Subgroups — #26224431

Order 12032.

770 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253708	C₂	1	1	yes	maximal, characteristic
2	#20252320	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252098	C₂	1	1	yes	maximal, characteristic
4	#20244363	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244214	C₂	1	1	yes	maximal, characteristic
6	#20244094	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244093	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244090	C₂	1	1	yes	maximal, characteristic, complemented
9	#20244089	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243524	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243227	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243225	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243223	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1764	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13094030	C₂²	1	1	yes	characteristic
17	#15689676	C₂²	1	1	yes	characteristic
18	#15689669	C₂²	1	1	yes	characteristic
19	#15689479	C₄	1	2	yes	complemented
20	#15689476	C₄	1	2	yes	complemented
21	#15689472	C₄	1	2	yes	complemented
22	#15689468	C₄	1	2	yes	complemented
23	#15689251	—	2	2	no	—
24	C₈×Dic₉₄	—	2	2	no	—
25	#15689199	—	2	2	no	—
26	C₈×C₂²⋊D₄₇	—	2	2	no	—
27	#15689151	C₂²	1	1	yes	characteristic
28	#15689150	C₂²	1	1	yes	characteristic
29	#15689146	C₂²	1	1	yes	characteristic
30	#15689146	C₂²	1	1	yes	characteristic
31	C₂×#13093952	C₂²	1	1	yes	characteristic
32	C₂×#13093951	C₂²	1	1	yes	characteristic
33	C₂×#13093950	C₂²	1	1	yes	characteristic
34	#15689120	C₂²	1	1	yes	characteristic
35	#15689119	C₂²	1	1	yes	characteristic
36	#15689117	C₂²	1	1	yes	characteristic
37	#15689091	C₂²	1	1	yes	characteristic
38	#15689090	C₂²	1	1	yes	characteristic
39	#15689078	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
42	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
45	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
46	#15688888	C₂²	1	1	yes	characteristic
47	#15688887	C₂²	1	1	yes	characteristic
48	#15688887	C₂²	1	1	yes	characteristic
49	#15688884	C₂²	1	1	yes	characteristic
50	#15688883	C₂²	1	1	yes	characteristic
51	#15688882	C₂²	1	1	yes	characteristic
52	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×#104×C₄₇	C₂²	1	1	yes	characteristic
54	C₄₇×#416	C₂²	1	1	yes	characteristic
55	C₄₇×#405	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
57	C₄₇×#341	C₂²	1	1	yes	characteristic
58	C₄₇×#339	C₂²	1	1	yes	characteristic
59	C₂×#10625350	C₂³	1	1	yes	characteristic
60	#13094030	—	2	2	no	—
61	#13094030	—	2	2	no	—
62	C₂×#10625329	C₂³	1	1	yes	characteristic
63	C₂×#10625329	C₂³	1	1	yes	characteristic
64	C₂×#10625324	—	2	1	no	—
65	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₄₇	—	2	1	no	—
