Subgroups — #26215292

Order 12032.

974 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689195	C₂	1	1	yes	maximal, characteristic
2	#20245853	C₂	1	1	yes	maximal, characteristic
3	#20243265	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243260	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄⋊C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243174	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243169	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243162	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243156	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243156	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243136	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243086	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243084	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₇×#435	C₂	1	1	yes	maximal, characteristic
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×#13093983	C₂²	1	1	yes	characteristic
19	C₂×#13093983	C₂²	1	1	yes	characteristic
20	#15689195	C₄	1	8	yes	complemented
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×#13093935	C₂²	1	1	yes	characteristic
25	C₂×#13093934	C₂²	1	1	yes	characteristic
26	C₂×#13093934	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
31	#15689026	C₄	1	2	yes	—
32	#15689022	C₄	1	2	yes	—
33	#15689016	C₄	1	2	yes	—
34	#15689016	C₄	1	2	yes	—
35	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
38	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
39	#15688877	C₂²	1	1	yes	characteristic
40	#15688877	C₂²	1	1	yes	characteristic
41	#15688877	C₂²	1	1	yes	characteristic
42	#15688877	C₂²	1	1	yes	characteristic
43	#15688877	C₂²	1	1	yes	characteristic
44	#15688877	C₂²	1	1	yes	characteristic
45	#15688877	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	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
50	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
52	C₄₇×#435	C₄	1	8	yes	complemented
53	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
56	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×#10625329	—	4	1	no	—
58	C₂×#10625329	—	4	1	no	—
59	C₂×#10625329	C₂×C₄	1	4	yes	—
60	C₂²×C₄₇⋊C₈	—	4	1	no	—
61	C₂²×C₄₇⋊C₈	—	4	1	no	—
62	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
63	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
67	#13093983	—	4	1	no	—
68	#13093983	—	4	1	no	—
69	#13093983	—	4	1	no	—
70	#13093983	—	4	1	no	—
71	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
74	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
77	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
78	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
79	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
80	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
84	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
85	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
86	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
87	#13093935	C₂×C₄	1	4	yes	—
88	#13093934	—	4	1	no	—
89	#13093934	—	4	1	no	—
90	C₈×Dic₄₇	—	4	1	no	—
91	C₈×Dic₄₇	—	4	1	no	—
92	C₈×Dic₄₇	—	4	1	no	—
93	C₈×Dic₄₇	—	4	1	no	—
94	C₄₇⋊#95	C₂×C₄	1	2	yes	—
95	C₄₇⋊#95	C₂×C₄	1	2	yes	—
96	C₄₇⋊#95	C₂×C₄	1	2	yes	—
97	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
98	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₄₇	—	4	1	no	—
101	C₂×M₁₆×C₄₇	—	4	1	no	—
102	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
103	C₂²×C₈×C₄₇	—	4	1	no	—
104	C₂²×C₈×C₄₇	—	4	1	no	—
