Finite Group Databasebeta

← #24991265

Subgroups — #24991265

Order 11008.

510 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 119 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
2C4×#13063323C211yesmaximal, characteristic
3#19132991C212yesmaximal
4#19132427C212yesmaximal
5C43×#1461C211yesmaximal, characteristic
6C2×#13063323C411yescharacteristic
7C2×C4×Dic86C2211yescharacteristic
8#14583030—24no—
9#14582956—22no—
10#14582952C2212yes—
11#14582806C411yescharacteristic
12#14582804C411yescharacteristic
13#14582794—22no—
14#14582768C411yescharacteristic
15C4×Dic43⋊C4—22no—
16C42×Dic43C2211yescharacteristic
17#14582631—24no—
18C2×C4×Q8×C43C2211yescharacteristic
19C43×#431C2212yes—
20C43×#324—22no—
21C22×Dic86C2×C411yescharacteristic
22#13063323—22no—
23#13063323—22no—
24C4×Dic86—22no—
25C4×Dic86—22no—
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×Dic43⋊C4—22no—
28C2×Dic43⋊C4—22no—
29C2×Dic43⋊C4—21no—
30C2×C4×Dic43—21no—
31C2×C4×Dic43—21no—
32C2×C4×Dic43—21no—
33C2×C4×Dic43C2×C411yescharacteristic
34C2×C4×Dic43C2×C411yescharacteristic
35C4⋊(C43⋊C8)—24no—
36C4⋊(C43⋊C8)D414yes—
37C22⋊(C43⋊C8)—22no—
38#13063236—24no—
39C4×C43⋊C8—22no—
40C43⋊#95—22no—
41C43⋊#95—22no—
42C22×Q8×C43C2×C411yescharacteristic
43C4×Q8×C43—22no—
44C4×Q8×C43—22no—
45C2×C4⋊C4×C43C2×C411yescharacteristic
46C2×C4⋊C4×C43D412yes—
47C2×C42×C43D412yes—
48C2×C42×C43C2311yescharacteristic
49C4⋊C8×C43—22no—
50C22⋊C8×C43—22no—
51C4×C8×C43—22no—
52C2×Q8×C43—22no—
53C2×Q8×C43—21no—
54C2×Q8×C43—21no—
55C2×Q8×C43—22no—
56C22×C4×C43C22⋊C412yes—
57C22×C4×C43C22⋊C412yes—
58C22×C4×C43C22×C411yescharacteristic
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×Dic43—21no—
62C22×Dic43—21no—
63C22×Dic43—21no—
64C22×Dic43—21no—
65C2×Dic86—22no—
66C2×Dic86—22no—
67C2×Dic86—21no—
68C2×Dic86M1612yes—
69C2×C8×C43—42no—
70C4⋊C4×C43—22no—
71C4⋊C4×C43—24no—
72C42×C43—22no—
73C42×C43—22no—
74C42×C43C2×D412yes—
75C42×C43#4112yes—
76C4⋊Dic43—22no—
77Dic43⋊C4—28no—
78Dic43⋊C4—44no—
79Dic43⋊C4—42no—
80C4×Dic43—24no—
81C4×Dic43—21no—
82C4×Dic43—22no—
83C4×Dic43—42no—
84C4×Dic43—41no—
85C4×Dic43—41no—
86C4×Dic43M1612yes—
87C2×C43⋊C8—24no—
88C23×C43C2×C22⋊C411yescharacteristic
89Q8×C43—42no—
90Q8×C43—42no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—41no—
97C2×C4×C43—42no—
98C2×C4×C43C4×D412yes—
99C2×C4×C43#12011yescharacteristic
100C2×C4×C43#12112yes—
101C2×C4×C43#12311yescharacteristic
102C2×C4×C43C2×M1611yescharacteristic
103C2×C4×C43C2×M1611yescharacteristic
104C2×C4×C43#13112yes—
105C2×Dic43—22no—
106C2×Dic43—22no—
107C2×Dic43—22no—
108C2×Dic43—22no—
109C2×Dic43—22no—
110C2×Dic43—41no—
111C2×Dic43—41no—
112C2×Dic43—41no—
113C2×Dic43—41no—
114C2×Dic43—42no—
115C2×Dic43—41no—
116Dic86—24no—
117Dic86—42no—
118C8×C43—82no—
119C43⋊C8—44no—
120#8962—431nomaximal, Sylow
121C22×C43—21no—
122C22×C43—21no—
123C22×C43#38611yescharacteristic
124C22×C43#40711yescharacteristic
125C22×C43#40811yescharacteristic
126C4×C43—22no—
127C4×C43—21no—
128C4×C43—42no—
129C4×C43—42no—
130C4×C43#43512yes—
131C4×C43#43612yes—
132C4×C43#45612yes—
133Dic43—24no—
134Dic43—42no—
135Dic43—42no—
136Dic43—81no—
137#2983—431no—
