Finite Group Databasebeta

← #30595018

Subgroups — #30595018

Order 15616.

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

normal subgroups only

This group has 182 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#21460701C211yesmaximal, characteristic
3#21447336C211yesmaximal, characteristic
4D61⋊(C22⋊C8)—21no—
5#16840658—21no—
6#16839811—21no—
7#16839811C411yescharacteristic
8#16839725—21no—
9#16839725C2211yescharacteristic
10C61×#338C411yescharacteristic
11C2×D61⋊C8—41no—
12#14519851—41no—
13#14519834—22no—
14C22⋊#92420—41no—
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×D61Q1611yescharacteristic
25C22×C4×C61C22⋊C411yescharacteristic
26C22×Dic61SD1611yescharacteristic
27C2×C4×D61—21no—
28C2×C4×D61—21no—
29C2×C4×D61—41no—
30C2×C4×D61—41no—
31C2×#92420—42no—
32D61⋊C8—81no—
33D61⋊C8—81no—
34M16×C61—41no—
35M16×C61—41no—
36M16×C61—41no—
37C2×C8×C61—22no—
38C2×C8×C61—21no—
39#11758194—41no—
40#11758194—41no—
41#11758194—41no—
42C2×#92418—21no—
43C2×#92418—41no—
44#11758187—81no—
45C23×C61#10311yescharacteristic
46C22×D61—21no—
47C22×D61—42no—
48C22×D61—41no—
49C2×C4×C61—21no—
50C2×C4×C61—21no—
51C2×C4×C61#9911yescharacteristic
52C2×C4×C61#10411yescharacteristic
53C2×Dic61—21no—
54C2×Dic61—41no—
55C4×D61—41no—
56C4×D61—41no—
57C4×D61—81no—
58#92420—82no—
59C8×C61—42no—
60C8×C61—41no—
61#92418—41no—
62#92418—81no—
63#7433—611nomaximal, Sylow
64C22×C61—21no—
65C22×C61—41no—
66C22×C61#32811yescharacteristic
67C2×D61—22no—
68C2×D61—41no—
69C2×D61—41no—
70C2×D61—42no—
71C2×D61—81no—
72C4×C61—21no—
73C4×C61#35211yescharacteristic
74C4×C61#35311yescharacteristic
75Dic61—41no—
76#2091—611no—
77#1320—611no—
78#1298—611no—
79C2×C61—21no—
80C2×C61—41no—
81C2×C61#135211yescharacteristic
82D61—42no—
83#430—611no—
84#430—1221no—
85#407—611no—
86#407—1221no—
87C2×C22⋊C8—1221no—
88#349—1221no—
89#338#692311yescharacteristic
90C61#743311yescharacteristic, complemented, Sylow
91C23×C4—611no—
92C2×M16—21no—
93C2×M16—611no—
94C2×M16—1221no—
95C2×M16C2×#692311yescharacteristic
96C22×C8—2441no—
97M32—2441no—
98#108—2441no—
99#108—2442no—
100C22⋊C8—1222no—
101C22⋊C8—2441no—
102C22⋊C8—2442no—
103C22⋊C8—2441no—
104C24—611no—
105C22×C4—611no—
106C22×C4—1221no—
107C22×C4—1221no—
108C22×C4—2441no—
109C22×C4—2441no—
110C22×C4C22⋊#692311yescharacteristic
111M16—41no—
112M16—41no—
113M16—41no—
114M16—2441no—
115M16—2441no—
116M16—2441no—
117C2×C8—22no—
118C2×C8—21no—
119C2×C8—1221no—
120C2×C8—4881no—
121C2×C8—4881no—
122C2×C8—2441no—
123C2×C8—2442no—
124C16—4881no—
125C23—1221no—
126C23—2441no—
127C23—2442no—
128C23#1451984011yescharacteristic
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—1221no—
132C2×C4—4881no—
133C2×C4—2441no—
134C2×C4—2441no—
135C2×C4—2441no—
136C2×C4#1451983611yescharacteristic
137C2×C4#1451984111yescharacteristic
138C8—42no—
139C8—41no—
140C8—4882no—
141C8—4881no—
142C8—2441no—
143C22—21no—
144C22—41no—
145C22—1222no—
146C22—4881no—
147C22—2441no—
148C22—2442no—
149C22—2441no—
150C22#1684061511yescharacteristic
151C4—21no—
152C4—2441no—
153C4#1684066511yescharacteristic
154C4#1684066711yescharacteristic
155C2—21no—
156C2—41no—
157C2—2442no—
158C2#2146081511yescharacteristic
subgroupG/H
centerC4#16840667
commutatorC2×M16×C61C2×C4
FrattiniC2×M16C2×#6923
FittingC61×#338C4
socleC2×C61#1352
prime radicalC23×D61Q16
cosocle#16839725C22
hypercenter#338#6923
hypocenterC61#7433
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
90. C61#7433semidirect

Maximal subgroups

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

subgroupindex
#214607522
#214607012
#214473362
#743361