Subgroups — #26123697

Order 12032.

930 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093959	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13093950	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689117	C₂	1	1	yes	maximal, characteristic
4	C₂×#15689089	C₂	1	1	yes	maximal, characteristic
5	C₂×#15688882	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688877	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1729	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625350	C₂²	1	1	yes	characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂×#13093959	—	2	2	no	—
13	C₂×#13093959	—	2	2	no	—
14	C₂×#13093959	—	2	2	no	—
15	C₂×#13093950	—	2	2	no	—
16	C₂×#13093950	—	2	2	no	—
17	C₂×#13093950	—	2	2	no	—
18	#15689117	—	2	2	no	—
19	#15689117	—	2	2	no	—
20	C₂×#13093947	C₄	1	1	yes	characteristic, complemented
21	C₂×#13093947	C₄	1	1	yes	characteristic, complemented
22	C₂×#13093944	C₄	1	1	yes	characteristic, complemented
23	C₂×#13093944	C₄	1	1	yes	characteristic, complemented
24	#15689089	—	2	2	no	—
25	#15689089	—	2	2	no	—
26	C₂×(C₂×D₄₇)⋊C₈	—	2	2	no	—
27	#15688882	—	2	2	no	—
28	#15688877	—	2	2	no	—
29	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
30	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#336	—	2	2	no	—
33	C₂×#10625350	—	2	1	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	—	2	1	no	—
43	C₂×#10625350	D₄	1	2	yes	—
44	C₂×#10625350	Q₈	1	2	yes	—
45	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₂²⋊D₄₇	—	2	1	no	—
48	C₂³×Dic₄₇	—	2	1	no	—
49	C₂²×C₄×D₄₇	—	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	D₄	1	2	yes	—
56	C₂²×C₄₇⋊C₈	—	2	1	no	—
57	C₂²×C₄₇⋊C₈	—	2	1	no	—
58	C₂²×C₄₇⋊C₈	—	2	1	no	—
59	C₂²×C₄₇⋊C₈	—	2	1	no	—
60	C₂²×C₄₇⋊C₈	—	2	1	no	—
61	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
64	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
65	C₂×C₄×Dic₄₇	—	2	1	no	—
66	C₂×C₄×Dic₄₇	—	2	1	no	—
67	C₂×C₄×Dic₄₇	—	2	1	no	—
68	C₂×C₄×Dic₄₇	—	2	1	no	—
69	C₂×C₄×Dic₄₇	—	2	1	no	—
70	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
71	#13093959	—	2	8	no	—
72	#13093950	—	2	8	no	—
73	#13093947	—	2	2	no	—
74	#13093947	—	2	2	no	—
75	#13093944	—	2	2	no	—
76	#13093944	—	2	2	no	—
77	(C₂×D₄₇)⋊C₈	—	2	8	no	—
78	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×M₁₆×C₄₇	—	2	1	no	—
80	C₂×M₁₆×C₄₇	—	2	1	no	—
81	C₂×M₁₆×C₄₇	—	2	1	no	—
82	C₂×M₁₆×C₄₇	—	2	1	no	—
83	C₂×M₁₆×C₄₇	—	2	1	no	—
84	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
85	C₂²×C₈×C₄₇	—	2	1	no	—
86	C₂²×C₈×C₄₇	—	2	1	no	—
87	C₂²×C₈×C₄₇	—	2	1	no	—
88	C₂²×C₈×C₄₇	—	2	1	no	—
89	C₂²×C₈×C₄₇	—	2	1	no	—
90	C₂²×C₈×C₄₇	—	2	1	no	—
91	C₂²×C₈×C₄₇	—	2	1	no	—
