Finite Group Databasebeta

← #16855316

Subgroups — #16855316

Order 3968.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#92469C211yesmaximal, characteristic, complemented
2#14521556C212yesmaximal, complemented
3#14521304C212yesmaximal, complemented
4#14521299C212yesmaximal, complemented
5#14521292C214yesmaximal, complemented
6#14521087C211yesmaximal, characteristic, complemented
7#14521045C212yesmaximal, complemented
8C2×C31×#135C211yesmaximal, characteristic, complemented
9C2×#41×C31C2212yes—
10C22×C4×D31C2211yescharacteristic
11C31×#135—24no—
12C2×Q16×C31C2211yescharacteristic, complemented
13C2×SD16×C31C2212yescomplemented
14C2×D8×C31C2211yescharacteristic, complemented
15C22×C8×C31C2211yescharacteristic
16#11758523C2214yes—
17#11758515C2214yes—
18#11758514—22no—
19#11758512—22no—
20C4×C22⋊D31—24no—
21#11758503C2212yes—
22C22×C31⋊C8C2211yescharacteristic
23C2×#92469—24no—
24C2×#92469C2212yes—
25C2×#92469C2212yes—
26#11758423C2214yescomplemented
27#11758420C2214yescomplemented
28#11758406C2212yescomplemented
29#11758405C2212yescomplemented
30C23×D31D411yescharacteristic
31#41×C31—24no—
32#41×C31—24no—
33C2×Q8×C31C2312yes—
34C2×D4×C31—22no—
35C2×D4×C31C2312yes—
36C22×C4×C31—22no—
37C22×C4×C31C2311yescharacteristic
38C2×C22⋊D31—24no—
39C22×Dic31D411yescharacteristic
40C2×C4×D31—22no—
41C2×C4×D31—22no—
42C2×C4×D31D412yes—
43C2×C4×D31C2312yes—
44Q16×C31—22no—
45SD16×C31—24no—
46D8×C31—22no—
47C2×C8×C31D414yescomplemented
48C2×C8×C31C2311yescharacteristic
49C2×C8×C31C2311yescharacteristic
50C22⋊Dic31—22no—
51C22⋊Dic31—24no—
52(C2×D31)⋊C4—24no—
53C4⋊Dic31C2314yes—
54Dic31⋊C4—24no—
55C4×Dic31—22no—
56C2×C31⋊C8—22no—
57C2×C31⋊C8C2312yes—
58#92469—24no—
59#92469—24no—
60C23×C31—22no—
61C23×C31C2×D411yescharacteristic
62C22×D31—22no—
63C22×D31—42no—
64C22×D31C2×D412yes—
65Q8×C31—22no—
66Q8×C31—22no—
67D4×C31—22no—
68D4×C31—22no—
69D4×C31—44no—
70C2×C4×C31—22no—
71C2×C4×C31—44no—
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31C2×D412yes—
74C2×C4×C31#4112yes—
75C2×C4×C31C2411yescharacteristic
76C22⋊D31—48no—
77C2×Dic31—22no—
78C2×Dic31—24no—
79C2×Dic31C2×D412yes—
80C4×D31—24no—
81C4×D31—22no—
82C4×D31—22no—
83C8×C31C2×D412yes—
84C8×C31C2×D412yes—
85C31⋊C8—22no—
86#3054—311nomaximal, Sylow
87C22×C31—22no—
88C22×C31—42no—
89C22×C31—44no—
90C22×C31#12112yes—
91C22×C31C22×D411yescharacteristic
92C2×D31—22no—
93C2×D31—24no—
94C2×D31—44no—
95C4×C31—42no—
96C4×C31#12112yes—
97C4×C31C22×D411yescharacteristic
98C4×C31C2×#4111yescharacteristic
99Dic31—22no—
100Dic31—44no—
101C2×#135D3111yescharacteristic, complemented
102C22×M16—311no—
103#525—312no—
104#470—312no—
105#469—312no—
106#468—314no—
107#427—311no—
108#416—312no—
109C2×C31—22no—
110C2×C31—82no—
111C2×C31C2×#12111yescharacteristic
112C2×C31#57512yes—
113D31—42no—
114C2×#41C2×D3112yes—
