Subgroups — #26221765

Order 12032.

710 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20245784	C₂	1	1	yes	maximal, characteristic
2	#20244000	C₂	1	1	yes	maximal, characteristic
3	#20243999	C₂	1	1	yes	maximal, characteristic
4	#20243995	C₂	1	1	yes	maximal, characteristic
5	#20243994	C₂	1	1	yes	maximal, characteristic
6	#20243954	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243951	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243946	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243247	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243244	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243149	C₂	1	1	yes	maximal, characteristic
12	#20243145	C₂	1	1	yes	maximal, characteristic
13	#20243138	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243074	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1916	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×(C₂×D₄₇)⋊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×#13093934	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	#15688990	C₄	1	1	yes	characteristic
32	#15688990	C₄	1	1	yes	characteristic
33	#15688988	C₄	1	1	yes	characteristic
34	#15688988	C₄	1	1	yes	characteristic
35	#15688985	C₄	1	1	yes	characteristic
36	#15688985	C₄	1	1	yes	characteristic
37	#15688980	C₄	1	1	yes	characteristic
38	#15688980	C₄	1	1	yes	characteristic
39	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
40	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
41	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
42	#15688969	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	#15688878	C₂²	1	1	yes	characteristic
47	#15688878	C₂²	1	1	yes	characteristic
48	#15688877	C₂²	1	1	yes	characteristic
49	#15688877	C₂²	1	1	yes	characteristic
50	#15688877	C₂²	1	1	yes	characteristic
51	#15688877	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
55	C₄₇×#336	C₂²	1	1	yes	characteristic
56	C₄₇×#336	C₂²	1	1	yes	characteristic
57	C₄₇×#336	C₂²	1	1	yes	characteristic
58	C₄₇×#336	C₂²	1	1	yes	characteristic
59	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
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	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
77	C₄²×D₄₇	—	2	2	no	—
78	C₄²×D₄₇	—	2	2	no	—
79	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
80	Dic₄₇⋊C₈	—	2	2	no	—
81	Dic₄₇⋊C₈	—	2	2	no	—
82	(C₂×D₄₇)⋊C₈	—	2	2	no	—
83	(C₂×D₄₇)⋊C₈	—	2	2	no	—
84	(C₂×D₄₇)⋊C₈	—	2	2	no	—
85	(C₂×D₄₇)⋊C₈	—	2	2	no	—
86	#13093935	—	2	2	no	—
87	#13093934	—	2	2	no	—
88	#13093934	—	2	2	no	—
89	#13093934	—	2	2	no	—
90	C₈×Dic₄₇	—	2	2	no	—
91	C₈×Dic₄₇	—	2	2	no	—
92	C₈×Dic₄₇	—	2	2	no	—
93	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
94	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
95	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
96	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
97	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
98	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
99	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
100	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
