Subgroups — #27124814

Order 12032.

11534 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#41×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#20257061	C₂	1	8	yes	maximal, complemented
3	#20257050	C₂	1	8	yes	maximal, complemented
4	#20257043	C₂	1	2	yes	maximal, complemented
5	#20257036	C₂	1	2	yes	maximal, complemented
6	#20257028	C₂	1	6	yes	maximal, complemented
7	#20257019	C₂	1	6	yes	maximal, complemented
8	#41×C₂²⋊D₄₇	C₂	1	16	yes	maximal, complemented
9	#20256717	C₂	1	6	yes	maximal, complemented
10	C₂×#15689630	C₂	1	6	yes	maximal, complemented
11	#20256591	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄₇×#585	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#10625354	C₂²	1	1	yes	characteristic, complemented
14	C₂²×#10625350	C₂²	1	3	yes	complemented
15	C₂²×#10625352	C₂²	1	3	yes	complemented
16	C₂×#41×D₄₇	—	2	16	no	—
17	C₂×#41×D₄₇	C₂²	1	8	yes	complemented
18	C₂×#41×D₄₇	C₂²	1	8	yes	complemented
19	C₂²×Q₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₄×D₄₇	C₂²	1	3	yes	complemented
21	C₂³×C₄×D₄₇	C₂²	1	3	yes	complemented
22	#15689792	C₂²	1	16	yes	complemented
23	Q₈×C₂²⋊D₄₇	C₂²	1	16	yes	complemented
24	#15689784	C₂²	1	16	yes	complemented
25	#15689780	C₂²	1	16	yes	complemented
26	#15689772	C₂²	1	48	yes	complemented
27	#15689767	C₂²	1	48	yes	complemented
28	#15689761	C₂²	1	48	yes	complemented
29	D₄×C₂²⋊D₄₇	C₂²	1	48	yes	complemented
30	#15689701	C₂²	1	24	yes	complemented
31	#15689697	C₂²	1	12	yes	complemented
32	#15689694	C₂²	1	12	yes	complemented
33	#15689690	C₂²	1	12	yes	complemented
34	#15689687	C₂²	1	12	yes	complemented
35	#15689682	C₂²	1	24	yes	complemented
36	#15689669	C₂²	1	24	yes	complemented
37	#15689634	C₂²	1	24	yes	complemented
38	#15689630	C₂²	1	12	yes	complemented
39	#15689630	C₂²	1	4	yes	complemented
40	#15689630	C₂²	1	12	yes	complemented
41	#15689630	C₂²	1	12	yes	complemented
42	#15689630	C₂²	1	24	yes	complemented
43	#15689630	C₂²	1	24	yes	complemented
44	C₂×#13094005	C₂²	1	12	yes	complemented
45	C₂×#13094000	C₂²	1	12	yes	complemented
46	C₂×#13093995	C₂²	1	12	yes	complemented
47	C₂×#13093992	C₂²	1	12	yes	complemented
48	#15689606	C₂²	1	8	yes	complemented
49	#15689601	C₂²	1	2	yes	complemented
50	#15689598	C₂²	1	6	yes	complemented
51	#41×Dic₄₇	C₂²	1	8	yes	complemented
52	C₂×C₄×C₂²⋊D₄₇	C₂²	1	24	yes	complemented
53	C₂×#13093983	C₂²	1	6	yes	complemented
54	C₄₇×#585	—	2	16	no	—
55	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	2	yes	complemented
56	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	4	yes	complemented
57	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	6	yes	complemented
58	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	4	yes	complemented
59	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
60	C₂²×#41×C₄₇	C₂²	1	6	yes	complemented
61	C₂²×#41×C₄₇	C₂²	1	8	yes	complemented
62	C₂⁴×D₄₇	C₂³	1	3	yes	—
63	C₂×#10625354	—	2	8	no	—
64	C₂×#10625354	C₂³	1	8	yes	—
65	C₂×#10625350	—	2	24	no	—
66	C₂×#10625350	C₂³	1	12	yes	—
