Finite Group Databasebeta

← #21455103

Subgroups — #21455103

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×#14519803C211yesmaximal, characteristic, complemented
3C22×#11758200C211yesmaximal, characteristic, complemented
4#16839905C214yesmaximal, complemented
5#16839900C214yesmaximal, complemented
6#16839770C211yesmaximal, characteristic, complemented
7#16839756C211yesmaximal, characteristic, complemented
8#16839729C211yesmaximal, characteristic, complemented
9C61×#535C211yesmaximal, 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—
19#14519803—24no—
20C2×#11758200—24no—
21C2×#11758200C2214yes—
22C2×#11758200C2212yes—
23C2×#11758199C2212yes—
24C2×#11758194C2211yescharacteristic
25C22×#92418C2211yescharacteristic
26#14519700C2212yescomplemented
27#14519700C2214yescomplemented
28#14519697C2212yescomplemented
29C22⋊#92418C2214yescomplemented
30C2×#41×C61C2211yescharacteristic
31C22×D4×C61C2211yescharacteristic
32#127×C61—21no—
33#124×C61—21no—
34#121×C61C2214yes—
35#120×C61—22no—
36#117×C61C2211yescharacteristic
37C24×C61—21no—
38#41×C61—22no—
39#41×C61—22no—
40C2×Q8×C61D411yescharacteristic
41C2×D4×C61—24no—
42C2×D4×C61—22no—
43C2×D4×C61—22no—
44C2×D4×C61—21no—
45C2×D4×C61D412yes—
46C2×D4×C61D411yescharacteristic
47C2×D4×C61C2312yes—
48C22×C4×C61C2312yes—
49C22×C4×C61C2311yescharacteristic
50C2×C22⋊D61—21no—
51C2×C22⋊D61—22no—
52C22×Dic61—21no—
53C22×Dic61—22no—
54Q8×D61—28no—
55#11758224—216no—
56#11758224—28no—
57#11758222—22no—
58#11758222—24no—
59#11758222—24no—
60#11758222D414yescomplemented
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
72C4⋊C4×C61C2312yes—
73C22⋊C4×C61—21no—
74C22⋊C4×C61—24no—
75C42×C61—21no—
76#11758200—28no—
77#11758200—24no—
78#11758199—24no—
79#11758194—22no—
80C2×#92418—22no—
81C2×#92418C2312yes—
82C2×#92418C2312yes—
83C23×C61—22no—
84C23×C61—42no—
85C23×C61—82no—
86C23×C61C2×D412yes—
87C23×C61C2×D411yescharacteristic
88C22×D61—21no—
89Q8×C61—22no—
90D4×C61—24no—
91D4×C61—22no—
92D4×C61—22no—
93D4×C61—22no—
94D4×C61—42no—
95D4×C61—84no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61C2×D412yes—
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61C2×D412yes—
102C2×C4×C61C2×D412yes—
103C2×C4×C61C2411yescharacteristic
104C22⋊D61—28no—
105C22⋊D61—24no—
106C2×Dic61—28no—
107C2×Dic61—24no—
108C2×Dic61—22no—
109C2×Dic61—21no—
110D244—21no—
111D244C2×D412yes—
112C4×D61—28no—
113C4×D61—24no—
114Dic122—28no—
115Dic122—24no—
116Dic122—22no—
117Dic122—21no—
118Dic122C2×D412yes—
119Dic122C2×D414yes—
120#92418—22no—
121#92418—22no—
122C22×C61—22no—
123C22×C61—22no—
124C22×C61—24no—
125C22×C61—42no—
126C22×C61—44no—
127C22×C61—84no—
128C22×C61#12012yes—
129C22×C61C22×D411yescharacteristic
130C2×D61—22no—
131C2×D61—42no—
132C4×C61—22no—
133C4×C61—42no—
134C4×C61#12012yes—
135C4×C61C22×D411yescharacteristic
136C4×C61C22×D411yescharacteristic
137Dic61—22no—
138Dic61—24no—
139#3010—611nomaximal, Sylow
