Subgroups — #26234096

Order 12032.

724 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20245795	C₂	1	1	yes	maximal, characteristic
2	#20244111	C₂	1	2	yes	maximal, complemented
3	#20243951	C₂	1	2	yes	maximal, complemented
4	#20243944	C₂	1	2	yes	maximal, complemented
5	#20243370	C₂	1	2	yes	maximal
6	#20243368	C₂	1	1	yes	maximal, characteristic
7	#20243260	C₂	1	2	yes	maximal, complemented
8	#20243156	C₂	1	2	yes	maximal
9	C₄₇×#1749	C₂	1	1	yes	maximal, characteristic
10	C₂×#13093983	C₂²	1	2	yes	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
12	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
13	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
14	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
15	C₂×#13093934	C₂²	1	2	yes	—
16	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
17	#15688993	C₄	1	1	yes	characteristic
18	#15688993	C₄	1	1	yes	characteristic
19	#15688989	C₄	1	2	yes	—
20	#15688983	C₄	1	2	yes	—
21	#15688983	C₄	1	1	yes	characteristic
22	#15688983	C₄	1	1	yes	characteristic
23	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
26	#15688878	C₂²	1	1	yes	characteristic
27	#15688878	C₂²	1	1	yes	characteristic
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	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#97×C₄₇	C₂²	1	2	yes	—
36	C₄₇×#336	C₂²	1	2	yes	—
37	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
38	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
39	#13093983	—	4	2	no	—
40	#13093983	—	4	2	no	—
41	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
42	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
49	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
50	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
51	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
52	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
53	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
54	Dic₄₇⋊C₈	—	4	2	no	—
55	Dic₄₇⋊C₈	—	4	2	no	—
56	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
57	#13093934	—	4	2	no	—
58	C₈×Dic₄₇	—	4	2	no	—
59	C₄₇⋊#95	C₂×C₄	1	2	yes	—
60	C₄₇⋊#95	C₂×C₄	1	2	yes	—
61	C₄₇⋊#95	C₂×C₄	1	2	yes	—
62	C₄₇⋊#95	C₂×C₄	1	2	yes	—
63	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
67	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₄₇	—	2	4	no	—
69	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
73	C₂²⋊C₈×C₄₇	—	2	2	no	—
74	C₂²⋊C₈×C₄₇	Q₈	1	4	yes	—
75	#97×C₄₇	—	2	4	no	—
76	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	—	2	2	no	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	4	1	no	—
83	C₂²×C₄×C₄₇	—	4	1	no	—
84	C₂²×C₄×C₄₇	—	4	1	no	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₄₇	#41	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
93	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
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	C₂×C₈×C₄₇	—	2	2	no	—
98	C₂×C₈×C₄₇	—	2	2	no	—
99	C₂×C₈×C₄₇	—	2	2	no	—
100	C₂×C₈×C₄₇	—	2	2	no	—
101	C₂×C₈×C₄₇	—	2	2	no	—
102	C₂×C₈×C₄₇	C₂×Q₈	1	4	yes	—
103	C₄²×C₄₇	—	2	2	no	—
104	C₄²×C₄₇	—	2	2	no	—
105	C₄²×C₄₇	—	2	2	no	—
106	C₄²×C₄₇	#41	1	4	yes	—
107	C₂²⋊Dic₄₇	—	4	2	no	—
108	C₂²⋊Dic₄₇	—	4	2	no	—
109	C₄⋊Dic₄₇	—	2	4	no	—
110	C₄⋊Dic₄₇	—	4	1	no	—
111	C₄⋊Dic₄₇	—	4	1	no	—
112	C₄⋊Dic₄₇	—	4	2	no	—
113	C₄⋊Dic₄₇	—	4	1	no	—
114	C₄⋊Dic₄₇	—	4	1	no	—
115	C₄⋊Dic₄₇	—	4	2	no	—
116	C₄⋊Dic₄₇	—	4	2	no	—
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	C₂×C₄₇⋊C₈	—	2	2	no	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	—	2	2	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂³×C₄₇	—	2	1	no	—
128	C₂³×C₄₇	—	2	1	no	—
129	C₂³×C₄₇	—	2	1	no	—
130	C₂³×C₄₇	—	2	1	no	—
131	C₂³×C₄₇	—	2	1	no	—