105	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
106	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
110	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
111	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
112	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
117	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
118	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
119	#97×C₄₇	C₂×C₄	1	4	yes	—
120	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂×D₄×C₄₇	—	4	2	no	—
123	C₂×D₄×C₄₇	C₄²	1	4	yes	—
124	C₂²×C₄×C₄₇	—	2	1	no	—
125	C₂²×C₄×C₄₇	—	2	1	no	—
126	C₂²×C₄×C₄₇	—	2	1	no	—
127	C₂²×C₄×C₄₇	—	2	1	no	—
128	C₂²×C₄×C₄₇	—	2	1	no	—
129	C₂²×C₄×C₄₇	—	2	1	no	—
130	C₂²×C₄×C₄₇	—	2	1	no	—
131	C₂²×C₄×C₄₇	—	2	1	no	—
132	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
141	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
142	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
143	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
144	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
145	M₁₆×C₄₇	—	4	4	no	—
146	C₂×C₈×C₄₇	—	2	1	no	—
147	C₂×C₈×C₄₇	—	2	1	no	—
148	C₂×C₈×C₄₇	—	2	1	no	—
149	C₂×C₈×C₄₇	—	2	1	no	—
150	C₂×C₈×C₄₇	—	2	1	no	—
151	C₂×C₈×C₄₇	—	2	1	no	—
152	C₂×C₈×C₄₇	—	2	1	no	—
153	C₂×C₈×C₄₇	—	2	1	no	—
154	C₂×C₈×C₄₇	—	4	4	no	—
155	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
156	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
157	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
158	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
159	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
160	C₂²⋊C₄×C₄₇	C₄²	1	4	yes	—
161	C₂²⋊C₄×C₄₇	C₄²	1	4	yes	—
162	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
163	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
164	C₂²⋊Dic₄₇	—	2	4	no	—
165	C₂²⋊Dic₄₇	—	2	4	no	—
166	C₂²⋊Dic₄₇	—	4	2	no	—
167	C₂²⋊Dic₄₇	—	4	2	no	—
168	C₄⋊Dic₄₇	—	4	2	no	—
169	C₄⋊Dic₄₇	—	4	2	no	—
170	C₄⋊Dic₄₇	—	4	2	no	—
171	C₄×Dic₄₇	—	2	1	no	—
172	C₄×Dic₄₇	—	2	1	no	—
173	C₄×Dic₄₇	—	2	1	no	—
174	C₄×Dic₄₇	—	2	1	no	—
175	C₄×Dic₄₇	—	2	1	no	—
176	C₄×Dic₄₇	—	2	1	no	—
177	C₄×Dic₄₇	—	2	1	no	—
178	C₄×Dic₄₇	—	2	1	no	—
179	C₄×Dic₄₇	—	2	4	no	—
180	C₄×Dic₄₇	—	4	2	no	—
181	#10625329	—	4	4	no	—
182	C₂×C₄₇⋊C₈	—	2	1	no	—
183	C₂×C₄₇⋊C₈	—	2	1	no	—
184	C₂×C₄₇⋊C₈	—	2	1	no	—
185	C₂×C₄₇⋊C₈	—	2	1	no	—
186	C₂×C₄₇⋊C₈	—	2	1	no	—
187	C₂×C₄₇⋊C₈	—	2	1	no	—
188	C₂×C₄₇⋊C₈	—	2	1	no	—
189	C₂×C₄₇⋊C₈	—	2	1	no	—
190	C₂×C₄₇⋊C₈	—	4	4	no	—
191	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
192	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
193	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
194	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
195	C₂³×C₄₇	—	2	1	no	—
196	C₂³×C₄₇	—	2	1	no	—
197	C₂³×C₄₇	—	2	1	no	—
198	C₂³×C₄₇	—	2	1	no	—
199	C₂³×C₄₇	—	2	2	no	—
200	C₂³×C₄₇	—	2	2	no	—
201	C₂³×C₄₇	—	2	2	no	—
202	C₂³×C₄₇	—	2	2	no	—
203	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
204	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
205	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
206	D₄×C₄₇	—	4	4	no	—
207	C₂×C₄×C₄₇	—	2	1	no	—
208	C₂×C₄×C₄₇	—	2	1	no	—
209	C₂×C₄×C₄₇	—	2	1	no	—
210	C₂×C₄×C₄₇	—	2	1	no	—
211	C₂×C₄×C₄₇	—	2	2	no	—
212	C₂×C₄×C₄₇	—	2	2	no	—
213	C₂×C₄×C₄₇	—	2	2	no	—
214	C₂×C₄×C₄₇	—	2	2	no	—
215	C₂×C₄×C₄₇	—	2	2	no	—
216	C₂×C₄×C₄₇	—	2	2	no	—
217	C₂×C₄×C₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	2	2	no	—
219	C₂×C₄×C₄₇	—	2	2	no	—
220	C₂×C₄×C₄₇	—	2	2	no	—
