Subgroups — #27094799

Order 12032.

1874 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256952	C₂	1	2	yes	maximal, complemented
2	#20255820	C₂	1	1	yes	maximal, characteristic, complemented
3	#20255812	C₂	1	1	yes	maximal, characteristic, complemented
4	#20255803	C₂	1	2	yes	maximal, complemented
5	#20255792	C₂	1	2	yes	maximal, complemented
6	#20255782	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255772	C₂	1	4	yes	maximal, complemented
8	#20255758	C₂	1	2	yes	maximal, complemented
9	#20255747	C₂	1	2	yes	maximal, complemented
10	#20255737	C₂	1	1	yes	maximal, characteristic, complemented
11	#20253902	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253299	C₂	1	4	yes	maximal, complemented
13	#20253176	C₂	1	2	yes	maximal, complemented
14	#20252965	C₂	1	2	yes	maximal, complemented
15	C₂×C₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
16	#427×D₄₇	C₂	1	2	yes	maximal, complemented
17	C₄×#135×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
19	#15689846	C₂²	1	2	yes	—
20	#15689838	C₂²	1	2	yes	—
21	#15689833	C₂²	1	2	yes	—
22	#15689823	C₂²	1	4	yes	—
23	#15689814	C₂²	1	4	yes	—
24	#15689813	—	2	2	no	—
25	#15689802	—	2	4	no	—
26	#15689778	C₂²	1	2	yes	—
27	#15689769	—	2	2	no	—
28	#15689680	C₂²	1	2	yes	—
29	#15689657	—	2	2	no	—
30	#15689651	—	2	4	no	—
31	#15689630	C₂²	1	4	yes	—
32	C₄×#10625350	—	2	2	no	—
33	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
34	#117×D₄₇	C₂²	1	4	yes	—
35	#15689528	C₂²	1	1	yes	characteristic, complemented
36	#15689528	C₂²	1	1	yes	characteristic, complemented
37	#15689525	C₂²	1	2	yes	complemented
38	#15689525	C₂²	1	2	yes	complemented
39	#15689521	C₂²	1	2	yes	complemented
40	#15689463	C₂²	1	4	yes	complemented
41	#15689462	C₂²	1	4	yes	complemented
42	#15689457	C₂²	1	4	yes	complemented
43	#15689452	C₂²	1	4	yes	complemented
44	#15689446	C₂²	1	4	yes	complemented
45	#15689445	C₂²	1	4	yes	complemented
46	#15689440	C₂²	1	4	yes	complemented
47	#15689435	C₂²	1	4	yes	complemented
48	#15689430	C₂²	1	4	yes	complemented
49	#15689423	C₂²	1	4	yes	complemented
50	#15689418	C₂²	1	2	yes	complemented
51	#15689413	C₂²	1	2	yes	complemented
52	#15689408	C₂²	1	2	yes	complemented
53	#15689403	C₂²	1	2	yes	complemented
54	#15689361	C₂²	1	2	yes	complemented
55	#15689361	C₂²	1	2	yes	complemented
56	#15689356	C₂²	1	2	yes	complemented
57	#15689356	C₂²	1	2	yes	complemented
58	#15689349	C₂²	1	4	yes	complemented
59	#15689349	C₂²	1	4	yes	complemented
60	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
61	C₈×D₁₈₈	C₂²	1	2	yes	—
62	C₈×D₁₈₈	C₂²	1	2	yes	—
63	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
64	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
65	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
66	#15689161	C₂²	1	2	yes	—
67	#15689161	C₂²	1	2	yes	—
68	#15689160	C₂²	1	2	yes	complemented
69	#15689160	C₂²	1	2	yes	complemented
70	#15689159	C₂²	1	4	yes	—
71	#15689158	C₂²	1	4	yes	complemented
72	#107×D₄₇	C₂²	1	2	yes	complemented
73	#107×D₄₇	C₂²	1	2	yes	complemented
74	#106×D₄₇	C₂²	1	4	yes	complemented
75	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
