Subgroups — C₄₇×#60722 #26100420

Order 12032.

2006 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3184	C₂	1	2	yes	maximal, complemented
4	C₄₇×#3182	C₂	1	2	yes	maximal, complemented
5	C₄₇×#3179	C₂	1	8	yes	maximal, complemented
6	C₄₇×#3169	C₂	1	2	yes	maximal, complemented
7	C₄₇×#3167	C₂	1	2	yes	maximal, complemented
8	C₄₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#3151	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#486	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#3062	C₂	1	4	yes	maximal, complemented
13	C₄₇×#2946	C₂	1	4	yes	maximal, complemented
14	C₄×#131×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	4	yes	—
16	C₂×#131×C₄₇	C₂²	1	2	yes	—
17	C₄₇×#559	—	2	1	no	—
18	C₄₇×#559	—	2	1	no	—
19	C₄₇×#556	—	2	1	no	—
20	C₄₇×#555	—	2	1	no	—
21	C₄₇×#554	—	2	1	no	—
22	C₄₇×#553	—	2	2	no	—
23	C₄₇×#550	—	2	1	no	—
24	C₄₇×#550	—	2	1	no	—
25	C₄₇×#548	—	2	2	no	—
26	C₄₇×#547	—	2	1	no	—
27	C₄₇×#546	—	2	2	no	—
28	C₄₇×#546	—	2	2	no	—
29	C₄₇×#542	C₂²	1	4	yes	complemented
30	C₄₇×#540	C₂²	1	4	yes	—
31	C₄₇×#537	C₂²	1	2	yes	—
32	C₄₇×#535	C₂²	1	2	yes	—
33	C₄₇×#533	C₂²	1	1	yes	characteristic
34	C₄₇×#533	C₂²	1	2	yes	complemented
35	C₄₇×#532	C₂²	1	1	yes	characteristic
36	C₄₇×#532	C₂²	1	2	yes	—
37	C₄₇×#532	C₂²	1	2	yes	—
38	C₄₇×#532	C₂²	1	2	yes	complemented
39	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#520	C₂²	1	2	yes	—
42	C₄₇×#518	C₂²	1	2	yes	—
43	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
44	C₄₇×#501	C₂²	1	4	yes	complemented
45	C₄₇×#500	C₂²	1	2	yes	complemented
46	C₄₇×#498	C₂²	1	2	yes	complemented
47	C₄₇×#496	C₂²	1	4	yes	—
48	C₄₇×#493	C₂²	1	2	yes	—
49	C₄₇×#492	C₂²	1	2	yes	—
50	C₄₇×#488	C₂²	1	4	yes	complemented
51	C₄₇×#487	C₂²	1	1	yes	characteristic, complemented
52	C₄₇×#487	C₂²	1	1	yes	characteristic, complemented
53	C₄₇×#486	C₂²	1	2	yes	—
54	C₄₇×#486	C₂²	1	4	yes	—
55	C₄₇×#486	C₂²	1	2	yes	—
56	C₄₇×#486	C₂²	1	1	yes	characteristic, complemented
57	C₄₇×#486	C₂²	1	1	yes	characteristic, complemented
58	C₄₇×#469	C₂²	1	8	yes	complemented
59	C₄₇×#468	C₂²	1	8	yes	complemented
60	C₄₇×#466	C₂²	1	8	yes	complemented
61	C₄₇×#465	C₂²	1	8	yes	complemented
62	C₄₇×#442	C₂²	1	8	yes	complemented
63	C₄₇×#440	C₂²	1	8	yes	complemented
64	C₄×SD₁₆×C₄₇	C₂²	1	8	yes	complemented
65	C₄×D₈×C₄₇	C₂²	1	8	yes	complemented
66	C₄₇×#428	C₂²	1	4	yes	—
67	C₄₇×#416	C₂²	1	4	yes	—
68	C₂×#102×C₄₇	C₂²	1	4	yes	—
69	C₄₇×#405	C₂²	1	2	yes	—
70	C₄₇×#405	C₂²	1	4	yes	complemented
71	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
72	C₄×M₁₆×C₄₇	C₂²	1	2	yes	complemented
73	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
74	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	complemented
75	C₂×#41×C₄₇	—	2	2	no	—
76	C₂×#41×C₄₇	—	2	2	no	—
77	C₂×#41×C₄₇	—	2	2	no	—
78	C₂×#41×C₄₇	C₂³	1	2	yes	—
79	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₄₇	—	2	1	no	—
81	C₂²×D₄×C₄₇	—	2	1	no	—
82	C₂²×D₄×C₄₇	—	2	1	no	—
83	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
84	AGL(1,ℤ/8)×C₄₇	—	2	16	no	—
