Subgroups — C₄₇×#17779 #26057477

Order 12032.

1112 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3499	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2990	C₂	1	2	yes	maximal, complemented
3	C₄₇×#1560	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1558	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1551	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1548	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1543	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#333	C₂	1	2	yes	maximal, complemented
9	C₂×2₋¹⁺⁴×C₄₇	C₄	1	2	yes	—
10	D₄×Q₈×C₄₇	—	2	2	no	—
11	C₄₇×#547	—	2	2	no	—
12	C₄₇×#547	—	2	4	no	—
13	C₄₇×#536	C₄	1	4	yes	—
14	C₄₇×#536	C₄	1	2	yes	—
15	C₄₇×#532	C₂²	1	1	yes	characteristic
16	C₄₇×#532	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
18	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#446	—	2	2	no	—
21	C₄₇×#435	—	2	4	no	—
22	C₈×D₄×C₄₇	—	2	2	no	—
23	C₄₇×#432	C₂²	1	4	yes	—
24	C₄₇×#431	C₂²	1	2	yes	—
25	C₄₇×#423	C₂²	1	2	yes	—
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	4	yes	—
27	C₄₇×#333	C₂²	1	1	yes	characteristic
28	C₄₇×#333	C₂²	1	4	yes	—
29	C₄₇×#333	C₂²	1	2	yes	—
30	C₄₇×#333	C₂²	1	1	yes	characteristic
31	C₄₇×#333	C₂²	1	4	yes	—
32	C₄₇×#331	C₂²	1	2	yes	—
33	C₄₇×#331	C₂²	1	2	yes	—
34	2₋¹⁺⁴×C₄₇	—	4	8	no	—
35	C₂×#41×C₄₇	—	2	4	no	—
36	C₂×#41×C₄₇	—	2	2	no	—
37	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
38	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
39	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂²×Q₈×C₄₇	—	2	2	no	—
41	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
42	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
43	C₂×M₁₆×C₄₇	—	2	2	no	—
44	C₂²×C₈×C₄₇	—	2	4	no	—
45	C₄⋊Q₈×C₄₇	—	2	2	no	—
46	C₄⋊Q₈×C₄₇	—	2	4	no	—
47	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
48	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
49	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
50	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
51	#127×C₄₇	C₂³	1	1	yes	characteristic
52	#124×C₄₇	C₂×C₄	1	2	yes	—
53	#124×C₄₇	C₂×C₄	1	4	yes	—
54	#123×C₄₇	—	2	4	no	—
55	#123×C₄₇	—	2	8	no	—
56	C₂²⋊Q₈×C₄₇	—	2	8	no	—
57	C₂²⋊Q₈×C₄₇	—	2	4	no	—
58	#121×C₄₇	—	2	4	no	—
59	#121×C₄₇	—	2	2	no	—
60	C₄×Q₈×C₄₇	D₄	1	2	yes	—
61	C₄×D₄×C₄₇	—	2	2	no	—
62	C₄×D₄×C₄₇	—	2	4	no	—
63	C₄×D₄×C₄₇	D₄	1	2	yes	—
64	C₄×D₄×C₄₇	D₄	1	4	yes	—
65	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
66	#117×C₄₇	C₂×C₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
70	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₄₇	—	2	4	no	—
72	C₄⋊C₈×C₄₇	—	2	2	no	—
73	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
74	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
75	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
76	C₂²⋊C₈×C₄₇	—	2	2	no	—
77	C₂²⋊C₈×C₄₇	—	2	4	no	—
78	#97×C₄₇	—	2	4	no	—
79	C₄×C₈×C₄₇	—	2	2	no	—
