Subgroups — #26204124

Order 12032.

900 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20254331	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253943	C₂	1	1	yes	maximal, characteristic, complemented
3	#20253930	C₂	1	1	yes	maximal, characteristic, complemented
4	#20253841	C₂	1	1	yes	maximal, characteristic
5	C₂×#15689497	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243018	C₂	1	2	yes	maximal, complemented
7	#20243013	C₂	1	2	yes	maximal, complemented
8	#20242979	C₂	1	2	yes	maximal, complemented
9	#20242976	C₂	1	2	yes	maximal, complemented
10	#20241669	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3227	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094049	—	2	2	no	—
13	C₂²×#10625336	—	2	2	no	—
14	#15689680	C₂²	1	1	yes	characteristic
15	C₂×#13094021	C₂²	1	1	yes	characteristic
16	#15689529	—	2	2	no	—
17	#15689526	C₂²	1	2	yes	complemented
18	#15689519	C₂²	1	1	yes	characteristic, complemented
19	#15689519	C₂²	1	2	yes	complemented
20	#15689513	—	2	2	no	—
21	#15689499	C₂²	1	2	yes	—
22	#15689497	—	2	2	no	—
23	#15689497	C₂²	1	2	yes	—
24	#15689497	C₂²	1	2	yes	—
25	#15689497	C₂²	1	2	yes	—
26	#15689496	C₂²	1	2	yes	—
27	#15689495	C₂²	1	1	yes	characteristic, complemented
28	#15689475	C₂²	1	1	yes	characteristic, complemented
29	#15689470	C₂²	1	2	yes	—
30	#15689469	C₂²	1	1	yes	characteristic, complemented
31	#15689350	—	2	2	no	—
32	#15689324	—	2	2	no	—
33	#15689276	—	2	2	no	—
34	C₄×#10625335	—	2	2	no	—
35	#15689163	—	2	2	no	—
36	C₄×#10625329	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	#15688845	C₂²	1	2	yes	complemented
39	C₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
40	C₄₇×#532	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#498	C₂²	1	2	yes	complemented
43	C₄₇×#486	C₂²	1	2	yes	complemented
44	C₄₇×#481	—	2	2	no	—
45	C₄₇×#476	—	2	2	no	—
46	C₄₇×#431	C₂²	1	1	yes	characteristic
47	C₂²×D₁₈₈	—	2	1	no	—
48	C₂²×D₁₈₈	—	2	1	no	—
49	C₂²×D₁₈₈	—	2	1	no	—
50	#13094049	—	4	8	no	—
51	C₂×#10625325	—	2	4	no	—
52	C₂×#10625335	—	2	2	no	—
53	C₂×#10625336	—	2	4	no	—
54	C₂×#10625336	—	2	4	no	—
55	C₂×#10625336	—	2	4	no	—
56	C₂×#10625336	—	4	8	no	—
57	C₂×#10625334	—	2	4	no	—
58	C₂×#10625329	D₄	1	2	yes	—
59	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
60	#13094024	C₂³	1	1	yes	characteristic
61	#13094024	C₂³	1	1	yes	characteristic
62	#13094021	—	2	1	no	—
63	#13094021	—	2	1	no	—
64	#13094021	—	2	1	no	—
65	#13094021	C₂³	1	2	yes	—
66	#13094016	—	2	1	no	—
67	#13094003	—	2	1	no	—
68	#13094003	—	2	1	no	—
69	C₄×Dic₉₄	—	2	1	no	—
70	C₄×Dic₉₄	—	2	1	no	—
71	#13093983	—	2	1	no	—
72	#13093957	—	2	4	no	—
73	#13093955	—	2	4	no	—
74	#13093955	—	2	2	no	—
75	#13093947	—	2	2	no	—
76	#13093946	—	2	4	no	—
77	#13093945	—	2	2	no	—
78	#13093935	D₄	1	2	yes	—
79	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
