Subgroups — #26216434

Order 12032.

914 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689148	C₂	1	2	yes	maximal
2	C₄×#13093981	C₂	1	1	yes	maximal, characteristic
3	#20243507	C₂	1	2	yes	maximal, complemented
4	#20243506	C₂	1	2	yes	maximal, complemented
5	#20243505	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243503	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243503	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243083	C₂	1	2	yes	maximal
9	#20243080	C₂	1	1	yes	maximal, characteristic
10	#336×D₄₇	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	2	yes	—
13	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
14	C₂×#13093981	C₂²	1	1	yes	characteristic
15	C₂×#13093981	C₂²	1	1	yes	characteristic
16	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
17	#15689148	—	2	8	no	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
19	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
20	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
21	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
22	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
23	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
24	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
25	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
26	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
27	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
28	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
29	#15688969	C₂²	1	1	yes	characteristic
30	#15688969	C₂²	1	1	yes	characteristic
31	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
32	#15688878	C₂²	1	1	yes	characteristic
33	#15688878	C₂²	1	1	yes	characteristic
34	#15688878	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	#15688877	C₂²	1	2	yes	—
38	#15688877	C₂²	1	2	yes	—
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
40	C₄³×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#336	C₂²	1	1	yes	characteristic
42	C₄₇×#336	C₂²	1	1	yes	characteristic
43	C₄₇×#336	C₂²	1	2	yes	—
44	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
47	C₂×#10625324	—	2	4	no	—
48	C₂×#10625324	—	2	4	no	—
49	C₂×#10625324	—	2	4	no	—
50	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
51	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
52	C₂×C₈×D₄₇	—	2	4	no	—
53	C₂×C₈×D₄₇	—	2	4	no	—
54	C₂×C₈×D₄₇	—	2	4	no	—
55	#13093981	—	2	4	no	—
56	#13093981	D₄	1	4	yes	—
57	#13093981	Q₈	1	4	yes	—
58	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
74	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
75	C₄²×D₄₇	—	2	4	no	—
76	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
77	Dic₄₇⋊C₈	—	2	4	no	—
78	Dic₄₇⋊C₈	—	2	4	no	—
79	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
80	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
81	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
82	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