76	#15689119	C₂²	1	4	yes	—
77	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
78	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
79	C₄×#41×C₄₇	C₂²	1	2	yes	—
80	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
81	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
82	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
83	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
84	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
85	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
86	C₄₇×#427	C₂²	1	1	yes	characteristic
87	C₄₇×#416	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
89	C₂×#10625350	—	2	2	no	—
90	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
91	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
92	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
93	C₂×C₈×D₄₇	—	2	8	no	—
94	C₂×C₈×D₄₇	C₂³	1	2	yes	—
95	C₂×C₈×D₄₇	C₂³	1	2	yes	—
96	C₂×C₈×D₄₇	C₂³	1	2	yes	—
97	C₂×C₈×D₄₇	C₂³	1	2	yes	—
98	#13094024	C₂³	1	2	yes	—
99	#13094024	C₂³	1	2	yes	—
100	#13094019	—	2	4	no	—
101	#13094018	—	2	4	no	—
102	#13094017	—	2	4	no	—
103	#13094016	—	2	2	no	—
104	#13094016	C₂³	1	4	yes	—
105	#13094014	—	2	4	no	—
106	#13094012	—	2	2	no	—
107	#13094010	—	2	4	no	—
108	#13094009	—	2	4	no	—
109	#13094007	—	2	4	no	—
110	#13094006	—	2	4	no	—
111	#13094005	—	2	4	no	—
112	#13094003	—	2	2	no	—
113	#13094003	—	2	2	no	—
114	#13094003	—	2	2	no	—
115	#13094002	—	2	4	no	—
116	#13094000	C₂³	1	4	yes	—
117	#13094000	C₂³	1	4	yes	—
118	#13093998	—	2	2	no	—
119	#13093997	—	2	4	no	—
120	#13093995	C₂³	1	4	yes	—
121	#13093995	C₂³	1	4	yes	—
122	#13093992	—	2	4	no	—
123	C₄×Dic₉₄	—	2	2	no	—
124	C₄×Dic₉₄	—	2	2	no	—
125	C₄×Dic₉₄	—	2	2	no	—
126	C₄×D₁₈₈	—	2	2	no	—
127	C₄×D₁₈₈	D₄	1	1	yes	characteristic
128	C₄×D₁₈₈	D₄	1	2	yes	—
129	C₄×D₁₈₈	D₄	1	1	yes	characteristic
130	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
131	C₄×D₁₈₈	C₂³	1	2	yes	—
132	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
133	C₄×C₂²⋊D₄₇	—	2	4	no	—
134	C₄×C₂²⋊D₄₇	—	2	4	no	—
135	C₄×C₂²⋊D₄₇	—	2	4	no	—
136	#13093983	—	2	2	no	—
137	#13093983	C₂³	1	4	yes	—
138	#13093982	C₂³	1	4	yes	—
139	#13093982	C₂³	1	4	yes	—
140	#13093981	—	2	4	no	—
141	#13093981	—	2	4	no	—
142	#13093980	—	2	4	no	—
143	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
144	C₄⋊C₄×D₄₇	C₂³	1	4	yes	—
145	C₄⋊C₄×D₄₇	C₂³	1	4	yes	—
146	C₂×(C₂×D₄₇)⋊C₄	D₄	1	2	yes	—
147	C₂²⋊C₄×D₄₇	—	2	4	no	—
148	C₄²×D₄₇	—	2	4	no	—
149	#13093958	C₂³	1	2	yes	—
150	#13093958	C₂³	1	2	yes	—
151	#13093958	C₂³	1	2	yes	—
152	#13093958	C₂³	1	2	yes	—
153	#13093957	C₂³	1	4	yes	—
154	#13093957	C₂³	1	4	yes	—
155	#13093956	C₂³	1	4	yes	—
156	#13093956	C₂³	1	4	yes	—
157	#13093955	C₂³	1	4	yes	—
158	#13093955	C₂³	1	4	yes	—
159	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
160	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
161	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
162	#13093948	C₂³	1	4	yes	—
163	#13093948	C₂³	1	4	yes	—
164	#13093945	C₂³	1	4	yes	—
165	#13093945	C₂³	1	4	yes	—
166	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