80	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
81	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
82	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
83	C₂×#41×C₄₇	—	2	1	no	—
84	C₂²×Q₈×C₄₇	—	2	1	no	—
85	C₄⋊Q₈×C₄₇	—	2	1	no	—
86	C₄⋊Q₈×C₄₇	—	2	1	no	—
87	C₄⋊Q₈×C₄₇	—	2	1	no	—
88	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
89	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
90	#127×C₄₇	C₂³	1	1	yes	characteristic
91	#124×C₄₇	—	2	1	no	—
92	#121×C₄₇	—	2	1	no	—
93	#121×C₄₇	—	2	1	no	—
94	C₄×D₄×C₄₇	—	2	1	no	—
95	C₄×D₄×C₄₇	—	2	1	no	—
96	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
97	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	#106×C₄₇	—	2	4	no	—
100	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
101	#102×C₄₇	—	2	4	no	—
102	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
103	C₄×C₈×C₄₇	C₂³	1	2	yes	—
104	C₂³×D₄₇	—	4	1	no	—
105	#41×C₄₇	—	4	4	no	—
106	C₂×Q₈×C₄₇	—	2	1	no	—
107	C₂×Q₈×C₄₇	—	2	2	no	—
108	C₂×Q₈×C₄₇	—	4	4	no	—
109	C₂×Q₈×C₄₇	—	4	1	no	—
110	C₂×D₄×C₄₇	—	2	1	no	—
111	C₂×D₄×C₄₇	—	2	1	no	—
112	C₂×D₄×C₄₇	—	2	1	no	—
113	C₂×D₄×C₄₇	—	4	1	no	—
114	C₂²×C₄×C₄₇	—	4	1	no	—
115	C₂²×C₄×C₄₇	—	4	1	no	—
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂×D₁₈₈	—	2	2	no	—
120	C₂×D₁₈₈	—	2	2	no	—
121	C₂×D₁₈₈	—	2	2	no	—
122	C₂×D₁₈₈	—	4	4	no	—
123	C₂×D₁₈₈	—	4	4	no	—
124	C₂×D₁₈₈	—	4	1	no	—
125	C₂×D₁₈₈	—	4	1	no	—
126	C₂×D₁₈₈	—	4	1	no	—
127	C₂×D₁₈₈	—	8	2	no	—
128	C₂×Dic₉₄	—	2	1	no	—
129	C₂×Dic₉₄	—	2	1	no	—
130	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
131	C₄⋊C₄×C₄₇	—	2	1	no	—
132	C₄⋊C₄×C₄₇	—	2	2	no	—
133	C₄⋊C₄×C₄₇	—	2	2	no	—
134	C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₄⋊C₄×C₄₇	—	4	1	no	—
136	C₄⋊C₄×C₄₇	—	4	1	no	—
137	C₂²⋊C₄×C₄₇	—	4	1	no	—
138	C₂²⋊C₄×C₄₇	—	4	1	no	—
139	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
143	C₂²⋊Dic₄₇	—	4	1	no	—
144	#10625336	—	4	8	no	—
145	#10625336	—	4	8	no	—
146	#10625336	—	4	8	no	—
147	#10625335	—	4	4	no	—
148	#10625334	—	4	8	no	—
149	C₄⋊Dic₄₇	—	2	1	no	—
150	C₄⋊Dic₄₇	—	2	1	no	—
151	C₄⋊Dic₄₇	—	2	1	no	—
152	C₄⋊Dic₄₇	—	2	1	no	—
153	Dic₄₇⋊C₄	—	4	1	no	—
154	Dic₄₇⋊C₄	—	4	1	no	—
155	C₄×Dic₄₇	—	4	1	no	—
156	#10625329	SD₁₆	1	8	yes	complemented
157	C₂×C₄₇⋊C₈	—	2	4	no	—
158	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
159	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
160	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
161	#10625325	—	8	4	no	—
162	C₂³×C₄₇	—	4	1	no	—
163	C₂³×C₄₇	#127	1	1	yes	characteristic
164	C₂²×D₄₇	—	4	2	no	—
165	C₂²×D₄₇	—	8	2	no	—
166	C₂²×D₄₇	—	8	2	no	—
167	C₂²×D₄₇	—	8	2	no	—
168	Q₈×C₄₇	—	4	2	no	—
169	Q₈×C₄₇	—	4	4	no	—
170	Q₈×C₄₇	—	8	2	no	—
171	D₄×C₄₇	—	4	2	no	—
172	D₄×C₄₇	—	4	2	no	—
173	D₄×C₄₇	—	4	2	no	—