83	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
84	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
85	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
86	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
88	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
89	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₄₇	—	2	4	no	—
97	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₄₇	—	2	2	no	—
113	C₂×C₄×D₄₇	—	2	2	no	—
114	C₂×C₄×D₄₇	—	2	2	no	—
115	C₂×C₄×D₄₇	—	2	2	no	—
116	C₂×C₄×D₄₇	—	4	1	no	—
117	C₂×C₄×D₄₇	—	4	1	no	—
118	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
119	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
120	C₂×C₄×D₄₇	#41	1	4	yes	—
121	C₂×C₄×D₄₇	#41	1	4	yes	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	—	2	2	no	—
129	C₄²×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	—	2	2	no	—
131	C₄²×C₄₇	—	2	2	no	—
132	C₄²×C₄₇	—	4	1	no	—
133	C₄²×C₄₇	—	4	1	no	—
134	C₄²×C₄₇	C₂×D₄	1	2	yes	—
135	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
136	(C₂×D₄₇)⋊C₄	—	2	2	no	—
137	(C₂×D₄₇)⋊C₄	—	2	2	no	—
138	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	4	yes	—
139	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	4	yes	—
140	Dic₄₇⋊C₄	—	2	2	no	—
141	Dic₄₇⋊C₄	—	2	2	no	—
142	Dic₄₇⋊C₄	C₄⋊C₄	1	4	yes	—
143	Dic₄₇⋊C₄	C₄⋊C₄	1	4	yes	—
144	C₄×Dic₄₇	—	2	2	no	—
145	C₄×Dic₄₇	—	2	2	no	—
146	C₄×Dic₄₇	—	2	2	no	—
147	C₄×Dic₄₇	—	2	2	no	—
148	C₄×Dic₄₇	—	2	2	no	—
149	C₄×Dic₄₇	—	2	2	no	—
150	C₄×Dic₄₇	—	4	1	no	—
151	C₄×Dic₄₇	—	4	1	no	—
152	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
153	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	—	2	2	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂×C₄₇⋊C₈	—	2	2	no	—
159	C₂×C₄₇⋊C₈	—	2	2	no	—
160	#10625324	—	4	8	no	—
161	C₈×D₄₇	—	4	8	no	—
162	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
163	C₂²×D₄₇	—	2	1	no	—
164	C₂²×D₄₇	—	2	1	no	—
165	C₂²×D₄₇	—	2	1	no	—
166	C₂²×D₄₇	—	2	1	no	—
167	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
168	C₂²×D₄₇	#117	1	2	yes	—
169	C₂²×D₄₇	#117	1	2	yes	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	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	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
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	C₂×C₄⋊C₄	1	2	yes	—
185	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
186	C₂×C₄×C₄₇	#131	1	2	yes	—
187	C₂×C₄×C₄₇	#131	1	2	yes	—
188	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
191	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
192	C₂×Dic₄₇	—	2	1	no	—
193	C₂×Dic₄₇	—	2	1	no	—
194	C₂×Dic₄₇	—	2	1	no	—
195	C₂×Dic₄₇	—	2	1	no	—
196	C₂×Dic₄₇	—	2	1	no	—
197	C₂×Dic₄₇	—	2	1	no	—
198	C₂×Dic₄₇	—	2	1	no	—
199	C₂×Dic₄₇	—	2	1	no	—
200	C₂×Dic₄₇	—	2	1	no	—
201	C₂×Dic₄₇	—	2	1	no	—
202	C₂×Dic₄₇	—	2	1	no	—
203	C₂×Dic₄₇	—	2	1	no	—
204	C₂×Dic₄₇	—	2	1	no	—
205	C₂×Dic₄₇	—	2	1	no	—
