Finite Group Databasebeta

← #21454112

Subgroups — #21454112

Order 7808.

1102 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C23×C4×D61C211yesmaximal, characteristic, complemented
2C2×#14519761C211yesmaximal, characteristic, complemented
3C2×#14519760C211yesmaximal, characteristic, complemented
4C2×#14519747C211yesmaximal, characteristic
5#16839640C214yesmaximal, complemented
6#16839636C214yesmaximal, complemented
7#16839623C211yesmaximal, characteristic, complemented
8#16839617C211yesmaximal, characteristic, complemented
9C61×#381C211yesmaximal, characteristic, complemented
10C24×D61C2211yescharacteristic
11C22×D244C2212yes—
12C22×C22⋊D61C2211yescharacteristic
13C23×Dic61C2211yescharacteristic
14C22×C4×D61—24no—
15C22×C4×D61—24no—
16C22×C4×D61—24no—
17C22×C4×D61C2214yes—
18#14519761—24no—
19#14519760—24no—
20#14519747—24no—
21C2×C4⋊Dic61C2212yescomplemented
22C2×#11758196C2212yescomplemented
23C2×C22⋊Dic61C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2214yes—
26C2×#11758198C2212yescomplemented
27C2×#11758198C2212yescomplemented
28#14519684C2214yescomplemented
29C23×C4×C61C2211yescharacteristic
30C2×C22⋊C4×C61C2211yescharacteristic
31C2×C22⋊C4×C61C2211yescharacteristic
32#95×C61C2214yescomplemented
33C24×C61C2311yescharacteristic
34C23×D61—22no—
35C23×D61—22no—
36C23×D61—28no—
37C23×D61D414yes—
38C23×D61C2311yescharacteristic
39C23×D61C2312yes—
40C22×C4×C61—22no—
41C22×C4×C61—22no—
42C22×C4×C61D414yescomplemented
43C22×C4×C61C2312yes—
44C22×C4×C61C2312yes—
45C22×C4×C61C2312yes—
46C2×C22⋊D61—22no—
47C2×C22⋊D61—22no—
48C2×C22⋊D61—22no—
49C22×Dic61—22no—
50C22×Dic61—22no—
51C22×Dic61D414yescomplemented
52C22×Dic61C2311yescharacteristic
53C22×Dic61C2312yes—
54C22×Dic61C2312yes—
55C2×D244—24no—
56C2×D244—28no—
57C2×C4×D61—232no—
58C2×C4×D61—28no—
59C2×C4×D61—28no—
60C2×C4×D61—28no—
61C22⋊C4×C61—22no—
62C22⋊C4×C61—22no—
63C22⋊Dic61—22no—
64#11758198—24no—
65#11758198—28no—
66#11758198—24no—
67#11758198—24no—
68C4⋊Dic61—24no—
69#11758196—24no—
70C23×C61—24no—
71C23×C61C2×D412yes—
72C23×C61C2×D412yes—
73C23×C61C2×D412yes—
74C23×C61C2411yescharacteristic
75C22×D61—216no—
76C22×D61—216no—
77C22×D61—28no—
78C22×D61—22no—
79C22×D61—22no—
80C22×D61—24no—
81C22×D61—216no—
82C22×D61—21no—
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—24no—
86C22×D61C2×D414yes—
87C22×D61#4118yes—
88C2×C4×C61—28no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—24no—
94C2×C4×C61—24no—
95C2×C4×C61C2×D414yes—
96C22⋊D61—44no—
97C2×Dic61—28no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—24no—
105C2×Dic61C2×D414yes—
106D244—48no—
107C4×D61—232no—
108C22×C61—24no—
109C22×C61—24no—
110C22×C61—24no—
111C22×C61#12014yes—
112C22×C61C22×D411yescharacteristic
113C22×C61C22×D411yescharacteristic
114C22×C61C22×D411yescharacteristic
115C22×C61C2×#4114yes—
116C2×D61—232no—
117C2×D61—24no—
118C2×D61—24no—
119C2×D61—28no—
120C2×D61—28no—
121C2×D61—41no—
122C2×D61—42no—
123C2×D61—42no—
124C2×D61—42no—
125C2×D61#12318yescomplemented
126C4×C61—24no—
127C4×C61—42no—
128C4×C61—42no—
129Dic61—24no—
130Dic61—41no—
131Dic61—42no—
132#2849—611nomaximal, Sylow
133C2×C61—24no—
134C2×C61C2×#12011yescharacteristic
135C2×C61C2×#12312yes—
136C2×C61#52512yes—
137C2×C61#52512yes—
138D61—28no—
139D61—81no—
140C24×C4—611no—
141C2×#123—611no—
