Finite Group Databasebeta

← #15675407

Subgroups — #15675407

Order 2944.

260 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 41 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#13093154C211yesmaximal, characteristic, complemented
2#13092608C211yesmaximal, characteristic, complemented
3#13092605C211yesmaximal, characteristic, complemented
4#13092584C211yesmaximal, characteristic, complemented
5#13092206C211yesmaximal, characteristic, complemented
6#13092203C211yesmaximal, characteristic, complemented
7C23×#353C211yesmaximal, characteristic, complemented
8#10625155C2211yescharacteristic
9C23×#127C2211yescharacteristic
10#10625110—21no—
11#10625110—21no—
12#10625110—21no—
13#10625108—21no—
14#10625108C2211yescharacteristic
15#10625106—21no—
16#10625106C2211yescharacteristic
17#10625103—21no—
18#10625057—21no—
19#10625053—21no—
20#10625047—21no—
21C23×#99C2211yescharacteristic
22C23×#99C2211yescharacteristic
23#10625015C2211yescharacteristic
24#10624988—21no—
25#10624988—21no—
26#10624987—21no—
27C23×D23D411yescharacteristic
28C2×D4×C23—21no—
29C2×D4×C23—21no—
30C2×D4×C23D411yescharacteristic, complemented
31C2×D4×C23C2311yescharacteristic
32C2×C22⋊D23—21no—
33C2×C22⋊D23—21no—
34C2×C22⋊D23—21no—
35C2×C22⋊D23—21no—
36C2×C22⋊D23—21no—
37C22×Dic23—21no—
38C22×Dic23D411yescharacteristic, complemented
39#67290—41no—
40D4×D23—41no—
41#67288—21no—
42C2×D92—41no—
43C22⋊C4×C23—21no—
44C22⋊C4×C23—21no—
45C42×C23D411yescharacteristic, complemented
46C22⋊Dic23—21no—
47C22⋊Dic23—21no—
48C22⋊Dic23D411yescharacteristic
49C22⋊Dic23D411yescharacteristic, complemented
50#67273—41no—
51#67272—41no—
52(C2×D23)⋊C4—21no—
53(C2×D23)⋊C4—21no—
54(C2×D23)⋊C4—21no—
55(C2×D23)⋊C4—41no—
56(C2×D23)⋊C4—41no—
57C4⋊Dic23—41no—
58Dic23⋊C4—21no—
59Dic23⋊C4—21no—
60Dic23⋊C4—21no—
61#67267—21no—
62C23×C23—21no—
63C23×C23C2×D411yescharacteristic
64C23×C23C2×D411yescharacteristic
65C22×D23—21no—
66C22×D23—21no—
67C22×D23—21no—
68C22×D23—41no—
69C22×D23—81no—
70D4×C23—41no—
71D4×C23—41no—
72D4×C23—81no—
73D4×C23—81no—
74C2×C4×C23—21no—
75C2×C4×C23—41no—
76C2×C4×C23—41no—
77C2×C4×C23C2×D411yescharacteristic
78C22⋊D23—41no—
79C22⋊D23—41no—
80C22⋊D23—41no—
81C22⋊D23—81no—
82C22⋊D23—81no—
83C22⋊D23—81no—
84C2×Dic23—21no—
85C2×Dic23—21no—
86C2×Dic23—21no—
87C2×Dic23—21no—
88C2×Dic23—21no—
89C2×Dic23—41no—
90C2×Dic23—81no—
91D92—21no—
92D92—82no—
93C4×D23—41no—
94Dic46—21no—
95C23⋊C8—41no—
96#2200—231nomaximal, Sylow
97C22×C23—21no—
98C22×C23—21no—
99C22×C23—41no—
100C22×C23—41no—
101C22×C23—41no—
102C22×C23—41no—
103C22×C23—41no—
104C22×C23#12011yescharacteristic
105C2×D23—41no—
106C2×D23—41no—
107C2×D23—42no—
108C2×D23—41no—
109C2×D23—41no—
110C2×D23—81no—
111C2×D23—81no—
112C2×D23—81no—
113C4×C23—21no—
114C4×C23—41no—
115C4×C23—81no—
116C4×C23—81no—
117Dic23—41no—
118Dic23—41no—
119Dic23—41no—
120Dic23—41no—
121#560—231no—
122#458—231no—
123B(4,𝔽2)—231no—
124#453—231no—
125#353D2311yescharacteristic, complemented