67	C₂×#10625350	C₂³	1	12	yes	—
68	C₂×#10625352	—	2	24	no	—
69	C₂×#10625352	C₂³	1	24	yes	—
70	#41×D₄₇	—	2	64	no	—
71	#41×D₄₇	—	2	64	no	—
72	C₂²×Dic₉₄	C₂³	1	3	yes	—
73	C₂×Q₈×D₄₇	—	2	8	no	—
74	C₂×Q₈×D₄₇	C₂³	1	8	yes	—
75	C₂²×D₁₈₈	C₂³	1	3	yes	—
76	C₂²×C₂²⋊D₄₇	C₂³	1	6	yes	—
77	C₂²×C₂²⋊D₄₇	C₂³	1	24	yes	—
78	C₂×D₄×D₄₇	—	2	24	no	—
79	C₂×D₄×D₄₇	C₂³	1	24	yes	—
80	C₂³×Dic₄₇	C₂³	1	3	yes	—
81	C₂²×C₄×D₄₇	—	2	24	no	—
82	C₂²×C₄×D₄₇	C₂³	1	12	yes	—
83	C₂²×C₄×D₄₇	C₂³	1	12	yes	—
84	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
85	C₂²×C₄×D₄₇	C₂³	1	3	yes	—
86	C₂²×C₄×D₄₇	C₂³	1	3	yes	—
87	C₂²×C₄×D₄₇	C₂³	1	3	yes	—
88	#13094022	C₂³	1	24	yes	complemented
89	#13094020	C₂³	1	24	yes	complemented
90	#13094013	C₂³	1	24	yes	complemented
91	#13094011	C₂³	1	24	yes	complemented
92	#13094007	C₂³	1	48	yes	complemented
93	#13094005	C₂³	1	8	yes	—
94	#13094005	C₂³	1	24	yes	—
95	#13094005	C₂³	1	48	yes	complemented
96	#13094003	C₂³	1	48	yes	complemented
97	#13094000	C₂³	1	24	yes	—
98	#13094000	C₂³	1	8	yes	—
99	#13094000	C₂³	1	24	yes	complemented
100	#13094000	C₂³	1	24	yes	complemented
101	#13093998	C₂³	1	48	yes	complemented
102	#13093996	C₂³	1	96	yes	complemented
103	#13093995	C₂³	1	24	yes	—
104	#13093995	C₂³	1	8	yes	—
105	#13093995	C₂³	1	24	yes	complemented
106	#13093995	C₂³	1	24	yes	complemented
107	#13093993	C₂³	1	48	yes	complemented
108	#13093992	C₂³	1	48	yes	—
109	#13093992	C₂³	1	8	yes	—
110	#13093992	C₂³	1	24	yes	—
111	Q₈×Dic₄₇	C₂³	1	16	yes	complemented
112	D₄×Dic₄₇	C₂³	1	48	yes	complemented
113	C₄×C₂²⋊D₄₇	C₂³	1	48	yes	—
114	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
115	C₄×C₂²⋊D₄₇	C₂³	1	48	yes	complemented
116	C₄×C₂²⋊D₄₇	C₂³	1	48	yes	complemented
117	#13093983	C₂³	1	4	yes	—
118	#13093983	C₂³	1	12	yes	—
119	#13093983	C₂³	1	12	yes	complemented
120	#13093983	C₂³	1	12	yes	complemented
121	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	complemented
122	C₂×Dic₄₇⋊C₄	C₂³	1	24	yes	complemented
123	C₂×C₂²⋊Dic₄₇	C₂³	1	12	yes	—
124	C₂×C₂²⋊Dic₄₇	C₂³	1	24	yes	complemented
125	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	24	yes	—
126	C₂×C₄×Dic₄₇	C₂³	1	12	yes	complemented
127	2₋¹⁺⁴×C₄₇	—	2	32	no	—
128	2₋¹⁺⁴×C₄₇	—	2	16	no	—
129	H(5,𝔽₂)×C₄₇	—	2	32	no	—
130	H(5,𝔽₂)×C₄₇	—	2	48	no	—
131	C₂×#41×C₄₇	—	2	64	no	—
132	C₂×#41×C₄₇	—	2	48	no	—
133	C₂×#41×C₄₇	D₄	1	16	yes	complemented
134	C₂×#41×C₄₇	C₂³	1	4	yes	—
135	C₂×#41×C₄₇	C₂³	1	12	yes	—
136	C₂×#41×C₄₇	C₂³	1	4	yes	—
137	C₂×#41×C₄₇	C₂³	1	4	yes	—
138	C₂×#41×C₄₇	C₂³	1	24	yes	complemented
139	C₂×#41×C₄₇	C₂³	1	8	yes	complemented
140	C₂×#41×C₄₇	C₂³	1	12	yes	complemented
141	C₂×#41×C₄₇	C₂³	1	12	yes	complemented
142	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
143	C₂²×Q₈×C₄₇	C₂³	1	8	yes	complemented
144	C₂²×Q₈×C₄₇	C₂³	1	6	yes	complemented
145	C₂²×D₄×C₄₇	C₂³	1	12	yes	—
146	C₂²×D₄×C₄₇	C₂³	1	3	yes	—
147	C₂²×D₄×C₄₇	C₂³	1	24	yes	complemented
148	C₂²×D₄×C₄₇	C₂³	1	6	yes	complemented
149	C₂³×C₄×C₄₇	C₂³	1	3	yes	—
150	C₂³×C₄×C₄₇	C₂³	1	12	yes	complemented
151	C₂⁴×C₄₇	C₂⁴	1	12	yes	—
