Finite Group Databasebeta

← #15672413

Subgroups — #15672413

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#13093005C211yesmaximal, characteristic
2#13092748C211yesmaximal, characteristic, complemented
3#13092731C211yesmaximal, characteristic, complemented
4#13092342C211yesmaximal, characteristic, complemented
5#13092155C211yesmaximal, characteristic, complemented
6#13092152C211yesmaximal, characteristic, complemented
7C23×#323C211yesmaximal, characteristic, complemented
8C2×C22⋊C4×C23C2211yescharacteristic
9#10625124—21no—
10C2×C22⋊Dic23—21no—
11#10625101C2211yescharacteristic
12C4×C22⋊D23—21no—
13C2×C4⋊Dic23C2211yescharacteristic
14#10625095C2211yescharacteristic
15#10625056—21no—
16#10625055—21no—
17#10625054—21no—
18#10625050—21no—
19C23×C22⋊C8C2211yescharacteristic
20C23×C22⋊C8C2211yescharacteristic
21C23⋊#95—21no—
22C23⋊#95C2211yescharacteristic
23#10625003—21no—
24#10625000—21no—
25#10624999—21no—
26#10624998—21no—
27C24×C23D411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×C4×C23C2311yescharacteristic
30C2×C22⋊D23—21no—
31C2×C22⋊D23—21no—
32C2×C22⋊D23—21no—
33C22×Dic23—21no—
34C22×Dic23—21no—
35C2×D92D411yescharacteristic
36C2×C4×D23—21no—
37C2×Dic46D411yescharacteristic
38C2×C8×C23—21no—
39C2×C8×C23—21no—
40C22⋊C4×C23—21no—
41C22⋊C4×C23—21no—
42C22⋊Dic23—21no—
43C22⋊Dic23—21no—
44C22⋊Dic23—21no—
45C22⋊Dic23—42no—
46(C2×D23)⋊C4—21no—
47(C2×D23)⋊C4—21no—
48C4⋊Dic23—21no—
49C4⋊Dic23—21no—
50C4⋊Dic23D411yescharacteristic
51C4⋊Dic23D411yescharacteristic
52Dic23⋊C4—21no—
53Dic23⋊C4—21no—
54C4×Dic23—21no—
55C23×C23—21no—
56C23×C23—21no—
57C23×C23—21no—
58C23×C23—41no—
59C23×C23—41no—
60C23×C23C2×D411yescharacteristic
61C22×D23—21no—
62C2×C4×C23—21no—
63C2×C4×C23—41no—
64C2×C4×C23—41no—
65C2×C4×C23C2×D411yescharacteristic
66C2×C4×C23C2×D411yescharacteristic
67C22⋊D23—41no—
68C22⋊D23—41no—
69C22⋊D23—81no—
70C22⋊D23—81no—
71C2×Dic23—21no—
72C2×Dic23—21no—
73C2×Dic23—21no—
74C2×Dic23—41no—
75C2×Dic23—41no—
76C2×Dic23—41no—
77C2×Dic23—41no—
78C2×Dic23—41no—
79C2×Dic23—41no—
80D92—41no—
81C4×D23—81no—
82Dic46—41no—
83C8×C23—41no—
84C8×C23—41no—
85#1612—231nomaximal, Sylow
86C22×C23—21no—
87C22×C23—21no—
88C22×C23—42no—
89C22×C23—41no—
90C22×C23—41no—
91C22×C23—41no—
92C22×C23—81no—
93C22×C23#12011yescharacteristic
94C22×C23#13511yescharacteristic
95C22×C23AGL(1,ℤ/8)11yescharacteristic
96C2×D23—41no—
97C2×D23—41no—
98C2×D23—41no—
99C4×C23—21no—
100C4×C23—21no—
101C4×C23—41no—
102Dic23—41no—
103Dic23—41no—
104Dic23—41no—
105Dic23—81no—
106Dic23—81no—
107#538—231no—
108#483—231no—
109#480—231no—
110#397—231no—
111#328—231no—
112#327—231no—
113#323D2311yescharacteristic, complemented
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—231no—
126#121—461no—
127#120—461no—
128C4×D4—461no—
129C2×C4⋊C4—231no—
130C2×C22⋊C4—461no—
131C2×C22⋊C4C2×D2311yescharacteristic
132#107—461no—
133#106—461no—
134#103—461no—
135#102—461no—
136C22⋊C8C2×D2311yescharacteristic
137C22⋊C8C2×D2311yescharacteristic
138#95—231no—
139#95—461no—
140C23#161211yescharacteristic, complemented, Sylow
141C24D9211yescharacteristic
142C2×Q8—231no—
143C2×D4—231no—
144C2×D4—461no—
145C2×D4—461no—
146C2×D4—461no—
147C22×C4—461no—
148C22×C4—461no—
149C22×C4—461no—
150C22×C4D9211yescharacteristic
151C22×C4C22×D2311yescharacteristic
152C2×C8—21no—
153C2×C8—21no—
154C4⋊C4—231no—
155C4⋊C4—231no—
156C4⋊C4—461no—
157C4⋊C4—461no—
158C4⋊C4—461no—
159C4⋊C4—461no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—461no—
163C22⋊C4—461no—
164C22⋊C4—461no—
165C22⋊C4—461no—
166C22⋊C4—461no—
167C22⋊C4—922no—
168C42—461no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—461no—
175C23C2×D9211yescharacteristic
176Q8—921no—
177D4—921no—
178D4—921no—
179D4—921no—
180D4—1841no—
181D4—1841no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—461no—
186C2×C4—461no—
187C2×C4—461no—
188C2×C4—921no—
189C2×C4—921no—
190C2×C4—921no—
191C2×C4—921no—
192C2×C4—921no—
193C2×C4—921no—
194C2×C4—1841no—
195C2×C4D4×D2311yescharacteristic
196C2×C4D4×D2311yescharacteristic
197C8—41no—
198C8—41no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—921no—
207C22—921no—
208C22—921no—
209C22#1062505311yescharacteristic
210C22#1062507511yescharacteristic
211C22#1062507911yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—921no—
216C4—921no—
217C4—921no—
218C4—1841no—
219C4—1841no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—1841no—
224C2#1309256411yescharacteristic
225C2#1309259711yescharacteristic
226C2#1309260811yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#323C2
socleC22×C23#120
prime radical#13093005C2
hypercenter#323D23
hypocenterC23#1612
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #13092748C2semidirect
3. #13092731C2semidirect
4. #13092342C2semidirect
5. #13092155C2semidirect
6. #13092152C2semidirect
7. C23×#323C2semidirect
113. #323D23semidirect
140. C23#1612semidirect

Maximal subgroups

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

subgroupindex
#130930052
#130927482
#130927312
#130923422
#130921552
#130921522
C23×#3232
#161223