Subgroups — #26124539

Order 12032.

886 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15688885	C₂	1	2	yes	maximal
2	C₂×#15688885	C₂	1	2	yes	maximal
3	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
4	#20241618	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#384	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₄₇⋊#95	—	2	1	no	—
10	C₂×C₄₇⋊#95	—	2	1	no	—
11	#15688885	—	2	4	no	—
12	#15688885	—	2	4	no	—
13	#15688878	C₄	1	4	yes	complemented
14	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
15	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#384	—	2	4	no	—
19	C₂³×Dic₄₇	—	2	1	no	—
20	C₂³×Dic₄₇	—	2	1	no	—
21	C₂²×C₄₇⋊C₈	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	—	2	2	no	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₂²×C₄₇⋊C₈	—	2	2	no	—
27	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	1	no	—
33	C₂×C₄⋊Dic₄₇	—	2	1	no	—
34	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
35	C₂×C₄⋊Dic₄₇	Q₈	1	2	yes	—
36	C₄₇⋊#95	—	4	2	no	—
37	C₄₇⋊#95	—	4	2	no	—
38	C₂³×C₄×C₄₇	—	2	2	no	—
39	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
50	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
51	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
52	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
53	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
54	C₂×C₄²×C₄₇	—	2	2	no	—
55	C₂×C₄²×C₄₇	—	2	2	no	—
56	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
58	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₄₇	—	2	1	no	—
60	C₂²×C₄×C₄₇	—	2	1	no	—
61	C₂²×C₄×C₄₇	—	2	1	no	—
62	C₂²×C₄×C₄₇	—	2	1	no	—
63	C₂²×C₄×C₄₇	—	2	1	no	—
64	C₂²×C₄×C₄₇	—	2	1	no	—
65	C₂²×C₄×C₄₇	—	2	1	no	—
66	C₂²×C₄×C₄₇	—	2	1	no	—
67	C₂²×C₄×C₄₇	—	2	4	no	—
68	C₂²×C₄×C₄₇	—	4	2	no	—
69	C₂²×C₄×C₄₇	—	4	2	no	—
70	C₂²×C₄×C₄₇	—	4	2	no	—
71	C₂²×C₄×C₄₇	—	4	2	no	—
72	C₂²×C₄×C₄₇	—	4	2	no	—
73	C₂²×C₄×C₄₇	—	4	2	no	—
74	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
75	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
76	C₂²×C₄×C₄₇	D₈	1	2	yes	—
77	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
78	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
79	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
80	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	#41	1	2	yes	—
86	C₂²×C₄×C₄₇	#41	1	2	yes	—
87	C₂²×C₄×C₄₇	#41	1	2	yes	—
88	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
90	C₂²×Dic₄₇	—	2	2	no	—
91	C₂²×Dic₄₇	—	2	2	no	—
92	C₂²×Dic₄₇	—	4	1	no	—
93	C₂²×Dic₄₇	—	4	1	no	—
94	C₂²×Dic₄₇	—	4	1	no	—
95	C₂²×Dic₄₇	—	4	1	no	—
96	C₂²×Dic₄₇	—	4	1	no	—
97	C₂²×Dic₄₇	—	4	1	no	—
98	C₂²×Dic₄₇	—	4	1	no	—
99	C₂²×Dic₄₇	—	4	1	no	—
100	C₂²×Dic₄₇	—	4	1	no	—
101	C₂²×Dic₄₇	—	4	1	no	—
102	C₂²×Dic₄₇	—	4	1	no	—
103	C₂²×Dic₄₇	—	4	1	no	—
104	C₄⋊C₄×C₄₇	—	2	4	no	—
105	C₄⋊C₄×C₄₇	—	2	4	no	—
106	C₄⋊C₄×C₄₇	—	4	8	no	—
107	C₄⋊C₄×C₄₇	—	4	8	no	—
108	C₄⋊C₄×C₄₇	—	4	2	no	—
109	C₄⋊C₄×C₄₇	—	4	2	no	—
110	C₄²×C₄₇	—	2	4	no	—
111	C₄²×C₄₇	—	2	4	no	—
112	C₄⋊Dic₄₇	—	2	4	no	—
113	C₄⋊Dic₄₇	—	2	4	no	—
