Finite Group Databasebeta

← #15673810

Subgroups — #15673810

Order 2944.

386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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×#10625106C211yesmaximal, characteristic
2C2×#10625016C211yesmaximal, characteristic
3#13092278C212yesmaximal, complemented
4#13092184C212yesmaximal, complemented
5C23×#518C211yesmaximal, characteristic
6C22×D4×C23C2211yescharacteristic
7C23×Dic23C2211yescharacteristic
8C4×D4×C23—24no—
9C23×#117—21no—
10C2×C22⋊C4×C23—21no—
11C2×C22⋊C4×C23C2212yes—
12C2×C22⋊Dic23—21no—
13C2×C22⋊Dic23C2212yes—
14C2×C22⋊Dic23C2211yescharacteristic
15#10625106—22no—
16#10625106C414yescomplemented
17C2×Dic23⋊C4—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—22no—
27C22×C4×C23D411yescharacteristic
28C22×C4×C23D414yes—
29C22×Dic23—21no—
30C22×Dic23—21no—
31C22×Dic23—21no—
32C22×Dic23—22no—
33C22×Dic23—22no—
34C22×Dic23—22no—
35C22×Dic23C2×C412yescomplemented
36C4⋊C4×C23—22no—
37C22⋊C4×C23—22no—
38C22⋊C4×C23—22no—
39C22⋊C4×C23—22no—
40C42×C23—22no—
41C22⋊Dic23—24no—
42C22⋊Dic23—21no—
43C22⋊Dic23—22no—
44C22⋊Dic23—22no—
45C22⋊Dic23C2×C412yescomplemented
46Dic23⋊C4—24no—
47C23×C23—21no—
48C23×C23—21no—
49C23×C23—42no—
50C23×C23—42no—
51C23×C23C22⋊C412yes—
52C23×C23C22×C411yescharacteristic
53C23×C23C2×D411yescharacteristic
54C23×C23C2×D411yescharacteristic
55C23×C23C2×D412yes—
56C23×C23#4112yes—
57D4×C23—24no—
58D4×C23—24no—
59C2×C4×C23—21no—
60C2×C4×C23—21no—
61C2×C4×C23—24no—
62C2×C4×C23—44no—
63C2×C4×C23—82no—
64C2×C4×C23C22⋊C412yes—
65C2×Dic23—22no—
66C2×Dic23—22no—
67C2×Dic23—24no—
68C2×Dic23—42no—
69C2×Dic23—41no—
70C2×Dic23—42no—
71C2×Dic23—41no—
72C2×Dic23—44no—
73C2×Dic23—42no—
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—44no—
91Dic23—42no—
92Dic23—42no—
93Dic23—82no—
94C2×#123—231no—
95#518D2311yescharacteristic
96C2×#99—231no—
97#381—232no—
98#342—232no—
99C2×C23—21no—
100C2×C23—22no—
101C2×C23—21no—
102C2×C23—22no—
103C2×C23—42no—
104C2×C23#38611yescharacteristic
105C2×C23#45812yes—
106C22×D4C2×D2311yescharacteristic
107C23×C4—231no—
108#123—234no—
109#123—462no—
110C4×D4—24no—
111#117—21no—
112C2×C4⋊C4—461no—
113C2×C22⋊C4—21no—
114C2×C22⋊C4—231no—
115C2×C22⋊C4—232no—
116C2×C22⋊C4—461no—
117C2×C22⋊C4C2×D2312yes—
118#99—462no—
119#95—464no—
120C23#189011yescharacteristic, complemented, Sylow
121C24C22⋊D2311yescharacteristic
122C24C22×D2311yescharacteristic
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C4×D2312yes—
126C2×D4D9212yes—
127C22×C4—22no—
128C22×C4—232no—
129C22×C4—461no—
130C22×C4—462no—
131C22×C4—462no—
132C22×C4—461no—
133C22×C4—461no—
134C22×C4—462no—
135C22×C4C22⋊D2311yescharacteristic
136C22×C4C22⋊D2314yes—
137C4⋊C4—22no—
138C4⋊C4—464no—
139C22⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4—232no—
143C22⋊C4—464no—
144C22⋊C4—461no—
145C22⋊C4—462no—
146C22⋊C4—462no—
147C42—22no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—42no—
152C23(C2×D23)⋊C412yes—
153C23C2×C4×D2311yescharacteristic
154C23C2×D9211yescharacteristic
155C23#6728812yes—
156C23C2×C22⋊D2311yescharacteristic
157C23C2×C22⋊D2312yes—
158D4—24no—
159D4—24no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—24no—
163C2×C4—44no—
164C2×C4—82no—
165C2×C4—462no—
166C2×C4—462no—
167C2×C4—464no—
168C2×C4—922no—
169C2×C4—921no—
170C2×C4—922no—
171C2×C4—921no—
172C2×C4—924no—
173C2×C4—922no—
174C2×C4(C2×D23)⋊C412yes—
175C22—24no—
176C22—22no—
177C22—22no—
178C22—41no—
179C22—41no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—81no—
184C22C2×(C2×D23)⋊C411yescharacteristic
185C22C4×C22⋊D2312yes—
186C22#1062510011yescharacteristic
187C22#1062510112yes—
188C22#1062512411yescharacteristic
189C4—22no—
190C4—44no—
191C4—922no—
192C4—922no—
193C4—1842no—
194C2—21no—
195C2—22no—
196C2—21no—
197C2—22no—
198C2—42no—
199C2#1309229611yescharacteristic
200C2#1309260712yes—
subgroupG/H
centerC22#10625124
commutatorC23×C23C22×C4
FrattiniC24C22×D23
FittingC23×#518C2
socleC22×C23#120
prime radicalC22×D4×C23C22
cosocleC24×C23C23
hypercenter#518D23
hypocenterC23#1890
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #518

Complements

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

NH ≅ G/Ntype
3. #13092278C2semidirect
4. #13092184C2semidirect
16. #10625106C4semidirect
35. C22×Dic23C2×C4semidirect
45. C22⋊Dic23C2×C4semidirect
120. C23#1890semidirect

Maximal subgroups

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

subgroupindex
C2×#106251062
C2×#106250162
#130922782
#130921842
C23×#5182
#189023