Subgroups — #26216871

Order 12032.

930 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	#20245790	C₂	1	2	yes	maximal
3	#20243546	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243543	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243514	C₂	1	2	yes	maximal, complemented
6	#20243421	C₂	1	1	yes	maximal, characteristic
7	#20243419	C₂	1	2	yes	maximal
8	#20243288	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243287	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243284	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1809	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂×#13093980	—	2	2	no	—
14	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
15	C₂×#13093958	C₂²	1	1	yes	characteristic
16	C₂×#13093957	C₂²	1	2	yes	—
17	C₂×#13093956	C₂²	1	1	yes	characteristic
18	C₂×#13093955	C₂²	1	2	yes	—
19	M₁₆×Dic₄₇	C₄	1	8	yes	complemented
20	C₂×#13093934	C₂²	1	1	yes	characteristic
21	C₂×#13093934	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
24	#15688992	C₂²	1	2	yes	—
25	#15688992	C₂²	1	2	yes	—
26	#15688987	—	2	2	no	—
27	#15688983	C₂²	1	2	yes	—
28	#15688981	—	2	2	no	—
29	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
30	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
31	#15688974	—	2	2	no	—
32	#15688886	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#380	C₂²	1	2	yes	—
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₂³×Dic₄₇	D₄	1	2	yes	—
41	C₂×#10625329	—	2	2	no	—
42	C₂×#10625329	—	2	2	no	—
43	C₂×#10625329	C₂×C₄	1	4	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	#13093980	—	4	8	no	—
47	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
49	C₂×Dic₄₇⋊C₄	—	2	2	no	—
50	C₂×Dic₄₇⋊C₄	—	2	2	no	—
51	C₂×Dic₄₇⋊C₄	—	2	2	no	—
52	C₂×Dic₄₇⋊C₄	—	2	2	no	—
53	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
54	C₂×C₄×Dic₄₇	—	2	2	no	—
55	C₂×C₄×Dic₄₇	—	2	2	no	—
56	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
57	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
58	C₂×C₄×Dic₄₇	Q₈	1	4	yes	—
59	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
61	#13093958	—	2	2	no	—
62	#13093957	—	2	4	no	—
63	#13093956	—	2	2	no	—
64	#13093955	—	2	4	no	—
65	#13093934	C₂×C₄	1	4	yes	—
66	#13093934	C₂×C₄	1	4	yes	—
67	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
68	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
69	C₄₇⋊#95	—	2	2	no	—
70	C₄₇⋊#95	—	2	2	no	—
71	C₄₇⋊#95	—	2	2	no	—
72	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×M₁₆×C₄₇	—	2	2	no	—
74	C₂×M₁₆×C₄₇	—	2	2	no	—
75	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
76	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
80	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
81	#107×C₄₇	—	2	2	no	—
82	#106×C₄₇	—	2	2	no	—
83	#95×C₄₇	—	2	2	no	—
84	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	—	2	1	no	—
86	C₂²×C₄×C₄₇	—	2	1	no	—
87	C₂²×C₄×C₄₇	—	2	1	no	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
95	C₂²×Dic₄₇	—	2	4	no	—
96	C₂²×Dic₄₇	—	2	4	no	—
97	C₂²×Dic₄₇	—	2	2	no	—
98	C₂²×Dic₄₇	—	2	2	no	—
99	C₂²×Dic₄₇	C₄⋊C₄	1	8	yes	—
100	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
101	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
102	M₁₆×C₄₇	—	2	8	no	—
103	C₂×C₈×C₄₇	—	2	1	no	—
104	C₂×C₈×C₄₇	—	2	1	no	—
105	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₄₇	#41	1	2	yes	—
108	C₂×C₈×C₄₇	#41	1	2	yes	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₂²⋊C₄×C₄₇	—	4	4	no	—
114	C₂²⋊Dic₄₇	—	4	4	no	—
115	C₄⋊Dic₄₇	—	2	2	no	—
116	C₄⋊Dic₄₇	—	2	2	no	—
117	C₄⋊Dic₄₇	—	2	2	no	—
118	C₄⋊Dic₄₇	—	2	2	no	—
119	Dic₄₇⋊C₄	—	4	4	no	—
120	Dic₄₇⋊C₄	—	4	4	no	—
121	Dic₄₇⋊C₄	—	4	4	no	—
122	Dic₄₇⋊C₄	—	4	4	no	—
123	C₄×Dic₄₇	—	4	4	no	—
124	C₄×Dic₄₇	—	4	4	no	—
125	C₄×Dic₄₇	C₄⋊C₄	1	8	yes	—
126	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
127	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
128	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
