Subgroups — #26185996

Order 12032.

660 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252506	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13094046	C₂	1	1	yes	maximal, characteristic
4	#20242258	C₂	1	2	yes	maximal, complemented
5	#20242251	C₂	1	2	yes	maximal, complemented
6	#20242230	C₂	1	2	yes	maximal, complemented
7	#20242223	C₂	1	2	yes	maximal, complemented
8	#20241773	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241773	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241680	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#334	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	C₄	1	1	yes	characteristic
13	C₄×#10625350	C₂²	1	1	yes	characteristic
14	C₄×#10625350	C₂²	1	1	yes	characteristic
15	#15689250	C₂²	1	2	yes	—
16	#15689247	C₂²	1	2	yes	—
17	C₄×Dic₁₈₈	C₄	1	1	yes	characteristic
18	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic
19	C₄×#10625325	C₄	1	1	yes	characteristic
20	C₄×#10625325	C₄	1	1	yes	characteristic
21	C₄×#10625325	C₂²	1	1	yes	characteristic
22	C₄×#10625325	C₂²	1	1	yes	characteristic
23	C₄×D₃₇₆	C₄	1	1	yes	characteristic
24	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
25	#15689200	C₂²	1	2	yes	—
26	#15689194	—	2	2	no	—
27	#15689188	C₂²	1	2	yes	—
28	C₈×C₂²⋊D₄₇	—	2	2	no	—
29	#15689179	—	2	1	no	—
30	#15689176	C₂²	1	1	yes	characteristic
31	#15689176	C₂²	1	1	yes	characteristic
32	#15689175	—	2	1	no	—
33	#15689161	C₄	1	1	yes	characteristic
34	#15689145	—	2	1	no	—
35	C₄⋊C₈×D₄₇	—	2	1	no	—
36	#15689120	C₄	1	1	yes	characteristic
37	#15689120	C₄	1	1	yes	characteristic
38	#15688853	C₂²	1	2	yes	—
39	#15688853	C₂²	1	2	yes	—
40	#15688850	C₂²	1	2	yes	—
41	#15688850	C₂²	1	2	yes	—
42	#15688845	C₂²	1	2	yes	—
43	#15688845	C₂²	1	2	yes	—
44	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₄₇×#334	C₂²	1	2	yes	—
48	C₄₇×#334	C₂²	1	2	yes	—
49	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
50	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
51	#13094046	—	2	4	no	—
52	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic
53	C₂×#10625325	C₂×C₄	1	1	yes	characteristic
54	C₂×#10625325	C₂×C₄	1	1	yes	characteristic
55	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
56	C₂×#10625324	—	2	2	no	—
57	C₂×C₈×D₄₇	—	2	2	no	—
58	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
59	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
60	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
61	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
62	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
63	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
64	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
65	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
66	C₄×C₂²⋊D₄₇	—	2	1	no	—
67	C₄×C₂²⋊D₄₇	—	2	1	no	—
68	C₄×C₂²⋊D₄₇	—	2	1	no	—
69	C₄×C₂²⋊D₄₇	—	2	1	no	—
70	#13093983	C₂×C₄	1	1	yes	characteristic
71	#13093983	C₂×C₄	1	1	yes	characteristic
72	#13093981	—	2	1	no	—
73	#13093981	—	2	1	no	—
74	C₄²×D₄₇	—	2	1	no	—
75	C₄²×D₄₇	—	2	1	no	—
76	#13093958	C₂×C₄	1	1	yes	characteristic
77	#13093958	C₂×C₄	1	1	yes	characteristic
78	#13093956	C₂×C₄	1	1	yes	characteristic
79	#13093956	C₂×C₄	1	1	yes	characteristic
