Finite Group Databasebeta

← #15673811

Subgroups — #15673811

Order 2944.

386 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 97 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#13092892C211yesmaximal, characteristic
2C2×#10625016C211yesmaximal, characteristic
3#13092280C212yesmaximal, complemented
4#13092183C212yesmaximal, complemented
5C2×C23×#123C211yesmaximal, characteristic
6C22×D4×C23C2211yescharacteristic
7C23×C4×C23C2211yescharacteristic
8C23×#123—22no—
9C23×#123C414yescomplemented
10C2×C4⋊C4×C23—21no—
11C2×C22⋊C4×C23—21no—
12C2×C22⋊C4×C23C2211yescharacteristic
13C2×C22⋊Dic23—21no—
14C2×C22⋊Dic23C2212yes—
15C2×C22⋊Dic23C2212yes—
16D4×Dic23—24no—
17#10625097—21no—
18#10625016—22no—
19C23⋊#95—24no—
20C24×C23D411yescharacteristic
21C24×C23C2311yescharacteristic
22C2×D4×C23—22no—
23C2×D4×C23—22no—
24C2×D4×C23C2×C412yes—
25C2×D4×C23D412yes—
26C22×C4×C23—21no—
27C22×C4×C23—21no—
28C22×C4×C23—21no—
29C22×C4×C23—22no—
30C22×C4×C23—22no—
31C22×C4×C23C2×C412yescomplemented
32C22×C4×C23D411yescharacteristic
33C22×Dic23—22no—
34C22×Dic23—22no—
35C22×Dic23D414yes—
36C4⋊C4×C23—24no—
37C22⋊C4×C23—24no—
38C22⋊C4×C23—21no—
39C22⋊C4×C23C2×C412yescomplemented
40C22⋊Dic23—22no—
41C22⋊Dic23—22no—
42C22⋊Dic23—22no—
43C22⋊Dic23—22no—
44C22⋊Dic23—22no—
45C4⋊Dic23—22no—
46C4×Dic23—22no—
47C23×C23—21no—
48C23×C23—21no—
49C23×C23—42no—
50C23×C23—42no—
51C23×C23C22⋊C412yes—
52C23×C23C22×C411yescharacteristic
53C23×C23C2×D412yes—
54C23×C23C2×D411yescharacteristic
55C23×C23C2×D411yescharacteristic
56C23×C23#4112yes—
57D4×C23—24no—
58D4×C23—24no—
59C2×C4×C23—21no—
60C2×C4×C23—21no—
61C2×C4×C23—22no—
62C2×C4×C23—22no—
63C2×C4×C23—24no—
64C2×C4×C23—42no—
65C2×C4×C23—41no—
66C2×C4×C23—42no—
67C2×C4×C23—41no—
68C2×C4×C23C22⋊C412yes—
69C2×Dic23—24no—
70C2×Dic23—44no—
71C2×Dic23—44no—
72C2×Dic23—42no—
73C2×Dic23—82no—
74#1890—231nomaximal, Sylow
75C22×C23—24no—
76C22×C23—22no—
77C22×C23—22no—
78C22×C23—41no—
79C22×C23—41no—
80C22×C23—42no—
81C22×C23—42no—
82C22×C23—42no—
83C22×C23—81no—
84C22×C23C2×C22⋊C411yescharacteristic
85C22×C23C4×D412yes—
86C22×C23#12011yescharacteristic
87C22×C23#12112yes—
88C22×C23#12311yescharacteristic
89C4×C23—22no—
90C4×C23—42no—
91C4×C23—42no—
92Dic23—44no—
93Dic23—82no—
94C2×#123D2311yescharacteristic
95#518—231no—
96C2×#99—231no—
97#381—232no—
98#342—232no—
99C2×C23—22no—
100C2×C23—21no—
101C2×C23—21no—
102C2×C23—22no—
103C2×C23—42no—
104C2×C23#38611yescharacteristic
105C2×C23#45812yes—
106C22×D4C2×D2311yescharacteristic
107C23×C4C2×D2311yescharacteristic
108#123—22no—
109#123Dic2314yescomplemented
110C4×D4—464no—
111#117—461no—
112C2×C4⋊C4—21no—
113C2×C22⋊C4—21no—
114C2×C22⋊C4—232no—
115C2×C22⋊C4—232no—
116C2×C22⋊C4—461no—
117C2×C22⋊C4C2×D2311yescharacteristic
118#99—462no—
119#95—464no—
120C23#189011yescharacteristic, complemented, Sylow
121C24C22⋊D2311yescharacteristic
122C24C22×D2311yescharacteristic
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C2×Dic2312yes—
126C2×D4C22⋊D2312yes—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—234no—
133C22×C4—462no—
134C22×C4—462no—
135C22×C4C2×Dic2312yescomplemented
136C22×C4C22⋊D2311yescharacteristic
137C4⋊C4—24no—
138C4⋊C4—462no—
139C22⋊C4—24no—
140C22⋊C4—21no—
141C22⋊C4—462no—
142C22⋊C4—462no—
143C22⋊C4—462no—
144C22⋊C4—462no—
145C22⋊C4—462no—
146C22⋊C4C2×Dic2312yescomplemented
147C42—462no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—42no—
152C23C22⋊Dic2312yes—
153C23D4×D2312yes—
154C23#6729012yes—
155C23C22×Dic2311yescharacteristic
156C23C2×C22⋊D2311yescharacteristic
157C23C2×C22⋊D2311yescharacteristic
158D4—24no—
159D4—24no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—24no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—42no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—464no—
170C2×C4—924no—
171C2×C4—924no—
172C2×C4—922no—
173C2×C4—1842no—
174C2×C4C22⋊Dic2312yes—
175C22—22no—
176C22—24no—
177C22—22no—
178C22—42no—
179C22—41no—
180C22—41no—
181C22—42no—
182C22—42no—
183C22—81no—
184C22D4×Dic2312yes—
185C22#1062510611yescharacteristic
186C22#1062510811yescharacteristic
187C22#1062511012yes—
188C22C2×C22⋊Dic2311yescharacteristic
189C4—22no—
190C4—42no—
191C4—42no—
192C4—924no—
193C4—1842no—
194C2—21no—
195C2—22no—
196C2—21no—
197C2—22no—
198C2—42no—
199C2#1309229711yescharacteristic
200C2#1309260612yes—
subgroupG/H
centerC22#10625108
commutatorC23×C23C22×C4
FrattiniC24C22×D23
FittingC2×C23×#123C2
socleC22×C23#120
prime radicalC22×D4×C23C22
cosocleC24×C23C23
hypercenterC2×#123D23
hypocenterC23#1890
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
3. #13092280C2semidirect
4. #13092183C2semidirect
9. C23×#123C4semidirect
31. C22×C4×C23C2×C4semidirect
39. C22⋊C4×C23C2×C4semidirect
109. #123Dic23semidirect
120. C23#1890semidirect
135. C22×C4C2×Dic23semidirect
146. C22⋊C4C2×Dic23semidirect

Maximal subgroups

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

subgroupindex
#130928922
C2×#106250162
#130922802
#130921832
C2×C23×#1232
#189023