Subgroups — #26185857

Order 12032.

748 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	#20252349	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13094050	C₂	1	1	yes	maximal, characteristic
3	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242249	C₂	1	2	yes	maximal, complemented
5	#20242242	C₂	1	2	yes	maximal, complemented
6	#20242221	C₂	1	2	yes	maximal, complemented
7	#20242214	C₂	1	2	yes	maximal, complemented
8	#20242141	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241776	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241678	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1478	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094050	C₄	1	1	yes	characteristic
13	C₂³×C₄₇⋊C₈	—	2	1	no	—
14	C₄×#10625350	C₂²	1	1	yes	characteristic
15	#15689250	C₂²	1	1	yes	characteristic, complemented
16	#15689250	C₂²	1	1	yes	characteristic, complemented
17	#15689233	C₄	1	2	yes	—
18	#15689223	C₄	1	2	yes	—
19	C₄×#10625335	C₂²	1	2	yes	—
20	C₄×#10625334	C₂²	1	2	yes	—
21	#15689200	C₂²	1	1	yes	characteristic, complemented
22	#15689200	C₂²	1	1	yes	characteristic, complemented
23	#15689191	—	2	1	no	—
24	#15689191	—	2	1	no	—
25	D₄×C₄₇⋊C₈	—	2	1	no	—
26	D₄×C₄₇⋊C₈	—	2	1	no	—
27	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
28	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
29	#15689174	—	2	1	no	—
30	#15689163	C₄	1	1	yes	characteristic
31	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
32	#15689128	C₄	1	1	yes	characteristic
33	#15689122	C₄	1	1	yes	characteristic
34	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
35	C₄×#10625329	C₂²	1	1	yes	characteristic
36	C₄×#10625324	—	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	#15688855	C₂²	1	2	yes	complemented
41	#15688852	C₂²	1	2	yes	complemented
42	#15688845	C₂²	1	2	yes	complemented
43	#15688844	C₂²	1	2	yes	complemented
44	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#431	C₂²	1	1	yes	characteristic
46	C₄₇×#431	C₂²	1	1	yes	characteristic
47	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
48	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
49	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
50	#13094050	—	2	4	no	—
51	C₂×#10625335	C₂×C₄	1	2	yes	—
52	C₂×#10625334	C₂×C₄	1	2	yes	—
53	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
54	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
55	C₂×#10625324	—	2	1	no	—
56	C₂×#10625324	—	2	1	no	—
57	C₂²×C₄₇⋊C₈	—	2	1	no	—
58	C₂²×C₄₇⋊C₈	—	2	2	no	—
59	C₂²×C₄₇⋊C₈	—	2	2	no	—
60	C₂²×C₄₇⋊C₈	—	4	4	no	—
61	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
62	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
63	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
64	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
65	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
