Subgroups — #26215101

Order 12032.

894 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689175	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689145	C₂	1	1	yes	maximal, characteristic
3	#20245780	C₂	1	1	yes	maximal, characteristic
4	#20243256	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243254	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243249	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243247	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243247	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243245	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243173	C₂	1	1	yes	maximal, characteristic
12	#20243171	C₂	1	1	yes	maximal, characteristic
13	#20243170	C₂	1	1	yes	maximal, characteristic
14	#20243168	C₂	1	1	yes	maximal, characteristic
15	C₄₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625324	C₂²	1	1	yes	characteristic
17	C₂²×#10625324	C₂²	1	1	yes	characteristic
18	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
19	#15689175	C₄	1	8	yes	complemented
20	#15689145	C₄	1	8	yes	complemented
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×#13093935	C₂²	1	1	yes	characteristic
28	C₂×#13093934	C₂²	1	1	yes	characteristic
29	C₂×#13093934	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
35	#15688990	C₄	1	2	yes	—
36	#15688987	C₄	1	2	yes	—
37	#15688985	C₄	1	2	yes	—
38	#15688982	C₄	1	2	yes	—
39	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
41	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
42	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
43	#15688969	C₂²	1	1	yes	characteristic
44	#15688878	C₂²	1	1	yes	characteristic
45	#15688878	C₂²	1	1	yes	characteristic
46	#15688877	C₂²	1	1	yes	characteristic
47	#15688877	C₂²	1	1	yes	characteristic
48	#15688877	C₂²	1	1	yes	characteristic
49	#15688877	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
51	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
52	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
54	C₄₇×#376	C₂²	1	1	yes	characteristic
55	C₄₇×#336	C₂²	1	1	yes	characteristic
56	C₄₇×#336	C₂²	1	1	yes	characteristic
57	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
60	C₂×#10625324	—	4	1	no	—
61	C₂×#10625324	—	4	1	no	—
62	C₂×#10625324	—	4	1	no	—
63	C₂×#10625324	—	4	1	no	—
64	C₂×#10625324	C₂×C₄	1	4	yes	—
65	C₂×#10625324	C₂×C₄	1	4	yes	—
66	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
70	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
71	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
73	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
74	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
79	C₄²×D₄₇	C₂×C₄	1	4	yes	—
80	C₄²×D₄₇	C₂×C₄	1	4	yes	—
81	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
82	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
83	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
84	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
85	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
86	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
87	#13093935	—	4	1	no	—
