Subgroups — #27080620

Order 12032.

2604 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20258161	C₂	1	1	yes	maximal, characteristic
2	#20258101	C₂	1	2	yes	maximal, complemented
3	#20252303	C₂	1	2	yes	maximal, complemented
4	#20252300	C₂	1	4	yes	maximal, complemented
5	#20252299	C₂	1	1	yes	maximal, characteristic, complemented
6	#20252296	C₂	1	4	yes	maximal, complemented
7	#20252291	C₂	1	1	yes	maximal, characteristic, complemented
8	#20252290	C₂	1	1	yes	maximal, characteristic, complemented
9	#20252286	C₂	1	4	yes	maximal, complemented
10	C₂×#15689242	C₂	1	2	yes	maximal, complemented
11	#444×D₄₇	C₂	1	4	yes	maximal, complemented
12	#20251998	C₂	1	1	yes	maximal, characteristic, complemented
13	#20251932	C₂	1	2	yes	maximal, complemented
14	#20251817	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#2956	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689959	C₂²	1	2	yes	—
17	#15689939	C₄	1	4	yes	complemented
18	#15689933	C₄	1	4	yes	complemented
19	#15689932	C₄	1	4	yes	complemented
20	#15689927	C₄	1	4	yes	complemented
21	#15689923	C₂²	1	1	yes	characteristic
22	#15689920	C₂²	1	4	yes	—
23	C₂×#13094044	C₂²	1	2	yes	—
24	#135×D₄₇	C₂²	1	4	yes	—
25	#15689889	—	2	4	no	—
26	#15689889	C₂²	1	2	yes	—
27	#15689889	C₂²	1	2	yes	complemented
28	#15689888	—	2	4	no	—
29	#15689888	C₂²	1	8	yes	complemented
30	C₂×#13094032	—	2	4	no	—
31	C₂×#13094032	C₂²	1	1	yes	characteristic
32	C₂×#13094032	C₂²	1	1	yes	characteristic
33	C₂×#13094032	C₂²	1	2	yes	complemented
34	C₂×#13094031	C₂²	1	2	yes	complemented
35	#131×D₄₇	—	2	4	no	—
36	#131×D₄₇	C₂²	1	8	yes	complemented
37	C₄×#10625350	C₂²	1	1	yes	characteristic
38	#15689246	C₂²	1	4	yes	complemented
39	#15689245	C₂²	1	4	yes	complemented
40	#15689244	C₂²	1	4	yes	complemented
41	#15689243	C₂²	1	8	yes	complemented
42	#15689242	C₂²	1	4	yes	complemented
43	#15689242	C₂²	1	4	yes	complemented
44	#15689242	C₂²	1	4	yes	complemented
45	#15689242	C₂²	1	4	yes	complemented
46	#15689241	C₂²	1	4	yes	complemented
47	#15689240	C₂²	1	4	yes	complemented
48	#15689239	C₂²	1	4	yes	complemented
49	#15689238	C₂²	1	8	yes	complemented
50	#15689172	C₂²	1	1	yes	characteristic, complemented
51	#15689170	C₂²	1	4	yes	complemented
52	C₂×#13093959	C₂²	1	2	yes	complemented
53	#108×D₄₇	C₂²	1	4	yes	complemented
54	#15689140	C₂²	1	2	yes	complemented
55	#15689139	C₂²	1	2	yes	complemented
56	#15689138	C₂²	1	8	yes	complemented
57	C₂×#13093952	C₂²	1	2	yes	complemented
58	#104×D₄₇	C₂²	1	8	yes	complemented
59	#15689081	C₂²	1	1	yes	characteristic, complemented
60	#15689081	C₂²	1	1	yes	characteristic, complemented
61	#15689077	C₂²	1	2	yes	complemented
62	#15689077	C₂²	1	2	yes	complemented
63	#15689075	C₂²	1	2	yes	complemented
64	C₂×#13093935	C₂²	1	1	yes	characteristic, complemented
65	#97×D₄₇	C₂²	1	2	yes	complemented
66	C₄₇×#575	C₂²	1	1	yes	characteristic
67	C₄₇×#568	C₂²	1	2	yes	complemented
68	C₄₇×#444	C₂²	1	4	yes	complemented
69	C₄₇×#443	C₂²	1	4	yes	complemented
70	C₄₇×#430	C₂²	1	1	yes	characteristic, complemented
71	C₂×#104×C₄₇	C₂²	1	2	yes	complemented
