Finite Group Databasebeta

← #15673865

Subgroups — #15673865

Order 2944.

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

normal subgroups only

This group has 338 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
1C2×#10625095C211yesmaximal, characteristic
2C2×#10625006C212yesmaximal, complemented
3#13092381C211yesmaximal, characteristic
4#13092185C212yesmaximal, complemented
5C22×M16×C23C211yesmaximal, characteristic
6C23×C4×C23C2211yescharacteristic
7C22×Dic46C2211yescharacteristic
8C2×M16×C23—21no—
9C2×M16×C23—24no—
10C2×M16×C23C2212yes—
11C22×C8×C23—21no—
12C2×C22⋊Dic23C412yes—
13C2×C4⋊Dic23C2211yescharacteristic
14#10625095—21no—
15#10625095—21no—
16#10625095—21no—
17#10625095—21no—
18C2×Dic23⋊C4C412yes—
19C2×#67267C2212yes—
20C22⋊(C23⋊C8)—21no—
21C22⋊(C23⋊C8)—21no—
22#10625006—24no—
23C24×C23C2×C411yescharacteristic
24C22×C4×C23—22no—
25C22×C4×C23—22no—
26C22×C4×C23C2×C411yescharacteristic
27C22×C4×C23D411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×C4×C23D411yescharacteristic
30C22×C4×C23D411yescharacteristic
31C22×C4×C23C2311yescharacteristic
32C22×Dic23C2×C412yes—
33C22×Dic23C2×C412yes—
34C2×Dic46—21no—
35C2×Dic46—21no—
36C2×Dic46—22no—
37C2×Dic46—22no—
38M16×C23—24no—
39M16×C23—22no—
40M16×C23D414yes—
41C2×C8×C23—24no—
42C2×C8×C23—22no—
43C22⋊Dic23—22no—
44C22⋊Dic23—22no—
45C4⋊Dic23—21no—
46C4⋊Dic23—21no—
47Dic23⋊C4—22no—
48Dic23⋊C4—22no—
49#67267—22no—
50#67267—22no—
51C2×C23⋊C8—22no—
52C23×C23—22no—
53C23×C23—22no—
54C23×C23—41no—
55C23×C23C22⋊C411yescharacteristic
56C23×C23C22⋊C411yescharacteristic
57C23×C23C22×C411yescharacteristic
58C2×C4×C23—22no—
59C2×C4×C23—21no—
60C2×C4×C23—21no—
61C2×C4×C23—22no—
62C2×C4×C23—22no—
63C2×C4×C23—21no—
64C2×C4×C23—21no—
65C2×C4×C23C22⋊C411yescharacteristic
66C2×C4×C23C22⋊C411yescharacteristic
67C2×C4×C23C2×D411yescharacteristic
68C2×C4×C23C2×D412yes—
69C2×C4×C23C2×D411yescharacteristic
70C2×C4×C23#4112yes—
71C2×Dic23—22no—
72C2×Dic23—22no—
73C2×Dic23—24no—
74C2×Dic23—42no—
75Dic46—41no—
76Dic46—42no—
77Dic46—41no—
78C8×C23—24no—
79C23⋊C8—42no—
80#1901—231nomaximal, Sylow
81C22×C23—21no—
82C22×C23—21no—
83C22×C23—21no—
84C22×C23—21no—
85C22×C23—21no—
86C22×C23—21no—
87C22×C23—21no—
88C22×C23—44no—
89C22×C23#10112yescomplemented
90C22×C23C2×C22⋊C411yescharacteristic
91C22×C23C4×D412yes—
92C4×C23—21no—
93C4×C23—21no—
94C4×C23#12011yescharacteristic
95C4×C23#12112yes—
96C4×C23#12311yescharacteristic
97Dic23—42no—
98Dic23—42no—
99C22×M16D2311yescharacteristic
100C2×C22⋊Q8—231no—
101C2×#101—232no—
102#407—231no—
103#343—232no—
104C2×C23—22no—
105C2×C23—22no—
106C2×C23—41no—
107C2×C23#38611yescharacteristic
108C2×C23C2×#10111yescharacteristic
109C2×C23#41311yescharacteristic
110C22×Q8—231no—
111C23×C4C2×D2311yescharacteristic
112C2×M16—21no—
113C2×M16—24no—
114C2×M16—232no—
115C2×M16C2×D2312yes—
116C22×C8—21no—
117C22⋊Q8—461no—
118C22⋊Q8—461no—
119C22⋊Q8—461no—
120C22⋊Q8—461no—
121C2×C4⋊C4—232no—
122C2×C4⋊C4—231no—
123C2×C22⋊C4—232no—
124#101—464no—
125C22⋊C8—461no—
126C22⋊C8—461no—
127C23#190111yescharacteristic, complemented, Sylow
128C24C4×D2311yescharacteristic
129C2×Q8—461no—
130C2×Q8—462no—
131C2×Q8—462no—
132C2×Q8—461no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—232no—
136C22×C4—232no—
137C22×C4C4×D2311yescharacteristic
138C22×C4D9211yescharacteristic
139C22×C4D9211yescharacteristic
140C22×C4C22⋊D2311yescharacteristic
141C22×C4C22⋊D2311yescharacteristic
142C22×C4C22×D2311yescharacteristic
143M16—24no—
144M16—22no—
145M16—462no—
146M16—462no—
147M16C22⋊D2314yes—
148C2×C8—24no—
149C2×C8—22no—
150C2×C8—462no—
151C4⋊C4—462no—
152C4⋊C4—462no—
153C4⋊C4—461no—
154C4⋊C4—461no—
155C22⋊C4—462no—
156C22⋊C4—462no—
157C23—22no—
158C23—22no—
159C23—41no—
160C23(C2×D23)⋊C411yescharacteristic
161C23(C2×D23)⋊C411yescharacteristic
162C23C2×C4×D2311yescharacteristic
163Q8—921no—
164Q8—922no—
165Q8—921no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—462no—
174C2×C4—462no—
175C2×C4—464no—
176C2×C4—922no—
177C2×C4(C2×D23)⋊C411yescharacteristic
178C2×C4(C2×D23)⋊C411yescharacteristic
179C2×C4C2×D9211yescharacteristic
180C2×C4#6728812yes—
181C2×C4C2×C22⋊D2311yescharacteristic
182C2×C4C2×C22⋊D2312yes—
183C8—24no—
184C8—922no—
185C22—21no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—44no—
193C22#1062500612yescomplemented
194C22C2×(C2×D23)⋊C411yescharacteristic
195C22C4×C22⋊D2312yes—
196C4—21no—
197C4—21no—
198C4—922no—
199C4—922no—
200C4#1062510011yescharacteristic
201C4#1062510112yes—
202C4#1062512411yescharacteristic
203C2—22no—
204C2—22no—
205C2—41no—
206C2#1309229611yescharacteristic
207C2C2×#1062500611yescharacteristic
208C2#1309239911yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC22×M16×C23C2
socleC22×C23C2×C22⋊C4
prime radicalC24×C23C2×C4
cosocleC22×C4×C23C23
hypercenterC22×M16D23
hypocenterC23#1901
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#10625006C2semidirect
4. #13092185C2semidirect
89. C22×C23#101semidirect
127. C23#1901semidirect
193. C22#10625006semidirect

Maximal subgroups

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

subgroupindex
C2×#106250952
C2×#106250062
#130923812
#130921852
C22×M16×C232
#190123