68	#13094023	C₂×C₄	1	2	yes	—
69	#13094022	C₂×C₄	1	1	yes	characteristic
70	#13094020	C₂×C₄	1	1	yes	characteristic
71	#13094015	C₂×C₄	1	2	yes	—
72	#13094013	C₂×C₄	1	1	yes	characteristic
73	#13094011	C₂×C₄	1	1	yes	characteristic
74	#13094001	—	2	2	no	—
75	#13093996	—	2	2	no	—
76	C₄×Dic₉₄	—	2	2	no	—
77	C₄×C₂²⋊D₄₇	—	2	2	no	—
78	#13093983	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₄₇	—	2	2	no	—
80	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
82	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
83	Dic₄₇⋊C₈	—	2	2	no	—
84	Dic₄₇⋊C₈	—	2	2	no	—
85	Dic₄₇⋊C₈	—	2	2	no	—
86	#13093952	—	2	2	no	—
87	#13093951	—	2	2	no	—
88	#13093950	—	2	2	no	—
89	#13093949	C₂×C₄	1	2	yes	—
90	#13093948	C₂×C₄	1	2	yes	—
91	#13093947	C₂×C₄	1	2	yes	—
92	#13093946	C₂×C₄	1	2	yes	—
93	#13093945	C₂×C₄	1	2	yes	—
94	#13093944	C₂×C₄	1	2	yes	—
95	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
96	(C₂×D₄₇)⋊C₈	—	2	2	no	—
97	#13093934	—	2	1	no	—
98	C₄×C₄₇⋊C₈	—	2	2	no	—
99	C₈×Dic₄₇	—	2	1	no	—
100	C₈×Dic₄₇	—	2	2	no	—
101	C₈×Dic₄₇	—	2	2	no	—
102	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
103	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
104	C₈×Dic₄₇	D₄	1	2	yes	—
105	C₈×Dic₄₇	D₄	1	2	yes	—
106	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
107	#131×C₄₇	—	2	2	no	—
108	#131×C₄₇	—	2	2	no	—
109	C₂×M₁₆×C₄₇	—	2	1	no	—
110	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
111	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₄₇	—	2	1	no	—
113	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
115	#117×C₄₇	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
117	#104×C₄₇	—	2	2	no	—
118	#103×C₄₇	C₂×C₄	1	2	yes	—
119	#102×C₄₇	C₂×C₄	1	2	yes	—
120	#97×C₄₇	—	2	1	no	—
121	C₄×C₈×C₄₇	—	2	1	no	—
122	C₄×C₈×C₄₇	—	2	2	no	—
123	#41×C₄₇	—	2	1	no	—
124	#41×C₄₇	—	2	1	no	—
125	#41×C₄₇	—	2	1	no	—
126	#41×C₄₇	—	2	1	no	—
127	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₄×C₄₇	—	2	1	no	—
129	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	—	2	1	no	—
131	C₂²×C₄×C₄₇	—	2	1	no	—
132	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
133	C₂×C₂²⋊D₄₇	—	2	1	no	—
134	C₂×C₂²⋊D₄₇	—	2	2	no	—
135	C₂²×Dic₄₇	—	2	1	no	—
136	C₂²×Dic₄₇	#41	1	2	yes	—
137	#10625350	—	2	1	no	—
138	#10625350	—	2	1	no	—
139	#10625350	—	2	1	no	—
140	#10625350	—	2	1	no	—
141	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄×D₄₇	—	2	1	no	—
143	C₂×Dic₉₄	—	2	2	no	—
144	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
145	M₁₆×C₄₇	—	2	1	no	—
146	M₁₆×C₄₇	—	2	1	no	—
147	M₁₆×C₄₇	—	2	1	no	—
148	M₁₆×C₄₇	—	2	1	no	—
149	M₁₆×C₄₇	—	4	2	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	—	4	2	no	—
155	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
