Finite Group Databasebeta

← #15673858

Subgroups — #15673858

Order 2944.

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

normal subgroups only

This group has 390 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
1C22×#67267C211yesmaximal, characteristic, complemented
2C2×#10625101C211yesmaximal, characteristic
3C2×#10625005C212yesmaximal, complemented
4#13092185C212yesmaximal, complemented
5C23×#407C211yesmaximal, characteristic, complemented
6C23×C4×C23C2211yescharacteristic
7C22×C22⋊D23C412yes—
8C22×D92C2211yescharacteristic
9C2×M16×C23C2212yes—
10#10625101—21no—
11#10625101—21no—
12#10625101—21no—
13#10625101—21no—
14C2×(C2×D23)⋊C4C412yes—
15C2×C4⋊Dic23C2211yescharacteristic
16C2×#67267—21no—
17C2×#67267—24no—
18C2×#67267C2212yes—
19C22×C23⋊C8—21no—
20C23×C22⋊C8—21no—
21C23×C22⋊C8—21no—
22#10625005—24no—
23C24×C23C2×C411yescharacteristic
24C23×D23C2×C412yes—
25C22×C4×C23—22no—
26C22×C4×C23—22no—
27C22×C4×C23C2×C411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×C4×C23D411yescharacteristic
30C22×C4×C23D411yescharacteristic
31C22×C4×C23D411yescharacteristic
32C22×C4×C23C2311yescharacteristic
33C2×C22⋊D23—22no—
34C2×C22⋊D23—22no—
35C2×C22⋊D23—44no—
36C22×Dic23C2×C412yes—
37C2×D92—21no—
38C2×D92—21no—
39C2×D92—22no—
40C2×D92—22no—
41M16×C23—22no—
42M16×C23—22no—
43C2×C8×C23—22no—
44(C2×D23)⋊C4—22no—
45(C2×D23)⋊C4—22no—
46C4⋊Dic23—21no—
47C4⋊Dic23—21no—
48#67267—24no—
49#67267—22no—
50#67267D414yescomplemented
51C2×C23⋊C8—24no—
52C2×C23⋊C8—22no—
53C23×C23—22no—
54C23×C23—22no—
55C23×C23—41no—
56C23×C23C22⋊C411yescharacteristic
57C23×C23C22⋊C411yescharacteristic
58C23×C23C22×C411yescharacteristic
59C22×D23—22no—
60C22×D23—24no—
61C22×D23—42no—
62C22×D23—42no—
63C2×C4×C23—22no—
64C2×C4×C23—21no—
65C2×C4×C23—21no—
66C2×C4×C23—22no—
67C2×C4×C23—22no—
68C2×C4×C23—21no—
69C2×C4×C23—21no—
70C2×C4×C23C22⋊C411yescharacteristic
71C2×C4×C23C22⋊C411yescharacteristic
72C2×C4×C23C2×D411yescharacteristic
73C2×C4×C23C2×D412yes—
74C2×C4×C23C2×D411yescharacteristic
75C2×C4×C23#4112yes—
76C22⋊D23—44no—
77C22⋊D23—44no—
78C2×Dic23—22no—
79C2×Dic23—42no—
80D92—41no—
81D92—42no—
82D92—41no—
83C8×C23—42no—
84C23⋊C8—24no—
85#1900—231nomaximal, Sylow
86C22×C23—21no—
87C22×C23—21no—
88C22×C23—21no—
89C22×C23—21no—
90C22×C23—21no—
91C22×C23—21no—
92C22×C23—21no—
93C22×C23—44no—
94C22×C23#10012yescomplemented
95C22×C23C2×C22⋊C411yescharacteristic
96C22×C23C4×D412yes—
97C2×D23—42no—
98C2×D23—42no—
99C2×D23—42no—
100C2×D23—84no—
101C4×C23—21no—
102C4×C23—21no—
103C4×C23#12011yescharacteristic
104C4×C23#12112yes—
105C4×C23#12311yescharacteristic
106Dic23—42no—
107C22×M16—231no—
108C2×#121—231no—
109C2×#100—232no—
110#407D2311yescharacteristic, complemented
111#343—232no—
112C2×C23—22no—
113C2×C23—22no—
