Subgroups — #26204227

Order 12032.

922 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20254506	C₂	1	1	yes	maximal, characteristic, complemented
2	#20254303	C₂	1	1	yes	maximal, characteristic, complemented
3	#20253848	C₂	1	1	yes	maximal, characteristic, complemented
4	#20253841	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15689470	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243058	C₂	1	2	yes	maximal, complemented
7	#20243053	C₂	1	2	yes	maximal, complemented
8	#20242992	C₂	1	2	yes	maximal, complemented
9	#20242979	C₂	1	2	yes	maximal, complemented
10	C₈×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094054	—	2	2	no	—
13	C₂×#13094049	—	2	2	no	—
14	C₂×#13094024	C₂²	1	1	yes	characteristic
15	C₂×#13094021	C₂²	1	1	yes	characteristic
16	#15689526	C₂²	1	2	yes	complemented
17	#15689518	—	2	2	no	—
18	#15689513	—	2	2	no	—
19	#15689502	C₂²	1	2	yes	complemented
20	#15689499	C₂²	1	2	yes	—
21	#15689499	C₂²	1	2	yes	—
22	#15689497	C₂²	1	2	yes	—
23	#15689495	C₂²	1	2	yes	complemented
24	#15689471	C₂²	1	2	yes	—
25	#15689470	—	2	2	no	—
26	#15689470	C₂²	1	2	yes	—
27	#15689470	C₂²	1	2	yes	—
28	#15689469	C₂²	1	2	yes	complemented
29	#15689434	—	2	2	no	—
30	#15689403	—	2	2	no	—
31	#15689318	—	2	2	no	—
32	#15689256	—	2	2	no	—
33	#15689176	C₂²	1	1	yes	characteristic
34	C₂×#13093946	—	2	2	no	—
35	C₄×#10625329	C₂²	1	1	yes	characteristic
36	#15688845	C₂²	1	2	yes	complemented
37	C₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
38	C₄₇×#532	C₂²	1	1	yes	characteristic
39	C₄₇×#532	C₂²	1	1	yes	characteristic
40	C₄₇×#500	C₂²	1	1	yes	characteristic, complemented
41	C₄₇×#493	C₂²	1	1	yes	characteristic, complemented
42	C₄₇×#486	C₂²	1	1	yes	characteristic, complemented
43	C₄₇×#486	C₂²	1	1	yes	characteristic, complemented
44	C₄₇×#466	—	2	2	no	—
45	C₄×D₈×C₄₇	—	2	2	no	—
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂²×Dic₉₄	—	2	1	no	—
48	C₂²×D₁₈₈	—	2	1	no	—
49	C₂²×D₁₈₈	—	2	1	no	—
50	C₂²×D₁₈₈	—	2	1	no	—
51	#13094054	—	4	8	no	—
52	#13094049	—	4	8	no	—
53	C₂×#10625337	—	2	4	no	—
54	C₂×#10625335	—	2	4	no	—
55	C₂×#10625336	—	2	4	no	—
56	C₂×#10625334	—	2	4	no	—
57	C₂×#10625334	—	2	4	no	—
58	C₂×#10625329	D₄	1	2	yes	—
59	#13094024	—	2	1	no	—
60	#13094024	—	2	1	no	—
61	#13094024	—	2	1	no	—
62	#13094024	C₂³	1	2	yes	—
63	#13094021	—	2	1	no	—
64	#13094021	—	2	1	no	—
65	#13094021	—	2	1	no	—
66	#13094021	C₂³	1	2	yes	—
67	C₂×C₄⋊Dic₄₇	—	2	1	no	—
68	C₂×C₄⋊Dic₄₇	—	2	1	no	—
69	#13093957	—	2	4	no	—
70	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
71	#13093946	—	2	4	no	—
72	#13093946	—	2	4	no	—
73	#13093945	—	2	4	no	—
74	#13093944	—	2	4	no	—
75	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
76	#13093935	D₄	1	2	yes	—
77	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
78	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