167	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
168	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
169	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
170	C₂×#41×C₄₇	C₂³	1	2	yes	—
171	#135×C₄₇	—	2	4	no	—
172	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
173	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
174	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
178	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
179	C₄×D₄×C₄₇	—	2	2	no	—
180	C₄×D₄×C₄₇	—	2	2	no	—
181	C₄×D₄×C₄₇	C₂³	1	2	yes	—
182	C₄×D₄×C₄₇	C₂³	1	2	yes	—
183	#117×C₄₇	—	2	2	no	—
184	#117×C₄₇	C₂³	1	2	yes	—
185	C₂×C₄²×C₄₇	—	2	2	no	—
186	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
187	#107×C₄₇	C₂³	1	1	yes	characteristic
188	#107×C₄₇	C₂³	1	1	yes	characteristic
189	#106×C₄₇	C₂³	1	2	yes	—
190	#103×C₄₇	C₂³	1	2	yes	—
191	#103×C₄₇	C₂³	1	2	yes	—
192	#102×C₄₇	C₂³	1	2	yes	—
193	#102×C₄₇	C₂³	1	2	yes	—
194	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
198	C₂³×D₄₇	C₂×D₄	1	2	yes	—
199	#41×C₄₇	—	2	4	no	—
200	#41×C₄₇	—	2	4	no	—
201	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
202	C₂×D₄×C₄₇	—	2	2	no	—
203	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₄₇	—	2	2	no	—
205	C₂²×C₄×C₄₇	—	2	2	no	—
206	C₂²×C₄×C₄₇	—	2	2	no	—
207	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
210	C₂×C₂²⋊D₄₇	—	2	4	no	—
211	C₂×C₂²⋊D₄₇	—	2	4	no	—
212	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
213	#10625350	—	4	8	no	—
214	C₂×D₁₈₈	—	2	4	no	—
215	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
216	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
217	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
218	C₂×C₄×D₄₇	—	2	4	no	—
219	C₂×C₄×D₄₇	—	2	4	no	—
220	C₂×C₄×D₄₇	—	2	4	no	—
221	C₂×C₄×D₄₇	—	2	4	no	—
222	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
223	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
224	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
225	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
226	C₂×Dic₉₄	—	2	2	no	—
227	C₂×Dic₉₄	—	2	2	no	—
228	Q₁₆×C₄₇	—	2	2	no	—
229	SD₁₆×C₄₇	—	2	4	no	—
230	D₈×C₄₇	—	2	2	no	—
231	C₂×C₈×C₄₇	—	2	2	no	—
232	C₂×C₈×C₄₇	#41	1	4	yes	complemented
233	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
234	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
235	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
236	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
237	C₄⋊C₄×C₄₇	—	2	2	no	—
238	C₄⋊C₄×C₄₇	—	2	2	no	—
239	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
240	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
241	C₂²⋊C₄×C₄₇	—	2	2	no	—
242	C₂²⋊C₄×C₄₇	—	2	2	no	—
243	C₂²⋊C₄×C₄₇	—	2	2	no	—
244	C₄²×C₄₇	—	2	2	no	—
245	C₄²×C₄₇	—	2	2	no	—
246	C₄²×C₄₇	—	2	2	no	—
247	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
248	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
249	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
250	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
251	C₂²⋊Dic₄₇	—	2	4	no	—
252	C₂²⋊Dic₄₇	—	2	4	no	—
253	C₂²⋊Dic₄₇	—	2	4	no	—
254	(C₂×D₄₇)⋊C₄	—	2	4	no	—
