Subgroups — #26233660

Order 12032.

864 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13093983	C₂	1	1	yes	maximal, characteristic
2	#20243946	C₂	1	2	yes	maximal, complemented
3	#20243944	C₂	1	2	yes	maximal, complemented
4	#20243566	C₂	1	2	yes	maximal
5	#20243530	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243503	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243456	C₂	1	1	yes	maximal, characteristic
8	#20243236	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal
10	#20243132	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic
12	C₂×#13093983	C₄	1	1	yes	characteristic
13	C₂×#13093983	C₄	1	1	yes	characteristic
14	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
15	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
16	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
18	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
19	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
20	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
21	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
23	C₄×C₂²⋊Dic₄₇	C₄	1	1	yes	characteristic
24	C₄×C₂²⋊Dic₄₇	C₄	1	1	yes	characteristic
25	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
27	#15688969	C₄	1	1	yes	characteristic
28	#15688969	C₄	1	1	yes	characteristic
29	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
30	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
31	#15688878	C₂²	1	1	yes	characteristic
32	#15688878	C₂²	1	1	yes	characteristic
33	#15688878	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	#15688877	C₂²	1	2	yes	—
38	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
39	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#336	C₂²	1	1	yes	characteristic
41	C₄₇×#336	C₂²	1	1	yes	characteristic
42	C₄₇×#336	C₂²	1	2	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	#13093983	—	2	4	no	—
46	#13093983	C₈	1	8	yes	complemented
47	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
64	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
67	Dic₄₇⋊C₈	—	2	4	no	—
68	Dic₄₇⋊C₈	—	4	2	no	—
69	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
70	C₈×Dic₄₇	—	2	4	no	—
71	C₈×Dic₄₇	—	4	2	no	—
72	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
73	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
74	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
75	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
76	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
77	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
78	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
79	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
80	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₇	—	2	4	no	—
84	C₂²×C₈×C₄₇	—	2	4	no	—
85	C₂²×C₈×C₄₇	—	4	2	no	—
86	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
87	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
88	C₂×C₄²×C₄₇	—	2	4	no	—
89	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
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	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	4	1	no	—
102	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	#41	1	4	yes	—
109	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
110	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₄₇	—	2	2	no	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	4	8	no	—