174	D₄×C₄₇	—	8	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	4	1	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	8	2	no	—
180	C₂×C₄×C₄₇	—	8	2	no	—
181	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
182	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
183	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
185	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×Dic₄₇	—	4	1	no	—
189	C₂×Dic₄₇	—	4	1	no	—
190	D₁₈₈	—	4	4	no	—
191	D₁₈₈	—	4	4	no	—
192	D₁₈₈	—	4	4	no	—
193	D₁₈₈	—	8	2	no	—
194	D₁₈₈	—	8	2	no	—
195	D₁₈₈	—	8	2	no	—
196	Dic₉₄	—	4	2	no	—
197	Dic₉₄	—	4	2	no	—
198	C₈×C₄₇	—	2	4	no	—
199	C₄₇⋊C₈	—	2	2	no	—
200	C₄₇⋊C₈	C₂×SD₁₆	1	8	yes	complemented
201	C₄₇⋊C₈	AGL(1,ℤ/8)	1	4	yes	complemented
202	#19621	—	47	1	no	maximal, Sylow
203	C₂²×C₄₇	—	2	1	no	—
204	C₂²×C₄₇	—	2	1	no	—
205	C₂²×C₄₇	—	8	1	no	—
206	C₂²×C₄₇	—	8	1	no	—
207	C₂²×C₄₇	—	8	1	no	—
208	C₂²×C₄₇	#492	1	2	yes	—
209	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
210	C₂×D₄₇	—	8	2	no	—
211	C₂×D₄₇	—	8	2	no	—
212	C₂×D₄₇	—	8	2	no	—
213	C₂×D₄₇	—	16	4	no	—
214	C₄×C₄₇	—	2	1	no	—
215	C₄×C₄₇	—	2	1	no	—
216	C₄×C₄₇	—	8	1	no	—
217	C₄×C₄₇	—	8	2	no	—
218	C₄×C₄₇	#492	1	2	yes	—
219	C₄×C₄₇	C₂²×SD₁₆	1	2	yes	—
220	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
221	C₄×C₄₇	#577	1	2	yes	—
222	Dic₄₇	—	8	1	no	—
223	Dic₄₇	—	8	1	no	—
224	#3227	D₄₇	1	1	yes	characteristic, complemented
225	#3208	—	47	1	no	—
226	#3167	—	47	1	no	—
227	#3165	—	47	1	no	—
228	#3151	—	47	1	no	—
229	C₂×#492	—	47	1	no	—
230	#1715	—	47	2	no	—
231	#1714	—	47	2	no	—
232	#1706	—	47	2	no	—
233	#1705	—	47	2	no	—
234	C₈×M₁₆	—	47	1	no	—
235	C₂×C₄₇	—	2	2	no	—
236	C₂×C₄₇	—	16	1	no	—
237	C₂×C₄₇	C₂×#492	1	1	yes	characteristic
238	C₂×C₄₇	#3151	1	1	yes	characteristic
239	C₂×C₄₇	#3154	1	1	yes	characteristic
240	D₄₇	—	16	2	no	—
241	C₂×AGL(1,ℤ/8)	—	94	2	no	—
242	C₂²×SD₁₆	—	94	2	no	—
243	#533	—	47	1	no	—
244	#532	C₂×D₄₇	1	1	yes	characteristic
245	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
246	C₂×#127	—	47	1	no	—
247	#501	—	94	2	no	—
248	#500	—	47	2	no	—
249	#498	—	47	2	no	—
250	#498	—	47	1	no	—
251	#498	C₂×D₄₇	1	2	yes	complemented
252	#496	—	94	2	no	—
253	#493	—	47	2	no	—
254	#492	—	47	2	no	—
255	#492	—	47	2	no	—
256	#492	—	47	2	no	—
257	#492	—	47	1	no	—
258	#492	—	47	2	no	—
259	#492	—	94	2	no	—
260	#487	—	47	1	no	—
261	#486	—	47	1	no	—
262	#486	—	47	2	no	—
263	#486	C₂×D₄₇	1	2	yes	complemented
264	#481	—	2	2	no	—
265	#476	—	2	2	no	—
266	#465	—	94	2	no	—
267	#460	—	94	2	no	—
268	#450	—	94	2	no	—
269	C₄×SD₁₆	—	94	2	no	—
270	#431	C₂×D₄₇	1	1	yes	characteristic
271	#428	—	94	2	no	—
272	C₄×M₁₆	—	47	1	no	—
273	C₂×C₄×C₈	—	47	1	no	—
274	#322	—	47	2	no	—
275	C₈²	—	47	2	no	—
276	C₄₇	#19621	1	1	yes	characteristic, complemented, Sylow
277	C₂×#41	—	2	1	no	—
278	C₂²×Q₈	—	2	1	no	—
279	C₂²×D₄	—	94	1	no	—
