Subgroups — #26223181

Order 12032.

938 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	AGL(1,ℤ/8)×Dic₄₇	C₂	1	2	yes	maximal, complemented
2	C₂×#15689235	C₂	1	1	yes	maximal, characteristic, complemented
3	#20251814	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244299	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244169	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244052	C₂	1	2	yes	maximal, complemented
7	#20243898	C₂	1	2	yes	maximal, complemented
8	#20243447	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243296	C₂	1	1	yes	maximal, characteristic, complemented
10	#100×Dic₄₇	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#472	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	C₂²	1	1	yes	characteristic
13	#41×Dic₄₇	C₂²	1	1	yes	characteristic
14	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
15	#15689235	—	2	2	no	—
16	#15689235	—	2	1	no	—
17	#15689235	—	2	1	no	—
18	#15689235	—	2	1	no	—
19	#15689235	—	2	1	no	—
20	#15689224	—	2	2	no	—
21	SD₁₆×Dic₄₇	—	2	2	no	—
22	D₈×Dic₄₇	—	2	2	no	—
23	C₂×#13093960	C₂²	1	1	yes	characteristic
24	#15689165	C₂²	1	2	yes	—
25	C₂×#13093956	C₂²	1	1	yes	characteristic
26	#15689128	C₂²	1	2	yes	—
27	#15689124	C₂²	1	2	yes	—
28	C₂×#13093945	C₂²	1	2	yes	—
29	C₂×#13093941	C₂²	1	2	yes	—
30	#15689081	—	2	1	no	—
31	#15689081	C₂²	1	1	yes	characteristic
32	#15689078	—	2	1	no	—
33	#15689078	C₂²	1	1	yes	characteristic
34	M₁₆×Dic₄₇	—	2	1	no	—
35	M₁₆×Dic₄₇	C₂²	1	2	yes	—
36	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
37	C₂×#13093934	—	2	1	no	—
38	C₂×#13093934	C₂²	1	1	yes	characteristic
39	#15688891	C₂²	1	2	yes	—
40	#15688891	C₂²	1	2	yes	—
41	#15688887	C₂²	1	2	yes	—
42	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	2	yes	—
43	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#472	C₄	1	8	yes	complemented
46	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#100×C₄₇	C₂²	1	2	yes	—
48	C₂³×Dic₄₇	—	2	2	no	—
49	#13094031	—	2	2	no	—
50	#13094031	—	2	2	no	—
51	C₂×#10625329	—	2	1	no	—
52	C₂×#10625329	C₂³	1	2	yes	—
53	C₂×#10625329	C₂³	1	1	yes	characteristic
54	C₂²×C₄₇⋊C₈	—	2	1	no	—
55	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
56	Q₈×Dic₄₇	D₄	1	2	yes	—
57	D₄×Dic₄₇	—	2	2	no	—
58	D₄×Dic₄₇	—	2	2	no	—
59	D₄×Dic₄₇	—	2	2	no	—
60	D₄×Dic₄₇	—	2	2	no	—
61	D₄×Dic₄₇	—	2	2	no	—
62	D₄×Dic₄₇	D₄	1	2	yes	—
63	#13093983	—	2	1	no	—
64	#13093983	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
66	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
67	C₂×C₄×Dic₄₇	—	2	1	no	—
68	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
69	#13093960	—	2	2	no	—
70	#13093958	—	2	2	no	—
71	#13093956	—	2	1	no	—
72	#13093956	—	2	1	no	—
73	#13093956	—	2	2	no	—
74	#13093948	—	2	2	no	—
75	#13093945	—	2	2	no	—
76	#13093945	—	2	2	no	—
77	#13093945	—	2	2	no	—
78	#13093945	—	2	2	no	—
79	#13093945	—	2	2	no	—
80	#13093941	—	2	4	no	—
81	#13093934	—	2	1	no	—
82	#13093934	—	2	2	no	—
83	#13093934	—	2	1	no	—
84	#13093934	—	2	1	no	—
85	#13093934	D₄	1	1	yes	characteristic
86	#13093934	D₄	1	1	yes	characteristic
