Subgroups — #26230218

Order 12032.

814 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13094000	C₂	1	1	yes	maximal, characteristic
2	#20244325	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244105	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244103	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243946	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243945	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243944	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243943	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243567	C₂	1	1	yes	maximal, characteristic
10	#20243564	C₂	1	1	yes	maximal, characteristic
11	#20243367	C₂	1	1	yes	maximal, characteristic
12	C₈×(C₂×D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic
13	#20243158	C₂	1	1	yes	maximal, characteristic
14	#336×D₄₇	C₂	1	1	yes	maximal, characteristic
15	C₄₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
18	C₂×#13094000	C₄	1	1	yes	characteristic
19	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
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×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
30	#15689030	C₄	1	1	yes	characteristic
31	#15689019	C₄	1	1	yes	characteristic
32	#15689004	C₄	1	1	yes	characteristic
33	#15689004	C₄	1	1	yes	characteristic
34	#15688994	C₄	1	1	yes	characteristic
35	#15688994	C₄	1	1	yes	characteristic
36	#15688980	C₄	1	1	yes	characteristic
37	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×Dic₄₇⋊C₄	C₂²	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	#15688878	C₂²	1	1	yes	characteristic
43	#15688878	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	#15688877	C₂²	1	1	yes	characteristic
51	#15688877	C₂²	1	1	yes	characteristic
52	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₈×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×C₈×D₄₇	—	2	2	no	—
67	C₂×C₈×D₄₇	—	4	1	no	—
68	C₂×C₈×D₄₇	—	4	1	no	—
69	C₂×C₈×D₄₇	—	4	1	no	—
70	C₂×C₈×D₄₇	—	4	1	no	—
71	C₂×C₈×D₄₇	Q₈	1	4	yes	complemented
72	#13094000	C₈	1	8	yes	complemented
73	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×Dic₄₇⋊C₄	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×Dic₄₇⋊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×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
88	C₄²×D₄₇	—	4	1	no	—
89	C₄²×D₄₇	—	4	1	no	—
90	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
91	Dic₄₇⋊C₈	—	4	1	no	—
92	Dic₄₇⋊C₈	—	4	1	no	—
93	Dic₄₇⋊C₈	—	4	1	no	—
94	Dic₄₇⋊C₈	—	4	1	no	—
95	(C₂×D₄₇)⋊C₈	—	2	2	no	—
96	(C₂×D₄₇)⋊C₈	—	2	2	no	—
97	C₄×C₄₇⋊C₈	—	4	1	no	—
98	C₈×Dic₄₇	—	4	1	no	—
99	C₈×Dic₄₇	—	4	1	no	—
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	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	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
111	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
115	C₄×Q₈×C₄₇	—	4	1	no	—
116	C₄×Q₈×C₄₇	—	4	1	no	—
117	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
123	C₄⋊C₈×C₄₇	—	4	1	no	—
124	C₄×C₈×C₄₇	—	4	1	no	—
125	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₂×Q₈×C₄₇	—	4	1	no	—
127	C₂×Q₈×C₄₇	—	4	1	no	—
128	C₂×Q₈×C₄₇	C₂×C₈	1	4	yes	complemented
