Subgroups — #26230225

Order 12032.

722 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	#20246656	C₂	1	1	yes	maximal, characteristic
2	#20244322	C₂	1	2	yes	maximal, complemented
3	#20244103	C₂	1	2	yes	maximal, complemented
4	#20243946	C₂	1	2	yes	maximal, complemented
5	#20243942	C₂	1	2	yes	maximal, complemented
6	#20243570	C₂	1	2	yes	maximal
7	#20243162	C₂	1	2	yes	maximal
8	#20243085	C₂	1	1	yes	maximal, characteristic
9	C₄₇×#1798	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
13	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
14	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
15	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
16	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
17	#15689062	C₄	1	1	yes	characteristic
18	#15689059	C₄	1	1	yes	characteristic
19	#15689056	C₄	1	2	yes	—
20	#15689046	C₄	1	2	yes	—
21	#15689043	C₄	1	1	yes	characteristic
22	#15689035	C₄	1	1	yes	characteristic
23	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
24	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
26	#15688878	C₂²	1	2	yes	—
27	#15688878	C₂²	1	2	yes	—
28	#15688877	C₂²	1	2	yes	—
29	#15688877	C₂²	1	2	yes	—
30	#15688877	C₂²	1	2	yes	—
31	#15688877	C₂²	1	2	yes	—
32	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
36	C₄₇×#336	C₂²	1	2	yes	—
37	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
38	C₂×#10625329	—	2	2	no	—
39	C₂×#10625329	—	4	1	no	—
40	C₂×#10625329	—	4	1	no	—
41	C₂²×C₄₇⋊C₈	—	4	1	no	—
42	C₂²×C₄₇⋊C₈	—	4	1	no	—
43	C₂²×C₄₇⋊C₈	Q₈	1	4	yes	complemented
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	C₄×Dic₉₄	—	4	1	no	—
47	C₄×Dic₉₄	—	4	1	no	—
48	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
56	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
57	Dic₄₇⋊C₈	—	4	2	no	—
58	Dic₄₇⋊C₈	—	4	2	no	—
59	C₈×Dic₄₇	—	4	2	no	—
60	C₈×Dic₄₇	—	4	2	no	—
61	C₄₇⋊#95	C₂×C₄	1	2	yes	—
62	C₄₇⋊#95	C₂×C₄	1	2	yes	—
63	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
64	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
65	C₄₇⋊#95	C₂×C₄	1	2	yes	—
66	C₄₇⋊#95	C₂×C₄	1	2	yes	—
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
69	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
70	#117×C₄₇	—	4	1	no	—
71	#117×C₄₇	—	4	1	no	—
72	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₄₇	—	4	1	no	—
79	C₄⋊C₈×C₄₇	—	4	1	no	—
80	C₂²⋊C₈×C₄₇	—	2	4	no	—
81	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	—	2	1	no	—
83	C₂²×C₄×C₄₇	—	2	1	no	—
84	C₂²×C₄×C₄₇	—	2	1	no	—
85	C₂²×C₄×C₄₇	—	2	1	no	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₄₇	#41	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
98	C₂×Dic₉₄	—	2	4	no	—
99	C₂×Dic₉₄	—	4	1	no	—
100	C₂×C₈×C₄₇	—	2	2	no	—
101	C₂×C₈×C₄₇	—	2	2	no	—
102	C₂×C₈×C₄₇	—	2	2	no	—
103	C₂×C₈×C₄₇	—	2	2	no	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₄⋊C₄×C₄₇	—	4	1	no	—
107	C₄⋊C₄×C₄₇	—	4	1	no	—
108	C₂²⋊C₄×C₄₇	—	4	1	no	—
109	C₂²⋊C₄×C₄₇	—	4	1	no	—
110	C₄²×C₄₇	—	2	1	no	—
111	C₄²×C₄₇	—	2	1	no	—
112	C₄²×C₄₇	—	2	1	no	—
113	C₄²×C₄₇	—	2	1	no	—
114	C₂²⋊Dic₄₇	—	2	4	no	—
115	C₂²⋊Dic₄₇	—	2	4	no	—
116	C₄⋊Dic₄₇	—	2	4	no	—
117	C₄⋊Dic₄₇	—	4	1	no	—
118	Dic₄₇⋊C₄	—	2	4	no	—
119	Dic₄₇⋊C₄	—	2	4	no	—
120	Dic₄₇⋊C₄	—	4	2	no	—
121	C₄×Dic₄₇	—	2	2	no	—
122	C₄×Dic₄₇	—	2	2	no	—
123	C₄×Dic₄₇	—	2	2	no	—
124	C₄×Dic₄₇	—	2	2	no	—
125	#10625329	—	4	4	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	—	4	4	no	—
132	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
133	C₂³×C₄₇	—	2	1	no	—
134	C₂³×C₄₇	—	2	1	no	—
135	C₂³×C₄₇	—	2	2	no	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