114	C₄⋊Dic₄₇	—	4	2	no	—
115	C₄⋊Dic₄₇	—	4	2	no	—
116	C₂×C₄₇⋊C₈	—	2	4	no	—
117	C₂×C₄₇⋊C₈	—	2	4	no	—
118	C₂×C₄₇⋊C₈	—	2	4	no	—
119	C₂×C₄₇⋊C₈	—	4	2	no	—
120	C₂×C₄₇⋊C₈	—	4	2	no	—
121	C₂×C₄₇⋊C₈	—	4	2	no	—
122	C₂×C₄₇⋊C₈	—	4	2	no	—
123	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂³×C₄₇	#120	1	1	yes	characteristic
125	C₂³×C₄₇	#121	1	1	yes	characteristic
126	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
127	C₂³×C₄₇	#123	1	1	yes	characteristic
128	C₂³×C₄₇	#124	1	1	yes	characteristic
129	C₂³×C₄₇	#124	1	1	yes	characteristic
130	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
131	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
132	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
133	C₂³×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
134	C₂³×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
135	C₂³×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
136	C₂³×C₄₇	#137	1	1	yes	characteristic
137	C₂³×C₄₇	#137	1	1	yes	characteristic
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	4	4	no	—
151	C₂×C₄×C₄₇	—	4	4	no	—
152	C₂×C₄×C₄₇	—	4	4	no	—
153	C₂×C₄×C₄₇	—	8	2	no	—
154	C₂×C₄×C₄₇	—	8	2	no	—
155	C₂×C₄×C₄₇	—	8	2	no	—
156	C₂×C₄×C₄₇	—	8	2	no	—
157	C₂×C₄×C₄₇	#106	1	4	yes	—
158	C₂×C₄×C₄₇	#107	1	4	yes	—
159	C₂×C₄×C₄₇	#117	1	2	yes	—
160	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₄₇	#121	1	2	yes	—
164	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
165	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
166	C₂×C₄×C₄₇	#123	1	2	yes	—
167	C₂×C₄×C₄₇	#123	1	2	yes	—
168	C₂×C₄×C₄₇	#124	1	2	yes	—
169	C₂×C₄×C₄₇	#125	1	2	yes	—
170	C₂×C₄×C₄₇	#125	1	2	yes	—
171	C₂×C₄×C₄₇	#125	1	1	yes	characteristic
172	C₂×C₄×C₄₇	#126	1	2	yes	—
173	C₂×C₄×C₄₇	#126	1	2	yes	—
174	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
175	C₂×Dic₄₇	—	4	2	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	4	2	no	—
178	C₂×Dic₄₇	—	4	2	no	—
179	C₂×Dic₄₇	—	4	2	no	—
180	C₂×Dic₄₇	—	4	2	no	—
181	C₂×Dic₄₇	—	8	1	no	—
182	C₂×Dic₄₇	—	8	1	no	—
183	C₂×Dic₄₇	—	8	1	no	—
184	C₂×Dic₄₇	—	8	1	no	—
185	C₂×Dic₄₇	—	8	1	no	—
186	C₂×Dic₄₇	—	8	1	no	—
187	C₂×Dic₄₇	—	8	1	no	—
188	C₂×Dic₄₇	—	8	1	no	—
189	C₄₇⋊C₈	—	4	4	no	—
190	#11267	—	47	1	no	maximal, Sylow
191	C₂²×C₄₇	#382	1	1	yes	characteristic
192	C₂²×C₄₇	#385	1	1	yes	characteristic
193	C₂²×C₄₇	#389	1	1	yes	characteristic
194	C₂²×C₄₇	#393	1	1	yes	characteristic
195	C₂²×C₄₇	#394	1	1	yes	characteristic
196	C₂²×C₄₇	#397	1	1	yes	characteristic
197	C₂²×C₄₇	#400	1	1	yes	characteristic
198	C₂²×C₄₇	C₂×#106	1	1	yes	characteristic
199	C₂²×C₄₇	C₂×#107	1	1	yes	characteristic
200	C₂²×C₄₇	#428	1	1	yes	characteristic
201	C₂²×C₄₇	#428	1	1	yes	characteristic
202	C₂²×C₄₇	#447	1	1	yes	characteristic
203	C₂²×C₄₇	#448	1	1	yes	characteristic
204	C₂²×C₄₇	#450	1	1	yes	characteristic
205	C₂²×C₄₇	#451	1	1	yes	characteristic
206	C₂²×C₄₇	#459	1	1	yes	characteristic
207	C₂²×C₄₇	#460	1	1	yes	characteristic
208	C₂²×C₄₇	#461	1	1	yes	characteristic
209	C₂²×C₄₇	#462	1	1	yes	characteristic
