Subgroups — #26121627

Order 12032.

1246 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689889	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689105	C₂	1	1	yes	maximal, characteristic
3	#20245878	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688895	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15688894	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243082	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1728	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625350	C₂²	1	1	yes	characteristic
9	#15689889	—	2	2	no	—
10	#15689889	—	2	2	no	—
11	#15689889	—	2	2	no	—
12	#15689889	C₄	1	4	yes	complemented
13	C₂×#13094032	—	2	2	no	—
14	C₂×#13094030	—	2	2	no	—
15	C₂²×#10625329	C₂²	1	1	yes	characteristic
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×D₄₇	—	2	2	no	—
18	C₂×#13093983	C₂²	1	1	yes	characteristic
19	#15689105	—	2	2	no	—
20	#15689105	C₄	1	4	yes	complemented
21	C₂×#13093942	—	2	1	no	—
22	C₂×#13093940	—	2	1	no	—
23	#15689029	—	2	1	no	—
24	#15689025	—	2	1	no	—
25	#15689002	C₄	1	4	yes	—
26	C₄×(C₂×D₄₇)⋊C₄	—	2	2	no	—
27	#15688895	—	2	2	no	—
28	#15688894	—	2	2	no	—
29	#15688878	—	2	2	no	—
30	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
33	C₄₇×#336	—	2	2	no	—
34	C₂×#10625350	—	2	1	no	—
35	C₂×#10625350	—	2	1	no	—
36	C₂×#10625350	—	2	1	no	—
37	C₂×#10625350	—	2	1	no	—
38	C₂×#10625350	—	2	1	no	—
39	C₂×#10625350	—	2	1	no	—
40	C₂×#10625350	—	2	1	no	—
41	C₂×#10625350	—	2	1	no	—
42	C₂×#10625350	C₂×C₄	1	2	yes	—
43	C₂×#10625350	C₂×C₄	1	2	yes	—
44	C₂×#10625350	D₄	1	2	yes	—
45	C₂×#10625350	Q₈	1	2	yes	—
46	C₂²×Dic₉₄	D₄	1	1	yes	characteristic
47	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
48	C₂²×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
49	C₂²×C₄×D₄₇	D₄	1	2	yes	—
50	#13094032	—	2	8	no	—
51	#13094032	—	2	8	no	—
52	#13094030	—	2	8	no	—
53	#13094030	—	2	8	no	—
54	C₂×#10625329	—	2	1	no	—
55	C₂×#10625329	—	2	1	no	—
56	C₂×#10625329	—	2	1	no	—
57	C₂×#10625329	—	2	1	no	—
58	C₂×#10625329	—	2	1	no	—
59	C₂×#10625329	—	2	1	no	—
60	C₂×#10625329	—	2	1	no	—
61	C₂×#10625329	—	2	1	no	—
62	C₂×#10625329	—	2	1	no	—
63	C₂×#10625329	C₂×C₄	1	2	yes	—
64	C₂×#10625329	C₂×C₄	1	2	yes	—
65	C₂×#10625329	D₄	1	2	yes	—
66	C₂×#10625324	—	2	4	no	—
67	M₁₆×D₄₇	—	2	8	no	—
68	M₁₆×D₄₇	—	2	8	no	—
69	C₂²×C₄₇⋊C₈	—	2	1	no	—
70	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
71	C₂×C₈×D₄₇	—	2	4	no	—
72	#13093983	—	2	1	no	—
73	#13093983	—	2	1	no	—
74	#13093983	—	2	1	no	—
75	#13093983	—	2	1	no	—
76	C₂×C₄⋊Dic₄₇	—	2	1	no	—
77	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
78	C₂×(C₂×D₄₇)⋊C₄	—	2	4	no	—
79	C₂×C₄×Dic₄₇	—	2	1	no	—
80	#13093942	—	2	4	no	—