114C2×C23—41no—
115C2×C23#38611yescharacteristic
116C2×C23C2×#10011yescharacteristic
117C2×C23#41311yescharacteristic
118D23—82no—
119C22×D4—232no—
120C22×D4—231no—
121C23×C4C2×D2311yescharacteristic
122C2×M16—232no—
123C2×M16—464no—
124C2×M16—461no—
125C2×M16C2×D2312yes—
126C22×C8—461no—
127#121—461no—
128#121—461no—
129#121—461no—
130#121—461no—
131C2×C4⋊C4—231no—
132C2×C22⋊C4—232no—
133#100—464no—
134C22⋊C8—21no—
135C22⋊C8—21no—
136C23#190011yescharacteristic, complemented, Sylow
137C24—232no—
138C24C4×D2311yescharacteristic
139C2×D4—462no—
140C2×D4—462no—
141C2×D4—461no—
142C2×D4—462no—
143C2×D4—462no—
144C2×D4—461no—
145C2×D4—924no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—232no—
149C22×C4C4×D2311yescharacteristic
150C22×C4D9211yescharacteristic
151C22×C4D9211yescharacteristic
152C22×C4C22⋊D2311yescharacteristic
153C22×C4C22⋊D2311yescharacteristic
154C22×C4C22×D2311yescharacteristic
155M16—22no—
156M16—22no—
157M16—234no—
158M16—464no—
159M16—462no—
160C2×C8—22no—
161C2×C8—464no—
162C2×C8—462no—
163C4⋊C4—461no—
164C4⋊C4—461no—
165C22⋊C4—462no—
166C22⋊C4—462no—
167C23—22no—
168C23—22no—
169C23—41no—
170C23—462no—
171C23—464no—
172C23—922no—
173C23—922no—
174C23(C2×D23)⋊C411yescharacteristic
175C23(C2×D23)⋊C411yescharacteristic
176C23C2×C4×D2311yescharacteristic
177D4—924no—
178D4—924no—
179D4—921no—
180D4—921no—
181D4—922no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—462no—
190C2×C4—922no—
191C2×C4(C2×D23)⋊C411yescharacteristic
192C2×C4(C2×D23)⋊C411yescharacteristic
193C2×C4C2×D9211yescharacteristic
194C2×C4D4×D2312yes—
195C2×C4#6729012yes—
196C2×C4C2×C22⋊D2311yescharacteristic
197C8—42no—
198C8—464no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—44no—
207C22—922no—
208C22—922no—
209C22—922no—
210C22—1844no—
211C22#1062500512yescomplemented
212C22(C22⋊D23)⋊C412yes—
213C22C2×(C2×D23)⋊C411yescharacteristic
214C4—21no—
215C4—21no—
216C4—922no—
217C4#1062505311yescharacteristic
218C4#1062505711yescharacteristic
219C4#1062511012yes—
220C2—22no—
221C2—22no—
222C2—41no—
223C2—1842no—
224C2#1309229411yescharacteristic
225C2C2×#1062500511yescharacteristic
226C2#1309239911yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#407C2
socleC22×C23C2×C22⋊C4
prime radicalC2×#10625101C2
cosocleC22×C4×C23C23
hypercenter#407D23
hypocenterC23#1900
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C22×#67267C2semidirect
3. C2×#10625005C2semidirect
4. #13092185C2semidirect
5. C23×#407C2semidirect
50. #67267D4semidirect
94. C22×C23#100semidirect
110. #407D23semidirect
136. C23#1900semidirect
211. C22#10625005semidirect

Maximal subgroups

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

subgroupindex
C22×#672672
C2×#106251012
C2×#106250052
#130921852
C23×#4072
#190023