87	#13093934	D₄	1	1	yes	characteristic
88	#13093934	D₄	1	1	yes	characteristic
89	C₈×Dic₄₇	—	2	1	no	—
90	C₈×Dic₄₇	—	2	1	no	—
91	C₈×Dic₄₇	—	2	2	no	—
92	C₈×Dic₄₇	—	2	1	no	—
93	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
95	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
96	AGL(1,ℤ/8)×C₄₇	C₂×C₄	1	8	yes	complemented
97	C₂×SD₁₆×C₄₇	—	2	2	no	—
98	C₂×D₈×C₄₇	—	2	2	no	—
99	C₂×D₈×C₄₇	—	2	1	no	—
100	C₂×D₈×C₄₇	—	2	1	no	—
101	C₂×D₈×C₄₇	—	2	2	no	—
102	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	complemented
103	#131×C₄₇	—	2	2	no	—
104	#131×C₄₇	C₂×C₄	1	4	yes	complemented
105	C₂×M₁₆×C₄₇	—	2	1	no	—
106	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
108	C₂²×C₈×C₄₇	—	2	1	no	—
109	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
110	#108×C₄₇	C₂×C₄	1	4	yes	complemented
111	#100×C₄₇	C₂×C₄	1	8	yes	complemented
112	C₂⁴×C₄₇	—	2	2	no	—
113	#41×C₄₇	—	2	1	no	—
114	#41×C₄₇	—	2	1	no	—
115	#41×C₄₇	C₂²×C₄	1	2	yes	—
116	#41×C₄₇	#41	1	2	yes	—
117	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂×D₄×C₄₇	—	2	1	no	—
119	C₂×D₄×C₄₇	—	2	2	no	—
120	C₂×D₄×C₄₇	—	2	2	no	—
121	C₂×D₄×C₄₇	—	2	2	no	—
122	C₂×D₄×C₄₇	—	2	2	no	—
123	C₂×D₄×C₄₇	—	2	2	no	—
124	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
125	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	—	2	1	no	—
127	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
128	C₂²×Dic₄₇	—	2	2	no	—
129	C₂²×Dic₄₇	—	2	2	no	—
130	C₂²×Dic₄₇	—	4	2	no	—
131	C₂²×Dic₄₇	—	4	2	no	—
132	C₂²×Dic₄₇	—	8	4	no	—
133	C₂²×Dic₄₇	#41	1	2	yes	—
134	SD₁₆×C₄₇	—	2	8	no	—
135	D₈×C₄₇	—	2	8	no	—
136	D₈×C₄₇	—	2	4	no	—
137	D₈×C₄₇	—	2	4	no	—
138	M₁₆×C₄₇	—	2	1	no	—
139	M₁₆×C₄₇	—	2	2	no	—
140	M₁₆×C₄₇	—	2	4	no	—
141	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
142	M₁₆×C₄₇	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₄₇	—	2	1	no	—
144	C₂×C₈×C₄₇	—	2	2	no	—
145	C₂×C₈×C₄₇	—	2	4	no	—
146	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₄₇	#41	1	2	yes	—
150	C₂²⋊Dic₄₇	—	2	1	no	—
151	C₂²⋊Dic₄₇	—	2	2	no	—
152	C₂²⋊Dic₄₇	—	4	2	no	—
153	C₂²⋊Dic₄₇	—	4	2	no	—
154	C₄⋊Dic₄₇	—	2	2	no	—
155	C₄⋊Dic₄₇	—	2	2	no	—
156	C₄⋊Dic₄₇	—	2	2	no	—
157	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
158	C₄×Dic₄₇	—	2	1	no	—
159	C₄×Dic₄₇	—	2	2	no	—
160	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
161	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
162	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
163	#10625329	—	2	4	no	—
164	#10625329	—	2	1	no	—
165	#10625329	—	2	2	no	—
166	#10625329	—	2	2	no	—
167	#10625329	#41	1	2	yes	—
168	C₂×C₄₇⋊C₈	—	2	4	no	—
169	C₂×C₄₇⋊C₈	—	2	1	no	—
170	C₂×C₄₇⋊C₈	—	2	1	no	—
171	C₂×C₄₇⋊C₈	—	2	1	no	—
172	C₂×C₄₇⋊C₈	—	2	2	no	—
173	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
174	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
175	C₂³×C₄₇	—	2	1	no	—
176	C₂³×C₄₇	—	2	4	no	—
177	C₂³×C₄₇	—	4	2	no	—
178	C₂³×C₄₇	—	4	2	no	—
179	C₂³×C₄₇	—	8	2	no	—
180	C₂³×C₄₇	—	8	2	no	—
181	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
182	Q₈×C₄₇	—	2	1	no	—
183	Q₈×C₄₇	C₄×D₄	1	2	yes	—