92	C₂²×C₈×C₄₇	D₄	1	2	yes	—
93	#117×C₄₇	—	2	1	no	—
94	#117×C₄₇	—	2	1	no	—
95	#117×C₄₇	—	2	1	no	—
96	#117×C₄₇	—	2	1	no	—
97	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
100	C₂×C₄²×C₄₇	—	2	1	no	—
101	C₂⁴×C₄₇	#41	1	1	yes	characteristic
102	C₂³×D₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	C₂²×C₄	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×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×Q₈	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×C₄×C₄₇	#41	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
119	C₂×C₂²⋊D₄₇	—	2	2	no	—
120	C₂×C₂²⋊D₄₇	—	2	2	no	—
121	C₂×C₂²⋊D₄₇	—	4	1	no	—
122	C₂×C₂²⋊D₄₇	—	4	1	no	—
123	C₂×C₂²⋊D₄₇	—	4	1	no	—
124	C₂×C₂²⋊D₄₇	—	4	1	no	—
125	C₂²×Dic₄₇	—	2	4	no	—
126	C₂²×Dic₄₇	—	2	1	no	—
127	C₂²×Dic₄₇	—	2	2	no	—
128	C₂²×Dic₄₇	—	4	2	no	—
129	C₂²×Dic₄₇	—	4	1	no	—
130	C₂²×Dic₄₇	—	4	1	no	—
131	#10625350	—	2	2	no	—
132	#10625350	—	2	2	no	—
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	—	4	1	no	—
140	#10625350	—	4	1	no	—
141	#10625350	—	4	1	no	—
142	#10625350	—	4	1	no	—
143	#10625350	—	4	1	no	—
144	#10625350	—	4	1	no	—
145	#10625350	—	4	1	no	—
146	#10625350	—	4	1	no	—
147	C₂×D₁₈₈	—	2	1	no	—
148	C₂×D₁₈₈	—	2	1	no	—
149	C₂×D₁₈₈	—	2	1	no	—
150	C₂×D₁₈₈	—	2	1	no	—
151	C₂×D₁₈₈	—	2	1	no	—
152	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
153	C₂×C₄×D₄₇	—	2	2	no	—
154	C₂×C₄×D₄₇	—	2	2	no	—
155	C₂×C₄×D₄₇	—	4	1	no	—
156	C₂×C₄×D₄₇	—	4	1	no	—
157	C₂×C₄×D₄₇	—	4	1	no	—
158	C₂×C₄×D₄₇	—	4	1	no	—
159	C₂×Dic₉₄	—	2	1	no	—
160	C₂×Dic₉₄	—	2	1	no	—
161	C₂×Dic₉₄	—	2	1	no	—
162	C₂×Dic₉₄	—	2	1	no	—
163	C₂×Dic₉₄	—	2	1	no	—
164	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
165	M₁₆×C₄₇	—	2	2	no	—
166	M₁₆×C₄₇	—	2	2	no	—
167	M₁₆×C₄₇	—	4	1	no	—
168	M₁₆×C₄₇	—	4	1	no	—
169	C₂×C₈×C₄₇	—	2	2	no	—
170	C₂×C₈×C₄₇	—	2	2	no	—
171	C₂×C₈×C₄₇	—	2	2	no	—
172	C₂×C₈×C₄₇	—	2	2	no	—
173	C₂×C₈×C₄₇	—	4	1	no	—
174	C₂×C₈×C₄₇	—	4	1	no	—
175	C₂×C₈×C₄₇	—	4	1	no	—
176	C₂×C₈×C₄₇	—	4	1	no	—
177	C₂×C₈×C₄₇	—	4	1	no	—
178	C₂×C₈×C₄₇	—	4	1	no	—
179	C₄⋊C₄×C₄₇	—	2	1	no	—
180	C₄⋊C₄×C₄₇	—	2	1	no	—
181	C₄⋊C₄×C₄₇	—	2	1	no	—
182	C₄⋊C₄×C₄₇	—	2	1	no	—
183	C₂²⋊C₄×C₄₇	—	4	1	no	—
184	C₂²⋊C₄×C₄₇	—	4	1	no	—
185	C₄²×C₄₇	—	4	1	no	—
186	C₄²×C₄₇	—	4	1	no	—
187	C₄×Dic₄₇	—	2	2	no	—
188	C₄×Dic₄₇	—	2	2	no	—
189	C₄×Dic₄₇	—	4	1	no	—
190	C₄×Dic₄₇	—	4	1	no	—
191	#10625329	—	2	2	no	—
192	#10625329	—	2	2	no	—
193	#10625329	—	4	1	no	—
194	#10625329	—	4	1	no	—
195	C₂×C₄₇⋊C₈	—	2	1	no	—
196	C₂×C₄₇⋊C₈	—	2	1	no	—
197	C₂×C₄₇⋊C₈	—	2	1	no	—
198	C₂×C₄₇⋊C₈	—	2	1	no	—
199	C₂×C₄₇⋊C₈	—	2	2	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	—	2	2	no	—
204	C₂×C₄₇⋊C₈	—	4	1	no	—
205	C₂×C₄₇⋊C₈	—	4	1	no	—