138	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	—	2	1	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
154	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
157	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
158	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
159	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
160	C₂×Dic₄₇	—	2	2	no	—
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	2	2	no	—
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	—	2	2	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	#131	1	4	yes	—
171	C₂×Dic₄₇	#131	1	4	yes	—
172	Dic₉₄	—	4	4	no	—
173	C₈×C₄₇	—	4	2	no	—
174	C₈×C₄₇	—	4	2	no	—
175	C₄₇⋊C₈	—	2	4	no	—
176	C₄₇⋊C₈	—	4	2	no	—
177	#22288	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	—	2	2	no	—
179	C₂²×C₄₇	—	2	4	no	—
180	C₂²×C₄₇	—	4	1	no	—
181	C₂²×C₄₇	—	4	1	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
184	C₂²×C₄₇	#518	1	1	yes	characteristic
185	C₂²×C₄₇	#520	1	1	yes	characteristic
186	C₂²×C₄₇	C₂×#131	1	2	yes	—
187	C₂²×C₄₇	C₂×#131	1	2	yes	—
188	C₄×C₄₇	—	2	2	no	—
189	C₄×C₄₇	—	4	1	no	—
190	C₄×C₄₇	—	4	1	no	—
191	C₄×C₄₇	—	4	1	no	—
192	C₄×C₄₇	—	4	1	no	—
193	C₄×C₄₇	#538	1	1	yes	characteristic
194	C₄×C₄₇	#539	1	1	yes	characteristic
195	C₄×C₄₇	#543	1	1	yes	characteristic
196	C₄×C₄₇	#544	1	1	yes	characteristic
197	Dic₄₇	—	2	4	no	—
198	Dic₄₇	—	2	4	no	—
199	Dic₄₇	—	4	2	no	—
200	Dic₄₇	—	4	2	no	—
201	#2396	—	47	1	no	—
202	#1984	—	47	2	no	—
203	#1939	—	47	2	no	—
204	#1916	—	47	2	no	—
205	#1916	—	47	2	no	—
206	#1851	—	47	2	no	—
207	#1798	D₄₇	1	1	yes	characteristic
208	C₈×C₂²⋊C₄	—	47	2	no	—
209	#1729	—	47	1	no	—
210	C₂×C₄₇	—	4	2	no	—
211	C₂×C₄₇	#2329	1	1	yes	characteristic
212	C₂×C₄₇	#2960	1	2	yes	—
213	C₂×C₄₇	#2977	1	1	yes	characteristic
214	C₂×C₄₇	#2979	1	1	yes	characteristic
215	C₂×C₄₇	#2994	1	2	yes	—
216	C₂²×M₁₆	—	47	1	no	—
217	C₂³×C₈	—	47	1	no	—
218	C₂×C₄×Q₈	—	47	1	no	—
219	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
220	C₂×C₄⋊C₈	—	47	2	no	—
221	C₂×C₄⋊C₈	—	47	2	no	—
222	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
223	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
224	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
225	C₂×C₄×C₈	—	47	2	no	—
226	C₂×C₄×C₈	—	47	2	no	—
227	#400	—	47	1	no	—
228	#399	—	47	1	no	—
229	#398	—	47	2	no	—
230	#396	—	47	2	no	—
231	#395	—	47	1	no	—
232	#393	—	47	1	no	—
233	C₄×C₄⋊C₄	—	47	1	no	—
234	C₄×C₄⋊C₄	—	47	2	no	—
235	C₄×C₂²⋊C₄	—	47	2	no	—
236	#336	—	47	2	no	—
237	#336	—	47	2	no	—
238	#336	—	47	2	no	—
239	#336	—	47	2	no	—
240	#336	—	47	2	no	—
241	#336	—	47	2	no	—
242	#336	C₂×D₄₇	1	2	yes	—
243	C₄₇	#22288	1	1	yes	characteristic, complemented, Sylow
244	C₂²×Q₈	—	47	1	no	—
245	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
246	C₂×M₁₆	—	94	2	no	—
247	C₂×M₁₆	—	188	1	no	—
248	C₂×M₁₆	—	188	1	no	—
249	C₂²×C₈	—	47	2	no	—
250	C₂²×C₈	—	47	4	no	—
251	C₂²×C₈	—	47	2	no	—
252	C₂²×C₈	—	188	1	no	—
253	C₂²×C₈	—	188	1	no	—
254	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
255	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
256	C₄×Q₈	—	188	1	no	—
257	C₄×Q₈	—	188	1	no	—
258	#117	—	4	1	no	—
259	#117	—	4	1	no	—
260	C₂×C₄⋊C₄	—	47	2	no	—
261	C₂×C₄⋊C₄	—	47	2	no	—
262	C₂×C₄⋊C₄	—	47	2	no	—
263	C₂×C₄⋊C₄	—	47	2	no	—
264	C₂×C₄⋊C₄	—	47	1	no	—
265	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	—	47	2	no	—
268	C₂×C₂²⋊C₄	—	47	2	no	—
269	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
271	C₂×C₄²	—	47	2	no	—
272	C₂×C₄²	—	47	2	no	—
273	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
274	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
275	C₄⋊C₈	—	4	1	no	—
