Subgroups — #26186268

Order 12032.

700 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253442	C₂	1	1	yes	maximal, characteristic
2	C₈×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242264	C₂	1	2	yes	maximal, complemented
4	#20242250	C₂	1	2	yes	maximal, complemented
5	C₈×#10625335	C₂	1	2	yes	maximal, complemented
6	C₈×#10625334	C₂	1	2	yes	maximal, complemented
7	#20242179	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241825	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241805	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#10625350	C₂²	1	1	yes	characteristic
13	#15689444	C₄	1	2	yes	—
14	#15689415	C₄	1	1	yes	characteristic
15	#15689410	C₄	1	1	yes	characteristic
16	#15689320	C₄	1	1	yes	characteristic
17	#15689315	C₄	1	1	yes	characteristic
18	#15689266	C₄	1	2	yes	—
19	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
20	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
21	C₄×#10625335	C₂²	1	2	yes	—
22	C₄×#10625334	C₂²	1	2	yes	—
23	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
24	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
25	C₈×C₂²⋊D₄₇	—	2	1	no	—
26	C₈×C₂²⋊D₄₇	—	2	1	no	—
27	#15689176	C₂²	1	1	yes	characteristic
28	#15689176	C₂²	1	1	yes	characteristic
29	#15689174	—	2	1	no	—
30	C₄×#10625329	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₄₇	—	2	1	no	—
32	#15688875	C₂²	1	2	yes	—
33	#15688873	C₂²	1	2	yes	—
34	#15688853	C₂²	1	2	yes	—
35	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
36	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
37	#15688850	C₂²	1	2	yes	—
38	#15688845	C₂²	1	2	yes	—
39	C₈×C₄₇⋊C₈	C₂²	1	2	yes	—
40	C₂×#131×C₄₇	—	2	1	no	—
41	C₄₇×#532	C₂²	1	1	yes	characteristic
42	C₄₇×#436	—	2	1	no	—
43	C₄₇×#436	C₂²	1	2	yes	—
44	C₈×D₄×C₄₇	—	2	1	no	—
45	C₈×D₄×C₄₇	C₂²	1	2	yes	—
46	C₄₇×#423	C₂²	1	1	yes	characteristic
47	C₄₇×#408	—	2	1	no	—
48	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
49	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
50	C₂×#10625335	C₂×C₄	1	2	yes	—
51	C₂×#10625334	C₂×C₄	1	2	yes	—
52	C₂×#10625329	—	2	1	no	—
53	C₂×C₈×D₄₇	—	2	1	no	—
54	C₂×C₈×D₄₇	—	2	1	no	—
55	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
56	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
57	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
58	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
59	C₄×C₂²⋊D₄₇	—	2	1	no	—
60	C₄×C₂²⋊D₄₇	—	2	1	no	—
61	#13093983	C₂×C₄	1	1	yes	characteristic
62	#13093981	—	2	1	no	—
63	C₄²×D₄₇	—	2	1	no	—
64	#13093957	C₂×C₄	1	2	yes	—
65	#13093955	C₂×C₄	1	2	yes	—
66	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
67	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
69	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
70	Dic₄₇⋊C₈	—	2	1	no	—
71	Dic₄₇⋊C₈	—	2	1	no	—
72	#13093947	C₂×C₄	1	2	yes	—
73	#13093945	C₂×C₄	1	2	yes	—
74	#13093945	C₂×C₄	1	2	yes	—
75	#13093944	C₂×C₄	1	2	yes	—
76	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
