Subgroups — #26215107

Order 12032.

966 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689177	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689146	C₂	1	1	yes	maximal, characteristic
3	C₄×#13093980	C₂	1	1	yes	maximal, characteristic
4	#20243264	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243262	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243261	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243259	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243242	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243240	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243236	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243174	C₂	1	1	yes	maximal, characteristic
13	#20243172	C₂	1	1	yes	maximal, characteristic
14	#20243169	C₂	1	1	yes	maximal, characteristic
15	C₄₇×#1753	C₂	1	1	yes	maximal, characteristic
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂×#13093980	C₄	1	2	yes	—
18	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
19	#15689177	C₄	1	8	yes	complemented
20	#15689146	C₄	1	8	yes	complemented
21	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×Dic₄₇⋊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×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×#13093935	C₂²	1	1	yes	characteristic
29	C₂×#13093934	C₂²	1	1	yes	characteristic
30	C₂×#13093934	C₂²	1	1	yes	characteristic
31	C₂×#13093934	C₂²	1	1	yes	characteristic
32	C₂×#13093934	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
36	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
38	#15688974	C₄	1	2	yes	—
39	C₂²⋊C₄×Dic₄₇	C₄	1	2	yes	—
40	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
41	#15688968	C₄	1	2	yes	—
42	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
43	C₄²×Dic₄₇	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	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊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	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
55	C₄₇×#336	C₂²	1	1	yes	characteristic
56	C₄₇×#336	C₂²	1	1	yes	characteristic
57	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×#10625329	—	4	1	no	—
60	C₂×#10625329	—	4	1	no	—
61	C₂×#10625329	C₂×C₄	1	4	yes	—
62	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
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	#13093980	—	2	8	no	—
67	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
68	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
70	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
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	1	yes	characteristic
74	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
76	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
77	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
78	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
82	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
83	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
84	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
85	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
86	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
87	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
88	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
89	#13093935	—	4	1	no	—
90	#13093934	—	4	1	no	—
91	#13093934	—	4	1	no	—
92	#13093934	C₂×C₄	1	4	yes	—
93	#13093934	C₂×C₄	1	4	yes	—
94	C₄×C₄₇⋊C₈	—	4	1	no	—
95	C₈×Dic₄₇	—	4	1	no	—
96	C₈×Dic₄₇	—	4	1	no	—
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	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₄₇	—	4	1	no	—
102	C₂×M₁₆×C₄₇	—	4	1	no	—
103	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
104	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
109	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
111	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
112	#97×C₄₇	—	4	1	no	—
113	C₄×C₈×C₄₇	—	4	1	no	—
