Subgroups — #26124461

Order 12032.

846 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688878	C₂	1	2	yes	maximal
3	C₂×#15688878	C₂	1	2	yes	maximal
4	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
5	C₄×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
7	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
8	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
11	#15688878	—	2	4	no	—
12	#15688878	—	2	4	no	—
13	#15688878	—	2	2	no	—
14	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#95×C₄₇	C₄	1	2	yes	—
17	C₂×#95×C₄₇	C₄	1	1	yes	characteristic
18	C₂×#95×C₄₇	C₄	1	1	yes	characteristic
19	C₂²×C₄₇⋊C₈	—	2	2	no	—
20	C₂²×C₄₇⋊C₈	—	2	1	no	—
21	C₂²×C₄₇⋊C₈	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	—	2	1	no	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₂²×C₄₇⋊C₈	—	2	1	no	—
27	C₂²×C₄₇⋊C₈	—	2	2	no	—
28	C₂²×C₄₇⋊C₈	—	2	1	no	—
29	C₂²×C₄₇⋊C₈	—	2	2	no	—
30	C₂²×C₄₇⋊C₈	—	2	2	no	—
31	C₂²×C₄₇⋊C₈	—	2	2	no	—
32	C₂²×C₄₇⋊C₈	—	2	2	no	—
33	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
34	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
35	C₂²×C₄₇⋊C₈	Q₈	1	2	yes	—
36	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
37	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂×C₄²×C₄₇	—	2	2	no	—
43	C₂×C₄²×C₄₇	—	2	2	no	—
44	C₂×C₄²×C₄₇	—	2	2	no	—
45	C₂×C₄²×C₄₇	—	2	2	no	—
46	C₂×C₄²×C₄₇	—	2	2	no	—
47	C₂×C₄²×C₄₇	—	2	2	no	—
48	C₂×C₄²×C₄₇	—	2	2	no	—
49	C₂×C₄²×C₄₇	—	2	2	no	—
50	C₂×C₄²×C₄₇	D₄	1	2	yes	—
51	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
52	#95×C₄₇	—	2	4	no	—
53	#95×C₄₇	—	2	2	no	—
54	#95×C₄₇	C₈	1	4	yes	complemented
55	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₇	—	2	2	no	—
57	C₂²×C₄×C₄₇	—	2	2	no	—
58	C₂²×C₄×C₄₇	—	2	2	no	—
59	C₂²×C₄×C₄₇	—	2	2	no	—
60	C₂²×C₄×C₄₇	—	2	2	no	—
61	C₂²×C₄×C₄₇	—	2	2	no	—
62	C₂²×C₄×C₄₇	—	2	2	no	—
63	C₂²×C₄×C₄₇	—	2	2	no	—
64	C₂²×C₄×C₄₇	—	2	2	no	—
65	C₂²×C₄×C₄₇	—	2	2	no	—
66	C₂²×C₄×C₄₇	—	2	2	no	—
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	2	1	no	—
69	C₂²×C₄×C₄₇	—	2	1	no	—
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
75	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
76	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
77	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
78	C₂²×C₄×C₄₇	M₁₆	1	4	yes	—
79	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
80	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
81	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	#41	1	2	yes	—
87	C₂²×C₄×C₄₇	#41	1	2	yes	—
88	C₂²×C₄×C₄₇	#41	1	2	yes	—
89	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
90	C₄²×C₄₇	—	2	2	no	—
91	C₄²×C₄₇	—	2	4	no	—
92	C₄²×C₄₇	—	2	2	no	—
93	C₄²×C₄₇	—	4	2	no	—
94	C₄²×C₄₇	—	4	2	no	—
95	C₄²×C₄₇	—	4	2	no	—
96	C₄²×C₄₇	—	4	2	no	—
97	C₂×C₄₇⋊C₈	—	2	4	no	—
98	C₂×C₄₇⋊C₈	—	2	4	no	—
99	C₂×C₄₇⋊C₈	—	2	2	no	—
100	C₂×C₄₇⋊C₈	—	2	4	no	—
101	C₂×C₄₇⋊C₈	—	2	2	no	—
102	C₂×C₄₇⋊C₈	—	2	4	no	—
103	C₂×C₄₇⋊C₈	—	2	4	no	—
104	C₂×C₄₇⋊C₈	—	4	1	no	—
105	C₂×C₄₇⋊C₈	—	4	2	no	—
106	C₂×C₄₇⋊C₈	—	4	2	no	—
107	C₂×C₄₇⋊C₈	—	4	2	no	—
108	C₂×C₄₇⋊C₈	—	4	1	no	—
109	C₂×C₄₇⋊C₈	—	4	2	no	—
110	C₂×C₄₇⋊C₈	—	4	1	no	—
111	C₂×C₄₇⋊C₈	—	4	2	no	—
112	C₂×C₄₇⋊C₈	—	4	1	no	—
113	C₂×C₄₇⋊C₈	—	4	2	no	—
