Subgroups — #26186883

Order 12032.

662 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253983	C₂	1	1	yes	maximal, characteristic
2	#20252357	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252099	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242277	C₂	1	2	yes	maximal, complemented
5	#20242272	C₂	1	2	yes	maximal, complemented
6	#20242211	C₂	1	2	yes	maximal, complemented
7	#20242199	C₂	1	2	yes	maximal, complemented
8	#20241856	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241851	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1569	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094032	—	2	1	no	—
13	#15689673	C₂²	1	1	yes	characteristic
14	#15689657	C₂²	1	1	yes	characteristic
15	#15689532	C₄	1	1	yes	characteristic
16	#15689512	C₄	1	1	yes	characteristic
17	#15689488	C₄	1	1	yes	characteristic
18	#15689483	C₄	1	1	yes	characteristic
19	#15689376	C₄	1	2	yes	—
20	#15689369	C₄	1	2	yes	—
21	#15689250	C₂²	1	1	yes	characteristic
22	#15689247	C₂²	1	1	yes	characteristic
23	C₄×#10625325	C₂²	1	2	yes	—
24	C₄×D₃₇₆	C₂²	1	2	yes	—
25	#15689200	—	2	1	no	—
26	#15689200	C₂²	1	1	yes	characteristic
27	#15689200	C₂²	1	2	yes	—
28	#15689191	—	2	1	no	—
29	#15689188	—	2	1	no	—
30	#15689188	C₂²	1	2	yes	—
31	#15689188	C₂²	1	1	yes	characteristic
32	(C₂²⋊D₄₇)⋊C₈	—	2	1	no	—
33	#15689185	—	2	1	no	—
34	#15689176	C₂²	1	1	yes	characteristic
35	#15689091	—	2	1	no	—
36	#15689080	—	2	1	no	—
37	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	#15688853	C₂²	1	2	yes	—
39	#15688850	C₂²	1	2	yes	—
40	#15688850	C₂²	1	2	yes	—
41	#15688850	C₂²	1	2	yes	—
42	#15688844	C₂²	1	2	yes	—
43	C₈×C₄₇⋊C₈	C₂²	1	2	yes	—
44	C₄₇×#432	C₂²	1	1	yes	characteristic
45	C₄₇×#423	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
47	C₄₇×#335	C₂²	1	2	yes	—
48	C₄₇×#334	C₂²	1	2	yes	—
49	C₂×#10625350	—	2	1	no	—
50	C₂×#10625325	C₂×C₄	1	2	yes	—
51	C₂×D₃₇₆	C₂×C₄	1	2	yes	—
52	#13094032	—	4	4	no	—
53	C₂×#10625324	—	2	1	no	—
54	C₂×#10625324	—	2	2	no	—
55	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
56	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
57	C₂×C₈×D₄₇	—	2	1	no	—
58	C₂×C₈×D₄₇	—	2	2	no	—
59	#13094024	C₂×C₄	1	1	yes	characteristic
60	#13094021	C₂×C₄	1	1	yes	characteristic
61	#13094018	—	2	1	no	—
62	#13094016	C₂×C₄	1	1	yes	characteristic
63	#13094012	—	2	1	no	—
64	#13094012	C₂×C₄	1	1	yes	characteristic
65	#13094007	—	2	1	no	—
66	#13094003	C₂×C₄	1	1	yes	characteristic
67	#13093998	—	2	1	no	—
68	#13093998	C₂×C₄	1	2	yes	—
69	#13093998	C₂×C₄	1	1	yes	characteristic
70	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
71	C₄×D₁₈₈	—	2	1	no	—
72	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
73	C₄×D₁₈₈	C₂³	1	2	yes	—
74	C₄×C₂²⋊D₄₇	—	2	1	no	—
75	#13093981	—	2	1	no	—
76	#13093958	C₂×C₄	1	2	yes	—
