Subgroups — #486×Dic₄₇ #26224246

Order 12032.

1046 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#127×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#20244350	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244195	C₂	1	1	yes	maximal, characteristic
5	#20244073	C₂	1	4	yes	maximal, complemented
6	#20243516	C₂	1	1	yes	maximal, characteristic, complemented
7	#102×Dic₄₇	C₂	1	4	yes	maximal, complemented
8	C₄×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₇×#486	C₂	1	1	yes	maximal, characteristic
10	C₂×Q₈×Dic₄₇	—	2	1	no	—
11	C₂×D₄×Dic₄₇	—	2	1	no	—
12	C₂×D₄×Dic₄₇	—	2	1	no	—
13	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
14	C₂×#13093945	C₂²	1	4	yes	—
15	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
17	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
18	#15689030	—	2	1	no	—
19	#15689026	—	2	1	no	—
20	#15689026	—	2	1	no	—
21	#15689026	C₂²	1	2	yes	—
22	#15689022	—	2	1	no	—
23	#15689022	C₂²	1	2	yes	—
24	#15688993	C₂²	1	1	yes	characteristic
25	#15688993	C₂²	1	1	yes	characteristic
26	C₄⋊C₄×Dic₄₇	—	2	1	no	—
27	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
28	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
29	#15688886	C₂²	1	4	yes	—
30	#15688885	C₂²	1	4	yes	—
31	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
33	C₄₇×#486	C₄	1	8	yes	complemented
34	C₂×#102×C₄₇	C₂²	1	4	yes	—
35	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂³×Dic₄₇	—	2	2	no	—
37	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
38	Q₈×Dic₄₇	—	4	4	no	—
39	D₄×Dic₄₇	—	2	8	no	—
40	D₄×Dic₄₇	—	4	4	no	—
41	D₄×Dic₄₇	—	4	4	no	—
42	C₂×C₄⋊Dic₄₇	—	2	1	no	—
43	C₂×C₄⋊Dic₄₇	—	2	1	no	—
44	C₂×C₄⋊Dic₄₇	—	2	1	no	—
45	C₂×C₄⋊Dic₄₇	—	2	1	no	—
46	C₂×C₄⋊Dic₄₇	—	2	2	no	—
47	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
49	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
50	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
51	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
52	C₂×C₄×Dic₄₇	—	2	2	no	—
53	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
54	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
59	#13093945	—	2	8	no	—
60	C₄×C₄₇⋊C₈	—	2	2	no	—
61	C₈×Dic₄₇	—	2	4	no	—
62	C₈×Dic₄₇	—	2	4	no	—
63	C₄₇⋊#95	—	2	2	no	—
64	C₄₇⋊#95	—	2	2	no	—
65	C₂²×Q₈×C₄₇	—	2	1	no	—
66	C₂²×D₄×C₄₇	—	2	1	no	—
67	C₂²×D₄×C₄₇	—	2	1	no	—
68	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
69	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
70	C₄⋊Q₈×C₄₇	—	2	2	no	—
71	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
72	#127×C₄₇	—	2	2	no	—
73	#127×C₄₇	C₂×C₄	1	4	yes	—
74	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	#102×C₄₇	C₂×C₄	1	16	yes	complemented
78	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
79	C₂⁴×C₄₇	—	2	2	no	—
80	C₂×Q₈×C₄₇	—	2	4	no	—
81	C₂×Q₈×C₄₇	—	4	2	no	—
82	C₂×Q₈×C₄₇	—	4	2	no	—
83	C₂×D₄×C₄₇	—	2	4	no	—
84	C₂×D₄×C₄₇	—	2	4	no	—
85	C₂×D₄×C₄₇	—	2	4	no	—
86	C₂×D₄×C₄₇	—	2	4	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	4	2	no	—
89	C₂×D₄×C₄₇	—	4	2	no	—
90	C₂×D₄×C₄₇	—	4	2	no	—
91	C₂×D₄×C₄₇	—	4	2	no	—
92	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
97	C₂²×Dic₄₇	—	2	2	no	—
98	C₂²×Dic₄₇	—	2	2	no	—
99	C₂²×Dic₄₇	—	4	4	no	—
