Subgroups — C₄₇×#20392 #26060090

Order 12032.

1834 conjugacy classes of subgroups.

The subgroup lattice has 352 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	C₂²×#99×C₄₇	C₂	1	2	yes	maximal
3	C₄₇×#2273	C₂	1	2	yes	maximal, complemented
4	C₄×#99×C₄₇	C₂	1	8	yes	maximal, complemented
5	C₂×C₄₇×#342	C₂	1	2	yes	maximal, complemented
6	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₄₇×#518	—	2	8	no	—
8	C₂×C₄×D₄×C₄₇	C₄	1	4	yes	complemented
9	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	—
10	C₂×#117×C₄₇	C₄	1	2	yes	complemented
11	C₂²×C₂²⋊C₄×C₄₇	C₄	1	2	yes	complemented
12	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
14	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#99×C₄₇	C₄	1	16	yes	complemented
16	C₂×#99×C₄₇	C₂²	1	8	yes	—
17	C₄×C₂²⋊C₄×C₄₇	—	2	8	no	—
18	C₄×C₂²⋊C₄×C₄₇	C₂²	1	8	yes	complemented
19	C₄₇×#342	C₂²	1	8	yes	complemented
20	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
21	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
22	C₂²×D₄×C₄₇	—	2	4	no	—
23	C₂²×D₄×C₄₇	—	2	4	no	—
24	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
25	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
26	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
27	C₂³×C₄×C₄₇	—	2	4	no	—
28	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
30	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	complemented
31	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
32	C₄×D₄×C₄₇	—	2	16	no	—
33	C₄×D₄×C₄₇	—	2	16	no	—
34	#117×C₄₇	—	2	8	no	—
35	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	complemented
36	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
37	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
38	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
39	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
40	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
41	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
42	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
43	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	complemented
44	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	complemented
45	C₂×C₂²⋊C₄×C₄₇	D₄	1	8	yes	—
46	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
47	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
48	C₂×C₄²×C₄₇	—	2	8	no	—
49	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	complemented
50	#99×C₄₇	C₂×C₄	1	32	yes	complemented
51	#95×C₄₇	—	2	8	no	—
52	C₂⁴×C₄₇	—	2	2	no	—
53	C₂⁴×C₄₇	—	2	2	no	—
54	C₂⁴×C₄₇	—	8	2	no	—
55	C₂⁴×C₄₇	—	8	2	no	—
56	C₂⁴×C₄₇	C₄²	1	4	yes	complemented
57	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
58	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
59	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
60	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
61	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
62	C₂⁴×C₄₇	#41	1	4	yes	—
63	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
64	C₂×D₄×C₄₇	—	2	4	no	—
65	C₂×D₄×C₄₇	—	2	4	no	—
66	C₂×D₄×C₄₇	—	2	16	no	—
67	C₂×D₄×C₄₇	—	2	16	no	—
68	C₂×D₄×C₄₇	—	2	4	no	—
69	C₂×D₄×C₄₇	—	2	4	no	—
70	C₂×D₄×C₄₇	C₄²	1	8	yes	complemented
71	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	—	2	8	no	—
75	C₂²×C₄×C₄₇	—	2	4	no	—
76	C₂²×C₄×C₄₇	—	2	16	no	—
77	C₂²×C₄×C₄₇	—	2	8	no	—
78	C₂²×C₄×C₄₇	—	8	2	no	—
79	C₂²×C₄×C₄₇	—	8	8	no	—
80	C₂²×C₄×C₄₇	—	8	2	no	—
81	C₂²×C₄×C₄₇	—	8	4	no	—
82	C₂²×C₄×C₄₇	C₄²	1	4	yes	complemented