80	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
81	C₄⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
82	C₄⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
83	Dic₄₇⋊C₈	—	2	2	no	—
84	Dic₄₇⋊C₈	—	2	2	no	—
85	#13093949	C₂×C₄	1	1	yes	characteristic
86	#13093949	C₂×C₄	1	1	yes	characteristic
87	#13093949	C₂×C₄	1	1	yes	characteristic
88	#13093949	C₂×C₄	1	1	yes	characteristic
89	#13093946	C₂×C₄	1	1	yes	characteristic
90	#13093946	C₂×C₄	1	1	yes	characteristic
91	#13093946	C₂×C₄	1	1	yes	characteristic
92	#13093946	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
94	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
95	(C₂×D₄₇)⋊C₈	—	2	2	no	—
96	(C₂×D₄₇)⋊C₈	—	2	2	no	—
97	#13093934	—	2	2	no	—
98	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
99	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
100	C₈×Dic₄₇	—	2	2	no	—
101	C₂²×C₈×C₄₇	—	2	1	no	—
102	C₂²×C₈×C₄₇	—	2	1	no	—
103	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
104	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
106	C₄⋊C₈×C₄₇	—	2	1	no	—
107	C₄⋊C₈×C₄₇	—	2	1	no	—
108	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
109	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
110	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
111	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
112	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
113	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
117	C₂×C₂²⋊D₄₇	—	2	1	no	—
118	C₂×C₂²⋊D₄₇	—	2	1	no	—
119	#10625350	—	2	2	no	—
120	#10625350	—	2	2	no	—
121	#10625350	—	2	2	no	—
122	#10625350	M₁₆	1	4	yes	complemented
123	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
124	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×D₄₇	—	2	1	no	—
126	C₂×C₄×D₄₇	—	2	1	no	—
127	C₂×C₄×D₄₇	—	2	1	no	—
128	C₂×C₄×D₄₇	—	2	1	no	—
129	C₂×C₄×D₄₇	—	2	1	no	—
130	C₂×C₄×D₄₇	—	2	1	no	—
131	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
132	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₄₇	—	2	2	no	—
134	C₂×C₈×C₄₇	—	2	2	no	—
135	C₂×C₈×C₄₇	—	2	2	no	—
136	C₂×C₈×C₄₇	—	2	2	no	—
137	C₂×C₈×C₄₇	—	8	1	no	—
138	C₂×C₈×C₄₇	—	8	1	no	—
139	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₄₇	#41	1	1	yes	characteristic
146	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
147	C₂²⋊Dic₄₇	—	2	1	no	—
148	C₂²⋊Dic₄₇	—	2	1	no	—
149	(C₂×D₄₇)⋊C₄	—	2	1	no	—
150	(C₂×D₄₇)⋊C₄	—	2	1	no	—
151	(C₂×D₄₇)⋊C₄	—	2	1	no	—
152	(C₂×D₄₇)⋊C₄	—	2	1	no	—
153	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
154	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
155	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
157	Dic₄₇⋊C₄	—	2	1	no	—
158	Dic₄₇⋊C₄	—	2	1	no	—
159	Dic₄₇⋊C₄	—	2	1	no	—
160	Dic₄₇⋊C₄	—	2	1	no	—
161	C₄×Dic₄₇	—	2	1	no	—
162	C₄×Dic₄₇	—	2	1	no	—
163	C₄×Dic₄₇	—	2	1	no	—
164	C₄×Dic₄₇	—	2	1	no	—
165	C₄×Dic₄₇	—	2	1	no	—
166	C₄×Dic₄₇	—	2	1	no	—
167	C₂×C₄₇⋊C₈	—	2	2	no	—
168	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
169	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
170	Dic₁₈₈	—	2	2	no	—
171	D₃₇₆	—	2	2	no	—
172	#10625325	—	2	2	no	—
173	#10625325	—	2	2	no	—
174	#10625324	—	8	2	no	—
