Subgroups — #26216837

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×#15689077	C₂	1	1	yes	maximal, characteristic
2	#20245993	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	#20243420	C₂	1	2	yes	maximal
7	#20243410	C₂	1	1	yes	maximal, characteristic
8	#20243410	C₂	1	1	yes	maximal, characteristic
9	#20243286	C₂	1	2	yes	maximal, complemented
10	C₄×#13093956	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#106×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	C₂×#13093981	C₂²	1	1	yes	characteristic
15	C₂×#13093957	C₂²	1	2	yes	—
16	C₂×#13093956	C₂²	1	1	yes	characteristic
17	C₂×#13093956	C₂²	1	1	yes	characteristic
18	C₂×#13093955	C₂²	1	2	yes	—
19	#15689077	C₄	1	8	yes	complemented
20	C₂×#13093935	C₂²	1	1	yes	characteristic
21	C₂×#13093934	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
23	#15689014	—	2	2	no	—
24	#15689012	—	2	2	no	—
25	#15689007	—	2	2	no	—
26	#15689005	—	2	2	no	—
27	#15688992	C₂²	1	2	yes	—
28	#15688988	C₂²	1	2	yes	—
29	#15688980	C₂²	1	2	yes	—
30	#15688980	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	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
41	C₂×#10625324	—	2	2	no	—
42	C₂×#10625324	—	2	2	no	—
43	C₂×#10625324	C₂×C₄	1	4	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂×C₈×D₄₇	—	2	2	no	—
47	C₂×C₈×D₄₇	—	2	2	no	—
48	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
49	#13093981	C₂×C₄	1	4	yes	—
50	#13093981	Q₈	1	4	yes	—
51	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
52	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
53	C₂×Dic₄₇⋊C₄	—	2	2	no	—
54	C₂×Dic₄₇⋊C₄	—	2	2	no	—
55	C₂×Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
56	C₂×Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
57	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
58	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
59	C₂×(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
60	C₂×(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	—	2	2	no	—
62	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
63	#13093957	—	2	4	no	—
64	#13093956	—	2	2	no	—
65	#13093956	—	2	2	no	—
66	#13093955	—	2	4	no	—
67	#13093935	C₂×C₄	1	4	yes	—
68	#13093934	C₂×C₄	1	4	yes	—
69	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
70	C₄₇⋊#95	—	2	2	no	—
71	C₄₇⋊#95	—	2	2	no	—
72	C₄₇⋊#95	—	2	2	no	—
73	C₄₇⋊#95	—	2	2	no	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
79	C₂×C₄²×C₄₇	—	2	2	no	—
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	#106×C₄₇	—	2	2	no	—
82	#106×C₄₇	—	2	2	no	—
83	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	—
84	#95×C₄₇	—	2	2	no	—
85	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
91	C₂²×Dic₄₇	—	2	2	no	—
92	C₂²×Dic₄₇	—	2	2	no	—
93	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂×C₄×D₄₇	—	2	1	no	—
97	C₂×C₄×D₄₇	—	2	1	no	—
98	C₂×C₄×D₄₇	—	2	1	no	—
99	C₂×C₄×D₄₇	—	2	1	no	—
100	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
101	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
102	C₂×C₈×C₄₇	—	2	1	no	—
103	C₂×C₈×C₄₇	—	2	1	no	—
104	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₄₇	#41	1	2	yes	—
107	C₂×C₈×C₄₇	#41	1	2	yes	—
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄²×C₄₇	—	8	2	no	—
113	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
114	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
115	(C₂×D₄₇)⋊C₄	—	8	2	no	—
