Subgroups — #26123297

Order 12032.

1006 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689127	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13093946	C₂	1	1	yes	maximal, characteristic
3	C₂²×#13093940	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688891	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15688888	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243109	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
12	#15689127	—	2	2	no	—
13	#15689127	C₄	1	4	yes	complemented
14	C₂×#13093946	—	2	2	no	—
15	C₂×#13093946	—	2	2	no	—
16	C₂×#13093946	—	2	2	no	—
17	C₂×#13093944	—	2	2	no	—
18	C₂×#13093940	—	2	2	no	—
19	C₂×#13093940	—	2	2	no	—
20	C₂×#13093940	—	2	2	no	—
21	#15688891	—	2	2	no	—
22	#15688888	—	2	2	no	—
23	#15688885	—	2	2	no	—
24	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
25	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
27	C₄₇×#424	—	2	2	no	—
28	C₄₇×#424	—	2	2	no	—
29	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
30	C₂⁴×D₄₇	—	2	1	no	—
31	C₂²×D₁₈₈	—	2	1	no	—
32	C₂²×D₁₈₈	—	2	1	no	—
33	C₂²×D₁₈₈	—	2	1	no	—
34	C₂²×D₁₈₈	—	2	1	no	—
35	C₂²×D₁₈₈	—	2	1	no	—
36	C₂²×D₁₈₈	—	2	1	no	—
37	C₂²×D₁₈₈	—	2	1	no	—
38	C₂²×D₁₈₈	—	2	1	no	—
39	C₂²×D₁₈₈	—	2	1	no	—
40	C₂²×D₁₈₈	—	2	1	no	—
41	C₂²×D₁₈₈	—	2	1	no	—
42	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
43	C₂²×D₁₈₈	D₄	1	2	yes	—
44	C₂²×D₁₈₈	Q₈	1	2	yes	—
45	C₂³×Dic₄₇	—	2	1	no	—
46	C₂×#10625329	—	2	1	no	—
47	C₂×#10625329	—	2	1	no	—
48	C₂×#10625329	—	2	1	no	—
49	C₂×#10625329	—	2	1	no	—
50	C₂×#10625329	—	2	1	no	—
51	C₂×#10625329	—	2	1	no	—
52	C₂×#10625329	—	2	1	no	—
53	C₂×#10625329	—	2	1	no	—
54	C₂×#10625329	—	2	1	no	—
55	C₂×#10625329	—	2	1	no	—
56	C₂×#10625329	C₂×C₄	1	2	yes	—
57	C₂×#10625329	D₄	1	2	yes	—
58	C₂²×C₄₇⋊C₈	—	2	1	no	—
59	C₂²×C₄₇⋊C₈	—	2	1	no	—
60	C₂×C₄⋊Dic₄₇	—	2	1	no	—
61	C₂×C₄⋊Dic₄₇	—	2	1	no	—
62	C₂×C₄⋊Dic₄₇	—	2	1	no	—
63	C₂×C₄⋊Dic₄₇	—	2	1	no	—
64	C₂×C₄⋊Dic₄₇	—	2	1	no	—
65	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
66	#13093946	—	2	8	no	—
67	#13093944	—	2	8	no	—
68	#13093940	—	2	8	no	—
69	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
70	C₂×M₁₆×C₄₇	—	2	1	no	—
71	C₂×M₁₆×C₄₇	—	2	1	no	—
72	C₂×M₁₆×C₄₇	—	2	1	no	—
73	C₂×M₁₆×C₄₇	—	2	1	no	—
74	C₂×M₁₆×C₄₇	—	2	1	no	—
75	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
76	C₂²×C₈×C₄₇	—	2	1	no	—
77	C₂²×C₈×C₄₇	—	2	1	no	—
78	C₂²×C₈×C₄₇	—	2	1	no	—
79	C₂²×C₈×C₄₇	—	2	1	no	—
80	C₂²×C₈×C₄₇	—	2	1	no	—
81	C₂²×C₈×C₄₇	—	2	1	no	—
82	C₂²×C₈×C₄₇	—	2	1	no	—