66	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
67	C₄×C₂²⋊D₄₇	—	2	1	no	—
68	C₄×C₂²⋊D₄₇	—	2	1	no	—
69	#13093983	C₂×C₄	1	1	yes	characteristic
70	#13093981	—	2	1	no	—
71	C₄²×D₄₇	—	2	1	no	—
72	#13093957	C₂×C₄	1	2	yes	—
73	#13093955	C₂×C₄	1	2	yes	—
74	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
75	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
76	Dic₄₇⋊C₈	—	2	1	no	—
77	Dic₄₇⋊C₈	—	2	1	no	—
78	#13093947	C₂×C₄	1	2	yes	—
79	#13093945	C₂×C₄	1	2	yes	—
80	#13093945	C₂×C₄	1	2	yes	—
81	#13093944	C₂×C₄	1	2	yes	—
82	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
83	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
84	(C₂×D₄₇)⋊C₈	—	2	1	no	—
85	(C₂×D₄₇)⋊C₈	—	2	1	no	—
86	#13093935	C₂×C₄	1	2	yes	—
87	#13093934	—	2	1	no	—
88	#13093934	—	2	1	no	—
89	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
90	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
91	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
92	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
93	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂³×C₄×C₄₇	—	2	1	no	—
96	C₄×D₄×C₄₇	—	2	1	no	—
97	C₄×D₄×C₄₇	—	2	1	no	—
98	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
99	C₄×D₄×C₄₇	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
102	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₄₇	—	2	1	no	—
104	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
106	C₂²⋊C₈×C₄₇	—	2	1	no	—
107	C₂²⋊C₈×C₄₇	—	2	1	no	—
108	C₄×C₈×C₄₇	—	2	1	no	—
109	C₄×C₈×C₄₇	C₂³	1	2	yes	—
110	C₂⁴×C₄₇	—	2	1	no	—
111	C₂×D₄×C₄₇	—	2	1	no	—
112	C₂×D₄×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	M₁₆	1	4	yes	complemented
114	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₄₇	—	2	1	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	4	2	no	—
119	C₂²×C₄×C₄₇	—	4	2	no	—
120	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
123	C₂×C₂²⋊D₄₇	—	2	1	no	—
124	#10625350	—	2	2	no	—
125	#10625350	—	2	2	no	—
126	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₄₇	—	2	1	no	—
128	C₂×C₄×D₄₇	—	2	1	no	—
129	C₂×C₄×D₄₇	—	2	1	no	—
130	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₄₇	—	2	1	no	—
132	C₂×C₈×C₄₇	—	2	1	no	—
133	C₂×C₈×C₄₇	—	2	2	no	—
134	C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
136	C₂²⋊C₄×C₄₇	—	2	2	no	—
137	C₂²⋊C₄×C₄₇	—	2	2	no	—
138	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₇	#41	1	1	yes	characteristic
141	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
142	C₂²⋊Dic₄₇	—	2	1	no	—
143	#10625335	—	2	4	no	—
144	#10625334	—	2	4	no	—
145	(C₂×D₄₇)⋊C₄	—	2	1	no	—
146	(C₂×D₄₇)⋊C₄	—	2	1	no	—
147	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
149	Dic₄₇⋊C₄	—	2	1	no	—
150	Dic₄₇⋊C₄	—	2	1	no	—
151	C₄×Dic₄₇	—	2	1	no	—
152	C₄×Dic₄₇	—	2	1	no	—
153	C₄×Dic₄₇	—	2	1	no	—
154	#10625329	—	2	2	no	—
155	#10625329	—	2	2	no	—