81	#13093940	—	2	4	no	—
82	C₄₇⋊#95	—	2	4	no	—
83	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
84	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₄₇	—	2	1	no	—
86	C₂×M₁₆×C₄₇	—	2	1	no	—
87	C₂×M₁₆×C₄₇	—	2	1	no	—
88	C₂×M₁₆×C₄₇	—	2	1	no	—
89	C₂×M₁₆×C₄₇	—	2	1	no	—
90	C₂×M₁₆×C₄₇	—	2	1	no	—
91	C₂×M₁₆×C₄₇	—	2	1	no	—
92	C₂×M₁₆×C₄₇	—	2	1	no	—
93	C₂×M₁₆×C₄₇	—	2	1	no	—
94	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
95	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
96	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
97	C₂²×C₈×C₄₇	—	2	1	no	—
98	C₂²×C₈×C₄₇	D₄	1	2	yes	—
99	C₂×C₄²×C₄₇	—	2	1	no	—
100	C₂×C₄²×C₄₇	—	2	1	no	—
101	C₂×C₄²×C₄₇	—	2	1	no	—
102	C₂×C₄²×C₄₇	—	2	1	no	—
103	C₂×C₄²×C₄₇	—	2	1	no	—
104	C₂×C₄²×C₄₇	—	2	1	no	—
105	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂³×D₄₇	C₂²⋊C₄	1	2	yes	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	4	4	no	—
111	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
125	C₂×C₂²⋊D₄₇	—	2	2	no	—
126	C₂×C₂²⋊D₄₇	—	2	2	no	—
127	C₂×C₂²⋊D₄₇	—	2	2	no	—
128	C₂×C₂²⋊D₄₇	—	2	2	no	—
129	C₂×C₂²⋊D₄₇	C₄²	1	4	yes	—
130	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	4	yes	—
131	C₂²×Dic₄₇	—	2	2	no	—
132	C₂²×Dic₄₇	C₂²⋊C₄	1	2	yes	—
133	#10625350	—	2	2	no	—
134	#10625350	—	2	2	no	—
135	#10625350	—	2	2	no	—
136	#10625350	—	2	2	no	—
137	#10625350	—	2	2	no	—
138	#10625350	—	2	2	no	—
139	#10625350	—	2	2	no	—
140	#10625350	—	2	2	no	—
141	#10625350	—	2	2	no	—
142	#10625350	—	2	2	no	—
143	#10625350	—	2	2	no	—
144	#10625350	—	2	2	no	—
145	#10625350	—	2	2	no	—
146	#10625350	—	2	2	no	—
147	#10625350	—	2	2	no	—
148	#10625350	—	2	2	no	—
149	C₂×D₁₈₈	—	2	1	no	—
150	C₂×D₁₈₈	—	2	1	no	—
151	C₂×D₁₈₈	—	2	1	no	—
152	C₂×D₁₈₈	—	2	1	no	—
153	C₂×D₁₈₈	C₂²⋊C₄	1	2	yes	—
154	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
155	C₂×C₄×D₄₇	—	2	2	no	—
156	C₂×C₄×D₄₇	—	2	2	no	—
157	C₂×C₄×D₄₇	—	2	2	no	—
158	C₂×C₄×D₄₇	—	2	2	no	—
159	C₂×C₄×D₄₇	C₂²⋊C₄	1	4	yes	—
160	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
161	C₂×Dic₉₄	—	2	1	no	—
162	C₂×Dic₉₄	—	2	1	no	—
163	C₂×Dic₉₄	—	2	1	no	—
164	C₂×Dic₉₄	—	2	1	no	—
165	C₂×Dic₉₄	C₂²⋊C₄	1	2	yes	—
166	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
167	M₁₆×C₄₇	—	2	2	no	—
168	M₁₆×C₄₇	—	2	2	no	—
169	M₁₆×C₄₇	—	2	2	no	—
170	M₁₆×C₄₇	—	2	2	no	—
171	M₁₆×C₄₇	—	2	2	no	—
172	M₁₆×C₄₇	—	2	2	no	—
173	M₁₆×C₄₇	—	4	1	no	—
174	M₁₆×C₄₇	—	4	1	no	—
175	C₂×C₈×C₄₇	—	2	2	no	—
176	C₂×C₈×C₄₇	—	2	2	no	—
177	C₂×C₈×C₄₇	—	2	2	no	—
178	C₂×C₈×C₄₇	—	4	1	no	—
179	C₂×C₈×C₄₇	—	4	1	no	—
180	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	complemented
181	C₄²×C₄₇	—	4	1	no	—
182	C₄²×C₄₇	—	4	1	no	—
183	C₄²×C₄₇	—	4	1	no	—
