Finite Group Databasebeta

← #24994471

Subgroups — #24994471

Order 11008.

522 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 115 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#19139500C211yesmaximal, characteristic
2#19134591C211yesmaximal, characteristic, complemented
3#19133021C212yesmaximal
4#19132454C212yesmaximal, complemented
5C43×#2983C211yesmaximal, characteristic, complemented
6C2×#13063301—21no—
7C2×C4×D172C2211yescharacteristic
8#14582923C2212yes—
9C2×#13063244—21no—
10#14582829C412yes—
11#14582816C412yes—
12#14582790—22no—
13#14582765C2211yescharacteristic
14#14582756—21no—
15#14582668—21no—
16#14582628—24no—
17C2×C4×Q8×C43C2211yescharacteristic
18C43×#446—24no—
19C43×#432—22no—
20C43×#431C2212yes—
21C22×D172C2×C411yescharacteristic
22C22×C4×D43—21no—
23C2×#10621877—22no—
24#13063301—44no—
25C4×D172—22no—
26C4×D172—22no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×Dic43⋊C4—22no—
30C2×(C2×D43)⋊C4—22no—
31C2×(C2×D43)⋊C4—22no—
32C2×(C2×D43)⋊C4—21no—
33C4⋊(C43⋊C8)—22no—
34C4⋊(C43⋊C8)—22no—
35#13063244—42no—
36C43⋊#95—22no—
37C43⋊#95—21no—
38C43⋊#95C2×C412yes—
39C22×Q8×C43D411yescharacteristic
40C4×Q8×C43—22no—
41C4×Q8×C43—22no—
42C2×C4⋊C4×C43C2×C412yes—
43C2×C4⋊C4×C43D411yescharacteristic
44C2×C42×C43D412yes—
45C2×C42×C43C2311yescharacteristic
46C4⋊C8×C43—24no—
47C4⋊C8×C43—22no—
48C22⋊C8×C43—22no—
49#97×C43—24no—
50C4×C8×C43D414yes—
51C23×D43—21no—
52C2×Q8×C43—22no—
53C2×Q8×C43—21no—
54C2×Q8×C43—22no—
55C2×Q8×C43—21no—
56C22×C4×C43C22⋊C412yes—
57C22×C4×C43C22⋊C412yes—
58C22×C4×C43C22×C411yescharacteristic
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×Dic43—22no—
62C22×Dic43—21no—
63C2×D172—22no—
64C2×D172—42no—
65C2×C4×D43—42no—
66C2×C4×D43—42no—
67C2×C4×D43—41no—
68C2×C4×D43—41no—
69C2×C8×C43—24no—
70C4⋊C4×C43—24no—
71C4⋊C4×C43—22no—
72C42×C43—22no—
73C42×C43—22no—
74C42×C43C2×D412yes—
75C42×C43#4112yes—
76(C2×D43)⋊C4—44no—
77(C2×D43)⋊C4—44no—
78(C2×D43)⋊C4—41no—
79(C2×D43)⋊C4—41no—
80C4⋊Dic43—22no—
81C4⋊Dic43—42no—
82Dic43⋊C4—44no—
83#10621877—42no—
84#10621877—42no—
85C2×C43⋊C8—42no—
86C23×C43C2×C22⋊C411yescharacteristic
87C22×D43—22no—
88C22×D43—41no—
89C22×D43—41no—
90C22×D43—41no—
91C22×D43—41no—
92C22×D43—41no—
93C22×D43—41no—
94Q8×C43—42no—
95Q8×C43—42no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—41no—
101C2×C4×C43—41no—
102C2×C4×C43—42no—
103C2×C4×C43C4×D412yes—
104C2×C4×C43#12011yescharacteristic
105C2×C4×C43#12112yes—
106C2×C4×C43#12311yescharacteristic
107C2×C4×C43AGL(1,ℤ/8)12yes—
108C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
109C2×C4×C43#13711yescharacteristic
110C2×Dic43—42no—
111C2×Dic43—42no—
112C2×Dic43—41no—
113C2×Dic43—41no—
114C2×Dic43—41no—
115C2×Dic43—42no—
116D172—24no—
117D172—42no—
118C4×D43—82no—
119C4×D43—82no—
120C8×C43—44no—
121C43⋊C8—82no—
122#9490—431nomaximal, Sylow
123C22×C43—21no—
124C22×C43—21no—
125C22×C43#38611yescharacteristic
126C22×C43#41711yescharacteristic
127C22×C43#41811yescharacteristic
128C2×D43—42no—
129C2×D43—42no—
130C2×D43—42no—
131C2×D43—81no—
132C2×D43—81no—
133C2×D43—81no—
134C2×D43—81no—
135C4×C43—22no—
136C4×C43—21no—
137C4×C43—21no—
138C4×C43—42no—
139C4×C43—42no—
140C4×C43#46812yes—
141C4×C43#46912yes—
142Dic43—82no—
143Dic43—81no—
144#2983D4311yescharacteristic, complemented
145#2536—431no—
146#1801—431no—
147#1486—432no—