101	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
102	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
103	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
104	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
105	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
106	C₄₇⋊#95	C₂×C₄	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	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₄₇	—	2	2	no	—
117	C₄×C₈×C₄₇	—	2	2	no	—
118	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
119	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
120	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
128	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
135	C₂×C₄×D₄₇	—	2	2	no	—
136	C₂×C₄×D₄₇	—	2	2	no	—
137	C₂×C₄×D₄₇	—	2	1	no	—
138	C₂×C₄×D₄₇	—	2	1	no	—
139	C₂×C₄×D₄₇	—	2	1	no	—
140	C₂×C₄×D₄₇	—	2	1	no	—
141	C₂×C₄×D₄₇	—	2	1	no	—
142	C₂×C₄×D₄₇	—	2	1	no	—
143	C₂×C₄×D₄₇	—	2	2	no	—
144	C₂×C₄×D₄₇	—	2	2	no	—
145	C₂×C₄×D₄₇	—	4	1	no	—
146	C₂×C₄×D₄₇	—	4	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	—	2	1	no	—
155	C₂×C₈×C₄₇	—	2	1	no	—
156	C₂×C₈×C₄₇	—	2	1	no	—
157	C₂×C₈×C₄₇	#41	1	2	yes	—
158	C₂×C₈×C₄₇	#41	1	2	yes	—
159	C₄⋊C₄×C₄₇	—	2	2	no	—
160	C₄⋊C₄×C₄₇	—	4	1	no	—
161	C₄²×C₄₇	—	2	1	no	—
162	C₄²×C₄₇	—	2	1	no	—
163	C₄²×C₄₇	—	2	1	no	—
164	C₄²×C₄₇	—	2	1	no	—
165	C₄²×C₄₇	—	2	1	no	—
166	C₄²×C₄₇	—	2	1	no	—
167	(C₂×D₄₇)⋊C₄	—	2	2	no	—
168	(C₂×D₄₇)⋊C₄	—	2	2	no	—
169	(C₂×D₄₇)⋊C₄	—	4	1	no	—
170	(C₂×D₄₇)⋊C₄	—	4	1	no	—
171	C₄⋊Dic₄₇	—	2	2	no	—
172	C₄⋊Dic₄₇	—	4	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	2	no	—
178	C₄×Dic₄₇	—	2	2	no	—
179	C₄×Dic₄₇	#41	1	2	yes	—
180	C₄×Dic₄₇	#41	1	2	yes	—
181	C₂×C₄₇⋊C₈	—	2	1	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	—	2	1	no	—
191	C₂×C₄₇⋊C₈	#41	1	2	yes	—
192	C₂×C₄₇⋊C₈	#41	1	2	yes	—
193	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
194	C₂²×D₄₇	—	2	1	no	—
195	C₂²×D₄₇	—	2	1	no	—
196	C₂²×D₄₇	—	2	1	no	—
197	C₂²×D₄₇	—	2	1	no	—
198	C₂²×D₄₇	—	2	1	no	—
199	C₂²×D₄₇	—	2	1	no	—
200	C₂²×D₄₇	#131	1	2	yes	—
201	C₂×C₄×C₄₇	—	2	1	no	—
202	C₂×C₄×C₄₇	—	2	1	no	—
203	C₂×C₄×C₄₇	—	2	1	no	—
204	C₂×C₄×C₄₇	—	2	1	no	—
205	C₂×C₄×C₄₇	—	2	1	no	—
206	C₂×C₄×C₄₇	—	2	1	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	1	no	—
212	C₂×C₄×C₄₇	—	2	1	no	—
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	#131	1	2	yes	—
219	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
225	C₂×Dic₄₇	—	2	1	no	—
226	C₂×Dic₄₇	—	2	1	no	—
227	C₂×Dic₄₇	—	2	1	no	—
228	C₂×Dic₄₇	—	2	1	no	—
229	C₂×Dic₄₇	—	2	1	no	—
230	C₂×Dic₄₇	—	2	1	no	—
231	C₂×Dic₄₇	—	2	1	no	—
232	C₂×Dic₄₇	—	2	1	no	—
233	C₂×Dic₄₇	—	2	1	no	—
234	C₂×Dic₄₇	—	2	1	no	—
235	C₂×Dic₄₇	—	2	1	no	—
236	C₂×Dic₄₇	—	2	1	no	—
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	#117	1	2	yes	—
245	C₂×Dic₄₇	#117	1	2	yes	—
246	C₄×D₄₇	—	4	4	no	—
247	C₄×D₄₇	—	4	4	no	—
248	C₄×D₄₇	—	4	1	no	—
249	C₄×D₄₇	—	4	1	no	—
250	C₄×D₄₇	—	4	1	no	—
251	C₄×D₄₇	—	4	1	no	—
252	C₈×C₄₇	—	2	2	no	—
253	C₈×C₄₇	—	2	2	no	—
254	C₈×C₄₇	—	4	1	no	—
255	C₈×C₄₇	—	4	1	no	—
256	C₄₇⋊C₈	—	2	2	no	—
257	C₄₇⋊C₈	—	2	2	no	—
258	C₄₇⋊C₈	—	4	1	no	—
