Subgroups — #26123580

Order 12032.

910 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	C₂²×#13093958	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689124	C₂	1	2	yes	maximal
3	C₂×#15688891	C₂	1	2	yes	maximal, complemented
4	C₂×#15688888	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₇×#408	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂×#13093958	—	2	4	no	—
9	C₂×#13093958	—	2	2	no	—
10	#15689124	—	2	4	no	—
11	#15689124	—	2	4	no	—
12	C₂×#13093948	—	2	2	no	—
13	C₂×#13093945	—	2	2	no	—
14	#15688891	—	2	4	no	—
15	#15688888	—	2	2	no	—
16	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#408	—	2	2	no	—
20	C₄₇×#408	C₄	1	4	yes	complemented
21	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
22	C₂³×Dic₄₇	—	2	2	no	—
23	C₂×#10625329	—	2	2	no	—
24	C₂×#10625329	—	2	2	no	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	D₄	1	4	yes	—
29	C₂²×C₄₇⋊C₈	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	2	no	—
33	C₂×C₄⋊Dic₄₇	—	2	2	no	—
34	C₂×C₄⋊Dic₄₇	—	2	2	no	—
35	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
36	#13093958	—	2	8	no	—
37	#13093948	—	2	8	no	—
38	#13093945	—	2	8	no	—
39	C₂×#41×C₄₇	—	2	1	no	—
40	C₂×#41×C₄₇	—	2	1	no	—
41	C₂×#41×C₄₇	—	2	2	no	—
42	C₂×#41×C₄₇	—	2	2	no	—
43	C₂×#41×C₄₇	—	2	2	no	—
44	C₂×#41×C₄₇	—	2	2	no	—
45	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
46	C₂×#41×C₄₇	Q₈	1	2	yes	—
47	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₄₇	—	2	1	no	—
49	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	—	2	1	no	—
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₄₇	—	2	1	no	—
53	C₂×M₁₆×C₄₇	—	2	2	no	—
54	C₂×M₁₆×C₄₇	—	2	2	no	—
55	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
56	C₂²×C₈×C₄₇	—	2	2	no	—
57	C₂²×C₈×C₄₇	—	2	2	no	—
58	C₂²×C₈×C₄₇	—	2	1	no	—
59	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
60	C₂²×C₈×C₄₇	D₄	1	2	yes	—
61	C₂²×C₈×C₄₇	D₄	1	2	yes	—
62	C₂²⋊C₈×C₄₇	—	2	8	no	—
63	C₂⁴×C₄₇	—	2	1	no	—
64	C₂⁴×C₄₇	#41	1	1	yes	characteristic
65	#41×C₄₇	—	2	4	no	—
66	#41×C₄₇	—	2	4	no	—
67	#41×C₄₇	—	2	4	no	—
68	#41×C₄₇	—	2	4	no	—
69	#41×C₄₇	—	4	2	no	—
70	#41×C₄₇	—	4	2	no	—
71	#41×C₄₇	—	4	2	no	—
72	#41×C₄₇	—	4	2	no	—
73	C₂×Q₈×C₄₇	—	2	1	no	—
74	C₂×Q₈×C₄₇	—	2	2	no	—
75	C₂×Q₈×C₄₇	—	2	2	no	—
76	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
77	C₂×D₄×C₄₇	—	2	2	no	—
78	C₂×D₄×C₄₇	—	2	2	no	—
79	C₂×D₄×C₄₇	—	2	2	no	—
80	C₂×D₄×C₄₇	—	2	1	no	—
81	C₂×D₄×C₄₇	—	2	2	no	—
82	C₂×D₄×C₄₇	—	4	2	no	—
83	C₂×D₄×C₄₇	—	4	2	no	—
84	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
85	C₂²×C₄×C₄₇	—	2	1	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	4	1	no	—
89	C₂²×C₄×C₄₇	—	4	1	no	—
90	C₂²×C₄×C₄₇	—	4	1	no	—
91	C₂²×C₄×C₄₇	—	4	1	no	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	#41	1	2	yes	—
100	C₂²×C₄×C₄₇	#41	1	2	yes	—
101	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
102	C₂²×Dic₄₇	—	2	4	no	—
103	C₂²×Dic₄₇	—	4	2	no	—
104	C₂²×Dic₄₇	—	4	2	no	—
105	C₂²×Dic₄₇	—	8	4	no	—
106	M₁₆×C₄₇	—	2	4	no	—
