Finite Group Databasebeta

← #24994432

Subgroups — #24994432

Order 11008.

518 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 107 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#19137198C211yesmaximal, characteristic
2#19134694C212yesmaximal
3#19132925C211yesmaximal, characteristic
4#19132447C212yesmaximal
5C43×#2484C211yesmaximal, characteristic
6#14582863C2212yes—
7#14582785—24no—
8#14582762—21no—
9#14582759—21no—
10C4×C22⋊Dic43C2212yes—
11#14582658—24no—
12#14582625—22no—
13C2×#117×C43C2211yescharacteristic
14C22×C4⋊C4×C43C2211yescharacteristic
15C43×#400C412yescomplemented
16C43×#398C412yescomplemented
17C43×#387—22no—
18C43×#385—21no—
19C43×#381—21no—
20C43×#381C2211yescharacteristic
21C2×#10621877—22no—
22C2×C4⋊Dic43—22no—
23C2×C22⋊Dic43—22no—
24C2×C4×Dic43D414yes—
25C22⋊(C43⋊C8)—22no—
26C22⋊(C43⋊C8)—22no—
27C43⋊#95—22no—
28C43⋊#95—24no—
29C43⋊#95—22no—
30C23×C4×C43D411yescharacteristic
31C23×C4×C43D411yescharacteristic
32C23×C4×C43C2311yescharacteristic
33#117×C43—22no—
34#117×C43—22no—
35C2×C4⋊C4×C43—22no—
36C2×C4⋊C4×C43—22no—
37C2×C4⋊C4×C43—22no—
38C2×C4⋊C4×C43C2×C411yescharacteristic
39C2×C4⋊C4×C43C2×C411yescharacteristic
40C2×C4⋊C4×C43C2×C412yes—
41C2×C4⋊C4×C43D412yes—
42C2×C22⋊C4×C43—21no—
43C2×C22⋊C4×C43—21no—
44C2×C42×C43—21no—
45#95×C43—22no—
46#95×C43—22no—
47#95×C43—22no—
48#95×C43—21no—
49#95×C43C2×C412yes—
50C24×C43C2×D411yescharacteristic
51C22×C4×C43—22no—
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—42no—
59C22×C4×C43—42no—
60C22×C4×C43—42no—
61C22×C4×C43C22⋊C412yes—
62C22×C4×C43C22⋊C412yes—
63C22×C4×C43C22×C411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D412yes—
66C22×C4×C43#4112yes—
67C22×Dic43—24no—
68C4⋊C4×C43—24no—
69C4⋊C4×C43—24no—
70C4⋊C4×C43—22no—
71C4⋊C4×C43—22no—
72C4⋊C4×C43—44no—
73C22⋊C4×C43—42no—
74C22⋊C4×C43—41no—
75C22⋊C4×C43—41no—
76C42×C43—42no—
77C22⋊Dic43—44no—
78C4⋊Dic43—82no—
79C4×Dic43—44no—
80#10621877—44no—
81C2×C43⋊C8—42no—
82C23×C43—22no—
83C23×C43—22no—
84C23×C43—41no—
85C23×C43C2×C22⋊C411yescharacteristic
86C23×C43#12011yescharacteristic
87C23×C43#12311yescharacteristic
88C2×C4×C43—24no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43—42no—
96C2×C4×C43—42no—
97C2×C4×C43—42no—
98C2×C4×C43—42no—
99C2×C4×C43—42no—
100C2×C4×C43—42no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43—42no—
106C2×C4×C43—42no—
107C2×C4×C43—81no—
108C2×C4×C43C4×D412yes—
109C2×C4×C43#12112yes—
110C2×Dic43—44no—
111C2×Dic43—44no—
112C2×Dic43—44no—
113C43⋊C8—82no—
114#9482—431nomaximal, Sylow
115C22×C43—21no—
116C22×C43—21no—
117C22×C43—21no—
118C22×C43—21no—
119C22×C43—21no—
120C22×C43—21no—
121C22×C43—21no—
122C22×C43—44no—
123C22×C43#38611yescharacteristic
124C22×C43#42112yes—
125C22×C43#45812yes—
126C4×C43—22no—
127C4×C43—22no—
128C4×C43—42no—
129C4×C43—42no—
130C4×C43—82no—
131C4×C43—81no—
132C4×C43—81no—
133Dic43—84no—
134#2484D4311yescharacteristic