114	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
115	C₂³×C₄₇	#117	1	2	yes	—
116	C₂³×C₄₇	C₄×D₄	1	2	yes	—
117	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
118	C₂³×C₄₇	C₄×Q₈	1	1	yes	characteristic
119	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
120	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
121	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
122	C₂³×C₄₇	#131	1	2	yes	—
123	C₂³×C₄₇	#131	1	1	yes	characteristic
124	C₂³×C₄₇	#131	1	1	yes	characteristic
125	C₂×C₄×C₄₇	—	2	2	no	—
126	C₂×C₄×C₄₇	—	2	2	no	—
127	C₂×C₄×C₄₇	—	2	4	no	—
128	C₂×C₄×C₄₇	—	2	4	no	—
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	2	no	—
131	C₂×C₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	2	4	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	2	4	no	—
135	C₂×C₄×C₄₇	—	2	4	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	2	4	no	—
138	C₂×C₄×C₄₇	—	4	2	no	—
139	C₂×C₄×C₄₇	—	4	2	no	—
140	C₂×C₄×C₄₇	—	4	2	no	—
141	C₂×C₄×C₄₇	—	4	2	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	C₄⋊C₈	1	4	yes	—
149	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
150	C₂×C₄×C₄₇	#121	1	2	yes	—
151	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
153	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
154	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#123	1	2	yes	—
156	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
157	C₂×C₄×C₄₇	#123	1	2	yes	—
158	C₂×C₄×C₄₇	#124	1	2	yes	—
159	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
160	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
161	C₂×C₄×C₄₇	#125	1	2	yes	—
162	C₂×C₄×C₄₇	#125	1	1	yes	characteristic
163	C₂×C₄×C₄₇	#125	1	2	yes	—
164	C₂×C₄×C₄₇	#126	1	2	yes	—
165	C₂×C₄×C₄₇	#126	1	2	yes	—
166	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
167	C₄₇⋊C₈	—	4	2	no	—
168	C₄₇⋊C₈	—	4	4	no	—
169	C₄₇⋊C₈	—	4	2	no	—
170	#11255	—	47	1	no	maximal, Sylow
171	C₂²×C₄₇	#382	1	1	yes	characteristic
172	C₂²×C₄₇	#385	1	1	yes	characteristic
173	C₂²×C₄₇	#387	1	2	yes	—
174	C₂²×C₄₇	#388	1	2	yes	—
175	C₂²×C₄₇	#389	1	1	yes	characteristic
176	C₂²×C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic
177	C₂²×C₄₇	#423	1	1	yes	characteristic
178	C₂²×C₄₇	#424	1	1	yes	characteristic
179	C₂²×C₄₇	#424	1	1	yes	characteristic
180	C₂²×C₄₇	#431	1	2	yes	—
181	C₂²×C₄₇	#432	1	2	yes	—
182	C₂²×C₄₇	#433	1	2	yes	—
183	C₂²×C₄₇	#433	1	2	yes	—
184	C₂²×C₄₇	C₈×D₄	1	2	yes	—
185	C₂²×C₄₇	C₈×D₄	1	1	yes	characteristic
186	C₂²×C₄₇	#435	1	2	yes	—
187	C₂²×C₄₇	#435	1	2	yes	—
188	C₂²×C₄₇	#435	1	2	yes	—
189	C₂²×C₄₇	#436	1	2	yes	—
190	C₂²×C₄₇	#436	1	1	yes	characteristic
191	C₂²×C₄₇	C₈×Q₈	1	1	yes	characteristic
192	C₂²×C₄₇	#446	1	2	yes	—
193	C₂²×C₄₇	#446	1	1	yes	characteristic
194	C₄×C₄₇	—	2	4	no	—
195	C₄×C₄₇	—	4	2	no	—
196	C₄×C₄₇	—	4	4	no	—
197	C₄×C₄₇	—	4	4	no	—
198	C₄×C₄₇	#393	1	1	yes	characteristic
199	C₄×C₄₇	#394	1	1	yes	characteristic
200	C₄×C₄₇	#397	1	1	yes	characteristic
201	C₄×C₄₇	#398	1	2	yes	—
202	C₄×C₄₇	#400	1	1	yes	characteristic
203	C₄×C₄₇	#400	1	2	yes	—
204	C₂²×C₄⋊C₈	—	47	1	no	—
205	C₂×#336	—	47	2	no	—
206	C₂×#336	—	47	2	no	—
207	C₂×#336	—	47	1	no	—
208	C₄×#95	D₄₇	1	1	yes	characteristic
209	C₂×C₄₇	#1442	1	1	yes	characteristic
210	C₂×C₄₇	#1831	1	1	yes	characteristic
