Finite Group Databasebeta

← #30595016

Subgroups — #30595016

Order 15616.

210 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 32 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#21460752C211yesmaximal, characteristic
2#21460699C211yesmaximal, characteristic
3#21447336C211yesmaximal, characteristic
4C4×C22⋊#6923—21no—
5#16840658—21no—
6#16839811—21no—
7#16839811C411yescharacteristic, complemented
8#16839725—21no—
9#16839725C2211yescharacteristic
10C61×#338C411yescharacteristic, complemented
11C2×C22⋊#6923—41no—
12C2×C4×#6923—41no—
13#14519851—41no—
14(C2×#6923)⋊C4—22no—
15C22×C4×D61D411yescharacteristic
16C2×#11758194—21no—
17C2×#11758194D411yescharacteristic
18#14519713—42no—
19#14519713—41no—
20#14519689—41no—
21#14519689—42no—
22C2×M16×C61—21no—
23C2×M16×C61C2×C411yescharacteristic
24C23×D61SD1611yescharacteristic
25C22×#6923—42no—
26C22×C4×C61C22⋊C411yescharacteristic
27C22×Dic61Q1611yescharacteristic
28C2×C4×D61—21no—
29C2×C4×D61—21no—
30C2×C4×D61—41no—
31C2×C4×D61—41no—
32C22⋊#6923—44no—
33C4×#6923—81no—
34C4×#6923—81no—
35M16×C61—41no—
36M16×C61—41no—
37M16×C61—41no—
38C2×C8×C61—22no—
39C2×C8×C61—21no—
40#11758194—41no—
41#11758194—41no—
42#11758194—41no—
43C2×#92418—21no—
44C2×#92418—41no—
45#11758187—81no—
46C23×C61#10311yescharacteristic
47C22×D61—21no—
48C22×D61—42no—
49C22×D61—41no—
50C2×#6923—44no—
51C2×#6923—82no—
52C2×#6923—82no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61#9911yescharacteristic
56C2×C4×C61#10411yescharacteristic
57C2×Dic61—21no—
58C2×Dic61—41no—
59C4×D61—41no—
60C4×D61—41no—
61C4×D61—81no—
62C8×C61—42no—
63C8×C61—41no—
64#92418—41no—
65#92418—81no—
66#7432—611nomaximal, Sylow
67C22×C61—21no—
68C22×C61—41no—
69C22×C61#32811yescharacteristic
70C2×D61—22no—
71C2×D61—41no—
72C2×D61—41no—
73C2×D61—42no—
74C2×D61—81no—
75#6923—84no—
76C4×C61—21no—
77C4×C61#35211yescharacteristic
78C4×C61#35311yescharacteristic
79Dic61—41no—
80#2091—611no—
81#1320—611no—
82#1297—611no—
83C2×C61—21no—
84C2×C61—41no—
85C2×C61#135211yescharacteristic
86D61—42no—
87#430—611no—
88#430—1221no—
89#407—611no—
90#407—1221no—
91C4×C22⋊C4—1221no—
92#349—1221no—
93#338#692311yescharacteristic, complemented
94C61#743211yescharacteristic, complemented, Sylow
95C23×C4—611no—
96C2×M16—21no—
97C2×M16—611no—
98C2×M16—1221no—
99C2×M16C2×#692311yescharacteristic
100C2×C22⋊C4—2441no—
101C2×C42—2441no—
102M32—2441no—
103#108—2441no—
104#108—2442no—
105C22⋊C8—2441no—
106C22⋊C8—2442no—
107#95—1222no—
108C24—611no—
109C22×C4—611no—
110C22×C4—1221no—
111C22×C4—1221no—
112C22×C4—2441no—
113C22×C4—2441no—
114C22×C4—2442no—
115C22×C4C22⋊#692311yescharacteristic
116M16—41no—
117M16—41no—
118M16—41no—
119M16—2441no—
120M16—2441no—
121M16—2441no—
122C2×C8—22no—
123C2×C8—21no—
124C2×C8—1221no—
125C2×C8—2441no—
126C22⋊C4—2444no—
127C42—4881no—
128C42—4881no—
129C16—4881no—
130C23—1221no—
131C23—2441no—
132C23—2442no—
133C23#1451984011yescharacteristic
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—1221no—
137C2×C4—4881no—
138C2×C4—4882no—
139C2×C4—4882no—
140C2×C4—2444no—
141C2×C4—2441no—
142C2×C4—2441no—
143C2×C4—2441no—
144C2×C4#1451983611yescharacteristic
145C2×C4#1451984111yescharacteristic
146C8—42no—
147C8—41no—
148C8—4881no—
149C8—2441no—
150C22—21no—
151C22—41no—
152C22—1222no—
153C22—4881no—
154C22—2441no—
155C22—2442no—
156C22—2441no—
157C22#1684061511yescharacteristic
158C4—21no—
159C4—4884no—
160C4—2441no—
161C4#1684066511yescharacteristic
162C4#1684066711yescharacteristic
163C2—21no—
164C2—41no—
165C2—2442no—
166C2#2146081511yescharacteristic
subgroupG/H
centerC4#16840667
commutatorC2×M16×C61C2×C4
FrattiniC2×M16C2×#6923
FittingC61×#338C4
socleC2×C61#1352
prime radicalC23×D61SD16
cosocle#16839725C22
hypercenter#338#6923
hypocenterC61#7432
LCSG ▷ C2×M16×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ #338

Complements

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

NH ≅ G/Ntype
7. #16839811C4semidirect
10. C61×#338C4semidirect
93. #338#6923semidirect
94. C61#7432semidirect

Maximal subgroups

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

subgroupindex
#214607522
#214606992
#214473362
#743261