88	#13093934	—	4	1	no	—
89	#13093934	—	4	1	no	—
90	C₄×C₄₇⋊C₈	—	4	1	no	—
91	C₈×Dic₄₇	—	4	1	no	—
92	C₈×Dic₄₇	—	4	1	no	—
93	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
94	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
95	C₄₇⋊#95	C₂×C₄	1	2	yes	—
96	C₄₇⋊#95	C₂×C₄	1	2	yes	—
97	C₄₇⋊#95	C₂×C₄	1	2	yes	—
98	C₄₇⋊#95	C₂×C₄	1	2	yes	—
99	C₄₇⋊#95	C₂×C₄	1	2	yes	—
100	C₄₇⋊#95	C₂×C₄	1	2	yes	—
101	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
108	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
109	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
110	#97×C₄₇	—	4	1	no	—
111	C₄×C₈×C₄₇	—	4	1	no	—
112	#95×C₄₇	C₂×C₄	1	2	yes	—
113	#95×C₄₇	C₂×C₄	1	2	yes	—
114	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
120	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
121	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
122	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×D₄₇	—	2	1	no	—
126	C₂×C₄×D₄₇	—	2	1	no	—
127	C₂×C₄×D₄₇	—	2	1	no	—
128	C₂×C₄×D₄₇	—	2	1	no	—
129	C₂×C₄×D₄₇	—	2	4	no	—
130	C₂×C₄×D₄₇	—	4	2	no	—
131	C₂×C₄×D₄₇	C₄²	1	4	yes	—
132	C₂×C₄×D₄₇	C₄²	1	4	yes	—
133	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
134	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₄₇	—	2	1	no	—
136	C₂×C₈×C₄₇	—	2	1	no	—
137	C₂×C₈×C₄₇	—	2	1	no	—
138	C₂×C₈×C₄₇	—	2	1	no	—
139	C₂×C₈×C₄₇	—	2	1	no	—
140	C₂×C₈×C₄₇	—	2	1	no	—
141	C₂×C₈×C₄₇	—	2	1	no	—
142	C₂×C₈×C₄₇	—	2	1	no	—
143	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
147	C₄²×C₄₇	—	2	1	no	—
148	C₄²×C₄₇	—	2	1	no	—
149	C₄²×C₄₇	—	2	1	no	—
150	C₄²×C₄₇	—	2	1	no	—
151	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
152	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
153	(C₂×D₄₇)⋊C₄	—	4	2	no	—
154	(C₂×D₄₇)⋊C₄	—	4	2	no	—
155	Dic₄₇⋊C₄	—	2	4	no	—
156	Dic₄₇⋊C₄	—	2	4	no	—
157	C₄×Dic₄₇	—	2	1	no	—
158	C₄×Dic₄₇	—	2	1	no	—
159	C₄×Dic₄₇	—	2	1	no	—
160	C₄×Dic₄₇	—	2	1	no	—
161	C₄×Dic₄₇	C₄²	1	4	yes	—
162	C₄×Dic₄₇	C₄²	1	4	yes	—
163	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
164	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
165	C₂×C₄₇⋊C₈	—	2	1	no	—
166	C₂×C₄₇⋊C₈	—	2	1	no	—
167	C₂×C₄₇⋊C₈	—	2	1	no	—
168	C₂×C₄₇⋊C₈	—	2	1	no	—
169	C₂×C₄₇⋊C₈	—	2	1	no	—
170	C₂×C₄₇⋊C₈	—	2	1	no	—
171	C₂×C₄₇⋊C₈	—	2	1	no	—
172	C₂×C₄₇⋊C₈	—	2	1	no	—
173	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
174	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
175	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
176	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
177	#10625324	—	4	4	no	—
178	#10625324	—	4	4	no	—
179	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
180	C₂²×D₄₇	—	2	1	no	—
181	C₂²×D₄₇	—	2	1	no	—
182	C₂²×D₄₇	—	2	2	no	—
183	C₂²×D₄₇	—	2	2	no	—
184	C₂²×D₄₇	C₂×C₄²	1	2	yes	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	2	2	no	—
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	2	2	no	—
193	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
194	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
195	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