184	D₄×C₄₇	—	2	2	no	—
185	D₄×C₄₇	—	2	2	no	—
186	D₄×C₄₇	—	2	4	no	—
187	D₄×C₄₇	—	2	4	no	—
188	D₄×C₄₇	—	2	1	no	—
189	D₄×C₄₇	—	4	2	no	—
190	D₄×C₄₇	—	4	2	no	—
191	D₄×C₄₇	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₄₇	—	2	1	no	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	2	2	no	—
195	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
201	C₂×Dic₄₇	—	2	2	no	—
202	C₂×Dic₄₇	—	4	2	no	—
203	C₂×Dic₄₇	—	4	2	no	—
204	C₂×Dic₄₇	—	8	2	no	—
205	C₂×Dic₄₇	—	8	4	no	—
206	C₂×Dic₄₇	—	8	4	no	—
207	C₂×Dic₄₇	—	8	2	no	—
208	C₂×Dic₄₇	#121	1	2	yes	—
209	C₂×Dic₄₇	#121	1	2	yes	—
210	C₈×C₄₇	—	2	2	no	—
211	C₈×C₄₇	—	2	4	no	—
212	C₈×C₄₇	C₄×D₄	1	2	yes	—
213	C₈×C₄₇	C₄×D₄	1	2	yes	—
214	C₄₇⋊C₈	—	2	1	no	—
215	C₄₇⋊C₈	—	2	2	no	—
216	C₄₇⋊C₈	—	2	1	no	—
217	C₄₇⋊C₈	—	4	2	no	—
218	#21555	—	47	1	no	maximal, Sylow
219	C₂²×C₄₇	—	2	2	no	—
220	C₂²×C₄₇	—	2	2	no	—
221	C₂²×C₄₇	—	4	2	no	—
222	C₂²×C₄₇	—	4	4	no	—
223	C₂²×C₄₇	—	8	4	no	—
224	C₂²×C₄₇	—	8	4	no	—
225	C₂²×C₄₇	—	8	2	no	—
226	C₂²×C₄₇	—	8	2	no	—
227	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
228	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
229	C₂²×C₄₇	#529	1	1	yes	characteristic
230	C₄×C₄₇	—	2	2	no	—
231	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
232	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
233	C₄×C₄₇	#525	1	1	yes	characteristic
234	C₄×C₄₇	#532	1	1	yes	characteristic
235	Dic₄₇	—	2	2	no	—
236	Dic₄₇	—	2	2	no	—
237	Dic₄₇	—	4	2	no	—
238	Dic₄₇	—	8	2	no	—
239	C₂×#472	D₄₇	1	1	yes	characteristic
240	C₄×AGL(1,ℤ/8)	—	47	2	no	—
241	C₂×#442	—	47	1	no	—
242	#2875	—	47	1	no	—
243	#1978	—	47	1	no	—
244	#1951	—	47	1	no	—
245	#1931	—	47	2	no	—
246	#1907	—	47	2	no	—
247	#1815	—	47	1	no	—
248	#1778	—	47	1	no	—
249	C₄×#100	—	47	2	no	—
250	C₂×C₄₇	—	2	1	no	—
251	C₂×C₄₇	—	2	1	no	—
252	C₂×C₄₇	—	4	2	no	—
253	C₂×C₄₇	—	8	4	no	—
254	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
255	C₂×C₄₇	#3068	1	2	yes	—
256	C₂×AGL(1,ℤ/8)	C₂×D₄₇	1	2	yes	—
257	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
258	C₂×#131	—	47	1	no	—
259	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
260	C₄×#41	—	47	1	no	—
261	C₂×C₄×D₄	—	47	2	no	—
262	#472	Dic₄₇	1	8	yes	complemented
263	#442	—	94	1	no	—
264	#442	—	94	1	no	—
265	#442	—	94	1	no	—
266	#442	—	94	1	no	—
267	#442	—	94	2	no	—
268	#440	—	94	2	no	—
269	C₄×SD₁₆	—	94	2	no	—
270	C₄×D₈	—	94	2	no	—
271	C₂×#108	—	47	1	no	—
272	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
273	#428	—	47	2	no	—
274	C₂×#106	—	47	1	no	—
275	#418	—	47	2	no	—
276	#417	—	47	2	no	—
277	C₂×#102	—	47	2	no	—
278	C₂×#100	—	47	2	no	—
279	C₂×#100	C₂×D₄₇	1	2	yes	—
280	#405	—	47	1	no	—
281	#405	—	47	1	no	—
282	#405	—	94	1	no	—
283	#405	—	94	1	no	—
284	C₄×M₁₆	—	47	1	no	—
285	C₄×M₁₆	—	47	2	no	—
286	C₄×M₁₆	—	94	1	no	—
287	C₂×#97	—	47	1	no	—
288	C₂×#97	—	94	1	no	—
289	#343	—	47	2	no	—
290	#343	—	47	2	no	—
291	#341	—	47	2	no	—
292	C₄₇	#21555	1	1	yes	characteristic, complemented, Sylow
293	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
294	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