77	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
78	(C₂×D₄₇)⋊C₈	—	2	1	no	—
79	(C₂×D₄₇)⋊C₈	—	2	1	no	—
80	#13093935	—	2	1	no	—
81	C₄×C₄₇⋊C₈	—	2	1	no	—
82	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
83	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
84	C₈×Dic₄₇	—	2	1	no	—
85	C₈×Dic₄₇	—	2	1	no	—
86	C₂×#41×C₄₇	—	2	1	no	—
87	#131×C₄₇	—	4	4	no	—
88	C₂×M₁₆×C₄₇	—	2	1	no	—
89	C₂×M₁₆×C₄₇	—	2	2	no	—
90	C₂²×C₈×C₄₇	—	2	2	no	—
91	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
92	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
93	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
94	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
95	#124×C₄₇	—	2	1	no	—
96	#121×C₄₇	—	2	1	no	—
97	#121×C₄₇	C₂×C₄	1	2	yes	—
98	C₄×D₄×C₄₇	—	2	1	no	—
99	C₄×D₄×C₄₇	C₂³	1	2	yes	—
100	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₄₇	—	2	1	no	—
102	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
103	C₂²⋊C₈×C₄₇	—	2	2	no	—
104	C₂²⋊C₈×C₄₇	—	2	2	no	—
105	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
106	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
107	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
109	#41×C₄₇	—	4	2	no	—
110	#41×C₄₇	—	4	2	no	—
111	C₂×Q₈×C₄₇	—	2	1	no	—
112	C₂×D₄×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	—	2	1	no	—
114	C₂×D₄×C₄₇	—	2	1	no	—
115	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
120	C₂×C₂²⋊D₄₇	—	2	1	no	—
121	#10625350	—	2	2	no	—
122	#10625350	—	2	2	no	—
123	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₄×D₄₇	—	2	1	no	—
125	C₂×C₄×D₄₇	—	2	1	no	—
126	C₂×C₄×D₄₇	—	2	1	no	—
127	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
128	M₁₆×C₄₇	—	4	4	no	—
129	M₁₆×C₄₇	—	4	2	no	—
130	C₂×C₈×C₄₇	—	2	2	no	—
131	C₂×C₈×C₄₇	—	2	2	no	—
132	C₂×C₈×C₄₇	—	4	1	no	—
133	C₂×C₈×C₄₇	—	4	4	no	—
134	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₄⋊C₄×C₄₇	—	2	1	no	—
139	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
140	C₂²⋊C₄×C₄₇	—	2	2	no	—
141	C₂²⋊C₄×C₄₇	—	2	2	no	—
142	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₄₇	#41	1	1	yes	characteristic
145	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
146	C₂²⋊Dic₄₇	—	2	1	no	—
147	#10625335	—	2	4	no	—
148	#10625334	—	2	4	no	—
149	(C₂×D₄₇)⋊C₄	—	2	1	no	—
150	(C₂×D₄₇)⋊C₄	—	2	1	no	—
151	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
153	Dic₄₇⋊C₄	—	2	1	no	—
154	Dic₄₇⋊C₄	—	2	1	no	—
155	C₄×Dic₄₇	—	2	1	no	—
156	C₄×Dic₄₇	—	2	1	no	—
157	C₄×Dic₄₇	—	2	1	no	—
158	#10625329	—	2	4	no	—
159	C₂×C₄₇⋊C₈	—	2	2	no	—
160	C₂×C₄₇⋊C₈	—	2	1	no	—
161	C₂×C₄₇⋊C₈	—	2	1	no	—
162	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
163	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
164	C₈×D₄₇	—	4	2	no	—
165	C₈×D₄₇	—	4	2	no	—
166	C₂³×C₄₇	—	2	2	no	—
167	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
168	C₂²×D₄₇	—	2	1	no	—
169	Q₈×C₄₇	—	4	2	no	—
170	D₄×C₄₇	—	2	2	no	—
171	D₄×C₄₇	—	2	2	no	—
