Subgroups — #26214123

Order 12032.

1474 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689140	C₂	1	1	yes	maximal, characteristic
2	#20251907	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689078	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689078	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243230	C₂	1	4	yes	maximal, complemented
6	#20243223	C₂	1	4	yes	maximal, complemented
7	#20243114	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243099	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#131×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂²×#10625329	C₂²	1	1	yes	characteristic
12	C₂×#13093983	C₂²	1	1	yes	characteristic
13	C₂×#13093983	C₂²	1	1	yes	characteristic
14	#15689140	C₄	1	8	yes	complemented
15	C₂×#13093951	C₂²	1	4	yes	—
16	#15689132	C₄	1	2	yes	complemented
17	#15689128	C₄	1	2	yes	complemented
18	#15689124	C₄	1	4	yes	complemented
19	#15689119	C₂²	1	4	yes	—
20	#15689078	—	2	1	no	—
21	#15689078	—	2	1	no	—
22	#15689078	—	2	4	no	—
23	#15689078	C₂²	1	2	yes	complemented
24	#15689078	C₂²	1	2	yes	complemented
25	C₂×#13093934	—	2	1	no	—
26	C₂×#13093934	C₂²	1	2	yes	complemented
27	C₂×C₈×Dic₄₇	—	2	1	no	—
28	C₂×C₈×Dic₄₇	C₂²	1	2	yes	complemented
29	#15688887	C₂²	1	4	yes	complemented
30	#15688884	C₂²	1	4	yes	complemented
31	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#131×C₄₇	—	2	4	no	—
33	C₂×#131×C₄₇	—	2	1	no	—
34	C₂×#131×C₄₇	—	2	1	no	—
35	C₂×#131×C₄₇	C₄	1	8	yes	complemented
36	C₂×#131×C₄₇	C₂²	1	2	yes	—
37	C₂×#131×C₄₇	C₂²	1	2	yes	—
38	C₂²×M₁₆×C₄₇	—	2	1	no	—
39	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
40	C₂³×C₈×C₄₇	—	2	1	no	—
41	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#10625329	—	2	1	no	—
43	C₂×#10625329	—	2	2	no	—
44	C₂×#10625329	—	2	2	no	—
45	C₂×#10625329	—	2	2	no	—
46	C₂×#10625329	C₂×C₄	1	4	yes	—
47	C₂×#10625329	C₂×C₄	1	2	yes	—
48	C₂×#10625329	C₂×C₄	1	2	yes	—
49	C₂×#10625329	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	—	2	1	no	—
51	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
52	#13093983	—	2	1	no	—
53	#13093983	—	2	2	no	—
54	#13093983	—	2	1	no	—
55	#13093983	C₂×C₄	1	2	yes	—
56	#13093983	C₂×C₄	1	4	yes	—
57	#13093983	C₂³	1	2	yes	—
58	C₂×C₄⋊Dic₄₇	—	2	1	no	—
59	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
61	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
62	C₂×C₄×Dic₄₇	—	2	1	no	—
63	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
64	#13093951	C₂×C₄	1	16	yes	complemented
65	#13093948	C₂×C₄	1	8	yes	—
66	#13093945	C₂×C₄	1	8	yes	—
67	#13093934	—	2	2	no	—
68	#13093934	—	2	2	no	—
69	#13093934	—	2	4	no	—
70	C₈×Dic₄₇	—	2	2	no	—
71	C₈×Dic₄₇	—	2	2	no	—
72	C₈×Dic₄₇	—	2	4	no	—
73	C₂×#41×C₄₇	—	2	2	no	—
74	C₂×#41×C₄₇	—	2	1	no	—
75	C₂×#41×C₄₇	—	2	1	no	—
76	C₂×#41×C₄₇	—	2	2	no	—
77	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
78	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
79	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
80	C₂×#41×C₄₇	C₂³	1	2	yes	—
81	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂²×D₄×C₄₇	—	2	1	no	—
83	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₄×C₄₇	—	2	1	no	—
85	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
86	#131×C₄₇	—	2	8	no	—
87	#131×C₄₇	—	2	8	no	—
88	#131×C₄₇	—	2	4	no	—
89	#131×C₄₇	—	2	4	no	—
90	#131×C₄₇	C₂×C₄	1	8	yes	complemented
91	#131×C₄₇	C₂×C₄	1	8	yes	complemented
92	C₂×M₁₆×C₄₇	—	2	2	no	—
93	C₂×M₁₆×C₄₇	—	2	1	no	—
94	C₂×M₁₆×C₄₇	—	2	8	no	—
95	C₂×M₁₆×C₄₇	—	2	2	no	—
96	C₂×M₁₆×C₄₇	—	2	2	no	—
97	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
98	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
99	C₂²×C₈×C₄₇	—	2	1	no	—
100	C₂²×C₈×C₄₇	—	2	8	no	—
101	C₂²×C₈×C₄₇	—	2	2	no	—
102	C₂²×C₈×C₄₇	—	2	2	no	—