135#2313—431no—
136#1826—432no—
137#1463—431no—
138#1284—432no—
139C2×C43—22no—
140C2×C43—22no—
141C2×C43—41no—
142C2×C43#189011yescharacteristic
143C2×C43#189711yescharacteristic
144C2×C43#191211yescharacteristic
145C2×#117C2×D4311yescharacteristic
146C22×C4⋊C4C2×D4311yescharacteristic
147#407—432no—
148#400Dic4312yescomplemented
149#398Dic4312yescomplemented
150#387—22no—
151#387—864no—
152#385—21no—
153#381—21no—
154#381—861no—
155#381C2×D4311yescharacteristic
156#380—861no—
157C4×C22⋊C4—432no—
158#339—864no—
159#324—862no—
160C43#948211yescharacteristic, complemented, Sylow
161C23×C4C22⋊D4311yescharacteristic
162C23×C4C22⋊D4311yescharacteristic
163C23×C4C22×D4311yescharacteristic
164C2×M16—862no—
165#117—22no—
166#117—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—862no—
171C2×C4⋊C4C2×Dic4311yescharacteristic
172C2×C4⋊C4C2×Dic4311yescharacteristic
173C2×C4⋊C4C2×Dic4312yes—
174C2×C4⋊C4C22⋊D4312yes—
175C2×C22⋊C4—21no—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—862no—
178C2×C42—21no—
179C2×C42—434no—
180C22⋊C8—862no—
181C22⋊C8—862no—
182#95—22no—
183#95—22no—
184#95—22no—
185#95—21no—
186#95—862no—
187#95—864no—
188#95—862no—
189#95C2×Dic4312yes—
190C24C2×C22⋊D4311yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—864no—
202C22×C4C22⋊Dic4312yes—
203C22×C4C22⋊Dic4312yes—
204C22×C4D4×D4312yes—
205C22×C4#1062190012yes—
206C22×C4C22×Dic4311yescharacteristic
207C22×C4C2×C22⋊D4311yescharacteristic
208M16—1724no—
209C2×C8—1722no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—44no—
215C4⋊C4—3442no—
216C22⋊C4—42no—
217C22⋊C4—41no—
218C22⋊C4—41no—
219C22⋊C4—1724no—
220C42—42no—
221C42—1724no—
222C23—22no—
223C23—22no—
224C23—41no—
225C23C2×C22⋊Dic4311yescharacteristic
226C23#1306329311yescharacteristic
227C23#1306330611yescharacteristic
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—81no—
248C2×C4—1724no—
249C2×C4—1724no—
250C2×C4—1724no—
251C2×C4D4×Dic4312yes—
252C2×C4#1306329712yes—
253C8—3442no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—44no—
262C22#1458277911yescharacteristic
263C22#1458291612yes—
264C22#1458308812yes—
265C4—22no—
266C4—22no—
267C4—42no—
268C4—42no—
269C4—82no—
270C4—81no—
271C4—81no—
272C4—3444no—
273C2—22no—
274C2—22no—
275C2—41no—
276C2#1913500911yescharacteristic
277C2#1913504411yescharacteristic
278C2#1913513311yescharacteristic
subgroupG/H
centerC22#14582779
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2484C2
socleC22×C43#386
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#2484D43
hypocenterC43#9482
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
15. C43×#400C4semidirect
16. C43×#398C4semidirect
148. #400Dic43semidirect
149. #398Dic43semidirect
160. C43#9482semidirect

Maximal subgroups

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

subgroupindex
#191371982
#191346942
#191329252
#191324472
C43×#24842
#948243