Subgroups — #26238819

Order 12032.

892 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252969	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689241	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252109	C₂	1	2	yes	maximal, complemented
4	C₂²×#13093960	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244276	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244136	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244037	C₂	1	2	yes	maximal, complemented
8	#20243688	C₂	1	2	yes	maximal, complemented
9	#20243666	C₂	1	2	yes	maximal, complemented
10	#20243267	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	C₂²	1	1	yes	characteristic
13	C₂×#13094030	C₂²	1	2	yes	—
14	C₂²×#10625329	C₂²	1	2	yes	—
15	#15689634	C₂²	1	2	yes	—
16	#15689364	C₄	1	1	yes	characteristic, complemented
17	#15689364	C₄	1	1	yes	characteristic, complemented
18	#15689359	C₄	1	1	yes	characteristic, complemented
19	#15689359	C₄	1	1	yes	characteristic, complemented
20	#15689352	C₄	1	2	yes	complemented
21	#15689352	C₄	1	2	yes	complemented
22	#15689241	—	2	4	no	—
23	#15689198	—	2	2	no	—
24	#15689197	—	2	2	no	—
25	#15689191	—	2	2	no	—
26	(C₂²⋊D₄₇)⋊C₈	—	2	2	no	—
27	C₂×#13093960	—	2	4	no	—
28	C₂×#13093960	C₂²	1	1	yes	characteristic
29	C₂×#13093960	C₂²	1	2	yes	—
30	C₂×#13093960	C₂²	1	1	yes	characteristic
31	#15689161	C₂²	1	1	yes	characteristic
32	#15689149	C₂²	1	2	yes	—
33	C₂×#13093952	C₂²	1	2	yes	—
34	C₂×#13093952	C₂²	1	2	yes	—
35	#15689120	C₂²	1	2	yes	—
36	#15689089	C₂²	1	2	yes	—
37	#15689078	C₂²	1	2	yes	—
38	#15688883	C₂²	1	2	yes	—
39	#15688883	C₂²	1	2	yes	—
40	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
44	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#336	C₂²	1	1	yes	characteristic
46	C₄₇×#336	C₂²	1	1	yes	characteristic
47	C₂×#10625350	C₂³	1	2	yes	—
48	#13094046	—	2	2	no	—
49	#13094046	—	2	2	no	—
50	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic
51	C₂×#10625325	C₂×C₄	1	2	yes	—
52	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
53	#13094030	—	2	4	no	—
54	#13094030	—	4	2	no	—
55	C₂×#10625329	—	2	2	no	—
56	C₂×#10625329	—	2	4	no	—
57	C₂×#10625329	—	4	2	no	—
58	C₂×#10625329	C₂³	1	2	yes	—
59	C₂×#10625329	C₂³	1	2	yes	—
60	C₂×#10625324	—	2	2	no	—
61	C₂²×C₄₇⋊C₈	—	2	2	no	—
62	C₂×C₈×D₄₇	—	2	2	no	—
63	#13094007	—	2	2	no	—
64	#13094003	C₂×C₄	1	2	yes	—
65	#13094003	C₂×C₄	1	2	yes	—
66	#13093998	C₂×C₄	1	2	yes	—
67	#13093998	C₂×C₄	1	2	yes	—
68	#13093993	—	2	2	no	—
69	C₄×C₂²⋊D₄₇	—	2	2	no	—
70	C₄×C₂²⋊D₄₇	—	2	2	no	—
71	#13093983	C₂³	1	2	yes	—
72	#13093960	—	2	2	no	—
73	#13093960	—	2	4	no	—
74	#13093960	D₄	1	4	yes	complemented
75	#13093958	C₂×C₄	1	1	yes	characteristic
76	#13093958	C₂×C₄	1	1	yes	characteristic
77	#13093956	C₂×C₄	1	2	yes	—
78	Dic₄₇⋊C₈	—	2	2	no	—
79	Dic₄₇⋊C₈	—	2	2	no	—
80	#13093952	—	2	4	no	—
81	#13093952	—	4	2	no	—
82	#13093949	C₂×C₄	1	2	yes	—
83	#13093949	C₂×C₄	1	2	yes	—
84	#13093946	C₂×C₄	1	2	yes	—
85	#13093946	C₂×C₄	1	2	yes	—
86	(C₂×D₄₇)⋊C₈	—	2	2	no	—
87	(C₂×D₄₇)⋊C₈	—	2	2	no	—
88	#13093934	—	2	2	no	—
89	C₈×Dic₄₇	—	2	2	no	—
90	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₄₇	—	2	2	no	—