184	C₄²×C₄₇	—	4	1	no	—
185	C₂²⋊Dic₄₇	—	2	2	no	—
186	C₂²⋊Dic₄₇	—	2	2	no	—
187	(C₂×D₄₇)⋊C₄	—	4	8	no	—
188	C₄⋊Dic₄₇	—	4	1	no	—
189	C₄⋊Dic₄₇	—	4	1	no	—
190	C₄×Dic₄₇	—	4	1	no	—
191	C₄×Dic₄₇	—	4	1	no	—
192	#10625329	—	2	2	no	—
193	#10625329	—	2	2	no	—
194	#10625329	—	2	2	no	—
195	#10625329	—	2	2	no	—
196	#10625329	—	2	2	no	—
197	#10625329	—	2	2	no	—
198	#10625329	—	4	1	no	—
199	#10625329	—	4	1	no	—
200	C₂×C₄₇⋊C₈	—	2	2	no	—
201	C₂×C₄₇⋊C₈	—	2	2	no	—
202	C₂×C₄₇⋊C₈	—	2	2	no	—
203	C₂×C₄₇⋊C₈	—	4	1	no	—
204	C₂×C₄₇⋊C₈	—	4	1	no	—
205	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	complemented
206	#10625324	—	2	16	no	—
207	C₈×D₄₇	—	2	16	no	—
208	C₂³×C₄₇	—	4	2	no	—
209	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
210	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
213	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
214	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
215	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
216	C₂²×D₄₇	—	2	2	no	—
217	C₂²×D₄₇	—	2	2	no	—
218	C₂²×D₄₇	—	4	4	no	—
219	C₂²×D₄₇	#95	1	4	yes	—
220	C₂×C₄×C₄₇	—	2	4	no	—
221	C₂×C₄×C₄₇	—	2	4	no	—
222	C₂×C₄×C₄₇	—	2	4	no	—
223	C₂×C₄×C₄₇	—	4	2	no	—
224	C₂×C₄×C₄₇	—	4	2	no	—
225	C₂×C₄×C₄₇	—	4	2	no	—
226	C₂×C₄×C₄₇	—	4	2	no	—
227	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
234	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
235	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
240	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
241	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
242	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
243	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
244	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
245	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
246	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
247	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
251	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
252	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
253	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
254	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
255	C₂²⋊D₄₇	—	2	4	no	—
256	C₂²⋊D₄₇	—	2	4	no	—
257	C₂²⋊D₄₇	—	2	4	no	—
258	C₂²⋊D₄₇	—	2	4	no	—
259	C₂×Dic₄₇	—	2	2	no	—
260	C₂×Dic₄₇	—	2	2	no	—
261	C₂×Dic₄₇	—	4	4	no	—
262	C₂×Dic₄₇	—	4	2	no	—
263	C₂×Dic₄₇	#95	1	4	yes	—
264	D₁₈₈	—	2	2	no	—
265	D₁₈₈	—	2	2	no	—
266	D₁₈₈	—	2	2	no	—
267	D₁₈₈	—	2	2	no	—
268	C₄×D₄₇	—	2	4	no	—
269	C₄×D₄₇	—	2	4	no	—
270	C₄×D₄₇	—	2	4	no	—
271	C₄×D₄₇	—	2	4	no	—
272	Dic₉₄	—	2	2	no	—
273	Dic₉₄	—	2	2	no	—
274	Dic₉₄	—	2	2	no	—
275	Dic₉₄	—	2	2	no	—
276	C₈×C₄₇	—	2	4	no	—
277	C₈×C₄₇	—	4	2	no	—
