Finite Group Databasebeta

← #24984820

Subgroups — #24984820

Order 11008.

874 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 874 conjugacy classes of subgroups — too many to draw. Only its 139 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#19134357C212yesmaximal, complemented
2#19132416C214yesmaximal, complemented
3C2×C43×#390C211yesmaximal, characteristic
4C2×C22⋊(C43⋊C8)—22no—
5C2×#13063236—22no—
6#14582654C2214yescomplemented
7C23×D4×C43C411yescharacteristic
8C22×C4⋊C4×C43C411yescharacteristic
9C22×C22⋊C4×C43—22no—
10C22×C42×C43C2211yescharacteristic
11C43×#390—22no—
12C43×#390C412yes—
13C43×#390C2212yes—
14C22×C43⋊C8—24no—
15C22⋊(C43⋊C8)—28no—
16#13063236—44no—
17C25×C43—21no—
18C22×D4×C43—24no—
19C22×D4×C43—21no—
20C22×D4×C43—42no—
21C22×D4×C43—42no—
22C22×D4×C43C2×C412yes—
23C23×C4×C43—21no—
24C23×C4×C43C2×C411yescharacteristic
25C23×C4×C43D412yes—
26C2×C4⋊C4×C43—21no—
27C2×C4⋊C4×C43—42no—
28C2×C4⋊C4×C43C2×C412yes—
29C2×C22⋊C4×C43—24no—
30C2×C22⋊C4×C43—24no—
31C2×C22⋊C4×C43—48no—
32C2×C42×C43—42no—
33C2×C42×C43C2×C411yescharacteristic
34C2×C42×C43D412yes—
35C2×C42×C43C2311yescharacteristic
36C24×C43—24no—
37C24×C43—22no—
38C24×C43—44no—
39C24×C43—42no—
40C24×C43—42no—
41C24×C43—44no—
42C24×C43C22⋊C411yescharacteristic
43C2×D4×C43—24no—
44C2×D4×C43—22no—
45C2×D4×C43—416no—
46C2×D4×C43—42no—
47C2×D4×C43—42no—
48C2×D4×C43—42no—
49C2×D4×C43—42no—
50C2×D4×C43M1614yes—
51C22×C4×C43—22no—
52C22×C4×C43—22no—
53C22×C4×C43—24no—
54C22×C4×C43—22no—
55C22×C4×C43—24no—
56C22×C4×C43—22no—
57C22×C4×C43—42no—
58C22×C4×C43—44no—
59C22×C4×C43—42no—
60C22×C4×C43C22⋊C412yes—
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D412yes—
64C4⋊C4×C43—42no—
65C4⋊C4×C43—42no—
66C22⋊C4×C43—48no—
67C22⋊C4×C43—48no—
68C42×C43—24no—
69C42×C43—41no—
70C42×C43—41no—
71C2×C43⋊C8—28no—
72C2×C43⋊C8—44no—
73C2×C43⋊C8—44no—
74C23×C43—21no—
75C23×C43—21no—
76C23×C43—22no—
77C23×C43—24no—
78C23×C43—48no—
79C23×C43—416no—
80C23×C43—42no—
81C23×C43—42no—
82C23×C43—44no—
83C23×C43—44no—
84C23×C43—84no—
85C23×C43—88no—
86C23×C43—84no—
87C23×C43#10012yes—
88C23×C43#10414yes—
89C23×C43C2×C22⋊C411yescharacteristic
90D4×C43—44no—
91D4×C43—48no—
92D4×C43—44no—
93C2×C4×C43—28no—
94C2×C4×C43—21no—
95C2×C4×C43—22no—
96C2×C4×C43—21no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—48no—
104C2×C4×C43—42no—
105C2×C4×C43—44no—
106C2×C4×C43—84no—
107C2×C4×C43#9912yes—
108C2×C4×C43C2×M1612yes—
109C2×C4×C43AGL(1,ℤ/8)14yes—
110C43⋊C8—48no—
111#7626—431nomaximal, Sylow
112C22×C43—22no—
113C22×C43—22no—
114C22×C43—24no—
115C22×C43—24no—
116C22×C43—44no—
117C22×C43—48no—
118C22×C43—816no—
119C22×C43—82no—
120C22×C43—84no—
121C22×C43—82no—
122C22×C43#32914yes—
123C22×C43#40711yescharacteristic
124C22×C43C2×#9911yescharacteristic
125C22×C43C2×#10011yescharacteristic
126C22×C43#41812yes—
127C22×C43C2×#10412yes—
128C4×C43—22no—
129C4×C43—22no—
130C4×C43—24no—
131C4×C43—42no—
132C4×C43—82no—
133C2×#390D4311yescharacteristic
134#1749—432no—
135#1270—434no—
136C2×C43—24no—
137C2×C43—84no—
138C2×C43#146211yescharacteristic
