Subgroups — #26235446

Order 12032.

874 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10625336	C₂	1	1	yes	maximal, characteristic
2	#20246339	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244086	C₂	1	2	yes	maximal
5	#20243969	C₂	1	2	yes	maximal, complemented
6	#20243741	C₂	1	2	yes	maximal
7	#20243515	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243389	C₂	1	1	yes	maximal, characteristic
9	#20243258	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243220	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625336	C₂²	1	1	yes	characteristic
13	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	C₂×#13093982	—	2	1	no	—
16	C₄×#10625336	C₄	1	8	yes	complemented
17	C₂×#13093955	C₂²	1	1	yes	characteristic
18	C₂×#13093948	C₂²	1	1	yes	characteristic
19	C₂×#13093946	C₂²	1	2	yes	—
20	C₂×#13093944	C₂²	1	1	yes	characteristic
21	C₂×#13093934	C₂²	1	2	yes	—
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	#15689024	C₂²	1	2	yes	—
24	#15689022	—	2	2	no	—
25	#15689022	C₂²	1	2	yes	—
26	#15689013	—	2	2	no	—
27	#15688993	—	2	1	no	—
28	#15688993	C₂²	1	1	yes	characteristic
29	#15688980	—	2	1	no	—
30	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
31	C₄×C₄⋊Dic₄₇	—	2	1	no	—
32	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
33	#15688886	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#103×C₄₇	C₂²	1	2	yes	—
40	C₄₇×#384	C₂²	1	1	yes	characteristic
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄×D₄₇	—	2	1	no	—
44	C₂×#10625336	—	2	2	no	—
45	C₂×#10625336	—	2	2	no	—
46	C₂×#10625336	C₂×C₄	1	4	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	Q₈×Dic₄₇	—	2	4	no	—
50	Q₈×Dic₄₇	—	4	2	no	—
51	C₄×D₁₈₈	—	2	2	no	—
52	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
53	#13093982	—	4	4	no	—
54	C₂×C₄⋊Dic₄₇	—	2	1	no	—
55	C₂×C₄⋊Dic₄₇	—	2	2	no	—
56	C₂×C₄⋊Dic₄₇	—	2	1	no	—
57	C₂×C₄⋊Dic₄₇	—	2	2	no	—
58	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
59	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
60	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
61	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
62	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
63	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
64	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
65	C₂×C₄×Dic₄₇	—	2	2	no	—
66	C₂×C₄×Dic₄₇	—	2	2	no	—
67	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
68	#13093955	C₂×C₄	1	4	yes	—
69	#13093948	C₂×C₄	1	4	yes	—
70	#13093946	—	4	2	no	—
71	#13093944	C₂×C₄	1	4	yes	—
72	#13093934	—	4	2	no	—
73	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₄₇⋊#95	—	2	2	no	—
76	C₄₇⋊#95	D₄	1	2	yes	—
77	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
79	C₄×Q₈×C₄₇	—	2	2	no	—
80	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	—
