Subgroups — #26222812

Order 12032.

1066 conjugacy classes of subgroups.

The subgroup lattice has 522 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	C₂×#15689078	C₂	1	1	yes	maximal, characteristic, complemented
3	#20246083	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	#20244087	C₂	1	2	yes	maximal, complemented
7	#20243827	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	#20243215	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#466	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
14	C₂×#13093983	C₂²	1	1	yes	characteristic
15	D₈×Dic₄₇	—	2	4	no	—
16	C₂×#13093958	C₂²	1	1	yes	characteristic
17	C₂×#13093958	C₂²	1	1	yes	characteristic
18	C₂×#13093945	C₂²	1	2	yes	—
19	C₂×#13093945	C₂²	1	2	yes	—
20	#15689078	—	2	4	no	—
21	C₂×#13093934	C₂²	1	1	yes	characteristic
22	C₂×#13093934	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
25	#15689026	—	2	2	no	—
26	#15689026	C₂²	1	2	yes	—
27	#15689022	C₂²	1	2	yes	—
28	#15689016	—	2	2	no	—
29	#15689003	—	2	2	no	—
30	#15688998	—	2	2	no	—
31	#15688983	C₂²	1	2	yes	—
32	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
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	C₂×#10625329	—	2	2	no	—
44	C₂×#10625329	—	2	2	no	—
45	C₂×#10625329	—	2	2	no	—
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	D₄×Dic₄₇	—	2	4	no	—
49	D₄×Dic₄₇	—	2	4	no	—
50	#13093983	—	2	2	no	—
51	#13093983	—	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	C₂³	1	2	yes	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
57	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
58	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
59	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
60	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
61	C₂×C₂²⋊Dic₄₇	D₄	1	1	yes	characteristic
62	C₂×C₂²⋊Dic₄₇	D₄	1	1	yes	characteristic
63	C₂×C₄×Dic₄₇	—	2	2	no	—
64	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
66	#13093958	—	2	2	no	—
67	#13093958	—	2	2	no	—
68	#13093945	—	2	4	no	—
69	#13093945	—	2	4	no	—
70	#13093934	—	2	2	no	—
71	#13093934	—	2	2	no	—
72	C₈×Dic₄₇	—	2	2	no	—
73	C₈×Dic₄₇	D₄	1	4	yes	complemented
74	C₄₇⋊#95	—	2	2	no	—
75	C₄₇⋊#95	—	2	2	no	—
76	C₄₇⋊#95	—	2	2	no	—
77	C₂²×D₄×C₄₇	—	2	2	no	—
78	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
79	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×D₈×C₄₇	—	2	2	no	—
81	C₂×D₈×C₄₇	—	2	2	no	—
82	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	—
83	C₂²×C₈×C₄₇	—	2	2	no	—
84	C₂²×C₈×C₄₇	—	2	2	no	—
85	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
86	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
88	#121×C₄₇	—	2	4	no	—
89	#121×C₄₇	C₂×C₄	1	8	yes	complemented
90	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
92	#107×C₄₇	C₂×C₄	1	4	yes	complemented
93	#102×C₄₇	C₂×C₄	1	8	yes	complemented
94	C₂⁴×C₄₇	—	2	2	no	—
