Subgroups — #26121759

Order 12032.

1254 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×#15689140	C₂	1	2	yes	maximal
2	#20243127	C₂	1	1	yes	maximal, characteristic, complemented
3	#20243121	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243107	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#520	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂×#13093983	C₂²	1	2	yes	—
8	#15689140	—	2	4	no	—
9	#15689140	C₄	1	8	yes	complemented
10	C₂×#13093951	—	2	4	no	—
11	#15688892	—	2	1	no	—
12	#15688892	—	2	1	no	—
13	#15688890	—	2	2	no	—
14	#15688885	—	2	4	no	—
15	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#520	—	2	4	no	—
17	C₄₇×#520	—	2	4	no	—
18	C₂×C₄×Q₈×C₄₇	C₄	1	2	yes	complemented
19	C₂×C₄×D₄×C₄₇	—	2	2	no	—
20	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	complemented
21	C₂×#117×C₄₇	—	2	1	no	—
22	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
24	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	—	2	2	no	—
29	C₂×#10625329	—	2	2	no	—
30	C₂×#10625329	C₂×C₄	1	4	yes	complemented
31	C₂²×C₄₇⋊C₈	—	2	2	no	—
32	#13093983	—	2	2	no	—
33	#13093983	—	2	2	no	—
34	#13093983	—	2	2	no	—
35	#13093983	C₂×C₄	1	4	yes	complemented
36	C₂×C₄⋊Dic₄₇	—	2	2	no	—
37	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
38	C₂×C₄×Dic₄₇	—	2	2	no	—
39	#13093951	—	2	16	no	—
40	C₂×#41×C₄₇	—	2	2	no	—
41	C₂×#41×C₄₇	—	2	2	no	—
42	C₂×#41×C₄₇	—	2	1	no	—
43	C₂×#41×C₄₇	—	2	1	no	—
44	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
45	C₂×#41×C₄₇	D₄	1	4	yes	—
46	C₂×#41×C₄₇	D₄	1	2	yes	—
47	C₂×#41×C₄₇	Q₈	1	2	yes	—
48	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₄×C₄₇	—	2	1	no	—
50	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	—	2	1	no	—
52	C₂³×C₄×C₄₇	—	2	1	no	—
53	C₂³×C₄×C₄₇	—	2	2	no	—
54	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
55	C₄×Q₈×C₄₇	—	2	4	no	—
56	C₄×Q₈×C₄₇	—	2	4	no	—
57	C₄×D₄×C₄₇	—	2	16	no	—
58	C₄×D₄×C₄₇	—	2	4	no	—
59	C₄×D₄×C₄₇	—	2	4	no	—
60	#117×C₄₇	—	2	8	no	—
61	#117×C₄₇	—	2	2	no	—
62	#117×C₄₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
73	C₂×C₄²×C₄₇	—	2	2	no	—
74	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
75	C₂⁴×C₄₇	—	2	1	no	—
76	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
77	#41×C₄₇	—	2	4	no	—
78	#41×C₄₇	—	2	4	no	—
79	#41×C₄₇	—	2	4	no	—
80	#41×C₄₇	—	2	4	no	—
81	#41×C₄₇	—	2	4	no	—
82	#41×C₄₇	—	2	4	no	—
83	#41×C₄₇	C₂²⋊C₄	1	8	yes	—
84	#41×C₄₇	C₄⋊C₄	1	8	yes	—
85	C₂×Q₈×C₄₇	—	2	1	no	—
86	C₂×Q₈×C₄₇	—	2	1	no	—
87	C₂×Q₈×C₄₇	—	2	1	no	—
88	C₂×Q₈×C₄₇	C₄²	1	2	yes	—
89	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
90	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
91	C₂×D₄×C₄₇	—	2	4	no	—
92	C₂×D₄×C₄₇	—	2	4	no	—
93	C₂×D₄×C₄₇	—	2	2	no	—
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	—	2	1	no	—
96	C₂×D₄×C₄₇	—	2	1	no	—
97	C₂×D₄×C₄₇	—	2	1	no	—
98	C₂×D₄×C₄₇	C₄²	1	2	yes	—
99	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
100	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	4	no	—
103	C₂²×C₄×C₄₇	—	2	4	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	2	8	no	—
108	C₂²×C₄×C₄₇	—	2	4	no	—
109	C₂²×C₄×C₄₇	—	8	2	no	—
110	C₂²×C₄×C₄₇	—	8	4	no	—
111	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	#41	1	2	yes	—
123	C₂²×Dic₄₇	—	4	2	no	—