221	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
222	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
223	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
224	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
225	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
229	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
230	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
231	C₂×Dic₄₇	—	2	2	no	—
232	C₂×Dic₄₇	—	2	2	no	—
233	C₂×Dic₄₇	—	2	2	no	—
234	C₂×Dic₄₇	—	2	2	no	—
235	C₂×Dic₄₇	—	2	2	no	—
236	C₂×Dic₄₇	—	2	2	no	—
237	C₂×Dic₄₇	—	2	2	no	—
238	C₂×Dic₄₇	—	2	2	no	—
239	C₂×Dic₄₇	—	2	2	no	—
240	C₂×Dic₄₇	—	2	2	no	—
241	C₂×Dic₄₇	—	2	2	no	—
242	C₂×Dic₄₇	#131	1	4	yes	—
243	C₈×C₄₇	—	2	2	no	—
244	C₈×C₄₇	—	2	2	no	—
245	C₈×C₄₇	—	2	2	no	—
246	C₈×C₄₇	—	2	2	no	—
247	C₄₇⋊C₈	—	2	2	no	—
248	C₄₇⋊C₈	—	2	2	no	—
249	C₄₇⋊C₈	—	2	2	no	—
250	C₄₇⋊C₈	—	2	2	no	—
251	#20566	—	47	1	no	maximal, Sylow
252	C₂²×C₄₇	—	2	2	no	—
253	C₂²×C₄₇	—	2	2	no	—
254	C₂²×C₄₇	—	2	2	no	—
255	C₂²×C₄₇	—	2	2	no	—
256	C₂²×C₄₇	—	2	2	no	—
257	C₂²×C₄₇	—	2	2	no	—
258	C₂²×C₄₇	—	4	2	no	—
259	C₂²×C₄₇	—	4	2	no	—
260	C₂²×C₄₇	—	4	2	no	—
261	C₂²×C₄₇	—	4	2	no	—
262	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
263	C₂²×C₄₇	#518	1	1	yes	characteristic
264	C₂²×C₄₇	#520	1	1	yes	characteristic
265	C₂²×C₄₇	C₂×#131	1	2	yes	—
266	C₂²×C₄₇	#568	1	2	yes	—
267	C₄×C₄₇	—	2	2	no	—
268	C₄×C₄₇	—	2	2	no	—
269	C₄×C₄₇	—	2	2	no	—
270	C₄×C₄₇	—	2	2	no	—
271	C₄×C₄₇	#518	1	1	yes	characteristic
272	C₄×C₄₇	#518	1	1	yes	characteristic
273	C₄×C₄₇	#520	1	1	yes	characteristic
274	C₄×C₄₇	#520	1	1	yes	characteristic
275	Dic₄₇	—	2	4	no	—
276	Dic₄₇	—	4	2	no	—
277	Dic₄₇	—	4	2	no	—
278	Dic₄₇	—	4	2	no	—
279	C₂×#435	—	47	1	no	—
280	C₂×#435	D₄₇	1	1	yes	characteristic
281	#2293	—	47	1	no	—
282	#1771	—	47	1	no	—
283	#1771	—	47	1	no	—
284	C₄×C₄⋊C₈	—	47	1	no	—
285	#1753	—	47	1	no	—
286	#1753	—	47	1	no	—
287	C₈×C₂²⋊C₄	—	47	1	no	—
288	C₈×C₂²⋊C₄	—	47	1	no	—
289	#1750	—	47	1	no	—
290	#1750	—	47	1	no	—
291	#1745	—	47	1	no	—
292	#1729	—	47	1	no	—
293	#1729	—	47	1	no	—
294	C₂×C₄₇	—	4	2	no	—
295	C₂×C₄₇	—	4	2	no	—
296	C₂×C₄₇	#2275	1	1	yes	characteristic
297	C₂×C₄₇	#2873	1	1	yes	characteristic
298	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
299	C₂×C₄₇	#2981	1	2	yes	—
300	C₂×C₄₇	#2992	1	2	yes	—
301	C₂²×M₁₆	—	47	1	no	—
302	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
303	C₂³×C₈	—	47	1	no	—
304	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
306	C₂×#117	—	47	1	no	—
307	C₂×#117	—	47	1	no	—
308	#435	—	47	8	no	—
309	#435	Dic₄₇	1	8	yes	complemented
310	C₂×C₄⋊C₈	—	47	1	no	—
311	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
312	C₂×C₂²⋊C₈	—	47	1	no	—
313	C₂×C₂²⋊C₈	—	47	1	no	—
314	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
315	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
316	C₂×#97	—	47	1	no	—
317	C₂×#97	—	47	1	no	—
318	C₂×#97	—	47	1	no	—
319	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
320	C₂×C₄×C₈	—	47	1	no	—
321	C₂×C₄×C₈	—	47	1	no	—
322	C₂×C₄×C₈	—	47	1	no	—
323	C₂×C₄×C₈	—	47	1	no	—
324	#390	—	47	2	no	—
325	#389	—	47	2	no	—
326	#388	—	47	2	no	—
327	#388	—	47	2	no	—
328	C₄×C₄⋊C₄	—	47	1	no	—
329	C₄×C₂²⋊C₄	—	47	1	no	—
330	C₄×C₂²⋊C₄	—	47	1	no	—
331	C₄³	—	47	1	no	—
332	#336	—	47	1	no	—
333	#336	—	47	1	no	—
334	#336	—	47	1	no	—
335	#336	—	47	1	no	—
336	#336	—	47	1	no	—
337	#336	—	47	1	no	—
338	#336	—	47	1	no	—
339	#336	—	47	1	no	—
340	#336	—	47	1	no	—
341	#336	—	47	1	no	—