278	C₄₇⋊C₈	—	2	4	no	—
279	C₄₇⋊C₈	—	4	2	no	—
280	#10746	—	47	1	no	maximal, Sylow
281	C₂²×C₄₇	—	2	2	no	—
282	C₂²×C₄₇	—	2	2	no	—
283	C₂²×C₄₇	—	2	2	no	—
284	C₂²×C₄₇	—	4	1	no	—
285	C₂²×C₄₇	—	4	1	no	—
286	C₂²×C₄₇	—	4	1	no	—
287	C₂²×C₄₇	—	4	1	no	—
288	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
289	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
290	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
291	C₂²×C₄₇	#385	1	1	yes	characteristic
292	C₂²×C₄₇	#385	1	1	yes	characteristic
293	C₂²×C₄₇	#386	1	1	yes	characteristic
294	C₂²×C₄₇	#386	1	1	yes	characteristic
295	C₂×D₄₇	—	2	4	no	—
296	C₂×D₄₇	—	4	4	no	—
297	C₂×D₄₇	—	4	4	no	—
298	C₂×D₄₇	—	8	2	no	—
299	C₄×C₄₇	—	4	4	no	—
300	C₄×C₄₇	#379	1	1	yes	characteristic
301	C₄×C₄₇	#380	1	1	yes	characteristic
302	C₄×C₄₇	#380	1	1	yes	characteristic
303	C₄×C₄₇	#381	1	1	yes	characteristic
304	C₄×C₄₇	#385	1	1	yes	characteristic
305	C₄×C₄₇	#385	1	1	yes	characteristic
306	C₄×C₄₇	#386	1	1	yes	characteristic
307	C₄×C₄₇	#386	1	1	yes	characteristic
308	Dic₄₇	—	2	4	no	—
309	Dic₄₇	—	8	2	no	—
310	C₂×#568	—	47	1	no	—
311	C₂×#413	—	47	1	no	—
312	#2297	—	47	1	no	—
313	C₂×#344	—	47	1	no	—
314	C₂×#344	—	47	1	no	—
315	#1728	—	47	1	no	—
316	#1728	D₄₇	1	1	yes	characteristic, complemented
317	C₂×C₄₇	—	2	1	no	—
318	C₂×C₄₇	—	2	1	no	—
319	C₂×C₄₇	—	2	1	no	—
320	C₂×C₄₇	—	2	1	no	—
321	C₂×C₄₇	—	2	1	no	—
322	C₂×C₄₇	—	2	1	no	—
323	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
324	C₂×C₄₇	#1891	1	2	yes	—
325	D₄₇	—	4	4	no	—
326	C₂²×#41	—	47	1	no	—
327	#568	—	47	4	no	—
328	#568	—	94	2	no	—
329	#568	—	94	2	no	—
330	#568	—	94	2	no	—
331	C₂×#131	—	94	2	no	—
332	C₂×#131	—	94	2	no	—
333	C₂²×M₁₆	—	47	1	no	—
334	C₂²×M₁₆	—	47	1	no	—
335	C₂²×M₁₆	—	94	2	no	—
336	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
337	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
338	C₂×#117	—	47	1	no	—
339	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
340	#413	—	47	4	no	—
341	#413	—	94	2	no	—
342	C₂×#101	—	94	1	no	—
343	C₂×#100	—	94	1	no	—
344	#391	—	94	1	no	—
345	#390	—	94	1	no	—
346	#386	—	47	4	no	—
347	C₄×C₂²⋊C₄	—	94	2	no	—
348	#344	—	94	2	no	—
349	#344	—	94	2	no	—
350	#336	—	2	2	no	—
351	#336	—	94	2	no	—
352	C₄₇	#10746	1	1	yes	characteristic, complemented, Sylow
353	C₂×#41	—	47	2	no	—
354	C₂×#41	—	47	2	no	—
355	C₂×#41	—	47	2	no	—
356	C₂×#41	—	47	2	no	—
357	C₂×#41	—	94	1	no	—
358	C₂×#41	—	94	1	no	—
359	C₂×#41	—	94	1	no	—
360	C₂×#41	—	94	1	no	—
361	C₂×#41	—	94	1	no	—
362	C₂×#41	—	94	1	no	—
363	C₂×#41	—	94	1	no	—
364	C₂×#41	—	94	1	no	—
365	C₂²×Q₈	—	47	1	no	—
366	C₂²×D₄	—	47	2	no	—
367	C₂²×D₄	—	47	1	no	—
368	C₂³×C₄	—	47	2	no	—
369	C₂³×C₄	C₄×D₄₇	1	2	yes	—