95	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂×D₄×C₄₇	—	2	8	no	—
97	C₂×D₄×C₄₇	—	2	2	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	—	8	2	no	—
103	C₂×D₄×C₄₇	—	8	2	no	—
104	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
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	2	no	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	#41	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
114	C₂²×Dic₄₇	—	2	2	no	—
115	C₂²×Dic₄₇	—	2	2	no	—
116	C₂²×Dic₄₇	—	4	4	no	—
117	C₂²×Dic₄₇	—	8	2	no	—
118	C₂²×Dic₄₇	—	8	2	no	—
119	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
123	D₈×C₄₇	—	2	8	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	2	1	no	—
126	C₂×C₈×C₄₇	—	2	8	no	—
127	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₄₇	#41	1	2	yes	—
131	C₄⋊C₄×C₄₇	—	2	2	no	—
132	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
133	C₂²⋊C₄×C₄₇	—	2	8	no	—
134	C₂²⋊Dic₄₇	—	2	2	no	—
135	C₂²⋊Dic₄₇	—	2	2	no	—
136	C₂²⋊Dic₄₇	—	4	4	no	—
137	C₂²⋊Dic₄₇	—	8	2	no	—
138	C₂²⋊Dic₄₇	—	8	2	no	—
139	C₂²⋊Dic₄₇	—	8	2	no	—
140	C₄⋊Dic₄₇	—	2	2	no	—
141	C₄⋊Dic₄₇	—	2	2	no	—
142	C₄⋊Dic₄₇	—	2	2	no	—
143	C₄⋊Dic₄₇	—	2	2	no	—
144	C₄⋊Dic₄₇	—	2	2	no	—
145	C₄⋊Dic₄₇	—	2	2	no	—
146	C₄⋊Dic₄₇	—	8	2	no	—
147	C₄×Dic₄₇	—	2	1	no	—
148	C₄×Dic₄₇	—	2	1	no	—
149	C₄×Dic₄₇	—	8	2	no	—
150	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
151	C₄×Dic₄₇	#41	1	2	yes	—
152	#10625329	—	2	8	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	1	no	—
155	C₂×C₄₇⋊C₈	—	2	1	no	—
156	C₂×C₄₇⋊C₈	—	2	1	no	—
157	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
158	C₂×C₄₇⋊C₈	#41	1	2	yes	—
159	C₂³×C₄₇	—	2	1	no	—
160	C₂³×C₄₇	—	2	1	no	—
161	C₂³×C₄₇	—	2	1	no	—
162	C₂³×C₄₇	—	2	1	no	—
163	C₂³×C₄₇	—	2	1	no	—
164	C₂³×C₄₇	—	2	1	no	—
165	C₂³×C₄₇	—	2	4	no	—
166	C₂³×C₄₇	—	4	2	no	—
167	C₂³×C₄₇	—	4	2	no	—
168	C₂³×C₄₇	—	4	2	no	—
169	C₂³×C₄₇	—	4	2	no	—
170	C₂³×C₄₇	—	4	2	no	—
171	C₂³×C₄₇	—	4	2	no	—
172	C₂³×C₄₇	C₄×D₄	1	2	yes	—
173	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	D₄×C₄₇	—	2	4	no	—
175	D₄×C₄₇	—	2	4	no	—
176	D₄×C₄₇	—	4	2	no	—
177	D₄×C₄₇	—	4	2	no	—
178	D₄×C₄₇	—	8	8	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	2	no	—
185	C₂×C₄×C₄₇	—	2	4	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
189	C₂×C₄×C₄₇	C₂³×C₄	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	C₂×#41	1	1	yes	characteristic
195	C₂×Dic₄₇	—	2	1	no	—
196	C₂×Dic₄₇	—	2	1	no	—
197	C₂×Dic₄₇	—	2	1	no	—
198	C₂×Dic₄₇	—	2	1	no	—
199	C₂×Dic₄₇	—	2	1	no	—
200	C₂×Dic₄₇	—	2	1	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	—	4	2	no	—
206	C₂×Dic₄₇	—	4	2	no	—
207	C₂×Dic₄₇	—	4	2	no	—
208	C₂×Dic₄₇	—	4	2	no	—
209	C₂×Dic₄₇	—	4	2	no	—
210	C₂×Dic₄₇	—	4	2	no	—
211	C₂×Dic₄₇	—	8	8	no	—
212	C₂×Dic₄₇	#121	1	2	yes	—
213	C₂×Dic₄₇	#121	1	2	yes	—
214	C₈×C₄₇	—	2	2	no	—
215	C₈×C₄₇	C₄×D₄	1	4	yes	—
216	C₄₇⋊C₈	—	2	2	no	—
217	C₄₇⋊C₈	—	2	2	no	—
