Finite Group Databasebeta

← C4×#14273697 #21426600

Subgroups — C4×#14273697 #21426600

Order 7552.

1224 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D59C211yesmaximal, characteristic, complemented
2C2×#14273697C211yesmaximal, characteristic
3C2×C4×D236C212yesmaximal, complemented
4C2×C4×C22⋊D59C211yesmaximal, characteristic, complemented
5#16837280C212yesmaximal, complemented
6#16837279C211yesmaximal, characteristic, complemented
7#16837277C211yesmaximal, characteristic, complemented
8#16837276C212yesmaximal, complemented
9#16837257C211yesmaximal, characteristic, complemented
10C4×(C2×D59)⋊C4C212yesmaximal, complemented
11C4×C22⋊C4×C59C211yesmaximal, characteristic, complemented
12C24×D59C2211yescharacteristic
13C22×D236C2212yes—
14C22×C22⋊D59C2211yescharacteristic
15C23×Dic59C2211yescharacteristic
16C22×C4×D59—24no—
17C22×C4×D59—28no—
18C22×C4×D59C2212yes—
19C22×C4×D59C2212yes—
20C22×C4×D59C2211yescharacteristic, complemented
21#14273697C418yesdirect product factor
22C4×D236—28no—
23C4×C22⋊D59—24no—
24C2×C4⋊Dic59C2212yescomplemented
25C2×Dic59⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic59C2211yescharacteristic
27C2×(C2×D59)⋊C4C2212yes—
28C2×(C2×D59)⋊C4C2212yes—
29C2×(C2×D59)⋊C4C2212yes—
30C2×(C2×D59)⋊C4C2212yescomplemented
31C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
32C2×C4×Dic59C2211yescharacteristic, complemented
33C59⋊#95C2212yescomplemented
34C59⋊#95C2212yescomplemented
35C23×C4×C59C2211yescharacteristic
36C2×C22⋊C4×C59C2211yescharacteristic
37C2×C22⋊C4×C59C2211yescharacteristic
38C2×C42×C59C2212yescomplemented
39#95×C59C2212yescomplemented
40C24×C59C2311yescharacteristic
41C23×D59—22no—
42C23×D59—22no—
43C23×D59—24no—
44C23×D59—24no—
45C23×D59C2×C414yescomplemented
46C23×D59C2311yescharacteristic
47C23×D59C2312yes—
48C22×C4×C59—24no—
49C22×C4×C59D414yescomplemented
50C22×C4×C59C2312yes—
51C22×C4×C59C2312yes—
52C22×C4×C59C2311yescharacteristic
53C22×C4×C59C2311yescharacteristic
54C2×C22⋊D59—22no—
55C2×C22⋊D59—22no—
56C2×C22⋊D59C2×C414yescomplemented
57C22×Dic59—22no—
58C22×Dic59—24no—
59C22×Dic59C2311yescharacteristic
60C22×Dic59C2311yescharacteristic
61C22×Dic59C2311yescharacteristic
62C22×Dic59C2312yes—
63C2×D236—24no—
64C2×D236—24no—
65C2×D236C2×C418yescomplemented
66C2×C4×D59—232no—
67C2×C4×D59—24no—
68C2×C4×D59—24no—
69C2×C4×D59—24no—
70C2×C4×D59—24no—
71C2×C4×D59—24no—
72C2×C4×D59—22no—
73C2×C4×D59—24no—
74C2×C4×D59D418yescomplemented
75C22⋊C4×C59—22no—
76C22⋊C4×C59C2×C414yescomplemented
77C42×C59—24no—
78C22⋊Dic59—22no—
79(C2×D59)⋊C4—24no—
80(C2×D59)⋊C4—24no—
81(C2×D59)⋊C4—22no—
82(C2×D59)⋊C4—24no—
83(C2×D59)⋊C4C2×C418yescomplemented
84C4⋊Dic59—24no—
85Dic59⋊C4—22no—
86C4×Dic59—22no—
87C23×C59—22no—
88C23×C59—22no—
89C23×C59C22×C412yes—
90C23×C59C2×D412yes—
91C23×C59#4112yes—
92C23×C59C2411yescharacteristic
93C22×D59—28no—
94C22×D59—216no—
95C22×D59—28no—
96C22×D59—28no—
97C22×D59—22no—
98C22×D59—22no—
99C22×D59—22no—
100C22×D59—22no—
101C22×D59—216no—
102C22×D59—22no—
103C22×D59—21no—
104C22×D59—22no—
105C22×D59—21no—
106C22×D59C22×C414yes—
107C22×D59C22×C412yescomplemented
