Subgroups — D₄₇×#1951 #26219814

Order 12032.

918 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#108×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#428×D₄₇	C₂	1	2	yes	maximal
3	C₂×#106×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#405×D₄₇	C₂	1	1	yes	maximal, characteristic
5	#20244169	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244168	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244167	C₂	1	2	yes	maximal, complemented
8	#20244166	C₂	1	1	yes	maximal, characteristic, complemented
9	#20244165	C₂	1	2	yes	maximal, complemented
10	#343×D₄₇	C₂	1	2	yes	maximal
11	C₄₇×#1951	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₄₇	C₂²	1	2	yes	—
13	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
15	#117×D₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
17	C₂×#13093960	C₂²	1	1	yes	characteristic
18	C₂×#13093959	C₂²	1	2	yes	—
19	#108×D₄₇	C₄	1	8	yes	complemented
20	#15689166	C₂²	1	2	yes	—
21	#15689165	C₂²	1	2	yes	—
22	#15689164	—	2	2	no	—
23	#15689163	C₂²	1	2	yes	—
24	#15689162	—	2	2	no	—
25	#107×D₄₇	—	2	2	no	—
26	C₂×#13093956	C₂²	1	1	yes	characteristic
27	C₂×#13093955	C₂²	1	2	yes	—
28	#106×D₄₇	—	2	1	no	—
29	#106×D₄₇	—	2	1	no	—
30	#106×D₄₇	—	2	1	no	—
31	#106×D₄₇	—	2	1	no	—
32	#106×D₄₇	—	2	2	no	—
33	#15689081	C₂²	1	1	yes	characteristic
34	#15689080	—	2	1	no	—
35	#15689079	C₂²	1	1	yes	characteristic
36	#15689078	C₂²	1	1	yes	characteristic
37	#15689077	—	2	1	no	—
38	#97×D₄₇	—	2	1	no	—
39	C₄×C₈×D₄₇	—	2	1	no	—
40	#15688892	C₂²	1	2	yes	—
41	#15688891	C₂²	1	2	yes	—
42	#15688891	C₂²	1	2	yes	—
43	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
44	C₄₇×#428	C₂²	1	2	yes	—
45	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
46	C₄₇×#405	C₂²	1	1	yes	characteristic
47	C₄₇×#343	C₂²	1	2	yes	—
48	C₂²×C₄×D₄₇	—	2	2	no	—
49	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
50	C₂×#10625329	C₂³	1	2	yes	—
51	C₂×#10625329	C₂³	1	1	yes	characteristic
52	C₂×#10625324	—	2	1	no	—
53	C₂×#10625324	—	2	2	no	—
54	M₁₆×D₄₇	—	2	4	no	—
55	M₁₆×D₄₇	—	2	2	no	—
56	M₁₆×D₄₇	C₂×C₄	1	8	yes	—
57	M₁₆×D₄₇	Q₈	1	4	yes	—
58	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₄₇	—	2	1	no	—
60	C₂×C₈×D₄₇	—	2	2	no	—
61	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
62	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
63	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
64	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
65	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
66	C₂×C₈×D₄₇	Q₈	1	4	yes	—
67	#13093983	C₂³	1	1	yes	characteristic
68	#13093982	D₄	1	2	yes	—
69	#13093981	—	2	1	no	—
70	#13093980	—	2	1	no	—
71	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
72	C₂×Dic₄₇⋊C₄	—	2	2	no	—
73	C₄⋊C₄×D₄₇	—	2	2	no	—
74	C₄⋊C₄×D₄₇	—	2	2	no	—
75	C₄⋊C₄×D₄₇	—	2	2	no	—
76	C₄⋊C₄×D₄₇	—	2	2	no	—
77	C₄⋊C₄×D₄₇	D₄	1	2	yes	—
78	C₂²⋊C₄×D₄₇	—	2	1	no	—
79	C₄²×D₄₇	—	2	1	no	—
80	#13093960	C₂×C₄	1	4	yes	complemented
81	#13093959	C₂×C₄	1	8	yes	complemented
82	#13093958	—	2	2	no	—