152	C₂⁴×C₄₇	C₂⁴	1	3	yes	—
153	C₂³×D₄₇	—	2	12	no	—
154	C₂³×D₄₇	—	4	12	no	—
155	C₂³×D₄₇	C₂⁴	1	1	yes	characteristic
156	C₂³×D₄₇	C₂⁴	1	12	yes	—
157	C₂³×D₄₇	C₂⁴	1	3	yes	—
158	#41×C₄₇	—	2	32	no	—
159	#41×C₄₇	—	2	96	no	—
160	#41×C₄₇	—	2	16	no	—
161	#41×C₄₇	—	2	48	no	—
162	#41×C₄₇	—	2	48	no	—
163	#41×C₄₇	—	2	48	no	—
164	#41×C₄₇	C₂×D₄	1	32	yes	complemented
165	#41×C₄₇	C₂×D₄	1	32	yes	complemented
166	C₂×Q₈×C₄₇	—	2	32	no	—
167	C₂×Q₈×C₄₇	—	2	24	no	—
168	C₂×Q₈×C₄₇	C₂×D₄	1	8	yes	complemented
169	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
170	C₂×Q₈×C₄₇	C₂⁴	1	12	yes	—
171	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
172	C₂×D₄×C₄₇	—	2	48	no	—
173	C₂×D₄×C₄₇	—	2	96	no	—
174	C₂×D₄×C₄₇	—	2	24	no	—
175	C₂×D₄×C₄₇	C₂×D₄	1	24	yes	complemented
176	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
177	C₂×D₄×C₄₇	C₂⁴	1	24	yes	—
178	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
179	C₂×D₄×C₄₇	C₂⁴	1	12	yes	—
180	C₂×D₄×C₄₇	C₂⁴	1	12	yes	—
181	C₂²×C₄×C₄₇	—	2	48	no	—
182	C₂²×C₄×C₄₇	C₂×D₄	1	24	yes	complemented
183	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
184	C₂²×C₄×C₄₇	C₂⁴	1	12	yes	—
185	C₂²×C₄×C₄₇	C₂⁴	1	24	yes	—
186	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
188	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
189	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
190	C₂×C₂²⋊D₄₇	—	2	24	no	—
191	C₂×C₂²⋊D₄₇	—	4	48	no	—
192	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
193	C₂×C₂²⋊D₄₇	C₂⁴	1	24	yes	—
194	C₂×C₂²⋊D₄₇	C₂⁴	1	48	yes	—
195	C₂²×Dic₄₇	—	2	12	no	—
196	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
197	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
198	C₂²×Dic₄₇	C₂⁴	1	3	yes	—
199	C₂²×Dic₄₇	C₂⁴	1	24	yes	—
200	#10625354	—	2	32	no	—
201	Q₈×D₄₇	—	2	32	no	—
202	#10625352	—	2	96	no	—
203	D₄×D₄₇	—	2	96	no	—
204	#10625350	—	2	48	no	—
205	#10625350	—	2	48	no	—
206	C₂×D₁₈₈	—	2	12	no	—
207	C₂×D₁₈₈	C₂⁴	1	12	yes	—
208	C₂×C₄×D₄₇	—	2	4	no	—
209	C₂×C₄×D₄₇	—	2	12	no	—
210	C₂×C₄×D₄₇	—	2	48	no	—
211	C₂×C₄×D₄₇	—	2	48	no	—
212	C₂×C₄×D₄₇	—	2	12	no	—
213	C₂×C₄×D₄₇	—	2	12	no	—
214	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
215	C₂×C₄×D₄₇	C₂⁴	1	12	yes	—
216	C₂×C₄×D₄₇	C₂⁴	1	6	yes	—
217	C₂×C₄×D₄₇	C₂⁴	1	12	yes	—
218	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
219	C₂×C₄×D₄₇	C₂⁴	1	6	yes	—
220	C₂×Dic₉₄	—	2	12	no	—
221	C₂×Dic₉₄	C₂⁴	1	12	yes	—
222	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
223	C₂²⋊Dic₄₇	C₂⁴	1	24	yes	—
224	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
225	C₂²⋊Dic₄₇	C₂⁴	1	48	yes	—
226	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
227	(C₂×D₄₇)⋊C₄	C₂⁴	1	48	yes	—
228	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
229	C₄⋊Dic₄₇	C₂⁴	1	24	yes	—
230	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
231	Dic₄₇⋊C₄	C₂⁴	1	48	yes	—
232	C₄×Dic₄₇	C₂⁴	1	8	yes	—
233	C₄×Dic₄₇	C₂⁴	1	24	yes	—
234	C₂³×C₄₇	—	2	24	no	—
235	C₂³×C₄₇	—	4	6	no	—
236	C₂³×C₄₇	—	4	24	no	—
237	C₂³×C₄₇	C₂²×D₄	1	12	yes	—
238	C₂³×C₄₇	C₂⁵	1	8	yes	—
