Subgroups — C₄₇×#25051 #26064749

Order 12032.

736 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3099	C₂	1	2	yes	maximal, complemented
2	C₄₇×#3060	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2952	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2079	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2039	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1974	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1951	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1859	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1844	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1815	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
14	C₄₇×#537	C₂²	1	2	yes	—
15	C₄₇×#520	C₂²	1	2	yes	—
16	C₄₇×#485	—	2	2	no	—
17	C₄₇×#483	—	2	2	no	—
18	C₄₇×#482	—	2	2	no	—
19	C₄₇×#481	—	2	2	no	—
20	C₄₇×#470	—	2	1	no	—
21	C₄₇×#469	—	2	1	no	—
22	C₄₇×#465	—	2	2	no	—
23	C₄₇×#442	—	2	1	no	—
24	C₄₇×#441	—	2	1	no	—
25	C₄×SD₁₆×C₄₇	—	2	2	no	—
26	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
27	C₄₇×#428	C₂²	1	2	yes	—
28	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×#106×C₄₇	C₂²	1	2	yes	—
31	C₂×#104×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#104×C₄₇	C₂²	1	2	yes	—
33	C₄₇×#417	C₂²	1	2	yes	—
34	C₄₇×#417	C₂²	1	2	yes	—
35	C₄₇×#417	C₂²	1	2	yes	—
36	C₄₇×#416	C₂²	1	1	yes	characteristic
37	C₄₇×#408	C₂²	1	2	yes	—
38	C₄₇×#405	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#384	C₂²	1	2	yes	—
41	C₄₇×#343	C₂²	1	2	yes	—
42	C₄₇×#343	C₂²	1	2	yes	—
43	C₄₇×#341	C₂²	1	1	yes	characteristic
44	C₄₇×#339	C₂²	1	1	yes	characteristic
45	C₂×#41×C₄₇	C₂³	1	2	yes	—
46	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
47	#135×C₄₇	—	2	2	no	—
48	#135×C₄₇	—	2	2	no	—
49	C₂×Q₁₆×C₄₇	D₄	1	1	yes	characteristic
50	C₂×SD₁₆×C₄₇	D₄	1	2	yes	—
51	C₂×D₈×C₄₇	D₄	1	1	yes	characteristic
52	#131×C₄₇	—	2	2	no	—
53	#131×C₄₇	—	2	2	no	—
54	C₂×M₁₆×C₄₇	—	2	1	no	—
55	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
58	C₂²×C₈×C₄₇	—	2	1	no	—
59	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
61	C₂²⋊Q₈×C₄₇	—	2	2	no	—
62	C₂²⋊Q₈×C₄₇	—	2	2	no	—
63	#121×C₄₇	—	2	2	no	—
64	#121×C₄₇	—	2	2	no	—
65	#121×C₄₇	—	4	2	no	—
66	C₄×Q₈×C₄₇	—	2	2	no	—
67	C₄×D₄×C₄₇	—	2	2	no	—
68	C₄×D₄×C₄₇	—	4	2	no	—
69	#117×C₄₇	—	2	2	no	—
70	#117×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
75	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	#108×C₄₇	—	2	2	no	—
77	#107×C₄₇	—	2	2	no	—
78	#106×C₄₇	—	2	1	no	—
79	#106×C₄₇	—	2	1	no	—
80	#106×C₄₇	—	2	2	no	—
81	#106×C₄₇	—	2	2	no	—
82	#106×C₄₇	—	2	1	no	—
83	#106×C₄₇	—	2	1	no	—
84	#106×C₄₇	—	2	2	no	—
85	#104×C₄₇	—	2	2	no	—
86	#104×C₄₇	—	2	4	no	—
87	#103×C₄₇	—	2	2	no	—
88	#103×C₄₇	—	2	2	no	—
89	#103×C₄₇	—	2	2	no	—
90	#103×C₄₇	D₄	1	2	yes	—
91	#102×C₄₇	—	2	2	no	—
92	#102×C₄₇	—	2	2	no	—
93	#102×C₄₇	—	2	2	no	—
94	#102×C₄₇	D₄	1	2	yes	—
95	C₂²⋊C₈×C₄₇	—	2	2	no	—
96	C₂²⋊C₈×C₄₇	—	2	2	no	—
97	#97×C₄₇	—	2	1	no	—
98	C₄×C₈×C₄₇	—	2	1	no	—
99	C₄×C₈×C₄₇	—	2	2	no	—
100	#41×C₄₇	—	2	2	no	—
101	#41×C₄₇	—	2	1	no	—
102	#41×C₄₇	—	2	1	no	—
103	#41×C₄₇	—	2	1	no	—
104	#41×C₄₇	—	2	2	no	—
105	#41×C₄₇	—	2	2	no	—
106	#41×C₄₇	—	2	2	no	—
107	#41×C₄₇	—	2	1	no	—
108	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₄₇	—	2	2	no	—
