Subgroups — #26218526

Order 12032.

798 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20251976	C₂	1	1	yes	maximal, characteristic
2	#424×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#405×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20243990	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243989	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243988	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243987	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243986	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243985	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243984	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243113	C₂	1	1	yes	maximal, characteristic
12	#20243096	C₂	1	1	yes	maximal, characteristic
13	#20243096	C₂	1	1	yes	maximal, characteristic
14	#20243083	C₂	1	1	yes	maximal, characteristic
15	C₄₇×#1922	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625324	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
20	C₂×#13093981	C₂²	1	1	yes	characteristic
21	#117×D₄₇	C₂²	1	1	yes	characteristic
22	#117×D₄₇	C₂²	1	1	yes	characteristic
23	#15689164	C₄	1	1	yes	characteristic, complemented
24	#15689164	C₄	1	1	yes	characteristic, complemented
25	#15689164	C₄	1	1	yes	characteristic, complemented
26	#15689164	C₄	1	1	yes	characteristic, complemented
27	#15689162	C₄	1	1	yes	characteristic, complemented
28	#15689162	C₄	1	1	yes	characteristic, complemented
29	#15689162	C₄	1	1	yes	characteristic, complemented
30	#15689162	C₄	1	1	yes	characteristic, complemented
31	#15689161	C₂²	1	1	yes	characteristic
32	#15689159	C₂²	1	1	yes	characteristic
33	#15689159	C₂²	1	1	yes	characteristic
34	#15689151	C₂²	1	1	yes	characteristic
35	#15689150	C₂²	1	1	yes	characteristic
36	#15689149	C₂²	1	1	yes	characteristic
37	#15689148	—	2	1	no	—
38	#15689148	—	2	1	no	—
39	C₄⋊C₈×D₄₇	—	2	1	no	—
40	C₄⋊C₈×D₄₇	—	2	1	no	—
41	#15689081	C₂²	1	1	yes	characteristic
42	#15689080	—	2	1	no	—
43	#15689079	C₂²	1	1	yes	characteristic
44	#15689078	C₂²	1	1	yes	characteristic
45	#15689077	—	2	1	no	—
46	#97×D₄₇	—	2	1	no	—
47	C₄×C₈×D₄₇	—	2	1	no	—
48	#15688888	C₂²	1	1	yes	characteristic
49	#15688887	C₂²	1	1	yes	characteristic
50	#15688887	C₂²	1	1	yes	characteristic
51	#15688884	C₂²	1	1	yes	characteristic
52	#15688884	C₂²	1	1	yes	characteristic
53	#15688883	C₂²	1	1	yes	characteristic
54	#15688883	C₂²	1	1	yes	characteristic
55	#15688882	C₂²	1	1	yes	characteristic
56	#15688882	C₂²	1	1	yes	characteristic
57	#15688878	C₂²	1	1	yes	characteristic
58	#15688877	C₂²	1	1	yes	characteristic
59	#15688877	C₂²	1	1	yes	characteristic