83	C₂²×C₈×C₄₇	D₄	1	2	yes	—
84	#117×C₄₇	—	2	1	no	—
85	#117×C₄₇	—	2	1	no	—
86	#117×C₄₇	C₂×C₄	1	2	yes	—
87	#117×C₄₇	D₄	1	2	yes	—
88	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
90	C₂×C₄²×C₄₇	—	2	1	no	—
91	C₄⋊C₈×C₄₇	—	2	8	no	—
92	C₂⁴×C₄₇	#41	1	1	yes	characteristic
93	C₂³×D₄₇	—	2	2	no	—
94	C₂³×D₄₇	—	2	2	no	—
95	C₂³×D₄₇	—	2	2	no	—
96	C₂³×D₄₇	—	4	1	no	—
97	C₂³×D₄₇	—	4	1	no	—
98	C₂³×D₄₇	—	4	1	no	—
99	C₂³×D₄₇	—	4	1	no	—
100	C₂³×D₄₇	—	8	2	no	—
101	C₂³×D₄₇	—	8	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
117	C₂²×Dic₄₇	—	2	2	no	—
118	C₂²×Dic₄₇	—	4	1	no	—
119	C₂²×Dic₄₇	—	4	1	no	—
120	C₂²×Dic₄₇	—	8	2	no	—
121	C₂×D₁₈₈	—	2	2	no	—
122	C₂×D₁₈₈	—	2	2	no	—
123	C₂×D₁₈₈	—	2	2	no	—
124	C₂×D₁₈₈	—	2	2	no	—
125	C₂×D₁₈₈	—	2	2	no	—
126	C₂×D₁₈₈	—	2	2	no	—
127	C₂×D₁₈₈	—	2	2	no	—
128	C₂×D₁₈₈	—	2	2	no	—
129	C₂×D₁₈₈	—	2	2	no	—
130	C₂×D₁₈₈	—	2	2	no	—
131	C₂×D₁₈₈	—	2	2	no	—
132	C₂×D₁₈₈	—	2	2	no	—
133	C₂×D₁₈₈	—	2	2	no	—
134	C₂×D₁₈₈	—	2	2	no	—
135	C₂×D₁₈₈	—	2	2	no	—
136	C₂×D₁₈₈	—	4	1	no	—
137	C₂×D₁₈₈	—	4	1	no	—
138	C₂×D₁₈₈	—	4	1	no	—
139	C₂×D₁₈₈	—	4	1	no	—
140	C₂×D₁₈₈	—	4	1	no	—
141	C₂×D₁₈₈	—	4	1	no	—
142	C₂×D₁₈₈	—	4	1	no	—
143	C₂×D₁₈₈	—	4	1	no	—
144	C₂×D₁₈₈	—	4	1	no	—
145	C₂×D₁₈₈	—	4	1	no	—
146	C₂×D₁₈₈	—	4	1	no	—
147	C₂×D₁₈₈	—	4	1	no	—
148	C₂×D₁₈₈	C₄⋊C₄	1	4	yes	—
149	M₁₆×C₄₇	—	2	2	no	—
150	M₁₆×C₄₇	—	2	2	no	—
151	M₁₆×C₄₇	—	4	1	no	—
152	M₁₆×C₄₇	—	4	1	no	—
153	C₂×C₈×C₄₇	—	2	2	no	—
154	C₂×C₈×C₄₇	—	2	2	no	—
155	C₂×C₈×C₄₇	—	2	2	no	—
156	C₂×C₈×C₄₇	—	2	2	no	—
157	C₂×C₈×C₄₇	—	4	1	no	—
158	C₂×C₈×C₄₇	—	4	1	no	—
159	C₂×C₈×C₄₇	—	4	1	no	—
160	C₂×C₈×C₄₇	—	4	1	no	—
161	C₂×C₈×C₄₇	—	4	1	no	—
162	C₂×C₈×C₄₇	—	4	1	no	—
163	C₄⋊C₄×C₄₇	—	2	2	no	—
164	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
165	C₂²⋊C₄×C₄₇	—	2	2	no	—
166	C₂²⋊C₄×C₄₇	—	2	2	no	—
167	C₄²×C₄₇	—	2	2	no	—
168	C₄²×C₄₇	—	2	2	no	—
169	C₄⋊Dic₄₇	—	2	2	no	—
170	C₄⋊Dic₄₇	—	2	2	no	—
171	C₄⋊Dic₄₇	—	4	1	no	—
172	C₄⋊Dic₄₇	—	4	1	no	—
173	#10625329	—	2	2	no	—
174	#10625329	—	2	2	no	—
175	#10625329	—	2	2	no	—
176	#10625329	—	2	2	no	—
177	#10625329	—	4	1	no	—
178	#10625329	—	4	1	no	—
179	#10625329	—	4	1	no	—
180	#10625329	—	4	1	no	—
181	C₂×C₄₇⋊C₈	—	2	2	no	—
182	C₂×C₄₇⋊C₈	—	2	2	no	—
183	C₂×C₄₇⋊C₈	—	4	1	no	—
184	C₂×C₄₇⋊C₈	—	4	1	no	—
185	C₂×C₄₇⋊C₈	—	4	1	no	—
186	C₂×C₄₇⋊C₈	—	4	1	no	—
187	C₂³×C₄₇	—	2	2	no	—
188	C₂³×C₄₇	—	2	2	no	—
189	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
190	C₂³×C₄₇	#121	1	1	yes	characteristic
191	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
192	C₂³×C₄₇	#123	1	1	yes	characteristic