124	C₄⋊C₄×C₄₇	—	2	8	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	—	2	4	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
130	C₂²⋊C₄×C₄₇	—	2	8	no	—
131	C₂²⋊C₄×C₄₇	—	2	4	no	—
132	C₄²×C₄₇	—	2	8	no	—
133	C₄²×C₄₇	—	2	2	no	—
134	C₄²×C₄₇	—	2	2	no	—
135	C₂²⋊Dic₄₇	—	2	4	no	—
136	C₂²⋊Dic₄₇	—	4	2	no	—
137	C₄⋊Dic₄₇	—	2	4	no	—
138	C₄⋊Dic₄₇	—	4	2	no	—
139	C₄×Dic₄₇	—	2	4	no	—
140	C₄×Dic₄₇	—	4	2	no	—
141	#10625329	—	2	4	no	—
142	#10625329	—	2	4	no	—
143	#10625329	—	4	2	no	—
144	#10625329	—	4	2	no	—
145	C₂×C₄₇⋊C₈	—	2	4	no	—
146	C₂×C₄₇⋊C₈	—	4	2	no	—
147	C₂×C₄₇⋊C₈	—	4	2	no	—
148	C₂³×C₄₇	—	2	2	no	—
149	C₂³×C₄₇	—	2	2	no	—
150	C₂³×C₄₇	—	2	2	no	—
151	C₂³×C₄₇	—	4	1	no	—
152	C₂³×C₄₇	—	4	1	no	—
153	C₂³×C₄₇	—	4	2	no	—
154	C₂³×C₄₇	—	4	2	no	—
155	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂³×C₄₇	C₄×D₄	1	2	yes	—
157	C₂³×C₄₇	#120	1	2	yes	—
158	C₂³×C₄₇	#121	1	1	yes	characteristic
159	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
160	Q₈×C₄₇	—	2	2	no	—
161	Q₈×C₄₇	—	2	2	no	—
162	Q₈×C₄₇	—	2	2	no	—
163	Q₈×C₄₇	#95	1	4	yes	—
164	D₄×C₄₇	—	2	8	no	—
165	D₄×C₄₇	—	2	8	no	—
166	D₄×C₄₇	—	2	2	no	—
167	D₄×C₄₇	—	2	2	no	—
168	D₄×C₄₇	—	2	2	no	—
169	D₄×C₄₇	#95	1	4	yes	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	8	no	—
174	C₂×C₄×C₄₇	—	2	8	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	4	no	—
178	C₂×C₄×C₄₇	—	4	4	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	8	4	no	—
182	C₂×C₄×C₄₇	—	8	8	no	—
183	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
185	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
188	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
190	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
193	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
194	C₂×C₄×C₄₇	#120	1	2	yes	—
195	C₂×C₄×C₄₇	#121	1	2	yes	—
196	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
198	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
199	C₂×C₄×C₄₇	#123	1	2	yes	—
200	C₂×C₄×C₄₇	#123	1	2	yes	—
201	C₂×Dic₄₇	—	4	4	no	—
202	C₂×Dic₄₇	—	8	2	no	—
203	C₂×Dic₄₇	—	8	2	no	—
204	C₄₇⋊C₈	—	4	4	no	—
205	#10775	—	47	1	no	maximal, Sylow
206	C₂²×C₄₇	—	2	2	no	—
207	C₂²×C₄₇	—	2	1	no	—
208	C₂²×C₄₇	—	2	2	no	—
209	C₂²×C₄₇	—	2	1	no	—
210	C₂²×C₄₇	—	2	4	no	—
211	C₂²×C₄₇	—	4	2	no	—
212	C₂²×C₄₇	—	4	1	no	—
213	C₂²×C₄₇	—	4	1	no	—
214	C₂²×C₄₇	—	4	4	no	—
215	C₂²×C₄₇	—	4	4	no	—
216	C₂²×C₄₇	—	4	2	no	—
217	C₂²×C₄₇	—	4	2	no	—
218	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
219	C₂²×C₄₇	#379	1	1	yes	characteristic
220	C₂²×C₄₇	#380	1	1	yes	characteristic
221	C₂²×C₄₇	#385	1	2	yes	—
222	C₂²×C₄₇	#386	1	2	yes	—
223	C₄×C₄₇	—	2	4	no	—
224	C₄×C₄₇	—	4	4	no	—
225	C₄×C₄₇	—	4	2	no	—
226	C₄×C₄₇	—	4	2	no	—
227	C₄×C₄₇	C₂×#95	1	1	yes	characteristic
228	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
229	C₄×C₄₇	#380	1	1	yes	characteristic
230	C₄×C₄₇	#381	1	1	yes	characteristic
231	C₄×C₄₇	#385	1	2	yes	—
232	C₄×C₄₇	#386	1	2	yes	—
233	Dic₄₇	—	8	4	no	—
234	C₂×#520	D₄₇	1	1	yes	characteristic
235	C₂×#421	—	47	2	no	—
236	#1742	—	47	1	no	—
237	#1740	—	47	1	no	—
238	#1736	—	47	2	no	—
239	C₂×C₄₇	—	2	2	no	—
240	C₂×C₄₇	—	2	1	no	—
241	C₂×C₄₇	—	2	1	no	—
242	C₂×C₄₇	—	2	2	no	—
243	C₂×C₄₇	—	4	4	no	—
244	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
245	C₂×C₄₇	#1795	1	1	yes	characteristic
