Finite Group Databasebeta

← #16847695

Subgroups — #16847695

Order 3968.

354 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 45 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#14521235C212yesmaximal, complemented
2#14521216C211yesmaximal, characteristic, complemented
3#14520842C211yesmaximal, characteristic, complemented
4#14520836C212yesmaximal, complemented
5D42×C31C211yesmaximal, characteristic, complemented
6C22×D4×C31—22no—
7#11758561C2211yescharacteristic, complemented
8C31×#127C2211yescharacteristic
9C31×#121—22no—
10C31×#120—21no—
11C31×#120C2212yes—
12C4×D4×C31—21no—
13#11758530—22no—
14#11758509—21no—
15#11758422C2212yescomplemented
16#11758421C2211yescharacteristic, complemented
17#11758394—22no—
18#11758393—21no—
19C24×C31—21no—
20C24×C31D412yescomplemented
21C2×D4×C31—21no—
22C2×D4×C31—22no—
23C2×D4×C31—22no—
24C2×D4×C31—22no—
25C2×D4×C31—48no—
26C2×D4×C31D411yescharacteristic, complemented
27C2×D4×C31C2311yescharacteristic
28C22×C4×C31—22no—
29C2×C22⋊D31—22no—
30C2×C22⋊D31—42no—
31#92497—41no—
32D4×D31—41no—
33#92495—21no—
34C4⋊C4×C31—21no—
35C22⋊C4×C31—21no—
36C22⋊C4×C31—22no—
37C22⋊C4×C31D412yescomplemented
38C42×C31D411yescharacteristic, complemented
39C22⋊Dic31—22no—
40C22⋊Dic31—42no—
41#92480—41no—
42#92479—41no—
43#92474—21no—
44C23×C31—22no—
45C23×C31—21no—
46C23×C31—42no—
47C23×C31—44no—
48C23×C31—44no—
49C23×C31—81no—
50C23×C31C2×D412yes—
51C22×D31—22no—
52D4×C31—24no—
53D4×C31—41no—
54D4×C31—41no—
55D4×C31—44no—
56D4×C31—44no—
57D4×C31—44no—
58C2×C4×C31—21no—
59C2×C4×C31—22no—
60C2×C4×C31—44no—
61C2×C4×C31C2×D411yescharacteristic
62C22⋊D31—42no—
63C22⋊D31—41no—
64C22⋊D31—84no—
65C2×Dic31—22no—
66C2×Dic31—42no—
67D124—21no—
68C4×D31—41no—
69Dic62—21no—
70C31⋊C8—41no—
71#2196—311nomaximal, Sylow
72C22×C31—24no—
73C22×C31—22no—
74C22×C31—42no—
75C22×C31—42no—
76C22×C31—42no—
77C22×C31—44no—
78C22×C31—42no—
79C22×C31—41no—
80C22×C31—82no—
81C22×C31—84no—
82C22×C31#12011yescharacteristic
83C2×D31—41no—
84C2×D31—82no—
85C4×C31—22no—
86C4×C31—21no—
87C4×C31—42no—
88Dic31—41no—
89Dic31—82no—
90D42D3111yescharacteristic, complemented
91B(4,𝔽2)—312no—
92#453—311no—
93#353—311no—
94AΣL(1,𝔽16)—312no—
95C2×C31—21no—
96C2×C31—42no—
97C2×C31—44no—
98C2×C31—81no—
99C2×C31B(4,𝔽2)11yescharacteristic
100D31—81no—
101H(5,𝔽2)—311no—
102C22×D4—22no—
103AGL(1,ℤ/8)—621no—
104#127C2×D3111yescharacteristic
105#121—22no—
106#120—21no—
107#120—622no—
108#120C2×D3112yes—
109C4×D4—21no—
110#104—621no—
111#100—311no—
112#99—312no—
113#99—622no—
114C31#219611yescharacteristic, complemented, Sylow
115C24—21no—
116C24C22⋊D3112yescomplemented
117#41—621no—
118#41—1241no—
119C2×D4—21no—
120C2×D4—22no—
121C2×D4—22no—
122C2×D4—22no—
123C2×D4—48no—
124C2×D4—622no—
125C2×D4—1241no—
126C2×D4—1242no—
127C2×D4C22⋊D3111yescharacteristic, complemented
128C2×D4C22×D3111yescharacteristic
129C22×C4—22no—
130SD16—1241no—
131D8—1241no—
132M16—621no—
133C4⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—22no—
136C22⋊C4—622no—
137C22⋊C4—1242no—
138C22⋊C4C22⋊D3112yescomplemented
139C42C22⋊D3111yescharacteristic, complemented
140C23—22no—
141C23—21no—
142C23—42no—
143C23—44no—
144C23—44no—
145C23—81no—
146C23—622no—
147C23C2×C22⋊D3112yes—
148Q8—621no—
149D4—24no—
150D4—41no—
151D4—41no—
152D4—44no—
153D4—44no—
154D4—44no—
155D4—621no—
156D4—1242no—
157D4—1241no—
158D4—2484no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—44no—
162C2×C4—622no—
163C2×C4—1241no—
164C2×C4—1242no—
165C2×C4C2×C22⋊D3111yescharacteristic
166C8—1241no—
167C22—24no—
168C22—22no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—44no—
173C22—42no—
174C22—41no—
175C22—82no—
176C22—84no—
177C22—1241no—
178C22—2482no—
179C22#1175853011yescharacteristic
180C4—22no—
181C4—21no—
182C4—42no—
183C4—1241no—
184C4—2482no—
185C2—21no—
186C2—42no—
187C2—44no—
188C2—81no—
189C2—2481no—
190C2#1452123611yescharacteristic
subgroupG/H
centerC2#14521236
commutator, cosocleC2×D4×C31C23
FrattiniC2×D4C22×D31
FittingD42×C31C2
socleC2×C31B(4,𝔽2)
hypercenterD42D31
hypocenterC31#2196
LCSG ▷ C2×D4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #14521235C2semidirect
2. #14521216C2semidirect
3. #14520842C2semidirect
4. #14520836C2semidirect
5. D42×C31C2semidirect
7. #11758561C22semidirect
15. #11758422C22semidirect
16. #11758421C22semidirect
20. C24×C31D4semidirect
26. C2×D4×C31D4semidirect
37. C22⋊C4×C31D4semidirect
38. C42×C31D4semidirect
90. D42D31semidirect
114. C31#2196semidirect
116. C24C22⋊D31semidirect
127. C2×D4C22⋊D31semidirect
138. C22⋊C4C22⋊D31semidirect
139. C42C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
#145212352
#145212162
#145208422
#145208362
D42×C312
#219631