Finite Group Databasebeta

← #29567839

Subgroups — #29567839

Order 15616.

148 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 25 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#21444938C211yesmaximal, characteristic
2#21443986C211yesmaximal, characteristic
3C61×#1359C211yesmaximal, characteristic
4#16840498C411yescharacteristic
5#16840054—21no—
6#16839561—21no—
7#16839506C411yescharacteristic
8#16839494—21no—
9C61×#492C2211yescharacteristic
10C61×#364—21no—
11#14519764—41no—
12#14519758—41no—
13C4×Dic122—21no—
14D4×Dic61—41no—
15#14519710—41no—
16C4⋊#92418—21no—
17#14519700—41no—
18#14519696—41no—
19C2×SD16×C61—41no—
20C4⋊Q8×C61D411yescharacteristic
21#127×C61C2×C411yescharacteristic
22M32×C61—41no—
23C4×C8×C61D411yescharacteristic
24C2×Q8×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—41no—
27C22×Dic61—41no—
28C2×Dic122—21no—
29SD16×C61—81no—
30SD16×C61—81no—
31C2×C8×C61—21no—
32C4⋊C4×C61—41no—
33C42×C61C22⋊C411yescharacteristic
34C22⋊Dic61—42no—
35C22⋊Dic61—41no—
36C4⋊Dic61—21no—
37#11758196—41no—
38C4×Dic61—41no—
39#11758194—81no—
40C2×#92418—41no—
41C16×C61—81no—
42C23×C61—41no—
43Q8×C61—81no—
44D4×C61—81no—
45D4×C61—81no—
46D4×C61—81no—
47C2×C4×C61—21no—
48C2×C4×C61—41no—
49C2×C4×C61#9911yescharacteristic
50C2×Dic61—41no—
51C2×Dic61—41no—
52C2×Dic61—161no—
53Dic122—41no—
54Dic122—41no—
55C8×C61—21no—
56C8×C61—21no—
57#92418—81no—
58#92418—161no—
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—
67Dic61—81no—
68Dic61—81no—
69#1630—611no—
70#1410—611no—
71#1359D6111yescharacteristic
72C2×C61—21no—
73C2×C61—161no—
74C2×C61#140211yescharacteristic
75#559—611no—
76#492C2×D6111yescharacteristic
77#477—1221no—
78#364—21no—
79#356—1221no—
80#331—611no—
81Q8⋊C8—1221no—
82C61#751811yescharacteristic, complemented, Sylow
83C2×SD16—41no—
84C4⋊Q8D24411yescharacteristic
85#127C4×D6111yescharacteristic
86#124—2441no—
87#123—2441no—
88C4×Q8—1221no—
89C4×D4—2441no—
90M32—41no—
91#107—2441no—
92C4⋊C8—1221no—
93#103—2441no—
94#101—2441no—
95C4×C8C22⋊D6111yescharacteristic
96C2×Q8—21no—
97C2×Q8—1221no—
98C2×D4—21no—
99C2×D4—41no—
100C22×C4—2441no—
101SD16—81no—
102SD16—81no—
103M16—4881no—
104C2×C8—21no—
105C2×C8—2441no—
106C4⋊C4—41no—
107C4⋊C4—1221no—
108C4⋊C4—2441no—
109C22⋊C4—2442no—
110C22⋊C4—2441no—
111C42—2441no—
112C42#1175819811yescharacteristic
113C16—81no—
114C23—41no—
115Q8—81no—
116Q8—2441no—
117Q8—2441no—
118D4—81no—
119D4—81no—
120D4—81no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—9761no—
124C2×C4—2441no—
125C2×C4—2441no—
126C2×C4#1451969111yescharacteristic
127C8—21no—
128C8—21no—
129C8—9761no—
130C8—4881no—
131C22—82no—
132C22—81no—
133C22#1683955011yescharacteristic
134C4—21no—
135C4—21no—
136C4—21no—
137C4—81no—
138C4—4881no—
139C4—4881no—
140C2—21no—
141C2—161no—
142C2#2144396511yescharacteristic
subgroupG/H
centerC2#21443965
commutator, prime radical#127×C61C2×C4
Frattini#492C2×D61
FittingC61×#1359C2
socleC2×C61#1402
cosocleC61×#492C22
hypercenter#1359D61
hypocenterC61#7518
LCSG ▷ #127×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1359

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
#214449382
#214439862
C61×#13592
#751861