200	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
201	C₂×Dic₄₇	—	2	1	no	—
202	C₂×Dic₄₇	—	2	1	no	—
203	C₂×Dic₄₇	—	2	2	no	—
204	C₂×Dic₄₇	—	2	2	no	—
205	C₂×Dic₄₇	—	2	2	no	—
206	C₂×Dic₄₇	—	2	2	no	—
207	C₂×Dic₄₇	—	2	2	no	—
208	C₂×Dic₄₇	—	2	2	no	—
209	C₂×Dic₄₇	—	2	2	no	—
210	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
211	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
212	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
213	C₂×Dic₄₇	#131	1	4	yes	—
214	C₄×D₄₇	—	2	2	no	—
215	C₄×D₄₇	—	2	2	no	—
216	C₄×D₄₇	—	2	2	no	—
217	C₄×D₄₇	—	2	2	no	—
218	C₄×D₄₇	—	2	8	no	—
219	C₄×D₄₇	—	4	4	no	—
220	C₈×C₄₇	—	2	2	no	—
221	C₈×C₄₇	—	2	2	no	—
222	C₈×C₄₇	—	2	2	no	—
223	C₈×C₄₇	—	2	2	no	—
224	C₄₇⋊C₈	—	2	2	no	—
225	C₄₇⋊C₈	—	2	2	no	—
226	C₄₇⋊C₈	—	2	2	no	—
227	C₄₇⋊C₈	—	2	2	no	—
228	#20548	—	47	1	no	maximal, Sylow
229	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
230	C₂²×C₄₇	#520	1	1	yes	characteristic
231	C₂²×C₄₇	#520	1	1	yes	characteristic
232	C₂²×C₄₇	C₂×#131	1	2	yes	—
233	C₂²×C₄₇	#568	1	2	yes	—
234	C₂×D₄₇	—	2	2	no	—
235	C₂×D₄₇	—	2	2	no	—
236	C₂×D₄₇	—	2	2	no	—
237	C₂×D₄₇	—	4	2	no	—
238	C₂×D₄₇	—	4	2	no	—
239	C₄×C₄₇	—	2	2	no	—
240	C₄×C₄₇	—	2	2	no	—
241	C₄×C₄₇	—	4	2	no	—
242	C₄×C₄₇	—	4	2	no	—
243	C₄×C₄₇	#518	1	1	yes	characteristic
244	C₄×C₄₇	#519	1	1	yes	characteristic
245	C₄×C₄₇	#520	1	1	yes	characteristic
246	C₄×C₄₇	#520	1	1	yes	characteristic
247	Dic₄₇	—	2	2	no	—
248	Dic₄₇	—	2	2	no	—
249	Dic₄₇	—	4	2	no	—
250	Dic₄₇	—	4	2	no	—
251	Dic₄₇	#405	1	4	yes	—
252	C₂×#431	—	47	1	no	—
253	C₂×#423	—	47	1	no	—
254	#2283	—	47	1	no	—
255	#1770	—	47	1	no	—
256	#1770	—	47	1	no	—
257	C₈×C₄⋊C₄	—	47	1	no	—
258	C₈×C₄⋊C₄	—	47	1	no	—
259	#1768	—	47	1	no	—
260	#1768	—	47	1	no	—
261	#1768	—	47	1	no	—
262	#1768	D₄₇	1	1	yes	characteristic, complemented
263	#1753	—	47	1	no	—
264	#1753	—	47	1	no	—
265	#1753	—	47	1	no	—
266	#1753	—	47	1	no	—
267	C₂×C₄₇	#2274	1	1	yes	characteristic
268	C₂×C₄₇	C₂×#405	1	1	yes	characteristic
269	C₂×C₄₇	#2873	1	1	yes	characteristic
270	C₂×C₄₇	#2993	1	2	yes	—
271	C₂×C₄₇	#2993	1	2	yes	—
272	D₄₇	—	4	2	no	—
273	C₂²×M₁₆	—	47	1	no	—
274	C₂²×M₁₆	—	47	1	no	—
275	C₂²×C₄²	—	47	1	no	—
276	#431	—	47	8	no	—
277	#423	—	47	8	no	—
278	C₂×C₄⋊C₈	—	47	1	no	—
279	C₂×C₄⋊C₈	—	47	1	no	—
280	C₂×C₄⋊C₈	—	47	1	no	—
281	C₂×C₄⋊C₈	—	47	1	no	—
282	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
283	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	—	47	1	no	—
285	C₂×C₂²⋊C₈	—	47	1	no	—
286	C₂×#97	—	47	1	no	—
287	C₂×#97	—	47	1	no	—
288	C₂×#97	—	47	1	no	—
289	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
290	C₂×C₄×C₈	—	47	1	no	—
291	C₂×C₄×C₈	—	47	1	no	—
292	C₂×C₄×C₈	—	47	1	no	—
293	C₂×C₄×C₈	—	47	1	no	—
294	C₂×C₄×C₈	—	47	1	no	—
295	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
296	#383	—	47	2	no	—
297	#382	—	47	2	no	—
298	#381	—	47	2	no	—
299	#380	—	47	2	no	—
300	C₄×C₄⋊C₄	—	47	1	no	—
301	C₄×C₄⋊C₄	—	47	1	no	—
302	C₄×C₂²⋊C₄	—	47	1	no	—
303	C₄×C₂²⋊C₄	—	47	1	no	—
304	#376	—	47	1	no	—
305	#376	C₂×D₄₇	1	1	yes	characteristic
306	#336	—	47	1	no	—
307	#336	—	47	1	no	—