81	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	—	2	1	no	—
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₄₇	—	2	2	no	—
89	#103×C₄₇	—	2	4	no	—
90	C₂³×D₄₇	—	2	1	no	—
91	C₂×Q₈×C₄₇	—	2	1	no	—
92	C₂×Q₈×C₄₇	—	2	1	no	—
93	C₂×Q₈×C₄₇	—	2	1	no	—
94	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂×Q₈×C₄₇	#41	1	2	yes	—
96	C₂×Q₈×C₄₇	#41	1	2	yes	—
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
103	C₂²×Dic₄₇	—	2	1	no	—
104	C₂²×Dic₄₇	—	2	2	no	—
105	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
106	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
107	C₂×D₁₈₈	—	2	1	no	—
108	C₂×D₁₈₈	—	2	1	no	—
109	C₂×D₁₈₈	—	2	1	no	—
110	C₂×D₁₈₈	—	2	1	no	—
111	C₂×D₁₈₈	—	2	1	no	—
112	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
113	C₂×C₄×D₄₇	—	2	4	no	—
114	C₂×C₄×D₄₇	—	4	2	no	—
115	C₂×C₄×D₄₇	—	4	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	4	no	—
120	C₄⋊C₄×C₄₇	—	2	1	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	4	2	no	—
124	C₄⋊C₄×C₄₇	—	8	1	no	—
125	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
126	C₄²×C₄₇	—	2	4	no	—
127	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
128	C₄²×C₄₇	#41	1	2	yes	—
129	#10625336	—	2	8	no	—
130	(C₂×D₄₇)⋊C₄	—	2	4	no	—
131	(C₂×D₄₇)⋊C₄	—	4	4	no	—
132	(C₂×D₄₇)⋊C₄	—	8	2	no	—
133	C₄⋊Dic₄₇	—	2	2	no	—
134	C₄⋊Dic₄₇	—	2	2	no	—
135	C₄⋊Dic₄₇	—	2	1	no	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	4	4	no	—
139	C₄⋊Dic₄₇	—	4	2	no	—
140	C₄⋊Dic₄₇	—	8	2	no	—
141	C₄⋊Dic₄₇	—	8	1	no	—
142	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
143	C₄×Dic₄₇	—	2	2	no	—
144	C₄×Dic₄₇	—	2	2	no	—
145	C₄×Dic₄₇	—	4	4	no	—
146	C₄×Dic₄₇	—	4	4	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
152	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
153	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	C₂²×D₄₇	—	2	2	no	—
155	C₂²×D₄₇	—	4	1	no	—
156	C₂²×D₄₇	—	4	1	no	—
157	C₂²×D₄₇	—	4	1	no	—
158	C₂²×D₄₇	—	4	1	no	—
159	C₂²×D₄₇	—	4	1	no	—
160	C₂²×D₄₇	—	4	1	no	—
161	Q₈×C₄₇	—	2	2	no	—
162	Q₈×C₄₇	—	2	2	no	—
163	Q₈×C₄₇	—	2	2	no	—
164	Q₈×C₄₇	#117	1	4	yes	complemented
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	4	1	no	—
172	C₂×C₄×C₄₇	—	4	1	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
179	C₂×C₄×C₄₇	#137	1	2	yes	—
180	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
186	C₂×Dic₄₇	—	2	2	no	—
187	C₂×Dic₄₇	—	2	2	no	—
188	C₂×Dic₄₇	—	2	2	no	—
189	C₂×Dic₄₇	—	2	2	no	—
190	C₂×Dic₄₇	—	2	2	no	—
191	C₂×Dic₄₇	—	2	2	no	—
192	C₂×Dic₄₇	—	2	2	no	—
193	C₂×Dic₄₇	—	4	1	no	—
194	C₂×Dic₄₇	—	4	1	no	—
195	C₂×Dic₄₇	—	4	2	no	—
196	C₂×Dic₄₇	—	4	2	no	—
197	C₂×Dic₄₇	—	4	2	no	—
198	D₁₈₈	—	2	2	no	—
199	D₁₈₈	—	2	2	no	—
200	D₁₈₈	—	4	1	no	—
201	D₁₈₈	—	4	1	no	—
202	C₄×D₄₇	—	4	8	no	—
203	C₈×C₄₇	—	4	2	no	—