255	(C₂×D₄₇)⋊C₄	—	2	4	no	—
256	(C₂×D₄₇)⋊C₄	—	2	4	no	—
257	(C₂×D₄₇)⋊C₄	—	2	4	no	—
258	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
259	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
260	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
261	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
262	C₄⋊Dic₄₇	—	2	2	no	—
263	C₄⋊Dic₄₇	—	2	2	no	—
264	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
265	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
266	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
267	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
268	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
269	Dic₄₇⋊C₄	—	2	4	no	—
270	Dic₄₇⋊C₄	—	2	4	no	—
271	Dic₄₇⋊C₄	—	2	4	no	—
272	Dic₄₇⋊C₄	—	2	4	no	—
273	Dic₄₇⋊C₄	—	2	4	no	—
274	Dic₄₇⋊C₄	—	2	4	no	—
275	C₄×Dic₄₇	—	2	4	no	—
276	C₄×Dic₄₇	—	2	4	no	—
277	C₄×Dic₄₇	—	2	4	no	—
278	C₂×C₄₇⋊C₈	—	2	4	no	—
279	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
280	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
281	C₈×D₄₇	—	2	4	no	—
282	C₈×D₄₇	—	2	4	no	—
283	C₈×D₄₇	—	2	4	no	—
284	C₈×D₄₇	—	2	4	no	—
285	C₂³×C₄₇	—	2	2	no	—
286	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
287	C₂²×D₄₇	—	2	4	no	—
288	C₂²×D₄₇	—	2	4	no	—
289	C₂²×D₄₇	—	4	2	no	—
290	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
291	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
292	Q₈×C₄₇	—	2	2	no	—
293	Q₈×C₄₇	—	2	2	no	—
294	D₄×C₄₇	—	2	2	no	—
295	D₄×C₄₇	—	2	2	no	—
296	D₄×C₄₇	—	4	4	no	—
297	C₂×C₄×C₄₇	—	2	2	no	—
298	C₂×C₄×C₄₇	—	2	2	no	—
299	C₂×C₄×C₄₇	—	2	2	no	—
300	C₂×C₄×C₄₇	—	2	2	no	—
301	C₂×C₄×C₄₇	—	4	1	no	—
302	C₂×C₄×C₄₇	—	4	4	no	—
303	C₂×C₄×C₄₇	—	4	4	no	—
304	C₂×C₄×C₄₇	—	8	2	no	—
305	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
311	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
312	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
313	C₂²⋊D₄₇	—	4	8	no	—
314	C₂²⋊D₄₇	—	8	4	no	—
315	C₂×Dic₄₇	—	2	4	no	—
316	C₂×Dic₄₇	—	2	4	no	—
317	C₂×Dic₄₇	—	2	4	no	—
318	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
319	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
320	D₁₈₈	—	2	4	no	—
321	D₁₈₈	—	2	2	no	—
322	D₁₈₈	#135	1	4	yes	complemented
323	C₄×D₄₇	—	2	4	no	—
324	C₄×D₄₇	—	2	4	no	—
325	C₄×D₄₇	—	2	2	no	—
326	C₄×D₄₇	—	2	2	no	—
327	C₄×D₄₇	—	2	2	no	—
328	C₄×D₄₇	—	2	2	no	—
329	C₄×D₄₇	—	4	8	no	—
330	C₄×D₄₇	—	8	4	no	—
331	Dic₉₄	—	4	4	no	—
332	Dic₉₄	—	8	2	no	—
333	C₈×C₄₇	—	2	1	no	—
334	C₈×C₄₇	—	2	1	no	—
335	C₈×C₄₇	C₂×#41	1	2	yes	—
336	C₈×C₄₇	C₂×#41	1	2	yes	—
337	C₄₇⋊C₈	—	2	2	no	—
338	C₄₇⋊C₈	—	2	2	no	—
339	#61234	—	47	1	no	maximal, Sylow
340	C₂²×C₄₇	—	2	1	no	—
341	C₂²×C₄₇	—	2	1	no	—
342	C₂²×C₄₇	—	4	2	no	—
343	C₂²×C₄₇	—	4	2	no	—
344	C₂²×C₄₇	—	4	2	no	—
345	C₂²×C₄₇	#547	1	2	yes	—
346	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
347	C₂×D₄₇	—	2	2	no	—
348	C₂×D₄₇	—	2	2	no	—
349	C₂×D₄₇	—	2	2	no	—
350	C₂×D₄₇	—	2	2	no	—
351	C₂×D₄₇	—	2	2	no	—
352	C₂×D₄₇	—	4	8	no	—
353	C₂×D₄₇	C₂×#135	1	4	yes	—
354	C₄×C₄₇	—	2	1	no	—
355	C₄×C₄₇	—	2	1	no	—
356	C₄×C₄₇	—	2	1	no	—
357	C₄×C₄₇	—	4	2	no	—
358	C₄×C₄₇	—	4	2	no	—
