Subgroups — #26226780

Order 12032.

774 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689182	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689148	C₂	1	1	yes	maximal, characteristic
3	#20245881	C₂	1	1	yes	maximal, characteristic
4	#20244112	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244109	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244106	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243572	C₂	1	1	yes	maximal, characteristic
8	#20243569	C₂	1	1	yes	maximal, characteristic
9	#20243567	C₂	1	1	yes	maximal, characteristic
10	#20243564	C₂	1	1	yes	maximal, characteristic
11	#20243541	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243539	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243506	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243503	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625324	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
18	C₂×#13093981	C₂²	1	1	yes	characteristic
19	#15689182	—	2	4	no	—
20	#15689148	—	2	4	no	—
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₄₇⋊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×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×#13093935	C₂²	1	1	yes	characteristic
35	#15689015	C₄	1	1	yes	characteristic
36	#15689015	C₄	1	1	yes	characteristic
37	#15689013	C₄	1	1	yes	characteristic
38	#15689013	C₄	1	1	yes	characteristic
39	#15689010	C₄	1	1	yes	characteristic
40	#15689010	C₄	1	1	yes	characteristic
41	#15689004	C₄	1	1	yes	characteristic
42	#15689004	C₄	1	1	yes	characteristic
43	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
44	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
46	#15688969	C₂²	1	1	yes	characteristic
47	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
48	#15688878	C₂²	1	1	yes	characteristic
49	#15688878	C₂²	1	1	yes	characteristic
50	#15688877	C₂²	1	1	yes	characteristic
51	#15688877	C₂²	1	1	yes	characteristic
52	#15688877	C₂²	1	1	yes	characteristic
53	#15688877	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
59	C₄₇×#336	C₂²	1	1	yes	characteristic
60	C₄₇×#336	C₂²	1	1	yes	characteristic
61	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
62	C₂×#10625324	—	2	2	no	—
63	C₂×#10625324	—	4	1	no	—
64	C₂×#10625324	—	4	1	no	—
65	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
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	C₂×C₈×D₄₇	—	2	2	no	—
70	C₂×C₈×D₄₇	—	4	1	no	—
71	C₂×C₈×D₄₇	—	4	1	no	—
72	#13093981	D₄	1	4	yes	—
73	#13093981	Q₈	1	4	yes	—
74	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
90	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
91	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
92	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
93	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
94	Dic₄₇⋊C₈	—	2	2	no	—
95	Dic₄₇⋊C₈	—	2	2	no	—
96	Dic₄₇⋊C₈	—	2	2	no	—