211	C₂×C₄₇	#1832	1	1	yes	characteristic
212	C₂×C₄₇	#1850	1	1	yes	characteristic
213	C₂×C₄₇	#1851	1	1	yes	characteristic
214	C₂×C₄₇	#1916	1	2	yes	—
215	C₂×C₄₇	#1917	1	2	yes	—
216	C₂×C₄₇	#1923	1	2	yes	—
217	C₂×C₄₇	#1924	1	2	yes	—
218	C₂×C₄₇	#1939	1	1	yes	characteristic
219	C₂×C₄₇	#1940	1	1	yes	characteristic
220	C₂³×C₈	—	47	2	no	—
221	C₂³×C₈	—	47	1	no	—
222	C₂³×C₈	—	47	1	no	—
223	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
224	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
225	C₂×C₄⋊C₈	—	94	4	no	—
226	C₂×C₄⋊C₈	—	94	2	no	—
227	C₂×#95	Dic₄₇	1	2	yes	—
228	C₂×#95	Dic₄₇	1	1	yes	characteristic
229	C₂×#95	Dic₄₇	1	1	yes	characteristic
230	#336	—	94	4	no	—
231	#336	—	94	4	no	—
232	#336	—	94	2	no	—
233	C₄₇	#11255	1	1	yes	characteristic, complemented, Sylow
234	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
235	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
236	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
237	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
238	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
239	C₂²×C₈	—	47	2	no	—
240	C₂²×C₈	—	47	4	no	—
241	C₂²×C₈	—	47	2	no	—
242	C₂²×C₈	—	94	1	no	—
243	C₂²×C₈	—	94	1	no	—
244	C₂²×C₈	—	94	2	no	—
245	C₂²×C₈	—	94	2	no	—
246	C₂²×C₈	—	94	2	no	—
247	C₂²×C₈	—	94	2	no	—
248	C₂²×C₈	—	94	2	no	—
249	C₂²×C₈	—	94	2	no	—
250	C₂²×C₈	—	94	2	no	—
251	C₂²×C₈	—	94	2	no	—
252	C₂²×C₈	—	94	1	no	—
253	C₂²×C₈	—	94	2	no	—
254	C₂²×C₈	—	94	1	no	—
255	C₂²×C₈	—	94	2	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	—	2	2	no	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	Dic₉₄	1	2	yes	—
265	C₂×C₄²	D₁₈₈	1	2	yes	—
266	C₄⋊C₈	—	94	8	no	—
267	#95	—	2	4	no	—
268	#95	—	2	2	no	—
269	#95	C₄₇⋊C₈	1	4	yes	complemented
270	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
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	C₂×C₄₇⋊C₈	1	4	yes	—
290	C₂²×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
291	C₂²×C₄	#10625329	1	4	yes	—
292	C₂²×C₄	#10625329	1	2	yes	—
293	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
294	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
295	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
297	C₂²×C₄	#10625350	1	2	yes	—
298	C₂²×C₄	#10625350	1	2	yes	—
299	C₂²×C₄	D₄×D₄₇	1	2	yes	—
300	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
301	C₂²×C₄	#10625352	1	2	yes	—
302	C₂²×C₄	#10625352	1	1	yes	characteristic
303	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
304	C₂²×C₄	#10625354	1	1	yes	characteristic
305	C₂×C₈	—	94	4	no	—
306	C₂×C₈	—	94	4	no	—
307	C₂×C₈	—	94	2	no	—
308	C₂×C₈	—	94	4	no	—
309	C₂×C₈	—	94	2	no	—
310	C₂×C₈	—	94	4	no	—
311	C₂×C₈	—	94	4	no	—
312	C₂×C₈	—	188	1	no	—
313	C₂×C₈	—	188	2	no	—
314	C₂×C₈	—	188	2	no	—
315	C₂×C₈	—	188	1	no	—
316	C₂×C₈	—	188	2	no	—
317	C₂×C₈	—	188	2	no	—
318	C₂×C₈	—	188	1	no	—
319	C₂×C₈	—	188	2	no	—
320	C₂×C₈	—	188	1	no	—
321	C₂×C₈	—	188	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	4	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	4	2	no	—
326	C₄²	—	4	2	no	—
327	C₄²	—	4	2	no	—
328	C₄²	—	4	2	no	—
329	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
330	C₂³	#13093983	1	2	yes	—
331	C₂³	D₄×Dic₄₇	1	2	yes	—