370	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
371	#131	—	94	8	no	—
372	#131	—	94	8	no	—
373	#131	—	94	8	no	—
374	#131	—	94	8	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	1	no	—
384	C₂×M₁₆	—	47	2	no	—
385	C₂×M₁₆	—	47	2	no	—
386	C₂×M₁₆	—	47	2	no	—
387	C₂×M₁₆	—	94	4	no	—
388	C₂×M₁₆	—	94	8	no	—
389	C₂×M₁₆	—	94	8	no	—
390	C₂×M₁₆	—	94	1	no	—
391	C₂×M₁₆	—	94	1	no	—
392	C₂×M₁₆	—	94	1	no	—
393	C₂×M₁₆	—	94	1	no	—
394	C₂×M₁₆	—	94	1	no	—
395	C₂×M₁₆	—	94	1	no	—
396	C₂×M₁₆	—	94	1	no	—
397	C₂×M₁₆	—	94	1	no	—
398	C₂×M₁₆	—	94	1	no	—
399	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
400	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
401	C₂×M₁₆	D₁₈₈	1	2	yes	—
402	C₂²×C₈	—	2	1	no	—
403	C₂²×C₈	—	47	2	no	—
404	C₂²×C₈	—	94	4	no	—
405	C₂²×C₈	—	94	1	no	—
406	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
407	#117	—	94	1	no	—
408	#117	—	94	1	no	—
409	#117	—	94	1	no	—
410	#117	—	94	1	no	—
411	C₂×C₄⋊C₄	—	94	1	no	—
412	C₂×C₂²⋊C₄	—	47	2	no	—
413	C₂×C₂²⋊C₄	—	94	4	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	—	2	1	no	—
417	C₂×C₄²	—	2	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	—	94	1	no	—
421	#101	—	94	4	no	—
422	#100	—	94	4	no	—
423	#95	—	94	4	no	—
424	C₂⁴	—	47	2	no	—
425	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
426	#41	—	94	2	no	—
427	#41	—	94	2	no	—
428	#41	—	94	2	no	—
429	#41	—	94	2	no	—
430	#41	—	94	2	no	—
431	#41	—	94	2	no	—
432	#41	—	94	2	no	—
433	#41	—	94	2	no	—
434	#41	—	94	2	no	—
435	#41	—	94	2	no	—
436	#41	—	94	2	no	—
437	#41	—	94	2	no	—
438	#41	—	94	2	no	—
439	#41	—	94	2	no	—
440	#41	—	94	2	no	—
441	#41	—	94	2	no	—
442	C₂×Q₈	—	47	2	no	—
443	C₂×Q₈	—	47	2	no	—
444	C₂×Q₈	—	94	1	no	—
445	C₂×Q₈	—	94	1	no	—
446	C₂×Q₈	—	94	1	no	—
447	C₂×Q₈	—	94	1	no	—
448	C₂×D₄	—	47	4	no	—
449	C₂×D₄	—	47	4	no	—
450	C₂×D₄	—	47	2	no	—
451	C₂×D₄	—	47	2	no	—
452	C₂×D₄	—	94	2	no	—
453	C₂×D₄	—	94	2	no	—
454	C₂×D₄	—	94	2	no	—
455	C₂×D₄	—	94	2	no	—
456	C₂×D₄	—	94	1	no	—
457	C₂×D₄	—	94	1	no	—
458	C₂×D₄	—	94	1	no	—
459	C₂×D₄	—	94	1	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	4	4	no	—
464	C₂²×C₄	—	47	2	no	—
465	C₂²×C₄	—	47	4	no	—
466	C₂²×C₄	—	47	4	no	—
467	C₂²×C₄	—	94	2	no	—
468	C₂²×C₄	—	94	2	no	—
469	C₂²×C₄	—	94	2	no	—
470	C₂²×C₄	—	94	2	no	—
471	C₂²×C₄	—	94	2	no	—
472	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
475	C₂²×C₄	#10625350	1	1	yes	characteristic
476	C₂²×C₄	#10625350	1	1	yes	characteristic
477	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
478	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
479	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
480	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