359	C₄×C₄₇	—	4	2	no	—
360	C₄×C₄₇	#547	1	2	yes	—
361	C₄×C₄₇	C₂×#135	1	2	yes	—
362	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
363	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
364	Dic₄₇	—	2	2	no	—
365	Dic₄₇	—	2	2	no	—
366	Dic₄₇	—	4	4	no	—
367	Dic₄₇	—	4	4	no	—
368	#3475	—	47	2	no	—
369	#3342	—	47	1	no	—
370	#3341	—	47	1	no	—
371	#3340	—	47	2	no	—
372	#3339	—	47	2	no	—
373	#3338	—	47	1	no	—
374	#3337	—	47	4	no	—
375	#3336	—	47	2	no	—
376	#3335	—	47	2	no	—
377	#3334	—	47	1	no	—
378	#3160	—	47	1	no	—
379	#3091	—	47	4	no	—
380	#3076	—	47	2	no	—
381	#3050	—	47	2	no	—
382	C₄×#135	D₄₇	1	1	yes	characteristic, complemented
383	C₂×C₈×D₄	—	47	1	no	—
384	C₂×#427	—	47	2	no	—
385	C₂×C₄₇	—	2	2	no	—
386	C₂×C₄₇	—	8	2	no	—
387	C₂×C₄₇	C₂×#547	1	1	yes	characteristic
388	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
389	C₂×C₄₇	#3584	1	1	yes	characteristic
390	D₄₇	—	2	4	no	—
391	D₄₇	—	4	2	no	—
392	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
393	C₂³×C₈	—	47	2	no	—
394	#556	—	47	2	no	—
395	#555	—	47	2	no	—
396	#554	—	47	2	no	—
397	#553	—	47	4	no	—
398	#552	—	47	4	no	—
399	#552	—	94	2	no	—
400	#551	—	94	4	no	—
401	#547	—	47	2	no	—
402	#546	—	94	2	no	—
403	#533	—	47	2	no	—
404	#529	—	94	2	no	—
405	#529	—	94	4	no	—
406	#525	—	47	4	no	—
407	C₄×#41	—	94	2	no	—
408	C₄×#41	C₂×D₄₇	1	2	yes	—
409	C₂×C₄×D₄	—	47	1	no	—
410	C₂×#117	—	47	4	no	—
411	#500	—	47	1	no	—
412	#500	—	47	1	no	—
413	#499	—	47	2	no	—
414	#499	—	47	2	no	—
415	#498	—	47	2	no	—
416	#485	—	47	4	no	—
417	#485	—	47	4	no	—
418	#484	—	47	4	no	—
419	#483	—	47	4	no	—
420	#482	—	47	4	no	—
421	#482	—	47	4	no	—
422	#481	—	47	4	no	—
423	#480	—	47	4	no	—
424	#479	—	47	4	no	—
425	#478	—	47	4	no	—
426	#477	—	47	2	no	—
427	#476	—	47	2	no	—
428	#475	—	47	2	no	—
429	#474	—	47	2	no	—
430	#467	—	47	2	no	—
431	#467	—	47	2	no	—
432	#466	—	47	2	no	—
433	#466	—	47	2	no	—
434	#465	—	47	4	no	—
435	#465	—	47	4	no	—
436	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
437	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
438	C₄×SD₁₆	C₂×D₄₇	1	2	yes	complemented
439	C₄×SD₁₆	C₂×D₄₇	1	2	yes	complemented
440	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
441	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
442	C₈×D₄	—	47	1	no	—
443	C₈×D₄	—	47	1	no	—
444	C₈×D₄	—	47	2	no	—
445	C₈×D₄	—	47	2	no	—
446	C₈×D₄	—	47	1	no	—
447	C₈×D₄	—	47	1	no	—
448	#427	—	47	2	no	—
449	#427	—	47	2	no	—
450	#427	—	47	4	no	—
451	#427	—	47	2	no	—
452	#427	—	47	2	no	—
453	#427	—	47	4	no	—
454	#427	C₂×D₄₇	1	1	yes	characteristic
455	C₂×#107	—	47	2	no	—
456	C₂×#107	—	47	2	no	—
457	C₂×#106	—	47	4	no	—
458	C₂×C₄⋊C₈	—	47	1	no	—
459	#416	—	47	4	no	—
460	#416	C₂×D₄₇	1	2	yes	—
461	C₂×C₂²⋊C₈	—	47	2	no	—
462	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
463	C₄₇	#61234	1	1	yes	characteristic, complemented, Sylow
464	C₂×#41	—	94	2	no	—
465	C₂×#41	C₂²×D₄₇	1	2	yes	—
466	C₂²×D₄	—	47	1	no	—
467	C₂³×C₄	—	47	2	no	—
468	#135	—	2	4	no	—
469	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
470	C₂×SD₁₆	C₂²×D₄₇	1	2	yes	—
471	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