218	#21524	—	47	1	no	maximal, Sylow
219	C₂²×C₄₇	—	2	2	no	—
220	C₂²×C₄₇	—	2	2	no	—
221	C₂²×C₄₇	—	2	2	no	—
222	C₂²×C₄₇	—	4	1	no	—
223	C₂²×C₄₇	—	4	1	no	—
224	C₂²×C₄₇	—	4	1	no	—
225	C₂²×C₄₇	—	4	1	no	—
226	C₂²×C₄₇	—	4	4	no	—
227	C₂²×C₄₇	—	4	4	no	—
228	C₂²×C₄₇	—	4	4	no	—
229	C₂²×C₄₇	—	8	2	no	—
230	C₂²×C₄₇	—	8	2	no	—
231	C₂²×C₄₇	—	8	2	no	—
232	C₂²×C₄₇	—	8	2	no	—
233	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
234	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
235	C₂²×C₄₇	#532	1	1	yes	characteristic
236	C₂²×C₄₇	#576	1	1	yes	characteristic
237	C₂²×C₄₇	#576	1	1	yes	characteristic
238	C₂²×C₄₇	#576	1	1	yes	characteristic
239	C₂²×C₄₇	#578	1	1	yes	characteristic
240	C₄×C₄₇	—	2	2	no	—
241	C₄×C₄₇	—	4	4	no	—
242	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
243	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
244	C₄×C₄₇	#525	1	1	yes	characteristic
245	C₄×C₄₇	#529	1	1	yes	characteristic
246	Dic₄₇	—	2	2	no	—
247	Dic₄₇	—	2	2	no	—
248	Dic₄₇	—	4	1	no	—
249	Dic₄₇	—	4	1	no	—
250	Dic₄₇	—	8	2	no	—
251	Dic₄₇	—	8	2	no	—
252	C₂×#466	D₄₇	1	1	yes	characteristic
253	C₂×C₄×D₈	—	47	1	no	—
254	C₂×#405	—	47	1	no	—
255	#2324	—	47	2	no	—
256	#1970	—	47	1	no	—
257	#1942	—	47	1	no	—
258	#1936	—	47	2	no	—
259	#1895	—	47	2	no	—
260	#1808	—	47	1	no	—
261	C₄×#107	—	47	1	no	—
262	#1762	—	47	2	no	—
263	C₂×C₄₇	—	4	2	no	—
264	C₂×C₄₇	—	8	4	no	—
265	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
266	C₂×C₄₇	#2948	1	1	yes	characteristic
267	C₂×C₄₇	#2951	1	1	yes	characteristic
268	C₂×C₄₇	#3058	1	1	yes	characteristic
269	C₂×C₄₇	#3061	1	1	yes	characteristic
270	C₂×C₄₇	#3175	1	1	yes	characteristic
271	C₂×C₄₇	#3176	1	1	yes	characteristic
272	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
273	C₂²×M₁₆	—	47	1	no	—
274	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
275	C₂×#121	C₂×D₄₇	1	2	yes	—
276	C₂×C₄×D₄	—	47	2	no	—
277	C₂×#117	—	47	1	no	—
278	#466	Dic₄₇	1	8	yes	complemented
279	C₄×D₈	—	94	4	no	—
280	C₂×#107	—	47	1	no	—
281	C₂×#107	—	47	1	no	—
282	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
283	C₂×#102	—	47	2	no	—
284	C₂×#102	—	47	2	no	—
285	C₂×#102	C₂×D₄₇	1	2	yes	—
286	#405	—	94	4	no	—
287	C₂×#97	—	47	1	no	—
288	C₂×#97	—	47	1	no	—
289	C₂×C₄×C₈	—	47	1	no	—
290	C₂×C₄×C₈	—	47	1	no	—
291	#390	—	47	2	no	—
292	#390	—	94	2	no	—
293	#389	—	47	2	no	—
294	#388	—	94	2	no	—
295	#386	—	94	2	no	—
296	#385	—	94	2	no	—
297	#380	—	47	2	no	—
298	C₄×C₄⋊C₄	—	47	2	no	—
299	#340	—	47	2	no	—
300	#340	—	47	2	no	—
301	#340	—	47	2	no	—
302	C₄₇	#21524	1	1	yes	characteristic, complemented, Sylow
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
305	C₂³×C₄	—	94	2	no	—
306	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
307	C₂×D₈	—	2	2	no	—
308	C₂×D₈	—	2	2	no	—
309	C₂×D₈	C₂×Dic₄₇	1	4	yes	—
310	C₂×M₁₆	—	94	2	no	—
311	C₂×M₁₆	—	94	2	no	—
