C₂×SD₁₆×C₄₇	—	2	2	no	—
51	C₂×SD₁₆×C₄₇	—	2	2	no	—
52	C₂×D₈×C₄₇	—	2	1	no	—
53	C₂×D₈×C₄₇	—	2	1	no	—
54	C₄⋊Q₈×C₄₇	—	2	2	no	—
55	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
56	#127×C₄₇	C₂³	1	2	yes	—
57	#125×C₄₇	—	2	2	no	—
58	#125×C₄₇	—	4	2	no	—
59	#124×C₄₇	—	2	2	no	—
60	#124×C₄₇	—	2	2	no	—
61	#123×C₄₇	—	4	2	no	—
62	C₄×Q₈×C₄₇	—	2	2	no	—
63	C₄×Q₈×C₄₇	—	2	2	no	—
64	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
65	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
66	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
67	C₄×D₄×C₄₇	—	2	2	no	—
68	C₄×D₄×C₄₇	—	2	2	no	—
69	#107×C₄₇	D₄	1	1	yes	characteristic
70	#107×C₄₇	D₄	1	1	yes	characteristic
71	#106×C₄₇	—	2	2	no	—
72	C₄⋊C₈×C₄₇	—	2	1	no	—
73	C₄⋊C₈×C₄₇	—	2	1	no	—
74	C₄⋊C₈×C₄₇	—	2	2	no	—
75	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
77	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
78	#103×C₄₇	—	2	2	no	—
79	#103×C₄₇	—	2	2	no	—
80	#103×C₄₇	D₄	1	2	yes	—
81	#103×C₄₇	D₄	1	1	yes	characteristic
82	#103×C₄₇	D₄	1	1	yes	characteristic
83	#102×C₄₇	—	2	2	no	—
84	#102×C₄₇	—	2	2	no	—
85	#102×C₄₇	—	2	2	no	—
86	#102×C₄₇	—	2	2	no	—
87	#102×C₄₇	—	4	2	no	—
88	C₄×C₈×C₄₇	—	2	2	no	—
89	C₄×C₈×C₄₇	—	2	1	no	—
90	C₄×C₈×C₄₇	—	2	1	no	—
91	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
97	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	4	2	no	—
102	Q₁₆×C₄₇	—	2	2	no	—
103	Q₁₆×C₄₇	—	2	2	no	—
104	Q₁₆×C₄₇	—	4	2	no	—
105	Q₁₆×C₄₇	—	8	1	no	—
106	Q₁₆×C₄₇	—	8	2	no	—
107	SD₁₆×C₄₇	—	4	4	no	—
108	SD₁₆×C₄₇	—	8	2	no	—
109	D₈×C₄₇	—	4	2	no	—
110	D₈×C₄₇	—	8	1	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	1	no	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₄⋊C₄×C₄₇	—	2	1	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	1	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	4	2	no	—
125	C₄⋊C₄×C₄₇	—	4	2	no	—
126	C₄⋊C₄×C₄₇	—	4	2	no	—
127	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²⋊C₄×C₄₇	—	4	2	no	—
131	C₂²⋊C₄×C₄₇	—	4	2	no	—
132	C₂²⋊C₄×C₄₇	—	4	2	no	—
133	C₄²×C₄₇	—	2	1	no	—
134	C₄²×C₄₇	—	2	2	no	—
135	C₄²×C₄₇	—	2	1	no	—
136	C₄²×C₄₇	—	4	2	no	—
137	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
138	C₂³×C₄₇	—	4	2	no	—
139	Q₈×C₄₇	—	2	1	no	—
140	Q₈×C₄₇	—	2	1	no	—
141	Q₈×C₄₇	—	2	2	no	—
142	Q₈×C₄₇	—	2	2	no	—
143	Q₈×C₄₇	—	2	1	no	—
144	Q₈×C₄₇	—	4	2	no	—
145	Q₈×C₄₇	—	4	2	no	—
146	Q₈×C₄₇	#135	1	2	yes	—
147	D₄×C₄₇	—	4	2	no	—
148	D₄×C₄₇	—	4	2	no	—
149	D₄×C₄₇	—	4	2	no	—
150	D₄×C₄₇	—	4	2	no	—
151	D₄×C₄₇	—	8	2	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	16	2	no	—
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
163	C₈×C₄₇	—	2	1	no	—
164	C₈×C₄₇	—	2	1	no	—
165	C₈×C₄₇	—	2	1	no	—
166	C₈×C₄₇	—	4	1	no	—
167	C₈×C₄₇	—	4	2	no	—
168	C₈×C₄₇	—	4	1	no	—
169	C₈×C₄₇	—	4	1	no	—
170	C₈×C₄₇	#135	1	2	yes	—
171	#20015	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂²×C₄₇	—	8	2	no	—
173	C₂²×C₄₇	—	8	2	no	—
174	C₂²×C₄₇	—	8	2	no	—
175	C₂²×C₄₇	D₄²	1	1	yes	characteristic
176	C₄×C₄₇	—	2	2	no	—
177	C₄×C₄₇	—	2	1	no	—
178	C₄×C₄₇	—	4	1	no	—
179	C₄×C₄₇	—	4	2	no	—
180	C₄×C₄₇	—	4	1	no	—
181	C₄×C₄₇	—	4	2	no	—
182	C₄×C₄₇	—	4	1	no	—
