Finite Group Databasebeta

← #15672412

Subgroups — #15672412

Order 2944.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#13093004C211yesmaximal, characteristic
2#13092748C211yesmaximal, characteristic, complemented
3#13092728C211yesmaximal, characteristic, complemented
4#13092344C211yesmaximal, characteristic, complemented
5#13092153C211yesmaximal, characteristic, complemented
6#13092140C211yesmaximal, characteristic, complemented
7C23×#327C211yesmaximal, characteristic, complemented
8C23×#121C2211yescharacteristic
9#10625110—21no—
10#10625108—21no—
11D4×Dic23—21no—
12C2×(C2×D23)⋊C4—21no—
13C2×(C2×D23)⋊C4C2211yescharacteristic
14C2×C4⋊Dic23C2211yescharacteristic
15#10625095C2211yescharacteristic
16#10625069—21no—
17#10625057—21no—
18#10625056—21no—
19C23×C22⋊C8C2211yescharacteristic
20C23×#95C2211yescharacteristic
21#10625014—21no—
22C23⋊#95—21no—
23C22⋊(C23⋊C8)C2211yescharacteristic
24#10624999—21no—
25#10624998—21no—
26#10624989—21no—
27C23×D23D411yescharacteristic
28C2×D4×C23—21no—
29C2×D4×C23D411yescharacteristic
30C22×C4×C23—21no—
31C22×C4×C23C2311yescharacteristic
32C2×C22⋊D23—21no—
33C2×C22⋊D23—21no—
34C22×Dic23—21no—
35C22×Dic23—21no—
36C22×Dic23D411yescharacteristic
37C2×Dic46D411yescharacteristic
38C2×C8×C23—21no—
39C4⋊C4×C23D411yescharacteristic
40C22⋊C4×C23—21no—
41C22⋊Dic23—21no—
42C22⋊Dic23—21no—
43(C2×D23)⋊C4—21no—
44(C2×D23)⋊C4—21no—
45(C2×D23)⋊C4—21no—
46(C2×D23)⋊C4—21no—
47(C2×D23)⋊C4—42no—
48C4⋊Dic23—21no—
49C4⋊Dic23—21no—
50C4⋊Dic23—21no—
51C4⋊Dic23D411yescharacteristic
52Dic23⋊C4—21no—
53C4×Dic23—21no—
54C2×C23⋊C8—21no—
55C23×C23—21no—
56C23×C23C2×D411yescharacteristic
57C22×D23—21no—
58C22×D23—21no—
59C22×D23—21no—
60C22×D23—41no—
61C22×D23—41no—
62D4×C23—41no—
63D4×C23—41no—
64D4×C23—41no—
65C2×C4×C23—21no—
66C2×C4×C23—41no—
67C2×C4×C23—41no—
68C2×C4×C23—41no—
69C2×C4×C23—41no—
70C2×C4×C23C2×D411yescharacteristic
71C2×C4×C23C2×D411yescharacteristic
72C22⋊D23—81no—
73C22⋊D23—81no—
74C2×Dic23—21no—
75C2×Dic23—21no—
76C2×Dic23—21no—
77C2×Dic23—41no—
78C2×Dic23—41no—
79C2×Dic23—41no—
80C2×Dic23—41no—
81C2×Dic23—81no—
82Dic46—41no—
83C8×C23—41no—
84C23⋊C8—41no—
85#1612—231nomaximal, Sylow
86C22×C23—21no—
87C22×C23—21no—
88C22×C23—41no—
89C22×C23—41no—
90C22×C23—41no—
91C22×C23#12011yescharacteristic
92C22×C23#13511yescharacteristic
93C22×C23AGL(1,ℤ/8)11yescharacteristic
94C2×D23—42no—
95C2×D23—41no—
96C2×D23—41no—
97C2×D23—41no—
98C2×D23—81no—
99C4×C23—21no—
100C4×C23—21no—
101C4×C23—41no—
102C4×C23—81no—
103Dic23—41no—
104Dic23—41no—
105Dic23—41no—
106Dic23—81no—
107#538—231no—
108#483—231no—
109#480—231no—
110#397—231no—
111#328—231no—
112#327D2311yescharacteristic, complemented
113#323—231no—
114C2×C23—21no—
115C2×C23—21no—
116C2×C23—81no—
117C2×C23#44911yescharacteristic
118C2×C23#45511yescharacteristic
119C2×C23#45811yescharacteristic
120D23—81no—
121#126—461no—
122#124—461no—
123#123—461no—
124C22⋊Q8—231no—
125#121—461no—
126#121C2×D2311yescharacteristic
127#120—461no—
128C4×D4—461no—
129C2×C4⋊C4—231no—
130C2×C22⋊C4—231no—
131C2×C22⋊C4—461no—
132#107—461no—
133#106—461no—
134#103—461no—
135#102—461no—
136C22⋊C8—231no—
137C22⋊C8C2×D2311yescharacteristic
138#95—461no—
139#95C2×D2311yescharacteristic
140C23#161211yescharacteristic, complemented, Sylow
141C24—231no—
142C2×Q8—231no—
143C2×D4—21no—
144C2×D4—461no—
145C2×D4—461no—
146C2×D4D9211yescharacteristic
147C22×C4—21no—
148C22×C4—231no—
149C22×C4—461no—
150C22×C4—461no—
151C22×C4C22×D2311yescharacteristic
152C2×C8—21no—
153C2×C8—461no—
154C4⋊C4—231no—
155C4⋊C4—461no—
156C4⋊C4—461no—
157C4⋊C4—461no—
158C4⋊C4—461no—
159C4⋊C4D9211yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—461no—
162C22⋊C4—461no—
163C22⋊C4—461no—
164C22⋊C4—461no—
165C22⋊C4—461no—
166C22⋊C4—461no—
167C22⋊C4—922no—
168C42—461no—
169C23—21no—
170C23—461no—
171C23—461no—
172C23—461no—
173C23—921no—
174C23—921no—
175C23D4×D2311yescharacteristic
176Q8—921no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—1841no—
181D4—1841no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—461no—
188C2×C4—461no—
189C2×C4—461no—
190C2×C4—921no—
191C2×C4—921no—
192C2×C4—921no—
193C2×C4—921no—
194C2×C4—1841no—
195C2×C4C2×D9211yescharacteristic
196C2×C4D4×D2311yescharacteristic
197C8—41no—
198C8—921no—
199C22—21no—
200C22—21no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—922no—
205C22—921no—
206C22—921no—
207C22—921no—
208C22—1841no—
209C22#1062505311yescharacteristic
210C22#1062508211yescharacteristic
211C22#1062508711yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—921no—
217C4—921no—
218C4—921no—
219C4—1841no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—1841no—
224C2#1309256311yescharacteristic
225C2#1309259611yescharacteristic
226C2#1309260811yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#327C2
socleC22×C23#120
prime radical#13093004C2
hypercenter#327D23
hypocenterC23#1612
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #13092748C2semidirect
3. #13092728C2semidirect
4. #13092344C2semidirect
5. #13092153C2semidirect
6. #13092140C2semidirect
7. C23×#327C2semidirect
112. #327D23semidirect
140. C23#1612semidirect

Maximal subgroups

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

subgroupindex
#130930042
#130927482
#130927282
#130923442
#130921532
#130921402
C23×#3272
#161223