140C2×C61—22no—
141C2×C61—42no—
142C2×C61—82no—
143C2×C61C2×#12011yescharacteristic
144C2×C61#57712yes—
145D61—42no—
146C2×2−1+4—611no—
147C2×AGL(1,ℤ/8)—611no—
148C22×SD16—611no—
149#535D6111yescharacteristic, complemented
150#449—614no—
151#448—614no—
152#419—611no—
153#416—611no—
154#408—611no—
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×D4C2×D6111yescharacteristic
167AGL(1,ℤ/8)—1224no—
168C2×SD16—614no—
169C2×SD16—612no—
170C2×SD16—1224no—
171C2×D8—612no—
172C2×M16—611no—
173C22×C8—611no—
174#127—21no—
175#124—21no—
176#121C2×D6114yes—
177#120—22no—
178#117C2×D6111yescharacteristic
179#103—612no—
180#103—614no—
181#102—612no—
182C22⋊C8—614no—
183C24—21no—
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—1222no—
200C2×Q8—1221no—
201C2×Q8C22⋊D6111yescharacteristic
202C2×D4—24no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—21no—
206C2×D4—611no—
207C2×D4—1222no—
208C2×D4—1221no—
209C2×D4C22⋊D6112yes—
210C2×D4C22⋊D6111yescharacteristic
211C2×D4C22×D6112yes—
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—1222no—
222C2×C8—612no—
223C2×C8—612no—
224C2×C8—1222no—
225C4⋊C4C22×D6112yes—
226C22⋊C4—21no—
227C22⋊C4—24no—
228C42—21no—
229C23—22no—
230C23—42no—
231C23—82no—
232C23—1221no—
233C23C2×C22⋊D6112yes—
234C23C2×C22⋊D6111yescharacteristic
235Q8—22no—
236Q8—614no—
237Q8—612no—
238Q8—1228no—
239Q8—1222no—
240Q8—1221no—
241Q8—1224no—
242D4—24no—
243D4—22no—
244D4—22no—
245D4—22no—
246D4—42no—
247D4—84no—
248D4—612no—
249D4—1228no—
250D4—1224no—
251D4—1221no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—1228no—
256C2×C4—1228no—
257C2×C4—1222no—
258C2×C4—1221no—
259C2×C4—1224no—
260C2×C4—1224no—
261C2×C4D4×D6112yes—
262C2×C4D4×D6112yes—
263C2×C4C2×C22⋊D6112yes—
264C2×C4C2×C22⋊D6111yescharacteristic
265C2×C4C23×D6111yescharacteristic
266C8—1222no—
267C8—1222no—
268C22—22no—
269C22—22no—
270C22—24no—
271C22—42no—
272C22—44no—
273C22—84no—
274C22—1222no—
275C22—2442no—
276C22#1451974512yes—
277C22C22×C22⋊D6111yescharacteristic
278C4—22no—
279C4—42no—
280C4—1224no—
281C4—1222no—
282C4#1451974512yes—
283C4C2×D4×D6111yescharacteristic
284C4C2×D4×D6111yescharacteristic
285C2—22no—
286C2—42no—
287C2—82no—
288C2—2442no—
289C2C2×#1451974511yescharacteristic
290C2#1684057312yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#535C2
socleC22×C61C22×D4
hypercenter#535D61
hypocenterC61#3010
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#14519824C2semidirect
2. C2×#14519803C2semidirect
3. C22×#11758200C2semidirect
4. #16839905C2semidirect
5. #16839900C2semidirect
6. #16839770C2semidirect
7. #16839756C2semidirect
8. #16839729C2semidirect
9. C61×#535C2semidirect
13. C2×#11758222C22semidirect
17. C22×Dic122C22semidirect
26. #14519700C22semidirect
27. #14519700C22semidirect
28. #14519697C22semidirect
29. C22⋊#92418C22semidirect
60. #11758222D4semidirect
69. C2×Dic122D4semidirect
149. #535D61semidirect
155. C61#3010semidirect