Finite Group Databasebeta

← #29567848

Subgroups — #29567848

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#21444962C211yesmaximal, characteristic
2#21443988C211yesmaximal, characteristic, complemented
3C61×#1358C211yesmaximal, characteristic, complemented
4#16840478C411yescharacteristic
5#16840049—21no—
6#16839561—21no—
7#16839511C411yescharacteristic
8#16839491—21no—
9C61×#494C2211yescharacteristic
10C61×#364—21no—
11#14519766—41no—
12#14519752—41no—
13C4×D244—21no—
14#14519735—41no—
15#14519708—41no—
16C4⋊#92418—21no—
17#14519697—41no—
18#14519696—41no—
19C2×Q16×C61—41no—
20C4⋊Q8×C61C2×C411yescharacteristic
21C4⋊Q8×C61D411yescharacteristic
22M32×C61—41no—
23C4×C8×C61D411yescharacteristic
24C2×Q8×C61—21no—
25C2×Q8×C61—21no—
26C2×D244—21no—
27C2×D244—41no—
28C2×C4×D61—41no—
29Q16×C61—81no—
30Q16×C61—81no—
31C2×C8×C61—21no—
32C4⋊C4×C61—41no—
33C4⋊C4×C61—41no—
34C42×C61C22⋊C411yescharacteristic
35#11758198—42no—
36#11758198—41no—
37C4⋊Dic61—21no—
38C4×Dic61—41no—
39#11758194—81no—
40C2×#92418—41no—
41C16×C61—81no—
42C22×D61—41no—
43Q8×C61—81no—
44Q8×C61—81no—
45C2×C4×C61—21no—
46C2×C4×C61—41no—
47C2×C4×C61—41no—
48C2×C4×C61#9911yescharacteristic
49C2×Dic61—41no—
50D244—41no—
51D244—41no—
52D244—161no—
53C4×D61—81no—
54C4×D61—81no—
55C8×C61—21no—
56C8×C61—21no—
57#92418—81no—
58#92418—161no—
59#7521—611nomaximal, Sylow
60C22×C61AΣL(1,𝔽16)11yescharacteristic
61C2×D61—81no—
62C2×D61—81no—
63C2×D61—81no—
64C4×C61—21no—
65C4×C61—21no—
66C4×C61—21no—
67C4×C61—81no—
68C4×C61—81no—
69Dic61—81no—
70#1634—611no—
71#1411—611no—
72#1358D6111yescharacteristic, complemented
73C2×C61—21no—
74C2×C61#140211yescharacteristic
75D61—161no—
76#555—611no—
77#494C2×D6111yescharacteristic
78#476—1221no—
79#364—21no—
80#356—1221no—
81#333—611no—
82D4⋊C8—1221no—
83C61#752111yescharacteristic, complemented, Sylow
84C2×Q16—41no—
85C4⋊Q8C4×D6111yescharacteristic
86C4⋊Q8D24411yescharacteristic
87#124—2441no—
88#121—2441no—
89C4×D4—1221no—
90#117—2441no—
91M32—41no—
92#106—2441no—
93C4⋊C8—1221no—
94#102—2441no—
95#101—2441no—
96C4×C8C22⋊D6111yescharacteristic
97C2×Q8—21no—
98C2×Q8—21no—
99C2×D4—1221no—
100C2×D4—2441no—
101C22×C4—2441no—
102Q16—81no—
103Q16—81no—
104M16—4881no—
105C2×C8—21no—
106C2×C8—2441no—
107C4⋊C4—41no—
108C4⋊C4—41no—
109C4⋊C4—1221no—
110C22⋊C4—2442no—
111C22⋊C4—2441no—
112C42—2441no—
113C42#1175819811yescharacteristic
114C16—81no—
115C23—2441no—
116Q8—81no—
117Q8—81no—
118D4—9761no—
119D4—2441no—
120D4—2441no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—4881no—
125C2×C4—4881no—
126C2×C4—2441no—
127C2×C4#1451969111yescharacteristic
128C8—21no—
129C8—21no—
130C8—9761no—
131C8—4881no—
132C22—4881no—
133C22—4881no—
134C22—4881no—
135C22#1683955011yescharacteristic
136C4—21no—
137C4—21no—
138C4—21no—
139C4—81no—
140C4—81no—
141C4—4881no—
142C2—21no—
143C2—9761no—
144C2#2144396511yescharacteristic
subgroupG/H
centerC2#21443965
commutatorC4⋊Q8×C61C2×C4
Frattini#494C2×D61
FittingC61×#1358C2
socleC2×C61#1402
prime radical#16840478C4
cosocleC61×#494C22
hypercenter#1358D61
hypocenterC61#7521
LCSG ▷ C4⋊Q8×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #494 ◁ #1358

Complements

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

NH ≅ G/Ntype
2. #21443988C2semidirect
3. C61×#1358C2semidirect
72. #1358D61semidirect
83. C61#7521semidirect

Maximal subgroups

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

subgroupindex
#214449622
#214439882
C61×#13582
#752161