295	C₂³×C₄	—	94	2	no	—
296	AGL(1,ℤ/8)	—	2	4	no	—
297	AGL(1,ℤ/8)	C₂×Dic₄₇	1	8	yes	complemented
298	C₂×SD₁₆	—	2	2	no	—
299	C₂×D₈	—	2	2	no	—
300	C₂×D₈	—	2	1	no	—
301	C₂×D₈	—	2	1	no	—
302	C₂×D₈	—	2	2	no	—
303	C₂×D₈	C₂×Dic₄₇	1	4	yes	complemented
304	#131	—	2	2	no	—
305	#131	—	94	2	no	—
306	#131	—	94	2	no	—
307	#131	C₂×Dic₄₇	1	4	yes	complemented
308	C₂×M₁₆	—	2	1	no	—
309	C₂×M₁₆	—	47	1	no	—
310	C₂×M₁₆	—	47	2	no	—
311	C₂×M₁₆	—	94	1	no	—
312	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
313	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
314	C₂²×C₈	—	2	1	no	—
315	C₂²×C₈	—	47	1	no	—
316	C₂²×C₈	—	94	1	no	—
317	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
318	C₄×Q₈	—	47	2	no	—
319	C₄×D₄	—	47	2	no	—
320	C₄×D₄	—	94	2	no	—
321	C₄×D₄	—	94	2	no	—
322	C₄×D₄	—	94	2	no	—
323	C₄×D₄	—	94	2	no	—
324	C₄×D₄	—	94	2	no	—
325	#117	—	47	1	no	—
326	#117	—	94	1	no	—
327	C₂×C₄⋊C₄	—	47	2	no	—
328	C₂×C₂²⋊C₄	—	94	2	no	—
329	C₂×C₄²	—	47	1	no	—
330	C₂×C₄²	—	94	1	no	—
331	#108	—	94	2	no	—
332	#108	C₂×Dic₄₇	1	4	yes	complemented
333	#107	—	94	2	no	—
334	#106	—	94	2	no	—
335	#106	—	94	1	no	—
336	#106	—	94	1	no	—
337	#103	—	94	2	no	—
338	#102	—	94	2	no	—
339	#102	—	94	2	no	—
340	#102	—	94	2	no	—
341	#102	—	94	2	no	—
342	#102	—	94	2	no	—
343	#100	—	94	4	no	—
344	#100	C₂×Dic₄₇	1	8	yes	complemented
345	#97	—	47	1	no	—
346	#97	—	47	1	no	—
347	#97	—	47	1	no	—
348	#97	—	47	1	no	—
349	#97	—	94	1	no	—
350	#97	—	94	2	no	—
351	#97	—	94	1	no	—
352	#97	—	94	1	no	—
353	C₄×C₈	—	94	1	no	—
354	C₄×C₈	—	94	2	no	—
355	C₄×C₈	—	94	1	no	—
356	C₄×C₈	—	94	1	no	—
357	C₂⁴	—	2	2	no	—
358	#41	—	2	1	no	—
359	#41	—	2	1	no	—
360	#41	#10625352	1	2	yes	—
361	#41	C₂²×Dic₄₇	1	2	yes	—
362	C₂×Q₈	D₄×D₄₇	1	1	yes	characteristic
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
370	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	47	2	no	—
373	C₂²×C₄	—	94	2	no	—
374	C₂²×C₄	—	94	2	no	—
375	C₂²×C₄	—	376	4	no	—
376	C₂²×C₄	—	188	2	no	—
377	C₂²×C₄	—	188	2	no	—
378	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
379	SD₁₆	—	2	8	no	—
380	D₈	—	2	8	no	—
381	D₈	—	2	4	no	—
382	D₈	—	2	4	no	—
383	M₁₆	—	2	1	no	—
384	M₁₆	—	2	2	no	—
385	M₁₆	—	2	4	no	—
386	M₁₆	—	47	2	no	—
387	M₁₆	—	94	4	no	—
388	M₁₆	—	94	1	no	—
389	M₁₆	—	94	2	no	—
390	M₁₆	—	94	2	no	—
391	M₁₆	C₂²×Dic₄₇	1	2	yes	—
392	M₁₆	C₂²×Dic₄₇	1	4	yes	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	4	no	—
396	C₂×C₈	—	47	1	no	—
397	C₂×C₈	—	47	1	no	—
398	C₂×C₈	—	94	4	no	—
399	C₂×C₈	—	94	1	no	—
400	C₂×C₈	—	94	1	no	—
401	C₂×C₈	—	94	1	no	—
402	C₂×C₈	—	94	2	no	—
403	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
404	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
405	C₂×C₈	#10625352	1	2	yes	—
406	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
407	C₄⋊C₄	—	47	2	no	—
408	C₄⋊C₄	—	94	2	no	—
409	C₄⋊C₄	—	94	2	no	—
410	C₄⋊C₄	—	94	2	no	—
411	C₂²⋊C₄	—	94	2	no	—
412	C₂²⋊C₄	—	94	1	no	—
413	C₂²⋊C₄	—	188	2	no	—
414	C₂²⋊C₄	—	188	2	no	—
415	C₄²	—	47	1	no	—
416	C₄²	—	47	2	no	—
417	C₄²	—	47	1	no	—
418	C₄²	—	94	2	no	—