156	C₂×C₄₇⋊C₈	—	2	2	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂×C₄₇⋊C₈	—	4	1	no	—
159	C₂×C₄₇⋊C₈	—	4	4	no	—
160	C₂×C₄₇⋊C₈	—	4	2	no	—
161	C₂×C₄₇⋊C₈	—	4	4	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	#10625324	—	4	2	no	—
169	#10625324	—	4	2	no	—
170	C₂³×C₄₇	—	2	2	no	—
171	C₂³×C₄₇	—	2	4	no	—
172	C₂³×C₄₇	—	4	2	no	—
173	C₂³×C₄₇	—	4	2	no	—
174	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
175	C₂²×D₄₇	—	2	1	no	—
176	D₄×C₄₇	—	2	2	no	—
177	D₄×C₄₇	—	2	4	no	—
178	D₄×C₄₇	C₂×M₁₆	1	4	yes	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	4	1	no	—
183	C₂×C₄×C₄₇	—	4	4	no	—
184	C₂×C₄×C₄₇	—	4	2	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
191	C₂×C₄×C₄₇	#131	1	2	yes	—
192	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
195	C₂²⋊D₄₇	—	4	2	no	—
196	C₂×Dic₄₇	—	2	1	no	—
197	C₂×Dic₄₇	—	2	1	no	—
198	C₂×Dic₄₇	—	2	1	no	—
199	D₁₈₈	—	2	1	no	—
200	D₁₈₈	—	2	1	no	—
201	C₄×D₄₇	—	4	2	no	—
202	C₄×D₄₇	—	4	1	no	—
203	C₄×D₄₇	—	4	1	no	—
204	C₄×D₄₇	—	4	2	no	—
205	Dic₉₄	—	2	1	no	—
206	Dic₉₄	—	2	1	no	—
207	C₈×C₄₇	—	4	2	no	—
208	C₈×C₄₇	—	4	1	no	—
209	C₈×C₄₇	—	4	1	no	—
210	C₄₇⋊C₈	—	2	2	no	—
211	C₄₇⋊C₈	—	2	2	no	—
212	C₄₇⋊C₈	—	2	1	no	—
213	C₄₇⋊C₈	—	2	1	no	—
214	C₄₇⋊C₈	—	2	1	no	—
215	C₄₇⋊C₈	—	4	2	no	—
216	C₄₇⋊C₈	AGL(1,ℤ/8)	1	2	yes	complemented
217	#17869	—	47	1	no	maximal, Sylow
218	C₂²×C₄₇	—	2	1	no	—
219	C₂²×C₄₇	—	2	1	no	—
220	C₂²×C₄₇	—	2	4	no	—
221	C₂²×C₄₇	—	4	8	no	—
222	C₂²×C₄₇	—	4	2	no	—
223	C₂²×C₄₇	—	4	2	no	—
224	C₂²×C₄₇	#435	1	2	yes	—
225	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
226	C₂×D₄₇	—	4	1	no	—
227	C₂×D₄₇	—	4	1	no	—
228	C₂×D₄₇	—	4	1	no	—
229	C₄×C₄₇	—	2	1	no	—
230	C₄×C₄₇	—	2	1	no	—
231	C₄×C₄₇	—	2	1	no	—
232	C₄×C₄₇	—	4	2	no	—
233	C₄×C₄₇	#435	1	2	yes	—
234	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
235	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
236	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
237	C₄×C₄₇	#575	1	1	yes	characteristic
238	Dic₄₇	—	4	1	no	—
239	Dic₄₇	—	4	1	no	—
240	Dic₄₇	—	4	1	no	—
241	#2965	—	47	1	no	—
242	C₄×AGL(1,ℤ/8)	—	47	1	no	—
243	C₂×C₈×D₄	—	47	1	no	—
244	#1586	—	47	2	no	—
245	#1585	—	47	2	no	—
246	#1582	—	47	2	no	—
247	#1581	—	47	2	no	—
248	#1565	—	47	1	no	—
249	#1478	D₄₇	1	1	yes	characteristic, complemented
250	#1477	—	47	1	no	—
251	#1451	—	47	1	no	—
252	C₂×C₄₇	—	2	2	no	—
253	C₂×C₄₇	—	4	4	no	—
254	C₂×C₄₇	C₂×#435	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	—	8	1	no	—
258	C₂×AGL(1,ℤ/8)	—	47	1	no	—
259	C₂³×C₈	—	94	1	no	—
260	C₄×#41	—	47	1	no	—
261	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
262	#446	—	47	1	no	—
263	#446	—	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	#436	—	47	1	no	—
269	#436	—	47	1	no	—
270	#435	—	94	1	no	—
271	#435	—	94	1	no	—
272	C₈×D₄	—	47	2	no	—
273	C₈×D₄	—	47	2	no	—
274	C₈×D₄	—	94	1	no	—
275	C₈×D₄	—	94	1	no	—
276	#431	—	94	1	no	—
277	#431	C₂×D₄₇	1	1	yes	characteristic