79	C₂×#41×C₄₇	—	2	1	no	—
80	C₂×#41×C₄₇	—	2	1	no	—
81	C₂×D₈×C₄₇	—	2	2	no	—
82	C₂²×C₈×C₄₇	D₄	1	2	yes	—
83	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
85	#127×C₄₇	C₂³	1	1	yes	characteristic
86	#127×C₄₇	C₂³	1	1	yes	characteristic
87	#124×C₄₇	—	2	1	no	—
88	#124×C₄₇	—	2	1	no	—
89	#121×C₄₇	—	2	1	no	—
90	#121×C₄₇	—	2	1	no	—
91	#121×C₄₇	—	2	1	no	—
92	#121×C₄₇	—	2	1	no	—
93	C₄×D₄×C₄₇	—	2	1	no	—
94	C₄×D₄×C₄₇	—	2	1	no	—
95	C₄×D₄×C₄₇	—	2	1	no	—
96	C₄×D₄×C₄₇	—	2	1	no	—
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	#107×C₄₇	—	2	2	no	—
99	#102×C₄₇	—	2	2	no	—
100	#102×C₄₇	—	2	2	no	—
101	C₄×C₈×C₄₇	D₄	1	2	yes	—
102	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
104	C₂³×D₄₇	—	4	1	no	—
105	#41×C₄₇	—	4	4	no	—
106	#41×C₄₇	—	4	4	no	—
107	C₂×Q₈×C₄₇	—	2	1	no	—
108	C₂×Q₈×C₄₇	—	2	1	no	—
109	C₂×D₄×C₄₇	—	2	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	—	2	1	no	—
114	C₂×D₄×C₄₇	—	2	1	no	—
115	C₂×D₄×C₄₇	—	4	1	no	—
116	C₂×D₄×C₄₇	—	4	1	no	—
117	C₂²×C₄×C₄₇	—	4	1	no	—
118	C₂²×C₄×C₄₇	—	4	1	no	—
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×Dic₄₇	—	4	1	no	—
123	C₂×D₁₈₈	—	2	2	no	—
124	C₂×D₁₈₈	—	2	2	no	—
125	C₂×D₁₈₈	—	2	2	no	—
126	C₂×D₁₈₈	—	4	4	no	—
127	C₂×D₁₈₈	—	4	4	no	—
128	C₂×D₁₈₈	—	4	1	no	—
129	C₂×D₁₈₈	—	4	1	no	—
130	C₂×D₁₈₈	—	4	1	no	—
131	C₂×D₁₈₈	—	8	2	no	—
132	C₂×Dic₉₄	—	2	2	no	—
133	C₂×Dic₉₄	—	4	4	no	—
134	C₂×Dic₉₄	—	4	1	no	—
135	D₈×C₄₇	—	4	4	no	—
136	C₂×C₈×C₄₇	—	4	2	no	—
137	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₄₇	—	2	1	no	—
140	C₄⋊C₄×C₄₇	—	2	1	no	—
141	C₄⋊C₄×C₄₇	—	2	1	no	—
142	C₄⋊C₄×C₄₇	—	2	1	no	—
143	C₂²⋊C₄×C₄₇	—	4	1	no	—
144	C₂²⋊C₄×C₄₇	—	4	1	no	—
145	C₂²⋊C₄×C₄₇	—	4	1	no	—
146	C₂²⋊C₄×C₄₇	—	4	1	no	—
147	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
151	#10625337	—	4	8	no	—
152	#10625336	—	4	8	no	—
153	#10625335	—	4	8	no	—
154	#10625334	—	4	8	no	—
155	#10625334	—	8	4	no	—
156	C₄⋊Dic₄₇	—	2	2	no	—
157	C₄⋊Dic₄₇	—	2	2	no	—
158	C₄⋊Dic₄₇	—	4	1	no	—
159	C₄⋊Dic₄₇	—	4	1	no	—
160	#10625329	D₈	1	8	yes	complemented
161	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
162	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
163	C₂³×C₄₇	—	4	1	no	—
164	C₂³×C₄₇	—	4	1	no	—
165	C₂³×C₄₇	#127	1	1	yes	characteristic
166	C₂²×D₄₇	—	4	2	no	—
167	C₂²×D₄₇	—	8	2	no	—
168	C₂²×D₄₇	—	8	2	no	—
169	C₂²×D₄₇	—	8	2	no	—
170	Q₈×C₄₇	—	4	2	no	—
171	Q₈×C₄₇	—	4	2	no	—
172	D₄×C₄₇	—	4	2	no	—
173	D₄×C₄₇	—	4	2	no	—
174	D₄×C₄₇	—	4	2	no	—
175	D₄×C₄₇	—	4	2	no	—
176	D₄×C₄₇	—	4	2	no	—
177	D₄×C₄₇	—	4	2	no	—
178	D₄×C₄₇	—	8	2	no	—
179	D₄×C₄₇	—	8	2	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	4	1	no	—
183	C₂×C₄×C₄₇	—	4	1	no	—
184	C₂×C₄×C₄₇	—	8	2	no	—
185	C₂×C₄×C₄₇	—	8	2	no	—
186	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
187	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