193	C₂³×C₄₇	#123	1	1	yes	characteristic
194	C₂³×C₄₇	#123	1	1	yes	characteristic
195	C₂³×C₄₇	#126	1	1	yes	characteristic
196	C₂²×D₄₇	—	2	4	no	—
197	C₂²×D₄₇	—	4	2	no	—
198	C₂²×D₄₇	—	4	2	no	—
199	C₂²×D₄₇	—	4	2	no	—
200	C₂²×D₄₇	—	4	2	no	—
201	C₂²×D₄₇	—	4	2	no	—
202	C₂²×D₄₇	—	4	2	no	—
203	C₂²×D₄₇	—	8	4	no	—
204	C₂²×D₄₇	—	8	4	no	—
205	C₂²×D₄₇	—	8	2	no	—
206	C₂²×D₄₇	—	8	2	no	—
207	C₂²×D₄₇	—	8	2	no	—
208	C₂²×D₄₇	—	8	2	no	—
209	C₂²×D₄₇	—	8	4	no	—
210	C₂²×D₄₇	—	8	4	no	—
211	C₂²×D₄₇	—	8	2	no	—
212	C₂²×D₄₇	—	8	2	no	—
213	C₂×C₄×C₄₇	—	2	4	no	—
214	C₂×C₄×C₄₇	—	4	2	no	—
215	C₂×C₄×C₄₇	—	4	2	no	—
216	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
219	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
223	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
224	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
225	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
226	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
227	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
228	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
229	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
230	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
231	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
232	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
234	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
235	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
236	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
237	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
238	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
239	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
240	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
241	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
242	C₂×C₄×C₄₇	#126	1	1	yes	characteristic
243	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
244	C₂×Dic₄₇	—	4	2	no	—
245	C₂×Dic₄₇	—	8	2	no	—
246	C₂×Dic₄₇	—	8	2	no	—
247	C₂×Dic₄₇	—	8	2	no	—
248	D₁₈₈	—	2	4	no	—
249	D₁₈₈	—	2	4	no	—
250	D₁₈₈	—	4	2	no	—
251	D₁₈₈	—	4	2	no	—
252	D₁₈₈	—	4	2	no	—
253	D₁₈₈	—	4	2	no	—
254	D₁₈₈	—	4	2	no	—
255	D₁₈₈	—	4	2	no	—
256	C₈×C₄₇	—	4	2	no	—
257	C₈×C₄₇	—	4	2	no	—
258	C₄₇⋊C₈	—	4	2	no	—
259	C₄₇⋊C₈	—	4	2	no	—
260	#11061	—	47	1	no	maximal, Sylow
261	C₂²×C₄₇	—	2	2	no	—
262	C₂²×C₄₇	—	2	2	no	—
263	C₂²×C₄₇	—	2	2	no	—
264	C₂²×C₄₇	—	2	2	no	—
265	C₂²×C₄₇	—	2	1	no	—
266	C₂²×C₄₇	—	2	1	no	—
267	C₂²×C₄₇	—	2	1	no	—
268	C₂²×C₄₇	—	2	1	no	—
269	C₂²×C₄₇	#385	1	1	yes	characteristic