342	C₄₇	#20566	1	1	yes	characteristic, complemented, Sylow
343	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
344	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
345	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
346	C₂×M₁₆	—	4	1	no	—
347	C₂×M₁₆	—	4	1	no	—
348	C₂×M₁₆	—	47	4	no	—
349	C₂×M₁₆	—	188	1	no	—
350	C₂×M₁₆	—	188	1	no	—
351	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
352	C₂²×C₈	—	4	1	no	—
353	C₂²×C₈	—	4	1	no	—
354	C₂²×C₈	—	47	1	no	—
355	C₂²×C₈	—	47	1	no	—
356	C₂²×C₈	—	47	1	no	—
357	C₂²×C₈	—	47	1	no	—
358	C₂²×C₈	—	47	4	no	—
359	C₂²×C₈	—	188	1	no	—
360	C₂²×C₈	—	188	1	no	—
361	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
362	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
363	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
364	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
365	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
366	C₄×D₄	C₄×D₄₇	1	4	yes	—
367	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
368	#117	—	188	1	no	—
369	#117	—	188	1	no	—
370	#117	—	188	1	no	—
371	#117	—	188	1	no	—
372	C₂×C₄⋊C₄	—	47	2	no	—
373	C₂×C₄⋊C₄	—	47	2	no	—
374	C₂×C₄⋊C₄	—	47	2	no	—
375	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	—	47	2	no	—
377	C₂×C₂²⋊C₄	—	47	2	no	—
378	C₂×C₂²⋊C₄	—	47	2	no	—
379	C₂×C₂²⋊C₄	—	47	2	no	—
380	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
382	C₂×C₄²	—	47	2	no	—
383	C₂×C₄²	—	47	1	no	—
384	C₂×C₄²	—	47	1	no	—
385	C₂×C₄²	—	47	1	no	—
386	C₂×C₄²	—	47	1	no	—
387	C₂×C₄²	—	47	2	no	—
388	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
389	C₄⋊C₈	—	47	4	no	—
390	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	—
391	C₂²⋊C₈	—	47	4	no	—
392	C₂²⋊C₈	—	47	4	no	—
393	C₂²⋊C₈	C₂×Dic₄₇	1	4	yes	—
394	C₂²⋊C₈	C₂×Dic₄₇	1	4	yes	—
395	#97	—	47	4	no	—
396	#97	—	188	1	no	—
397	#97	—	188	1	no	—
398	#97	C₂×Dic₄₇	1	4	yes	—
399	C₄×C₈	—	188	1	no	—
400	C₄×C₈	—	188	1	no	—
401	C₄×C₈	—	188	1	no	—
402	C₄×C₈	—	188	1	no	—
403	#95	—	47	2	no	—
404	#95	—	47	2	no	—
405	#95	—	47	2	no	—
406	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
407	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
408	C₂×D₄	—	4	2	no	—
409	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	47	2	no	—
419	C₂²×C₄	—	47	2	no	—
420	C₂²×C₄	—	47	2	no	—
421	C₂²×C₄	—	47	2	no	—
422	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
423	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
424	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
425	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
426	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
427	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
428	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
429	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
430	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
431	M₁₆	—	4	4	no	—
432	M₁₆	—	188	4	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	4	4	no	—
442	C₂×C₈	—	47	2	no	—
443	C₂×C₈	—	47	2	no	—
444	C₂×C₈	—	47	2	no	—
445	C₂×C₈	—	47	2	no	—
446	C₂×C₈	—	94	1	no	—
447	C₂×C₈	—	94	1	no	—
448	C₂×C₈	—	94	1	no	—
449	C₂×C₈	—	94	1	no	—
450	C₂×C₈	—	94	1	no	—
451	C₂×C₈	—	94	1	no	—
452	C₂×C₈	—	94	1	no	—
453	C₂×C₈	—	94	1	no	—
454	C₂×C₈	—	188	4	no	—
455	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
456	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
457	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
458	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
459	C₄⋊C₄	—	188	2	no	—
460	C₄⋊C₄	—	188	2	no	—
