Finite Group Databasebeta

← #15673843

Subgroups — #15673843

Order 2944.

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

normal subgroups only

This group has 358 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#13092928C211yesmaximal, characteristic
2C2×#10625097C211yesmaximal, characteristic, complemented
3C2×#10625007C212yesmaximal, complemented
4#13092178C212yesmaximal, complemented
5C23×#407C211yesmaximal, characteristic, complemented
6C23×C4×C23C2211yescharacteristic
7C2×#67288C2211yescharacteristic
8C2×M16×C23C2212yes—
9#10625124—21no—
10C2×C22⋊Dic23—21no—
11#10625101C412yescomplemented
12#10625100—21no—
13C4×C22⋊D23—22no—
14#10625097—24no—
15#10625097C2211yescharacteristic
16C2×C4⋊Dic23—21no—
17#10625095C412yescomplemented
18C2×C4×Dic23C2212yes—
19C23×C22⋊C8—22no—
20#10625007—24no—
21C24×C23D411yescharacteristic
22C22×C4×C23—22no—
23C22×C4×C23—22no—
24C22×C4×C23C2×C412yes—
25C22×C4×C23D411yescharacteristic
26C22×C4×C23D412yes—
27C22×C4×C23C2311yescharacteristic
28C2×C22⋊D23—22no—
29C2×C22⋊D23—21no—
30C22×Dic23—22no—
31#67288—22no—
32#67288—22no—
33C2×D92C2×C411yescharacteristic
34C2×C4×D23—21no—
35C2×Dic46C2×C411yescharacteristic
36M16×C23—22no—
37M16×C23—22no—
38C2×C8×C23—22no—
39C22⋊Dic23—24no—
40C22⋊Dic23—22no—
41C22⋊Dic23—21no—
42(C2×D23)⋊C4—22no—
43C4⋊Dic23—24no—
44C4⋊Dic23C2×C412yes—
45Dic23⋊C4—22no—
46C4×Dic23—22no—
47C4×Dic23—21no—
48C4×Dic23D414yescomplemented
49C23×C23—21no—
50C23×C23—21no—
51C23×C23—42no—
52C23×C23C22⋊C412yes—
53C23×C23C2×D411yescharacteristic
54C22×D23—21no—
55C2×C4×C23—21no—
56C2×C4×C23—21no—
57C2×C4×C23—24no—
58C2×C4×C23—24no—
59C2×C4×C23C22⋊C412yes—
60C2×C4×C23C22×C411yescharacteristic
61C2×C4×C23C2×D412yes—
62C2×C4×C23C2×D411yescharacteristic
63C2×C4×C23#4112yes—
64C22⋊D23—44no—
65C22⋊D23—41no—
66C22⋊D23—41no—
67C2×Dic23—22no—
68C2×Dic23—21no—
69C2×Dic23—24no—
70C2×Dic23—44no—
71D92—22no—
72C4×D23—42no—
73Dic46—22no—
74C8×C23—42no—
75#1897—231nomaximal, Sylow
76C22×C23—22no—
77C22×C23—22no—
78C22×C23—22no—
79C22×C23—22no—
80C22×C23—42no—
81C22×C23—42no—
82C22×C23C2×C22⋊C411yescharacteristic
83C22×C23#12011yescharacteristic
84C22×C23#12311yescharacteristic
85C2×D23—41no—
86C2×D23—42no—
87C4×C23—22no—
88C4×C23C4×D412yes—
89C4×C23#12112yes—
90Dic23—44no—
91Dic23—41no—
92Dic23—42no—
93#525—231no—
94C2×#117—231no—
95C2×#104—232no—
96#407D2311yescharacteristic, complemented
97#339—232no—
98C2×C23—21no—
99C2×C23—21no—
100C2×C23—42no—
101C2×C23#38611yescharacteristic
102C2×C23#42112yes—
103D23—81no—
104C2×#41—231no—
105C23×C4C2×D2311yescharacteristic
106C2×M16C2×D2312yes—
107#123—461no—
108C22⋊Q8—232no—
109#121—232no—
110#120—461no—
111C4×D4—462no—
112#117—231no—
113#117—464no—
114C2×C4⋊C4—461no—
115C2×C22⋊C4—461no—
116C2×C42—232no—
117#104—464no—
118C22⋊C8—22no—
119C23#189711yescharacteristic, complemented, Sylow
120C24D9211yescharacteristic
121#41—462no—
122#41—462no—
123C2×Q8—231no—
124C2×D4—231no—
125C2×D4—462no—
126C2×D4—461no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—462no—
130C22×C4—461no—
131C22×C4C4×D2312yes—
132C22×C4D9211yescharacteristic
133C22×C4C22⋊D2312yes—
134C22×C4C22×D2311yescharacteristic
135M16—22no—
136M16—22no—
137C2×C8—22no—
138C4⋊C4—232no—
139C4⋊C4—464no—
140C4⋊C4—462no—
141C22⋊C4—464no—
142C22⋊C4—462no—
143C22⋊C4—461no—
144C22⋊C4—462no—
145C42—234no—
146C42—462no—
147C42—461no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—461no—
152C23(C2×D23)⋊C412yes—
153C23C2×D9211yescharacteristic
154Q8—462no—
155D4—462no—
156D4—924no—
157D4—921no—
158D4—921no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—464no—
164C2×C4—462no—
165C2×C4—461no—
166C2×C4—924no—
167C2×C4—922no—
168C2×C4(C2×D23)⋊C412yes—
169C2×C4C2×C4×D2311yescharacteristic
170C2×C4D4×D2312yes—
171C2×C4#6729012yes—
172C2×C4C2×C22⋊D2311yescharacteristic
173C8—42no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—922no—
181C22—921no—
182C22#1062505311yescharacteristic
183C22#1062505711yescharacteristic
184C22C2×(C2×D23)⋊C411yescharacteristic
185C4—22no—
186C4—924no—
187C4—922no—
188C4—921no—
189C4(C22⋊D23)⋊C412yes—
190C4#1062511012yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—1841no—
195C2#1309229411yescharacteristic
196C2#1309243312yes—
subgroupG/H
centerC2×C4C2×C22⋊D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#407C2
socleC22×C23C2×C22⋊C4
prime radical#13092928C2
cosocleC22×C4×C23C23
hypercenter#407D23
hypocenterC23#1897
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#10625097C2semidirect
3. C2×#10625007C2semidirect
4. #13092178C2semidirect
5. C23×#407C2semidirect
11. #10625101C4semidirect
17. #10625095C4semidirect
48. C4×Dic23D4semidirect
96. #407D23semidirect
119. C23#1897semidirect

Maximal subgroups

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

subgroupindex
#130929282
C2×#106250972
C2×#106250072
#130921782
C23×#4072
#189723