Finite Group Databasebeta

← #24994055

Subgroups — #24994055

Order 11008.

526 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 99 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#19139975C211yesmaximal, characteristic
2#19137198C211yesmaximal, characteristic
3#19133116C212yesmaximal
4#19132480C212yesmaximal
5C43×#1463C211yesmaximal, characteristic
6C2×#13063304C2211yescharacteristic
7#14582829C412yescomplemented
8#14582819C412yescomplemented
9#14582794—22no—
10#14582785—24no—
11#14582772—21no—
12#14582772—21no—
13#14582762—21no—
14#14582759—21no—
15C4×C22⋊Dic43C2211yescharacteristic
16C4×C22⋊Dic43C2212yes—
17#14582637—24no—
18C22×C4⋊C4×C43C2211yescharacteristic
19C43×#407C2212yes—
20C43×#324—22no—
21C22×Dic86C2×C411yescharacteristic
22#13063304—22no—
23#13063304—22no—
24C2×C4⋊Dic43—22no—
25C2×C4⋊Dic43C2×C411yescharacteristic
26C2×Dic43⋊C4—22no—
27C2×Dic43⋊C4—21no—
28C2×Dic43⋊C4—22no—
29C2×C22⋊Dic43—21no—
30C2×C22⋊Dic43—21no—
31C2×C22⋊Dic43—22no—
32C2×C4×Dic43—22no—
33C2×C4×Dic43—21no—
34C43⋊#95—22no—
35C43⋊#95—24no—
36C43⋊#95—22no—
37C43⋊#95—22no—
38C43⋊#95C2×C412yes—
39C43⋊#95D414yes—
40C23×C4×C43D411yescharacteristic
41C23×C4×C43D411yescharacteristic
42C23×C4×C43C2311yescharacteristic
43C2×M16×C43—22no—
44C2×C4⋊C4×C43—22no—
45C2×C4⋊C4×C43—22no—
46C2×C4⋊C4×C43C2×C412yes—
47C2×C4⋊C4×C43D412yes—
48C22⋊C8×C43—22no—
49C22⋊C8×C43—22no—
50C24×C43C2×D411yescharacteristic
51C22×C4×C43—21no—
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—42no—
56C22×C4×C43—81no—
57C22×C4×C43—81no—
58C22×C4×C43C22⋊C412yes—
59C22×C4×C43C22⋊C412yes—
60C22×C4×C43C22×C411yescharacteristic
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43C2×D412yes—
63C22×C4×C43#4112yes—
64C22×Dic43—22no—
65C22×Dic43—21no—
66C22×Dic43—21no—
67C22×Dic43—24no—
68C2×Dic86—22no—
69C2×Dic86—81no—
70M16×C43—82no—
71C2×C8×C43—42no—
72C4⋊C4×C43—24no—
73C4⋊C4×C43—24no—
74C22⋊Dic43—24no—
75C22⋊Dic43—44no—
76C22⋊Dic43—41no—
77C22⋊Dic43—41no—
78C4⋊Dic43—22no—
79C4⋊Dic43—82no—
80Dic43⋊C4—44no—
81Dic43⋊C4—42no—
82Dic43⋊C4—82no—
83C4×Dic43—81no—
84C4×Dic43—82no—
85C23×C43—22no—
86C23×C43—22no—
87C23×C43—41no—
88C23×C43C2×C22⋊C411yescharacteristic
89C23×C43#12011yescharacteristic
90C23×C43#12311yescharacteristic
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—42no—
96C2×C4×C43—41no—
97C2×C4×C43—42no—
98C2×C4×C43—41no—
99C2×C4×C43—42no—
100C2×C4×C43—42no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43—81no—
104C2×C4×C43C4×D412yes—
105C2×C4×C43#12112yes—
106C2×Dic43—24no—
107C2×Dic43—42no—
108C2×Dic43—42no—
109C2×Dic43—44no—
110C2×Dic43—42no—
111C2×Dic43—44no—
112C2×Dic43—41no—
113C2×Dic43—41no—
114C2×Dic43—42no—
115C2×Dic43—44no—
116Dic86—82no—
117C8×C43—82no—
118#9412—431nomaximal, Sylow
119C22×C43—21no—
120C22×C43—21no—
121C22×C43—21no—
122C22×C43—21no—
123C22×C43—21no—
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—44no—
127C22×C43#38611yescharacteristic
128C22×C43#42112yes—
129C22×C43#45612yes—
130C4×C43—22no—
131C4×C43—22no—
132C4×C43—42no—
133C4×C43—42no—
134Dic43—44no—
135Dic43—84no—
136Dic43—81no—
