Subgroups — #26185697

Order 12032.

802 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13094049	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689188	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242209	C₂	1	2	yes	maximal, complemented
5	#20242203	C₂	1	2	yes	maximal, complemented
6	#20242185	C₂	1	2	yes	maximal, complemented
7	#20242180	C₂	1	2	yes	maximal, complemented
8	#20242138	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241780	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241669	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094049	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	—	2	1	no	—
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
16	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
17	#15689233	C₄	1	2	yes	—
18	#15689221	C₄	1	2	yes	—
19	C₄×#10625336	C₂²	1	2	yes	—
20	C₄×#10625334	C₂²	1	2	yes	—
21	D₄×C₄₇⋊C₈	—	2	1	no	—
22	D₄×C₄₇⋊C₈	—	2	1	no	—
23	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
24	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
25	#15689188	—	2	1	no	—
26	#15689188	—	2	1	no	—
27	#15689188	C₂²	1	2	yes	—
28	#15689188	C₂²	1	2	yes	—
29	#15689176	—	2	1	no	—
30	#15689176	C₂²	1	1	yes	characteristic
31	#15689166	C₄	1	1	yes	characteristic
32	#15689127	C₄	1	1	yes	characteristic
33	#15689124	C₄	1	1	yes	characteristic
34	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
35	C₄×#10625329	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
37	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	#15688875	C₂²	1	2	yes	complemented
39	#15688873	C₂²	1	2	yes	complemented
40	#15688852	C₂²	1	2	yes	—
41	#15688852	C₂²	1	2	yes	—
42	#15688845	C₂²	1	2	yes	complemented
43	C₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
44	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#431	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
48	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
49	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₄₇	—	2	1	no	—
51	#13094049	C₈	1	8	yes	complemented
52	C₂×#10625336	C₂×C₄	1	2	yes	—
53	C₂×#10625334	C₂×C₄	1	2	yes	—
54	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
55	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₄₇⋊C₈	—	2	1	no	—
57	C₂²×C₄₇⋊C₈	—	2	1	no	—
58	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
59	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
60	C₂×C₈×D₄₇	—	2	2	no	—
61	C₂×C₈×D₄₇	—	2	2	no	—
62	C₂×C₈×D₄₇	—	4	4	no	—
63	C₄×D₁₈₈	—	2	1	no	—
64	C₄×D₁₈₈	—	2	1	no	—
65	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
66	C₄×D₁₈₈	C₂³	1	2	yes	—
67	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
69	#13093957	C₂×C₄	1	2	yes	—
70	#13093955	C₂×C₄	1	2	yes	—
71	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
72	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
73	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
74	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
75	#13093948	C₂×C₄	1	2	yes	—
76	#13093945	C₂×C₄	1	2	yes	—
77	#13093944	C₂×C₄	1	2	yes	—
78	#13093944	C₂×C₄	1	2	yes	—
79	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
80	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
81	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