83	#13093957	—	2	2	no	—
84	#13093957	—	2	2	no	—
85	#13093956	—	2	1	no	—
86	#13093956	—	2	1	no	—
87	#13093956	—	2	2	no	—
88	#13093955	—	2	2	no	—
89	#13093955	—	2	2	no	—
90	#13093955	—	2	2	no	—
91	#13093955	—	2	2	no	—
92	#13093935	—	2	1	no	—
93	#13093934	—	2	1	no	—
94	#13093934	—	2	1	no	—
95	C₄×C₄₇⋊C₈	—	2	1	no	—
96	C₈×Dic₄₇	—	2	1	no	—
97	C₈×Dic₄₇	—	2	1	no	—
98	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
99	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
101	#117×C₄₇	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
103	#108×C₄₇	C₂×C₄	1	4	yes	complemented
104	#107×C₄₇	—	2	2	no	—
105	#106×C₄₇	—	2	1	no	—
106	#106×C₄₇	—	2	1	no	—
107	#106×C₄₇	—	2	2	no	—
108	#97×C₄₇	—	2	1	no	—
109	C₄×C₈×C₄₇	—	2	1	no	—
110	C₂³×D₄₇	#41	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
113	C₂²×Dic₄₇	—	2	2	no	—
114	C₂²×Dic₄₇	#41	1	1	yes	characteristic
115	C₂×C₄×D₄₇	—	2	2	no	—
116	C₂×C₄×D₄₇	—	4	2	no	—
117	C₂×C₄×D₄₇	—	4	2	no	—
118	C₂×C₄×D₄₇	—	8	4	no	—
119	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
120	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
125	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
126	C₂×C₄×D₄₇	#41	1	2	yes	—
127	M₁₆×C₄₇	—	2	2	no	—
128	M₁₆×C₄₇	—	2	1	no	—
129	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
130	M₁₆×C₄₇	C₂×Q₈	1	2	yes	—
131	C₂×C₈×C₄₇	—	2	2	no	—
132	C₂×C₈×C₄₇	—	2	1	no	—
133	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
137	C₄⋊C₄×C₄₇	—	2	2	no	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
140	C₂²⋊C₄×C₄₇	—	2	1	no	—
141	C₄²×C₄₇	—	2	1	no	—
142	C₂²⋊Dic₄₇	—	2	1	no	—
143	(C₂×D₄₇)⋊C₄	—	2	2	no	—
144	C₄⋊Dic₄₇	—	2	2	no	—
145	C₄⋊Dic₄₇	—	2	2	no	—
146	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
147	Dic₄₇⋊C₄	—	2	2	no	—
148	Dic₄₇⋊C₄	—	4	2	no	—
149	Dic₄₇⋊C₄	—	4	2	no	—
150	C₄×Dic₄₇	—	2	1	no	—
151	C₄×Dic₄₇	—	2	2	no	—
152	#10625329	—	2	2	no	—
153	#10625329	—	2	1	no	—
154	#10625329	C₂²×C₄	1	4	yes	—
155	#10625329	C₂×Q₈	1	2	yes	—
156	C₂×C₄₇⋊C₈	—	2	1	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
159	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
162	#10625324	—	2	8	no	—
163	#10625324	—	2	4	no	—
164	C₈×D₄₇	—	2	8	no	—
165	C₈×D₄₇	—	2	4	no	—
166	C₈×D₄₇	C₄⋊C₄	1	4	yes	—
167	C₈×D₄₇	C₄⋊C₄	1	4	yes	—
168	C₈×D₄₇	C₄⋊C₄	1	4	yes	—
169	C₈×D₄₇	C₄⋊C₄	1	4	yes	—
170	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
171	C₂²×D₄₇	—	2	4	no	—
172	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
173	C₂²×D₄₇	#121	1	1	yes	characteristic
174	C₂²×D₄₇	#121	1	1	yes	characteristic
175	C₂²×D₄₇	#125	1	2	yes	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	8	2	no	—
179	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
185	C₂×Dic₄₇	—	2	2	no	—
186	C₂×Dic₄₇	—	4	2	no	—
187	C₂×Dic₄₇	—	8	2	no	—
188	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
189	C₂×Dic₄₇	#121	1	1	yes	characteristic
190	C₂×Dic₄₇	#121	1	1	yes	characteristic
191	C₂×Dic₄₇	#125	1	2	yes	—
192	C₄×D₄₇	—	4	4	no	—
193	C₄×D₄₇	—	8	4	no	—
194	C₄×D₄₇	—	8	4	no	—
195	C₄×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
