Finite Group Databasebeta

← #21455064

Subgroups — #21455064

Order 7808.

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×#11758222C211yesmaximal, characteristic, complemented
2C2×#14519810C211yesmaximal, characteristic, complemented
3C2×#14519805C211yesmaximal, characteristic, complemented
4#16840273C211yesmaximal, characteristic, complemented
5#16839926C214yesmaximal, complemented
6#16839909C214yesmaximal, complemented
7#16839772C211yesmaximal, characteristic, complemented
8#16839768C211yesmaximal, characteristic, complemented
9C61×#407C211yesmaximal, characteristic, complemented
10C2×#11758222—22no—
11C2×#11758222—24no—
12C2×#11758222—24no—
13C2×#11758222C2211yescharacteristic
14C2×#11758222C2214yes—
15C22×Dic122C2211yescharacteristic
16C22×D244C2211yescharacteristic
17C22×C22⋊D61—21no—
18C22×C4×D61—21no—
19#14519810—24no—
20#14519805—24no—
21C2×Dic244C2212yescomplemented
22C2×#11758190C2212yescomplemented
23C2×#11758190C2212yescomplemented
24C2×D488C2212yescomplemented
25#14519760—21no—
26#14519756C2212yescomplemented
27#14519751C2212yescomplemented
28#14519746—21no—
29C4×C22⋊D61—22no—
30#14519736C2211yescharacteristic
31#14519702C2214yescomplemented
32#14519699C2214yescomplemented
33C23×C4×C61C2211yescharacteristic
34C2×M16×C61C2211yescharacteristic
35C2×M16×C61C2211yescharacteristic
36C22⋊C8×C61C2214yescomplemented
37C24×C61D411yescharacteristic
38C23×D61—21no—
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61D411yescharacteristic
42C22×C4×C61D412yes—
43C22×C4×C61C2312yes—
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—28no—
46C2×C22⋊D61—24no—
47C2×C22⋊D61—21no—
48C2×C22⋊D61—22no—
49C22×Dic61—21no—
50#11758222—216no—
51#11758222—28no—
52#11758222—22no—
53#11758222—22no—
54#11758222—28no—
55C2×D244—21no—
56C2×D244—22no—
57C2×D244D414yescomplemented
58C2×D244C2311yescharacteristic
59C2×D244C2312yes—
60C2×C4×D61—28no—
61C2×C4×D61—24no—
62C2×C4×D61—21no—
63C2×Dic122—21no—
64C2×Dic122—22no—
65C2×Dic122D414yescomplemented
66C2×Dic122C2311yescharacteristic
67C2×Dic122C2312yes—
68M16×C61—22no—
69M16×C61—22no—
70C2×C8×C61C2312yes—
71C2×C8×C61C2312yes—
72C22⋊Dic61—21no—
73C22⋊Dic61—22no—
74#11758198—22no—
75C4⋊Dic61C2312yes—
76#11758196—22no—
77C4×Dic61—21no—
78Dic244—24no—
79D488—24no—
80#11758190—24no—
81#11758190—24no—
82C23×C61—22no—
83C23×C61—42no—
84C23×C61C2×D412yes—
85C23×C61C2×D411yescharacteristic
86C22×D61—24no—
87C22×D61—22no—
88C22×D61—21no—
89C22×D61—44no—
90C2×C4×C61—22no—
91C2×C4×C61—24no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61C2×D412yes—
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2×D412yes—
97C2×C4×C61C2×D412yes—
98C2×C4×C61C2411yescharacteristic
99C22⋊D61—216no—
100C22⋊D61—44no—
101C22⋊D61—42no—
102C2×Dic61—24no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—21no—
106D244—24no—
107D244—22no—
108D244—21no—
109D244—21no—
110D244C2×D414yes—
111C4×D61—216no—
112C4×D61—42no—
113Dic122—24no—
114Dic122—22no—
115Dic122—21no—
116Dic122—21no—
117Dic122C2×D414yes—
118C8×C61—22no—
119C8×C61—22no—
120C22×C61—22no—
121C22×C61—22no—
122C22×C61—22no—
123C22×C61—22no—
124C22×C61—44no—
125C22×C61#12012yes—
126C22×C61C22×D411yescharacteristic
127C2×D61—24no—
128C2×D61—48no—
129C2×D61—44no—
130C2×D61—41no—
131C2×D61—42no—
132C4×C61—22no—
133C4×C61#12012yes—
134C4×C61C22×D411yescharacteristic
135C4×C61C22×D411yescharacteristic
136Dic61—24no—
137Dic61—41no—
138Dic61—42no—
139#3005—611nomaximal, Sylow
140C2×C61—22no—
141C2×C61—42no—
142C2×C61C2×#12011yescharacteristic