183	C₄×C₄₇	—	8	2	no	—
184	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
185	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
186	C₄×C₄₇	#576	1	1	yes	characteristic
187	C₄×C₄₇	#578	1	1	yes	characteristic
188	#3396	C₂×C₄₇	1	1	yes	characteristic
189	#3395	C₂×C₄₇	1	1	yes	characteristic, complemented
190	#3365	C₂×C₄₇	1	2	yes	complemented
191	#1709	C₂×C₄₇	1	1	yes	characteristic
192	#1682	C₂×C₄₇	1	2	yes	complemented
193	#1670	C₂×C₄₇	1	1	yes	characteristic, complemented
194	#1668	C₂×C₄₇	1	1	yes	characteristic
195	#1640	C₂×C₄₇	1	2	yes	complemented
196	#1626	C₂×C₄₇	1	2	yes	complemented
197	C₈×Q₁₆	C₂×C₄₇	1	1	yes	characteristic, complemented
198	C₈×Q₁₆	C₂×C₄₇	1	1	yes	characteristic, complemented
199	C₂×C₄₇	—	16	2	no	—
200	C₂×C₄₇	#3285	1	1	yes	characteristic
201	C₂×C₄₇	#3287	1	1	yes	characteristic
202	C₂×C₄₇	#3290	1	1	yes	characteristic
203	#559	C₂²×C₄₇	1	2	yes	—
204	#557	C₂²×C₄₇	1	2	yes	—
205	#495	—	2	1	no	—
206	#494	—	2	1	no	—
207	#494	C₂²×C₄₇	1	1	yes	characteristic
208	#493	C₂²×C₄₇	1	1	yes	characteristic
209	#488	—	2	2	no	—
210	#486	C₂²×C₄₇	1	2	yes	—
211	#486	C₂²×C₄₇	1	2	yes	—
212	#478	—	2	2	no	—
213	#475	C₂²×C₄₇	1	2	yes	—
214	#464	—	2	2	no	—
215	#463	—	2	2	no	—
216	#462	—	2	2	no	—
217	#462	C₂²×C₄₇	1	2	yes	—
218	#460	C₂²×C₄₇	1	2	yes	—
219	#460	C₂²×C₄₇	1	2	yes	—
220	C₈×Q₈	C₂²×C₄₇	1	2	yes	—
221	C₈×Q₈	C₂²×C₄₇	1	1	yes	characteristic
222	C₈×Q₈	C₂²×C₄₇	1	1	yes	characteristic
223	C₄×Q₁₆	—	2	1	no	—
224	C₄×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
225	C₄×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
226	C₄×SD₁₆	—	2	2	no	—
227	C₄×D₈	—	2	1	no	—
228	#335	C₂²×C₄₇	1	1	yes	characteristic
229	#335	C₂²×C₄₇	1	1	yes	characteristic
230	#332	C₂²×C₄₇	1	2	yes	—
231	#331	C₂²×C₄₇	1	2	yes	—
232	Q₈⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
233	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
234	Q₈⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
235	C₈²	C₂²×C₄₇	1	1	yes	characteristic
236	C₄₇	#20015	1	1	yes	characteristic, direct product factor, Sylow
237	C₂×Q₁₆	—	2	2	no	—
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×Q₁₆	—	2	1	no	—
240	C₂×Q₁₆	D₄×C₄₇	1	1	yes	characteristic
241	C₂×Q₁₆	D₄×C₄₇	1	1	yes	characteristic
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×SD₁₆	—	2	2	no	—
244	C₂×D₈	—	2	1	no	—
245	C₂×D₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	2	no	—
247	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
248	#127	C₂³×C₄₇	1	2	yes	—
249	#125	—	2	2	no	—
250	#125	—	4	2	no	—
251	#124	—	2	2	no	—
252	#124	—	2	2	no	—
253	#123	—	4	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
257	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
258	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	2	2	no	—
261	#107	D₄×C₄₇	1	1	yes	characteristic
262	#107	D₄×C₄₇	1	1	yes	characteristic
263	#106	—	2	2	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
268	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
269	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
270	#103	—	2	2	no	—
271	#103	—	2	2	no	—