472	C₂²×C₈	—	47	2	no	—
473	C₂²×C₈	—	47	2	no	—
474	C₂²×C₈	—	47	2	no	—
475	C₂²×C₈	—	47	2	no	—
476	C₂²×C₈	—	47	2	no	—
477	C₂²×C₈	—	94	8	no	—
478	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
479	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
480	C₄⋊Q₈	—	47	2	no	—
481	C₄⋊Q₈	—	47	2	no	—
482	#126	—	94	4	no	—
483	#126	—	94	4	no	—
484	#126	—	94	4	no	—
485	#125	—	47	4	no	—
486	#125	—	94	2	no	—
487	#125	—	94	4	no	—
488	#124	—	94	2	no	—
489	#124	—	94	4	no	—
490	#123	—	94	4	no	—
491	#123	—	94	4	no	—
492	#123	—	94	4	no	—
493	#123	—	94	4	no	—
494	C₂²⋊Q₈	—	47	4	no	—
495	C₂²⋊Q₈	—	47	4	no	—
496	C₂²⋊Q₈	—	94	4	no	—
497	C₂²⋊Q₈	—	94	2	no	—
498	C₂²⋊Q₈	—	94	2	no	—
499	C₂²⋊Q₈	—	94	2	no	—
500	#121	—	47	4	no	—
501	#121	—	47	4	no	—
502	#121	—	94	4	no	—
503	#121	—	94	2	no	—
504	#120	—	94	4	no	—
505	C₄×Q₈	—	94	2	no	—
506	C₄×Q₈	—	94	2	no	—
507	C₄×Q₈	—	94	2	no	—
508	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
509	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	47	1	no	—
513	C₄×D₄	—	47	1	no	—
514	C₄×D₄	—	47	2	no	—
515	C₄×D₄	—	47	1	no	—
516	C₄×D₄	—	47	2	no	—
517	C₄×D₄	—	47	1	no	—
518	C₄×D₄	—	94	2	no	—
519	C₄×D₄	—	94	4	no	—
520	C₄×D₄	—	94	4	no	—
521	C₄×D₄	—	94	4	no	—
522	C₄×D₄	C₂²×D₄₇	1	2	yes	—
523	C₄×D₄	C₂²×D₄₇	1	2	yes	—
524	#117	—	2	2	no	—
525	#117	—	47	4	no	—
526	#117	—	47	4	no	—
527	#117	—	47	4	no	—
528	#117	—	94	4	no	—
529	#117	—	94	4	no	—
530	#117	—	94	4	no	—
531	#117	—	94	2	no	—
532	#117	C₂²×D₄₇	1	2	yes	—
533	C₂×C₄⋊C₄	—	47	1	no	—
534	C₂×C₄⋊C₄	—	47	4	no	—
535	C₂×C₄⋊C₄	—	47	4	no	—
536	C₂×C₂²⋊C₄	—	47	2	no	—
537	C₂×C₂²⋊C₄	—	94	4	no	—
538	C₂×C₄²	—	2	2	no	—
539	C₂×C₄²	—	94	4	no	—
540	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
541	#107	—	47	2	no	—
542	#107	—	47	2	no	—
543	#107	—	47	2	no	—
544	#107	—	47	2	no	—
545	#107	—	47	4	no	—
546	#107	—	47	4	no	—
547	#107	C₂²×D₄₇	1	1	yes	characteristic
548	#107	C₂²×D₄₇	1	1	yes	characteristic
549	#106	—	47	4	no	—
550	#106	—	47	4	no	—
551	#106	—	47	4	no	—
552	#106	—	47	4	no	—
553	#106	C₂²×D₄₇	1	2	yes	—
554	C₄⋊C₈	—	47	1	no	—
555	C₄⋊C₈	—	47	1	no	—
556	C₄⋊C₈	—	47	2	no	—
557	#103	—	47	4	no	—
558	#103	—	47	4	no	—
559	#103	C₂²×D₄₇	1	2	yes	—
560	#103	C₂²×D₄₇	1	2	yes	—
561	#102	—	47	4	no	—
562	#102	—	47	4	no	—
563	#102	C₂²×D₄₇	1	2	yes	—
564	#102	C₂²×D₄₇	1	2	yes	—
565	C₂²⋊C₈	—	47	2	no	—
566	C₂²⋊C₈	—	47	2	no	—
567	C₂²⋊C₈	—	47	2	no	—
568	C₂²⋊C₈	—	47	2	no	—
569	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
570	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
571	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
572	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
573	C₂⁴	—	47	2	no	—
574	#41	—	2	4	no	—
575	#41	—	2	4	no	—
576	#41	—	188	8	no	—
577	C₂×Q₈	—	94	2	no	—
578	C₂×Q₈	—	94	2	no	—
579	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	47	1	no	—
582	C₂×D₄	—	47	2	no	—
583	C₂×D₄	—	47	1	no	—
584	C₂×D₄	—	94	4	no	—
585	C₂×D₄	—	94	4	no	—
586	C₂×D₄	—	94	4	no	—
587	C₂×D₄	C₂³×D₄₇	1	2	yes	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	47	2	no	—
592	C₂²×C₄	—	47	2	no	—
593	C₂²×C₄	—	47	2	no	—
594	C₂²×C₄	—	47	2	no	—
