Subgroups — #26233634

Order 12032.

906 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252042	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689119	C₂	1	1	yes	maximal, characteristic
3	#20244095	C₂	1	2	yes	maximal, complemented
4	#20244033	C₂	1	2	yes	maximal, complemented
5	#20243663	C₂	1	2	yes	maximal, complemented
6	#20243485	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243424	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243332	C₂	1	1	yes	maximal, characteristic
9	#20243223	C₂	1	2	yes	maximal, complemented
10	#20243162	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2880	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×#13093983	C₂²	1	1	yes	characteristic
14	#15689181	—	2	2	no	—
15	#15689177	—	2	1	no	—
16	#15689173	—	2	1	no	—
17	C₂×#13093959	C₂²	1	2	yes	complemented
18	#15689149	C₂²	1	2	yes	complemented
19	C₂×#13093951	C₂²	1	2	yes	—
20	C₂×#13093951	C₂²	1	2	yes	—
21	#15689119	C₄	1	1	yes	characteristic, complemented
22	#15689119	C₄	1	1	yes	characteristic, complemented
23	#15689119	C₄	1	1	yes	characteristic, complemented
24	#15689119	C₄	1	1	yes	characteristic, complemented
25	#15689119	C₂²	1	1	yes	characteristic
26	#15689119	C₂²	1	1	yes	characteristic
27	#15689119	C₂²	1	1	yes	characteristic
28	#15689119	C₂²	1	1	yes	characteristic
29	C₂×#13093948	C₄	1	1	yes	characteristic, complemented
30	C₂×#13093948	C₄	1	1	yes	characteristic, complemented
31	C₂×#13093945	C₄	1	1	yes	characteristic, complemented
32	C₂×#13093945	C₄	1	1	yes	characteristic, complemented
33	#15689087	C₂²	1	1	yes	characteristic
34	#15689078	C₂²	1	2	yes	complemented
35	C₂×C₈×Dic₄₇	C₂²	1	2	yes	complemented
36	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
37	#15688887	C₂²	1	2	yes	complemented
38	#15688884	C₂²	1	2	yes	complemented
39	#15688884	C₂²	1	2	yes	complemented
40	#15688877	C₂²	1	2	yes	complemented
41	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#131×C₄₇	C₂²	1	2	yes	—
43	C₄₇×#408	—	2	2	no	—
44	C₄₇×#408	C₂²	1	2	yes	—
45	C₄₇×#407	—	2	1	no	—
46	C₄₇×#407	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
48	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
49	C₂×#10625329	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	—	4	2	no	—
51	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
57	#13093983	—	2	1	no	—
58	#13093983	—	2	1	no	—
59	#13093983	C₂×C₄	1	1	yes	characteristic
60	#13093983	C₂×C₄	1	1	yes	characteristic
61	#13093983	C₂³	1	1	yes	characteristic
62	#13093983	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
66	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
67	C₂×C₄×Dic₄₇	—	2	1	no	—
68	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
69	#13093959	—	4	2	no	—
70	Dic₄₇⋊C₈	—	2	2	no	—
71	Dic₄₇⋊C₈	—	2	2	no	—
72	#13093951	—	2	4	no	—
73	#13093951	—	4	2	no	—
74	#13093948	C₂×C₄	1	1	yes	characteristic
75	#13093948	C₂×C₄	1	1	yes	characteristic
76	#13093948	C₂×C₄	1	1	yes	characteristic