239	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
240	C₂³×C₄₇	C₂⁵	1	6	yes	—
241	C₂²×D₄₇	—	2	2	no	—
242	C₂²×D₄₇	—	2	4	no	—
243	C₂²×D₄₇	—	2	6	no	—
244	C₂²×D₄₇	—	2	24	no	—
245	C₂²×D₄₇	—	2	24	no	—
246	C₂²×D₄₇	—	4	12	no	—
247	C₂²×D₄₇	—	4	6	no	—
248	C₂²×D₄₇	—	4	48	no	—
249	C₂²×D₄₇	C₂⁵	1	6	yes	—
250	C₂²×D₄₇	C₂⁵	1	2	yes	—
251	Q₈×C₄₇	—	2	24	no	—
252	Q₈×C₄₇	—	2	8	no	—
253	Q₈×C₄₇	C₂²×D₄	1	16	yes	—
254	D₄×C₄₇	—	2	16	no	—
255	D₄×C₄₇	—	2	48	no	—
256	D₄×C₄₇	—	2	24	no	—
257	D₄×C₄₇	—	2	8	no	—
258	D₄×C₄₇	C₂²×D₄	1	48	yes	—
259	C₂×C₄×C₄₇	—	2	24	no	—
260	C₂×C₄×C₄₇	—	2	16	no	—
261	C₂×C₄×C₄₇	—	2	48	no	—
262	C₂×C₄×C₄₇	C₂²×D₄	1	12	yes	—
263	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
264	C₂×C₄×C₄₇	C₂²×D₄	1	24	yes	—
265	C₂×C₄×C₄₇	C₂²×D₄	1	24	yes	—
266	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
267	C₂×C₄×C₄₇	C₂⁵	1	6	yes	—
268	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
269	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
270	C₂²⋊D₄₇	—	2	48	no	—
271	C₂²⋊D₄₇	—	2	32	no	—
272	C₂²⋊D₄₇	—	4	48	no	—
273	C₂×Dic₄₇	—	2	6	no	—
274	C₂×Dic₄₇	—	2	2	no	—
275	C₂×Dic₄₇	—	2	24	no	—
276	C₂×Dic₄₇	—	4	24	no	—
277	C₂×Dic₄₇	C₂⁵	1	16	yes	—
278	C₂×Dic₄₇	C₂⁵	1	6	yes	—
279	C₂×Dic₄₇	C₂⁵	1	2	yes	—
280	D₁₈₈	—	2	24	no	—
281	C₄×D₄₇	—	2	4	no	—
282	C₄×D₄₇	—	2	4	no	—
283	C₄×D₄₇	—	2	12	no	—
284	C₄×D₄₇	—	2	12	no	—
285	C₄×D₄₇	—	2	24	no	—
286	C₄×D₄₇	—	2	24	no	—
287	Dic₉₄	—	2	24	no	—
288	#62811	—	47	1	no	maximal, Sylow
289	C₂²×C₄₇	—	2	12	no	—
290	C₂²×C₄₇	—	2	2	no	—
291	C₂²×C₄₇	—	2	8	no	—
292	C₂²×C₄₇	—	2	16	no	—
293	C₂²×C₄₇	—	4	12	no	—
294	C₂²×C₄₇	—	8	24	no	—
295	C₂²×C₄₇	C₂³×D₄	1	2	yes	—
296	C₂²×C₄₇	C₂³×D₄	1	12	yes	—
297	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
298	C₂×D₄₇	—	2	8	no	—
299	C₂×D₄₇	—	2	2	no	—
300	C₂×D₄₇	—	2	2	no	—
301	C₂×D₄₇	—	2	6	no	—
302	C₂×D₄₇	—	2	12	no	—
303	C₂×D₄₇	—	4	48	no	—
304	C₂×D₄₇	—	4	12	no	—
305	C₂×D₄₇	#585	1	4	yes	complemented
306	C₄×C₄₇	—	2	8	no	—
307	C₄×C₄₇	C₂³×D₄	1	12	yes	—
308	C₄×C₄₇	C₂³×D₄	1	2	yes	—
309	C₄×C₄₇	C₂³×D₄	1	2	yes	—
310	Dic₄₇	—	2	6	no	—
311	Dic₄₇	—	2	2	no	—
312	Dic₄₇	—	2	16	no	—
313	C₂×#585	D₄₇	1	1	yes	characteristic, complemented
314	C₂³×#41	—	47	1	no	—
315	#3489	—	47	8	no	—
316	#3488	—	47	8	no	—
317	#3487	—	47	2	no	—
318	#3486	—	47	2	no	—
319	#3485	—	47	6	no	—
320	#3484	—	47	6	no	—
321	D₄×#41	—	47	16	no	—
322	#3449	—	47	6	no	—
323	C₂×#525	—	47	6	no	—
324	#3428	—	47	1	no	—
325	C₂×C₄₇	—	2	2	no	—
326	C₂×C₄₇	—	2	12	no	—
327	C₂×C₄₇	—	4	8	no	—
328	C₂×C₄₇	C₂⁴×D₄	1	1	yes	characteristic
329	C₂×C₄₇	C₂×#585	1	2	yes	—
330	D₄₇	—	2	4	no	—
331	D₄₇	—	4	6	no	—
332	#585	—	2	16	no	—
333	C₂×2₋¹⁺⁴	C₂×D₄₇	1	2	yes	complemented
334	C₂×2₋¹⁺⁴	C₂×D₄₇	1	4	yes	complemented
335	C₂×H(5,𝔽₂)	C₂×D₄₇	1	6	yes	complemented
336	C₂×H(5,𝔽₂)	C₂×D₄₇	1	4	yes	complemented
337	C₂²×#41	—	47	8	no	—
338	C₂²×#41	—	47	8	no	—
339	C₂²×#41	—	47	1	no	—
340	C₂²×#41	—	47	3	no	—
341	C₂²×#41	—	47	3	no	—
342	C₂²×#41	—	94	16	no	—
343	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
344	C₂²×#41	C₂×D₄₇	1	6	yes	complemented