175	C₈×D₄₇	—	8	2	no	—
176	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
177	C₂²×D₄₇	—	2	1	no	—
178	C₂²×D₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
186	C₂×C₄×C₄₇	#131	1	2	yes	—
187	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
190	C₂²⋊D₄₇	—	2	4	no	—
191	C₂²⋊D₄₇	—	4	2	no	—
192	C₂×Dic₄₇	—	2	1	no	—
193	C₂×Dic₄₇	—	2	1	no	—
194	C₂×Dic₄₇	—	2	1	no	—
195	C₂×Dic₄₇	—	2	1	no	—
196	C₂×Dic₄₇	—	2	1	no	—
197	C₂×Dic₄₇	—	2	1	no	—
198	D₁₈₈	—	2	1	no	—
199	D₁₈₈	—	2	1	no	—
200	D₁₈₈	—	2	1	no	—
201	D₁₈₈	C₂×M₁₆	1	2	yes	—
202	C₄×D₄₇	—	2	4	no	—
203	C₄×D₄₇	—	4	1	no	—
204	C₄×D₄₇	—	4	1	no	—
205	C₄×D₄₇	—	4	1	no	—
206	C₄×D₄₇	—	4	1	no	—
207	C₄×D₄₇	—	4	2	no	—
208	C₄×D₄₇	—	8	1	no	—
209	C₄×D₄₇	—	8	1	no	—
210	Dic₉₄	—	2	1	no	—
211	Dic₉₄	—	2	1	no	—
212	Dic₉₄	—	2	1	no	—
213	Dic₉₄	C₂×M₁₆	1	2	yes	—
214	C₈×C₄₇	—	2	1	no	—
215	C₈×C₄₇	—	2	1	no	—
216	C₈×C₄₇	—	2	1	no	—
217	C₈×C₄₇	—	2	1	no	—
218	C₈×C₄₇	—	4	2	no	—
219	C₈×C₄₇	—	4	2	no	—
220	C₄₇⋊C₈	—	2	2	no	—
221	C₄₇⋊C₈	—	2	2	no	—
222	C₄₇⋊C₈	—	4	2	no	—
223	#17882	—	47	1	no	maximal, Sylow
224	C₂²×C₄₇	—	2	1	no	—
225	C₂²×C₄₇	—	2	1	no	—
226	C₂²×C₄₇	#435	1	2	yes	—
227	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂×D₄₇	—	2	2	no	—
229	C₂×D₄₇	—	4	1	no	—
230	C₂×D₄₇	—	4	1	no	—
231	C₂×D₄₇	—	4	1	no	—
232	C₂×D₄₇	—	4	1	no	—
233	C₂×D₄₇	—	4	1	no	—
234	C₄×C₄₇	—	2	1	no	—
235	C₄×C₄₇	—	2	1	no	—
236	C₄×C₄₇	—	2	1	no	—
237	C₄×C₄₇	#435	1	2	yes	—
238	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
239	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
240	C₄×C₄₇	#577	1	1	yes	characteristic
241	C₄×C₄₇	#577	1	1	yes	characteristic
242	Dic₄₇	—	2	2	no	—
243	Dic₄₇	—	4	1	no	—
244	Dic₄₇	—	4	1	no	—
245	Dic₄₇	—	4	1	no	—
246	Dic₄₇	—	4	1	no	—
247	Dic₄₇	—	4	1	no	—
248	#2989	—	47	1	no	—
249	#2988	—	47	1	no	—
250	C₄×#135	—	47	1	no	—
251	#1587	—	47	2	no	—
252	#1586	—	47	2	no	—
253	#1583	—	47	2	no	—
254	#1582	—	47	2	no	—
255	C₂×#334	D₄₇	1	1	yes	characteristic, complemented
256	#1477	—	47	1	no	—
257	#1477	—	47	1	no	—
258	#1452	—	47	1	no	—
259	C₂×C₄₇	—	2	2	no	—
260	C₂×C₄₇	C₂×#435	1	1	yes	characteristic
261	C₂×C₄₇	#2952	1	1	yes	characteristic
262	C₂×C₄₇	#2957	1	1	yes	characteristic
263	D₄₇	—	4	2	no	—
264	D₄₇	—	8	1	no	—
265	C₂×#135	—	47	1	no	—
266	C₄×#41	—	47	1	no	—
267	C₄×#41	—	47	1	no	—
268	#446	—	47	2	no	—
269	C₈×Q₈	—	47	2	no	—
270	C₄×Q₁₆	—	47	1	no	—
271	C₄×Q₁₆	—	47	1	no	—
272	C₄×SD₁₆	—	47	1	no	—
273	C₄×SD₁₆	—	47	1	no	—
274	C₄×SD₁₆	—	47	1	no	—
275	C₄×SD₁₆	—	47	1	no	—
276	C₄×D₈	—	47	1	no	—
277	C₄×D₈	—	47	1	no	—
278	#436	—	47	2	no	—
279	#435	—	94	2	no	—
280	C₈×D₄	—	47	2	no	—
281	C₈×D₄	—	94	2	no	—
282	#432	—	94	1	no	—
283	#431	—	47	1	no	—
284	#431	—	47	1	no	—
285	#431	—	94	1	no	—
286	#427	—	47	1	no	—
287	#423	—	94	1	no	—
288	C₂×C₄⋊C₈	—	94	1	no	—
289	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
290	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
291	#416	—	47	1	no	—
292	#416	—	47	1	no	—
293	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
294	#334	C₂×D₄₇	1	2	yes	—
295	#334	C₂×D₄₇	1	2	yes	—
296	Q₈⋊C₈	—	47	2	no	—
297	Q₈⋊C₈	—	47	2	no	—
298	D₄⋊C₈	—	47	2	no	—
299	D₄⋊C₈	—	47	2	no	—
300	#322	—	47	2	no	—
301	#322	—	47	2	no	—
