Subgroups — #26112414

Order 12032.

578 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×#15689410	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689188	C₂	1	1	yes	maximal, characteristic
3	#20244350	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243389	C₂	1	1	yes	maximal, characteristic
5	#20241272	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241222	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×#333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₄₇	—	2	1	no	—
9	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
10	#15689410	—	2	2	no	—
11	#15689410	C₄	1	4	yes	complemented
12	#15689188	—	2	2	no	—
13	#15689188	—	2	2	no	—
14	C₂×#13093955	—	2	1	no	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×#13093946	—	2	1	no	—
17	C₂×#13093944	—	2	1	no	—
18	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
19	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	#15688993	C₂²	1	1	yes	characteristic
21	#15688886	—	2	1	no	—
22	#15688885	—	2	1	no	—
23	#15688885	—	2	1	no	—
24	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₄₇×#333	—	2	2	no	—
28	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₄₇	—	2	1	no	—
30	C₂²×C₄₇⋊C₈	—	2	1	no	—
31	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
32	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
33	C₂×C₈×D₄₇	—	2	4	no	—
34	C₂×C₈×D₄₇	—	4	2	no	—
35	C₂×C₈×D₄₇	—	4	2	no	—
36	C₄×D₁₈₈	—	2	1	no	—
37	C₄×D₁₈₈	—	2	1	no	—
38	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
39	C₄×D₁₈₈	D₄	1	2	yes	—
40	C₂×C₄⋊Dic₄₇	—	2	1	no	—
41	C₂×C₄⋊Dic₄₇	—	2	1	no	—
42	C₂×C₄⋊Dic₄₇	—	2	1	no	—
43	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
44	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
45	#13093955	—	2	4	no	—
46	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
47	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
48	#13093946	—	4	2	no	—
49	#13093944	—	2	4	no	—
50	(C₂×D₄₇)⋊C₈	—	2	4	no	—
51	C₄×C₄₇⋊C₈	—	2	1	no	—
52	C₄×C₄₇⋊C₈	—	2	1	no	—
53	C₂²×Q₈×C₄₇	—	2	1	no	—
54	C₂²×C₈×C₄₇	—	2	1	no	—
55	C₂²×C₈×C₄₇	—	2	1	no	—
56	C₄⋊Q₈×C₄₇	—	2	1	no	—
57	C₄⋊Q₈×C₄₇	—	2	1	no	—
58	C₄⋊Q₈×C₄₇	—	2	1	no	—
59	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
62	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₄₇	—	2	1	no	—
64	C₄⋊C₈×C₄₇	—	2	1	no	—
65	C₄⋊C₈×C₄₇	—	2	1	no	—
66	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
67	C₂³×D₄₇	—	2	1	no	—
68	C₂×Q₈×C₄₇	—	2	2	no	—
69	C₂×Q₈×C₄₇	—	4	1	no	—