103	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
104	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
105	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
106	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
107	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
108	C₂²×C₈×C₄₇	D₄	1	4	yes	—
109	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
111	C₂⁴×C₄₇	—	2	1	no	—
112	C₂⁴×C₄₇	#41	1	1	yes	characteristic
113	#41×C₄₇	—	2	4	no	—
114	#41×C₄₇	—	2	4	no	—
115	#41×C₄₇	—	2	4	no	—
116	#41×C₄₇	—	2	4	no	—
117	#41×C₄₇	—	2	4	no	—
118	#41×C₄₇	—	2	2	no	—
119	#41×C₄₇	—	2	2	no	—
120	#41×C₄₇	C₄²	1	8	yes	—
121	#41×C₄₇	C₂²×C₄	1	4	yes	—
122	#41×C₄₇	C₂²×C₄	1	4	yes	—
123	C₂×Q₈×C₄₇	—	2	1	no	—
124	C₂×Q₈×C₄₇	—	2	2	no	—
125	C₂×Q₈×C₄₇	C₄²	1	4	yes	—
126	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂×D₄×C₄₇	—	2	4	no	—
128	C₂×D₄×C₄₇	—	2	2	no	—
129	C₂×D₄×C₄₇	—	2	4	no	—
130	C₂×D₄×C₄₇	—	2	2	no	—
131	C₂×D₄×C₄₇	—	2	2	no	—
132	C₂×D₄×C₄₇	—	2	1	no	—
133	C₂×D₄×C₄₇	C₄²	1	4	yes	—
134	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₄₇	—	2	1	no	—
136	C₂²×C₄×C₄₇	—	2	4	no	—
137	C₂²×C₄×C₄₇	—	2	2	no	—
138	C₂²×C₄×C₄₇	—	2	4	no	—
139	C₂²×C₄×C₄₇	—	2	2	no	—
140	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
148	C₂²×C₄×C₄₇	#41	1	2	yes	—
149	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
150	C₂²×Dic₄₇	—	2	2	no	—
151	C₂²×Dic₄₇	—	2	2	no	—
152	M₁₆×C₄₇	—	2	4	no	—
153	M₁₆×C₄₇	—	2	2	no	—
154	M₁₆×C₄₇	—	2	8	no	—
155	M₁₆×C₄₇	—	2	8	no	—
156	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
157	C₂×C₈×C₄₇	—	2	4	no	—
158	C₂×C₈×C₄₇	—	2	2	no	—
159	C₂×C₈×C₄₇	—	2	8	no	—
160	C₂×C₈×C₄₇	—	2	8	no	—
161	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
162	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
163	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
164	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
165	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
166	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
167	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
171	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
172	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
173	C₂²⋊Dic₄₇	—	2	2	no	—
174	C₂²⋊Dic₄₇	—	2	4	no	—
175	C₂²⋊Dic₄₇	—	2	2	no	—
176	C₄⋊Dic₄₇	—	2	4	no	—
177	C₄⋊Dic₄₇	—	2	2	no	—
178	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
179	C₄×Dic₄₇	—	2	2	no	—
180	C₄×Dic₄₇	—	2	2	no	—
181	C₄×Dic₄₇	—	2	2	no	—
182	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
183	#10625329	—	2	4	no	—
184	#10625329	—	2	4	no	—
185	#10625329	—	2	4	no	—
186	#10625329	—	2	2	no	—
187	#10625329	C₂²×C₄	1	4	yes	—
188	C₂×C₄₇⋊C₈	—	2	4	no	—
189	C₂×C₄₇⋊C₈	—	2	2	no	—
190	C₂×C₄₇⋊C₈	—	2	2	no	—
191	C₂×C₄₇⋊C₈	—	2	2	no	—
192	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
193	C₂³×C₄₇	—	2	2	no	—
194	C₂³×C₄₇	—	2	4	no	—
195	C₂³×C₄₇	—	4	2	no	—
196	C₂³×C₄₇	—	4	4	no	—
197	C₂³×C₄₇	#117	1	2	yes	—
198	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
199	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
200	C₂³×C₄₇	C₄×D₄	1	2	yes	—
201	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
202	Q₈×C₄₇	—	2	2	no	—
203	Q₈×C₄₇	—	2	4	no	—
204	Q₈×C₄₇	C₂×C₄²	1	4	yes	—
205	D₄×C₄₇	—	2	4	no	—
206	D₄×C₄₇	—	2	4	no	—
207	D₄×C₄₇	—	2	8	no	—
208	D₄×C₄₇	—	2	2	no	—
209	D₄×C₄₇	—	2	4	no	—
210	D₄×C₄₇	C₂×C₄²	1	4	yes	—
211	C₂×C₄×C₄₇	—	2	2	no	—
212	C₂×C₄×C₄₇	—	2	4	no	—
213	C₂×C₄×C₄₇	—	2	4	no	—
214	C₂×C₄×C₄₇	—	2	4	no	—
215	C₂×C₄×C₄₇	—	2	8	no	—
216	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
217	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
218	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
220	C₂×C₄×C₄₇	#117	1	2	yes	—
221	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