142C2×#123—611no—
143C2×#120—611no—
144#386—614no—
145#385—614no—
146#381—611no—
147#381D6111yescharacteristic, complemented
148#379—611no—
149C61#284911yescharacteristic, complemented, Sylow
150C25—611no—
151C22×D4—611no—
152C22×D4—612no—
153C23×C4—611no—
154C23×C4—614no—
155C23×C4—1224no—
156C23×C4—1224no—
157C23×C4—1224no—
158C23×C4C2×D6111yescharacteristic
159#123—1224no—
160#123—1224no—
161#120—1224no—
162C2×C4⋊C4—612no—
163C2×C4⋊C4—612no—
164C2×C22⋊C4—611no—
165C2×C22⋊C4—612no—
166C2×C22⋊C4—612no—
167C2×C22⋊C4—612no—
168C2×C22⋊C4—614no—
169C2×C22⋊C4C2×D6111yescharacteristic
170C2×C22⋊C4C2×D6111yescharacteristic
171#95—614no—
172#95C2×D6114yescomplemented
173C24—612no—
174C24—614no—
175C24—611no—
176C24—1228no—
177C24—1222no—
178C24—1222no—
179C24C22×D6111yescharacteristic
180C2×D4—1224no—
181C2×D4—1228no—
182C2×D4—1222no—
183C2×D4—1222no—
184C2×D4—1222no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—614no—
188C22×C4—612no—
189C22×C4—612no—
190C22×C4—611no—
191C22×C4—1228no—
192C22×C4—1228no—
193C22×C4—12232no—
194C22×C4—1222no—
195C22×C4—1222no—
196C22×C4—1228no—
197C22×C4D24414yescomplemented
198C22×C4C22×D6112yes—
199C22×C4C22×D6112yes—
200C22×C4C22×D6112yes—
201C4⋊C4—1224no—
202C4⋊C4—1224no—
203C22⋊C4—22no—
204C22⋊C4—22no—
205C22⋊C4—1224no—
206C22⋊C4—1228no—
207C22⋊C4—1224no—
208C22⋊C4—1222no—
209C22⋊C4—1224no—
210C23—24no—
211C23—614no—
212C23—618no—
213C23—12216no—
214C23—12216no—
215C23—12216no—
216C23—1222no—
217C23—1222no—
218C23—1224no—
219C23—1228no—
220C23—1221no—
221C23—1221no—
222C23—1221no—
223C23—1224no—
224C23C2×D24412yes—
225C23D4×D6112yes—
226C23D4×D6112yes—
227C23C23×D6111yescharacteristic
228D4—2448no—
229D4—2444no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—28no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—24no—
236C2×C4—24no—
237C2×C4—614no—
238C2×C4—12232no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4—1228no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1222no—
245C2×C4—1221no—
246C2×C4—1224no—
247C2×C4C2×D24414yes—
248C22—24no—
249C22—24no—
250C22—24no—
251C22—618no—
252C22—12232no—
253C22—1224no—
254C22—1224no—
255C22—1228no—
256C22—1228no—
257C22—2441no—
258C22—2442no—
259C22—2442no—
260C22—2442no—
261C22#1451974714yes—
262C22C2×D4×D6111yescharacteristic
263C22C2×D4×D6111yescharacteristic
264C22C22×D24411yescharacteristic
265C22#41×D6114yes—
266C4—24no—
267C4—42no—
268C4—42no—
269C4—1224no—
270C4—2441no—
271C4—2442no—
272C2—24no—
273C2—1228no—
274C2—4881no—
275C2C2×#1451974711yescharacteristic
276C2#123×D6112yes—
277C2#1684027012yes—
278C2#1684027412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#381C2
hypercenter#381D61
hypocenterC61#2849
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C23×C4×D61C2semidirect
2. C2×#14519761C2semidirect
3. C2×#14519760C2semidirect
5. #16839640C2semidirect
6. #16839636C2semidirect
7. #16839623C2semidirect
8. #16839617C2semidirect
9. C61×#381C2semidirect
21. C2×C4⋊Dic61C22semidirect
22. C2×#11758196C22semidirect
26. C2×#11758198C22semidirect
27. C2×#11758198C22semidirect
28. #14519684C22semidirect
32. #95×C61C22semidirect
42. C22×C4×C61D4semidirect
51. C22×Dic61D4semidirect
125. C2×D61#123semidirect
147. #381D61semidirect
149. C61#2849semidirect
172. #95C2×D61semidirect
197. C22×C4D244semidirect