100	C₂²×Dic₄₇	—	4	4	no	—
101	C₂²×Dic₄₇	—	4	4	no	—
102	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
109	C₄⋊C₄×C₄₇	—	2	4	no	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
112	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
113	C₄²×C₄₇	#41	1	2	yes	—
114	C₂²⋊Dic₄₇	—	4	4	no	—
115	C₂²⋊Dic₄₇	—	4	4	no	—
116	C₂²⋊Dic₄₇	—	4	4	no	—
117	C₄⋊Dic₄₇	—	2	4	no	—
118	C₄⋊Dic₄₇	—	2	4	no	—
119	C₄⋊Dic₄₇	—	4	2	no	—
120	C₄⋊Dic₄₇	—	4	2	no	—
121	C₄⋊Dic₄₇	—	4	2	no	—
122	C₄⋊Dic₄₇	—	4	2	no	—
123	C₄⋊Dic₄₇	—	4	4	no	—
124	C₄×Dic₄₇	—	2	2	no	—
125	C₄×Dic₄₇	—	2	2	no	—
126	C₄×Dic₄₇	—	2	2	no	—
127	C₄×Dic₄₇	—	4	4	no	—
128	C₄×Dic₄₇	D₈	1	4	yes	—
129	C₄×Dic₄₇	SD₁₆	1	4	yes	—
130	C₄×Dic₄₇	#41	1	4	yes	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	#41	1	4	yes	—
134	C₂³×C₄₇	—	2	4	no	—
135	C₂³×C₄₇	—	4	2	no	—
136	C₂³×C₄₇	—	4	2	no	—
137	C₂³×C₄₇	—	4	2	no	—
138	C₂³×C₄₇	—	4	2	no	—
139	C₂³×C₄₇	—	4	2	no	—
140	C₂³×C₄₇	—	4	2	no	—
141	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
142	Q₈×C₄₇	—	4	8	no	—
143	D₄×C₄₇	—	2	8	no	—
144	D₄×C₄₇	—	4	4	no	—
145	D₄×C₄₇	—	4	8	no	—
146	D₄×C₄₇	—	4	8	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
153	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
154	C₂×C₄×C₄₇	#135	1	2	yes	—
155	C₂×C₄×C₄₇	#135	1	2	yes	—
156	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
158	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
159	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
160	C₂×Dic₄₇	—	2	1	no	—
161	C₂×Dic₄₇	—	2	1	no	—
162	C₂×Dic₄₇	—	2	1	no	—
163	C₂×Dic₄₇	—	2	1	no	—
164	C₂×Dic₄₇	—	2	1	no	—
165	C₂×Dic₄₇	—	2	1	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	—	4	2	no	—
172	C₂×Dic₄₇	—	8	8	no	—
173	C₂×Dic₄₇	#124	1	2	yes	—
174	C₂×Dic₄₇	#124	1	2	yes	—
175	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
176	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
177	C₂×Dic₄₇	C₂×SD₁₆	1	2	yes	—
178	C₂×Dic₄₇	C₂×SD₁₆	1	2	yes	—
179	C₈×C₄₇	—	2	4	no	—
180	C₄₇⋊C₈	—	2	4	no	—
181	C₄×#486	—	47	1	no	maximal, Sylow
182	C₂²×C₄₇	—	4	4	no	—
183	C₂²×C₄₇	—	4	4	no	—
184	C₂²×C₄₇	—	4	4	no	—
185	C₂²×C₄₇	—	8	2	no	—
186	C₂²×C₄₇	—	8	2	no	—
187	C₂²×C₄₇	—	8	2	no	—
188	C₂²×C₄₇	—	8	2	no	—
189	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
190	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
191	C₂²×C₄₇	#532	1	1	yes	characteristic
192	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
193	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
194	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
195	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
196	C₄×C₄₇	—	4	4	no	—
197	C₄×C₄₇	C₄×D₈	1	4	yes	—
198	C₄×C₄₇	C₄×SD₁₆	1	4	yes	—
199	C₄×C₄₇	C₄×#41	1	2	yes	—
200	C₄×C₄₇	#529	1	2	yes	—
201	Dic₄₇	—	2	2	no	—
202	Dic₄₇	—	2	2	no	—
203	Dic₄₇	—	2	2	no	—
204	Dic₄₇	—	8	2	no	—
205	Dic₄₇	—	8	2	no	—
206	Dic₄₇	#486	1	4	yes	direct product factor
207	C₂×#486	D₄₇	1	1	yes	characteristic
208	C₄×C₄⋊Q₈	—	47	1	no	—
209	C₄×#127	—	47	1	no	—
210	#1990	—	47	1	no	—
211	#1957	—	47	1	no	—
212	#1934	—	47	4	no	—
213	#1834	—	47	1	no	—
214	C₄×#102	—	47	4	no	—
215	C₄²×C₈	—	47	1	no	—
216	C₂×C₄₇	—	8	4	no	—
217	C₂×C₄₇	C₄×#124	1	1	yes	characteristic
218	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
