Subgroups — D₄₇×#1942 #26219601

Order 12032.

1182 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#107×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#107×D₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#389×D₄₇	C₂	1	2	yes	maximal
5	#20244122	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244121	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244120	C₂	1	2	yes	maximal, complemented
8	#20244119	C₂	1	1	yes	maximal, characteristic, complemented
9	#20244118	C₂	1	2	yes	maximal, complemented
10	#340×D₄₇	C₂	1	2	yes	maximal
11	C₄₇×#1942	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×D₄₇	—	2	2	no	—
15	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
16	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
17	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
18	C₂×#13093958	C₂²	1	1	yes	characteristic
19	C₂×#13093958	C₂²	1	1	yes	characteristic
20	C₂×#13093957	C₂²	1	2	yes	—
21	C₂×#13093957	C₂²	1	2	yes	—
22	#107×D₄₇	—	2	4	no	—
23	#107×D₄₇	C₄	1	8	yes	complemented
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₄₇	—	2	4	no	—
28	#15689022	C₂²	1	2	yes	—
29	#15689021	C₂²	1	2	yes	—
30	#15689020	—	2	2	no	—
31	#15689019	C₂²	1	2	yes	—
32	#15689018	—	2	2	no	—
33	#95×D₄₇	—	2	2	no	—
34	#15688886	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	#15688885	C₂²	1	2	yes	—
37	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#389	C₂²	1	2	yes	—
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₂²×C₄×D₄₇	—	2	2	no	—
43	C₂²×C₄×D₄₇	—	2	2	no	—
44	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
46	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂×C₈×D₄₇	—	2	2	no	—
50	C₂×C₈×D₄₇	—	2	2	no	—
51	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
52	C₂×C₈×D₄₇	D₄	1	4	yes	—
53	C₂×C₈×D₄₇	Q₈	1	4	yes	—
54	C₂×C₈×D₄₇	Q₈	1	4	yes	—
55	C₂×C₄⋊Dic₄₇	—	2	2	no	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
58	C₂×Dic₄₇⋊C₄	—	2	2	no	—
59	C₂×Dic₄₇⋊C₄	—	2	2	no	—
60	C₂×Dic₄₇⋊C₄	—	2	2	no	—
61	C₂×Dic₄₇⋊C₄	—	2	2	no	—
62	C₄⋊C₄×D₄₇	—	2	4	no	—
63	C₄⋊C₄×D₄₇	—	2	4	no	—
64	C₄⋊C₄×D₄₇	—	2	4	no	—
65	C₄⋊C₄×D₄₇	—	4	8	no	—
66	C₄⋊C₄×D₄₇	C₂×C₄	1	8	yes	—
67	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
68	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
69	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
70	C₄²×D₄₇	—	2	2	no	—
71	C₄²×D₄₇	—	2	2	no	—
72	#13093958	—	2	2	no	—
73	#13093958	C₂×C₄	1	4	yes	complemented
74	#13093957	—	2	4	no	—
75	#13093957	C₂×C₄	1	8	yes	complemented
76	C₄×C₄₇⋊C₈	—	2	2	no	—
77	C₈×Dic₄₇	—	2	2	no	—
78	C₈×Dic₄₇	—	2	2	no	—
79	C₄₇⋊#95	—	2	2	no	—
80	C₄₇⋊#95	—	2	2	no	—
81	C₄₇⋊#95	—	2	2	no	—
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	#107×C₄₇	—	2	2	no	—
89	#107×C₄₇	C₂×C₄	1	4	yes	complemented
90	C₄×C₈×C₄₇	—	2	2	no	—
91	#95×C₄₇	—	2	2	no	—
92	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
98	C₂²×Dic₄₇	—	2	2	no	—
99	C₂²×Dic₄₇	—	2	2	no	—
100	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₄₇	—	2	2	no	—