481	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
482	C₂²×C₄	#10625352	1	1	yes	characteristic
483	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
484	C₂²×C₄	#10625354	1	1	yes	characteristic
485	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	2	2	no	—
489	M₁₆	—	2	2	no	—
490	M₁₆	—	2	2	no	—
491	M₁₆	—	2	2	no	—
492	M₁₆	—	4	1	no	—
493	M₁₆	—	4	1	no	—
494	M₁₆	—	94	16	no	—
495	M₁₆	—	94	2	no	—
496	M₁₆	—	94	2	no	—
497	M₁₆	—	94	2	no	—
498	M₁₆	—	94	2	no	—
499	M₁₆	—	94	2	no	—
500	M₁₆	—	94	2	no	—
501	M₁₆	—	188	1	no	—
502	M₁₆	—	188	1	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	4	1	no	—
507	C₂×C₈	—	4	1	no	—
508	C₂×C₈	—	47	4	no	—
509	C₂×C₈	—	94	16	no	—
510	C₂×C₈	—	94	2	no	—
511	C₂×C₈	—	94	2	no	—
512	C₂×C₈	—	94	2	no	—
513	C₂×C₈	—	188	1	no	—
514	C₂×C₈	—	188	1	no	—
515	C₂×C₈	(C₂×D₄₇)⋊C₄	1	4	yes	complemented
516	C₄⋊C₄	—	188	1	no	—
517	C₄⋊C₄	—	188	1	no	—
518	C₂²⋊C₄	—	94	2	no	—
519	C₂²⋊C₄	—	94	2	no	—
520	C₂²⋊C₄	—	188	8	no	—
521	C₄²	—	4	1	no	—
522	C₄²	—	4	1	no	—
523	C₄²	—	4	1	no	—
524	C₄²	—	4	1	no	—
525	C₄²	—	188	1	no	—
526	C₄²	—	188	1	no	—
527	C₂³	—	4	2	no	—
528	C₂³	—	47	4	no	—
529	C₂³	—	94	2	no	—
530	C₂³	—	94	2	no	—
531	C₂³	—	188	4	no	—
532	C₂³	C₄²×D₄₇	1	1	yes	characteristic
533	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
534	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
535	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
536	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
537	C₂³	#13093986	1	1	yes	characteristic
538	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
539	Q₈	—	94	2	no	—
540	Q₈	—	94	2	no	—
541	Q₈	—	94	2	no	—
542	Q₈	—	94	2	no	—
543	D₄	—	94	4	no	—
544	D₄	—	94	4	no	—
545	D₄	—	94	4	no	—
546	D₄	—	94	4	no	—
547	D₄	—	94	2	no	—
548	D₄	—	94	2	no	—
549	D₄	—	94	2	no	—
550	D₄	—	94	2	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	47	4	no	—
559	C₂×C₄	—	94	2	no	—
560	C₂×C₄	—	94	2	no	—
561	C₂×C₄	—	94	4	no	—
562	C₂×C₄	—	94	4	no	—
563	C₂×C₄	—	94	4	no	—
564	C₂×C₄	—	94	4	no	—
565	C₂×C₄	—	188	4	no	—
566	C₂×C₄	—	188	2	no	—
567	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
568	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
569	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
570	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
571	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
572	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
573	C₂×C₄	#13093981	1	1	yes	characteristic
574	C₂×C₄	#13093982	1	1	yes	characteristic
575	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
576	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
577	C₂×C₄	#13093986	1	1	yes	characteristic
578	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