222	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
223	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
224	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
225	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
234	C₂×Dic₄₇	—	2	4	no	—
235	C₂×Dic₄₇	—	2	4	no	—
236	C₂×Dic₄₇	—	4	4	no	—
237	C₂×Dic₄₇	—	4	4	no	—
238	C₈×C₄₇	—	2	4	no	—
239	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
240	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
241	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
242	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
243	C₄₇⋊C₈	—	2	4	no	—
244	C₄₇⋊C₈	—	2	4	no	—
245	#20420	—	47	1	no	maximal, Sylow
246	C₂²×C₄₇	—	2	2	no	—
247	C₂²×C₄₇	—	2	2	no	—
248	C₂²×C₄₇	—	2	2	no	—
249	C₂²×C₄₇	—	2	4	no	—
250	C₂²×C₄₇	—	4	2	no	—
251	C₂²×C₄₇	—	4	2	no	—
252	C₂²×C₄₇	—	4	8	no	—
253	C₂²×C₄₇	—	4	4	no	—
254	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
255	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
256	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
257	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
259	C₄×C₄₇	—	2	4	no	—
260	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
261	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
262	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
263	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
264	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
265	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
266	Dic₄₇	—	4	4	no	—
267	Dic₄₇	—	4	4	no	—
268	C₂²×#131	D₄₇	1	1	yes	characteristic
269	C₂×#421	—	47	1	no	—
270	#2896	—	47	1	no	—
271	C₂×#405	—	47	1	no	—
272	C₂×#405	—	47	1	no	—
273	#1765	—	47	4	no	—
274	#1764	—	47	4	no	—
275	#1738	—	47	1	no	—
276	#1733	—	47	1	no	—
277	C₂×C₄₇	—	2	1	no	—
278	C₂×C₄₇	—	2	2	no	—
279	C₂×C₄₇	—	2	1	no	—
280	C₂×C₄₇	—	2	2	no	—
281	C₂×C₄₇	—	4	4	no	—
282	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
283	C₂×C₄₇	#2955	1	2	yes	—
284	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
285	C₂×#131	—	2	4	no	—
286	C₂×#131	—	2	1	no	—
287	C₂×#131	—	2	1	no	—
288	C₂×#131	Dic₄₇	1	8	yes	complemented
289	C₂×#131	C₂×D₄₇	1	2	yes	—
290	C₂×#131	C₂×D₄₇	1	2	yes	—
291	C₂²×M₁₆	—	2	1	no	—
292	C₂²×M₁₆	—	47	1	no	—
293	C₂²×M₁₆	—	47	1	no	—
294	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
295	C₂³×C₈	—	2	1	no	—
296	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
297	C₂×#117	—	47	1	no	—
298	C₂×#117	—	47	1	no	—
299	#421	—	47	8	no	—
300	C₂×#104	—	47	4	no	—
301	#419	—	47	2	no	—
302	#418	—	47	2	no	—
303	#417	—	47	4	no	—
304	#416	—	47	4	no	—
305	#405	—	47	2	no	—
306	#405	—	47	2	no	—
307	#405	—	94	4	no	—
308	#405	—	94	1	no	—
309	#405	—	94	1	no	—
310	C₂×#97	—	47	2	no	—
311	C₂×#97	—	94	1	no	—
312	C₂×C₄×C₈	—	47	2	no	—
313	C₂×C₄×C₈	—	94	1	no	—
314	#341	—	47	4	no	—
315	#339	—	47	4	no	—
316	C₄₇	#20420	1	1	yes	characteristic, complemented, Sylow
317	C₂×#41	—	2	1	no	—
318	C₂×#41	—	2	2	no	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	—	2	1	no	—
321	C₂×#41	C₄×D₄₇	1	4	yes	—
322	C₂×#41	C₄×D₄₇	1	2	yes	—
323	C₂×#41	C₂×Dic₄₇	1	4	yes	—
324	C₂×#41	C₂²×D₄₇	1	2	yes	—
325	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
328	C₂³×C₄	—	2	1	no	—
329	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
330	#131	—	2	8	no	—
331	#131	—	2	8	no	—
332	#131	—	2	4	no	—
333	#131	—	2	4	no	—
334	#131	C₂×Dic₄₇	1	8	yes	complemented
335	#131	C₂×Dic₄₇	1	8	yes	complemented
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	—	2	1	no	—
338	C₂×M₁₆	—	2	8	no	—
339	C₂×M₁₆	—	2	2	no	—
340	C₂×M₁₆	—	2	2	no	—
341	C₂×M₁₆	—	47	2	no	—
342	C₂×M₁₆	—	47	2	no	—
343	C₂×M₁₆	—	47	4	no	—
344	C₂×M₁₆	—	47	2	no	—
345	C₂×M₁₆	—	94	2	no	—
346	C₂×M₁₆	—	94	2	no	—
347	C₂×M₁₆	—	94	2	no	—
348	C₂×M₁₆	—	94	1	no	—