259	C₄₇⋊C₈	—	4	1	no	—
260	#21437	—	47	1	no	maximal, Sylow
261	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
262	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
263	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
264	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
265	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
266	C₂²×C₄₇	#568	1	1	yes	characteristic
267	C₂²×C₄₇	#568	1	1	yes	characteristic
268	C₂×D₄₇	—	2	2	no	—
269	C₂×D₄₇	—	2	2	no	—
270	C₂×D₄₇	—	2	2	no	—
271	C₂×D₄₇	—	4	1	no	—
272	C₂×D₄₇	—	4	1	no	—
273	C₂×D₄₇	—	4	1	no	—
274	C₂×D₄₇	—	4	1	no	—
275	C₄×C₄₇	—	2	2	no	—
276	C₄×C₄₇	—	4	1	no	—
277	C₄×C₄₇	—	4	1	no	—
278	C₄×C₄₇	—	4	1	no	—
279	C₄×C₄₇	—	4	1	no	—
280	C₄×C₄₇	—	4	1	no	—
281	C₄×C₄₇	#529	1	1	yes	characteristic
282	C₄×C₄₇	#529	1	1	yes	characteristic
283	C₄×C₄₇	#529	1	1	yes	characteristic
284	C₄×C₄₇	#529	1	1	yes	characteristic
285	Dic₄₇	—	2	2	no	—
286	Dic₄₇	—	2	2	no	—
287	Dic₄₇	—	4	1	no	—
288	Dic₄₇	—	4	1	no	—
289	Dic₄₇	—	4	1	no	—
290	Dic₄₇	—	4	1	no	—
291	Dic₄₇	—	4	1	no	—
292	#2283	—	47	1	no	—
293	#1924	—	47	1	no	—
294	#1924	—	47	1	no	—
295	#1923	—	47	1	no	—
296	#1923	—	47	1	no	—
297	#1917	—	47	1	no	—
298	#1917	—	47	1	no	—
299	#1916	—	47	1	no	—
300	#1916	D₄₇	1	1	yes	characteristic, complemented
301	#1768	—	47	1	no	—
302	#1768	—	47	1	no	—
303	#1749	—	47	1	no	—
304	C₄×C₂²⋊C₈	—	47	1	no	—
305	#1746	—	47	1	no	—
306	#1726	—	47	1	no	—
307	C₂×C₄₇	#2298	1	1	yes	characteristic
308	C₂×C₄₇	#2924	1	1	yes	characteristic
309	C₂×C₄₇	#2924	1	1	yes	characteristic
310	C₂×C₄₇	#2966	1	1	yes	characteristic
311	C₂×C₄₇	#2967	1	1	yes	characteristic
312	C₂×C₄₇	#2968	1	1	yes	characteristic
313	C₂×C₄₇	#2969	1	1	yes	characteristic
314	D₄₇	—	4	2	no	—
315	C₂²×C₄²	—	47	1	no	—
316	C₂×C₄⋊C₈	—	47	1	no	—
317	C₂×C₄⋊C₈	—	47	1	no	—
318	C₂×C₄⋊C₈	—	47	1	no	—
319	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
320	C₂×C₂²⋊C₈	—	47	1	no	—
321	C₂×C₂²⋊C₈	—	47	1	no	—
322	C₂×C₂²⋊C₈	—	47	1	no	—
323	C₂×C₂²⋊C₈	—	47	1	no	—
324	C₂×#97	—	47	1	no	—
325	C₂×#97	—	47	1	no	—
326	C₂×#97	—	47	1	no	—
327	C₂×#97	—	47	1	no	—
328	C₂×C₄×C₈	—	47	1	no	—
329	C₂×C₄×C₈	—	47	1	no	—
330	C₂×C₄×C₈	—	47	1	no	—
331	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
332	#383	—	47	1	no	—
333	#383	—	47	1	no	—
334	#382	—	47	1	no	—
335	#382	—	47	1	no	—
336	#381	—	47	1	no	—
337	#381	—	47	1	no	—
338	#380	—	47	1	no	—
339	#380	—	47	1	no	—
340	C₄×C₄⋊C₄	—	47	1	no	—
341	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
342	C₄×C₂²⋊C₄	—	47	1	no	—
343	C₄×C₂²⋊C₄	—	47	1	no	—
344	#376	—	47	1	no	—
345	#376	—	47	1	no	—
346	#336	—	47	1	no	—
347	#336	—	47	1	no	—
348	#336	—	47	1	no	—
349	#336	—	47	1	no	—
350	#336	—	47	1	no	—
351	#336	—	47	1	no	—
352	#336	—	47	1	no	—
353	#336	—	47	1	no	—
354	#336	C₂×D₄₇	1	1	yes	characteristic
355	#336	C₂×D₄₇	1	1	yes	characteristic
356	#336	C₂×D₄₇	1	1	yes	characteristic
357	#336	C₂×D₄₇	1	1	yes	characteristic
358	C₄₇	#21437	1	1	yes	characteristic, complemented, Sylow
359	C₂³×C₄	—	47	1	no	—
360	C₂³×C₄	—	47	1	no	—
361	C₂³×C₄	—	47	1	no	—
362	C₂²×C₈	—	47	1	no	—
363	C₂²×C₈	—	47	1	no	—
364	C₂²×C₈	—	47	1	no	—