419	C₄²	—	94	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	4	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	8	2	no	—
425	C₂³	—	8	2	no	—
426	C₂³	#41×D₄₇	1	1	yes	characteristic
427	Q₈	—	2	1	no	—
428	Q₈	D₄×Dic₄₇	1	2	yes	—
429	D₄	—	2	2	no	—
430	D₄	—	2	2	no	—
431	D₄	—	2	4	no	—
432	D₄	—	2	4	no	—
433	D₄	—	2	1	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	D₄×Dic₄₇	1	2	yes	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	47	2	no	—
441	C₂×C₄	—	47	2	no	—
442	C₂×C₄	—	94	2	no	—
443	C₂×C₄	—	376	4	no	—
444	C₂×C₄	—	376	4	no	—
445	C₂×C₄	—	376	2	no	—
446	C₂×C₄	—	376	2	no	—
447	C₂×C₄	—	188	2	no	—
448	C₂×C₄	—	188	2	no	—
449	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
450	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
451	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
452	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
453	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
454	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
455	C₈	—	2	2	no	—
456	C₈	—	2	4	no	—
457	C₈	—	94	1	no	—
458	C₈	—	94	1	no	—
459	C₈	—	94	2	no	—
460	C₈	—	188	2	no	—
461	C₈	D₄×Dic₄₇	1	2	yes	—
462	C₈	D₄×Dic₄₇	1	2	yes	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	8	4	no	—
468	C₂²	—	8	4	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	2	no	—
471	C₂²	#41×Dic₄₇	1	1	yes	characteristic
472	C₂²	#121×D₄₇	1	1	yes	characteristic
473	C₂²	#15689654	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	94	2	no	—
476	C₄	—	94	2	no	—
477	C₄	—	376	2	no	—
478	C₄	—	188	2	no	—
479	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
480	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
481	C₄	#15689633	1	1	yes	characteristic
482	C₄	#15689668	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	4	2	no	—
486	C₂	—	8	4	no	—
487	C₂	#121×Dic₄₇	1	1	yes	characteristic
488	C₂	#20253114	1	2	yes	—

	subgroup	G/H
center	C₂²	#121×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#472	C₂
socle	C₂²×C₄₇	C₂×#121
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#472	D₄₇
hypocenter	C₄₇	#21555
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#472

Complements

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

N	H ≅ G/N	type
1. AGL(1,ℤ/8)×Dic₄₇	C₂	semidirect
2. C₂×#15689235	C₂	semidirect
3. #20251814	C₂	semidirect
4. #20244299	C₂	semidirect
5. #20244169	C₂	semidirect
6. #20244052	C₂	semidirect
7. #20243898	C₂	semidirect
8. #20243447	C₂	semidirect
9. #20243296	C₂	semidirect
10. #100×Dic₄₇	C₂	semidirect
45. C₄₇×#472	C₄	semidirect
96. AGL(1,ℤ/8)×C₄₇	C₂×C₄	semidirect
102. C₂×D₈×C₄₇	C₂×C₄	semidirect
104. #131×C₄₇	C₂×C₄	semidirect
110. #108×C₄₇	C₂×C₄	semidirect
111. #100×C₄₇	C₂×C₄	semidirect
262. #472	Dic₄₇	semidirect
292. C₄₇	#21555	semidirect
297. AGL(1,ℤ/8)	C₂×Dic₄₇	semidirect
303. C₂×D₈	C₂×Dic₄₇	semidirect
307. #131	C₂×Dic₄₇	semidirect
332. #108	C₂×Dic₄₇	semidirect
344. #100	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
AGL(1,ℤ/8)×Dic₄₇	2
C₂×#15689235	2
#20251814	2
#20244299	2
#20244169	2
#20244052	2
#20243898	2
#20243447	2
#20243296	2
#100×Dic₄₇	2
C₂×C₄₇×#472	2
#21555	47