Finite Group Databasebeta

← #30595271

Subgroups — #30595271

Order 15616.

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

normal subgroups only

This group has 138 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#21460961C211yesmaximal, characteristic, complemented
2#21460826C211yesmaximal, characteristic, complemented
3#21445143C211yesmaximal, characteristic
4#16840673—21no—
5#16840654—21no—
6#16840510C411yescharacteristic
7#16840132C2211yescharacteristic
8#16840122—21no—
9#16839501—21no—
10C61×#330C411yescharacteristic
11#14519851—41no—
12#14519838—41no—
13#14519777D411yescharacteristic
14#14519765—21no—
15#14519762—41no—
16#14519755—41no—
17#14519752—41no—
18#14519702—41no—
19#14519700—41no—
20#14519699—41no—
21#14519688D411yescharacteristic
22#125×C61C2×C411yescharacteristic
23#97×C61—21no—
24C2×D244—21no—
25C2×D244—41no—
26C2×C4×D61—41no—
27C2×Dic122—21no—
28C2×Dic122—21no—
29#11758217—81no—
30C2×C8×C61—41no—
31C4⋊C4×C61—21no—
32C4⋊C4×C61—41no—
33C42×C61C22⋊C411yescharacteristic
34#11758198—41no—
35#11758198—41no—
36#11758198—41no—
37C4⋊Dic61—41no—
38#11758196—41no—
39C2×#92418—21no—
40#11758187—42no—
41C22×D61—41no—
42C2×C4×C61—21no—
43C2×C4×C61—41no—
44C2×C4×C61#9911yescharacteristic
45C2×Dic61—41no—
46C2×Dic61—41no—
47D244—81no—
48D244—161no—
49C4×D61—161no—
50Dic122—81no—
51Dic122—81no—
52#92420—161no—
53C8×C61—81no—
54#92418—41no—
55#7525—611nomaximal, Sylow
56C22×C61AΣL(1,𝔽16)11yescharacteristic
57C2×D61—81no—
58C2×D61—81no—
59C2×D61—81no—
60C4×C61—21no—
61C4×C61—41no—
62C4×C61—81no—
63Dic61—81no—
64Dic61—81no—
65#1662—611no—
66#1413—611no—
67#1356—611no—
68C2×C61—21no—
69C2×C61#140411yescharacteristic
70D61—161no—
71#562—611no—
72#491—611no—
73#489—1221no—
74#356—1221no—
75#347—1221no—
76#330#692311yescharacteristic
77#329—1221no—
78C61#752511yescharacteristic, complemented, Sylow
79C4⋊Q8—611no—
80#125C2×#692311yescharacteristic
81#124—1221no—
82#123—2441no—
83C22⋊Q8—2441no—
84#121—2441no—
85M32—2441no—
86#103—2441no—
87#103—2441no—
88#102—2441no—
89#101—2441no—
90#97—21no—
91#97—611no—
92C2×Q8—1221no—
93C2×Q8—1221no—
94C2×D4—1221no—
95C2×D4—2441no—
96C22×C4—2441no—
97M16—4881no—
98C2×C8—41no—
99C2×C8—1221no—
100C4⋊C4—21no—
101C4⋊C4—41no—
102C4⋊C4—2441no—
103C4⋊C4—2441no—
104C22⋊C4—2441no—
105C22⋊C4—2441no—
106C22⋊C4—2441no—
107C42C22⋊#692311yescharacteristic
108C16—2442no—
109C23—2441no—
110Q8—4881no—
111Q8—4881no—
112D4—9761no—
113D4—4881no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—9761no—
117C2×C4—2441no—
118C2×C4—2441no—
119C2×C4#1451983611yescharacteristic
120C8—81no—
121C8—9761no—
122C8—2441no—
123C22—4881no—
124C22—4881no—
125C22—4881no—
126C22#1684066311yescharacteristic
127C4—21no—
128C4—41no—
129C4—81no—
130C4—4881no—
131C4—4881no—
132C2—21no—
133C2—9761no—
134C2#2146094311yescharacteristic
subgroupG/H
centerC2#21460943
commutator#125×C61C2×C4
Frattini#125C2×#6923
FittingC61×#330C4
socleC2×C61#1404
prime radical#16840510C4
cosocle#16840132C22
hypercenter#330#6923
hypocenterC61#7525
LCSG ▷ #125×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #125 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #21460961C2semidirect
2. #21460826C2semidirect
78. C61#7525semidirect

Maximal subgroups

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

subgroupindex
#214609612
#214608262
#214451432
#752561