107	M₁₆×C₄₇	—	4	2	no	—
108	C₂×C₈×C₄₇	—	2	4	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	4	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	4	1	no	—
114	C₂×C₈×C₄₇	—	4	1	no	—
115	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
116	C₄⋊Dic₄₇	—	2	4	no	—
117	C₄⋊Dic₄₇	—	2	4	no	—
118	C₄⋊Dic₄₇	—	4	2	no	—
119	C₄⋊Dic₄₇	—	4	2	no	—
120	#10625329	—	2	4	no	—
121	#10625329	—	2	4	no	—
122	#10625329	—	4	2	no	—
123	#10625329	—	4	2	no	—
124	C₂×C₄₇⋊C₈	—	2	4	no	—
125	C₂×C₄₇⋊C₈	—	4	2	no	—
126	C₂×C₄₇⋊C₈	—	4	2	no	—
127	C₂³×C₄₇	—	2	2	no	—
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	—	2	2	no	—
130	C₂³×C₄₇	—	4	1	no	—
131	C₂³×C₄₇	—	4	1	no	—
132	C₂³×C₄₇	—	4	2	no	—
133	C₂³×C₄₇	—	4	2	no	—
134	C₂³×C₄₇	#117	1	1	yes	characteristic
135	C₂³×C₄₇	#121	1	2	yes	—
136	C₂³×C₄₇	#121	1	1	yes	characteristic
137	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
138	C₂³×C₄₇	#126	1	2	yes	—
139	Q₈×C₄₇	—	2	4	no	—
140	Q₈×C₄₇	—	4	2	no	—
141	D₄×C₄₇	—	2	4	no	—
142	D₄×C₄₇	—	4	4	no	—
143	D₄×C₄₇	—	4	4	no	—
144	D₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	4	1	no	—
147	C₂×C₄×C₄₇	—	4	1	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×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
155	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
156	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
157	C₂×C₄×C₄₇	#120	1	2	yes	—
158	C₂×C₄×C₄₇	#121	1	2	yes	—
159	C₂×C₄×C₄₇	#121	1	2	yes	—
160	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
162	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
163	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
164	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
165	C₂×C₄×C₄₇	#123	1	2	yes	—
166	C₂×C₄×C₄₇	#123	1	2	yes	—
167	C₂×C₄×C₄₇	#124	1	2	yes	—
168	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
169	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
170	C₂×Dic₄₇	—	4	4	no	—
171	C₂×Dic₄₇	—	8	4	no	—
172	C₂×Dic₄₇	—	8	4	no	—
173	C₂×Dic₄₇	—	8	4	no	—
174	C₈×C₄₇	—	2	4	no	—
175	C₈×C₄₇	—	4	2	no	—
176	C₄₇⋊C₈	—	4	4	no	—
177	#11107	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	—	2	2	no	—
179	C₂²×C₄₇	—	2	2	no	—
180	C₂²×C₄₇	—	2	4	no	—
181	C₂²×C₄₇	—	2	2	no	—
182	C₂²×C₄₇	—	2	2	no	—
183	C₂²×C₄₇	—	4	4	no	—
184	C₂²×C₄₇	—	4	2	no	—
185	C₂²×C₄₇	—	8	2	no	—
186	C₂²×C₄₇	—	8	1	no	—
187	C₂²×C₄₇	—	8	1	no	—
188	C₂²×C₄₇	#380	1	1	yes	characteristic
189	C₂²×C₄₇	#388	1	2	yes	—
190	C₂²×C₄₇	#392	1	1	yes	characteristic
191	C₂²×C₄₇	#396	1	2	yes	—
192	C₂²×C₄₇	#397	1	1	yes	characteristic
193	C₂²×C₄₇	#472	1	2	yes	—
194	C₂²×C₄₇	#473	1	2	yes	—
195	C₄×C₄₇	—	4	2	no	—
196	C₄×C₄₇	#385	1	2	yes	—
197	C₄×C₄₇	#386	1	1	yes	characteristic
198	C₄×C₄₇	#390	1	1	yes	characteristic
199	C₄×C₄₇	#393	1	1	yes	characteristic
200	C₄×C₄₇	#394	1	2	yes	—
201	C₄×C₄₇	#399	1	1	yes	characteristic
202	Dic₄₇	—	8	4	no	—
203	C₂²×#107	—	47	1	no	—
204	C₂×#417	—	47	2	no	—
205	C₂×#408	D₄₇	1	1	yes	characteristic
206	C₂×#343	—	47	2	no	—
207	C₂×#341	—	47	1	no	—
