Finite Group Databasebeta

← #21433342

Subgroups — #21433342

Order 7552.

758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#11745689C211yesmaximal, characteristic, complemented
2C2×#14273758C211yesmaximal, characteristic, complemented
3C2×#14273755C211yesmaximal, characteristic, complemented
4#16837914C211yesmaximal, characteristic, complemented
5#16837567C214yesmaximal, complemented
6#16837550C214yesmaximal, complemented
7#16837406C211yesmaximal, characteristic, complemented
8#16837365C211yesmaximal, characteristic, complemented
9C59×#419C211yesmaximal, characteristic, complemented
10C2×#11745689—24no—
11C2×#11745689—24no—
12C2×#11745689—22no—
13C2×#11745689C2214yes—
14C2×#11745685C2211yescharacteristic
15C22×D236—21no—
16C22×D236C2211yescharacteristic
17C22×C4×D59—21no—
18C22×C4×D59C2211yescharacteristic
19#14273758—24no—
20#14273755—24no—
21C2×#11745672C2212yescomplemented
22C2×#11745660C2212yescomplemented
23C2×#11745671C2212yescomplemented
24C2×D472C2212yescomplemented
25C2×#11745664C2211yescharacteristic
26#14273711—21no—
27#14273707C2212yescomplemented
28#14273702C2212yescomplemented
29#14273697—21no—
30C4×D236—22no—
31#14273647C2214yescomplemented
32(C2×D59)⋊C8C2214yescomplemented
33C22×Q8×C59C2211yescharacteristic
34C2×M16×C59C2211yescharacteristic
35#117×C59C2211yescharacteristic
36#103×C59C2214yescomplemented
37C23×D59—21no—
38C23×D59D411yescharacteristic
39C2×Q8×C59—22no—
40C2×Q8×C59—21no—
41C2×Q8×C59D414yescomplemented
42C2×Q8×C59C2312yes—
43C22×C4×C59—21no—
44C22×C4×C59C2311yescharacteristic
45C2×C22⋊D59—21no—
46C22×Dic59D411yescharacteristic
47#11745689—216no—
48#11745689—28no—
49#11745689—28no—
50#11745685—22no—
51#11745685—22no—
52C2×D236—28no—
53C2×D236—24no—
54C2×D236—21no—
55C2×D236—22no—
56C2×D236—22no—
57C2×D236D414yescomplemented
58C2×D236C2311yescharacteristic
59C2×D236C2312yes—
60C2×C4×D59—28no—
61C2×C4×D59—22no—
62C2×C4×D59—22no—
63C2×C4×D59—24no—
64C2×C4×D59—21no—
65C2×C4×D59D412yes—
66C2×C4×D59C2312yes—
67C2×Dic118C2311yescharacteristic
68M16×C59—22no—
69C2×C8×C59C2312yes—
70C4⋊C4×C59C2312yes—
71C22⋊C4×C59—21no—
72C42×C59—21no—
73#11745672—24no—
74#11745671—24no—
75(C2×D59)⋊C4—22no—
76(C2×D59)⋊C4—22no—
77C4⋊Dic59—22no—
78#11745664—22no—
79C2×C59⋊C8C2312yes—
80D472—24no—
81#11745660—24no—
82C23×C59C2×D411yescharacteristic
83C22×D59—22no—
84C22×D59—24no—
85C22×D59—22no—
86C22×D59—21no—
87C22×D59—42no—
88C22×D59—44no—
89C22×D59C2×D412yes—
90Q8×C59—24no—
91Q8×C59—22no—
92Q8×C59C2×D414yes—
93C2×C4×C59—24no—
94C2×C4×C59—22no—
95C2×C4×C59—22no—
96C2×C4×C59C2×D412yes—
97C2×C4×C59C2×D411yescharacteristic
98C2×C4×C59C2×D412yes—
99C2×C4×C59C2411yescharacteristic
100C22⋊D59—42no—
101C2×Dic59—22no—
102C2×Dic59—21no—
103C2×Dic59C2×D412yes—
104D236—216no—
105D236—24no—
106D236—22no—
107D236—21no—
108D236—21no—
109D236—44no—
110D236C2×D414yes—
111C4×D59—216no—
112C4×D59—24no—
113C4×D59—22no—
114C4×D59—22no—
115C4×D59—42no—
116Dic118—21no—
117Dic118—21no—
118C8×C59—22no—
119C59⋊C8—22no—
120C22×C59—22no—
121C22×C59#12012yes—
122C22×C59C22×D411yescharacteristic
123C2×D59—22no—
124C2×D59—24no—
125C2×D59—22no—
126C2×D59—22no—
127C2×D59—44no—
128C2×D59—48no—
129C2×D59—44no—
130C2×D59—41no—
131C2×D59—42no—
132C4×C59—24no—
133C4×C59—42no—
134C4×C59#12012yes—
135C4×C59C22×D411yescharacteristic
136C4×C59C22×D411yescharacteristic
137Dic59—22no—
138Dic59—41no—
139#3005—591nomaximal, Sylow
140C2×C59—22no—
141C2×C59C2×#12011yescharacteristic
142C2×C59#57512yes—
143D59—42no—
144D59—44no—