77	#13093956	C₂×C₄	1	2	yes	—
78	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
79	Dic₄₇⋊C₈	—	2	1	no	—
80	Dic₄₇⋊C₈	—	2	1	no	—
81	#13093949	C₂×C₄	1	2	yes	—
82	#13093946	C₂×C₄	1	2	yes	—
83	#13093946	C₂×C₄	1	2	yes	—
84	#13093946	C₂×C₄	1	2	yes	—
85	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
86	(C₂×D₄₇)⋊C₈	—	2	2	no	—
87	(C₂×D₄₇)⋊C₈	—	2	2	no	—
88	(C₂×D₄₇)⋊C₈	—	2	1	no	—
89	(C₂×D₄₇)⋊C₈	—	2	1	no	—
90	#13093934	—	2	1	no	—
91	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
92	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
93	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
94	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
95	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
96	C₈×Dic₄₇	—	2	1	no	—
97	C₂×M₁₆×C₄₇	—	2	1	no	—
98	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
99	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₄₇	—	2	1	no	—
101	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
104	C₂²⋊C₈×C₄₇	—	2	1	no	—
105	#97×C₄₇	—	2	1	no	—
106	#97×C₄₇	C₂×C₄	1	1	yes	characteristic
107	#97×C₄₇	C₂×C₄	1	1	yes	characteristic
108	C₄×C₈×C₄₇	C₂³	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₄₇	—	2	1	no	—
113	C₂×C₂²⋊D₄₇	—	2	2	no	—
114	#10625350	—	4	2	no	—
115	#10625350	—	4	2	no	—
116	C₂×D₁₈₈	—	2	1	no	—
117	C₂×D₁₈₈	—	2	1	no	—
118	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
119	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
120	C₂×C₄×D₄₇	—	2	1	no	—
121	C₂×C₄×D₄₇	—	2	2	no	—
122	C₂×Dic₉₄	—	2	1	no	—
123	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
124	M₁₆×C₄₇	—	2	4	no	—
125	M₁₆×C₄₇	—	4	2	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	2	1	no	—
128	C₂×C₈×C₄₇	—	2	1	no	—
129	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
131	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₄₇	#41	1	1	yes	characteristic
134	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
135	C₂²⋊Dic₄₇	—	2	1	no	—
136	(C₂×D₄₇)⋊C₄	—	2	1	no	—
137	(C₂×D₄₇)⋊C₄	—	2	1	no	—
138	(C₂×D₄₇)⋊C₄	—	2	1	no	—
139	(C₂×D₄₇)⋊C₄	—	2	2	no	—
140	(C₂×D₄₇)⋊C₄	—	2	2	no	—
141	(C₂×D₄₇)⋊C₄	—	2	1	no	—
142	C₄⋊Dic₄₇	—	2	1	no	—
143	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
146	Dic₄₇⋊C₄	—	2	1	no	—
147	Dic₄₇⋊C₄	—	2	1	no	—
148	Dic₄₇⋊C₄	—	2	1	no	—
149	Dic₄₇⋊C₄	—	2	1	no	—
150	C₄×Dic₄₇	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	4	1	no	—
154	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
158	D₃₇₆	—	2	4	no	—
159	#10625325	—	2	4	no	—
160	#10625324	—	4	2	no	—
161	#10625324	—	4	4	no	—
162	C₈×D₄₇	—	4	2	no	—
163	C₈×D₄₇	—	4	4	no	—
164	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
165	C₂²×D₄₇	—	2	1	no	—
166	C₂²×D₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	4	1	no	—
171	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