172	D₄×C₄₇	—	4	2	no	—
173	D₄×C₄₇	—	4	4	no	—
174	D₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
189	C₂²⋊D₄₇	—	2	4	no	—
190	C₂×Dic₄₇	—	2	1	no	—
191	C₂×Dic₄₇	—	2	1	no	—
192	C₂×Dic₄₇	—	2	1	no	—
193	D₁₈₈	—	2	1	no	—
194	D₁₈₈	#131	1	2	yes	complemented
195	C₄×D₄₇	—	2	4	no	—
196	C₄×D₄₇	—	4	1	no	—
197	C₄×D₄₇	—	4	1	no	—
198	C₄×D₄₇	—	4	2	no	—
199	Dic₉₄	—	2	1	no	—
200	Dic₉₄	#131	1	2	yes	complemented
201	C₈×C₄₇	—	2	1	no	—
202	C₈×C₄₇	—	2	1	no	—
203	C₈×C₄₇	—	2	1	no	—
204	C₈×C₄₇	—	4	2	no	—
205	C₈×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
206	C₄₇⋊C₈	—	2	4	no	—
207	C₄₇⋊C₈	—	2	2	no	—
208	C₄₇⋊C₈	—	2	2	no	—
209	C₄₇⋊C₈	—	4	1	no	—
210	C₄₇⋊C₈	—	4	1	no	—
211	#17912	—	47	1	no	maximal, Sylow
212	C₂²×C₄₇	—	2	1	no	—
213	C₂²×C₄₇	—	2	1	no	—
214	C₂²×C₄₇	—	2	1	no	—
215	C₂²×C₄₇	—	4	2	no	—
216	C₂²×C₄₇	—	4	2	no	—
217	C₂²×C₄₇	—	4	2	no	—
218	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
219	C₂×D₄₇	—	2	2	no	—
220	C₂×D₄₇	—	4	1	no	—
221	C₂×D₄₇	—	4	1	no	—
222	C₄×C₄₇	—	2	1	no	—
223	C₄×C₄₇	—	2	1	no	—
224	C₄×C₄₇	—	2	1	no	—
225	C₄×C₄₇	—	4	2	no	—
226	C₄×C₄₇	#443	1	2	yes	—
227	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
228	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
229	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
230	C₄×C₄₇	#575	1	1	yes	characteristic
231	Dic₄₇	—	2	2	no	—
232	Dic₄₇	—	4	1	no	—
233	Dic₄₇	—	4	1	no	—
234	#3106	—	47	1	no	—
235	C₈×#41	—	47	1	no	—
236	#2931	D₄₇	1	1	yes	characteristic, complemented
237	#1588	—	47	2	no	—
238	#1586	—	47	2	no	—
239	C₈×SD₁₆	—	47	2	no	—
240	C₈×D₈	—	47	2	no	—
241	#1574	—	47	1	no	—
242	#1489	—	47	1	no	—
243	#1484	—	47	1	no	—
244	C₈×M₁₆	—	47	1	no	—
245	C₂×C₄₇	—	4	1	no	—
246	C₂×C₄₇	—	8	2	no	—
247	C₂×C₄₇	#2929	1	1	yes	characteristic
248	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
249	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
250	D₄₇	—	4	2	no	—
251	C₂×#131	—	2	1	no	—
252	#532	C₂×D₄₇	1	1	yes	characteristic
253	C₄×#41	—	47	1	no	—
254	#482	—	47	2	no	—
255	#477	—	47	1	no	—
256	#476	—	47	1	no	—
257	#460	—	47	1	no	—
258	#459	—	47	1	no	—
259	#449	—	47	2	no	—
260	C₈×Q₈	—	47	1	no	—
261	C₈×Q₈	—	47	1	no	—
262	C₄×SD₁₆	—	47	2	no	—
263	C₄×D₈	—	47	2	no	—
264	#436	—	2	1	no	—
265	#436	C₂×D₄₇	1	2	yes	—
266	C₈×D₄	—	2	1	no	—
267	C₈×D₄	—	47	1	no	—
268	C₈×D₄	—	47	1	no	—
269	C₈×D₄	—	94	1	no	—
270	C₈×D₄	—	94	1	no	—
271	C₈×D₄	C₂×D₄₇	1	2	yes	—
272	#431	—	47	1	no	—
273	#431	—	47	1	no	—
274	#431	—	94	1	no	—
275	#423	C₂×D₄₇	1	1	yes	characteristic
276	#408	—	2	1	no	—
277	C₄×M₁₆	—	47	1	no	—
278	C₂×C₄×C₈	—	94	1	no	—
279	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
280	#335	—	47	2	no	—
281	#334	—	47	2	no	—
282	Q₈⋊C₈	—	47	2	no	—
283	D₄⋊C₈	—	47	2	no	—
284	D₄⋊C₈	—	47	2	no	—
285	D₄⋊C₈	—	47	2	no	—
286	#322	—	47	2	no	—
287	C₈²	—	47	2	no	—
288	C₄₇	#17912	1	1	yes	characteristic, complemented, Sylow
289	C₂×#41	—	2	1	no	—
290	C₂×#41	—	47	1	no	—
291	C₂×SD₁₆	—	47	2	no	—
292	C₂×D₈	—	47	2	no	—
293	#131	—	4	4	no	—