332	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
333	C₂³	Q₈×Dic₄₇	1	1	yes	characteristic
334	C₂³	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
335	C₂³	C₂×#10625329	1	1	yes	characteristic
336	C₂³	C₂×#10625329	1	2	yes	—
337	C₂³	#13094031	1	1	yes	characteristic
338	C₂³	#13094031	1	2	yes	—
339	C₂³	#13094031	1	1	yes	characteristic
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	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	C₄⋊(C₄₇⋊C₈)	1	4	yes	—
364	C₂×C₄	#13093994	1	1	yes	characteristic
365	C₂×C₄	#13093997	1	2	yes	—
366	C₂×C₄	#13093999	1	1	yes	characteristic
367	C₂×C₄	#13094001	1	2	yes	—
368	C₂×C₄	#13094002	1	2	yes	—
369	C₂×C₄	#13094004	1	1	yes	characteristic
370	C₂×C₄	#13094006	1	2	yes	—
371	C₂×C₄	#13094008	1	1	yes	characteristic
372	C₂×C₄	#13094009	1	2	yes	—
373	C₂×C₄	#13094010	1	2	yes	—
374	C₂×C₄	#13094012	1	1	yes	characteristic
375	C₂×C₄	#13094012	1	1	yes	characteristic
376	C₂×C₄	#13094014	1	2	yes	—
377	C₂×C₄	#13094015	1	1	yes	characteristic
378	C₂×C₄	#13094016	1	2	yes	—
379	C₂×C₄	#13094017	1	2	yes	—
380	C₂×C₄	#13094019	1	2	yes	—
381	C₂×C₄	#13094023	1	1	yes	characteristic
382	C₈	—	188	2	no	—
383	C₈	—	188	4	no	—
384	C₈	—	188	2	no	—
385	C₂²	#15688989	1	1	yes	characteristic
386	C₂²	#15688998	1	1	yes	characteristic
387	C₂²	#15689009	1	2	yes	—
388	C₂²	#15689016	1	2	yes	—
389	C₂²	#15689022	1	1	yes	characteristic
390	C₂²	C₂×C₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic
391	C₂²	#15689147	1	1	yes	characteristic
392	C₂²	#15689150	1	1	yes	characteristic
393	C₂²	#15689150	1	1	yes	characteristic
394	C₂²	#15689176	1	2	yes	—
395	C₂²	#15689180	1	2	yes	—
396	C₂²	#15689184	1	2	yes	—
397	C₂²	#15689184	1	2	yes	—
398	C₂²	D₄×C₄₇⋊C₈	1	1	yes	characteristic
399	C₂²	D₄×C₄₇⋊C₈	1	2	yes	—
400	C₂²	#15689195	1	2	yes	—
401	C₂²	#15689195	1	2	yes	—
402	C₂²	#15689195	1	2	yes	—
403	C₂²	#15689201	1	2	yes	—
404	C₂²	#15689201	1	1	yes	characteristic
405	C₂²	Q₈×C₄₇⋊C₈	1	1	yes	characteristic
406	C₂²	#15689254	1	1	yes	characteristic
407	C₂²	#15689254	1	2	yes	—
408	C₄	—	2	4	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	2	no	—
412	C₄	#15689036	1	1	yes	characteristic
413	C₄	#15689041	1	1	yes	characteristic
414	C₄	#15689050	1	1	yes	characteristic
415	C₄	#15689057	1	2	yes	—
416	C₄	#15689063	1	1	yes	characteristic
417	C₄	#15689065	1	2	yes	—
418	C₂	#20241645	1	1	yes	characteristic
419	C₂	#20243505	1	1	yes	characteristic
420	C₂	#20243508	1	1	yes	characteristic
421	C₂	#20243568	1	1	yes	characteristic
422	C₂	#20243573	1	1	yes	characteristic
423	C₂	#20243947	1	2	yes	—
424	C₂	#20243954	1	2	yes	—
425	C₂	#20243996	1	2	yes	—
426	C₂	#20244003	1	2	yes	—
427	C₂	#20244107	1	1	yes	characteristic
428	C₂	#20244112	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂²×C₈
Fitting	C₄×#95×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₄×#95	D₄₇
hypocenter	C₄₇	#11255
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₄×#95

Complements

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

N	H ≅ G/N	type
54. #95×C₄₇	C₈	semidirect
233. C₄₇	#11255	semidirect
269. #95	C₄₇⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊(C₄₇⋊C₈)	2
C₂×#15688878	2
C₄×#95×C₄₇	2
#11255	47