132	C₂³×C₄₇	—	2	1	no	—
133	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
134	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₄₇	—	2	1	no	—
136	C₂×C₄×C₄₇	—	2	1	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	2	1	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	1	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	4	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	—	4	4	no	—
149	C₂×C₄×C₄₇	—	4	4	no	—
150	C₂×C₄×C₄₇	#117	1	2	yes	—
151	C₂×C₄×C₄₇	#117	1	2	yes	—
152	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
153	C₂×C₄×C₄₇	#131	1	2	yes	—
154	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
156	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
158	C₂×Dic₄₇	—	2	2	no	—
159	C₂×Dic₄₇	—	2	2	no	—
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	C₈×C₄₇	—	2	4	no	—
171	C₈×C₄₇	—	4	2	no	—
172	C₄₇⋊C₈	—	4	2	no	—
173	C₄₇⋊C₈	—	4	2	no	—
174	#22628	—	47	1	no	maximal, Sylow
175	C₂²×C₄₇	—	2	2	no	—
176	C₂²×C₄₇	—	2	2	no	—
177	C₂²×C₄₇	—	2	2	no	—
178	C₂²×C₄₇	—	4	1	no	—
179	C₂²×C₄₇	—	4	1	no	—
180	C₂²×C₄₇	—	4	1	no	—
181	C₂²×C₄₇	—	4	1	no	—
182	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
183	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
184	C₂²×C₄₇	#518	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
186	C₂²×C₄₇	#568	1	1	yes	characteristic
187	C₂²×C₄₇	#568	1	1	yes	characteristic
188	C₂²×C₄₇	#568	1	1	yes	characteristic
189	C₄×C₄₇	—	2	2	no	—
190	C₄×C₄₇	—	2	2	no	—
191	C₄×C₄₇	—	2	2	no	—
192	C₄×C₄₇	—	2	2	no	—
193	C₄×C₄₇	—	4	1	no	—
194	C₄×C₄₇	#553	1	2	yes	—
195	C₄×C₄₇	#554	1	2	yes	—
196	Dic₄₇	—	4	2	no	—
197	Dic₄₇	—	4	2	no	—
198	Dic₄₇	—	4	2	no	—
199	Dic₄₇	—	4	2	no	—
200	#2285	—	47	1	no	—
201	#1940	—	47	2	no	—
202	#1917	—	47	2	no	—
203	#1916	—	47	2	no	—
204	#1798	—	47	2	no	—
205	#1797	—	47	1	no	—
206	#1771	—	47	2	no	—
207	#1750	—	47	2	no	—
208	#1749	D₄₇	1	1	yes	characteristic
209	C₂×C₄₇	—	4	2	no	—
210	C₂×C₄₇	#2345	1	1	yes	characteristic
211	C₂×C₄₇	#2921	1	1	yes	characteristic
212	C₂×C₄₇	#2924	1	1	yes	characteristic
213	C₂×C₄₇	#2961	1	1	yes	characteristic
214	C₂×C₄₇	#2962	1	1	yes	characteristic
215	C₂×C₄₇	#2980	1	1	yes	characteristic
216	C₂×C₄₇	#2981	1	1	yes	characteristic
217	C₂×#117	—	47	2	no	—
218	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
219	C₂×C₄⋊C₈	—	47	2	no	—
220	C₂×C₄⋊C₈	—	47	2	no	—
221	C₂×C₄⋊C₈	—	47	2	no	—
222	C₂×C₂²⋊C₈	—	47	2	no	—
223	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
224	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
225	C₂×#97	—	47	2	no	—
226	C₂×#97	C₂×D₄₇	1	2	yes	—
227	C₂×C₄×C₈	—	47	2	no	—
228	#384	—	47	1	no	—
229	#384	—	47	1	no	—
230	#382	—	47	2	no	—
231	#380	—	47	2	no	—
232	#380	—	47	1	no	—
233	#380	—	47	1	no	—
234	C₄×C₄⋊C₄	—	47	2	no	—
235	C₄×C₄⋊C₄	—	47	1	no	—
236	C₄×C₄⋊C₄	—	47	1	no	—
237	#336	—	47	2	no	—
238	#336	—	47	2	no	—
239	#336	—	47	2	no	—
240	#336	—	47	2	no	—
241	#336	—	47	1	no	—
242	#336	—	47	1	no	—
243	#336	C₂×D₄₇	1	2	yes	—
244	C₄₇	#22628	1	1	yes	characteristic, complemented, Sylow
245	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
246	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
247	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
248	C₂²×C₈	—	47	2	no	—
249	C₂²×C₈	—	47	2	no	—
250	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
251	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
252	#117	—	188	2	no	—
253	#117	—	188	2	no	—
254	C₂×C₄⋊C₄	—	47	2	no	—
255	C₂×C₄⋊C₄	—	47	2	no	—
256	C₂×C₄⋊C₄	—	47	2	no	—
257	C₂×C₄⋊C₄	—	47	1	no	—
258	C₂×C₄⋊C₄	—	47	1	no	—
259	C₂×C₄⋊C₄	—	47	1	no	—
260	C₂×C₄⋊C₄	—	47	1	no	—
261	C₂×C₄⋊C₄	—	47	2	no	—
262	C₂×C₂²⋊C₄	—	47	2	no	—
263	C₂×C₂²⋊C₄	—	47	2	no	—
264	C₂×C₄²	—	2	4	no	—
