Finite Group Databasebeta

← #30594993

Subgroups — #30594993

Order 15616.

150 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 34 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#21460935C211yesmaximal, characteristic, complemented
2#21460887C211yesmaximal, characteristic, complemented
3#21447923C211yesmaximal, characteristic
4#16840772—21no—
5#16840694—21no—
6C2×D976C411yescharacteristic, complemented
7C2×#14519716C2211yescharacteristic
8#16839999—21no—
9#16839562—21no—
10C61×#367C411yescharacteristic, complemented
11#14519856—41no—
12#14519846—41no—
13#14519845—22no—
14#14519827—41no—
15C2×D488—21no—
16C2×C8×D61D411yescharacteristic
17#14519752—41no—
18D976—41no—
19#14519716—41no—
20C2×#11758185D411yescharacteristic
21#14519697—41no—
22C2×C16×C61C2×C411yescharacteristic
23#107×C61—21no—
24C2×D244—41no—
25C2×D244—81no—
26C2×C4×D61D811yescharacteristic
27C22⋊#6923—81no—
28C4⋊#6923—42no—
29C4×#6923—81no—
30C2×C8×C61C22⋊C411yescharacteristic
31C4⋊C4×C61—41no—
32#11758198—81no—
33C2×#92418SD1611yescharacteristic
34D488—41no—
35D488—41no—
36C8×D61—21no—
37C8×D61—21no—
38C16×C61—21no—
39#11758185—21no—
40C22×D61—81no—
41C22×D61D1611yescharacteristic
42C2×#6923—82no—
43C2×C4×C61—81no—
44C2×C4×C61#10211yescharacteristic
45C2×Dic61SD3211yescharacteristic
46D244—81no—
47D244—81no—
48D244—162no—
49C4×D61—21no—
50C4×D61—21no—
51C8×C61#9911yescharacteristic
52C8×C61#10411yescharacteristic
53#92418—21no—
54#7422—611nomaximal, Sylow
55C22×C61#35711yescharacteristic
56C2×D61—21no—
57C2×D61—41no—
58C2×D61—161no—
59C2×D61—161no—
60C2×D61—161no—
61#6923—162no—
62C4×C61—161no—
63C4×C61#32711yescharacteristic
64C4×C61#36011yescharacteristic
65Dic61—21no—
66#2218—611no—
67#1400—611no—
68#1384—611no—
69C2×C61—21no—
70C2×C61#134711yescharacteristic
71D61—41no—
72D61—321no—
73C2×D16—611no—
74C2×M32—611no—
75#466—1221no—
76#427—1221no—
77M64—1221no—
78#367#692311yescharacteristic, complemented
79#357—1221no—
80C61#742211yescharacteristic, complemented, Sylow
81C2×D8—1221no—
82C22×C8—611no—
83#121—2441no—
84#117—2441no—
85D16—2441no—
86M32—2441no—
87C2×C16—611no—
88C2×C16C2×#692311yescharacteristic
89#107—21no—
90#107—2441no—
91#106—1222no—
92#102—2441no—
93C32—2441no—
94C2×D4—4881no—
95C2×D4—2441no—
96C22×C4—611no—
97D8—2441no—
98D8—2441no—
99C2×C8—611no—
100C2×C8—1221no—
101C2×C8—1221no—
102C2×C8C22⋊#692311yescharacteristic
103C4⋊C4—41no—
104C4⋊C4—2442no—
105C22⋊C4—4881no—
106C22⋊C4—4881no—
107C42—4881no—
108C16—21no—
109C16—1221no—
110C23—611no—
111C23—4881no—
112D4—9762no—
113D4—4881no—
114D4—4881no—
115C2×C4—81no—
116C2×C4—611no—
117C2×C4—1221no—
118C2×C4—1221no—
119C2×C4—4882no—
120C2×C4#1451983911yescharacteristic
121C8—1221no—
122C8#1451983611yescharacteristic
123C8#1451984211yescharacteristic
124C22—1221no—
125C22—9761no—
126C22—9761no—
127C22—9761no—
128C22—2441no—
129C22#1684067411yescharacteristic
130C4—161no—
131C4—1221no—
132C4—9762no—
133C4#1684061411yescharacteristic
134C4#1684067911yescharacteristic
135C2—21no—
136C2—19521no—
137C2—2441no—
138C2#2146080611yescharacteristic
subgroupG/H
centerC2#21460806
commutatorC2×C16×C61C2×C4
FrattiniC2×C16C2×#6923
FittingC61×#367C4
socleC2×C61#1347
prime radical#21447923C2
cosocleC2×#14519716C22
hypercenter#367#6923
hypocenterC61#7422
LCSG ▷ C2×C16×C61 ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #367

Complements

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

NH ≅ G/Ntype
1. #21460935C2semidirect
2. #21460887C2semidirect
6. C2×D976C4semidirect
10. C61×#367C4semidirect
78. #367#6923semidirect
80. C61#7422semidirect

Maximal subgroups

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

subgroupindex
#214609352
#214608872
#214479232
#742261