72	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
73	#13094072	C₂×C₄	1	4	yes	—
74	#13094071	—	2	2	no	—
75	#13094071	C₂×C₄	1	4	yes	—
76	#13094070	—	2	2	no	—
77	#13094070	C₂×C₄	1	4	yes	—
78	#13094069	—	2	4	no	—
79	#13094069	C₂×C₄	1	4	yes	—
80	C₂×#10625350	—	2	4	no	—
81	C₂×#10625350	C₂³	1	2	yes	—
82	C₂×#10625350	C₂³	1	1	yes	characteristic
83	#41×D₄₇	—	2	4	no	—
84	#41×D₄₇	C₂³	1	8	yes	—
85	#13094057	C₂×C₄	1	4	yes	complemented
86	#13094056	C₂×C₄	1	8	yes	complemented
87	#13094053	C₂×C₄	1	8	yes	complemented
88	#13094052	C₂×C₄	1	4	yes	complemented
89	#13094051	C₂×C₄	1	8	yes	complemented
90	#13094048	C₂×C₄	1	8	yes	complemented
91	#13094047	C₂×C₄	1	4	yes	complemented
92	#13094046	C₂³	1	4	yes	—
93	#13094045	C₂×C₄	1	8	yes	complemented
94	#13094044	C₂×C₄	1	4	yes	complemented
95	#13094044	C₂×C₄	1	4	yes	complemented
96	#13094044	C₂³	1	4	yes	—
97	#13094044	C₂³	1	4	yes	—
98	#13094043	C₂×C₄	1	4	yes	complemented
99	C₂×#10625337	C₂×C₄	1	2	yes	complemented
100	Q₁₆×D₄₇	C₂×C₄	1	4	yes	complemented
101	C₂×#10625335	C₂×C₄	1	2	yes	complemented
102	C₂×#10625336	C₂×C₄	1	2	yes	complemented
103	SD₁₆×D₄₇	C₂×C₄	1	8	yes	complemented
104	C₂×#10625334	C₂×C₄	1	2	yes	complemented
105	D₈×D₄₇	C₂×C₄	1	4	yes	complemented
106	#13094032	—	2	4	no	—
107	#13094032	—	2	4	no	—
108	#13094032	—	2	2	no	—
109	#13094032	—	2	2	no	—
110	#13094032	—	2	8	no	—
111	#13094032	—	2	8	no	—
112	#13094032	C₂×C₄	1	4	yes	—
113	#13094032	C₂×C₄	1	4	yes	—
114	#13094032	D₄	1	4	yes	—
115	#13094032	D₄	1	4	yes	—
116	#13094032	C₂³	1	4	yes	—
117	#13094032	C₂³	1	4	yes	—
118	#13094031	—	2	2	no	—
119	#13094031	—	2	2	no	—
120	#13094031	C₂³	1	4	yes	—
121	#13094031	C₂³	1	4	yes	—
122	#13094030	—	2	4	no	—
123	#13094030	—	2	8	no	—
124	#13094030	—	2	8	no	—
125	#13094030	C₂³	1	8	yes	—
126	C₂×#10625329	—	2	2	no	—
127	C₂×#10625329	C₂³	1	2	yes	—
128	C₂×#10625324	—	2	2	no	—
129	C₂×#10625324	—	2	8	no	—
130	C₂×#10625324	C₂³	1	2	yes	—
131	C₂×#10625324	C₂³	1	2	yes	—
132	M₁₆×D₄₇	—	2	4	no	—
133	M₁₆×D₄₇	—	2	8	no	—
134	M₁₆×D₄₇	—	2	8	no	—
135	M₁₆×D₄₇	C₂³	1	8	yes	—
136	C₂²×C₄₇⋊C₈	—	2	2	no	—
137	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
138	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
139	C₂×C₈×D₄₇	—	2	2	no	—
140	C₂×C₈×D₄₇	—	2	8	no	—
141	C₂×C₈×D₄₇	C₂³	1	2	yes	—
142	C₂×C₈×D₄₇	C₂³	1	2	yes	—
143	C₄×Dic₉₄	—	2	1	no	—
144	C₄×D₁₈₈	—	2	1	no	—
145	C₄×C₂²⋊D₄₇	—	2	2	no	—
146	#13093983	C₂³	1	1	yes	characteristic
147	#13093981	C₂³	1	2	yes	—
148	C₄²×D₄₇	C₂³	1	2	yes	—
149	#13093960	C₂³	1	4	yes	—
150	#13093959	C₂³	1	4	yes	—
151	#13093959	C₂³	1	4	yes	—
152	#13093952	C₂³	1	4	yes	—
153	#13093952	C₂³	1	4	yes	—
154	#13093951	C₂³	1	8	yes	—
155	#13093950	C₂³	1	8	yes	—
156	#13093935	C₂³	1	1	yes	characteristic
157	#13093935	C₂³	1	1	yes	characteristic
158	#13093935	C₂³	1	1	yes	characteristic
159	#13093935	C₂³	1	1	yes	characteristic
160	#13093934	C₂³	1	2	yes	—
161	#13093934	C₂³	1	2	yes	—
162	C₈×Dic₄₇	C₂³	1	2	yes	—
163	C₈×Dic₄₇	C₂³	1	2	yes	—
164	C₂×#41×C₄₇	C₂³	1	2	yes	—
165	#137×C₄₇	C₂×C₄	1	4	yes	complemented
