Finite Group Databasebeta

← #16856100

Subgroups — #16856100

Order 3968.

400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#11758452C211yesmaximal, characteristic
2#14521411C214yesmaximal, complemented
3#14521406C214yesmaximal, complemented
4#14521057C212yesmaximal, complemented
5#14521053C212yesmaximal
6C4×#92474C211yesmaximal, characteristic, complemented
7C31×#533C211yesmaximal, characteristic, complemented
8C22×D124C2211yescharacteristic
9C22×Dic62C2211yescharacteristic
10C31×C4⋊Q8C2212yescomplemented
11C31×#125C2212yescomplemented
12C31×C22⋊Q8—22no—
13C4×Q8×C31—22no—
14C31×#117C2212yes—
15C2×C42×C31C2211yescharacteristic
16C2×(C2×D31)⋊C4—22no—
17C2×#92474C2212yes—
18#11758452—22no—
19#11758452C2212yes—
20#11758452C2212yes—
21#11758398C2218yescomplemented
22#11758397C2218yes—
23#11758391C2212yescomplemented
24C4×C31⋊C8C2212yescomplemented
25C23×D31—21no—
26C2×Q8×C31—22no—
27C22×C4×C31D412yes—
28C22×C4×C31C2311yescharacteristic
29C22×Dic31—21no—
30C2×D124—24no—
31C2×D124—21no—
32C2×D124C2312yes—
33C2×Dic62—24no—
34C2×Dic62—21no—
35C2×Dic62C2312yes—
36C4⋊C4×C31—24no—
37C4⋊C4×C31—22no—
38C4⋊C4×C31C2314yes—
39C22⋊C4×C31—22no—
40C42×C31—22no—
41C42×C31D412yes—
42C42×C31C2311yescharacteristic
43C42×C31C2311yescharacteristic
44(C2×D31)⋊C4—24no—
45(C2×D31)⋊C4—24no—
46#92474—24no—
47C2×C31⋊C8C2314yes—
48C23×C31C2×D411yescharacteristic
49C22×D31—22no—
50C22×D31—44no—
51C22×D31—42no—
52Q8×C31—44no—
53C2×C4×C31—24no—
54C2×C4×C31—42no—
55C2×C4×C31C2×D412yes—
56C2×C4×C31C2×D412yes—
57C2×C4×C31C2×D411yescharacteristic
58C2×C4×C31#4114yes—
59C2×C4×C31C2411yescharacteristic
60C2×Dic31—22no—
61C2×Dic31—42no—
62D124—24no—
63D124—42no—
64Dic62—24no—
65Dic62—42no—
66C31⋊C8—24no—
67#3140—311nomaximal, Sylow
68C22×C31—22no—
69C22×C31#12412yes—
70C22×C31C22×D411yescharacteristic
71C2×D31—42no—
72C2×D31—44no—
73C2×D31—84no—
74C4×C31—22no—
75C4×C31—22no—
76C4×C31—44no—
77C4×C31#12412yes—
78C4×C31C2×#4112yes—
79Dic31—42no—
80#533D3111yescharacteristic, complemented
81C2×#124—311no—
82#489—314no—
83#488—314no—
84#419—312no—
85#418—312no—
86C4×M16—311no—
87C2×C31—22no—
88C2×C31C2×#12411yescharacteristic
89C2×C31#57512yes—
90D31—82no—
91C22×Q8—311no—
92C22×D4—311no—
93C2×M16—312no—
94C4⋊Q8C2×D3112yescomplemented
95#125C2×D3112yescomplemented
96#124—312no—
97#124—312no—
98#124—622no—
99C22⋊Q8—22no—
100C4×Q8—22no—
101#117C2×D3112yes—
102C2×C22⋊C4—622no—
103C2×C42C2×D3111yescharacteristic
104#103—318no—
105#102—318no—
106#97—312no—
107C4×C8—312no—
108C31#314011yescharacteristic, complemented, Sylow
109C24—621no—
110C2×Q8—22no—
111C2×Q8—312no—
112C2×Q8—621no—
113C2×Q8—624no—
114C2×D4—312no—
115C2×D4—624no—
116C2×D4—621no—
117C22×C4—621no—
118C22×C4C22⋊D3112yes—
119C22×C4C22×D3111yescharacteristic
120M16—624no—
121C2×C8—314no—
122C4⋊C4—24no—
123C4⋊C4—22no—
124C4⋊C4C22×D3114yes—
125C22⋊C4—22no—
126C22⋊C4—624no—
127C22⋊C4—624no—
128C42—22no—
129C42C22⋊D3112yes—
130C42C22×D3111yescharacteristic
131C42C22×D3111yescharacteristic
132C23—622no—
133C23—1244no—
134C23—1242no—
135C23C2×C22⋊D3111yescharacteristic
136Q8—44no—
137Q8—624no—
138Q8—1242no—
139D4—624no—
140D4—1242no—
141C2×C4—24no—
142C2×C4—42no—
143C2×C4—622no—
144C2×C4—1242no—
145C2×C4#9249914yes—
146C2×C4C2×C22⋊D3112yes—
147C2×C4C2×C22⋊D3112yes—
148C2×C4C2×C22⋊D3111yescharacteristic
149C2×C4C23×D3111yescharacteristic
150C8—624no—
151C22—22no—
152C22—1242no—
153C22—1244no—
154C22—2484no—
155C22#1175852412yes—
156C22C22×C22⋊D3111yescharacteristic
157C4—22no—
158C4—22no—
159C4—44no—
160C4—1242no—
161C4#1175852412yes—
162C4C2×#9249912yes—
163C2—22no—
164C2—2482no—
165C2C2×#1175852411yescharacteristic
166C2#1452184712yes—
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#533C2
socleC22×C31C22×D4
prime radicalC22×D124C22
hypercenter#533D31
hypocenterC31#3140
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #14521411C2semidirect
3. #14521406C2semidirect
4. #14521057C2semidirect
6. C4×#92474C2semidirect
7. C31×#533C2semidirect
10. C31×C4⋊Q8C22semidirect
11. C31×#125C22semidirect
21. #11758398C22semidirect
23. #11758391C22semidirect
24. C4×C31⋊C8C22semidirect
80. #533D31semidirect
94. C4⋊Q8C2×D31semidirect
95. #125C2×D31semidirect
108. C31#3140semidirect

Maximal subgroups

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

subgroupindex
C2×#117584522
#145214112
#145214062
#145210572
#145210532
C4×#924742
C31×#5332
#314031