126#352—231no—
127AΣL(1,𝔽16)—231no—
128C2×C23—21no—
129C2×C23—41no—
130C2×C23—41no—
131C2×C23—81no—
132C2×C23B(4,𝔽2)11yescharacteristic
133D23—81no—
134D23—81no—
135H(5,𝔽2)—231no—
136AGL(1,ℤ/8)—461no—
137#127C2×D2311yescharacteristic
138#126—461no—
139#123—231no—
140#123—461no—
141#123—461no—
142#121—461no—
143#121—461no—
144#121—461no—
145#120—231no—
146#120—461no—
147#120—461no—
148#104—461no—
149#100—231no—
150#99—461no—
151#99—461no—
152#99C2×D2311yescharacteristic
153#99C2×D2311yescharacteristic
154C23#220011yescharacteristic, complemented, Sylow
155C24—231no—
156#41—461no—
157#41—921no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—461no—
161C2×D4—461no—
162C2×D4—461no—
163C2×D4—461no—
164C2×D4—461no—
165C2×D4—921no—
166C2×D4—921no—
167C2×D4D9211yescharacteristic, complemented
168C2×D4C22×D2311yescharacteristic
169C22×C4—231no—
170C22×C4—461no—
171SD16—921no—
172D8—921no—
173M16—461no—
174C4⋊C4—461no—
175C4⋊C4—461no—
176C4⋊C4—461no—
177C4⋊C4—921no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—231no—
181C22⋊C4—231no—
182C22⋊C4—461no—
183C22⋊C4—461no—
184C22⋊C4—461no—
185C22⋊C4—461no—
186C22⋊C4—461no—
187C22⋊C4—921no—
188C22⋊C4—921no—
189C42D9211yescharacteristic, complemented
190C23—21no—
191C23—461no—
192C23—461no—
193C23—461no—
194C23—921no—
195C23—1841no—
196C23D4×D2311yescharacteristic
197C23D4×D2311yescharacteristic
198Q8—461no—
199D4—41no—
200D4—41no—
201D4—81no—
202D4—81no—
203D4—461no—
204D4—921no—
205D4—921no—
206D4—921no—
207D4—1842no—
208D4—1841no—
209D4—1841no—
210D4—1841no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—461no—
215C2×C4—461no—
216C2×C4—461no—
217C2×C4—461no—
218C2×C4—461no—
219C2×C4—921no—
220C2×C4—921no—
221C2×C4—1841no—
222C2×C4C2×D9211yescharacteristic
223C8—921no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—921no—
232C22—921no—
233C22—922no—
234C22—921no—
235C22—921no—
236C22—1841no—
237C22—1841no—
238C22—1841no—
239C22#1062505311yescharacteristic
240C4—21no—
241C4—41no—
242C4—81no—
243C4—81no—
244C4—921no—
245C4—921no—
246C4—921no—
247C4—921no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—1841no—
253C2—1841no—
254C2#1309260511yescharacteristic
subgroupG/H
centerC2#13092605
commutator, cosocleC2×D4×C23C23
FrattiniC2×D4C22×D23
FittingC23×#353C2
socleC2×C23B(4,𝔽2)
hypercenter#353D23
hypocenterC23#2200
LCSG ▷ C2×D4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
1. #13093154C2semidirect
2. #13092608C2semidirect
3. #13092605C2semidirect
4. #13092584C2semidirect
5. #13092206C2semidirect
6. #13092203C2semidirect
7. C23×#353C2semidirect
30. C2×D4×C23D4semidirect
38. C22×Dic23D4semidirect
45. C42×C23D4semidirect
49. C22⋊Dic23D4semidirect
125. #353D23semidirect
154. C23#2200semidirect
167. C2×D4D92semidirect
189. C42D92semidirect

Maximal subgroups

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

subgroupindex
#130931542
#130926082
#130926052
#130925842
#130922062
#130922032
C23×#3532
#220023