579	C₂×C₄	#13093992	1	1	yes	characteristic
580	C₂×C₄	#13093992	1	1	yes	characteristic
581	C₂×C₄	#13093994	1	1	yes	characteristic
582	C₂×C₄	#13093994	1	1	yes	characteristic
583	C₂×C₄	#13093995	1	1	yes	characteristic
584	C₂×C₄	#13093997	1	1	yes	characteristic
585	C₂×C₄	#13093997	1	1	yes	characteristic
586	C₂×C₄	#13093999	1	1	yes	characteristic
587	C₂×C₄	#13094000	1	1	yes	characteristic
588	C₂×C₄	#13094002	1	1	yes	characteristic
589	C₂×C₄	#13094002	1	1	yes	characteristic
590	C₂×C₄	#13094004	1	1	yes	characteristic
591	C₂×C₄	#13094006	1	1	yes	characteristic
592	C₂×C₄	#13094006	1	1	yes	characteristic
593	C₂×C₄	#13094009	1	1	yes	characteristic
594	C₂×C₄	#13094009	1	1	yes	characteristic
595	C₈	—	2	4	no	—
596	C₈	—	4	2	no	—
597	C₈	—	94	4	no	—
598	C₈	—	188	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	94	4	no	—
607	C₂²	—	376	2	no	—
608	C₂²	—	188	4	no	—
609	C₂²	—	188	4	no	—
610	C₂²	#95×D₄₇	1	1	yes	characteristic
611	C₂²	#15688970	1	1	yes	characteristic
612	C₂²	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
613	C₂²	#15688994	1	1	yes	characteristic
614	C₂²	#15688997	1	1	yes	characteristic
615	C₂²	#15688999	1	1	yes	characteristic
616	C₂²	#15689001	1	1	yes	characteristic
617	C₄	—	4	4	no	—
618	C₄	—	94	4	no	—
619	C₄	—	376	2	no	—
620	C₄	#15688978	1	1	yes	characteristic
621	C₄	#15688980	1	1	yes	characteristic
622	C₄	#15688982	1	1	yes	characteristic
623	C₄	#15688985	1	1	yes	characteristic
624	C₄	#15688994	1	1	yes	characteristic
625	C₄	#15688997	1	1	yes	characteristic
626	C₄	#15688999	1	1	yes	characteristic
627	C₄	#15689001	1	1	yes	characteristic
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	2	1	no	—
633	C₂	—	2	1	no	—
634	C₂	—	188	4	no	—
635	C₂	(C₂×D₄₇)⋊#95	1	1	yes	characteristic
636	C₂	#20243803	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13093992
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄₇×#1728	C₂
socle	C₂²×C₄₇	#386
prime radical	C₂²×#10625350	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	#1728	D₄₇
hypocenter	C₄₇	#10746
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1728

Complements

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

N	H ≅ G/N	type
4. C₂×#15688895	C₂	semidirect
5. C₂×#15688894	C₂	semidirect
6. #20243082	C₂	semidirect
7. C₄₇×#1728	C₂	semidirect
12. #15689889	C₄	semidirect
20. #15689105	C₄	semidirect
180. C₂×C₈×C₄₇	C₂²⋊C₄	semidirect
205. C₂×C₄₇⋊C₈	C₂²⋊C₄	semidirect
316. #1728	D₄₇	semidirect
352. C₄₇	#10746	semidirect
515. C₂×C₈	(C₂×D₄₇)⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689889	2
C₂×#15689105	2
#20245878	2
C₂×#15688895	2
C₂×#15688894	2
#20243082	2
C₄₇×#1728	2
#10746	47