Subgroups — C₄₇×#20856 #26060554

Order 12032.

1578 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#518	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2911	C₂	1	2	yes	maximal, complemented
3	C₂²×#100×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2309	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1856	C₂	1	8	yes	maximal, complemented
6	C₄₇×#1733	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
9	C₄₇×#518	—	2	2	no	—
10	C₄₇×#518	—	2	4	no	—
11	C₄₇×#518	C₂²	1	4	yes	—
12	C₂×C₄×D₄×C₄₇	—	2	4	no	—
13	C₂×#117×C₄₇	C₂²	1	2	yes	—
14	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₄₇	—	2	2	no	—
17	C₄₇×#428	—	2	4	no	—
18	C₄₇×#428	C₂²	1	8	yes	complemented
19	C₄₇×#427	—	2	4	no	—
20	C₂×#100×C₄₇	C₄	1	8	yes	complemented
21	C₂×#100×C₄₇	C₂²	1	4	yes	—
22	C₄₇×#390	—	2	2	no	—
23	C₄₇×#390	C₂²	1	4	yes	—
24	C₄₇×#379	—	2	2	no	—
25	C₄₇×#339	C₂²	1	8	yes	complemented
26	C₂⁵×C₄₇	D₄	1	2	yes	—
27	C₂²×D₄×C₄₇	—	2	2	no	—
28	C₂²×D₄×C₄₇	—	2	2	no	—
29	C₂²×D₄×C₄₇	—	2	4	no	—
30	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
31	C₂²×D₄×C₄₇	D₄	1	2	yes	—
32	C₂²×D₄×C₄₇	Q₈	1	4	yes	—
33	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
34	C₂³×C₄×C₄₇	—	2	4	no	—
35	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₄₇	—	2	2	no	—
37	C₂×M₁₆×C₄₇	—	2	4	no	—
38	C₂×M₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
39	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
40	C₂²×C₈×C₄₇	—	2	2	no	—
41	C₄×D₄×C₄₇	—	2	16	no	—
42	C₄×D₄×C₄₇	—	2	16	no	—
43	#117×C₄₇	—	2	2	no	—
44	#117×C₄₇	—	2	2	no	—
45	#117×C₄₇	—	2	4	no	—
46	#117×C₄₇	—	2	2	no	—
47	#117×C₄₇	—	2	2	no	—
48	#117×C₄₇	D₄	1	4	yes	—
49	#117×C₄₇	C₂³	1	4	yes	—
50	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
52	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
53	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
54	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
55	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
57	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
60	C₂×C₄²×C₄₇	—	2	2	no	—
61	C₂×C₄²×C₄₇	—	2	1	no	—
62	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
63	#107×C₄₇	—	2	8	no	—
64	#106×C₄₇	—	2	8	no	—
65	#100×C₄₇	C₂×C₄	1	16	yes	complemented
66	C₂⁴×C₄₇	—	2	2	no	—
67	C₂⁴×C₄₇	—	2	2	no	—
68	C₂⁴×C₄₇	—	2	4	no	—
69	C₂⁴×C₄₇	—	8	4	no	—
70	C₂⁴×C₄₇	C₄⋊C₄	1	8	yes	—
71	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
72	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
73	C₂×D₄×C₄₇	—	2	8	no	—
74	C₂×D₄×C₄₇	—	2	8	no	—
75	C₂×D₄×C₄₇	—	2	4	no	—
76	C₂×D₄×C₄₇	—	2	8	no	—
77	C₂×D₄×C₄₇	—	2	8	no	—
78	C₂×D₄×C₄₇	—	2	4	no	—
79	C₂×D₄×C₄₇	—	2	4	no	—
80	C₂×D₄×C₄₇	—	2	4	no	—
81	C₂×D₄×C₄₇	C₄⋊C₄	1	8	yes	—
82	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
83	C₂×D₄×C₄₇	C₂×Q₈	1	4	yes	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	16	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	8	8	no	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₄₇	#41	1	4	yes	—
95	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