345	C₂²×#41	C₂×D₄₇	1	8	yes	complemented
346	C₂³×Q₈	—	47	1	no	—
347	C₂³×D₄	—	47	3	no	—
348	C₂⁴×C₄	—	47	3	no	—
349	#550	—	47	16	no	—
350	D₄×Q₈	—	47	16	no	—
351	#548	—	47	16	no	—
352	#548	—	47	16	no	—
353	#547	—	47	48	no	—
354	#546	—	47	48	no	—
355	#546	—	47	48	no	—
356	D₄²	—	47	48	no	—
357	#537	—	47	24	no	—
358	#536	—	47	12	no	—
359	#536	—	47	12	no	—
360	#535	—	47	12	no	—
361	#535	—	47	12	no	—
362	#534	—	47	24	no	—
363	#532	—	47	24	no	—
364	#525	—	47	4	no	—
365	#525	—	47	12	no	—
366	#525	—	47	12	no	—
367	#525	—	47	12	no	—
368	#525	—	47	24	no	—
369	#525	—	47	24	no	—
370	#525	—	47	24	no	—
371	C₂×#123	—	47	12	no	—
372	C₂×C₂²⋊Q₈	—	47	12	no	—
373	C₂×#121	—	47	12	no	—
374	C₂×#120	—	47	12	no	—
375	#520	—	47	8	no	—
376	#519	—	47	2	no	—
377	#518	—	47	6	no	—
378	C₄×#41	—	47	8	no	—
379	C₂×C₄×D₄	—	47	24	no	—
380	C₂×#117	—	47	6	no	—
381	C₄₇	#62811	1	1	yes	characteristic, complemented, Sylow
382	C₂⁵	—	47	3	no	—
383	2₋¹⁺⁴	—	2	32	no	—
384	2₋¹⁺⁴	—	2	16	no	—
385	H(5,𝔽₂)	—	2	32	no	—
386	H(5,𝔽₂)	—	2	48	no	—
387	C₂×#41	—	2	64	no	—
388	C₂×#41	—	2	48	no	—
389	C₂×#41	—	47	8	no	—
390	C₂×#41	—	47	24	no	—
391	C₂×#41	—	47	12	no	—
392	C₂×#41	—	47	12	no	—
393	C₂×#41	—	94	64	no	—
394	C₂×#41	—	94	64	no	—
395	C₂×#41	—	94	8	no	—
396	C₂×#41	—	94	24	no	—
397	C₂×#41	—	94	24	no	—
398	C₂×#41	C₂²⋊D₄₇	1	16	yes	complemented
399	C₂×#41	C₂²×D₄₇	1	4	yes	—
400	C₂×#41	C₂²×D₄₇	1	12	yes	—
401	C₂×#41	C₂²×D₄₇	1	4	yes	—
402	C₂×#41	C₂²×D₄₇	1	4	yes	—
403	C₂×#41	C₂²×D₄₇	1	12	yes	complemented
404	C₂×#41	C₂²×D₄₇	1	12	yes	complemented
405	C₂×#41	C₂²×D₄₇	1	24	yes	complemented
406	C₂×#41	C₂²×D₄₇	1	8	yes	complemented
407	C₂²×Q₈	—	47	8	no	—
408	C₂²×Q₈	—	47	3	no	—
409	C₂²×Q₈	—	94	8	no	—
410	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
411	C₂²×Q₈	C₂²×D₄₇	1	6	yes	complemented
412	C₂²×Q₈	C₂²×D₄₇	1	8	yes	complemented
413	C₂²×D₄	—	47	6	no	—
414	C₂²×D₄	—	47	24	no	—
415	C₂²×D₄	—	47	24	no	—
416	C₂²×D₄	—	47	3	no	—
417	C₂²×D₄	—	94	24	no	—
418	C₂²×D₄	C₂²×D₄₇	1	12	yes	—
419	C₂²×D₄	C₂²×D₄₇	1	3	yes	—
420	C₂²×D₄	C₂²×D₄₇	1	6	yes	complemented
421	C₂²×D₄	C₂²×D₄₇	1	24	yes	complemented
422	C₂³×C₄	—	47	3	no	—
423	C₂³×C₄	—	47	12	no	—
424	C₂³×C₄	—	47	12	no	—
425	C₂³×C₄	—	47	1	no	—
426	C₂³×C₄	—	47	3	no	—
427	C₂³×C₄	—	47	3	no	—
428	C₂³×C₄	—	47	3	no	—
429	C₂³×C₄	—	94	24	no	—
430	C₂³×C₄	C₂²×D₄₇	1	3	yes	—
431	C₂³×C₄	C₂²×D₄₇	1	12	yes	complemented
432	C₄⋊Q₈	—	47	24	no	—
433	#127	—	47	24	no	—
434	#124	—	47	24	no	—
435	#124	—	47	24	no	—
436	#123	—	47	8	no	—
437	#123	—	47	24	no	—
438	#123	—	47	48	no	—
439	#123	—	47	48	no	—
440	C₂²⋊Q₈	—	47	8	no	—
441	C₂²⋊Q₈	—	47	24	no	—
442	C₂²⋊Q₈	—	47	24	no	—
443	C₂²⋊Q₈	—	47	24	no	—
444	C₂²⋊Q₈	—	47	48	no	—
445	#121	—	47	8	no	—
446	#121	—	47	24	no	—
447	#121	—	47	24	no	—
448	#121	—	47	24	no	—
449	#121	—	47	96	no	—
450	#121	—	47	48	no	—
451	#120	—	47	48	no	—
452	#120	—	47	8	no	—
453	#120	—	47	24	no	—
454	#120	—	47	48	no	—
455	C₄×Q₈	—	47	16	no	—
456	C₄×D₄	—	47	48	no	—
457	C₄×D₄	—	47	16	no	—
458	C₄×D₄	—	47	48	no	—
459	C₄×D₄	—	47	48	no	—