156	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₄₇	#41	1	2	yes	—
159	C₂×C₈×C₄₇	#41	1	2	yes	—
160	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
161	C₂²⋊C₄×C₄₇	—	2	1	no	—
162	C₄²×C₄₇	—	2	1	no	—
163	C₄²×C₄₇	—	2	1	no	—
164	C₄²×C₄₇	#41	1	2	yes	—
165	C₂²⋊Dic₄₇	—	2	1	no	—
166	C₂²⋊Dic₄₇	—	2	2	no	—
167	(C₂×D₄₇)⋊C₄	—	2	2	no	—
168	C₄⋊Dic₄₇	—	2	2	no	—
169	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
170	Dic₄₇⋊C₄	—	2	2	no	—
171	Dic₄₇⋊C₄	—	2	2	no	—
172	Dic₄₇⋊C₄	—	2	2	no	—
173	C₄×Dic₄₇	—	2	8	no	—
174	C₄×Dic₄₇	—	2	1	no	—
175	C₄×Dic₄₇	—	2	1	no	—
176	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
177	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
178	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
179	C₄×Dic₄₇	#41	1	2	yes	—
180	#10625329	—	2	1	no	—
181	#10625329	—	2	1	no	—
182	#10625329	—	2	1	no	—
183	#10625329	—	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	C₂²×C₄	1	2	yes	—
191	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
192	#10625324	—	4	2	no	—
193	C₈×D₄₇	—	4	2	no	—
194	C₂³×C₄₇	—	2	1	no	—
195	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
196	C₂²×D₄₇	—	2	1	no	—
197	Q₈×C₄₇	—	2	1	no	—
198	Q₈×C₄₇	—	2	1	no	—
199	D₄×C₄₇	—	2	1	no	—
200	D₄×C₄₇	—	2	1	no	—
201	D₄×C₄₇	—	4	1	no	—
202	D₄×C₄₇	—	4	1	no	—
203	C₂×C₄×C₄₇	—	2	4	no	—
204	C₂×C₄×C₄₇	—	2	2	no	—
205	C₂×C₄×C₄₇	—	2	2	no	—
206	C₂×C₄×C₄₇	—	2	1	no	—
207	C₂×C₄×C₄₇	—	4	1	no	—
208	C₂×C₄×C₄₇	—	4	1	no	—
209	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
215	C₂²⋊D₄₇	—	4	1	no	—
216	C₂²⋊D₄₇	—	4	1	no	—
217	C₂²⋊D₄₇	—	4	4	no	—
218	C₂×Dic₄₇	—	2	4	no	—
219	C₂×Dic₄₇	—	2	2	no	—
220	C₂×Dic₄₇	—	2	4	no	—
221	C₂×Dic₄₇	—	2	2	no	—
222	C₂×Dic₄₇	—	2	1	no	—
223	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
224	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
225	D₁₈₈	—	2	1	no	—
226	D₁₈₈	—	2	1	no	—
227	C₄×D₄₇	—	4	1	no	—
228	C₄×D₄₇	—	4	1	no	—
229	Dic₉₄	—	2	1	no	—
230	Dic₉₄	—	2	1	no	—
231	Dic₉₄	—	4	4	no	—
232	C₈×C₄₇	—	2	2	no	—
233	C₈×C₄₇	—	4	1	no	—
234	C₈×C₄₇	—	4	1	no	—
235	C₈×C₄₇	#124	1	2	yes	—
236	C₈×C₄₇	#124	1	2	yes	—
237	C₄₇⋊C₈	—	2	2	no	—
238	C₄₇⋊C₈	—	2	2	no	—
239	C₄₇⋊C₈	—	4	1	no	—
240	C₄₇⋊C₈	—	4	1	no	—
241	#21658	—	47	1	no	maximal, Sylow
242	C₂²×C₄₇	—	2	2	no	—
243	C₂²×C₄₇	—	4	2	no	—
244	C₂²×C₄₇	—	4	1	no	—
245	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
246	C₂²×C₄₇	#529	1	1	yes	characteristic
247	C₂²×C₄₇	#529	1	1	yes	characteristic
248	C₂×D₄₇	—	4	2	no	—
249	C₂×D₄₇	—	4	1	no	—
250	C₄×C₄₇	—	2	4	no	—
251	C₄×C₄₇	—	4	2	no	—
252	C₄×C₄₇	—	4	1	no	—
253	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
254	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
255	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
256	C₄×C₄₇	#532	1	1	yes	characteristic