166	AGL(1,ℤ/8)×C₄₇	C₂×C₄	1	4	yes	complemented
167	#135×C₄₇	C₂³	1	4	yes	—
168	#131×C₄₇	—	2	4	no	—
169	#131×C₄₇	C₂³	1	8	yes	—
170	C₂×M₁₆×C₄₇	—	2	4	no	—
171	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
172	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
173	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
175	#108×C₄₇	C₂³	1	4	yes	—
176	#104×C₄₇	C₂³	1	4	yes	—
177	#104×C₄₇	C₂³	1	4	yes	—
178	#97×C₄₇	C₂³	1	2	yes	—
179	C₄×C₈×C₄₇	C₂³	1	2	yes	—
180	#41×C₄₇	—	2	2	no	—
181	#41×C₄₇	—	2	2	no	—
182	#41×C₄₇	C₂²×C₄	1	4	yes	—
183	#41×C₄₇	C₂⁴	1	4	yes	—
184	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
185	C₂×D₄×C₄₇	—	2	2	no	—
186	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
187	C₂²×C₄×C₄₇	—	2	2	no	—
188	C₂²×C₄×C₄₇	—	2	1	no	—
189	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
190	C₂×C₂²⋊D₄₇	—	2	2	no	—
191	C₂×C₂²⋊D₄₇	—	2	8	no	—
192	C₂×C₂²⋊D₄₇	#41	1	2	yes	—
193	#10625354	—	2	4	no	—
194	#10625354	C₂²×C₄	1	8	yes	—
195	Q₈×D₄₇	—	2	4	no	—
196	Q₈×D₄₇	C₂²×C₄	1	8	yes	—
197	#10625352	—	2	8	no	—
198	#10625352	—	2	8	no	—
199	#10625352	—	2	4	no	—
200	#10625352	C₂²×C₄	1	8	yes	—
201	D₄×D₄₇	—	2	8	no	—
202	D₄×D₄₇	—	2	8	no	—
203	D₄×D₄₇	—	2	4	no	—
204	D₄×D₄₇	C₂²×C₄	1	8	yes	—
205	#10625350	—	2	2	no	—
206	#10625350	—	2	2	no	—
207	#10625350	—	2	8	no	—
208	#10625350	—	2	4	no	—
209	#10625350	—	2	8	no	—
210	#10625350	—	2	4	no	—
211	#10625350	C₂²×C₄	1	4	yes	—
212	#10625350	C₂²×C₄	1	4	yes	—
213	#10625350	C₂×D₄	1	4	yes	—
214	#10625350	C₂⁴	1	4	yes	—
215	C₂×D₁₈₈	—	2	4	no	—
216	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
217	C₂×D₁₈₈	#41	1	1	yes	characteristic
218	C₂×C₄×D₄₇	—	2	2	no	—
219	C₂×C₄×D₄₇	—	2	8	no	—
220	C₂×C₄×D₄₇	—	2	2	no	—
221	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
222	C₂×Dic₉₄	—	2	4	no	—
223	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
224	C₂×Dic₉₄	#41	1	1	yes	characteristic
225	Q₁₆×C₄₇	C₂²×C₄	1	4	yes	—
226	SD₁₆×C₄₇	C₂²×C₄	1	8	yes	—
227	D₈×C₄₇	C₂²×C₄	1	4	yes	—
228	M₁₆×C₄₇	—	2	2	no	—
229	M₁₆×C₄₇	—	2	8	no	—
230	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
231	M₁₆×C₄₇	C₂×D₄	1	4	yes	—
232	M₁₆×C₄₇	C₂⁴	1	4	yes	—
233	C₂×C₈×C₄₇	—	2	2	no	—
234	C₂×C₈×C₄₇	—	2	8	no	—
235	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
236	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
237	C₄²×C₄₇	—	2	1	no	—
238	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
239	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
240	C₂²⋊Dic₄₇	—	2	1	no	—
241	#10625337	C₂²×C₄	1	4	yes	—
242	#10625337	C₂²×C₄	1	4	yes	—
243	#10625336	C₂²×C₄	1	4	yes	—
244	#10625336	C₂²×C₄	1	4	yes	—
245	#10625335	C₂²×C₄	1	4	yes	—
246	#10625335	C₂²×C₄	1	4	yes	—
247	#10625334	C₂²×C₄	1	4	yes	—
248	#10625334	C₂²×C₄	1	4	yes	—
249	(C₂×D₄₇)⋊C₄	—	2	2	no	—
250	C₄⋊Dic₄₇	—	2	1	no	—
251	Dic₄₇⋊C₄	—	2	2	no	—
252	C₄×Dic₄₇	—	2	2	no	—
253	C₄×Dic₄₇	C₂⁴	1	2	yes	—
254	#10625329	—	2	2	no	—
255	#10625329	—	2	4	no	—
256	#10625329	—	2	4	no	—
257	#10625329	C₂⁴	1	4	yes	—
258	C₂×C₄₇⋊C₈	—	2	2	no	—
259	C₂×C₄₇⋊C₈	—	2	4	no	—
260	C₂×C₄₇⋊C₈	—	2	4	no	—