294	C₂×M₁₆	—	2	1	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	94	1	no	—
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	94	1	no	—
299	C₂²×C₈	—	94	1	no	—
300	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
301	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
302	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
303	#127	C₄×D₄₇	1	1	yes	characteristic
304	#124	—	2	1	no	—
305	#121	—	2	1	no	—
306	#121	C₄×D₄₇	1	2	yes	—
307	C₄×Q₈	—	47	1	no	—
308	C₄×Q₈	—	47	1	no	—
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	—	47	1	no	—
311	C₄×D₄	—	47	1	no	—
312	C₄×D₄	—	94	1	no	—
313	C₄×D₄	—	94	1	no	—
314	C₄×D₄	C₂²×D₄₇	1	2	yes	—
315	#117	—	47	1	no	—
316	#117	—	94	1	no	—
317	C₂×C₄²	—	94	1	no	—
318	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
319	#107	—	47	2	no	—
320	#106	—	47	2	no	—
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	—	47	1	no	—
323	C₄⋊C₈	—	47	1	no	—
324	C₄⋊C₈	—	47	1	no	—
325	C₄⋊C₈	—	47	1	no	—
326	C₄⋊C₈	—	94	1	no	—
327	C₄⋊C₈	—	94	1	no	—
328	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
329	#103	—	47	2	no	—
330	#102	—	47	2	no	—
331	#102	—	47	2	no	—
332	#102	—	47	2	no	—
333	C₂²⋊C₈	—	2	2	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	C₂²⋊C₈	—	47	2	no	—
336	C₂²⋊C₈	—	94	1	no	—
337	C₂²⋊C₈	—	94	1	no	—
338	C₂²⋊C₈	—	94	1	no	—
339	#97	—	94	1	no	—
340	C₄×C₈	—	47	2	no	—
341	C₄×C₈	—	47	2	no	—
342	C₄×C₈	—	94	1	no	—
343	C₄×C₈	—	94	1	no	—
344	C₄×C₈	—	94	1	no	—
345	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
346	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
347	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
348	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
349	#41	—	4	2	no	—
350	#41	—	4	2	no	—
351	#41	—	94	2	no	—
352	#41	—	94	2	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	47	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	47	1	no	—
359	C₂×D₄	—	94	1	no	—
360	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	94	1	no	—
363	C₂²×C₄	—	94	1	no	—
364	C₂²×C₄	—	94	1	no	—
365	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
366	C₂²×C₄	#10625350	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
368	SD₁₆	—	94	4	no	—
369	D₈	—	94	4	no	—
370	M₁₆	—	4	4	no	—
371	M₁₆	—	4	2	no	—
372	M₁₆	—	94	4	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	4	1	no	—
376	C₂×C₈	—	4	4	no	—
377	C₂×C₈	—	47	2	no	—
378	C₂×C₈	—	47	2	no	—
379	C₂×C₈	—	94	2	no	—
380	C₂×C₈	—	94	1	no	—
381	C₂×C₈	—	94	1	no	—
382	C₂×C₈	—	188	2	no	—
383	C₂×C₈	—	188	2	no	—
384	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
385	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
386	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
387	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	47	1	no	—
390	C₄⋊C₄	—	47	1	no	—
391	C₄⋊C₄	—	94	1	no	—
392	C₄⋊C₄	—	94	1	no	—
393	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	94	1	no	—
397	C₂²⋊C₄	—	94	1	no	—
398	C₂²⋊C₄	—	94	1	no	—