104	C₂×C₄×D₄₇	—	2	2	no	—
105	C₂×C₄×D₄₇	—	2	2	no	—
106	C₂×C₄×D₄₇	—	2	2	no	—
107	C₂×C₄×D₄₇	—	2	8	no	—
108	C₂×C₄×D₄₇	—	4	4	no	—
109	C₂×C₄×D₄₇	—	4	4	no	—
110	C₂×C₄×D₄₇	—	4	4	no	—
111	C₂×C₄×D₄₇	—	4	4	no	—
112	C₂×C₄×D₄₇	—	4	4	no	—
113	C₂×C₄×D₄₇	D₈	1	4	yes	—
114	C₂×C₄×D₄₇	Q₁₆	1	4	yes	—
115	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
116	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
117	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
118	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
119	C₂×C₄×D₄₇	#41	1	2	yes	—
120	C₂×C₄×D₄₇	#41	1	2	yes	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
126	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
127	C₄⋊C₄×C₄₇	—	2	2	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	—	4	4	no	—
131	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
132	C₄²×C₄₇	—	2	1	no	—
133	C₄²×C₄₇	—	2	1	no	—
134	C₄⋊Dic₄₇	—	2	2	no	—
135	C₄⋊Dic₄₇	—	2	2	no	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	—	4	4	no	—
138	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
139	Dic₄₇⋊C₄	—	2	8	no	—
140	Dic₄₇⋊C₄	—	4	4	no	—
141	Dic₄₇⋊C₄	—	4	4	no	—
142	Dic₄₇⋊C₄	—	4	4	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	2	1	no	—
145	C₄×Dic₄₇	—	2	2	no	—
146	C₄×Dic₄₇	—	2	2	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
150	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
151	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
152	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
153	C₈×D₄₇	—	2	8	no	—
154	C₈×D₄₇	C₄⋊C₄	1	16	yes	complemented
155	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
156	C₂²×D₄₇	C₄×D₄	1	2	yes	—
157	C₂²×D₄₇	#121	1	2	yes	—
158	C₂²×D₄₇	C₄⋊Q₈	1	2	yes	—
159	C₂²×D₄₇	C₂×D₈	1	2	yes	—
160	C₂²×D₄₇	C₂×Q₁₆	1	2	yes	—
161	C₂²×D₄₇	#135	1	2	yes	—
162	C₂²×D₄₇	#135	1	2	yes	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	4	no	—
168	C₂×C₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
174	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
175	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂×Dic₄₇	—	2	1	no	—
182	C₂×Dic₄₇	—	2	1	no	—
183	C₂×Dic₄₇	—	2	1	no	—
184	C₂×Dic₄₇	—	2	1	no	—
185	C₂×Dic₄₇	—	2	4	no	—
186	C₂×Dic₄₇	—	4	2	no	—
187	C₂×Dic₄₇	—	4	2	no	—
188	C₂×Dic₄₇	—	4	2	no	—
189	C₂×Dic₄₇	—	4	2	no	—
190	C₂×Dic₄₇	—	4	2	no	—
191	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
192	C₂×Dic₄₇	#121	1	2	yes	—
193	C₂×Dic₄₇	C₄⋊Q₈	1	2	yes	—
194	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
195	C₂×Dic₄₇	C₂×Q₁₆	1	2	yes	—
196	C₄×D₄₇	—	2	8	no	—
197	C₄×D₄₇	—	2	8	no	—
198	C₄×D₄₇	—	4	16	no	—
199	C₄×D₄₇	—	8	8	no	—
200	C₄×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
201	C₄×D₄₇	C₄×Q₈	1	4	yes	—
202	C₄×D₄₇	C₂²⋊Q₈	1	4	yes	—
203	C₄×D₄₇	#125	1	4	yes	—
204	C₈×C₄₇	—	2	2	no	—
205	C₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	complemented
206	C₄₇⋊C₈	—	2	2	no	—
207	C₄₇⋊C₈	C₂×C₄⋊C₄	1	4	yes	complemented
208	C₂×#1942	—	47	1	no	maximal, Sylow