137Dic43—81no—
138#2583—431no—
139#2313—431no—
140#1508—432no—
141#1463D4311yescharacteristic
142#1297—432no—
143C2×C43—22no—
144C2×C43—22no—
145C2×C43—41no—
146C2×C43#188611yescharacteristic
147C2×C43#189711yescharacteristic
148C2×C43#191311yescharacteristic
149C2×C22⋊Q8—431no—
150C22×C4⋊C4C2×D4311yescharacteristic
151#407C2×D4312yes—
152#398—432no—
153#395—432no—
154#389—862no—
155#387—864no—
156#385—861no—
157#385—861no—
158#381—861no—
159#380—861no—
160C4×C22⋊C4—432no—
161C4×C22⋊C4—431no—
162#328—864no—
163#324—22no—
164C43#941211yescharacteristic, complemented, Sylow
165C22×Q8—431no—
166C23×C4D17211yescharacteristic
167C23×C4D17211yescharacteristic
168C23×C4C22×D4311yescharacteristic
169C2×M16—22no—
170C22⋊Q8—862no—
171C22⋊Q8—862no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—431no—
175C2×C4⋊C4—862no—
176C2×C4⋊C4—862no—
177C2×C4⋊C4—862no—
178C2×C4⋊C4—861no—
179C2×C4⋊C4C4×D4312yes—
180C2×C4⋊C4C22⋊D4312yes—
181C2×C22⋊C4—861no—
182C2×C22⋊C4—861no—
183C2×C22⋊C4—862no—
184C2×C42—862no—
185C2×C42—861no—
186C22⋊C8—22no—
187C22⋊C8—22no—
188#95—432no—
189#95—434no—
190#95—862no—
191#95—864no—
192#95—862no—
193#95—862no—
194C24C2×D17211yescharacteristic
195C2×Q8—862no—
196C2×Q8—3441no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—42no—
202C22×C4—81no—
203C22×C4—81no—
204C22×C4—862no—
205C22×C4—861no—
206C22×C4—861no—
207C22×C4—864no—
208C22×C4(C2×D43)⋊C412yes—
209C22×C4(C2×D43)⋊C412yes—
210C22×C4C2×C4×D4311yescharacteristic
211C22×C4D4×D4312yes—
212C22×C4#1062190012yes—
213C22×C4C2×C22⋊D4311yescharacteristic
214M16—82no—
215C2×C8—42no—
216C4⋊C4—24no—
217C4⋊C4—24no—
218C4⋊C4—862no—
219C4⋊C4—3442no—
220C4⋊C4—3442no—
221C4⋊C4—1724no—
222C4⋊C4—1722no—
223C22⋊C4—864no—
224C22⋊C4—1724no—
225C22⋊C4—1721no—
226C22⋊C4—1721no—
227C42—3442no—
228C42—3441no—
229C23—22no—
230C23—22no—
231C23—41no—
232C23C2×(C2×D43)⋊C411yescharacteristic
233C23#1306329511yescharacteristic
234C23#1306330911yescharacteristic
235Q8—3442no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—81no—
249C2×C4—864no—
250C2×C4—1724no—
251C2×C4—1724no—
252C2×C4—1722no—
253C2×C4—1724no—
254C2×C4—1722no—
255C2×C4—1721no—
256C2×C4—1721no—
257C2×C4—1722no—
258C2×C4—1722no—
259C2×C4(C22⋊D43)⋊C412yes—
260C2×C4#1306329712yes—
261C8—82no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—44no—
270C22#1458277611yescharacteristic
271C22#1458291512yes—
272C22#1458308412yes—
273C4—22no—
274C4—22no—
275C4—42no—
276C4—42no—
277C4—3444no—
278C4—3441no—
279C4—3441no—
280C4—1724no—
281C2—22no—
282C2—22no—
283C2—41no—
284C2#1913498611yescharacteristic
285C2#1913504111yescharacteristic
286C2#1913513511yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1463C2
socleC22×C43#386
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1463D43
hypocenterC43#9412
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
7. #14582829C4semidirect
8. #14582819C4semidirect
164. C43#9412semidirect

Maximal subgroups

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

subgroupindex
#191399752
#191371982
#191331162
#191324802
C43×#14632
#941243