83	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
87	C₄⋊C₄×C₄₇	—	2	8	no	—
88	C₂²⋊C₄×C₄₇	—	2	4	no	—
89	C₂²⋊C₄×C₄₇	—	2	16	no	—
90	C₂²⋊C₄×C₄₇	—	2	4	no	—
91	C₂²⋊C₄×C₄₇	—	2	8	no	—
92	C₂²⋊C₄×C₄₇	—	2	8	no	—
93	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
94	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
95	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
96	C₄²×C₄₇	—	2	8	no	—
97	C₄²×C₄₇	—	8	8	no	—
98	C₂³×C₄₇	—	2	2	no	—
99	C₂³×C₄₇	—	2	2	no	—
100	C₂³×C₄₇	—	2	8	no	—
101	C₂³×C₄₇	—	4	2	no	—
102	C₂³×C₄₇	—	4	8	no	—
103	C₂³×C₄₇	—	4	2	no	—
104	C₂³×C₄₇	—	4	2	no	—
105	C₂³×C₄₇	—	4	4	no	—
106	C₂³×C₄₇	—	8	4	no	—
107	C₂³×C₄₇	—	8	4	no	—
108	C₂³×C₄₇	—	8	4	no	—
109	C₂³×C₄₇	—	8	4	no	—
110	C₂³×C₄₇	—	8	4	no	—
111	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
112	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
113	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
114	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
115	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
116	C₂³×C₄₇	#117	1	2	yes	—
117	C₂³×C₄₇	#117	1	2	yes	—
118	C₂³×C₄₇	C₄×D₄	1	8	yes	—
119	C₂³×C₄₇	C₄×D₄	1	8	yes	—
120	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
121	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
122	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
123	C₂³×C₄₇	C₂×#41	1	2	yes	—
124	D₄×C₄₇	—	2	16	no	—
125	D₄×C₄₇	—	2	16	no	—
126	C₂×C₄×C₄₇	—	2	2	no	—
127	C₂×C₄×C₄₇	—	2	2	no	—
128	C₂×C₄×C₄₇	—	2	8	no	—
129	C₂×C₄×C₄₇	—	2	4	no	—
130	C₂×C₄×C₄₇	—	2	16	no	—
131	C₂×C₄×C₄₇	—	4	8	no	—
132	C₂×C₄×C₄₇	—	4	4	no	—
133	C₂×C₄×C₄₇	—	4	16	no	—
134	C₂×C₄×C₄₇	—	4	4	no	—
135	C₂×C₄×C₄₇	—	8	8	no	—
136	C₂×C₄×C₄₇	—	8	4	no	—
137	C₂×C₄×C₄₇	—	8	16	no	—
138	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
139	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
140	#20392	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂²×C₄₇	—	2	4	no	—
142	C₂²×C₄₇	—	2	2	no	—
143	C₂²×C₄₇	—	2	4	no	—
144	C₂²×C₄₇	—	2	4	no	—
145	C₂²×C₄₇	—	2	4	no	—
146	C₂²×C₄₇	—	4	8	no	—
147	C₂²×C₄₇	—	4	2	no	—
148	C₂²×C₄₇	—	4	2	no	—
149	C₂²×C₄₇	—	4	2	no	—
150	C₂²×C₄₇	—	4	2	no	—
151	C₂²×C₄₇	—	4	8	no	—
152	C₂²×C₄₇	—	4	2	no	—
153	C₂²×C₄₇	—	4	2	no	—
154	C₂²×C₄₇	—	4	4	no	—
155	C₂²×C₄₇	—	4	4	no	—
156	C₂²×C₄₇	—	4	4	no	—
157	C₂²×C₄₇	—	8	8	no	—
158	C₂²×C₄₇	C₄×C₂²⋊C₄	1	4	yes	—
159	C₂²×C₄₇	C₄×C₂²⋊C₄	1	4	yes	—
160	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
161	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
163	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
164	C₄×C₄₇	—	2	8	no	—
165	C₄×C₄₇	—	2	4	no	—
166	C₄×C₄₇	—	4	16	no	—
167	C₄×C₄₇	—	4	4	no	—
168	C₂×#518	C₂×C₄₇	1	1	yes	characteristic
169	C₂²×#99	C₂×C₄₇	1	2	yes	—
170	#2273	C₂×C₄₇	1	2	yes	complemented
171	C₄×#99	C₂×C₄₇	1	8	yes	complemented
172	C₂×#342	C₂×C₄₇	1	2	yes	complemented
173	C₂×C₄₇	—	2	4	no	—
174	C₂×C₄₇	—	2	1	no	—
175	C₂×C₄₇	—	2	1	no	—
176	C₂×C₄₇	—	2	4	no	—
177	C₂×C₄₇	—	2	4	no	—
178	C₂×C₄₇	—	4	4	no	—
179	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₄₇	#2883	1	2	yes	—
181	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
182	#518	—	2	8	no	—
183	C₂×C₄×D₄	C₄×C₄₇	1	4	yes	complemented
184	C₂×C₄×D₄	C₂²×C₄₇	1	4	yes	—
185	C₂×#117	C₄×C₄₇	1	2	yes	complemented
186	C₂²×C₂²⋊C₄	C₄×C₄₇	1	2	yes	complemented
187	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
188	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
189	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
190	C₂×#99	C₄×C₄₇	1	16	yes	complemented