114	#95×C₄₇	C₂×C₄	1	2	yes	—
115	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	—	2	1	no	—
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	—	2	1	no	—
119	C₂²×C₄×C₄₇	—	2	1	no	—
120	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
126	C₂²×Dic₄₇	—	2	4	no	—
127	C₂²×Dic₄₇	—	4	2	no	—
128	C₂²×Dic₄₇	C₄²	1	4	yes	—
129	C₂²×Dic₄₇	C₄²	1	4	yes	—
130	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
131	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
135	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
136	M₁₆×C₄₇	—	4	4	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	—	2	1	no	—
144	C₂×C₈×C₄₇	—	2	1	no	—
145	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
149	C₂²⋊C₄×C₄₇	—	2	4	no	—
150	C₄²×C₄₇	—	2	1	no	—
151	C₄²×C₄₇	—	2	1	no	—
152	C₄²×C₄₇	—	2	1	no	—
153	C₄²×C₄₇	—	2	1	no	—
154	C₂²⋊Dic₄₇	—	2	4	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	—	2	4	no	—
162	C₄×Dic₄₇	—	4	2	no	—
163	C₄×Dic₄₇	—	4	2	no	—
164	C₄×Dic₄₇	C₄²	1	4	yes	—
165	C₄×Dic₄₇	C₄²	1	4	yes	—
166	C₄×Dic₄₇	M₁₆	1	8	yes	complemented
167	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
168	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
169	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
170	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
171	#10625329	—	4	4	no	—
172	C₂×C₄₇⋊C₈	—	2	1	no	—
173	C₂×C₄₇⋊C₈	—	2	1	no	—
174	C₂×C₄₇⋊C₈	—	2	1	no	—
175	C₂×C₄₇⋊C₈	—	2	1	no	—
176	C₂×C₄₇⋊C₈	—	2	1	no	—
177	C₂×C₄₇⋊C₈	—	2	1	no	—
178	C₂×C₄₇⋊C₈	—	2	1	no	—
179	C₂×C₄₇⋊C₈	—	2	1	no	—
180	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
181	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
182	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
183	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
184	C₂³×C₄₇	—	2	1	no	—
185	C₂³×C₄₇	—	2	1	no	—
186	C₂³×C₄₇	—	2	2	no	—
187	C₂³×C₄₇	—	2	2	no	—
188	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
189	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	—	2	1	no	—
192	C₂×C₄×C₄₇	—	2	1	no	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	2	2	no	—
195	C₂×C₄×C₄₇	—	2	2	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	2	2	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
202	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
203	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
206	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
207	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
208	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
209	C₂×Dic₄₇	—	2	2	no	—
210	C₂×Dic₄₇	—	2	2	no	—
211	C₂×Dic₄₇	—	2	2	no	—
212	C₂×Dic₄₇	—	2	2	no	—
213	C₂×Dic₄₇	—	2	2	no	—
214	C₂×Dic₄₇	—	2	8	no	—
215	C₂×Dic₄₇	—	2	2	no	—
216	C₂×Dic₄₇	—	2	2	no	—
217	C₂×Dic₄₇	—	2	2	no	—
218	C₂×Dic₄₇	—	4	4	no	—
219	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
220	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
221	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
222	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
223	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
224	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
225	C₈×C₄₇	—	2	2	no	—
226	C₈×C₄₇	—	2	2	no	—
227	C₈×C₄₇	—	2	2	no	—
228	C₈×C₄₇	—	2	2	no	—
229	C₄₇⋊C₈	—	2	2	no	—
230	C₄₇⋊C₈	—	2	2	no	—
231	C₄₇⋊C₈	—	2	2	no	—
232	C₄₇⋊C₈	—	2	2	no	—
233	#20549	—	47	1	no	maximal, Sylow
234	C₂²×C₄₇	—	2	2	no	—
235	C₂²×C₄₇	—	2	2	no	—
236	C₂²×C₄₇	—	2	2	no	—
237	C₂²×C₄₇	—	4	2	no	—
238	C₂²×C₄₇	—	4	2	no	—
239	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
240	C₂²×C₄₇	#520	1	1	yes	characteristic
241	C₂²×C₄₇	#520	1	1	yes	characteristic
242	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
243	C₂²×C₄₇	#568	1	2	yes	—
244	C₄×C₄₇	—	2	4	no	—
245	C₄×C₄₇	—	2	2	no	—
246	C₄×C₄₇	—	4	2	no	—
247	C₄×C₄₇	#518	1	1	yes	characteristic
248	C₄×C₄₇	#519	1	1	yes	characteristic
249	C₄×C₄₇	#520	1	1	yes	characteristic
250	C₄×C₄₇	#520	1	1	yes	characteristic