143C2×C61#57512yes—
144D61—44no—
145D61—81no—
146C22×#41—611no—
147C2×#137—611no—
148C2×AGL(1,ℤ/8)—611no—
149#525—611no—
150#452—614no—
151#449—614no—
152#419—611no—
153#418—611no—
154#407D6111yescharacteristic, complemented
155C61#300511yescharacteristic, complemented, Sylow
156C2×#41—611no—
157C2×#41—614no—
158C2×#41—1224no—
159C2×#41—1224no—
160C2×#41—1222no—
161C22×Q8—611no—
162C22×D4—611no—
163C22×D4—1221no—
164C23×C4—1221no—
165C23×C4C2×D6111yescharacteristic
166#137—1224no—
167AGL(1,ℤ/8)—1224no—
168C2×Q16—612no—
169C2×SD16—612no—
170C2×SD16—612no—
171C2×D8—612no—
172C2×M16C2×D6111yescharacteristic
173C2×M16C2×D6111yescharacteristic
174#123—1221no—
175C22⋊Q8—612no—
176#121—612no—
177#120—1221no—
178C4×D4—1222no—
179#117—611no—
180#103—614no—
181#102—614no—
182C22⋊C8C2×D6114yescomplemented
183C24—1221no—
184C24D24411yescharacteristic
185#41—1228no—
186#41—1228no—
187#41—12216no—
188#41—1222no—
189#41—1222no—
190C2×Q8—614no—
191C2×Q8—612no—
192C2×Q8—611no—
193C2×Q8—1221no—
194C2×Q8—1222no—
195C2×D4—614no—
196C2×D4—612no—
197C2×D4—611no—
198C2×D4—1228no—
199C2×D4—1224no—
200C2×D4—1222no—
201C2×D4—1221no—
202C2×D4—1221no—
203C2×D4—1222no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—1228no—
207C22×C4—1221no—
208C22×C4—1224no—
209C22×C4—1221no—
210C22×C4D24412yes—
211C22×C4D24411yescharacteristic
212C22×C4C22×D6112yes—
213C22×C4C22×D6111yescharacteristic
214Q16—1224no—
215SD16—1224no—
216SD16—1224no—
217D8—1224no—
218M16—22no—
219M16—22no—
220C2×C8C22×D6112yes—
221C2×C8C22×D6112yes—
222C4⋊C4—612no—
223C4⋊C4—1222no—
224C22⋊C4—1221no—
225C22⋊C4—1222no—
226C22⋊C4—1222no—
227C42—1221no—
228C23—22no—
229C23—42no—
230C23—1222no—
231C23—1224no—
232C23—1221no—
233C23—2444no—
234C23C2×D24412yes—
235C23C2×D24411yescharacteristic
236Q8—614no—
237Q8—1222no—
238Q8—1224no—
239Q8—1221no—
240Q8—1221no—
241D4—614no—
242D4—12216no—
243D4—1222no—
244D4—1221no—
245D4—1221no—
246D4—1224no—
247D4—2444no—
248D4—2442no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—24no—
253C2×C4—12216no—
254C2×C4—1222no—
255C2×C4—1224no—
256C2×C4—1222no—
257C2×C4—1221no—
258C2×C4—2442no—
259C2×C4C2×D24412yes—
260C2×C4C2×D24411yescharacteristic
261C2×C4D4×D6112yes—
262C2×C4D4×D6112yes—
263C2×C4C23×D6111yescharacteristic
264C8—22no—
265C8—22no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—44no—
271C22—1224no—
272C22—2448no—
273C22—2441no—
274C22—2442no—
275C22—2444no—
276C22#1451974712yes—
277C22C22×D24411yescharacteristic
278C4—22no—
279C4—1224no—
280C4—2441no—
281C4—2442no—
282C4#1451974712yes—
283C4C2×D4×D6111yescharacteristic
284C4C2×D4×D6111yescharacteristic
285C2—22no—
286C2—42no—
287C2—4881no—
288C2—2444no—
289C2C2×#1451974711yescharacteristic
290C2#1684056212yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#407C2
socleC22×C61C22×D4
hypercenter#407D61
hypocenterC61#3005
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C22×#11758222C2semidirect
2. C2×#14519810C2semidirect
3. C2×#14519805C2semidirect
4. #16840273C2semidirect
5. #16839926C2semidirect
6. #16839909C2semidirect
7. #16839772C2semidirect
8. #16839768C2semidirect
9. C61×#407C2semidirect
21. C2×Dic244C22semidirect
22. C2×#11758190C22semidirect
23. C2×#11758190C22semidirect
24. C2×D488C22semidirect
26. #14519756C22semidirect
27. #14519751C22semidirect
31. #14519702C22semidirect
32. #14519699C22semidirect
36. C22⋊C8×C61C22semidirect
57. C2×D244D4semidirect
65. C2×Dic122D4semidirect
154. #407D61semidirect
155. C61#3005semidirect
182. C22⋊C8C2×D61semidirect