270	C₂²×C₄₇	#386	1	1	yes	characteristic
271	C₂²×C₄₇	#388	1	1	yes	characteristic
272	C₂²×C₄₇	#394	1	1	yes	characteristic
273	C₂²×C₄₇	#396	1	1	yes	characteristic
274	C₂²×C₄₇	#397	1	1	yes	characteristic
275	C₂²×C₄₇	#399	1	1	yes	characteristic
276	C₂²×C₄₇	#471	1	2	yes	—
277	C₂²×C₄₇	#472	1	2	yes	—
278	C₂×D₄₇	—	4	4	no	—
279	C₂×D₄₇	—	8	4	no	—
280	C₂×D₄₇	—	8	4	no	—
281	C₂×D₄₇	—	8	4	no	—
282	C₂×D₄₇	—	8	4	no	—
283	C₂×D₄₇	—	8	4	no	—
284	C₂×D₄₇	—	8	2	no	—
285	C₂×D₄₇	—	8	2	no	—
286	C₂×D₄₇	—	8	4	no	—
287	C₄×C₄₇	—	4	4	no	—
288	C₄×C₄₇	#380	1	1	yes	characteristic
289	C₄×C₄₇	#385	1	1	yes	characteristic
290	C₄×C₄₇	#388	1	1	yes	characteristic
291	C₄×C₄₇	#390	1	1	yes	characteristic
292	C₄×C₄₇	#392	1	1	yes	characteristic
293	C₄×C₄₇	#393	1	1	yes	characteristic
294	C₄×C₄₇	#394	1	1	yes	characteristic
295	C₄×C₄₇	#396	1	1	yes	characteristic
296	Dic₄₇	—	8	2	no	—
297	C₂×#424	D₄₇	1	1	yes	characteristic, complemented
298	C₂×#418	—	47	1	no	—
299	C₂²×#102	—	47	1	no	—
300	C₂²×#100	—	47	1	no	—
301	C₂×#343	—	47	1	no	—
302	C₂×#341	—	47	1	no	—
303	#1736	—	47	1	no	—
304	C₂×C₄₇	—	2	1	no	—
305	C₂×C₄₇	—	2	1	no	—
306	C₂×C₄₇	—	2	1	no	—
307	C₂×C₄₇	—	2	1	no	—
308	C₂×C₄₇	#1439	1	1	yes	characteristic
309	C₂×C₄₇	#1907	1	2	yes	—
310	C₂×C₄₇	#2045	1	1	yes	characteristic
311	C₂×C₄₇	#2046	1	1	yes	characteristic
312	C₂×C₄₇	#2063	1	2	yes	—
313	D₄₇	—	8	4	no	—
314	C₂³×D₄	—	47	1	no	—
315	C₂²×M₁₆	—	47	1	no	—
316	C₂²×M₁₆	—	47	1	no	—
317	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
318	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
319	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
320	C₂²×C₄⋊C₄	—	47	1	no	—
321	#424	—	2	2	no	—
322	#424	—	2	2	no	—
323	C₂×C₄⋊C₈	—	2	2	no	—
324	#418	—	47	4	no	—
325	#418	—	94	2	no	—
326	C₂×#102	—	94	2	no	—
327	C₂×#102	—	94	2	no	—
328	C₂×#102	—	94	2	no	—
329	C₂×#102	—	94	2	no	—
330	C₂×#100	—	94	2	no	—
331	C₂×#100	—	94	2	no	—
332	C₂×#100	—	94	2	no	—
333	#343	—	94	2	no	—
334	#341	—	94	2	no	—
335	#340	—	94	2	no	—
336	C₄₇	#11061	1	1	yes	characteristic, complemented, Sylow
337	C₂⁵	—	94	1	no	—
338	C₂²×D₄	—	47	2	no	—
339	C₂²×D₄	—	47	2	no	—
340	C₂²×D₄	—	47	2	no	—
341	C₂²×D₄	—	94	1	no	—
342	C₂²×D₄	—	94	1	no	—
343	C₂²×D₄	—	94	1	no	—
344	C₂²×D₄	—	94	1	no	—
345	C₂²×D₄	—	94	1	no	—
346	C₂²×D₄	—	94	1	no	—
347	C₂²×D₄	—	94	1	no	—
348	C₂²×D₄	—	94	1	no	—
349	C₂²×D₄	—	94	1	no	—
350	C₂²×D₄	—	94	1	no	—
351	C₂²×D₄	—	94	1	no	—
352	C₂³×C₄	—	94	1	no	—
353	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	47	2	no	—
360	C₂×M₁₆	—	47	2	no	—