209	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
210	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
211	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
212	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
213	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
214	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
215	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
216	C₂×D₄₇	#389	1	4	yes	—
217	C₂×D₄₇	C₄×D₈	1	4	yes	—
218	C₂×D₄₇	C₄×Q₁₆	1	4	yes	—
219	C₂×D₄₇	#466	1	4	yes	—
220	C₂×D₄₇	#467	1	4	yes	—
221	C₂×D₄₇	#499	1	4	yes	—
222	C₂×D₄₇	#500	1	4	yes	—
223	C₄×C₄₇	—	2	2	no	—
224	C₄×C₄₇	—	2	2	no	—
225	C₄×C₄₇	—	4	4	no	—
226	C₄×C₄₇	—	8	2	no	—
227	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
228	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
229	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
230	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
231	Dic₄₇	—	2	2	no	—
232	Dic₄₇	—	2	2	no	—
233	Dic₄₇	—	4	4	no	—
234	Dic₄₇	—	8	2	no	—
235	Dic₄₇	#389	1	4	yes	—
236	C₂²×#107	—	47	1	no	—
237	C₂²×#107	—	47	1	no	—
238	C₂²×C₄×C₈	—	47	1	no	—
239	C₂×#389	—	47	2	no	—
240	#1942	—	47	1	no	—
241	#1942	—	47	1	no	—
242	#1942	—	47	1	no	—
243	#1942	—	47	2	no	—
244	#1942	—	47	2	no	—
245	#1942	D₄₇	1	1	yes	characteristic, direct product factor
246	C₂×#340	—	47	2	no	—
247	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
248	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
249	C₂×C₄₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
250	C₂×C₄₇	C₂×#466	1	1	yes	characteristic
251	C₂×C₄₇	C₂×#467	1	1	yes	characteristic
252	C₂×C₄₇	C₂×#499	1	1	yes	characteristic
253	C₂×C₄₇	C₂×#500	1	1	yes	characteristic
254	D₄₇	#1942	1	8	yes	direct product factor
255	C₂³×C₈	—	47	1	no	—
256	C₂³×C₈	—	47	1	no	—
257	C₂²×C₄⋊C₄	—	47	2	no	—
258	C₂²×C₄⋊C₄	—	47	2	no	—
259	C₂²×C₄⋊C₄	—	94	2	no	—
260	C₂²×C₄²	—	47	1	no	—
261	C₂×#107	—	47	1	no	—
262	C₂×#107	—	47	2	no	—
263	C₂×#107	—	47	8	no	—
264	C₂×#107	—	47	1	no	—
265	C₂×#107	—	47	2	no	—
266	C₂×#107	—	94	4	no	—
267	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
268	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
269	C₂×C₄×C₈	—	47	1	no	—
270	C₂×C₄×C₈	—	47	1	no	—
271	C₂×C₄×C₈	—	47	1	no	—
272	C₂×C₄×C₈	—	94	4	no	—
273	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
274	#389	—	47	2	no	—
275	#389	—	47	2	no	—
276	#389	—	47	2	no	—
277	#389	—	94	2	no	—
278	#389	—	94	2	no	—
279	#389	C₂×D₄₇	1	2	yes	—
280	C₂×#95	—	94	2	no	—
281	#340	—	47	2	no	—
282	#340	—	47	2	no	—
283	#340	—	47	2	no	—
284	#340	C₂×D₄₇	1	2	yes	—
285	C₄₇	C₂×#1942	1	1	yes	characteristic, complemented, Sylow
286	C₂³×C₄	—	47	1	no	—
287	C₂³×C₄	—	47	1	no	—
288	C₂³×C₄	—	47	1	no	—
289	C₂³×C₄	—	94	2	no	—
290	C₂³×C₄	—	94	2	no	—
291	C₂²×C₈	—	47	1	no	—
292	C₂²×C₈	—	47	4	no	—
293	C₂²×C₈	—	47	4	no	—
294	C₂²×C₈	—	47	4	no	—
295	C₂²×C₈	—	47	1	no	—
296	C₂²×C₈	—	47	4	no	—
297	C₂²×C₈	—	94	2	no	—
298	C₂²×C₈	—	94	2	no	—
299	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
