Finite Group Databasebeta

← #21446844

Subgroups — #21446844

Order 7808.

382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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×#14519805C211yesmaximal, characteristic
2#16840338C211yesmaximal, characteristic, complemented
3C2×#14519765C211yesmaximal, characteristic, complemented
4C2×#14519705C211yesmaximal, characteristic, complemented
5#16839766C211yesmaximal, characteristic, complemented
6C2×#14519695C211yesmaximal, characteristic, complemented
7C61×#339C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×Dic122C2211yescharacteristic
10C22×D244C2211yescharacteristic
11#14519805—22no—
12#14519805—22no—
13C2×#11758190—21no—
14C2×D488—21no—
15C2×#11758194C2211yescharacteristic
16#14519777—21no—
17#14519765—22no—
18#14519765—21no—
19#14519765—22no—
20#14519761—22no—
21#14519757—22no—
22C2×#11758198—22no—
23#14519705—22no—
24#14519697—22no—
25#14519695—22no—
26C2×M16×C61C2211yescharacteristic
27#117×C61C2211yescharacteristic
28C2×C42×C61C2211yescharacteristic
29C23×D61—21no—
30C22×C4×C61—21no—
31C22×C4×C61C2311yescharacteristic
32C2×C22⋊D61—21no—
33C22×Dic61D412yes—
34#11758222—21no—
35#11758222—21no—
36#11758222—21no—
37#11758222—21no—
38C2×D244—21no—
39C2×D244—21no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244—21no—
43C2×D244D412yes—
44C2×D244D411yescharacteristic
45C2×C4×D61—21no—
46C2×Dic122—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122—21no—
51C2×Dic122—21no—
52C2×Dic122D411yescharacteristic
53M16×C61—21no—
54M16×C61D412yes—
55C2×C8×C61—21no—
56C4⋊C4×C61D412yes—
57C22⋊C4×C61—21no—
58C42×C61—21no—
59C42×C61—21no—
60C42×C61D412yes—
61#11758198—28no—
62#11758198—24no—
63C4⋊Dic61—24no—
64#11758194—21no—
65#11758194—21no—
66C2×#92418—21no—
67D488—24no—
68#11758190—24no—
69C23×C61C2×D411yescharacteristic
70C22×D61—21no—
71C22×D61—22no—
72C22×D61—44no—
73C22×D61—41no—
74C22×D61—41no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—42no—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61#4111yescharacteristic
84C22⋊D61—41no—
85C22⋊D61—41no—
86C2×Dic61—21no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90D244—22no—
91D244—21no—
92D244—22no—
93D244—21no—
94D244—41no—
95D244—41no—
96C4×D61—41no—
97C4×D61—41no—
98Dic122—21no—
99Dic122—21no—
100Dic122—41no—
101Dic122—41no—
102Dic122—41no—
103Dic122—41no—
104C8×C61—22no—
105#92418—41no—
106C22×C61—22no—
107C22×C61#12011yescharacteristic
108C22×C61#12011yescharacteristic
109C22×C61#12111yescharacteristic
110C2×D61—44no—
111C2×D61—41no—
112C2×D61—42no—
113C2×D61—42no—
114C2×D61—82no—
115C2×D61—82no—
116C4×C61—42no—
117C4×C61—42no—
118C4×C61#12011yescharacteristic
119C4×C61#12111yescharacteristic
120C4×C61#12111yescharacteristic
121C4×C61#12711yescharacteristic
122Dic61—41no—
123Dic61—42no—
124#2003—611nomaximal, Sylow
125C2×C61—21no—
126C2×C61—21no—
127C2×C61#39211yescharacteristic
128C2×C61#45412yes—