276	C₄⋊C₈	—	4	1	no	—
277	C₄⋊C₈	—	188	2	no	—
278	C₄⋊C₈	—	188	2	no	—
279	C₂²⋊C₈	—	2	4	no	—
280	C₄×C₈	—	188	2	no	—
281	C₄×C₈	—	188	2	no	—
282	#95	—	47	2	no	—
283	#95	—	47	2	no	—
284	#95	—	47	2	no	—
285	#95	—	47	1	no	—
286	#95	—	47	1	no	—
287	#95	—	47	2	no	—
288	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
289	C₂×Q₈	—	94	4	no	—
290	C₂×Q₈	—	188	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	47	2	no	—
296	C₂²×C₄	—	47	2	no	—
297	C₂²×C₄	—	47	2	no	—
298	C₂²×C₄	—	47	2	no	—
299	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
304	C₂²×C₄	#10625352	1	2	yes	—
305	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
306	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
307	M₁₆	—	188	4	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	47	4	no	—
315	C₂×C₈	—	94	2	no	—
316	C₂×C₈	—	94	2	no	—
317	C₂×C₈	—	94	2	no	—
318	C₂×C₈	—	94	2	no	—
319	C₂×C₈	—	94	2	no	—
320	C₂×C₈	—	188	4	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	94	4	no	—
324	C₄⋊C₄	—	94	4	no	—
325	C₄⋊C₄	—	94	4	no	—
326	C₄⋊C₄	—	188	2	no	—
327	C₄⋊C₄	—	188	1	no	—
328	C₂²⋊C₄	—	4	1	no	—
329	C₂²⋊C₄	—	4	1	no	—
330	C₂²⋊C₄	—	94	4	no	—
331	C₂²⋊C₄	—	94	4	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	94	2	no	—
337	C₄²	—	94	2	no	—
338	C₄²	—	94	2	no	—
339	C₄²	—	94	2	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	#13093989	1	2	yes	—
345	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
346	Q₈	—	188	4	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
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	—	47	4	no	—
362	C₂×C₄	—	47	4	no	—
363	C₂×C₄	—	94	2	no	—
364	C₂×C₄	—	94	2	no	—
365	C₂×C₄	—	94	2	no	—
366	C₂×C₄	—	94	2	no	—
367	C₂×C₄	—	94	2	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	#13093989	1	2	yes	—
374	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
375	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
376	C₂×C₄	#13094069	1	1	yes	characteristic
377	C₂×C₄	#13094069	1	1	yes	characteristic
378	C₂×C₄	#13094070	1	1	yes	characteristic
379	C₂×C₄	#13094071	1	1	yes	characteristic
380	C₈	—	4	2	no	—
381	C₈	—	4	2	no	—
382	C₈	—	94	4	no	—
383	C₈	—	188	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	2	no	—
389	C₂²	C₂×#13093989	1	1	yes	characteristic
390	C₂²	#15689596	1	1	yes	characteristic
391	C₂²	#15689603	1	1	yes	characteristic
392	C₂²	#131×D₄₇	1	2	yes	—
393	C₂²	#131×D₄₇	1	2	yes	—
394	C₄	—	2	2	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	1	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	1	no	—
399	C₄	—	94	4	no	—
400	C₄	—	94	4	no	—
401	C₄	—	188	2	no	—
402	C₄	—	188	2	no	—
403	C₄	#15689710	1	1	yes	characteristic
404	C₄	#15689718	1	1	yes	characteristic
405	C₄	#15689748	1	1	yes	characteristic
406	C₄	#15689752	1	1	yes	characteristic
407	C₂	—	4	2	no	—
408	C₂	#20246118	1	1	yes	characteristic
409	C₂	#20252321	1	2	yes	—
410	C₂	#20252440	1	1	yes	characteristic
411	C₂	#20252452	1	1	yes	characteristic
412	C₂	#20252542	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1798	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1798	D₄₇
hypocenter	C₄₇	#22288
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1798

Complements

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

N	H ≅ G/N	type
2. #20244322	C₂	semidirect
3. #20244103	C₂	semidirect
4. #20243946	C₂	semidirect
5. #20243942	C₂	semidirect
43. C₂²×C₄₇⋊C₈	Q₈	semidirect
243. C₄₇	#22288	semidirect

Maximal subgroups

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

subgroup	index
#20246656	2
#20244322	2
#20244103	2
#20243946	2
#20243942	2
#20243570	2
#20243162	2
#20243085	2
C₄₇×#1798	2
#22288	47