191	C₂×#99	C₂²×C₄₇	1	8	yes	—
192	C₄×C₂²⋊C₄	—	2	8	no	—
193	C₄×C₂²⋊C₄	C₂²×C₄₇	1	8	yes	complemented
194	#342	C₂²×C₄₇	1	8	yes	complemented
195	C₄₇	#20392	1	1	yes	characteristic, direct product factor, Sylow
196	C₂⁵	C₂×C₄×C₄₇	1	1	yes	characteristic
197	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
198	C₂²×D₄	—	2	4	no	—
199	C₂²×D₄	—	2	4	no	—
200	C₂²×D₄	C₂×C₄×C₄₇	1	8	yes	—
201	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
202	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
203	C₂³×C₄	—	2	4	no	—
204	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
205	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
206	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	complemented
207	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
208	C₄×D₄	—	2	16	no	—
209	C₄×D₄	—	2	16	no	—
210	#117	—	2	8	no	—
211	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	complemented
212	C₂×C₂²⋊C₄	—	2	4	no	—
213	C₂×C₂²⋊C₄	—	2	4	no	—
214	C₂×C₂²⋊C₄	—	2	8	no	—
215	C₂×C₂²⋊C₄	—	2	8	no	—
216	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
217	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
218	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
219	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	complemented
220	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	16	yes	complemented
221	C₂×C₂²⋊C₄	D₄×C₄₇	1	8	yes	—
222	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
223	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
224	C₂×C₄²	—	2	8	no	—
225	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	complemented
226	#99	C₂×C₄×C₄₇	1	32	yes	complemented
227	#95	—	2	8	no	—
228	C₂⁴	—	2	2	no	—
229	C₂⁴	—	2	2	no	—
230	C₂⁴	—	8	2	no	—
231	C₂⁴	—	8	2	no	—
232	C₂⁴	C₄²×C₄₇	1	4	yes	complemented
233	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
234	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
235	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
236	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
237	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
238	C₂⁴	#41×C₄₇	1	4	yes	—
239	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
240	C₂×D₄	—	2	4	no	—
241	C₂×D₄	—	2	4	no	—
242	C₂×D₄	—	2	16	no	—
243	C₂×D₄	—	2	16	no	—
244	C₂×D₄	—	2	4	no	—
245	C₂×D₄	—	2	4	no	—
246	C₂×D₄	C₄²×C₄₇	1	8	yes	complemented
247	C₂×D₄	C₂²×C₄×C₄₇	1	8	yes	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	8	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	16	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	8	2	no	—
255	C₂²×C₄	—	8	8	no	—
256	C₂²×C₄	—	8	2	no	—
257	C₂²×C₄	—	8	4	no	—
258	C₂²×C₄	C₄²×C₄₇	1	4	yes	complemented
259	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
260	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
261	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
262	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
263	C₄⋊C₄	—	2	8	no	—
264	C₂²⋊C₄	—	2	4	no	—
265	C₂²⋊C₄	—	2	16	no	—
266	C₂²⋊C₄	—	2	4	no	—
267	C₂²⋊C₄	—	2	8	no	—
268	C₂²⋊C₄	—	2	8	no	—
269	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	8	yes	—
270	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	8	yes	—
271	C₂²⋊C₄	C₂²×C₄×C₄₇	1	16	yes	—
272	C₄²	—	2	8	no	—
273	C₄²	—	8	8	no	—
274	C₂³	—	2	2	no	—
275	C₂³	—	2	2	no	—
276	C₂³	—	2	8	no	—
277	C₂³	—	4	2	no	—
278	C₂³	—	4	8	no	—
279	C₂³	—	4	2	no	—
280	C₂³	—	4	2	no	—
281	C₂³	—	4	4	no	—
282	C₂³	—	8	4	no	—
283	C₂³	—	8	4	no	—
284	C₂³	—	8	4	no	—
285	C₂³	—	8	4	no	—
