Subgroups — #26228237

Order 12032.

794 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689254	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689176	C₂	1	1	yes	maximal, characteristic
3	#20244325	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244112	C₂	1	2	yes	maximal, complemented
5	#20244107	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244003	C₂	1	2	yes	maximal
7	#20244003	C₂	1	2	yes	maximal
8	#20243954	C₂	1	2	yes	maximal, complemented
9	#20243368	C₂	1	1	yes	maximal, characteristic
10	#20243257	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
12	#15689254	—	2	4	no	—
13	#15689176	—	2	4	no	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
20	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
23	C₂×#13093935	C₂²	1	2	yes	—
24	C₂×#13093935	C₂²	1	2	yes	—
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	#15688878	C₂²	1	2	yes	—
28	#15688878	C₂²	1	2	yes	—
29	#15688878	C₂²	1	2	yes	—
30	#15688878	C₂²	1	2	yes	—
31	#15688878	C₂²	1	2	yes	—
32	C₂×C₂²⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#391	C₄	1	1	yes	characteristic
36	C₄₇×#389	C₄	1	1	yes	characteristic
37	C₄₇×#387	C₄	1	2	yes	—
38	C₄₇×#385	C₄	1	2	yes	—
39	C₄₇×#380	C₄	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
42	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
50	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
51	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
52	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
54	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
55	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
56	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
57	C₂²⋊(C₄₇⋊C₈)	—	4	2	no	—
58	#13093935	—	2	4	no	—
59	#13093935	—	4	2	no	—
60	C₄×C₄₇⋊C₈	—	2	2	no	—
61	C₄×C₄₇⋊C₈	D₄	1	4	yes	—
62	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
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⋊Q₈×C₄₇	—	2	4	no	—
67	C₄×Q₈×C₄₇	—	2	2	no	—
68	C₄×Q₈×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
77	C₂×C₄²×C₄₇	—	2	2	no	—
78	C₂×C₄²×C₄₇	—	2	2	no	—
79	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
83	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	#95×C₄₇	C₂×C₄	1	2	yes	—
86	#95×C₄₇	C₂×C₄	1	2	yes	—
87	#95×C₄₇	C₂×C₄	1	2	yes	—
88	#95×C₄₇	C₂×C₄	1	2	yes	—
89	#95×C₄₇	C₂×C₄	1	2	yes	—
90	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂×Q₈×C₄₇	—	2	2	no	—
92	C₂×Q₈×C₄₇	—	2	2	no	—
93	C₂×Q₈×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	4	1	no	—
104	C₂²×C₄×C₄₇	—	4	1	no	—
105	C₂²×C₄×C₄₇	M₁₆	1	4	yes	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₄⋊C₄×C₄₇	—	2	2	no	—
117	C₄⋊C₄×C₄₇	—	2	4	no	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	4	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	4	2	no	—
122	C₂²⋊C₄×C₄₇	—	2	4	no	—
123	C₂²⋊C₄×C₄₇	—	4	2	no	—
124	C₄²×C₄₇	—	2	2	no	—
125	C₄²×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	—	2	1	no	—
127	C₄²×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	—	2	1	no	—
129	C₄²×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	—	2	2	no	—
131	C₄²×C₄₇	—	2	2	no	—
132	C₄²×C₄₇	C₂×D₄	1	2	yes	—
133	C₄²×C₄₇	#41	1	2	yes	—
134	C₂×C₄₇⋊C₈	—	2	1	no	—
135	C₂×C₄₇⋊C₈	—	2	1	no	—
136	C₂×C₄₇⋊C₈	—	2	1	no	—
137	C₂×C₄₇⋊C₈	—	2	1	no	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	—	2	1	no	—
140	C₂×C₄₇⋊C₈	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	—	2	2	no	—
144	C₂×C₄₇⋊C₈	—	2	1	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₂×C₄₇⋊C₈	—	2	2	no	—
150	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
151	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
152	C₂³×C₄₇	—	2	1	no	—
153	C₂³×C₄₇	—	2	1	no	—
154	C₂³×C₄₇	—	2	1	no	—
155	C₂³×C₄₇	—	2	1	no	—
156	C₂³×C₄₇	—	2	1	no	—
157	C₂³×C₄₇	—	2	1	no	—
158	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
159	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
160	Q₈×C₄₇	—	4	4	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	8	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	1	no	—
184	C₂×C₄×C₄₇	—	4	4	no	—
185	C₂×C₄×C₄₇	—	4	1	no	—
186	C₂×C₄×C₄₇	—	4	1	no	—
