Finite Group Databasebeta

← #21446124

Subgroups — #21446124

Order 7808.

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

normal subgroups only

This group has 404 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
1C2×#14519756C211yesmaximal, characteristic
2C22×C4⋊Dic61C211yesmaximal, characteristic
3C2×#14519702C212yesmaximal, complemented
4#16839525C212yesmaximal, complemented
5C2×C22⋊C8×C61C211yesmaximal, characteristic
6C22×Dic122C2211yescharacteristic
7C23×Dic61—21no—
8#14519756—22no—
9#14519756C414yescomplemented
10C2×C4⋊Dic61—21no—
11C2×C4⋊Dic61—24no—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2212yes—
14C2×#11758196—21no—
15C2×C22⋊Dic61—21no—
16#14519702—24no—
17C23×C4×C61C2211yescharacteristic
18C22×C8×C61C2212yes—
19C22⋊C8×C61—22no—
20C24×C61D411yescharacteristic
21C22×C4×C61—22no—
22C22×C4×C61—22no—
23C22×C4×C61C2×C412yes—
24C22×C4×C61D411yescharacteristic
25C22×C4×C61D412yes—
26C22×C4×C61C2311yescharacteristic
27C22×Dic61—24no—
28C22×Dic61—22no—
29C22×Dic61—21no—
30C22×Dic61—21no—
31C22×Dic61—42no—
32C22×Dic61—42no—
33C2×Dic122—22no—
34C2×Dic122—22no—
35C2×Dic122—21no—
36C2×Dic122C2×C412yescomplemented
37C2×C8×C61—22no—
38C2×C8×C61—22no—
39C2×C8×C61—22no—
40C22⋊Dic61—24no—
41C4⋊Dic61—24no—
42C4⋊Dic61—22no—
43C4⋊Dic61—21no—
44C4⋊Dic61C2×C412yescomplemented
45C4⋊Dic61D414yes—
46#11758196—24no—
47C23×C61—21no—
48C23×C61—21no—
49C23×C61—21no—
50C23×C61—21no—
51C23×C61C22⋊C412yes—
52C23×C61SD1612yes—
53C23×C61Q1612yes—
54C23×C61C2×D411yescharacteristic
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—24no—
58C2×C4×C61—24no—
59C2×C4×C61C22⋊C412yes—
60C2×C4×C61C22×C411yescharacteristic
61C2×C4×C61C2×D412yes—
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61#4112yes—
64C2×Dic61—22no—
65C2×Dic61—22no—
66C2×Dic61—24no—
67C2×Dic61—48no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61—42no—
71C2×Dic61—41no—
72C2×Dic61—42no—
73C2×Dic61—41no—
74Dic122—24no—
75Dic122—42no—
76C8×C61—42no—
77C22×C61—22no—
78C22×C61—22no—
79C22×C61—22no—
80C22×C61—22no—
81C22×C61—22no—
82C22×C61—22no—
83C22×C61#10314yescomplemented
84C22×C61C2×C22⋊C411yescharacteristic
85C22×C61#12011yescharacteristic
86C22×C61#12311yescharacteristic
87C22×C61C2×SD1611yescharacteristic
88C22×C61C2×Q1611yescharacteristic
89C22×C61AGL(1,ℤ/8)11yescharacteristic
90C22×C61#13711yescharacteristic
91C4×C61—22no—
92C4×C61C4×D412yes—
93C4×C61#12112yes—
94Dic61—42no—
95Dic61—42no—
96Dic61—44no—
97#1872—611nomaximal, Sylow
98C2×C61—24no—
99C2×C61#38611yescharacteristic
100C2×C61C2×#10311yescharacteristic
101C2×C61#41711yescharacteristic
102C2×C61#45011yescharacteristic
103C2×C61#45111yescharacteristic
104C2×C61#48311yescharacteristic
105C2×C61#48411yescharacteristic
106C2×C22⋊Q8—611no—
107C22×C4⋊C4—611no—
108C2×#103—612no—
109C2×C22⋊C8D6111yescharacteristic
110#340—612no—
111C61#187211yescharacteristic, complemented, Sylow
112C22×Q8—611no—
113C23×C4—1221no—
114C23×C4C2×D6111yescharacteristic
115C22×C8C2×D6112yes—
116C22⋊Q8—614no—
117C22⋊Q8—1222no—
118C2×C4⋊C4—612no—
119C2×C4⋊C4—611no—
120C2×C4⋊C4—1224no—
121C2×C4⋊C4—1221no—
122C2×C4⋊C4—1221no—
123C2×C22⋊C4—1221no—
124#103—1224no—
125C22⋊C8—22no—
126C24D24411yescharacteristic
127C2×Q8—612no—
128C2×Q8—1221no—
129C2×Q8—1222no—
130C2×Q8—1222no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—1224no—
134C22×C4—1221no—
135C22×C4—1221no—
136C22×C4—1222no—
137C22×C4—2442no—
138C22×C4—2442no—
139C22×C4C4×D6112yes—
140C22×C4D24411yescharacteristic
141C22×C4C22⋊D6112yes—
142C22×C4C22×D6111yescharacteristic
143C2×C8—22no—
144C2×C8—22no—
145C2×C8—22no—
146C4⋊C4—612no—
147C4⋊C4—614no—
148C4⋊C4—1224no—
149C4⋊C4—1224no—
150C4⋊C4—1222no—
151C4⋊C4—1221no—
152C22⋊C4—1224no—
153C23—21no—
154C23—21no—
155C23—21no—
156C23—21no—
157C23#1175819012yes—
158C23Dic24412yes—
159C23#1175819812yes—
160C23C2×D24411yescharacteristic
161Q8—1224no—
162Q8—2442no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—1222no—
168C2×C4—1222no—
169C2×C4—1224no—
170C2×C4—2448no—
171C2×C4—2441no—
172C2×C4—2441no—
173C2×C4—2441no—
174C2×C4—2442no—
175C2×C4—2441no—
176C2×C4—2442no—
177C2×C4#1175819812yes—
178C2×C4C2×C4×D6111yescharacteristic
179C2×C4D4×D6112yes—
180C2×C4#1175822412yes—
181C2×C4C2×C22⋊D6111yescharacteristic
182C8—42no—
183C22—22no—
184C22—22no—
185C22—22no—
186C22—22no—
187C22—22no—
188C22—22no—
189C22#1451970214yescomplemented
190C22C2×#1175819811yescharacteristic
191C22#1451974711yescharacteristic
192C22#1451976111yescharacteristic
193C22C2×#1175819011yescharacteristic
194C22C2×Dic24411yescharacteristic
195C22#1451980511yescharacteristic
196C22#1451981011yescharacteristic
197C4—22no—
198C4—2442no—
199C4—2442no—
200C4—2444no—
201C4#1451973712yes—
202C4#1451974912yes—
203C2—24no—
204C2#1683963911yescharacteristic
205C2C2×#1451970211yescharacteristic
206C2#1683976411yescharacteristic
207C2#1683991511yescharacteristic
208C2#1683992011yescharacteristic
209C2#1684009311yescharacteristic
210C2#1684009811yescharacteristic
subgroupG/H
centerC23C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×C22⋊C8×C61C2
socleC23×C61C2×D4
hypercenterC2×C22⋊C8D61
hypocenterC61#1872
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#14519702C2semidirect
4. #16839525C2semidirect
9. #14519756C4semidirect
36. C2×Dic122C2×C4semidirect
44. C4⋊Dic61C2×C4semidirect
83. C22×C61#103semidirect
111. C61#1872semidirect
189. C22#14519702semidirect