Subgroups — #466×Dic₄₇ #26222775

Order 12032.

1222 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#121×Dic₄₇	C₂	1	2	yes	maximal, complemented
4	#20244255	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244122	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244073	C₂	1	2	yes	maximal, complemented
7	#20243817	C₂	1	2	yes	maximal, complemented
8	#20243417	C₂	1	1	yes	maximal, characteristic, complemented
9	#107×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#102×Dic₄₇	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#466	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×D₄×Dic₄₇	—	2	2	no	—
14	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
15	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
16	D₈×Dic₄₇	—	2	4	no	—
17	C₂×#13093958	C₂²	1	1	yes	characteristic
18	C₂×#13093958	C₂²	1	1	yes	characteristic
19	C₂×#13093945	C₂²	1	2	yes	—
20	C₂×#13093945	C₂²	1	2	yes	—
21	C₂×C₈×Dic₄₇	—	2	4	no	—
22	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
26	#15689026	C₂²	1	2	yes	—
27	#15689022	C₂²	1	2	yes	—
28	#15689016	—	2	2	no	—
29	#15689003	—	2	2	no	—
30	#15688983	C₂²	1	2	yes	—
31	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
32	C₂²⋊C₄×Dic₄₇	—	2	2	no	—
33	#15688886	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#121×C₄₇	C₂²	1	2	yes	—
39	C₄₇×#466	C₄	1	8	yes	complemented
40	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#102×C₄₇	C₂²	1	2	yes	—
42	C₂³×Dic₄₇	—	2	2	no	—
43	C₂³×Dic₄₇	D₄	1	1	yes	characteristic
44	C₂³×Dic₄₇	D₄	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	—	2	2	no	—
46	C₂²×C₄₇⋊C₈	—	2	2	no	—
47	C₂²×C₄₇⋊C₈	—	2	2	no	—
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	D₄×Dic₄₇	—	2	4	no	—
51	D₄×Dic₄₇	—	2	4	no	—
52	D₄×Dic₄₇	—	4	8	no	—
53	C₂×C₄⋊Dic₄₇	—	2	2	no	—
54	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
56	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
57	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
58	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
59	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
60	C₂×C₄×Dic₄₇	—	2	2	no	—
61	C₂×C₄×Dic₄₇	—	2	2	no	—
62	C₂×C₄×Dic₄₇	—	2	2	no	—
63	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
64	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
65	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
67	#13093958	—	2	2	no	—
68	#13093958	—	2	2	no	—
69	#13093945	—	2	4	no	—
70	#13093945	—	2	4	no	—
71	C₈×Dic₄₇	—	2	2	no	—
72	C₈×Dic₄₇	—	2	2	no	—
73	C₈×Dic₄₇	—	2	2	no	—
74	C₈×Dic₄₇	D₄	1	4	yes	complemented
75	C₄₇⋊#95	—	2	2	no	—
76	C₄₇⋊#95	—	2	2	no	—
77	C₄₇⋊#95	—	2	2	no	—
78	C₂²×D₄×C₄₇	—	2	2	no	—
79	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