188	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂×D₈	1	4	yes	—
190	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×Dic₄₇	—	4	2	no	—
194	C₂×Dic₄₇	—	8	2	no	—
195	D₁₈₈	—	4	4	no	—
196	D₁₈₈	—	4	4	no	—
197	D₁₈₈	—	4	4	no	—
198	D₁₈₈	—	8	2	no	—
199	D₁₈₈	—	8	2	no	—
200	D₁₈₈	—	8	2	no	—
201	Dic₉₄	—	4	4	no	—
202	Dic₉₄	—	8	2	no	—
203	C₈×C₄₇	—	2	2	no	—
204	C₈×C₄₇	—	2	2	no	—
205	C₄₇⋊C₈	—	2	4	no	—
206	C₄₇⋊C₈	C₂×D₈	1	8	yes	—
207	#19631	—	47	1	no	maximal, Sylow
208	C₂²×C₄₇	—	2	1	no	—
209	C₂²×C₄₇	—	2	1	no	—
210	C₂²×C₄₇	—	8	1	no	—
211	C₂²×C₄₇	—	8	1	no	—
212	C₂²×C₄₇	—	8	1	no	—
213	C₂²×C₄₇	—	8	1	no	—
214	C₂²×C₄₇	—	8	1	no	—
215	C₂²×C₄₇	—	8	1	no	—
216	C₂²×C₄₇	#493	1	2	yes	—
217	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
218	C₂×D₄₇	—	8	2	no	—
219	C₂×D₄₇	—	8	2	no	—
220	C₂×D₄₇	—	8	2	no	—
221	C₂×D₄₇	—	16	4	no	—
222	C₄×C₄₇	—	2	1	no	—
223	C₄×C₄₇	—	2	1	no	—
224	C₄×C₄₇	—	8	1	no	—
225	C₄×C₄₇	—	8	1	no	—
226	C₄×C₄₇	#493	1	2	yes	—
227	C₄×C₄₇	C₂²×D₈	1	2	yes	—
228	C₄×C₄₇	#575	1	2	yes	—
229	C₄×C₄₇	#577	1	2	yes	—
230	Dic₄₇	—	8	2	no	—
231	#3226	—	47	1	no	—
232	#3205	—	47	1	no	—
233	#3169	D₄₇	1	1	yes	characteristic, complemented
234	#3152	—	47	1	no	—
235	#3151	—	47	1	no	—
236	C₂×#486	—	47	1	no	—
237	#1722	—	47	2	no	—
238	#1721	—	47	2	no	—
239	#1709	—	47	2	no	—
240	#1706	—	47	2	no	—
241	C₈×M₁₆	—	47	1	no	—
242	C₂×C₄₇	—	2	2	no	—
243	C₂×C₄₇	—	16	1	no	—
244	C₂×C₄₇	—	16	1	no	—
245	C₂×C₄₇	C₂×#493	1	1	yes	characteristic
246	C₂×C₄₇	#3153	1	1	yes	characteristic
247	C₂×C₄₇	#3154	1	1	yes	characteristic
248	D₄₇	—	16	2	no	—
249	C₂×#137	—	94	2	no	—
250	C₂×AGL(1,ℤ/8)	—	94	2	no	—
251	#532	C₂×D₄₇	1	1	yes	characteristic
252	#532	C₂×D₄₇	1	1	yes	characteristic
253	C₂×C₄⋊Q₈	—	47	1	no	—
254	C₂×#127	—	47	1	no	—
255	#500	—	47	2	no	—
256	#500	C₂×D₄₇	1	1	yes	characteristic, complemented
257	#497	—	94	2	no	—
258	#496	—	94	2	no	—
259	#494	—	47	2	no	—
260	#493	—	47	2	no	—
261	#493	—	47	2	no	—
262	#493	C₂×D₄₇	1	1	yes	characteristic, complemented
263	#492	—	47	2	no	—
264	#492	—	47	2	no	—
265	#486	—	47	2	no	—
266	#486	—	47	2	no	—
267	#486	—	47	2	no	—
268	#486	—	47	2	no	—
269	#486	—	94	2	no	—
270	#486	C₂×D₄₇	1	1	yes	characteristic, complemented
271	#486	C₂×D₄₇	1	1	yes	characteristic, complemented
272	#480	—	94	2	no	—
273	#474	—	94	2	no	—
274	#466	—	2	2	no	—
275	#459	—	94	2	no	—
276	#447	—	94	2	no	—
277	C₄×D₈	—	2	2	no	—
278	#431	—	47	1	no	—
279	C₂×#102	—	94	2	no	—
280	C₄×M₁₆	—	47	1	no	—
281	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
282	#322	—	47	2	no	—
283	C₈²	—	47	2	no	—
284	C₄₇	#19631	1	1	yes	characteristic, complemented, Sylow
285	C₂×#41	—	2	1	no	—
286	C₂×#41	—	2	1	no	—
287	C₂²×Q₈	—	94	1	no	—
288	C₂²×D₄	—	94	1	no	—
289	C₂²×D₄	—	94	1	no	—
290	C₂²×D₄	—	94	1	no	—
291	#137	—	188	8	no	—
292	AGL(1,ℤ/8)	—	188	8	no	—
293	C₂×Q₁₆	—	94	4	no	—
294	C₂×SD₁₆	—	94	4	no	—
