Finite Group Databasebeta

← #21446346

Subgroups — #21446346

Order 7808.

344 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 89 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#16840326C211yesmaximal, characteristic
2#16839768C212yesmaximal, complemented
3#16839736C211yesmaximal, characteristic, complemented
4#16839519C212yesmaximal, complemented
5C61×#568C211yesmaximal, characteristic, complemented
6C22×D244C2211yescharacteristic
7#14519773C412yescomplemented
8#14519766C412yescomplemented
9#14519751—22no—
10#14519745—22no—
11#14519736C2212yes—
12#14519736C2211yescharacteristic
13#14519699—24no—
14#14519692—22no—
15C2×#41×C61C2211yescharacteristic
16#131×C61—24no—
17C2×M16×C61—22no—
18C2×M16×C61C2212yes—
19C23×D61—21no—
20#41×C61—22no—
21#41×C61—22no—
22C2×Q8×C61C2×C411yescharacteristic
23C2×D4×C61C2×C411yescharacteristic
24C2×D4×C61D412yes—
25C22×C4×C61D412yes—
26C22×C4×C61C2311yescharacteristic
27C2×C22⋊D61—24no—
28C2×D244—22no—
29C2×D244—22no—
30C2×D244—21no—
31C2×D244C2×C412yes—
32M16×C61—24no—
33M16×C61—22no—
34M16×C61—22no—
35C2×C8×C61—24no—
36C2×C8×C61D414yescomplemented
37C22⋊Dic61—21no—
38C22⋊Dic61—22no—
39#11758198—24no—
40C4⋊Dic61—21no—
41C4⋊Dic61—22no—
42C4×Dic61—22no—
43C4×Dic61C2×C412yes—
44C23×C61C22⋊C412yes—
45C23×C61C2×D411yescharacteristic
46C22×D61—22no—
47C22×D61—42no—
48C22×D61—82no—
49Q8×C61—22no—
50D4×C61—24no—
51D4×C61—22no—
52C2×C4×C61—22no—
53C2×C4×C61—22no—
54C2×C4×C61C22⋊C412yes—
55C2×C4×C61C22×C411yescharacteristic
56C2×C4×C61C2×D412yes—
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61#4112yes—
59C22⋊D61—84no—
60C2×Dic61—22no—
61C2×Dic61—42no—
62D244—24no—
63D244—41no—
64D244—41no—
65C8×C61—24no—
66C22×C61—22no—
67C22×C61—41no—
68C22×C61—42no—
69C22×C61C2×C22⋊C411yescharacteristic
70C22×C61#12112yes—
71C2×D61—44no—
72C2×D61—42no—
73C2×D61—84no—
74C4×C61—22no—
75C4×C61C4×D412yes—
76C4×C61#12011yescharacteristic
77C4×C61#12311yescharacteristic
78Dic61—42no—
79Dic61—82no—
80#1910—611nomaximal, Sylow
81C2×C61—21no—
82C2×C61—22no—
83C2×C61—42no—
84C2×C61#38611yescharacteristic
85D61—82no—
86#568D6111yescharacteristic, complemented
87#535—611no—
88#418—612no—
89#410—611no—
90H(3,ℤ/4)—612no—
91C61#191011yescharacteristic, complemented, Sylow
92C2×#41C2×D6111yescharacteristic
93C22×D4—611no—
94#131—24no—
95C2×M16—22no—
96C2×M16C2×D6112yes—
97#127—612no—
98#124—612no—
99#121—1222no—
100#120—1222no—
101#117—611no—
102#117—612no—
103#102—1224no—
104#99—1222no—
105C24—1221no—
106#41—22no—
107#41—22no—
108C2×Q8C4×D6111yescharacteristic
109C2×D4—612no—
110C2×D4—1224no—
111C2×D4—1222no—
112C2×D4—1222no—
113C2×D4—1221no—
114C2×D4C4×D6111yescharacteristic
115C2×D4D24412yes—
116C22×C4C22⋊D6112yes—
117C22×C4C22×D6111yescharacteristic
118M16—24no—
119M16—22no—
120M16—22no—
121C2×C8—24no—
122C2×C8C22⋊D6114yescomplemented
123C4⋊C4—1221no—
124C4⋊C4—1222no—
125C22⋊C4—1221no—
126C22⋊C4—1224no—
127C22⋊C4—1222no—
128C42—612no—
129C42—1222no—
130C23—1222no—
131C23—4882no—
132C23—2442no—
133C23#1175819812yes—
134C23C2×D24411yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—1224no—
139D4—4884no—
140D4—2441no—
141D4—2441no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—1222no—
145C2×C4—2442no—
146C2×C4#1175819812yes—
147C2×C4C2×C4×D6111yescharacteristic
148C2×C4#1175822212yes—
149C2×C4C2×C22⋊D6112yes—
150C2×C4C2×C22⋊D6111yescharacteristic
151C8—24no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—4884no—
156C22—2444no—
157C22—2442no—
158C22C2×#1175819811yescharacteristic
159C22#1451975112yes—
160C4—22no—
161C4—4882no—
162C4—2442no—
163C4C4×C22⋊D6112yes—
164C4#1451974611yescharacteristic
165C4#1451976011yescharacteristic
166C2—22no—
167C2—21no—
168C2—42no—
169C2—4882no—
170C2#1683964111yescharacteristic
subgroupG/H
centerC2#16839641
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#568C2
socleC2×C61#386
hypercenter#568D61
hypocenterC61#1910
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #16839768C2semidirect
3. #16839736C2semidirect
4. #16839519C2semidirect
5. C61×#568C2semidirect
7. #14519773C4semidirect
8. #14519766C4semidirect
36. C2×C8×C61D4semidirect
86. #568D61semidirect
91. C61#1910semidirect
122. C2×C8C22⋊D61semidirect