60	C₄₇×#427	C₂²	1	1	yes	characteristic
61	C₄₇×#424	C₂²	1	1	yes	characteristic
62	C₄₇×#405	C₂²	1	1	yes	characteristic
63	C₄₇×#341	C₂²	1	1	yes	characteristic
64	C₄₇×#339	C₂²	1	1	yes	characteristic
65	C₄₇×#339	C₂²	1	1	yes	characteristic
66	C₄₇×#336	C₂²	1	1	yes	characteristic
67	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
68	C₂×#10625329	C₂³	1	1	yes	characteristic
69	C₂×#10625329	C₂³	1	1	yes	characteristic
70	C₂×#10625324	—	2	1	no	—
71	C₂×#10625324	—	2	2	no	—
72	C₂×#10625324	—	2	2	no	—
73	C₂×#10625324	—	2	1	no	—
74	C₂×#10625324	C₂×C₄	1	1	yes	characteristic
75	C₂×#10625324	C₂×C₄	1	1	yes	characteristic
76	C₂×#10625324	C₂×C₄	1	1	yes	characteristic
77	C₂×#10625324	C₂×C₄	1	1	yes	characteristic
78	M₁₆×D₄₇	—	2	2	no	—
79	M₁₆×D₄₇	—	2	2	no	—
80	M₁₆×D₄₇	—	2	2	no	—
81	M₁₆×D₄₇	Q₈	1	4	yes	—
82	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
84	C₂×C₈×D₄₇	—	2	1	no	—
85	C₂×C₈×D₄₇	—	2	2	no	—
86	C₂×C₈×D₄₇	—	2	2	no	—
87	C₂×C₈×D₄₇	—	2	1	no	—
88	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
89	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
90	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
91	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
92	#13093983	C₂³	1	1	yes	characteristic
93	#13093983	C₂³	1	1	yes	characteristic
94	#13093982	C₂×C₄	1	1	yes	characteristic
95	#13093982	C₂×C₄	1	1	yes	characteristic
96	#13093982	C₂×C₄	1	1	yes	characteristic
97	#13093982	C₂×C₄	1	1	yes	characteristic
98	#13093981	—	2	1	no	—
99	#13093981	—	2	1	no	—
100	#13093981	—	2	2	no	—
101	#13093981	—	2	2	no	—
102	#13093980	—	2	1	no	—
103	#13093980	—	2	1	no	—
104	C₂×Dic₄₇⋊C₄	—	2	1	no	—
105	C₄⋊C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
106	C₄⋊C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
107	C₄⋊C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
108	C₄⋊C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
109	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
110	C₂²⋊C₄×D₄₇	—	2	1	no	—
111	C₂²⋊C₄×D₄₇	—	2	1	no	—
112	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
113	C₄²×D₄₇	—	2	1	no	—
114	C₄²×D₄₇	—	2	1	no	—
115	#13093958	C₂×C₄	1	1	yes	characteristic
116	#13093958	C₂×C₄	1	1	yes	characteristic
117	#13093957	C₂×C₄	1	1	yes	characteristic
118	#13093957	C₂×C₄	1	1	yes	characteristic
119	#13093957	C₂×C₄	1	1	yes	characteristic
120	#13093957	C₂×C₄	1	1	yes	characteristic
121	#13093956	C₂×C₄	1	1	yes	characteristic
122	#13093956	C₂×C₄	1	1	yes	characteristic
123	#13093955	C₂×C₄	1	1	yes	characteristic
124	#13093955	C₂×C₄	1	1	yes	characteristic
125	#13093955	C₂×C₄	1	1	yes	characteristic
126	#13093955	C₂×C₄	1	1	yes	characteristic