82	(C₂×D₄₇)⋊C₈	—	2	2	no	—
83	(C₂×D₄₇)⋊C₈	—	2	2	no	—
84	#13093935	C₂×C₄	1	2	yes	—
85	C₄×C₄₇⋊C₈	—	2	1	no	—
86	C₄×C₄₇⋊C₈	—	2	1	no	—
87	C₄×C₄₇⋊C₈	—	2	1	no	—
88	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
89	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
90	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
91	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
92	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
93	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂²×C₈×C₄₇	—	2	1	no	—
95	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
96	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₄₇	—	2	1	no	—
98	C₄×D₄×C₄₇	—	2	1	no	—
99	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
100	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
101	#117×C₄₇	—	2	1	no	—
102	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₇	—	2	1	no	—
104	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₄₇	—	2	1	no	—
106	C₄⋊C₈×C₄₇	—	2	1	no	—
107	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
108	C₂²⋊C₈×C₄₇	—	2	1	no	—
109	C₄×C₈×C₄₇	C₂³	1	2	yes	—
110	C₂³×D₄₇	—	2	1	no	—
111	#41×C₄₇	—	2	2	no	—
112	#41×C₄₇	C₂×C₈	1	4	yes	complemented
113	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₄×C₄₇	—	2	1	no	—
115	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	—	2	1	no	—
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	—	2	1	no	—
119	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
122	C₂²×Dic₄₇	—	2	1	no	—
123	C₂×D₁₈₈	—	2	1	no	—
124	C₂×D₁₈₈	—	2	2	no	—
125	C₂×D₁₈₈	C₂×C₈	1	4	yes	complemented
126	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
127	C₂×C₄×D₄₇	—	2	2	no	—
128	C₂×C₄×D₄₇	—	2	2	no	—
129	C₂×C₄×D₄₇	—	4	2	no	—
130	C₂×C₄×D₄₇	—	4	2	no	—
131	C₂×C₈×C₄₇	—	2	2	no	—
132	C₂×C₈×C₄₇	—	2	2	no	—
133	C₂×C₈×C₄₇	—	4	2	no	—
134	C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₄⋊C₄×C₄₇	—	2	1	no	—
136	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²⋊C₄×C₄₇	—	2	1	no	—
139	C₂²⋊C₄×C₄₇	—	2	1	no	—
140	C₂²⋊C₄×C₄₇	—	2	1	no	—
141	C₄²×C₄₇	—	2	1	no	—
142	C₄²×C₄₇	—	2	1	no	—
143	C₄²×C₄₇	—	2	1	no	—
144	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₄₇	#41	1	1	yes	characteristic
147	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
148	#10625336	C₂×C₈	1	8	yes	complemented
149	#10625334	C₂×C₈	1	8	yes	complemented
150	(C₂×D₄₇)⋊C₄	—	2	2	no	—
151	(C₂×D₄₇)⋊C₄	—	2	2	no	—
152	C₄⋊Dic₄₇	—	2	1	no	—
153	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
154	#10625329	—	2	2	no	—
155	#10625329	C₂×C₈	1	4	yes	complemented
156	C₂×C₄₇⋊C₈	—	2	2	no	—
157	C₂×C₄₇⋊C₈	—	2	1	no	—
158	C₂×C₄₇⋊C₈	—	2	1	no	—
159	C₂×C₄₇⋊C₈	—	4	1	no	—
160	C₂×C₄₇⋊C₈	—	4	2	no	—
161	C₂×C₄₇⋊C₈	—	4	2	no	—
162	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
163	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
164	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
167	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
168	C₈×D₄₇	—	4	4	no	—
169	C₈×D₄₇	—	4	4	no	—
170	C₂³×C₄₇	—	2	1	no	—
171	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
172	C₂²×D₄₇	—	2	2	no	—
173	C₂²×D₄₇	—	2	4	no	—
174	C₂²×D₄₇	—	4	2	no	—
175	C₂²×D₄₇	—	4	2	no	—
176	Q₈×C₄₇	—	2	1	no	—
177	Q₈×C₄₇	C₂²×C₈	1	2	yes	complemented
