Finite Group Databasebeta

← #15673929

Subgroups — #15673929

Order 2944.

362 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 89 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#13092984C211yesmaximal, characteristic
2#13092435C212yesmaximal, complemented
3C2×#10625015C211yesmaximal, characteristic, complemented
4#13092173C212yesmaximal, complemented
5C23×#518C211yesmaximal, characteristic, complemented
6C22×D4×C23C2211yescharacteristic
7C2×#67288C2211yescharacteristic
8C4×D4×C23—24no—
9C23×#117C2212yes—
10C2×C22⋊C4×C23—22no—
11#10625124—22no—
12#10625111C412yescomplemented
13#10625109—22no—
14#10625107C412yescomplemented
15#10625097C2211yescharacteristic
16C2×#67267C2212yes—
17#10625015—22no—
18#10624987—24no—
19C24×C23D412yes—
20C2×D4×C23—22no—
21C2×D4×C23—22no—
22C2×D4×C23C2×C412yes—
23C2×D4×C23D412yes—
24C22×C4×C23—24no—
25C22×C4×C23C2311yescharacteristic
26C2×C22⋊D23—21no—
27C2×C22⋊D23—24no—
28#67288—22no—
29#67288—22no—
30C2×D92C2×C411yescharacteristic, complemented
31C2×C4×D23—21no—
32C2×Dic46C2×C411yescharacteristic, complemented
33C4⋊C4×C23—22no—
34C22⋊C4×C23—24no—
35C22⋊C4×C23—22no—
36C42×C23D414yescomplemented
37C22⋊Dic23—24no—
38C22⋊Dic23—21no—
39C4⋊Dic23—21no—
40C4×Dic23C2×C412yescomplemented
41#67267—22no—
42#67267—22no—
43C2×C23⋊C8—22no—
44C23×C23—22no—
45C23×C23—22no—
46C23×C23—82no—
47C23×C23C22⋊C414yes—
48C23×C23C2×D411yescharacteristic
49C22×D23—21no—
50D4×C23—24no—
51D4×C23—24no—
52C2×C4×C23—24no—
53C2×C4×C23—84no—
54C2×C4×C23C22×C411yescharacteristic
55C2×C4×C23C2×D411yescharacteristic
56C2×C4×C23C2×D412yes—
57C2×C4×C23#4112yes—
58C22⋊D23—41no—
59C22⋊D23—41no—
60C22⋊D23—84no—
61C2×Dic23—22no—
62C2×Dic23—21no—
63D92—22no—
64C4×D23—42no—
65Dic46—22no—
66C23⋊C8—42no—
67#1911—231nomaximal, Sylow
68C22×C23—24no—
69C22×C23—41no—
70C22×C23—44no—
71C22×C23—44no—
72C22×C23—82no—
73C22×C23C2×C22⋊C411yescharacteristic
74C22×C23#12011yescharacteristic
75C22×C23#12311yescharacteristic
76C2×D23—42no—
77C2×D23—41no—
78C4×C23—44no—
79C4×C23C4×D412yes—
80C4×C23#12112yes—
81Dic23—42no—
82Dic23—41no—
83#535—231no—
84#518D2311yescharacteristic, complemented
85#421—232no—
86C2×#100—231no—
87H(3,ℤ/4)—232no—
88C2×C23—21no—
89C2×C23—21no—
90C2×C23—21no—
91C2×C23—44no—
92C2×C23#38611yescharacteristic
93D23—81no—
94C2×#41—231no—
95C22×D4C2×D2311yescharacteristic
96C2×M16—232no—
97#127—232no—
98#124—232no—
99#121—462no—
100#120—462no—
101C4×D4—24no—
102#117—231no—
103#117C2×D2312yes—
104C2×C22⋊C4—22no—
105#104—464no—
106#100—462no—
107C23#191111yescharacteristic, complemented, Sylow
108C24C22⋊D2312yes—
109#41—462no—
110#41—462no—
111C2×Q8—231no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—231no—
115C2×D4—461no—
116C2×D4—464no—
117C2×D4C4×D2312yes—
118C2×D4D9212yes—
119C22×C4—24no—
120C22×C4—461no—
121C22×C4C22×D2311yescharacteristic
122M16—462no—
123M16—462no—
124C2×C8—462no—
125C4⋊C4—22no—
126C4⋊C4—461no—
127C22⋊C4—24no—
128C22⋊C4—22no—
129C22⋊C4—464no—
130C22⋊C4—461no—
131C42—232no—
132C42C22⋊D2314yescomplemented
133C23—22no—
134C23—22no—
135C23—82no—
136C23—461no—
137C23(C2×D23)⋊C414yes—
138C23C2×C22⋊D2311yescharacteristic
139Q8—462no—
140D4—24no—
141D4—24no—
142D4—462no—
143D4—921no—
144D4—921no—
145D4—1844no—
146C2×C4—24no—
147C2×C4—84no—
148C2×C4—462no—
149C2×C4—461no—
150C2×C4—922no—
151C2×C4C2×C4×D2311yescharacteristic
152C2×C4C2×D9211yescharacteristic
153C2×C4#6728812yes—
154C2×C4C2×C22⋊D2312yes—
155C8—922no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—82no—
161C22—922no—
162C22—921no—
163C22C2×(C2×D23)⋊C411yescharacteristic
164C22#1062510011yescharacteristic
165C22#1062512411yescharacteristic
166C4—44no—
167C4—922no—
168C4—921no—
169C4C4×C22⋊D2312yes—
170C4#1062510112yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—1841no—
176C2#1309229611yescharacteristic
subgroupG/H
centerC2#13092296
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#518C2
socleC2×C23#386
prime radical#13092984C2
cosocleC22×C4×C23C23
hypercenter#518D23
hypocenterC23#1911
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #13092435C2semidirect
3. C2×#10625015C2semidirect
4. #13092173C2semidirect
5. C23×#518C2semidirect
12. #10625111C4semidirect
14. #10625107C4semidirect
30. C2×D92C2×C4semidirect
32. C2×Dic46C2×C4semidirect
36. C42×C23D4semidirect
40. C4×Dic23C2×C4semidirect
84. #518D23semidirect
107. C23#1911semidirect
132. C42C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
#130929842
#130924352
C2×#106250152
#130921732
C23×#5182
#191123