Finite Group Databasebeta

← #15683002

Subgroups — #15683002

Order 2944.

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×#67262C211yesmaximal, characteristic, complemented
2#13092924C212yesmaximal, complemented
3#13092672C212yesmaximal, complemented
4#13092667C212yesmaximal, complemented
5#13092660C214yesmaximal, complemented
6#13092455C211yesmaximal, characteristic, complemented
7#13092413C212yesmaximal, complemented
8C2×C23×#135C211yesmaximal, characteristic, complemented
9C2×#41×C23C2212yes—
10C22×C4×D23C2211yescharacteristic
11C23×#135—24no—
12C2×Q16×C23C2211yescharacteristic, complemented
13C2×SD16×C23C2212yescomplemented
14C2×D8×C23C2211yescharacteristic, complemented
15C22×C8×C23C2211yescharacteristic
16#10625117C2214yes—
17#10625109C2214yes—
18#10625108—22no—
19#10625106—22no—
20C4×C22⋊D23—24no—
21#10625097C2212yes—
22C22×C23⋊C8C2211yescharacteristic
23C2×#67262—24no—
24C2×#67262C2212yes—
25C2×#67262C2212yes—
26#10625017C2214yescomplemented
27#10625014C2214yescomplemented
28#10625000C2212yescomplemented
29#10624999C2212yescomplemented
30C23×D23D411yescharacteristic
31#41×C23—24no—
32#41×C23—24no—
33C2×Q8×C23C2312yes—
34C2×D4×C23—22no—
35C2×D4×C23C2312yes—
36C22×C4×C23—22no—
37C22×C4×C23C2311yescharacteristic
38C2×C22⋊D23—24no—
39C22×Dic23D411yescharacteristic
40C2×C4×D23—22no—
41C2×C4×D23—22no—
42C2×C4×D23D412yes—
43C2×C4×D23C2312yes—
44Q16×C23—22no—
45SD16×C23—24no—
46D8×C23—22no—
47C2×C8×C23D414yescomplemented
48C2×C8×C23C2311yescharacteristic
49C2×C8×C23C2311yescharacteristic
50C22⋊Dic23—22no—
51C22⋊Dic23—24no—
52(C2×D23)⋊C4—24no—
53C4⋊Dic23C2314yes—
54Dic23⋊C4—24no—
55C4×Dic23—22no—
56C2×C23⋊C8—22no—
57C2×C23⋊C8C2312yes—
58#67262—24no—
59#67262—24no—
60C23×C23—22no—
61C23×C23C2×D411yescharacteristic
62C22×D23—22no—
63C22×D23—42no—
64C22×D23C2×D412yes—
65Q8×C23—22no—
66Q8×C23—22no—
67D4×C23—22no—
68D4×C23—22no—
69D4×C23—44no—
70C2×C4×C23—22no—
71C2×C4×C23—44no—
72C2×C4×C23C2×D411yescharacteristic
73C2×C4×C23C2×D412yes—
74C2×C4×C23#4112yes—
75C2×C4×C23C2411yescharacteristic
76C22⋊D23—48no—
77C2×Dic23—22no—
78C2×Dic23—24no—
79C2×Dic23C2×D412yes—
80C4×D23—24no—
81C4×D23—22no—
82C4×D23—22no—
83C8×C23C2×D412yes—
84C8×C23C2×D412yes—
85C23⋊C8—22no—
86#3054—231nomaximal, Sylow
87C22×C23—22no—
88C22×C23—42no—
89C22×C23—44no—
90C22×C23#12112yes—
91C22×C23C22×D411yescharacteristic
92C2×D23—22no—
93C2×D23—24no—
94C2×D23—44no—
95C4×C23—42no—
96C4×C23#12112yes—
97C4×C23C22×D411yescharacteristic
98C4×C23C2×#4111yescharacteristic
99Dic23—22no—
100Dic23—44no—
101C2×#135D2311yescharacteristic, complemented
102C22×M16—231no—
103#525—232no—
104#470—232no—
105#469—232no—
106#468—234no—
107#427—231no—
108#416—232no—
109C2×C23—22no—
110C2×C23—82no—
111C2×C23C2×#12111yescharacteristic
112C2×C23#57512yes—
113D23—42no—
114C2×#41C2×D2312yes—