124	C₂×C₈×C₄₇	#41	1	4	yes	—
125	C₄²×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	—	2	2	no	—
129	C₂²⋊Dic₄₇	—	2	2	no	—
130	C₂²⋊Dic₄₇	C₂×C₈	1	4	yes	—
131	C₂²⋊Dic₄₇	C₂×C₈	1	4	yes	—
132	C₂²⋊Dic₄₇	M₁₆	1	4	yes	—
133	C₄⋊Dic₄₇	—	2	2	no	—
134	C₄⋊Dic₄₇	—	2	2	no	—
135	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	complemented
136	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	complemented
137	C₄×Dic₄₇	—	2	2	no	—
138	C₄×Dic₄₇	—	2	2	no	—
139	C₄×Dic₄₇	—	2	2	no	—
140	C₄×Dic₄₇	—	2	2	no	—
141	C₄×Dic₄₇	—	2	1	no	—
142	C₄×Dic₄₇	—	2	1	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	2	1	no	—
145	C₄×Dic₄₇	—	2	2	no	—
146	C₄×Dic₄₇	—	2	2	no	—
147	C₄×Dic₄₇	—	4	1	no	—
148	C₄×Dic₄₇	—	4	1	no	—
149	C₄×Dic₄₇	C₂×C₈	1	4	yes	complemented
150	C₄×Dic₄₇	C₂×C₈	1	4	yes	complemented
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	—	2	2	no	—
157	C₂³×C₄₇	—	2	1	no	—
158	C₂³×C₄₇	—	2	1	no	—
159	C₂³×C₄₇	—	2	1	no	—
160	C₂³×C₄₇	—	2	1	no	—
161	C₂³×C₄₇	#117	1	2	yes	—
162	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
163	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
164	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
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	8	no	—
174	C₂×C₄×C₄₇	—	2	4	no	—
175	C₂×C₄×C₄₇	—	2	4	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	—	4	4	no	—
180	C₂×C₄×C₄₇	#117	1	2	yes	—
181	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
182	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
183	C₂×C₄×C₄₇	#131	1	2	yes	—
184	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
185	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
186	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
188	C₂×Dic₄₇	—	2	1	no	—
189	C₂×Dic₄₇	—	2	1	no	—
190	C₂×Dic₄₇	—	2	1	no	—
191	C₂×Dic₄₇	—	2	1	no	—
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	C₂²×C₈	1	2	yes	—
207	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
208	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
209	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
210	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
211	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
212	C₈×C₄₇	—	2	4	no	—
213	C₈×C₄₇	—	4	2	no	—
214	C₄₇⋊C₈	—	4	2	no	—
215	C₄₇⋊C₈	—	4	2	no	—
216	#22589	—	47	1	no	maximal, Sylow
217	C₂²×C₄₇	—	2	2	no	—
218	C₂²×C₄₇	—	2	2	no	—
219	C₂²×C₄₇	—	2	2	no	—
220	C₂²×C₄₇	—	2	2	no	—
221	C₂²×C₄₇	—	2	2	no	—
222	C₂²×C₄₇	—	2	2	no	—
223	C₂²×C₄₇	#431	1	4	yes	—
224	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
225	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
226	C₂²×C₄₇	#520	1	1	yes	characteristic
227	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
228	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
229	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
230	C₂²×C₄₇	#568	1	1	yes	characteristic
231	C₄×C₄₇	—	2	2	no	—
232	C₄×C₄₇	—	2	2	no	—
233	C₄×C₄₇	—	2	2	no	—
234	C₄×C₄₇	—	2	2	no	—
235	C₄×C₄₇	—	4	1	no	—
236	C₄×C₄₇	#551	1	2	yes	—
237	C₄×C₄₇	#552	1	2	yes	—
238	Dic₄₇	—	2	2	no	—
239	Dic₄₇	—	2	2	no	—
240	Dic₄₇	—	2	2	no	—
241	Dic₄₇	—	2	2	no	—
242	Dic₄₇	—	2	2	no	—
243	Dic₄₇	—	2	2	no	—
244	Dic₄₇	—	4	1	no	—
245	Dic₄₇	—	4	1	no	—
246	C₄×#117	—	47	1	no	—
247	#1916	—	47	2	no	—
248	#1916	—	47	2	no	—
249	#1850	—	47	2	no	—
250	#1839	—	47	1	no	—
251	#1831	—	47	1	no	—
252	#1817	—	47	1	no	—
253	C₄×C₄⋊C₈	—	47	1	no	—