70	C₂×Q₈×C₄₇	—	8	1	no	—
71	C₂×Q₈×C₄₇	—	8	1	no	—
72	C₂²×C₄×C₄₇	—	4	1	no	—
73	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
76	C₂²×Dic₄₇	—	2	1	no	—
77	C₂²×Dic₄₇	—	4	1	no	—
78	C₂×D₁₈₈	—	2	1	no	—
79	C₂×D₁₈₈	—	2	1	no	—
80	C₂×D₁₈₈	—	2	1	no	—
81	C₂×D₁₈₈	C₂²⋊C₄	1	2	yes	—
82	C₂×D₁₈₈	SD₁₆	1	2	yes	—
83	C₂×D₁₈₈	Q₁₆	1	2	yes	—
84	C₂×C₄×D₄₇	—	2	2	no	—
85	C₂×C₄×D₄₇	—	2	2	no	—
86	C₂×C₄×D₄₇	—	4	1	no	—
87	C₂×C₄×D₄₇	—	4	1	no	—
88	C₂×C₄×D₄₇	—	4	1	no	—
89	C₂×C₄×D₄₇	—	4	1	no	—
90	C₂×C₈×C₄₇	—	2	2	no	—
91	C₂×C₈×C₄₇	—	4	1	no	—
92	C₂×C₈×C₄₇	—	4	1	no	—
93	C₂×C₈×C₄₇	—	4	1	no	—
94	C₂×C₈×C₄₇	—	4	1	no	—
95	C₂×C₈×C₄₇	—	4	1	no	—
96	C₄⋊C₄×C₄₇	—	2	2	no	—
97	C₄⋊C₄×C₄₇	—	2	2	no	—
98	C₄⋊C₄×C₄₇	—	4	1	no	—
99	C₄⋊C₄×C₄₇	—	4	1	no	—
100	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₄₇	#41	1	1	yes	characteristic
104	(C₂×D₄₇)⋊C₄	—	2	2	no	—
105	(C₂×D₄₇)⋊C₄	—	2	2	no	—
106	C₄⋊Dic₄₇	—	2	1	no	—
107	C₄⋊Dic₄₇	—	4	1	no	—
108	C₄⋊Dic₄₇	—	4	1	no	—
109	C₄⋊Dic₄₇	—	4	1	no	—
110	C₄⋊Dic₄₇	—	4	1	no	—
111	C₄⋊Dic₄₇	—	8	1	no	—
112	C₄⋊Dic₄₇	C₂²⋊C₄	1	2	yes	—
113	C₂×C₄₇⋊C₈	—	2	1	no	—
114	C₂×C₄₇⋊C₈	—	2	1	no	—
115	C₂×C₄₇⋊C₈	—	2	2	no	—
116	C₂×C₄₇⋊C₈	—	2	1	no	—
117	C₂×C₄₇⋊C₈	—	2	1	no	—
118	C₂×C₄₇⋊C₈	—	2	1	no	—
119	C₂×C₄₇⋊C₈	—	4	1	no	—
120	C₂×C₄₇⋊C₈	—	4	1	no	—
121	C₂×C₄₇⋊C₈	SD₁₆	1	2	yes	—
122	C₈×D₄₇	—	4	8	no	—
123	C₂³×C₄₇	#121	1	1	yes	characteristic
124	C₂²×D₄₇	—	2	2	no	—
125	C₂²×D₄₇	—	2	2	no	—
126	C₂²×D₄₇	—	2	2	no	—
127	C₂²×D₄₇	—	4	1	no	—
128	C₂²×D₄₇	—	4	1	no	—
129	C₂²×D₄₇	—	4	1	no	—
130	C₂²×D₄₇	—	4	1	no	—
131	Q₈×C₄₇	—	8	2	no	—
132	Q₈×C₄₇	—	8	2	no	—
133	C₂×C₄×C₄₇	—	2	1	no	—
134	C₂×C₄×C₄₇	—	2	1	no	—
135	C₂×C₄×C₄₇	—	4	2	no	—
136	C₂×C₄×C₄₇	—	8	1	no	—
137	C₂×C₄×C₄₇	—	8	1	no	—
138	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
142	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
143	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
150	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
152	C₂×Dic₄₇	—	2	2	no	—
153	C₂×Dic₄₇	—	4	1	no	—
154	C₂×Dic₄₇	—	4	1	no	—
155	C₂×Dic₄₇	—	8	1	no	—
156	C₂×Dic₄₇	—	8	1	no	—
157	C₂×Dic₄₇	—	8	1	no	—
158	D₁₈₈	—	2	2	no	—
159	D₁₈₈	—	2	2	no	—
160	D₁₈₈	—	2	2	no	—
161	D₁₈₈	#103	1	4	yes	—
162	C₄×D₄₇	—	4	2	no	—
163	C₄×D₄₇	—	4	2	no	—
164	C₄×D₄₇	—	4	2	no	—
165	C₄×D₄₇	—	4	2	no	—
166	C₈×C₄₇	—	4	2	no	—
167	C₈×C₄₇	—	8	1	no	—
168	C₄₇⋊C₈	—	2	2	no	—
169	C₄₇⋊C₈	—	4	2	no	—
170	C₄₇⋊C₈	—	4	1	no	—
171	#9215	—	47	1	no	maximal, Sylow
172	C₂²×C₄₇	#386	1	1	yes	characteristic
173	C₂²×C₄₇	#461	1	1	yes	characteristic