210	C₂²×C₄₇	#474	1	1	yes	characteristic
211	C₂²×C₄₇	#475	1	1	yes	characteristic
212	C₂²×C₄₇	#476	1	1	yes	characteristic
213	C₂²×C₄₇	#477	1	1	yes	characteristic
214	C₂²×C₄₇	#480	1	1	yes	characteristic
215	C₂²×C₄₇	#481	1	1	yes	characteristic
216	C₂²×C₄₇	#483	1	1	yes	characteristic
217	C₂²×C₄₇	#484	1	1	yes	characteristic
218	C₂²×C₄₇	#486	1	1	yes	characteristic
219	C₂²×C₄₇	#486	1	1	yes	characteristic
220	C₂²×C₄₇	#487	1	1	yes	characteristic
221	C₂²×C₄₇	#487	1	1	yes	characteristic
222	C₂²×C₄₇	#489	1	1	yes	characteristic
223	C₂²×C₄₇	#489	1	1	yes	characteristic
224	C₂²×C₄₇	#490	1	1	yes	characteristic
225	C₂²×C₄₇	#491	1	1	yes	characteristic
226	C₄×C₄₇	—	2	4	no	—
227	C₄×C₄₇	—	2	4	no	—
228	C₄×C₄₇	—	8	4	no	—
229	C₄×C₄₇	#387	1	2	yes	—
230	C₄×C₄₇	#388	1	2	yes	—
231	C₄×C₄₇	#398	1	2	yes	—
232	C₄×C₄₇	#400	1	2	yes	—
233	Dic₄₇	—	8	2	no	—
234	Dic₄₇	—	8	2	no	—
235	C₂×#384	D₄₇	1	1	yes	characteristic
236	C₂×#340	—	47	2	no	—
237	C₂×#340	—	47	2	no	—
238	C₂×#336	—	47	1	no	—
239	C₄⋊#95	—	47	1	no	—
240	C₂×C₄₇	#1442	1	1	yes	characteristic
241	C₂×C₄₇	#1834	1	1	yes	characteristic
242	C₂×C₄₇	#1836	1	1	yes	characteristic
243	C₂×C₄₇	#1852	1	1	yes	characteristic
244	C₂×C₄₇	#1853	1	1	yes	characteristic
245	C₂×C₄₇	#1947	1	1	yes	characteristic
246	C₂×C₄₇	#1948	1	1	yes	characteristic
247	C₂×C₄₇	#2023	1	1	yes	characteristic
248	C₂×C₄₇	#2024	1	1	yes	characteristic
249	C₂×C₄₇	#2041	1	1	yes	characteristic
250	C₂×C₄₇	#2043	1	1	yes	characteristic
251	C₂×C₄₇	#2071	1	1	yes	characteristic
252	C₂×C₄₇	#2072	1	1	yes	characteristic
253	C₂×C₄₇	#2099	1	1	yes	characteristic
254	C₂×C₄₇	#2100	1	1	yes	characteristic
255	C₂³×C₈	—	47	2	no	—
256	C₂²×C₄⋊C₄	—	2	1	no	—
257	C₂²×C₄⋊C₄	—	2	1	no	—
258	C₂²×C₄⋊C₄	—	47	1	no	—
259	C₂²×C₄⋊C₄	—	47	1	no	—
260	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
261	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
262	#384	—	2	4	no	—
263	C₂×#95	—	94	1	no	—
264	C₂×#95	—	94	1	no	—
265	#340	—	94	4	no	—
266	#340	—	94	4	no	—
267	#336	—	47	4	no	—
268	C₄₇	#11267	1	1	yes	characteristic, complemented, Sylow
269	C₂³×C₄	—	2	2	no	—
270	C₂³×C₄	—	94	1	no	—
271	C₂³×C₄	—	94	1	no	—
272	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
273	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
274	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
275	C₂²×C₈	—	47	4	no	—
276	C₂²×C₈	—	94	2	no	—
277	C₂²×C₈	—	94	2	no	—
278	C₂²×C₈	—	94	2	no	—
279	C₂²×C₈	—	94	2	no	—
280	C₂²×C₈	—	94	2	no	—
281	C₂²×C₈	—	94	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	4	no	—
287	C₂×C₄⋊C₄	—	2	4	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	4	2	no	—
290	C₂×C₄⋊C₄	—	4	2	no	—
291	C₂×C₄⋊C₄	—	4	2	no	—
292	C₂×C₄⋊C₄	—	4	2	no	—
293	C₂×C₄⋊C₄	—	47	2	no	—
294	C₂×C₄⋊C₄	—	47	2	no	—
295	C₂×C₄⋊C₄	—	94	2	no	—
296	C₂×C₄⋊C₄	—	94	2	no	—
297	C₂×C₄⋊C₄	—	94	2	no	—
298	C₂×C₄⋊C₄	—	94	2	no	—
299	C₂×C₄⋊C₄	—	94	1	no	—
300	C₂×C₄⋊C₄	—	94	1	no	—
301	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	4	yes	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	Dic₉₄	1	2	yes	—