129	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	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	C₂⁴	1	1	yes	characteristic
136	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×Dic₄₇	C₂²×C₄	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	C₂×C₄×D₄₇	—	2	1	no	—
144	C₂×C₄×D₄₇	—	2	1	no	—
145	C₂×C₄×D₄₇	—	2	1	no	—
146	C₂×C₄×D₄₇	—	2	1	no	—
147	C₂×C₄×D₄₇	—	2	2	no	—
148	C₂×C₄×D₄₇	—	4	1	no	—
149	C₂×C₄×D₄₇	—	4	1	no	—
150	C₂×C₄×D₄₇	—	4	1	no	—
151	C₂×C₄×D₄₇	—	4	1	no	—
152	C₂×C₄×D₄₇	C₂×C₈	1	4	yes	—
153	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
154	C₂×C₄×D₄₇	#41	1	2	yes	—
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	C₂×C₈×C₄₇	—	2	1	no	—
164	C₂×C₈×C₄₇	—	2	1	no	—
165	C₂×C₈×C₄₇	—	2	1	no	—
166	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
167	C₄⋊C₄×C₄₇	—	4	1	no	—
168	C₄⋊C₄×C₄₇	—	4	1	no	—
169	C₄⋊C₄×C₄₇	—	4	1	no	—
170	C₄²×C₄₇	—	2	1	no	—
171	C₄²×C₄₇	—	2	1	no	—
172	C₄²×C₄₇	—	2	1	no	—
173	C₄²×C₄₇	—	2	1	no	—
174	C₄²×C₄₇	—	2	1	no	—
175	C₄²×C₄₇	—	2	1	no	—
176	(C₂×D₄₇)⋊C₄	—	2	2	no	—
177	(C₂×D₄₇)⋊C₄	—	2	2	no	—
178	(C₂×D₄₇)⋊C₄	C₂×C₈	1	4	yes	—
179	(C₂×D₄₇)⋊C₄	C₂×C₈	1	4	yes	—
180	C₄⋊Dic₄₇	—	4	1	no	—
181	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	complemented
182	Dic₄₇⋊C₄	—	4	1	no	—
183	Dic₄₇⋊C₄	—	4	1	no	—
184	Dic₄₇⋊C₄	C₂×C₈	1	4	yes	complemented
185	Dic₄₇⋊C₄	C₂×C₈	1	4	yes	complemented
186	C₄×Dic₄₇	—	2	1	no	—
187	C₄×Dic₄₇	—	2	1	no	—
188	C₄×Dic₄₇	—	2	1	no	—
189	C₄×Dic₄₇	—	2	1	no	—
190	C₄×Dic₄₇	—	2	1	no	—
191	C₄×Dic₄₇	—	2	1	no	—
192	C₄×Dic₄₇	—	4	1	no	—
193	C₄×Dic₄₇	—	4	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	C₂×C₄₇⋊C₈	—	2	1	no	—
204	C₂×C₄₇⋊C₈	—	2	1	no	—
205	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
206	C₈×D₄₇	—	4	4	no	—
207	C₈×D₄₇	—	4	4	no	—
208	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
209	C₂²×D₄₇	—	2	1	no	—
210	C₂²×D₄₇	—	2	1	no	—
211	C₂²×D₄₇	—	2	1	no	—
212	C₂²×D₄₇	—	2	1	no	—
213	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
214	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
215	C₂²×D₄₇	#131	1	2	yes	—
216	Q₈×C₄₇	—	4	4	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	—	2	1	no	—
229	C₂×C₄×C₄₇	—	2	1	no	—
230	C₂×C₄×C₄₇	—	2	1	no	—
231	C₂×C₄×C₄₇	—	2	1	no	—
232	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
233	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
234	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
235	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
236	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
239	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
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	—	2	1	no	—
255	C₂×Dic₄₇	—	2	1	no	—
256	C₂×Dic₄₇	—	2	1	no	—
257	C₂×Dic₄₇	—	2	1	no	—
258	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
259	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
260	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
261	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
262	C₄×D₄₇	—	2	2	no	—
263	C₄×D₄₇	—	2	2	no	—
264	C₄×D₄₇	—	2	2	no	—
265	C₄×D₄₇	—	2	2	no	—
266	C₄×D₄₇	—	4	4	no	—
267	C₄×D₄₇	—	4	4	no	—
268	C₈×C₄₇	—	2	2	no	—
269	C₈×C₄₇	—	4	1	no	—
270	C₈×C₄₇	—	4	1	no	—
271	C₈×C₄₇	—	4	1	no	—
272	C₄₇⋊C₈	—	2	2	no	—
273	C₄₇⋊C₈	—	4	1	no	—