206	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
207	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
208	C₂³×C₄₇	—	2	2	no	—
209	C₂³×C₄₇	—	2	2	no	—
210	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
211	C₂³×C₄₇	#121	1	1	yes	characteristic
212	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
213	C₂³×C₄₇	#123	1	1	yes	characteristic
214	C₂³×C₄₇	#124	1	1	yes	characteristic
215	C₂³×C₄₇	#124	1	1	yes	characteristic
216	C₂³×C₄₇	#126	1	1	yes	characteristic
217	C₂²×D₄₇	—	2	2	no	—
218	C₂²×D₄₇	—	4	1	no	—
219	C₂²×D₄₇	—	4	1	no	—
220	C₂²×D₄₇	—	4	2	no	—
221	C₂²×D₄₇	—	4	2	no	—
222	C₂×C₄×C₄₇	—	4	1	no	—
223	C₂×C₄×C₄₇	—	4	1	no	—
224	C₂×C₄×C₄₇	—	4	2	no	—
225	C₂×C₄×C₄₇	—	4	2	no	—
226	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
233	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
234	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
235	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
236	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
237	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
238	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
239	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
240	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
241	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
242	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
244	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
245	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
246	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
247	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
248	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
249	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
250	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
251	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
252	C₂×C₄×C₄₇	#126	1	1	yes	characteristic
253	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
254	C₂²⋊D₄₇	—	4	2	no	—
255	C₂²⋊D₄₇	—	4	2	no	—
256	C₂²⋊D₄₇	—	4	2	no	—
257	C₂²⋊D₄₇	—	4	2	no	—
258	C₂×Dic₄₇	—	2	4	no	—
259	C₂×Dic₄₇	—	2	2	no	—
260	C₂×Dic₄₇	—	4	4	no	—
261	C₂×Dic₄₇	—	4	4	no	—
262	C₂×Dic₄₇	—	4	2	no	—
263	C₂×Dic₄₇	—	4	1	no	—
264	C₂×Dic₄₇	—	4	1	no	—
265	C₂×Dic₄₇	—	4	2	no	—
266	D₁₈₈	—	2	2	no	—
267	D₁₈₈	—	2	2	no	—
268	D₁₈₈	—	4	1	no	—
269	D₁₈₈	—	4	1	no	—
270	C₄×D₄₇	—	4	2	no	—
271	C₄×D₄₇	—	4	2	no	—
272	C₄×D₄₇	—	4	2	no	—
273	C₄×D₄₇	—	4	2	no	—
274	Dic₉₄	—	2	2	no	—
275	Dic₉₄	—	2	2	no	—
276	Dic₉₄	—	4	1	no	—
277	Dic₉₄	—	4	1	no	—
278	C₈×C₄₇	—	4	2	no	—
279	C₈×C₄₇	—	4	2	no	—
280	C₄₇⋊C₈	—	2	2	no	—
281	C₄₇⋊C₈	—	2	2	no	—
282	C₄₇⋊C₈	—	4	2	no	—
283	#11125	—	47	1	no	maximal, Sylow