261	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
262	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
263	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
264	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
265	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
266	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
267	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
268	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
269	Dic₁₈₈	C₂²×C₄	1	4	yes	—
270	D₃₇₆	C₂²×C₄	1	4	yes	—
271	#10625325	C₂²×C₄	1	8	yes	—
272	#10625324	—	2	8	no	—
273	#10625324	—	2	8	no	—
274	#10625324	—	2	4	no	—
275	#10625324	—	2	4	no	—
276	#10625324	C₂²×C₄	1	8	yes	—
277	#10625324	C₂×D₄	1	4	yes	—
278	#10625324	C₂×D₄	1	4	yes	—
279	C₈×D₄₇	—	2	8	no	—
280	C₈×D₄₇	—	2	8	no	—
281	C₈×D₄₇	—	2	4	no	—
282	C₈×D₄₇	—	2	4	no	—
283	C₈×D₄₇	C₂²×C₄	1	4	yes	—
284	C₈×D₄₇	C₂²×C₄	1	4	yes	—
285	C₈×D₄₇	C₂×D₄	1	8	yes	—
286	C₂³×C₄₇	—	2	2	no	—
287	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
288	C₂²×D₄₇	—	2	2	no	—
289	C₂²×D₄₇	—	2	8	no	—
290	C₂²×D₄₇	C₂×#41	1	2	yes	—
291	Q₈×C₄₇	—	2	2	no	—
292	Q₈×C₄₇	C₂³×C₄	1	4	yes	—
293	D₄×C₄₇	—	2	4	no	—
294	D₄×C₄₇	—	2	4	no	—
295	D₄×C₄₇	—	2	2	no	—
296	D₄×C₄₇	C₂³×C₄	1	4	yes	—
297	C₂×C₄×C₄₇	—	2	2	no	—
298	C₂×C₄×C₄₇	—	2	4	no	—
299	C₂×C₄×C₄₇	—	2	4	no	—
300	C₂×C₄×C₄₇	—	2	1	no	—
301	C₂×C₄×C₄₇	—	2	1	no	—
302	C₂×C₄×C₄₇	—	8	1	no	—
303	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
304	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
307	C₂²⋊D₄₇	—	2	4	no	—
308	C₂²⋊D₄₇	—	2	4	no	—
309	C₂²⋊D₄₇	—	2	8	no	—
310	C₂²⋊D₄₇	—	2	8	no	—
311	C₂²⋊D₄₇	C₄×D₄	1	8	yes	—
312	C₂×Dic₄₇	—	2	2	no	—
313	C₂×Dic₄₇	—	2	8	no	—
314	C₂×Dic₄₇	—	2	2	no	—
315	C₂×Dic₄₇	C₂×#41	1	2	yes	—
316	D₁₈₈	—	2	8	no	—
317	D₁₈₈	—	2	2	no	—
318	D₁₈₈	C₄×D₄	1	4	yes	—
319	D₁₈₈	C₂³×C₄	1	4	yes	—
320	C₄×D₄₇	—	2	8	no	—
321	C₄×D₄₇	—	2	4	no	—
322	C₄×D₄₇	—	2	4	no	—
323	C₄×D₄₇	—	2	8	no	—
324	C₄×D₄₇	—	8	2	no	—
325	C₄×D₄₇	C₂³×C₄	1	4	yes	—
326	C₄×D₄₇	C₂²×D₄	1	4	yes	—
327	Dic₉₄	—	2	2	no	—
328	Dic₉₄	—	2	8	no	—
329	Dic₉₄	C₄×D₄	1	4	yes	—
330	Dic₉₄	C₂³×C₄	1	4	yes	—
331	C₈×C₄₇	—	2	4	no	—
332	C₈×C₄₇	C₂³×C₄	1	4	yes	—
333	C₈×C₄₇	C₂²×D₄	1	4	yes	—
334	C₄₇⋊C₈	—	2	4	no	—
335	C₄₇⋊C₈	C₂³×C₄	1	1	yes	characteristic
336	C₄₇⋊C₈	C₂³×C₄	1	1	yes	characteristic
337	C₄₇⋊C₈	C₂³×C₄	1	2	yes	—
338	C₄₇⋊C₈	C₂²×D₄	1	1	yes	characteristic
339	C₄₇⋊C₈	C₂²×D₄	1	2	yes	—
340	C₄₇⋊C₈	C₂²×D₄	1	1	yes	characteristic
341	#60184	—	47	1	no	maximal, Sylow
342	C₂²×C₄₇	—	2	4	no	—
343	C₂²×C₄₇	—	4	1	no	—
344	C₂²×C₄₇	—	8	2	no	—
345	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
346	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
347	C₂×D₄₇	—	2	4	no	—
348	C₂×D₄₇	—	4	2	no	—
349	C₂×D₄₇	—	8	8	no	—
350	C₂×D₄₇	—	8	2	no	—
351	C₂×D₄₇	C₂×C₄×D₄	1	4	yes	—
352	C₄×C₄₇	—	2	4	no	—
353	C₄×C₄₇	—	4	1	no	—
354	C₄×C₄₇	—	4	1	no	—
355	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
356	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
357	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
358	Dic₄₇	—	2	4	no	—
359	Dic₄₇	—	4	2	no	—