80	#41×C₄₇	—	2	4	no	—
81	#41×C₄₇	—	4	8	no	—
82	#41×C₄₇	—	4	4	no	—
83	#41×C₄₇	—	4	16	no	—
84	#41×C₄₇	—	4	8	no	—
85	C₂×Q₈×C₄₇	—	2	4	no	—
86	C₂×Q₈×C₄₇	—	2	2	no	—
87	C₂×Q₈×C₄₇	—	4	4	no	—
88	C₂×Q₈×C₄₇	—	4	8	no	—
89	C₂×Q₈×C₄₇	—	4	8	no	—
90	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
92	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂×D₄×C₄₇	—	2	2	no	—
94	C₂×D₄×C₄₇	—	2	4	no	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
97	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	4	no	—
101	C₂²×C₄×C₄₇	—	2	4	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
107	M₁₆×C₄₇	—	8	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	4	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	8	4	no	—
112	C₄⋊C₄×C₄₇	—	2	4	no	—
113	C₄⋊C₄×C₄₇	—	2	8	no	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	2	4	no	—
116	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
117	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
118	C₂²⋊C₄×C₄₇	—	2	4	no	—
119	C₂²⋊C₄×C₄₇	—	2	8	no	—
120	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
121	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
122	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
123	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₄₇	C₂×D₄	1	2	yes	—
125	C₄²×C₄₇	C₂×D₄	1	4	yes	—
126	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
127	C₂³×C₄₇	—	2	2	no	—
128	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
130	Q₈×C₄₇	—	2	2	no	—
131	Q₈×C₄₇	—	4	4	no	—
132	Q₈×C₄₇	—	4	2	no	—
133	Q₈×C₄₇	—	4	8	no	—
134	Q₈×C₄₇	—	4	4	no	—
135	D₄×C₄₇	—	2	4	no	—
136	D₄×C₄₇	—	4	2	no	—
137	D₄×C₄₇	—	4	4	no	—
138	D₄×C₄₇	—	4	8	no	—
139	D₄×C₄₇	—	4	2	no	—
140	D₄×C₄₇	—	4	2	no	—
141	D₄×C₄₇	#100	1	4	yes	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	4	8	no	—
151	C₂×C₄×C₄₇	—	4	4	no	—
152	C₂×C₄×C₄₇	—	4	8	no	—
153	C₂×C₄×C₄₇	—	4	4	no	—
154	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
156	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
160	C₈×C₄₇	—	4	2	no	—
161	C₈×C₄₇	—	4	4	no	—
162	C₈×C₄₇	—	4	2	no	—
163	#17779	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂²×C₄₇	—	2	4	no	—
165	C₂²×C₄₇	—	2	1	no	—
166	C₂²×C₄₇	—	2	2	no	—
167	C₂²×C₄₇	—	4	2	no	—
168	C₂²×C₄₇	—	4	4	no	—
169	C₂²×C₄₇	C₂×#100	1	4	yes	—
170	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
171	C₄×C₄₇	—	2	1	no	—
172	C₄×C₄₇	—	2	2	no	—
173	C₄×C₄₇	—	2	4	no	—
174	C₄×C₄₇	—	2	2	no	—
175	C₄×C₄₇	—	4	4	no	—
176	C₄×C₄₇	—	4	2	no	—
177	C₄×C₄₇	C₂×#100	1	2	yes	—
178	C₄×C₄₇	#577	1	2	yes	—
179	C₄×C₄₇	#578	1	2	yes	—
180	#3499	C₂×C₄₇	1	1	yes	characteristic
181	#2990	C₂×C₄₇	1	2	yes	complemented
182	#1560	C₂×C₄₇	1	1	yes	characteristic, complemented
183	#1558	C₂×C₄₇	1	2	yes	complemented
184	#1551	C₂×C₄₇	1	4	yes	complemented
185	#1548	C₂×C₄₇	1	2	yes	complemented
186	#1543	C₂×C₄₇	1	1	yes	characteristic, complemented
187	C₂×#333	C₂×C₄₇	1	2	yes	complemented
188	C₂×C₄₇	—	2	4	no	—