305	C₂×C₄²	C₄×D₄₇	1	2	yes	—
306	#95	—	188	2	no	—
307	#95	—	188	2	no	—
308	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	94	2	no	—
325	C₂²×C₄	—	94	2	no	—
326	C₂²×C₄	—	188	1	no	—
327	C₂²×C₄	—	188	1	no	—
328	C₂²×C₄	—	188	1	no	—
329	C₂²×C₄	—	188	1	no	—
330	C₂²×C₄	—	188	1	no	—
331	C₂²×C₄	—	188	1	no	—
332	C₂²×C₄	—	188	1	no	—
333	C₂²×C₄	—	188	1	no	—
334	C₂²×C₄	—	188	1	no	—
335	C₂²×C₄	—	188	1	no	—
336	C₂²×C₄	—	188	1	no	—
337	C₂²×C₄	—	188	1	no	—
338	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
339	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
340	C₂²×C₄	#10625334	1	2	yes	—
341	C₂²×C₄	#10625335	1	2	yes	—
342	C₂²×C₄	#10625336	1	2	yes	—
343	C₂²×C₄	#10625337	1	2	yes	—
344	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
346	C₂²×C₄	#10625350	1	2	yes	—
347	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
348	C₂²×C₄	#10625352	1	2	yes	—
349	C₂²×C₄	#10625352	1	1	yes	characteristic
350	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
351	C₂²×C₄	#10625354	1	2	yes	—
352	C₂²×C₄	#10625354	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
354	C₂×C₈	—	94	4	no	—
355	C₂×C₈	—	94	4	no	—
356	C₂×C₈	—	94	4	no	—
357	C₂×C₈	—	188	2	no	—
358	C₂×C₈	—	188	2	no	—
359	C₂×C₈	—	188	2	no	—
360	C₂×C₈	—	188	2	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	4	8	no	—
364	C₄⋊C₄	—	4	8	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	94	4	no	—
368	C₄⋊C₄	—	94	4	no	—
369	C₄⋊C₄	—	188	2	no	—
370	C₄⋊C₄	—	188	2	no	—
371	C₄²	—	2	4	no	—
372	C₄²	—	2	4	no	—
373	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
374	C₂³	#13093993	1	1	yes	characteristic
375	C₂³	#13093995	1	1	yes	characteristic
376	C₂³	#13094000	1	1	yes	characteristic
377	C₂³	#13094007	1	1	yes	characteristic
378	C₂³	#13094011	1	1	yes	characteristic
379	C₂³	#13094013	1	1	yes	characteristic
380	C₂³	C₂×#10625334	1	1	yes	characteristic
381	C₂³	C₂×#10625336	1	1	yes	characteristic
382	C₂³	C₂×#10625335	1	1	yes	characteristic
383	C₂³	C₂×#10625337	1	1	yes	characteristic
384	C₂³	#13094050	1	1	yes	characteristic
385	C₂³	#13094050	1	1	yes	characteristic
386	C₂³	#13094055	1	1	yes	characteristic
387	C₂³	#13094055	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	—	8	2	no	—
407	C₂×C₄	—	376	1	no	—
408	C₂×C₄	—	376	1	no	—
409	C₂×C₄	—	376	1	no	—
410	C₂×C₄	—	376	1	no	—
411	C₂×C₄	—	376	1	no	—
412	C₂×C₄	—	376	1	no	—
413	C₂×C₄	—	376	1	no	—
414	C₂×C₄	—	376	1	no	—
415	C₂×C₄	—	188	2	no	—
416	C₂×C₄	—	188	2	no	—
417	C₂×C₄	—	188	2	no	—
418	C₂×C₄	—	188	2	no	—
419	C₂×C₄	—	188	2	no	—
420	C₂×C₄	—	188	2	no	—
421	C₂×C₄	#13093955	1	4	yes	—
422	C₂×C₄	#13093957	1	4	yes	—
423	C₂×C₄	#13093982	1	2	yes	—
424	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
425	C₂×C₄	#13093986	1	1	yes	characteristic
426	C₂×C₄	#13093989	1	1	yes	characteristic
427	C₂×C₄	#13093996	1	2	yes	—
428	C₂×C₄	#13094000	1	2	yes	—
429	C₂×C₄	#13094003	1	2	yes	—
430	C₂×C₄	#13094005	1	2	yes	—
431	C₂×C₄	#13094009	1	2	yes	—