129	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
130	#10625329	—	2	8	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	—	2	1	no	—
133	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
134	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
135	C₂×C₄₇⋊C₈	#41	1	2	yes	—
136	C₂×C₄₇⋊C₈	#41	1	2	yes	—
137	C₂³×C₄₇	—	2	1	no	—
138	C₂³×C₄₇	—	2	1	no	—
139	C₂³×C₄₇	—	2	2	no	—
140	C₂³×C₄₇	—	2	2	no	—
141	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
142	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	1	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	—	4	2	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
156	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₂×Dic₄₇	—	2	2	no	—
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	16	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
172	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
173	C₂×Dic₄₇	AGL(1,ℤ/8)	1	4	yes	—
174	C₂×Dic₄₇	#137	1	4	yes	—
175	C₈×C₄₇	—	2	2	no	—
176	C₈×C₄₇	#117	1	4	yes	complemented
177	C₄₇⋊C₈	—	2	2	no	—
178	C₄₇⋊C₈	#117	1	4	yes	complemented
179	#20824	—	47	1	no	maximal, Sylow
180	C₂²×C₄₇	—	2	4	no	—
181	C₂²×C₄₇	—	2	2	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	—	4	1	no	—
184	C₂²×C₄₇	—	4	1	no	—
185	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
186	C₂²×C₄₇	#532	1	1	yes	characteristic
187	C₂²×C₄₇	#532	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
189	C₂²×C₄₇	C₂×#137	1	2	yes	—
190	C₄×C₄₇	—	2	2	no	—
191	C₄×C₄₇	—	8	2	no	—
192	C₄×C₄₇	—	8	2	no	—
193	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
194	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
195	C₄×C₄₇	#533	1	1	yes	characteristic
196	C₄×C₄₇	#533	1	1	yes	characteristic
197	Dic₄₇	—	2	4	no	—
198	Dic₄₇	—	8	2	no	—
199	Dic₄₇	—	8	2	no	—
200	Dic₄₇	#428	1	8	yes	—
201	C₂×C₄×M₁₆	—	47	1	no	—
202	#2285	—	47	2	no	—
203	#1845	—	47	1	no	—
204	#1844	—	47	1	no	—
205	#1834	—	47	2	no	—
206	#1809	—	47	2	no	—
207	#1809	—	47	1	no	—
208	#1809	D₄₇	1	1	yes	characteristic
209	#1776	—	47	1	no	—
210	#1776	—	47	1	no	—
211	#1776	—	47	2	no	—
212	C₂×C₄₇	—	4	2	no	—
213	C₂×C₄₇	#2285	1	1	yes	characteristic
214	C₂×C₄₇	C₂×#428	1	2	yes	—
215	C₂×C₄₇	#3182	1	2	yes	—
216	C₂×C₄₇	#3184	1	1	yes	characteristic
217	C₂×C₄₇	#3185	1	1	yes	characteristic
218	C₂²×M₁₆	—	47	1	no	—
219	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
220	C₂×#117	—	94	2	no	—
221	C₂²×C₄²	—	47	1	no	—
222	C₂×#107	—	47	1	no	—
223	C₂×#107	—	47	2	no	—
224	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
225	C₂×#106	—	47	1	no	—
226	C₂×#106	—	47	2	no	—
227	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
228	C₄×M₁₆	—	47	8	no	—
229	C₂×#97	—	47	1	no	—
230	C₂×#97	—	47	1	no	—
231	C₂×C₄×C₈	—	47	1	no	—
232	C₂×C₄×C₈	—	47	1	no	—
233	#384	—	47	2	no	—
234	#384	—	47	2	no	—
235	#382	—	94	2	no	—
236	#380	—	47	2	no	—
237	#380	—	94	2	no	—
238	#380	C₂×D₄₇	1	2	yes	—
239	C₄×C₄⋊C₄	—	47	2	no	—
240	C₄×C₄⋊C₄	—	47	2	no	—
241	C₄×C₄⋊C₄	—	94	2	no	—
242	#340	—	47	2	no	—
243	#340	—	47	2	no	—
244	#340	—	47	2	no	—
245	#340	C₂×D₄₇	1	2	yes	—
246	C₄₇	#20824	1	1	yes	characteristic, complemented, Sylow
247	C₂³×C₄	—	47	2	no	—
248	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	47	4	no	—
252	C₂×M₁₆	—	94	2	no	—
253	C₂×M₁₆	—	94	2	no	—
254	C₂×M₁₆	C₄×D₄₇	1	4	yes	—
255	C₂²×C₈	—	47	1	no	—
256	C₂²×C₈	—	47	1	no	—
257	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
258	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
259	#117	—	188	8	no	—
260	C₂×C₄⋊C₄	—	47	2	no	—
261	C₂×C₄⋊C₄	—	47	2	no	—
262	C₂×C₄⋊C₄	—	94	2	no	—
263	C₂×C₄⋊C₄	—	94	2	no	—
264	C₂×C₄⋊C₄	—	94	2	no	—
265	C₂×C₄⋊C₄	—	94	2	no	—
266	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
267	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	94	2	no	—
270	C₂×C₄²	—	47	4	no	—
271	C₂×C₄²	—	47	2	no	—
272	C₂×C₄²	—	47	4	no	—
273	C₂×C₄²	—	47	1	no	—
274	C₂×C₄²	—	47	1	no	—
275	C₂×C₄²	—	94	2	no	—
