Finite Group Databasebeta

← #21447122

Subgroups — #21447122

Order 7808.

264 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 67 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#16839790C211yesmaximal, characteristic, complemented
2#16839758C212yesmaximal, complemented
3#16839736C212yesmaximal, complemented
4#16839519C211yesmaximal, characteristic, complemented
5C61×#575C211yesmaximal, characteristic
6C22×#92418C2211yescharacteristic
7#14519736C2212yes—
8#14519736C2211yescharacteristic
9#14519706—22no—
10#14519701—22no—
11#14519698—22no—
12#14519692—24no—
13C2×#41×C61C2212yes—
14#137×C61—22no—
15AGL(1,ℤ/8)×C61—22no—
16#135×C61—22no—
17C2×M16×C61C2211yescharacteristic
18#41×C61—22no—
19#41×C61—22no—
20#41×C61—22no—
21#41×C61—22no—
22C2×Q8×C61D412yes—
23C2×D4×C61—22no—
24C2×D4×C61D412yes—
25C22×C4×C61—22no—
26C22×C4×C61C2311yescharacteristic
27Q16×C61—22no—
28SD16×C61—24no—
29D8×C61—22no—
30M16×C61—22no—
31C2×C8×C61D412yes—
32C22⋊Dic61—22no—
33C22⋊Dic61D412yes—
34C4⋊Dic61—21no—
35C4⋊Dic61—22no—
36C4×Dic61—21no—
37C4×Dic61—22no—
38C2×#92418—22no—
39C2×#92418—21no—
40C23×C61—22no—
41C23×C61C2×D411yescharacteristic
42Q8×C61—22no—
43Q8×C61—22no—
44D4×C61—22no—
45D4×C61—22no—
46D4×C61—42no—
47D4×C61—42no—
48C2×C4×C61—22no—
49C2×C4×C61—42no—
50C2×C4×C61—42no—
51C2×C4×C61C2×D412yes—
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61#4111yescharacteristic
54C2×C4×C61#4112yes—
55C2×Dic61—22no—
56C2×Dic61—42no—
57C8×C61—22no—
58#92418—41no—
59C22×C61—41no—
60C22×C61—42no—
61C22×C61—82no—
62C22×C61#12111yescharacteristic
63C22×C61#12112yes—
64C4×C61—42no—
65C4×C61#12011yescharacteristic
66C4×C61#12312yes—
67C4×C61#12411yescharacteristic
68Dic61—42no—
69Dic61—82no—
70#2053—611nomaximal, Sylow
71C2×C61—21no—
72C2×C61—22no—
73C2×C61—82no—
74C2×C61#39411yescharacteristic
75#575D6111yescharacteristic
76#424—611no—
77#416—612no—
78#410—612no—
79H(3,ℤ/4)—611no—
80C61#205311yescharacteristic, complemented, Sylow
81C2×#41C2×D6112yes—
82#137—22no—
83AGL(1,ℤ/8)—22no—
84#135—22no—
85C2×M16C2×D6111yescharacteristic
86C22×C8—611no—
87#117—611no—
88#117—612no—
89C4⋊C8—1222no—
90#103—1222no—
91#102—1222no—
92#99—1224no—
93#41—22no—
94#41—22no—
95#41—22no—
96#41—22no—
97C2×Q8C22⋊D6112yes—
98C2×D4—22no—
99C2×D4C22⋊D6112yes—
100C22×C4—22no—
101C22×C4C22×D6111yescharacteristic
102Q16—22no—
103SD16—24no—
104D8—22no—
105M16—22no—
106C2×C8—1222no—
107C2×C8—1221no—
108C2×C8C22⋊D6112yes—
109C4⋊C4—1221no—
110C4⋊C4—1222no—
111C22⋊C4—612no—
112C22⋊C4—1222no—
113C42—1221no—
114C42—1222no—
115C23—22no—
116C23D4×D6111yescharacteristic
117Q8—22no—
118Q8—22no—
119D4—22no—
120D4—22no—
121D4—42no—
122D4—42no—
123C2×C4—22no—
124C2×C4—42no—
125C2×C4—42no—
126C2×C4—1222no—
127C2×C4—2442no—
128C2×C4#1175822411yescharacteristic
129C2×C4#1175822412yes—
130C2×C4C2×C22⋊D6112yes—
131C2×C4C2×C22⋊D6111yescharacteristic
132C8—22no—
133C8—2441no—
134C22—41no—
135C22—42no—
136C22—82no—
137C22#1451974811yescharacteristic
138C22#1451974912yes—
139C4—42no—
140C4—4882no—
141C4—2442no—
142C4#1451974611yescharacteristic
143C4#1451975812yes—
144C4#1451976411yescharacteristic
145C2—22no—
146C2—21no—
147C2—82no—
148C2#1683967611yescharacteristic
subgroupG/H
centerC4#14519764
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#575C2
socleC2×C61#394
hypercenter#575D61
hypocenterC61#2053
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #16839790C2semidirect
2. #16839758C2semidirect
3. #16839736C2semidirect
4. #16839519C2semidirect
80. C61#2053semidirect