111	C₂×D₄×C₄₇	—	2	1	no	—
112	C₂×D₄×C₄₇	—	4	2	no	—
113	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
114	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	—	2	1	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	4	2	no	—
121	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
122	Q₁₆×C₄₇	—	2	2	no	—
123	SD₁₆×C₄₇	—	2	4	no	—
124	D₈×C₄₇	—	2	2	no	—
125	M₁₆×C₄₇	—	2	2	no	—
126	M₁₆×C₄₇	—	2	1	no	—
127	M₁₆×C₄₇	—	2	2	no	—
128	M₁₆×C₄₇	—	2	1	no	—
129	M₁₆×C₄₇	—	2	1	no	—
130	M₁₆×C₄₇	—	2	1	no	—
131	M₁₆×C₄₇	—	4	2	no	—
132	C₂×C₈×C₄₇	—	2	1	no	—
133	C₂×C₈×C₄₇	—	2	1	no	—
134	C₂×C₈×C₄₇	—	2	1	no	—
135	C₂×C₈×C₄₇	—	2	1	no	—
136	C₂×C₈×C₄₇	—	2	2	no	—
137	C₂×C₈×C₄₇	—	4	2	no	—
138	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₄₇	#41	1	2	yes	—
142	C₂×C₈×C₄₇	#41	1	2	yes	—
143	C₄⋊C₄×C₄₇	—	2	2	no	—
144	C₄⋊C₄×C₄₇	—	2	2	no	—
145	C₄⋊C₄×C₄₇	—	2	2	no	—
146	C₄⋊C₄×C₄₇	—	2	2	no	—
147	C₄⋊C₄×C₄₇	—	4	2	no	—
148	C₄⋊C₄×C₄₇	—	4	2	no	—
149	C₄⋊C₄×C₄₇	—	8	4	no	—
150	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
151	C₂²⋊C₄×C₄₇	—	2	1	no	—
152	C₂²⋊C₄×C₄₇	—	4	2	no	—
153	C₂²⋊C₄×C₄₇	—	4	2	no	—
154	C₂²⋊C₄×C₄₇	—	4	2	no	—
155	C₄²×C₄₇	—	2	1	no	—
156	C₄²×C₄₇	—	2	1	no	—
157	C₄²×C₄₇	—	4	2	no	—
158	C₄²×C₄₇	#41	1	2	yes	—
159	C₂³×C₄₇	—	2	2	no	—
160	C₂³×C₄₇	—	2	1	no	—
161	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
162	Q₈×C₄₇	—	2	2	no	—
163	Q₈×C₄₇	—	2	1	no	—
164	Q₈×C₄₇	—	2	1	no	—
165	Q₈×C₄₇	—	2	2	no	—
166	D₄×C₄₇	—	2	2	no	—
167	D₄×C₄₇	—	2	1	no	—
168	D₄×C₄₇	—	2	1	no	—
169	D₄×C₄₇	—	2	2	no	—
170	D₄×C₄₇	—	4	2	no	—
171	D₄×C₄₇	—	4	1	no	—
172	D₄×C₄₇	—	4	2	no	—
173	D₄×C₄₇	—	4	1	no	—
174	D₄×C₄₇	—	16	2	no	—
175	C₂×C₄×C₄₇	—	2	4	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	4	1	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	1	no	—
184	C₂×C₄×C₄₇	—	4	2	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	8	2	no	—
187	C₂×C₄×C₄₇	—	8	2	no	—
188	C₂×C₄×C₄₇	—	16	2	no	—
189	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
195	C₈×C₄₇	—	2	2	no	—
196	C₈×C₄₇	—	4	1	no	—
197	C₈×C₄₇	—	4	2	no	—
198	C₈×C₄₇	—	4	1	no	—
199	C₈×C₄₇	#123	1	2	yes	—
200	C₈×C₄₇	#123	1	2	yes	—
201	#25051	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₄₇	—	2	2	no	—
203	C₂²×C₄₇	—	4	1	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	—	4	2	no	—
206	C₂²×C₄₇	—	4	2	no	—
207	C₂²×C₄₇	—	4	2	no	—
208	C₂²×C₄₇	#542	1	1	yes	characteristic
209	C₂²×C₄₇	D₄²	1	1	yes	characteristic
210	C₂²×C₄₇	#553	1	1	yes	characteristic
211	C₄×C₄₇	—	2	4	no	—
212	C₄×C₄₇	—	4	2	no	—
213	C₄×C₄₇	—	4	1	no	—
214	C₄×C₄₇	—	4	2	no	—
215	C₄×C₄₇	—	8	2	no	—
216	C₄×C₄₇	—	8	2	no	—
217	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
218	C₄×C₄₇	#532	1	1	yes	characteristic
219	C₄×C₄₇	#547	1	1	yes	characteristic
220	C₄×C₄₇	#547	1	1	yes	characteristic
221	#3099	C₂×C₄₇	1	2	yes	complemented
222	#3060	C₂×C₄₇	1	1	yes	characteristic
223	#2952	C₂×C₄₇	1	1	yes	characteristic, complemented
224	#2079	C₂×C₄₇	1	2	yes	complemented
225	#2039	C₂×C₄₇	1	2	yes	complemented
226	#1974	C₂×C₄₇	1	1	yes	characteristic, complemented
227	#1951	C₂×C₄₇	1	1	yes	characteristic, complemented
228	#1859	C₂×C₄₇	1	2	yes	complemented
229	#1844	C₂×C₄₇	1	1	yes	characteristic, complemented
230	#1815	C₂×C₄₇	1	1	yes	characteristic, complemented