92	C₂²×C₈×C₄₇	—	2	2	no	—
93	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
96	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
97	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
102	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
104	C₂²⋊C₈×C₄₇	D₄	1	1	yes	characteristic
105	C₂²⋊C₈×C₄₇	D₄	1	1	yes	characteristic
106	C₂²⋊C₈×C₄₇	D₄	1	1	yes	characteristic
107	C₂²⋊C₈×C₄₇	D₄	1	1	yes	characteristic
108	C₄×C₈×C₄₇	—	2	2	no	—
109	C₄×C₈×C₄₇	—	2	2	no	—
110	#95×C₄₇	—	2	1	no	—
111	C₂⁴×C₄₇	#41	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	1	no	—
116	C₂²×C₄×C₄₇	—	2	1	no	—
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
124	C₂×C₂²⋊D₄₇	—	2	2	no	—
125	C₂×C₂²⋊D₄₇	—	2	2	no	—
126	C₂×C₂²⋊D₄₇	—	2	2	no	—
127	#10625350	—	2	2	no	—
128	#10625350	—	2	2	no	—
129	#10625350	—	2	2	no	—
130	#10625350	—	2	2	no	—
131	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
132	C₂×C₄×D₄₇	—	2	2	no	—
133	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₄₇	—	2	1	no	—
135	C₂×C₈×C₄₇	—	2	1	no	—
136	C₂×C₈×C₄₇	—	2	1	no	—
137	C₂×C₈×C₄₇	—	2	1	no	—
138	C₂×C₈×C₄₇	—	2	1	no	—
139	C₂×C₈×C₄₇	—	2	1	no	—
140	C₂×C₈×C₄₇	—	2	2	no	—
141	C₂×C₈×C₄₇	—	2	2	no	—
142	C₂×C₈×C₄₇	—	2	2	no	—
143	C₂×C₈×C₄₇	—	2	2	no	—
144	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₄₇	#41	1	2	yes	—
154	C₂²⋊C₄×C₄₇	—	2	4	no	—
155	C₄²×C₄₇	—	2	1	no	—
156	C₄²×C₄₇	—	2	1	no	—
157	C₄²×C₄₇	—	2	1	no	—
158	C₄²×C₄₇	—	2	1	no	—
159	C₂²⋊Dic₄₇	—	2	2	no	—
160	C₂²⋊Dic₄₇	—	2	2	no	—
161	C₂²⋊Dic₄₇	—	2	2	no	—
162	(C₂×D₄₇)⋊C₄	—	2	2	no	—
163	(C₂×D₄₇)⋊C₄	—	2	2	no	—
164	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
165	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
166	Dic₄₇⋊C₄	—	2	2	no	—
167	Dic₄₇⋊C₄	—	2	2	no	—
168	C₄×Dic₄₇	—	2	2	no	—
169	#10625329	—	2	2	no	—
170	#10625329	—	2	2	no	—
171	#10625329	—	2	2	no	—
172	#10625329	—	4	4	no	—
173	#10625329	C₂×D₄	1	4	yes	—
174	C₂×C₄₇⋊C₈	—	2	2	no	—
175	C₂×C₄₇⋊C₈	—	2	2	no	—
176	C₂×C₄₇⋊C₈	—	4	4	no	—
177	Dic₁₈₈	—	2	2	no	—
178	D₃₇₆	—	2	2	no	—
179	#10625325	—	2	4	no	—
180	#10625324	—	4	4	no	—
181	C₈×D₄₇	—	4	4	no	—
182	C₂³×C₄₇	—	2	1	no	—
183	C₂³×C₄₇	—	2	1	no	—
184	C₂³×C₄₇	—	2	2	no	—
185	C₂³×C₄₇	—	4	1	no	—
186	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
187	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
188	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
189	C₂²×D₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	1	no	—
191	C₂×C₄×C₄₇	—	2	1	no	—
192	C₂×C₄×C₄₇	—	2	1	no	—
193	C₂×C₄×C₄₇	—	2	1	no	—
194	C₂×C₄×C₄₇	—	2	1	no	—
195	C₂×C₄×C₄₇	—	2	1	no	—
196	C₂×C₄×C₄₇	—	2	1	no	—
197	C₂×C₄×C₄₇	—	2	1	no	—
198	C₂×C₄×C₄₇	—	2	1	no	—
199	C₂×C₄×C₄₇	—	2	1	no	—
200	C₂×C₄×C₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	—	2	2	no	—
202	C₂×C₄×C₄₇	—	4	1	no	—
203	C₂×C₄×C₄₇	—	4	1	no	—
204	C₂×C₄×C₄₇	—	4	1	no	—
205	C₂×C₄×C₄₇	—	4	1	no	—
206	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
214	C₂²⋊D₄₇	—	4	2	no	—
215	C₂²⋊D₄₇	—	4	2	no	—
216	C₂²⋊D₄₇	—	4	4	no	—
217	C₂²⋊D₄₇	—	8	2	no	—
218	C₂×Dic₄₇	—	2	2	no	—
219	C₂×Dic₄₇	—	2	2	no	—
220	C₂×Dic₄₇	—	2	2	no	—
221	D₁₈₈	—	2	2	no	—
222	D₁₈₈	—	2	2	no	—
223	C₄×D₄₇	—	4	2	no	—
