Subgroups — #26216834

Order 12032.

810 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689078	C₂	1	1	yes	maximal, characteristic
2	#20245995	C₂	1	2	yes	maximal
3	#20243549	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243543	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243520	C₂	1	2	yes	maximal, complemented
6	#20243419	C₂	1	2	yes	maximal
7	#20243413	C₂	1	1	yes	maximal, characteristic
8	#20243284	C₂	1	2	yes	maximal, complemented
9	#106×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#106×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1807	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂×#13093983	C₂²	1	1	yes	characteristic
14	C₂×#13093957	C₂²	1	2	yes	—
15	C₂×#13093956	C₂²	1	1	yes	characteristic
16	C₂×#13093956	C₂²	1	1	yes	characteristic
17	C₂×#13093955	C₂²	1	2	yes	—
18	#15689078	C₄	1	8	yes	complemented
19	C₂×#13093934	C₂²	1	1	yes	characteristic
20	C₂×#13093934	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
23	#15689017	—	2	2	no	—
24	#15689011	—	2	2	no	—
25	#15689008	—	2	2	no	—
26	#15689006	—	2	2	no	—
27	#15688992	C₂²	1	2	yes	—
28	#15688988	C₂²	1	2	yes	—
29	#15688983	C₂²	1	2	yes	—
30	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
31	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
32	#15688886	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#106×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	C₂×#10625329	—	2	2	no	—
41	C₂×#10625329	—	2	2	no	—
42	C₂×#10625329	C₂×C₄	1	4	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	#13093983	C₂×C₄	1	4	yes	—
46	#13093983	Q₈	1	4	yes	—
47	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
48	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
51	C₂×Dic₄₇⋊C₄	—	2	2	no	—
52	C₂×Dic₄₇⋊C₄	—	2	2	no	—
53	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
54	C₂×C₂²⋊Dic₄₇	D₄	1	1	yes	characteristic
55	C₂×C₂²⋊Dic₄₇	D₄	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	—	2	2	no	—
57	C₂×C₄×Dic₄₇	—	2	2	no	—
58	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
60	#13093957	—	2	4	no	—
61	#13093956	—	2	2	no	—
62	#13093956	—	2	2	no	—
63	#13093955	—	2	4	no	—
64	#13093934	C₂×C₄	1	4	yes	—
65	#13093934	C₂×C₄	1	4	yes	—
66	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
67	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
68	C₄₇⋊#95	—	2	2	no	—
69	C₄₇⋊#95	—	2	2	no	—
70	C₄₇⋊#95	—	2	2	no	—
71	C₄₇⋊#95	—	2	2	no	—
72	C₄₇⋊#95	—	2	2	no	—
73	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	—	2	2	no	—
75	C₂²×C₈×C₄₇	—	2	2	no	—
76	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
77	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
81	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
82	#106×C₄₇	—	2	2	no	—
83	#106×C₄₇	—	2	2	no	—
84	#95×C₄₇	—	2	2	no	—
85	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
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	1	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
96	C₂²×Dic₄₇	—	2	2	no	—
97	C₂²×Dic₄₇	—	2	2	no	—
98	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₄₇	—	2	1	no	—
103	C₂×C₈×C₄₇	—	2	1	no	—
104	C₂×C₈×C₄₇	—	2	8	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	—	8	2	no	—
114	C₂²⋊Dic₄₇	—	8	2	no	—
115	C₂²⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
116	C₂²⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
117	C₄⋊Dic₄₇	—	2	2	no	—
118	C₄⋊Dic₄₇	—	2	2	no	—
119	C₄⋊Dic₄₇	—	2	2	no	—
120	C₄⋊Dic₄₇	—	2	2	no	—
121	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
122	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
123	Dic₄₇⋊C₄	—	8	2	no	—
124	Dic₄₇⋊C₄	—	8	2	no	—
125	C₄×Dic₄₇	—	8	2	no	—
126	C₄×Dic₄₇	—	8	2	no	—
127	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
128	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
129	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
130	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
131	#10625329	—	2	8	no	—
132	C₂×C₄₇⋊C₈	—	2	1	no	—
133	C₂×C₄₇⋊C₈	—	2	1	no	—