365	C₂²×C₈	—	47	1	no	—
366	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
367	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
368	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
369	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
370	C₂×C₄⋊C₄	—	47	1	no	—
371	C₂×C₄⋊C₄	—	47	1	no	—
372	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	—	47	1	no	—
375	C₂×C₂²⋊C₄	—	47	1	no	—
376	C₂×C₂²⋊C₄	—	47	1	no	—
377	C₂×C₂²⋊C₄	—	47	1	no	—
378	C₂×C₄²	—	47	1	no	—
379	C₂×C₄²	—	47	1	no	—
380	C₂×C₄²	—	47	1	no	—
381	C₂×C₄²	—	47	1	no	—
382	C₂×C₄²	—	47	1	no	—
383	C₂×C₄²	—	94	2	no	—
384	C₂×C₄²	—	94	2	no	—
385	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
386	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
387	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
388	C₄⋊C₈	—	2	2	no	—
389	C₄⋊C₈	—	94	2	no	—
390	C₄⋊C₈	—	94	2	no	—
391	C₄⋊C₈	—	94	2	no	—
392	C₂²⋊C₈	—	94	2	no	—
393	C₂²⋊C₈	—	94	2	no	—
394	C₂²⋊C₈	—	94	2	no	—
395	C₂²⋊C₈	—	94	2	no	—
396	#97	—	94	2	no	—
397	#97	—	94	2	no	—
398	#97	—	94	2	no	—
399	#97	—	94	2	no	—
400	C₄×C₈	—	2	2	no	—
401	C₄×C₈	—	94	2	no	—
402	C₄×C₈	—	94	2	no	—
403	C₄×C₈	—	94	2	no	—
404	#95	—	47	1	no	—
405	#95	—	47	1	no	—
406	#95	—	47	1	no	—
407	#95	—	47	1	no	—
408	#95	—	47	1	no	—
409	#95	—	47	1	no	—
410	#95	—	47	1	no	—
411	#95	—	47	1	no	—
412	#95	—	47	1	no	—
413	#95	—	47	1	no	—
414	#95	—	47	1	no	—
415	#95	—	47	1	no	—
416	#95	—	47	1	no	—
417	#95	—	47	1	no	—
418	#95	C₄×D₄₇	1	1	yes	characteristic
419	#95	C₄×D₄₇	1	1	yes	characteristic
420	C₂⁴	—	47	1	no	—
421	C₂²×C₄	—	47	1	no	—
422	C₂²×C₄	—	47	1	no	—
423	C₂²×C₄	—	47	1	no	—
424	C₂²×C₄	—	47	1	no	—
425	C₂²×C₄	—	47	1	no	—
426	C₂²×C₄	—	47	1	no	—
427	C₂²×C₄	—	47	1	no	—
428	C₂²×C₄	—	94	2	no	—
429	C₂²×C₄	—	94	2	no	—
430	C₂²×C₄	—	94	2	no	—
431	C₂²×C₄	—	94	2	no	—
432	C₂²×C₄	—	94	1	no	—
433	C₂²×C₄	—	94	1	no	—
434	C₂²×C₄	—	94	1	no	—
435	C₂²×C₄	—	94	1	no	—
436	C₂²×C₄	—	94	1	no	—
437	C₂²×C₄	—	94	1	no	—
438	C₂²×C₄	—	188	1	no	—
439	C₂²×C₄	—	188	1	no	—
440	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
441	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
443	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
446	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	47	2	no	—
458	C₂×C₈	—	47	2	no	—
459	C₂×C₈	—	94	1	no	—
460	C₂×C₈	—	94	1	no	—
461	C₂×C₈	—	94	1	no	—
462	C₂×C₈	—	94	1	no	—
463	C₂×C₈	—	94	1	no	—
464	C₂×C₈	—	94	1	no	—
465	C₂×C₈	—	94	1	no	—
466	C₂×C₈	—	94	1	no	—
467	C₂×C₈	—	94	1	no	—
468	C₂×C₈	—	94	1	no	—
469	C₂×C₈	#10625352	1	2	yes	—
470	C₂×C₈	#10625354	1	2	yes	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	—	94	2	no	—
474	C₄⋊C₄	—	188	1	no	—
475	C₂²⋊C₄	—	94	2	no	—
476	C₂²⋊C₄	—	94	2	no	—
477	C₂²⋊C₄	—	188	1	no	—
478	C₂²⋊C₄	—	188	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	47	2	no	—
486	C₄²	—	47	2	no	—
487	C₄²	—	94	2	no	—
488	C₄²	—	94	2	no	—
489	C₄²	—	94	1	no	—
490	C₄²	—	94	1	no	—
491	C₄²	—	94	1	no	—
492	C₄²	—	94	1	no	—
493	C₂³	—	47	2	no	—
494	C₂³	—	94	1	no	—
495	C₂³	—	94	1	no	—
496	C₂³	—	94	1	no	—
497	C₂³	—	94	1	no	—
498	C₂³	—	94	1	no	—
499	C₂³	—	94	1	no	—
