Finite Group Databasebeta

← #21455186

Subgroups — #21455186

Order 7808.

698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14519825C211yesmaximal, characteristic, complemented
2#16840562C212yesmaximal, complemented
3#16840336C211yesmaximal, characteristic, complemented
4#16839947C214yesmaximal, complemented
5#16839937C214yesmaximal, complemented
6#16839778C212yesmaximal, complemented
7C2×#101×C61C211yesmaximal, characteristic, complemented
8#14519825—22no—
9#14519825—24no—
10#14519825C2214yes—
11C2×#11758226—22no—
12C2×#11758222—22no—
13C2×#11758222C2212yes—
14C2×#11758222C2211yescharacteristic
15C2×Q8×D61—22no—
16#14519810—22no—
17#14519810C2214yescomplemented
18#14519805—22no—
19#14519805C2214yescomplemented
20#14519799—24no—
21#14519775C2212yescomplemented
22#14519766C2212yescomplemented
23#14519760—22no—
24#14519753—22no—
25#14519736C2211yescharacteristic
26#14519703C2218yescomplemented
27C22×Q8×C61C2211yescharacteristic
28C2×M16×C61C2212yes—
29#101×C61C2214yescomplemented
30C2×Q8×C61—22no—
31C2×Q8×C61—22no—
32C2×Q8×C61D412yes—
33C2×Q8×C61C2312yes—
34C22×C4×C61D412yes—
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—22no—
37C2×C22⋊D61—21no—
38#11758226—28no—
39#11758226—28no—
40Q8×D61—28no—
41Q8×D61—28no—
42#11758222—28no—
43#11758222—28no—
44#11758222—22no—
45#11758222—22no—
46#11758222—22no—
47#11758222—22no—
48#11758222D414yes—
49#11758222C2314yes—
50C2×D244—22no—
51C2×D244D412yes—
52C2×D244C2311yescharacteristic
53C2×C4×D61—24no—
54C2×C4×D61—22no—
55C2×C4×D61—21no—
56C2×Dic122—22no—
57C2×Dic122D412yes—
58C2×Dic122C2311yescharacteristic
59M16×C61—22no—
60M16×C61C2314yes—
61C2×C8×C61—22no—
62C22⋊Dic61—21no—
63#11758198—24no—
64C4⋊Dic61—21no—
65#11758196—24no—
66C4×Dic61C2312yes—
67Dic244—24no—
68D488—24no—
69#11758190—24no—
70#11758190—24no—
71C23×C61C2×D411yescharacteristic
72C22×D61—22no—
73C22×D61—21no—
74Q8×C61—24no—
75Q8×C61—24no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61C2×D414yes—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D412yes—
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2411yescharacteristic
83C22⋊D61—24no—
84C22⋊D61—24no—
85C22⋊D61—41no—
86C22⋊D61—41no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—21no—
90D244—28no—
91D244—22no—
92D244—22no—
93D244C2×D414yes—
94C4×D61—216no—
95C4×D61—24no—
96C4×D61—24no—
97C4×D61—42no—
98Dic122—28no—
99Dic122—22no—
100Dic122—22no—
101Dic122C2×D414yes—
102C8×C61—24no—
103C22×C61—41no—
104C22×C61#12011yescharacteristic
105C22×C61#12011yescharacteristic
106C22×C61C22×D411yescharacteristic
107C2×D61—24no—
108C2×D61—44no—
109C2×D61—42no—
110C2×D61—41no—
111C4×C61—24no—
112C4×C61#12012yes—
113C4×C61C22×D412yes—
114Dic61—24no—
115Dic61—42no—
116Dic61—41no—
117#3020—611nomaximal, Sylow
118C2×C61—21no—
119C2×C61—21no—
120C2×C61—21no—
121C2×C61C2×#12011yescharacteristic
122D61—44no—
123D61—81no—
124C2×2−1+4—611no—
