Finite Group Databasebeta

← #16846864

Subgroups — #16846864

Order 3968.

282 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 71 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#14521053C212yesmaximal
2#14520950C211yesmaximal, characteristic
3#14520818C211yesmaximal, characteristic, complemented
4#14520808C212yesmaximal, complemented
5C31×#544C211yesmaximal, characteristic, complemented
6C22×D124C2211yescharacteristic
7C31×C4⋊Q8—22no—
8C31×#125—22no—
9C31×C22⋊Q8—22no—
10C31×#117C2212yes—
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×(C2×D31)⋊C4—22no—
13C2×C4×Dic31C2211yescharacteristic
14C2×#92474C2212yes—
15#11758397—22no—
16#11758397—22no—
17C23×D31—21no—
18C2×Q8×C31—22no—
19C22×C4×C31D412yes—
20C22×C4×C31C2311yescharacteristic
21C22×Dic31—21no—
22C2×D124—22no—
23C2×D124—22no—
24C2×D124—21no—
25C2×D124Q812yescomplemented
26C4⋊C4×C31—22no—
27C4⋊C4×C31—24no—
28C4⋊C4×C31—22no—
29C4⋊C4×C31D412yes—
30C4⋊C4×C31D412yes—
31C22⋊C4×C31—22no—
32C42×C31—22no—
33(C2×D31)⋊C4—44no—
34C4×Dic31—22no—
35#92474—22no—
36#92474—22no—
37C2×C31⋊C8—22no—
38C23×C31C2×D411yescharacteristic
39C22×D31—22no—
40C22×D31—42no—
41C22×D31—42no—
42C22×D31—41no—
43C22×D31—41no—
44Q8×C31—82no—
45C2×C4×C31—22no—
46C2×C4×C31—22no—
47C2×C4×C31—22no—
48C2×C4×C31—42no—
49C2×C4×C31C2×D412yes—
50C2×C4×C31C2×Q811yescharacteristic
51C2×C4×C31#4112yes—
52C2×C4×C31#4111yescharacteristic
53C2×Dic31—22no—
54C2×Dic31—41no—
55C2×Dic31—41no—
56D124—24no—
57D124—42no—
58C31⋊C8—42no—
59#2027—311nomaximal, Sylow
60C22×C31—21no—
61C22×C31—21no—
62C22×C31#12011yescharacteristic
63C22×C31C22⋊Q811yescharacteristic
64C22×C31#12411yescharacteristic
65C2×D31—44no—
66C2×D31—42no—
67C2×D31—82no—
68C2×D31—81no—
69C2×D31—81no—
70C4×C31—42no—
71C4×C31—42no—
72C4×C31—42no—
73C4×C31C22⋊Q812yes—
74C4×C31#12412yes—
75Dic31—42no—
76#544D3111yescharacteristic, complemented
77#418—312no—
78#390—311no—
79#343—311no—
80#339—312no—
81C2×C31—21no—
82C2×C31—21no—
83C2×C31#39311yescharacteristic
84C2×C31#45311yescharacteristic
85C2×C31#45411yescharacteristic
86D31—82no—
87C22×D4—311no—
88C2×M16—312no—
89C4⋊Q8—22no—
90#125—22no—
91C22⋊Q8—22no—
92#117C2×D3112yes—
93C2×C4⋊C4C2×D3111yescharacteristic
94C2×C22⋊C4—622no—
95C2×C42—311no—
96#102—622no—
97#102—622no—
98C31#202711yescharacteristic, complemented, Sylow
99C24—621no—
100C2×Q8—22no—
101C2×D4—312no—
102C2×D4—622no—
103C2×D4—621no—
104C2×D4—622no—
105C22×C4—621no—
106C22×C4C22⋊D3112yes—
107C22×C4C22×D3111yescharacteristic
108M16—622no—
109M16—622no—
110C2×C8—622no—
111C4⋊C4—22no—
112C4⋊C4—24no—
113C4⋊C4—22no—
114C4⋊C4C22⋊D3112yes—
115C4⋊C4C22⋊D3112yes—
116C22⋊C4—22no—
117C22⋊C4—1244no—
118C42—22no—
119C42—622no—
120C23—622no—
121C23—1242no—
122C23—1242no—
123C23—1241no—
124C23—1241no—
125C23C2×C22⋊D3111yescharacteristic
126Q8—82no—
127D4—624no—
128D4—1242no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—42no—
133C2×C4—622no—
134C2×C4—1241no—
135C2×C4—1241no—
136C2×C4Q8×D3111yescharacteristic
137C2×C4#9249912yes—
138C2×C4#9249911yescharacteristic
139C2×C4C2×C22⋊D3112yes—
140C8—1242no—
141C22—21no—
142C22—21no—
143C22—1244no—
144C22—1242no—
145C22—2482no—
146C22—2481no—
147C22—2481no—
148C22#1175852311yescharacteristic
149C22#1175852411yescharacteristic
150C22#1175853011yescharacteristic
151C4—42no—
152C4—42no—
153C4—42no—
154C4—1242no—
155C4#1175852312yes—
156C4#1175852412yes—
157C2—21no—
158C2—21no—
159C2—2482no—
160C2#1452096011yescharacteristic
161C2#1452121711yescharacteristic
162C2#1452122211yescharacteristic
subgroupG/H
centerC22#11758530
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#544C2
socleC22×C31#120
prime radicalC22×D124C22
hypercenter#544D31
hypocenterC31#2027
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #14520818C2semidirect
4. #14520808C2semidirect
5. C31×#544C2semidirect
25. C2×D124Q8semidirect
76. #544D31semidirect
98. C31#2027semidirect

Maximal subgroups

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

subgroupindex
#145210532
#145209502
#145208182
#145208082
C31×#5442
#202731