Subgroups — #26110855

Order 12032.

672 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#20244183	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241223	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₄₇⋊C₈	—	2	1	no	—
9	D₄×C₄₇⋊C₈	—	2	2	no	—
10	D₄×C₄₇⋊C₈	—	2	2	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
14	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
15	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
16	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	D₄⋊(C₄₇⋊C₈)	—	2	2	no	—
19	D₄⋊(C₄₇⋊C₈)	—	2	2	no	—
20	C₂²×D₈×C₄₇	C₄	1	1	yes	characteristic
21	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
23	C₄×D₈×C₄₇	—	2	2	no	—
24	C₄×D₈×C₄₇	—	2	2	no	—
25	C₂×#107×C₄₇	C₄	1	1	yes	characteristic
26	C₂×#102×C₄₇	C₄	1	1	yes	characteristic
27	C₂×#102×C₄₇	C₄	1	1	yes	characteristic
28	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄₇⋊C₈	—	2	4	no	—
30	C₂²×C₄₇⋊C₈	—	2	1	no	—
31	C₂²×C₄₇⋊C₈	—	2	1	no	—
32	C₂²×C₄₇⋊C₈	—	2	1	no	—
33	C₂²×C₄₇⋊C₈	—	4	2	no	—
34	C₂²×C₄₇⋊C₈	—	4	2	no	—
35	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
36	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
37	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
38	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
39	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
40	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
41	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
42	C₂²⋊(C₄₇⋊C₈)	—	4	2	no	—
43	C₂²⋊(C₄₇⋊C₈)	—	4	2	no	—
44	C₄×C₄₇⋊C₈	—	2	1	no	—
45	C₄×C₄₇⋊C₈	—	2	1	no	—
46	C₄×C₄₇⋊C₈	—	2	1	no	—
47	C₄×C₄₇⋊C₈	—	2	1	no	—
48	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	—	2	1	no	—
51	C₂³×C₄×C₄₇	—	2	1	no	—
52	C₂×D₈×C₄₇	—	2	2	no	—
53	C₂×D₈×C₄₇	—	2	2	no	—
54	C₂×D₈×C₄₇	C₈	1	4	yes	complemented
55	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
57	C₄×D₄×C₄₇	—	2	1	no	—
58	C₄×D₄×C₄₇	—	2	1	no	—
59	C₄×D₄×C₄₇	—	2	1	no	—
60	C₄×D₄×C₄₇	—	2	1	no	—
61	C₄×D₄×C₄₇	—	2	1	no	—
62	C₄×D₄×C₄₇	—	2	1	no	—
63	C₄×D₄×C₄₇	D₄	1	2	yes	—
64	C₄×D₄×C₄₇	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
70	#107×C₄₇	—	2	2	no	—
71	#102×C₄₇	—	2	2	no	—
72	#102×C₄₇	—	2	2	no	—
73	C₄×C₈×C₄₇	—	2	1	no	—
74	C₄×C₈×C₄₇	—	2	1	no	—
75	C₂⁴×C₄₇	—	2	1	no	—
76	C₂⁴×C₄₇	—	2	1	no	—
77	C₂×D₄×C₄₇	—	2	1	no	—
78	C₂×D₄×C₄₇	—	2	1	no	—
79	C₂×D₄×C₄₇	—	2	1	no	—
80	C₂×D₄×C₄₇	—	2	1	no	—
81	C₂×D₄×C₄₇	—	2	1	no	—
82	C₂×D₄×C₄₇	—	2	1	no	—
83	C₂×D₄×C₄₇	—	2	1	no	—
84	C₂×D₄×C₄₇	—	2	1	no	—
85	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
86	C₂×D₄×C₄₇	C₂×C₈	1	2	yes	—
87	C₂×D₄×C₄₇	C₂×C₈	1	2	yes	complemented