278	#431	C₂×D₄₇	1	1	yes	characteristic
279	#428	—	47	1	no	—
280	C₂×C₄⋊C₈	—	47	1	no	—
281	#418	—	47	1	no	—
282	#417	—	47	1	no	—
283	C₂×C₂²⋊C₈	—	94	1	no	—
284	C₄×M₁₆	—	47	1	no	—
285	C₄×M₁₆	—	94	1	no	—
286	C₂×C₄×C₈	—	47	1	no	—
287	#335	—	47	2	no	—
288	#334	—	47	2	no	—
289	Q₈⋊C₈	—	47	2	no	—
290	D₄⋊C₈	—	47	2	no	—
291	D₄⋊C₈	C₂×D₄₇	1	2	yes	—
292	D₄⋊C₈	C₂×D₄₇	1	2	yes	—
293	#322	—	47	2	no	—
294	#322	—	47	2	no	—
295	C₄₇	#17869	1	1	yes	characteristic, complemented, Sylow
296	C₂×#41	—	47	1	no	—
297	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
298	C₂³×C₄	—	2	1	no	—
299	AGL(1,ℤ/8)	—	94	4	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	C₂×M₁₆	—	94	1	no	—
305	C₂×M₁₆	—	94	1	no	—
306	C₂²×C₈	—	47	1	no	—
307	C₂²×C₈	—	47	1	no	—
308	C₂²×C₈	—	94	2	no	—
309	C₂²×C₈	—	94	2	no	—
310	C₂²×C₈	—	94	1	no	—
311	C₂²×C₈	—	188	4	no	—
312	C₄×Q₈	—	47	1	no	—
313	C₄×Q₈	—	47	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	47	1	no	—
317	C₄×D₄	—	47	1	no	—
318	C₄×D₄	—	94	1	no	—
319	C₄×D₄	—	94	1	no	—
320	C₄×D₄	C₄×D₄₇	1	2	yes	—
321	C₄×D₄	C₂²×D₄₇	1	2	yes	—
322	#117	—	47	1	no	—
323	#117	—	94	1	no	—
324	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₄²	—	94	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	—	47	2	no	—
332	C₄⋊C₈	—	94	1	no	—
333	C₄⋊C₈	—	94	1	no	—
334	C₄⋊C₈	—	94	1	no	—
335	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
336	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
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	—	2	1	no	—
343	C₂²⋊C₈	—	94	1	no	—
344	C₂²⋊C₈	—	94	1	no	—
345	C₂²⋊C₈	—	94	2	no	—
346	C₂²⋊C₈	—	94	2	no	—
347	#97	—	47	2	no	—
348	#97	—	94	1	no	—
349	#97	—	94	1	no	—
350	C₄×C₈	—	2	1	no	—
351	C₄×C₈	—	47	1	no	—
352	C₄×C₈	—	47	1	no	—
353	C₄×C₈	—	47	2	no	—
354	C₄×C₈	—	47	1	no	—
355	C₄×C₈	—	47	1	no	—
356	C₄×C₈	C₂²×D₄₇	1	2	yes	—
357	C₂⁴	—	2	1	no	—
358	#41	—	94	2	no	—
359	#41	—	94	2	no	—
360	C₂×Q₈	—	47	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	47	1	no	—
364	C₂×D₄	—	94	1	no	—
365	C₂×D₄	#10625324	1	4	yes	complemented
366	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	94	1	no	—
373	C₂²×C₄	—	94	1	no	—
374	C₂²×C₄	—	94	1	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	—	94	4	no	—
379	D₈	—	94	4	no	—
380	M₁₆	—	94	2	no	—
381	M₁₆	—	94	2	no	—
382	M₁₆	—	188	2	no	—
383	M₁₆	—	188	2	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	47	1	no	—
388	C₂×C₈	—	47	2	no	—
389	C₂×C₈	—	47	2	no	—
390	C₂×C₈	—	47	1	no	—
391	C₂×C₈	—	47	1	no	—
392	C₂×C₈	—	47	1	no	—
393	C₂×C₈	—	94	2	no	—
394	C₂×C₈	—	94	2	no	—
395	C₂×C₈	—	188	4	no	—
396	C₂×C₈	—	188	1	no	—
397	C₂×C₈	—	188	4	no	—
398	C₂×C₈	—	188	2	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	47	1	no	—
401	C₄⋊C₄	—	47	1	no	—
402	C₄⋊C₄	—	94	1	no	—
403	C₄⋊C₄	—	94	1	no	—
404	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	94	1	no	—
408	C₂²⋊C₄	—	94	1	no	—
