Subgroups — #26226938

Order 12032.

800 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20243996	C₂	1	2	yes	maximal, complemented
2	#20243947	C₂	1	2	yes	maximal, complemented
3	#20243681	C₂	1	2	yes	maximal
4	#20243568	C₂	1	2	yes	maximal, complemented
5	#20243533	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243508	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243459	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243372	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15688878	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2290	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
15	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
19	#15688878	C₂²	1	1	yes	characteristic
20	#15688878	C₂²	1	1	yes	characteristic
21	#15688878	C₂²	1	2	yes	—
22	#15688878	C₂²	1	2	yes	—
23	#15688878	C₂²	1	2	yes	—
24	#15688878	C₂²	1	1	yes	characteristic
25	#15688878	C₂²	1	2	yes	—
26	#15688878	C₂²	1	1	yes	characteristic
27	#15688878	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#388	C₄	1	2	yes	—
32	C₄₇×#387	C₄	1	2	yes	—
33	C₄₇×#386	C₄	1	2	yes	—
34	C₄₇×#385	C₄	1	2	yes	—
35	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#376	C₂²	1	1	yes	characteristic
39	C₂²×C₄₇⋊C₈	—	2	4	no	—
40	C₂²×C₄₇⋊C₈	—	4	2	no	—
41	C₂²×C₄₇⋊C₈	—	4	2	no	—
42	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
47	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
48	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
49	C₂²⋊(C₄₇⋊C₈)	—	4	2	no	—
50	C₂²⋊(C₄₇⋊C₈)	—	4	2	no	—
51	C₄×C₄₇⋊C₈	—	4	2	no	—
52	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
54	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
56	C₄×D₄×C₄₇	—	2	4	no	—
57	#117×C₄₇	—	4	2	no	—
58	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₄₇	—	4	2	no	—
67	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
73	#95×C₄₇	C₂×C₄	1	2	yes	—
74	#95×C₄₇	C₂×C₄	1	2	yes	—
75	#95×C₄₇	C₂×C₄	1	2	yes	—
76	#95×C₄₇	C₂×C₄	1	2	yes	—
77	#95×C₄₇	C₂×C₄	1	2	yes	—
78	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
79	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
80	C₂×D₄×C₄₇	—	2	2	no	—
81	C₂×D₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	1	no	—
84	C₂²×C₄×C₄₇	—	2	1	no	—
85	C₂²×C₄×C₄₇	—	2	4	no	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	1	no	—
91	C₂²×C₄×C₄₇	—	4	2	no	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	#41	1	4	yes	—
101	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
102	C₄⋊C₄×C₄₇	—	2	2	no	—
103	C₄⋊C₄×C₄₇	—	2	4	no	—
104	C₄⋊C₄×C₄₇	—	4	2	no	—
105	C₂²⋊C₄×C₄₇	—	2	2	no	—
106	C₂²⋊C₄×C₄₇	—	2	4	no	—
107	C₂²⋊C₄×C₄₇	—	2	2	no	—
108	C₂²⋊C₄×C₄₇	—	2	4	no	—
109	C₂²⋊C₄×C₄₇	—	4	2	no	—
110	C₄²×C₄₇	—	2	2	no	—
111	C₄²×C₄₇	—	2	2	no	—
112	C₄²×C₄₇	—	2	2	no	—
113	C₄²×C₄₇	—	2	2	no	—
114	C₄²×C₄₇	—	2	1	no	—
115	C₄²×C₄₇	—	2	1	no	—
116	C₄²×C₄₇	—	4	2	no	—
117	C₂×C₄₇⋊C₈	—	2	2	no	—
118	C₂×C₄₇⋊C₈	—	2	2	no	—
119	C₂×C₄₇⋊C₈	—	2	2	no	—
120	C₂×C₄₇⋊C₈	—	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	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	4	8	no	—
130	C₂³×C₄₇	—	2	1	no	—
131	C₂³×C₄₇	—	2	1	no	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	—	2	1	no	—
134	C₂³×C₄₇	—	2	1	no	—
135	C₂³×C₄₇	—	2	1	no	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	#117	1	2	yes	—
139	C₂³×C₄₇	#131	1	4	yes	—
140	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
141	D₄×C₄₇	—	4	4	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	2	1	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	4	8	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	#117	1	2	yes	—