178	D₄×C₄₇	—	2	4	no	—
179	D₄×C₄₇	—	2	1	no	—
180	D₄×C₄₇	C₂²×C₈	1	2	yes	complemented
181	C₂×C₄×C₄₇	—	2	1	no	—
182	C₂×C₄×C₄₇	—	2	1	no	—
183	C₂×C₄×C₄₇	—	2	1	no	—
184	C₂×C₄×C₄₇	—	2	4	no	—
185	C₂×C₄×C₄₇	—	2	1	no	—
186	C₂×C₄×C₄₇	—	2	1	no	—
187	C₂×C₄×C₄₇	—	4	1	no	—
188	C₂×C₄×C₄₇	—	4	2	no	—
189	C₂×C₄×C₄₇	—	4	1	no	—
190	C₂×C₄×C₄₇	—	4	1	no	—
191	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
195	C₂×C₄×C₄₇	#131	1	2	yes	—
196	C₂×C₄×C₄₇	C₂³×C₄	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×Dic₄₇	—	2	2	no	—
200	C₂×Dic₄₇	—	4	2	no	—
201	D₁₈₈	—	2	2	no	—
202	D₁₈₈	—	2	4	no	—
203	D₁₈₈	C₂²×C₈	1	4	yes	—
204	C₄×D₄₇	—	4	4	no	—
205	C₄×D₄₇	—	4	2	no	—
206	C₄×D₄₇	—	4	2	no	—
207	C₈×C₄₇	—	4	2	no	—
208	C₈×C₄₇	—	4	2	no	—
209	C₄₇⋊C₈	—	2	2	no	—
210	C₄₇⋊C₈	—	2	1	no	—
211	C₄₇⋊C₈	—	2	1	no	—
212	C₄₇⋊C₈	—	2	1	no	—
213	C₄₇⋊C₈	—	4	1	no	—
214	C₄₇⋊C₈	—	4	1	no	—
215	C₄₇⋊C₈	C₂²×C₈	1	4	yes	complemented
216	C₄₇⋊C₈	AGL(1,ℤ/8)	1	2	yes	complemented
217	C₈×AGL(1,ℤ/8)	—	47	1	no	maximal, Sylow
218	C₂²×C₄₇	—	2	1	no	—
219	C₂²×C₄₇	—	2	1	no	—
220	C₂²×C₄₇	—	2	2	no	—
221	C₂²×C₄₇	—	4	1	no	—
222	C₂²×C₄₇	—	4	1	no	—
223	C₂²×C₄₇	C₈×D₄	1	2	yes	—
224	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
225	C₂×D₄₇	—	2	4	no	—
226	C₂×D₄₇	—	4	8	no	—
227	C₂×D₄₇	—	4	2	no	—
228	C₂×D₄₇	—	4	2	no	—
229	C₄×C₄₇	—	2	2	no	—
230	C₄×C₄₇	—	2	1	no	—
231	C₄×C₄₇	—	2	1	no	—
232	C₄×C₄₇	—	2	1	no	—
233	C₄×C₄₇	—	4	1	no	—
234	C₄×C₄₇	—	4	1	no	—
235	C₄×C₄₇	C₈×D₄	1	2	yes	—
236	C₄×C₄₇	C₂³×C₈	1	1	yes	characteristic
237	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
238	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
239	C₄×C₄₇	#575	1	1	yes	characteristic
240	Dic₄₇	—	4	2	no	—
241	C₈×#41	—	47	1	no	—
242	C₄×AGL(1,ℤ/8)	—	47	1	no	—
243	C₂×C₈×D₄	—	47	1	no	—
244	#1580	—	47	2	no	—
245	SD₁₆⋊C₈	—	47	2	no	—
246	C₈×SD₁₆	—	47	2	no	—
247	C₈×D₈	—	47	2	no	—
248	#1565	—	47	1	no	—
249	#1478	—	47	1	no	—
250	#1477	D₄₇	1	1	yes	characteristic, complemented
251	C₈×M₁₆	—	47	1	no	—
252	C₂×C₄₇	—	2	2	no	—
253	C₂×C₄₇	—	4	2	no	—
254	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
255	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₂×C₄₇	#2955	1	1	yes	characteristic
257	D₄₇	—	4	4	no	—
258	C₂×AGL(1,ℤ/8)	—	47	1	no	—
259	C₂³×C₈	—	94	1	no	—
260	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
261	C₂×C₄×D₄	—	47	1	no	—
262	C₈×Q₈	—	47	1	no	—
263	C₈×Q₈	—	47	1	no	—
264	#442	—	47	2	no	—
265	#440	—	47	2	no	—
266	C₄×SD₁₆	—	47	2	no	—
267	C₄×D₈	—	47	2	no	—
268	C₈×D₄	—	47	1	no	—
269	C₈×D₄	—	47	1	no	—
270	C₈×D₄	—	47	2	no	—
271	C₈×D₄	—	47	2	no	—
272	C₈×D₄	—	94	1	no	—
273	C₈×D₄	—	94	1	no	—
274	C₈×D₄	—	94	1	no	—
275	C₈×D₄	—	94	1	no	—
276	#431	—	47	1	no	—
277	#431	—	94	1	no	—
278	#431	C₂×D₄₇	1	1	yes	characteristic
279	#428	—	47	1	no	—
280	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
281	#418	—	47	1	no	—
282	#417	—	47	1	no	—
283	C₂×C₂²⋊C₈	—	94	1	no	—
284	C₄×M₁₆	—	47	1	no	—
285	C₂×C₄×C₈	—	47	1	no	—
286	C₂×C₄×C₈	—	94	1	no	—
287	#335	—	47	2	no	—
288	#334	—	47	2	no	—
289	Q₈⋊C₈	C₂×D₄₇	1	2	yes	complemented
290	D₄⋊C₈	—	47	2	no	—
291	D₄⋊C₈	—	47	2	no	—
292	D₄⋊C₈	C₂×D₄₇	1	2	yes	complemented
293	#322	—	47	2	no	—
294	C₈²	—	47	2	no	—
295	C₄₇	C₈×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
