Finite Group Databasebeta

← #15683863

Subgroups — #15683863

Order 2944.

572 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C2×#10625080C212yesmaximal, complemented
2C2×#10625079C212yesmaximal, complemented
3#13092967C211yesmaximal, characteristic, complemented
4C2×#10625046C211yesmaximal, characteristic, complemented
5#13092811C212yesmaximal, complemented
6#13092806C212yesmaximal, complemented
7#13092801C214yesmaximal, complemented
8C4×M16×C23C211yesmaximal, characteristic, complemented
9C2×#67288C2212yes—
10C22×D92C2211yescharacteristic
11C22×Dic46C2211yescharacteristic
12C2×M16×C23C2212yes—
13C2×C42×C23C2211yescharacteristic
14#10625101—22no—
15C2×(C2×D23)⋊C4—22no—
16#10625080—28no—
17#10625079—28no—
18C2×Dic92C2214yescomplemented
19C2×D184C2214yes—
20C2×#67263C2214yes—
21C2×#67263C2214yescomplemented
22#10625046—22no—
23#10625046C2212yes—
24#10625046C2212yes—
25#10625046C2212yescomplemented
26#10625045C2211yescharacteristic, complemented
27C4×D92—22no—
28#10625040C2211yescharacteristic, complemented
29C23×#97C2212yescomplemented
30C4×C8×C23C2212yescomplemented
31C23×D23—21no—
32C22×C4×C23D412yes—
33C22×C4×C23C2311yescharacteristic
34C2×C22⋊D23—22no—
35C22×Dic23—21no—
36#67288—24no—
37#67288—24no—
38C2×D92—24no—
39C2×D92—22no—
40C2×D92—21no—
41C2×D92C2312yes—
42C2×D92C2312yes—
43C2×C4×D23—22no—
44C2×Dic46—24no—
45C2×Dic46—21no—
46C2×Dic46C2312yes—
47C2×Dic46C2312yes—
48M16×C23D418yescomplemented
49C2×C8×C23C2314yes—
50C42×C23D412yes—
51C42×C23C2311yescharacteristic
52C42×C23C2311yescharacteristic
53(C2×D23)⋊C4—24no—
54(C2×D23)⋊C4—24no—
55(C2×D23)⋊C4—24no—
56C4⋊Dic23—22no—
57Dic92—28no—
58D184—28no—
59#67263—28no—
60#67263—28no—
61C23×C23C2×D411yescharacteristic
62C22×D23—22no—
63C22×D23—22no—
64C22×D23—44no—
65C22×D23—42no—
66C2×C4×C23—42no—
67C2×C4×C23C2×D412yes—
68C2×C4×C23C2×D412yes—
69C2×C4×C23C2×D411yescharacteristic
70C2×C4×C23C2×D414yes—
71C2×C4×C23C2411yescharacteristic
72C22⋊D23—44no—
73C2×Dic23—22no—
74C2×Dic23—22no—
75C2×Dic23—42no—
76D92—22no—
77D92—24no—
78D92—22no—
79D92—44no—
80D92—42no—
81C4×D23—44no—
82Dic46—22no—
83Dic46—24no—
84Dic46—22no—
85Dic46—42no—
86C8×C23C2×D418yes—
87#3153—231nomaximal, Sylow
88C22×C23—22no—
89C22×C23#12712yes—
90C22×C23C22×D411yescharacteristic
91C2×D23—42no—
92C2×D23—42no—
93C2×D23—44no—
94C2×D23—44no—
95C2×D23—84no—
96C4×C23—22no—
97C4×C23—22no—
98C4×C23#12712yes—
99C4×C23C22×D412yes—
100Dic23—42no—
101Dic23—42no—
102C2×#137—232no—
103C2×AGL(1,ℤ/8)—232no—
104#532—231no—
105C2×#124—231no—
106#497—232no—
107#496—232no—
108#495—234no—
109C4×M16D2311yescharacteristic, complemented
110C2×C23—22no—
111C2×C23C2×#12711yescharacteristic
112C2×C23#57512yes—
113D23—82no—