254	C₈×C₂²⋊C₄	—	47	2	no	—
255	#1744	—	47	1	no	—
256	C₂×#336	D₄₇	1	1	yes	characteristic
257	C₂×C₄₇	—	2	4	no	—
258	C₂×C₄₇	#2343	1	1	yes	characteristic
259	C₂×C₄₇	C₂×#431	1	1	yes	characteristic
260	C₂×C₄₇	#2924	1	1	yes	characteristic
261	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
262	C₂×C₄₇	#2970	1	1	yes	characteristic
263	C₂×C₄₇	#2988	1	1	yes	characteristic
264	C₂×C₄₇	#2990	1	1	yes	characteristic
265	C₂³×C₈	C₂×D₄₇	1	2	yes	—
266	C₂×#117	—	47	1	no	—
267	C₂×#117	—	47	1	no	—
268	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
269	C₂×C₄⋊C₈	—	47	2	no	—
270	C₂×C₄⋊C₈	—	47	2	no	—
271	C₂×C₂²⋊C₈	—	47	2	no	—
272	C₂×C₄×C₈	—	47	2	no	—
273	C₂×C₄×C₈	—	47	2	no	—
274	C₄×C₄⋊C₄	—	47	1	no	—
275	C₄×C₄⋊C₄	—	47	1	no	—
276	C₄×C₄⋊C₄	—	47	1	no	—
277	C₄×C₄⋊C₄	—	47	1	no	—
278	C₄×C₂²⋊C₄	—	47	1	no	—
279	C₄×C₂²⋊C₄	—	47	1	no	—
280	C₄×C₂²⋊C₄	—	47	1	no	—
281	C₄×C₂²⋊C₄	—	47	1	no	—
282	#376	—	47	1	no	—
283	#376	—	47	1	no	—
284	C₄³	—	47	1	no	—
285	C₄³	—	47	1	no	—
286	#336	—	47	2	no	—
287	#336	—	47	2	no	—
288	#336	—	47	2	no	—
289	#336	—	47	2	no	—
290	#336	—	47	1	no	—
291	#336	—	47	1	no	—
292	#336	—	47	2	no	—
293	#336	C₂×D₄₇	1	1	yes	characteristic
294	#336	C₂×D₄₇	1	2	yes	—
295	#336	C₂×D₄₇	1	1	yes	characteristic
296	C₄₇	#22589	1	1	yes	characteristic, complemented, Sylow
297	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
298	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
299	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
300	C₂²×C₈	—	2	4	no	—
301	C₂²×C₈	—	2	4	no	—
302	C₂²×C₈	—	4	2	no	—
303	C₂²×C₈	—	47	2	no	—
304	C₂²×C₈	—	47	2	no	—
305	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
306	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
307	#117	—	47	8	no	—
308	#117	—	94	4	no	—
309	C₂×C₄⋊C₄	—	47	1	no	—
310	C₂×C₄⋊C₄	—	47	1	no	—
311	C₂×C₄⋊C₄	—	47	1	no	—
312	C₂×C₄⋊C₄	—	47	1	no	—
313	C₂×C₂²⋊C₄	—	47	1	no	—
314	C₂×C₂²⋊C₄	—	47	1	no	—
315	C₂×C₂²⋊C₄	—	47	1	no	—
316	C₂×C₂²⋊C₄	—	47	1	no	—
317	C₂×C₄²	—	2	4	no	—
318	C₂×C₄²	—	47	1	no	—
319	C₂×C₄²	—	47	1	no	—
320	C₂×C₄²	—	47	1	no	—
321	C₂×C₄²	—	47	1	no	—
322	C₂×C₄²	—	47	1	no	—
323	C₂×C₄²	—	47	1	no	—
324	C₂×C₄²	—	47	1	no	—
325	C₂×C₄²	—	47	1	no	—
326	C₂×C₄²	—	47	1	no	—
327	C₂×C₄²	—	47	1	no	—
328	C₂×C₄²	—	47	1	no	—
329	C₂×C₄²	—	47	1	no	—
330	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
331	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
332	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
333	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
334	C₄⋊C₈	—	94	4	no	—
335	C₄⋊C₈	—	188	2	no	—
336	C₂²⋊C₈	—	94	4	no	—
337	C₄×C₈	—	94	4	no	—
338	C₄×C₈	—	188	2	no	—
339	#95	—	47	1	no	—
340	#95	—	47	1	no	—
341	#95	—	47	1	no	—
342	#95	—	47	1	no	—
343	#95	—	47	1	no	—
344	#95	—	47	1	no	—
345	#95	—	47	1	no	—
346	#95	—	47	1	no	—
347	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	—	47	1	no	—
357	C₂²×C₄	—	47	1	no	—
358	C₂²×C₄	—	47	1	no	—
359	C₂²×C₄	—	47	1	no	—
360	C₂²×C₄	—	47	1	no	—
361	C₂²×C₄	—	47	1	no	—
362	C₂²×C₄	—	47	1	no	—
363	C₂²×C₄	—	47	1	no	—
364	C₂²×C₄	C₈×D₄₇	1	4	yes	—
365	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
370	C₂²×C₄	#10625352	1	4	yes	—
371	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	4	8	no	—
378	C₂×C₈	—	94	2	no	—
379	C₂×C₈	—	94	2	no	—
380	C₂×C₈	—	94	2	no	—
381	C₂×C₈	—	94	2	no	—
382	C₂×C₈	—	94	2	no	—
383	C₂×C₈	—	94	2	no	—
384	C₂×C₈	#10625350	1	4	yes	—