361	C₂×M₁₆	—	94	1	no	—
362	C₂×M₁₆	—	94	1	no	—
363	C₂×M₁₆	—	94	1	no	—
364	C₂×M₁₆	—	94	1	no	—
365	C₂×M₁₆	—	94	1	no	—
366	C₂×M₁₆	—	94	1	no	—
367	C₂×M₁₆	—	94	1	no	—
368	C₂×M₁₆	—	94	1	no	—
369	C₂×M₁₆	—	94	1	no	—
370	C₂×M₁₆	—	94	1	no	—
371	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	2	1	no	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	94	1	no	—
380	C₂²×C₈	—	94	1	no	—
381	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
382	#117	—	2	1	no	—
383	#117	—	2	1	no	—
384	#117	C₄×D₄₇	1	2	yes	—
385	#117	C₂²⋊D₄₇	1	2	yes	—
386	C₂×C₄⋊C₄	—	47	2	no	—
387	C₂×C₄⋊C₄	—	94	1	no	—
388	C₂×C₄⋊C₄	—	94	1	no	—
389	C₂×C₄⋊C₄	—	94	1	no	—
390	C₂×C₄⋊C₄	—	94	1	no	—
391	C₂×C₄⋊C₄	—	94	1	no	—
392	C₂×C₄⋊C₄	D₁₈₈	1	2	yes	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₄²	—	2	1	no	—
395	C₄⋊C₈	—	2	8	no	—
396	#102	—	94	8	no	—
397	#102	—	94	8	no	—
398	#100	—	94	8	no	—
399	C₂⁴	—	94	2	no	—
400	C₂⁴	—	94	2	no	—
401	C₂⁴	—	94	2	no	—
402	C₂⁴	—	376	2	no	—
403	C₂⁴	—	376	2	no	—
404	C₂⁴	—	188	1	no	—
405	C₂⁴	—	188	1	no	—
406	C₂⁴	—	188	1	no	—
407	C₂⁴	—	188	1	no	—
408	C₂⁴	#10625350	1	1	yes	characteristic
409	C₂×D₄	—	47	4	no	—
410	C₂×D₄	—	94	2	no	—
411	C₂×D₄	—	94	2	no	—
412	C₂×D₄	—	94	2	no	—
413	C₂×D₄	—	94	2	no	—
414	C₂×D₄	—	94	2	no	—
415	C₂×D₄	—	94	2	no	—
416	C₂×D₄	—	94	2	no	—
417	C₂×D₄	—	94	2	no	—
418	C₂×D₄	—	94	2	no	—
419	C₂×D₄	—	94	2	no	—
420	C₂×D₄	—	94	2	no	—
421	C₂×D₄	—	94	2	no	—
422	C₂×D₄	—	94	2	no	—
423	C₂×D₄	—	94	2	no	—
424	C₂×D₄	—	94	2	no	—
425	C₂×D₄	—	188	1	no	—
426	C₂×D₄	—	188	1	no	—
427	C₂×D₄	—	188	1	no	—
428	C₂×D₄	—	188	1	no	—
429	C₂×D₄	—	188	1	no	—
430	C₂×D₄	—	188	1	no	—
431	C₂×D₄	—	188	1	no	—
432	C₂×D₄	—	188	1	no	—
433	C₂×D₄	—	188	1	no	—
434	C₂×D₄	—	188	1	no	—
435	C₂×D₄	—	188	1	no	—
436	C₂×D₄	—	188	1	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	94	2	no	—
439	C₂²×C₄	—	376	2	no	—
440	C₂²×C₄	—	188	1	no	—
441	C₂²×C₄	—	188	1	no	—
442	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
444	C₂²×C₄	#10625350	1	1	yes	characteristic
445	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
446	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
447	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
448	C₂²×C₄	#10625352	1	1	yes	characteristic
449	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
450	C₂²×C₄	#10625354	1	1	yes	characteristic
451	C₂²×C₄	#10625354	1	1	yes	characteristic
452	C₂²×C₄	#10625354	1	1	yes	characteristic
453	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
454	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