206	C₂×Dic₄₇	—	2	1	no	—
207	C₂×Dic₄₇	—	2	1	no	—
208	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
209	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
210	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
211	C₂×Dic₄₇	#117	1	2	yes	—
212	C₂×Dic₄₇	#117	1	2	yes	—
213	C₄×D₄₇	—	4	4	no	—
214	C₄×D₄₇	—	4	4	no	—
215	C₄×D₄₇	#124	1	8	yes	—
216	C₄×D₄₇	#125	1	8	yes	—
217	C₈×C₄₇	—	4	2	no	—
218	C₈×C₄₇	—	4	2	no	—
219	C₄₇⋊C₈	—	4	2	no	—
220	C₄₇⋊C₈	—	4	2	no	—
221	#20754	—	47	1	no	maximal, Sylow
222	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
223	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
224	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
225	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
226	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
227	C₂²×C₄₇	#568	1	1	yes	characteristic
228	C₂²×C₄₇	#568	1	1	yes	characteristic
229	C₂×D₄₇	—	2	2	no	—
230	C₂×D₄₇	—	2	2	no	—
231	C₂×D₄₇	—	2	2	no	—
232	C₂×D₄₇	—	2	2	no	—
233	C₂×D₄₇	—	2	2	no	—
234	C₂×D₄₇	—	2	2	no	—
235	C₂×D₄₇	#382	1	4	yes	—
236	C₄×C₄₇	—	2	2	no	—
237	C₄×C₄₇	—	2	2	no	—
238	C₄×C₄₇	—	2	2	no	—
239	C₄×C₄₇	—	2	2	no	—
240	C₄×C₄₇	—	4	1	no	—
241	C₄×C₄₇	—	4	1	no	—
242	C₄×C₄₇	C₂×#124	1	2	yes	—
243	C₄×C₄₇	C₂×#125	1	2	yes	—
244	Dic₄₇	—	2	2	no	—
245	Dic₄₇	—	2	2	no	—
246	Dic₄₇	—	4	1	no	—
247	Dic₄₇	—	4	1	no	—
248	Dic₄₇	—	4	1	no	—
249	Dic₄₇	—	4	1	no	—
250	Dic₄₇	#382	1	4	yes	—
251	C₂×#424	—	47	2	no	—
252	C₄×#117	—	47	1	no	—
253	#1832	—	47	2	no	—
254	#1832	—	47	2	no	—
255	#1831	—	47	1	no	—
256	#1831	—	47	1	no	—
257	#1831	—	47	1	no	—
258	#1831	D₄₇	1	1	yes	characteristic, complemented
259	#1729	—	47	2	no	—
260	#1728	—	47	1	no	—
261	C₂×#336	—	47	1	no	—
262	C₂×C₄₇	C₂×#382	1	1	yes	characteristic
263	C₂×C₄₇	#2906	1	1	yes	characteristic
264	C₂×C₄₇	#2906	1	1	yes	characteristic
265	C₂×C₄₇	#2922	1	1	yes	characteristic
266	C₂×C₄₇	#2923	1	1	yes	characteristic
267	C₂×C₄₇	#2924	1	1	yes	characteristic
268	C₂×C₄₇	#2924	1	1	yes	characteristic
269	D₄₇	—	2	4	no	—
270	C₂²×M₁₆	—	47	2	no	—
271	C₂³×C₈	—	47	2	no	—
272	C₂×#117	—	47	1	no	—
273	C₂×#117	—	47	1	no	—
274	C₂²×C₄²	—	47	1	no	—
275	#424	—	94	8	no	—
276	C₂×C₄⋊C₈	—	47	2	no	—
277	C₂×C₄⋊C₈	—	47	2	no	—
278	C₂×C₄⋊C₈	—	47	2	no	—
279	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
280	C₄×C₄⋊C₄	—	47	1	no	—
281	C₄×C₄⋊C₄	—	47	1	no	—
282	C₄×C₄⋊C₄	—	47	1	no	—
283	C₄×C₄⋊C₄	—	47	1	no	—
284	C₄×C₂²⋊C₄	—	47	1	no	—
285	C₄×C₂²⋊C₄	—	47	1	no	—
286	C₄×C₂²⋊C₄	—	47	1	no	—
287	C₄×C₂²⋊C₄	—	47	1	no	—
288	#376	—	47	1	no	—
289	#376	—	47	1	no	—
290	C₄³	—	47	1	no	—
291	C₄³	C₂×D₄₇	1	1	yes	characteristic
292	#336	—	47	2	no	—
293	#336	—	47	2	no	—
294	#336	—	47	2	no	—
295	#336	—	47	2	no	—
296	#336	—	47	1	no	—
297	#336	—	47	1	no	—
298	#336	—	47	2	no	—
299	#336	C₂×D₄₇	1	1	yes	characteristic
300	#336	C₂×D₄₇	1	1	yes	characteristic
301	#336	C₂×D₄₇	1	2	yes	—
302	C₄₇	#20754	1	1	yes	characteristic, complemented, Sylow