177	C₂²⋊D₄₇	—	4	4	no	—
178	C₂²⋊D₄₇	—	4	2	no	—
179	C₂×Dic₄₇	—	2	1	no	—
180	C₂×Dic₄₇	—	2	1	no	—
181	C₂×Dic₄₇	—	2	1	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	D₁₈₈	—	2	2	no	—
184	D₁₈₈	—	2	2	no	—
185	D₁₈₈	—	2	2	no	—
186	D₁₈₈	—	4	2	no	—
187	D₁₈₈	—	4	2	no	—
188	C₄×D₄₇	—	4	2	no	—
189	C₄×D₄₇	—	4	1	no	—
190	C₄×D₄₇	—	4	1	no	—
191	C₄×D₄₇	—	4	2	no	—
192	Dic₉₄	—	2	2	no	—
193	Dic₉₄	—	4	2	no	—
194	C₈×C₄₇	—	2	2	no	—
195	C₈×C₄₇	—	4	2	no	—
196	C₈×C₄₇	—	4	1	no	—
197	C₈×C₄₇	—	4	1	no	—
198	C₈×C₄₇	#131	1	4	yes	complemented
199	C₄₇⋊C₈	—	2	1	no	—
200	C₄₇⋊C₈	—	2	1	no	—
201	C₄₇⋊C₈	—	2	1	no	—
202	C₄₇⋊C₈	—	4	2	no	—
203	C₄₇⋊C₈	AGL(1,ℤ/8)	1	2	yes	—
204	#17966	—	47	1	no	maximal, Sylow
205	C₂²×C₄₇	—	2	1	no	—
206	C₂²×C₄₇	—	2	1	no	—
207	C₂²×C₄₇	—	2	1	no	—
208	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
209	C₂×D₄₇	—	4	2	no	—
210	C₂×D₄₇	—	4	1	no	—
211	C₂×D₄₇	—	4	2	no	—
212	C₂×D₄₇	—	4	1	no	—
213	C₂×D₄₇	—	4	2	no	—
214	C₂×D₄₇	—	4	1	no	—
215	C₄×C₄₇	—	2	1	no	—
216	C₄×C₄₇	—	2	1	no	—
217	C₄×C₄₇	—	2	1	no	—
218	C₄×C₄₇	—	2	1	no	—
219	C₄×C₄₇	C₂×#131	1	2	yes	—
220	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₄×C₄₇	#575	1	1	yes	characteristic
222	Dic₄₇	—	4	1	no	—
223	Dic₄₇	—	4	2	no	—
224	Dic₄₇	—	4	1	no	—
225	Dic₄₇	—	4	1	no	—
226	#3171	—	47	1	no	—
227	#2966	—	47	1	no	—
228	#2931	—	47	1	no	—
229	#1590	—	47	2	no	—
230	#1589	—	47	2	no	—
231	#1580	—	47	2	no	—
232	SD₁₆⋊C₈	—	47	2	no	—
233	#1569	D₄₇	1	1	yes	characteristic, complemented
234	#1496	—	47	1	no	—
235	#1495	—	47	1	no	—
236	C₈×M₁₆	—	47	1	no	—
237	C₂×C₄₇	—	4	1	no	—
238	C₂×C₄₇	#2931	1	1	yes	characteristic
239	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
240	C₂×C₄₇	#2955	1	1	yes	characteristic
241	D₄₇	—	8	2	no	—
242	D₄₇	—	8	1	no	—
243	C₂×#131	—	94	1	no	—
244	#532	—	47	1	no	—
245	#529	—	47	1	no	—
246	#501	—	47	1	no	—
247	#496	—	47	1	no	—
248	#490	—	47	1	no	—
249	#489	—	47	1	no	—
250	#469	—	47	2	no	—
251	#468	—	47	2	no	—
252	#446	—	47	1	no	—
253	C₈×Q₈	—	47	1	no	—
254	C₄×SD₁₆	—	47	2	no	—
255	C₄×D₈	—	47	2	no	—
256	#436	—	47	1	no	—
257	#436	—	47	2	no	—
258	#436	—	94	1	no	—
259	#435	—	94	1	no	—
260	C₈×D₄	—	47	2	no	—
261	C₈×D₄	—	47	1	no	—
262	C₈×D₄	—	94	1	no	—
263	C₈×D₄	—	94	1	no	—
264	#433	—	94	1	no	—
265	#432	C₂×D₄₇	1	1	yes	characteristic
266	#431	—	47	1	no	—
267	#423	C₂×D₄₇	1	1	yes	characteristic
268	#408	—	94	1	no	—
269	#405	—	94	1	no	—
270	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
271	C₂×C₄×C₈	—	47	1	no	—
272	#335	C₂×D₄₇	1	2	yes	—
273	#334	C₂×D₄₇	1	2	yes	—
274	Q₈⋊C₈	—	47	2	no	—
275	D₄⋊C₈	—	47	2	no	—
276	D₄⋊C₈	—	47	2	no	—
277	D₄⋊C₈	—	47	2	no	—
278	#322	—	47	2	no	—
279	C₈²	—	47	2	no	—
280	C₄₇	#17966	1	1	yes	characteristic, complemented, Sylow
281	C₂×#41	—	94	1	no	—
282	C₂×SD₁₆	—	47	2	no	—
283	C₂×D₈	—	47	2	no	—