284	C₂²×C₄₇	—	2	2	no	—
285	C₂²×C₄₇	—	2	2	no	—
286	C₂²×C₄₇	—	2	2	no	—
287	C₂²×C₄₇	—	2	2	no	—
288	C₂²×C₄₇	—	2	1	no	—
289	C₂²×C₄₇	—	2	1	no	—
290	C₂²×C₄₇	—	2	1	no	—
291	C₂²×C₄₇	—	2	1	no	—
292	C₂²×C₄₇	#385	1	1	yes	characteristic
293	C₂²×C₄₇	#388	1	1	yes	characteristic
294	C₂²×C₄₇	#390	1	1	yes	characteristic
295	C₂²×C₄₇	#393	1	1	yes	characteristic
296	C₂²×C₄₇	#394	1	1	yes	characteristic
297	C₂²×C₄₇	#396	1	1	yes	characteristic
298	C₂²×C₄₇	#397	1	1	yes	characteristic
299	C₂²×C₄₇	#443	1	2	yes	—
300	C₂²×C₄₇	#444	1	2	yes	—
301	C₂×D₄₇	—	4	4	no	—
302	C₂×D₄₇	—	4	2	no	—
303	C₂×D₄₇	—	8	2	no	—
304	C₂×D₄₇	—	8	1	no	—
305	C₂×D₄₇	—	8	1	no	—
306	C₄×C₄₇	—	8	1	no	—
307	C₄×C₄₇	—	8	1	no	—
308	C₄×C₄₇	#380	1	1	yes	characteristic
309	C₄×C₄₇	#385	1	1	yes	characteristic
310	C₄×C₄₇	#386	1	1	yes	characteristic
311	C₄×C₄₇	#388	1	1	yes	characteristic
312	C₄×C₄₇	#392	1	1	yes	characteristic
313	C₄×C₄₇	#394	1	1	yes	characteristic
314	C₄×C₄₇	#396	1	1	yes	characteristic
315	C₄×C₄₇	#399	1	1	yes	characteristic
316	Dic₄₇	—	4	4	no	—
317	Dic₄₇	—	4	2	no	—
318	C₂²×#108	—	47	1	no	—
319	C₂²×#104	—	47	1	no	—
320	C₂×#416	—	47	1	no	—
321	C₂×#408	—	47	1	no	—
322	C₂×#339	—	47	1	no	—
323	#1729	D₄₇	1	1	yes	characteristic, complemented
324	C₂×#336	—	47	1	no	—
325	C₂×C₄₇	—	2	1	no	—
326	C₂×C₄₇	—	2	1	no	—
327	C₂×C₄₇	—	2	1	no	—
328	C₂×C₄₇	—	2	1	no	—
329	C₂×C₄₇	#1439	1	1	yes	characteristic
330	C₂×C₄₇	#1866	1	2	yes	—
331	C₂×C₄₇	#1929	1	2	yes	—
332	C₂×C₄₇	#1974	1	1	yes	characteristic
333	C₂×C₄₇	#1975	1	1	yes	characteristic
334	D₄₇	—	8	2	no	—
335	C₂²×#41	—	47	1	no	—
336	C₂²×M₁₆	—	47	1	no	—
337	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
338	C₂³×C₈	—	47	1	no	—
339	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
340	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
341	C₂²×C₄²	—	47	1	no	—
342	C₂×#108	—	94	2	no	—
343	C₂×#108	—	94	2	no	—
344	C₂×#108	—	94	2	no	—
345	C₂×#104	—	94	2	no	—
346	C₂×#104	—	94	2	no	—
347	C₂×#104	—	94	2	no	—
348	#416	—	94	2	no	—
349	#416	—	94	2	no	—
350	C₂×#103	—	47	1	no	—
351	C₂×#103	—	47	1	no	—
352	C₂×#102	—	47	1	no	—
353	C₂×#102	—	47	1	no	—
354	#408	—	94	2	no	—
355	#408	—	94	2	no	—
356	C₂×C₂²⋊C₈	—	94	2	no	—
357	#339	—	94	2	no	—
358	#336	—	2	2	no	—
359	#336	—	94	2	no	—
360	C₄₇	#11125	1	1	yes	characteristic, complemented, Sylow
361	C₂×#41	—	47	2	no	—
362	C₂×#41	—	47	2	no	—
363	C₂×#41	—	94	1	no	—
364	C₂×#41	—	94	1	no	—
365	C₂×#41	—	94	1	no	—
366	C₂×#41	—	94	1	no	—
367	C₂×#41	—	94	1	no	—
368	C₂×#41	—	94	1	no	—
369	C₂×#41	—	94	1	no	—
370	C₂×#41	—	94	1	no	—
371	C₂×#41	—	94	1	no	—
372	C₂×#41	—	94	1	no	—
373	C₂²×Q₈	—	47	1	no	—
374	C₂²×D₄	—	47	1	no	—
375	C₂²×D₄	—	94	1	no	—
376	C₂³×C₄	—	94	1	no	—