127	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
128	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
129	Dic₄₇⋊C₈	—	2	1	no	—
130	Dic₄₇⋊C₈	—	2	1	no	—
131	Dic₄₇⋊C₈	—	2	1	no	—
132	Dic₄₇⋊C₈	—	2	1	no	—
133	#13093935	—	2	1	no	—
134	#13093934	—	2	1	no	—
135	#13093934	—	2	1	no	—
136	C₄×C₄₇⋊C₈	—	2	1	no	—
137	C₈×Dic₄₇	—	2	1	no	—
138	C₈×Dic₄₇	—	2	1	no	—
139	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
143	#117×C₄₇	C₂³	1	1	yes	characteristic
144	#117×C₄₇	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
146	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
147	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
148	#106×C₄₇	C₂×C₄	1	1	yes	characteristic
149	#106×C₄₇	C₂×C₄	1	1	yes	characteristic
150	C₄⋊C₈×C₄₇	—	2	1	no	—
151	C₄⋊C₈×C₄₇	—	2	1	no	—
152	#97×C₄₇	—	2	1	no	—
153	C₄×C₈×C₄₇	—	2	1	no	—
154	C₂³×D₄₇	#41	1	1	yes	characteristic
155	C₂²×C₄×C₄₇	—	2	1	no	—
156	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
157	C₂²×Dic₄₇	—	2	1	no	—
158	C₂²×Dic₄₇	#41	1	1	yes	characteristic
159	C₂×C₄×D₄₇	—	2	1	no	—
160	C₂×C₄×D₄₇	—	2	1	no	—
161	C₂×C₄×D₄₇	—	2	1	no	—
162	C₂×C₄×D₄₇	—	2	1	no	—
163	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
167	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
168	C₂×C₄×D₄₇	#41	1	2	yes	—
169	C₂×C₄×D₄₇	#41	1	2	yes	—
170	C₂×C₄×D₄₇	#41	1	2	yes	—
171	M₁₆×C₄₇	—	2	1	no	—
172	M₁₆×C₄₇	—	2	1	no	—
173	M₁₆×C₄₇	—	2	1	no	—
174	M₁₆×C₄₇	C₂×Q₈	1	2	yes	—
175	C₂×C₈×C₄₇	—	2	1	no	—
176	C₂×C₈×C₄₇	—	2	1	no	—
177	C₂×C₈×C₄₇	—	2	1	no	—
178	C₂×C₈×C₄₇	—	2	1	no	—
179	C₂×C₈×C₄₇	—	2	1	no	—
180	C₂×C₈×C₄₇	—	2	1	no	—
181	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
185	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
186	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
187	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
188	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
189	C₂²⋊C₄×C₄₇	—	2	1	no	—
190	C₂²⋊C₄×C₄₇	—	2	1	no	—
191	C₄²×C₄₇	—	2	1	no	—
192	C₄²×C₄₇	—	2	1	no	—
193	C₄²×C₄₇	—	2	1	no	—
194	C₄²×C₄₇	—	2	1	no	—
195	C₂²⋊Dic₄₇	—	2	1	no	—
196	C₂²⋊Dic₄₇	—	2	1	no	—
197	(C₂×D₄₇)⋊C₄	—	2	1	no	—
198	(C₂×D₄₇)⋊C₄	—	2	1	no	—
199	(C₂×D₄₇)⋊C₄	—	2	1	no	—
200	(C₂×D₄₇)⋊C₄	—	2	1	no	—
201	(C₂×D₄₇)⋊C₄	—	4	2	no	—
202	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
203	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
204	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
205	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
206	Dic₄₇⋊C₄	—	2	1	no	—
207	Dic₄₇⋊C₄	—	2	1	no	—
208	Dic₄₇⋊C₄	—	2	1	no	—
209	Dic₄₇⋊C₄	—	2	1	no	—
210	Dic₄₇⋊C₄	—	4	2	no	—
211	C₄×Dic₄₇	—	2	1	no	—
212	C₄×Dic₄₇	—	2	1	no	—
213	C₄×Dic₄₇	—	2	1	no	—
