Finite Group Databasebeta

← #21455107

Subgroups — #21455107

Order 7808.

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

normal subgroups only

This group has 732 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
1C2×#14519824C211yesmaximal, characteristic, complemented
2C2×#14519805C211yesmaximal, characteristic, complemented
3C22×#11758190C211yesmaximal, characteristic, complemented
4#16840326C211yesmaximal, characteristic, complemented
5#16839909C214yesmaximal, complemented
6#16839903C214yesmaximal, complemented
7#16839772C211yesmaximal, characteristic, complemented
8#16839759C211yesmaximal, characteristic, complemented
9C61×#408C211yesmaximal, characteristic, complemented
10#14519824—24no—
11#14519824—24no—
12C2×#11758222C2211yescharacteristic
13C2×#11758222C2212yescomplemented
14C2×#11758224—21no—
15C2×#11758224—22no—
16C22×Dic122C2211yescharacteristic
17C22×Dic122C2212yescomplemented
18C2×Q8×D61—21no—
19C22×D244C2211yescharacteristic
20#14519805—24no—
21C2×#11758190—24no—
22C2×#11758190C2214yes—
23C2×#11758190C2212yes—
24C2×D488C2212yes—
25#14519773—21no—
26#14519766—21no—
27#14519751C2214yes—
28#14519745—22no—
29#14519736C2211yescharacteristic
30#14519702C2212yescomplemented
31#14519702C2214yescomplemented
32#14519699C2212yescomplemented
33C2×#41×C61C2211yescharacteristic
34C2×M16×C61C2211yescharacteristic
35C22×C8×C61C2211yescharacteristic
36C22⋊C8×C61C2214yescomplemented
37C23×D61—21no—
38#41×C61—22no—
39#41×C61—22no—
40C2×Q8×C61D411yescharacteristic
41C2×D4×C61D412yes—
42C2×D4×C61D411yescharacteristic
43C22×C4×C61C2312yes—
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—21no—
46C2×C22⋊D61—22no—
47C2×C22⋊D61—24no—
48C22×Dic61—21no—
49C22×Dic61—22no—
50Q8×D61—28no—
51#11758224—216no—
52#11758224—28no—
53#11758222—22no—
54#11758222—24no—
55#11758222—24no—
56#11758222D414yescomplemented
57C2×D244—22no—
58C2×D244—22no—
59C2×D244—21no—
60C2×D244C2312yes—
61C2×D244C2311yescharacteristic
62C2×C4×D61—21no—
63C2×C4×D61—22no—
64C2×Dic122—21no—
65C2×Dic122—22no—
66C2×Dic122—22no—
67C2×Dic122—24no—
68C2×Dic122—24no—
69C2×Dic122D414yescomplemented
70C2×Dic122C2312yes—
71C2×Dic122C2311yescharacteristic
72M16×C61—22no—
73C2×C8×C61—22no—
74C2×C8×C61C2312yes—
75C2×C8×C61C2312yes—
76C22⋊Dic61—21no—
77#11758198—24no—
78C4⋊Dic61C2312yes—
79C4×Dic61—21no—
80D488—24no—
81#11758190—28no—
82#11758190—24no—
83C23×C61C2×D412yes—
84C23×C61C2×D411yescharacteristic
85C22×D61—21no—
86C22×D61—22no—
87C22×D61—42no—
88C22×D61—82no—
89Q8×C61—22no—
90D4×C61—24no—
91D4×C61—22no—
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—28no—
100C22⋊D61—24no—
101C22⋊D61—84no—
102C2×Dic61—28no—
103C2×Dic61—24no—
104C2×Dic61—22no—
105C2×Dic61—21no—
106C2×Dic61—22no—
107D244—21no—
108D244—22no—
109D244—22no—
110D244—42no—
111D244C2×D412yes—
112C4×D61—28no—
113C4×D61—24no—
114Dic122—28no—
115Dic122—24no—
116Dic122—22no—
117Dic122—21no—
118Dic122C2×D412yes—
119Dic122C2×D414yes—
120C8×C61—22no—
121C8×C61—22no—
122C22×C61—22no—
123C22×C61—22no—
124C22×C61—24no—
125C22×C61#12012yes—
126C22×C61C22×D411yescharacteristic
127C2×D61—22no—
128C2×D61—42no—
129C2×D61—42no—
130C2×D61—44no—
131C2×D61—84no—
132C4×C61—22no—
133C4×C61#12012yes—
134C4×C61C22×D411yescharacteristic
135C4×C61C22×D411yescharacteristic
136Dic61—22no—
137Dic61—24no—
138Dic61—42no—
139#3010—611nomaximal, Sylow
140C2×C61—22no—
141C2×C61—42no—
142C2×C61C2×#12011yescharacteristic