296	C₂×#41	C₄×D₄₇	1	1	yes	characteristic
297	C₂²×D₄	—	47	1	no	—
298	C₂³×C₄	—	94	1	no	—
299	AGL(1,ℤ/8)	—	47	8	no	—
300	C₂×SD₁₆	—	47	2	no	—
301	C₂×D₈	—	47	2	no	—
302	C₂×M₁₆	—	47	1	no	—
303	C₂×M₁₆	—	47	1	no	—
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	47	1	no	—
306	C₂²×C₈	—	47	1	no	—
307	C₂²×C₈	—	94	2	no	—
308	C₂²×C₈	—	94	2	no	—
309	C₂²×C₈	—	94	1	no	—
310	C₂²×C₈	—	94	1	no	—
311	C₂²×C₈	—	188	4	no	—
312	C₄×Q₈	C₄×D₄₇	1	1	yes	characteristic
313	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	47	2	no	—
317	C₄×D₄	—	47	2	no	—
318	C₄×D₄	—	94	1	no	—
319	C₄×D₄	—	94	1	no	—
320	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
321	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
322	#117	—	2	1	no	—
323	#117	C₄×D₄₇	1	1	yes	characteristic
324	C₂×C₄⋊C₄	—	47	1	no	—
325	C₂×C₂²⋊C₄	—	94	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
328	#107	—	47	2	no	—
329	#106	—	47	2	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	—	47	1	no	—
333	C₄⋊C₈	—	47	1	no	—
334	C₄⋊C₈	—	94	1	no	—
335	C₄⋊C₈	—	94	1	no	—
336	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
337	#103	—	47	2	no	—
338	#102	—	47	2	no	—
339	#102	—	47	2	no	—
340	#102	—	47	2	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	94	2	no	—
343	C₂²⋊C₈	—	94	2	no	—
344	C₂²⋊C₈	—	94	1	no	—
345	C₂²⋊C₈	—	94	1	no	—
346	C₂²⋊C₈	—	94	1	no	—
347	#97	—	47	2	no	—
348	C₄×C₈	—	47	1	no	—
349	C₄×C₈	—	47	1	no	—
350	C₄×C₈	—	47	1	no	—
351	C₄×C₈	—	47	2	no	—
352	C₄×C₈	—	47	1	no	—
353	C₄×C₈	—	94	1	no	—
354	C₄×C₈	—	94	1	no	—
355	C₄×C₈	—	94	1	no	—
356	C₄×C₈	C₂²×D₄₇	1	2	yes	—
357	C₂⁴	—	94	1	no	—
358	#41	—	2	2	no	—
359	#41	C₈×D₄₇	1	4	yes	complemented
360	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	47	4	no	—
363	C₂×D₄	—	47	2	no	—
364	C₂×D₄	—	94	1	no	—
365	C₂×D₄	—	94	2	no	—
366	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	94	1	no	—
371	C₂²×C₄	—	94	2	no	—
372	C₂²×C₄	—	94	2	no	—
373	C₂²×C₄	—	188	2	no	—
374	C₂²×C₄	—	188	2	no	—
375	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
376	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
377	C₂²×C₄	#10625352	1	1	yes	characteristic
378	SD₁₆	—	47	8	no	—
379	D₈	—	47	8	no	—
380	M₁₆	—	47	4	no	—
381	M₁₆	—	94	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	4	2	no	—
385	C₂×C₈	—	47	2	no	—
386	C₂×C₈	—	47	1	no	—
387	C₂×C₈	—	47	2	no	—
388	C₂×C₈	—	47	1	no	—
389	C₂×C₈	—	47	1	no	—
390	C₂×C₈	—	47	1	no	—
391	C₂×C₈	—	94	2	no	—
392	C₂×C₈	—	94	1	no	—
393	C₂×C₈	—	94	1	no	—
394	C₂×C₈	—	188	4	no	—
395	C₂×C₈	—	188	4	no	—
396	C₂×C₈	—	188	2	no	—
397	C₂×C₈	—	188	1	no	—
398	C₂×C₈	—	188	2	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	47	2	no	—
402	C₄⋊C₄	—	94	1	no	—
403	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
404	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	94	2	no	—
409	C₂²⋊C₄	—	94	2	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
414	C₄²	D₄×D₄₇	1	1	yes	characteristic
415	C₄²	#10625352	1	1	yes	characteristic
416	C₄²	C₂³×D₄₇	1	1	yes	characteristic
417	C₂³	—	2	1	no	—
418	C₂³	—	94	2	no	—
419	C₂³	—	94	4	no	—
420	C₂³	—	188	2	no	—
421	C₂³	—	188	2	no	—
422	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
423	Q₈	—	2	1	no	—
424	Q₈	C₂×C₈×D₄₇	1	2	yes	complemented
425	D₄	—	2	4	no	—