432	C₂×C₄	#13094013	1	2	yes	—
433	C₂×C₄	#13094014	1	2	yes	—
434	C₂×C₄	#13094015	1	2	yes	—
435	C₂×C₄	#13094015	1	1	yes	characteristic
436	C₂×C₄	#13094019	1	2	yes	—
437	C₂×C₄	#13094019	1	2	yes	—
438	C₂×C₄	#13094023	1	1	yes	characteristic
439	C₈	—	188	4	no	—
440	C₂²	#15688988	1	1	yes	characteristic
441	C₂²	#15688996	1	1	yes	characteristic
442	C₂²	#15689019	1	1	yes	characteristic
443	C₂²	#15689034	1	1	yes	characteristic
444	C₂²	#15689037	1	1	yes	characteristic
445	C₂²	#15689049	1	1	yes	characteristic
446	C₂²	#15689061	1	1	yes	characteristic
447	C₂²	C₂×#13093955	1	1	yes	characteristic
448	C₂²	C₂×#13093957	1	1	yes	characteristic
449	C₂²	#15689163	1	1	yes	characteristic
450	C₂²	#15689163	1	1	yes	characteristic
451	C₂²	#15689257	1	1	yes	characteristic
452	C₂²	#15689262	1	1	yes	characteristic
453	C₂²	#15689274	1	1	yes	characteristic
454	C₂²	#15689279	1	1	yes	characteristic
455	C₂²	#15689315	1	1	yes	characteristic
456	C₂²	#15689320	1	1	yes	characteristic
457	C₂²	#15689325	1	1	yes	characteristic
458	C₂²	#15689330	1	1	yes	characteristic
459	C₂²	#15689400	1	1	yes	characteristic
460	C₂²	#15689405	1	1	yes	characteristic
461	C₂²	#15689410	1	1	yes	characteristic
462	C₂²	#15689415	1	1	yes	characteristic
463	C₂²	#15689436	1	1	yes	characteristic
464	C₂²	#15689441	1	1	yes	characteristic
465	C₂²	#15689453	1	1	yes	characteristic
466	C₂²	#15689458	1	1	yes	characteristic
467	C₂²	#15689469	1	1	yes	characteristic
468	C₂²	#15689471	1	1	yes	characteristic
469	C₂²	#15689473	1	1	yes	characteristic
470	C₂²	#15689475	1	1	yes	characteristic
471	C₂²	#15689485	1	1	yes	characteristic
472	C₂²	#15689485	1	1	yes	characteristic
473	C₂²	#15689487	1	1	yes	characteristic
474	C₂²	#15689491	1	1	yes	characteristic
475	C₄	—	2	4	no	—
476	C₄	—	2	4	no	—
477	C₄	—	8	4	no	—
478	C₄	—	376	2	no	—
479	C₄	—	376	2	no	—
480	C₄	#15689004	1	2	yes	—
481	C₄	#15689013	1	2	yes	—
482	C₄	#15689056	1	2	yes	—
483	C₄	#15689062	1	2	yes	—
484	C₂	#20241647	1	1	yes	characteristic
485	C₂	#20243515	1	1	yes	characteristic
486	C₂	#20243523	1	1	yes	characteristic
487	C₂	#20243576	1	1	yes	characteristic
488	C₂	#20243581	1	1	yes	characteristic
489	C₂	#20244144	1	1	yes	characteristic
490	C₂	#20244149	1	1	yes	characteristic
491	C₂	#20244521	1	1	yes	characteristic
492	C₂	#20244526	1	1	yes	characteristic
493	C₂	#20244619	1	1	yes	characteristic
494	C₂	#20244631	1	1	yes	characteristic
495	C₂	#20244792	1	1	yes	characteristic
496	C₂	#20244797	1	1	yes	characteristic
497	C₂	#20244945	1	1	yes	characteristic
498	C₂	#20244950	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#384	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#384	D₄₇
hypocenter	C₄₇	#11267
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#384

Complements

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

N	H ≅ G/N	type
13. #15688878	C₄	semidirect
268. C₄₇	#11267	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15688885	2
C₂×#15688878	2
#20241618	2
C₂×C₄₇×#384	2
#11267	47