224	C₄×D₄₇	—	4	2	no	—
225	Dic₉₄	—	2	2	no	—
226	Dic₉₄	—	2	2	no	—
227	C₈×C₄₇	—	2	1	no	—
228	C₈×C₄₇	—	2	1	no	—
229	C₈×C₄₇	—	2	1	no	—
230	C₈×C₄₇	—	2	1	no	—
231	C₈×C₄₇	—	2	1	no	—
232	C₈×C₄₇	—	2	1	no	—
233	C₈×C₄₇	C₄×D₄	1	2	yes	—
234	C₈×C₄₇	C₄×D₄	1	2	yes	—
235	C₄₇⋊C₈	—	2	4	no	—
236	C₄₇⋊C₈	—	4	2	no	—
237	#23018	—	47	1	no	maximal, Sylow
238	C₂²×C₄₇	—	2	1	no	—
239	C₂²×C₄₇	—	2	1	no	—
240	C₂²×C₄₇	—	2	1	no	—
241	C₂²×C₄₇	—	2	1	no	—
242	C₂²×C₄₇	—	2	1	no	—
243	C₂²×C₄₇	—	2	1	no	—
244	C₂²×C₄₇	—	2	1	no	—
245	C₂²×C₄₇	—	4	2	no	—
246	C₂²×C₄₇	—	4	2	no	—
247	C₂²×C₄₇	#443	1	2	yes	complemented
248	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
249	C₂²×C₄₇	#548	1	1	yes	characteristic
250	C₂²×C₄₇	#553	1	1	yes	characteristic
251	C₂×D₄₇	—	4	2	no	—
252	C₂×D₄₇	—	4	2	no	—
253	C₂×D₄₇	—	4	2	no	—
254	C₄×C₄₇	—	2	1	no	—
255	C₄×C₄₇	—	2	1	no	—
256	C₄×C₄₇	—	4	2	no	—
257	C₄×C₄₇	—	4	2	no	—
258	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
259	C₄×C₄₇	#520	1	1	yes	characteristic
260	C₄×C₄₇	D₄²	1	1	yes	characteristic
261	C₄×C₄₇	#547	1	1	yes	characteristic
262	Dic₄₇	—	4	2	no	—
263	Dic₄₇	—	4	2	no	—
264	Dic₄₇	—	4	2	no	—
265	#3050	—	47	1	no	—
266	C₂×#443	—	47	1	no	—
267	#2933	—	47	2	no	—
268	C₂²×#108	—	47	1	no	—
269	#1974	—	47	1	no	—
270	#1945	—	47	1	no	—
271	#1929	—	47	2	no	—
272	#1871	—	47	2	no	—
273	#1866	—	47	2	no	—
274	#1772	—	47	1	no	—
275	C₈×C₂²⋊C₄	D₄₇	1	1	yes	characteristic, complemented
276	C₂×C₄₇	—	2	1	no	—
277	C₂×C₄₇	—	2	1	no	—
278	C₂×C₄₇	—	2	2	no	—
279	C₂×C₄₇	—	4	1	no	—
280	C₂×C₄₇	#2361	1	1	yes	characteristic
281	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
282	C₂×C₄₇	#2957	1	1	yes	characteristic
283	D₄₇	—	8	2	no	—
284	C₂×#135	—	47	1	no	—
285	C₂×#131	—	47	2	no	—
286	C₂²×M₁₆	—	47	2	no	—
287	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
288	#525	—	47	2	no	—
289	#467	—	47	1	no	—
290	#467	—	47	1	no	—
291	#466	—	47	1	no	—
292	#466	—	47	1	no	—
293	#465	—	47	2	no	—
294	#465	—	47	2	no	—
295	#443	—	94	4	no	—
296	#436	—	94	2	no	—
297	#435	—	94	2	no	—
298	#435	—	94	2	no	—
299	C₈×D₄	—	94	2	no	—
300	C₂×#108	—	47	1	no	—
301	C₂×#108	—	47	2	no	—
302	C₂×#108	—	47	1	no	—
303	C₂×#108	—	94	4	no	—
304	#427	—	47	1	no	—
305	#424	—	47	2	no	—
306	C₂×#104	—	47	2	no	—
307	C₂×#104	—	47	2	no	—
308	#416	—	47	2	no	—
309	#408	—	47	2	no	—
310	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
311	#405	—	47	2	no	—
312	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
313	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
314	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
315	#339	—	47	2	no	—
316	#339	—	47	2	no	—
317	#336	C₂×D₄₇	1	1	yes	characteristic
318	#336	C₂×D₄₇	1	1	yes	characteristic
319	C₄₇	#23018	1	1	yes	characteristic, complemented, Sylow
320	C₂×#41	—	47	2	no	—
321	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
322	#135	—	94	2	no	—
323	#135	—	94	2	no	—
324	C₂×Q₁₆	—	47	1	no	—
325	C₂×SD₁₆	—	47	2	no	—
326	C₂×D₈	—	47	1	no	—
327	#131	—	94	4	no	—
328	#131	—	188	2	no	—
329	C₂×M₁₆	—	47	2	no	—
330	C₂×M₁₆	—	47	2	no	—
331	C₂×M₁₆	—	94	2	no	—
332	C₂×M₁₆	—	94	2	no	—
333	C₂×M₁₆	—	94	4	no	—
334	C₂×M₁₆	—	188	2	no	—
