Finite Group Databasebeta

← #24994279

Subgroups — #24994279

Order 11008.

468 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 103 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#19143680C211yesmaximal, characteristic
2#19139580C211yesmaximal, characteristic
3#19133320C212yesmaximal
4#19132450C212yesmaximal
5C43×#1467C211yesmaximal, characteristic
6C2×#13063325C2211yescharacteristic
7C2×#13063323C412yes—
8#14583030—24no—
9#14582956—21no—
10#14582956C2212yes—
11#14582952—21no—
12#14582829—21no—
13#14582829—21no—
14#14582804C412yes—
15#14582797—21no—
16#14582797—21no—
17C4×C4⋊Dic43C2211yescharacteristic
18#14582647—24no—
19C2×C4×Q8×C43C2211yescharacteristic
20C43×#432C2212yes—
21C43×#324—21no—
22C43×#324—21no—
23C22×Dic86C2×C412yes—
24#13063325—22no—
25#13063325—22no—
26#13063323—44no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×Dic43⋊C4—22no—
31C2×Dic43⋊C4—22no—
32C2×C4×Dic43C2×C412yes—
33C4⋊(C43⋊C8)—22no—
34C4⋊(C43⋊C8)—22no—
35C4⋊(C43⋊C8)D414yes—
36C22⋊(C43⋊C8)—22no—
37#13063236—22no—
38#13063236—22no—
39C4×C43⋊C8—22no—
40C43⋊#95—22no—
41C43⋊#95—22no—
42C43⋊#95—21no—
43C22×Q8×C43C2×C411yescharacteristic
44C4×Q8×C43—22no—
45C4×Q8×C43—22no—
46C2×C4⋊C4×C43C2×C411yescharacteristic
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C42×C43D411yescharacteristic
50C2×C42×C43D411yescharacteristic
51C2×C42×C43C2311yescharacteristic
52C4⋊C8×C43—22no—
53C22⋊C8×C43—22no—
54#97×C43—22no—
55C2×Q8×C43—22no—
56C2×Q8×C43—22no—
57C2×Q8×C43—41no—
58C22×C4×C43C22⋊C411yescharacteristic
59C22×C4×C43C22⋊C411yescharacteristic
60C22×C4×C43C22⋊C411yescharacteristic
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×Dic43—22no—
66C22×Dic43—22no—
67C2×Dic86—24no—
68C2×Dic86—42no—
69C2×Dic86—42no—
70C2×C8×C43—42no—
71C4⋊C4×C43—22no—
72C4⋊C4×C43—22no—
73C4⋊C4×C43—22no—
74C42×C43—21no—
75C42×C43—21no—
76C42×C43—21no—
77C42×C43—21no—
78C42×C43C2×D412yes—
79C42×C43#4112yes—
80C4⋊Dic43—24no—
81C4⋊Dic43—41no—
82C4⋊Dic43—42no—
83C4⋊Dic43—41no—
84Dic43⋊C4—44no—
85Dic43⋊C4—44no—
86C4×Dic43—42no—
87C2×C43⋊C8—24no—
88C23×C43C2×C22⋊C411yescharacteristic
89Q8×C43—44no—
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—22no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—41no—
101C2×C4×C43—41no—
102C2×C4×C43—41no—
103C2×C4×C43#10012yes—
104C2×C4×C43C4×D412yes—
105C2×C4×C43#12011yescharacteristic
106C2×C4×C43#12112yes—
107C2×C4×C43#12311yescharacteristic
108C2×Dic43—24no—
109C2×Dic43—42no—
110C2×Dic43—42no—
111C2×Dic43—42no—
112C2×Dic43—42no—
113C2×Dic43—42no—
114Dic86—84no—
115C8×C43—82no—
116C43⋊C8—44no—
117#9452—431nomaximal, Sylow
118C22×C43—21no—
119C22×C43—21no—
120C22×C43#38611yescharacteristic
121C22×C43C2×#10011yescharacteristic
122C22×C43#41311yescharacteristic
123C4×C43—21no—
124C4×C43—22no—
125C4×C43—22no—
126C4×C43—22no—
127C4×C43—41no—
128C4×C43—41no—
129C4×C43—41no—
130C4×C43#45612yes—
131Dic43—44no—
132Dic43—82no—
133#2983—431no—
134#2546—431no—
135#1558—432no—
136#1467D4311yescharacteristic
137#1285—432no—