80	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×D₈×C₄₇	—	2	2	no	—
82	C₂×D₈×C₄₇	—	2	2	no	—
83	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	complemented
84	C₂²×C₈×C₄₇	—	2	2	no	—
85	C₂²×C₈×C₄₇	—	2	2	no	—
86	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
87	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
89	#121×C₄₇	—	2	4	no	—
90	#121×C₄₇	C₂×C₄	1	8	yes	complemented
91	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
92	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
93	#107×C₄₇	C₂×C₄	1	4	yes	complemented
94	#102×C₄₇	C₂×C₄	1	8	yes	complemented
95	C₂⁴×C₄₇	—	2	2	no	—
96	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₄₇	—	2	8	no	—
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	4	4	no	—
104	C₂×D₄×C₄₇	—	4	4	no	—
105	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₄₇	—	2	1	no	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	1	no	—
109	C₂²×C₄×C₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	#41	1	2	yes	—
114	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
115	C₂²×Dic₄₇	—	2	2	no	—
116	C₂²×Dic₄₇	—	2	2	no	—
117	C₂²×Dic₄₇	—	2	2	no	—
118	C₂²×Dic₄₇	—	2	2	no	—
119	C₂²×Dic₄₇	—	2	2	no	—
120	C₂²×Dic₄₇	—	2	2	no	—
121	C₂²×Dic₄₇	—	2	2	no	—
122	C₂²×Dic₄₇	—	4	4	no	—
123	C₂²×Dic₄₇	—	4	4	no	—
124	C₂²×Dic₄₇	—	4	4	no	—
125	C₂²×Dic₄₇	D₈	1	4	yes	complemented
126	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
130	D₈×C₄₇	—	2	8	no	—
131	C₂×C₈×C₄₇	—	2	1	no	—
132	C₂×C₈×C₄₇	—	2	1	no	—
133	C₂×C₈×C₄₇	—	2	8	no	—
134	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₄₇	#41	1	2	yes	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
140	C₂²⋊C₄×C₄₇	—	2	8	no	—
141	C₂²⋊Dic₄₇	—	4	4	no	—
142	C₂²⋊Dic₄₇	—	4	4	no	—
143	C₂²⋊Dic₄₇	—	4	4	no	—
144	C₂²⋊Dic₄₇	—	4	4	no	—
145	C₄⋊Dic₄₇	—	2	2	no	—
146	C₄⋊Dic₄₇	—	2	2	no	—
147	C₄⋊Dic₄₇	—	2	2	no	—
148	C₄⋊Dic₄₇	—	2	2	no	—
149	C₄⋊Dic₄₇	—	4	4	no	—
150	C₄×Dic₄₇	—	2	1	no	—
151	C₄×Dic₄₇	—	2	1	no	—
152	C₄×Dic₄₇	—	2	2	no	—
153	C₄×Dic₄₇	—	2	2	no	—
154	C₄×Dic₄₇	—	4	4	no	—
155	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
156	C₄×Dic₄₇	#41	1	2	yes	—
157	C₂×C₄₇⋊C₈	—	2	8	no	—
158	C₂×C₄₇⋊C₈	—	2	1	no	—
159	C₂×C₄₇⋊C₈	—	2	1	no	—
160	C₂×C₄₇⋊C₈	—	2	1	no	—
161	C₂×C₄₇⋊C₈	—	2	1	no	—
162	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
163	C₂×C₄₇⋊C₈	#41	1	2	yes	—
164	C₂³×C₄₇	—	2	1	no	—
165	C₂³×C₄₇	—	2	1	no	—
166	C₂³×C₄₇	—	2	1	no	—
167	C₂³×C₄₇	—	2	1	no	—
168	C₂³×C₄₇	—	2	4	no	—
169	C₂³×C₄₇	—	4	2	no	—
170	C₂³×C₄₇	—	4	2	no	—
171	C₂³×C₄₇	—	4	2	no	—
172	C₂³×C₄₇	—	4	2	no	—
173	C₂³×C₄₇	—	4	2	no	—
174	C₂³×C₄₇	—	4	2	no	—
175	C₂³×C₄₇	C₄×D₄	1	2	yes	—
176	C₂³×C₄₇	C₂×D₈	1	2	yes	—
177	C₂³×C₄₇	#135	1	2	yes	—