456	M₁₆	—	2	2	no	—
457	M₁₆	—	2	2	no	—
458	M₁₆	—	4	1	no	—
459	M₁₆	—	4	1	no	—
460	M₁₆	—	94	2	no	—
461	M₁₆	—	94	2	no	—
462	M₁₆	—	94	2	no	—
463	M₁₆	—	94	2	no	—
464	M₁₆	—	188	1	no	—
465	M₁₆	—	188	1	no	—
466	M₁₆	—	188	1	no	—
467	M₁₆	—	188	1	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	4	1	no	—
473	C₂×C₈	—	4	1	no	—
474	C₂×C₈	—	4	1	no	—
475	C₂×C₈	—	4	1	no	—
476	C₂×C₈	—	4	1	no	—
477	C₂×C₈	—	4	1	no	—
478	C₂×C₈	—	94	2	no	—
479	C₂×C₈	—	94	2	no	—
480	C₂×C₈	—	188	1	no	—
481	C₂×C₈	—	188	1	no	—
482	C₂×C₈	—	188	1	no	—
483	C₂×C₈	—	188	1	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	94	2	no	—
486	C₄⋊C₄	—	94	2	no	—
487	C₄⋊C₄	—	188	1	no	—
488	C₄⋊C₄	—	188	1	no	—
489	C₄⋊C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	94	4	no	—
497	C₂³	—	376	4	no	—
498	C₂³	—	376	2	no	—
499	C₂³	—	376	2	no	—
500	C₂³	—	376	4	no	—
501	C₂³	—	376	4	no	—
502	C₂³	—	376	2	no	—
503	C₂³	—	376	2	no	—
504	C₂³	—	376	4	no	—
505	C₂³	—	376	2	no	—
506	C₂³	—	376	2	no	—
507	C₂³	—	188	2	no	—
508	C₂³	—	188	2	no	—
509	C₂³	—	188	2	no	—
510	C₂³	—	188	2	no	—
511	C₂³	—	188	2	no	—
512	C₂³	—	188	2	no	—
513	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
514	C₂³	#13093998	1	1	yes	characteristic
515	C₂³	#13094002	1	1	yes	characteristic
516	C₂³	#13094007	1	1	yes	characteristic
517	C₂³	#13094009	1	1	yes	characteristic
518	C₂³	#13094009	1	1	yes	characteristic
519	C₂³	#13094019	1	1	yes	characteristic
520	D₄	—	94	4	no	—
521	D₄	—	94	4	no	—
522	D₄	—	188	2	no	—
523	D₄	—	188	2	no	—
524	D₄	—	188	2	no	—
525	D₄	—	188	2	no	—
526	D₄	—	188	2	no	—
527	D₄	—	188	2	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	376	2	no	—
532	C₂×C₄	—	376	2	no	—
533	C₂×C₄	—	376	2	no	—
534	C₂×C₄	—	188	2	no	—
535	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
536	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
537	C₂×C₄	#13093982	1	1	yes	characteristic
538	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
539	C₂×C₄	#13093986	1	1	yes	characteristic
540	C₂×C₄	#13093986	1	1	yes	characteristic
541	C₂×C₄	#13093992	1	1	yes	characteristic
542	C₂×C₄	#13093992	1	1	yes	characteristic
543	C₂×C₄	#13093993	1	1	yes	characteristic
544	C₂×C₄	#13093995	1	1	yes	characteristic
545	C₂×C₄	#13093996	1	1	yes	characteristic
546	C₂×C₄	#13093996	1	1	yes	characteristic
547	C₂×C₄	#13093998	1	1	yes	characteristic
548	C₂×C₄	#13093999	1	1	yes	characteristic
549	C₂×C₄	#13093999	1	1	yes	characteristic
550	C₂×C₄	#13093999	1	1	yes	characteristic
551	C₂×C₄	#13094000	1	1	yes	characteristic
