Finite Group Databasebeta

← #20244855

Subgroups — #20244855

Order 6016.

184 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 59 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#15689171C211yesmaximal, characteristic
2#15689132C211yesmaximal, characteristic
3#15689132C211yesmaximal, characteristic
4#15688895C211yesmaximal, characteristic
5#15688894C211yesmaximal, characteristic
6#15688880C211yesmaximal, characteristic
7C2×#101×C47C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10#13093983C2211yescharacteristic
11#13093983C2211yescharacteristic
12#13093959—22no—
13#13093948—22no—
14#13093948—22no—
15C22×Q8×C47C2211yescharacteristic
16C2×M16×C47C2211yescharacteristic
17C2×M16×C47C2211yescharacteristic
18#101×C47—22no—
19C2×Q8×C47—21no—
20C2×Q8×C47—21no—
21C2×Q8×C47—21no—
22C2×Q8×C47—21no—
23C2×Q8×C47—21no—
24C2×Q8×C47D412yes—
25C22×C4×C47—21no—
26C22×C4×C47C2311yescharacteristic
27M16×C47—21no—
28M16×C47—21no—
29M16×C47—21no—
30M16×C47—21no—
31C2×C8×C47—21no—
32C2×C8×C47—21no—
33C22⋊Dic47—21no—
34C22⋊Dic47—21no—
35C4⋊Dic47—21no—
36C4⋊Dic47—21no—
37C4×Dic47—21no—
38C4×Dic47—21no—
39#10625329—21no—
40#10625329—21no—
41#10625329—21no—
42#10625329—21no—
43C2×C47⋊C8—21no—
44C2×C47⋊C8D412yes—
45C23×C47#4111yescharacteristic
46Q8×C47—22no—
47Q8×C47—22no—
48Q8×C47—41no—
49Q8×C47—41no—
50C2×C4×C47—22no—
51C2×C4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47C2×D411yescharacteristic
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47#4111yescharacteristic
56C2×C4×C47#4111yescharacteristic
57C2×C4×C47#4111yescharacteristic
58C2×C4×C47#4111yescharacteristic
59C2×Dic47—41no—
60C2×Dic47—41no—
61C8×C47—41no—
62C8×C47—41no—
63C47⋊C8—22no—
64C47⋊C8—41no—
65C22×C47—41no—
66C22×C47#12311yescharacteristic
67C22×C47#12411yescharacteristic
68C22×C47#12611yescharacteristic
69C4×C47—42no—
70C4×C47#12111yescharacteristic
71C4×C47#12311yescharacteristic
72C4×C47#12311yescharacteristic
73C4×C47#12611yescharacteristic
74Dic47—81no—
75Dic47—81no—
76#2082—471nomaximal, Sylow
77C2×C47—21no—
78C2×C47—21no—
79C2×C47—21no—
80C2×C47#39711yescharacteristic
81#430—471no—
82#419—471no—
83#419—471no—
84C2×#101D4711yescharacteristic
85#344—471no—
86#344—471no—
87H(3,ℤ/4)—471no—
88C47#208211yescharacteristic, complemented, Sylow
89C22×Q8C2×D4711yescharacteristic
90C2×M16—471no—
91C2×M16—471no—
92C2×M16C2×D4711yescharacteristic
93C2×M16C2×D4711yescharacteristic
94#117—471no—
95#117—471no—
96#108—942no—
97#103—942no—
98#103—942no—
99#101—22no—
100C2×Q8—21no—
101C2×Q8—21no—
102C2×Q8—21no—
103C2×Q8—21no—
104C2×Q8—21no—
105C2×Q8C22⋊D4712yes—
106C22×C4—21no—
107C22×C4C22×D4711yescharacteristic
108M16—21no—
109M16—21no—
110M16—21no—
111M16—21no—
112M16—941no—
113M16—941no—
114M16—941no—
115M16—941no—
116C2×C8—21no—
117C2×C8—21no—
118C2×C8—472no—
119C2×C8—941no—
120C4⋊C4—941no—
121C4⋊C4—941no—
122C22⋊C4—941no—
123C22⋊C4—941no—
124C42—941no—
125C42—941no—
126C23#1062535011yescharacteristic
127Q8—22no—
128Q8—22no—
129Q8—41no—
130Q8—41no—
131C2×C4—22no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—1881no—
135C2×C4—1881no—
136C2×C4#1062535011yescharacteristic
137C2×C4D4×D4711yescharacteristic
138C2×C4#1062535211yescharacteristic
139C2×C4#1062535211yescharacteristic
140C2×C4#1062535211yescharacteristic
141C2×C4C2×C22⋊D4711yescharacteristic
142C8—41no—
143C8—41no—
144C8—942no—
145C8—1881no—
146C22—41no—
147C22#1309400711yescharacteristic
148C22#1309401011yescharacteristic
149C22#1309401711yescharacteristic
150C4—42no—
151C4—3761no—
152C4—3761no—
153C4#1309399611yescharacteristic
154C4#1309400511yescharacteristic
155C4#1309400611yescharacteristic
156C4#1309401711yescharacteristic
157C2—21no—
158C2—21no—
159C2—21no—
160C2#1568905111yescharacteristic
subgroupG/H
centerC2#15689051
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#101×C47C2
socleC2×C47#397
hypercenterC2×#101D47
hypocenterC47#2082
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
88. C47#2082semidirect