Finite Group Databasebeta

← #29567641

Subgroups — #29567641

Order 15616.

194 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 41 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#21447169C211yesmaximal, characteristic
2#21443700C211yesmaximal, characteristic
3C61×#1324C211yesmaximal, characteristic
4#16840393C411yescharacteristic
5#16839802—21no—
6C2×#14519688—21no—
7#16839531C411yescharacteristic
8#16839522—21no—
9C61×#382C2211yescharacteristic
10C61×#324—21no—
11C2×#11758194—21no—
12C22×#92418—41no—
13#14519776—41no—
14#14519768—41no—
15#14519756—41no—
16#14519736—21no—
17#14519710—41no—
18#14519708—41no—
19#14519688—22no—
20#14519688—41no—
21C2×C4⋊C4×C61C2×C411yescharacteristic
22C2×C4⋊C4×C61D411yescharacteristic
23C2×C42×C61D411yescharacteristic
24C22⋊C8×C61—41no—
25#95×C61—41no—
26C22×C4×C61—21no—
27C22×C4×C61—21no—
28C22×C4×C61—21no—
29C22×C4×C61C22⋊C411yescharacteristic
30C2×Dic122—41no—
31C2×C8×C61—81no—
32C4⋊C4×C61—41no—
33C4⋊C4×C61—41no—
34C42×C61—21no—
35C42×C61SD1611yescharacteristic
36C42×C61Q1611yescharacteristic
37C22⋊Dic61—41no—
38C4⋊Dic61—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61—41no—
41#11758196—42no—
42C4×Dic61—41no—
43#11758194—22no—
44#11758194—41no—
45C2×#92418—42no—
46C2×#92418—41no—
47C2×#92418—42no—
48C2×#92418—42no—
49C23×C61#9911yescharacteristic
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61—41no—
58C2×C4×C61—81no—
59C2×C4×C61—81no—
60C2×C4×C61#10311yescharacteristic
61C2×C4×C61#10411yescharacteristic
62C2×Dic61—41no—
63C2×Dic61—41no—
64Dic122—161no—
65C8×C61—161no—
66#92418—42no—
67#92418—44no—
68#7442—611nomaximal, Sylow
69C22×C61—21no—
70C22×C61—21no—
71C22×C61#32811yescharacteristic
72C22×C61AΣL(1,𝔽16)11yescharacteristic
73C22×C61#35611yescharacteristic
74C4×C61—21no—
75C4×C61—21no—
76C4×C61—41no—
77C4×C61—41no—
78C4×C61—81no—
79C4×C61—81no—
80Dic61—81no—
81Dic61—81no—
82#2061—611no—
83#1324D6111yescharacteristic
84#1295—611no—
85C2×C61—21no—
86C2×C61—21no—
87C2×C61#135411yescharacteristic
88C2×C61#140311yescharacteristic
89C2×C61#140411yescharacteristic
90#544—611no—
91#428—1221no—
92C2×#97—1221no—
93#382C2×D6111yescharacteristic
94#343—611no—
95#339—1221no—
96#324—21no—
97C61#744211yescharacteristic, complemented, Sylow
98C2×M16—1221no—
99C22×C8—2441no—
100C4⋊Q8—2441no—
101#125—2441no—
102C22⋊Q8—2441no—
103#117—1221no—
104C2×C4⋊C4C4×D6111yescharacteristic
105C2×C4⋊C4C22⋊D6111yescharacteristic
106C2×C42D24411yescharacteristic
107#107—2441no—
108#106—2441no—
109C22⋊C8—41no—
110#97—1222no—
111#97—2441no—
112#95—41no—
113C2×Q8—2441no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4#1175819811yescharacteristic
118M16—1222no—
119M16—2441no—
120C2×C8—81no—
121C2×C8—2442no—
122C2×C8—2441no—
123C2×C8—2442no—
124C2×C8—2442no—
125C4⋊C4—41no—
126C4⋊C4—41no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4—2441no—
130C4⋊C4—2442no—
131C22⋊C4—2441no—
132C42—21no—
133C42—2441no—
134C42#1175819011yescharacteristic
135C42Dic24411yescharacteristic
136C23#1451969111yescharacteristic
137Q8—9761no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—81no—
147C2×C4—81no—
148C2×C4—2441no—
149C2×C4—2441no—
150C2×C4#1451970211yescharacteristic
151C2×C4#1451970311yescharacteristic
152C8—161no—
153C8—2442no—
154C8—2444no—
155C22—21no—
156C22—21no—
157C22#1683950011yescharacteristic
158C22#1683954811yescharacteristic
159C22#1683956011yescharacteristic
160C4—21no—
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—81no—
166C4—4881no—
167C4—4881no—
168C2—21no—
169C2—21no—
170C2#2144385011yescharacteristic
171C2#2144396611yescharacteristic
172C2#2144396911yescharacteristic
subgroupG/H
centerC22#16839548
commutatorC2×C4⋊C4×C61C2×C4
Frattini#382C2×D61
FittingC61×#1324C2
socleC22×C61AΣL(1,𝔽16)
prime radicalC23×C61#99
cosocleC61×#382C22
hypercenter#1324D61
hypocenterC61#7442
LCSG ▷ C2×C4⋊C4×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #382 ◁ #1324

Complements

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

NH ≅ G/Ntype
97. C61#7442semidirect

Maximal subgroups

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

subgroupindex
#214471692
#214437002
C61×#13242
#744261