377	C₂³×C₄	—	94	1	no	—
378	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
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	—	94	1	no	—
386	C₂×M₁₆	—	94	1	no	—
387	C₂×M₁₆	—	94	1	no	—
388	C₂×M₁₆	—	94	1	no	—
389	C₂×M₁₆	—	94	1	no	—
390	C₂×M₁₆	D₁₈₈	1	2	yes	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	—	2	1	no	—
394	C₂²×C₈	—	2	1	no	—
395	C₂²×C₈	—	2	1	no	—
396	C₂²×C₈	—	2	1	no	—
397	C₂²×C₈	—	2	1	no	—
398	C₂²×C₈	—	47	1	no	—
399	C₂²×C₈	—	47	1	no	—
400	C₂²×C₈	—	47	2	no	—
401	C₂²×C₈	—	47	2	no	—
402	C₂²×C₈	—	94	1	no	—
403	C₂²×C₈	—	94	1	no	—
404	C₂²×C₈	—	94	1	no	—
405	C₂²×C₈	—	94	1	no	—
406	C₂²×C₈	—	94	1	no	—
407	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
408	#117	—	2	1	no	—
409	#117	—	2	1	no	—
410	#117	—	2	1	no	—
411	#117	—	2	1	no	—
412	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	—	47	2	no	—
417	C₂×C₄²	—	94	1	no	—
418	C₂×C₄²	—	94	1	no	—
419	C₂×C₄²	—	94	1	no	—
420	C₂×C₄²	—	94	1	no	—
421	C₂×C₄²	—	94	1	no	—
422	#108	—	94	8	no	—
423	#104	—	94	8	no	—
424	#103	—	94	2	no	—
425	#103	—	94	2	no	—
426	#102	—	94	2	no	—
427	#102	—	94	2	no	—
428	C₂²⋊C₈	—	94	8	no	—
429	C₂⁴	—	94	1	no	—
430	C₂⁴	#10625350	1	1	yes	characteristic
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	—	188	1	no	—
440	#41	—	188	1	no	—
441	#41	—	188	1	no	—
442	#41	—	188	1	no	—
443	#41	—	188	1	no	—
444	#41	—	188	1	no	—
445	#41	—	188	1	no	—
446	#41	—	188	1	no	—
447	C₂×Q₈	—	47	2	no	—
448	C₂×Q₈	—	94	1	no	—
449	C₂×Q₈	—	94	1	no	—
450	C₂×Q₈	—	94	1	no	—
451	C₂×Q₈	—	94	1	no	—
452	C₂×Q₈	—	94	1	no	—
453	C₂×D₄	—	47	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	C₂×D₄	—	94	1	no	—
461	C₂×D₄	—	188	1	no	—
462	C₂×D₄	—	188	1	no	—
463	C₂×D₄	—	188	1	no	—
464	C₂×D₄	—	188	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	94	4	no	—
468	C₂²×C₄	—	94	1	no	—
469	C₂²×C₄	—	94	2	no	—
470	C₂²×C₄	—	94	2	no	—
471	C₂²×C₄	—	94	2	no	—
472	C₂²×C₄	—	188	2	no	—
473	C₂²×C₄	—	188	1	no	—
474	C₂²×C₄	—	188	1	no	—
475	C₂²×C₄	—	188	1	no	—
476	C₂²×C₄	—	188	1	no	—
477	C₂²×C₄	—	188	1	no	—
478	C₂²×C₄	—	188	1	no	—
479	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
481	C₂²×C₄	#10625350	1	1	yes	characteristic
482	C₂²×C₄	#10625350	1	1	yes	characteristic
483	C₂²×C₄	#10625350	1	1	yes	characteristic
484	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
485	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
486	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
487	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
488	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
489	C₂²×C₄	#10625352	1	1	yes	characteristic
490	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