116	(C₂×D₄₇)⋊C₄	—	8	2	no	—
117	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	4	yes	—
118	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	4	yes	—
119	C₄⋊Dic₄₇	—	2	2	no	—
120	C₄⋊Dic₄₇	—	2	2	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	—	2	2	no	—
123	Dic₄₇⋊C₄	—	8	2	no	—
124	Dic₄₇⋊C₄	—	8	2	no	—
125	Dic₄₇⋊C₄	C₄⋊C₄	1	4	yes	—
126	Dic₄₇⋊C₄	C₄⋊C₄	1	4	yes	—
127	C₄×Dic₄₇	—	8	2	no	—
128	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
129	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
133	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
134	C₂×C₄₇⋊C₈	#41	1	2	yes	—
135	C₂×C₄₇⋊C₈	#41	1	2	yes	—
136	#10625324	—	2	8	no	—
137	C₈×D₄₇	—	2	8	no	—
138	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
139	C₂²×D₄₇	—	2	1	no	—
140	C₂²×D₄₇	—	2	1	no	—
141	C₂²×D₄₇	—	2	2	no	—
142	C₂²×D₄₇	—	2	2	no	—
143	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	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	C₂×C₄⋊C₄	1	2	yes	—
153	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
154	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	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×Dic₄₇	—	2	1	no	—
161	C₂×Dic₄₇	—	2	1	no	—
162	C₂×Dic₄₇	—	2	2	no	—
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	4	2	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	C₂×C₄⋊C₄	1	2	yes	—
171	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
172	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
173	C₄×D₄₇	—	2	2	no	—
174	C₄×D₄₇	—	2	2	no	—
175	C₄×D₄₇	—	2	2	no	—
176	C₄×D₄₇	—	2	2	no	—
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	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₂²×C₄₇	#532	1	1	yes	characteristic
184	C₂²×C₄₇	#532	1	1	yes	characteristic
185	C₂²×C₄₇	#577	1	2	yes	—
186	C₂²×C₄₇	#577	1	2	yes	—
187	C₂×D₄₇	—	2	2	no	—
188	C₂×D₄₇	—	2	2	no	—
189	C₂×D₄₇	—	2	2	no	—
190	C₂×D₄₇	—	4	2	no	—
191	C₂×D₄₇	—	4	2	no	—
192	C₄×C₄₇	—	2	2	no	—
193	C₄×C₄₇	—	2	2	no	—
194	C₄×C₄₇	—	8	2	no	—
195	C₄×C₄₇	—	8	2	no	—
196	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
197	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
198	C₄×C₄₇	#533	1	1	yes	characteristic
199	C₄×C₄₇	#533	1	1	yes	characteristic
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	—	47	1	no	—
213	#1776	—	47	2	no	—
214	C₄×#106	—	47	1	no	—
215	C₄×#106	D₄₇	1	1	yes	characteristic, complemented
216	C₂×C₄₇	#2285	1	1	yes	characteristic
217	C₂×C₄₇	#2912	1	1	yes	characteristic
218	C₂×C₄₇	#2912	1	1	yes	characteristic
219	C₂×C₄₇	#3173	1	2	yes	—
220	C₂×C₄₇	#3174	1	2	yes	—
221	D₄₇	—	4	2	no	—
222	C₂²×M₁₆	—	47	1	no	—
223	C₂³×C₈	—	47	1	no	—
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	C₂×D₄₇	1	1	yes	characteristic
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	—	47	2	no	—
244	C₄×C₄⋊C₄	—	47	2	no	—
245	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
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	—	47	1	no	—
252	C₂×M₁₆	—	47	4	no	—
253	C₂×M₁₆	—	94	2	no	—
254	C₂×M₁₆	—	94	2	no	—
255	C₂²×C₈	—	47	1	no	—
256	C₂²×C₈	—	47	1	no	—
257	C₂²×C₈	—	47	4	no	—
258	C₂²×C₈	—	94	2	no	—
259	C₂²×C₈	—	94	2	no	—
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	—	47	1	no	—
273	C₂×C₂²⋊C₄	—	47	1	no	—
274	C₂×C₂²⋊C₄	—	94	2	no	—
275	C₂×C₂²⋊C₄	—	94	2	no	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	—	47	1	no	—
278	C₂×C₄²	—	94	2	no	—