85	C₂×SD₁₆×C₄₇	C₂³	1	8	yes	—
86	C₂×D₈×C₄₇	C₂³	1	8	yes	—
87	#131×C₄₇	—	2	8	no	—
88	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
89	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
90	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
91	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
92	C₄⋊Q₈×C₄₇	—	2	1	no	—
93	C₄⋊Q₈×C₄₇	—	2	1	no	—
94	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
95	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
96	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
97	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
99	#127×C₄₇	—	2	2	no	—
100	#127×C₄₇	—	2	1	no	—
101	#127×C₄₇	—	2	1	no	—
102	#127×C₄₇	C₂³	1	2	yes	—
103	#127×C₄₇	C₂³	1	2	yes	—
104	#127×C₄₇	C₂³	1	1	yes	characteristic
105	#126×C₄₇	—	2	4	no	—
106	#125×C₄₇	—	2	2	no	—
107	#125×C₄₇	C₂³	1	2	yes	—
108	#124×C₄₇	—	2	2	no	—
109	#124×C₄₇	—	2	4	no	—
110	#124×C₄₇	—	2	2	no	—
111	#124×C₄₇	—	2	2	no	—
112	#124×C₄₇	—	2	2	no	—
113	#124×C₄₇	C₂³	1	2	yes	—
114	#123×C₄₇	—	2	4	no	—
115	#123×C₄₇	—	2	4	no	—
116	#123×C₄₇	—	2	4	no	—
117	C₂²⋊Q₈×C₄₇	—	2	2	no	—
118	C₂²⋊Q₈×C₄₇	—	2	1	no	—
119	C₂²⋊Q₈×C₄₇	—	2	1	no	—
120	C₂²⋊Q₈×C₄₇	—	2	2	no	—
121	C₂²⋊Q₈×C₄₇	—	2	4	no	—
122	C₂²⋊Q₈×C₄₇	C₂³	1	4	yes	—
123	#121×C₄₇	—	2	2	no	—
124	#121×C₄₇	—	2	4	no	—
125	#121×C₄₇	—	2	2	no	—
126	#121×C₄₇	—	2	2	no	—
127	#121×C₄₇	—	2	1	no	—
128	#121×C₄₇	—	2	1	no	—
129	#121×C₄₇	—	2	2	no	—
130	#121×C₄₇	—	2	4	no	—
131	#121×C₄₇	—	2	4	no	—
132	#121×C₄₇	C₂³	1	4	yes	—
133	#121×C₄₇	C₂³	1	4	yes	—
134	#121×C₄₇	C₂³	1	4	yes	—
135	#120×C₄₇	—	2	4	no	—
136	C₄×Q₈×C₄₇	—	2	1	no	—
137	C₄×Q₈×C₄₇	—	2	1	no	—
138	C₄×Q₈×C₄₇	—	2	2	no	—
139	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
140	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
141	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
142	C₄×D₄×C₄₇	—	2	2	no	—
143	C₄×D₄×C₄₇	—	2	2	no	—
144	C₄×D₄×C₄₇	—	2	4	no	—
145	C₄×D₄×C₄₇	—	2	2	no	—
146	C₄×D₄×C₄₇	—	2	2	no	—
147	C₄×D₄×C₄₇	—	2	1	no	—
148	C₄×D₄×C₄₇	—	2	1	no	—
149	C₄×D₄×C₄₇	—	2	2	no	—
150	C₄×D₄×C₄₇	D₄	1	2	yes	—
151	C₄×D₄×C₄₇	D₄	1	2	yes	—
152	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
153	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
154	C₄×D₄×C₄₇	C₂³	1	4	yes	—
155	C₄×D₄×C₄₇	C₂³	1	4	yes	—
156	C₄×D₄×C₄₇	C₂³	1	4	yes	—
157	#117×C₄₇	—	2	2	no	—
158	#117×C₄₇	—	2	2	no	—
159	#117×C₄₇	C₂³	1	2	yes	—
160	#117×C₄₇	C₂³	1	1	yes	characteristic
161	#117×C₄₇	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
163	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
164	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
166	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
168	#107×C₄₇	C₂³	1	8	yes	—
169	#106×C₄₇	C₂³	1	8	yes	—
170	#103×C₄₇	C₂³	1	4	yes	—
171	#103×C₄₇	C₂³	1	4	yes	—
172	#102×C₄₇	C₂³	1	8	yes	—
173	#102×C₄₇	C₂³	1	4	yes	—
174	#102×C₄₇	C₂³	1	8	yes	—
175	#102×C₄₇	C₂³	1	4	yes	—
176	#97×C₄₇	C₂³	1	2	yes	—
177	#97×C₄₇	C₂³	1	4	yes	—
178	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