178	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	D₄×C₄₇	—	2	4	no	—
180	D₄×C₄₇	—	2	4	no	—
181	D₄×C₄₇	—	4	16	no	—
182	D₄×C₄₇	—	4	2	no	—
183	D₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	—	2	1	no	—
185	C₂×C₄×C₄₇	—	2	1	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	2	2	no	—
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	4	no	—
191	C₂×C₄×C₄₇	—	4	2	no	—
192	C₂×C₄×C₄₇	—	4	2	no	—
193	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
194	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
200	C₂×Dic₄₇	—	2	8	no	—
201	C₂×Dic₄₇	—	2	1	no	—
202	C₂×Dic₄₇	—	2	1	no	—
203	C₂×Dic₄₇	—	2	1	no	—
204	C₂×Dic₄₇	—	2	1	no	—
205	C₂×Dic₄₇	—	2	1	no	—
206	C₂×Dic₄₇	—	2	1	no	—
207	C₂×Dic₄₇	—	2	8	no	—
208	C₂×Dic₄₇	—	4	2	no	—
209	C₂×Dic₄₇	—	4	2	no	—
210	C₂×Dic₄₇	—	4	2	no	—
211	C₂×Dic₄₇	—	4	2	no	—
212	C₂×Dic₄₇	—	4	2	no	—
213	C₂×Dic₄₇	—	4	2	no	—
214	C₂×Dic₄₇	—	8	8	no	—
215	C₂×Dic₄₇	#121	1	2	yes	—
216	C₂×Dic₄₇	#121	1	2	yes	—
217	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
218	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
219	C₂×Dic₄₇	#135	1	2	yes	—
220	C₂×Dic₄₇	#135	1	2	yes	—
221	C₈×C₄₇	—	2	2	no	—
222	C₈×C₄₇	C₄×D₄	1	4	yes	complemented
223	C₄₇⋊C₈	—	2	2	no	—
224	C₄₇⋊C₈	—	2	2	no	—
225	C₄×#466	—	47	1	no	maximal, Sylow
226	C₂²×C₄₇	—	2	2	no	—
227	C₂²×C₄₇	—	2	2	no	—
228	C₂²×C₄₇	—	2	2	no	—
229	C₂²×C₄₇	—	2	2	no	—
230	C₂²×C₄₇	—	2	2	no	—
231	C₂²×C₄₇	—	2	2	no	—
232	C₂²×C₄₇	—	4	4	no	—
233	C₂²×C₄₇	—	4	4	no	—
234	C₂²×C₄₇	—	4	4	no	—
235	C₂²×C₄₇	—	8	2	no	—
236	C₂²×C₄₇	—	8	2	no	—
237	C₂²×C₄₇	—	8	2	no	—
238	C₂²×C₄₇	—	8	2	no	—
239	C₂²×C₄₇	C₄×D₈	1	4	yes	complemented
240	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
241	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
242	C₂²×C₄₇	#532	1	1	yes	characteristic
243	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
244	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
245	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
246	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
247	C₄×C₄₇	—	2	2	no	—
248	C₄×C₄₇	—	4	4	no	—
249	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
250	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
251	C₄×C₄₇	#525	1	1	yes	characteristic
252	C₄×C₄₇	#529	1	1	yes	characteristic
253	Dic₄₇	—	2	2	no	—
254	Dic₄₇	—	2	2	no	—
255	Dic₄₇	—	2	2	no	—
256	Dic₄₇	—	8	2	no	—
257	Dic₄₇	—	8	2	no	—
258	Dic₄₇	#466	1	4	yes	direct product factor
259	C₂×#466	D₄₇	1	1	yes	characteristic
260	C₂×C₄×D₈	—	47	1	no	—
261	C₂²×C₄×C₈	—	47	1	no	—
262	C₄×#121	—	47	2	no	—
263	#1970	—	47	1	no	—
264	#1942	—	47	1	no	—
265	#1934	—	47	2	no	—
266	#1893	—	47	2	no	—
267	#1808	—	47	1	no	—
268	C₄×#107	—	47	1	no	—
269	C₄×#102	—	47	2	no	—