349	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
350	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
351	C₂²×C₈	—	2	1	no	—
352	C₂²×C₈	—	2	8	no	—
353	C₂²×C₈	—	2	2	no	—
354	C₂²×C₈	—	2	2	no	—
355	C₂²×C₈	—	47	2	no	—
356	C₂²×C₈	—	94	1	no	—
357	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
358	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
359	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
360	C₂²×C₈	C₂²⋊D₄₇	1	4	yes	—
361	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
362	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
363	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
364	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
365	#117	—	47	4	no	—
366	#117	—	47	2	no	—
367	#117	—	47	2	no	—
368	#117	—	94	1	no	—
369	#117	—	94	2	no	—
370	#117	—	94	1	no	—
371	C₂×C₄⋊C₄	—	47	2	no	—
372	C₂×C₄⋊C₄	—	94	1	no	—
373	C₂×C₂²⋊C₄	—	94	1	no	—
374	C₂×C₂²⋊C₄	—	94	1	no	—
375	C₂×C₄²	—	47	2	no	—
376	C₂×C₄²	—	94	1	no	—
377	#104	—	47	16	no	—
378	#103	—	47	8	no	—
379	#102	—	47	8	no	—
380	#97	—	94	4	no	—
381	#97	—	94	2	no	—
382	#97	—	94	2	no	—
383	C₄×C₈	—	94	4	no	—
384	C₄×C₈	—	94	2	no	—
385	C₄×C₈	—	94	2	no	—
386	C₂⁴	—	2	1	no	—
387	C₂⁴	#10625350	1	1	yes	characteristic
388	#41	—	2	4	no	—
389	#41	—	2	4	no	—
390	#41	—	2	4	no	—
391	#41	—	2	4	no	—
392	#41	—	2	4	no	—
393	#41	—	2	2	no	—
394	#41	—	2	2	no	—
395	#41	C₄×Dic₄₇	1	8	yes	—
396	#41	C₂×C₄×D₄₇	1	4	yes	—
397	#41	C₂²×Dic₄₇	1	4	yes	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	C₄×Dic₄₇	1	4	yes	—
401	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
409	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	94	2	no	—
416	C₂²×C₄	—	94	2	no	—
417	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
418	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
419	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
420	C₂²×C₄	#10625350	1	1	yes	characteristic
421	C₂²×C₄	#10625350	1	2	yes	—
422	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
423	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
424	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
425	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
426	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
427	M₁₆	—	2	4	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	—	2	8	no	—
430	M₁₆	—	2	8	no	—
431	M₁₆	—	47	4	no	—
432	M₁₆	—	94	4	no	—
433	M₁₆	—	94	4	no	—
434	M₁₆	—	94	4	no	—
435	M₁₆	—	94	2	no	—
436	M₁₆	C₂²×Dic₄₇	1	4	yes	—
437	C₂×C₈	—	2	4	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	8	no	—
440	C₂×C₈	—	2	8	no	—
441	C₂×C₈	—	47	4	no	—
442	C₂×C₈	—	94	4	no	—
443	C₂×C₈	—	94	2	no	—
444	C₂×C₈	—	94	2	no	—
445	C₂×C₈	—	94	2	no	—
446	C₂×C₈	C₂²⋊Dic₄₇	1	4	yes	—
447	C₂×C₈	C₂²⋊Dic₄₇	1	4	yes	—
448	C₂×C₈	C₂²⋊Dic₄₇	1	4	yes	—
449	C₂×C₈	C₂²⋊Dic₄₇	1	4	yes	—
450	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
451	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
452	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
453	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
454	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
455	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
456	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
457	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
458	C₄⋊C₄	—	47	4	no	—
459	C₄⋊C₄	—	94	2	no	—
460	C₄⋊C₄	—	94	4	no	—
461	C₂²⋊C₄	—	94	4	no	—
462	C₂²⋊C₄	—	94	2	no	—
463	C₂²⋊C₄	—	94	2	no	—
464	C₄²	—	47	4	no	—
465	C₄²	—	94	2	no	—
466	C₄²	—	94	2	no	—
467	C₄²	—	94	2	no	—
468	C₂³	—	2	4	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	4	2	no	—
471	C₂³	—	4	4	no	—
472	C₂³	#13093983	1	2	yes	—
473	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
474	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