168	C₂×C₄×C₄₇	#131	1	4	yes	—
169	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
170	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
171	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
173	C₄₇⋊C₈	—	4	2	no	—
174	C₄₇⋊C₈	—	4	2	no	—
175	C₄₇⋊C₈	—	4	2	no	—
176	C₄₇⋊C₈	—	4	2	no	—
177	#21997	—	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	4	no	—
182	C₂²×C₄₇	—	4	1	no	—
183	C₂²×C₄₇	—	4	1	no	—
184	C₂²×C₄₇	—	4	1	no	—
185	C₂²×C₄₇	—	4	2	no	—
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	#433	1	4	yes	—
188	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
189	C₂²×C₄₇	#518	1	1	yes	characteristic
190	C₂²×C₄₇	#520	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×#131	1	2	yes	—
192	C₂²×C₄₇	C₂×#131	1	2	yes	—
193	C₄×C₄₇	—	2	2	no	—
194	C₄×C₄₇	—	2	4	no	—
195	C₄×C₄₇	—	4	1	no	—
196	C₄×C₄₇	—	4	1	no	—
197	C₄×C₄₇	—	4	1	no	—
198	C₄×C₄₇	—	4	2	no	—
199	C₄×C₄₇	—	4	2	no	—
200	C₄×C₄₇	—	4	2	no	—
201	C₄×C₄₇	#538	1	2	yes	—
202	C₄×C₄₇	#539	1	2	yes	—
203	#2290	D₄₇	1	1	yes	characteristic
204	#1923	—	47	2	no	—
205	#1916	—	47	2	no	—
206	#1869	—	47	2	no	—
207	#1850	—	47	2	no	—
208	#1840	—	47	1	no	—
209	#1832	—	47	1	no	—
210	#1818	—	47	1	no	—
211	#1798	—	47	1	no	—
212	C₄×C₂²⋊C₈	—	47	1	no	—
213	C₂×#336	—	47	1	no	—
214	C₂×C₄₇	—	2	4	no	—
215	C₂×C₄₇	—	8	1	no	—
216	C₂×C₄₇	#2318	1	1	yes	characteristic
217	C₂×C₄₇	C₂×#433	1	1	yes	characteristic
218	C₂×C₄₇	#2922	1	1	yes	characteristic
219	C₂×C₄₇	#2977	1	2	yes	—
220	C₂×C₄₇	#2994	1	2	yes	—
221	C₂³×C₈	—	47	2	no	—
222	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
223	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
224	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
225	C₂×C₄⋊C₈	—	47	2	no	—
226	C₂×C₄⋊C₈	—	47	2	no	—
227	C₂×C₂²⋊C₈	—	47	2	no	—
228	C₂×C₂²⋊C₈	—	47	2	no	—
229	C₂×C₂²⋊C₈	—	47	2	no	—
230	C₂×C₄×C₈	—	47	2	no	—
231	#388	Dic₄₇	1	2	yes	—
232	#387	Dic₄₇	1	2	yes	—
233	#386	Dic₄₇	1	2	yes	—
234	#385	Dic₄₇	1	2	yes	—
235	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
236	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
237	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
238	#376	C₂×D₄₇	1	1	yes	characteristic
239	#336	—	47	1	no	—
240	#336	—	47	1	no	—
241	#336	—	47	1	no	—
242	#336	—	47	1	no	—
243	#336	—	47	2	no	—
244	#336	—	47	2	no	—
245	#336	—	47	2	no	—
246	#336	—	47	2	no	—
247	#336	—	47	2	no	—
248	C₄₇	#21997	1	1	yes	characteristic, complemented, Sylow
249	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
250	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
251	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
252	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
253	C₂²×C₈	—	47	2	no	—
254	C₂²×C₈	—	47	2	no	—
255	C₂²×C₈	—	47	2	no	—
256	C₂²×C₈	—	47	2	no	—
257	C₂²×C₈	—	94	4	no	—
258	C₂²×C₈	—	188	2	no	—
259	C₂²×C₈	—	188	2	no	—
260	C₄×D₄	—	2	4	no	—
261	#117	—	4	2	no	—
262	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
264	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
265	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
269	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
270	C₂×C₄²	—	4	2	no	—
271	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
272	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
273	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
274	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