179	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
180	C₄×C₈×C₄₇	C₂³	1	2	yes	—
181	C₄×C₈×C₄₇	C₂³	1	2	yes	—
182	C₄×C₈×C₄₇	C₂³	1	4	yes	—
183	C₂⁴×C₄₇	—	2	2	no	—
184	#41×C₄₇	—	2	4	no	—
185	#41×C₄₇	—	2	8	no	—
186	#41×C₄₇	—	8	4	no	—
187	#41×C₄₇	—	8	4	no	—
188	#41×C₄₇	—	8	4	no	—
189	C₂×Q₈×C₄₇	—	2	1	no	—
190	C₂×Q₈×C₄₇	—	2	1	no	—
191	C₂×Q₈×C₄₇	—	2	2	no	—
192	C₂×Q₈×C₄₇	—	2	2	no	—
193	C₂×Q₈×C₄₇	—	8	2	no	—
194	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
195	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
196	C₂×D₄×C₄₇	—	2	2	no	—
197	C₂×D₄×C₄₇	—	2	4	no	—
198	C₂×D₄×C₄₇	—	2	4	no	—
199	C₂×D₄×C₄₇	—	2	4	no	—
200	C₂×D₄×C₄₇	—	2	1	no	—
201	C₂×D₄×C₄₇	—	2	2	no	—
202	C₂×D₄×C₄₇	—	2	1	no	—
203	C₂×D₄×C₄₇	—	2	2	no	—
204	C₂×D₄×C₄₇	—	2	2	no	—
205	C₂×D₄×C₄₇	—	2	2	no	—
206	C₂×D₄×C₄₇	—	2	2	no	—
207	C₂×D₄×C₄₇	—	2	8	no	—
208	C₂×D₄×C₄₇	—	8	2	no	—
209	C₂×D₄×C₄₇	—	8	2	no	—
210	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
211	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
212	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
213	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₄₇	—	2	2	no	—
215	C₂²×C₄×C₄₇	—	2	2	no	—
216	C₂²×C₄×C₄₇	—	2	4	no	—
217	C₂²×C₄×C₄₇	—	2	4	no	—
218	C₂²×C₄×C₄₇	—	2	4	no	—
219	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
223	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
225	SD₁₆×C₄₇	—	2	16	no	—
226	D₈×C₄₇	—	2	16	no	—
227	M₁₆×C₄₇	—	2	8	no	—
228	M₁₆×C₄₇	#41	1	8	yes	complemented
229	C₂×C₈×C₄₇	—	2	4	no	—
230	C₂×C₈×C₄₇	—	2	8	no	—
231	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
232	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
233	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
234	C₄⋊C₄×C₄₇	—	2	2	no	—
235	C₄⋊C₄×C₄₇	—	2	2	no	—
236	C₄⋊C₄×C₄₇	—	2	4	no	—
237	C₄⋊C₄×C₄₇	—	2	2	no	—
238	C₄⋊C₄×C₄₇	—	2	1	no	—
239	C₄⋊C₄×C₄₇	—	2	1	no	—
240	C₄⋊C₄×C₄₇	—	2	1	no	—
241	C₄⋊C₄×C₄₇	—	2	1	no	—
242	C₄⋊C₄×C₄₇	—	2	2	no	—
243	C₄⋊C₄×C₄₇	—	2	2	no	—
244	C₄⋊C₄×C₄₇	—	2	4	no	—
245	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
246	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
247	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
248	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
249	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
250	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
251	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
252	C₂²⋊C₄×C₄₇	—	2	2	no	—
253	C₂²⋊C₄×C₄₇	—	2	4	no	—
254	C₂²⋊C₄×C₄₇	—	2	4	no	—
255	C₂²⋊C₄×C₄₇	—	2	4	no	—
256	C₂²⋊C₄×C₄₇	—	2	4	no	—
257	C₂²⋊C₄×C₄₇	—	2	4	no	—
258	C₂²⋊C₄×C₄₇	—	2	4	no	—
259	C₂²⋊C₄×C₄₇	—	2	4	no	—
260	C₂²⋊C₄×C₄₇	—	2	2	no	—
261	C₂²⋊C₄×C₄₇	—	2	2	no	—
262	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
263	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
264	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
265	C₄²×C₄₇	—	2	4	no	—
266	C₄²×C₄₇	—	2	2	no	—
267	C₄²×C₄₇	C₂×D₄	1	2	yes	—
268	C₄²×C₄₇	C₂×D₄	1	2	yes	—
269	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