97	Dic₄₇⋊C₈	—	2	2	no	—
98	Dic₄₇⋊C₈	—	4	1	no	—
99	Dic₄₇⋊C₈	—	4	1	no	—
100	Dic₄₇⋊C₈	—	4	1	no	—
101	Dic₄₇⋊C₈	—	4	1	no	—
102	(C₂×D₄₇)⋊C₈	—	2	2	no	—
103	(C₂×D₄₇)⋊C₈	—	2	2	no	—
104	#13093935	—	2	2	no	—
105	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
106	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
107	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
108	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
109	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
110	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
111	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
112	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
113	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
114	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
115	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
121	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₄₇	—	2	2	no	—
125	C₄⋊C₈×C₄₇	—	4	1	no	—
126	C₄⋊C₈×C₄₇	—	4	1	no	—
127	C₄×C₈×C₄₇	—	2	2	no	—
128	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
129	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
130	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
138	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₄×D₄₇	—	2	1	no	—
146	C₂×C₄×D₄₇	—	2	1	no	—
147	C₂×C₄×D₄₇	—	2	1	no	—
148	C₂×C₄×D₄₇	—	2	1	no	—
149	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
150	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
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	—	2	1	no	—
155	C₂×C₈×C₄₇	—	2	1	no	—
156	C₂×C₈×C₄₇	—	2	1	no	—
157	C₂×C₈×C₄₇	—	2	1	no	—
158	C₂×C₈×C₄₇	—	2	1	no	—
159	C₂×C₈×C₄₇	—	2	1	no	—
160	C₂×C₈×C₄₇	—	2	1	no	—
161	C₂×C₈×C₄₇	—	2	1	no	—
162	C₂×C₈×C₄₇	—	2	1	no	—
163	C₄⋊C₄×C₄₇	—	2	2	no	—
164	C₄⋊C₄×C₄₇	—	4	1	no	—
165	C₄²×C₄₇	—	2	1	no	—
166	C₄²×C₄₇	—	2	1	no	—
167	C₄²×C₄₇	—	2	1	no	—
168	C₄²×C₄₇	—	2	1	no	—
169	C₄²×C₄₇	C₂×D₄	1	2	yes	—
170	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
171	(C₂×D₄₇)⋊C₄	—	2	2	no	—
172	(C₂×D₄₇)⋊C₄	—	2	2	no	—
173	(C₂×D₄₇)⋊C₄	—	4	1	no	—
174	(C₂×D₄₇)⋊C₄	—	4	1	no	—
175	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	4	yes	—
176	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	4	yes	—
177	C₄⋊Dic₄₇	—	2	2	no	—
178	C₄⋊Dic₄₇	—	4	1	no	—
179	Dic₄₇⋊C₄	C₄⋊C₄	1	4	yes	—
180	Dic₄₇⋊C₄	C₄⋊C₄	1	4	yes	—
181	C₄×Dic₄₇	—	2	2	no	—
182	C₄×Dic₄₇	—	2	1	no	—
183	C₄×Dic₄₇	—	2	1	no	—
184	C₄×Dic₄₇	—	2	1	no	—
185	C₄×Dic₄₇	—	2	1	no	—
186	C₄×Dic₄₇	—	2	2	no	—
187	C₄×Dic₄₇	—	4	1	no	—
188	C₄×Dic₄₇	—	4	1	no	—
189	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
190	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
191	C₂×C₄₇⋊C₈	—	2	1	no	—
192	C₂×C₄₇⋊C₈	—	2	1	no	—
193	C₂×C₄₇⋊C₈	—	2	1	no	—
194	C₂×C₄₇⋊C₈	—	2	1	no	—
195	C₂×C₄₇⋊C₈	—	2	1	no	—
196	C₂×C₄₇⋊C₈	—	2	1	no	—
197	C₂×C₄₇⋊C₈	—	2	1	no	—
198	C₂×C₄₇⋊C₈	—	2	1	no	—
199	C₂×C₄₇⋊C₈	—	2	1	no	—
