Finite Group Databasebeta

← #21455729

Subgroups — #21455729

Order 7808.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#16840272C211yesmaximal, characteristic
2C2×#14519735C211yesmaximal, characteristic, complemented
3#16840106C212yesmaximal, complemented
4#16840097C211yesmaximal, characteristic, complemented
5#16840093C211yesmaximal, characteristic, complemented
6#16840085C212yesmaximal, complemented
7#16840073C211yesmaximal, characteristic, complemented
8#16839797C212yesmaximal, complemented
9#16839755C212yesmaximal, complemented
10C22⋊C8×D61C211yesmaximal, characteristic, complemented
11C61×#481C211yesmaximal, characteristic, complemented
12C2×#11758224C2211yescharacteristic
13C22×C4×D61C2211yescharacteristic
14C2×C8×D61C2212yes—
15#14519759—21no—
16#14519757C2211yescharacteristic
17#14519756C2211yescharacteristic
18#14519748C2211yescharacteristic
19#14519745—21no—
20D4×Dic61—21no—
21#14519737—21no—
22#14519735—21no—
23#14519735—21no—
24#14519735C2212yes—
25#14519735C2212yes—
26#14519735C2211yescharacteristic
27C2×C4⋊Dic61C2211yescharacteristic
28C2×#11758198—21no—
29C2×C4×Dic61—21no—
30#14519710C2212yescomplemented
31#14519710C2212yescomplemented
32#14519709C2212yescomplemented
33#14519702C2212yescomplemented
34#14519700C2212yescomplemented
35#14519698C2212yescomplemented
36C22⋊#92418C2211yescharacteristic
37#14519689C2212yes—
38#121×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#106×C61C2212yescomplemented
41#102×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic
43C23×D61D411yescharacteristic
44C2×D4×C61—21no—
45C2×D4×C61C2311yescharacteristic
46C22×C4×C61—21no—
47C22×C4×C61C2311yescharacteristic
48C2×C22⋊D61—21no—
49C2×C22⋊D61—21no—
50C22×Dic61—21no—
51C22×Dic61—21no—
52C22×Dic61D411yescharacteristic
53#11758224—24no—
54C2×C4×D61—24no—
55C2×C4×D61D411yescharacteristic
56C2×C4×D61D411yescharacteristic
57C2×C4×D61C2311yescharacteristic
58C2×C4×D61C2311yescharacteristic
59C2×Dic122C2311yescharacteristic
60C2×C8×C61C2312yes—
61C4⋊C4×C61—21no—
62C4⋊C4×C61C2312yes—
63C4⋊C4×C61C2311yescharacteristic
64C22⋊C4×C61—21no—
65C22⋊Dic61—21no—
66C22⋊Dic61—21no—
67#11758198—22no—
68#11758198—22no—
69#11758198—21no—
70#11758198—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61—21no—
73C4⋊Dic61C2312yes—
74C4⋊Dic61C2311yescharacteristic
75#11758196—21no—
76C4×Dic61—22no—
77C4×Dic61—22no—
78C4×Dic61—21no—
79C2×#92418C2312yes—
80C8×D61—24no—
81C23×C61—21no—
82C23×C61C2×D411yescharacteristic
83C22×D61—22no—
84C22×D61—22no—
85C22×D61—41no—
86C22×D61C2×D411yescharacteristic
87C22×D61C2×D411yescharacteristic
88D4×C61—22no—
89D4×C61—42no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—21no—
93C2×C4×C61—42no—
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2411yescharacteristic
96C22⋊D61—42no—
97C22⋊D61—42no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104C2×Dic61C2×D411yescharacteristic
105C2×Dic61C2×D411yescharacteristic
106C4×D61—22no—
107C4×D61—22no—
108C4×D61—22no—
109C4×D61#4114yes—
110Dic122—22no—
111C8×C61—22no—
112#92418—22no—
113C22×C61—21no—
114C22×C61—21no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61—41no—
118C22×C61#13512yes—
119C22×C61C22×D411yescharacteristic
120C2×D61—21no—
121C2×D61—21no—
122C2×D61—21no—
123C2×D61—21no—
124C2×D61—21no—
125C2×D61—44no—
126C2×D61#12312yes—
127C4×C61—21no—
128C4×C61—41no—
129C4×C61—42no—
130C4×C61C2×#4112yes—
131Dic61—21no—
132Dic61—41no—
133Dic61—42no—
134Dic61—41no—
135Dic61#12312yes—