460	C₄×D₄	—	47	48	no	—
461	#117	—	47	4	no	—
462	#117	—	47	12	no	—
463	#117	—	47	12	no	—
464	#117	—	47	12	no	—
465	C₂×C₄⋊C₄	—	47	12	no	—
466	C₂×C₄⋊C₄	—	47	24	no	—
467	C₂×C₂²⋊C₄	—	47	12	no	—
468	C₂×C₂²⋊C₄	—	47	24	no	—
469	C₂×C₂²⋊C₄	—	47	24	no	—
470	C₂×C₄²	—	47	12	no	—
471	C₂⁴	—	47	1	no	—
472	C₂⁴	—	47	12	no	—
473	C₂⁴	—	47	3	no	—
474	C₂⁴	—	94	12	no	—
475	C₂⁴	—	188	12	no	—
476	C₂⁴	C₂³×D₄₇	1	12	yes	—
477	C₂⁴	C₂³×D₄₇	1	3	yes	—
478	#41	—	2	32	no	—
479	#41	—	2	96	no	—
480	#41	—	2	16	no	—
481	#41	—	2	48	no	—
482	#41	—	2	48	no	—
483	#41	—	2	48	no	—
484	#41	—	94	32	no	—
485	#41	—	94	96	no	—
486	#41	—	94	48	no	—
487	#41	—	94	48	no	—
488	#41	C₂×C₂²⋊D₄₇	1	32	yes	complemented
489	#41	C₂×C₂²⋊D₄₇	1	32	yes	complemented
490	C₂×Q₈	—	2	32	no	—
491	C₂×Q₈	—	2	24	no	—
492	C₂×Q₈	—	47	12	no	—
493	C₂×Q₈	—	94	32	no	—
494	C₂×Q₈	—	94	12	no	—
495	C₂×Q₈	C₂×C₂²⋊D₄₇	1	8	yes	complemented
496	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
497	C₂×Q₈	C₂³×D₄₇	1	12	yes	—
498	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
499	C₂×D₄	—	2	48	no	—
500	C₂×D₄	—	2	96	no	—
501	C₂×D₄	—	2	24	no	—
502	C₂×D₄	—	47	16	no	—
503	C₂×D₄	—	47	24	no	—
504	C₂×D₄	—	47	48	no	—
505	C₂×D₄	—	47	12	no	—
506	C₂×D₄	—	94	24	no	—
507	C₂×D₄	—	94	96	no	—
508	C₂×D₄	—	94	12	no	—
509	C₂×D₄	—	188	48	no	—
510	C₂×D₄	C₂×C₂²⋊D₄₇	1	24	yes	complemented
511	C₂×D₄	C₂³×D₄₇	1	8	yes	—
512	C₂×D₄	C₂³×D₄₇	1	24	yes	—
513	C₂×D₄	C₂³×D₄₇	1	4	yes	—
514	C₂×D₄	C₂³×D₄₇	1	12	yes	—
515	C₂×D₄	C₂³×D₄₇	1	12	yes	—
516	C₂²×C₄	—	2	48	no	—
517	C₂²×C₄	—	47	12	no	—
518	C₂²×C₄	—	47	1	no	—
519	C₂²×C₄	—	47	3	no	—
520	C₂²×C₄	—	47	24	no	—
521	C₂²×C₄	—	47	12	no	—
522	C₂²×C₄	—	47	12	no	—
523	C₂²×C₄	—	47	2	no	—
524	C₂²×C₄	—	47	6	no	—
525	C₂²×C₄	—	47	2	no	—
526	C₂²×C₄	—	47	6	no	—
527	C₂²×C₄	—	94	12	no	—
528	C₂²×C₄	—	94	4	no	—
529	C₂²×C₄	—	94	12	no	—
530	C₂²×C₄	—	94	12	no	—
531	C₂²×C₄	—	94	12	no	—
532	C₂²×C₄	—	94	48	no	—
533	C₂²×C₄	—	94	48	no	—
534	C₂²×C₄	C₂×C₂²⋊D₄₇	1	24	yes	complemented
535	C₂²×C₄	C₂³×D₄₇	1	12	yes	—
536	C₂²×C₄	C₂³×D₄₇	1	24	yes	—
537	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
538	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
539	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
540	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
541	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
542	C₄⋊C₄	—	47	16	no	—
543	C₄⋊C₄	—	47	48	no	—
544	C₄⋊C₄	—	47	8	no	—
545	C₄⋊C₄	—	47	24	no	—
546	C₂²⋊C₄	—	47	8	no	—
547	C₂²⋊C₄	—	47	16	no	—
548	C₂²⋊C₄	—	47	24	no	—
549	C₂²⋊C₄	—	47	48	no	—
550	C₂²⋊C₄	—	47	16	no	—
551	C₂²⋊C₄	—	47	48	no	—
552	C₄²	—	47	24	no	—
553	C₄²	—	47	8	no	—
554	C₂³	—	2	24	no	—
555	C₂³	—	4	6	no	—
556	C₂³	—	4	24	no	—
557	C₂³	—	47	2	no	—
558	C₂³	—	47	6	no	—
559	C₂³	—	94	4	no	—
560	C₂³	—	94	24	no	—
561	C₂³	—	94	2	no	—
562	C₂³	—	94	24	no	—
563	C₂³	—	94	6	no	—
564	C₂³	—	188	12	no	—
565	C₂³	—	188	6	no	—
566	C₂³	—	188	48	no	—
567	C₂³	C₂²×C₂²⋊D₄₇	1	12	yes	—
568	C₂³	C₂⁴×D₄₇	1	8	yes	—
569	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
570	C₂³	C₂⁴×D₄₇	1	6	yes	—