200	C₂×C₄₇⋊C₈	—	2	1	no	—
201	C₂×C₄₇⋊C₈	—	2	1	no	—
202	C₂×C₄₇⋊C₈	—	2	1	no	—
203	#10625324	—	4	4	no	—
204	C₈×D₄₇	—	4	4	no	—
205	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
206	C₂²×D₄₇	—	2	1	no	—
207	C₂²×D₄₇	—	2	1	no	—
208	C₂²×D₄₇	—	2	1	no	—
209	C₂²×D₄₇	—	2	1	no	—
210	C₂²×D₄₇	—	2	1	no	—
211	C₂²×D₄₇	—	2	1	no	—
212	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
213	C₂×C₄×C₄₇	—	2	1	no	—
214	C₂×C₄×C₄₇	—	2	1	no	—
215	C₂×C₄×C₄₇	—	2	1	no	—
216	C₂×C₄×C₄₇	—	2	1	no	—
217	C₂×C₄×C₄₇	—	2	1	no	—
218	C₂×C₄×C₄₇	—	2	1	no	—
219	C₂×C₄×C₄₇	—	2	1	no	—
220	C₂×C₄×C₄₇	—	2	1	no	—
221	C₂×C₄×C₄₇	—	2	1	no	—
222	C₂×C₄×C₄₇	—	2	1	no	—
223	C₂×C₄×C₄₇	—	2	1	no	—
224	C₂×C₄×C₄₇	—	2	1	no	—
225	C₂×C₄×C₄₇	—	2	1	no	—
226	C₂×C₄×C₄₇	—	2	1	no	—
227	C₂×C₄×C₄₇	—	2	1	no	—
228	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
229	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
230	C₂×C₄×C₄₇	#131	1	2	yes	—
231	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
233	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
236	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
237	C₂×Dic₄₇	—	2	1	no	—
238	C₂×Dic₄₇	—	2	1	no	—
239	C₂×Dic₄₇	—	2	1	no	—
240	C₂×Dic₄₇	—	2	1	no	—
241	C₂×Dic₄₇	—	2	1	no	—
242	C₂×Dic₄₇	—	2	1	no	—
243	C₂×Dic₄₇	—	2	1	no	—
244	C₂×Dic₄₇	—	2	1	no	—
245	C₂×Dic₄₇	—	2	1	no	—
246	C₂×Dic₄₇	—	2	1	no	—
247	C₂×Dic₄₇	—	2	1	no	—
248	C₂×Dic₄₇	—	2	1	no	—
249	C₂×Dic₄₇	—	2	1	no	—
250	C₂×Dic₄₇	—	2	1	no	—
251	C₂×Dic₄₇	—	2	1	no	—
252	C₂×Dic₄₇	—	2	1	no	—
253	C₂×Dic₄₇	—	2	1	no	—
254	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
255	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
256	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
257	C₂×Dic₄₇	#131	1	2	yes	—
258	C₄×D₄₇	—	2	2	no	—
259	C₄×D₄₇	—	2	2	no	—
260	C₄×D₄₇	—	2	2	no	—
261	C₄×D₄₇	—	2	2	no	—
262	C₈×C₄₇	—	4	1	no	—
263	C₈×C₄₇	—	4	1	no	—
264	C₈×C₄₇	—	4	1	no	—
265	C₈×C₄₇	—	4	1	no	—
266	C₄₇⋊C₈	—	4	1	no	—
267	C₄₇⋊C₈	—	4	1	no	—
268	C₄₇⋊C₈	—	4	1	no	—
269	C₄₇⋊C₈	—	4	1	no	—
270	#21980	—	47	1	no	maximal, Sylow
271	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
272	C₂²×C₄₇	#520	1	1	yes	characteristic
273	C₂²×C₄₇	#520	1	1	yes	characteristic
274	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
275	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
276	C₂²×C₄₇	#568	1	1	yes	characteristic
277	C₂²×C₄₇	#568	1	1	yes	characteristic
278	C₂×D₄₇	—	2	2	no	—
279	C₂×D₄₇	—	2	2	no	—
280	C₂×D₄₇	—	2	2	no	—
281	C₂×D₄₇	—	4	1	no	—
282	C₂×D₄₇	—	4	1	no	—
283	C₂×D₄₇	—	4	1	no	—
284	C₂×D₄₇	—	4	1	no	—
285	C₄×C₄₇	—	2	2	no	—
286	C₄×C₄₇	—	2	2	no	—
287	C₄×C₄₇	—	2	2	no	—
288	C₄×C₄₇	—	4	1	no	—
289	C₄×C₄₇	—	4	1	no	—
290	C₄×C₄₇	—	4	1	no	—
291	C₄×C₄₇	#535	1	1	yes	characteristic
292	C₄×C₄₇	#536	1	1	yes	characteristic
293	C₄×C₄₇	#544	1	1	yes	characteristic
294	C₄×C₄₇	#544	1	1	yes	characteristic
295	Dic₄₇	—	2	2	no	—