399	C₄²	—	94	1	no	—
400	C₄²	—	94	1	no	—
401	C₄²	—	94	1	no	—
402	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
403	C₄²	#10625350	1	1	yes	characteristic
404	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
405	C₄²	C₂³×D₄₇	1	1	yes	characteristic
406	C₂³	—	2	2	no	—
407	C₂³	—	94	1	no	—
408	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
409	Q₈	—	4	2	no	—
410	Q₈	—	47	2	no	—
411	Q₈	—	94	1	no	—
412	D₄	—	2	2	no	—
413	D₄	—	2	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	4	no	—
416	D₄	—	4	2	no	—
417	D₄	—	47	2	no	—
418	D₄	—	94	4	no	—
419	D₄	—	94	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	94	4	no	—
429	C₂×C₄	—	94	1	no	—
430	C₂×C₄	—	94	1	no	—
431	C₂×C₄	—	94	1	no	—
432	C₂×C₄	—	188	2	no	—
433	C₂×C₄	—	188	1	no	—
434	C₂×C₄	—	188	1	no	—
435	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
436	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
437	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
438	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
439	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
440	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
441	C₈	—	2	1	no	—
442	C₈	—	2	1	no	—
443	C₈	—	2	1	no	—
444	C₈	—	4	2	no	—
445	C₈	—	94	4	no	—
446	C₈	—	94	2	no	—
447	C₈	—	94	2	no	—
448	C₈	—	188	1	no	—
449	C₈	—	188	1	no	—
450	C₈	#13094050	1	2	yes	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	94	2	no	—
458	C₂²	—	188	1	no	—
459	C₂²	—	188	1	no	—
460	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	4	2	no	—
465	C₄	—	94	2	no	—
466	C₄	—	188	1	no	—
467	C₄	—	188	1	no	—
468	C₄	#15689238	1	2	yes	—
469	C₄	#131×D₄₇	1	1	yes	characteristic
470	C₄	#131×D₄₇	1	1	yes	characteristic
471	C₄	C₂×#13094050	1	1	yes	characteristic
472	C₄	#15689921	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	8	2	no	—
475	C₂	—	188	2	no	—
476	C₂	#20252080	1	1	yes	characteristic
477	C₂	C₄×#13094050	1	1	yes	characteristic
478	C₂	C₂×#15689238	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#2931	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20253442	C₂
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#2931	D₄₇
hypocenter	C₄₇	#17912
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2931

Complements

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

N	H ≅ G/N	type
2. C₈×#10625350	C₂	semidirect
3. #20242264	C₂	semidirect
4. #20242250	C₂	semidirect
5. C₈×#10625335	C₂	semidirect
6. C₈×#10625334	C₂	semidirect
7. #20242179	C₂	semidirect
8. #20241825	C₂	semidirect
9. #20241805	C₂	semidirect
10. C₈×#10625329	C₂	semidirect
11. C₄₇×#2931	C₂	semidirect
194. D₁₈₈	#131	semidirect
200. Dic₉₄	#131	semidirect
236. #2931	D₄₇	semidirect
288. C₄₇	#17912	semidirect

Maximal subgroups

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

subgroup	index
#20253442	2
C₈×#10625350	2
#20242264	2
#20242250	2
C₈×#10625335	2
C₈×#10625334	2
#20242179	2
#20241825	2
#20241805	2
C₈×#10625329	2
C₄₇×#2931	2
#17912	47