276	C₂×C₄²	—	94	2	no	—
277	#107	—	2	2	no	—
278	#107	—	94	4	no	—
279	#107	—	94	2	no	—
280	#106	—	2	2	no	—
281	#106	—	94	4	no	—
282	#106	—	94	2	no	—
283	#97	—	47	4	no	—
284	#97	—	47	4	no	—
285	C₄×C₈	—	47	4	no	—
286	C₄×C₈	—	47	4	no	—
287	#95	—	2	2	no	—
288	#95	—	94	2	no	—
289	#95	—	94	2	no	—
290	#95	—	94	2	no	—
291	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	47	2	no	—
299	C₂²×C₄	—	47	8	no	—
300	C₂²×C₄	—	47	2	no	—
301	C₂²×C₄	—	94	4	no	—
302	C₂²×C₄	—	94	4	no	—
303	C₂²×C₄	—	94	2	no	—
304	C₂²×C₄	—	94	2	no	—
305	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
306	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
307	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
308	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
309	M₁₆	—	2	8	no	—
310	M₁₆	—	94	8	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	47	2	no	—
314	C₂×C₈	—	47	2	no	—
315	C₂×C₈	—	47	2	no	—
316	C₂×C₈	—	47	2	no	—
317	C₂×C₈	—	94	1	no	—
318	C₂×C₈	—	94	1	no	—
319	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
320	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
321	C₂×C₈	#10625352	1	2	yes	—
322	C₂×C₈	#10625352	1	2	yes	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	94	2	no	—
328	C₄⋊C₄	—	94	2	no	—
329	C₄⋊C₄	—	94	2	no	—
330	C₄⋊C₄	—	94	2	no	—
331	C₄⋊C₄	—	188	4	no	—
332	C₄⋊C₄	—	188	4	no	—
333	C₄⋊C₄	—	188	4	no	—
334	C₄⋊C₄	—	188	4	no	—
335	C₂²⋊C₄	—	4	4	no	—
336	C₂²⋊C₄	—	188	4	no	—
337	C₄²	—	47	8	no	—
338	C₄²	—	47	2	no	—
339	C₄²	—	47	2	no	—
340	C₄²	—	47	2	no	—
341	C₄²	—	47	2	no	—
342	C₄²	—	188	4	no	—
343	C₄²	—	188	4	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	C₄⋊C₄×D₄₇	1	2	yes	—
349	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	47	4	no	—
363	C₂×C₄	—	47	4	no	—
364	C₂×C₄	—	47	4	no	—
365	C₂×C₄	—	47	4	no	—
366	C₂×C₄	—	94	16	no	—
367	C₂×C₄	—	94	2	no	—
368	C₂×C₄	—	94	2	no	—
369	C₂×C₄	—	188	2	no	—
370	C₂×C₄	—	188	2	no	—
371	C₂×C₄	—	188	2	no	—
372	C₂×C₄	—	188	2	no	—
373	C₂×C₄	—	188	2	no	—
374	C₂×C₄	—	188	2	no	—
375	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
376	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
377	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
378	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
379	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
381	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	47	4	no	—
384	C₈	—	94	2	no	—
385	C₈	#13093980	1	4	yes	complemented
386	C₂²	—	2	2	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
392	C₂²	#15689668	1	1	yes	characteristic
393	C₂²	#15689668	1	1	yes	characteristic
394	C₂²	AGL(1,ℤ/8)×D₄₇	1	2	yes	—
395	C₂²	#137×D₄₇	1	2	yes	—
396	C₄	—	2	2	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	2	no	—
399	C₄	—	47	8	no	—
400	C₄	—	94	4	no	—
401	C₄	—	376	2	no	—
402	C₄	—	376	2	no	—
403	C₄	#117×D₄₇	1	1	yes	characteristic
404	C₄	C₂×#13093980	1	1	yes	characteristic
405	C₄	#15689675	1	1	yes	characteristic
406	C₄	#15689675	1	1	yes	characteristic
407	C₂	—	4	2	no	—
408	C₂	#20245790	1	1	yes	characteristic
409	C₂	#428×D₄₇	1	2	yes	—
410	C₂	#20254101	1	2	yes	—
411	C₂	#20254121	1	1	yes	characteristic
412	C₂	#20254128	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1809	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1809	D₄₇
hypocenter	C₄₇	#20824
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #1809

Complements

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

N	H ≅ G/N	type
3. #20243546	C₂	semidirect
4. #20243543	C₂	semidirect
5. #20243514	C₂	semidirect
8. #20243288	C₂	semidirect
9. #20243287	C₂	semidirect
10. #20243284	C₂	semidirect
19. M₁₆×Dic₄₇	C₄	semidirect
176. C₈×C₄₇	#117	semidirect
178. C₄₇⋊C₈	#117	semidirect
246. C₄₇	#20824	semidirect
385. C₈	#13093980	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×Dic₄₇	2
#20245790	2
#20243546	2
#20243543	2
#20243514	2
#20243421	2
#20243419	2
#20243288	2
#20243287	2
#20243284	2
C₄₇×#1809	2
#20824	47