189	C₂×C₄₇	—	4	1	no	—
190	C₂×C₄₇	—	8	2	no	—
191	C₂×C₄₇	C₂²×#100	1	1	yes	characteristic
192	C₂×C₄₇	#2898	1	2	yes	—
193	C₂×2₋¹⁺⁴	C₄×C₄₇	1	2	yes	—
194	D₄×Q₈	—	2	2	no	—
195	#547	—	2	2	no	—
196	#547	—	2	4	no	—
197	#536	C₄×C₄₇	1	4	yes	—
198	#536	C₄×C₄₇	1	2	yes	—
199	#532	C₂²×C₄₇	1	1	yes	characteristic
200	#532	C₂²×C₄₇	1	2	yes	—
201	C₂×C₄⋊Q₈	C₂²×C₄₇	1	2	yes	—
202	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
203	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
204	#446	—	2	2	no	—
205	#435	—	2	4	no	—
206	C₈×D₄	—	2	2	no	—
207	#432	C₂²×C₄₇	1	4	yes	—
208	#431	C₂²×C₄₇	1	2	yes	—
209	#423	C₂²×C₄₇	1	2	yes	—
210	C₂×C₄⋊C₈	C₂²×C₄₇	1	4	yes	—
211	#333	C₂²×C₄₇	1	1	yes	characteristic
212	#333	C₂²×C₄₇	1	4	yes	—
213	#333	C₂²×C₄₇	1	2	yes	—
214	#333	C₂²×C₄₇	1	1	yes	characteristic
215	#333	C₂²×C₄₇	1	4	yes	—
216	#331	C₂²×C₄₇	1	2	yes	—
217	#331	C₂²×C₄₇	1	2	yes	—
218	C₄₇	#17779	1	1	yes	characteristic, direct product factor, Sylow
219	2₋¹⁺⁴	—	4	8	no	—
220	C₂×#41	—	2	4	no	—
221	C₂×#41	—	2	2	no	—
222	C₂×#41	C₂×C₄×C₄₇	1	4	yes	—
223	C₂×#41	C₂×C₄×C₄₇	1	2	yes	—
224	C₂×#41	C₂×C₄×C₄₇	1	1	yes	characteristic
225	C₂²×Q₈	—	2	2	no	—
226	C₂²×Q₈	C₂×C₄×C₄₇	1	2	yes	—
227	C₂²×Q₈	C₂×C₄×C₄₇	1	4	yes	—
228	C₂×M₁₆	—	2	2	no	—
229	C₂²×C₈	—	2	4	no	—
230	C₄⋊Q₈	—	2	2	no	—
231	C₄⋊Q₈	—	2	4	no	—
232	C₄⋊Q₈	C₂×C₄×C₄₇	1	4	yes	—
233	C₄⋊Q₈	C₂×C₄×C₄₇	1	2	yes	—
234	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
235	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
236	#127	C₂³×C₄₇	1	1	yes	characteristic
237	#124	C₂×C₄×C₄₇	1	2	yes	—
238	#124	C₂×C₄×C₄₇	1	4	yes	—
239	#123	—	2	4	no	—
240	#123	—	2	8	no	—
241	C₂²⋊Q₈	—	2	8	no	—
242	C₂²⋊Q₈	—	2	4	no	—
243	#121	—	2	4	no	—
244	#121	—	2	2	no	—
245	C₄×Q₈	D₄×C₄₇	1	2	yes	—
246	C₄×D₄	—	2	2	no	—
247	C₄×D₄	—	2	4	no	—
248	C₄×D₄	D₄×C₄₇	1	2	yes	—
249	C₄×D₄	D₄×C₄₇	1	4	yes	—
250	#117	C₂×C₄×C₄₇	1	1	yes	characteristic
251	#117	C₂×C₄×C₄₇	1	2	yes	—
252	C₂×C₄⋊C₄	—	2	4	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
255	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
256	C₄⋊C₈	—	2	4	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
259	C₄⋊C₈	C₂³×C₄₇	1	4	yes	—
260	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
261	C₂²⋊C₈	—	2	2	no	—
262	C₂²⋊C₈	—	2	4	no	—
263	#97	—	2	4	no	—
264	C₄×C₈	—	2	2	no	—
265	#41	—	2	4	no	—
266	#41	—	4	8	no	—
267	#41	—	4	4	no	—
268	#41	—	4	16	no	—
269	#41	—	4	8	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	4	4	no	—
273	C₂×Q₈	—	4	8	no	—
274	C₂×Q₈	—	4	8	no	—
275	C₂×Q₈	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
276	C₂×Q₈	C₂²×C₄×C₄₇	1	4	yes	—
277	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	C₂²⋊C₄×C₄₇	1	2	yes	—
282	C₂×D₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
283	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
289	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
291	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