296	Dic₄₇	—	2	2	no	—
297	Dic₄₇	—	2	2	no	—
298	Dic₄₇	—	2	2	no	—
299	Dic₄₇	—	4	1	no	—
300	Dic₄₇	—	4	1	no	—
301	Dic₄₇	—	4	1	no	—
302	C₂×#433	—	47	1	no	—
303	C₂×#424	—	47	1	no	—
304	#2298	—	47	1	no	—
305	#1940	—	47	1	no	—
306	#1940	—	47	1	no	—
307	#1939	—	47	1	no	—
308	#1939	D₄₇	1	1	yes	characteristic, complemented
309	#1851	—	47	1	no	—
310	#1851	—	47	1	no	—
311	#1850	—	47	1	no	—
312	#1850	—	47	1	no	—
313	#1843	—	47	1	no	—
314	#1842	—	47	1	no	—
315	#1832	—	47	1	no	—
316	#1831	—	47	1	no	—
317	C₂×C₄₇	#2317	1	1	yes	characteristic
318	C₂×C₄₇	#2906	1	1	yes	characteristic
319	C₂×C₄₇	#2906	1	1	yes	characteristic
320	C₂×C₄₇	#2992	1	1	yes	characteristic
321	C₂×C₄₇	#2993	1	1	yes	characteristic
322	C₂×C₄₇	#2994	1	1	yes	characteristic
323	C₂×C₄₇	#2995	1	1	yes	characteristic
324	D₄₇	—	4	2	no	—
325	C₂²×M₁₆	—	47	1	no	—
326	C₂³×C₈	—	47	1	no	—
327	C₂×#117	—	47	1	no	—
328	#433	—	94	4	no	—
329	#424	—	94	4	no	—
330	C₂×C₄⋊C₈	—	47	1	no	—
331	C₂×C₄⋊C₈	—	47	1	no	—
332	C₂×C₄⋊C₈	—	47	1	no	—
333	C₂×C₄⋊C₈	—	47	1	no	—
334	C₂×C₄⋊C₈	—	47	1	no	—
335	C₂×C₄⋊C₈	—	47	1	no	—
336	C₂×C₄⋊C₈	—	47	1	no	—
337	C₂×C₄⋊C₈	—	47	1	no	—
338	C₂×C₄⋊C₈	—	47	1	no	—
339	C₂×C₄⋊C₈	—	47	1	no	—
340	C₂×C₄⋊C₈	—	47	1	no	—
341	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
342	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
343	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
344	C₂×C₂²⋊C₈	—	47	1	no	—
345	C₂×C₂²⋊C₈	—	47	1	no	—
346	C₂×#97	—	47	1	no	—
347	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
348	#388	—	47	1	no	—
349	#388	—	47	1	no	—
350	#388	—	47	1	no	—
351	#388	—	47	1	no	—
352	#387	—	47	1	no	—
353	#387	—	47	1	no	—
354	#387	—	47	1	no	—
355	#387	—	47	1	no	—
356	C₄×C₄⋊C₄	—	47	1	no	—
357	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
358	C₄×C₂²⋊C₄	—	47	1	no	—
359	C₄×C₂²⋊C₄	—	47	1	no	—
360	#376	—	47	1	no	—
361	C₄³	—	47	1	no	—
362	#336	—	47	1	no	—
363	#336	—	47	1	no	—
364	#336	—	47	1	no	—
365	#336	—	47	1	no	—
366	#336	—	47	1	no	—
367	#336	—	47	1	no	—
368	#336	C₂×D₄₇	1	1	yes	characteristic
369	#336	C₂×D₄₇	1	1	yes	characteristic
370	C₄₇	#21980	1	1	yes	characteristic, complemented, Sylow
371	C₂³×C₄	—	47	1	no	—
372	C₂×M₁₆	—	94	2	no	—
373	C₂×M₁₆	—	188	1	no	—
374	C₂×M₁₆	—	188	1	no	—
375	C₂²×C₈	—	47	1	no	—
376	C₂²×C₈	—	47	1	no	—
377	C₂²×C₈	—	47	1	no	—
378	C₂²×C₈	—	47	1	no	—
379	C₂²×C₈	—	94	2	no	—
380	C₂²×C₈	—	188	1	no	—
381	C₂²×C₈	—	188	1	no	—
382	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
383	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
384	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
385	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
386	#117	—	47	4	no	—
387	#117	—	47	4	no	—
388	C₂×C₄⋊C₄	—	47	1	no	—
389	C₂×C₄⋊C₄	—	47	1	no	—
390	C₂×C₄⋊C₄	—	47	1	no	—
391	C₂×C₄⋊C₄	—	47	1	no	—
392	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	—	47	1	no	—