145D59—81no—
146C22×#41—591no—
147C2×#137—591no—
148C2×AGL(1,ℤ/8)—591no—
149#525—591no—
150#452—594no—
151#449—594no—
152#419D5911yescharacteristic, complemented
153#418—591no—
154#407—591no—
155C59#300511yescharacteristic, complemented, Sylow
156C2×#41—594no—
157C2×#41—591no—
158C2×#41—1182no—
159C2×#41—1184no—
160C2×#41—1184no—
161C22×Q8C2×D5911yescharacteristic
162C22×D4—591no—
163C22×D4—1181no—
164C23×C4—591no—
165C23×C4—1181no—
166#137—1184no—
167AGL(1,ℤ/8)—1184no—
168C2×Q16—592no—
169C2×SD16—592no—
170C2×SD16—592no—
171C2×D8—592no—
172C2×M16—591no—
173C2×M16C2×D5911yescharacteristic
174#123—1181no—
175C22⋊Q8—592no—
176#121—592no—
177#120—1181no—
178C4×D4—1182no—
179#117C2×D5911yescharacteristic
180#103C2×D5914yescomplemented
181#102—594no—
182C22⋊C8—594no—
183C24—591no—
184C24—1181no—
185#41—1188no—
186#41—11816no—
187#41—1188no—
188#41—1182no—
189#41—1182no—
190C2×Q8—22no—
191C2×Q8—21no—
192C2×Q8—591no—
193C2×Q8D23614yescomplemented
194C2×Q8C22×D5912yes—
195C2×D4—594no—
196C2×D4—592no—
197C2×D4—591no—
198C2×D4—1184no—
199C2×D4—1188no—
200C2×D4—1182no—
201C2×D4—1181no—
202C2×D4—1182no—
203C2×D4—1181no—
204C22×C4—21no—
205C22×C4—591no—
206C22×C4—592no—
207C22×C4—592no—
208C22×C4—1184no—
209C22×C4—1188no—
210C22×C4—1182no—
211C22×C4—1182no—
212C22×C4—1181no—
213C22×C4C22×D5911yescharacteristic
214Q16—1184no—
215SD16—1184no—
216SD16—1184no—
217D8—1184no—
218M16—22no—
219M16—1182no—
220C2×C8—592no—
221C2×C8C22×D5912yes—
222C4⋊C4—1182no—
223C4⋊C4C22×D5912yes—
224C22⋊C4—21no—
225C22⋊C4—1182no—
226C22⋊C4—1182no—
227C42—21no—
228C23—592no—
229C23—1184no—
230C23—1182no—
231C23—1182no—
232C23—1181no—
233C23—2362no—
234C23—2364no—
235C23D4×D5911yescharacteristic
236Q8—24no—
237Q8—22no—
238Q8—1181no—
239Q8—1181no—
240Q8C2×D23614yes—
241D4—594no—
242D4—11816no—
243D4—1184no—
244D4—1181no—
245D4—1182no—
246D4—1181no—
247D4—2364no—
248D4—2362no—
249C2×C4—24no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—592no—
253C2×C4—11816no—
254C2×C4—1182no—
255C2×C4—1184no—
256C2×C4—1182no—
257C2×C4—1182no—
258C2×C4—1181no—
259C2×C4—2362no—
260C2×C4C2×D23612yes—
261C2×C4D4×D5911yescharacteristic
262C2×C4D4×D5912yes—
263C2×C4C23×D5911yescharacteristic
264C8—22no—
265C8—1182no—
266C22—22no—
267C22—1184no—
268C22—1182no—
269C22—1182no—
270C22—1182no—
271C22—2364no—
272C22—2368no—
273C22—2361no—
274C22—2362no—
275C22—2364no—
276C22#1427369712yes—
277C22C2×D4×D5911yescharacteristic
278C4—24no—
279C4—42no—
280C4—1182no—
281C4—2361no—
282C4#1427369712yes—
283C4C2×D4×D5911yescharacteristic
284C4C22×D23611yescharacteristic
285C2—22no—
286C2—4721no—
287C2—2362no—
288C2—2364no—
289C2C2×#1427369711yescharacteristic
290C2#1683820112yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#419C2
socleC22×C59C22×D4
hypercenter#419D59
hypocenterC59#3005
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C22×#11745689C2semidirect
2. C2×#14273758C2semidirect
3. C2×#14273755C2semidirect
4. #16837914C2semidirect
5. #16837567C2semidirect
6. #16837550C2semidirect
7. #16837406C2semidirect
8. #16837365C2semidirect
9. C59×#419C2semidirect
21. C2×#11745672C22semidirect
22. C2×#11745660C22semidirect
23. C2×#11745671C22semidirect
24. C2×D472C22semidirect
27. #14273707C22semidirect
28. #14273702C22semidirect
31. #14273647C22semidirect
32. (C2×D59)⋊C8C22semidirect
36. #103×C59C22semidirect
41. C2×Q8×C59D4semidirect
57. C2×D236D4semidirect
152. #419D59semidirect
155. C59#3005semidirect
180. #103C2×D59semidirect
193. C2×Q8D236semidirect