136#3091—611nomaximal, Sylow
137C2×C61—22no—
138C2×C61—81no—
139C2×C61C2×#12311yescharacteristic
140C2×C61C2×#13511yescharacteristic
141C2×C61#57511yescharacteristic
142D61—22no—
143D61—41no—
144#525—611no—
145C2×#117—611no—
146#485—612no—
147#484—611no—
148#483—611no—
149#482—612no—
150#481D6111yescharacteristic, complemented
151#480—611no—
152#427—612no—
153#416—612no—
154C2×C22⋊C8—611no—
155C61#309111yescharacteristic, complemented, Sylow
156C2×#41—611no—
157C23×C4—611no—
158C22×C8—612no—
159#123—1221no—
160C22⋊Q8—611no—
161C22⋊Q8—611no—
162#121—611no—
163#121C2×D6111yescharacteristic
164#120—1221no—
165C4×D4—1221no—
166C4×D4—1221no—
167#117—612no—
168#117—612no—
169#117—611no—
170#117—1221no—
171#117—1221no—
172C2×C4⋊C4—611no—
173C2×C4⋊C4C2×D6111yescharacteristic
174C2×C22⋊C4—1221no—
175C2×C42—1221no—
176#107—612no—
177#107—612no—
178#106—612no—
179#106C2×D6112yescomplemented
180#103—612no—
181#103—612no—
182#102—612no—
183#102C2×D6112yescomplemented
184C22⋊C8—611no—
185C22⋊C8—612no—
186C22⋊C8C2×D6111yescharacteristic
187C24—611no—
188#41—1224no—
189C2×Q8—611no—
190C2×D4—21no—
191C2×D4—1221no—
192C2×D4—1221no—
193C2×D4C22×D6111yescharacteristic
194C22×C4—21no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—1224no—
201C22×C4—1221no—
202C22×C4—1221no—
203C22×C4C22×D6111yescharacteristic
204C2×C8—612no—
205C2×C8—1224no—
206C2×C8C22×D6112yes—
207C4⋊C4—21no—
208C4⋊C4—612no—
209C4⋊C4—611no—
210C4⋊C4—1221no—
211C4⋊C4—1221no—
212C4⋊C4—1221no—
213C4⋊C4C22×D6112yes—
214C4⋊C4C22×D6111yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—1222no—
217C22⋊C4—1222no—
218C22⋊C4—1221no—
219C22⋊C4—1221no—
220C22⋊C4—1221no—
221C22⋊C4—1221no—
222C42—1222no—
223C42—1222no—
224C42—1221no—
225C23—21no—
226C23—611no—
227C23—611no—
228C23—1222no—
229C23—1222no—
230C23—2441no—
231C23D4×D6111yescharacteristic
232Q8—1222no—
233D4—22no—
234D4—42no—
235D4—2442no—
236D4—2442no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—42no—
241C2×C4—611no—
242C2×C4—614no—
243C2×C4—611no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—1222no—
248C2×C4—1222no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—2442no—
252C2×C4—2442no—
253C2×C4D4×D6111yescharacteristic
254C2×C4C23×D6111yescharacteristic
255C8—22no—
256C8—1222no—
257C22—21no—
258C22—21no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—612no—
263C22—1221no—
264C22—1221no—
265C22—1221no—
266C22—1221no—
267C22—1221no—
268C22—2444no—
269C22#1451979812yes—
270C22C2×D4×D6111yescharacteristic
271C4—21no—
272C4—41no—
273C4—42no—
274C4—612no—
275C4—1221no—
276C4—2441no—
277C4—2442no—
278C4—2441no—
279C4#41×D6112yes—
280C2—22no—
281C2—81no—
282C2—1222no—
283C2—2441no—
284C2#123×D6111yescharacteristic
285C2C2×#1451979811yescharacteristic
286C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#481C2
socleC22×C61C22×D4
hypercenter#481D61
hypocenterC61#3091
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#14519735C2semidirect
3. #16840106C2semidirect
4. #16840097C2semidirect
5. #16840093C2semidirect
6. #16840085C2semidirect
7. #16840073C2semidirect
8. #16839797C2semidirect
9. #16839755C2semidirect
10. C22⋊C8×D61C2semidirect
11. C61×#481C2semidirect
30. #14519710C22semidirect
31. #14519710C22semidirect
32. #14519709C22semidirect
33. #14519702C22semidirect
34. #14519700C22semidirect
35. #14519698C22semidirect
40. #106×C61C22semidirect
41. #102×C61C22semidirect
150. #481D61semidirect
155. C61#3091semidirect
179. #106C2×D61semidirect
183. #102C2×D61semidirect