Finite Group Databasebeta

← #16846129

Subgroups — #16846129

Order 3968.

342 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 89 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#14521556C211yesmaximal, characteristic
2#14521033C211yesmaximal, characteristic, complemented
3#14521012C212yesmaximal, complemented
4#14520820C212yesmaximal, complemented
5C31×#568C211yesmaximal, characteristic, complemented
6C2×#41×C31C2211yescharacteristic
7C22×C4×D31C2211yescharacteristic
8C31×#131—24no—
9C2×M16×C31—22no—
10C2×M16×C31C2212yes—
11#11758523—21no—
12#11758515—21no—
13#11758514C412yes—
14#11758512C412yes—
15C4×C22⋊D31—22no—
16#11758503C2211yescharacteristic
17C2×#92474C2212yes—
18#11758424—21no—
19#11758421—21no—
20(C2×D31)⋊C8—24no—
21C23×D31C2×C411yescharacteristic
22#41×C31—22no—
23#41×C31—22no—
24C2×Q8×C31D411yescharacteristic
25C2×D4×C31C2×C412yes—
26C2×D4×C31D411yescharacteristic
27C22×C4×C31D412yes—
28C22×C4×C31C2311yescharacteristic
29C2×C22⋊D31—22no—
30C22×Dic31C2×C411yescharacteristic
31C2×C4×D31—22no—
32C2×C4×D31—21no—
33C2×C4×D31—21no—
34C2×C4×D31—22no—
35M16×C31—24no—
36M16×C31—22no—
37M16×C31—22no—
38C2×C8×C31—24no—
39C2×C8×C31D414yescomplemented
40C22⋊Dic31—22no—
41C22⋊Dic31C2×C412yes—
42(C2×D31)⋊C4—22no—
43C4⋊Dic31—21no—
44Dic31⋊C4—22no—
45C4×Dic31—21no—
46#92474—22no—
47#92474—22no—
48C2×C31⋊C8—22no—
49C23×C31C22⋊C412yes—
50C23×C31C22×C411yescharacteristic
51C22×D31—21no—
52C22×D31—22no—
53C22×D31—42no—
54Q8×C31—22no—
55D4×C31—24no—
56D4×C31—22no—
57C2×C4×C31—22no—
58C2×C4×C31—22no—
59C2×C4×C31C22⋊C412yes—
60C2×C4×C31C2×D411yescharacteristic
61C2×C4×C31C2×D412yes—
62C2×C4×C31C2×D411yescharacteristic
63C2×C4×C31#4112yes—
64C22⋊D31—44no—
65C2×Dic31—22no—
66C2×Dic31—21no—
67C2×Dic31—22no—
68C4×D31—41no—
69C4×D31—42no—
70C4×D31—41no—
71C8×C31—24no—
72C31⋊C8—42no—
73#1891—311nomaximal, Sylow
74C22×C31—22no—
75C22×C31—41no—
76C22×C31—42no—
77C22×C31C2×C22⋊C411yescharacteristic
78C22×C31C4×D412yes—
79C2×D31—22no—
80C2×D31—24no—
81C2×D31—41no—
82C2×D31—42no—
83C2×D31—41no—
84C4×C31—22no—
85C4×C31#12011yescharacteristic
86C4×C31#12112yes—
87C4×C31#12311yescharacteristic
88Dic31—42no—
89Dic31—41no—
90#568D3111yescharacteristic, complemented
91#525—311no—
92#413—311no—
93#407—312no—
94#344—312no—
95C2×C31—21no—
96C2×C31—22no—
97C2×C31—42no—
98C2×C31#38611yescharacteristic
99D31—42no—
100C2×#41C2×D3111yescharacteristic
101C23×C4—311no—
102#131—24no—
103C2×M16—22no—
104C2×M16—312no—
105C2×M16C2×D3112yes—
106#123—312no—
107C22⋊Q8—621no—
108#121—621no—
109#120—312no—
110C4×D4—622no—
111#117—311no—
112#101—621no—
113#100—621no—
114C22⋊C8—624no—
115C31#189111yescharacteristic, complemented, Sylow
116C24—311no—
117#41—22no—
118#41—22no—
119C2×Q8D12411yescharacteristic
120C2×D4—622no—
121C2×D4C4×D3112yes—
122C2×D4D12411yescharacteristic
123C22×C4—311no—
124C22×C4—621no—
125C22×C4—622no—
126C22×C4—622no—
127C22×C4—621no—
128C22×C4C22⋊D3112yes—
129C22×C4C22×D3111yescharacteristic
130M16—24no—
131M16—22no—
132M16—22no—
133M16—622no—
134M16—622no—
135C2×C8—24no—
136C2×C8—622no—
137C2×C8C22⋊D3114yescomplemented
138C4⋊C4—622no—
139C4⋊C4—621no—
140C22⋊C4—312no—
141C22⋊C4—622no—
142C22⋊C4—622no—
143C42—621no—
144C23—621no—
145C23—622no—
146C23—1242no—
147C23(C2×D31)⋊C412yes—
148C23C2×C4×D3111yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—1244no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—622no—
156C2×C4—621no—
157C2×C4—622no—
158C2×C4—1241no—
159C2×C4—1242no—
160C2×C4—1241no—
161C2×C4(C2×D31)⋊C412yes—
162C2×C4C2×D12411yescharacteristic
163C2×C4#9249512yes—
164C2×C4C2×C22⋊D3111yescharacteristic
165C2×C4C2×C22⋊D3112yes—
166C8—24no—
167C8—1242no—
168C22—22no—
169C22—41no—
170C22—42no—
171C22—622no—
172C22—624no—
173C22—1241no—
174C22—1242no—
175C22—1241no—
176C22C2×(C2×D31)⋊C411yescharacteristic
177C22C4×C22⋊D3112yes—
178C4—22no—
179C4—1242no—
180C4—1241no—
181C4#1175850611yescharacteristic
182C4#1175850712yes—
183C4#1175853011yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—1242no—
188C2#1452092811yescharacteristic
subgroupG/H
centerC4#11758530
commutatorC23×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#568C2
socleC2×C31#386
prime radical#14521556C2
cosocleC22×C4×C31C23
hypercenter#568D31
hypocenterC31#1891
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #14521033C2semidirect
3. #14521012C2semidirect
4. #14520820C2semidirect
5. C31×#568C2semidirect
39. C2×C8×C31D4semidirect
90. #568D31semidirect
115. C31#1891semidirect
137. C2×C8C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
#145215562
#145210332
#145210122
#145208202
C31×#5682
#189131