208	C₂×C₄₇	—	2	2	no	—
209	C₂×C₄₇	—	2	2	no	—
210	C₂×C₄₇	—	8	2	no	—
211	C₂×C₄₇	#1439	1	1	yes	characteristic
212	C₂×C₄₇	#1816	1	2	yes	—
213	C₂×C₄₇	#2018	1	1	yes	characteristic
214	C₂×C₄₇	#2020	1	1	yes	characteristic
215	C₂×C₄₇	#2078	1	2	yes	—
216	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
217	C₂²×M₁₆	—	47	2	no	—
218	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
219	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
220	C₂²×C₄⋊C₄	—	47	2	no	—
221	C₂×#107	—	94	4	no	—
222	C₂×#107	—	94	2	no	—
223	#417	—	94	4	no	—
224	#417	—	94	4	no	—
225	C₂×#103	—	94	2	no	—
226	C₂×#102	—	94	2	no	—
227	#408	—	2	2	no	—
228	#408	Dic₄₇	1	4	yes	complemented
229	C₂×C₂²⋊C₈	—	2	2	no	—
230	#343	—	94	4	no	—
231	#341	—	94	2	no	—
232	C₄₇	#11107	1	1	yes	characteristic, complemented, Sylow
233	C₂×#41	—	2	1	no	—
234	C₂×#41	—	2	1	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	—	2	2	no	—
237	C₂×#41	—	2	2	no	—
238	C₂×#41	—	2	2	no	—
239	C₂×#41	Dic₉₄	1	2	yes	—
240	C₂×#41	C₂×Dic₄₇	1	2	yes	—
241	C₂²×Q₈	D₁₈₈	1	1	yes	characteristic
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	D₁₈₈	1	1	yes	characteristic
244	C₂³×C₄	—	2	1	no	—
245	C₂³×C₄	—	94	2	no	—
246	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	47	4	no	—
251	C₂×M₁₆	—	94	2	no	—
252	C₂×M₁₆	—	94	2	no	—
253	C₂×M₁₆	—	94	2	no	—
254	C₂×M₁₆	—	94	2	no	—
255	C₂×M₁₆	—	94	2	no	—
256	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	—	2	2	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	94	2	no	—
261	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
262	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
263	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
264	C₂×C₄⋊C₄	—	47	4	no	—
265	C₂×C₄⋊C₄	—	94	2	no	—
266	C₂×C₄⋊C₄	—	94	2	no	—
267	C₂×C₄⋊C₄	—	94	2	no	—
268	C₂×C₄⋊C₄	—	94	2	no	—
269	C₂×C₄⋊C₄	—	94	2	no	—
270	#107	—	94	8	no	—
271	#103	—	94	8	no	—
272	#102	—	94	8	no	—
273	C₂²⋊C₈	—	2	8	no	—
274	C₂⁴	—	2	1	no	—
275	C₂⁴	#10625350	1	1	yes	characteristic
276	#41	—	2	4	no	—
277	#41	—	2	4	no	—
278	#41	—	2	4	no	—
279	#41	—	2	4	no	—
280	#41	—	4	2	no	—
281	#41	—	4	2	no	—
282	#41	—	4	2	no	—
283	#41	—	4	2	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	C₄⋊Dic₄₇	1	2	yes	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	C₄⋊Dic₄₇	1	2	yes	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	94	4	no	—
304	C₂²×C₄	—	376	4	no	—
305	C₂²×C₄	—	188	2	no	—
306	C₂²×C₄	—	188	2	no	—
307	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
309	C₂²×C₄	#10625350	1	1	yes	characteristic
310	C₂²×C₄	D₄×D₄₇	1	2	yes	—
311	C₂²×C₄	D₄×D₄₇	1	2	yes	—
312	C₂²×C₄	#10625352	1	2	yes	—
313	C₂²×C₄	#10625352	1	2	yes	—
314	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
317	M₁₆	—	2	4	no	—
318	M₁₆	—	4	2	no	—
319	M₁₆	—	94	4	no	—
320	M₁₆	—	94	4	no	—
321	M₁₆	—	188	2	no	—
322	M₁₆	—	188	2	no	—
323	C₂×C₈	—	2	4	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	4	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	94	4	no	—
331	C₂×C₈	—	188	2	no	—