335	C₂²×C₈	—	2	2	no	—
336	C₂²×C₈	—	2	2	no	—
337	C₂²×C₈	—	94	2	no	—
338	C₂²×C₈	—	94	2	no	—
339	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
340	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
341	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
342	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
343	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
344	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
345	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
346	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
347	#123	—	94	2	no	—
348	C₂²⋊Q₈	—	47	2	no	—
349	C₂²⋊Q₈	—	47	2	no	—
350	#121	—	47	2	no	—
351	#121	—	47	2	no	—
352	#120	—	94	2	no	—
353	C₄×D₄	—	94	2	no	—
354	C₄×D₄	—	94	2	no	—
355	#117	—	47	2	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
358	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
359	#108	—	47	4	no	—
360	#108	—	94	4	no	—
361	#108	—	94	2	no	—
362	#107	—	47	1	no	—
363	#107	—	47	1	no	—
364	#106	—	47	2	no	—
365	C₄⋊C₈	—	94	2	no	—
366	C₄⋊C₈	—	94	2	no	—
367	#104	—	94	4	no	—
368	#104	—	188	2	no	—
369	#103	—	47	2	no	—
370	#103	—	47	2	no	—
371	#102	—	47	2	no	—
372	#102	—	47	2	no	—
373	C₂²⋊C₈	—	94	2	no	—
374	C₂²⋊C₈	—	94	2	no	—
375	C₂²⋊C₈	D₁₈₈	1	1	yes	characteristic
376	C₂²⋊C₈	D₁₈₈	1	1	yes	characteristic
377	C₂²⋊C₈	D₁₈₈	1	1	yes	characteristic
378	C₂²⋊C₈	D₁₈₈	1	1	yes	characteristic
379	#97	—	94	2	no	—
380	C₄×C₈	—	2	2	no	—
381	C₄×C₈	—	2	2	no	—
382	C₄×C₈	—	94	2	no	—
383	#95	—	2	1	no	—
384	C₂⁴	#10625350	1	1	yes	characteristic
385	#41	—	94	2	no	—
386	#41	—	94	2	no	—
387	#41	—	94	2	no	—
388	#41	—	94	2	no	—
389	C₂×Q₈	—	47	2	no	—
390	C₂×D₄	—	47	2	no	—
391	C₂×D₄	—	94	2	no	—
392	C₂×D₄	—	94	2	no	—
393	C₂×D₄	—	94	2	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	94	2	no	—
401	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
402	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
405	C₂²×C₄	#10625350	1	1	yes	characteristic
406	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
407	Q₁₆	—	94	2	no	—
408	SD₁₆	—	94	4	no	—
409	D₈	—	94	2	no	—
410	M₁₆	—	47	4	no	—
411	M₁₆	—	94	2	no	—
412	M₁₆	—	94	2	no	—
413	M₁₆	—	94	2	no	—
414	M₁₆	—	188	4	no	—
415	M₁₆	—	188	4	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	94	2	no	—
427	C₂×C₈	—	94	2	no	—
428	C₂×C₈	—	188	4	no	—
429	C₂×C₈	—	188	4	no	—
430	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
431	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
432	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
433	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
434	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
435	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
436	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
437	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
438	C₂×C₈	D₄×D₄₇	1	2	yes	—
439	C₂×C₈	#10625352	1	2	yes	—
440	C₄⋊C₄	—	47	2	no	—
441	C₄⋊C₄	—	47	2	no	—
442	C₄⋊C₄	—	94	2	no	—
443	C₄⋊C₄	—	94	2	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	94	2	no	—
446	C₂²⋊C₄	—	94	2	no	—
447	C₂²⋊C₄	—	94	2	no	—
448	C₂²⋊C₄	—	94	2	no	—