300	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	47	2	no	—
303	C₂×C₄⋊C₄	—	47	8	no	—
304	C₂×C₄⋊C₄	—	47	2	no	—
305	C₂×C₄⋊C₄	—	94	4	no	—
306	C₂×C₄⋊C₄	—	94	4	no	—
307	C₂×C₄⋊C₄	—	94	4	no	—
308	C₂×C₄⋊C₄	—	94	2	no	—
309	C₂×C₄⋊C₄	—	94	2	no	—
310	C₂×C₄⋊C₄	—	94	2	no	—
311	C₂×C₄⋊C₄	—	94	2	no	—
312	C₂×C₄⋊C₄	—	94	2	no	—
313	C₂×C₄⋊C₄	—	188	8	no	—
314	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
315	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
316	C₂×C₄²	—	47	1	no	—
317	C₂×C₄²	—	47	1	no	—
318	C₂×C₄²	—	47	1	no	—
319	C₂×C₄²	—	94	2	no	—
320	C₂×C₄²	—	94	2	no	—
321	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
322	#107	—	2	2	no	—
323	#107	—	47	4	no	—
324	#107	—	47	8	no	—
325	#107	—	94	4	no	—
326	#107	—	94	2	no	—
327	#107	C₄×D₄₇	1	4	yes	complemented
328	C₄×C₈	—	2	2	no	—
329	C₄×C₈	—	94	2	no	—
330	C₄×C₈	—	94	2	no	—
331	C₄×C₈	—	94	2	no	—
332	#95	—	2	2	no	—
333	#95	—	94	2	no	—
334	#95	—	94	2	no	—
335	#95	—	94	2	no	—
336	C₂⁴	—	47	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	47	1	no	—
340	C₂²×C₄	—	47	2	no	—
341	C₂²×C₄	—	47	2	no	—
342	C₂²×C₄	—	47	2	no	—
343	C₂²×C₄	—	47	2	no	—
344	C₂²×C₄	—	47	2	no	—
345	C₂²×C₄	—	47	2	no	—
346	C₂²×C₄	—	47	1	no	—
347	C₂²×C₄	—	47	1	no	—
348	C₂²×C₄	—	47	4	no	—
349	C₂²×C₄	—	47	4	no	—
350	C₂²×C₄	—	94	2	no	—
351	C₂²×C₄	—	94	2	no	—
352	C₂²×C₄	—	94	2	no	—
353	C₂²×C₄	—	94	2	no	—
354	C₂²×C₄	—	94	8	no	—
355	C₂²×C₄	—	94	2	no	—
356	C₂²×C₄	—	94	2	no	—
357	C₂²×C₄	—	188	4	no	—
358	C₂²×C₄	—	188	4	no	—
359	C₂²×C₄	—	188	4	no	—
360	C₂²×C₄	—	188	4	no	—
361	C₂²×C₄	—	188	4	no	—
362	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
363	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
364	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	47	2	no	—
368	C₂×C₈	—	47	2	no	—
369	C₂×C₈	—	47	2	no	—
370	C₂×C₈	—	47	16	no	—
371	C₂×C₈	—	47	2	no	—
372	C₂×C₈	—	94	8	no	—
373	C₂×C₈	—	94	1	no	—
374	C₂×C₈	—	94	1	no	—
375	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
376	C₂×C₈	D₄×D₄₇	1	2	yes	—
377	C₂×C₈	Q₈×D₄₇	1	2	yes	—
378	C₂×C₈	Q₈×D₄₇	1	2	yes	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄⋊C₄	—	47	4	no	—
384	C₄⋊C₄	—	94	8	no	—
385	C₄⋊C₄	—	94	2	no	—
386	C₄⋊C₄	—	94	2	no	—
387	C₄⋊C₄	—	94	2	no	—
388	C₄⋊C₄	—	188	4	no	—
389	C₄⋊C₄	—	188	4	no	—
390	C₄⋊C₄	—	188	4	no	—
391	C₄⋊C₄	—	188	4	no	—
392	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	94	2	no	—
396	C₄²	—	94	2	no	—
397	C₄²	—	94	1	no	—
398	C₄²	—	94	1	no	—
399	C₂³	—	47	2	no	—
400	C₂³	—	47	2	no	—
401	C₂³	—	47	2	no	—
402	C₂³	—	47	2	no	—
403	C₂³	—	47	2	no	—
404	C₂³	—	47	2	no	—
405	C₂³	—	47	2	no	—
406	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	47	2	no	—
418	C₂×C₄	—	47	2	no	—
419	C₂×C₄	—	47	2	no	—
420	C₂×C₄	—	47	4	no	—
421	C₂×C₄	—	47	4	no	—
422	C₂×C₄	—	47	4	no	—
423	C₂×C₄	—	47	4	no	—
424	C₂×C₄	—	47	2	no	—
425	C₂×C₄	—	47	2	no	—
426	C₂×C₄	—	94	8	no	—
427	C₂×C₄	—	94	8	no	—
428	C₂×C₄	—	94	1	no	—
429	C₂×C₄	—	94	1	no	—
430	C₂×C₄	—	94	1	no	—
431	C₂×C₄	—	94	1	no	—