257	Dic₄₇	—	2	4	no	—
258	Dic₄₇	—	2	2	no	—
259	Dic₄₇	—	4	2	no	—
260	Dic₄₇	—	4	1	no	—
261	Dic₄₇	#443	1	4	yes	—
262	#3131	—	47	1	no	—
263	#2960	—	47	1	no	—
264	#2931	—	47	1	no	—
265	#1994	—	47	1	no	—
266	#1962	—	47	1	no	—
267	#1937	—	47	1	no	—
268	#1937	—	47	1	no	—
269	#1937	—	47	1	no	—
270	#1937	—	47	1	no	—
271	#1837	—	47	1	no	—
272	#1764	—	47	1	no	—
273	#1764	—	47	1	no	—
274	#1764	—	47	1	no	—
275	#1764	D₄₇	1	1	yes	characteristic, complemented
276	C₄²×C₈	—	47	1	no	—
277	C₂×C₄₇	—	2	1	no	—
278	C₂×C₄₇	—	2	1	no	—
279	C₂×C₄₇	—	8	1	no	—
280	C₂×C₄₇	C₄×#124	1	1	yes	characteristic
281	C₂×C₄₇	C₂×#443	1	2	yes	—
282	D₄₇	—	8	1	no	—
283	C₂×#131	—	47	1	no	—
284	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
285	#533	—	47	1	no	—
286	#532	—	47	1	no	—
287	#488	—	47	2	no	—
288	#488	—	47	2	no	—
289	#487	—	47	2	no	—
290	#486	—	47	2	no	—
291	#446	—	94	2	no	—
292	C₈×Q₈	—	94	2	no	—
293	#436	—	94	2	no	—
294	C₈×D₄	—	94	2	no	—
295	#424	—	47	1	no	—
296	#424	—	47	1	no	—
297	#423	—	47	1	no	—
298	#423	—	47	1	no	—
299	C₂×#104	—	47	1	no	—
300	C₂×#104	—	47	1	no	—
301	C₂×#104	—	47	1	no	—
302	C₂×#104	C₂×D₄₇	1	1	yes	characteristic
303	#416	—	47	1	no	—
304	#416	—	47	1	no	—
305	#416	—	47	1	no	—
306	#416	C₂×D₄₇	1	1	yes	characteristic
307	#408	—	47	1	no	—
308	#408	—	47	1	no	—
309	#405	—	47	1	no	—
310	#405	C₂×D₄₇	1	1	yes	characteristic
311	C₂×C₄×C₈	—	47	1	no	—
312	C₂×C₄×C₈	—	47	1	no	—
313	C₂×C₄×C₈	—	47	1	no	—
314	C₂×C₄×C₈	—	47	1	no	—
315	C₂×C₄×C₈	—	47	1	no	—
316	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
317	C₄³	—	47	1	no	—
318	#341	—	47	1	no	—
319	#341	—	47	1	no	—
320	#341	—	47	1	no	—
321	#341	C₂×D₄₇	1	1	yes	characteristic
322	#339	—	47	1	no	—
323	#339	—	47	1	no	—
324	#339	—	47	1	no	—
325	#339	C₂×D₄₇	1	1	yes	characteristic
326	C₄₇	#21658	1	1	yes	characteristic, complemented, Sylow
327	C₂×#41	—	47	1	no	—
328	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
329	#131	—	2	2	no	—
330	#131	—	2	2	no	—
331	#131	—	94	2	no	—
332	#131	—	94	2	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	47	1	no	—
335	C₂×M₁₆	—	47	1	no	—
336	C₂×M₁₆	—	94	1	no	—
337	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
338	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
339	C₂²×C₈	—	2	1	no	—
340	C₂²×C₈	—	47	1	no	—
341	C₂²×C₈	—	47	1	no	—
342	C₂²×C₈	—	94	1	no	—
343	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
344	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
345	C₄⋊Q₈	—	47	2	no	—
346	C₄⋊Q₈	—	47	1	no	—
347	#127	—	47	1	no	—
348	#125	—	47	2	no	—
349	#124	—	47	1	no	—
350	#124	—	47	1	no	—
351	C₂²⋊Q₈	—	94	2	no	—
352	#121	—	94	2	no	—
353	C₄×Q₈	—	94	2	no	—
354	C₄×D₄	—	94	2	no	—
355	#117	—	47	1	no	—
356	#117	C₂²×D₄₇	1	1	yes	characteristic
357	C₂×C₄²	—	47	1	no	—