274	C₄₇⋊C₈	—	4	1	no	—
275	C₄₇⋊C₈	—	4	1	no	—
276	#22287	—	47	1	no	maximal, Sylow
277	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
278	C₂²×C₄₇	#518	1	1	yes	characteristic
279	C₂²×C₄₇	#520	1	1	yes	characteristic
280	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
281	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
282	C₂²×C₄₇	#568	1	1	yes	characteristic
283	C₂²×C₄₇	#568	1	1	yes	characteristic
284	C₂×D₄₇	—	2	2	no	—
285	C₂×D₄₇	—	2	2	no	—
286	C₂×D₄₇	—	2	2	no	—
287	C₂×D₄₇	—	2	2	no	—
288	C₂×D₄₇	—	2	2	no	—
289	C₂×D₄₇	—	2	2	no	—
290	C₂×D₄₇	C₈×Q₈	1	4	yes	—
291	C₄×C₄₇	—	2	2	no	—
292	C₄×C₄₇	—	2	2	no	—
293	C₄×C₄₇	—	2	2	no	—
294	C₄×C₄₇	—	4	1	no	—
295	C₄×C₄₇	—	4	1	no	—
296	C₄×C₄₇	—	4	1	no	—
297	C₄×C₄₇	#538	1	1	yes	characteristic
298	C₄×C₄₇	#539	1	1	yes	characteristic
299	C₄×C₄₇	#543	1	1	yes	characteristic
300	C₄×C₄₇	#544	1	1	yes	characteristic
301	Dic₄₇	—	2	2	no	—
302	Dic₄₇	—	2	2	no	—
303	Dic₄₇	—	2	2	no	—
304	Dic₄₇	—	2	2	no	—
305	Dic₄₇	—	4	1	no	—
306	Dic₄₇	—	4	1	no	—
307	Dic₄₇	—	4	1	no	—
308	C₄×C₂²⋊Q₈	—	47	1	no	—
309	#1984	—	47	1	no	—
310	#1984	D₄₇	1	1	yes	characteristic, complemented
311	#1939	—	47	1	no	—
312	#1939	—	47	1	no	—
313	#1916	—	47	1	no	—
314	#1916	—	47	1	no	—
315	#1916	—	47	1	no	—
316	#1916	—	47	1	no	—
317	#1850	—	47	1	no	—
318	#1850	—	47	1	no	—
319	#1797	—	47	1	no	—
320	C₈×C₂²⋊C₄	—	47	1	no	—
321	C₈×C₂²⋊C₄	—	47	1	no	—
322	C₂×#336	—	47	1	no	—
323	C₂×C₄₇	#2329	1	1	yes	characteristic
324	C₂×C₄₇	C₂×C₈×Q₈	1	1	yes	characteristic
325	C₂×C₄₇	#2961	1	1	yes	characteristic
326	C₂×C₄₇	#2972	1	1	yes	characteristic
327	C₂×C₄₇	#2976	1	1	yes	characteristic
328	C₂×C₄₇	#2988	1	1	yes	characteristic
329	C₂×C₄₇	#2992	1	1	yes	characteristic
330	D₄₇	—	2	4	no	—
331	C₂³×C₈	—	47	1	no	—
332	C₂³×C₈	—	47	1	no	—
333	C₂×C₂²⋊Q₈	—	47	1	no	—
334	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
335	C₂²×C₄²	—	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×C₂²⋊C₈	—	47	1	no	—
343	C₂×C₂²⋊C₈	—	47	1	no	—
344	C₂×C₄×C₈	—	47	1	no	—
345	C₂×C₄×C₈	—	47	1	no	—
346	C₂×C₄×C₈	—	47	1	no	—
347	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
348	#391	—	47	1	no	—
349	#389	—	47	1	no	—
350	#387	—	47	1	no	—
351	#387	—	47	1	no	—
352	#385	—	47	1	no	—
353	#385	—	47	1	no	—
354	#380	—	47	1	no	—
355	C₄×C₄⋊C₄	—	47	1	no	—
356	C₄×C₄⋊C₄	—	47	1	no	—
357	C₄×C₄⋊C₄	—	47	1	no	—
358	C₄×C₂²⋊C₄	—	47	1	no	—
359	C₄×C₂²⋊C₄	—	47	1	no	—
360	#336	—	47	1	no	—
361	#336	—	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	—	47	1	no	—
369	#336	—	47	1	no	—
370	#336	C₂×D₄₇	1	1	yes	characteristic
371	#336	C₂×D₄₇	1	1	yes	characteristic
372	#336	C₂×D₄₇	1	1	yes	characteristic
373	#336	C₂×D₄₇	1	1	yes	characteristic
374	C₄₇	#22287	1	1	yes	characteristic, complemented, Sylow
375	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
376	C₂³×C₄	—	47	1	no	—
377	C₂³×C₄	—	47	1	no	—
378	C₂³×C₄	—	47	1	no	—
379	C₂²×C₈	—	47	1	no	—
380	C₂²×C₈	—	47	4	no	—
381	C₂²×C₈	—	47	1	no	—
382	C₂²×C₈	—	47	1	no	—
383	C₂²×C₈	—	47	1	no	—
384	C₂²×C₈	—	94	2	no	—
385	C₂²×C₈	—	188	1	no	—
386	C₂²×C₈	—	188	1	no	—
387	C₂²×C₈	—	188	1	no	—
388	C₂²×C₈	—	188	1	no	—
389	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
