Finite Group Databasebeta

← #30595270

Subgroups — #30595270

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#21460962C211yesmaximal, characteristic, complemented
2#21460826C211yesmaximal, characteristic, complemented
3#21445142C211yesmaximal, characteristic
4#16840673—21no—
5#16840654—21no—
6#16840132C2211yescharacteristic
7#16840121—21no—
8#16839504C411yescharacteristic
9#16839502—21no—
10C61×#562C411yescharacteristic
11#14519851—41no—
12#14519838—41no—
13#14519777D411yescharacteristic
14#14519701—41no—
15#14519700—41no—
16#14519698—41no—
17#14519688—21no—
18#14519688D411yescharacteristic
19#125×C61C2×C411yescharacteristic
20#124×C61—21no—
21#123×C61—41no—
22C22⋊Q8×C61—41no—
23#121×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—
32C4⋊C4×C61—41no—
33C22⋊C4×C61—41no—
34C22⋊C4×C61—41no—
35C22⋊C4×C61—41no—
36C42×C61C22⋊C411yescharacteristic
37C4⋊Dic61—41no—
38C2×#92418—21no—
39C2×#92418—41no—
40#11758187—42no—
41C23×C61—41no—
42Q8×C61—81no—
43D4×C61—81no—
44D4×C61—161no—
45C2×C4×C61—21no—
46C2×C4×C61—41no—
47C2×C4×C61—41no—
48C2×C4×C61—161no—
49C2×C4×C61#9911yescharacteristic
50C2×Dic61—41no—
51Dic122—81no—
52#92420—161no—
53#92418—41no—
54#92418—81no—
55#7525—611nomaximal, Sylow
56C22×C61—81no—
57C22×C61—81no—
58C22×C61—81no—
59C22×C61AΣL(1,𝔽16)11yescharacteristic
60C4×C61—21no—
61C4×C61—41no—
62C4×C61—81no—
63C4×C61—81no—
64Dic61—81no—
65#1662—611no—
66#1413—611no—
67#1356—611no—
68C2×C61—21no—
69C2×C61—161no—
70C2×C61#140411yescharacteristic
71#562#692311yescharacteristic
72#491—611no—
73#489—1221no—
74#356—1221no—
75#347—1221no—
76#330—611no—
77#329—1221no—
78C61#752511yescharacteristic, complemented, Sylow
79C4⋊Q8—611no—
80#125C2×#692311yescharacteristic
81#124—21no—
82#123—41no—
83C22⋊Q8—41no—
84#121—41no—
85M32—2441no—
86#103—2441no—
87#103—2441no—
88#102—2441no—
89#101—2441no—
90#97—611no—
91#97—1221no—
92C2×Q8—21no—
93C2×Q8—1221no—
94C2×D4—21no—
95C2×D4—41no—
96C22×C4—41no—
97M16—4881no—
98C2×C8—1221no—
99C2×C8—2441no—
100C4⋊C4—21no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—2441no—
104C22⋊C4—41no—
105C22⋊C4—41no—
106C22⋊C4—41no—
107C42C22⋊#692311yescharacteristic
108C16—2442no—
109C23—41no—
110Q8—81no—
111Q8—4881no—
112D4—81no—
113D4—161no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—161no—
118C2×C4—2441no—
119C2×C4#1451983511yescharacteristic
120C8—9761no—
121C8—4881no—
122C8—2441no—
123C22—81no—
124C22—81no—
125C22—81no—
126C22#1684066211yescharacteristic
127C4—21no—
128C4—41no—
129C4—81no—
130C4—81no—
131C4—4881no—
132C2—21no—
133C2—161no—
134C2#2146094211yescharacteristic
subgroupG/H
centerC2#21460942
commutator#125×C61C2×C4
Frattini#125C2×#6923
Fitting, prime radicalC61×#562C4
socleC2×C61#1404
cosocle#16840132C22
hypercenter#562#6923
hypocenterC61#7525
LCSG ▷ #125×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #125 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #21460962C2semidirect
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
#214609622
#214608262
#214451422
#752561