214	C₄×Dic₄₇	—	2	1	no	—
215	C₄×Dic₄₇	—	2	1	no	—
216	C₄×Dic₄₇	—	2	1	no	—
217	C₄×Dic₄₇	—	2	1	no	—
218	C₄×Dic₄₇	—	2	1	no	—
219	#10625329	—	2	1	no	—
220	#10625329	—	2	1	no	—
221	#10625329	—	2	1	no	—
222	#10625329	C₂×Q₈	1	2	yes	—
223	C₂×C₄₇⋊C₈	—	2	1	no	—
224	C₂×C₄₇⋊C₈	—	2	1	no	—
225	C₂×C₄₇⋊C₈	—	2	1	no	—
226	C₂×C₄₇⋊C₈	—	2	1	no	—
227	C₂×C₄₇⋊C₈	—	2	1	no	—
228	C₂×C₄₇⋊C₈	—	2	1	no	—
229	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
230	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
231	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
232	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
233	#10625324	—	2	2	no	—
234	#10625324	—	2	2	no	—
235	#10625324	—	2	2	no	—
236	#10625324	—	2	2	no	—
237	#10625324	—	2	4	no	—
238	#10625324	—	4	2	no	—
239	C₈×D₄₇	—	2	4	no	—
240	C₈×D₄₇	—	2	2	no	—
241	C₈×D₄₇	—	2	2	no	—
242	C₈×D₄₇	—	2	2	no	—
243	C₈×D₄₇	—	2	2	no	—
244	C₈×D₄₇	—	4	2	no	—
245	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
246	C₂²×D₄₇	—	4	1	no	—
247	C₂²×D₄₇	—	4	1	no	—
248	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
249	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
250	C₂²×D₄₇	#125	1	2	yes	—
251	C₂²×D₄₇	#126	1	2	yes	—
252	C₂×C₄×C₄₇	—	2	1	no	—
253	C₂×C₄×C₄₇	—	2	1	no	—
254	C₂×C₄×C₄₇	—	2	1	no	—
255	C₂×C₄×C₄₇	—	2	1	no	—
256	C₂×C₄×C₄₇	—	4	1	no	—
257	C₂×C₄×C₄₇	—	4	1	no	—
258	C₂×C₄×C₄₇	—	4	1	no	—
259	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
260	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
262	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
265	C₂×Dic₄₇	—	2	1	no	—
266	C₂×Dic₄₇	—	2	1	no	—
267	C₂×Dic₄₇	—	2	1	no	—
268	C₂×Dic₄₇	—	2	1	no	—
269	C₂×Dic₄₇	—	4	1	no	—
270	C₂×Dic₄₇	—	4	1	no	—
271	C₂×Dic₄₇	—	4	1	no	—
272	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
273	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
274	C₂×Dic₄₇	#125	1	2	yes	—
275	C₂×Dic₄₇	#126	1	2	yes	—
276	C₄×D₄₇	—	4	2	no	—
277	C₄×D₄₇	—	4	2	no	—
278	C₄×D₄₇	—	4	2	no	—
279	C₄×D₄₇	—	4	2	no	—
280	C₄×D₄₇	#117	1	2	yes	—
281	C₄×D₄₇	#117	1	2	yes	—
282	C₄×D₄₇	C₄×Q₈	1	2	yes	—
283	C₄×D₄₇	C₄×Q₈	1	2	yes	—
284	C₄×D₄₇	C₂²⋊Q₈	1	2	yes	—
285	C₄×D₄₇	C₂²⋊Q₈	1	2	yes	—
286	C₄×D₄₇	#123	1	2	yes	—
287	C₄×D₄₇	#123	1	2	yes	—
288	C₈×C₄₇	—	2	1	no	—
289	C₈×C₄₇	—	2	1	no	—
290	C₈×C₄₇	—	2	2	no	—
291	C₈×C₄₇	—	2	1	no	—
292	C₈×C₄₇	—	2	1	no	—
293	C₈×C₄₇	—	4	1	no	—
294	C₄₇⋊C₈	—	2	1	no	—
295	C₄₇⋊C₈	—	2	1	no	—
296	C₄₇⋊C₈	—	2	2	no	—
297	C₄₇⋊C₈	—	2	1	no	—
298	C₄₇⋊C₈	—	2	1	no	—
299	C₄₇⋊C₈	—	4	1	no	—
300	#21041	—	47	1	no	maximal, Sylow
301	C₂²×C₄₇	—	2	1	no	—
302	C₂²×C₄₇	—	2	1	no	—
303	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