115C23×C4—311no—
116#135—24no—
117C2×Q16C2×D3111yescharacteristic, complemented
118C2×SD16C2×D3112yescomplemented
119C2×D8C2×D3111yescharacteristic, complemented
120C2×M16—312no—
121C2×M16—312no—
122C2×M16—624no—
123C22×C8—311no—
124C22×C8C2×D3111yescharacteristic
125#123—622no—
126C22⋊Q8—314no—
127#121—314no—
128#120—622no—
129C4×D4—624no—
130#117—312no—
131#107—312no—
132#106—312no—
133#103—314no—
134#102—314no—
135C31#305411yescharacteristic, complemented, Sylow
136C24—311no—
137#41—24no—
138#41—24no—
139C2×Q8C22×D3112yes—
140C2×D4—22no—
141C2×D4—624no—
142C2×D4C22×D3112yes—
143C22×C4—22no—
144C22×C4—311no—
145C22×C4—312no—
146C22×C4—312no—
147C22×C4—622no—
148C22×C4—622no—
149C22×C4C22×D3111yescharacteristic
150Q16—22no—
151SD16—24no—
152D8—22no—
153M16—624no—
154M16—624no—
155C2×C8—312no—
156C2×C8—622no—
157C2×C8C22⋊D3114yescomplemented
158C2×C8C22×D3111yescharacteristic
159C2×C8C22×D3111yescharacteristic
160C4⋊C4—314no—
161C4⋊C4—624no—
162C22⋊C4—624no—
163C22⋊C4—624no—
164C22⋊C4—622no—
165C42—622no—
166C23—22no—
167C23—312no—
168C23—622no—
169C23—1242no—
170C23D4×D3111yescharacteristic
171Q8—22no—
172Q8—22no—
173D4—22no—
174D4—22no—
175D4—44no—
176D4—1248no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—312no—
180C2×C4—622no—
181C2×C4—624no—
182C2×C4—622no—
183C2×C4—622no—
184C2×C4—624no—
185C2×C4D4×D3111yescharacteristic
186C2×C4#9249712yes—
187C2×C4C2×C22⋊D3112yes—
188C2×C4C23×D3111yescharacteristic
189C8—622no—
190C8C2×C22⋊D3112yes—
191C8C2×C22⋊D3112yes—
192C22—22no—
193C22—42no—
194C22—44no—
195C22—622no—
196C22—624no—
197C22—1244no—
198C22#1175851512yes—
199C22C2×D4×D3111yescharacteristic
200C4—42no—
201C4—622no—
202C4—1244no—
203C4#1175851512yes—
204C4C2×#9249711yescharacteristic
205C4C22×C22⋊D3111yescharacteristic
206C2—22no—
207C2—82no—
208C2—1242no—
209C2C2×#1175851511yescharacteristic
210C2#1452184612yes—
subgroupG/H
centerC2×C4D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#135C2
socleC22×C31C22×D4
hypercenterC2×#135D31
hypocenterC31#3054
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C22×#92469C2semidirect
2. #14521556C2semidirect
3. #14521304C2semidirect
4. #14521299C2semidirect
5. #14521292C2semidirect
6. #14521087C2semidirect
7. #14521045C2semidirect
8. C2×C31×#135C2semidirect
12. C2×Q16×C31C22semidirect
13. C2×SD16×C31C22semidirect
14. C2×D8×C31C22semidirect
26. #11758423C22semidirect
27. #11758420C22semidirect
28. #11758406C22semidirect
29. #11758405C22semidirect
47. C2×C8×C31D4semidirect
101. C2×#135D31semidirect
117. C2×Q16C2×D31semidirect
118. C2×SD16C2×D31semidirect
119. C2×D8C2×D31semidirect
135. C31#3054semidirect
157. C2×C8C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C22×#924692
#145215562
#145213042
#145212992
#145212922
#145210872
#145210452
C2×C31×#1352
#305431