Finite Group Databasebeta

← #16846159

Subgroups — #16846159

Order 3968.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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#14521560C211yesmaximal, characteristic
2C2×#11758393C212yesmaximal, complemented
3#14521013C211yesmaximal, characteristic, complemented
4#14520809C212yesmaximal, complemented
5C2×C31×#117C211yesmaximal, characteristic, complemented
6C23×C4×C31C2211yescharacteristic
7C2×#92495C2211yescharacteristic
8C31×#117—24no—
9C2×C4⋊C4×C31—21no—
10C2×C22⋊C4×C31—21no—
11C2×C42×C31C2212yes—
12#11758530—21no—
13#11758507C412yescomplemented
14#11758506—21no—
15C4×C22⋊D31—22no—
16#11758503C2211yescharacteristic
17#11758501C412yescomplemented
18C2×#92474C2212yes—
19C22⋊(C31⋊C8)—22no—
20#11758393—24no—
21C24×C31D411yescharacteristic
22C22×C4×C31—22no—
23C22×C4×C31—22no—
24C22×C4×C31—22no—
25C22×C4×C31C2×C412yes—
26C22×C4×C31D411yescharacteristic
27C22×C4×C31D412yes—
28C22×C4×C31C2311yescharacteristic
29C2×C22⋊D31—22no—
30C2×C22⋊D31—21no—
31#92495—22no—
32#92495—22no—
33C2×D124C2×C411yescharacteristic
34C2×C4×D31—21no—
35C2×Dic62C2×C411yescharacteristic
36C4⋊C4×C31—24no—
37C22⋊C4×C31—24no—
38C42×C31—22no—
39C42×C31D414yescomplemented
40C22⋊Dic31—22no—
41C22⋊Dic31—21no—
42(C2×D31)⋊C4—22no—
43C4⋊Dic31C2×C412yes—
44Dic31⋊C4—22no—
45C4×Dic31—21no—
46#92474—22no—
47#92474—22no—
48C2×C31⋊C8—22no—
49C23×C31—21no—
50C23×C31—21no—
51C23×C31—42no—
52C23×C31C22⋊C412yes—
53C23×C31C2×D411yescharacteristic
54C22×D31—21no—
55C2×C4×C31—21no—
56C2×C4×C31—21no—
57C2×C4×C31—24no—
58C2×C4×C31—24no—
59C2×C4×C31—24no—
60C2×C4×C31—44no—
61C2×C4×C31C22⋊C412yes—
62C2×C4×C31C22×C411yescharacteristic
63C2×C4×C31C2×D411yescharacteristic
64C2×C4×C31C2×D412yes—
65C2×C4×C31#4112yes—
66C22⋊D31—44no—
67C22⋊D31—41no—
68C22⋊D31—41no—
69C2×Dic31—22no—
70C2×Dic31—21no—
71D124—22no—
72C4×D31—42no—
73Dic62—22no—
74C31⋊C8—42no—
75#1897—311nomaximal, Sylow
76C22×C31—22no—
77C22×C31—22no—
78C22×C31—22no—
79C22×C31—22no—
80C22×C31—42no—
81C22×C31—42no—
82C22×C31C2×C22⋊C411yescharacteristic
83C22×C31#12011yescharacteristic
84C22×C31#12311yescharacteristic
85C2×D31—41no—
86C2×D31—42no—
87C4×C31—22no—
88C4×C31—44no—
89C4×C31C4×D412yes—
90C4×C31#12112yes—
91Dic31—41no—
92Dic31—42no—
93#525—311no—
94C2×#117D3111yescharacteristic, complemented
95C2×#104—312no—
96#407—311no—
97#339—312no—
98C2×C31—21no—
99C2×C31—21no—
100C2×C31—42no—
101C2×C31#38611yescharacteristic
102C2×C31#42112yes—
103D31—81no—
104C2×#41—311no—
105C23×C4C2×D3111yescharacteristic
106C2×M16—312no—
107#123—621no—
108C22⋊Q8—312no—
109#121—312no—
110#120—621no—
111C4×D4—622no—
112#117—24no—
113#117—311no—
114C2×C4⋊C4—21no—
115C2×C22⋊C4—21no—
116C2×C42C2×D3112yes—
117#104—624no—
118C22⋊C8—622no—
119C31#189711yescharacteristic, complemented, Sylow
120C24C22⋊D3111yescharacteristic
121#41—622no—
122#41—622no—
123C2×Q8—311no—
124C2×D4—311no—
125C2×D4—622no—
126C2×D4—621no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—621no—
131C22×C4C4×D3112yes—
132C22×C4D12412yes—
133C22×C4C22⋊D3111yescharacteristic
134C22×C4C22×D3111yescharacteristic
135M16—622no—
136M16—622no—
137C2×C8—622no—
138C4⋊C4—24no—
139C4⋊C4—312no—
140C4⋊C4—622no—
141C22⋊C4—24no—
142C22⋊C4—622no—
143C22⋊C4—621no—
144C22⋊C4—622no—
145C42—22no—
146C42—621no—
147C42C22⋊D3114yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—621no—
152C23(C2×D31)⋊C412yes—
153C23C2×C22⋊D3111yescharacteristic
154Q8—622no—
155D4—622no—
156D4—1244no—
157D4—1241no—
158D4—1241no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—622no—
166C2×C4—621no—
167C2×C4—1242no—
168C2×C4(C2×D31)⋊C412yes—
169C2×C4C2×C4×D3111yescharacteristic
170C2×C4C2×D12411yescharacteristic
171C2×C4#9249512yes—
172C2×C4C2×C22⋊D3112yes—
173C8—1242no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—1241no—
181C22—1242no—
182C22C2×(C2×D31)⋊C411yescharacteristic
183C22#1175850611yescharacteristic
184C22#1175853011yescharacteristic
185C4—22no—
186C4—44no—
187C4—1241no—
188C4—1242no—
189C4C4×C22⋊D3112yes—
190C4#1175850712yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—2481no—
195C2#1452092811yescharacteristic
196C2#1452106712yes—
subgroupG/H
centerC2×C4C2×D124
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#117C2
socleC22×C31C2×C22⋊C4
prime radical#14521560C2
cosocleC22×C4×C31C23
hypercenterC2×#117D31
hypocenterC31#1897
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#11758393C2semidirect
3. #14521013C2semidirect
4. #14520809C2semidirect
5. C2×C31×#117C2semidirect
13. #11758507C4semidirect
17. #11758501C4semidirect
39. C42×C31D4semidirect
94. C2×#117D31semidirect
119. C31#1897semidirect
147. C42C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
#145215602
C2×#117583932
#145210132
#145208092
C2×C31×#1172
#189731