295	C₂×SD₁₆	—	94	4	no	—
296	C₂×D₈	—	2	2	no	—
297	C₂×D₈	—	94	4	no	—
298	C₂×D₈	—	94	4	no	—
299	C₂×M₁₆	—	47	2	no	—
300	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
301	C₄⋊Q₈	—	47	2	no	—
302	C₄⋊Q₈	—	94	1	no	—
303	C₄⋊Q₈	—	94	1	no	—
304	C₄⋊Q₈	—	94	1	no	—
305	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
306	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
307	#127	—	47	2	no	—
308	#127	—	94	1	no	—
309	#127	—	94	1	no	—
310	#127	—	94	1	no	—
311	#127	C₂²×D₄₇	1	1	yes	characteristic
312	#127	C₂²×D₄₇	1	1	yes	characteristic
313	#124	—	2	1	no	—
314	#124	—	2	1	no	—
315	#121	—	2	1	no	—
316	#121	—	2	1	no	—
317	#121	—	2	1	no	—
318	#121	—	2	1	no	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	94	1	no	—
324	C₂×C₄⋊C₄	—	94	1	no	—
325	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
326	#107	—	2	2	no	—
327	#107	—	94	4	no	—
328	C₄⋊C₈	—	47	2	no	—
329	#102	—	2	2	no	—
330	#102	—	2	2	no	—
331	#102	—	94	4	no	—
332	#102	—	94	4	no	—
333	#102	—	94	4	no	—
334	#102	—	94	4	no	—
335	C₂²⋊C₈	—	47	2	no	—
336	#97	—	47	2	no	—
337	C₄×C₈	—	47	2	no	—
338	C₄×C₈	—	47	2	no	—
339	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
340	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
341	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
342	C₂⁴	—	188	1	no	—
343	#41	—	4	4	no	—
344	#41	—	4	4	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	94	2	no	—
348	C₂×Q₈	—	188	4	no	—
349	C₂×Q₈	—	188	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	4	1	no	—
357	C₂×D₄	—	4	1	no	—
358	C₂×D₄	—	94	2	no	—
359	C₂×D₄	—	94	2	no	—
360	C₂×D₄	—	94	2	no	—
361	C₂×D₄	—	376	2	no	—
362	C₂×D₄	—	188	4	no	—
363	C₂×D₄	—	188	1	no	—
364	C₂×D₄	—	188	1	no	—
365	C₂×D₄	—	188	1	no	—
366	C₂×D₄	—	188	4	no	—
367	C₂²×C₄	—	4	1	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	—	188	1	no	—
370	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
371	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
372	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
373	Q₁₆	—	188	8	no	—
374	SD₁₆	—	188	8	no	—
375	SD₁₆	—	188	8	no	—
376	D₈	—	4	4	no	—
377	D₈	—	376	4	no	—
378	D₈	—	188	8	no	—
379	M₁₆	—	47	8	no	—
380	C₂×C₈	—	4	2	no	—
381	C₂×C₈	—	47	4	no	—
382	C₂×C₈	—	47	4	no	—
383	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
384	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	94	2	no	—
390	C₄⋊C₄	—	94	2	no	—
391	C₄⋊C₄	—	188	1	no	—
392	C₄⋊C₄	—	188	1	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₂²⋊C₄	—	4	1	no	—
396	C₂²⋊C₄	—	4	1	no	—
397	C₄²	D₄×D₄₇	1	1	yes	characteristic
398	C₄²	D₄×D₄₇	1	1	yes	characteristic
399	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
400	C₄²	C₂³×D₄₇	1	1	yes	characteristic
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	376	2	no	—
404	C₂³	—	376	2	no	—
405	C₂³	—	376	2	no	—
406	C₂³	—	188	2	no	—