270	C₂×C₄₇	—	2	4	no	—
271	C₂×C₄₇	—	8	4	no	—
272	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
273	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
274	C₂×C₄₇	C₄×#135	1	1	yes	characteristic
275	C₂×C₄₇	C₂×#466	1	1	yes	characteristic
276	C₂×C₄₇	#3050	1	1	yes	characteristic
277	C₂×C₄₇	#3168	1	1	yes	characteristic
278	C₂×C₄₇	#3169	1	1	yes	characteristic
279	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
280	C₂³×C₈	—	47	1	no	—
281	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
282	C₂×#121	C₂×D₄₇	1	2	yes	—
283	C₂×C₄×D₄	—	47	2	no	—
284	C₂×C₄×D₄	—	94	2	no	—
285	C₂²×C₄²	—	47	1	no	—
286	#466	Dic₄₇	1	8	yes	direct product factor
287	C₄×D₈	—	94	4	no	—
288	C₂×#107	—	47	1	no	—
289	C₂×#107	—	47	1	no	—
290	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
291	C₂×#102	—	47	2	no	—
292	C₂×#102	—	47	2	no	—
293	C₂×#102	C₂×D₄₇	1	2	yes	—
294	C₂×C₄×C₈	—	47	1	no	—
295	C₂×C₄×C₈	—	47	1	no	—
296	C₂×C₄×C₈	—	47	1	no	—
297	C₂×C₄×C₈	—	47	1	no	—
298	C₂×C₄×C₈	—	94	4	no	—
299	#390	—	47	2	no	—
300	#389	—	47	2	no	—
301	#388	—	94	2	no	—
302	#386	—	94	2	no	—
303	#380	—	47	2	no	—
304	C₄×C₄⋊C₄	—	47	2	no	—
305	C₄×C₂²⋊C₄	—	94	2	no	—
306	#340	—	47	2	no	—
307	#340	—	47	2	no	—
308	#340	—	47	2	no	—
309	C₄₇	C₄×#466	1	1	yes	characteristic, complemented, Sylow
310	C₂²×D₄	—	2	2	no	—
311	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
312	C₂³×C₄	—	47	1	no	—
313	C₂³×C₄	—	47	1	no	—
314	C₂³×C₄	—	94	2	no	—
315	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
316	C₂×D₈	—	2	2	no	—
317	C₂×D₈	—	2	2	no	—
318	C₂×D₈	C₂×Dic₄₇	1	4	yes	complemented
319	C₂²×C₈	—	2	2	no	—
320	C₂²×C₈	—	2	2	no	—
321	C₂²×C₈	—	47	1	no	—
322	C₂²×C₈	—	47	1	no	—
323	C₂²×C₈	—	94	2	no	—
324	C₂²×C₈	—	94	2	no	—
325	C₂²×C₈	—	94	2	no	—
326	C₂²×C₈	C₂×Dic₄₇	1	4	yes	complemented
327	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
328	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
329	#121	—	2	4	no	—
330	#121	C₂×Dic₄₇	1	8	yes	complemented
331	C₄×D₄	—	94	4	no	—
332	C₄×D₄	—	94	4	no	—
333	C₄×D₄	—	188	8	no	—
334	C₂×C₄⋊C₄	—	47	2	no	—
335	C₂×C₄⋊C₄	—	47	2	no	—
336	C₂×C₄⋊C₄	—	94	2	no	—
337	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	94	2	no	—
340	C₂×C₂²⋊C₄	—	94	2	no	—
341	C₂×C₂²⋊C₄	—	94	2	no	—
342	C₂×C₂²⋊C₄	—	94	2	no	—
343	C₂×C₄²	—	47	1	no	—
344	C₂×C₄²	—	47	1	no	—
345	C₂×C₄²	—	47	1	no	—
346	C₂×C₄²	—	47	1	no	—
347	C₂×C₄²	—	94	2	no	—
348	C₂×C₄²	—	94	2	no	—
349	C₂×C₄²	—	94	2	no	—
350	#107	—	94	2	no	—
351	#107	—	94	2	no	—
352	#107	C₂×Dic₄₇	1	4	yes	complemented
353	#102	—	94	4	no	—
354	#102	—	94	4	no	—
355	#102	C₂×Dic₄₇	1	8	yes	complemented
356	C₄×C₈	—	47	4	no	—
357	C₄×C₈	—	94	2	no	—
358	C₄×C₈	—	94	2	no	—
359	C₄×C₈	—	94	2	no	—
360	#95	—	94	2	no	—
