Finite Group Databasebeta

← #21455059

Subgroups — #21455059

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×#14519807C211yesmaximal, characteristic, complemented
3C2×#14519802C211yesmaximal, characteristic, complemented
4#16839922C214yesmaximal, complemented
5#16839905C214yesmaximal, complemented
6#16839770C211yesmaximal, characteristic, complemented
7#16839766C211yesmaximal, characteristic, complemented
8#16839726C211yesmaximal, characteristic, complemented
9C61×#525C211yesmaximal, characteristic, complemented
10C2×#11758222—22no—
11C2×#11758222—24no—
12C2×#11758222—24no—
13C2×#11758222C2214yes—
14C22×Dic122C2211yescharacteristic
15C22×D244C2211yescharacteristic
16C22×C22⋊D61—21no—
17C22×C4×D61—21no—
18#14519807—24no—
19#14519802—24no—
20C2×#11758202C2212yescomplemented
21C2×#11758200C2212yescomplemented
22C2×#11758201C2212yescomplemented
23C2×#11758199C2212yescomplemented
24C2×#11758194C2211yescharacteristic
25C2×#11758194C2211yescharacteristic
26#14519700C2214yescomplemented
27#14519697C2214yescomplemented
28C22⋊#92418C2214yescomplemented
29C2×#41×C61C2211yescharacteristic
30C23×C4×C61C2211yescharacteristic
31#123×C61—21no—
32C22⋊Q8×C61C2212yescomplemented
33#121×C61C2212yescomplemented
34#120×C61—21no—
35C4×D4×C61—22no—
36#117×C61C2211yescharacteristic
37C24×C61D411yescharacteristic
38C23×D61—21no—
39#41×C61—22no—
40#41×C61—22no—
41C2×Q8×C61C2311yescharacteristic
42C2×D4×C61—22no—
43C2×D4×C61—21no—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—22no—
46C22×C4×C61—22no—
47C22×C4×C61—21no—
48C22×C4×C61D411yescharacteristic
49C22×C4×C61D412yes—
50C22×C4×C61C2312yes—
51C22×C4×C61C2311yescharacteristic
52C2×C22⋊D61—28no—
53C2×C22⋊D61—24no—
54C22×Dic61—21no—
55#11758222—216no—
56#11758222—28no—
57#11758222—28no—
58C2×D244—21no—
59C2×D244—22no—
60C2×D244D414yescomplemented
61C2×D244C2312yes—
62C2×C4×D61—28no—
63C2×C4×D61—24no—
64C2×Dic122—21no—
65C2×Dic122—22no—
66C2×Dic122D414yescomplemented
67C2×Dic122C2312yes—
68C4⋊C4×C61—22no—
69C4⋊C4×C61C2312yes—
70C22⋊C4×C61—21no—
71C22⋊C4×C61—22no—
72C22⋊C4×C61—22no—
73C42×C61—21no—
74#11758202—24no—
75#11758201—24no—
76#11758200—24no—
77#11758199—24no—
78#11758194—22no—
79#11758194—22no—
80C2×#92418C2312yes—
81C2×#92418C2312yes—
82C23×C61—22no—
83C23×C61—21no—
84C23×C61—42no—
85C23×C61C2×D412yes—
86C23×C61C2×D411yescharacteristic
87C22×D61—24no—
88C22×D61—22no—
89C22×D61—44no—
90Q8×C61—21no—
91Q8×C61—21no—
92D4×C61—21no—
93D4×C61—21no—
94D4×C61—44no—
95D4×C61—42no—
96C2×C4×C61—22no—
97C2×C4×C61—24no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—21no—
102C2×C4×C61—42no—
103C2×C4×C61C2×D412yes—
104C2×C4×C61C2×D411yescharacteristic
105C2×C4×C61C2×D412yes—
106C2×C4×C61C2×D412yes—
107C2×C4×C61C2411yescharacteristic
108C22⋊D61—216no—
109C2×Dic61—24no—
110C2×Dic61—22no—
111D244—24no—
112D244—22no—
113D244C2×D414yes—
114C4×D61—216no—
115Dic122—24no—
116Dic122—22no—
117Dic122C2×D414yes—
118#92418—22no—
119#92418—22no—
120C22×C61—22no—
121C22×C61—22no—
122C22×C61—22no—
123C22×C61—22no—
124C22×C61—44no—
125C22×C61—41no—
126C22×C61—42no—
127C22×C61#12012yes—
128C22×C61C22×D411yescharacteristic
129C2×D61—24no—
130C2×D61—48no—
131C2×D61—44no—
132C4×C61—22no—
133C4×C61—41no—
134C4×C61—42no—
135C4×C61#12012yes—
136C4×C61C22×D411yescharacteristic
137C4×C61C22×D411yescharacteristic
138Dic61—24no—
139#3005—611nomaximal, Sylow
140C2×C61—22no—
141C2×C61—42no—
142C2×C61—81no—