77	#13093948	C₂×C₄	1	1	yes	characteristic
78	#13093948	C₂×C₄	1	1	yes	characteristic
79	#13093948	C₂×C₄	1	1	yes	characteristic
80	#13093948	C₂×C₄	1	1	yes	characteristic
81	#13093948	C₂×C₄	1	1	yes	characteristic
82	#13093945	C₂×C₄	1	1	yes	characteristic
83	#13093945	C₂×C₄	1	1	yes	characteristic
84	#13093945	C₂×C₄	1	1	yes	characteristic
85	#13093945	C₂×C₄	1	1	yes	characteristic
86	#13093945	C₂×C₄	1	1	yes	characteristic
87	#13093945	C₂×C₄	1	1	yes	characteristic
88	#13093945	C₂×C₄	1	1	yes	characteristic
89	#13093945	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
91	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
92	#13093934	—	2	2	no	—
93	C₈×Dic₄₇	—	2	2	no	—
94	C₈×Dic₄₇	—	4	2	no	—
95	C₄₇⋊#95	—	2	1	no	—
96	C₂×#41×C₄₇	—	2	1	no	—
97	C₂×#41×C₄₇	—	2	1	no	—
98	C₂×#41×C₄₇	—	2	4	no	—
99	C₂×#41×C₄₇	—	4	2	no	—
100	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
101	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
102	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
103	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
104	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
105	C₂²×D₄×C₄₇	—	2	1	no	—
106	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
107	C₂³×C₄×C₄₇	—	2	1	no	—
108	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
109	#131×C₄₇	—	2	4	no	—
110	#131×C₄₇	—	4	2	no	—
111	C₂×M₁₆×C₄₇	—	2	2	no	—
112	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
113	C₂²×C₈×C₄₇	—	2	2	no	—
114	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
115	C₂²⋊C₈×C₄₇	—	2	1	no	—
116	C₂²⋊C₈×C₄₇	—	2	1	no	—
117	C₂²⋊C₈×C₄₇	—	2	2	no	—
118	C₂²⋊C₈×C₄₇	—	2	2	no	—
119	C₂²⋊C₈×C₄₇	D₄	1	1	yes	characteristic
120	C₂²⋊C₈×C₄₇	D₄	1	1	yes	characteristic
121	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
122	C₂⁴×C₄₇	—	2	1	no	—
123	C₂⁴×C₄₇	#41	1	1	yes	characteristic
124	#41×C₄₇	—	2	2	no	—
125	#41×C₄₇	—	2	2	no	—
126	#41×C₄₇	—	2	2	no	—
127	#41×C₄₇	—	2	2	no	—
128	#41×C₄₇	—	2	2	no	—
129	#41×C₄₇	—	4	4	no	—
130	#41×C₄₇	—	4	1	no	—
131	#41×C₄₇	—	4	1	no	—
132	#41×C₄₇	—	4	4	no	—
133	#41×C₄₇	#41	1	4	yes	—
134	C₂×Q₈×C₄₇	—	2	1	no	—
135	C₂×Q₈×C₄₇	—	2	2	no	—
136	C₂×Q₈×C₄₇	—	4	1	no	—
137	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
138	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×D₄×C₄₇	—	2	1	no	—
140	C₂×D₄×C₄₇	—	2	2	no	—
141	C₂×D₄×C₄₇	—	2	1	no	—
142	C₂×D₄×C₄₇	—	2	1	no	—
143	C₂×D₄×C₄₇	—	2	1	no	—
144	C₂×D₄×C₄₇	—	2	1	no	—
145	C₂×D₄×C₄₇	—	4	1	no	—
146	C₂×D₄×C₄₇	—	4	4	no	—
147	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	—	2	1	no	—
150	C₂²×C₄×C₄₇	—	2	2	no	—
151	C₂²×C₄×C₄₇	—	2	2	no	—
152	C₂²×C₄×C₄₇	—	2	1	no	—
153	C₂²×C₄×C₄₇	—	2	1	no	—
154	C₂²×C₄×C₄₇	—	2	1	no	—
155	C₂²×C₄×C₄₇	—	2	1	no	—
156	C₂²×C₄×C₄₇	—	4	4	no	—
157	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
162	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
163	C₂²×Dic₄₇	—	2	1	no	—
164	C₂²×Dic₄₇	—	2	2	no	—
165	C₂²×Dic₄₇	—	2	1	no	—
