Finite Group Databasebeta

← #21454108

Subgroups — #21454108

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×#14519758C211yesmaximal, characteristic, complemented
3C2×#14519745C211yesmaximal, characteristic
4#16839638C214yesmaximal, complemented
5#16839633C214yesmaximal, complemented
6#16839625C211yesmaximal, characteristic, complemented
7#16839623C211yesmaximal, characteristic, complemented
8#16839617C211yesmaximal, characteristic, complemented
9C2×#123×C61C211yesmaximal, characteristic, complemented
10C24×D61C2211yescharacteristic
11C22×C22⋊D61C2212yes—
12C23×Dic61C2211yescharacteristic
13C22×C4×D61—24no—
14C22×C4×D61—24no—
15C22×C4×D61—24no—
16C22×C4×D61C2214yes—
17#14519758—24no—
18#14519745—24no—
19C2×#11758196C2212yescomplemented
20C2×C22⋊Dic61C2211yescharacteristic
21C2×C22⋊Dic61C2211yescharacteristic
22C2×C22⋊Dic61C2212yescomplemented
23C2×#11758198C2212yes—
24C2×#11758198C2214yes—
25#14519684C2214yescomplemented
26#14519684C2214yescomplemented
27C22×D4×C61C2211yescharacteristic
28C23×C4×C61C2211yescharacteristic
29#123×C61—24no—
30C2×C4⋊C4×C61C2212yescomplemented
31C2×C22⋊C4×C61C2211yescharacteristic
32C2×C22⋊C4×C61C2212yescomplemented
33C24×C61C2311yescharacteristic
34C24×C61C2311yescharacteristic
35C23×D61—22no—
36C23×D61—22no—
37C23×D61—28no—
38C23×D61D414yes—
39C23×D61C2312yes—
40C2×D4×C61—22no—
41C2×D4×C61—22no—
42C2×D4×C61—22no—
43C22×C4×C61—22no—
44C22×C4×C61—22no—
45C22×C4×C61D414yescomplemented
46C22×C4×C61C2312yes—
47C22×C4×C61C2311yescharacteristic
48C22×C4×C61C2312yes—
49C2×C22⋊D61—24no—
50C2×C22⋊D61—28no—
51C22×Dic61—22no—
52C22×Dic61—22no—
53C22×Dic61D414yescomplemented
54C22×Dic61C2312yes—
55C22×Dic61C2312yes—
56C22×Dic61C2312yes—
57C2×C4×D61—232no—
58C2×C4×D61—28no—
59C2×C4×D61—28no—
60C2×C4×D61—28no—
61C4⋊C4×C61—24no—
62C22⋊C4×C61—22no—
63C22⋊C4×C61—24no—
64C22⋊Dic61—22no—
65C22⋊Dic61—22no—
66C22⋊Dic61—24no—
67#11758198—24no—
68#11758198—28no—
69#11758196—24no—
70C23×C61—24no—
71C23×C61—21no—
72C23×C61—21no—
73C23×C61—21no—
74C23×C61—24no—
75C23×C61C2×D412yes—
76C23×C61C2×D412yes—
77C23×C61C2×D412yes—
78C23×C61C2411yescharacteristic
79C22×D61—216no—
80C22×D61—216no—
81C22×D61—28no—
82C22×D61—22no—
83C22×D61—22no—
84C22×D61—24no—
85C22×D61—216no—
86C22×D61C2×D414yes—
87C22×D61#4118yes—
88D4×C61—44no—
89C2×C4×C61—28no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—22no—
95C2×C4×C61—21no—
96C2×C4×C61—24no—
97C2×C4×C61C2×D414yes—
98C22⋊D61—48no—
99C2×Dic61—28no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—24no—
105C2×Dic61—24no—
106C2×Dic61C2×D414yes—
107C4×D61—232no—
108C22×C61—24no—
109C22×C61—24no—
110C22×C61—24no—
111C22×C61—41no—
112C22×C61—42no—
113C22×C61—42no—
114C22×C61—42no—
115C22×C61#12014yes—
116C22×C61C22×D411yescharacteristic
117C22×C61C22×D411yescharacteristic
118C22×C61C22×D411yescharacteristic
119C22×C61C2×#4114yes—
120C2×D61—232no—
121C2×D61—24no—
122C2×D61—24no—
123C2×D61—28no—
124C2×D61—28no—
125C2×D61#12318yescomplemented
126C4×C61—24no—
127C4×C61—41no—
128C4×C61—42no—
129Dic61—24no—
130Dic61—42no—
131Dic61—42no—
132#2849—611nomaximal, Sylow
133C2×C61—24no—
134C2×C61—81no—
135C2×C61C2×#12011yescharacteristic
136C2×C61C2×#12312yes—
137C2×C61#52512yes—
138C2×C61#52512yes—
139D61—28no—
140C24×C4—611no—
141C2×#123—611no—
142C2×#123D6111yescharacteristic, complemented