595	C₂²×C₄	—	47	2	no	—
596	C₂²×C₄	—	94	4	no	—
597	C₂²×C₄	—	94	4	no	—
598	C₂²×C₄	—	94	4	no	—
599	C₂²×C₄	—	94	4	no	—
600	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
601	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
602	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
603	Q₁₆	—	2	2	no	—
604	SD₁₆	—	2	4	no	—
605	D₈	—	2	2	no	—
606	C₂×C₈	—	2	2	no	—
607	C₂×C₈	—	47	2	no	—
608	C₂×C₈	—	47	2	no	—
609	C₂×C₈	—	94	4	no	—
610	C₂×C₈	—	94	4	no	—
611	C₂×C₈	—	94	4	no	—
612	C₂×C₈	—	94	4	no	—
613	C₂×C₈	—	94	4	no	—
614	C₂×C₈	#10625350	1	4	yes	complemented
615	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
616	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
617	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
618	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	47	1	no	—
622	C₄⋊C₄	—	47	1	no	—
623	C₄⋊C₄	—	47	2	no	—
624	C₄⋊C₄	—	47	4	no	—
625	C₄⋊C₄	—	47	4	no	—
626	C₄⋊C₄	—	94	4	no	—
627	C₄⋊C₄	—	94	4	no	—
628	C₄⋊C₄	—	94	4	no	—
629	C₄⋊C₄	—	94	4	no	—
630	C₄⋊C₄	—	94	4	no	—
631	C₄⋊C₄	—	94	4	no	—
632	C₄⋊C₄	—	94	2	no	—
633	C₄⋊C₄	—	94	2	no	—
634	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
635	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	47	2	no	—
640	C₂²⋊C₄	—	47	2	no	—
641	C₂²⋊C₄	—	47	2	no	—
642	C₂²⋊C₄	—	47	2	no	—
643	C₂²⋊C₄	—	94	4	no	—
644	C₂²⋊C₄	—	94	4	no	—
645	C₂²⋊C₄	—	94	4	no	—
646	C₂²⋊C₄	—	94	4	no	—
647	C₂²⋊C₄	—	94	4	no	—
648	C₂²⋊C₄	—	94	4	no	—
649	C₂²⋊C₄	—	94	4	no	—
650	C₄²	—	2	2	no	—
651	C₄²	—	2	2	no	—
652	C₄²	—	2	2	no	—
653	C₄²	—	94	4	no	—
654	C₄²	—	94	4	no	—
655	C₄²	—	94	4	no	—
656	C₄²	D₄×D₄₇	1	1	yes	characteristic
657	C₄²	D₄×D₄₇	1	1	yes	characteristic
658	C₄²	C₂³×D₄₇	1	1	yes	characteristic
659	C₄²	C₂³×D₄₇	1	1	yes	characteristic
660	C₂³	—	2	2	no	—
661	C₂³	—	47	2	no	—
662	C₂³	—	47	2	no	—
663	C₂³	—	94	4	no	—
664	C₂³	—	94	4	no	—
665	C₂³	—	188	2	no	—
666	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
667	Q₈	—	2	2	no	—
668	Q₈	—	2	2	no	—
669	Q₈	—	376	2	no	—
670	Q₈	—	188	4	no	—
671	D₄	—	2	2	no	—
672	D₄	—	2	2	no	—
673	D₄	—	4	4	no	—
674	D₄	—	47	4	no	—
675	D₄	—	94	4	no	—
676	D₄	—	94	2	no	—
677	D₄	—	376	4	no	—
678	D₄	—	188	8	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	4	no	—
685	C₂×C₄	—	4	4	no	—
686	C₂×C₄	—	8	2	no	—
687	C₂×C₄	—	47	2	no	—
688	C₂×C₄	—	47	2	no	—
689	C₂×C₄	—	94	4	no	—
690	C₂×C₄	—	94	4	no	—
691	C₂×C₄	—	94	4	no	—
692	C₂×C₄	—	94	2	no	—
693	C₂×C₄	—	94	2	no	—
694	C₂×C₄	—	94	2	no	—
695	C₂×C₄	—	94	2	no	—
696	C₂×C₄	—	94	4	no	—
697	C₂×C₄	—	94	4	no	—
698	C₂×C₄	—	376	4	no	—
699	C₂×C₄	—	188	8	no	—
700	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
701	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
702	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
703	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
704	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
705	C₂×C₄	C₂×#10625350	1	2	yes	—
706	C₂×C₄	#13094071	1	2	yes	—
707	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
708	C₈	—	2	1	no	—
709	C₈	—	2	1	no	—
710	C₈	—	94	2	no	—
711	C₈	—	94	2	no	—
712	C₈	C₂×#10625350	1	2	yes	—