134	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
135	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
136	C₂×C₄₇⋊C₈	#41	1	2	yes	—
137	C₂×C₄₇⋊C₈	#41	1	2	yes	—
138	C₂³×C₄₇	—	2	1	no	—
139	C₂³×C₄₇	—	2	1	no	—
140	C₂³×C₄₇	—	2	2	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
143	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	1	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	—	2	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	—	4	2	no	—
156	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂²×Q₈	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×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	2	no	—
165	C₂×Dic₄₇	—	2	2	no	—
166	C₂×Dic₄₇	—	2	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	—	4	2	no	—
172	C₂×Dic₄₇	—	4	2	no	—
173	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
176	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
177	C₈×C₄₇	—	2	2	no	—
178	C₈×C₄₇	#117	1	4	yes	—
179	C₄₇⋊C₈	—	2	2	no	—
180	C₄₇⋊C₈	#117	1	4	yes	—
181	#20820	—	47	1	no	maximal, Sylow
182	C₂²×C₄₇	—	2	2	no	—
183	C₂²×C₄₇	—	2	2	no	—
184	C₂²×C₄₇	—	2	2	no	—
185	C₂²×C₄₇	—	4	2	no	—
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
188	C₂²×C₄₇	#532	1	1	yes	characteristic
189	C₂²×C₄₇	#532	1	1	yes	characteristic
190	C₂²×C₄₇	#577	1	2	yes	—
191	C₂²×C₄₇	#577	1	2	yes	—
192	C₄×C₄₇	—	2	2	no	—
193	C₄×C₄₇	—	8	2	no	—
194	C₄×C₄₇	—	8	2	no	—
195	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
196	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
197	C₄×C₄₇	#533	1	1	yes	characteristic
198	C₄×C₄₇	#533	1	1	yes	characteristic
199	Dic₄₇	—	2	2	no	—
200	Dic₄₇	—	2	2	no	—
201	Dic₄₇	—	2	2	no	—
202	Dic₄₇	—	2	2	no	—
203	Dic₄₇	—	8	2	no	—
204	Dic₄₇	—	8	2	no	—
205	C₂×#405	—	47	1	no	—
206	#2314	—	47	2	no	—
207	#1846	—	47	1	no	—
208	#1844	—	47	1	no	—
209	#1836	—	47	2	no	—
210	#1809	—	47	2	no	—
211	#1807	—	47	1	no	—
212	#1807	D₄₇	1	1	yes	characteristic
213	#1776	—	47	2	no	—
214	C₄×#106	—	47	1	no	—
215	C₄×#106	—	47	1	no	—
216	C₂×C₄₇	—	4	2	no	—
217	C₂×C₄₇	#2285	1	1	yes	characteristic
218	C₂×C₄₇	#2912	1	1	yes	characteristic
219	C₂×C₄₇	#2912	1	1	yes	characteristic
220	C₂×C₄₇	#3173	1	2	yes	—
221	C₂×C₄₇	#3174	1	2	yes	—
222	C₂²×M₁₆	—	47	1	no	—
223	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
224	C₂×#117	—	47	1	no	—
225	C₂×#107	—	47	2	no	—
226	C₂×#106	—	47	1	no	—
227	C₂×#106	—	47	1	no	—
228	C₂×#106	—	47	2	no	—
229	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
230	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
231	#405	—	47	8	no	—
232	C₂×#97	—	47	1	no	—
233	C₂×#97	—	47	1	no	—
234	C₂×C₄×C₈	—	47	1	no	—
235	C₂×C₄×C₈	—	47	1	no	—
236	#388	—	94	2	no	—
237	#388	—	94	2	no	—
238	#387	—	94	2	no	—
239	#387	—	94	2	no	—
240	#384	—	47	2	no	—
241	#382	—	47	2	no	—
242	#380	—	47	2	no	—
243	#380	C₂×D₄₇	1	2	yes	—
244	C₄×C₄⋊C₄	—	47	2	no	—
245	C₄×C₄⋊C₄	—	47	2	no	—
246	#340	—	47	2	no	—
247	#340	—	47	2	no	—
248	#340	—	47	2	no	—
249	#340	C₂×D₄₇	1	2	yes	—
250	C₄₇	#20820	1	1	yes	characteristic, complemented, Sylow
251	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
252	C₂×M₁₆	—	47	4	no	—
253	C₂×M₁₆	—	94	2	no	—
254	C₂×M₁₆	—	94	2	no	—
255	C₂²×C₈	—	2	2	no	—
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	—	47	1	no	—
258	C₂²×C₈	—	47	1	no	—
259	C₂²×C₈	C₄×D₄₇	1	4	yes	—
260	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
261	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
262	#117	—	47	4	no	—
263	#117	—	47	4	no	—
264	C₂×C₄⋊C₄	—	47	1	no	—
265	C₂×C₄⋊C₄	—	47	1	no	—
266	C₂×C₄⋊C₄	—	47	2	no	—
267	C₂×C₄⋊C₄	—	47	2	no	—
268	C₂×C₄⋊C₄	—	94	2	no	—
269	C₂×C₄⋊C₄	—	94	2	no	—
270	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
271	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	47	1	no	—
274	C₂×C₂²⋊C₄	—	47	1	no	—
275	C₂×C₂²⋊C₄	—	94	2	no	—
276	C₂×C₄²	—	47	1	no	—
277	C₂×C₄²	—	47	1	no	—
278	C₂×C₄²	—	94	2	no	—
279	C₂×C₄²	—	94	2	no	—
280	#107	—	94	4	no	—
281	#106	—	2	2	no	—
282	#106	—	2	2	no	—