390	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
391	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
392	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
393	C₂²⋊Q₈	—	47	8	no	—
394	C₄×Q₈	—	4	1	no	—
395	C₄×Q₈	—	4	1	no	—
396	C₂×C₄⋊C₄	—	47	1	no	—
397	C₂×C₄⋊C₄	—	47	1	no	—
398	C₂×C₄⋊C₄	—	47	1	no	—
399	C₂×C₄⋊C₄	—	47	1	no	—
400	C₂×C₄⋊C₄	—	47	1	no	—
401	C₂×C₄⋊C₄	—	47	1	no	—
402	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	—	47	1	no	—
406	C₂×C₂²⋊C₄	—	47	1	no	—
407	C₂×C₂²⋊C₄	—	47	1	no	—
408	C₂×C₂²⋊C₄	—	47	1	no	—
409	C₂×C₄²	—	47	1	no	—
410	C₂×C₄²	—	47	1	no	—
411	C₂×C₄²	—	47	1	no	—
412	C₂×C₄²	—	47	1	no	—
413	C₂×C₄²	—	47	1	no	—
414	C₂×C₄²	—	188	1	no	—
415	C₂×C₄²	—	188	1	no	—
416	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
417	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
418	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
419	C₄⋊C₈	—	4	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	C₄⋊C₈	—	188	1	no	—
425	C₂²⋊C₈	—	94	2	no	—
426	C₂²⋊C₈	—	94	2	no	—
427	C₄×C₈	—	4	1	no	—
428	C₄×C₈	—	188	1	no	—
429	C₄×C₈	—	188	1	no	—
430	C₄×C₈	—	188	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	—	47	1	no	—
439	#95	—	47	1	no	—
440	#95	—	47	1	no	—
441	C₂⁴	—	47	1	no	—
442	C₂×Q₈	—	4	1	no	—
443	C₂×Q₈	—	4	1	no	—
444	C₂×Q₈	C₈×D₄₇	1	4	yes	complemented
445	C₂²×C₄	—	47	1	no	—
446	C₂²×C₄	—	47	1	no	—
447	C₂²×C₄	—	47	1	no	—
448	C₂²×C₄	—	47	1	no	—
449	C₂²×C₄	—	47	2	no	—
450	C₂²×C₄	—	47	2	no	—
451	C₂²×C₄	—	47	4	no	—
452	C₂²×C₄	—	47	1	no	—
453	C₂²×C₄	—	47	1	no	—
454	C₂²×C₄	—	47	1	no	—
455	C₂²×C₄	—	94	2	no	—
456	C₂²×C₄	—	94	1	no	—
457	C₂²×C₄	—	94	1	no	—
458	C₂²×C₄	—	94	1	no	—
459	C₂²×C₄	—	94	1	no	—
460	C₂²×C₄	—	188	1	no	—
461	C₂²×C₄	—	188	1	no	—
462	C₂²×C₄	—	188	1	no	—
463	C₂²×C₄	—	188	1	no	—
464	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
466	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
468	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
470	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	47	2	no	—
483	C₂×C₈	—	94	1	no	—
484	C₂×C₈	—	94	1	no	—
485	C₂×C₈	—	94	1	no	—
486	C₂×C₈	—	94	1	no	—
487	C₂×C₈	—	94	1	no	—
488	C₂×C₈	—	94	1	no	—
489	C₂×C₈	—	94	1	no	—
490	C₂×C₈	—	94	1	no	—
491	C₂×C₈	—	94	1	no	—
492	C₂×C₈	—	94	1	no	—
493	C₂×C₈	—	94	1	no	—
494	C₂×C₈	—	188	4	no	—
495	C₂×C₈	—	188	4	no	—
496	C₂×C₈	Q₈×D₄₇	1	2	yes	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	47	4	no	—
501	C₄⋊C₄	—	47	4	no	—
502	C₄⋊C₄	—	47	4	no	—
503	C₄⋊C₄	—	188	1	no	—
504	C₄⋊C₄	—	188	1	no	—
505	C₄⋊C₄	—	188	1	no	—
506	C₂²⋊C₄	—	47	4	no	—
507	C₂²⋊C₄	—	47	4	no	—
508	C₂²⋊C₄	—	94	2	no	—
509	C₂²⋊C₄	—	94	2	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	94	1	no	—
517	C₄²	—	94	1	no	—
518	C₄²	—	94	1	no	—
519	C₄²	—	94	1	no	—
520	C₄²	—	94	1	no	—
521	C₄²	—	94	1	no	—
522	C₄²	—	188	1	no	—
523	C₄²	—	188	1	no	—
524	C₂³	—	47	2	no	—
525	C₂³	—	47	2	no	—
526	C₂³	—	47	2	no	—
527	C₂³	—	94	1	no	—
528	C₂³	—	94	1	no	—
529	C₂³	—	94	1	no	—
530	C₂³	—	94	1	no	—
531	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
532	Q₈	—	4	4	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	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	47	2	no	—
549	C₂×C₄	—	47	2	no	—
550	C₂×C₄	—	47	2	no	—