308	#336	—	47	1	no	—
309	#336	—	47	1	no	—
310	#336	—	47	1	no	—
311	#336	—	47	1	no	—
312	#336	C₂×D₄₇	1	1	yes	characteristic
313	#336	C₂×D₄₇	1	1	yes	characteristic
314	C₄₇	#20548	1	1	yes	characteristic, complemented, Sylow
315	C₂³×C₄	—	47	1	no	—
316	C₂³×C₄	—	47	1	no	—
317	C₂³×C₄	—	47	1	no	—
318	C₂×M₁₆	—	47	4	no	—
319	C₂×M₁₆	—	47	4	no	—
320	C₂×M₁₆	—	188	1	no	—
321	C₂×M₁₆	—	188	1	no	—
322	C₂×M₁₆	—	188	1	no	—
323	C₂×M₁₆	—	188	1	no	—
324	C₂²×C₈	—	47	1	no	—
325	C₂²×C₈	—	47	1	no	—
326	C₂²×C₈	—	47	1	no	—
327	C₂²×C₈	—	47	1	no	—
328	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
329	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
330	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
331	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
332	C₂×C₄⋊C₄	—	47	2	no	—
333	C₂×C₄⋊C₄	—	47	2	no	—
334	C₂×C₂²⋊C₄	—	47	2	no	—
335	C₂×C₂²⋊C₄	—	47	2	no	—
336	C₂×C₄²	—	47	1	no	—
337	C₂×C₄²	—	47	1	no	—
338	C₂×C₄²	—	47	1	no	—
339	C₂×C₄²	—	47	4	no	—
340	C₂×C₄²	—	47	4	no	—
341	C₂×C₄²	—	47	1	no	—
342	C₂×C₄²	—	47	1	no	—
343	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
344	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
345	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
346	C₄⋊C₈	—	47	4	no	—
347	C₄⋊C₈	—	47	4	no	—
348	C₄⋊C₈	—	47	4	no	—
349	C₄⋊C₈	—	47	4	no	—
350	C₄⋊C₈	C₄×D₄₇	1	4	yes	—
351	C₄⋊C₈	C₄×D₄₇	1	4	yes	—
352	C₂²⋊C₈	—	47	4	no	—
353	C₂²⋊C₈	—	47	4	no	—
354	#97	—	4	1	no	—
355	#97	—	188	1	no	—
356	#97	—	188	1	no	—
357	#97	—	188	1	no	—
358	C₄×C₈	—	4	1	no	—
359	C₄×C₈	—	47	4	no	—
360	C₄×C₈	—	47	4	no	—
361	C₄×C₈	—	188	1	no	—
362	C₄×C₈	—	188	1	no	—
363	C₄×C₈	—	188	1	no	—
364	#95	—	47	2	no	—
365	#95	—	47	2	no	—
366	#95	—	47	2	no	—
367	#95	—	47	2	no	—
368	#95	—	47	2	no	—
369	#95	—	47	2	no	—
370	#95	C₄×D₄₇	1	2	yes	—
371	#95	C₄×D₄₇	1	2	yes	—
372	C₂⁴	—	47	1	no	—
373	C₂²×C₄	—	47	1	no	—
374	C₂²×C₄	—	47	1	no	—
375	C₂²×C₄	—	47	1	no	—
376	C₂²×C₄	—	47	4	no	—
377	C₂²×C₄	—	47	2	no	—
378	C₂²×C₄	—	47	2	no	—
379	C₂²×C₄	—	47	4	no	—
380	C₂²×C₄	—	47	2	no	—
381	C₂²×C₄	—	47	2	no	—
382	C₂²×C₄	—	94	4	no	—
383	C₂²×C₄	—	94	1	no	—
384	C₂²×C₄	—	94	1	no	—
385	C₂²×C₄	—	94	1	no	—
386	C₂²×C₄	—	94	1	no	—
387	C₂²×C₄	—	188	2	no	—
388	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
389	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
390	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
391	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
392	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
393	M₁₆	—	188	4	no	—
394	M₁₆	—	188	4	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	47	2	no	—
404	C₂×C₈	—	47	2	no	—
405	C₂×C₈	—	47	2	no	—
406	C₂×C₈	—	47	2	no	—
407	C₂×C₈	—	94	1	no	—
408	C₂×C₈	—	94	1	no	—
409	C₂×C₈	—	94	1	no	—
410	C₂×C₈	—	94	1	no	—
411	C₂×C₈	—	94	1	no	—
412	C₂×C₈	—	94	1	no	—
413	C₂×C₈	—	94	1	no	—
414	C₂×C₈	—	94	1	no	—
415	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
416	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
417	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
418	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
419	C₄⋊C₄	—	94	4	no	—