303	C₂³×C₄	—	47	1	no	—
304	C₂³×C₄	—	47	1	no	—
305	C₂³×C₄	—	47	1	no	—
306	C₂×M₁₆	—	94	4	no	—
307	C₂×M₁₆	—	94	4	no	—
308	C₂×M₁₆	—	94	4	no	—
309	C₂²×C₈	—	47	2	no	—
310	C₂²×C₈	—	47	2	no	—
311	C₂²×C₈	—	94	4	no	—
312	C₂²×C₈	—	94	4	no	—
313	C₂²×C₈	—	94	4	no	—
314	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
315	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
316	#117	—	47	4	no	—
317	#117	—	47	4	no	—
318	#117	—	94	4	no	—
319	C₂×C₄⋊C₄	—	47	1	no	—
320	C₂×C₄⋊C₄	—	47	1	no	—
321	C₂×C₄⋊C₄	—	47	1	no	—
322	C₂×C₄⋊C₄	—	47	1	no	—
323	C₂×C₂²⋊C₄	—	47	1	no	—
324	C₂×C₂²⋊C₄	—	47	1	no	—
325	C₂×C₂²⋊C₄	—	47	1	no	—
326	C₂×C₂²⋊C₄	—	47	1	no	—
327	C₂×C₄²	—	47	1	no	—
328	C₂×C₄²	—	47	1	no	—
329	C₂×C₄²	—	47	1	no	—
330	C₂×C₄²	—	47	1	no	—
331	C₂×C₄²	—	47	1	no	—
332	C₂×C₄²	—	47	1	no	—
333	C₂×C₄²	—	47	1	no	—
334	C₂×C₄²	—	47	1	no	—
335	C₂×C₄²	—	47	1	no	—
336	C₂×C₄²	—	94	4	no	—
337	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
338	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
339	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
340	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
341	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
342	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
343	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
344	C₄⋊C₈	—	2	4	no	—
345	C₄⋊C₈	—	94	4	no	—
346	C₄⋊C₈	—	94	4	no	—
347	C₄⋊C₈	—	94	4	no	—
348	#95	—	47	1	no	—
349	#95	—	47	1	no	—
350	#95	—	47	1	no	—
351	#95	—	47	1	no	—
352	#95	—	47	1	no	—
353	#95	—	47	1	no	—
354	#95	—	47	1	no	—
355	#95	—	47	1	no	—
356	C₂⁴	—	47	1	no	—
357	C₂²×C₄	—	47	1	no	—
358	C₂²×C₄	—	47	2	no	—
359	C₂²×C₄	—	47	2	no	—
360	C₂²×C₄	—	47	4	no	—
361	C₂²×C₄	—	47	4	no	—
362	C₂²×C₄	—	47	1	no	—
363	C₂²×C₄	—	47	1	no	—
364	C₂²×C₄	—	47	1	no	—
365	C₂²×C₄	—	47	1	no	—
366	C₂²×C₄	—	47	1	no	—
367	C₂²×C₄	—	47	1	no	—
368	C₂²×C₄	—	94	2	no	—
369	C₂²×C₄	—	94	2	no	—
370	C₂²×C₄	—	94	2	no	—
371	C₂²×C₄	—	94	2	no	—
372	C₂²×C₄	—	188	1	no	—
373	C₂²×C₄	—	188	1	no	—
374	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
378	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
379	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
380	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
381	M₁₆	—	188	8	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	94	2	no	—
389	C₂×C₈	—	94	2	no	—
390	C₂×C₈	—	94	2	no	—
391	C₂×C₈	—	94	2	no	—
392	C₂×C₈	—	94	2	no	—
393	C₂×C₈	—	94	2	no	—
394	C₂×C₈	—	188	8	no	—
395	C₄⋊C₄	—	47	4	no	—
396	C₄⋊C₄	—	47	4	no	—
397	C₄⋊C₄	—	94	2	no	—
398	C₄⋊C₄	—	94	2	no	—
399	C₂²⋊C₄	—	47	4	no	—
400	C₂²⋊C₄	—	47	4	no	—
401	C₂²⋊C₄	—	94	2	no	—
402	C₂²⋊C₄	—	94	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	4	1	no	—
408	C₄²	—	4	1	no	—
409	C₄²	—	47	2	no	—
410	C₄²	—	47	2	no	—
411	C₄²	—	94	2	no	—
412	C₄²	—	94	2	no	—
413	C₄²	—	94	2	no	—
414	C₄²	—	94	2	no	—
415	C₄²	—	94	2	no	—
416	C₄²	—	94	2	no	—
417	C₄²	—	188	1	no	—
418	C₄²	—	188	1	no	—
419	C₄²	D₄×D₄₇	1	2	yes	—