275	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
276	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
277	C₄⋊C₈	—	188	2	no	—
278	C₄⋊C₈	—	188	2	no	—
279	C₂²⋊C₈	—	94	4	no	—
280	C₂²⋊C₈	—	188	2	no	—
281	C₂²⋊C₈	—	188	2	no	—
282	C₄×C₈	—	188	2	no	—
283	#95	C₂×Dic₄₇	1	2	yes	—
284	#95	C₂×Dic₄₇	1	2	yes	—
285	#95	C₂×Dic₄₇	1	2	yes	—
286	#95	C₂×Dic₄₇	1	2	yes	—
287	#95	C₂×Dic₄₇	1	2	yes	—
288	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
289	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	#10625350	1	4	yes	—
303	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
304	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
305	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
306	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
307	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
308	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
309	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
310	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
311	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
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	—	94	2	no	—
317	C₂×C₈	—	94	2	no	—
318	C₂×C₈	—	94	2	no	—
319	C₂×C₈	—	94	2	no	—
320	C₂×C₈	—	94	2	no	—
321	C₂×C₈	—	94	2	no	—
322	C₂×C₈	—	94	2	no	—
323	C₂×C₈	—	94	2	no	—
324	C₂×C₈	—	188	8	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₂²⋊C₄	—	4	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	4	2	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	#13093983	1	2	yes	—
349	C₂³	#13094031	1	4	yes	—
350	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
351	D₄	—	4	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	8	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	#13093983	1	2	yes	—
378	C₂×C₄	#13094031	1	4	yes	—
379	C₂×C₄	C₂×#10625350	1	2	yes	—
380	C₂×C₄	#13094069	1	2	yes	—
381	C₂×C₄	#13094070	1	1	yes	characteristic
382	C₂×C₄	#13094071	1	1	yes	characteristic
383	C₈	—	188	2	no	—
384	C₈	—	188	2	no	—
385	C₈	—	188	2	no	—
386	C₈	—	188	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	2	no	—
396	C₂²	#15689184	1	4	yes	—
397	C₂²	C₂×#13093983	1	1	yes	characteristic
398	C₂²	#15689598	1	1	yes	characteristic
399	C₂²	#15689606	1	1	yes	characteristic
400	C₂²	C₂×#13094031	1	2	yes	—
401	C₂²	C₂×#13094031	1	2	yes	—
402	C₄	—	2	2	no	—
403	C₄	—	2	4	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	2	no	—
410	C₄	#15689706	1	2	yes	—
411	C₄	#15689715	1	2	yes	—
412	C₂	—	2	4	no	—
413	C₂	—	8	1	no	—
414	C₂	#20246021	1	1	yes	characteristic
415	C₂	C₂×#15689184	1	1	yes	characteristic
416	C₂	#20252032	1	1	yes	characteristic
417	C₂	#20252444	1	2	yes	—
418	C₂	#20252548	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#2290	C₂
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2290	D₄₇
hypocenter	C₄₇	#21997
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2290

Complements

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

N	H ≅ G/N	type
1. #20243996	C₂	semidirect
2. #20243947	C₂	semidirect
4. #20243568	C₂	semidirect
5. #20243533	C₂	semidirect
6. #20243508	C₂	semidirect
7. #20243459	C₂	semidirect
8. #20243372	C₂	semidirect
9. C₄×C₂²⋊(C₄₇⋊C₈)	C₂	semidirect
10. C₂×#15688878	C₂	semidirect
248. C₄₇	#21997	semidirect

Maximal subgroups

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

subgroup	index
#20243996	2
#20243947	2
#20243681	2
#20243568	2
#20243533	2
#20243508	2
#20243459	2
#20243372	2
C₄×C₂²⋊(C₄₇⋊C₈)	2
C₂×#15688878	2
C₄₇×#2290	2
#21997	47