219	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
220	C₂×C₄₇	C₂×#486	1	1	yes	characteristic
221	C₂×C₄₇	#3131	1	1	yes	characteristic
222	C₂×C₄₇	#3167	1	1	yes	characteristic
223	C₂×C₄₇	#3169	1	1	yes	characteristic
224	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
225	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
226	C₂×C₄×Q₈	—	94	1	no	—
227	C₂×C₄×D₄	—	47	2	no	—
228	C₂×C₄×D₄	—	94	1	no	—
229	C₂×C₄×D₄	—	94	1	no	—
230	#486	Dic₄₇	1	8	yes	direct product factor
231	C₂×#102	—	47	4	no	—
232	C₂×#102	C₂×D₄₇	1	4	yes	—
233	C₂×C₄×C₈	—	47	2	no	—
234	C₂×C₄×C₈	—	47	2	no	—
235	C₂×C₄×C₈	—	47	1	no	—
236	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
237	#391	—	94	1	no	—
238	#390	—	47	2	no	—
239	#390	—	94	1	no	—
240	#390	—	94	1	no	—
241	#389	—	47	2	no	—
242	#389	—	94	1	no	—
243	#384	—	47	1	no	—
244	#384	—	47	1	no	—
245	C₄×C₄⋊C₄	—	47	2	no	—
246	C₄×C₄⋊C₄	—	94	1	no	—
247	C₄³	—	47	1	no	—
248	#340	—	47	4	no	—
249	#340	—	47	4	no	—
250	C₄₇	C₄×#486	1	1	yes	characteristic, complemented, Sylow
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
255	C₂³×C₄	—	94	2	no	—
256	C₂²×C₈	—	47	2	no	—
257	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
258	C₄⋊Q₈	—	2	2	no	—
259	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
260	#127	—	2	2	no	—
261	#127	C₂×Dic₄₇	1	4	yes	—
262	C₄×Q₈	—	188	4	no	—
263	C₄×D₄	—	94	8	no	—
264	C₄×D₄	—	188	4	no	—
265	C₄×D₄	—	188	4	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	47	2	no	—
268	C₂×C₄⋊C₄	—	47	2	no	—
269	C₂×C₄⋊C₄	—	94	2	no	—
270	C₂×C₄⋊C₄	—	94	1	no	—
271	C₂×C₄⋊C₄	—	94	1	no	—
272	C₂×C₄⋊C₄	—	94	1	no	—
273	C₂×C₄⋊C₄	—	94	1	no	—
274	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
275	C₂×C₂²⋊C₄	—	94	2	no	—
276	C₂×C₂²⋊C₄	—	94	2	no	—
277	C₂×C₂²⋊C₄	—	94	2	no	—
278	C₂×C₄²	—	47	1	no	—
279	C₂×C₄²	—	47	1	no	—
280	C₂×C₄²	—	47	1	no	—
281	C₂×C₄²	—	47	1	no	—
282	C₂×C₄²	—	47	1	no	—
283	C₂×C₄²	—	47	1	no	—
284	C₂×C₄²	—	94	2	no	—
285	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
286	#102	—	94	8	no	—
287	#102	C₂×Dic₄₇	1	16	yes	complemented
288	C₄×C₈	—	94	4	no	—
289	C₄×C₈	—	94	4	no	—
290	C₄×C₈	—	94	2	no	—
291	C₄×C₈	C₂×Dic₄₇	1	4	yes	complemented
292	#95	—	94	2	no	—
293	#95	—	94	2	no	—
294	C₂⁴	—	2	2	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	4	2	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	47	1	no	—
310	C₂²×C₄	—	47	1	no	—
311	C₂²×C₄	—	47	1	no	—
312	C₂²×C₄	—	47	1	no	—
313	C₂²×C₄	—	94	2	no	—
314	C₂²×C₄	—	94	2	no	—
315	C₂²×C₄	—	188	4	no	—
316	C₂²×C₄	—	188	4	no	—
317	C₂²×C₄	—	188	4	no	—
318	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
319	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
320	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	47	4	no	—
324	C₂×C₈	—	94	2	no	—
325	C₂×C₈	—	94	2	no	—
326	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	94	4	no	—
330	C₄⋊C₄	—	94	4	no	—
331	C₄⋊C₄	—	188	4	no	—
332	C₄⋊C₄	—	188	2	no	—
333	C₄⋊C₄	—	188	2	no	—
334	C₄⋊C₄	—	188	2	no	—
335	C₄⋊C₄	—	188	2	no	—
336	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
337	C₂²⋊C₄	—	188	4	no	—
338	C₂²⋊C₄	—	188	4	no	—
339	C₂²⋊C₄	—	188	4	no	—
340	C₄²	—	47	4	no	—
341	C₄²	—	47	4	no	—
342	C₄²	—	47	4	no	—
343	C₄²	—	94	2	no	—
344	C₄²	—	94	2	no	—