204	C₄₇⋊C₈	—	2	2	no	—
205	C₄₇⋊C₈	—	2	2	no	—
206	#22759	—	47	1	no	maximal, Sylow
207	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂²×C₄₇	#546	1	1	yes	characteristic
209	C₂²×C₄₇	#548	1	1	yes	characteristic
210	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
211	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
212	C₂²×C₄₇	#577	1	1	yes	characteristic
213	C₂²×C₄₇	#577	1	1	yes	characteristic
214	C₂×D₄₇	—	4	2	no	—
215	C₂×D₄₇	—	4	2	no	—
216	C₂×D₄₇	—	4	2	no	—
217	C₂×D₄₇	—	8	1	no	—
218	C₂×D₄₇	—	8	1	no	—
219	C₂×D₄₇	—	8	1	no	—
220	C₂×D₄₇	—	8	1	no	—
221	C₄×C₄₇	—	2	4	no	—
222	C₄×C₄₇	—	2	2	no	—
223	C₄×C₄₇	—	4	2	no	—
224	C₄×C₄₇	—	8	2	no	—
225	C₄×C₄₇	#440	1	4	yes	—
226	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
227	C₄×C₄₇	#520	1	1	yes	characteristic
228	C₄×C₄₇	#552	1	1	yes	characteristic
229	C₄×C₄₇	#553	1	1	yes	characteristic
230	Dic₄₇	—	4	2	no	—
231	Dic₄₇	—	4	2	no	—
232	Dic₄₇	—	4	2	no	—
233	Dic₄₇	—	8	2	no	—
234	C₂×C₄×SD₁₆	—	47	1	no	—
235	#2354	—	47	1	no	—
236	Q₈×C₄⋊C₄	—	47	1	no	—
237	#1936	—	47	2	no	—
238	#1919	—	47	2	no	—
239	#1880	—	47	2	no	—
240	#1834	—	47	1	no	—
241	#1803	D₄₇	1	1	yes	characteristic, complemented
242	#1802	—	47	1	no	—
243	#1770	—	47	1	no	—
244	#1763	—	47	2	no	—
245	C₂×C₄₇	#2352	1	1	yes	characteristic
246	C₂×C₄₇	C₂×#440	1	1	yes	characteristic
247	C₂×C₄₇	#2952	1	1	yes	characteristic
248	C₂×C₄₇	#3329	1	1	yes	characteristic
249	C₂×C₄₇	#3332	1	1	yes	characteristic
250	C₂×C₄₇	#3368	1	1	yes	characteristic
251	C₂×C₄₇	#3369	1	1	yes	characteristic
252	D₄₇	—	8	2	no	—
253	C₂²×SD₁₆	—	47	1	no	—
254	C₂×C₄×Q₈	—	47	2	no	—
255	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
256	C₂×C₄×D₄	—	47	1	no	—
257	C₂×#117	—	94	1	no	—
258	C₄×SD₁₆	—	47	8	no	—
259	C₂×#106	—	47	1	no	—
260	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
261	C₂×#103	—	47	1	no	—
262	C₂×#103	C₂×D₄₇	1	2	yes	—
263	C₂×#102	—	47	1	no	—
264	C₂×#102	—	47	2	no	—
265	C₂×#97	—	47	2	no	—
266	C₂×C₄×C₈	—	47	1	no	—
267	#390	—	47	2	no	—
268	#389	—	47	2	no	—
269	#389	—	94	2	no	—
270	#388	—	94	2	no	—
271	#384	—	47	1	no	—
272	#384	—	94	1	no	—
273	#384	C₂×D₄₇	1	1	yes	characteristic
274	#380	—	94	1	no	—
275	C₄×C₄⋊C₄	—	47	1	no	—
276	C₄×C₄⋊C₄	—	47	2	no	—
277	C₄×C₄⋊C₄	—	94	1	no	—
278	#340	—	47	2	no	—
279	#340	—	47	2	no	—
280	#340	—	47	2	no	—
281	#340	C₂×D₄₇	1	2	yes	—
282	#336	—	47	2	no	—
283	C₄₇	#22759	1	1	yes	characteristic, complemented, Sylow
284	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
285	C₂²×D₄	—	47	1	no	—
286	C₂³×C₄	—	94	1	no	—
287	C₂×SD₁₆	—	47	4	no	—
288	C₂×SD₁₆	—	94	2	no	—
289	C₂×SD₁₆	—	94	2	no	—
290	C₂²×C₈	—	47	1	no	—
291	C₂²×C₈	—	47	1	no	—
292	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	—	94	4	no	—
295	C₄×Q₈	—	188	2	no	—
296	C₄×Q₈	C₄×D₄₇	1	4	yes	—