302	C₄₇	#17882	1	1	yes	characteristic, complemented, Sylow
303	C₂×#41	—	47	1	no	—
304	C₂×#41	—	47	1	no	—
305	#135	—	94	4	no	—
306	C₂×Q₁₆	—	47	1	no	—
307	C₂×SD₁₆	—	47	1	no	—
308	C₂×SD₁₆	—	47	1	no	—
309	C₂×D₈	—	47	1	no	—
310	C₂×M₁₆	—	94	2	no	—
311	C₂²×C₈	—	2	1	no	—
312	C₂²×C₈	—	2	1	no	—
313	C₂²×C₈	—	94	2	no	—
314	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
315	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
316	C₄×Q₈	—	47	1	no	—
317	C₄×Q₈	—	47	1	no	—
318	C₄×Q₈	—	47	1	no	—
319	C₄×Q₈	—	47	1	no	—
320	C₄×D₄	—	47	1	no	—
321	C₄×D₄	—	47	1	no	—
322	C₄×D₄	—	47	1	no	—
323	C₄×D₄	—	47	1	no	—
324	C₄×D₄	—	94	1	no	—
325	C₄×D₄	—	94	1	no	—
326	C₄×D₄	—	94	1	no	—
327	C₄×D₄	—	94	1	no	—
328	#117	—	47	1	no	—
329	#117	—	47	1	no	—
330	#117	—	94	1	no	—
331	#117	—	94	1	no	—
332	C₂×C₄²	—	94	1	no	—
333	C₂×C₄²	—	94	1	no	—
334	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
335	#107	—	47	1	no	—
336	#107	—	47	1	no	—
337	#106	—	47	1	no	—
338	#106	—	47	1	no	—
339	C₄⋊C₈	—	2	1	no	—
340	C₄⋊C₈	—	2	1	no	—
341	C₄⋊C₈	—	47	1	no	—
342	C₄⋊C₈	—	47	1	no	—
343	C₄⋊C₈	—	94	2	no	—
344	C₄⋊C₈	—	94	2	no	—
345	C₄⋊C₈	—	94	1	no	—
346	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
347	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
348	#103	—	47	1	no	—
349	#103	—	47	1	no	—
350	#103	—	47	1	no	—
351	#103	—	47	1	no	—
352	#102	—	47	1	no	—
353	#102	—	47	1	no	—
354	#102	—	47	1	no	—
355	#102	—	47	1	no	—
356	C₂²⋊C₈	—	47	2	no	—
357	C₂²⋊C₈	—	94	2	no	—
358	C₂²⋊C₈	—	94	2	no	—
359	C₂²⋊C₈	—	94	1	no	—
360	#97	—	94	2	no	—
361	C₄×C₈	—	47	2	no	—
362	C₄×C₈	—	47	2	no	—
363	C₄×C₈	—	94	2	no	—
364	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
365	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
366	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
367	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
368	#41	—	47	4	no	—
369	#41	—	94	2	no	—
370	#41	—	94	2	no	—
371	#41	—	94	2	no	—
372	C₂×Q₈	—	47	1	no	—
373	C₂×Q₈	—	47	1	no	—
374	C₂×D₄	—	47	1	no	—
375	C₂×D₄	—	47	1	no	—
376	C₂×D₄	—	94	1	no	—
377	C₂×D₄	—	94	1	no	—
378	C₂²×C₄	—	94	1	no	—
379	C₂²×C₄	—	94	1	no	—
380	C₂²×C₄	—	94	1	no	—
381	C₂²×C₄	—	94	1	no	—
382	C₂²×C₄	—	94	1	no	—
383	C₂²×C₄	—	94	1	no	—
384	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
385	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
386	C₂²×C₄	#10625354	1	1	yes	characteristic
387	Q₁₆	—	94	2	no	—
388	SD₁₆	—	94	2	no	—
389	SD₁₆	—	94	2	no	—
390	D₈	—	94	2	no	—
391	M₁₆	—	376	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	8	1	no	—
397	C₂×C₈	—	8	1	no	—
398	C₂×C₈	—	47	2	no	—
399	C₂×C₈	—	47	2	no	—
400	C₂×C₈	—	94	2	no	—
401	C₂×C₈	—	376	2	no	—
402	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
403	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
404	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
405	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
406	C₄⋊C₄	—	47	1	no	—
407	C₄⋊C₄	—	47	1	no	—
408	C₄⋊C₄	—	47	1	no	—
409	C₄⋊C₄	—	47	1	no	—
410	C₄⋊C₄	—	94	1	no	—
411	C₄⋊C₄	—	94	1	no	—
412	C₄⋊C₄	—	94	1	no	—
413	C₄⋊C₄	—	94	1	no	—
414	C₂²⋊C₄	—	94	1	no	—
415	C₂²⋊C₄	—	94	1	no	—
416	C₂²⋊C₄	—	94	1	no	—
417	C₂²⋊C₄	—	94	1	no	—