280	C₂²×D₄	—	94	1	no	—
281	C₂²×D₄	—	94	1	no	—
282	AGL(1,ℤ/8)	—	188	8	no	—
283	C₂×SD₁₆	—	94	2	no	—
284	C₂×SD₁₆	—	94	4	no	—
285	C₂×SD₁₆	—	94	4	no	—
286	C₂×SD₁₆	—	94	4	no	—
287	C₂×SD₁₆	—	94	4	no	—
288	C₂×SD₁₆	—	188	8	no	—
289	C₂×D₈	—	94	4	no	—
290	C₂×M₁₆	—	47	2	no	—
291	C₂²×C₈	—	47	2	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	—	2	1	no	—
294	C₄⋊Q₈	—	2	1	no	—
295	C₄⋊Q₈	—	47	1	no	—
296	C₄⋊Q₈	—	47	1	no	—
297	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
298	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
299	#127	—	47	2	no	—
300	#127	—	94	1	no	—
301	#127	—	94	1	no	—
302	#127	—	94	1	no	—
303	#127	C₂²×D₄₇	1	1	yes	characteristic
304	#125	—	94	1	no	—
305	#124	—	2	1	no	—
306	C₂²⋊Q₈	—	94	1	no	—
307	C₂²⋊Q₈	—	94	1	no	—
308	#121	—	2	1	no	—
309	#121	—	2	1	no	—
310	C₄×Q₈	—	94	1	no	—
311	C₄×Q₈	—	94	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	2	1	no	—
314	#117	—	94	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
318	#107	—	94	4	no	—
319	#106	—	2	4	no	—
320	#106	—	94	4	no	—
321	#106	—	94	2	no	—
322	C₄⋊C₈	C₂²⋊D₄₇	1	2	yes	—
323	#103	—	94	2	no	—
324	#102	—	2	4	no	—
325	#102	—	94	2	no	—
326	#102	—	94	4	no	—
327	C₂²⋊C₈	C₂²⋊D₄₇	1	2	yes	—
328	#97	—	47	2	no	—
329	C₄×C₈	—	47	2	no	—
330	C₄×C₈	—	47	1	no	—
331	C₄×C₈	—	47	2	no	—
332	C₄×C₈	—	47	1	no	—
333	C₄×C₈	C₂²×D₄₇	1	2	yes	—
334	C₂⁴	—	188	1	no	—
335	#41	—	4	4	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	4	4	no	—
339	C₂×Q₈	—	4	1	no	—
340	C₂×Q₈	—	94	1	no	—
341	C₂×Q₈	—	94	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	94	2	no	—
347	C₂×D₄	—	94	2	no	—
348	C₂×D₄	—	94	2	no	—
349	C₂×D₄	—	376	2	no	—
350	C₂×D₄	—	188	4	no	—
351	C₂×D₄	—	188	1	no	—
352	C₂×D₄	—	188	1	no	—
353	C₂×D₄	—	188	1	no	—
354	C₂×D₄	—	188	4	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
358	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
360	SD₁₆	—	376	4	no	—
361	SD₁₆	—	188	4	no	—
362	SD₁₆	—	188	8	no	—
363	SD₁₆	—	188	8	no	—
364	SD₁₆	—	188	8	no	—
365	D₈	—	188	8	no	—
366	M₁₆	—	47	8	no	—
367	C₂×C₈	—	47	2	no	—
368	C₂×C₈	—	47	4	no	—
369	C₂×C₈	—	47	2	no	—
370	C₂×C₈	—	94	4	no	—
371	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	—	94	1	no	—
379	C₄⋊C₄	—	94	1	no	—
380	C₄⋊C₄	—	94	1	no	—
381	C₄⋊C₄	—	94	1	no	—
382	C₄⋊C₄	—	188	1	no	—
383	C₄⋊C₄	—	188	1	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₂²⋊C₄	—	188	1	no	—
387	C₄²	—	188	1	no	—
388	C₄²	D₄×D₄₇	1	1	yes	characteristic
389	C₄²	D₄×D₄₇	1	1	yes	characteristic
390	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
391	C₄²	C₂³×D₄₇	1	1	yes	characteristic
392	C₂³	—	4	1	no	—
393	C₂³	—	376	2	no	—
394	C₂³	—	376	2	no	—
395	C₂³	—	376	2	no	—
396	C₂³	—	188	2	no	—
397	C₂³	#13094020	1	1	yes	characteristic
398	Q₈	—	4	2	no	—
399	Q₈	—	4	4	no	—
400	Q₈	—	8	2	no	—
401	Q₈	—	188	2	no	—
402	Q₈	—	188	2	no	—