297	C₄×D₄	—	47	4	no	—
298	C₄×D₄	—	94	2	no	—
299	#117	—	188	4	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	47	1	no	—
304	C₂×C₄⋊C₄	—	47	1	no	—
305	C₂×C₄⋊C₄	—	47	1	no	—
306	C₂×C₄⋊C₄	—	47	2	no	—
307	C₂×C₄⋊C₄	—	94	2	no	—
308	C₂×C₄⋊C₄	—	94	1	no	—
309	C₂×C₄⋊C₄	—	94	2	no	—
310	C₂×C₄⋊C₄	—	94	1	no	—
311	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
312	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	—	94	1	no	—
314	C₂×C₂²⋊C₄	—	94	2	no	—
315	C₂×C₂²⋊C₄	—	94	2	no	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	—	47	2	no	—
318	C₂×C₄²	—	94	2	no	—
319	C₂×C₄²	—	94	2	no	—
320	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
321	#106	—	47	4	no	—
322	C₄⋊C₈	—	2	2	no	—
323	#103	—	2	4	no	—
324	#103	—	47	4	no	—
325	#102	—	47	4	no	—
326	#102	—	188	2	no	—
327	#97	—	188	2	no	—
328	C₄×C₈	—	47	4	no	—
329	#95	—	47	2	no	—
330	#95	—	94	2	no	—
331	#95	—	94	2	no	—
332	C₂⁴	—	94	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
337	C₂×Q₈	#10625352	1	2	yes	—
338	C₂×Q₈	#10625354	1	2	yes	—
339	C₂×D₄	—	47	2	no	—
340	C₂×D₄	—	94	1	no	—
341	C₂×D₄	—	94	1	no	—
342	C₂×D₄	—	94	1	no	—
343	C₂×D₄	—	94	1	no	—
344	C₂×D₄	—	94	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	47	2	no	—
349	C₂²×C₄	—	47	2	no	—
350	C₂²×C₄	—	94	1	no	—
351	C₂²×C₄	—	94	4	no	—
352	C₂²×C₄	—	94	2	no	—
353	C₂²×C₄	—	188	2	no	—
354	C₂²×C₄	—	188	2	no	—
355	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
356	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
357	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
358	SD₁₆	—	94	8	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	47	2	no	—
363	C₂×C₈	—	47	2	no	—
364	C₂×C₈	—	94	1	no	—
365	C₂×C₈	—	94	1	no	—
366	C₂×C₈	—	94	1	no	—
367	C₂×C₈	—	94	1	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	8	1	no	—
374	C₄⋊C₄	—	47	2	no	—
375	C₄⋊C₄	—	94	2	no	—
376	C₄⋊C₄	—	94	2	no	—
377	C₄⋊C₄	—	94	1	no	—
378	C₄⋊C₄	—	94	2	no	—
379	C₄⋊C₄	—	94	2	no	—
380	C₄⋊C₄	—	376	1	no	—
381	C₄⋊C₄	—	376	2	no	—
382	C₄⋊C₄	—	188	4	no	—
383	C₄⋊C₄	—	188	2	no	—
384	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
385	C₂²⋊C₄	—	94	4	no	—
386	C₂²⋊C₄	—	376	2	no	—
387	C₂²⋊C₄	—	188	4	no	—
388	C₄²	—	2	4	no	—
389	C₄²	—	94	2	no	—
390	C₄²	—	94	2	no	—
391	C₄²	—	188	4	no	—
392	C₄²	—	188	4	no	—
393	C₄²	C₂×C₄×D₄₇	1	2	yes	—
394	C₄²	#10625352	1	2	yes	—
395	C₂³	—	94	2	no	—
396	C₂³	—	188	1	no	—
397	C₂³	—	188	1	no	—
398	C₂³	—	188	1	no	—
399	C₂³	—	188	1	no	—
400	C₂³	—	188	1	no	—
401	C₂³	—	188	1	no	—
402	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
403	Q₈	—	2	2	no	—
404	Q₈	—	2	2	no	—
405	Q₈	—	2	2	no	—
406	Q₈	#13093982	1	4	yes	complemented
407	D₄	—	94	2	no	—
408	D₄	—	94	2	no	—
409	D₄	—	188	1	no	—
410	D₄	—	188	1	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	94	2	no	—