272	C₄²×C₄₇	C₂⁴	1	2	yes	—
273	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
274	C₂³×C₄₇	—	2	2	no	—
275	C₂³×C₄₇	—	2	4	no	—
276	C₂³×C₄₇	—	4	4	no	—
277	C₂³×C₄₇	—	8	2	no	—
278	C₂³×C₄₇	—	8	2	no	—
279	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
280	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
281	Q₈×C₄₇	—	2	2	no	—
282	Q₈×C₄₇	—	2	4	no	—
283	Q₈×C₄₇	—	4	4	no	—
284	Q₈×C₄₇	—	4	2	no	—
285	Q₈×C₄₇	—	4	2	no	—
286	Q₈×C₄₇	—	8	2	no	—
287	D₄×C₄₇	—	2	4	no	—
288	D₄×C₄₇	—	2	2	no	—
289	D₄×C₄₇	—	2	4	no	—
290	D₄×C₄₇	—	2	8	no	—
291	D₄×C₄₇	—	4	4	no	—
292	D₄×C₄₇	—	4	4	no	—
293	D₄×C₄₇	—	4	4	no	—
294	D₄×C₄₇	—	4	2	no	—
295	D₄×C₄₇	—	4	2	no	—
296	D₄×C₄₇	—	4	4	no	—
297	D₄×C₄₇	—	8	2	no	—
298	D₄×C₄₇	—	8	2	no	—
299	D₄×C₄₇	—	8	4	no	—
300	D₄×C₄₇	—	8	4	no	—
301	D₄×C₄₇	—	8	4	no	—
302	C₂×C₄×C₄₇	—	2	2	no	—
303	C₂×C₄×C₄₇	—	2	4	no	—
304	C₂×C₄×C₄₇	—	2	2	no	—
305	C₂×C₄×C₄₇	—	2	4	no	—
306	C₂×C₄×C₄₇	—	2	4	no	—
307	C₂×C₄×C₄₇	—	2	2	no	—
308	C₂×C₄×C₄₇	—	2	2	no	—
309	C₂×C₄×C₄₇	—	2	2	no	—
310	C₂×C₄×C₄₇	—	2	4	no	—
311	C₂×C₄×C₄₇	—	4	4	no	—
312	C₂×C₄×C₄₇	—	8	4	no	—
313	C₂×C₄×C₄₇	—	8	4	no	—
314	C₂×C₄×C₄₇	—	8	4	no	—
315	C₂×C₄×C₄₇	—	8	2	no	—
316	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
325	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
326	C₈×C₄₇	—	2	2	no	—
327	C₈×C₄₇	—	2	2	no	—
328	C₈×C₄₇	C₂×#41	1	8	yes	—
329	#60722	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
330	C₂²×C₄₇	—	2	1	no	—
331	C₂²×C₄₇	—	2	1	no	—
332	C₂²×C₄₇	—	2	2	no	—
333	C₂²×C₄₇	—	2	2	no	—
334	C₂²×C₄₇	—	2	2	no	—
335	C₂²×C₄₇	—	4	2	no	—
336	C₂²×C₄₇	—	4	4	no	—
337	C₂²×C₄₇	—	4	2	no	—
338	C₂²×C₄₇	—	4	4	no	—
339	C₂²×C₄₇	—	4	4	no	—
340	C₂²×C₄₇	—	4	2	no	—
341	C₂²×C₄₇	—	16	4	no	—
342	C₂²×C₄₇	#532	1	2	yes	—
343	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
344	C₄×C₄₇	—	2	2	no	—
345	C₄×C₄₇	—	2	2	no	—
346	C₄×C₄₇	—	2	1	no	—
347	C₄×C₄₇	—	2	2	no	—
348	C₄×C₄₇	—	2	1	no	—
349	C₄×C₄₇	—	4	2	no	—
350	C₄×C₄₇	—	4	2	no	—
351	C₄×C₄₇	—	4	4	no	—
352	C₄×C₄₇	—	4	2	no	—
353	C₄×C₄₇	#532	1	2	yes	—
354	C₄×C₄₇	#576	1	2	yes	—
355	C₄×C₄₇	#577	1	2	yes	—
356	C₄×C₄₇	C₂²×#41	1	2	yes	—
357	#3511	C₂×C₄₇	1	1	yes	characteristic, complemented
358	#3508	C₂×C₄₇	1	1	yes	characteristic, complemented
359	#3184	C₂×C₄₇	1	2	yes	complemented
360	#3182	C₂×C₄₇	1	2	yes	complemented
361	#3179	C₂×C₄₇	1	8	yes	complemented
362	#3169	C₂×C₄₇	1	2	yes	complemented
363	#3167	C₂×C₄₇	1	2	yes	complemented
364	#3165	C₂×C₄₇	1	1	yes	characteristic, complemented
365	#3151	C₂×C₄₇	1	1	yes	characteristic, complemented
366	#3131	C₂×C₄₇	1	1	yes	characteristic, complemented
367	C₂×#486	C₂×C₄₇	1	1	yes	characteristic, complemented
368	#3062	C₂×C₄₇	1	4	yes	complemented
369	#2946	C₂×C₄₇	1	4	yes	complemented
370	C₄×#131	C₂×C₄₇	1	1	yes	characteristic, complemented
371	C₂×C₄₇	—	2	2	no	—
372	C₂×C₄₇	—	4	2	no	—
373	C₂×C₄₇	—	8	2	no	—
374	C₂×C₄₇	—	8	4	no	—
375	C₂×C₄₇	C₂×#532	1	1	yes	characteristic
376	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
377	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