174	C₂²×C₄₇	#463	1	1	yes	characteristic
175	C₂²×C₄₇	#465	1	1	yes	characteristic
176	C₂²×C₄₇	#467	1	1	yes	characteristic
177	C₂²×C₄₇	#471	1	1	yes	characteristic
178	C₂²×C₄₇	#472	1	1	yes	characteristic
179	C₂×D₄₇	—	2	4	no	—
180	C₂×D₄₇	—	4	2	no	—
181	C₂×D₄₇	—	4	2	no	—
182	C₂×D₄₇	—	4	2	no	—
183	C₂×D₄₇	—	4	2	no	—
184	C₂×D₄₇	—	4	2	no	—
185	C₂×D₄₇	—	4	2	no	—
186	C₄×C₄₇	—	2	1	no	—
187	C₄×C₄₇	—	2	1	no	—
188	C₄×C₄₇	—	8	2	no	—
189	C₄×C₄₇	C₂×#103	1	1	yes	characteristic
190	C₄×C₄₇	#416	1	1	yes	characteristic
191	C₄×C₄₇	C₄×SD₁₆	1	1	yes	characteristic
192	C₄×C₄₇	#440	1	1	yes	characteristic
193	C₄×C₄₇	#450	1	1	yes	characteristic
194	C₄×C₄₇	#452	1	1	yes	characteristic
195	C₄×C₄₇	#465	1	1	yes	characteristic
196	C₄×C₄₇	#467	1	1	yes	characteristic
197	Dic₄₇	—	4	2	no	—
198	Dic₄₇	—	16	1	no	—
199	C₂×#476	—	47	1	no	—
200	C₂×C₈×D₄	—	47	1	no	—
201	#1990	—	47	1	no	—
202	#1802	—	47	1	no	—
203	C₂×#333	D₄₇	1	1	yes	characteristic, complemented
204	#1296	—	47	1	no	—
205	#1277	—	47	1	no	—
206	C₂×C₄₇	#1671	1	1	yes	characteristic
207	C₂×C₄₇	#1675	1	1	yes	characteristic
208	C₂×C₄₇	#1677	1	1	yes	characteristic
209	C₂×C₄₇	#1683	1	1	yes	characteristic
210	C₂×C₄₇	#1877	1	1	yes	characteristic
211	C₂×C₄₇	#1892	1	1	yes	characteristic
212	C₂×C₄₇	#1907	1	1	yes	characteristic
213	D₄₇	—	4	4	no	—
214	C₂³×C₈	—	94	1	no	—
215	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
216	C₂×C₄×D₄	—	47	1	no	—
217	#476	—	47	4	no	—
218	#476	—	94	2	no	—
219	C₈×D₄	—	94	2	no	—
220	C₈×D₄	—	94	2	no	—
221	C₂×#106	—	94	1	no	—
222	C₂×C₄⋊C₈	—	47	1	no	—
223	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
225	C₂×#102	—	94	1	no	—
226	C₂×#102	—	94	1	no	—
227	C₂×C₂²⋊C₈	—	94	1	no	—
228	C₂×C₄×C₈	—	47	1	no	—
229	#384	—	47	1	no	—
230	#340	—	94	1	no	—
231	#340	—	94	1	no	—
232	#340	—	94	1	no	—
233	#333	—	2	2	no	—
234	C₄₇	#9215	1	1	yes	characteristic, complemented, Sylow
235	C₂²×Q₈	—	2	1	no	—
236	C₂²×D₄	—	47	1	no	—
237	C₂³×C₄	—	94	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	47	1	no	—
241	C₂²×C₈	—	47	1	no	—
242	C₂²×C₈	—	94	4	no	—
243	C₂²×C₈	—	94	1	no	—
244	C₂²×C₈	—	188	2	no	—
245	C₂²×C₈	—	188	2	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	C₄×D₄₇	1	2	yes	—
250	C₄×D₄	—	47	2	no	—
251	C₄×D₄	—	47	2	no	—
252	C₄×D₄	—	94	1	no	—
253	C₄×D₄	—	94	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	47	1	no	—
257	C₂×C₄⋊C₄	—	94	1	no	—
258	C₂×C₄⋊C₄	—	94	1	no	—
259	C₂×C₄⋊C₄	—	94	1	no	—
260	C₂×C₂²⋊C₄	—	94	1	no	—