361	#95	—	94	2	no	—
362	#95	—	94	2	no	—
363	C₂⁴	—	2	2	no	—
364	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	47	1	no	—
380	C₂²×C₄	—	47	4	no	—
381	C₂²×C₄	—	47	1	no	—
382	C₂²×C₄	—	47	1	no	—
383	C₂²×C₄	—	47	1	no	—
384	C₂²×C₄	—	94	2	no	—
385	C₂²×C₄	—	94	2	no	—
386	C₂²×C₄	—	94	2	no	—
387	C₂²×C₄	—	94	2	no	—
388	C₂²×C₄	—	94	2	no	—
389	C₂²×C₄	—	94	2	no	—
390	C₂²×C₄	—	94	2	no	—
391	C₂²×C₄	—	188	4	no	—
392	C₂²×C₄	—	188	4	no	—
393	C₂²×C₄	—	188	4	no	—
394	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
395	C₂²×C₄	#10625352	1	2	yes	—
396	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
397	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
398	D₈	—	2	8	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	8	no	—
402	C₂×C₈	—	47	2	no	—
403	C₂×C₈	—	47	2	no	—
404	C₂×C₈	—	94	8	no	—
405	C₂×C₈	—	94	1	no	—
406	C₂×C₈	—	94	1	no	—
407	C₂×C₈	—	94	1	no	—
408	C₂×C₈	—	94	1	no	—
409	C₂×C₈	D₄×D₄₇	1	2	yes	—
410	C₂×C₈	#10625352	1	2	yes	—
411	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
412	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	94	2	no	—
415	C₄⋊C₄	—	94	2	no	—
416	C₄⋊C₄	—	94	2	no	—
417	C₄⋊C₄	—	94	2	no	—
418	C₄⋊C₄	—	188	4	no	—
419	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	188	4	no	—
422	C₂²⋊C₄	—	188	4	no	—
423	C₂²⋊C₄	—	188	4	no	—
424	C₂²⋊C₄	—	188	4	no	—
425	C₄²	—	47	2	no	—
426	C₄²	—	47	2	no	—
427	C₄²	—	94	2	no	—
428	C₄²	—	94	2	no	—
429	C₄²	—	94	1	no	—
430	C₄²	—	94	1	no	—
431	C₄²	—	188	4	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	D₄×Dic₄₇	1	2	yes	—
444	C₂³	D₈×D₄₇	1	2	yes	—
445	C₂³	#13094043	1	2	yes	—
446	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
447	D₄	—	2	4	no	—
448	D₄	—	2	4	no	—
449	D₄	—	4	16	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	47	2	no	—
462	C₂×C₄	—	47	2	no	—
463	C₂×C₄	—	47	2	no	—
464	C₂×C₄	—	47	2	no	—
465	C₂×C₄	—	47	2	no	—
466	C₂×C₄	—	47	2	no	—
467	C₂×C₄	—	94	8	no	—
468	C₂×C₄	—	94	8	no	—
469	C₂×C₄	—	94	1	no	—
470	C₂×C₄	—	94	1	no	—
471	C₂×C₄	—	94	1	no	—
472	C₂×C₄	—	94	1	no	—
473	C₂×C₄	—	94	1	no	—
474	C₂×C₄	—	94	1	no	—
475	C₂×C₄	—	376	8	no	—
476	C₂×C₄	—	188	2	no	—
477	C₂×C₄	—	188	2	no	—
478	C₂×C₄	—	188	2	no	—
479	C₂×C₄	—	188	2	no	—
480	C₂×C₄	—	188	2	no	—
481	C₂×C₄	—	188	2	no	—
482	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
483	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
484	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
485	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
486	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
487	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
488	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
489	C₈	—	2	2	no	—
490	C₈	—	94	2	no	—
