Finite Group Databasebeta

← #30595280

Subgroups — #30595280

Order 15616.

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

normal subgroups only

This group has 142 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#21460955C211yesmaximal, characteristic
2#21460953C211yesmaximal, characteristic
3#21445490C211yesmaximal, characteristic
4#16840673—21no—
5#16840667—21no—
6#16840167—21no—
7#16840142C411yescharacteristic, complemented
8#16840135C2211yescharacteristic
9#16840109—21no—
10C61×#322C411yescharacteristic, complemented
11#14519838—41no—
12#14519836—41no—
13C2×Dic244—41no—
14C2×#11758190—41no—
15#14519777—21no—
16#14519777D411yescharacteristic
17#14519774D411yescharacteristic
18#14519711—42no—
19#14519699—42no—
20C4×C8×C61—21no—
21C4×C8×C61C2×C411yescharacteristic
22C2×D244—21no—
23C2×D244—41no—
24C2×Dic122—21no—
25C2×Dic122—41no—
26C22⋊#6923—81no—
27#11758217—81no—
28C2×C8×C61—21no—
29C2×C8×C61—22no—
30C42×C61C22⋊C411yescharacteristic
31C4⋊Dic61—41no—
32C4⋊Dic61—41no—
33C4⋊Dic61—41no—
34Dic244—82no—
35#11758190—82no—
36C22×D61—41no—
37C2×#6923—161no—
38C2×C4×C61—21no—
39C2×C4×C61#9911yescharacteristic
40C2×Dic61—41no—
41C2×Dic61—81no—
42D244—81no—
43D244—82no—
44Dic122—81no—
45Dic122—82no—
46#92420—161no—
47C8×C61—22no—
48C8×C61—42no—
49#7528—611nomaximal, Sylow
50C22×C61#35311yescharacteristic
51C2×D61—81no—
52C2×D61—161no—
53#6923—321no—
54C4×C61—22no—
55C4×C61—21no—
56Dic61—81no—
57Dic61—161no—
58#1722—611no—
59#1410—611no—
60#1409—611no—
61C2×C61—21no—
62C2×C61#140811yescharacteristic
63D61—161no—
64#500—1221no—
65#494—611no—
66#492—611no—
67#486—1221no—
68#356—1221no—
69#353—1221no—
70#322#692311yescharacteristic, complemented
71C61#752811yescharacteristic, complemented, Sylow
72C2×Q16—2441no—
73C2×SD16—2441no—
74C4⋊Q8—611no—
75C4⋊Q8—1221no—
76#127—611no—
77#107—2442no—
78#102—2442no—
79#101—2441no—
80#99—2441no—
81C4×C8—21no—
82C4×C8C2×#692311yescharacteristic
83C2×Q8—1221no—
84C2×Q8—2441no—
85C2×D4—1221no—
86C2×D4—2441no—
87Q16—4882no—
88SD16—4882no—
89M16—4881no—
90C2×C8—21no—
91C2×C8—22no—
92C4⋊C4—2441no—
93C4⋊C4—2441no—
94C4⋊C4—2441no—
95C22⋊C4—4881no—
96C42C22⋊#692311yescharacteristic
97C23—2441no—
98Q8—4882no—
99Q8—4881no—
100D4—4882no—
101D4—4881no—
102C2×C4—21no—
103C2×C4—9761no—
104C2×C4—4881no—
105C2×C4—2441no—
106C2×C4#1451983611yescharacteristic
107C8—22no—
108C8—42no—
109C8—9761no—
110C22—9761no—
111C22—4881no—
112C22#1684066711yescharacteristic
113C4—22no—
114C4—21no—
115C4—19521no—
116C4—9761no—
117C4—4881no—
118C2—21no—
119C2—9761no—
120C2#2146095111yescharacteristic
subgroupG/H
centerC2#21460951
commutatorC4×C8×C61C2×C4
FrattiniC4×C8C2×#6923
FittingC61×#322C4
socleC2×C61#1408
prime radical#14519774D4
cosocle#16840135C22
hypercenter#322#6923
hypocenterC61#7528
LCSG ▷ C4×C8×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #322

Complements

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

NH ≅ G/Ntype
7. #16840142C4semidirect
10. C61×#322C4semidirect
70. #322#6923semidirect
71. C61#7528semidirect

Maximal subgroups

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

subgroupindex
#214609552
#214609532
#214454902
#752861