129D61—81no—
130D61—82no—
131C2×AGL(1,ℤ/8)—611no—
132#536—611no—
133C2×#124—611no—
134C2×#104—611no—
135#418—611no—
136C2×#101—611no—
137#339D6111yescharacteristic, complemented
138C61#200311yescharacteristic, complemented, Sylow
139C2×#41—611no—
140C22×Q8—611no—
141C22×D4—611no—
142AGL(1,ℤ/8)—1222no—
143AGL(1,ℤ/8)—1222no—
144C2×SD16—1221no—
145C2×D8—1221no—
146C2×M16—611no—
147C2×M16C2×D6111yescharacteristic
148C4⋊Q8—1221no—
149#124—1222no—
150#124—1221no—
151#124—1222no—
152#123—1222no—
153C22⋊Q8—1222no—
154#117C2×D6111yescharacteristic
155C2×C22⋊C4—1222no—
156C2×C42C2×D6111yescharacteristic
157#104—1222no—
158#102—1222no—
159#101—1222no—
160C24—1221no—
161#41—1221no—
162#41—1221no—
163#41—1221no—
164#41—1221no—
165C2×Q8—611no—
166C2×Q8—1221no—
167C2×Q8—1221no—
168C2×Q8—1221no—
169C2×Q8—1221no—
170C2×Q8—1221no—
171C2×Q8—1221no—
172C2×D4—611no—
173C2×D4—612no—
174C2×D4—1221no—
175C2×D4—1221no—
176C2×D4—1221no—
177C2×D4—1221no—
178C2×D4—1221no—
179C2×D4—1221no—
180C22×C4—21no—
181C22×C4—612no—
182C22×C4—1221no—
183C22×C4C22×D6111yescharacteristic
184SD16—1224no—
185D8—1224no—
186M16—21no—
187M16—1221no—
188M16—1221no—
189M16D24412yes—
190C2×C8—21no—
191C2×C8—1221no—
192C4⋊C4—1224no—
193C4⋊C4D24412yes—
194C22⋊C4—21no—
195C22⋊C4—1228no—
196C22⋊C4—1224no—
197C42—21no—
198C42—21no—
199C42D24412yes—
200C23—1222no—
201C23—1221no—
202C23—2444no—
203C23—2441no—
204C23—2441no—
205C23D4×D6111yescharacteristic
206Q8—1221no—
207Q8—1221no—
208Q8—2441no—
209Q8—2441no—
210Q8—2441no—
211Q8—2441no—
212D4—1221no—
213D4—1222no—
214D4—1222no—
215D4—1221no—
216D4—2441no—
217D4—2441no—
218D4—2441no—
219D4—2441no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—42no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1221no—
226C2×C4—1222no—
227C2×C4—2441no—
228C2×C4—2441no—
229C2×C4C2×D24411yescharacteristic
230C2×C4C2×D24411yescharacteristic
231C2×C4C2×D24411yescharacteristic
232C2×C4D4×D6111yescharacteristic
233C2×C4D4×D6111yescharacteristic
234C2×C4#1175822611yescharacteristic
235C8—22no—
236C8—2441no—
237C22—22no—
238C22—4882no—
239C22—4882no—
240C22—2444no—
241C22—2442no—
242C22—2441no—
243C22—2442no—
244C22#1451974711yescharacteristic
245C22#1451974711yescharacteristic
246C22#1451975211yescharacteristic
247C4—42no—
248C4—42no—
249C4—2442no—
250C4—2441no—
251C4#1451974711yescharacteristic
252C4#1451975211yescharacteristic
253C4#1451975211yescharacteristic
254C4#1451977411yescharacteristic
255C2—21no—
256C2—21no—
257C2—4882no—
258C2—4881no—
259C2#1683967211yescharacteristic
260C2#1683993612yes—
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#339C2
socleC22×C61#120
hypercenter#339D61
hypocenterC61#2003
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #16840338C2semidirect
3. C2×#14519765C2semidirect
4. C2×#14519705C2semidirect
5. #16839766C2semidirect
6. C2×#14519695C2semidirect
7. C61×#339C2semidirect
137. #339D61semidirect
138. C61#2003semidirect