332	C₂×C₈	—	188	2	no	—
333	C₂×C₈	C₂²⋊Dic₄₇	1	4	yes	—
334	C₄⋊C₄	—	94	4	no	—
335	C₄⋊C₄	—	94	4	no	—
336	C₄⋊C₄	—	188	2	no	—
337	C₄⋊C₄	—	188	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	4	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	#13093983	1	1	yes	characteristic
346	C₂³	#13093997	1	2	yes	—
347	C₂³	#13093998	1	1	yes	characteristic
348	C₂³	#13094003	1	1	yes	characteristic
349	C₂³	#13094017	1	2	yes	—
350	Q₈	—	2	4	no	—
351	Q₈	—	4	2	no	—
352	D₄	—	2	4	no	—
353	D₄	—	4	4	no	—
354	D₄	—	4	4	no	—
355	D₄	—	4	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	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	—	376	4	no	—
364	C₂×C₄	—	376	4	no	—
365	C₂×C₄	—	376	4	no	—
366	C₂×C₄	—	188	4	no	—
367	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
368	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
369	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
370	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
371	C₂×C₄	#13093992	1	1	yes	characteristic
372	C₂×C₄	#13093994	1	2	yes	—
373	C₂×C₄	#13093995	1	2	yes	—
374	C₂×C₄	#13093996	1	2	yes	—
375	C₂×C₄	#13093998	1	1	yes	characteristic
376	C₂×C₄	#13094001	1	2	yes	—
377	C₂×C₄	#13094001	1	2	yes	—
378	C₂×C₄	#13094003	1	1	yes	characteristic
379	C₂×C₄	#13094005	1	1	yes	characteristic
380	C₂×C₄	#13094006	1	2	yes	—
381	C₂×C₄	#13094008	1	2	yes	—
382	C₂×C₄	#13094010	1	2	yes	—
383	C₂×C₄	#13094011	1	1	yes	characteristic
384	C₂×C₄	#13094020	1	1	yes	characteristic
385	C₈	—	2	4	no	—
386	C₈	—	4	2	no	—
387	C₈	—	188	4	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	8	1	no	—
397	C₂²	—	8	2	no	—
398	C₂²	#15688983	1	1	yes	characteristic
399	C₂²	#15689016	1	2	yes	—
400	C₂²	#15689032	1	1	yes	characteristic
401	C₂²	#15689046	1	2	yes	—
402	C₂²	#15689048	1	1	yes	characteristic
403	C₂²	#15689393	1	2	yes	—
404	C₂²	#15689398	1	2	yes	—
405	C₄	—	4	2	no	—
406	C₄	—	376	4	no	—
407	C₄	#15688998	1	2	yes	—
408	C₄	#15689003	1	1	yes	characteristic
409	C₄	#15689026	1	1	yes	characteristic
410	C₄	#15689035	1	1	yes	characteristic
411	C₄	#15689039	1	2	yes	—
412	C₄	#15689059	1	1	yes	characteristic
413	C₂	—	2	2	no	—
414	C₂	—	2	2	no	—
415	C₂	—	8	2	no	—
416	C₂	#20241633	1	1	yes	characteristic
417	C₂	#20243452	1	2	yes	—
418	C₂	#20244497	1	1	yes	characteristic
419	C₂	#20244509	1	1	yes	characteristic
420	C₂	#20244828	1	2	yes	—

	subgroup	G/H
center	C₂³	#13093998
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#408	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#408	D₄₇
hypocenter	C₄₇	#11107
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#408

Complements

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

N	H ≅ G/N	type
1. C₂²×#13093958	C₂	semidirect
3. C₂×#15688891	C₂	semidirect
4. C₂×#15688888	C₂	semidirect
20. C₄₇×#408	C₄	semidirect
228. #408	Dic₄₇	semidirect
232. C₄₇	#11107	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13093958	2
C₂×#15689124	2
C₂×#15688891	2
C₂×#15688888	2
C₂×C₄₇×#408	2
#11107	47