304	C₂²×C₄₇	C₂×#125	1	1	yes	characteristic
305	C₂²×C₄₇	C₂×#126	1	1	yes	characteristic
306	C₂×D₄₇	—	2	1	no	—
307	C₂×D₄₇	—	2	1	no	—
308	C₂×D₄₇	—	2	1	no	—
309	C₂×D₄₇	—	2	1	no	—
310	C₂×D₄₇	—	4	2	no	—
311	C₂×D₄₇	—	4	2	no	—
312	C₂×D₄₇	#387	1	2	yes	—
313	C₂×D₄₇	#387	1	2	yes	—
314	C₄×C₄₇	—	4	1	no	—
315	C₄×C₄₇	—	4	1	no	—
316	C₄×C₄₇	—	4	1	no	—
317	C₄×C₄₇	—	4	1	no	—
318	C₄×C₄₇	—	8	1	no	—
319	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
320	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
321	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
322	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
323	Dic₄₇	—	4	1	no	—
324	Dic₄₇	—	4	1	no	—
325	Dic₄₇	—	4	1	no	—
326	Dic₄₇	—	4	1	no	—
327	Dic₄₇	—	8	1	no	—
328	Dic₄₇	#387	1	2	yes	—
329	Dic₄₇	#387	1	2	yes	—
330	#2911	—	47	1	no	—
331	C₂×#424	—	47	1	no	—
332	C₂×#405	—	47	1	no	—
333	#1922	—	47	1	no	—
334	#1922	—	47	1	no	—
335	#1922	—	47	1	no	—
336	#1922	—	47	1	no	—
337	#1922	—	47	1	no	—
338	#1922	—	47	1	no	—
339	#1922	—	47	1	no	—
340	#1922	D₄₇	1	1	yes	characteristic, complemented
341	#1738	—	47	1	no	—
342	#1733	—	47	1	no	—
343	#1733	—	47	1	no	—
344	#1729	—	47	1	no	—
345	C₂×C₄₇	—	2	1	no	—
346	C₂×C₄₇	—	2	1	no	—
347	C₂×C₄₇	C₂×#387	1	1	yes	characteristic
348	C₂×C₄₇	#2955	1	1	yes	characteristic
349	C₂×C₄₇	#2955	1	1	yes	characteristic
350	D₄₇	—	2	2	no	—
351	D₄₇	—	2	2	no	—
352	C₂²×M₁₆	—	47	1	no	—
353	C₂²×M₁₆	—	47	1	no	—
354	C₂²×M₁₆	—	47	1	no	—
355	C₂³×C₈	—	47	1	no	—
356	C₂×#117	—	47	1	no	—
357	C₂×#117	—	47	1	no	—
358	C₂×#117	—	47	1	no	—
359	#428	—	47	1	no	—
360	#428	—	47	1	no	—
361	#428	—	47	1	no	—
362	#428	—	47	1	no	—
363	#428	—	47	1	no	—
364	#428	—	47	1	no	—
365	#428	—	47	1	no	—
366	#428	—	47	1	no	—
367	#427	—	47	1	no	—
368	#427	—	47	1	no	—
369	#427	—	47	1	no	—
370	#427	C₂×D₄₇	1	1	yes	characteristic
371	#424	—	47	1	no	—
372	#424	—	47	1	no	—
373	#424	—	47	1	no	—
374	#424	—	94	1	no	—
375	#424	—	94	1	no	—
376	#424	C₂×D₄₇	1	1	yes	characteristic
377	C₂×C₄⋊C₈	—	94	1	no	—
378	C₂×C₄⋊C₈	—	94	1	no	—
379	#405	—	47	1	no	—
380	#405	—	47	1	no	—
381	#405	—	47	1	no	—
382	#405	—	94	1	no	—
383	#405	—	94	1	no	—
384	#405	C₂×D₄₇	1	1	yes	characteristic
385	C₂×#97	—	94	1	no	—
386	C₂×C₄×C₈	—	94	1	no	—
387	#341	—	47	1	no	—
388	#341	—	47	1	no	—
389	#341	—	47	1	no	—
390	#341	C₂×D₄₇	1	1	yes	characteristic
391	#339	—	47	1	no	—
392	#339	—	47	1	no	—
393	#339	—	47	1	no	—
394	#339	—	47	1	no	—
395	#339	—	47	1	no	—
396	#339	—	47	1	no	—
397	#339	C₂×D₄₇	1	1	yes	characteristic
398	#339	C₂×D₄₇	1	1	yes	characteristic
399	#336	—	47	1	no	—
400	#336	—	47	1	no	—
401	#336	—	47	1	no	—
402	#336	C₂×D₄₇	1	1	yes	characteristic
403	C₄₇	#21041	1	1	yes	characteristic, complemented, Sylow