284	#131	—	188	4	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	—	94	2	no	—
287	C₂×M₁₆	—	94	1	no	—
288	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
289	C₂²×C₈	—	47	1	no	—
290	C₂²×C₈	—	47	1	no	—
291	C₂²×C₈	—	94	2	no	—
292	C₂²×C₈	—	94	1	no	—
293	C₄⋊Q₈	—	47	1	no	—
294	#127	—	47	1	no	—
295	#126	—	94	1	no	—
296	#125	—	47	1	no	—
297	#124	—	47	1	no	—
298	#124	—	94	1	no	—
299	#123	—	94	1	no	—
300	C₂²⋊Q₈	—	47	1	no	—
301	#121	—	47	1	no	—
302	#121	—	47	2	no	—
303	#121	—	94	1	no	—
304	C₄×Q₈	—	47	1	no	—
305	C₄×D₄	—	47	1	no	—
306	C₄×D₄	—	47	2	no	—
307	C₄×D₄	—	94	1	no	—
308	C₄×D₄	—	94	1	no	—
309	#117	—	94	1	no	—
310	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
311	#107	—	47	2	no	—
312	#106	—	47	2	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	94	1	no	—
315	C₄⋊C₈	—	94	1	no	—
316	C₄⋊C₈	—	94	1	no	—
317	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
318	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
319	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
320	#103	—	47	2	no	—
321	#102	—	47	2	no	—
322	#102	—	47	2	no	—
323	#102	—	47	2	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	94	2	no	—
326	C₂²⋊C₈	—	94	2	no	—
327	C₂²⋊C₈	—	94	1	no	—
328	C₂²⋊C₈	—	94	1	no	—
329	C₂²⋊C₈	—	94	1	no	—
330	#97	—	2	1	no	—
331	#97	—	94	1	no	—
332	#97	C₄×D₄₇	1	1	yes	characteristic
333	#97	C₄×D₄₇	1	1	yes	characteristic
334	C₄×C₈	—	47	1	no	—
335	C₄×C₈	—	47	1	no	—
336	C₄×C₈	—	47	1	no	—
337	C₄×C₈	—	47	1	no	—
338	C₄×C₈	—	47	2	no	—
339	C₄×C₈	—	94	1	no	—
340	C₄×C₈	C₂²×D₄₇	1	2	yes	—
341	#41	—	188	2	no	—
342	#41	—	188	2	no	—
343	C₂×Q₈	—	47	1	no	—
344	C₂×Q₈	—	94	1	no	—
345	C₂×D₄	—	47	1	no	—
346	C₂×D₄	—	47	2	no	—
347	C₂×D₄	—	94	1	no	—
348	C₂×D₄	—	94	2	no	—
349	C₂×D₄	—	94	1	no	—
350	C₂×D₄	—	94	1	no	—
351	C₂²×C₄	—	94	1	no	—
352	C₂²×C₄	—	94	2	no	—
353	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
354	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
355	C₂²×C₄	#10625354	1	1	yes	characteristic
356	SD₁₆	—	94	4	no	—
357	D₈	—	94	4	no	—
358	M₁₆	—	2	4	no	—
359	M₁₆	—	4	2	no	—
360	M₁₆	—	188	2	no	—
361	M₁₆	—	188	4	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	47	1	no	—
366	C₂×C₈	—	47	1	no	—
367	C₂×C₈	—	47	1	no	—
368	C₂×C₈	—	47	1	no	—
369	C₂×C₈	—	94	2	no	—
370	C₂×C₈	—	94	2	no	—
371	C₂×C₈	—	188	2	no	—
372	C₂×C₈	—	188	4	no	—
373	C₂×C₈	—	188	1	no	—
374	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
375	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
376	C₄⋊C₄	—	47	1	no	—
377	C₄⋊C₄	—	47	1	no	—
378	C₄⋊C₄	—	47	2	no	—
379	C₄⋊C₄	—	94	1	no	—
380	C₄⋊C₄	—	94	1	no	—
381	C₄⋊C₄	—	94	1	no	—
382	C₄⋊C₄	—	94	1	no	—
383	C₄⋊C₄	—	94	1	no	—
384	C₂²⋊C₄	—	94	1	no	—
385	C₂²⋊C₄	—	94	1	no	—
386	C₂²⋊C₄	—	94	1	no	—
387	C₂²⋊C₄	—	94	2	no	—
388	C₂²⋊C₄	—	94	1	no	—