378	C₂×AGL(1,ℤ/8)	C₂²×C₄₇	1	4	yes	—
379	C₂×#131	C₂²×C₄₇	1	2	yes	—
380	#559	—	2	1	no	—
381	#559	—	2	1	no	—
382	#556	—	2	1	no	—
383	#555	—	2	1	no	—
384	#554	—	2	1	no	—
385	#553	—	2	2	no	—
386	#550	—	2	1	no	—
387	#550	—	2	1	no	—
388	#548	—	2	2	no	—
389	#547	—	2	1	no	—
390	#546	—	2	2	no	—
391	#546	—	2	2	no	—
392	#542	C₂²×C₄₇	1	4	yes	complemented
393	#540	C₂²×C₄₇	1	4	yes	—
394	#537	C₂²×C₄₇	1	2	yes	—
395	#535	C₂²×C₄₇	1	2	yes	—
396	#533	C₂²×C₄₇	1	1	yes	characteristic
397	#533	C₂²×C₄₇	1	2	yes	complemented
398	#532	C₂²×C₄₇	1	1	yes	characteristic
399	#532	C₂²×C₄₇	1	2	yes	—
400	#532	C₂²×C₄₇	1	2	yes	—
401	#532	C₂²×C₄₇	1	2	yes	complemented
402	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
403	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
404	#520	C₂²×C₄₇	1	2	yes	—
405	#518	C₂²×C₄₇	1	2	yes	—
406	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
407	#501	C₂²×C₄₇	1	4	yes	complemented
408	#500	C₂²×C₄₇	1	2	yes	complemented
409	#498	C₂²×C₄₇	1	2	yes	complemented
410	#496	C₂²×C₄₇	1	4	yes	—
411	#493	C₂²×C₄₇	1	2	yes	—
412	#492	C₂²×C₄₇	1	2	yes	—
413	#488	C₂²×C₄₇	1	4	yes	complemented
414	#487	C₂²×C₄₇	1	1	yes	characteristic, complemented
415	#487	C₂²×C₄₇	1	1	yes	characteristic, complemented
416	#486	C₂²×C₄₇	1	2	yes	—
417	#486	C₂²×C₄₇	1	4	yes	—
418	#486	C₂²×C₄₇	1	2	yes	—
419	#486	C₂²×C₄₇	1	1	yes	characteristic, complemented
420	#486	C₂²×C₄₇	1	1	yes	characteristic, complemented
421	#469	C₂²×C₄₇	1	8	yes	complemented
422	#468	C₂²×C₄₇	1	8	yes	complemented
423	#466	C₂²×C₄₇	1	8	yes	complemented
424	#465	C₂²×C₄₇	1	8	yes	complemented
425	#442	C₂²×C₄₇	1	8	yes	complemented
426	#440	C₂²×C₄₇	1	8	yes	complemented
427	C₄×SD₁₆	C₂²×C₄₇	1	8	yes	complemented
428	C₄×D₈	C₂²×C₄₇	1	8	yes	complemented
429	#428	C₂²×C₄₇	1	4	yes	—
430	#416	C₂²×C₄₇	1	4	yes	—
431	C₂×#102	C₂²×C₄₇	1	4	yes	—
432	#405	C₂²×C₄₇	1	2	yes	—
433	#405	C₂²×C₄₇	1	4	yes	complemented
434	C₄×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
435	C₄×M₁₆	C₂²×C₄₇	1	2	yes	complemented
436	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
437	C₂×C₄×C₈	C₂²×C₄₇	1	2	yes	complemented
438	C₄₇	#60722	1	1	yes	characteristic, direct product factor, Sylow
439	C₂×#41	—	2	2	no	—
440	C₂×#41	—	2	2	no	—
441	C₂×#41	—	2	2	no	—
442	C₂×#41	C₂³×C₄₇	1	2	yes	—
443	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
444	C₂²×Q₈	—	2	1	no	—
445	C₂²×D₄	—	2	1	no	—
446	C₂²×D₄	—	2	1	no	—
447	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
448	AGL(1,ℤ/8)	—	2	16	no	—
449	C₂×SD₁₆	C₂³×C₄₇	1	8	yes	—
450	C₂×D₈	C₂³×C₄₇	1	8	yes	—
451	#131	—	2	8	no	—
452	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
453	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
454	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
455	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
456	C₄⋊Q₈	—	2	1	no	—
457	C₄⋊Q₈	—	2	1	no	—
458	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
459	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
460	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