114D23—82no—
115C2×#41—232no—
116C22×Q8—231no—
117C22×D4—231no—
118#137—468no—
119AGL(1,ℤ/8)—468no—
120C2×Q16—234no—
121C2×SD16—234no—
122C2×SD16—234no—
123C2×D8—234no—
124C2×M16C2×D2312yes—
125C4⋊Q8—231no—
126#127—231no—
127#124—232no—
128#124—232no—
129#124—232no—
130#124—462no—
131#121—462no—
132C4×D4—462no—
133C2×C22⋊C4—462no—
134C2×C42C2×D2311yescharacteristic
135#97C2×D2312yescomplemented
136C4×C8C2×D2312yescomplemented
137C23#315311yescharacteristic, complemented, Sylow
138C24—461no—
139#41—464no—
140#41—464no—
141C2×Q8—232no—
142C2×Q8—232no—
143C2×Q8—461no—
144C2×Q8—464no—
145C2×D4—232no—
146C2×D4—232no—
147C2×D4—462no—
148C2×D4—464no—
149C2×D4—462no—
150C2×D4—461no—
151C22×C4—461no—
152C22×C4—462no—
153C22×C4D9212yes—
154C22×C4C22×D2311yescharacteristic
155Q16—468no—
156SD16—468no—
157SD16—468no—
158D8—468no—
159M16D9218yescomplemented
160C2×C8C22×D2314yes—
161C4⋊C4—462no—
162C22⋊C4—464no—
163C22⋊C4—464no—
164C22⋊C4—464no—
165C42D9212yes—
166C42C22×D2311yescharacteristic
167C42C22×D2311yescharacteristic
168C23—462no—
169C23—462no—
170C23—924no—
171C23—922no—
172C23C2×D9211yescharacteristic
173Q8—462no—
174Q8—464no—
175Q8—462no—
176Q8—922no—
177D4—462no—
178D4—464no—
179D4—462no—
180D4—924no—
181D4—924no—
182D4—922no—
183C2×C4—42no—
184C2×C4—462no—
185C2×C4—462no—
186C2×C4—922no—
187C2×C4—924no—
188C2×C4C2×D9212yes—
189C2×C4C2×D9212yes—
190C2×C4C2×D9211yescharacteristic
191C2×C4C2×D9214yes—
192C2×C4C23×D2311yescharacteristic
193C8C2×D9218yes—
194C22—22no—
195C22—922no—
196C22—922no—
197C22—924no—
198C22—924no—
199C22—1844no—
200C22#1062504512yes—
201C22C22×D9211yescharacteristic
202C4—22no—
203C4—22no—
204C4—922no—
205C4—922no—
206C4#1062504512yes—
207C4C22×D9212yes—
208C2—22no—
209C2—1842no—
210C2—1842no—
211C2C2×#1062504511yescharacteristic
212C2#1309321712yes—
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC4×M16×C23C2
socleC22×C23C22×D4
hypercenterC4×M16D23
hypocenterC23#3153
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#10625080C2semidirect
2. C2×#10625079C2semidirect
3. #13092967C2semidirect
4. C2×#10625046C2semidirect
5. #13092811C2semidirect
6. #13092806C2semidirect
7. #13092801C2semidirect
8. C4×M16×C23C2semidirect
18. C2×Dic92C22semidirect
21. C2×#67263C22semidirect
25. #10625046C22semidirect
26. #10625045C22semidirect
28. #10625040C22semidirect
29. C23×#97C22semidirect
30. C4×C8×C23C22semidirect
48. M16×C23D4semidirect
109. C4×M16D23semidirect
135. #97C2×D23semidirect
136. C4×C8C2×D23semidirect
137. C23#3153semidirect
159. M16D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106250802
C2×#106250792
#130929672
C2×#106250462
#130928112
#130928062
#130928012
C4×M16×C232
#315323