166	M₁₆×C₄₇	—	2	2	no	—
167	M₁₆×C₄₇	—	2	2	no	—
168	M₁₆×C₄₇	—	4	4	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	—	4	4	no	—
173	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
174	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
175	C₂²⋊Dic₄₇	—	2	4	no	—
176	C₂²⋊Dic₄₇	—	2	1	no	—
177	C₂²⋊Dic₄₇	—	2	1	no	—
178	C₂²⋊Dic₄₇	—	2	1	no	—
179	C₂²⋊Dic₄₇	—	2	1	no	—
180	C₄⋊Dic₄₇	—	2	1	no	—
181	C₄⋊Dic₄₇	—	2	1	no	—
182	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
183	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
184	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
185	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
186	C₄×Dic₄₇	—	2	1	no	—
187	C₄×Dic₄₇	—	2	1	no	—
188	C₄×Dic₄₇	—	2	1	no	—
189	C₄×Dic₄₇	—	2	1	no	—
190	C₄×Dic₄₇	—	2	2	no	—
191	C₄×Dic₄₇	—	2	2	no	—
192	#10625329	—	2	2	no	—
193	#10625329	—	2	2	no	—
194	C₂×C₄₇⋊C₈	—	2	2	no	—
195	C₂×C₄₇⋊C₈	—	2	2	no	—
196	C₂×C₄₇⋊C₈	—	2	2	no	—
197	C₂×C₄₇⋊C₈	—	4	1	no	—
198	C₂×C₄₇⋊C₈	—	4	1	no	—
199	C₂×C₄₇⋊C₈	—	4	1	no	—
200	C₂×C₄₇⋊C₈	—	4	1	no	—
201	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
205	C₂³×C₄₇	—	2	1	no	—
206	C₂³×C₄₇	—	2	2	no	—
207	C₂³×C₄₇	—	2	2	no	—
208	C₂³×C₄₇	—	2	1	no	—
209	C₂³×C₄₇	—	4	1	no	—
210	C₂³×C₄₇	—	4	2	no	—
211	C₂³×C₄₇	—	4	2	no	—
212	C₂³×C₄₇	—	8	1	no	—
213	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
214	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
215	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
216	Q₈×C₄₇	—	2	1	no	—
217	Q₈×C₄₇	—	2	1	no	—
218	Q₈×C₄₇	—	2	1	no	—
219	Q₈×C₄₇	—	4	2	no	—
220	Q₈×C₄₇	#117	1	2	yes	—
221	D₄×C₄₇	—	2	4	no	—
222	D₄×C₄₇	—	2	1	no	—
223	D₄×C₄₇	—	2	1	no	—
224	D₄×C₄₇	—	2	1	no	—
225	D₄×C₄₇	—	4	2	no	—
226	D₄×C₄₇	—	4	2	no	—
227	D₄×C₄₇	—	4	2	no	—
228	D₄×C₄₇	—	4	2	no	—
229	D₄×C₄₇	#117	1	2	yes	—
230	C₂×C₄×C₄₇	—	2	1	no	—
231	C₂×C₄×C₄₇	—	2	2	no	—
232	C₂×C₄×C₄₇	—	2	1	no	—
233	C₂×C₄×C₄₇	—	2	1	no	—
234	C₂×C₄×C₄₇	—	2	1	no	—
235	C₂×C₄×C₄₇	—	2	1	no	—
236	C₂×C₄×C₄₇	—	2	4	no	—
237	C₂×C₄×C₄₇	—	2	2	no	—
238	C₂×C₄×C₄₇	—	2	2	no	—
239	C₂×C₄×C₄₇	—	2	1	no	—
240	C₂×C₄×C₄₇	—	4	2	no	—
241	C₂×C₄×C₄₇	—	4	2	no	—
242	C₂×C₄×C₄₇	—	4	2	no	—
243	C₂×C₄×C₄₇	—	4	2	no	—
244	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
249	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
250	C₂×Dic₄₇	—	2	4	no	—
251	C₂×Dic₄₇	—	2	1	no	—
252	C₂×Dic₄₇	—	2	1	no	—
253	C₂×Dic₄₇	—	2	1	no	—
254	C₂×Dic₄₇	—	2	1	no	—
255	C₂×Dic₄₇	—	4	2	no	—
256	C₂×Dic₄₇	—	4	2	no	—
257	C₂×Dic₄₇	—	4	2	no	—
258	C₂×Dic₄₇	—	8	1	no	—
259	C₈×C₄₇	—	2	2	no	—
260	C₈×C₄₇	—	2	2	no	—
261	C₈×C₄₇	—	4	2	no	—
262	C₄₇⋊C₈	—	2	1	no	—
263	C₄₇⋊C₈	—	2	1	no	—
264	C₄₇⋊C₈	—	2	1	no	—
265	C₄₇⋊C₈	—	2	1	no	—
266	C₄₇⋊C₈	—	4	2	no	—
267	#22587	—	47	1	no	maximal, Sylow
268	C₂²×C₄₇	—	2	1	no	—
269	C₂²×C₄₇	—	2	1	no	—
270	C₂²×C₄₇	—	2	1	no	—
271	C₂²×C₄₇	—	2	1	no	—
272	C₂²×C₄₇	—	2	1	no	—
273	C₂²×C₄₇	—	2	2	no	—
274	C₂²×C₄₇	—	2	1	no	—
275	C₂²×C₄₇	—	2	1	no	—
276	C₂²×C₄₇	—	4	4	no	—
277	C₂²×C₄₇	—	4	1	no	—