279	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
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	C₄×D₄₇	1	4	yes	—
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	—	47	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	47	1	no	—
300	C₂²×C₄	—	47	1	no	—
301	C₂²×C₄	—	47	1	no	—
302	C₂²×C₄	—	47	2	no	—
303	C₂²×C₄	—	47	2	no	—
304	C₂²×C₄	—	94	1	no	—
305	C₂²×C₄	—	94	1	no	—
306	C₂²×C₄	—	94	1	no	—
307	C₂²×C₄	—	94	1	no	—
308	C₂²×C₄	—	94	2	no	—
309	C₂²×C₄	—	94	2	no	—
310	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
311	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
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	—	47	2	no	—
317	C₂×C₈	—	47	2	no	—
318	C₂×C₈	—	47	2	no	—
319	C₂×C₈	—	47	2	no	—
320	C₂×C₈	—	94	1	no	—
321	C₂×C₈	—	94	1	no	—
322	C₂×C₈	—	94	8	no	—
323	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
324	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
325	C₂×C₈	#10625350	1	2	yes	—
326	C₂×C₈	#10625350	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	—	47	4	no	—
340	C₂²⋊C₄	—	47	4	no	—
341	C₂²⋊C₄	—	376	2	no	—
342	C₂²⋊C₄	—	376	2	no	—
343	C₄²	—	8	2	no	—
344	C₄²	—	47	2	no	—
345	C₄²	—	47	2	no	—
346	C₄²	—	376	2	no	—
347	C₄²	C₂×C₄×D₄₇	1	2	yes	—
348	C₄²	Q₈×D₄₇	1	2	yes	—
349	C₂³	—	47	2	no	—
350	C₂³	—	94	1	no	—
351	C₂³	—	94	1	no	—
352	C₂³	—	94	2	no	—
353	C₂³	—	94	2	no	—
354	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	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	—	4	2	no	—
363	C₂×C₄	—	47	2	no	—
364	C₂×C₄	—	47	2	no	—
365	C₂×C₄	—	47	2	no	—
366	C₂×C₄	—	94	1	no	—
367	C₂×C₄	—	94	1	no	—
368	C₂×C₄	—	94	2	no	—
369	C₂×C₄	—	94	2	no	—
370	C₂×C₄	—	94	2	no	—
371	C₂×C₄	—	94	2	no	—
372	C₂×C₄	—	94	2	no	—
373	C₂×C₄	—	94	2	no	—
374	C₂×C₄	—	188	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	C₄⋊C₄×D₄₇	1	2	yes	—
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×#10625350	1	1	yes	characteristic
387	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
388	C₈	—	2	2	no	—
389	C₈	—	47	4	no	—
390	C₈	—	94	2	no	—
391	C₈	#13093981	1	4	yes	—
392	C₂²	—	94	2	no	—
393	C₂²	—	94	2	no	—
394	C₂²	—	94	2	no	—
395	C₂²	—	188	2	no	—
396	C₂²	—	188	2	no	—
397	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
398	C₂²	#15689670	1	1	yes	characteristic
399	C₂²	#15689670	1	1	yes	characteristic
400	C₂²	#15689929	1	2	yes	—
401	C₂²	#15689930	1	2	yes	—
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	8	2	no	—
405	C₄	—	8	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×#13093981	1	1	yes	characteristic
413	C₄	#15689677	1	1	yes	characteristic
414	C₄	#15689677	1	1	yes	characteristic
415	C₂	—	188	2	no	—
416	C₂	#20245792	1	1	yes	characteristic
417	C₂	#20251979	1	1	yes	characteristic
418	C₂	#20251980	1	1	yes	characteristic
419	C₂	#20254001	1	2	yes	—
420	C₂	#20254012	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×#106×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#106	D₄₇
hypocenter	C₄₇	#20820
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#106

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
9. #20243286	C₂	semidirect
10. C₄×#13093956	C₂	semidirect
11. C₄×#106×C₄₇	C₂	semidirect
19. #15689077	C₄	semidirect
215. C₄×#106	D₄₇	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×#15689077	2
#20245993	2
#20243549	2
#20243543	2
#20243520	2
#20243420	2
#20243410	2
#20243286	2
C₄×#13093956	2
C₄×#106×C₄₇	2
#20820	47