143C2×C61C2×#12011yescharacteristic
144C2×C61#57512yes—
145D61—44no—
146C22×#41—611no—
147C2×#137—611no—
148C2×AGL(1,ℤ/8)—611no—
149#525D6111yescharacteristic, complemented
150#452—614no—
151#449—614no—
152#419—611no—
153#418—611no—
154#407—611no—
155C61#300511yescharacteristic, complemented, Sylow
156C2×#41—614no—
157C2×#41—1224no—
158C2×#41—1224no—
159C2×#41—1222no—
160C2×#41C2×D6111yescharacteristic
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×M16—611no—
173C2×M16—611no—
174#123—21no—
175C22⋊Q8C2×D6112yescomplemented
176#121C2×D6112yescomplemented
177#120—21no—
178C4×D4—22no—
179#117C2×D6111yescharacteristic
180#103—614no—
181#102—614no—
182C22⋊C8—614no—
183C24—1221no—
184C24C22⋊D6111yescharacteristic
185#41—22no—
186#41—22no—
187#41—1228no—
188#41—1228no—
189#41—12216no—
190C2×Q8—614no—
191C2×Q8—612no—
192C2×Q8—1222no—
193C2×Q8—1221no—
194C2×Q8C22×D6111yescharacteristic
195C2×D4—22no—
196C2×D4—21no—
197C2×D4—614no—
198C2×D4—612no—
199C2×D4—1228no—
200C2×D4—1224no—
201C2×D4—1222no—
202C2×D4—1221no—
203C2×D4C22×D6111yescharacteristic
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—21no—
207C22×C4—1228no—
208C22×C4—1221no—
209C22×C4—1224no—
210C22×C4C22⋊D6112yes—
211C22×C4C22⋊D6111yescharacteristic
212C22×C4C22×D6112yes—
213C22×C4C22×D6111yescharacteristic
214Q16—1224no—
215SD16—1224no—
216SD16—1224no—
217D8—1224no—
218M16—1222no—
219M16—1222no—
220C2×C8—612no—
221C2×C8—612no—
222C4⋊C4—22no—
223C4⋊C4C22×D6112yes—
224C22⋊C4—21no—
225C22⋊C4—22no—
226C22⋊C4—22no—
227C42—21no—
228C23—22no—
229C23—21no—
230C23—42no—
231C23—1222no—
232C23—1224no—
233C23—2444no—
234C23C2×C22⋊D6112yes—
235C23C2×C22⋊D6111yescharacteristic
236Q8—21no—
237Q8—21no—
238Q8—614no—
239Q8—1222no—
240Q8—1224no—
241D4—21no—
242D4—21no—
243D4—44no—
244D4—42no—
245D4—614no—
246D4—12216no—
247D4—1222no—
248D4—1224no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—24no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—12216no—
257C2×C4—1222no—
258C2×C4—1224no—
259C2×C4D4×D6112yes—
260C2×C4D4×D6112yes—
261C2×C4C2×C22⋊D6112yes—
262C2×C4C2×C22⋊D6111yescharacteristic
263C2×C4C23×D6111yescharacteristic
264C8—1222no—
265C8—1222no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—44no—
271C22—41no—
272C22—42no—
273C22—1224no—
274C22—2448no—
275C22—2444no—
276C22#1451974512yes—
277C22C22×C22⋊D6111yescharacteristic
278C4—22no—
279C4—41no—
280C4—42no—
281C4—1224no—
282C4#1451974512yes—
283C4C2×D4×D6111yescharacteristic
284C4C2×D4×D6111yescharacteristic
285C2—22no—
286C2—42no—
287C2—81no—
288C2—2444no—
289C2C2×#1451974511yescharacteristic
290C2#1684056012yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#525C2
socleC22×C61C22×D4
hypercenter#525D61
hypocenterC61#3005
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×#11758222C2semidirect
2. C2×#14519807C2semidirect
3. C2×#14519802C2semidirect
4. #16839922C2semidirect
5. #16839905C2semidirect
6. #16839770C2semidirect
7. #16839766C2semidirect
8. #16839726C2semidirect
9. C61×#525C2semidirect
20. C2×#11758202C22semidirect
21. C2×#11758200C22semidirect
22. C2×#11758201C22semidirect
23. C2×#11758199C22semidirect
26. #14519700C22semidirect
27. #14519697C22semidirect
28. C22⋊#92418C22semidirect
32. C22⋊Q8×C61C22semidirect
33. #121×C61C22semidirect
60. C2×D244D4semidirect
66. C2×Dic122D4semidirect
149. #525D61semidirect
155. C61#3005semidirect
175. C22⋊Q8C2×D61semidirect
176. #121C2×D61semidirect