Finite Group Databasebeta

← #15673838

Subgroups — #15673838

Order 2944.

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

normal subgroups only

This group has 442 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#13092928C211yesmaximal, characteristic
2C22×C4×Dic23C211yesmaximal, characteristic, complemented
3C2×#10625007C212yesmaximal, complemented
4#13092178C212yesmaximal, complemented
5C23×#407C211yesmaximal, characteristic, complemented
6C23×C4×C23C2211yescharacteristic
7C23×Dic23—21no—
8C2×#67288C2211yescharacteristic
9C2×M16×C23C2212yes—
10#10625124—21no—
11#10625101C412yescomplemented
12#10625100—21no—
13C4×C22⋊D23—22no—
14#10625097C2211yescharacteristic
15#10625095C412yescomplemented
16C2×C4×Dic23—21no—
17C2×C4×Dic23—24no—
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—24no—
31C22×Dic23—28no—
32C22×Dic23—22no—
33#67288—22no—
34#67288—22no—
35C2×D92C2×C411yescharacteristic, complemented
36C2×C4×D23—21no—
37C2×Dic46C2×C411yescharacteristic, complemented
38M16×C23—22no—
39M16×C23—22no—
40C2×C8×C23—22no—
41C22⋊Dic23—22no—
42C22⋊Dic23—21no—
43(C2×D23)⋊C4—22no—
44C4⋊Dic23C2×C412yescomplemented
45Dic23⋊C4—22no—
46C4×Dic23—24no—
47C4×Dic23—22no—
48C4×Dic23—21no—
49C4×Dic23D414yescomplemented
50C23×C23—24no—
51C23×C23—21no—
52C23×C23—21no—
53C23×C23C22⋊C412yes—
54C23×C23C2×D411yescharacteristic
55C22×D23—21no—
56C2×C4×C23—21no—
57C2×C4×C23—21no—
58C2×C4×C23—24no—
59C2×C4×C23—24no—
60C2×C4×C23C22⋊C412yes—
61C2×C4×C23C22×C411yescharacteristic
62C2×C4×C23C2×D412yes—
63C2×C4×C23C2×D411yescharacteristic
64C2×C4×C23#4112yes—
65C22⋊D23—44no—
66C22⋊D23—41no—
67C22⋊D23—41no—
68C2×Dic23—216no—
69C2×Dic23—28no—
70C2×Dic23—24no—
71C2×Dic23—22no—
72C2×Dic23—21no—
73D92—22no—
74C4×D23—42no—
75Dic46—22no—
76C8×C23—42no—
77#1896—231nomaximal, Sylow
78C22×C23—24no—
79C22×C23—24no—
80C22×C23—22no—
81C22×C23—22no—
82C22×C23—22no—
83C22×C23#10414yescomplemented
84C22×C23C2×C22⋊C411yescharacteristic
85C22×C23#12011yescharacteristic
86C22×C23#12311yescharacteristic
87C2×D23—41no—
88C2×D23—42no—
89C4×C23—22no—
90C4×C23C4×D412yes—
91C4×C23#12112yes—
92Dic23—28no—
93Dic23—41no—
94Dic23—42no—
95#525—231no—
96C22×C42—231no—
97C2×#104—232no—
98#407D2311yescharacteristic, complemented
99#339—232no—
100C2×C23—21no—
101C2×C23—24no—
102C2×C23—21no—
103C2×C23#38611yescharacteristic
104C2×C23C2×#10412yes—
105D23—81no—
106C2×#41—231no—
107C23×C4—461no—
108C23×C4C2×D2311yescharacteristic
109C2×M16C2×D2312yes—
110#123—461no—
111C22⋊Q8—232no—
112#121—232no—
113#120—461no—
114C4×D4—462no—
115#117—231no—
116C2×C42—232no—
117C2×C42—464no—
118C2×C42—461no—
119#104—464no—
120C22⋊C8—22no—
121C23#189611yescharacteristic, complemented, Sylow
122C24D9211yescharacteristic
123#41—462no—
124#41—462no—
125C2×Q8—231no—
126C2×D4—231no—
127C2×D4—462no—
128C2×D4—461no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—464no—
132C22×C4—468no—
133C22×C4—462no—
134C22×C4—461no—
135C22×C4C4×D2312yes—
136C22×C4D9211yescharacteristic
137C22×C4C22⋊D2312yes—
138C22×C4C22×D2311yescharacteristic
139M16—22no—
140M16—22no—
141C2×C8—22no—
142C4⋊C4—232no—
143C4⋊C4—462no—
144C22⋊C4—462no—
145C22⋊C4—461no—
146C22⋊C4—462no—
147C42—234no—
148C42—464no—
149C42—462no—
150C42—461no—
151C23—21no—
152C23—21no—
153C23—24no—
154C23—461no—
155C23(C2×D23)⋊C412yes—
156C23C2×D9211yescharacteristic
157Q8—462no—
158D4—462no—
159D4—921no—
160D4—921no—
161D4—924no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—4616no—
167C2×C4—468no—
168C2×C4—464no—
169C2×C4—462no—
170C2×C4—461no—
171C2×C4—922no—
172C2×C4(C2×D23)⋊C412yes—
173C2×C4C2×C4×D2311yescharacteristic
174C2×C4D4×D2312yes—
175C2×C4#6729012yes—
176C2×C4C2×C22⋊D2311yescharacteristic
177C8—42no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—922no—
184C22—921no—
185C22#1062500714yescomplemented
186C22#1062505311yescharacteristic
187C22#1062505711yescharacteristic
188C22C2×(C2×D23)⋊C411yescharacteristic
189C4—22no—
190C4—468no—
191C4—922no—
192C4—921no—
193C4(C22⋊D23)⋊C412yes—
194C4#1062511012yes—
195C2—21no—
196C2—21no—
197C2—24no—
198C2—1841no—
199C2#1309229411yescharacteristic
200C2C2×#1062500712yes—
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#1896
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. C22×C4×Dic23C2semidirect
3. C2×#10625007C2semidirect
4. #13092178C2semidirect
5. C23×#407C2semidirect
11. #10625101C4semidirect
15. #10625095C4semidirect
35. C2×D92C2×C4semidirect
37. C2×Dic46C2×C4semidirect
44. C4⋊Dic23C2×C4semidirect
49. C4×Dic23D4semidirect
83. C22×C23#104semidirect
98. #407D23semidirect
121. C23#1896semidirect
185. C22#10625007semidirect

Maximal subgroups

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

subgroupindex
#130929282
C22×C4×Dic232
C2×#106250072
#130921782
C23×#4072
#189623