713	C₈	C₂×#10625350	1	2	yes	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	47	4	no	—
720	C₂²	—	94	2	no	—
721	C₂²	—	94	2	no	—
722	C₂²	—	94	2	no	—
723	C₂²	—	94	2	no	—
724	C₂²	—	94	2	no	—
725	C₂²	—	188	8	no	—
726	C₂²	#15689778	1	2	yes	—
727	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	—	94	2	no	—
735	C₄	—	94	2	no	—
736	C₄	—	188	4	no	—
737	C₄	—	188	4	no	—
738	C₄	#15689778	1	2	yes	—
739	C₄	#135×D₄₇	1	2	yes	—
740	C₄	C₂²×#10625350	1	1	yes	characteristic
741	C₄	C₂×#13094071	1	1	yes	characteristic
742	C₂	—	2	2	no	—
743	C₂	—	8	2	no	—
744	C₂	—	94	4	no	—
745	C₂	—	188	2	no	—
746	C₂	C₂×#15689778	1	1	yes	characteristic
747	C₂	C₂×#135×D₄₇	1	1	yes	characteristic
748	C₂	#20258157	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄×#135×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	C₄×#135	D₄₇
hypocenter	C₄₇	#61234
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #20256952	C₂	semidirect
2. #20255820	C₂	semidirect
3. #20255812	C₂	semidirect
4. #20255803	C₂	semidirect
5. #20255792	C₂	semidirect
6. #20255782	C₂	semidirect
7. #20255772	C₂	semidirect
8. #20255758	C₂	semidirect
9. #20255747	C₂	semidirect
10. #20255737	C₂	semidirect
11. #20253902	C₂	semidirect
12. #20253299	C₂	semidirect
13. #20253176	C₂	semidirect
14. #20252965	C₂	semidirect
15. C₂×C₈×D₁₈₈	C₂	semidirect
16. #427×D₄₇	C₂	semidirect
17. C₄×#135×C₄₇	C₂	semidirect
35. #15689528	C₂²	semidirect
36. #15689528	C₂²	semidirect
37. #15689525	C₂²	semidirect
38. #15689525	C₂²	semidirect
39. #15689521	C₂²	semidirect
40. #15689463	C₂²	semidirect
41. #15689462	C₂²	semidirect
42. #15689457	C₂²	semidirect
43. #15689452	C₂²	semidirect
44. #15689446	C₂²	semidirect
45. #15689445	C₂²	semidirect
46. #15689440	C₂²	semidirect
47. #15689435	C₂²	semidirect
48. #15689430	C₂²	semidirect
49. #15689423	C₂²	semidirect
50. #15689418	C₂²	semidirect
51. #15689413	C₂²	semidirect
52. #15689408	C₂²	semidirect
53. #15689403	C₂²	semidirect
54. #15689361	C₂²	semidirect
55. #15689361	C₂²	semidirect
56. #15689356	C₂²	semidirect
57. #15689356	C₂²	semidirect
58. #15689349	C₂²	semidirect
59. #15689349	C₂²	semidirect
68. #15689160	C₂²	semidirect
69. #15689160	C₂²	semidirect
71. #15689158	C₂²	semidirect
72. #107×D₄₇	C₂²	semidirect
73. #107×D₄₇	C₂²	semidirect
74. #106×D₄₇	C₂²	semidirect
80. C₄×Q₁₆×C₄₇	C₂²	semidirect
81. C₄×Q₁₆×C₄₇	C₂²	semidirect
82. C₄×SD₁₆×C₄₇	C₂²	semidirect
83. C₄×SD₁₆×C₄₇	C₂²	semidirect
84. C₄×D₈×C₄₇	C₂²	semidirect
85. C₄×D₈×C₄₇	C₂²	semidirect
232. C₂×C₈×C₄₇	#41	semidirect
322. D₁₈₈	#135	semidirect
382. C₄×#135	D₄₇	semidirect
436. C₄×Q₁₆	C₂×D₄₇	semidirect
437. C₄×Q₁₆	C₂×D₄₇	semidirect
438. C₄×SD₁₆	C₂×D₄₇	semidirect
439. C₄×SD₁₆	C₂×D₄₇	semidirect
440. C₄×D₈	C₂×D₄₇	semidirect
441. C₄×D₈	C₂×D₄₇	semidirect
463. C₄₇	#61234	semidirect
614. C₂×C₈	#10625350	semidirect

Maximal subgroups

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

subgroup	index
#20256952	2
#20255820	2
#20255812	2
#20255803	2
#20255792	2
#20255782	2
#20255772	2
#20255758	2
#20255747	2
#20255737	2
#20253902	2
#20253299	2
#20253176	2
#20252965	2
C₂×C₈×D₁₈₈	2
#427×D₄₇	2
C₄×#135×C₄₇	2
#61234	47