246	C₂×C₄₇	#1796	1	1	yes	characteristic
247	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
248	C₂²×M₁₆	—	47	2	no	—
249	#520	—	2	4	no	—
250	#520	—	2	4	no	—
251	C₂×C₄×Q₈	Dic₄₇	1	2	yes	complemented
252	C₂×C₄×D₄	—	2	2	no	—
253	C₂×C₄×D₄	Dic₄₇	1	2	yes	complemented
254	C₂×#117	—	2	1	no	—
255	C₂×#117	—	47	2	no	—
256	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
257	C₂²×C₄⋊C₄	—	2	1	no	—
258	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
259	#421	—	47	8	no	—
260	#421	—	94	4	no	—
261	C₂×#104	—	94	4	no	—
262	#343	—	94	1	no	—
263	#343	—	94	1	no	—
264	#342	—	94	2	no	—
265	#340	—	94	4	no	—
266	C₄₇	#10775	1	1	yes	characteristic, complemented, Sylow
267	C₂×#41	—	2	2	no	—
268	C₂×#41	—	2	1	no	—
269	C₂×#41	—	2	1	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	Dic₉₄	1	2	yes	—
272	C₂×#41	C₄×D₄₇	1	4	yes	—
273	C₂×#41	D₁₈₈	1	2	yes	—
274	C₂×#41	C₂²⋊D₄₇	1	4	yes	—
275	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	—	2	1	no	—
280	C₂³×C₄	—	2	2	no	—
281	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
282	C₂×M₁₆	—	47	4	no	—
283	C₂×M₁₆	—	94	2	no	—
284	C₂×M₁₆	—	94	2	no	—
285	C₂×M₁₆	—	94	2	no	—
286	C₂×M₁₆	—	94	2	no	—
287	C₂×M₁₆	—	94	2	no	—
288	C₂²×C₈	—	94	2	no	—
289	C₄×Q₈	—	2	4	no	—
290	C₄×Q₈	—	2	4	no	—
291	C₄×D₄	—	2	16	no	—
292	C₄×D₄	—	2	4	no	—
293	C₄×D₄	—	2	4	no	—
294	#117	—	2	8	no	—
295	#117	—	2	2	no	—
296	#117	—	2	2	no	—
297	#117	—	47	4	no	—
298	#117	—	94	2	no	—
299	#117	—	94	2	no	—
300	#117	—	94	2	no	—
301	C₂×C₄⋊C₄	—	2	8	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	94	2	no	—
306	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
307	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	4	yes	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	94	2	no	—
312	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
313	C₂×C₄²	—	2	2	no	—
314	C₂×C₄²	—	94	2	no	—
315	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
316	#104	—	94	16	no	—
317	C₂⁴	—	2	1	no	—
318	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
319	#41	—	2	4	no	—
320	#41	—	2	4	no	—
321	#41	—	2	4	no	—
322	#41	—	2	4	no	—
323	#41	—	2	4	no	—
324	#41	—	2	4	no	—
325	#41	Dic₄₇⋊C₄	1	8	yes	—
326	#41	(C₂×D₄₇)⋊C₄	1	8	yes	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	C₄×Dic₄₇	1	2	yes	—
331	C₂×Q₈	C₄⋊Dic₄₇	1	2	yes	—
332	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	C₄×Dic₄₇	1	2	yes	—
341	C₂×D₄	C₄⋊Dic₄₇	1	2	yes	—
342	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	8	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	8	2	no	—
352	C₂²×C₄	—	8	4	no	—
353	C₂²×C₄	—	188	2	no	—
354	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
355	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
356	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
358	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
359	C₂²×C₄	#10625350	1	1	yes	characteristic
360	C₂²×C₄	#10625350	1	1	yes	characteristic
361	C₂²×C₄	#10625350	1	2	yes	—
362	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
364	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
365	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
366	M₁₆	—	94	4	no	—
367	M₁₆	—	94	4	no	—
368	M₁₆	—	188	2	no	—
369	M₁₆	—	188	2	no	—
370	C₂×C₈	—	94	4	no	—
371	C₂×C₈	—	188	2	no	—
372	C₂×C₈	—	188	2	no	—