261	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
262	#106	—	94	4	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	47	2	no	—
267	C₄⋊C₈	—	94	1	no	—
268	C₄⋊C₈	C₂²⋊D₄₇	1	2	yes	—
269	#102	—	94	4	no	—
270	#102	—	188	2	no	—
271	C₂²⋊C₈	—	94	4	no	—
272	C₄×C₈	—	94	1	no	—
273	C₄×C₈	—	94	1	no	—
274	C₂⁴	—	94	1	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	4	1	no	—
277	C₂×Q₈	—	8	1	no	—
278	C₂×Q₈	—	8	1	no	—
279	C₂×D₄	—	47	2	no	—
280	C₂×D₄	—	47	2	no	—
281	C₂×D₄	—	47	2	no	—
282	C₂×D₄	—	94	1	no	—
283	C₂×D₄	—	94	1	no	—
284	C₂×D₄	—	94	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	94	1	no	—
287	C₂²×C₄	—	94	2	no	—
288	C₂²×C₄	—	94	2	no	—
289	C₂²×C₄	—	188	1	no	—
290	C₂²×C₄	—	188	1	no	—
291	C₂²×C₄	—	188	1	no	—
292	C₂²×C₄	—	188	1	no	—
293	C₂²×C₄	—	188	1	no	—
294	C₂²×C₄	#10625350	1	1	yes	characteristic
295	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
296	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	4	1	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	47	2	no	—
304	C₂×C₈	—	94	1	no	—
305	C₂×C₈	—	94	1	no	—
306	C₂×C₈	—	94	2	no	—
307	C₂×C₈	—	94	1	no	—
308	C₂×C₈	—	94	1	no	—
309	C₂×C₈	—	94	1	no	—
310	C₂×C₈	—	188	8	no	—
311	C₂×C₈	—	188	1	no	—
312	C₂×C₈	—	188	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	47	2	no	—
318	C₄⋊C₄	—	94	1	no	—
319	C₄⋊C₄	—	376	1	no	—
320	C₄⋊C₄	—	188	1	no	—
321	C₄⋊C₄	—	188	1	no	—
322	C₄⋊C₄	—	188	1	no	—
323	C₄⋊C₄	—	188	1	no	—
324	C₂²⋊C₄	—	94	2	no	—
325	C₂²⋊C₄	—	94	2	no	—
326	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
327	C₄²	D₄×D₄₇	1	1	yes	characteristic
328	C₄²	#10625352	1	1	yes	characteristic
329	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
330	C₂³	—	94	2	no	—
331	C₂³	—	94	2	no	—
332	C₂³	—	94	2	no	—
333	C₂³	—	188	1	no	—
334	C₂³	—	188	1	no	—
335	C₂³	—	188	1	no	—
336	C₂³	—	188	1	no	—
337	C₂³	#13093997	1	1	yes	characteristic
338	Q₈	—	8	2	no	—
339	Q₈	—	8	2	no	—
340	D₄	—	47	4	no	—
341	D₄	—	94	2	no	—
342	D₄	—	94	2	no	—
343	D₄	—	94	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	8	1	no	—
348	C₂×C₄	—	8	1	no	—
349	C₂×C₄	—	94	2	no	—
350	C₂×C₄	—	376	1	no	—
351	C₂×C₄	—	376	1	no	—
352	C₂×C₄	—	376	1	no	—
353	C₂×C₄	—	188	1	no	—
354	C₂×C₄	—	188	1	no	—
355	C₂×C₄	—	188	2	no	—
356	C₂×C₄	—	188	2	no	—
357	C₂×C₄	—	188	2	no	—
358	C₂×C₄	—	188	2	no	—
359	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
360	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
361	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