418	C₂²⋊C₄	—	94	1	no	—
419	C₂²⋊C₄	—	94	1	no	—
420	C₄²	—	94	1	no	—
421	C₄²	—	94	1	no	—
422	C₄²	—	94	1	no	—
423	C₄²	—	94	1	no	—
424	C₄²	—	94	1	no	—
425	C₄²	—	94	1	no	—
426	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
427	C₄²	D₄×D₄₇	1	1	yes	characteristic
428	C₄²	#10625354	1	1	yes	characteristic
429	C₄²	C₂³×D₄₇	1	1	yes	characteristic
430	C₂³	—	94	1	no	—
431	C₂³	—	94	1	no	—
432	C₂³	#13093986	1	1	yes	characteristic
433	Q₈	—	47	2	no	—
434	Q₈	—	94	1	no	—
435	Q₈	—	94	1	no	—
436	Q₈	—	94	1	no	—
437	D₄	—	47	2	no	—
438	D₄	—	94	4	no	—
439	D₄	—	94	1	no	—
440	D₄	—	94	1	no	—
441	D₄	—	94	1	no	—
442	D₄	—	188	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	94	1	no	—
447	C₂×C₄	—	94	4	no	—
448	C₂×C₄	—	94	1	no	—
449	C₂×C₄	—	94	1	no	—
450	C₂×C₄	—	94	1	no	—
451	C₂×C₄	—	94	1	no	—
452	C₂×C₄	—	94	1	no	—
453	C₂×C₄	—	376	1	no	—
454	C₂×C₄	—	376	1	no	—
455	C₂×C₄	—	188	1	no	—
456	C₂×C₄	—	188	1	no	—
457	C₂×C₄	—	188	1	no	—
458	C₂×C₄	—	188	1	no	—
459	C₂×C₄	—	188	2	no	—
460	C₂×C₄	#13093986	1	1	yes	characteristic
461	C₂×C₄	#13093986	1	1	yes	characteristic
462	C₂×C₄	#13093986	1	1	yes	characteristic
463	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
464	C₂×C₄	#13094030	1	2	yes	—
465	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
466	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
467	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
468	C₈	—	2	1	no	—
469	C₈	—	2	1	no	—
470	C₈	—	2	1	no	—
471	C₈	—	2	1	no	—
472	C₈	—	4	2	no	—
473	C₈	—	4	2	no	—
474	C₈	—	94	2	no	—
475	C₈	—	94	2	no	—
476	C₈	—	188	2	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	94	2	no	—
480	C₂²	—	188	1	no	—
481	C₂²	—	188	1	no	—
482	C₂²	—	188	1	no	—
483	C₂²	—	188	1	no	—
484	C₂²	—	188	1	no	—
485	C₂²	#15689193	1	2	yes	—
486	C₂²	C₂×#13093986	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	94	2	no	—
491	C₄	—	188	1	no	—
492	C₄	—	188	1	no	—
493	C₄	—	188	1	no	—
494	C₄	—	188	1	no	—
495	C₄	—	188	1	no	—
496	C₄	#15689193	1	2	yes	—
497	C₄	C₂×M₁₆×D₄₇	1	1	yes	characteristic
498	C₄	C₂×#13094030	1	1	yes	characteristic
499	C₄	#15689929	1	1	yes	characteristic
500	C₄	#15689929	1	1	yes	characteristic
501	C₂	—	2	2	no	—
502	C₂	—	376	1	no	—
503	C₂	—	188	2	no	—
504	C₂	C₂×#15689193	1	1	yes	characteristic
505	C₂	#20252271	1	1	yes	characteristic
506	C₂	#20252304	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#334	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094046	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂×#334	D₄₇
hypocenter	C₄₇	#17882
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
1. #20252506	C₂	semidirect
2. #20252497	C₂	semidirect
4. #20242258	C₂	semidirect
5. #20242251	C₂	semidirect
6. #20242230	C₂	semidirect
7. #20242223	C₂	semidirect
8. #20241773	C₂	semidirect
9. #20241773	C₂	semidirect
10. #20241680	C₂	semidirect
11. C₂×C₄₇×#334	C₂	semidirect
122. #10625350	M₁₆	semidirect
255. C₂×#334	D₄₇	semidirect
302. C₄₇	#17882	semidirect

Maximal subgroups

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

subgroup	index
#20252506	2
#20252497	2
C₄×#13094046	2
#20242258	2
#20242251	2
#20242230	2
#20242223	2
#20241773	2
#20241680	2
C₂×C₄₇×#334	2
#17882	47