475	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
476	C₂³	C₂×#10625350	1	1	yes	characteristic
477	Q₈	—	2	4	no	—
478	Q₈	—	2	2	no	—
479	Q₈	C₂×C₄×Dic₄₇	1	4	yes	—
480	D₄	—	2	8	no	—
481	D₄	—	2	4	no	—
482	D₄	—	2	4	no	—
483	D₄	—	2	4	no	—
484	D₄	—	2	2	no	—
485	D₄	C₂×C₄×Dic₄₇	1	4	yes	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	8	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	94	4	no	—
492	C₂×C₄	—	94	4	no	—
493	C₂×C₄	—	188	4	no	—
494	C₂×C₄	—	188	4	no	—
495	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
496	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
497	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
498	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
499	C₂×C₄	#13093983	1	2	yes	—
500	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
501	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
502	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
503	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
504	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
505	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
506	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
507	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
508	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
509	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
510	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
511	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
512	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
513	C₈	—	2	4	no	—
514	C₈	—	94	4	no	—
515	C₈	—	94	4	no	—
516	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
517	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
518	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
519	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	8	no	—
527	C₂²	—	4	4	no	—
528	C₂²	C₄×C₂²⋊Dic₄₇	1	2	yes	—
529	C₂²	C₄×C₂²⋊Dic₄₇	1	2	yes	—
530	C₂²	C₂×#13093983	1	1	yes	characteristic
531	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
532	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
533	C₄	—	2	4	no	—
534	C₄	—	188	4	no	—
535	C₄	—	188	4	no	—
536	C₄	C₄×C₂²⋊Dic₄₇	1	2	yes	—
537	C₄	C₄×C₂²⋊Dic₄₇	1	2	yes	—
538	C₄	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
539	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
540	C₄	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
541	C₄	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
542	C₂	—	2	1	no	—
543	C₂	—	2	2	no	—
544	C₂	—	2	2	no	—
545	C₂	—	2	1	no	—
546	C₂	—	4	4	no	—
547	C₂	C₂×C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
548	C₂	#20252289	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×#131×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#131	D₄₇
hypocenter	C₄₇	#20420
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ C₂²×#131

Complements

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

N	H ≅ G/N	type
3. C₂×#15689078	C₂	semidirect
4. C₂×#15689078	C₂	semidirect
5. #20243230	C₂	semidirect
6. #20243223	C₂	semidirect
7. #20243114	C₂	semidirect
8. #20243099	C₂	semidirect
14. #15689140	C₄	semidirect
16. #15689132	C₄	semidirect
17. #15689128	C₄	semidirect
18. #15689124	C₄	semidirect
23. #15689078	C₂²	semidirect
24. #15689078	C₂²	semidirect
26. C₂×#13093934	C₂²	semidirect
28. C₂×C₈×Dic₄₇	C₂²	semidirect
29. #15688887	C₂²	semidirect
30. #15688884	C₂²	semidirect
35. C₂×#131×C₄₇	C₄	semidirect
64. #13093951	C₂×C₄	semidirect
90. #131×C₄₇	C₂×C₄	semidirect
91. #131×C₄₇	C₂×C₄	semidirect
288. C₂×#131	Dic₄₇	semidirect
316. C₄₇	#20420	semidirect
334. #131	C₂×Dic₄₇	semidirect
335. #131	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689140	2
#20251907	2
C₂×#15689078	2
#20243230	2
#20243223	2
#20243114	2
#20243099	2
C₂²×#131×C₄₇	2
#20420	47