500	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	47	2	no	—
519	C₂×C₄	—	47	2	no	—
520	C₂×C₄	—	94	1	no	—
521	C₂×C₄	—	94	1	no	—
522	C₂×C₄	—	94	1	no	—
523	C₂×C₄	—	94	1	no	—
524	C₂×C₄	—	94	1	no	—
525	C₂×C₄	—	94	1	no	—
526	C₂×C₄	—	94	1	no	—
527	C₂×C₄	—	94	1	no	—
528	C₂×C₄	—	94	1	no	—
529	C₂×C₄	—	94	1	no	—
530	C₂×C₄	—	94	1	no	—
531	C₂×C₄	—	94	1	no	—
532	C₂×C₄	—	94	1	no	—
533	C₂×C₄	—	94	1	no	—
534	C₂×C₄	—	94	1	no	—
535	C₂×C₄	—	94	1	no	—
536	C₂×C₄	—	94	1	no	—
537	C₂×C₄	—	94	1	no	—
538	C₂×C₄	—	94	1	no	—
539	C₂×C₄	—	188	4	no	—
540	C₂×C₄	—	188	4	no	—
541	C₂×C₄	—	188	1	no	—
542	C₂×C₄	—	188	1	no	—
543	C₂×C₄	—	188	1	no	—
544	C₂×C₄	—	188	1	no	—
545	C₂×C₄	#13094030	1	2	yes	—
546	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
547	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
548	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
549	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
550	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
551	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
552	C₈	—	2	2	no	—
553	C₈	—	2	2	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	94	2	no	—
557	C₈	—	94	2	no	—
558	C₈	—	188	1	no	—
559	C₈	—	188	1	no	—
560	C₂²	—	94	2	no	—
561	C₂²	—	94	2	no	—
562	C₂²	—	94	2	no	—
563	C₂²	—	188	1	no	—
564	C₂²	—	188	1	no	—
565	C₂²	—	188	1	no	—
566	C₂²	—	188	1	no	—
567	C₂²	#117×D₄₇	1	1	yes	characteristic
568	C₂²	C₄×#10625352	1	1	yes	characteristic
569	C₂²	C₄×#10625354	1	1	yes	characteristic
570	C₂²	#131×D₄₇	1	1	yes	characteristic
571	C₂²	C₂×#13094030	1	1	yes	characteristic
572	C₂²	#15689888	1	1	yes	characteristic
573	C₂²	#15689889	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	94	2	no	—
581	C₄	—	94	2	no	—
582	C₄	—	188	1	no	—
583	C₄	—	188	1	no	—
584	C₄	—	188	1	no	—
585	C₄	—	188	1	no	—
586	C₄	—	188	1	no	—
587	C₄	#15689650	1	1	yes	characteristic
588	C₄	#15689656	1	1	yes	characteristic
589	C₄	#15689658	1	1	yes	characteristic
590	C₄	#15689659	1	1	yes	characteristic
591	C₂	—	188	2	no	—
592	C₂	#20245880	1	1	yes	characteristic
593	C₂	#20252041	1	1	yes	characteristic
594	C₂	#20252044	1	1	yes	characteristic
595	C₂	#20252365	1	1	yes	characteristic
596	C₂	#20252372	1	1	yes	characteristic
597	C₂	#20252379	1	1	yes	characteristic
598	C₂	#20252389	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1916	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1916	D₄₇
hypocenter	C₄₇	#21437
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1916

Complements

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

N	H ≅ G/N	type
6. #20243954	C₂	semidirect
7. #20243951	C₂	semidirect
8. #20243946	C₂	semidirect
9. #20243247	C₂	semidirect
10. #20243244	C₂	semidirect
13. #20243138	C₂	semidirect
14. #20243074	C₂	semidirect
15. C₄₇×#1916	C₂	semidirect
300. #1916	D₄₇	semidirect
358. C₄₇	#21437	semidirect

Maximal subgroups

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

subgroup	index
#20245784	2
#20244000	2
#20243999	2
#20243995	2
#20243994	2
#20243954	2
#20243951	2
#20243946	2
#20243247	2
#20243244	2
#20243149	2
#20243145	2
#20243138	2
#20243074	2
C₄₇×#1916	2
#21437	47