96	M₁₆×C₄₇	—	2	8	no	—
97	M₁₆×C₄₇	—	2	4	no	—
98	M₁₆×C₄₇	C₂²×C₄	1	8	yes	complemented
99	C₂×C₈×C₄₇	—	2	8	no	—
100	C₂×C₈×C₄₇	—	2	4	no	—
101	C₄⋊C₄×C₄₇	—	2	4	no	—
102	C₄⋊C₄×C₄₇	—	2	4	no	—
103	C₄⋊C₄×C₄₇	—	4	2	no	—
104	C₄⋊C₄×C₄₇	C₂×D₄	1	8	yes	—
105	C₂²⋊C₄×C₄₇	—	2	16	no	—
106	C₂²⋊C₄×C₄₇	—	2	4	no	—
107	C₂²⋊C₄×C₄₇	—	2	4	no	—
108	C₂²⋊C₄×C₄₇	—	4	1	no	—
109	C₂²⋊C₄×C₄₇	—	4	1	no	—
110	C₂²⋊C₄×C₄₇	—	4	2	no	—
111	C₂²⋊C₄×C₄₇	—	8	8	no	—
112	C₄²×C₄₇	—	2	4	no	—
113	C₄²×C₄₇	—	2	4	no	—
114	C₄²×C₄₇	—	2	4	no	—
115	C₄²×C₄₇	—	4	2	no	—
116	C₂³×C₄₇	—	2	4	no	—
117	C₂³×C₄₇	—	2	8	no	—
118	C₂³×C₄₇	—	2	4	no	—
119	C₂³×C₄₇	—	2	8	no	—
120	C₂³×C₄₇	—	4	2	no	—
121	C₂³×C₄₇	—	4	8	no	—
122	C₂³×C₄₇	—	4	8	no	—
123	C₂³×C₄₇	—	8	4	no	—
124	C₂³×C₄₇	—	8	8	no	—
125	C₂³×C₄₇	—	8	8	no	—
126	C₂³×C₄₇	C₂×C₄⋊C₄	1	8	yes	—
127	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
128	C₂³×C₄₇	#120	1	1	yes	characteristic
129	C₂³×C₄₇	#120	1	1	yes	characteristic
130	C₂³×C₄₇	#123	1	2	yes	—
131	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
132	D₄×C₄₇	—	2	8	no	—
133	D₄×C₄₇	—	2	8	no	—
134	D₄×C₄₇	—	2	16	no	—
135	C₂×C₄×C₄₇	—	2	8	no	—
136	C₂×C₄×C₄₇	—	4	8	no	—
137	C₂×C₄×C₄₇	—	4	4	no	—
138	C₂×C₄×C₄₇	—	4	4	no	—
139	C₂×C₄×C₄₇	—	4	2	no	—
140	C₂×C₄×C₄₇	—	4	2	no	—
141	C₂×C₄×C₄₇	—	8	16	no	—
142	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
144	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
145	C₂×C₄×C₄₇	#120	1	2	yes	—
146	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
147	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
148	C₂×C₄×C₄₇	#123	1	2	yes	—
149	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
153	C₈×C₄₇	—	2	8	no	—
154	#20856	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂²×C₄₇	—	2	2	no	—
156	C₂²×C₄₇	—	2	2	no	—
157	C₂²×C₄₇	—	2	2	no	—
158	C₂²×C₄₇	—	2	8	no	—
159	C₂²×C₄₇	—	4	2	no	—
160	C₂²×C₄₇	—	4	2	no	—
161	C₂²×C₄₇	—	4	8	no	—
162	C₂²×C₄₇	—	4	16	no	—
163	C₂²×C₄₇	—	4	8	no	—
164	C₂²×C₄₇	—	8	4	no	—
165	C₂²×C₄₇	—	8	8	no	—
166	C₂²×C₄₇	#385	1	2	yes	—
167	C₂²×C₄₇	#385	1	2	yes	—
168	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
169	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
170	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
171	C₄×C₄₇	—	4	8	no	—
172	C₄×C₄₇	—	8	2	no	—
173	C₄×C₄₇	—	8	2	no	—
174	C₄×C₄₇	#385	1	4	yes	—
175	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
176	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
177	C₂×#518	C₂×C₄₇	1	1	yes	characteristic
178	#2911	C₂×C₄₇	1	2	yes	complemented
179	C₂²×#100	C₂×C₄₇	1	1	yes	characteristic
180	#2309	C₂×C₄₇	1	1	yes	characteristic
181	#1856	C₂×C₄₇	1	8	yes	complemented
182	#1733	C₂×C₄₇	1	2	yes	complemented
183	C₂×C₄₇	—	2	1	no	—
184	C₂×C₄₇	—	2	1	no	—
185	C₂×C₄₇	—	2	2	no	—
186	C₂×C₄₇	—	2	2	no	—
187	C₂×C₄₇	—	4	8	no	—
188	C₂×C₄₇	C₂×#385	1	1	yes	characteristic
189	C₂×C₄₇	#3019	1	2	yes	—
190	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
191	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
192	#518	—	2	2	no	—