360	Dic₄₇	C₂×C₄×D₄	1	4	yes	—
361	#3584	—	47	1	no	—
362	#3573	—	47	2	no	—
363	#2957	—	47	4	no	—
364	#2957	—	47	2	no	—
365	#2956	—	47	4	no	—
366	#2956	—	47	1	no	—
367	#2956	D₄₇	1	1	yes	characteristic, complemented
368	#2955	—	47	4	no	—
369	#2955	—	47	1	no	—
370	#2955	—	47	1	no	—
371	C₂×#444	—	47	4	no	—
372	C₂×#444	—	47	2	no	—
373	#2916	—	47	1	no	—
374	#2901	—	47	2	no	—
375	#2875	—	47	1	no	—
376	C₂×C₄₇	—	2	1	no	—
377	C₂×C₄₇	—	2	2	no	—
378	C₂×C₄₇	—	4	4	no	—
379	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
380	D₄₇	—	2	4	no	—
381	D₄₇	—	4	4	no	—
382	#585	—	47	2	no	—
383	#578	—	47	4	no	—
384	#577	—	47	4	no	—
385	#577	—	47	4	no	—
386	#576	—	47	4	no	—
387	#575	—	47	4	no	—
388	#575	—	47	1	no	—
389	#575	C₂×D₄₇	1	1	yes	characteristic
390	C₂×#135	—	47	2	no	—
391	C₂×#135	—	47	4	no	—
392	#568	—	47	2	no	—
393	#568	—	47	8	no	—
394	#568	—	47	2	no	—
395	#568	—	94	4	no	—
396	#568	—	94	4	no	—
397	#568	C₂×D₄₇	1	2	yes	complemented
398	C₂×#131	—	47	1	no	—
399	C₂×#131	—	47	1	no	—
400	C₂×#131	—	47	2	no	—
401	C₂×#131	—	47	8	no	—
402	C₂×#131	—	47	2	no	—
403	C₂×#131	—	94	4	no	—
404	C₂×#131	—	94	4	no	—
405	C₄×#41	—	47	1	no	—
406	#444	—	47	4	no	—
407	#444	—	47	8	no	—
408	#444	—	47	4	no	—
409	#444	—	47	4	no	—
410	#444	—	47	4	no	—
411	#444	—	47	4	no	—
412	#444	—	47	4	no	—
413	#444	—	47	4	no	—
414	#444	C₂×D₄₇	1	4	yes	complemented
415	#443	—	47	4	no	—
416	#443	—	47	8	no	—
417	#443	—	47	4	no	—
418	#443	—	47	4	no	—
419	#443	C₂×D₄₇	1	4	yes	complemented
420	#430	—	47	1	no	—
421	#430	—	47	4	no	—
422	#430	C₂×D₄₇	1	1	yes	characteristic, complemented
423	C₂×#108	—	47	2	no	—
424	C₂×#108	—	47	4	no	—
425	#421	—	47	2	no	—
426	#421	—	47	2	no	—
427	#421	—	47	8	no	—
428	C₂×#104	—	47	2	no	—
429	C₂×#104	—	47	8	no	—
430	C₂×#104	C₂×D₄₇	1	2	yes	complemented
431	#405	—	47	1	no	—
432	#405	—	47	1	no	—
433	#405	—	47	2	no	—
434	#405	—	47	2	no	—
435	C₄×M₁₆	—	47	2	no	—
436	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
437	C₂×#97	—	47	1	no	—
438	C₂×#97	—	47	2	no	—
439	C₄₇	#60184	1	1	yes	characteristic, complemented, Sylow
440	2₋¹⁺⁴	—	47	4	no	—
441	2₋¹⁺⁴	—	47	4	no	—
442	2₋¹⁺⁴	—	94	2	no	—
443	H(5,𝔽₂)	—	47	4	no	—
444	H(5,𝔽₂)	—	47	4	no	—
445	H(5,𝔽₂)	—	94	4	no	—
446	H(5,𝔽₂)	—	94	2	no	—
447	C₂×#41	—	47	1	no	—
448	C₂×#41	—	47	8	no	—
449	C₂×#41	—	47	2	no	—
450	C₂×#41	—	94	4	no	—
451	C₂×#41	—	94	4	no	—
452	C₂×#41	C₂²×D₄₇	1	2	yes	—
453	#137	—	47	8	no	—
454	#137	—	47	8	no	—
455	#137	—	47	4	no	—
456	#137	C₄×D₄₇	1	4	yes	complemented
457	AGL(1,ℤ/8)	—	47	8	no	—
458	AGL(1,ℤ/8)	—	47	8	no	—
459	AGL(1,ℤ/8)	—	47	4	no	—
460	AGL(1,ℤ/8)	C₄×D₄₇	1	4	yes	complemented
461	#135	—	47	4	no	—
462	#135	—	47	4	no	—
463	#135	—	47	4	no	—
464	#135	—	47	4	no	—
465	#135	—	47	4	no	—
466	#135	—	47	8	no	—
467	#135	—	47	4	no	—
468	#135	—	47	4	no	—
469	#135	C₂²×D₄₇	1	4	yes	—
470	C₂×Q₁₆	—	47	2	no	—
471	C₂×Q₁₆	—	47	4	no	—
472	C₂×SD₁₆	—	47	2	no	—
473	C₂×SD₁₆	—	47	2	no	—
474	C₂×SD₁₆	—	47	8	no	—
475	C₂×D₈	—	47	2	no	—
476	C₂×D₈	—	47	4	no	—
477	#131	—	2	4	no	—
478	#131	—	47	4	no	—
479	#131	—	47	4	no	—
480	#131	—	47	4	no	—