491	C₂²×C₄	#10625354	1	1	yes	characteristic
492	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
493	M₁₆	—	2	2	no	—
494	M₁₆	—	2	2	no	—
495	M₁₆	—	4	1	no	—
496	M₁₆	—	4	1	no	—
497	M₁₆	—	94	2	no	—
498	M₁₆	—	94	2	no	—
499	M₁₆	—	188	1	no	—
500	M₁₆	—	188	1	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	4	1	no	—
506	C₂×C₈	—	4	1	no	—
507	C₂×C₈	—	4	1	no	—
508	C₂×C₈	—	4	1	no	—
509	C₂×C₈	—	4	1	no	—
510	C₂×C₈	—	4	1	no	—
511	C₂×C₈	—	47	2	no	—
512	C₂×C₈	—	47	2	no	—
513	C₂×C₈	—	94	1	no	—
514	C₂×C₈	—	94	1	no	—
515	C₂×C₈	—	94	1	no	—
516	C₂×C₈	—	94	1	no	—
517	C₂×C₈	—	94	2	no	—
518	C₂×C₈	—	94	2	no	—
519	C₂×C₈	—	94	2	no	—
520	C₂×C₈	—	94	2	no	—
521	C₂×C₈	—	94	2	no	—
522	C₂×C₈	—	188	1	no	—
523	C₂×C₈	—	188	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₂²⋊C₄	—	4	1	no	—
529	C₂²⋊C₄	—	4	1	no	—
530	C₄²	—	4	1	no	—
531	C₄²	—	4	1	no	—
532	C₄²	—	94	2	no	—
533	C₄²	—	94	2	no	—
534	C₄²	—	188	1	no	—
535	C₄²	—	188	1	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	94	2	no	—
539	C₂³	—	188	2	no	—
540	C₂³	—	188	2	no	—
541	C₂³	—	188	1	no	—
542	C₂³	—	188	1	no	—
543	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
544	C₂³	#13093997	1	1	yes	characteristic
545	C₂³	#13094002	1	1	yes	characteristic
546	C₂³	#13094009	1	1	yes	characteristic
547	C₂³	#13094010	1	1	yes	characteristic
548	C₂³	#13094012	1	1	yes	characteristic
549	C₂³	#13094018	1	1	yes	characteristic
550	Q₈	—	94	2	no	—
551	Q₈	—	94	2	no	—
552	Q₈	—	188	1	no	—
553	Q₈	—	188	1	no	—
554	D₄	—	94	2	no	—
555	D₄	—	94	2	no	—
556	D₄	—	188	2	no	—
557	D₄	—	188	2	no	—
558	D₄	—	188	2	no	—
559	D₄	—	188	2	no	—
560	D₄	—	188	1	no	—
561	D₄	—	188	1	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	94	4	no	—
567	C₂×C₄	—	94	2	no	—
568	C₂×C₄	—	188	2	no	—
569	C₂×C₄	—	188	4	no	—
570	C₂×C₄	—	188	4	no	—
571	C₂×C₄	—	188	1	no	—
572	C₂×C₄	—	188	1	no	—
573	C₂×C₄	—	188	2	no	—
574	C₂×C₄	—	188	2	no	—
575	C₂×C₄	—	188	2	no	—
576	C₂×C₄	—	188	2	no	—
577	C₂×C₄	—	188	2	no	—
578	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
579	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
580	C₂×C₄	#13093981	1	1	yes	characteristic
581	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
582	C₂×C₄	#13093986	1	1	yes	characteristic
583	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
584	C₂×C₄	#13093992	1	1	yes	characteristic
585	C₂×C₄	#13093994	1	1	yes	characteristic
586	C₂×C₄	#13093994	1	1	yes	characteristic
587	C₂×C₄	#13093996	1	1	yes	characteristic
588	C₂×C₄	#13093997	1	1	yes	characteristic
589	C₂×C₄	#13093997	1	1	yes	characteristic
590	C₂×C₄	#13093997	1	1	yes	characteristic
591	C₂×C₄	#13093997	1	1	yes	characteristic
592	C₂×C₄	#13093998	1	1	yes	characteristic
