Finite Group Databasebeta

← #15673813

Subgroups — #15673813

Order 2944.

342 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 85 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#13093184C211yesmaximal, characteristic, complemented
2#13092924C211yesmaximal, characteristic
3#13092380C212yesmaximal, complemented
4#13092189C212yesmaximal, complemented
5C23×#413C211yesmaximal, characteristic, complemented
6C2×#41×C23C2211yescharacteristic
7C22×C4×D23C2211yescharacteristic
8C2×M16×C23C2212yes—
9#10625119—24no—
10#10625117—21no—
11#10625109—21no—
12#10625108C412yes—
13#10625106C412yes—
14C4×C22⋊D23—22no—
15#10625097C2211yescharacteristic
16C2×#67267—22no—
17C2×#67267C2212yes—
18C23×#101—21no—
19C23×#100—21no—
20(C2×D23)⋊C8—24no—
21C23×D23C2×C411yescharacteristic
22#41×C23—22no—
23#41×C23—22no—
24C2×Q8×C23D411yescharacteristic
25C2×D4×C23C2×C412yes—
26C2×D4×C23D411yescharacteristic
27C22×C4×C23D412yes—
28C22×C4×C23C2311yescharacteristic
29C2×C22⋊D23—22no—
30C22×Dic23C2×C411yescharacteristic
31C2×C4×D23—21no—
32C2×C4×D23—21no—
33C2×C4×D23—22no—
34C2×C4×D23—22no—
35M16×C23—22no—
36M16×C23—22no—
37C2×C8×C23—22no—
38C22⋊Dic23—22no—
39C22⋊Dic23C2×C412yes—
40(C2×D23)⋊C4—22no—
41C4⋊Dic23—21no—
42Dic23⋊C4—22no—
43C4×Dic23—21no—
44#67267—24no—
45#67267—22no—
46#67267—22no—
47C2×C23⋊C8—24no—
48C2×C23⋊C8D414yescomplemented
49C23×C23C22⋊C412yes—
50C23×C23C22×C411yescharacteristic
51C22×D23—21no—
52C22×D23—22no—
53C22×D23—42no—
54Q8×C23—22no—
55D4×C23—24no—
56D4×C23—22no—
57C2×C4×C23—22no—
58C2×C4×C23—22no—
59C2×C4×C23C22⋊C412yes—
60C2×C4×C23C2×D411yescharacteristic
61C2×C4×C23C2×D412yes—
62C2×C4×C23C2×D411yescharacteristic
63C2×C4×C23#4112yes—
64C22⋊D23—44no—
65C2×Dic23—22no—
66C2×Dic23—21no—
67C2×Dic23—22no—
68C4×D23—41no—
69C4×D23—42no—
70C4×D23—41no—
71C8×C23—42no—
72C23⋊C8—24no—
73#1891—231nomaximal, Sylow
74C22×C23—22no—
75C22×C23—41no—
76C22×C23—42no—
77C22×C23C2×C22⋊C411yescharacteristic
78C22×C23C4×D412yes—
79C2×D23—22no—
80C2×D23—24no—
81C2×D23—41no—
82C2×D23—42no—
83C2×D23—41no—
84C4×C23—22no—
85C4×C23#12011yescharacteristic
86C4×C23#12112yes—
87C4×C23#12311yescharacteristic
88Dic23—42no—
89Dic23—41no—
90#568—231no—
91#525—231no—
92#413D2311yescharacteristic, complemented
93#407—232no—
94#344—232no—
95C2×C23—21no—
96C2×C23—22no—
97C2×C23—42no—
98C2×C23#38611yescharacteristic
99D23—42no—
100C2×#41C2×D2311yescharacteristic
101C23×C4—231no—
102#131—464no—
103C2×M16—232no—
104C2×M16—462no—
105C2×M16C2×D2312yes—
106#123—232no—
107C22⋊Q8—461no—
108#121—461no—
109#120—232no—
110C4×D4—462no—
111#117—231no—
112#101—21no—
113#100—21no—
114C22⋊C8—464no—
115C23#189111yescharacteristic, complemented, Sylow
116C24—231no—
117#41—22no—
118#41—22no—
119C2×Q8C22⋊D2311yescharacteristic
120C2×D4—462no—
121C2×D4C4×D2312yes—
122C2×D4C22⋊D2311yescharacteristic
123C22×C4—231no—
124C22×C4—461no—
125C22×C4—462no—
126C22×C4—462no—
127C22×C4—461no—
128C22×C4D9212yes—
129C22×C4C22×D2311yescharacteristic
130M16—22no—
131M16—22no—
132M16—464no—
133M16—462no—
134M16—462no—
135C2×C8—22no—
136C2×C8—234no—
137C2×C8—464no—
138C4⋊C4—462no—
139C4⋊C4—461no—
140C22⋊C4—232no—
141C22⋊C4—462no—
142C22⋊C4—462no—
143C42—461no—
144C23—462no—
145C23—461no—
146C23—922no—
147C23(C2×D23)⋊C412yes—
148C23C2×C4×D2311yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—924no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—462no—
156C2×C4—462no—
157C2×C4—461no—
158C2×C4—921no—
159C2×C4—921no—
160C2×C4—922no—
161C2×C4(C2×D23)⋊C412yes—
162C2×C4C2×D9211yescharacteristic
163C2×C4D4×D2312yes—
164C2×C4#6729012yes—
165C2×C4C2×C22⋊D2311yescharacteristic
166C8—42no—
167C8—464no—
168C22—22no—
169C22—41no—
170C22—42no—
171C22—462no—
172C22—464no—
173C22—921no—
174C22—922no—
175C22—921no—
176C22(C22⋊D23)⋊C412yes—
177C22C2×(C2×D23)⋊C411yescharacteristic
178C4—22no—
179C4—922no—
180C4—921no—
181C4#1062505311yescharacteristic
182C4#1062505711yescharacteristic
183C4#1062511012yes—
184C2—21no—
185C2—22no—
186C2—42no—
187C2—922no—
188C2#1309229411yescharacteristic
subgroupG/H
centerC4#10625053
commutatorC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#413C2
socleC2×C23#386
prime radical#13092924C2
cosocleC22×C4×C23C23
hypercenter#413D23
hypocenterC23#1891
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #13093184C2semidirect
3. #13092380C2semidirect
4. #13092189C2semidirect
5. C23×#413C2semidirect
48. C2×C23⋊C8D4semidirect
92. #413D23semidirect
115. C23#1891semidirect

Maximal subgroups

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

subgroupindex
#130931842
#130929242
#130923802
#130921892
C23×#4132
#189123