196	C₄×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
197	C₄×D₄₇	C₄×D₄	1	2	yes	—
198	C₄×D₄₇	C₄×D₄	1	2	yes	—
199	C₄×D₄₇	C₂²⋊Q₈	1	2	yes	—
200	C₄×D₄₇	C₂²⋊Q₈	1	2	yes	—
201	C₄×D₄₇	C₄⋊Q₈	1	2	yes	—
202	C₄×D₄₇	C₄⋊Q₈	1	2	yes	—
203	C₈×C₄₇	—	2	4	no	—
204	C₈×C₄₇	—	2	2	no	—
205	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
206	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
207	C₄₇⋊C₈	—	2	4	no	—
208	C₄₇⋊C₈	—	2	2	no	—
209	C₄₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
210	C₄₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
211	C₂×#1951	—	47	1	no	maximal, Sylow
212	C₂²×C₄₇	—	2	2	no	—
213	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
214	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
215	C₂²×C₄₇	C₂×#125	1	1	yes	characteristic
216	C₂×D₄₇	—	2	2	no	—
217	C₂×D₄₇	—	2	4	no	—
218	C₂×D₄₇	—	2	4	no	—
219	C₂×D₄₇	#389	1	2	yes	—
220	C₂×D₄₇	#389	1	2	yes	—
221	C₂×D₄₇	#471	1	4	yes	—
222	C₄×C₄₇	—	4	2	no	—
223	C₄×C₄₇	—	8	2	no	—
224	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
225	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
226	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
227	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
228	Dic₄₇	—	4	2	no	—
229	Dic₄₇	—	8	2	no	—
230	Dic₄₇	#389	1	2	yes	—
231	Dic₄₇	#389	1	2	yes	—
232	C₂²×#108	—	47	1	no	—
233	C₂×#428	—	47	2	no	—
234	C₂²×#106	—	47	1	no	—
235	C₂×#405	—	47	1	no	—
236	#1951	—	47	1	no	—
237	#1951	—	47	2	no	—
238	#1951	—	47	1	no	—
239	#1951	—	47	1	no	—
240	#1951	—	47	2	no	—
241	#1951	D₄₇	1	1	yes	characteristic, direct product factor
242	C₂×#343	—	47	2	no	—
243	C₂×C₄₇	—	2	1	no	—
244	C₂×C₄₇	—	2	1	no	—
245	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
246	C₂×C₄₇	C₂×#471	1	2	yes	—
247	D₄₇	—	2	2	no	—
248	D₄₇	#1951	1	4	yes	direct product factor
249	C₂²×M₁₆	—	47	1	no	—
250	C₂²×M₁₆	—	47	2	no	—
251	C₂³×C₈	—	47	1	no	—
252	C₂×#117	—	47	1	no	—
253	C₂²×C₄⋊C₄	—	47	2	no	—
254	C₂×#108	—	47	2	no	—
255	C₂×#108	—	47	1	no	—
256	C₂×#108	—	47	8	no	—
257	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
258	#428	—	47	2	no	—
259	#428	—	47	2	no	—
260	#428	—	47	2	no	—
261	#428	—	94	2	no	—
262	#428	—	94	2	no	—
263	#428	C₂×D₄₇	1	2	yes	—
264	C₂×#107	—	94	2	no	—
265	C₂×#106	—	47	1	no	—
266	C₂×#106	—	47	2	no	—
267	C₂×#106	—	94	2	no	—
268	C₂×#106	—	94	1	no	—
269	C₂×#106	—	94	1	no	—
270	C₂×#106	—	94	1	no	—
271	C₂×#106	—	94	1	no	—
272	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
273	#405	—	47	1	no	—
274	#405	—	47	1	no	—
275	#405	—	47	1	no	—
276	#405	—	94	1	no	—
277	#405	—	94	1	no	—
278	#405	C₂×D₄₇	1	1	yes	characteristic
279	C₂×#97	—	94	1	no	—
280	C₂×C₄×C₈	—	94	1	no	—
281	#343	—	47	2	no	—
282	#343	—	47	2	no	—
283	#343	—	47	2	no	—
284	#343	C₂×D₄₇	1	2	yes	—
285	C₄₇	C₂×#1951	1	1	yes	characteristic, complemented, Sylow
286	C₂³×C₄	—	47	1	no	—
287	C₂³×C₄	—	94	2	no	—
288	C₂×M₁₆	—	47	1	no	—
289	C₂×M₁₆	—	47	2	no	—
290	C₂×M₁₆	—	47	8	no	—
291	C₂×M₁₆	—	47	4	no	—
292	C₂×M₁₆	—	94	1	no	—
