Finite Group Databasebeta

← #30595291

Subgroups — #30595291

Order 15616.

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

normal subgroups only

This group has 128 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#21460957C211yesmaximal, characteristic
2#21460957C211yesmaximal, characteristic
3#21445453C211yesmaximal, characteristic
4#16840673—21no—
5#16840673—21no—
6#16840158—21no—
7#16840142C2211yescharacteristic
8#16840112—21no—
9#16839483C411yescharacteristic
10C61×#498C411yescharacteristic
11#14519838—41no—
12#14519838—41no—
13C2×Dic244—41no—
14#14519777D411yescharacteristic
15#14519777D411yescharacteristic
16#14519708—42no—
17#14519701—42no—
18C4×#92418—21no—
19C4⋊Q8×C61—21no—
20#106×C61—41no—
21C4×C8×C61C2×C411yescharacteristic
22C2×Q8×C61—41no—
23C2×Dic122—21no—
24C2×Dic122—21no—
25#11758217—81no—
26#11758217—81no—
27C2×C8×C61—21no—
28C4⋊C4×C61—41no—
29C4⋊C4×C61—41no—
30C42×C61C22⋊C411yescharacteristic
31C4⋊Dic61—41no—
32C4⋊Dic61—41no—
33C2×#92418—22no—
34Dic244—82no—
35Q8×C61—82no—
36C2×C4×C61—21no—
37C2×C4×C61—81no—
38C2×C4×C61#9911yescharacteristic
39C2×Dic61—41no—
40C2×Dic61—41no—
41Dic122—81no—
42Dic122—81no—
43#92420—161no—
44#92420—161no—
45C8×C61—22no—
46#92418—42no—
47#7534—611nomaximal, Sylow
48C22×C61#35311yescharacteristic
49C4×C61—22no—
50C4×C61—21no—
51C4×C61—161no—
52Dic61—81no—
53Dic61—81no—
54#1716—611no—
55#1411—611no—
56#1411—611no—
57C2×C61—21no—
58C2×C61#140911yescharacteristic
59#498—1221no—
60#498#692311yescharacteristic
61#494—611no—
62#487—1221no—
63#356—1221no—
64#356—1221no—
65#322—611no—
66C61#753411yescharacteristic, complemented, Sylow
67C2×Q16—2441no—
68C4⋊Q8—21no—
69C4⋊Q8—611no—
70C4⋊Q8—611no—
71#106—41no—
72#106—2442no—
73#103—2442no—
74#101—2441no—
75#101—2441no—
76C4×C8—1221no—
77C4×C8C2×#692311yescharacteristic
78C2×Q8—41no—
79C2×Q8—1221no—
80C2×Q8—1221no—
81Q16—4882no—
82M16—4881no—
83M16—4881no—
84C2×C8—21no—
85C2×C8—1222no—
86C4⋊C4—41no—
87C4⋊C4—41no—
88C4⋊C4—2441no—
89C4⋊C4—2441no—
90C42C22⋊#692311yescharacteristic
91Q8—82no—
92Q8—4881no—
93Q8—4881no—
94C2×C4—21no—
95C2×C4—81no—
96C2×C4—2441no—
97C2×C4—2441no—
98C2×C4#1451983511yescharacteristic
99C8—22no—
100C8—9761no—
101C8—9761no—
102C8—2442no—
103C22#1684066611yescharacteristic
104C4—22no—
105C4—21no—
106C4—161no—
107C4—4881no—
108C4—4881no—
109C2—21no—
110C2#2146095211yescharacteristic
subgroupG/H
centerC2#21460952
commutatorC4×C8×C61C2×C4
FrattiniC4×C8C2×#6923
FittingC61×#498C4
socleC2×C61#1409
prime radicalC22×C61#353
cosocle#16840142C22
hypercenter#498#6923
hypocenterC61#7534
LCSG ▷ C4×C8×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #498

Complements

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

NH ≅ G/Ntype
66. C61#7534semidirect

Maximal subgroups

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

subgroupindex
#214609572
#214454532
#753461