Finite Group Databasebeta

← #21447125

Subgroups — #21447125

Order 7808.

264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 65 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#16840562C211yesmaximal, characteristic
2#16839759C212yesmaximal, complemented
3#16839735C212yesmaximal, complemented
4#16839519C211yesmaximal, characteristic, complemented
5C61×#424C211yesmaximal, characteristic, complemented
6C2×#11758222C2212yes—
7#14519810—22no—
8#14519805—22no—
9#14519799—22no—
10#14519736C2212yes—
11#14519702—22no—
12#14519699—22no—
13#14519691—24no—
14C2×M16×C61C2211yescharacteristic
15C22×C8×C61C2211yescharacteristic
16#117×C61C2211yescharacteristic
17C4⋊C8×C61—22no—
18C22×C4×C61C2311yescharacteristic
19C2×C22⋊D61—22no—
20#11758222—22no—
21#11758222—22no—
22#11758222—22no—
23#11758222—22no—
24C2×D244D412yes—
25C2×C4×D61—22no—
26C2×Dic122D412yes—
27M16×C61—22no—
28C2×C8×C61—21no—
29C2×C8×C61—22no—
30C2×C8×C61D412yes—
31C4⋊C4×C61—21no—
32C22⋊C4×C61D412yes—
33C42×C61—21no—
34C22⋊Dic61—22no—
35C4⋊Dic61—22no—
36C4×Dic61—22no—
37Dic244—22no—
38D488—22no—
39#11758190—24no—
40C23×C61C2×D411yescharacteristic
41C22×D61—22no—
42C2×C4×C61—22no—
43C2×C4×C61C2×D412yes—
44C2×C4×C61C2×D411yescharacteristic
45C2×C4×C61#4111yescharacteristic
46C2×C4×C61#4112yes—
47C22⋊D61—42no—
48C22⋊D61—42no—
49C2×Dic61—22no—
50C2×Dic61—42no—
51D244—22no—
52D244—22no—
53C4×D61—42no—
54C4×D61—42no—
55Dic122—22no—
56Dic122—22no—
57C8×C61—22no—
58C8×C61—41no—
59C22×C61—41no—
60C22×C61#12111yescharacteristic
61C22×C61#12112yes—
62C2×D61—42no—
63C2×D61—82no—
64C4×C61—42no—
65C4×C61#12011yescharacteristic
66C4×C61#12312yes—
67C4×C61#12411yescharacteristic
68Dic61—42no—
69Dic61—82no—
70#2053—611nomaximal, Sylow
71C2×C61—22no—
72C2×C61—21no—
73C2×C61#39411yescharacteristic
74D61—82no—
75#575—611no—
76#424D6111yescharacteristic, complemented
77#416—612no—
78#410—612no—
79H(3,ℤ/4)—611no—
80C61#205311yescharacteristic, complemented, Sylow
81C2×#41—612no—
82#137—1222no—
83AGL(1,ℤ/8)—1222no—
84#135—1222no—
85C2×M16C2×D6111yescharacteristic
86C22×C8C2×D6111yescharacteristic
87#117—612no—
88#117C2×D6111yescharacteristic
89C4⋊C8—22no—
90#103—1222no—
91#102—1222no—
92#99—1224no—
93#41—1222no—
94#41—1222no—
95#41—1222no—
96#41—1222no—
97C2×Q8—612no—
98C2×D4—612no—
99C2×D4—1222no—
100C22×C4—1222no—
101C22×C4C22×D6111yescharacteristic
102Q16—1222no—
103SD16—1224no—
104D8—1222no—
105M16—22no—
106C2×C8—22no—
107C2×C8—21no—
108C2×C8C22⋊D6112yes—
109C4⋊C4—21no—
110C4⋊C4—1222no—
111C22⋊C4—1222no—
112C22⋊C4D24412yes—
113C42—21no—
114C42—1222no—
115C23—1222no—
116C23C2×D24411yescharacteristic
117Q8—1222no—
118Q8—1222no—
119D4—1222no—
120D4—1222no—
121D4—2442no—
122D4—2442no—
123C2×C4—22no—
124C2×C4—1222no—
125C2×C4—2442no—
126C2×C4—2442no—
127C2×C4—2442no—
128C2×C4#1175822211yescharacteristic
129C2×C4D4×D6112yes—
130C2×C4#1175822612yes—
131C2×C4C2×C22⋊D6111yescharacteristic
132C8—22no—
133C8—41no—
134C22—41no—
135C22—4882no—
136C22—2442no—
137C22#1451975111yescharacteristic
138C22#1451975212yes—
139C4—42no—
140C4—4882no—
141C4—2442no—
142C4#1451974511yescharacteristic
143C4#1451976212yes—
144C4#1451976611yescharacteristic
145C2—21no—
146C2—22no—
147C2—4882no—
148C2#1683967911yescharacteristic
subgroupG/H
centerC4#14519766
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#424C2
socleC2×C61#394
hypercenter#424D61
hypocenterC61#2053
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #16839759C2semidirect
3. #16839735C2semidirect
4. #16839519C2semidirect
5. C61×#424C2semidirect
76. #424D61semidirect
80. C61#2053semidirect