265	C₂×C₄²	—	47	2	no	—
266	C₂×C₄²	—	47	2	no	—
267	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
268	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
269	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
270	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
271	C₄⋊C₈	—	94	4	no	—
272	C₄⋊C₈	—	188	2	no	—
273	C₄⋊C₈	—	188	2	no	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₂²⋊C₈	—	94	4	no	—
276	C₂²⋊C₈	Dic₉₄	1	4	yes	—
277	#97	—	2	4	no	—
278	#97	—	188	2	no	—
279	C₄×C₈	—	188	2	no	—
280	#95	—	47	2	no	—
281	#95	—	47	2	no	—
282	#95	—	47	2	no	—
283	#95	—	47	2	no	—
284	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	47	2	no	—
294	C₂²×C₄	—	47	2	no	—
295	C₂²×C₄	—	47	2	no	—
296	C₂²×C₄	—	47	2	no	—
297	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
298	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
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	#10625350	1	2	yes	—
304	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	94	2	no	—
311	C₂×C₈	—	94	2	no	—
312	C₂×C₈	—	94	2	no	—
313	C₂×C₈	—	94	2	no	—
314	C₂×C₈	—	94	2	no	—
315	C₂×C₈	—	94	2	no	—
316	C₂×C₈	C₂×Dic₉₄	1	4	yes	—
317	C₄⋊C₄	—	94	4	no	—
318	C₄⋊C₄	—	188	1	no	—
319	C₄⋊C₄	—	188	1	no	—
320	C₄⋊C₄	—	188	1	no	—
321	C₄⋊C₄	—	188	1	no	—
322	C₄⋊C₄	—	188	2	no	—
323	C₄⋊C₄	—	188	2	no	—
324	C₄⋊C₄	—	188	2	no	—
325	C₂²⋊C₄	—	188	2	no	—
326	C₂²⋊C₄	—	188	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	94	2	no	—
331	C₄²	—	94	2	no	—
332	C₄²	—	94	2	no	—
333	C₄²	—	94	2	no	—
334	C₄²	#10625352	1	4	yes	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	C₄×Dic₉₄	1	2	yes	—
342	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	94	2	no	—
359	C₂×C₄	—	94	2	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	94	2	no	—
362	C₂×C₄	—	94	2	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	#13093980	1	2	yes	—
371	C₂×C₄	#13093980	1	2	yes	—
372	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
373	C₂×C₄	#13094032	1	2	yes	—
374	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
375	C₂×C₄	C₂×#10625352	1	2	yes	—
376	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
377	C₂×C₄	#13094070	1	2	yes	—
378	C₈	—	2	4	no	—
379	C₈	—	4	2	no	—
380	C₈	—	188	2	no	—
381	C₈	—	188	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	C₂×#13093980	1	1	yes	characteristic
390	C₂²	C₂×C₄×Dic₉₄	1	1	yes	characteristic
391	C₂²	#15689597	1	1	yes	characteristic
392	C₂²	C₂×#13094032	1	1	yes	characteristic
393	C₂²	#15689889	1	1	yes	characteristic
394	C₂²	#15689889	1	1	yes	characteristic
395	C₂²	#15689889	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	4	1	no	—
401	C₄	—	188	2	no	—
402	C₄	—	188	2	no	—
403	C₄	—	188	2	no	—
404	C₄	—	188	2	no	—
405	C₄	#15689819	1	2	yes	—
406	C₄	#15689830	1	2	yes	—
407	C₂	—	4	2	no	—
408	C₂	#20246263	1	1	yes	characteristic
409	C₂	#20252023	1	1	yes	characteristic
410	C₂	#20252048	1	1	yes	characteristic
411	C₂	#20252328	1	1	yes	characteristic
412	C₂	#20252335	1	1	yes	characteristic
413	C₂	#20252458	1	1	yes	characteristic
414	C₂	#20252466	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1749	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1749	D₄₇
hypocenter	C₄₇	#22628
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1749

Complements

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

N	H ≅ G/N	type
2. #20244111	C₂	semidirect
3. #20243951	C₂	semidirect
4. #20243944	C₂	semidirect
7. #20243260	C₂	semidirect
244. C₄₇	#22628	semidirect

Maximal subgroups

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

subgroup	index
#20245795	2
#20244111	2
#20243951	2
#20243944	2
#20243370	2
#20243368	2
#20243260	2
#20243156	2
C₄₇×#1749	2
#22628	47