278	C₂²×C₄₇	—	4	1	no	—
279	C₂²×C₄₇	—	4	1	no	—
280	C₂²×C₄₇	—	4	1	no	—
281	C₂²×C₄₇	—	4	1	no	—
282	C₂²×C₄₇	—	8	4	no	—
283	C₂²×C₄₇	#443	1	2	yes	—
284	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
285	C₂²×C₄₇	#551	1	2	yes	—
286	C₄×C₄₇	—	2	1	no	—
287	C₄×C₄₇	—	2	1	no	—
288	C₄×C₄₇	—	2	2	no	—
289	C₄×C₄₇	—	4	1	no	—
290	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
291	C₄×C₄₇	#518	1	1	yes	characteristic
292	C₄×C₄₇	#546	1	2	yes	—
293	Dic₄₇	—	4	4	no	—
294	Dic₄₇	—	4	1	no	—
295	Dic₄₇	—	4	1	no	—
296	Dic₄₇	—	4	1	no	—
297	Dic₄₇	—	4	1	no	—
298	#2924	—	47	1	no	—
299	C₂×#416	—	47	1	no	—
300	#2880	D₄₇	1	1	yes	characteristic
301	#1937	—	47	2	no	—
302	#1929	—	47	2	no	—
303	#1866	—	47	2	no	—
304	#1826	—	47	1	no	—
305	#1810	—	47	1	no	—
306	#1789	—	47	1	no	—
307	#1764	—	47	2	no	—
308	C₈×C₂²⋊C₄	—	47	1	no	—
309	C₂×C₄₇	—	2	2	no	—
310	C₂×C₄₇	—	2	2	no	—
311	C₂×C₄₇	—	4	1	no	—
312	C₂×C₄₇	—	4	2	no	—
313	C₂×C₄₇	—	8	1	no	—
314	C₂×C₄₇	#2342	1	1	yes	characteristic
315	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
316	C₂×C₄₇	#2957	1	1	yes	characteristic
317	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
318	C₂×#131	C₂×D₄₇	1	2	yes	—
319	C₂³×C₈	—	47	1	no	—
320	C₂×#117	—	47	1	no	—
321	#433	—	94	2	no	—
322	#432	—	94	1	no	—
323	#431	—	94	1	no	—
324	C₂×#108	—	47	2	no	—
325	#424	—	47	2	no	—
326	C₂×#104	—	47	2	no	—
327	C₂×#104	—	47	2	no	—
328	#416	—	47	1	no	—
329	#416	—	47	1	no	—
330	#416	—	47	1	no	—
331	#416	—	47	1	no	—
332	#416	—	47	1	no	—
333	#416	—	47	1	no	—
334	#416	—	47	1	no	—
335	#416	—	47	1	no	—
336	C₂×#103	—	47	1	no	—
337	C₂×#103	—	47	1	no	—
338	C₂×#102	—	47	1	no	—
339	C₂×#102	—	47	1	no	—
340	#408	—	2	2	no	—
341	#408	C₂×D₄₇	1	2	yes	—
342	#407	—	2	1	no	—
343	#407	—	47	1	no	—
344	#407	C₂×D₄₇	1	1	yes	characteristic
345	C₂×C₂²⋊C₈	—	2	1	no	—
346	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
347	#405	—	47	2	no	—
348	C₂×C₄×C₈	—	47	2	no	—
349	C₄×C₂²⋊C₄	—	47	1	no	—
350	#341	—	47	2	no	—
351	#339	—	47	2	no	—
352	#339	—	47	2	no	—
353	#336	—	47	2	no	—
354	C₄₇	#22587	1	1	yes	characteristic, complemented, Sylow
355	C₂×#41	—	2	1	no	—
356	C₂×#41	—	2	1	no	—
357	C₂×#41	—	2	4	no	—
358	C₂×#41	—	4	2	no	—
359	C₂×#41	C₄×D₄₇	1	1	yes	characteristic
360	C₂×#41	C₄×D₄₇	1	1	yes	characteristic
361	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
362	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
363	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
364	C₂²×D₄	—	2	1	no	—
365	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
366	C₂³×C₄	—	2	1	no	—
367	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
368	#131	—	2	4	no	—
369	#131	—	4	2	no	—
370	C₂×M₁₆	—	2	2	no	—
371	C₂×M₁₆	—	47	2	no	—
372	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
373	C₂²×C₈	—	2	2	no	—
374	C₂²×C₈	—	47	1	no	—
375	C₂²×C₈	—	47	1	no	—
376	C₂²×C₈	—	47	1	no	—
377	C₂²×C₈	—	47	1	no	—
378	C₂²×C₈	—	47	1	no	—
379	C₂²×C₈	—	47	1	no	—
380	C₂²×C₈	—	188	2	no	—