362	C₂×C₄	#13093992	1	1	yes	characteristic
363	C₂×C₄	#13093995	1	1	yes	characteristic
364	C₂×C₄	#13094006	1	1	yes	characteristic
365	C₂×C₄	SD₁₆×D₄₇	1	1	yes	characteristic
366	C₂×C₄	SD₁₆×D₄₇	1	1	yes	characteristic
367	C₂×C₄	Q₁₆×D₄₇	1	1	yes	characteristic
368	C₂×C₄	#13094045	1	1	yes	characteristic
369	C₂×C₄	#13094047	1	1	yes	characteristic
370	C₂×C₄	#13094047	1	1	yes	characteristic
371	C₂×C₄	#13094051	1	1	yes	characteristic
372	C₂×C₄	#13094056	1	1	yes	characteristic
373	C₈	—	4	2	no	—
374	C₈	—	8	1	no	—
375	C₈	—	94	2	no	—
376	C₈	—	188	1	no	—
377	C₈	—	188	2	no	—
378	C₂²	—	94	4	no	—
379	C₂²	—	188	2	no	—
380	C₂²	—	188	2	no	—
381	C₂²	—	188	2	no	—
382	C₂²	—	188	2	no	—
383	C₂²	—	188	2	no	—
384	C₂²	—	188	2	no	—
385	C₂²	#15688999	1	1	yes	characteristic
386	C₂²	#15689327	1	1	yes	characteristic
387	C₂²	#15689341	1	1	yes	characteristic
388	C₂²	#15689355	1	1	yes	characteristic
389	C₂²	#15689363	1	1	yes	characteristic
390	C₂²	#15689385	1	1	yes	characteristic
391	C₂²	#15689392	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	8	2	no	—
395	C₄	—	188	2	no	—
396	C₄	—	752	1	no	—
397	C₄	#103×D₄₇	1	1	yes	characteristic
398	C₄	#15689118	1	1	yes	characteristic
399	C₄	#15689208	1	1	yes	characteristic
400	C₄	#15689226	1	1	yes	characteristic
401	C₄	#15689272	1	1	yes	characteristic
402	C₄	#15689284	1	1	yes	characteristic
403	C₄	#15689349	1	1	yes	characteristic
404	C₄	#15689361	1	1	yes	characteristic
405	C₂	—	188	4	no	—
406	C₂	#20242766	1	1	yes	characteristic
407	C₂	#20242786	1	1	yes	characteristic
408	C₂	#20242800	1	1	yes	characteristic
409	C₂	#20242842	1	1	yes	characteristic
410	C₂	#20243719	1	1	yes	characteristic
411	C₂	#20243808	1	1	yes	characteristic
412	C₂	#20243893	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093997
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄₇×#333	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂²×D₁₈₈	D₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#333	D₄₇
hypocenter	C₄₇	#9215
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

Complements

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

N	H ≅ G/N	type
3. #20244350	C₂	semidirect
5. #20241272	C₂	semidirect
6. #20241222	C₂	semidirect
7. C₂×C₄₇×#333	C₂	semidirect
11. #15689410	C₄	semidirect
203. C₂×#333	D₄₇	semidirect
234. C₄₇	#9215	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689410	2
C₂×#15689188	2
#20244350	2
#20243389	2
#20241272	2
#20241222	2
C₂×C₄₇×#333	2
#9215	47