404	C₂³×C₄	—	47	1	no	—
405	C₂×M₁₆	—	47	1	no	—
406	C₂×M₁₆	—	47	1	no	—
407	C₂×M₁₆	—	47	1	no	—
408	C₂×M₁₆	—	47	1	no	—
409	C₂×M₁₆	—	47	1	no	—
410	C₂×M₁₆	—	47	4	no	—
411	C₂×M₁₆	—	47	1	no	—
412	C₂×M₁₆	—	94	2	no	—
413	C₂×M₁₆	—	94	2	no	—
414	C₂×M₁₆	—	94	1	no	—
415	C₂×M₁₆	—	94	1	no	—
416	C₂×M₁₆	—	94	2	no	—
417	C₂×M₁₆	—	94	2	no	—
418	C₂×M₁₆	—	94	2	no	—
419	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
420	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
421	C₂²×C₈	—	47	1	no	—
422	C₂²×C₈	—	47	1	no	—
423	C₂²×C₈	—	47	1	no	—
424	C₂²×C₈	—	47	1	no	—
425	C₂²×C₈	—	47	1	no	—
426	C₂²×C₈	—	47	1	no	—
427	C₂²×C₈	—	94	2	no	—
428	C₂²×C₈	—	94	2	no	—
429	C₂²×C₈	—	94	1	no	—
430	C₂²×C₈	—	94	1	no	—
431	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
432	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
433	#117	—	47	1	no	—
434	#117	—	47	1	no	—
435	#117	—	47	1	no	—
436	#117	—	47	1	no	—
437	#117	—	47	1	no	—
438	#117	—	47	1	no	—
439	#117	—	94	1	no	—
440	#117	—	94	1	no	—
441	#117	—	94	2	no	—
442	#117	—	94	2	no	—
443	#117	—	94	1	no	—
444	#117	—	94	1	no	—
445	#117	C₂²×D₄₇	1	1	yes	characteristic
446	#117	C₂²×D₄₇	1	1	yes	characteristic
447	C₂×C₄⋊C₄	—	47	1	no	—
448	C₂×C₄⋊C₄	—	47	1	no	—
449	C₂×C₄⋊C₄	—	47	1	no	—
450	C₂×C₄⋊C₄	—	47	1	no	—
451	C₂×C₄⋊C₄	—	94	1	no	—
452	C₂×C₂²⋊C₄	—	94	1	no	—
453	C₂×C₂²⋊C₄	—	94	1	no	—
454	C₂×C₂²⋊C₄	—	94	1	no	—
455	C₂×C₄²	—	47	1	no	—
456	C₂×C₄²	—	94	1	no	—
457	C₂×C₄²	—	94	1	no	—
458	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
459	#107	—	47	1	no	—
460	#107	—	47	1	no	—
461	#107	—	47	1	no	—
462	#107	—	47	1	no	—
463	#107	—	47	1	no	—
464	#107	—	47	1	no	—
465	#107	C₄×D₄₇	1	1	yes	characteristic
466	#107	C₄×D₄₇	1	1	yes	characteristic
467	#106	—	47	1	no	—
468	#106	—	47	1	no	—
469	#106	—	47	1	no	—
470	#106	—	47	1	no	—
471	#106	—	47	1	no	—
472	#106	—	47	1	no	—
473	#106	C₄×D₄₇	1	1	yes	characteristic
474	#106	C₄×D₄₇	1	1	yes	characteristic
475	C₄⋊C₈	—	2	1	no	—
476	C₄⋊C₈	—	2	1	no	—
477	C₄⋊C₈	—	94	1	no	—
478	C₄⋊C₈	—	94	1	no	—
479	C₄⋊C₈	—	94	1	no	—
480	C₄⋊C₈	—	94	1	no	—
481	C₄⋊C₈	—	94	1	no	—
482	C₄⋊C₈	—	94	1	no	—
483	#97	—	2	1	no	—
484	#97	—	94	1	no	—
485	#97	—	94	1	no	—
486	#97	—	94	1	no	—
487	C₄×C₈	—	2	1	no	—
488	C₄×C₈	—	94	1	no	—
489	C₄×C₈	—	94	1	no	—
490	C₄×C₈	—	94	1	no	—
491	C₂⁴	—	47	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	47	1	no	—
494	C₂²×C₄	—	47	1	no	—
495	C₂²×C₄	—	47	1	no	—
496	C₂²×C₄	—	47	1	no	—
497	C₂²×C₄	—	47	1	no	—
498	C₂²×C₄	—	47	2	no	—
499	C₂²×C₄	—	47	2	no	—
500	C₂²×C₄	—	47	2	no	—
501	C₂²×C₄	—	47	2	no	—
502	C₂²×C₄	—	94	1	no	—
503	C₂²×C₄	—	94	1	no	—
504	C₂²×C₄	—	94	1	no	—