251	Dic₄₇	—	2	2	no	—
252	Dic₄₇	—	2	2	no	—
253	Dic₄₇	—	2	2	no	—
254	Dic₄₇	—	2	4	no	—
255	Dic₄₇	—	4	2	no	—
256	Dic₄₇	C₄×M₁₆	1	4	yes	—
257	C₂×#432	—	47	1	no	—
258	C₂×#423	—	47	1	no	—
259	C₄×#117	—	47	1	no	—
260	#1771	—	47	1	no	—
261	#1771	—	47	1	no	—
262	#1771	—	47	1	no	—
263	#1771	—	47	1	no	—
264	#1767	—	47	1	no	—
265	#1767	—	47	1	no	—
266	C₄×C₄⋊C₈	—	47	1	no	—
267	C₄×C₄⋊C₈	—	47	1	no	—
268	#1753	—	47	1	no	—
269	#1753	—	47	1	no	—
270	#1753	—	47	1	no	—
271	#1753	D₄₇	1	1	yes	characteristic
272	C₂×C₄₇	—	4	2	no	—
273	C₂×C₄₇	#2274	1	1	yes	characteristic
274	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
275	C₂×C₄₇	#2873	1	1	yes	characteristic
276	C₂×C₄₇	#2989	1	2	yes	—
277	C₂×C₄₇	#2989	1	2	yes	—
278	C₂²×M₁₆	—	47	1	no	—
279	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
280	C₂×#117	—	47	2	no	—
281	C₂²×C₄²	—	47	1	no	—
282	#432	—	47	8	no	—
283	#423	—	47	8	no	—
284	C₂×C₄⋊C₈	—	47	1	no	—
285	C₂×C₄⋊C₈	—	47	1	no	—
286	C₂×C₄⋊C₈	—	47	1	no	—
287	C₂×C₄⋊C₈	—	47	1	no	—
288	C₂×C₄⋊C₈	—	47	1	no	—
289	C₂×C₄⋊C₈	—	47	1	no	—
290	C₂×C₂²⋊C₈	—	47	1	no	—
291	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
292	C₂×#97	—	47	1	no	—
293	C₂×#97	—	47	1	no	—
294	C₂×#97	—	47	1	no	—
295	C₂×#97	—	47	1	no	—
296	C₂×#97	—	47	1	no	—
297	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
298	C₂×C₄×C₈	—	47	1	no	—
299	C₂×C₄×C₈	—	47	1	no	—
300	C₂×C₄×C₈	—	47	1	no	—
301	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
302	C₄×C₄⋊C₄	—	47	1	no	—
303	C₄×C₄⋊C₄	—	47	1	no	—
304	C₄×C₄⋊C₄	—	47	2	no	—
305	C₄×C₂²⋊C₄	—	47	1	no	—
306	C₄×C₂²⋊C₄	—	47	2	no	—
307	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
308	#376	—	47	2	no	—
309	C₄³	—	47	1	no	—
310	C₄³	—	47	1	no	—
311	#336	—	47	1	no	—
312	#336	—	47	1	no	—
313	#336	—	47	1	no	—
314	#336	—	47	1	no	—
315	#336	—	47	1	no	—
316	#336	—	47	1	no	—
317	#336	C₂×D₄₇	1	1	yes	characteristic
318	#336	C₂×D₄₇	1	1	yes	characteristic
319	C₄₇	#20549	1	1	yes	characteristic, complemented, Sylow
320	C₂³×C₄	—	47	1	no	—
321	C₂³×C₄	—	47	1	no	—
322	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
323	C₂×M₁₆	—	4	1	no	—
324	C₂×M₁₆	—	4	1	no	—
325	C₂×M₁₆	—	47	4	no	—
326	C₂×M₁₆	—	188	1	no	—
327	C₂×M₁₆	—	188	1	no	—
328	C₂×M₁₆	C₄×D₄₇	1	4	yes	—
329	C₂²×C₈	—	47	1	no	—
330	C₂²×C₈	—	47	1	no	—
331	C₂²×C₈	—	47	1	no	—
332	C₂²×C₈	—	47	1	no	—
333	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
334	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
335	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
336	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
337	#117	—	94	8	no	—
338	C₂×C₄⋊C₄	—	47	2	no	—
339	C₂×C₄⋊C₄	—	47	2	no	—
340	C₂×C₂²⋊C₄	—	47	2	no	—
341	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
342	C₂×C₄²	—	47	2	no	—
343	C₂×C₄²	—	47	1	no	—
344	C₂×C₄²	—	47	1	no	—
345	C₂×C₄²	—	47	4	no	—
346	C₂×C₄²	—	47	4	no	—
347	C₂×C₄²	—	47	1	no	—
348	C₂×C₄²	—	47	1	no	—
349	C₂×C₄²	—	47	2	no	—
350	C₂×C₄²	—	47	1	no	—
351	C₂×C₄²	—	47	1	no	—
352	C₂×C₄²	—	47	2	no	—
353	C₂×C₄²	—	47	2	no	—
354	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
355	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
356	C₄⋊C₈	—	47	4	no	—
357	C₄⋊C₈	—	47	4	no	—
358	C₄⋊C₈	—	47	4	no	—
359	C₄⋊C₈	—	47	4	no	—
360	C₄⋊C₈	—	47	4	no	—
361	C₄⋊C₈	—	47	4	no	—
362	C₂²⋊C₈	—	47	4	no	—
363	C₂²⋊C₈	C₄×D₄₇	1	4	yes	—
364	#97	—	4	1	no	—
365	#97	—	47	4	no	—
366	#97	—	47	4	no	—
367	#97	—	188	1	no	—
368	#97	—	188	1	no	—
369	#97	—	188	1	no	—
370	C₄×C₈	—	4	1	no	—
371	C₄×C₈	—	188	1	no	—
372	C₄×C₈	—	188	1	no	—
373	C₄×C₈	—	188	1	no	—
374	#95	—	47	2	no	—
375	#95	—	47	2	no	—
376	#95	—	47	2	no	—
377	#95	C₄×D₄₇	1	2	yes	—
378	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	47	1	no	—
384	C₂²×C₄	—	47	4	no	—
385	C₂²×C₄	—	47	1	no	—
386	C₂²×C₄	—	47	2	no	—
387	C₂²×C₄	—	47	1	no	—
388	C₂²×C₄	—	47	1	no	—
389	C₂²×C₄	—	47	4	no	—
390	C₂²×C₄	—	47	2	no	—
391	C₂²×C₄	—	94	4	no	—
392	C₂²×C₄	—	188	2	no	—