193	#518	—	2	4	no	—
194	#518	C₂²×C₄₇	1	4	yes	—
195	C₂×C₄×D₄	—	2	4	no	—
196	C₂×#117	C₂²×C₄₇	1	2	yes	—
197	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
198	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
199	C₂²×C₂²⋊C₄	—	2	2	no	—
200	#428	—	2	4	no	—
201	#428	C₂²×C₄₇	1	8	yes	complemented
202	#427	—	2	4	no	—
203	C₂×#100	C₄×C₄₇	1	8	yes	complemented
204	C₂×#100	C₂²×C₄₇	1	4	yes	—
205	#390	—	2	2	no	—
206	#390	C₂²×C₄₇	1	4	yes	—
207	#379	—	2	2	no	—
208	#339	C₂²×C₄₇	1	8	yes	complemented
209	C₄₇	#20856	1	1	yes	characteristic, direct product factor, Sylow
210	C₂⁵	D₄×C₄₇	1	2	yes	—
211	C₂²×D₄	—	2	2	no	—
212	C₂²×D₄	—	2	2	no	—
213	C₂²×D₄	—	2	4	no	—
214	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	—
215	C₂²×D₄	D₄×C₄₇	1	2	yes	—
216	C₂²×D₄	Q₈×C₄₇	1	4	yes	—
217	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
218	C₂³×C₄	—	2	4	no	—
219	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	2	4	no	—
222	C₂×M₁₆	C₂×C₄×C₄₇	1	8	yes	complemented
223	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
224	C₂²×C₈	—	2	2	no	—
225	C₄×D₄	—	2	16	no	—
226	C₄×D₄	—	2	16	no	—
227	#117	—	2	2	no	—
228	#117	—	2	2	no	—
229	#117	—	2	4	no	—
230	#117	—	2	2	no	—
231	#117	—	2	2	no	—
232	#117	D₄×C₄₇	1	4	yes	—
233	#117	C₂³×C₄₇	1	4	yes	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	—
236	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
237	C₂×C₂²⋊C₄	—	2	4	no	—
238	C₂×C₂²⋊C₄	—	2	8	no	—
239	C₂×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₂²⋊C₄	—	2	8	no	—
241	C₂×C₂²⋊C₄	—	2	1	no	—
242	C₂×C₂²⋊C₄	—	2	1	no	—
243	C₂×C₂²⋊C₄	—	2	8	no	—
244	C₂×C₄²	—	2	2	no	—
245	C₂×C₄²	—	2	1	no	—
246	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
247	#107	—	2	8	no	—
248	#106	—	2	8	no	—
249	#100	C₂×C₄×C₄₇	1	16	yes	complemented
250	C₂⁴	—	2	2	no	—
251	C₂⁴	—	2	2	no	—
252	C₂⁴	—	2	4	no	—
253	C₂⁴	—	8	4	no	—
254	C₂⁴	C₄⋊C₄×C₄₇	1	8	yes	—
255	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
256	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
257	C₂×D₄	—	2	8	no	—
258	C₂×D₄	—	2	8	no	—
259	C₂×D₄	—	2	4	no	—
260	C₂×D₄	—	2	8	no	—
261	C₂×D₄	—	2	8	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	C₄⋊C₄×C₄₇	1	8	yes	—
266	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
267	C₂×D₄	C₂×Q₈×C₄₇	1	4	yes	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	16	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	8	8	no	—
273	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
274	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
277	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
278	C₂²×C₄	#41×C₄₇	1	4	yes	—
279	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
280	M₁₆	—	2	8	no	—
281	M₁₆	—	2	4	no	—
282	M₁₆	C₂²×C₄×C₄₇	1	8	yes	complemented
283	C₂×C₈	—	2	8	no	—
284	C₂×C₈	—	2	4	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	4	2	no	—
288	C₄⋊C₄	C₂×D₄×C₄₇	1	8	yes	—
289	C₂²⋊C₄	—	2	16	no	—
290	C₂²⋊C₄	—	2	4	no	—
291	C₂²⋊C₄	—	2	4	no	—
292	C₂²⋊C₄	—	4	1	no	—
