Finite Group Databasebeta

← #15685197

Subgroups — #15685197

Order 2944.

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

normal subgroups only

This group has 476 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#13093222C212yesmaximal, complemented
2#13093219C212yesmaximal, complemented
3#13092794C211yesmaximal, characteristic, complemented
4#13092688C212yesmaximal, complemented
5#13092687C212yesmaximal, complemented
6#13092586C214yesmaximal, complemented
7#13092535C211yesmaximal, characteristic, complemented
8C23×#443C211yesmaximal, characteristic, complemented
9#10625160C2214yescomplemented
10C23×#135C2211yescharacteristic
11C23×#131C2212yescomplemented
12#10625120C2214yescomplemented
13#10625090—22no—
14#10625085—24no—
15D8×D23—22no—
16#10625079—24no—
17#10625079C2214yescomplemented
18#10625075—22no—
19#10625075C2211yescharacteristic
20C2×D184—22no—
21C2×D184C2212yescomplemented
22C2×D184C2212yescomplemented
23#10625072C2212yescomplemented
24#10625045C2212yescomplemented
25C23×#108C2211yescharacteristic, complemented
26C23×#104C2212yescomplemented
27C4×C8×C23C2211yescharacteristic, complemented
28#10625005C2214yescomplemented
29#10625001C2211yescharacteristic, complemented
30#10624987C2212yescomplemented
31#41×C23C2312yes—
32#67292—24no—
33D4×D23—24no—
34D4×D23—44no—
35#67288—24no—
36#67288C2312yes—
37C2×D92—24no—
38C2×D92—42no—
39C2×D92C2314yes—
40Q16×C23D411yescharacteristic, complemented
41SD16×C23D412yescomplemented
42D8×C23D411yescharacteristic, complemented
43M16×C23—22no—
44M16×C23C2312yes—
45C2×C8×C23—22no—
46C2×C8×C23C2311yescharacteristic
47C2×C8×C23C2311yescharacteristic
48C42×C23C2311yescharacteristic
49#67274—24no—
50#67272—24no—
51#67267C2312yes—
52Dic92D411yescharacteristic, complemented
53D184—24no—
54D184—22no—
55D184—22no—
56D184—22no—
57D184—22no—
58D184D411yescharacteristic, complemented
59#67263—24no—
60#67263D412yescomplemented
61#67262—22no—
62C8×D23—22no—
63C22×D23—24no—
64C22×D23—44no—
65Q8×C23C2×D412yes—
66D4×C23—22no—
67D4×C23C2×D412yes—
68C2×C4×C23—21no—
69C2×C4×C23—22no—
70C2×C4×C23C2411yescharacteristic
71C22⋊D23—22no—
72C22⋊D23—44no—
73D92—24no—
74D92—24no—
75D92—44no—
76D92—84no—
77D92C2×D412yes—
78C4×D23—22no—
79C4×D23—44no—
80Dic46C2×D412yes—
81C8×C23—22no—
82C8×C23C2×D411yescharacteristic
83C8×C23C2×D411yescharacteristic
84C8×C23C2×D411yescharacteristic
85C8×C23C2×D411yescharacteristic
86C23⋊C8—22no—
87#3292—231nomaximal, Sylow
88C22×C23—22no—
89C22×C23H(5,𝔽2)11yescharacteristic
90C2×D23—22no—
91C2×D23—44no—
92C2×D23—84no—
93C2×D23—164no—
94C4×C23—22no—
95C4×C23—22no—
96C4×C23C22×D411yescharacteristic
97C4×C23C22×D411yescharacteristic
98Dic23—22no—
99#576—232no—
100#576—232no—
101#493—231no—
102#472—232no—
103#472—232no—
104#453—234no—
105#443—231no—
106#443D2311yescharacteristic, complemented
107C2×C23—21no—
108C2×C23—42no—
109C2×C23D4211yescharacteristic
110D23—42no—
111D23—84no—
112H(5,𝔽2)—234no—
113AGL(1,ℤ/8)—234no—
114AGL(1,ℤ/8)—234no—
115AGL(1,ℤ/8)—464no—
116AGL(1,ℤ/8)—464no—
117#135—231no—
118#135—462no—