423	C₂×C₄	—	94	2	no	—
424	C₂×C₄	—	94	2	no	—
425	C₂×C₄	—	94	2	no	—
426	C₂×C₄	—	94	2	no	—
427	C₂×C₄	—	94	2	no	—
428	C₂×C₄	—	94	2	no	—
429	C₂×C₄	—	188	2	no	—
430	C₂×C₄	—	188	2	no	—
431	C₂×C₄	—	188	2	no	—
432	C₂×C₄	—	188	1	no	—
433	C₂×C₄	—	188	1	no	—
434	C₂×C₄	—	188	8	no	—
435	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
436	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
437	C₂×C₄	#13094051	1	2	yes	—
438	C₂×C₄	#13094056	1	2	yes	—
439	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
440	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
441	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
442	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
443	C₂×C₄	#13094070	1	1	yes	characteristic
444	C₂×C₄	#13094071	1	1	yes	characteristic
445	C₈	—	4	2	no	—
446	C₈	—	94	2	no	—
447	C₈	—	94	2	no	—
448	C₂²	—	376	1	no	—
449	C₂²	—	376	1	no	—
450	C₂²	—	376	1	no	—
451	C₂²	—	376	1	no	—
452	C₂²	—	188	2	no	—
453	C₂²	—	188	2	no	—
454	C₂²	—	188	2	no	—
455	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
456	C₂²	#15689764	1	1	yes	characteristic
457	C₂²	#15689779	1	1	yes	characteristic
458	C₂²	C₂×#13094051	1	1	yes	characteristic
459	C₂²	C₂×#13094056	1	1	yes	characteristic
460	C₂²	#15689932	1	1	yes	characteristic
461	C₂²	#15689933	1	1	yes	characteristic
462	C₄	—	2	4	no	—
463	C₄	—	2	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	8	2	no	—
466	C₄	—	376	2	no	—
467	C₄	—	188	2	no	—
468	C₄	—	188	2	no	—
469	C₄	—	188	2	no	—
470	C₄	#15689226	1	4	yes	—
471	C₄	C₂×#13093982	1	1	yes	characteristic
472	C₄	#15689603	1	1	yes	characteristic
473	C₄	#15689815	1	1	yes	characteristic
474	C₄	#15689825	1	1	yes	characteristic
475	C₂	—	376	2	no	—
476	C₂	#20246319	1	1	yes	characteristic
477	C₂	C₂×#15689226	1	1	yes	characteristic
478	C₂	#20252267	1	1	yes	characteristic
479	C₂	#20255679	1	1	yes	characteristic
480	C₂	#20255712	1	1	yes	characteristic
481	C₂	#20256121	1	1	yes	characteristic
482	C₂	#20256132	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1803	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1803	D₄₇
hypocenter	C₄₇	#22759
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1803

Complements

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

N	H ≅ G/N	type
3. Q₈×C₄⋊Dic₄₇	C₂	semidirect
5. #20243969	C₂	semidirect
7. #20243515	C₂	semidirect
9. #20243258	C₂	semidirect
10. #20243220	C₂	semidirect
11. C₄₇×#1803	C₂	semidirect
16. C₄×#10625336	C₄	semidirect
164. Q₈×C₄₇	#117	semidirect
241. #1803	D₄₇	semidirect
283. C₄₇	#22759	semidirect
406. Q₈	#13093982	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10625336	2
#20246339	2
Q₈×C₄⋊Dic₄₇	2
#20244086	2
#20243969	2
#20243741	2
#20243515	2
#20243389	2
#20243258	2
#20243220	2
C₄₇×#1803	2
#22759	47