461	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
462	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
463	#127	—	2	2	no	—
464	#127	—	2	1	no	—
465	#127	—	2	1	no	—
466	#127	C₂³×C₄₇	1	2	yes	—
467	#127	C₂³×C₄₇	1	2	yes	—
468	#127	C₂³×C₄₇	1	1	yes	characteristic
469	#126	—	2	4	no	—
470	#125	—	2	2	no	—
471	#125	C₂³×C₄₇	1	2	yes	—
472	#124	—	2	2	no	—
473	#124	—	2	4	no	—
474	#124	—	2	2	no	—
475	#124	—	2	2	no	—
476	#124	—	2	2	no	—
477	#124	C₂³×C₄₇	1	2	yes	—
478	#123	—	2	4	no	—
479	#123	—	2	4	no	—
480	#123	—	2	4	no	—
481	C₂²⋊Q₈	—	2	2	no	—
482	C₂²⋊Q₈	—	2	1	no	—
483	C₂²⋊Q₈	—	2	1	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	4	no	—
486	C₂²⋊Q₈	C₂³×C₄₇	1	4	yes	—
487	#121	—	2	2	no	—
488	#121	—	2	4	no	—
489	#121	—	2	2	no	—
490	#121	—	2	2	no	—
491	#121	—	2	1	no	—
492	#121	—	2	1	no	—
493	#121	—	2	2	no	—
494	#121	—	2	4	no	—
495	#121	—	2	4	no	—
496	#121	C₂³×C₄₇	1	4	yes	—
497	#121	C₂³×C₄₇	1	4	yes	—
498	#121	C₂³×C₄₇	1	4	yes	—
499	#120	—	2	4	no	—
500	C₄×Q₈	—	2	1	no	—
501	C₄×Q₈	—	2	1	no	—
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
504	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
505	C₄×Q₈	C₂³×C₄₇	1	4	yes	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	4	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	1	no	—
512	C₄×D₄	—	2	1	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	D₄×C₄₇	1	2	yes	—
515	C₄×D₄	D₄×C₄₇	1	2	yes	—
516	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
517	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
518	C₄×D₄	C₂³×C₄₇	1	4	yes	—
519	C₄×D₄	C₂³×C₄₇	1	4	yes	—
520	C₄×D₄	C₂³×C₄₇	1	4	yes	—
521	#117	—	2	2	no	—
522	#117	—	2	2	no	—
523	#117	C₂³×C₄₇	1	2	yes	—
524	#117	C₂³×C₄₇	1	1	yes	characteristic
525	#117	C₂³×C₄₇	1	2	yes	—
526	C₂×C₄⋊C₄	—	2	1	no	—
527	C₂×C₄⋊C₄	—	2	2	no	—
528	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
529	C₂×C₂²⋊C₄	—	2	4	no	—
530	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
532	#107	C₂³×C₄₇	1	8	yes	—
533	#106	C₂³×C₄₇	1	8	yes	—
534	#103	C₂³×C₄₇	1	4	yes	—
535	#103	C₂³×C₄₇	1	4	yes	—
536	#102	C₂³×C₄₇	1	8	yes	—
537	#102	C₂³×C₄₇	1	8	yes	—
538	#102	C₂³×C₄₇	1	4	yes	—
539	#102	C₂³×C₄₇	1	4	yes	—
540	#97	C₂³×C₄₇	1	2	yes	—
541	#97	C₂³×C₄₇	1	4	yes	—
542	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
543	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
544	C₄×C₈	C₂³×C₄₇	1	2	yes	—
545	C₄×C₈	C₂³×C₄₇	1	2	yes	—
546	C₄×C₈	C₂³×C₄₇	1	4	yes	—
547	C₂⁴	—	2	2	no	—
548	#41	—	2	4	no	—
549	#41	—	2	8	no	—
550	#41	—	8	4	no	—
551	#41	—	8	4	no	—
552	#41	—	8	4	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	8	2	no	—
558	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
559	C₂×Q₈	C₂⁴×C₄₇	1	2	yes	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	8	no	—
572	C₂×D₄	—	8	2	no	—
573	C₂×D₄	—	8	2	no	—
574	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
575	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
576	C₂×D₄	C₂⁴×C₄₇	1	2	yes	—
577	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