119#135—462no—
120#135C2×D2311yescharacteristic
121C2×D8—232no—
122C2×D8—232no—
123C2×D8—462no—
124C2×D8—462no—
125#131—232no—
126#131C2×D2312yescomplemented
127#127—232no—
128#108—231no—
129#108C2×D2311yescharacteristic, complemented
130#104—232no—
131#104C2×D2312yescomplemented
132#100—234no—
133C4×C8C2×D2311yescharacteristic, complemented
134C23#329211yescharacteristic, complemented, Sylow
135#41—232no—
136#41—464no—
137#41—464no—
138#41C22×D2312yes—
139C2×D4—234no—
140C2×D4—464no—
141C2×D4—464no—
142C2×D4—922no—
143C2×D4—924no—
144Q16—231no—
145Q16D9211yescharacteristic, complemented
146SD16—232no—
147SD16—464no—
148SD16—464no—
149SD16D9212yescomplemented
150D8—231no—
151D8—464no—
152D8—464no—
153D8—462no—
154D8—462no—
155D8—462no—
156D8—462no—
157D8D9211yescharacteristic, complemented
158M16—22no—
159M16—232no—
160M16—462no—
161M16C22×D2312yes—
162C2×C8—22no—
163C2×C8—462no—
164C2×C8C22×D2311yescharacteristic
165C2×C8C22×D2311yescharacteristic
166C42C22×D2311yescharacteristic
167C23—464no—
168C23—924no—
169Q8—232no—
170Q8C2×D9212yes—
171D4—22no—
172D4—232no—
173D4—462no—
174D4—464no—
175D4—464no—
176D4—924no—
177D4—924no—
178D4—1844no—
179D4C2×D9212yes—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—462no—
183C2×C4—924no—
184C2×C4C23×D2311yescharacteristic
185C8—22no—
186C8—462no—
187C8C2×D9211yescharacteristic
188C8C2×D9211yescharacteristic
189C8D4×D2311yescharacteristic
190C8D4×D2311yescharacteristic
191C22—22no—
192C22—462no—
193C22—924no—
194C22—3684no—
195C22—1844no—
196C22#1062516011yescharacteristic
197C4—22no—
198C4—22no—
199C4—462no—
200C4C22×D9211yescharacteristic
201C4C2×D4×D2311yescharacteristic
202C2—21no—
203C2—42no—
204C2—922no—
205C2—1844no—
206C2D4×D9211yescharacteristic
subgroupG/H
centerC2D4×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#443C2
socleC2×C23D42
hypercenter#443D23
hypocenterC23#3292
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #13093222C2semidirect
2. #13093219C2semidirect
3. #13092794C2semidirect
4. #13092688C2semidirect
5. #13092687C2semidirect
6. #13092586C2semidirect
7. #13092535C2semidirect
8. C23×#443C2semidirect
9. #10625160C22semidirect
11. C23×#131C22semidirect
12. #10625120C22semidirect
17. #10625079C22semidirect
21. C2×D184C22semidirect
22. C2×D184C22semidirect
23. #10625072C22semidirect
24. #10625045C22semidirect
25. C23×#108C22semidirect
26. C23×#104C22semidirect
27. C4×C8×C23C22semidirect
28. #10625005C22semidirect
29. #10625001C22semidirect
30. #10624987C22semidirect
40. Q16×C23D4semidirect
41. SD16×C23D4semidirect
42. D8×C23D4semidirect
52. Dic92D4semidirect
58. D184D4semidirect
60. #67263D4semidirect
106. #443D23semidirect
126. #131C2×D23semidirect
129. #108C2×D23semidirect
131. #104C2×D23semidirect
133. C4×C8C2×D23semidirect
134. C23#3292semidirect
145. Q16D92semidirect
149. SD16D92semidirect
157. D8D92semidirect

Maximal subgroups

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

subgroupindex
#130932222
#130932192
#130927942
#130926882
#130926872
#130925862
#130925352
C23×#4432
#329223