231	#1764	C₂×C₄₇	1	1	yes	characteristic, complemented
232	C₂×C₄₇	—	2	1	no	—
233	C₂×C₄₇	—	2	1	no	—
234	C₂×C₄₇	—	8	2	no	—
235	C₂×C₄₇	—	8	1	no	—
236	C₂×C₄₇	#2422	1	1	yes	characteristic
237	C₂×C₄₇	#3291	1	2	yes	—
238	C₂×#135	C₂²×C₄₇	1	1	yes	characteristic
239	C₂×#131	C₂²×C₄₇	1	1	yes	characteristic
240	#537	C₂²×C₄₇	1	2	yes	—
241	#520	C₂²×C₄₇	1	2	yes	—
242	#485	—	2	2	no	—
243	#483	—	2	2	no	—
244	#482	—	2	2	no	—
245	#481	—	2	2	no	—
246	#470	—	2	1	no	—
247	#469	—	2	1	no	—
248	#465	—	2	2	no	—
249	#442	—	2	1	no	—
250	#441	—	2	1	no	—
251	C₄×SD₁₆	—	2	2	no	—
252	C₂×#108	C₂²×C₄₇	1	1	yes	characteristic
253	#428	C₂²×C₄₇	1	2	yes	—
254	C₂×#106	C₂²×C₄₇	1	1	yes	characteristic
255	C₂×#106	C₂²×C₄₇	1	2	yes	—
256	C₂×#106	C₂²×C₄₇	1	1	yes	characteristic
257	C₂×#104	C₂²×C₄₇	1	2	yes	—
258	C₂×#104	C₂²×C₄₇	1	1	yes	characteristic
259	#417	C₂²×C₄₇	1	2	yes	—
260	#417	C₂²×C₄₇	1	2	yes	—
261	#417	C₂²×C₄₇	1	2	yes	—
262	#416	C₂²×C₄₇	1	1	yes	characteristic
263	#408	C₂²×C₄₇	1	2	yes	—
264	#405	C₂²×C₄₇	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
266	#384	C₂²×C₄₇	1	2	yes	—
267	#343	C₂²×C₄₇	1	2	yes	—
268	#343	C₂²×C₄₇	1	2	yes	—
269	#341	C₂²×C₄₇	1	1	yes	characteristic
270	#339	C₂²×C₄₇	1	1	yes	characteristic
271	C₄₇	#25051	1	1	yes	characteristic, direct product factor, Sylow
272	C₂×#41	C₂³×C₄₇	1	2	yes	—
273	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
274	#135	—	2	2	no	—
275	#135	—	2	2	no	—
276	C₂×Q₁₆	D₄×C₄₇	1	1	yes	characteristic
277	C₂×SD₁₆	D₄×C₄₇	1	2	yes	—
278	C₂×D₈	D₄×C₄₇	1	1	yes	characteristic
279	#131	—	2	2	no	—
280	#131	—	2	2	no	—
281	C₂×M₁₆	—	2	1	no	—
282	C₂×M₁₆	C₂³×C₄₇	1	1	yes	characteristic
283	C₂×M₁₆	C₂³×C₄₇	1	1	yes	characteristic
284	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
285	C₂²×C₈	—	2	1	no	—
286	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
288	C₂²⋊Q₈	—	2	2	no	—
289	C₂²⋊Q₈	—	2	2	no	—
290	#121	—	2	2	no	—
291	#121	—	2	2	no	—
292	#121	—	4	2	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	4	2	no	—
296	#117	—	2	2	no	—
297	#117	C₂³×C₄₇	1	1	yes	characteristic
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	4	2	no	—
300	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
302	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
303	#108	—	2	2	no	—
304	#107	—	2	2	no	—
305	#106	—	2	1	no	—
306	#106	—	2	1	no	—
307	#106	—	2	1	no	—
308	#106	—	2	1	no	—
309	#106	—	2	2	no	—
310	#106	—	2	2	no	—
311	#106	—	2	2	no	—
312	#104	—	2	4	no	—
313	#104	—	2	2	no	—
314	#103	—	2	2	no	—
315	#103	—	2	2	no	—
316	#103	—	2	2	no	—
317	#103	D₄×C₄₇	1	2	yes	—
318	#102	—	2	2	no	—
319	#102	—	2	2	no	—
320	#102	—	2	2	no	—
321	#102	D₄×C₄₇	1	2	yes	—
322	C₂²⋊C₈	—	2	2	no	—
323	C₂²⋊C₈	—	2	2	no	—
324	#97	—	2	1	no	—
325	C₄×C₈	—	2	1	no	—
326	C₄×C₈	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	1	no	—
329	#41	—	2	1	no	—
330	#41	—	2	1	no	—
331	#41	—	2	2	no	—
332	#41	—	2	2	no	—
333	#41	—	2	2	no	—
334	#41	—	2	1	no	—
335	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
336	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
341	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
349	Q₁₆	—	2	2	no	—
350	SD₁₆	—	2	4	no	—
351	D₈	—	2	2	no	—
352	M₁₆	—	2	2	no	—
353	M₁₆	—	2	1	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	1	no	—