292	M₁₆	—	8	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	8	4	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	8	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
302	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
303	C₂²⋊C₄	—	2	4	no	—
304	C₂²⋊C₄	—	2	8	no	—
305	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
306	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
307	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
308	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
309	C₄²	C₂×D₄×C₄₇	1	2	yes	—
310	C₄²	C₂×D₄×C₄₇	1	4	yes	—
311	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
312	C₂³	—	2	2	no	—
313	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
314	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
315	Q₈	—	2	2	no	—
316	Q₈	—	4	4	no	—
317	Q₈	—	4	2	no	—
318	Q₈	—	4	8	no	—
319	Q₈	—	4	4	no	—
320	D₄	—	2	4	no	—
321	D₄	—	4	2	no	—
322	D₄	—	4	4	no	—
323	D₄	—	4	8	no	—
324	D₄	—	4	2	no	—
325	D₄	—	4	2	no	—
326	D₄	#100×C₄₇	1	4	yes	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	4	8	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	4	8	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
340	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
341	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
342	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
343	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
345	C₈	—	4	2	no	—
346	C₈	—	4	4	no	—
347	C₈	—	4	2	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	4	2	no	—
352	C₂²	—	4	4	no	—
353	C₂²	C₂×#100×C₄₇	1	4	yes	—
354	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
355	C₄	—	2	1	no	—
356	C₄	—	2	2	no	—
357	C₄	—	2	4	no	—
358	C₄	—	2	2	no	—
359	C₄	—	4	4	no	—
360	C₄	—	4	2	no	—
361	C₄	C₂×#100×C₄₇	1	2	yes	—
362	C₄	C₄₇×#577	1	2	yes	—
363	C₄	C₄₇×#578	1	2	yes	—
364	C₂	—	2	4	no	—
365	C₂	—	4	1	no	—
366	C₂	—	8	2	no	—
367	C₂	C₂²×#100×C₄₇	1	1	yes	characteristic
368	C₂	C₄₇×#2898	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₄²	C₂⁴×C₄₇
prime radical	C₄₇×#3499	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₄×#41×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2990	C₂	semidirect
3. C₄₇×#1560	C₂	semidirect
4. C₄₇×#1558	C₂	semidirect
5. C₄₇×#1551	C₂	semidirect
6. C₄₇×#1548	C₂	semidirect
7. C₄₇×#1543	C₂	semidirect
8. C₂×C₄₇×#333	C₂	semidirect
163. #17779	C₄₇	direct (N × H)
181. #2990	C₂×C₄₇	semidirect
182. #1560	C₂×C₄₇	semidirect
183. #1558	C₂×C₄₇	semidirect
184. #1551	C₂×C₄₇	semidirect
185. #1548	C₂×C₄₇	semidirect
186. #1543	C₂×C₄₇	semidirect
187. C₂×#333	C₂×C₄₇	semidirect
218. C₄₇	#17779	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×#3499	2
C₄₇×#2990	2
C₄₇×#1560	2
C₄₇×#1558	2
C₄₇×#1551	2
C₄₇×#1548	2
C₄₇×#1543	2
C₂×C₄₇×#333	2
#17779	47

Subgroups — C47×#17779 #26057477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#17779 #26057477