115C23×C4—231no—
116#135—24no—
117C2×Q16C2×D2311yescharacteristic, complemented
118C2×SD16C2×D2312yescomplemented
119C2×D8C2×D2311yescharacteristic, complemented
120C2×M16—232no—
121C2×M16—232no—
122C2×M16—464no—
123C22×C8—231no—
124C22×C8C2×D2311yescharacteristic
125#123—462no—
126C22⋊Q8—234no—
127#121—234no—
128#120—462no—
129C4×D4—464no—
130#117—232no—
131#107—232no—
132#106—232no—
133#103—234no—
134#102—234no—
135C23#305411yescharacteristic, complemented, Sylow
136C24—231no—
137#41—24no—
138#41—24no—
139C2×Q8C22×D2312yes—
140C2×D4—22no—
141C2×D4—464no—
142C2×D4C22×D2312yes—
143C22×C4—22no—
144C22×C4—231no—
145C22×C4—232no—
146C22×C4—232no—
147C22×C4—462no—
148C22×C4—462no—
149C22×C4C22×D2311yescharacteristic
150Q16—22no—
151SD16—24no—
152D8—22no—
153M16—464no—
154M16—464no—
155C2×C8—232no—
156C2×C8—462no—
157C2×C8C22⋊D2314yescomplemented
158C2×C8C22×D2311yescharacteristic
159C2×C8C22×D2311yescharacteristic
160C4⋊C4—234no—
161C4⋊C4—464no—
162C22⋊C4—464no—
163C22⋊C4—464no—
164C22⋊C4—462no—
165C42—462no—
166C23—22no—
167C23—232no—
168C23—462no—
169C23—922no—
170C23D4×D2311yescharacteristic
171Q8—22no—
172Q8—22no—
173D4—22no—
174D4—22no—
175D4—44no—
176D4—928no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—232no—
180C2×C4—462no—
181C2×C4—464no—
182C2×C4—462no—
183C2×C4—462no—
184C2×C4—464no—
185C2×C4D4×D2311yescharacteristic
186C2×C4#6729012yes—
187C2×C4C2×C22⋊D2312yes—
188C2×C4C23×D2311yescharacteristic
189C8—462no—
190C8C2×C22⋊D2312yes—
191C8C2×C22⋊D2312yes—
192C22—22no—
193C22—42no—
194C22—44no—
195C22—462no—
196C22—464no—
197C22—924no—
198C22#1062510912yes—
199C22C2×D4×D2311yescharacteristic
200C4—42no—
201C4—462no—
202C4—924no—
203C4#1062510912yes—
204C4C2×#6729011yescharacteristic
205C4C22×C22⋊D2311yescharacteristic
206C2—22no—
207C2—82no—
208C2—922no—
209C2C2×#1062510911yescharacteristic
210C2#1309321412yes—
subgroupG/H
centerC2×C4D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×#135C2
socleC22×C23C22×D4
hypercenterC2×#135D23
hypocenterC23#3054
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C22×#67262C2semidirect
2. #13092924C2semidirect
3. #13092672C2semidirect
4. #13092667C2semidirect
5. #13092660C2semidirect
6. #13092455C2semidirect
7. #13092413C2semidirect
8. C2×C23×#135C2semidirect
12. C2×Q16×C23C22semidirect
13. C2×SD16×C23C22semidirect
14. C2×D8×C23C22semidirect
26. #10625017C22semidirect
27. #10625014C22semidirect
28. #10625000C22semidirect
29. #10624999C22semidirect
47. C2×C8×C23D4semidirect
101. C2×#135D23semidirect
117. C2×Q16C2×D23semidirect
118. C2×SD16C2×D23semidirect
119. C2×D8C2×D23semidirect
135. C23#3054semidirect
157. C2×C8C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
C22×#672622
#130929242
#130926722
#130926672
#130926602
#130924552
#130924132
C2×C23×#1352
#305423