139C2×C43#149012yes—
140C2×C43#150712yes—
141C2×C43C2×#32911yescharacteristic
142C2×C43#155511yescharacteristic
143C23×D4Dic4311yescharacteristic
144C22×C4⋊C4Dic4311yescharacteristic
145C22×C22⋊C4—22no—
146C22×C42C2×D4311yescharacteristic
147C2×C22⋊C8—862no—
148C2×#97—862no—
149#390—22no—
150#390Dic4312yes—
151#390C2×D4312yes—
152#336—434no—
153C43#762611yescharacteristic, complemented, Sylow
154C25—21no—
155C22×D4—24no—
156C22×D4—21no—
157C22×D4—42no—
158C22×D4—42no—
159C22×D4C2×Dic4312yes—
160C23×C4—21no—
161C23×C4C2×Dic4311yescharacteristic
162C23×C4C22⋊D4312yes—
163C22×C8—864no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—42no—
166C2×C4⋊C4C2×Dic4312yes—
167C2×C22⋊C4—24no—
168C2×C22⋊C4—24no—
169C2×C22⋊C4—48no—
170C2×C42—42no—
171C2×C42C2×Dic4311yescharacteristic
172C2×C42C22⋊D4312yes—
173C2×C42C22×D4311yescharacteristic
174C22⋊C8—868no—
175#97—1724no—
176C24—24no—
177C24—22no—
178C24—44no—
179C24—42no—
180C24—42no—
181C24—44no—
182C24C22⋊Dic4311yescharacteristic
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—42no—
186C2×D4—42no—
187C2×D4—416no—
188C2×D4—42no—
189C2×D4—42no—
190C2×D4#1062187714yes—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—24no—
195C22×C4—24no—
196C22×C4—22no—
197C22×C4—42no—
198C22×C4—44no—
199C22×C4—42no—
200C22×C4C22⋊Dic4312yes—
201C22×C4C22⋊Dic4311yescharacteristic
202C22×C4C22×Dic4311yescharacteristic
203C22×C4C2×C22⋊D4312yes—
204C2×C8—868no—
205C2×C8—1724no—
206C2×C8—1724no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C22⋊C4—48no—
210C22⋊C4—48no—
211C42—24no—
212C42—41no—
213C42—41no—
214C23—21no—
215C23—21no—
216C23—22no—
217C23—24no—
218C23—48no—
219C23—416no—
220C23—42no—
221C23—42no—
222C23—44no—
223C23—44no—
224C23—84no—
225C23—88no—
226C23—84no—
227C23#1306324212yes—
228C23#1306325214yes—
229C23C2×C22⋊Dic4311yescharacteristic
230D4—44no—
231D4—48no—
232D4—44no—
233C2×C4—28no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—48no—
244C2×C4—42no—
245C2×C4—44no—
246C2×C4—84no—
247C2×C4#1306324012yes—
248C2×C4C2×#1062187712yes—
249C2×C4#1306335114yes—
250C8—1728no—
251C22—24no—
252C22—22no—
253C22—24no—
254C22—22no—
255C22—48no—
256C22—44no—
257C22—816no—
258C22—82no—
259C22—84no—
260C22—82no—
261C22#1458263914yes—
262C22#1458286311yescharacteristic
263C22C2×#1306324011yescharacteristic
264C22C2×#1306324211yescharacteristic
265C22#1458290412yes—
266C22C2×#1306325212yes—
267C4—24no—
268C4—22no—
269C4—22no—
270C4—42no—
271C4—82no—
272C2—24no—
273C2—84no—
274C2#1913292211yescharacteristic
275C2#1913303812yes—
276C2#1913311112yes—
277C2C2×#1458263911yescharacteristic
278C2#1913330911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#390C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D4×C43C4
cosocleC2×C42×C43C23
hypercenterC2×#390D43
hypocenterC43#7626
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. #19134357C2semidirect
2. #19132416C2semidirect
6. #14582654C22semidirect
153. C43#7626semidirect

Maximal subgroups

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

subgroupindex
#191343572
#191324162
C2×C43×#3902
#762643