Finite Group Databasebeta

← #16855963

Subgroups — #16855963

Order 3968.

394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 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#14521661C211yesmaximal, characteristic, complemented
2#14521390C212yesmaximal, complemented
3#14521349C212yesmaximal, complemented
4#14521254C212yesmaximal, complemented
5#14521200C212yesmaximal
6#14521149C212yesmaximal, complemented
7C4×#92480C212yesmaximal, complemented
8#14521110C211yesmaximal, characteristic, complemented
9C31×#518C211yesmaximal, characteristic
10C22×D4×C31C2211yescharacteristic
11C4×D4×C31—22no—
12C4×D4×C31C2212yes—
13C4×D4×C31C2212yes—
14C31×#117C2211yescharacteristic
15C31×#117C2211yescharacteristic
16C2×C22⋊C4×C31—22no—
17C2×#92480C2212yes—
18C2×#92480C2212yes—
19#11758501C2212yes—
20#11758466—22no—
21#11758456—22no—
22#11758447C2211yescharacteristic, complemented
23#11758446C2211yescharacteristic, complemented
24C4×Dic62C2212yescomplemented
25#11758420C2212yes—
26#11758420C2212yes—
27C22⋊(C31⋊C8)C2212yes—
28#11758398C2212yescomplemented
29#11758398C2212yescomplemented
30#11758396C2212yescomplemented
31#11758395C2212yescomplemented
32C4⋊(C31⋊C8)C2212yescomplemented
33#11758391C2211yescharacteristic, complemented
34C4×C31⋊C8C2211yescharacteristic, complemented
35C24×C31—21no—
36C2×D4×C31—24no—
37C2×D4×C31—21no—
38C2×D4×C31C2312yes—
39C22×C4×C31—22no—
40C22×C4×C31—22no—
41C22×C4×C31C2311yescharacteristic
42C2×Dic62C2312yes—
43C4⋊C4×C31D412yes—
44C4⋊C4×C31C2312yes—
45C22⋊C4×C31—21no—
46C22⋊C4×C31—22no—
47C22⋊C4×C31—22no—
48C22⋊C4×C31D412yes—
49C42×C31—21no—
50C42×C31C2311yescharacteristic
51C42×C31C2311yescharacteristic
52C22⋊Dic31—22no—
53#92480—24no—
54#92480—24no—
55C4⋊Dic31—22no—
56C4⋊Dic31C2312yes—
57Dic31⋊C4—22no—
58Dic31⋊C4—22no—
59Dic31⋊C4—22no—
60C4×Dic31—22no—
61C2×C31⋊C8C2312yes—
62C2×C31⋊C8C2312yes—
63C23×C31—24no—
64C23×C31—22no—
65C23×C31—82no—
66C23×C31C2×D411yescharacteristic
67D4×C31—24no—
68D4×C31—22no—
69D4×C31#4114yes—
70C2×C4×C31—22no—
71C2×C4×C31—22no—
72C2×C4×C31—82no—
73C2×C4×C31—82no—
74C2×C4×C31C2×D412yes—
75C2×C4×C31C2×D411yescharacteristic
76C2×C4×C31C2×D412yes—
77C2×C4×C31C2411yescharacteristic
78C2×Dic31—22no—
79C2×Dic31—22no—
80Dic62—22no—
81Dic62—22no—
82C31⋊C8—22no—
83C31⋊C8—22no—
84#3123—311nomaximal, Sylow
85C22×C31—21no—
86C22×C31—24no—
87C22×C31—22no—
88C22×C31—42no—
89C22×C31—42no—
90C22×C31—84no—
91C22×C31C22×D411yescharacteristic
92C4×C31—21no—
93C4×C31—22no—
94C4×C31—22no—
95C4×C31—42no—
96C4×C31C2×#4112yes—
97Dic31—42no—
98Dic31—42no—
99#541—311no—
100#518D3111yescharacteristic
101#485—312no—
102#478—312no—
103#461—312no—
104#450—312no—
105#440—312no—
106C4×SD16—312no—
107#433—311no—
108C2×C31—41no—
109C2×C31—44no—
110C2×C31#52511yescharacteristic
111C2×C31#57712yes—
112C22×D4C2×D3111yescharacteristic
113C2×SD16—312no—
114C2×SD16—312no—
115C4⋊Q8—311no—
116#126—622no—
117#125—311no—
118#125—622no—
119C22⋊Q8—312no—
120C4×Q8—312no—
121C4×D4—22no—
122C4×D4C2×D3112yes—
123C4×D4C2×D3112yes—
124#117C2×D3111yescharacteristic
125#117C2×D3111yescharacteristic
126C2×C22⋊C4—22no—
127#107—312no—
128#106—312no—
129C4⋊C8—312no—
130#103—312no—
131#103—312no—
132#102—312no—
133#102—312no—
134C22⋊C8—312no—
135#97—311no—
136C4×C8—311no—
137C31#312311yescharacteristic, complemented, Sylow
138C24—21no—
139C2×Q8—312no—
140C2×D4—24no—
141C2×D4—21no—
142C2×D4C22×D3112yes—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4C22×D3111yescharacteristic
146SD16—624no—
147SD16—624no—
148C2×C8—312no—
149C2×C8—312no—
150C4⋊C4—312no—
151C4⋊C4—622no—
152C4⋊C4—622no—
153C4⋊C4—622no—
154C4⋊C4—622no—
155C4⋊C4C22⋊D3112yes—
156C4⋊C4C22×D3112yes—
157C22⋊C4—21no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—622no—
161C22⋊C4C22⋊D3112yes—
162C42—21no—
163C42—622no—
164C42C22×D3111yescharacteristic
165C42C22×D3111yescharacteristic
166C23—24no—
167C23—22no—
168C23—82no—
169C23C2×C22⋊D3111yescharacteristic
170Q8—622no—
171Q8—622no—
172D4—24no—
173D4—22no—
174D4#9249514yes—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—622no—
180C2×C4—622no—
181C2×C4C2×C22⋊D3111yescharacteristic
182C2×C4C2×C22⋊D3112yes—
183C2×C4C2×C22⋊D3112yes—
184C2×C4C23×D3111yescharacteristic
185C8—622no—
186C8—622no—
187C22—22no—
188C22—21no—
189C22—24no—
190C22—42no—
191C22—42no—
192C22—84no—
193C22C22×C22⋊D3111yescharacteristic
194C4—22no—
195C4—22no—
196C4—21no—
197C4—42no—
198C4—1242no—
199C4—1242no—
200C4C2×#9249512yes—
201C2—41no—
202C2—44no—
203C2#1452156011yescharacteristic
204C2#1452186012yes—
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#518C2
socleC22×C31C22×D4
prime radicalC22×D4×C31C22
hypercenter#518D31
hypocenterC31#3123
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #14521661C2semidirect
2. #14521390C2semidirect
3. #14521349C2semidirect
4. #14521254C2semidirect
6. #14521149C2semidirect
7. C4×#92480C2semidirect
8. #14521110C2semidirect
22. #11758447C22semidirect
23. #11758446C22semidirect
24. C4×Dic62C22semidirect
28. #11758398C22semidirect
29. #11758398C22semidirect
30. #11758396C22semidirect
31. #11758395C22semidirect
32. C4⋊(C31⋊C8)C22semidirect
33. #11758391C22semidirect
34. C4×C31⋊C8C22semidirect
137. C31#3123semidirect

Maximal subgroups

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

subgroupindex
#145216612
#145213902
#145213492
#145212542
#145212002
#145211492
C4×#924802
#145211102
C31×#5182
#312331