293	C₂×M₁₆	—	94	2	no	—
294	C₂×M₁₆	—	94	2	no	—
295	C₂×M₁₆	—	94	4	no	—
296	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
297	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
298	C₂²×C₈	—	47	1	no	—
299	C₂²×C₈	—	47	4	no	—
300	C₂²×C₈	—	47	1	no	—
301	C₂²×C₈	—	47	1	no	—
302	C₂²×C₈	—	47	1	no	—
303	C₂²×C₈	—	47	1	no	—
304	C₂²×C₈	—	47	4	no	—
305	C₂²×C₈	—	94	1	no	—
306	C₂²×C₈	—	94	2	no	—
307	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
308	#117	—	47	1	no	—
309	#117	—	47	2	no	—
310	#117	—	94	1	no	—
311	#117	—	94	1	no	—
312	#117	C₂²×D₄₇	1	1	yes	characteristic
313	C₂×C₄⋊C₄	—	47	2	no	—
314	C₂×C₄⋊C₄	—	47	2	no	—
315	C₂×C₄⋊C₄	—	94	2	no	—
316	C₂×C₄⋊C₄	—	94	2	no	—
317	C₂×C₄⋊C₄	—	94	2	no	—
318	C₂×C₄⋊C₄	—	94	2	no	—
319	C₂×C₄⋊C₄	—	94	2	no	—
320	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
321	C₂×C₂²⋊C₄	—	94	1	no	—
322	C₂×C₄²	—	94	1	no	—
323	#108	—	47	8	no	—
324	#108	—	47	4	no	—
325	#108	C₄×D₄₇	1	4	yes	complemented
326	#107	—	2	2	no	—
327	#107	—	94	2	no	—
328	#107	—	94	2	no	—
329	#107	—	94	2	no	—
330	#106	—	2	1	no	—
331	#106	—	2	1	no	—
332	#106	—	2	2	no	—
333	#106	—	94	2	no	—
334	#106	—	94	2	no	—
335	#106	—	94	2	no	—
336	#106	—	94	2	no	—
337	#106	—	94	1	no	—
338	#106	—	94	1	no	—
339	#106	—	94	2	no	—
340	#97	—	2	1	no	—
341	#97	—	94	1	no	—
342	#97	—	94	1	no	—
343	#97	—	94	1	no	—
344	C₄×C₈	—	2	1	no	—
345	C₄×C₈	—	94	1	no	—
346	C₄×C₈	—	94	1	no	—
347	C₄×C₈	—	94	1	no	—
348	C₂⁴	—	47	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	47	1	no	—
351	C₂²×C₄	—	47	2	no	—
352	C₂²×C₄	—	47	1	no	—
353	C₂²×C₄	—	47	1	no	—
354	C₂²×C₄	—	47	1	no	—
355	C₂²×C₄	—	47	1	no	—
356	C₂²×C₄	—	47	2	no	—
357	C₂²×C₄	—	47	2	no	—
358	C₂²×C₄	—	47	2	no	—
359	C₂²×C₄	—	94	2	no	—
360	C₂²×C₄	—	94	2	no	—
361	C₂²×C₄	—	376	4	no	—
362	C₂²×C₄	—	188	2	no	—
363	C₂²×C₄	—	188	2	no	—
364	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
365	M₁₆	—	2	2	no	—
366	M₁₆	—	2	1	no	—
367	M₁₆	—	47	4	no	—
368	M₁₆	—	47	2	no	—
369	M₁₆	—	94	8	no	—
370	M₁₆	—	94	4	no	—
371	M₁₆	—	94	2	no	—
372	M₁₆	—	94	1	no	—
373	M₁₆	C₂×C₄×D₄₇	1	4	yes	—
374	M₁₆	Q₈×D₄₇	1	2	yes	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	47	2	no	—
378	C₂×C₈	—	47	1	no	—
379	C₂×C₈	—	47	1	no	—
380	C₂×C₈	—	47	2	no	—
381	C₂×C₈	—	47	4	no	—
382	C₂×C₈	—	47	4	no	—
383	C₂×C₈	—	47	4	no	—
384	C₂×C₈	—	47	4	no	—
385	C₂×C₈	—	94	8	no	—
386	C₂×C₈	—	94	4	no	—
387	C₂×C₈	—	94	1	no	—
388	C₂×C₈	—	94	2	no	—
389	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
390	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
391	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
392	C₂×C₈	Q₈×D₄₇	1	2	yes	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	47	2	no	—
396	C₄⋊C₄	—	94	2	no	—
397	C₄⋊C₄	—	94	2	no	—
398	C₄⋊C₄	—	94	2	no	—
399	C₄⋊C₄	—	188	2	no	—
400	C₄⋊C₄	—	188	2	no	—
401	C₄⋊C₄	D₄×D₄₇	1	2	yes	—
402	C₂²⋊C₄	—	2	1	no	—
403	C₂²⋊C₄	—	94	2	no	—
404	C₂²⋊C₄	—	94	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	94	2	no	—
407	C₄²	—	94	1	no	—
408	C₂³	—	47	1	no	—
409	C₂³	—	47	2	no	—
410	C₂³	—	47	1	no	—