407	C₂³	#13094020	1	1	yes	characteristic
408	Q₈	—	4	2	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	376	2	no	—
411	Q₈	—	188	4	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	8	2	no	—
419	D₄	—	8	2	no	—
420	D₄	—	376	2	no	—
421	D₄	—	376	2	no	—
422	D₄	—	376	2	no	—
423	D₄	—	188	4	no	—
424	D₄	—	188	4	no	—
425	D₄	—	188	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	8	2	no	—
431	C₂×C₄	—	8	2	no	—
432	C₂×C₄	—	376	2	no	—
433	C₂×C₄	—	188	2	no	—
434	C₂×C₄	#13094020	1	1	yes	characteristic
435	C₂×C₄	#13094020	1	1	yes	characteristic
436	C₂×C₄	#13094020	1	1	yes	characteristic
437	C₂×C₄	D₈×D₄₇	1	4	yes	—
438	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
439	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
440	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
441	C₈	—	2	2	no	—
442	C₈	—	2	2	no	—
443	C₈	—	47	8	no	—
444	C₈	—	94	4	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	376	2	no	—
454	C₂²	—	376	2	no	—
455	C₂²	—	376	2	no	—
456	C₂²	—	752	4	no	—
457	C₂²	#15689498	1	2	yes	—
458	C₂²	C₂×#13094020	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	8	1	no	—
462	C₄	—	8	1	no	—
463	C₄	—	376	2	no	—
464	C₄	#15689498	1	2	yes	—
465	C₄	C₂×D₈×D₄₇	1	2	yes	—
466	C₄	#15689921	1	2	yes	—
467	C₄	#15689930	1	2	yes	—
468	C₂	—	2	2	no	—
469	C₂	—	16	1	no	—
470	C₂	—	16	1	no	—
471	C₂	—	752	2	no	—
472	C₂	C₂×#15689498	1	1	yes	characteristic
473	C₂	#20253856	1	1	yes	characteristic
474	C₂	#20253865	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13094020
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3169	C₂
socle	C₂²×C₄₇	C₂×#127
hypercenter	#3169	D₄₇
hypocenter	C₄₇	#19631
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3169

Complements

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

N	H ≅ G/N	type
1. #20254506	C₂	semidirect
2. #20254303	C₂	semidirect
3. #20253848	C₂	semidirect
4. #20253841	C₂	semidirect
5. C₂×#15689470	C₂	semidirect
6. #20243058	C₂	semidirect
7. #20243053	C₂	semidirect
8. #20242992	C₂	semidirect
9. #20242979	C₂	semidirect
10. C₈×#10625329	C₂	semidirect
11. C₄₇×#3169	C₂	semidirect
16. #15689526	C₂²	semidirect
19. #15689502	C₂²	semidirect
23. #15689495	C₂²	semidirect
28. #15689469	C₂²	semidirect
36. #15688845	C₂²	semidirect
37. C₈×C₄₇⋊C₈	C₂²	semidirect
40. C₄₇×#500	C₂²	semidirect
41. C₄₇×#493	C₂²	semidirect
42. C₄₇×#486	C₂²	semidirect
43. C₄₇×#486	C₂²	semidirect
160. #10625329	D₈	semidirect
233. #3169	D₄₇	semidirect
256. #500	C₂×D₄₇	semidirect
262. #493	C₂×D₄₇	semidirect
270. #486	C₂×D₄₇	semidirect
271. #486	C₂×D₄₇	semidirect
284. C₄₇	#19631	semidirect

Maximal subgroups

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

subgroup	index
#20254506	2
#20254303	2
#20253848	2
#20253841	2
C₂×#15689470	2
#20243058	2
#20243053	2
#20242992	2
#20242979	2
C₈×#10625329	2
C₄₇×#3169	2
#19631	47