585	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
589	SD₁₆	—	2	16	no	—
590	D₈	—	2	16	no	—
591	M₁₆	—	2	8	no	—
592	M₁₆	#41×C₄₇	1	8	yes	complemented
593	C₂×C₈	—	2	4	no	—
594	C₂×C₈	—	2	8	no	—
595	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
596	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
597	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
610	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
611	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
612	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
613	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
614	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
615	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
627	C₂²⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
628	C₂²⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
629	C₄²	—	2	4	no	—
630	C₄²	—	2	2	no	—
631	C₄²	C₂×D₄×C₄₇	1	2	yes	—
632	C₄²	C₂×D₄×C₄₇	1	2	yes	—
633	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
634	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
635	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
636	C₄²	C₂⁴×C₄₇	1	2	yes	—
637	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
638	C₂³	—	2	2	no	—
639	C₂³	—	2	4	no	—
640	C₂³	—	4	4	no	—
641	C₂³	—	8	2	no	—
642	C₂³	—	8	2	no	—
643	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
644	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
645	Q₈	—	2	2	no	—
646	Q₈	—	2	4	no	—
647	Q₈	—	4	4	no	—
648	Q₈	—	4	2	no	—
649	Q₈	—	4	2	no	—
650	Q₈	—	8	2	no	—
651	D₄	—	2	4	no	—
652	D₄	—	2	2	no	—
653	D₄	—	2	4	no	—
654	D₄	—	2	8	no	—
655	D₄	—	4	4	no	—
656	D₄	—	4	4	no	—
657	D₄	—	4	4	no	—
658	D₄	—	4	2	no	—
659	D₄	—	4	2	no	—
660	D₄	—	4	4	no	—
661	D₄	—	8	2	no	—
662	D₄	—	8	2	no	—
663	D₄	—	8	4	no	—
664	D₄	—	8	4	no	—
665	D₄	—	8	4	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	4	4	no	—
676	C₂×C₄	—	8	4	no	—
677	C₂×C₄	—	8	4	no	—
678	C₂×C₄	—	8	4	no	—
679	C₂×C₄	—	8	2	no	—
680	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
681	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
682	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
684	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
685	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
686	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
687	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
688	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
689	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
690	C₈	—	2	2	no	—
691	C₈	—	2	2	no	—
692	C₈	C₂×#41×C₄₇	1	8	yes	—
693	C₂²	—	2	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	4	4	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	4	no	—
704	C₂²	—	16	4	no	—
705	C₂²	C₄₇×#532	1	2	yes	—
706	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
707	C₄	—	2	2	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	2	no	—
710	C₄	—	2	1	no	—
711	C₄	—	2	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	4	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	C₄₇×#532	1	2	yes	—