411	C₂³	—	47	2	no	—
412	C₂³	—	94	4	no	—
413	C₂³	#41×D₄₇	1	1	yes	characteristic
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	8	2	no	—
417	C₂×C₄	—	47	2	no	—
418	C₂×C₄	—	47	1	no	—
419	C₂×C₄	—	47	1	no	—
420	C₂×C₄	—	47	2	no	—
421	C₂×C₄	—	47	2	no	—
422	C₂×C₄	—	47	2	no	—
423	C₂×C₄	—	47	2	no	—
424	C₂×C₄	—	47	2	no	—
425	C₂×C₄	—	47	2	no	—
426	C₂×C₄	—	47	2	no	—
427	C₂×C₄	—	47	2	no	—
428	C₂×C₄	—	47	2	no	—
429	C₂×C₄	—	94	2	no	—
430	C₂×C₄	—	376	4	no	—
431	C₂×C₄	—	376	4	no	—
432	C₂×C₄	—	376	2	no	—
433	C₂×C₄	—	188	4	no	—
434	C₂×C₄	—	188	2	no	—
435	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
436	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
437	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
438	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
439	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
440	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
441	C₈	—	2	4	no	—
442	C₈	—	2	2	no	—
443	C₈	—	47	2	no	—
444	C₈	—	47	2	no	—
445	C₈	—	94	4	no	—
446	C₈	—	94	2	no	—
447	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
448	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
449	C₂²	—	2	2	no	—
450	C₂²	—	47	2	no	—
451	C₂²	—	47	4	no	—
452	C₂²	—	47	2	no	—
453	C₂²	—	94	4	no	—
454	C₂²	—	94	4	no	—
455	C₂²	—	94	2	no	—
456	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
457	C₂²	#121×D₄₇	1	1	yes	characteristic
458	C₂²	#125×D₄₇	1	1	yes	characteristic
459	C₄	—	4	2	no	—
460	C₄	—	8	2	no	—
461	C₄	—	47	2	no	—
462	C₄	—	47	2	no	—
463	C₄	—	376	2	no	—
464	C₄	—	188	2	no	—
465	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
466	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
467	C₄	C₂²⋊Q₈×D₄₇	1	1	yes	characteristic
468	C₄	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
469	C₂	—	2	1	no	—
470	C₂	—	2	1	no	—
471	C₂	—	47	4	no	—
472	C₂	—	94	2	no	—
473	C₂	#389×D₄₇	1	1	yes	characteristic
474	C₂	#471×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂²	#121×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1951	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	C₂³×D₄₇	#41
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1951	D₄₇
hypocenter	C₄₇	C₂×#1951
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1951

Complements

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

N	H ≅ G/N	type
5. #20244169	C₂	semidirect
6. #20244168	C₂	semidirect
7. #20244167	C₂	semidirect
8. #20244166	C₂	semidirect
9. #20244165	C₂	semidirect
11. C₄₇×#1951	C₂	semidirect
19. #108×D₄₇	C₄	semidirect
80. #13093960	C₂×C₄	semidirect
81. #13093959	C₂×C₄	semidirect
103. #108×C₄₇	C₂×C₄	semidirect
241. #1951	D₄₇	direct (N × H)
248. D₄₇	#1951	direct (N × H)
285. C₄₇	C₂×#1951	semidirect
325. #108	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#108×D₄₇	2
#428×D₄₇	2
C₂×#106×D₄₇	2
#405×D₄₇	2
#20244169	2
#20244168	2
#20244167	2
#20244166	2
#20244165	2
#343×D₄₇	2
C₄₇×#1951	2
C₂×#1951	47

Subgroups — D47×#1951 #26219814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#1951 #26219814