505	C₂²×C₄	—	94	1	no	—
506	C₂²×C₄	—	94	1	no	—
507	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
508	M₁₆	—	2	1	no	—
509	M₁₆	—	2	1	no	—
510	M₁₆	—	2	1	no	—
511	M₁₆	—	47	2	no	—
512	M₁₆	—	94	2	no	—
513	M₁₆	—	94	2	no	—
514	M₁₆	—	94	2	no	—
515	M₁₆	—	94	2	no	—
516	M₁₆	—	94	4	no	—
517	M₁₆	—	94	1	no	—
518	M₁₆	—	94	1	no	—
519	M₁₆	—	94	1	no	—
520	M₁₆	—	188	2	no	—
521	M₁₆	Q₈×D₄₇	1	2	yes	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	47	1	no	—
529	C₂×C₈	—	47	1	no	—
530	C₂×C₈	—	47	1	no	—
531	C₂×C₈	—	47	1	no	—
532	C₂×C₈	—	94	2	no	—
533	C₂×C₈	—	94	2	no	—
534	C₂×C₈	—	94	2	no	—
535	C₂×C₈	—	94	2	no	—
536	C₂×C₈	—	94	4	no	—
537	C₂×C₈	—	94	1	no	—
538	C₂×C₈	—	94	1	no	—
539	C₂×C₈	—	94	1	no	—
540	C₂×C₈	—	94	1	no	—
541	C₂×C₈	—	94	1	no	—
542	C₂×C₈	—	94	1	no	—
543	C₂×C₈	—	188	2	no	—
544	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
545	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
546	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
547	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
548	C₄⋊C₄	—	47	1	no	—
549	C₄⋊C₄	—	47	1	no	—
550	C₄⋊C₄	—	47	1	no	—
551	C₄⋊C₄	—	47	1	no	—
552	C₄⋊C₄	—	94	1	no	—
553	C₄⋊C₄	—	94	1	no	—
554	C₄⋊C₄	—	94	1	no	—
555	C₄⋊C₄	—	94	1	no	—
556	C₄⋊C₄	—	188	2	no	—
557	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
558	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
559	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
560	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
561	C₂²⋊C₄	—	2	1	no	—
562	C₂²⋊C₄	—	2	1	no	—
563	C₂²⋊C₄	—	94	1	no	—
564	C₂²⋊C₄	—	94	1	no	—
565	C₂²⋊C₄	—	94	1	no	—
566	C₂²⋊C₄	—	94	1	no	—
567	C₂²⋊C₄	—	94	1	no	—
568	C₂²⋊C₄	—	94	1	no	—
569	C₂²⋊C₄	—	188	2	no	—
570	C₄²	—	2	1	no	—
571	C₄²	—	2	1	no	—
572	C₄²	—	2	1	no	—
573	C₄²	—	2	1	no	—
574	C₄²	—	94	1	no	—
575	C₄²	—	94	1	no	—
576	C₄²	—	94	1	no	—
577	C₄²	—	94	1	no	—
578	C₄²	—	94	1	no	—
579	C₄²	—	94	1	no	—
580	C₄²	—	94	1	no	—
581	C₄²	—	94	1	no	—
582	C₂³	—	47	1	no	—
583	C₂³	—	47	1	no	—
584	C₂³	—	47	2	no	—
585	C₂³	—	47	2	no	—
586	C₂³	—	188	1	no	—
587	C₂³	—	188	1	no	—
588	C₂³	#41×D₄₇	1	1	yes	characteristic
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	47	1	no	—
597	C₂×C₄	—	47	1	no	—
598	C₂×C₄	—	47	2	no	—
599	C₂×C₄	—	47	2	no	—
600	C₂×C₄	—	47	2	no	—
601	C₂×C₄	—	47	2	no	—
602	C₂×C₄	—	47	2	no	—
603	C₂×C₄	—	47	2	no	—
604	C₂×C₄	—	47	2	no	—
605	C₂×C₄	—	47	2	no	—
606	C₂×C₄	—	47	2	no	—
607	C₂×C₄	—	47	2	no	—
608	C₂×C₄	—	94	1	no	—
609	C₂×C₄	—	94	1	no	—
610	C₂×C₄	—	94	1	no	—
611	C₂×C₄	—	94	1	no	—
612	C₂×C₄	—	188	2	no	—
613	C₂×C₄	—	188	2	no	—
614	C₂×C₄	—	188	2	no	—
615	C₂×C₄	—	188	2	no	—
616	C₂×C₄	—	188	1	no	—
617	C₂×C₄	—	188	1	no	—