293	C₂²⋊C₄	—	4	1	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₂²⋊C₄	—	8	8	no	—
296	C₄²	—	2	4	no	—
297	C₄²	—	2	4	no	—
298	C₄²	—	2	4	no	—
299	C₄²	—	4	2	no	—
300	C₂³	—	2	4	no	—
301	C₂³	—	2	8	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	8	no	—
304	C₂³	—	4	2	no	—
305	C₂³	—	4	8	no	—
306	C₂³	—	4	8	no	—
307	C₂³	—	8	4	no	—
308	C₂³	—	8	8	no	—
309	C₂³	—	8	8	no	—
310	C₂³	C₂×C₄⋊C₄×C₄₇	1	8	yes	—
311	C₂³	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
312	C₂³	#120×C₄₇	1	1	yes	characteristic
313	C₂³	#120×C₄₇	1	1	yes	characteristic
314	C₂³	#123×C₄₇	1	2	yes	—
315	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
316	D₄	—	2	8	no	—
317	D₄	—	2	8	no	—
318	D₄	—	2	16	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	4	8	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	8	16	no	—
326	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
327	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
328	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
329	C₂×C₄	#120×C₄₇	1	2	yes	—
330	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
331	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
332	C₂×C₄	#123×C₄₇	1	2	yes	—
333	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
334	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
335	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
336	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
337	C₈	—	2	8	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	8	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	8	no	—
345	C₂²	—	4	16	no	—
346	C₂²	—	4	8	no	—
347	C₂²	—	8	4	no	—
348	C₂²	—	8	8	no	—
349	C₂²	C₄₇×#385	1	2	yes	—
350	C₂²	C₄₇×#385	1	2	yes	—
351	C₂²	C₂²×C₄⋊C₄×C₄₇	1	1	yes	characteristic
352	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
353	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
354	C₄	—	4	8	no	—
355	C₄	—	8	2	no	—
356	C₄	—	8	2	no	—
357	C₄	C₄₇×#385	1	4	yes	—
358	C₄	C₂×C₄×D₄×C₄₇	1	2	yes	—
359	C₄	C₂×C₂²⋊Q₈×C₄₇	1	2	yes	—
360	C₂	—	2	1	no	—
361	C₂	—	2	1	no	—
362	C₂	—	2	2	no	—
363	C₂	—	2	2	no	—
364	C₂	—	4	8	no	—
365	C₂	C₂×C₄₇×#385	1	1	yes	characteristic
366	C₂	C₄₇×#3019	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2911	C₂	semidirect
5. C₄₇×#1856	C₂	semidirect
6. C₄₇×#1733	C₂	semidirect
18. C₄₇×#428	C₂²	semidirect
20. C₂×#100×C₄₇	C₄	semidirect
25. C₄₇×#339	C₂²	semidirect
38. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
65. #100×C₄₇	C₂×C₄	semidirect
98. M₁₆×C₄₇	C₂²×C₄	semidirect
154. #20856	C₄₇	direct (N × H)
178. #2911	C₂×C₄₇	semidirect
181. #1856	C₂×C₄₇	semidirect
182. #1733	C₂×C₄₇	semidirect
201. #428	C₂²×C₄₇	semidirect
203. C₂×#100	C₄×C₄₇	semidirect
208. #339	C₂²×C₄₇	semidirect
209. C₄₇	#20856	direct (N × H)
222. C₂×M₁₆	C₂×C₄×C₄₇	semidirect
249. #100	C₂×C₄×C₄₇	semidirect
282. M₁₆	C₂²×C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#518	2
C₄₇×#2911	2
C₂²×#100×C₄₇	2
C₄₇×#2309	2
C₄₇×#1856	2
C₄₇×#1733	2
#20856	47

Subgroups — C47×#20856 #26060554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20856 #26060554