432	C₂×C₄	—	94	4	no	—
433	C₂×C₄	—	376	8	no	—
434	C₂×C₄	—	188	16	no	—
435	C₂×C₄	—	188	2	no	—
436	C₂×C₄	—	188	2	no	—
437	C₂×C₄	—	188	2	no	—
438	C₂×C₄	—	188	2	no	—
439	C₂×C₄	—	188	2	no	—
440	C₂×C₄	D₈×D₄₇	1	2	yes	—
441	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
442	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
443	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
444	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
445	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
446	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
447	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
448	C₈	—	2	2	no	—
449	C₈	—	47	4	no	—
450	C₈	—	94	2	no	—
451	C₈	C₄⋊C₄×D₄₇	1	4	yes	complemented
452	C₂²	—	47	4	no	—
453	C₂²	—	47	4	no	—
454	C₂²	—	47	4	no	—
455	C₂²	—	47	4	no	—
456	C₂²	—	47	4	no	—
457	C₂²	—	47	4	no	—
458	C₂²	—	47	4	no	—
459	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
460	C₂²	#121×D₄₇	1	1	yes	characteristic
461	C₂²	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
462	C₂²	C₂×D₈×D₄₇	1	1	yes	characteristic
463	C₂²	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
464	C₂²	#135×D₄₇	1	1	yes	characteristic
465	C₂²	#135×D₄₇	1	1	yes	characteristic
466	C₄	—	2	2	no	—
467	C₄	—	2	2	no	—
468	C₄	—	4	4	no	—
469	C₄	—	8	2	no	—
470	C₄	—	47	4	no	—
471	C₄	—	94	2	no	—
472	C₄	—	94	2	no	—
473	C₄	—	376	2	no	—
474	C₄	—	188	4	no	—
475	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
476	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
477	C₄	C₂²⋊Q₈×D₄₇	1	1	yes	characteristic
478	C₄	#125×D₄₇	1	1	yes	characteristic
479	C₂	—	47	8	no	—
480	C₂	#389×D₄₇	1	1	yes	characteristic
481	C₂	C₄×D₈×D₄₇	1	1	yes	characteristic
482	C₂	C₄×Q₁₆×D₄₇	1	1	yes	characteristic
483	C₂	#466×D₄₇	1	1	yes	characteristic
484	C₂	#467×D₄₇	1	1	yes	characteristic
485	C₂	#499×D₄₇	1	1	yes	characteristic
486	C₂	#500×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1942	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1942	D₄₇
hypocenter	C₄₇	C₂×#1942
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1942

Complements

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

N	H ≅ G/N	type
5. #20244122	C₂	semidirect
6. #20244121	C₂	semidirect
7. #20244120	C₂	semidirect
8. #20244119	C₂	semidirect
9. #20244118	C₂	semidirect
11. C₄₇×#1942	C₂	semidirect
23. #107×D₄₇	C₄	semidirect
73. #13093958	C₂×C₄	semidirect
75. #13093957	C₂×C₄	semidirect
89. #107×C₄₇	C₂×C₄	semidirect
154. C₈×D₄₇	C₄⋊C₄	semidirect
205. C₈×C₄₇	C₂×C₄⋊C₄	semidirect
207. C₄₇⋊C₈	C₂×C₄⋊C₄	semidirect
245. #1942	D₄₇	direct (N × H)
254. D₄₇	#1942	direct (N × H)
285. C₄₇	C₂×#1942	semidirect
327. #107	C₄×D₄₇	semidirect
451. C₈	C₄⋊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×#107×D₄₇	2
C₂×C₄×C₈×D₄₇	2
#389×D₄₇	2
#20244122	2
#20244121	2
#20244120	2
#20244119	2
#20244118	2
#340×D₄₇	2
C₄₇×#1942	2
C₂×#1942	47

Subgroups — D47×#1942 #26219601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#1942 #26219601