312	C₂×M₁₆	—	94	2	no	—
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	—	2	2	no	—
315	C₂²×C₈	—	47	1	no	—
316	C₂²×C₈	—	47	1	no	—
317	C₂²×C₈	C₂×Dic₄₇	1	4	yes	complemented
318	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
319	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
320	#121	—	2	4	no	—
321	#121	C₂×Dic₄₇	1	8	yes	complemented
322	C₄×D₄	—	94	4	no	—
323	C₄×D₄	—	94	4	no	—
324	#117	—	94	2	no	—
325	#117	—	94	2	no	—
326	C₂×C₄⋊C₄	—	47	1	no	—
327	C₂×C₄⋊C₄	—	47	1	no	—
328	C₂×C₄⋊C₄	—	47	2	no	—
329	C₂×C₄⋊C₄	—	47	2	no	—
330	C₂×C₄⋊C₄	—	94	2	no	—
331	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	47	1	no	—
334	C₂×C₂²⋊C₄	—	47	1	no	—
335	C₂×C₂²⋊C₄	—	94	2	no	—
336	C₂×C₂²⋊C₄	—	94	2	no	—
337	C₂×C₂²⋊C₄	—	94	2	no	—
338	C₂×C₂²⋊C₄	—	94	2	no	—
339	C₂×C₄²	—	47	1	no	—
340	C₂×C₄²	—	47	1	no	—
341	C₂×C₄²	—	94	2	no	—
342	#107	—	94	2	no	—
343	#107	—	94	2	no	—
344	#107	C₂×Dic₄₇	1	4	yes	complemented
345	#102	—	94	4	no	—
346	#102	—	94	4	no	—
347	#102	C₂×Dic₄₇	1	8	yes	complemented
348	#97	—	94	2	no	—
349	#97	—	94	2	no	—
350	C₄×C₈	—	47	4	no	—
351	C₄×C₈	—	94	2	no	—
352	#95	—	94	2	no	—
353	#95	—	94	2	no	—
354	#95	—	94	2	no	—
355	C₂⁴	—	2	2	no	—
356	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	8	2	no	—
364	C₂×D₄	—	8	2	no	—
365	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	47	1	no	—
372	C₂²×C₄	—	47	1	no	—
373	C₂²×C₄	—	47	1	no	—
374	C₂²×C₄	—	47	1	no	—
375	C₂²×C₄	—	94	2	no	—
376	C₂²×C₄	—	94	2	no	—
377	C₂²×C₄	—	376	2	no	—
378	C₂²×C₄	—	376	2	no	—
379	C₂²×C₄	—	188	4	no	—
380	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
381	C₂²×C₄	#10625352	1	2	yes	—
382	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
383	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
384	D₈	—	2	8	no	—
385	M₁₆	—	94	8	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	8	no	—
389	C₂×C₈	—	47	2	no	—
390	C₂×C₈	—	47	2	no	—
391	C₂×C₈	—	94	1	no	—
392	C₂×C₈	—	94	1	no	—
393	C₂×C₈	—	94	1	no	—
394	C₂×C₈	—	94	1	no	—
395	C₂×C₈	D₄×D₄₇	1	2	yes	—
396	C₂×C₈	#10625352	1	2	yes	—
397	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
398	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	94	2	no	—
401	C₄⋊C₄	—	94	2	no	—
402	C₄⋊C₄	—	94	2	no	—
403	C₄⋊C₄	—	94	2	no	—
404	C₄⋊C₄	—	94	2	no	—
405	C₄⋊C₄	—	94	2	no	—
406	C₄⋊C₄	—	376	2	no	—
407	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	94	2	no	—
410	C₂²⋊C₄	—	94	2	no	—
411	C₂²⋊C₄	—	376	2	no	—
412	C₂²⋊C₄	—	376	2	no	—
413	C₂²⋊C₄	—	376	2	no	—
414	C₂²⋊C₄	—	188	4	no	—
415	C₄²	—	47	2	no	—
416	C₄²	—	47	2	no	—
417	C₄²	—	94	1	no	—
418	C₄²	—	94	1	no	—
419	C₄²	—	376	2	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	1	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	D₄×Dic₄₇	1	2	yes	—
434	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
435	D₄	—	2	4	no	—