593	C₂×C₄	#13093999	1	1	yes	characteristic
594	C₂×C₄	#13094000	1	1	yes	characteristic
595	C₂×C₄	#13094002	1	1	yes	characteristic
596	C₂×C₄	#13094002	1	1	yes	characteristic
597	C₂×C₄	#13094002	1	1	yes	characteristic
598	C₂×C₄	#13094004	1	1	yes	characteristic
599	C₂×C₄	#13094006	1	1	yes	characteristic
600	C₂×C₄	#13094007	1	1	yes	characteristic
601	C₂×C₄	#13094009	1	1	yes	characteristic
602	C₂×C₄	#13094009	1	1	yes	characteristic
603	C₂×C₄	#13094010	1	1	yes	characteristic
604	C₂×C₄	#13094019	1	1	yes	characteristic
605	C₂×C₄	#13094020	1	1	yes	characteristic
606	C₈	—	4	2	no	—
607	C₈	—	4	2	no	—
608	C₈	—	94	2	no	—
609	C₈	—	94	2	no	—
610	C₈	—	188	2	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	376	1	no	—
620	C₂²	—	376	1	no	—
621	C₂²	—	376	2	no	—
622	C₂²	—	188	4	no	—
623	C₂²	—	188	2	no	—
624	C₂²	#15688994	1	1	yes	characteristic
625	C₂²	#15689014	1	1	yes	characteristic
626	C₂²	#15689023	1	1	yes	characteristic
627	C₂²	#15689036	1	1	yes	characteristic
628	C₂²	#15689041	1	1	yes	characteristic
629	C₂²	#15689047	1	1	yes	characteristic
630	C₂²	#15689052	1	1	yes	characteristic
631	C₂²	#15689238	1	2	yes	—
632	C₂²	#15689243	1	2	yes	—
633	C₄	—	8	1	no	—
634	C₄	—	8	1	no	—
635	C₄	—	188	4	no	—
636	C₄	—	188	2	no	—
637	C₄	#15688982	1	1	yes	characteristic
638	C₄	#15688997	1	1	yes	characteristic
639	C₄	#15689001	1	1	yes	characteristic
640	C₄	#15689012	1	1	yes	characteristic
641	C₄	#15689032	1	1	yes	characteristic
642	C₄	#15689038	1	1	yes	characteristic
643	C₄	#15689045	1	1	yes	characteristic
644	C₄	#15689058	1	1	yes	characteristic
645	C₂	—	2	1	no	—
646	C₂	—	2	1	no	—
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	376	2	no	—
650	C₂	#20241632	1	1	yes	characteristic
651	C₂	#20243662	1	2	yes	—
652	C₂	#20244036	1	2	yes	—
653	C₂	#20244275	1	1	yes	characteristic
654	C₂	#20244280	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄₇×#1729	C₂
socle	C₂³×C₄₇	C₄×D₄
prime radical	C₂²×#10625350	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	#1729	D₄₇
hypocenter	C₄₇	#11125
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ #1729

Complements

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

N	H ≅ G/N	type
1. C₂²×#13093959	C₂	semidirect
5. C₂×#15688882	C₂	semidirect
6. C₂×#15688877	C₂	semidirect
7. C₄₇×#1729	C₂	semidirect
20. C₂×#13093947	C₄	semidirect
21. C₂×#13093947	C₄	semidirect
22. C₂×#13093944	C₄	semidirect
23. C₂×#13093944	C₄	semidirect
323. #1729	D₄₇	semidirect
360. C₄₇	#11125	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13093959	2
C₂²×#13093950	2
C₂×#15689117	2
C₂×#15689089	2
C₂×#15688882	2
C₂×#15688877	2
C₄₇×#1729	2
#11125	47