Finite Group Databasebeta

← #30594471

Subgroups — #30594471

Order 15616.

192 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 44 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#21462191C211yesmaximal, characteristic
2#21461749C211yesmaximal, characteristic
3#21444121C211yesmaximal, characteristic
4#16840685—21no—
5#16840659—21no—
6#16840655C412yescomplemented
7#16840644—21no—
8#16840633—21no—
9#16840631C411yescharacteristic
10#16840630C411yescharacteristic
11C4×#11758189—21no—
12C4×#11758189C2211yescharacteristic
13#16839483—21no—
14#16839483C411yescharacteristic, complemented
15C82×C61C411yescharacteristic, complemented
16D61⋊M16—21no—
17#14519856—21no—
18#14519851—22no—
19C2×#11758189—22no—
20C2×#11758189C2×C411yescharacteristic
21C2×#11758189D411yescharacteristic
22C42×D61D411yescharacteristic
23#14519687—22no—
24#14519687C2×C411yescharacteristic
25#14519687Q811yescharacteristic
26C4×#92418—21no—
27C4×#92418D411yescharacteristic
28C4×C8×C61—21no—
29C4×C8×C61C2×C411yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61C22⋊C411yescharacteristic
32C22⋊#6923—41no—
33#11758217—41no—
34C4⋊#6923—41no—
35C4×#6923—41no—
36#11758213—41no—
37D61⋊C8—41no—
38C2×C8×C61—22no—
39C2×C8×C61C4211yescharacteristic
40C2×C8×C61C4⋊C411yescharacteristic
41C42×C61C22⋊C411yescharacteristic
42C4×Dic61—21no—
43C4×Dic61C4⋊C411yescharacteristic
44C2×#92418—22no—
45C2×#92418C22⋊C411yescharacteristic
46C2×#92418C4⋊C411yescharacteristic
47#11758189—41no—
48#11758189—41no—
49#11758189—44no—
50#11758187—42no—
51C22×D61#10411yescharacteristic
52C2×#6923—81no—
53C2×C4×C61—21no—
54C2×C4×C61#9511yescharacteristic
55C2×Dic61—21no—
56C2×Dic61#10411yescharacteristic
57C4×D61—21no—
58C4×D61—21no—
59C4×D61—42no—
60#92420—81no—
61C8×C61—24no—
62C8×C61—21no—
63C8×C61—21no—
64#92418—21no—
65#92418—21no—
66#92418—42no—
67#7225—611nomaximal, Sylow
68C22×C61#33911yescharacteristic
69C2×D61—21no—
70C2×D61—41no—
71#6923—161no—
72C4×C61—22no—
73C4×C61H(3,ℤ/4)11yescharacteristic
74C4×C61#34411yescharacteristic
75Dic61—21no—
76Dic61—41no—
77#2165—611no—
78#1841—611no—
79#1455—611no—
80C2×C61—21no—
81C2×C61#128811yescharacteristic
82D61—41no—
83C4×M16—611no—
84C4×M16—1221no—
85#364—1221no—
86#349—1221no—
87#347—612no—
88#344—1221no—
89#339—1221no—
90#338—611no—
91H(3,ℤ/4)—611no—
92#322—611no—
93#322—1221no—
94C82#692311yescharacteristic, complemented
95C61#722511yescharacteristic, complemented, Sylow
96C2×M16—611no—
97C2×M16—611no—
98C2×M16—1222no—
99C2×M16—1221no—
100#117—1221no—
101C2×C42—611no—
102M32—1222no—
103#97—611no—
104#97—611no—
105#97—1222no—
106C4×C8—21no—
107C4×C8—611no—
108C4×C8—1221no—
109C4×C8C2×#692311yescharacteristic
110C22×C4—611no—
111C22×C4—1221no—
112M16—2441no—
113M16—2441no—
114M16—2444no—
115M16—2441no—
116M16—2441no—
117C2×C8—22no—
118C2×C8—611no—
119C2×C8—611no—
120C2×C8—1222no—
121C2×C8—2441no—
122C2×C8C4×#692311yescharacteristic
123C2×C8C4⋊#692311yescharacteristic
124C4⋊C4—2441no—
125C22⋊C4—2441no—
126C42—611no—
127C42—1221no—
128C42—2441no—
129C42C22⋊#692311yescharacteristic
130C16—2442no—
131C23—611no—
132C2×C4—21no—
133C2×C4—611no—
134C2×C4—1221no—
135C2×C4—1221no—
136C2×C4—1221no—
137C2×C4—4881no—
138C2×C4—2442no—
139C2×C4(C2×#6923)⋊C411yescharacteristic
140C8—24no—
141C8—21no—
142C8—21no—
143C8—1221no—
144C8—1221no—
145C8—4881no—
146C8—2442no—
147C22—1221no—
148C22—2441no—
149C22#1684063311yescharacteristic
150C4—22no—
151C4—1221no—
152C4—9761no—
153C4—2441no—
154C4#1684063011yescharacteristic
155C4#1684064411yescharacteristic
156C2—21no—
157C2—2441no—
158C2#2146067911yescharacteristic
subgroupG/H
centerC4#16840630
commutatorC2×C8×C61C42
FrattiniC4×C8C2×#6923
FittingC82×C61C4
socleC2×C61#1288
prime radicalC22×D61#104
cosocleC4×#11758189C22
hypercenterC82#6923
hypocenterC61#7225
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ C82

Complements

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

NH ≅ G/Ntype
6. #16840655C4semidirect
14. #16839483C4semidirect
15. C82×C61C4semidirect
94. C82#6923semidirect
95. C61#7225semidirect

Maximal subgroups

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

subgroupindex
#214621912
#214617492
#214441212
#722561