551	C₂×C₄	—	47	2	no	—
552	C₂×C₄	—	94	1	no	—
553	C₂×C₄	—	94	1	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	2	no	—
561	C₂×C₄	—	94	2	no	—
562	C₂×C₄	—	94	2	no	—
563	C₂×C₄	—	94	2	no	—
564	C₂×C₄	—	94	1	no	—
565	C₂×C₄	—	94	1	no	—
566	C₂×C₄	—	94	1	no	—
567	C₂×C₄	—	94	1	no	—
568	C₂×C₄	—	94	1	no	—
569	C₂×C₄	—	94	1	no	—
570	C₂×C₄	—	94	1	no	—
571	C₂×C₄	—	94	1	no	—
572	C₂×C₄	—	94	1	no	—
573	C₂×C₄	—	188	4	no	—
574	C₂×C₄	—	188	4	no	—
575	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
576	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
577	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
578	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
579	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
580	C₂×C₄	#13094069	1	1	yes	characteristic
581	C₂×C₄	#13094069	1	1	yes	characteristic
582	C₂×C₄	#13094070	1	1	yes	characteristic
583	C₂×C₄	#13094072	1	1	yes	characteristic
584	C₈	—	2	2	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₈	—	4	1	no	—
588	C₈	—	94	2	no	—
589	C₈	—	188	1	no	—
590	C₈	—	188	1	no	—
591	C₈	—	188	1	no	—
592	C₂²	—	47	4	no	—
593	C₂²	—	94	2	no	—
594	C₂²	—	94	2	no	—
595	C₂²	—	94	2	no	—
596	C₂²	—	94	2	no	—
597	C₂²	—	94	2	no	—
598	C₂²	—	94	2	no	—
599	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
600	C₂²	#15689596	1	1	yes	characteristic
601	C₂²	#15689605	1	1	yes	characteristic
602	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
603	C₂²	#131×D₄₇	1	1	yes	characteristic
604	C₂²	#15689888	1	1	yes	characteristic
605	C₂²	#15689889	1	1	yes	characteristic
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	94	2	no	—
613	C₄	—	94	2	no	—
614	C₄	—	94	2	no	—
615	C₄	—	94	2	no	—
616	C₄	—	188	1	no	—
617	C₄	—	188	1	no	—
618	C₄	—	188	1	no	—
619	C₄	#15689707	1	1	yes	characteristic
620	C₄	#15689719	1	1	yes	characteristic
621	C₄	#15689748	1	1	yes	characteristic
622	C₄	#15689750	1	1	yes	characteristic
623	C₂	—	94	4	no	—
624	C₂	#20246120	1	1	yes	characteristic
625	C₂	C₈×Q₈×D₄₇	1	1	yes	characteristic
626	C₂	#20252324	1	1	yes	characteristic
627	C₂	#20252410	1	1	yes	characteristic
628	C₂	#20252431	1	1	yes	characteristic
629	C₂	#20252498	1	1	yes	characteristic
630	C₂	#20252526	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#1984	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1984	D₄₇
hypocenter	C₄₇	#22287
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1984

Complements

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

N	H ≅ G/N	type
2. #20244325	C₂	semidirect
3. #20244105	C₂	semidirect
4. #20244103	C₂	semidirect
5. #20243946	C₂	semidirect
6. #20243945	C₂	semidirect
7. #20243944	C₂	semidirect
8. #20243943	C₂	semidirect
15. C₄₇×#1984	C₂	semidirect
71. C₂×C₈×D₄₇	Q₈	semidirect
72. #13094000	C₈	semidirect
128. C₂×Q₈×C₄₇	C₂×C₈	semidirect
181. C₄⋊Dic₄₇	C₂×C₈	semidirect
184. Dic₄₇⋊C₄	C₂×C₈	semidirect
185. Dic₄₇⋊C₄	C₂×C₈	semidirect
310. #1984	D₄₇	semidirect
374. C₄₇	#22287	semidirect
444. C₂×Q₈	C₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13094000	2
#20244325	2
#20244105	2
#20244103	2
#20243946	2
#20243945	2
#20243944	2
#20243943	2
#20243567	2
#20243564	2
#20243367	2
C₈×(C₂×D₄₇)⋊C₄	2
#20243158	2
#336×D₄₇	2
C₄₇×#1984	2
#22287	47