571	Q₈	—	2	24	no	—
572	Q₈	—	2	8	no	—
573	Q₈	—	94	24	no	—
574	Q₈	C₂²×C₂²⋊D₄₇	1	16	yes	—
575	D₄	—	2	48	no	—
576	D₄	—	2	16	no	—
577	D₄	—	2	24	no	—
578	D₄	—	2	8	no	—
579	D₄	—	94	32	no	—
580	D₄	—	94	48	no	—
581	D₄	—	94	24	no	—
582	D₄	—	188	48	no	—
583	D₄	C₂²×C₂²⋊D₄₇	1	48	yes	—
584	C₂×C₄	—	2	24	no	—
585	C₂×C₄	—	2	16	no	—
586	C₂×C₄	—	2	48	no	—
587	C₂×C₄	—	47	16	no	—
588	C₂×C₄	—	47	2	no	—
589	C₂×C₄	—	47	6	no	—
590	C₂×C₄	—	94	2	no	—
591	C₂×C₄	—	94	6	no	—
592	C₂×C₄	—	94	24	no	—
593	C₂×C₄	—	94	4	no	—
594	C₂×C₄	—	94	4	no	—
595	C₂×C₄	—	94	24	no	—
596	C₂×C₄	—	94	24	no	—
597	C₂×C₄	—	94	12	no	—
598	C₂×C₄	—	94	12	no	—
599	C₂×C₄	—	188	24	no	—
600	C₂×C₄	C₂²×C₂²⋊D₄₇	1	24	yes	—
601	C₂×C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
602	C₂×C₄	C₂²×C₂²⋊D₄₇	1	24	yes	—
603	C₂×C₄	C₂²×C₂²⋊D₄₇	1	12	yes	—
604	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
605	C₂×C₄	C₂⁴×D₄₇	1	6	yes	—
606	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
607	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
608	C₂²	—	2	12	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	8	no	—
611	C₂²	—	2	16	no	—
612	C₂²	—	4	12	no	—
613	C₂²	—	8	24	no	—
614	C₂²	—	47	4	no	—
615	C₂²	—	94	8	no	—
616	C₂²	—	94	2	no	—
617	C₂²	—	94	2	no	—
618	C₂²	—	94	6	no	—
619	C₂²	—	94	12	no	—
620	C₂²	—	188	48	no	—
621	C₂²	—	188	12	no	—
622	C₂²	C₂³×C₂²⋊D₄₇	1	12	yes	—
623	C₂²	C₂³×C₂²⋊D₄₇	1	2	yes	—
624	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
625	C₄	—	2	8	no	—
626	C₄	—	94	2	no	—
627	C₄	—	94	6	no	—
628	C₄	—	94	16	no	—
629	C₄	C₂³×C₂²⋊D₄₇	1	2	yes	—
630	C₄	C₂³×C₂²⋊D₄₇	1	12	yes	—
631	C₄	C₂³×C₂²⋊D₄₇	1	2	yes	—
632	C₂	—	2	2	no	—
633	C₂	—	2	12	no	—
634	C₂	—	4	8	no	—
635	C₂	—	94	4	no	—
636	C₂	—	188	6	no	—
637	C₂	C₂⁴×C₂²⋊D₄₇	1	1	yes	characteristic
638	C₂	#585×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×#585	C₂
hypercenter	C₂×#585	D₄₇
hypocenter	C₄₇	#62811
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#585

Complements

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

N	H ≅ G/N	type
1. C₂²×#41×D₄₇	C₂	semidirect
2. #20257061	C₂	semidirect
3. #20257050	C₂	semidirect
4. #20257043	C₂	semidirect
5. #20257036	C₂	semidirect
6. #20257028	C₂	semidirect
7. #20257019	C₂	semidirect
8. #41×C₂²⋊D₄₇	C₂	semidirect
9. #20256717	C₂	semidirect
10. C₂×#15689630	C₂	semidirect
11. #20256591	C₂	semidirect
12. C₂×C₄₇×#585	C₂	semidirect
13. C₂²×#10625354	C₂²	semidirect
14. C₂²×#10625350	C₂²	semidirect
15. C₂²×#10625352	C₂²	semidirect
17. C₂×#41×D₄₇	C₂²	semidirect
18. C₂×#41×D₄₇	C₂²	semidirect
19. C₂²×Q₈×D₄₇	C₂²	semidirect
20. C₂²×D₄×D₄₇	C₂²	semidirect
21. C₂³×C₄×D₄₇	C₂²	semidirect
22. #15689792	C₂²	semidirect
23. Q₈×C₂²⋊D₄₇	C₂²	semidirect
24. #15689784	C₂²	semidirect
25. #15689780	C₂²	semidirect
26. #15689772	C₂²	semidirect
27. #15689767	C₂²	semidirect
28. #15689761	C₂²	semidirect
29. D₄×C₂²⋊D₄₇	C₂²	semidirect
30. #15689701	C₂²	semidirect
31. #15689697	C₂²	semidirect
32. #15689694	C₂²	semidirect
33. #15689690	C₂²	semidirect
34. #15689687	C₂²	semidirect
