Finite Group Databasebeta

← #30595251

Subgroups — #30595251

Order 15616.

148 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 22 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#21460954C211yesmaximal, characteristic
2#21460829C211yesmaximal, characteristic
3#21444940C211yesmaximal, characteristic
4#16840685—21no—
5#16840673—21no—
6#16840134C2211yescharacteristic
7#16840057—21no—
8#16839506C411yescharacteristic
9Q8⋊#92418—21no—
10C61×#559C411yescharacteristic
11#14519851—41no—
12#14519838—41no—
13C2×#11758200—41no—
14#14519777D411yescharacteristic
15#14519710—41no—
16C4⋊#92418—21no—
17#14519701—41no—
18C4×#92418D411yescharacteristic
19#127×C61C2×C411yescharacteristic
20#124×C61—41no—
21#123×C61—41no—
22C4×Q8×C61—21no—
23C4×D4×C61—41no—
24C2×Q8×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—41no—
27C22×C4×C61—41no—
28C2×Dic122—21no—
29#11758217—81no—
30C4⋊C4×C61—21no—
31C4⋊C4×C61—41no—
32C22⋊C4×C61—42no—
33C22⋊C4×C61—41no—
34C42×C61—41no—
35C42×C61C22⋊C411yescharacteristic
36#11758200—81no—
37#11758200—81no—
38C4⋊Dic61—41no—
39C2×#92418—21no—
40C2×#92418—41no—
41#11758187—81no—
42C23×C61—41no—
43Q8×C61—41no—
44Q8×C61—41no—
45D4×C61—81no—
46D4×C61—81no—
47D4×C61—81no—
48C2×C4×C61—21no—
49C2×C4×C61—41no—
50C2×C4×C61—41no—
51C2×C4×C61—161no—
52C2×C4×C61#9911yescharacteristic
53C2×Dic61—41no—
54Dic122—81no—
55#92420—161no—
56#92418—21no—
57#92418—21no—
58#92418—81no—
59#7518—611nomaximal, Sylow
60C22×C61—82no—
61C22×C61—81no—
62C22×C61AΣL(1,𝔽16)11yescharacteristic
63C4×C61—21no—
64C4×C61—21no—
65C4×C61—21no—
66C4×C61—81no—
67C4×C61—81no—
68Dic61—81no—
69#1630—611no—
70#1410—611no—
71#1359—611no—
72C2×C61—21no—
73C2×C61—161no—
74C2×C61#140211yescharacteristic
75#559#692311yescharacteristic
76#492—611no—
77#477—1221no—
78#364—1221no—
79#356—1221no—
80#331—611no—
81Q8⋊C8—1221no—
82C61#751811yescharacteristic, complemented, Sylow
83C2×SD16—2441no—
84C4⋊Q8—611no—
85#127C2×#692311yescharacteristic
86#124—41no—
87#123—41no—
88C4×Q8—21no—
89C4×D4—41no—
90M32—2441no—
91#107—2441no—
92C4⋊C8—1221no—
93#103—2441no—
94#101—2441no—
95C4×C8—611no—
96C2×Q8—21no—
97C2×Q8—1221no—
98C2×D4—21no—
99C2×D4—41no—
100C22×C4—41no—
101SD16—4881no—
102SD16—4881no—
103M16—4881no—
104C2×C8—1221no—
105C2×C8—2441no—
106C4⋊C4—21no—
107C4⋊C4—41no—
108C4⋊C4—2441no—
109C22⋊C4—42no—
110C22⋊C4—41no—
111C42—41no—
112C42C22⋊#692311yescharacteristic
113C16—4881no—
114C23—41no—
115Q8—41no—
116Q8—41no—
117Q8—4881no—
118D4—81no—
119D4—81no—
120D4—81no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—161no—
125C2×C4—2441no—
126C2×C4#1451983511yescharacteristic
127C8—1221no—
128C8—1221no—
129C8—9761no—
130C8—4881no—
131C22—82no—
132C22—81no—
133C22#1684066211yescharacteristic
134C4—21no—
135C4—21no—
136C4—21no—
137C4—81no—
138C4—81no—
139C4—4881no—
140C2—21no—
141C2—161no—
142C2#2146093811yescharacteristic
subgroupG/H
centerC2#21460938
commutator, prime radical#127×C61C2×C4
Frattini#127C2×#6923
FittingC61×#559C4
socleC2×C61#1402
cosocle#16840134C22
hypercenter#559#6923
hypocenterC61#7518
LCSG ▷ #127×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #127 ◁ #559

Complements

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

NH ≅ G/Ntype
82. C61#7518semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214609542
#214608292
#214449402
#751861