88	C₂×D₄×C₄₇	M₁₆	1	2	yes	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	1	no	—
93	C₂²×C₄×C₄₇	—	4	1	no	—
94	C₂²×C₄×C₄₇	—	4	1	no	—
95	C₂²×C₄×C₄₇	—	4	1	no	—
96	C₂²×C₄×C₄₇	—	4	1	no	—
97	C₂²×C₄×C₄₇	—	4	1	no	—
98	C₂²×C₄×C₄₇	—	4	1	no	—
99	C₂²×C₄×C₄₇	—	4	1	no	—
100	C₂²×C₄×C₄₇	—	4	1	no	—
101	C₂²×C₄×C₄₇	—	4	1	no	—
102	C₂²×C₄×C₄₇	—	4	1	no	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
106	D₈×C₄₇	—	2	8	no	—
107	C₂×C₈×C₄₇	—	2	1	no	—
108	C₂×C₈×C₄₇	—	2	1	no	—
109	C₂×C₈×C₄₇	—	2	1	no	—
110	C₂×C₈×C₄₇	—	2	1	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	C₂×C₈	1	2	yes	complemented
113	C₄⋊C₄×C₄₇	—	2	1	no	—
114	C₄⋊C₄×C₄₇	—	2	1	no	—
115	C₄⋊C₄×C₄₇	—	2	1	no	—
116	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
117	C₂²⋊C₄×C₄₇	—	2	2	no	—
118	C₂²⋊C₄×C₄₇	—	2	2	no	—
119	C₂²⋊C₄×C₄₇	—	4	1	no	—
120	C₂²⋊C₄×C₄₇	—	4	1	no	—
121	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₄₇	#41	1	1	yes	characteristic
125	C₂×C₄₇⋊C₈	—	2	1	no	—
126	C₂×C₄₇⋊C₈	—	2	1	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	1	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	—	4	8	no	—
133	C₂×C₄₇⋊C₈	—	4	1	no	—
134	C₂×C₄₇⋊C₈	—	4	1	no	—
135	C₂×C₄₇⋊C₈	—	4	1	no	—
136	C₂×C₄₇⋊C₈	—	4	1	no	—
137	C₂×C₄₇⋊C₈	—	4	1	no	—
138	C₂×C₄₇⋊C₈	—	4	1	no	—
139	C₂×C₄₇⋊C₈	—	4	1	no	—
140	C₂×C₄₇⋊C₈	D₈	1	2	yes	complemented
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	—	2	2	no	—
144	C₂³×C₄₇	—	2	2	no	—
145	C₂³×C₄₇	—	4	1	no	—
146	C₂³×C₄₇	—	4	1	no	—
147	C₂³×C₄₇	—	4	1	no	—
148	C₂³×C₄₇	—	4	1	no	—
149	C₂³×C₄₇	—	4	1	no	—
150	C₂³×C₄₇	—	4	1	no	—
151	C₂³×C₄₇	—	4	1	no	—
152	C₂³×C₄₇	—	4	1	no	—
153	C₂³×C₄₇	—	4	1	no	—
154	C₂³×C₄₇	—	4	1	no	—
155	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
156	D₄×C₄₇	—	2	2	no	—
157	D₄×C₄₇	—	2	2	no	—
158	D₄×C₄₇	—	2	2	no	—
159	D₄×C₄₇	—	2	2	no	—
160	D₄×C₄₇	—	2	2	no	—
161	D₄×C₄₇	—	4	1	no	—
162	D₄×C₄₇	—	4	1	no	—
163	D₄×C₄₇	C₂²⋊C₈	1	4	yes	complemented
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	1	no	—
174	C₂×C₄×C₄₇	—	4	1	no	—
175	C₂×C₄×C₄₇	—	4	1	no	—
176	C₂×C₄×C₄₇	—	8	1	no	—
177	C₂×C₄×C₄₇	—	8	1	no	—
178	C₂×C₄×C₄₇	—	8	1	no	—
179	C₂×C₄×C₄₇	—	8	1	no	—
180	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
183	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
184	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
185	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
188	C₂×C₄×C₄₇	#131	1	1	yes	characteristic
189	C₂×C₄×C₄₇	#131	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
191	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