143C2×C61#57712yes—
144D61—42no—
145D61—82no—
146C2×2−1+4—611no—
147C2×AGL(1,ℤ/8)—611no—
148C22×SD16—611no—
149#535—611no—
150#449—614no—
151#448—614no—
152#419—611no—
153#416—611no—
154#408D6111yescharacteristic, complemented
155C61#301011yescharacteristic, complemented, Sylow
1562−1+4—1224no—
1572−1+4—1224no—
158C2×#41—611no—
159C2×#41—612no—
160C2×#41—1222no—
161C2×#41—1221no—
162C2×#41C2×D6111yescharacteristic
163C22×Q8—611no—
164C22×Q8—612no—
165C22×Q8—1221no—
166C22×D4—611no—
167AGL(1,ℤ/8)—1224no—
168C2×SD16—614no—
169C2×SD16—612no—
170C2×SD16—1224no—
171C2×D8—612no—
172C2×M16C2×D6111yescharacteristic
173C22×C8C2×D6111yescharacteristic
174#127—1221no—
175#124—1221no—
176#121—614no—
177#120—1222no—
178#117—611no—
179#103—612no—
180#103—614no—
181#102—612no—
182C22⋊C8C2×D6114yescomplemented
183C24—1221no—
184#41—22no—
185#41—22no—
186#41—614no—
187#41—1224no—
188#41—1224no—
189#41—12216no—
190#41—1228no—
191#41—1222no—
192C2×Q8—614no—
193C2×Q8—612no—
194C2×Q8—611no—
195C2×Q8—1224no—
196C2×Q8—1224no—
197C2×Q8—1228no—
198C2×Q8—1222no—
199C2×Q8—1221no—
200C2×Q8—1222no—
201C2×Q8D24411yescharacteristic
202C2×D4—611no—
203C2×D4—612no—
204C2×D4—1222no—
205C2×D4—1221no—
206C2×D4—1224no—
207C2×D4—1221no—
208C2×D4—1222no—
209C2×D4—1222no—
210C2×D4D24412yes—
211C2×D4D24411yescharacteristic
212C22×C4—1222no—
213C22×C4—1221no—
214C22×C4—1222no—
215C22×C4—1221no—
216C22×C4C22×D6112yes—
217C22×C4C22×D6111yescharacteristic
218SD16—1228no—
219SD16—1224no—
220D8—1224no—
221M16—22no—
222C2×C8—22no—
223C2×C8C22×D6112yes—
224C2×C8C22×D6112yes—
225C4⋊C4—612no—
226C22⋊C4—1221no—
227C22⋊C4—1224no—
228C42—1221no—
229C23—1221no—
230C23—1222no—
231C23—4882no—
232C23—2442no—
233C23C2×D24412yes—
234C23C2×D24411yescharacteristic
235Q8—22no—
236Q8—614no—
237Q8—612no—
238Q8—1228no—
239Q8—1222no—
240Q8—1221no—
241Q8—1224no—
242D4—24no—
243D4—22no—
244D4—612no—
245D4—1228no—
246D4—1224no—
247D4—1221no—
248D4—1222no—
249D4—1222no—
250D4—4884no—
251D4—2442no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—1228no—
255C2×C4—1228no—
256C2×C4—1222no—
257C2×C4—1221no—
258C2×C4—1224no—
259C2×C4—1224no—
260C2×C4—1222no—
261C2×C4C2×D24412yes—
262C2×C4C2×D24411yescharacteristic
263C2×C4D4×D6112yes—
264C2×C4D4×D6112yes—
265C2×C4C23×D6111yescharacteristic
266C8—22no—
267C8—22no—
268C22—22no—
269C22—22no—
270C22—24no—
271C22—1222no—
272C22—4884no—
273C22—2442no—
274C22—2444no—
275C22—2442no—
276C22#1451974712yes—
277C22C22×D24411yescharacteristic
278C4—22no—
279C4—1224no—
280C4—1222no—
281C4—2442no—
282C4#1451974712yes—
283C4C2×D4×D6111yescharacteristic
284C4C2×D4×D6111yescharacteristic
285C2—22no—
286C2—42no—
287C2—4882no—
288C2—2442no—
289C2C2×#1451974711yescharacteristic
290C2#1684057412yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#408C2
socleC22×C61C22×D4
hypercenter#408D61
hypocenterC61#3010
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×#14519824C2semidirect
2. C2×#14519805C2semidirect
3. C22×#11758190C2semidirect
4. #16840326C2semidirect
5. #16839909C2semidirect
6. #16839903C2semidirect
7. #16839772C2semidirect
8. #16839759C2semidirect
9. C61×#408C2semidirect
13. C2×#11758222C22semidirect
17. C22×Dic122C22semidirect
30. #14519702C22semidirect
31. #14519702C22semidirect
32. #14519699C22semidirect
36. C22⋊C8×C61C22semidirect
56. #11758222D4semidirect
69. C2×Dic122D4semidirect
154. #408D61semidirect
155. C61#3010semidirect
182. C22⋊C8C2×D61semidirect