420	C₄⋊C₄	—	94	4	no	—
421	C₂²⋊C₄	—	188	2	no	—
422	C₂²⋊C₄	—	188	2	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	47	4	no	—
428	C₄²	—	47	4	no	—
429	C₄²	—	47	2	no	—
430	C₄²	—	47	2	no	—
431	C₄²	—	94	1	no	—
432	C₄²	—	94	1	no	—
433	C₄²	—	94	1	no	—
434	C₄²	—	94	1	no	—
435	C₄²	C₂×C₄×D₄₇	1	2	yes	—
436	C₄²	C₂×C₄×D₄₇	1	2	yes	—
437	C₂³	—	47	2	no	—
438	C₂³	—	94	1	no	—
439	C₂³	—	94	1	no	—
440	C₂³	—	94	2	no	—
441	C₂³	—	94	2	no	—
442	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	47	2	no	—
452	C₂×C₄	—	47	4	no	—
453	C₂×C₄	—	47	2	no	—
454	C₂×C₄	—	47	2	no	—
455	C₂×C₄	—	94	8	no	—
456	C₂×C₄	—	94	1	no	—
457	C₂×C₄	—	94	1	no	—
458	C₂×C₄	—	94	2	no	—
459	C₂×C₄	—	94	2	no	—
460	C₂×C₄	—	94	2	no	—
461	C₂×C₄	—	94	2	no	—
462	C₂×C₄	—	94	2	no	—
463	C₂×C₄	—	94	2	no	—
464	C₂×C₄	—	94	2	no	—
465	C₂×C₄	—	94	2	no	—
466	C₂×C₄	—	94	2	no	—
467	C₂×C₄	—	94	2	no	—
468	C₂×C₄	—	94	2	no	—
469	C₂×C₄	—	188	4	no	—
470	C₂×C₄	C₄²×D₄₇	1	2	yes	—
471	C₂×C₄	C₄²×D₄₇	1	2	yes	—
472	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
473	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
474	C₂×C₄	#13094069	1	1	yes	characteristic
475	C₂×C₄	#13094070	1	1	yes	characteristic
476	C₂×C₄	#13094071	1	1	yes	characteristic
477	C₂×C₄	#13094072	1	1	yes	characteristic
478	C₈	—	2	2	no	—
479	C₈	—	2	2	no	—
480	C₈	—	2	2	no	—
481	C₈	—	2	2	no	—
482	C₈	—	94	2	no	—
483	C₈	—	94	2	no	—
484	C₈	—	94	2	no	—
485	C₈	—	94	2	no	—
486	C₂²	—	94	2	no	—
487	C₂²	—	94	2	no	—
488	C₂²	—	94	2	no	—
489	C₂²	—	188	2	no	—
490	C₂²	—	188	2	no	—
491	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
492	C₂²	#15689603	1	1	yes	characteristic
493	C₂²	#15689604	1	1	yes	characteristic
494	C₂²	#131×D₄₇	1	2	yes	—
495	C₂²	#15689888	1	2	yes	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	47	4	no	—
501	C₄	—	94	2	no	—
502	C₄	—	94	2	no	—
503	C₄	—	188	2	no	—
504	C₄	—	188	2	no	—
505	C₄	#15689595	1	1	yes	characteristic
506	C₄	#15689599	1	1	yes	characteristic
507	C₄	#15689602	1	1	yes	characteristic
508	C₄	#15689605	1	1	yes	characteristic
509	C₂	—	188	2	no	—
510	C₂	#20245742	1	1	yes	characteristic
511	C₂	#405×D₄₇	1	1	yes	characteristic
512	C₂	#20251804	1	1	yes	characteristic
513	C₂	#20252531	1	2	yes	—
514	C₂	#20252535	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄₇×#1768	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1768	D₄₇
hypocenter	C₄₇	#20548
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1768

Complements

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

N	H ≅ G/N	type
4. #20243256	C₂	semidirect
5. #20243254	C₂	semidirect
6. C₈×Dic₄₇⋊C₄	C₂	semidirect
7. #20243249	C₂	semidirect
8. #20243247	C₂	semidirect
9. #20243247	C₂	semidirect
10. #20243245	C₂	semidirect
15. C₄₇×#1768	C₂	semidirect
19. #15689175	C₄	semidirect
20. #15689145	C₄	semidirect
262. #1768	D₄₇	semidirect
314. C₄₇	#20548	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689175	2
C₂×#15689145	2
#20245780	2
#20243256	2
#20243254	2
C₈×Dic₄₇⋊C₄	2
#20243249	2
#20243247	2
#20243245	2
#20243173	2
#20243171	2
#20243170	2
#20243168	2
C₄₇×#1768	2
#20548	47