395	C₂×C₂²⋊C₄	—	47	1	no	—
396	C₂×C₂²⋊C₄	—	47	1	no	—
397	C₂×C₂²⋊C₄	—	47	1	no	—
398	C₂×C₂²⋊C₄	—	47	1	no	—
399	C₂×C₂²⋊C₄	—	47	1	no	—
400	C₂×C₄²	—	47	1	no	—
401	C₂×C₄²	—	47	1	no	—
402	C₂×C₄²	—	47	1	no	—
403	C₂×C₄²	—	47	1	no	—
404	C₂×C₄²	—	47	1	no	—
405	C₂×C₄²	—	47	1	no	—
406	C₂×C₄²	—	47	1	no	—
407	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
408	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
409	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
410	C₄⋊C₈	—	2	2	no	—
411	C₄⋊C₈	—	4	1	no	—
412	C₄⋊C₈	—	4	1	no	—
413	C₄⋊C₈	—	94	2	no	—
414	C₄⋊C₈	—	94	2	no	—
415	C₄⋊C₈	—	94	2	no	—
416	C₄⋊C₈	—	94	2	no	—
417	C₄⋊C₈	—	94	2	no	—
418	C₄⋊C₈	—	188	1	no	—
419	C₄⋊C₈	—	188	1	no	—
420	C₄⋊C₈	—	188	1	no	—
421	C₄⋊C₈	—	188	1	no	—
422	C₄⋊C₈	—	188	1	no	—
423	C₄⋊C₈	—	188	1	no	—
424	C₂²⋊C₈	—	94	2	no	—
425	C₂²⋊C₈	—	94	2	no	—
426	#97	—	94	2	no	—
427	C₄×C₈	—	2	2	no	—
428	#95	—	47	1	no	—
429	#95	—	47	1	no	—
430	#95	—	47	1	no	—
431	#95	—	47	1	no	—
432	#95	—	47	1	no	—
433	#95	—	47	1	no	—
434	#95	—	47	1	no	—
435	#95	—	47	1	no	—
436	#95	—	47	1	no	—
437	#95	—	47	1	no	—
438	#95	C₄×D₄₇	1	1	yes	characteristic
439	#95	C₄×D₄₇	1	1	yes	characteristic
440	C₂⁴	—	47	1	no	—
441	C₂²×C₄	—	47	1	no	—
442	C₂²×C₄	—	47	1	no	—
443	C₂²×C₄	—	47	1	no	—
444	C₂²×C₄	—	47	1	no	—
445	C₂²×C₄	—	47	2	no	—
446	C₂²×C₄	—	47	2	no	—
447	C₂²×C₄	—	47	1	no	—
448	C₂²×C₄	—	47	1	no	—
449	C₂²×C₄	—	47	1	no	—
450	C₂²×C₄	—	94	1	no	—
451	C₂²×C₄	—	94	1	no	—
452	C₂²×C₄	—	94	1	no	—
453	C₂²×C₄	—	94	1	no	—
454	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
456	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
460	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
461	M₁₆	—	188	4	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	94	1	no	—
475	C₂×C₈	—	94	1	no	—
476	C₂×C₈	—	94	1	no	—
477	C₂×C₈	—	94	1	no	—
478	C₂×C₈	—	94	1	no	—
479	C₂×C₈	—	94	1	no	—
480	C₂×C₈	—	94	1	no	—
481	C₂×C₈	—	94	1	no	—
482	C₂×C₈	—	94	1	no	—
483	C₂×C₈	—	94	1	no	—
484	C₂×C₈	—	94	1	no	—
485	C₂×C₈	—	94	1	no	—
486	C₂×C₈	—	188	4	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	47	4	no	—
490	C₄⋊C₄	—	47	4	no	—
491	C₄⋊C₄	—	94	2	no	—
492	C₄⋊C₄	—	188	1	no	—
493	C₂²⋊C₄	—	47	4	no	—
494	C₂²⋊C₄	—	47	4	no	—
495	C₂²⋊C₄	—	94	2	no	—
496	C₂²⋊C₄	—	94	2	no	—
497	C₂²⋊C₄	—	188	1	no	—
498	C₂²⋊C₄	—	188	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	47	2	no	—
504	C₄²	—	47	2	no	—
505	C₄²	—	94	2	no	—
506	C₄²	—	94	2	no	—
507	C₄²	—	94	1	no	—
508	C₄²	—	94	1	no	—
509	C₄²	—	94	1	no	—
510	C₄²	—	94	1	no	—
511	C₄²	—	188	1	no	—
512	C₄²	—	188	1	no	—
513	C₄²	D₄×D₄₇	1	2	yes	—
514	C₄²	Q₈×D₄₇	1	2	yes	—
515	C₂³	—	47	2	no	—
516	C₂³	—	94	1	no	—
517	C₂³	—	94	1	no	—
518	C₂³	—	94	1	no	—
519	C₂³	—	94	1	no	—
520	C₂³	—	94	1	no	—
521	C₂³	—	94	1	no	—
522	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	47	2	no	—
539	C₂×C₄	—	47	2	no	—
540	C₂×C₄	—	47	2	no	—
541	C₂×C₄	—	47	2	no	—