618	C₂×C₄	—	188	1	no	—
619	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
620	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
621	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
622	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
623	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
624	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
625	C₈	—	2	1	no	—
626	C₈	—	2	1	no	—
627	C₈	—	2	2	no	—
628	C₈	—	2	1	no	—
629	C₈	—	2	1	no	—
630	C₈	—	4	1	no	—
631	C₈	—	94	1	no	—
632	C₈	—	94	1	no	—
633	C₈	—	94	2	no	—
634	C₈	—	94	1	no	—
635	C₈	—	94	1	no	—
636	C₈	—	188	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	47	2	no	—
640	C₂²	—	47	2	no	—
641	C₂²	—	94	1	no	—
642	C₂²	—	94	1	no	—
643	C₂²	—	94	1	no	—
644	C₂²	—	94	1	no	—
645	C₂²	—	188	2	no	—
646	C₂²	—	188	2	no	—
647	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
648	C₂²	#125×D₄₇	1	1	yes	characteristic
649	C₂²	#126×D₄₇	1	1	yes	characteristic
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	8	1	no	—
655	C₄	—	47	2	no	—
656	C₄	—	47	2	no	—
657	C₄	—	376	1	no	—
658	C₄	—	188	1	no	—
659	C₄	—	188	1	no	—
660	C₄	—	188	1	no	—
661	C₄	—	188	1	no	—
662	C₄	#117×D₄₇	1	1	yes	characteristic
663	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
664	C₄	C₂²⋊Q₈×D₄₇	1	1	yes	characteristic
665	C₄	#123×D₄₇	1	1	yes	characteristic
666	C₂	—	2	1	no	—
667	C₂	—	2	1	no	—
668	C₂	—	94	2	no	—
669	C₂	—	94	2	no	—
670	C₂	#387×D₄₇	1	1	yes	characteristic
671	C₂	#20252286	1	1	yes	characteristic
672	C₂	#20252288	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1922	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂³×D₄₇	#41
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1922	D₄₇
hypocenter	C₄₇	#21041
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1922

Complements

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

N	H ≅ G/N	type
4. #20243990	C₂	semidirect
5. #20243989	C₂	semidirect
6. #20243988	C₂	semidirect
7. #20243987	C₂	semidirect
8. #20243986	C₂	semidirect
9. #20243985	C₂	semidirect
10. #20243984	C₂	semidirect
15. C₄₇×#1922	C₂	semidirect
23. #15689164	C₄	semidirect
24. #15689164	C₄	semidirect
25. #15689164	C₄	semidirect
26. #15689164	C₄	semidirect
27. #15689162	C₄	semidirect
28. #15689162	C₄	semidirect
29. #15689162	C₄	semidirect
30. #15689162	C₄	semidirect
340. #1922	D₄₇	semidirect
403. C₄₇	#21041	semidirect

Maximal subgroups

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

subgroup	index
#20251976	2
#424×D₄₇	2
#405×D₄₇	2
#20243990	2
#20243989	2
#20243988	2
#20243987	2
#20243986	2
#20243985	2
#20243984	2
#20243113	2
#20243096	2
#20243083	2
C₄₇×#1922	2
#21041	47