Finite Group Databasebeta

← #30594960

Subgroups — #30594960

Order 15616.

166 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 32 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#21460907C211yesmaximal, characteristic
2#21460754C211yesmaximal, characteristic
3#21447265C211yesmaximal, characteristic
4#16840741—21no—
5#16840658—21no—
6#16839761—21no—
7#16839728C2211yescharacteristic
8#16839531—21no—
9#16839527C411yescharacteristic, complemented
10C2×#106×C61C411yescharacteristic, complemented
11#14519856—41no—
12#14519851—41no—
13#14519836—41no—
14#14519835—22no—
15C2×#11758222D411yescharacteristic
16C2×#11758194—21no—
17C2×#11758194D411yescharacteristic
18#14519700—41no—
19#14519697—41no—
20#14519689—41no—
21C22×C8×C61C2×C411yescharacteristic
22C2×C4⋊C4×C61—21no—
23#106×C61—41no—
24C22×C4×C61—41no—
25C22×C4×C61C22⋊C411yescharacteristic
26C2×C22⋊D61—21no—
27#11758222—41no—
28#11758222—41no—
29C2×D244D811yescharacteristic
30C2×C4×D61—21no—
31C2×Dic122SD1611yescharacteristic
32C22⋊#6923—42no—
33C4⋊#6923—81no—
34C4×#6923—81no—
35C2×C8×C61—21no—
36C2×C8×C61—41no—
37C4⋊C4×C61—41no—
38C4⋊C4×C61—41no—
39#11758194—41no—
40#11758194—41no—
41#11758194—41no—
42C2×#92418—21no—
43C2×#92418—41no—
44#11758187—81no—
45C23×C61#10411yescharacteristic
46C22×D61—21no—
47C2×#6923—82no—
48C2×C4×C61—21no—
49C2×C4×C61—21no—
50C2×C4×C61—81no—
51C2×C4×C61—161no—
52C2×C4×C61#9911yescharacteristic
53C2×C4×C61#10211yescharacteristic
54C22⋊D61—81no—
55C2×Dic61—21no—
56D244—41no—
57C4×D61—41no—
58C4×D61—41no—
59Dic122—41no—
60C8×C61—41no—
61#92418—41no—
62#92418—81no—
63#7410—611nomaximal, Sylow
64C22×C61—21no—
65C22×C61—41no—
66C22×C61#32711yescharacteristic
67C2×D61—41no—
68C2×D61—81no—
69#6923—162no—
70C4×C61—21no—
71C4×C61—161no—
72C4×C61#35211yescharacteristic
73C4×C61#35411yescharacteristic
74Dic61—41no—
75#2079—611no—
76#1391—611no—
77#1321—611no—
78C2×C61—21no—
79C2×C61—41no—
80C2×C61#134411yescharacteristic
81D61—81no—
82C2×#106#692311yescharacteristic, complemented
83#417—1221no—
84#410—1221no—
85#408—611no—
86#349—1221no—
87#343—1221no—
88#341—611no—
89C61#741011yescharacteristic, complemented, Sylow
90C2×#41—611no—
91C2×M16—611no—
92C2×M16—1221no—
93C22×C8C2×#692311yescharacteristic
94#117—2441no—
95C2×C4⋊C4—21no—
96M32—2441no—
97#106—41no—
98#103—2441no—
99#102—2441no—
100#99—1222no—
101#99—2441no—
102C22⋊C8—2441no—
103#41—2441no—
104#41—2441no—
105C2×Q8—611no—
106C2×D4—611no—
107C2×D4—1221no—
108C22×C4—41no—
109C22×C4—1221no—
110C22×C4C22⋊#692311yescharacteristic
111M16—2441no—
112M16—2441no—
113M16—2441no—
114C2×C8—21no—
115C2×C8—41no—
116C2×C8—1221no—
117C2×C8—2441no—
118C4⋊C4—41no—
119C4⋊C4—41no—
120C4⋊C4—4881no—
121C22⋊C4—2442no—
122C42—4881no—
123C16—4881no—
124C23—1221no—
125C23#1451984111yescharacteristic
126Q8—2441no—
127D4—4881no—
128D4—2441no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—81no—
132C2×C4—161no—
133C2×C4—1221no—
134C2×C4—4882no—
135C2×C4—2441no—
136C2×C4—2441no—
137C2×C4#1451983511yescharacteristic
138C2×C4#1451983911yescharacteristic
139C8—41no—
140C8—4881no—
141C8—2441no—
142C22—21no—
143C22—41no—
144C22—4881no—
145C22—2441no—
146C22#1684061311yescharacteristic
147C4—21no—
148C4—161no—
149C4—9762no—
150C4—2441no—
151C4#1684066411yescharacteristic
152C4#1684066811yescharacteristic
153C2—21no—
154C2—41no—
155C2—4881no—
156C2#2146079911yescharacteristic
subgroupG/H
centerC2#21460799
commutatorC22×C8×C61C2×C4
FrattiniC22×C8C2×#6923
FittingC2×#106×C61C4
socleC2×C61#1344
prime radicalC2×#11758222D4
cosocle#16839728C22
hypercenterC2×#106#6923
hypocenterC61#7410
LCSG ▷ C22×C8×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
9. #16839527C4semidirect
10. C2×#106×C61C4semidirect
82. C2×#106#6923semidirect
89. C61#7410semidirect

Maximal subgroups

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

subgroupindex
#214609072
#214607542
#214472652
#741061