393	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
394	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
396	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
397	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
398	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
399	M₁₆	—	4	4	no	—
400	M₁₆	—	188	4	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	47	2	no	—
410	C₂×C₈	—	47	2	no	—
411	C₂×C₈	—	47	2	no	—
412	C₂×C₈	—	47	2	no	—
413	C₂×C₈	—	94	1	no	—
414	C₂×C₈	—	94	1	no	—
415	C₂×C₈	—	94	1	no	—
416	C₂×C₈	—	94	1	no	—
417	C₂×C₈	—	94	1	no	—
418	C₂×C₈	—	94	1	no	—
419	C₂×C₈	—	94	1	no	—
420	C₂×C₈	—	94	1	no	—
421	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
422	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
423	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
424	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
425	C₄⋊C₄	—	94	4	no	—
426	C₄⋊C₄	—	94	4	no	—
427	C₂²⋊C₄	—	2	4	no	—
428	C₂²⋊C₄	—	94	4	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	47	4	no	—
434	C₄²	—	47	4	no	—
435	C₄²	—	47	8	no	—
436	C₄²	—	47	2	no	—
437	C₄²	—	47	2	no	—
438	C₄²	—	47	2	no	—
439	C₄²	—	47	2	no	—
440	C₄²	—	94	4	no	—
441	C₄²	—	94	1	no	—
442	C₄²	—	94	1	no	—
443	C₄²	—	94	1	no	—
444	C₄²	—	94	1	no	—
445	C₄²	—	188	2	no	—
446	C₄²	—	188	2	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	C₄²×D₄₇	1	2	yes	—
452	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	47	2	no	—
465	C₂×C₄	—	47	4	no	—
466	C₂×C₄	—	47	2	no	—
467	C₂×C₄	—	47	2	no	—
468	C₂×C₄	—	47	2	no	—
469	C₂×C₄	—	47	4	no	—
470	C₂×C₄	—	94	8	no	—
471	C₂×C₄	—	94	2	no	—
472	C₂×C₄	—	94	2	no	—
473	C₂×C₄	—	94	2	no	—
474	C₂×C₄	—	94	2	no	—
475	C₂×C₄	—	94	2	no	—
476	C₂×C₄	—	94	2	no	—
477	C₂×C₄	—	94	2	no	—
478	C₂×C₄	—	94	2	no	—
479	C₂×C₄	—	188	4	no	—
480	C₂×C₄	C₄²×D₄₇	1	2	yes	—
481	C₂×C₄	M₁₆×D₄₇	1	4	yes	—
482	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
483	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
484	C₂×C₄	#13094069	1	1	yes	characteristic
485	C₂×C₄	#13094069	1	1	yes	characteristic
486	C₂×C₄	#13094071	1	1	yes	characteristic
487	C₂×C₄	#13094071	1	1	yes	characteristic
488	C₈	—	2	2	no	—
489	C₈	—	2	2	no	—
490	C₈	—	2	2	no	—
491	C₈	—	2	2	no	—
492	C₈	—	94	2	no	—
493	C₈	—	94	2	no	—
494	C₈	—	94	2	no	—
495	C₈	—	94	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
502	C₂²	#15689602	1	1	yes	characteristic
503	C₂²	#15689602	1	1	yes	characteristic
504	C₂²	C₂×M₁₆×D₄₇	1	2	yes	—
505	C₂²	#15689888	1	2	yes	—
506	C₄	—	2	4	no	—
507	C₄	—	2	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	47	4	no	—
510	C₄	—	94	4	no	—
511	C₄	—	94	2	no	—
512	C₄	—	94	2	no	—
513	C₄	—	94	2	no	—
514	C₄	—	188	2	no	—
515	C₄	#15689596	1	1	yes	characteristic
516	C₄	#15689600	1	1	yes	characteristic
517	C₄	#15689602	1	1	yes	characteristic
518	C₄	#15689602	1	1	yes	characteristic
519	C₂	—	4	2	no	—
520	C₂	#20245743	1	1	yes	characteristic
521	C₂	C₄×M₁₆×D₄₇	1	1	yes	characteristic
522	C₂	#20251804	1	1	yes	characteristic
523	C₂	#20252500	1	2	yes	—
524	C₂	#20252503	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄₇×#1753	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1753	D₄₇
hypocenter	C₄₇	#20549
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1753

Complements

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

N	H ≅ G/N	type
4. #20243264	C₂	semidirect
5. #20243262	C₂	semidirect
6. #20243261	C₂	semidirect
7. #20243259	C₂	semidirect
8. #20243242	C₂	semidirect
9. #20243240	C₂	semidirect
10. C₄×Dic₄₇⋊C₈	C₂	semidirect
11. #20243236	C₂	semidirect
19. #15689177	C₄	semidirect
20. #15689146	C₄	semidirect
166. C₄×Dic₄₇	M₁₆	semidirect
319. C₄₇	#20549	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689177	2
C₂×#15689146	2
C₄×#13093980	2
#20243264	2
#20243262	2
#20243261	2
#20243259	2
#20243242	2
#20243240	2
C₄×Dic₄₇⋊C₈	2
#20243236	2
#20243174	2
#20243172	2
#20243169	2
C₄₇×#1753	2
#20549	47