436	D₄	—	2	4	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	8	8	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	47	2	no	—
450	C₂×C₄	—	47	2	no	—
451	C₂×C₄	—	94	1	no	—
452	C₂×C₄	—	94	1	no	—
453	C₂×C₄	—	94	1	no	—
454	C₂×C₄	—	94	1	no	—
455	C₂×C₄	—	94	1	no	—
456	C₂×C₄	—	94	1	no	—
457	C₂×C₄	—	94	1	no	—
458	C₂×C₄	—	94	1	no	—
459	C₂×C₄	—	94	1	no	—
460	C₂×C₄	—	94	1	no	—
461	C₂×C₄	—	376	8	no	—
462	C₂×C₄	—	188	2	no	—
463	C₂×C₄	—	188	2	no	—
464	C₂×C₄	—	188	2	no	—
465	C₂×C₄	—	188	2	no	—
466	C₂×C₄	—	188	2	no	—
467	C₂×C₄	—	188	2	no	—
468	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
469	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
470	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
471	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
472	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
473	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
474	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
475	C₈	—	2	2	no	—
476	C₈	—	94	2	no	—
477	C₈	—	94	2	no	—
478	C₈	D₄×Dic₄₇	1	4	yes	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
494	C₂²	#121×D₄₇	1	1	yes	characteristic
495	C₂²	#15689668	1	1	yes	characteristic
496	C₂²	#15689924	1	1	yes	characteristic
497	C₂²	#15689924	1	1	yes	characteristic
498	C₂²	#15689925	1	1	yes	characteristic
499	C₂²	#15689937	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	4	4	no	—
502	C₄	—	94	2	no	—
503	C₄	—	94	2	no	—
504	C₄	—	376	2	no	—
505	C₄	—	376	2	no	—
506	C₄	—	188	1	no	—
507	C₄	—	188	1	no	—
508	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
509	C₄	#41×Dic₄₇	1	1	yes	characteristic
510	C₄	#15689633	1	1	yes	characteristic
511	C₄	#15689654	1	1	yes	characteristic
512	C₂	—	4	2	no	—
513	C₂	—	8	4	no	—
514	C₂	#121×Dic₄₇	1	1	yes	characteristic
515	C₂	#20252240	1	1	yes	characteristic
516	C₂	#20252264	1	1	yes	characteristic
517	C₂	#20253031	1	1	yes	characteristic
518	C₂	#20253053	1	1	yes	characteristic
519	C₂	#20254020	1	1	yes	characteristic
520	C₂	#20254031	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	#21524
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. C₂×#15689078	C₂	semidirect
3. #20246083	C₂	semidirect
4. #20244255	C₂	semidirect
5. #20244122	C₂	semidirect
6. #20244087	C₂	semidirect
7. #20243827	C₂	semidirect
8. #20243417	C₂	semidirect
9. #107×Dic₄₇	C₂	semidirect
10. #20243215	C₂	semidirect
39. C₄₇×#466	C₄	semidirect
73. C₈×Dic₄₇	D₄	semidirect
85. C₂²×C₈×C₄₇	C₂×C₄	semidirect
89. #121×C₄₇	C₂×C₄	semidirect
92. #107×C₄₇	C₂×C₄	semidirect
93. #102×C₄₇	C₂×C₄	semidirect
278. #466	Dic₄₇	semidirect
302. C₄₇	#21524	semidirect
317. C₂²×C₈	C₂×Dic₄₇	semidirect
321. #121	C₂×Dic₄₇	semidirect
344. #107	C₂×Dic₄₇	semidirect
347. #102	C₂×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
C₂×#15689078	2
#20246083	2
#20244255	2
#20244122	2
#20244087	2
#20243827	2
#20243417	2
#107×Dic₄₇	2
#20243215	2
C₂×C₄₇×#466	2
#21524	47