138C2×C43—21no—
139C2×C43—21no—
140C2×C43#188611yescharacteristic
141C2×C43#190011yescharacteristic
142C2×C43#190911yescharacteristic
143C2×C4⋊Q8—432no—
144C2×C4⋊Q8—431no—
145C2×C4×Q8C2×D4311yescharacteristic
146#446—864no—
147#432—432no—
148#432—861no—
149#432C2×D4312yes—
150#431—861no—
151#398—861no—
152#398—861no—
153#391—432no—
154#389—861no—
155#389—861no—
156C4×C4⋊C4—431no—
157#333—864no—
158#324—21no—
159#324—21no—
160C43#945211yescharacteristic, complemented, Sylow
161C22×Q8—432no—
162C22×Q8C4×D4311yescharacteristic
163C4⋊Q8—862no—
164C4⋊Q8—862no—
165C4⋊Q8—1724no—
166C4×Q8—22no—
167C4×Q8—22no—
168C2×C4⋊C4—861no—
169C2×C4⋊C4—862no—
170C2×C4⋊C4—862no—
171C2×C4⋊C4—861no—
172C2×C4⋊C4—861no—
173C2×C4⋊C4C4×D4311yescharacteristic
174C2×C4⋊C4C22⋊D4311yescharacteristic
175C2×C4⋊C4C22⋊D4311yescharacteristic
176C2×C42—432no—
177C2×C42D17211yescharacteristic
178C2×C42D17211yescharacteristic
179C2×C42C22×D4311yescharacteristic
180C4⋊C8—22no—
181C4⋊C8—434no—
182C4⋊C8—862no—
183C4⋊C8—862no—
184C22⋊C8—22no—
185C22⋊C8—862no—
186#97—22no—
187#97—862no—
188#97—862no—
189C4×C8—862no—
190#95—862no—
191#95—862no—
192#95—861no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—41no—
196C2×Q8—864no—
197C2×Q8—1722no—
198C2×Q8—1722no—
199C22×C4—862no—
200C22×C4—862no—
201C22×C4(C2×D43)⋊C411yescharacteristic
202C22×C4(C2×D43)⋊C411yescharacteristic
203C22×C4(C2×D43)⋊C411yescharacteristic
204C22×C4(C2×D43)⋊C411yescharacteristic
205C22×C4C2×C4×D4311yescharacteristic
206C22×C4C2×D17211yescharacteristic
207C22×C4C2×C22⋊D4311yescharacteristic
208C2×C8—42no—
209C2×C8—864no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—864no—
214C4⋊C4—1724no—
215C4⋊C4—1724no—
216C4⋊C4—1721no—
217C4⋊C4—1722no—
218C4⋊C4—1721no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—1722no—
224C42D4×D4312yes—
225C42#1062190012yes—
226C23C2×(C2×D43)⋊C411yescharacteristic
227Q8—44no—
228Q8—3444no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—864no—
243C2×C4—1722no—
244C2×C4—1722no—
245C2×C4—1722no—
246C2×C4—1722no—
247C2×C4—1722no—
248C2×C4#1306324112yes—
249C2×C4(C22⋊D43)⋊C412yes—
250C2×C4#1306329511yescharacteristic
251C2×C4#1306329712yes—
252C2×C4#1306330911yescharacteristic
253C8—82no—
254C8—1724no—
255C22—21no—
256C22—21no—
257C22#1458277611yescharacteristic
258C22C2×#1306324111yescharacteristic
259C22#1458288111yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—22no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—3442no—
268C4—1724no—
269C4#1458308412yes—
270C2—21no—
271C2—21no—
272C2#1913498611yescharacteristic
273C2#1913505611yescharacteristic
274C2#1913511511yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1467C2
socleC22×C43#386
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1467D43
hypocenterC43#9452
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
160. C43#9452semidirect

Maximal subgroups

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

subgroupindex
#191436802
#191395802
#191333202
#191324502
C43×#14672
#945243