143C2×#120—611no—
144#386—614no—
145#385—614no—
146#381—611no—
147#381—611no—
148#379—611no—
149C61#284911yescharacteristic, complemented, Sylow
150C25—611no—
151C22×D4—612no—
152C22×D4C2×D6111yescharacteristic
153C23×C4—611no—
154C23×C4—614no—
155C23×C4—1224no—
156C23×C4—1224no—
157C23×C4—1224no—
158C23×C4C2×D6111yescharacteristic
159#123—24no—
160#123—1224no—
161#120—1224no—
162C2×C4⋊C4—612no—
163C2×C4⋊C4C2×D6112yescomplemented
164C2×C22⋊C4—611no—
165C2×C22⋊C4—611no—
166C2×C22⋊C4—612no—
167C2×C22⋊C4—612no—
168C2×C22⋊C4—614no—
169C2×C22⋊C4C2×D6111yescharacteristic
170C2×C22⋊C4C2×D6112yescomplemented
171#95—614no—
172#95—614no—
173C24—612no—
174C24—614no—
175C24—1228no—
176C24—1222no—
177C24—1222no—
178C24C22×D6111yescharacteristic
179C24C22×D6111yescharacteristic
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4—1224no—
184C2×D4—1228no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—614no—
188C22×C4—612no—
189C22×C4—612no—
190C22×C4—612no—
191C22×C4—1228no—
192C22×C4—1228no—
193C22×C4—12232no—
194C22×C4—1222no—
195C22×C4—1222no—
196C22×C4—1228no—
197C22×C4C22⋊D6114yescomplemented
198C22×C4C22×D6112yes—
199C22×C4C22×D6111yescharacteristic
200C22×C4C22×D6112yes—
201C4⋊C4—24no—
202C4⋊C4—1224no—
203C22⋊C4—22no—
204C22⋊C4—24no—
205C22⋊C4—1228no—
206C22⋊C4—1224no—
207C22⋊C4—1224no—
208C22⋊C4—1222no—
209C22⋊C4—1222no—
210C23—24no—
211C23—21no—
212C23—21no—
213C23—21no—
214C23—24no—
215C23—614no—
216C23—618no—
217C23—12216no—
218C23—12216no—
219C23—12216no—
220C23—1222no—
221C23—1222no—
222C23—1224no—
223C23—1228no—
224C23D4×D6112yes—
225C23D4×D6112yes—
226C23C2×C22⋊D6112yes—
227C23C23×D6111yescharacteristic
228D4—44no—
229D4—2448no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—28no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—24no—
238C2×C4—614no—
239C2×C4—12232no—
240C2×C4—1222no—
241C2×C4—1222no—
242C2×C4—1228no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—1224no—
246C2×C4—1224no—
247C2×C4C2×C22⋊D6114yes—
248C22—24no—
249C22—24no—
250C22—24no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—618no—
256C22—12232no—
257C22—1224no—
258C22—1224no—
259C22—1228no—
260C22—1228no—
261C22#1451974514yes—
262C22C2×D4×D6111yescharacteristic
263C22C2×D4×D6111yescharacteristic
264C22C22×C22⋊D6111yescharacteristic
265C22#41×D6114yes—
266C4—24no—
267C4—41no—
268C4—42no—
269C4—1224no—
270C4—2442no—
271C4—2442no—
272C2—24no—
273C2—81no—
274C2—1228no—
275C2C2×#1451974511yescharacteristic
276C2#123×D6112yes—
277C2#1684026912yes—
278C2#1684027012yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#123×C61C2
hypercenterC2×#123D61
hypocenterC61#2849
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C23×C4×D61C2semidirect
2. C2×#14519758C2semidirect
4. #16839638C2semidirect
5. #16839633C2semidirect
6. #16839625C2semidirect
7. #16839623C2semidirect
8. #16839617C2semidirect
9. C2×#123×C61C2semidirect
19. C2×#11758196C22semidirect
22. C2×C22⋊Dic61C22semidirect
25. #14519684C22semidirect
26. #14519684C22semidirect
30. C2×C4⋊C4×C61C22semidirect
32. C2×C22⋊C4×C61C22semidirect
45. C22×C4×C61D4semidirect
53. C22×Dic61D4semidirect
125. C2×D61#123semidirect
142. C2×#123D61semidirect
149. C61#2849semidirect
163. C2×C4⋊C4C2×D61semidirect
170. C2×C22⋊C4C2×D61semidirect
197. C22×C4C22⋊D61semidirect