481	#131	—	47	4	no	—
482	#131	—	47	4	no	—
483	#131	—	47	4	no	—
484	#131	—	47	4	no	—
485	#131	—	47	4	no	—
486	#131	—	47	8	no	—
487	#131	—	94	8	no	—
488	#131	—	94	8	no	—
489	#131	—	94	4	no	—
490	#131	—	94	2	no	—
491	#131	—	94	8	no	—
492	#131	—	94	2	no	—
493	#131	—	94	2	no	—
494	#131	—	94	2	no	—
495	#131	—	94	8	no	—
496	#131	—	94	4	no	—
497	#131	—	94	4	no	—
498	#131	C₂²×D₄₇	1	8	yes	—
499	C₂×M₁₆	—	2	4	no	—
500	C₂×M₁₆	—	47	2	no	—
501	C₂×M₁₆	—	47	2	no	—
502	C₂×M₁₆	—	47	2	no	—
503	C₂×M₁₆	—	47	8	no	—
504	C₂×M₁₆	—	94	2	no	—
505	C₂×M₁₆	—	94	8	no	—
506	C₂×M₁₆	—	94	8	no	—
507	C₂×M₁₆	—	94	2	no	—
508	C₂×M₁₆	—	94	8	no	—
509	C₂×M₁₆	—	94	4	no	—
510	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
511	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
512	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
513	C₂²×C₈	—	47	1	no	—
514	C₂²×C₈	—	47	1	no	—
515	C₂²×C₈	—	47	2	no	—
516	C₂²×C₈	—	47	2	no	—
517	C₂²×C₈	—	94	2	no	—
518	C₂²×C₈	—	94	8	no	—
519	C₂²×C₈	—	94	2	no	—
520	C₄×Q₈	—	94	1	no	—
521	C₄×D₄	—	94	1	no	—
522	C₄×D₄	—	94	2	no	—
523	#117	—	47	1	no	—
524	#117	—	47	2	no	—
525	C₂×C₄²	—	47	2	no	—
526	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
527	#108	—	47	4	no	—
528	#108	—	47	4	no	—
529	#108	—	47	4	no	—
530	#108	C₂²×D₄₇	1	4	yes	—
531	#104	—	47	8	no	—
532	#104	—	47	8	no	—
533	#104	—	47	4	no	—
534	#104	—	47	4	no	—
535	#104	C₂²×D₄₇	1	4	yes	—
536	#104	C₂²×D₄₇	1	4	yes	—
537	#97	—	47	2	no	—
538	#97	—	47	2	no	—
539	#97	—	47	1	no	—
540	#97	—	47	1	no	—
541	#97	—	47	1	no	—
542	#97	—	47	1	no	—
543	#97	C₂²×D₄₇	1	2	yes	—
544	C₄×C₈	—	47	2	no	—
545	C₄×C₈	—	47	2	no	—
546	C₄×C₈	C₂²×D₄₇	1	2	yes	—
547	#41	—	2	2	no	—
548	#41	—	2	2	no	—
549	#41	—	47	4	no	—
550	#41	—	47	4	no	—
551	#41	—	47	8	no	—
552	#41	—	47	8	no	—
553	#41	—	47	4	no	—
554	#41	—	47	4	no	—
555	#41	—	94	8	no	—
556	#41	—	94	8	no	—
557	#41	—	94	4	no	—
558	#41	—	94	4	no	—
559	#41	—	94	8	no	—
560	#41	—	94	8	no	—
561	#41	—	94	4	no	—
562	#41	—	94	4	no	—
563	#41	—	94	2	no	—
564	#41	—	94	2	no	—
565	#41	C₂×C₄×D₄₇	1	4	yes	—
566	#41	C₂³×D₄₇	1	4	yes	—
567	C₂×Q₈	—	47	1	no	—
568	C₂×Q₈	—	47	8	no	—
569	C₂×Q₈	—	47	2	no	—
570	C₂×Q₈	—	94	4	no	—
571	C₂×Q₈	—	94	4	no	—
572	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	47	2	no	—
575	C₂×D₄	—	47	8	no	—
576	C₂×D₄	—	47	2	no	—
577	C₂×D₄	—	47	1	no	—
578	C₂×D₄	—	94	4	no	—
579	C₂×D₄	—	94	8	no	—
580	C₂×D₄	—	94	4	no	—
581	C₂×D₄	—	94	8	no	—
582	C₂×D₄	—	94	8	no	—
583	C₂×D₄	—	94	2	no	—
584	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	47	2	no	—
588	C₂²×C₄	—	94	8	no	—
589	C₂²×C₄	—	94	2	no	—
590	C₂²×C₄	—	94	2	no	—
591	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
592	Q₁₆	—	47	4	no	—
593	Q₁₆	—	47	4	no	—
594	Q₁₆	—	47	4	no	—
595	Q₁₆	C₂×C₄×D₄₇	1	4	yes	—
596	SD₁₆	—	47	4	no	—
597	SD₁₆	—	47	4	no	—
598	SD₁₆	—	47	4	no	—
599	SD₁₆	—	47	4	no	—
600	SD₁₆	—	47	8	no	—
601	SD₁₆	C₂×C₄×D₄₇	1	8	yes	—
602	D₈	—	47	4	no	—
603	D₈	—	47	4	no	—
604	D₈	—	47	4	no	—
605	D₈	C₂×C₄×D₄₇	1	4	yes	—
606	M₁₆	—	2	2	no	—
607	M₁₆	—	2	8	no	—
608	M₁₆	—	47	8	no	—
609	M₁₆	—	47	4	no	—
610	M₁₆	—	47	4	no	—