426	D₄	—	2	1	no	—
427	D₄	—	47	4	no	—
428	D₄	—	94	2	no	—
429	D₄	—	94	4	no	—
430	D₄	C₂×C₈×D₄₇	1	2	yes	complemented
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	94	2	no	—
442	C₂×C₄	—	188	4	no	—
443	C₂×C₄	—	188	2	no	—
444	C₂×C₄	—	188	2	no	—
445	C₂×C₄	—	188	2	no	—
446	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
447	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
448	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
449	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
450	C₂×C₄	#13094032	1	2	yes	—
451	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
452	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
453	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
454	C₈	—	4	2	no	—
455	C₈	—	4	2	no	—
456	C₈	—	47	4	no	—
457	C₈	—	47	2	no	—
458	C₈	—	94	2	no	—
459	C₈	—	94	1	no	—
460	C₈	—	94	1	no	—
461	C₈	—	94	1	no	—
462	C₈	—	188	1	no	—
463	C₈	—	188	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	94	4	no	—
470	C₂²	—	188	8	no	—
471	C₂²	—	188	2	no	—
472	C₂²	—	188	2	no	—
473	C₂²	(C₂²⋊D₄₇)⋊C₈	1	2	yes	—
474	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	188	2	no	—
482	C₄	(C₂²⋊D₄₇)⋊C₈	1	2	yes	—
483	C₄	C₂²×C₈×D₄₇	1	1	yes	characteristic
484	C₄	C₂×#13094032	1	1	yes	characteristic
485	C₄	AGL(1,ℤ/8)×D₄₇	1	1	yes	characteristic
486	C₄	#15689922	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	4	2	no	—
489	C₂	—	188	4	no	—
490	C₂	C₂×(C₂²⋊D₄₇)⋊C₈	1	1	yes	characteristic
491	C₂	#20252201	1	1	yes	characteristic
492	C₂	#20252287	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂³×C₈
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1477	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094049	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1477	D₄₇
hypocenter	C₄₇	C₈×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1477

Complements

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

N	H ≅ G/N	type
1. #41×C₄₇⋊C₈	C₂	semidirect
3. C₂×#15689188	C₂	semidirect
4. #20242209	C₂	semidirect
5. #20242203	C₂	semidirect
6. #20242185	C₂	semidirect
7. #20242180	C₂	semidirect
8. #20242138	C₂	semidirect
9. #20241780	C₂	semidirect
10. #20241669	C₂	semidirect
11. C₄₇×#1477	C₂	semidirect
15. Q₈×C₄₇⋊C₈	C₂²	semidirect
16. Q₈×C₄₇⋊C₈	C₂²	semidirect
23. D₄×C₄₇⋊C₈	C₂²	semidirect
24. D₄×C₄₇⋊C₈	C₂²	semidirect
38. #15688875	C₂²	semidirect
39. #15688873	C₂²	semidirect
42. #15688845	C₂²	semidirect
43. C₈×C₄₇⋊C₈	C₂²	semidirect
47. C₄₇×Q₈⋊C₈	C₂²	semidirect
48. C₄₇×D₄⋊C₈	C₂²	semidirect
51. #13094049	C₈	semidirect
112. #41×C₄₇	C₂×C₈	semidirect
125. C₂×D₁₈₈	C₂×C₈	semidirect
148. #10625336	C₂×C₈	semidirect
149. #10625334	C₂×C₈	semidirect
155. #10625329	C₂×C₈	semidirect
177. Q₈×C₄₇	C₂²×C₈	semidirect
180. D₄×C₄₇	C₂²×C₈	semidirect
215. C₄₇⋊C₈	C₂²×C₈	semidirect
216. C₄₇⋊C₈	AGL(1,ℤ/8)	semidirect
250. #1477	D₄₇	semidirect
289. Q₈⋊C₈	C₂×D₄₇	semidirect
292. D₄⋊C₈	C₂×D₄₇	semidirect
295. C₄₇	C₈×AGL(1,ℤ/8)	semidirect
359. #41	C₈×D₄₇	semidirect
424. Q₈	C₂×C₈×D₄₇	semidirect
430. D₄	C₂×C₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#41×C₄₇⋊C₈	2
C₄×#13094049	2
C₂×#15689188	2
#20242209	2
#20242203	2
#20242185	2
#20242180	2
#20242138	2
#20241780	2
#20241669	2
C₄₇×#1477	2
C₈×AGL(1,ℤ/8)	47