403	D₄	—	4	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	8	2	no	—
407	D₄	—	376	2	no	—
408	D₄	—	376	2	no	—
409	D₄	—	376	2	no	—
410	D₄	—	188	4	no	—
411	D₄	—	188	4	no	—
412	D₄	—	188	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	8	2	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	—	188	1	no	—
420	C₂×C₄	—	188	1	no	—
421	C₂×C₄	#13094020	1	1	yes	characteristic
422	C₂×C₄	#13094020	1	1	yes	characteristic
423	C₂×C₄	#13094020	1	1	yes	characteristic
424	C₂×C₄	SD₁₆×D₄₇	1	4	yes	—
425	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
426	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
427	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
428	C₈	—	2	4	no	—
429	C₈	—	47	8	no	—
430	C₈	—	47	4	no	—
431	C₈	—	94	2	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	8	1	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	376	2	no	—
438	C₂²	—	376	2	no	—
439	C₂²	—	376	2	no	—
440	C₂²	—	752	4	no	—
441	C₂²	#15689494	1	2	yes	—
442	C₂²	C₂×#13094020	1	1	yes	characteristic
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	2	no	—
447	C₄	—	376	1	no	—
448	C₄	—	376	1	no	—
449	C₄	#15689494	1	2	yes	—
450	C₄	C₂×SD₁₆×D₄₇	1	2	yes	—
451	C₄	AGL(1,ℤ/8)×D₄₇	1	2	yes	—
452	C₄	#15689931	1	2	yes	—
453	C₂	—	2	2	no	—
454	C₂	—	16	1	no	—
455	C₂	—	752	2	no	—
456	C₂	C₂×#15689494	1	1	yes	characteristic
457	C₂	#20253836	1	1	yes	characteristic
458	C₂	#20253866	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13094020
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3227	C₂
socle	C₂²×C₄₇	C₂×#127
prime radical	#20253841	C₂
hypercenter	#3227	D₄₇
hypocenter	C₄₇	#19621
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3227

Complements

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

N	H ≅ G/N	type
1. #20254331	C₂	semidirect
2. #20253943	C₂	semidirect
3. #20253930	C₂	semidirect
5. C₂×#15689497	C₂	semidirect
6. #20243018	C₂	semidirect
7. #20243013	C₂	semidirect
8. #20242979	C₂	semidirect
9. #20242976	C₂	semidirect
10. #20241669	C₂	semidirect
11. C₄₇×#3227	C₂	semidirect
17. #15689526	C₂²	semidirect
18. #15689519	C₂²	semidirect
19. #15689519	C₂²	semidirect
27. #15689495	C₂²	semidirect
28. #15689475	C₂²	semidirect
30. #15689469	C₂²	semidirect
38. #15688845	C₂²	semidirect
39. C₈×C₄₇⋊C₈	C₂²	semidirect
42. C₄₇×#498	C₂²	semidirect
43. C₄₇×#486	C₂²	semidirect
156. #10625329	SD₁₆	semidirect
200. C₄₇⋊C₈	C₂×SD₁₆	semidirect
201. C₄₇⋊C₈	AGL(1,ℤ/8)	semidirect
224. #3227	D₄₇	semidirect
251. #498	C₂×D₄₇	semidirect
263. #486	C₂×D₄₇	semidirect
276. C₄₇	#19621	semidirect

Maximal subgroups

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

subgroup	index
#20254331	2
#20253943	2
#20253930	2
#20253841	2
C₂×#15689497	2
#20243018	2
#20243013	2
#20242979	2
#20242976	2
#20241669	2
C₄₇×#3227	2
#19621	47