35. #15689682	C₂²	semidirect
36. #15689669	C₂²	semidirect
37. #15689634	C₂²	semidirect
38. #15689630	C₂²	semidirect
39. #15689630	C₂²	semidirect
40. #15689630	C₂²	semidirect
41. #15689630	C₂²	semidirect
42. #15689630	C₂²	semidirect
43. #15689630	C₂²	semidirect
44. C₂×#13094005	C₂²	semidirect
45. C₂×#13094000	C₂²	semidirect
46. C₂×#13093995	C₂²	semidirect
47. C₂×#13093992	C₂²	semidirect
48. #15689606	C₂²	semidirect
49. #15689601	C₂²	semidirect
50. #15689598	C₂²	semidirect
51. #41×Dic₄₇	C₂²	semidirect
52. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
53. C₂×#13093983	C₂²	semidirect
55. C₂×2₋¹⁺⁴×C₄₇	C₂²	semidirect
56. C₂×2₋¹⁺⁴×C₄₇	C₂²	semidirect
57. C₂×H(5,𝔽₂)×C₄₇	C₂²	semidirect
58. C₂×H(5,𝔽₂)×C₄₇	C₂²	semidirect
60. C₂²×#41×C₄₇	C₂²	semidirect
61. C₂²×#41×C₄₇	C₂²	semidirect
88. #13094022	C₂³	semidirect
89. #13094020	C₂³	semidirect
90. #13094013	C₂³	semidirect
91. #13094011	C₂³	semidirect
92. #13094007	C₂³	semidirect
95. #13094005	C₂³	semidirect
96. #13094003	C₂³	semidirect
99. #13094000	C₂³	semidirect
100. #13094000	C₂³	semidirect
101. #13093998	C₂³	semidirect
102. #13093996	C₂³	semidirect
105. #13093995	C₂³	semidirect
106. #13093995	C₂³	semidirect
107. #13093993	C₂³	semidirect
111. Q₈×Dic₄₇	C₂³	semidirect
112. D₄×Dic₄₇	C₂³	semidirect
115. C₄×C₂²⋊D₄₇	C₂³	semidirect
116. C₄×C₂²⋊D₄₇	C₂³	semidirect
119. #13093983	C₂³	semidirect
120. #13093983	C₂³	semidirect
121. C₂×C₄⋊Dic₄₇	C₂³	semidirect
122. C₂×Dic₄₇⋊C₄	C₂³	semidirect
124. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
126. C₂×C₄×Dic₄₇	C₂³	semidirect
133. C₂×#41×C₄₇	D₄	semidirect
138. C₂×#41×C₄₇	C₂³	semidirect
139. C₂×#41×C₄₇	C₂³	semidirect
140. C₂×#41×C₄₇	C₂³	semidirect
141. C₂×#41×C₄₇	C₂³	semidirect
143. C₂²×Q₈×C₄₇	C₂³	semidirect
144. C₂²×Q₈×C₄₇	C₂³	semidirect
147. C₂²×D₄×C₄₇	C₂³	semidirect
148. C₂²×D₄×C₄₇	C₂³	semidirect
150. C₂³×C₄×C₄₇	C₂³	semidirect
164. #41×C₄₇	C₂×D₄	semidirect
165. #41×C₄₇	C₂×D₄	semidirect
168. C₂×Q₈×C₄₇	C₂×D₄	semidirect
175. C₂×D₄×C₄₇	C₂×D₄	semidirect
182. C₂²×C₄×C₄₇	C₂×D₄	semidirect
305. C₂×D₄₇	#585	semidirect
313. C₂×#585	D₄₇	semidirect
333. C₂×2₋¹⁺⁴	C₂×D₄₇	semidirect
334. C₂×2₋¹⁺⁴	C₂×D₄₇	semidirect
335. C₂×H(5,𝔽₂)	C₂×D₄₇	semidirect
336. C₂×H(5,𝔽₂)	C₂×D₄₇	semidirect
344. C₂²×#41	C₂×D₄₇	semidirect
345. C₂²×#41	C₂×D₄₇	semidirect
381. C₄₇	#62811	semidirect
398. C₂×#41	C₂²⋊D₄₇	semidirect
403. C₂×#41	C₂²×D₄₇	semidirect
404. C₂×#41	C₂²×D₄₇	semidirect
405. C₂×#41	C₂²×D₄₇	semidirect
406. C₂×#41	C₂²×D₄₇	semidirect
411. C₂²×Q₈	C₂²×D₄₇	semidirect
412. C₂²×Q₈	C₂²×D₄₇	semidirect
420. C₂²×D₄	C₂²×D₄₇	semidirect
421. C₂²×D₄	C₂²×D₄₇	semidirect
431. C₂³×C₄	C₂²×D₄₇	semidirect
488. #41	C₂×C₂²⋊D₄₇	semidirect
489. #41	C₂×C₂²⋊D₄₇	semidirect
495. C₂×Q₈	C₂×C₂²⋊D₄₇	semidirect
510. C₂×D₄	C₂×C₂²⋊D₄₇	semidirect
534. C₂²×C₄	C₂×C₂²⋊D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#41×D₄₇	2
#20257061	2
#20257050	2
#20257043	2
#20257036	2
#20257028	2
#20257019	2
#41×C₂²⋊D₄₇	2
#20256717	2
C₂×#15689630	2
#20256591	2
C₂×C₄₇×#585	2
#62811	47