611	M₁₆	—	47	4	no	—
612	M₁₆	—	94	4	no	—
613	M₁₆	—	94	4	no	—
614	M₁₆	—	94	8	no	—
615	M₁₆	—	94	4	no	—
616	M₁₆	—	94	4	no	—
617	M₁₆	—	94	2	no	—
618	M₁₆	—	94	8	no	—
619	M₁₆	C₂×C₄×D₄₇	1	4	yes	—
620	M₁₆	D₄×D₄₇	1	4	yes	—
621	M₁₆	C₂³×D₄₇	1	4	yes	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	2	8	no	—
624	C₂×C₈	—	47	2	no	—
625	C₂×C₈	—	47	2	no	—
626	C₂×C₈	—	47	2	no	—
627	C₂×C₈	—	47	2	no	—
628	C₂×C₈	—	47	1	no	—
629	C₂×C₈	—	47	1	no	—
630	C₂×C₈	—	47	1	no	—
631	C₂×C₈	—	47	1	no	—
632	C₂×C₈	—	47	4	no	—
633	C₂×C₈	—	47	4	no	—
634	C₂×C₈	—	47	8	no	—
635	C₂×C₈	—	94	4	no	—
636	C₂×C₈	—	94	4	no	—
637	C₂×C₈	—	94	8	no	—
638	C₂×C₈	—	94	4	no	—
639	C₂×C₈	—	94	4	no	—
640	C₂×C₈	—	94	2	no	—
641	C₂×C₈	—	94	8	no	—
642	C₂×C₈	C₂³×D₄₇	1	2	yes	—
643	C₂×C₈	C₂³×D₄₇	1	2	yes	—
644	C₄⋊C₄	—	94	2	no	—
645	C₄⋊C₄	—	94	1	no	—
646	C₂²⋊C₄	—	94	2	no	—
647	C₂²⋊C₄	—	94	1	no	—
648	C₄²	—	2	1	no	—
649	C₄²	—	47	2	no	—
650	C₄²	—	94	2	no	—
651	C₄²	C₂³×D₄₇	1	1	yes	characteristic
652	C₄²	C₂³×D₄₇	1	1	yes	characteristic
653	C₂³	—	2	2	no	—
654	C₂³	—	47	2	no	—
655	C₂³	—	94	8	no	—
656	C₂³	—	94	2	no	—
657	C₂³	#41×D₄₇	1	1	yes	characteristic
658	Q₈	—	2	2	no	—
659	Q₈	—	47	4	no	—
660	Q₈	—	47	4	no	—
661	Q₈	—	94	8	no	—
662	Q₈	—	94	2	no	—
663	Q₈	C₂²×C₄×D₄₇	1	4	yes	—
664	D₄	—	2	4	no	—
665	D₄	—	2	4	no	—
666	D₄	—	2	2	no	—
667	D₄	—	47	8	no	—
668	D₄	—	47	4	no	—
669	D₄	—	47	4	no	—
670	D₄	—	94	8	no	—
671	D₄	—	94	8	no	—
672	D₄	—	94	8	no	—
673	D₄	—	94	4	no	—
674	D₄	—	94	4	no	—
675	D₄	—	94	2	no	—
676	D₄	C₂²×C₄×D₄₇	1	4	yes	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	8	1	no	—
683	C₂×C₄	—	47	2	no	—
684	C₂×C₄	—	47	4	no	—
685	C₂×C₄	—	47	4	no	—
686	C₂×C₄	—	94	8	no	—
687	C₂×C₄	—	94	8	no	—
688	C₂×C₄	—	94	8	no	—
689	C₂×C₄	—	94	2	no	—
690	C₂×C₄	—	94	4	no	—
691	C₂×C₄	—	94	4	no	—
692	C₂×C₄	—	94	2	no	—
693	C₂×C₄	—	376	2	no	—
694	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
695	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
696	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
697	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
698	C₈	—	2	4	no	—
699	C₈	—	47	1	no	—
700	C₈	—	47	1	no	—
701	C₈	—	47	2	no	—
702	C₈	—	47	2	no	—
703	C₈	—	47	1	no	—
704	C₈	—	47	1	no	—
705	C₈	—	94	4	no	—
706	C₈	C₂²×C₄×D₄₇	1	4	yes	—
707	C₈	C₂×D₄×D₄₇	1	4	yes	—
708	C₂²	—	2	4	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	8	2	no	—
711	C₂²	—	47	4	no	—
712	C₂²	—	94	4	no	—
713	C₂²	—	376	2	no	—
714	C₂²	—	376	8	no	—
715	C₂²	—	188	2	no	—
716	C₂²	C₄×D₄×D₄₇	1	2	yes	—
717	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
718	C₄	—	2	4	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	1	no	—
721	C₄	—	47	4	no	—
722	C₄	—	94	4	no	—
723	C₄	—	188	2	no	—
724	C₄	C₄×D₄×D₄₇	1	2	yes	—
725	C₄	C₂³×C₄×D₄₇	1	1	yes	characteristic
726	C₄	C₂²×D₄×D₄₇	1	1	yes	characteristic
727	C₂	—	2	1	no	—
728	C₂	—	2	2	no	—
729	C₂	—	4	4	no	—
730	C₂	—	94	4	no	—
731	C₂	—	188	4	no	—
732	C₂	C₂×C₄×D₄×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#2956	C₂
socle	C₂×C₄₇	C₂²×C₄×D₄
prime radical	#20258161	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2956	D₄₇