108C22×D59C2×D414yes—
109C22×D59#4114yes—
110C2×C4×C59—22no—
111C2×C4×C59—22no—
112C2×C4×C59—22no—
113C2×C4×C59—28no—
114C2×C4×C59—22no—
115C2×C4×C59—22no—
116C2×C4×C59—22no—
117C2×C4×C59C22×C414yescomplemented
118C2×C4×C59C2×D412yes—
119C2×C4×C59C2×D412yes—
120C2×C4×C59C2×D414yes—
121C22⋊D59—28no—
122C2×Dic59—28no—
123C2×Dic59—21no—
124C2×Dic59—22no—
125C2×Dic59—22no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—22no—
130C2×Dic59—22no—
131C2×Dic59C22×C412yescomplemented
132C2×Dic59C2×D414yes—
133D236—216no—
134C4×D59—216no—
135C4×D59—216no—
136C4×D59—44no—
137C22×C59—24no—
138C22×C59—22no—
139C22×C59—22no—
140C22×C59—24no—
141C22×C59C4×D414yescomplemented
142C22×C59C23×C411yescharacteristic
143C22×C59C22×D412yes—
144C22×C59C22×D411yescharacteristic
145C22×C59C2×#4112yes—
146C22×C59C2×#4111yescharacteristic
147C2×D59—232no—
148C2×D59—24no—
149C2×D59—24no—
150C2×D59—24no—
151C2×D59—24no—
152C2×D59—24no—
153C2×D59—24no—
154C2×D59—24no—
155C2×D59—22no—
156C2×D59—41no—
157C2×D59—42no—
158C2×D59—41no—
159C2×D59C4×D418yescomplemented
160C4×C59—24no—
161C4×C59—22no—
162C4×C59—42no—
163C4×C59#12014yescomplemented
164Dic59—22no—
165Dic59—24no—
166Dic59—41no—
167Dic59—41no—
168C4×#120—591nomaximal, Sylow
169C2×C59—24no—
170C2×C59C2×C4×D412yes—
171C2×C59C2×C4×D411yescharacteristic
172C2×C59C2×#12011yescharacteristic
173C2×C59#52512yes—
174C2×C59#52511yescharacteristic
175D59—28no—
176D59—42no—
177C24×C4—591no—
178C2×#120—591no—
179C2×C4×D4—591no—
180C2×C4×D4—592no—
181#386—591no—
182#386—592no—
183#385—591no—
184#385—592no—
185#379—591no—
186C4×C22⋊C4—592no—
187C4×C22⋊C4D5911yescharacteristic, complemented
188C59C4×#12011yescharacteristic, complemented, Sylow
189C25—591no—
190C22×D4—591no—
191C22×D4—592no—
192C23×C4—592no—
193C23×C4—591no—
194C23×C4—592no—
195C23×C4—591no—
196C23×C4—1188no—
197C23×C4—1184no—
198C23×C4C2×D5911yescharacteristic
199#120—598no—
200C4×D4—1188no—
201C4×D4—1184no—
202C2×C4⋊C4—591no—
203C2×C4⋊C4—592no—
204C2×C22⋊C4—592no—
205C2×C22⋊C4—591no—
206C2×C22⋊C4—592no—
207C2×C22⋊C4—592no—
208C2×C22⋊C4—591no—
209C2×C22⋊C4—592no—
210C2×C22⋊C4C2×D5911yescharacteristic
211C2×C22⋊C4C2×D5911yescharacteristic
212C2×C42—591no—
213C2×C42C2×D5912yescomplemented
214#95—592no—
215#95—592no—
216#95C2×D5912yescomplemented
217C24—592no—
218C24—594no—
219C24—591no—
220C24—1184no—
221C24—1184no—
222C24—1182no—
223C24—1182no—
224C24C22×D5911yescharacteristic
225C2×D4—594no—
226C2×D4—598no—
227C2×D4—1184no—
228C2×D4—1184no—
229C2×D4—1182no—
230C2×D4—1182no—
231C22×C4—24no—
232C22×C4—591no—
233C22×C4—592no—
234C22×C4—598no—
235C22×C4—591no—
236C22×C4—591no—
237C22×C4—1184no—
238C22×C4—1184no—
239C22×C4—11832no—
240C22×C4—1184no—
241C22×C4—1182no—
242C22×C4—1184no—
243C22×C4—1184no—
244C22×C4—1184no—
245C22×C4—1182no—
246C22×C4—1184no—
247C22×C4D23614yescomplemented
248C22×C4C22×D5912yes—
249C22×C4C22×D5912yes—
250C22×C4C22×D5911yescharacteristic
251C22×C4C22×D5911yescharacteristic
252C4⋊C4—1184no—
253C4⋊C4—1182no—
254C22⋊C4—22no—
255C22⋊C4—598no—
256C22⋊C4—1184no—
257C22⋊C4—1184no—
258C22⋊C4—1184no—
259C22⋊C4—1182no—