385	C₄⋊C₄	—	47	4	no	—
386	C₄⋊C₄	—	47	4	no	—
387	C₄⋊C₄	—	94	2	no	—
388	C₄⋊C₄	—	94	2	no	—
389	C₂²⋊C₄	—	47	4	no	—
390	C₂²⋊C₄	—	47	4	no	—
391	C₂²⋊C₄	—	47	4	no	—
392	C₂²⋊C₄	—	94	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	47	4	no	—
398	C₄²	—	47	4	no	—
399	C₄²	—	94	2	no	—
400	C₄²	—	94	2	no	—
401	C₄²	—	94	2	no	—
402	C₄²	—	94	2	no	—
403	C₄²	—	94	2	no	—
404	C₄²	—	94	2	no	—
405	C₄²	—	94	1	no	—
406	C₄²	—	94	1	no	—
407	C₄²	—	94	1	no	—
408	C₄²	—	94	1	no	—
409	C₄²	—	188	1	no	—
410	C₄²	—	188	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	#13093980	1	2	yes	—
416	C₂³	C₂×C₈×D₄₇	1	2	yes	—
417	C₂³	M₁₆×D₄₇	1	2	yes	—
418	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	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	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	47	2	no	—
435	C₂×C₄	—	47	2	no	—
436	C₂×C₄	—	47	2	no	—
437	C₂×C₄	—	47	2	no	—
438	C₂×C₄	—	47	2	no	—
439	C₂×C₄	—	47	2	no	—
440	C₂×C₄	—	94	1	no	—
441	C₂×C₄	—	94	1	no	—
442	C₂×C₄	—	94	1	no	—
443	C₂×C₄	—	94	1	no	—
444	C₂×C₄	—	94	1	no	—
445	C₂×C₄	—	94	1	no	—
446	C₂×C₄	—	94	1	no	—
447	C₂×C₄	—	94	1	no	—
448	C₂×C₄	—	94	1	no	—
449	C₂×C₄	—	94	1	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	#13093980	1	2	yes	—
459	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
460	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
461	C₂×C₄	#13094030	1	2	yes	—
462	C₂×C₄	C₂×#10625352	1	2	yes	—
463	C₂×C₄	C₂×#10625350	1	2	yes	—
464	C₂×C₄	#13094069	1	1	yes	characteristic
465	C₂×C₄	#13094072	1	1	yes	characteristic
466	C₈	—	2	4	no	—
467	C₈	—	4	2	no	—
468	C₈	—	188	2	no	—
469	C₈	—	188	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	#15689173	1	4	yes	—
477	C₂²	C₂×#13093980	1	1	yes	characteristic
478	C₂²	C₄×#10625350	1	1	yes	characteristic
479	C₂²	#15689604	1	1	yes	characteristic
480	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
481	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
482	C₂²	C₂×#13094030	1	1	yes	characteristic
483	C₂²	#15689889	1	1	yes	characteristic
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	2	no	—
487	C₄	—	2	2	no	—
488	C₄	—	4	1	no	—
489	C₄	—	94	2	no	—
490	C₄	—	94	2	no	—
491	C₄	—	94	2	no	—
492	C₄	—	94	2	no	—
493	C₄	—	94	2	no	—
494	C₄	—	94	2	no	—
495	C₄	—	188	1	no	—
496	C₄	—	188	1	no	—
497	C₄	#15689799	1	2	yes	—
498	C₄	#15689808	1	2	yes	—
499	C₂	—	2	4	no	—
500	C₂	#20246244	1	1	yes	characteristic
501	C₂	C₂×#15689173	1	1	yes	characteristic
502	C₂	#20252042	1	1	yes	characteristic
503	C₂	C₈×#10625350	1	1	yes	characteristic
504	C₂	#20252399	1	1	yes	characteristic
505	C₂	#20252497	1	1	yes	characteristic
506	C₂	#20252510	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₂×C₄₇×#336	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#336	D₄₇
hypocenter	C₄₇	#22589
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
2. #20243946	C₂	semidirect
3. #20243944	C₂	semidirect
5. #20243530	C₂	semidirect
6. #20243503	C₂	semidirect
8. #20243236	C₂	semidirect
10. #20243132	C₂	semidirect
46. #13093983	C₈	semidirect
135. C₄⋊Dic₄₇	C₂×C₈	semidirect
136. C₄⋊Dic₄₇	C₂×C₈	semidirect
149. C₄×Dic₄₇	C₂×C₈	semidirect
150. C₄×Dic₄₇	C₂×C₈	semidirect
296. C₄₇	#22589	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13093983	2
#20243946	2
#20243944	2
#20243566	2
#20243530	2
#20243503	2
#20243456	2
#20243236	2
C₈×C₂²⋊Dic₄₇	2
#20243132	2
C₂×C₄₇×#336	2
#22589	47