552	C₂×C₄	#13094000	1	1	yes	characteristic
553	C₂×C₄	#13094000	1	1	yes	characteristic
554	C₂×C₄	#13094002	1	1	yes	characteristic
555	C₂×C₄	#13094004	1	1	yes	characteristic
556	C₂×C₄	#13094009	1	1	yes	characteristic
557	C₂×C₄	#13094009	1	1	yes	characteristic
558	C₂×C₄	#13094013	1	1	yes	characteristic
559	C₂×C₄	#13094013	1	1	yes	characteristic
560	C₂×C₄	#13094013	1	1	yes	characteristic
561	C₂×C₄	#13094019	1	1	yes	characteristic
562	C₂×C₄	#13094020	1	1	yes	characteristic
563	C₈	—	4	2	no	—
564	C₈	—	4	2	no	—
565	C₈	—	188	2	no	—
566	C₈	—	188	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	376	4	no	—
576	C₂²	—	376	4	no	—
577	C₂²	—	376	4	no	—
578	C₂²	—	376	4	no	—
579	C₂²	—	376	4	no	—
580	C₂²	—	376	2	no	—
581	C₂²	—	376	2	no	—
582	C₂²	—	376	4	no	—
583	C₂²	—	188	4	no	—
584	C₂²	#15688994	1	1	yes	characteristic
585	C₂²	#15689002	1	1	yes	characteristic
586	C₂²	#15689013	1	1	yes	characteristic
587	C₂²	#15689040	1	1	yes	characteristic
588	C₂²	#15689045	1	1	yes	characteristic
589	C₂²	#15689049	1	1	yes	characteristic
590	C₂²	#15689058	1	1	yes	characteristic
591	C₂²	#15689386	1	2	yes	—
592	C₂²	#15689393	1	2	yes	—
593	C₄	—	4	4	no	—
594	C₄	—	376	2	no	—
595	C₄	#15688980	1	1	yes	characteristic
596	C₄	#15688994	1	1	yes	characteristic
597	C₄	#15689013	1	1	yes	characteristic
598	C₄	#15689024	1	1	yes	characteristic
599	C₄	#15689031	1	1	yes	characteristic
600	C₄	#15689034	1	1	yes	characteristic
601	C₄	#15689040	1	1	yes	characteristic
602	C₄	#15689045	1	1	yes	characteristic
603	C₂	—	2	1	no	—
604	C₂	—	2	1	no	—
605	C₂	—	2	1	no	—
606	C₂	—	2	1	no	—
607	C₂	—	376	4	no	—
608	C₂	#20241630	1	1	yes	characteristic
609	C₂	#20243896	1	2	yes	—
610	C₂	#20244644	1	1	yes	characteristic
611	C₂	#20244651	1	1	yes	characteristic
612	C₂	#20244747	1	2	yes	—

	subgroup	G/H
center	C₂³	#13093998
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#424	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂³×D₁₈₈	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#424	D₄₇
hypocenter	C₄₇	#11061
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#424

Complements

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

N	H ≅ G/N	type
4. C₂×#15688891	C₂	semidirect
5. C₂×#15688888	C₂	semidirect
6. #20243109	C₂	semidirect
7. C₂×C₄₇×#424	C₂	semidirect
13. #15689127	C₄	semidirect
297. C₂×#424	D₄₇	semidirect
336. C₄₇	#11061	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689127	2
C₂²×#13093946	2
C₂²×#13093940	2
C₂×#15688891	2
C₂×#15688888	2
#20243109	2
C₂×C₄₇×#424	2
#11061	47