125#575—612no—
126#536—611no—
127#456—614no—
128#454—614no—
129#421—612no—
130C2×#101D6111yescharacteristic, complemented
131C61#302011yescharacteristic, complemented, Sylow
1322−1+4—614no—
1332−1+4—1224no—
1342−1+4—1222no—
135C2×#41—612no—
136C2×#41—611no—
137C2×#41—1222no—
138C2×#41—1222no—
139C22×Q8—1222no—
140C22×Q8C2×D6111yescharacteristic
141#137—614no—
142#137—1222no—
143AGL(1,ℤ/8)—614no—
144AGL(1,ℤ/8)—1222no—
145#135—1224no—
146C2×M16C2×D6112yes—
147C4⋊Q8—612no—
148#124—612no—
149#123—1222no—
150C22⋊Q8—1222no—
151#117—611no—
152#104—618no—
153#101C2×D6114yescomplemented
154#41—614no—
155#41—614no—
156#41—1228no—
157#41—1228no—
158#41—1228no—
159#41—1222no—
160#41—1228no—
161#41—1222no—
162#41—1222no—
163#41—1222no—
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—612no—
167C2×Q8—611no—
168C2×Q8—1222no—
169C2×Q8—1228no—
170C2×Q8—1228no—
171C2×Q8D24412yes—
172C2×Q8C22×D6112yes—
173C2×D4—612no—
174C2×D4—611no—
175C2×D4—1222no—
176C2×D4—1222no—
177C2×D4—1221no—
178C22×C4—1224no—
179C22×C4—1222no—
180C22×C4—1221no—
181C22×C4D24412yes—
182C22×C4C22×D6111yescharacteristic
183Q16—1224no—
184SD16—1224no—
185SD16—1224no—
186D8—1224no—
187M16—22no—
188M16C22×D6114yes—
189C2×C8—22no—
190C4⋊C4—1224no—
191C4⋊C4—1221no—
192C22⋊C4—1221no—
193C22⋊C4—1224no—
194C42—612no—
195C23—1222no—
196C23—1221no—
197C23C2×D24411yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—614no—
201Q8—1228no—
202Q8—1222no—
203Q8—1222no—
204D4—614no—
205D4—1228no—
206D4—1224no—
207D4—1224no—
208D4—1222no—
209D4—1222no—
210D4—2441no—
211D4—2441no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—12216no—
215C2×C4—1222no—
216C2×C4—1224no—
217C2×C4—1224no—
218C2×C4—1222no—
219C2×C4—1221no—
220C2×C4—2442no—
221C2×C4C2×D24414yes—
222C2×C4C2×D24411yescharacteristic
223C2×C4D4×D6112yes—
224C2×C4D4×D6112yes—
225C2×C4C23×D6111yescharacteristic
226C8—24no—
227C22—41no—
228C22—1224no—
229C22—2442no—
230C22—2444no—
231C22—2441no—
232C22#1451974711yescharacteristic
233C22#1451974711yescharacteristic
234C22C22×D24411yescharacteristic
235C4—24no—
236C4—1224no—
237C4—2442no—
238C4—2441no—
239C4#1451974712yes—
240C4C2×D4×D6112yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—4881no—
245C2—2444no—
246C2C2×#1451974711yescharacteristic
subgroupG/H
centerC2C2×#14519747
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#101×C61C2
socleC2×C61C2×#120
hypercenterC2×#101D61
hypocenterC61#3020
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. C2×#14519825C2semidirect
2. #16840562C2semidirect
3. #16840336C2semidirect
4. #16839947C2semidirect
5. #16839937C2semidirect
6. #16839778C2semidirect
7. C2×#101×C61C2semidirect
17. #14519810C22semidirect
19. #14519805C22semidirect
21. #14519775C22semidirect
22. #14519766C22semidirect
26. #14519703C22semidirect
29. #101×C61C22semidirect
130. C2×#101D61semidirect
131. C61#3020semidirect
153. #101C2×D61semidirect