148#1286—432no—
149C2×C43—21no—
150C2×C43—21no—
151C2×C43#189111yescharacteristic
152C2×C43#189511yescharacteristic
153C2×C43#191211yescharacteristic
154D43—82no—
155C2×C22⋊Q8—861no—
156C2×C4×Q8C2×D4311yescharacteristic
157C2×C4×D4—431no—
158#446—24no—
159#432—22no—
160#431C2×D4312yes—
161#423—432no—
162C2×#101—861no—
163#398—432no—
164#394—432no—
165#388—862no—
166#382—431no—
167#380—861no—
168#343—861no—
169D4⋊C8—864no—
170C43#949011yescharacteristic, complemented, Sylow
171C22×Q8D17211yescharacteristic
172C22×D4—431no—
173C23×C4—861no—
174C2×M16—862no—
175C22⋊Q8—1724no—
176C4×Q8—22no—
177C4×Q8—22no—
178C4×D4—862no—
179C4×D4—862no—
180C2×C4⋊C4—431no—
181C2×C4⋊C4—862no—
182C2×C4⋊C4—861no—
183C2×C4⋊C4C4×D4312yes—
184C2×C4⋊C4D17211yescharacteristic
185C2×C22⋊C4—862no—
186C2×C22⋊C4—862no—
187C2×C22⋊C4—861no—
188C2×C42C22⋊D4312yes—
189C2×C42C22×D4311yescharacteristic
190C4⋊C8—24no—
191C4⋊C8—22no—
192C4⋊C8—862no—
193C4⋊C8—862no—
194#101—1722no—
195C22⋊C8—22no—
196#97—24no—
197C4×C8C22⋊D4314yes—
198#95—432no—
199#95—862no—
200#95—861no—
201C24—861no—
202C2×Q8—22no—
203C2×Q8—21no—
204C2×Q8—22no—
205C2×Q8—21no—
206C2×D4—862no—
207C2×D4—1722no—
208C22×C4—862no—
209C22×C4—861no—
210C22×C4—1722no—
211C22×C4—1722no—
212C22×C4—1721no—
213C22×C4—1721no—
214C22×C4(C2×D43)⋊C412yes—
215C22×C4(C2×D43)⋊C412yes—
216C22×C4C2×C4×D4311yescharacteristic
217C22×C4C2×D17211yescharacteristic
218C22×C4C2×C22⋊D4311yescharacteristic
219M16—1722no—
220M16—1722no—
221C2×C8—24no—
222C2×C8—1722no—
223C4⋊C4—24no—
224C4⋊C4—22no—
225C4⋊C4—862no—
226C4⋊C4—1724no—
227C4⋊C4—1722no—
228C22⋊C4—1724no—
229C22⋊C4—1724no—
230C22⋊C4—1721no—
231C22⋊C4—1721no—
232C42—22no—
233C42—22no—
234C42#1062189812yes—
235C42C2×C22⋊D4312yes—
236C23—862no—
237C23—1721no—
238C23—1721no—
239C23—1721no—
240C23—1721no—
241C23—1721no—
242C23—1721no—
243C23C2×(C2×D43)⋊C411yescharacteristic
244Q8—42no—
245Q8—42no—
246D4—864no—
247D4—1722no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—3442no—
256C2×C4—3442no—
257C2×C4—1722no—
258C2×C4—1722no—
259C2×C4—1721no—
260C2×C4—1722no—
261C2×C4—1721no—
262C2×C4—1721no—
263C2×C4C4×C22⋊D4312yes—
264C2×C4#1306329411yescharacteristic
265C2×C4#1306329912yes—
266C2×C4#1306330811yescharacteristic
267C2×C4#1306335312yes—
268C2×C4#1306335311yescharacteristic
269C2×C4#1306335811yescharacteristic
270C8—44no—
271C8—3442no—
272C22—21no—
273C22—21no—
274C22—3441no—
275C22—3441no—
276C22—3441no—
277C22—3441no—
278C22—1722no—
279C22—1722no—
280C22—1722no—
281C22#1458277811yescharacteristic
282C22#1458290111yescharacteristic
283C22#1458290511yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—42no—
288C4—42no—
289C4—3442no—
290C4—3441no—
291C4#1458314512yes—
292C4#1458315212yes—
293C2—21no—
294C2—21no—
295C2—3442no—
296C2#1913501311yescharacteristic
297C2#1913503311yescharacteristic
298C2#1913513211yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2983C2
socleC22×C43#386
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#2983D43
hypocenterC43#9490
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
2. #19134591C2semidirect
4. #19132454C2semidirect
5. C43×#2983C2semidirect
144. #2983D43semidirect
170. C43#9490semidirect

Maximal subgroups

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

subgroupindex
#191395002
#191345912
#191330212
#191324542
C43×#29832
#949043