192	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₈×C₄₇	—	2	2	no	—
195	C₈×C₄₇	—	4	1	no	—
196	C₄₇⋊C₈	—	2	2	no	—
197	C₄₇⋊C₈	—	4	2	no	—
198	C₄₇⋊C₈	—	4	2	no	—
199	C₄₇⋊C₈	—	4	1	no	—
200	C₄₇⋊C₈	—	8	1	no	—
201	#8947	—	47	1	no	maximal, Sylow
202	C₂²×C₄₇	—	2	4	no	—
203	C₂²×C₄₇	—	4	2	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	—	4	2	no	—
206	C₂²×C₄₇	—	4	2	no	—
207	C₂²×C₄₇	—	4	2	no	—
208	C₂²×C₄₇	—	4	2	no	—
209	C₂²×C₄₇	—	4	2	no	—
210	C₂²×C₄₇	—	4	2	no	—
211	C₂²×C₄₇	—	4	2	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	#386	1	1	yes	characteristic
217	C₂²×C₄₇	C₈×D₄	1	1	yes	characteristic
218	C₂²×C₄₇	#435	1	1	yes	characteristic
219	C₂²×C₄₇	C₄×D₈	1	1	yes	characteristic
220	C₂²×C₄₇	#442	1	1	yes	characteristic
221	C₂²×C₄₇	#443	1	1	yes	characteristic
222	C₂²×C₄₇	#444	1	1	yes	characteristic
223	C₄×C₄₇	—	2	1	no	—
224	C₄×C₄₇	—	2	1	no	—
225	C₄×C₄₇	—	4	2	no	—
226	C₄×C₄₇	—	8	1	no	—
227	C₄×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
228	C₄×C₄₇	#408	1	1	yes	characteristic
229	C₄×C₄₇	C₈×D₄	1	1	yes	characteristic
230	C₄×C₄₇	#435	1	1	yes	characteristic
231	C₄×C₄₇	#447	1	1	yes	characteristic
232	C₄×C₄₇	#449	1	1	yes	characteristic
233	C₄×C₄₇	#459	1	1	yes	characteristic
234	C₄×C₄₇	#463	1	1	yes	characteristic
235	C₂×C₄×D₈	D₄₇	1	1	yes	characteristic
236	C₂×C₈×D₄	—	47	1	no	—
237	#1954	—	47	1	no	—
238	C₂×D₄⋊C₈	—	47	1	no	—
239	C₂×D₄⋊C₈	—	47	1	no	—
240	#1277	—	47	1	no	—
241	#1273	—	47	1	no	—
242	C₂×C₄₇	—	4	4	no	—
243	C₂×C₄₇	—	8	2	no	—
244	C₂×C₄₇	C₈×D₈	1	1	yes	characteristic
245	C₂×C₄₇	#1580	1	1	yes	characteristic
246	C₂×C₄₇	#1581	1	1	yes	characteristic
247	C₂×C₄₇	#1586	1	1	yes	characteristic
248	C₂×C₄₇	#1869	1	1	yes	characteristic
249	C₂×C₄₇	#1876	1	1	yes	characteristic
250	C₂×C₄₇	#1879	1	1	yes	characteristic
251	C₂²×D₈	Dic₄₇	1	1	yes	characteristic
252	C₂³×C₈	—	94	1	no	—
253	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
255	C₄×D₈	—	2	2	no	—
256	C₄×D₈	—	2	2	no	—
257	C₈×D₄	—	94	2	no	—
258	C₈×D₄	—	94	2	no	—
259	C₂×#107	Dic₄₇	1	1	yes	characteristic
260	C₂×C₄⋊C₈	—	47	1	no	—
261	C₂×C₄⋊C₈	—	47	1	no	—
262	C₂×#102	Dic₄₇	1	1	yes	characteristic
263	C₂×#102	Dic₄₇	1	1	yes	characteristic
264	C₂×C₂²⋊C₈	—	94	1	no	—
265	C₂×C₂²⋊C₈	—	94	1	no	—
266	C₂×C₂²⋊C₈	—	94	1	no	—
267	C₂×C₄×C₈	—	47	1	no	—
268	C₂×C₄×C₈	—	47	1	no	—
269	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
270	D₄⋊C₈	—	94	2	no	—
271	D₄⋊C₈	—	94	2	no	—
272	C₄₇	#8947	1	1	yes	characteristic, complemented, Sylow
273	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
274	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