381	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
382	#117	—	47	1	no	—
383	#117	—	47	1	no	—
384	#117	—	47	1	no	—
385	#117	—	47	1	no	—
386	#117	—	94	1	no	—
387	#117	—	94	1	no	—
388	C₂×C₄⋊C₄	—	47	1	no	—
389	C₂×C₄⋊C₄	—	47	1	no	—
390	C₂×C₂²⋊C₄	—	94	1	no	—
391	C₂×C₂²⋊C₄	—	94	1	no	—
392	C₂×C₄²	—	47	2	no	—
393	C₂×C₄²	—	94	1	no	—
394	#108	—	188	2	no	—
395	C₄⋊C₈	—	94	2	no	—
396	C₄⋊C₈	—	94	2	no	—
397	#104	—	94	4	no	—
398	#104	—	188	2	no	—
399	#103	—	47	1	no	—
400	#103	—	47	1	no	—
401	#103	—	47	1	no	—
402	#103	—	47	1	no	—
403	#103	—	47	1	no	—
404	#103	—	47	1	no	—
405	#103	—	47	1	no	—
406	#103	—	47	1	no	—
407	#102	—	47	1	no	—
408	#102	—	47	1	no	—
409	#102	—	47	1	no	—
410	#102	—	47	1	no	—
411	#102	—	47	1	no	—
412	#102	—	47	1	no	—
413	#102	—	47	1	no	—
414	#102	—	47	1	no	—
415	C₂²⋊C₈	—	2	1	no	—
416	C₂²⋊C₈	—	2	1	no	—
417	C₂²⋊C₈	—	2	2	no	—
418	C₂²⋊C₈	—	2	2	no	—
419	C₂²⋊C₈	—	94	1	no	—
420	C₂²⋊C₈	—	94	1	no	—
421	C₂²⋊C₈	C₂²⋊D₄₇	1	1	yes	characteristic
422	C₂²⋊C₈	C₂²⋊D₄₇	1	1	yes	characteristic
423	C₂²⋊C₈	C₂²⋊D₄₇	1	2	yes	—
424	#97	—	94	2	no	—
425	C₄×C₈	—	94	2	no	—
426	C₄×C₈	—	188	2	no	—
427	#95	—	94	1	no	—
428	C₂⁴	—	2	1	no	—
429	C₂⁴	#10625350	1	1	yes	characteristic
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	2	2	no	—
435	#41	—	4	4	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	4	4	no	—
439	#41	#10625352	1	4	yes	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	4	1	no	—
443	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
444	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	4	1	no	—
452	C₂×D₄	—	4	4	no	—
453	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
454	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	4	4	no	—
463	C₂²×C₄	—	94	1	no	—
464	C₂²×C₄	—	94	1	no	—
465	C₂²×C₄	—	94	2	no	—
466	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
468	C₂²×C₄	#10625350	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
471	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	4	4	no	—
475	M₁₆	—	94	2	no	—
476	M₁₆	—	94	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	4	4	no	—
481	C₂×C₈	—	47	1	no	—
482	C₂×C₈	—	47	1	no	—
483	C₂×C₈	—	47	1	no	—
484	C₂×C₈	—	47	1	no	—
485	C₂×C₈	—	94	2	no	—
486	C₂×C₈	—	94	2	no	—
487	C₂×C₈	—	94	2	no	—
488	C₂×C₈	—	188	1	no	—
489	C₂×C₈	—	188	1	no	—
490	C₂×C₈	—	188	1	no	—
491	C₂×C₈	—	188	1	no	—
492	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
493	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
494	C₄⋊C₄	—	47	1	no	—
495	C₄⋊C₄	—	47	1	no	—
496	C₄⋊C₄	—	47	1	no	—
497	C₄⋊C₄	—	47	1	no	—
498	C₄⋊C₄	—	94	1	no	—
499	C₄⋊C₄	—	94	1	no	—
500	C₂²⋊C₄	—	94	4	no	—
501	C₂²⋊C₄	—	94	1	no	—
502	C₂²⋊C₄	—	94	1	no	—
503	C₂²⋊C₄	—	94	1	no	—
504	C₂²⋊C₄	—	94	1	no	—
505	C₄²	—	94	1	no	—
506	C₄²	—	94	1	no	—
507	C₄²	—	94	1	no	—
508	C₄²	—	94	1	no	—
509	C₄²	—	94	2	no	—
510	C₄²	—	94	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	8	1	no	—
519	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