hypocenter	C₄₇	#60184
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #2956

Complements

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

N	H ≅ G/N	type
2. #20258101	C₂	semidirect
3. #20252303	C₂	semidirect
4. #20252300	C₂	semidirect
5. #20252299	C₂	semidirect
6. #20252296	C₂	semidirect
7. #20252291	C₂	semidirect
8. #20252290	C₂	semidirect
9. #20252286	C₂	semidirect
10. C₂×#15689242	C₂	semidirect
11. #444×D₄₇	C₂	semidirect
12. #20251998	C₂	semidirect
13. #20251932	C₂	semidirect
14. #20251817	C₂	semidirect
15. C₄₇×#2956	C₂	semidirect
17. #15689939	C₄	semidirect
18. #15689933	C₄	semidirect
19. #15689932	C₄	semidirect
20. #15689927	C₄	semidirect
27. #15689889	C₂²	semidirect
29. #15689888	C₂²	semidirect
33. C₂×#13094032	C₂²	semidirect
34. C₂×#13094031	C₂²	semidirect
36. #131×D₄₇	C₂²	semidirect
38. #15689246	C₂²	semidirect
39. #15689245	C₂²	semidirect
40. #15689244	C₂²	semidirect
41. #15689243	C₂²	semidirect
42. #15689242	C₂²	semidirect
43. #15689242	C₂²	semidirect
44. #15689242	C₂²	semidirect
45. #15689242	C₂²	semidirect
46. #15689241	C₂²	semidirect
47. #15689240	C₂²	semidirect
48. #15689239	C₂²	semidirect
49. #15689238	C₂²	semidirect
50. #15689172	C₂²	semidirect
51. #15689170	C₂²	semidirect
52. C₂×#13093959	C₂²	semidirect
53. #108×D₄₇	C₂²	semidirect
54. #15689140	C₂²	semidirect
55. #15689139	C₂²	semidirect
56. #15689138	C₂²	semidirect
57. C₂×#13093952	C₂²	semidirect
58. #104×D₄₇	C₂²	semidirect
59. #15689081	C₂²	semidirect
60. #15689081	C₂²	semidirect
61. #15689077	C₂²	semidirect
62. #15689077	C₂²	semidirect
63. #15689075	C₂²	semidirect
64. C₂×#13093935	C₂²	semidirect
65. #97×D₄₇	C₂²	semidirect
67. C₄₇×#568	C₂²	semidirect
68. C₄₇×#444	C₂²	semidirect
69. C₄₇×#443	C₂²	semidirect
70. C₄₇×#430	C₂²	semidirect
71. C₂×#104×C₄₇	C₂²	semidirect
72. C₄×M₁₆×C₄₇	C₂²	semidirect
85. #13094057	C₂×C₄	semidirect
86. #13094056	C₂×C₄	semidirect
87. #13094053	C₂×C₄	semidirect
88. #13094052	C₂×C₄	semidirect
89. #13094051	C₂×C₄	semidirect
90. #13094048	C₂×C₄	semidirect
91. #13094047	C₂×C₄	semidirect
93. #13094045	C₂×C₄	semidirect
94. #13094044	C₂×C₄	semidirect
95. #13094044	C₂×C₄	semidirect
98. #13094043	C₂×C₄	semidirect
99. C₂×#10625337	C₂×C₄	semidirect
100. Q₁₆×D₄₇	C₂×C₄	semidirect
101. C₂×#10625335	C₂×C₄	semidirect
102. C₂×#10625336	C₂×C₄	semidirect
103. SD₁₆×D₄₇	C₂×C₄	semidirect
104. C₂×#10625334	C₂×C₄	semidirect
105. D₈×D₄₇	C₂×C₄	semidirect
165. #137×C₄₇	C₂×C₄	semidirect
166. AGL(1,ℤ/8)×C₄₇	C₂×C₄	semidirect
367. #2956	D₄₇	semidirect
397. #568	C₂×D₄₇	semidirect
414. #444	C₂×D₄₇	semidirect
419. #443	C₂×D₄₇	semidirect
422. #430	C₂×D₄₇	semidirect
430. C₂×#104	C₂×D₄₇	semidirect
436. C₄×M₁₆	C₂×D₄₇	semidirect
439. C₄₇	#60184	semidirect
456. #137	C₄×D₄₇	semidirect
460. AGL(1,ℤ/8)	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20258161	2
#20258101	2
#20252303	2
#20252300	2
#20252299	2
#20252296	2
#20252291	2
#20252290	2
#20252286	2
C₂×#15689242	2
#444×D₄₇	2
#20251998	2
#20251932	2
#20251817	2
C₄₇×#2956	2
#60184	47