275	C₂³×C₄	—	2	1	no	—
276	C₂³×C₄	—	2	1	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂×D₈	—	2	2	no	—
279	C₂×D₈	C₄₇⋊C₈	1	4	yes	complemented
280	C₂²×C₈	—	47	1	no	—
281	C₂²×C₈	—	47	1	no	—
282	C₂²×C₈	—	94	4	no	—
283	C₂²×C₈	—	94	1	no	—
284	C₂²×C₈	—	94	1	no	—
285	C₂²×C₈	—	94	1	no	—
286	C₂²×C₈	—	188	2	no	—
287	C₂²×C₈	—	188	2	no	—
288	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
289	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
297	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
298	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
303	#107	—	2	2	no	—
304	C₄⋊C₈	—	47	2	no	—
305	C₄⋊C₈	—	94	1	no	—
306	C₄⋊C₈	—	94	1	no	—
307	C₄⋊C₈	—	94	1	no	—
308	#102	—	2	2	no	—
309	#102	—	2	2	no	—
310	C₂²⋊C₈	—	94	4	no	—
311	C₂²⋊C₈	—	188	2	no	—
312	C₂²⋊C₈	—	188	2	no	—
313	C₄×C₈	—	2	1	no	—
314	C₄×C₈	—	2	1	no	—
315	C₄×C₈	—	94	1	no	—
316	C₄×C₈	—	94	1	no	—
317	C₄×C₈	—	94	1	no	—
318	C₄×C₈	—	94	1	no	—
319	C₂⁴	—	2	1	no	—
320	C₂⁴	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	C₂×C₄₇⋊C₈	1	2	yes	—
330	C₂×D₄	C₂×C₄₇⋊C₈	1	2	yes	complemented
331	C₂×D₄	#10625329	1	2	yes	—
332	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
348	C₂²×C₄	#10625352	1	1	yes	characteristic
349	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
350	D₈	—	2	8	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	47	2	no	—
357	C₂×C₈	—	94	1	no	—
358	C₂×C₈	—	94	1	no	—
359	C₂×C₈	—	94	2	no	—
360	C₂×C₈	—	94	1	no	—
361	C₂×C₈	—	94	2	no	—
362	C₂×C₈	—	94	1	no	—
363	C₂×C₈	—	94	1	no	—
364	C₂×C₈	—	188	8	no	—
365	C₂×C₈	—	188	1	no	—
366	C₂×C₈	—	188	1	no	—
367	C₂×C₈	—	188	1	no	—
368	C₂×C₈	—	188	1	no	—
369	C₂×C₈	—	188	1	no	—
370	C₂×C₈	—	188	1	no	—
371	C₂×C₈	—	188	1	no	—
372	C₂×C₈	C₂×C₄₇⋊C₈	1	2	yes	complemented
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	4	1	no	—
380	C₂²⋊C₄	—	4	1	no	—
381	C₄²	D₄×D₄₇	1	1	yes	characteristic
382	C₄²	#10625352	1	1	yes	characteristic
383	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
384	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
400	D₄	—	2	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	2	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	2	no	—
405	D₄	—	4	1	no	—
406	D₄	—	4	1	no	—
407	D₄	C₂²⋊(C₄₇⋊C₈)	1	4	yes	complemented
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	8	1	no	—
421	C₂×C₄	—	8	1	no	—
422	C₂×C₄	—	8	1	no	—
423	C₂×C₄	—	8	1	no	—
424	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
425	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
426	C₂×C₄	#13093992	1	1	yes	characteristic
