Finite Group Databasebeta

← #30594845

Subgroups — #30594845

Order 15616.

222 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 36 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#21460765C212yesmaximal, complemented
2#21446647C211yesmaximal, characteristic
3#16840658—22no—
4#16840312C411yescharacteristic
5#16839786C2211yescharacteristic
6C2×#14519705—22no—
7C43×C61C411yescharacteristic
8#14519851—42no—
9C2×#11758222—21no—
10C2×#11758194D412yes—
11#14519777C811yescharacteristic
12#14519774C811yescharacteristic
13#14519765—21no—
14#14519751—41no—
15C4×D244—41no—
16C4⋊#92418—41no—
17#14519705—44no—
18C2×C42×C61—21no—
19C2×C42×C61—41no—
20C2×C42×C61C2×C411yescharacteristic
21C22×C4×C61—21no—
22C22×C4×C61—41no—
23C22×C4×C61C22⋊C411yescharacteristic
24C2×C22⋊D61—41no—
25#11758222—42no—
26#11758222—42no—
27C2×D244—21no—
28C2×D244—41no—
29C2×C4×D61—41no—
30C2×Dic122—21no—
31C42×C61—21no—
32C42×C61—22no—
33C42×C61—41no—
34C42×C61—44no—
35C42×C61C2×C811yescharacteristic
36C42×C61M1611yescharacteristic
37#11758198—42no—
38C4⋊Dic61—41no—
39#11758194—42no—
40C2×#92418—22no—
41#11758187—82no—
42C23×C61#10011yescharacteristic
43C22×D61—41no—
44C2×C4×C61—21no—
45C2×C4×C61—21no—
46C2×C4×C61—21no—
47C2×C4×C61—21no—
48C2×C4×C61—42no—
49C2×C4×C61—42no—
50C2×C4×C61—44no—
51C2×C4×C61C22⋊C811yescharacteristic
52C2×C4×C61#9911yescharacteristic
53C22⋊D61—82no—
54C2×Dic61—41no—
55D244—42no—
56D244—82no—
57C4×D61—81no—
58C4×D61—81no—
59Dic122—42no—
60#92418—42no—
61#7357—611nomaximal, Sylow
62C22×C61—21no—
63C22×C61—41no—
64C22×C61#32311yescharacteristic
65C2×D61—82no—
66C2×D61—81no—
67C4×C61—22no—
68C4×C61—21no—
69C4×C61—41no—
70C4×C61—44no—
71C4×C61#35311yescharacteristic
72C4×C61#35511yescharacteristic
73Dic61—81no—
74#1962—611no—
75#1327—612no—
76C2×C61—21no—
77C2×C61—41no—
78C2×C61#131811yescharacteristic
79D61—161no—
80#532—611no—
81#423—611no—
82C2×#104—1222no—
83C43#692311yescharacteristic
84#349—1222no—
85C61#735711yescharacteristic, complemented, Sylow
86C2×#41—1221no—
87C2×M16—612no—
88C4⋊Q8—611no—
89#127—611no—
90#124—1221no—
91#121—2441no—
92C4×D4—2441no—
93C2×C42—21no—
94C2×C42—41no—
95C2×C42C2×#692311yescharacteristic
96M32—2442no—
97C4⋊C8—2441no—
98#104—2444no—
99#41—2442no—
100#41—2442no—
101C2×Q8—1221no—
102C2×D4—1221no—
103C2×D4—2441no—
104C2×D4—2441no—
105C22×C4—21no—
106C22×C4—41no—
107C22×C4—2441no—
108C22×C4C22⋊#692311yescharacteristic
109M16—2442no—
110C2×C8—1222no—
111C4⋊C4—2441no—
112C22⋊C4—2442no—
113C42—21no—
114C42—22no—
115C42—41no—
116C42—44no—
117C42D61⋊C811yescharacteristic
118C42#1175821311yescharacteristic
119C16—4882no—
120C23—2441no—
121C23#1451983711yescharacteristic
122Q8—2442no—
123D4—4882no—
124D4—4882no—
125D4—2442no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—42no—
131C2×C4—42no—
132C2×C4—44no—
133C2×C4—4881no—
134C2×C4—4881no—
135C2×C4—2441no—
136C2×C4#1451983411yescharacteristic
137C2×C4#1451983611yescharacteristic
138C8—2442no—
139C22—21no—
140C22—41no—
141C22—4882no—
142C22—4881no—
143C22#1684060611yescharacteristic
144C4—22no—
145C4—21no—
146C4—41no—
147C4—44no—
148C4—4881no—
149C4#1684066711yescharacteristic
150C4#1684067111yescharacteristic
151C2—21no—
152C2—41no—
153C2—9761no—
154C2#2146074811yescharacteristic
subgroupG/H
centerC4#16840667
commutatorC42×C61C2×C8
FrattiniC2×C42C2×#6923
FittingC43×C61C4
socleC2×C61#1318
prime radical#16840312C4
cosocle#16839786C22
hypercenterC43#6923
hypocenterC61#7357
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
1. #21460765C2semidirect
85. C61#7357semidirect

Maximal subgroups

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

subgroupindex
#214607652
#214466472
#735761