272	#103	D₄×C₄₇	1	1	yes	characteristic
273	#103	D₄×C₄₇	1	2	yes	—
274	#103	D₄×C₄₇	1	1	yes	characteristic
275	#102	—	2	2	no	—
276	#102	—	2	2	no	—
277	#102	—	2	2	no	—
278	#102	—	2	2	no	—
279	#102	—	4	2	no	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	—	2	2	no	—
282	C₄×C₈	—	2	1	no	—
283	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
288	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
289	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	Q₁₆	—	2	2	no	—
295	Q₁₆	—	2	2	no	—
296	Q₁₆	—	4	2	no	—
297	Q₁₆	—	8	1	no	—
298	Q₁₆	—	8	2	no	—
299	SD₁₆	—	4	4	no	—
300	SD₁₆	—	8	2	no	—
301	D₈	—	4	2	no	—
302	D₈	—	8	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
308	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
309	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
310	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
320	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
321	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	4	2	no	—
329	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
330	C₂³	—	4	2	no	—
331	Q₈	—	2	1	no	—
332	Q₈	—	2	2	no	—
333	Q₈	—	2	1	no	—
334	Q₈	—	2	2	no	—
335	Q₈	—	2	1	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	Q₈	#135×C₄₇	1	2	yes	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	8	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	16	2	no	—
352	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
353	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
354	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	—	4	1	no	—
359	C₈	—	4	2	no	—
360	C₈	—	4	1	no	—
361	C₈	—	4	1	no	—
362	C₈	#135×C₄₇	1	2	yes	—
363	C₂²	—	8	2	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	D₄²×C₄₇	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	2	2	no	—
369	C₄	—	4	2	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	1	no	—
373	C₄	—	4	1	no	—
374	C₄	—	8	2	no	—
375	C₄	C₂×#135×C₄₇	1	1	yes	characteristic
376	C₄	C₂×#135×C₄₇	1	1	yes	characteristic
377	C₄	C₄₇×#576	1	1	yes	characteristic
378	C₄	C₄₇×#578	1	1	yes	characteristic
379	C₂	—	16	2	no	—
380	C₂	C₄₇×#3285	1	1	yes	characteristic
381	C₂	C₄₇×#3287	1	1	yes	characteristic
382	C₂	C₄₇×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₇
prime radical	C₄₇×#493	C₂²
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
2. C₄₇×#3395	C₂	semidirect
3. C₄₇×#3365	C₂	semidirect
5. C₄₇×#1682	C₂	semidirect
6. C₄₇×#1670	C₂	semidirect
8. C₄₇×#1640	C₂	semidirect
9. C₄₇×#1626	C₂	semidirect
10. C₈×Q₁₆×C₄₇	C₂	semidirect
11. C₈×Q₁₆×C₄₇	C₂	semidirect
171. #20015	C₄₇	direct (N × H)
189. #3395	C₂×C₄₇	semidirect
190. #3365	C₂×C₄₇	semidirect
192. #1682	C₂×C₄₇	semidirect
193. #1670	C₂×C₄₇	semidirect
195. #1640	C₂×C₄₇	semidirect
196. #1626	C₂×C₄₇	semidirect
197. C₈×Q₁₆	C₂×C₄₇	semidirect
198. C₈×Q₁₆	C₂×C₄₇	semidirect
236. C₄₇	#20015	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#3396	2
C₄₇×#3395	2
C₄₇×#3365	2
C₄₇×#1709	2
C₄₇×#1682	2
C₄₇×#1670	2
C₄₇×#1668	2
C₄₇×#1640	2
C₄₇×#1626	2
C₈×Q₁₆×C₄₇	2
#20015	47

Subgroups — C47×#20015 #26059713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20015 #26059713