449	C₂²⋊C₄	—	94	2	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	94	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	94	2	no	—
460	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
461	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
462	C₂³	C₂×#10625350	1	1	yes	characteristic
463	Q₈	—	94	2	no	—
464	Q₈	—	94	2	no	—
465	D₄	—	94	2	no	—
466	D₄	—	94	2	no	—
467	D₄	—	376	2	no	—
468	D₄	—	188	4	no	—
469	D₄	—	188	2	no	—
470	D₄	—	188	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	94	2	no	—
488	C₂×C₄	—	94	2	no	—
489	C₂×C₄	—	94	2	no	—
490	C₂×C₄	—	188	2	no	—
491	C₂×C₄	—	188	2	no	—
492	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
493	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
494	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
495	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
497	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
498	C₂×C₄	#13094070	1	1	yes	characteristic
499	C₂×C₄	#13094071	1	1	yes	characteristic
500	C₈	—	2	1	no	—
501	C₈	—	2	1	no	—
502	C₈	—	2	1	no	—
503	C₈	—	2	1	no	—
504	C₈	—	2	1	no	—
505	C₈	—	2	1	no	—
506	C₈	—	94	4	no	—
507	C₈	—	188	2	no	—
508	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
509	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	188	2	no	—
520	C₂²	—	188	2	no	—
521	C₂²	—	188	2	no	—
522	C₂²	#15689241	1	2	yes	complemented
523	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
524	C₂²	#15689782	1	1	yes	characteristic
525	C₂²	#15689819	1	1	yes	characteristic
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	188	2	no	—
531	C₄	—	188	2	no	—
532	C₄	—	188	2	no	—
533	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
534	C₄	#15689603	1	1	yes	characteristic
535	C₄	D₄×D₁₈₈	1	1	yes	characteristic
536	C₄	#15689777	1	1	yes	characteristic
537	C₂	—	2	1	no	—
538	C₂	—	2	1	no	—
539	C₂	—	2	2	no	—
540	C₂	—	4	1	no	—
541	C₂	—	376	2	no	—
542	C₂	#20246402	1	1	yes	characteristic
543	C₂	C₂×#15689241	1	1	yes	characteristic
544	C₂	#20252306	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₈×C₂²⋊C₄×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20252969	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₈×C₂²⋊C₄	D₄₇
hypocenter	C₄₇	#23018
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₂²⋊C₈ ◁ C₈×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#15689241	C₂	semidirect
3. #20252109	C₂	semidirect
4. C₂²×#13093960	C₂	semidirect
5. #20244276	C₂	semidirect
6. #20244136	C₂	semidirect
7. #20244037	C₂	semidirect
8. #20243688	C₂	semidirect
9. #20243666	C₂	semidirect
10. #20243267	C₂	semidirect
11. C₈×C₂²⋊C₄×C₄₇	C₂	semidirect
16. #15689364	C₄	semidirect
17. #15689364	C₄	semidirect
18. #15689359	C₄	semidirect
19. #15689359	C₄	semidirect
20. #15689352	C₄	semidirect
21. #15689352	C₄	semidirect
74. #13093960	D₄	semidirect
247. C₂²×C₄₇	#443	semidirect
275. C₈×C₂²⋊C₄	D₄₇	semidirect
319. C₄₇	#23018	semidirect
522. C₂²	#15689241	semidirect

Maximal subgroups

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

subgroup	index
#20252969	2
C₂×#15689241	2
#20252109	2
C₂²×#13093960	2
#20244276	2
#20244136	2
#20244037	2
#20243688	2
#20243666	2
#20243267	2
C₈×C₂²⋊C₄×C₄₇	2
#23018	47