427	C₂×C₄	#13093996	1	1	yes	characteristic
428	C₂×C₄	#13093996	1	1	yes	characteristic
429	C₂×C₄	#13094005	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
431	C₂×C₄	C₂×#10625329	1	1	yes	characteristic
432	C₂×C₄	#13094031	1	1	yes	characteristic
433	C₂×C₄	#13094031	1	1	yes	characteristic
434	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
435	C₂×C₄	#13094043	1	1	yes	characteristic
436	C₂×C₄	#13094048	1	1	yes	characteristic
437	C₂×C₄	#13094048	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	4	1	no	—
440	C₈	—	94	2	no	—
441	C₈	—	376	1	no	—
442	C₈	—	188	2	no	—
443	C₈	—	188	2	no	—
444	C₈	—	188	1	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	#15689003	1	1	yes	characteristic
460	C₂²	D₄×C₄₇⋊C₈	1	1	yes	characteristic
461	C₂²	#15689195	1	1	yes	characteristic
462	C₂²	D₈×Dic₄₇	1	1	yes	characteristic
463	C₂²	#15689235	1	1	yes	characteristic
464	C₂²	#15689240	1	1	yes	characteristic
465	C₂²	#15689245	1	1	yes	characteristic
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	4	2	no	—
469	C₄	—	8	1	no	—
470	C₄	C₂×C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
471	C₄	#15689090	1	1	yes	characteristic
472	C₄	D₄×C₄₇⋊C₈	1	1	yes	characteristic
473	C₄	#15689195	1	1	yes	characteristic
474	C₄	#15689255	1	1	yes	characteristic
475	C₄	#15689265	1	1	yes	characteristic
476	C₄	#15689316	1	1	yes	characteristic
477	C₄	#15689336	1	1	yes	characteristic
478	C₂	—	4	4	no	—
479	C₂	—	8	2	no	—
480	C₂	D₈×C₄₇⋊C₈	1	1	yes	characteristic
481	C₂	#20242212	1	1	yes	characteristic
482	C₂	#20242218	1	1	yes	characteristic
483	C₂	#20242253	1	1	yes	characteristic
484	C₂	#20243681	1	1	yes	characteristic
485	C₂	#20243717	1	1	yes	characteristic
486	C₂	#20243738	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄×D₈×C₄₇	C₂
socle	C₂³×C₄₇	C₄×D₄
prime radical	C₂²×D₈×C₄₇	C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×C₄×D₈	D₄₇
hypocenter	C₄₇	#8947
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×C₄₇⋊C₈	C₂	semidirect
2. #20244183	C₂	semidirect
3. C₂×D₄⋊(C₄₇⋊C₈)	C₂	semidirect
4. C₂×D₄⋊(C₄₇⋊C₈)	C₂	semidirect
5. #20241223	C₂	semidirect
6. C₄₇⋊#1273	C₂	semidirect
54. C₂×D₈×C₄₇	C₈	semidirect
87. C₂×D₄×C₄₇	C₂×C₈	semidirect
112. C₂×C₈×C₄₇	C₂×C₈	semidirect
140. C₂×C₄₇⋊C₈	D₈	semidirect
163. D₄×C₄₇	C₂²⋊C₈	semidirect
272. C₄₇	#8947	semidirect
279. C₂×D₈	C₄₇⋊C₈	semidirect
330. C₂×D₄	C₂×C₄₇⋊C₈	semidirect
372. C₂×C₈	C₂×C₄₇⋊C₈	semidirect
407. D₄	C₂²⋊(C₄₇⋊C₈)	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₄₇⋊C₈	2
#20244183	2
C₂×D₄⋊(C₄₇⋊C₈)	2
#20241223	2
C₄₇⋊#1273	2
C₂×C₄×D₈×C₄₇	2
#8947	47