356	M₁₆	—	2	1	no	—
357	M₁₆	—	2	1	no	—
358	M₁₆	—	4	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	4	2	no	—
365	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
366	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
367	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
368	C₂×C₈	#41×C₄₇	1	2	yes	—
369	C₂×C₈	#41×C₄₇	1	2	yes	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	8	4	no	—
377	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
378	C₂²⋊C₄	—	2	1	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	4	2	no	—
385	C₄²	#41×C₄₇	1	2	yes	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	1	no	—
388	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
389	Q₈	—	2	2	no	—
390	Q₈	—	2	1	no	—
391	Q₈	—	2	1	no	—
392	Q₈	—	2	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	1	no	—
395	D₄	—	2	1	no	—
396	D₄	—	2	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	1	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	1	no	—
401	D₄	—	16	2	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	8	2	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	—	16	2	no	—
416	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
418	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
420	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
421	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
422	C₈	—	2	2	no	—
423	C₈	—	4	1	no	—
424	C₈	—	4	2	no	—
425	C₈	—	4	1	no	—
426	C₈	#123×C₄₇	1	2	yes	—
427	C₈	#123×C₄₇	1	2	yes	—
428	C₂²	—	2	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	2	no	—
434	C₂²	C₄₇×#542	1	1	yes	characteristic
435	C₂²	D₄²×C₄₇	1	1	yes	characteristic
436	C₂²	C₄₇×#553	1	1	yes	characteristic
437	C₄	—	2	4	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	8	2	no	—
442	C₄	—	8	2	no	—
443	C₄	C₂×#123×C₄₇	1	1	yes	characteristic
444	C₄	C₄₇×#532	1	1	yes	characteristic
445	C₄	C₄₇×#547	1	1	yes	characteristic
446	C₄	C₄₇×#547	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	8	2	no	—
450	C₂	—	8	1	no	—
451	C₂	C₄₇×#2422	1	1	yes	characteristic
452	C₂	C₄₇×#3291	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₇	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₄₇×#3060	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂²×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#3099	C₂	semidirect
3. C₄₇×#2952	C₂	semidirect
4. C₄₇×#2079	C₂	semidirect
5. C₄₇×#2039	C₂	semidirect
6. C₄₇×#1974	C₂	semidirect
7. C₄₇×#1951	C₂	semidirect
8. C₄₇×#1859	C₂	semidirect
9. C₄₇×#1844	C₂	semidirect
10. C₄₇×#1815	C₂	semidirect
11. C₄₇×#1764	C₂	semidirect
201. #25051	C₄₇	direct (N × H)
221. #3099	C₂×C₄₇	semidirect
223. #2952	C₂×C₄₇	semidirect
224. #2079	C₂×C₄₇	semidirect
225. #2039	C₂×C₄₇	semidirect
226. #1974	C₂×C₄₇	semidirect
227. #1951	C₂×C₄₇	semidirect
228. #1859	C₂×C₄₇	semidirect
229. #1844	C₂×C₄₇	semidirect
230. #1815	C₂×C₄₇	semidirect
231. #1764	C₂×C₄₇	semidirect
271. C₄₇	#25051	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×#3099	2
C₄₇×#3060	2
C₄₇×#2952	2
C₄₇×#2079	2
C₄₇×#2039	2
C₄₇×#1974	2
C₄₇×#1951	2
C₄₇×#1859	2
C₄₇×#1844	2
C₄₇×#1815	2
C₄₇×#1764	2
#25051	47

Subgroups — C47×#25051 #26064749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#25051 #26064749