420	C₄²	Q₈×D₄₇	1	2	yes	—
421	C₂³	—	47	2	no	—
422	C₂³	—	47	2	no	—
423	C₂³	—	47	2	no	—
424	C₂³	—	94	1	no	—
425	C₂³	—	94	1	no	—
426	C₂³	—	94	1	no	—
427	C₂³	—	94	1	no	—
428	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	47	2	no	—
444	C₂×C₄	—	47	2	no	—
445	C₂×C₄	—	47	2	no	—
446	C₂×C₄	—	47	8	no	—
447	C₂×C₄	—	47	8	no	—
448	C₂×C₄	—	47	2	no	—
449	C₂×C₄	—	47	2	no	—
450	C₂×C₄	—	94	1	no	—
451	C₂×C₄	—	94	1	no	—
452	C₂×C₄	—	94	1	no	—
453	C₂×C₄	—	94	1	no	—
454	C₂×C₄	—	94	1	no	—
455	C₂×C₄	—	94	1	no	—
456	C₂×C₄	—	94	1	no	—
457	C₂×C₄	—	94	1	no	—
458	C₂×C₄	—	94	1	no	—
459	C₂×C₄	—	94	1	no	—
460	C₂×C₄	—	94	1	no	—
461	C₂×C₄	—	94	1	no	—
462	C₂×C₄	—	94	1	no	—
463	C₂×C₄	—	94	1	no	—
464	C₂×C₄	—	94	1	no	—
465	C₂×C₄	—	94	1	no	—
466	C₂×C₄	—	188	4	no	—
467	C₂×C₄	—	188	4	no	—
468	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
469	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
470	C₂×C₄	#13094030	1	2	yes	—
471	C₂×C₄	#13094032	1	2	yes	—
472	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
473	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
474	C₂×C₄	#41×D₄₇	1	2	yes	—
475	C₂×C₄	#41×D₄₇	1	2	yes	—
476	C₈	—	4	2	no	—
477	C₈	—	4	2	no	—
478	C₈	—	188	2	no	—
479	C₈	—	188	2	no	—
480	C₂²	—	47	4	no	—
481	C₂²	—	94	2	no	—
482	C₂²	—	94	2	no	—
483	C₂²	—	94	2	no	—
484	C₂²	—	94	2	no	—
485	C₂²	—	94	2	no	—
486	C₂²	—	94	2	no	—
487	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
488	C₂²	#117×D₄₇	1	1	yes	characteristic
489	C₂²	#117×D₄₇	1	1	yes	characteristic
490	C₂²	C₂×#13094030	1	1	yes	characteristic
491	C₂²	C₂×#13094032	1	1	yes	characteristic
492	C₂²	#15689889	1	1	yes	characteristic
493	C₂²	#15689889	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	4	1	no	—
499	C₄	—	4	1	no	—
500	C₄	—	47	4	no	—
501	C₄	—	94	2	no	—
502	C₄	—	94	2	no	—
503	C₄	—	188	1	no	—
504	C₄	—	188	1	no	—
505	C₄	—	188	1	no	—
506	C₄	—	188	1	no	—
507	C₄	#124×D₄₇	1	2	yes	—
508	C₄	#125×D₄₇	1	2	yes	—
509	C₂	—	94	4	no	—
510	C₂	#382×D₄₇	1	1	yes	characteristic
511	C₂	#20251953	1	1	yes	characteristic
512	C₂	#20251957	1	1	yes	characteristic
513	C₂	#20252027	1	1	yes	characteristic
514	C₂	#20252034	1	1	yes	characteristic
515	C₂	#20252041	1	1	yes	characteristic
516	C₂	#20252047	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1831	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1831	D₄₇
hypocenter	C₄₇	#20754
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1831

Complements

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

N	H ≅ G/N	type
3. #20243507	C₂	semidirect
4. #20243506	C₂	semidirect
5. #20243505	C₂	semidirect
6. #20243503	C₂	semidirect
7. #20243503	C₂	semidirect
11. C₄₇×#1831	C₂	semidirect
258. #1831	D₄₇	semidirect
302. C₄₇	#20754	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689148	2
C₄×#13093981	2
#20243507	2
#20243506	2
#20243505	2
#20243503	2
#20243083	2
#20243080	2
#336×D₄₇	2
C₄₇×#1831	2
#20754	47