520	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
521	C₂³	C₂×#10625350	1	1	yes	characteristic
522	Q₈	—	2	1	no	—
523	Q₈	—	2	1	no	—
524	Q₈	—	2	1	no	—
525	Q₈	—	4	2	no	—
526	Q₈	#13093980	1	2	yes	—
527	D₄	—	2	4	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	#13093980	1	2	yes	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	94	4	no	—
551	C₂×C₄	—	94	1	no	—
552	C₂×C₄	—	94	1	no	—
553	C₂×C₄	—	94	1	no	—
554	C₂×C₄	—	94	1	no	—
555	C₂×C₄	—	376	1	no	—
556	C₂×C₄	—	188	2	no	—
557	C₂×C₄	—	188	2	no	—
558	C₂×C₄	—	188	2	no	—
559	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
560	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
561	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
562	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
563	C₂×C₄	C₂×#10625352	1	2	yes	—
564	C₂×C₄	#13094069	1	2	yes	—
565	C₈	—	2	2	no	—
566	C₈	—	2	2	no	—
567	C₈	—	4	2	no	—
568	C₈	—	94	1	no	—
569	C₈	—	94	1	no	—
570	C₈	—	94	1	no	—
571	C₈	—	94	1	no	—
572	C₈	—	188	2	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	8	4	no	—
588	C₂²	#15689238	1	2	yes	—
589	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
590	C₂²	#15689799	1	2	yes	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	1	no	—
595	C₄	—	188	4	no	—
596	C₄	—	188	1	no	—
597	C₄	—	188	1	no	—
598	C₄	—	188	1	no	—
599	C₄	—	188	1	no	—
600	C₄	C₂×#13093980	1	1	yes	characteristic
601	C₄	#15689596	1	1	yes	characteristic
602	C₄	#15689767	1	2	yes	—
603	C₂	—	2	2	no	—
604	C₂	—	2	2	no	—
605	C₂	—	4	1	no	—
606	C₂	—	4	2	no	—
607	C₂	—	8	1	no	—
608	C₂	#20246233	1	1	yes	characteristic
609	C₂	C₂×#15689238	1	1	yes	characteristic
610	C₂	#20252303	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2880	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2880	D₄₇
hypocenter	C₄₇	#22587
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₂²⋊C₈ ◁ #2880

Complements

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

N	H ≅ G/N	type
1. #20252042	C₂	semidirect
3. #20244095	C₂	semidirect
4. #20244033	C₂	semidirect
5. #20243663	C₂	semidirect
6. #20243485	C₂	semidirect
7. #20243424	C₂	semidirect
9. #20243223	C₂	semidirect
10. #20243162	C₂	semidirect
17. C₂×#13093959	C₂²	semidirect
18. #15689149	C₂²	semidirect
21. #15689119	C₄	semidirect
22. #15689119	C₄	semidirect
23. #15689119	C₄	semidirect
24. #15689119	C₄	semidirect
29. C₂×#13093948	C₄	semidirect
30. C₂×#13093948	C₄	semidirect
31. C₂×#13093945	C₄	semidirect
32. C₂×#13093945	C₄	semidirect
34. #15689078	C₂²	semidirect
35. C₂×C₈×Dic₄₇	C₂²	semidirect
37. #15688887	C₂²	semidirect
38. #15688884	C₂²	semidirect
39. #15688884	C₂²	semidirect
40. #15688877	C₂²	semidirect
354. C₄₇	#22587	semidirect

Maximal subgroups

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

subgroup	index
#20252042	2
C₂×#15689119	2
#20244095	2
#20244033	2
#20243663	2
#20243485	2
#20243424	2
#20243332	2
#20243223	2
#20243162	2
C₄₇×#2880	2
#22587	47