345	C₄²	—	94	2	no	—
346	C₄²	—	188	4	no	—
347	C₄²	#10625352	1	2	yes	—
348	C₄²	C₂²×Dic₄₇	1	2	yes	—
349	C₂³	—	2	4	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
357	Q₈	—	4	8	no	—
358	D₄	—	2	8	no	—
359	D₄	—	4	4	no	—
360	D₄	—	4	8	no	—
361	D₄	—	4	8	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	47	2	no	—
366	C₂×C₄	—	47	2	no	—
367	C₂×C₄	—	47	2	no	—
368	C₂×C₄	—	47	2	no	—
369	C₂×C₄	—	47	2	no	—
370	C₂×C₄	—	47	2	no	—
371	C₂×C₄	—	94	1	no	—
372	C₂×C₄	—	94	1	no	—
373	C₂×C₄	—	94	1	no	—
374	C₂×C₄	—	94	1	no	—
375	C₂×C₄	—	94	1	no	—
376	C₂×C₄	—	94	1	no	—
377	C₂×C₄	—	376	8	no	—
378	C₂×C₄	—	188	2	no	—
379	C₂×C₄	—	188	2	no	—
380	C₂×C₄	—	188	2	no	—
381	C₂×C₄	—	188	2	no	—
382	C₂×C₄	—	188	2	no	—
383	C₂×C₄	—	188	2	no	—
384	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
385	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
386	C₂×C₄	D₈×D₄₇	1	2	yes	—
387	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
388	C₂×C₄	#13094043	1	2	yes	—
389	C₂×C₄	#13094045	1	2	yes	—
390	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
391	C₂×C₄	#41×D₄₇	1	2	yes	—
392	C₂×C₄	#41×D₄₇	1	2	yes	—
393	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
394	C₈	—	2	4	no	—
395	C₈	—	94	4	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
404	C₂²	#124×D₄₇	1	1	yes	characteristic
405	C₂²	#15689672	1	1	yes	characteristic
406	C₂²	C₂×D₈×D₄₇	1	1	yes	characteristic
407	C₂²	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
408	C₂²	C₂×#13094043	1	1	yes	characteristic
409	C₂²	C₂×#13094045	1	1	yes	characteristic
410	C₄	—	4	4	no	—
411	C₄	—	47	4	no	—
412	C₄	—	94	2	no	—
413	C₄	—	94	2	no	—
414	C₄	—	94	2	no	—
415	C₄	—	376	2	no	—
416	C₄	—	376	2	no	—
417	C₄	D₈×Dic₄₇	1	4	yes	—
418	C₄	SD₁₆×Dic₄₇	1	4	yes	—
419	C₄	#41×Dic₄₇	1	2	yes	—
420	C₄	#15689652	1	2	yes	—
421	C₂	—	8	4	no	—
422	C₂	#124×Dic₄₇	1	1	yes	characteristic
423	C₂	C₂×D₈×Dic₄₇	1	1	yes	characteristic
424	C₂	C₂×SD₁₆×Dic₄₇	1	1	yes	characteristic
425	C₂	#486×D₄₇	1	1	yes	characteristic
426	C₂	#20253707	1	1	yes	characteristic
427	C₂	#20253946	1	1	yes	characteristic
428	C₂	#20253966	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#486	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂×#127×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#486	D₄₇
hypocenter	C₄₇	C₄×#486
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#486

Complements

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

N	H ≅ G/N	type
1. C₄⋊Q₈×Dic₄₇	C₂	semidirect
3. #20244350	C₂	semidirect
5. #20244073	C₂	semidirect
6. #20243516	C₂	semidirect
7. #102×Dic₄₇	C₂	semidirect
8. C₄×C₈×Dic₄₇	C₂	semidirect
33. C₄₇×#486	C₄	semidirect
71. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
77. #102×C₄₇	C₂×C₄	semidirect
78. C₄×C₈×C₄₇	C₂×C₄	semidirect
206. Dic₄₇	#486	direct (N × H)
230. #486	Dic₄₇	direct (N × H)
250. C₄₇	C₄×#486	semidirect
259. C₄⋊Q₈	C₂×Dic₄₇	semidirect
287. #102	C₂×Dic₄₇	semidirect
291. C₄×C₈	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊Q₈×Dic₄₇	2
#127×Dic₄₇	2
#20244350	2
#20244195	2
#20244073	2
#20243516	2
#102×Dic₄₇	2
C₄×C₈×Dic₄₇	2
C₂×C₄₇×#486	2
C₄×#486	47

Subgroups — #486×Dic47 #26224246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #486×Dic₄₇ #26224246