409	C₂²⋊C₄	—	94	1	no	—
410	C₄²	—	94	1	no	—
411	C₄²	—	94	1	no	—
412	C₄²	—	94	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	2	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	94	1	no	—
422	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
423	Q₈	—	94	1	no	—
424	Q₈	—	94	1	no	—
425	D₄	—	2	2	no	—
426	D₄	—	2	4	no	—
427	D₄	—	94	1	no	—
428	D₄	—	94	1	no	—
429	D₄	—	188	2	no	—
430	D₄	C₂×#10625324	1	4	yes	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	94	1	no	—
440	C₂×C₄	—	94	1	no	—
441	C₂×C₄	—	94	1	no	—
442	C₂×C₄	—	188	2	no	—
443	C₂×C₄	—	188	1	no	—
444	C₂×C₄	—	188	1	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×#10625324	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	1	no	—
456	C₈	—	4	1	no	—
457	C₈	—	47	2	no	—
458	C₈	—	94	2	no	—
459	C₈	—	94	2	no	—
460	C₈	—	94	1	no	—
461	C₈	—	94	1	no	—
462	C₈	—	94	1	no	—
463	C₈	—	188	2	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	4	no	—
467	C₂²	—	4	8	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	188	1	no	—
471	C₂²	—	188	1	no	—
472	C₂²	—	188	1	no	—
473	C₂²	#15689191	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	—	4	2	no	—
479	C₄	—	188	1	no	—
480	C₄	—	188	1	no	—
481	C₄	—	188	1	no	—
482	C₄	#15689191	1	2	yes	—
483	C₄	C₂²×#10625324	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	#15689919	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	4	4	no	—
489	C₂	—	376	1	no	—
490	C₂	C₂×#15689191	1	1	yes	characteristic
491	C₂	#20252192	1	1	yes	characteristic
492	C₂	#20252287	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1478	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094050	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1478	D₄₇
hypocenter	C₄₇	#17869
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1478

Complements

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

N	H ≅ G/N	type
1. #20252349	C₂	semidirect
3. C₂×D₄×C₄₇⋊C₈	C₂	semidirect
4. #20242249	C₂	semidirect
5. #20242242	C₂	semidirect
6. #20242221	C₂	semidirect
7. #20242214	C₂	semidirect
8. #20242141	C₂	semidirect
9. #20241776	C₂	semidirect
10. #20241678	C₂	semidirect
11. C₄₇×#1478	C₂	semidirect
15. #15689250	C₂²	semidirect
16. #15689250	C₂²	semidirect
21. #15689200	C₂²	semidirect
22. #15689200	C₂²	semidirect
38. #15688875	C₂²	semidirect
39. #15688873	C₂²	semidirect
40. #15688855	C₂²	semidirect
41. #15688852	C₂²	semidirect
42. #15688845	C₂²	semidirect
43. #15688844	C₂²	semidirect
113. C₂×D₄×C₄₇	M₁₆	semidirect
216. C₄₇⋊C₈	AGL(1,ℤ/8)	semidirect
249. #1478	D₄₇	semidirect
295. C₄₇	#17869	semidirect
365. C₂×D₄	#10625324	semidirect

Maximal subgroups

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

subgroup	index
#20252349	2
C₄×#13094050	2
C₂×D₄×C₄₇⋊C₈	2
#20242249	2
#20242242	2
#20242221	2
#20242214	2
#20242141	2
#20241776	2
#20241678	2
C₄₇×#1478	2
#17869	47