260C22⋊C4—1182no—
261C22⋊C4C4×D5914yescomplemented
262C42—24no—
263C42—1182no—
264C23—22no—
265C23—22no—
266C23—594no—
267C23—594no—
268C23—594no—
269C23—592no—
270C23—11816no—
271C23—1188no—
272C23—11816no—
273C23—1188no—
274C23—1188no—
275C23—1182no—
276C23—1182no—
277C23—1182no—
278C23—1182no—
279C23—1182no—
280C23—1181no—
281C23—1182no—
282C23—1181no—
283C23C2×C4×D5912yes—
284C23C2×D23612yes—
285C23#1174568512yes—
286C23C23×D5911yescharacteristic
287D4—11816no—
288D4—1188no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—28no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—592no—
297C2×C4—594no—
298C2×C4—11816no—
299C2×C4—1188no—
300C2×C4—1182no—
301C2×C4—1181no—
302C2×C4—1182no—
303C2×C4—1181no—
304C2×C4—11816no—
305C2×C4—1182no—
306C2×C4—1181no—
307C2×C4—1181no—
308C2×C4—1182no—
309C2×C4—2364no—
310C2×C4C2×C4×D5914yescomplemented
311C2×C4C2×D23612yes—
312C2×C4C2×D23612yes—
313C2×C4D4×D5914yes—
314C22—22no—
315C22—24no—
316C22—22no—
317C22—24no—
318C22—598no—
319C22—11832no—
320C22—1184no—
321C22—1184no—
322C22—1184no—
323C22—1184no—
324C22—1184no—
325C22—1184no—
326C22—1184no—
327C22—1182no—
328C22—2361no—
329C22—2362no—
330C22—2361no—
331C22C4×D23614yescomplemented
332C22C22×C4×D5911yescharacteristic
333C22C2×D4×D5912yes—
334C22C22×D23611yescharacteristic
335C22#41×D5912yes—
336C22C2×#1174568511yescharacteristic
337C4—22no—
338C4—24no—
339C4—42no—
340C4—1184no—
341C4—1182no—
342C4—2361no—
343C4—2361no—
344C4#1427369714yesdirect product factor
345C2—24no—
346C2—1188no—
347C2—2362no—
348C2C4×D4×D5912yes—
349C2C2×C4×D23611yescharacteristic
350C2C2×#1427369711yescharacteristic
351C2#1683791112yes—
352C2#1683791411yescharacteristic
subgroupG/H
centerC22×C4C22×D59
commutatorC22×C59C23×C4
FrattiniC23C23×D59
FittingC4×C22⋊C4×C59C2
socleC23×C59C24
hypercenterC4×C22⋊C4D59
hypocenterC59C4×#120
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C4×D59C2semidirect
3. C2×C4×D236C2semidirect
4. C2×C4×C22⋊D59C2semidirect
5. #16837280C2semidirect
6. #16837279C2semidirect
7. #16837277C2semidirect
8. #16837276C2semidirect
9. #16837257C2semidirect
10. C4×(C2×D59)⋊C4C2semidirect
11. C4×C22⋊C4×C59C2semidirect
20. C22×C4×D59C22semidirect
21. #14273697C4direct (N × H)
24. C2×C4⋊Dic59C22semidirect
25. C2×Dic59⋊C4C22semidirect
30. C2×(C2×D59)⋊C4C22semidirect
31. C2×(C2×D59)⋊C4C22semidirect
32. C2×C4×Dic59C22semidirect
33. C59⋊#95C22semidirect
34. C59⋊#95C22semidirect
38. C2×C42×C59C22semidirect
39. #95×C59C22semidirect
45. C23×D59C2×C4semidirect
49. C22×C4×C59D4semidirect
56. C2×C22⋊D59C2×C4semidirect
65. C2×D236C2×C4semidirect
74. C2×C4×D59D4semidirect
76. C22⋊C4×C59C2×C4semidirect
83. (C2×D59)⋊C4C2×C4semidirect
107. C22×D59C22×C4semidirect
117. C2×C4×C59C22×C4semidirect
131. C2×Dic59C22×C4semidirect
141. C22×C59C4×D4semidirect
159. C2×D59C4×D4semidirect
163. C4×C59#120semidirect
187. C4×C22⋊C4D59semidirect
188. C59C4×#120semidirect
213. C2×C42C2×D59semidirect
216. #95C2×D59semidirect
247. C22×C4D236semidirect
261. C22⋊C4C4×D59semidirect
310. C2×C4C2×C4×D59semidirect
331. C22C4×D236semidirect
344. C4#14273697direct (N × H)