491	C₈	—	94	2	no	—
492	C₈	D₄×Dic₄₇	1	4	yes	complemented
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	8	2	no	—
503	C₂²	—	8	2	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	2	no	—
506	C₂²	D₈×Dic₄₇	1	4	yes	complemented
507	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
508	C₂²	#121×D₄₇	1	1	yes	characteristic
509	C₂²	#15689668	1	1	yes	characteristic
510	C₂²	C₂×D₈×D₄₇	1	1	yes	characteristic
511	C₂²	#135×D₄₇	1	1	yes	characteristic
512	C₂²	#135×D₄₇	1	1	yes	characteristic
513	C₂²	C₂×#13094043	1	1	yes	characteristic
514	C₄	—	2	2	no	—
515	C₄	—	4	4	no	—
516	C₄	—	47	4	no	—
517	C₄	—	94	2	no	—
518	C₄	—	94	2	no	—
519	C₄	—	94	2	no	—
520	C₄	—	376	2	no	—
521	C₄	—	376	2	no	—
522	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
523	C₄	#41×Dic₄₇	1	1	yes	characteristic
524	C₄	#15689633	1	1	yes	characteristic
525	C₄	#15689654	1	1	yes	characteristic
526	C₂	—	2	4	no	—
527	C₂	—	8	4	no	—
528	C₂	#121×Dic₄₇	1	1	yes	characteristic
529	C₂	C₂×D₈×Dic₄₇	1	1	yes	characteristic
530	C₂	#135×Dic₄₇	1	1	yes	characteristic
531	C₂	#466×D₄₇	1	1	yes	characteristic
532	C₂	#20252967	1	1	yes	characteristic
533	C₂	#20253953	1	1	yes	characteristic
534	C₂	#20253962	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#466	C₂
socle	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#466	D₄₇
hypocenter	C₄₇	C₄×#466
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#466

Complements

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

N	H ≅ G/N	type
1. C₂×D₈×Dic₄₇	C₂	semidirect
2. C₂²×C₈×Dic₄₇	C₂	semidirect
3. #121×Dic₄₇	C₂	semidirect
4. #20244255	C₂	semidirect
5. #20244122	C₂	semidirect
6. #20244073	C₂	semidirect
7. #20243817	C₂	semidirect
8. #20243417	C₂	semidirect
9. #107×Dic₄₇	C₂	semidirect
10. #102×Dic₄₇	C₂	semidirect
39. C₄₇×#466	C₄	semidirect
74. C₈×Dic₄₇	D₄	semidirect
83. C₂×D₈×C₄₇	C₂×C₄	semidirect
86. C₂²×C₈×C₄₇	C₂×C₄	semidirect
90. #121×C₄₇	C₂×C₄	semidirect
93. #107×C₄₇	C₂×C₄	semidirect
94. #102×C₄₇	C₂×C₄	semidirect
125. C₂²×Dic₄₇	D₈	semidirect
222. C₈×C₄₇	C₄×D₄	semidirect
239. C₂²×C₄₇	C₄×D₈	semidirect
258. Dic₄₇	#466	direct (N × H)
286. #466	Dic₄₇	direct (N × H)
309. C₄₇	C₄×#466	semidirect
318. C₂×D₈	C₂×Dic₄₇	semidirect
326. C₂²×C₈	C₂×Dic₄₇	semidirect
330. #121	C₂×Dic₄₇	semidirect
352. #107	C₂×Dic₄₇	semidirect
355. #102	C₂×Dic₄₇	semidirect
492. C₈	D₄×Dic₄₇	semidirect
506. C₂²	D₈×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₈×Dic₄₇	2
C₂²×C₈×Dic₄₇	2
#121×Dic₄₇	2
#20244255	2
#20244122	2
#20244073	2
#20243817	2
#20243417	2
#107×Dic₄₇	2
#102×Dic₄₇	2
C₂×C₄₇×#466	2
C₄×#466	47

Subgroups — #466×Dic47 #26222775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #466×Dic₄₇ #26222775