461	C₄⋊C₄	—	188	2	no	—
462	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
463	C₂²⋊C₄	—	94	4	no	—
464	C₂²⋊C₄	—	94	4	no	—
465	C₂²⋊C₄	—	188	2	no	—
466	C₂²⋊C₄	—	188	2	no	—
467	C₂²⋊C₄	C₄×Dic₄₇	1	4	yes	—
468	C₂²⋊C₄	C₄×Dic₄₇	1	4	yes	—
469	C₄²	—	94	4	no	—
470	C₄²	—	94	1	no	—
471	C₄²	—	94	1	no	—
472	C₄²	—	94	1	no	—
473	C₄²	—	94	1	no	—
474	C₄²	—	94	1	no	—
475	C₄²	—	94	1	no	—
476	C₄²	—	94	1	no	—
477	C₄²	—	94	1	no	—
478	C₄²	—	188	2	no	—
479	C₄²	C₂×C₄×D₄₇	1	2	yes	—
480	C₄²	C₂²×Dic₄₇	1	2	yes	—
481	C₂³	—	2	1	no	—
482	C₂³	—	2	1	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	1	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
490	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
491	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
492	D₄	—	4	4	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	47	4	no	—
508	C₂×C₄	—	94	2	no	—
509	C₂×C₄	—	94	2	no	—
510	C₂×C₄	—	94	2	no	—
511	C₂×C₄	—	94	2	no	—
512	C₂×C₄	—	94	2	no	—
513	C₂×C₄	—	94	2	no	—
514	C₂×C₄	—	94	2	no	—
515	C₂×C₄	—	94	2	no	—
516	C₂×C₄	—	94	2	no	—
517	C₂×C₄	—	94	2	no	—
518	C₂×C₄	—	94	2	no	—
519	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
520	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
521	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
522	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
523	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
524	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
525	C₂×C₄	#13094069	1	1	yes	characteristic
526	C₂×C₄	#13094069	1	1	yes	characteristic
527	C₂×C₄	#13094070	1	1	yes	characteristic
528	C₂×C₄	#13094071	1	1	yes	characteristic
529	C₈	—	2	2	no	—
530	C₈	—	2	2	no	—
531	C₈	—	2	2	no	—
532	C₈	—	2	2	no	—
533	C₈	—	94	2	no	—
534	C₈	—	94	2	no	—
535	C₈	—	94	2	no	—
536	C₈	—	94	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
548	C₂²	#15689595	1	1	yes	characteristic
549	C₂²	#15689602	1	1	yes	characteristic
550	C₂²	#131×D₄₇	1	2	yes	—
551	C₂²	#15689889	1	2	yes	—
552	C₄	—	2	2	no	—
553	C₄	—	2	2	no	—
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	94	4	no	—
557	C₄	—	188	2	no	—
558	C₄	—	188	2	no	—
559	C₄	—	188	2	no	—
560	C₄	#15689595	1	1	yes	characteristic
561	C₄	#15689598	1	1	yes	characteristic
562	C₄	#15689602	1	1	yes	characteristic
563	C₄	#15689606	1	1	yes	characteristic
564	C₂	—	4	2	no	—
565	C₂	—	4	2	no	—
566	C₂	#20245749	1	1	yes	characteristic
567	C₂	#20251806	1	1	yes	characteristic
568	C₂	#131×Dic₄₇	1	1	yes	characteristic
569	C₂	#20252460	1	2	yes	—
570	C₂	#20252523	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₂×C₄₇×#435	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#435	D₄₇
hypocenter	C₄₇	#20566
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#435

Complements

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

N	H ≅ G/N	type
3. #20243265	C₂	semidirect
4. #20243260	C₂	semidirect
5. C₄⋊C₈×Dic₄₇	C₂	semidirect
6. #20243174	C₂	semidirect
7. #20243169	C₂	semidirect
8. #20243162	C₂	semidirect
9. C₈×C₂²⋊Dic₄₇	C₂	semidirect
10. #20243156	C₂	semidirect
11. #20243156	C₂	semidirect
12. #20243136	C₂	semidirect
13. #20243086	C₂	semidirect
14. #20243084	C₂	semidirect
20. #15689195	C₄	semidirect
52. C₄₇×#435	C₄	semidirect
309. #435	Dic₄₇	semidirect
342. C₄₇	#20566	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689195	2
#20245853	2
#20243265	2
#20243260	2
C₄⋊C₈×Dic₄₇	2
#20243174	2
#20243169	2
#20243162	2
C₈×C₂²⋊Dic₄₇	2
#20243156	2
#20243136	2
#20243086	2
#20243084	2
C₂×C₄₇×#435	2
#20566	47