187	C₂×C₄×C₄₇	—	4	1	no	—
188	C₂×C₄×C₄₇	—	4	1	no	—
189	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
190	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
191	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
192	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
193	C₂×C₄×C₄₇	#131	1	2	yes	—
194	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
198	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
199	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
200	C₄₇⋊C₈	—	2	2	no	—
201	C₄₇⋊C₈	—	2	2	no	—
202	C₄₇⋊C₈	—	4	1	no	—
203	C₄₇⋊C₈	—	4	1	no	—
204	C₄₇⋊C₈	—	4	2	no	—
205	C₄₇⋊C₈	—	4	2	no	—
206	#22104	—	47	1	no	maximal, Sylow
207	C₂²×C₄₇	—	2	2	no	—
208	C₂²×C₄₇	—	2	2	no	—
209	C₂²×C₄₇	—	2	2	no	—
210	C₂²×C₄₇	—	4	1	no	—
211	C₂²×C₄₇	—	4	1	no	—
212	C₂²×C₄₇	—	4	1	no	—
213	C₂²×C₄₇	—	4	1	no	—
214	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
215	C₂²×C₄₇	#519	1	1	yes	characteristic
216	C₂²×C₄₇	#520	1	1	yes	characteristic
217	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
218	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
219	C₂²×C₄₇	#568	1	1	yes	characteristic
220	C₂²×C₄₇	#568	1	1	yes	characteristic
221	C₄×C₄₇	—	2	2	no	—
222	C₄×C₄₇	—	2	2	no	—
223	C₄×C₄₇	—	4	1	no	—
224	C₄×C₄₇	—	4	2	no	—
225	C₄×C₄₇	—	4	2	no	—
226	C₄×C₄₇	—	4	1	no	—
227	C₄×C₄₇	—	4	2	no	—
228	C₄×C₄₇	—	4	2	no	—
229	C₄×C₄₇	#435	1	4	yes	—
230	C₄×C₄₇	#536	1	1	yes	characteristic
231	C₄×C₄₇	#537	1	1	yes	characteristic
232	C₄×C₄₇	#541	1	1	yes	characteristic
233	C₄×C₄₇	#542	1	1	yes	characteristic
234	C₂×#446	—	47	1	no	—
235	C₂×#431	—	47	1	no	—
236	C₄×C₂²⋊Q₈	D₄₇	1	1	yes	characteristic
237	#1984	—	47	1	no	—
238	#1940	—	47	2	no	—
239	#1939	—	47	1	no	—
240	#1924	—	47	2	no	—
241	#1924	—	47	2	no	—
242	#1917	—	47	2	no	—
243	#1797	—	47	1	no	—
244	#1770	—	47	1	no	—
245	C₂×C₄₇	—	4	2	no	—
246	C₂×C₄₇	#2323	1	1	yes	characteristic
247	C₂×C₄₇	C₂×#435	1	1	yes	characteristic
248	C₂×C₄₇	#2930	1	1	yes	characteristic
249	C₂×C₄₇	#2983	1	1	yes	characteristic
250	C₂×C₄₇	#2985	1	1	yes	characteristic
251	C₂×C₄₇	#2989	1	1	yes	characteristic
252	C₂×C₄₇	#2993	1	1	yes	characteristic
253	C₂×C₂²⋊Q₈	Dic₄₇	1	1	yes	characteristic
254	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
255	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
256	#446	—	94	4	no	—
257	#431	—	94	4	no	—
258	C₂×C₄⋊C₈	—	47	1	no	—
259	C₂×C₄⋊C₈	—	47	1	no	—
260	C₂×C₄⋊C₈	—	47	1	no	—
261	C₂×C₄⋊C₈	—	47	1	no	—
262	C₂×C₄⋊C₈	—	47	2	no	—
263	C₂×C₄⋊C₈	—	47	2	no	—
264	C₂×C₂²⋊C₈	—	47	1	no	—
265	C₂×C₂²⋊C₈	—	47	1	no	—
266	C₂×C₂²⋊C₈	—	47	2	no	—
267	C₂×#97	—	47	2	no	—
268	C₂×#97	—	47	2	no	—
269	C₂×C₄×C₈	—	47	1	no	—
270	C₂×C₄×C₈	—	47	1	no	—
271	#391	Dic₄₇	1	1	yes	characteristic
272	#389	Dic₄₇	1	1	yes	characteristic
273	#387	Dic₄₇	1	2	yes	—
274	#385	Dic₄₇	1	2	yes	—
275	#380	Dic₄₇	1	1	yes	characteristic
276	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
277	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
278	C₄×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
279	#336	—	47	2	no	—
280	#336	—	47	2	no	—
281	#336	—	47	2	no	—
282	#336	—	47	2	no	—
283	#336	—	47	2	no	—
284	C₄₇	#22104	1	1	yes	characteristic, complemented, Sylow
285	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
286	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
287	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
288	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
289	C₂²×C₈	—	47	1	no	—
290	C₂²×C₈	—	47	1	no	—
291	C₂²×C₈	—	47	1	no	—
292	C₂²×C₈	—	47	2	no	—
293	C₂²×C₈	—	47	1	no	—
294	C₂²×C₈	—	47	2	no	—
295	C₂²⋊Q₈	—	2	4	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×Q₈	—	2	2	no	—
298	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
300	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
301	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
304	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
305	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
306	C₂×C₄²	—	2	2	no	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
309	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