717	C₄	C₄₇×#576	1	2	yes	—
718	C₄	C₄₇×#577	1	2	yes	—
719	C₄	C₂²×#41×C₄₇	1	2	yes	—
720	C₂	—	2	2	no	—
721	C₂	—	4	2	no	—
722	C₂	—	8	4	no	—
723	C₂	—	8	2	no	—
724	C₂	C₂×C₄₇×#532	1	1	yes	characteristic
725	C₂	C₂×C₄₇×#576	1	1	yes	characteristic
726	C₂	C₂×C₄₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ 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
1. C₄₇×#3511	C₂	semidirect
2. C₄₇×#3508	C₂	semidirect
3. C₄₇×#3184	C₂	semidirect
4. C₄₇×#3182	C₂	semidirect
5. C₄₇×#3179	C₂	semidirect
6. C₄₇×#3169	C₂	semidirect
7. C₄₇×#3167	C₂	semidirect
8. C₄₇×#3165	C₂	semidirect
9. C₄₇×#3151	C₂	semidirect
10. C₄₇×#3131	C₂	semidirect
11. C₂×C₄₇×#486	C₂	semidirect
12. C₄₇×#3062	C₂	semidirect
13. C₄₇×#2946	C₂	semidirect
14. C₄×#131×C₄₇	C₂	semidirect
29. C₄₇×#542	C₂²	semidirect
34. C₄₇×#533	C₂²	semidirect
38. C₄₇×#532	C₂²	semidirect
44. C₄₇×#501	C₂²	semidirect
45. C₄₇×#500	C₂²	semidirect
46. C₄₇×#498	C₂²	semidirect
50. C₄₇×#488	C₂²	semidirect
51. C₄₇×#487	C₂²	semidirect
52. C₄₇×#487	C₂²	semidirect
56. C₄₇×#486	C₂²	semidirect
57. C₄₇×#486	C₂²	semidirect
58. C₄₇×#469	C₂²	semidirect
59. C₄₇×#468	C₂²	semidirect
60. C₄₇×#466	C₂²	semidirect
61. C₄₇×#465	C₂²	semidirect
62. C₄₇×#442	C₂²	semidirect
63. C₄₇×#440	C₂²	semidirect
64. C₄×SD₁₆×C₄₇	C₂²	semidirect
65. C₄×D₈×C₄₇	C₂²	semidirect
70. C₄₇×#405	C₂²	semidirect
72. C₄×M₁₆×C₄₇	C₂²	semidirect
74. C₂×C₄×C₈×C₄₇	C₂²	semidirect
228. M₁₆×C₄₇	#41	semidirect
329. #60722	C₄₇	direct (N × H)
357. #3511	C₂×C₄₇	semidirect
358. #3508	C₂×C₄₇	semidirect
359. #3184	C₂×C₄₇	semidirect
360. #3182	C₂×C₄₇	semidirect
361. #3179	C₂×C₄₇	semidirect
362. #3169	C₂×C₄₇	semidirect
363. #3167	C₂×C₄₇	semidirect
364. #3165	C₂×C₄₇	semidirect
365. #3151	C₂×C₄₇	semidirect
366. #3131	C₂×C₄₇	semidirect
367. C₂×#486	C₂×C₄₇	semidirect
368. #3062	C₂×C₄₇	semidirect
369. #2946	C₂×C₄₇	semidirect
370. C₄×#131	C₂×C₄₇	semidirect
392. #542	C₂²×C₄₇	semidirect
397. #533	C₂²×C₄₇	semidirect
401. #532	C₂²×C₄₇	semidirect
407. #501	C₂²×C₄₇	semidirect
408. #500	C₂²×C₄₇	semidirect
409. #498	C₂²×C₄₇	semidirect
413. #488	C₂²×C₄₇	semidirect
414. #487	C₂²×C₄₇	semidirect
415. #487	C₂²×C₄₇	semidirect
419. #486	C₂²×C₄₇	semidirect
420. #486	C₂²×C₄₇	semidirect
421. #469	C₂²×C₄₇	semidirect
422. #468	C₂²×C₄₇	semidirect
423. #466	C₂²×C₄₇	semidirect
424. #465	C₂²×C₄₇	semidirect
425. #442	C₂²×C₄₇	semidirect
426. #440	C₂²×C₄₇	semidirect
427. C₄×SD₁₆	C₂²×C₄₇	semidirect
428. C₄×D₈	C₂²×C₄₇	semidirect
433. #405	C₂²×C₄₇	semidirect
435. C₄×M₁₆	C₂²×C₄₇	semidirect
437. C₂×C₄×C₈	C₂²×C₄₇	semidirect
438. C₄₇	#60722	direct (N × H)
592. M₁₆	#41×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#3511	2
C₄₇×#3508	2
C₄₇×#3184	2
C₄₇×#3182	2
C₄₇×#3179	2
C₄₇×#3169	2
C₄₇×#3167	2
C₄₇×#3165	2
C₄₇×#3151	2
C₄₇×#3131	2
C₂×C₄₇×#486	2
C₄₇×#3062	2
C₄₇×#2946	2
C₄×#131×C₄₇	2
#60722	47

Subgroups — C47×#60722 #26100420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#60722 #26100420