389	C₂²⋊C₄	—	94	2	no	—
390	C₂²⋊C₄	—	94	1	no	—
391	C₄²	—	94	1	no	—
392	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
393	C₄²	D₄×D₄₇	1	1	yes	characteristic
394	C₄²	#10625354	1	1	yes	characteristic
395	C₄²	C₂³×D₄₇	1	1	yes	characteristic
396	C₂³	—	94	1	no	—
397	C₂³	—	94	2	no	—
398	C₂³	#13093986	1	1	yes	characteristic
399	Q₈	—	94	2	no	—
400	Q₈	—	188	2	no	—
401	D₄	—	94	2	no	—
402	D₄	—	94	2	no	—
403	D₄	—	94	2	no	—
404	D₄	—	188	2	no	—
405	D₄	—	188	2	no	—
406	D₄	—	188	2	no	—
407	D₄	—	188	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	94	1	no	—
413	C₂×C₄	—	94	1	no	—
414	C₂×C₄	—	94	1	no	—
415	C₂×C₄	—	94	2	no	—
416	C₂×C₄	—	188	2	no	—
417	C₂×C₄	—	188	1	no	—
418	C₂×C₄	—	188	1	no	—
419	C₂×C₄	—	188	2	no	—
420	C₂×C₄	#13093986	1	1	yes	characteristic
421	C₂×C₄	#13093986	1	1	yes	characteristic
422	C₂×C₄	#13093986	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
424	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
425	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	4	2	no	—
428	C₈	—	4	1	no	—
429	C₈	—	4	1	no	—
430	C₈	—	47	2	no	—
431	C₈	—	94	1	no	—
432	C₈	—	94	1	no	—
433	C₈	—	94	1	no	—
434	C₈	—	188	2	no	—
435	C₈	#13094032	1	4	yes	complemented
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	188	2	no	—
440	C₂²	—	188	1	no	—
441	C₂²	—	188	2	no	—
442	C₂²	—	188	1	no	—
443	C₂²	—	188	1	no	—
444	C₂²	—	188	2	no	—
445	C₂²	C₂×#13093986	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	188	2	no	—
451	C₄	—	188	1	no	—
452	C₄	—	188	1	no	—
453	C₄	—	188	1	no	—
454	C₄	C₂×#13094032	1	2	yes	—
455	C₄	AGL(1,ℤ/8)×D₄₇	1	1	yes	characteristic
456	C₄	#15689922	1	1	yes	characteristic
457	C₂	—	4	1	no	—
458	C₂	—	376	2	no	—
459	C₂	—	376	1	no	—
460	C₂	#20252099	1	1	yes	characteristic
461	C₂	#20252195	1	1	yes	characteristic
462	C₂	#20252290	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1569	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20253983	C₂
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1569	D₄₇
hypocenter	C₄₇	#17966
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1569

Complements

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

N	H ≅ G/N	type
2. #20252357	C₂	semidirect
3. #20252099	C₂	semidirect
4. #20242277	C₂	semidirect
5. #20242272	C₂	semidirect
6. #20242211	C₂	semidirect
7. #20242199	C₂	semidirect
8. #20241856	C₂	semidirect
9. #20241851	C₂	semidirect
10. M₁₆×C₄₇⋊C₈	C₂	semidirect
11. C₄₇×#1569	C₂	semidirect
198. C₈×C₄₇	#131	semidirect
233. #1569	D₄₇	semidirect
280. C₄₇	#17966	semidirect
435. C₈	#13094032	semidirect

Maximal subgroups

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

subgroup	index
#20253983	2
#20252357	2
#20252099	2
#20242277	2
#20242272	2
#20242211	2
#20242199	2
#20241856	2
#20241851	2
M₁₆×C₄₇⋊C₈	2
C₄₇×#1569	2
#17966	47