310	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
311	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
312	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
313	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
314	C₄⋊C₈	—	94	2	no	—
315	C₄⋊C₈	—	94	2	no	—
316	C₄⋊C₈	—	94	4	no	—
317	C₄⋊C₈	—	94	2	no	—
318	C₄⋊C₈	—	94	2	no	—
319	C₄⋊C₈	—	188	2	no	—
320	C₂²⋊C₈	—	94	2	no	—
321	C₂²⋊C₈	—	94	2	no	—
322	C₂²⋊C₈	—	188	2	no	—
323	#97	—	94	4	no	—
324	#97	—	188	2	no	—
325	C₄×C₈	—	47	4	no	—
326	C₄×C₈	—	94	2	no	—
327	#95	C₂×Dic₄₇	1	2	yes	—
328	#95	C₂×Dic₄₇	1	2	yes	—
329	#95	C₂×Dic₄₇	1	2	yes	—
330	#95	C₂×Dic₄₇	1	2	yes	—
331	#95	C₂×Dic₄₇	1	2	yes	—
332	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	#10625329	1	4	yes	—
348	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
349	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
350	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
351	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
352	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
353	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
354	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
355	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
356	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
357	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
358	C₂×C₈	—	47	2	no	—
359	C₂×C₈	—	47	2	no	—
360	C₂×C₈	—	94	1	no	—
361	C₂×C₈	—	94	1	no	—
362	C₂×C₈	—	94	1	no	—
363	C₂×C₈	—	94	1	no	—
364	C₂×C₈	—	94	1	no	—
365	C₂×C₈	—	94	1	no	—
366	C₂×C₈	—	94	2	no	—
367	C₂×C₈	—	94	2	no	—
368	C₂×C₈	—	94	2	no	—
369	C₂×C₈	—	94	2	no	—
370	C₂×C₈	—	94	1	no	—
371	C₂×C₈	—	94	1	no	—
372	C₂×C₈	—	94	2	no	—
373	C₂×C₈	—	94	1	no	—
374	C₂×C₈	—	94	1	no	—
375	C₂×C₈	—	94	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	D₄×D₄₇	1	2	yes	—
393	C₄²	#10625352	1	2	yes	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	1	no	—
400	C₂³	C₂×#10625329	1	2	yes	—
401	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
402	Q₈	—	4	4	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	8	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
432	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
433	C₂×C₄	C₂×#10625329	1	2	yes	—
434	C₂×C₄	C₂×#10625329	1	2	yes	—
435	C₂×C₄	#13094031	1	2	yes	—
436	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
437	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
438	C₂×C₄	#13094070	1	1	yes	characteristic
439	C₂×C₄	#13094071	1	1	yes	characteristic
440	C₂×C₄	#13094072	1	1	yes	characteristic
441	C₂×C₄	#13094072	1	1	yes	characteristic
442	C₈	—	94	2	no	—
443	C₈	—	94	2	no	—
444	C₈	—	188	2	no	—
445	C₈	—	188	1	no	—
446	C₈	—	188	1	no	—
447	C₈	—	188	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
456	C₂²	#15689601	1	1	yes	characteristic
457	C₂²	#15689606	1	1	yes	characteristic
458	C₂²	C₂²×#10625329	1	1	yes	characteristic
459	C₂²	C₂×#13094031	1	1	yes	characteristic
460	C₂²	#15689890	1	1	yes	characteristic
461	C₂²	#15689890	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	2	no	—
470	C₄	#15689195	1	4	yes	—
471	C₄	#15689696	1	1	yes	characteristic
472	C₄	#15689703	1	1	yes	characteristic
473	C₄	#15689733	1	1	yes	characteristic
474	C₄	#15689746	1	1	yes	characteristic
475	C₂	—	4	2	no	—
476	C₂	#20246072	1	1	yes	characteristic
477	C₂	C₂×#15689195	1	1	yes	characteristic
478	C₂	#20252092	1	1	yes	characteristic
479	C₂	#20252473	1	1	yes	characteristic
480	C₂	#20252483	1	1	yes	characteristic
481	C₂	#20252505	1	1	yes	characteristic
482	C₂	#20252537	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄×C₂²⋊Q₈×C₄₇	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×C₂²⋊Q₈	D₄₇
hypocenter	C₄₇	#22104
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#15689254	C₂	semidirect
3. #20244325	C₂	semidirect
4. #20244112	C₂	semidirect
5. #20244107	C₂	semidirect
8. #20243954	C₂	semidirect
10. #20243257	C₂	semidirect
284. C₄₇	#22104	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689254	2
C₂×#15689176	2
#20244325	2
#20244112	2
#20244107	2
#20244003	2
#20243954	2
#20243368	2
#20243257	2
C₄×C₂²⋊Q₈×C₄₇	2
#22104	47