138C4×C4⋊Q8—431no—
139#1479—432no—
140#1461D4311yescharacteristic
141#1276—432no—
142C2×C43—21no—
143C2×C43—21no—
144C2×C43#187011yescharacteristic
145C2×C43#188411yescharacteristic
146C2×C43#188611yescharacteristic
147C2×C4⋊Q8—431no—
148C2×C4×Q8—431no—
149C2×C4×Q8C2×D4311yescharacteristic
150#446—864no—
151#432—862no—
152#431—432no—
153#431C2×D4312yes—
154#391—431no—
155#391—431no—
156#389—862no—
157#384—431no—
158C4×C4⋊C4—862no—
159C43—431no—
160Q8⋊C8—864no—
161#324—22no—
162C43#896211yescharacteristic, complemented, Sylow
163C22×Q8—431no—
164C22×Q8C4×D4311yescharacteristic
165C4⋊Q8—862no—
166C4⋊Q8—862no—
167C4×Q8—22no—
168C4×Q8—22no—
169C4×Q8—862no—
170C4×Q8—862no—
171C2×C4⋊C4—431no—
172C2×C4⋊C4—862no—
173C2×C4⋊C4—862no—
174C2×C4⋊C4—861no—
175C2×C4⋊C4C4×D4311yescharacteristic
176C2×C4⋊C4C22⋊D4312yes—
177C2×C42—431no—
178C2×C42—431no—
179C2×C42—861no—
180C2×C42—861no—
181C2×C42—861no—
182C2×C42D17212yes—
183C2×C42C22×D4311yescharacteristic
184C4⋊C8—22no—
185C4⋊C8—434no—
186C4⋊C8—864no—
187C22⋊C8—22no—
188C22⋊C8—862no—
189#97—864no—
190C4×C8—22no—
191C4×C8—862no—
192#95—862no—
193#95—862no—
194C2×Q8—22no—
195C2×Q8—21no—
196C2×Q8—21no—
197C2×Q8—22no—
198C2×Q8—432no—
199C2×Q8—861no—
200C2×Q8—862no—
201C2×Q8—862no—
202C22×C4—861no—
203C22×C4—861no—
204C22×C4—861no—
205C22×C4—861no—
206C22×C4(C2×D43)⋊C412yes—
207C22×C4(C2×D43)⋊C412yes—
208C22×C4C2×C4×D4311yescharacteristic
209C22×C4C2×D17211yescharacteristic
210C22×C4C2×C22⋊D4311yescharacteristic
211C2×C8—42no—
212C2×C8—864no—
213C4⋊C4—22no—
214C4⋊C4—24no—
215C4⋊C4—868no—
216C4⋊C4—862no—
217C4⋊C4—1724no—
218C4⋊C4—1722no—
219C42—22no—
220C42—22no—
221C42—432no—
222C42—864no—
223C42—861no—
224C42—862no—
225C42—1722no—
226C42—1721no—
227C42—1721no—
228C42D4×D4312yes—
229C42#1062190012yes—
230C23C2×(C2×D43)⋊C411yescharacteristic
231Q8—42no—
232Q8—42no—
233Q8—864no—
234Q8—1722no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—862no—
243C2×C4—862no—
244C2×C4—862no—
245C2×C4—862no—
246C2×C4—862no—
247C2×C4—1722no—
248C2×C4—1721no—
249C2×C4—1721no—
250C2×C4—1721no—
251C2×C4—1721no—
252C2×C4—1721no—
253C2×C4(C22⋊D43)⋊C412yes—
254C2×C4#1306329511yescharacteristic
255C2×C4#1306329712yes—
256C2×C4#1306330911yescharacteristic
257C2×C4M16×D4311yescharacteristic
258C2×C4M16×D4311yescharacteristic
259C2×C4#1306333112yes—
260C8—82no—
261C8—1724no—
262C22—21no—
263C22—21no—
264C22#1458277611yescharacteristic
265C22#1458286211yescharacteristic
266C22#1458286511yescharacteristic
267C4—22no—
268C4—21no—
269C4—42no—
270C4—42no—
271C4—864no—
272C4—3441no—
273C4—1722no—
274C4—1722no—
275C4#1458297312yes—
276C4#1458297412yes—
277C4#1458308412yes—
278C2—21no—
279C2—21no—
280C2#1913489011yescharacteristic
281C2#1913497611yescharacteristic
282C2#1913498611yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1461C2
socleC22×C43#386
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1461D43
hypocenterC43#8962
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
162. C43#8962semidirect

Maximal subgroups

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

subgroupindex
#191436802
C4×#130633232
#191329912
#191324272
C43×#14612
#896243