Finite Group Databasebeta

← #29567883

Subgroups — #29567883

Order 15616.

128 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 128 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#21445450C211yesmaximal, characteristic
2#21443988C211yesmaximal, characteristic
3C61×#1411C211yesmaximal, characteristic
4#16840160C411yescharacteristic
5#16840158—21no—
6#16840114—21no—
7#16839561—21no—
8#16839483C411yescharacteristic
9C61×#494C2211yescharacteristic
10C61×#356—21no—
11#14519777—21no—
12#14519709—41no—
13#14519708—42no—
14#14519700—42no—
15#14519696—41no—
16C4×#92418—21no—
17C2×Q16×C61—41no—
18C4⋊Q8×C61D411yescharacteristic
19C4⋊Q8×C61D411yescharacteristic
20#101×C61—41no—
21C4×C8×C61C2×C411yescharacteristic
22C2×Q8×C61—21no—
23C2×Q8×C61—21no—
24C2×Dic122—41no—
25Q16×C61—82no—
26M16×C61—81no—
27C2×C8×C61—21no—
28C4⋊C4×C61—41no—
29C4⋊C4×C61—41no—
30C42×C61C22⋊C411yescharacteristic
31C4⋊Dic61—41no—
32C4⋊Dic61—41no—
33#11758194—81no—
34C2×#92418—22no—
35Q8×C61—81no—
36Q8×C61—81no—
37C2×C4×C61—21no—
38C2×C4×C61—41no—
39C2×C4×C61—41no—
40C2×C4×C61#9911yescharacteristic
41C2×Dic61—81no—
42Dic122—82no—
43C8×C61—22no—
44C8×C61—161no—
45#92418—42no—
46#92418—161no—
47#7534—611nomaximal, Sylow
48C22×C61#35311yescharacteristic
49C4×C61—22no—
50C4×C61—21no—
51C4×C61—81no—
52C4×C61—81no—
53Dic61—161no—
54#1716—611no—
55#1411—611no—
56#1411D6111yescharacteristic
57C2×C61—21no—
58C2×C61#140911yescharacteristic
59#498—611no—
60#498—1221no—
61#494C2×D6111yescharacteristic
62#487—1221no—
63#356—21no—
64#356—1221no—
65#322—611no—
66C61#753411yescharacteristic, complemented, Sylow
67C2×Q16—41no—
68C4⋊Q8—1221no—
69C4⋊Q8D24411yescharacteristic
70C4⋊Q8C22⋊D6111yescharacteristic
71#106—2442no—
72#106—2441no—
73#103—2442no—
74#101—41no—
75#101—2441no—
76C4×C8—1221no—
77C4×C8C4×D6111yescharacteristic
78C2×Q8—21no—
79C2×Q8—21no—
80C2×Q8—2441no—
81Q16—82no—
82M16—81no—
83M16—4881no—
84C2×C8—21no—
85C2×C8—1222no—
86C4⋊C4—41no—
87C4⋊C4—41no—
88C4⋊C4—2441no—
89C4⋊C4—2441no—
90C42#1175819811yescharacteristic
91Q8—81no—
92Q8—81no—
93Q8—4882no—
94C2×C4—21no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—4881no—
98C2×C4#1451969111yescharacteristic
99C8—22no—
100C8—161no—
101C8—9761no—
102C8—2442no—
103C22#1683955411yescharacteristic
104C4—22no—
105C4—21no—
106C4—81no—
107C4—81no—
108C4—9761no—
109C2—21no—
110C2#2144398311yescharacteristic
subgroupG/H
centerC2#21443983
commutatorC4×C8×C61C2×C4
Frattini#494C2×D61
FittingC61×#1411C2
socleC2×C61#1409
prime radicalC22×C61#353
cosocleC61×#494C22
hypercenter#1411D61
hypocenterC61#7534
LCSG ▷ C4×C8×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #494 ◁ #1411

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
#214454502
#214439882
C61×#14112
#753461