358	C₂×C₄²	—	47	1	no	—
359	C₂×C₄²	—	94	2	no	—
360	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
361	C₄⋊C₈	—	94	2	no	—
362	C₄⋊C₈	—	94	2	no	—
363	C₄⋊C₈	—	94	2	no	—
364	C₄⋊C₈	—	94	2	no	—
365	#104	—	2	2	no	—
366	#104	—	94	2	no	—
367	#104	—	94	2	no	—
368	#104	—	94	2	no	—
369	#103	—	47	2	no	—
370	#103	—	47	2	no	—
371	#103	—	47	2	no	—
372	#103	C₄×D₄₇	1	2	yes	—
373	#102	—	47	2	no	—
374	#102	—	47	2	no	—
375	#102	—	47	2	no	—
376	#102	C₄×D₄₇	1	2	yes	—
377	C₂²⋊C₈	—	94	2	no	—
378	C₂²⋊C₈	—	94	2	no	—
379	#97	—	2	1	no	—
380	#97	—	94	1	no	—
381	C₄×C₈	—	2	1	no	—
382	C₄×C₈	—	2	2	no	—
383	C₄×C₈	—	47	2	no	—
384	C₄×C₈	—	47	2	no	—
385	C₄×C₈	—	47	2	no	—
386	C₄×C₈	—	47	2	no	—
387	C₄×C₈	—	94	2	no	—
388	C₄×C₈	—	94	2	no	—
389	C₄×C₈	—	94	1	no	—
390	C₄×C₈	—	94	2	no	—
391	#41	—	2	1	no	—
392	#41	—	2	1	no	—
393	#41	—	2	1	no	—
394	#41	—	2	1	no	—
395	#41	—	94	1	no	—
396	#41	—	94	1	no	—
397	#41	—	94	1	no	—
398	#41	—	94	1	no	—
399	C₂×Q₈	—	47	1	no	—
400	C₂×Q₈	—	94	2	no	—
401	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	47	1	no	—
404	C₂×D₄	—	94	2	no	—
405	C₂×D₄	—	94	1	no	—
406	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	47	2	no	—
410	C₂²×C₄	—	94	1	no	—
411	C₂²×C₄	—	94	1	no	—
412	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
413	M₁₆	—	2	1	no	—
414	M₁₆	—	2	1	no	—
415	M₁₆	—	2	1	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	4	2	no	—
418	M₁₆	—	94	1	no	—
419	M₁₆	—	94	1	no	—
420	M₁₆	—	94	1	no	—
421	M₁₆	—	94	1	no	—
422	M₁₆	—	188	2	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	4	2	no	—
428	C₂×C₈	—	47	2	no	—
429	C₂×C₈	—	47	2	no	—
430	C₂×C₈	—	94	1	no	—
431	C₂×C₈	—	94	1	no	—
432	C₂×C₈	—	94	1	no	—
433	C₂×C₈	—	94	1	no	—
434	C₂×C₈	—	94	1	no	—
435	C₂×C₈	—	94	1	no	—
436	C₂×C₈	—	188	2	no	—
437	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
438	C₂×C₈	#10625350	1	2	yes	—
439	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
440	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
441	C₂×C₈	#10625352	1	2	yes	—
442	C₄⋊C₄	—	47	2	no	—
443	C₄⋊C₄	—	94	2	no	—
444	C₄⋊C₄	—	94	2	no	—
445	C₄⋊C₄	—	94	2	no	—
446	C₄⋊C₄	—	94	2	no	—
447	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
448	C₂²⋊C₄	—	2	1	no	—
449	C₂²⋊C₄	—	94	2	no	—
450	C₂²⋊C₄	—	94	2	no	—
451	C₂²⋊C₄	—	94	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	47	1	no	—
455	C₄²	—	47	1	no	—
456	C₄²	—	47	2	no	—
457	C₄²	—	47	2	no	—
458	C₄²	—	94	8	no	—
459	C₄²	—	94	1	no	—
460	C₄²	—	94	1	no	—
461	C₄²	#10625350	1	2	yes	—
462	C₂³	—	2	1	no	—
463	C₂³	—	94	1	no	—
464	C₂³	#41×D₄₇	1	1	yes	characteristic
465	Q₈	—	2	1	no	—
466	Q₈	—	2	1	no	—
467	Q₈	—	94	1	no	—
468	Q₈	—	94	1	no	—
469	Q₈	—	188	4	no	—
470	D₄	—	2	1	no	—
471	D₄	—	2	1	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	1	no	—