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	94	4	no	—
379	C₄⋊C₄	—	188	2	no	—
380	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	94	4	no	—
384	C₂²⋊C₄	—	188	2	no	—
385	C₄²	—	2	8	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	94	4	no	—
389	C₄²	—	188	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
398	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
399	C₂³	#13093993	1	2	yes	—
400	C₂³	#13093998	1	1	yes	characteristic
401	C₂³	#13094003	1	1	yes	characteristic
402	Q₈	—	2	2	no	—
403	Q₈	—	2	2	no	—
404	Q₈	—	2	2	no	—
405	Q₈	C₄₇⋊#95	1	4	yes	—
406	D₄	—	2	8	no	—
407	D₄	—	2	8	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	2	no	—
410	D₄	—	2	2	no	—
411	D₄	C₄₇⋊#95	1	4	yes	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	8	4	no	—
424	C₂×C₄	—	8	8	no	—
425	C₂×C₄	—	376	2	no	—
426	C₂×C₄	—	376	2	no	—
427	C₂×C₄	—	188	4	no	—
428	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
429	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
430	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
431	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
432	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
433	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
434	C₂×C₄	#13093983	1	1	yes	characteristic
435	C₂×C₄	#13093983	1	1	yes	characteristic
436	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
437	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
438	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
439	C₂×C₄	#13093993	1	2	yes	—
440	C₂×C₄	#13093998	1	2	yes	—
441	C₂×C₄	#13093998	1	1	yes	characteristic
442	C₂×C₄	#13094003	1	2	yes	—
443	C₂×C₄	#13094003	1	1	yes	characteristic
444	C₂×C₄	#13094007	1	2	yes	—
445	C₂×C₄	#13094007	1	2	yes	—
446	C₈	—	188	4	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
460	C₂²	#15688979	1	1	yes	characteristic
461	C₂²	#15688983	1	1	yes	characteristic
462	C₂²	#15688996	1	2	yes	—
463	C₂²	#15689002	1	2	yes	—
464	C₄	—	2	4	no	—
465	C₄	—	4	4	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	376	4	no	—
469	C₄	C₂×C₄₇⋊#95	1	1	yes	characteristic
470	C₄	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
471	C₄	#15688983	1	1	yes	characteristic
472	C₄	#15688986	1	1	yes	characteristic
473	C₄	#15688996	1	2	yes	—
474	C₄	#15689002	1	2	yes	—
475	C₂	—	2	2	no	—
476	C₂	—	2	1	no	—
477	C₂	—	2	1	no	—
478	C₂	—	2	2	no	—
479	C₂	—	4	4	no	—
480	C₂	#20241611	1	1	yes	characteristic
481	C₂	#20243358	1	1	yes	characteristic
482	C₂	#20243363	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15688979
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#520	C₂
socle	C₂²×C₄₇	#379
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#520	D₄₇
hypocenter	C₄₇	#10775
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#520

Complements

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

N	H ≅ G/N	type
2. #20243127	C₂	semidirect
3. #20243121	C₂	semidirect
4. #20243107	C₂	semidirect
9. #15689140	C₄	semidirect
18. C₂×C₄×Q₈×C₄₇	C₄	semidirect
20. C₂×C₄×D₄×C₄₇	C₄	semidirect
30. C₂×#10625329	C₂×C₄	semidirect
35. #13093983	C₂×C₄	semidirect
251. C₂×C₄×Q₈	Dic₄₇	semidirect
253. C₂×C₄×D₄	Dic₄₇	semidirect
266. C₄₇	#10775	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689140	2
#20243127	2
#20243121	2
#20243107	2
C₂×C₄₇×#520	2
#10775	47