542	C₂×C₄	—	94	1	no	—
543	C₂×C₄	—	94	1	no	—
544	C₂×C₄	—	94	1	no	—
545	C₂×C₄	—	94	1	no	—
546	C₂×C₄	—	94	1	no	—
547	C₂×C₄	—	94	1	no	—
548	C₂×C₄	—	94	1	no	—
549	C₂×C₄	—	94	1	no	—
550	C₂×C₄	—	94	2	no	—
551	C₂×C₄	—	94	2	no	—
552	C₂×C₄	—	94	2	no	—
553	C₂×C₄	—	94	2	no	—
554	C₂×C₄	—	94	1	no	—
555	C₂×C₄	—	94	1	no	—
556	C₂×C₄	—	94	1	no	—
557	C₂×C₄	—	94	1	no	—
558	C₂×C₄	—	94	1	no	—
559	C₂×C₄	—	94	1	no	—
560	C₂×C₄	—	94	1	no	—
561	C₂×C₄	—	94	1	no	—
562	C₂×C₄	—	94	1	no	—
563	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
564	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
565	C₂×C₄	#13094030	1	2	yes	—
566	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
567	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
568	C₂×C₄	#13094069	1	1	yes	characteristic
569	C₂×C₄	#13094070	1	1	yes	characteristic
570	C₂×C₄	#13094071	1	1	yes	characteristic
571	C₂×C₄	#13094072	1	1	yes	characteristic
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	—	188	1	no	—
577	C₈	—	188	1	no	—
578	C₈	—	188	1	no	—
579	C₈	—	188	1	no	—
580	C₂²	—	94	2	no	—
581	C₂²	—	94	2	no	—
582	C₂²	—	94	2	no	—
583	C₂²	—	188	1	no	—
584	C₂²	—	188	1	no	—
585	C₂²	—	188	1	no	—
586	C₂²	—	188	1	no	—
587	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
588	C₂²	#15689602	1	1	yes	characteristic
589	C₂²	#15689605	1	1	yes	characteristic
590	C₂²	#131×D₄₇	1	1	yes	characteristic
591	C₂²	C₂×#13094030	1	1	yes	characteristic
592	C₂²	#15689888	1	1	yes	characteristic
593	C₂²	#15689889	1	1	yes	characteristic
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	94	2	no	—
601	C₄	—	94	2	no	—
602	C₄	—	94	2	no	—
603	C₄	—	94	2	no	—
604	C₄	—	188	1	no	—
605	C₄	—	188	1	no	—
606	C₄	—	188	1	no	—
607	C₄	#15689689	1	1	yes	characteristic
608	C₄	#15689696	1	1	yes	characteristic
609	C₄	#15689750	1	1	yes	characteristic
610	C₄	#15689753	1	1	yes	characteristic
611	C₂	—	188	2	no	—
612	C₂	#20246010	1	1	yes	characteristic
613	C₂	#20251953	1	1	yes	characteristic
614	C₂	#20251955	1	1	yes	characteristic
615	C₂	#20252526	1	1	yes	characteristic
616	C₂	#20252536	1	1	yes	characteristic
617	C₂	#20252545	1	1	yes	characteristic
618	C₂	#20252552	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1939	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1939	D₄₇
hypocenter	C₄₇	#21980
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
4. #20244112	C₂	semidirect
5. #20244109	C₂	semidirect
6. #20244106	C₂	semidirect
11. #20243541	C₂	semidirect
12. #20243539	C₂	semidirect
13. #20243506	C₂	semidirect
14. #20243503	C₂	semidirect
15. C₄₇×#1939	C₂	semidirect
308. #1939	D₄₇	semidirect
370. C₄₇	#21980	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689182	2
C₂×#15689148	2
#20245881	2
#20244112	2
#20244109	2
#20244106	2
#20243572	2
#20243569	2
#20243567	2
#20243564	2
#20243541	2
#20243539	2
#20243506	2
#20243503	2
C₄₇×#1939	2
#21980	47