286	C₂³	—	8	4	no	—
287	C₂³	C₂×C₄²×C₄₇	1	4	yes	—
288	C₂³	C₂×C₄²×C₄₇	1	2	yes	—
289	C₂³	C₂×C₄²×C₄₇	1	2	yes	—
290	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
291	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
292	C₂³	#117×C₄₇	1	2	yes	—
293	C₂³	#117×C₄₇	1	2	yes	—
294	C₂³	C₄×D₄×C₄₇	1	8	yes	—
295	C₂³	C₄×D₄×C₄₇	1	8	yes	—
296	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
297	C₂³	C₂³×C₄×C₄₇	1	2	yes	—
298	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
299	C₂³	C₂×#41×C₄₇	1	2	yes	—
300	D₄	—	2	16	no	—
301	D₄	—	2	16	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	16	no	—
307	C₂×C₄	—	4	8	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	—	4	16	no	—
310	C₂×C₄	—	4	4	no	—
311	C₂×C₄	—	8	8	no	—
312	C₂×C₄	—	8	4	no	—
313	C₂×C₄	—	8	16	no	—
314	C₂×C₄	C₂×C₄²×C₄₇	1	4	yes	—
315	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	8	yes	—
316	C₂²	—	2	4	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	4	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	4	no	—
321	C₂²	—	4	8	no	—
322	C₂²	—	4	2	no	—
323	C₂²	—	4	2	no	—
324	C₂²	—	4	2	no	—
325	C₂²	—	4	2	no	—
326	C₂²	—	4	8	no	—
327	C₂²	—	4	2	no	—
328	C₂²	—	4	2	no	—
329	C₂²	—	4	4	no	—
330	C₂²	—	4	4	no	—
331	C₂²	—	4	4	no	—
332	C₂²	—	8	8	no	—
333	C₂²	C₄×C₂²⋊C₄×C₄₇	1	4	yes	—
334	C₂²	C₄×C₂²⋊C₄×C₄₇	1	4	yes	—
335	C₂²	C₂²×C₄²×C₄₇	1	1	yes	characteristic
336	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
337	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
338	C₂²	C₂×C₄×D₄×C₄₇	1	4	yes	—
339	C₄	—	2	4	no	—
340	C₄	—	2	8	no	—
341	C₄	—	4	16	no	—
342	C₄	—	4	4	no	—
343	C₂	—	2	4	no	—
344	C₂	—	2	1	no	—
345	C₂	—	2	1	no	—
346	C₂	—	2	4	no	—
347	C₂	—	2	4	no	—
348	C₂	—	4	4	no	—
349	C₂	C₂×C₄×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
350	C₂	C₄₇×#2883	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
commutator	C₂²	C₂²×C₄²×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂²×C₂²⋊C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₇×#2273	C₂	semidirect
4. C₄×#99×C₄₇	C₂	semidirect
5. C₂×C₄₇×#342	C₂	semidirect
8. C₂×C₄×D₄×C₄₇	C₄	semidirect
10. C₂×#117×C₄₇	C₄	semidirect
11. C₂²×C₂²⋊C₄×C₄₇	C₄	semidirect
15. C₂×#99×C₄₇	C₄	semidirect
18. C₄×C₂²⋊C₄×C₄₇	C₂²	semidirect
19. C₄₇×#342	C₂²	semidirect
30. C₂³×C₄×C₄₇	C₂×C₄	semidirect
35. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
43. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
44. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
49. C₂×C₄²×C₄₇	C₂×C₄	semidirect
50. #99×C₄₇	C₂×C₄	semidirect
56. C₂⁴×C₄₇	C₄²	semidirect
70. C₂×D₄×C₄₇	C₄²	semidirect
82. C₂²×C₄×C₄₇	C₄²	semidirect
140. #20392	C₄₇	direct (N × H)
170. #2273	C₂×C₄₇	semidirect
171. C₄×#99	C₂×C₄₇	semidirect
172. C₂×#342	C₂×C₄₇	semidirect
183. C₂×C₄×D₄	C₄×C₄₇	semidirect
185. C₂×#117	C₄×C₄₇	semidirect
186. C₂²×C₂²⋊C₄	C₄×C₄₇	semidirect
190. C₂×#99	C₄×C₄₇	semidirect
193. C₄×C₂²⋊C₄	C₂²×C₄₇	semidirect
194. #342	C₂²×C₄₇	semidirect
195. C₄₇	#20392	direct (N × H)
206. C₂³×C₄	C₂×C₄×C₄₇	semidirect
211. C₂×C₄⋊C₄	C₂×C₄×C₄₇	semidirect
219. C₂×C₂²⋊C₄	C₂×C₄×C₄₇	semidirect
220. C₂×C₂²⋊C₄	C₂×C₄×C₄₇	semidirect
225. C₂×C₄²	C₂×C₄×C₄₇	semidirect
226. #99	C₂×C₄×C₄₇	semidirect
232. C₂⁴	C₄²×C₄₇	semidirect
246. C₂×D₄	C₄²×C₄₇	semidirect
258. C₂²×C₄	C₄²×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
C₂²×#99×C₄₇	2
C₄₇×#2273	2
C₄×#99×C₄₇	2
C₂×C₄₇×#342	2
#20392	47

Subgroups — C47×#20392 #26060090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20392 #26060090