474	D₄	—	94	1	no	—
475	D₄	—	94	1	no	—
476	D₄	—	188	4	no	—
477	D₄	—	188	1	no	—
478	D₄	—	188	1	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	47	2	no	—
486	C₂×C₄	—	47	2	no	—
487	C₂×C₄	—	94	4	no	—
488	C₂×C₄	—	94	4	no	—
489	C₂×C₄	—	94	2	no	—
490	C₂×C₄	—	94	2	no	—
491	C₂×C₄	—	94	1	no	—
492	C₂×C₄	—	188	1	no	—
493	C₂×C₄	—	188	1	no	—
494	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
495	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
496	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
497	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
498	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
499	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
500	C₈	—	2	2	no	—
501	C₈	—	4	1	no	—
502	C₈	—	4	1	no	—
503	C₈	—	94	2	no	—
504	C₈	—	94	2	no	—
505	C₈	—	188	1	no	—
506	C₈	—	188	1	no	—
507	C₈	#13094010	1	2	yes	—
508	C₈	#13094010	1	2	yes	—
509	C₂²	—	2	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	188	2	no	—
513	C₂²	—	188	1	no	—
514	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
515	C₂²	#15689651	1	1	yes	characteristic
516	C₂²	#15689653	1	1	yes	characteristic
517	C₄	—	2	4	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	47	4	no	—
521	C₄	—	94	4	no	—
522	C₄	—	94	2	no	—
523	C₄	—	188	2	no	—
524	C₄	—	188	1	no	—
525	C₄	C₄×#10625352	1	1	yes	characteristic
526	C₄	C₄×#10625350	1	1	yes	characteristic
527	C₄	C₂×#13094010	1	1	yes	characteristic
528	C₄	#15689670	1	1	yes	characteristic
529	C₂	—	2	1	no	—
530	C₂	—	2	1	no	—
531	C₂	—	8	1	no	—
532	C₂	—	376	1	no	—
533	C₂	C₄×#13094010	1	1	yes	characteristic
534	C₂	#443×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1764	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#15689669	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1764	D₄₇
hypocenter	C₄₇	#21658
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1764

Complements

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

N	H ≅ G/N	type
2. #20252320	C₂	semidirect
4. #20244363	C₂	semidirect
6. #20244094	C₂	semidirect
7. #20244093	C₂	semidirect
8. #20244090	C₂	semidirect
9. #20244089	C₂	semidirect
10. #20243524	C₂	semidirect
11. #20243227	C₂	semidirect
12. #20243225	C₂	semidirect
13. #20243223	C₂	semidirect
14. C₄×C₈×Dic₄₇	C₂	semidirect
15. C₄₇×#1764	C₂	semidirect
19. #15689479	C₄	semidirect
20. #15689476	C₄	semidirect
21. #15689472	C₄	semidirect
22. #15689468	C₄	semidirect
275. #1764	D₄₇	semidirect
326. C₄₇	#21658	semidirect

Maximal subgroups

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

subgroup	index
#20253708	2
#20252320	2
#20252098	2
#20244363	2
#20244214	2
#20244094	2
#20244093	2
#20244090	2
#20244089	2
#20243524	2
#20243227	2
#20243225	2
#20243223	2
C₄×C₈×Dic₄₇	2
C₄₇×#1764	2
#21658	47