283	#106	—	94	4	no	—
284	#106	—	94	2	no	—
285	#106	—	94	2	no	—
286	#97	—	47	4	no	—
287	#97	—	47	4	no	—
288	C₄×C₈	—	47	4	no	—
289	C₄×C₈	—	47	4	no	—
290	#95	—	2	2	no	—
291	#95	—	94	2	no	—
292	#95	—	94	2	no	—
293	#95	—	94	2	no	—
294	#95	—	94	2	no	—
295	#95	—	94	2	no	—
296	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	47	1	no	—
304	C₂²×C₄	—	47	1	no	—
305	C₂²×C₄	—	47	1	no	—
306	C₂²×C₄	—	47	1	no	—
307	C₂²×C₄	—	94	2	no	—
308	C₂²×C₄	—	94	2	no	—
309	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
310	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
311	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
312	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
313	M₁₆	—	94	8	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	8	no	—
317	C₂×C₈	—	47	2	no	—
318	C₂×C₈	—	47	2	no	—
319	C₂×C₈	—	47	2	no	—
320	C₂×C₈	—	47	2	no	—
321	C₂×C₈	—	94	1	no	—
322	C₂×C₈	—	94	1	no	—
323	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
324	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
325	C₂×C₈	#10625352	1	2	yes	—
326	C₂×C₈	#10625352	1	2	yes	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	47	4	no	—
332	C₄⋊C₄	—	47	4	no	—
333	C₄⋊C₄	—	94	2	no	—
334	C₄⋊C₄	—	94	2	no	—
335	C₄⋊C₄	—	94	2	no	—
336	C₄⋊C₄	—	94	2	no	—
337	C₄⋊C₄	—	376	2	no	—
338	C₄⋊C₄	—	376	2	no	—
339	C₂²⋊C₄	—	8	2	no	—
340	C₂²⋊C₄	—	47	4	no	—
341	C₂²⋊C₄	—	47	4	no	—
342	C₂²⋊C₄	—	376	2	no	—
343	C₄²	—	47	2	no	—
344	C₄²	—	47	2	no	—
345	C₄²	—	47	2	no	—
346	C₄²	—	47	2	no	—
347	C₄²	—	376	2	no	—
348	C₄²	—	376	2	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	C₄⋊C₄×D₄₇	1	2	yes	—
354	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	47	2	no	—
368	C₂×C₄	—	47	2	no	—
369	C₂×C₄	—	47	2	no	—
370	C₂×C₄	—	47	2	no	—
371	C₂×C₄	—	94	2	no	—
372	C₂×C₄	—	94	2	no	—
373	C₂×C₄	—	94	2	no	—
374	C₂×C₄	—	94	2	no	—
375	C₂×C₄	—	188	2	no	—
376	C₂×C₄	—	188	2	no	—
377	C₂×C₄	—	188	2	no	—
378	C₂×C₄	—	188	2	no	—
379	C₂×C₄	—	188	2	no	—
380	C₂×C₄	—	188	2	no	—
381	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
382	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
383	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
384	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
385	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
386	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
387	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
388	C₈	—	2	2	no	—
389	C₈	—	47	4	no	—
390	C₈	—	94	2	no	—
391	C₈	#13093980	1	4	yes	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	2	no	—
397	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
398	C₂²	#15689668	1	1	yes	characteristic
399	C₂²	#15689668	1	1	yes	characteristic
400	C₂²	#15689929	1	2	yes	—
401	C₂²	#15689930	1	2	yes	—
402	C₄	—	2	2	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	2	no	—
405	C₄	—	94	2	no	—
406	C₄	—	94	2	no	—
407	C₄	—	94	2	no	—
408	C₄	—	94	2	no	—
409	C₄	—	376	2	no	—
410	C₄	—	376	2	no	—
411	C₄	#117×D₄₇	1	1	yes	characteristic
412	C₄	C₂×#13093980	1	1	yes	characteristic
413	C₄	#15689675	1	1	yes	characteristic
414	C₄	#15689675	1	1	yes	characteristic
415	C₂	—	4	2	no	—
416	C₂	#20245790	1	1	yes	characteristic
417	C₂	#20251979	1	1	yes	characteristic
418	C₂	#20251980	1	1	yes	characteristic
419	C₂	#20253998	1	2	yes	—
420	C₂	#20254009	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1807	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1807	D₄₇
hypocenter	C₄₇	#20820
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #1807

Complements

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

N	H ≅ G/N	type
3. #20243549	C₂	semidirect
4. #20243543	C₂	semidirect
5. #20243520	C₂	semidirect
8. #20243284	C₂	semidirect
9. #106×Dic₄₇	C₂	semidirect
10. #106×Dic₄₇	C₂	semidirect
18. #15689078	C₄	semidirect
250. C₄₇	#20820	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689078	2
#20245995	2
#20243549	2
#20243543	2
#20243520	2
#20243419	2
#20243413	2
#20243284	2
#106×Dic₄₇	2
C₄₇×#1807	2
#20820	47