Finite Group Databasebeta

← #24997248

Subgroups — #24997248

Order 11008.

602 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 79 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#19144535C212yesmaximal, complemented
2#19142619C211yesmaximal, characteristic
3#19133123C212yesmaximal, complemented
4#19132503C211yesmaximal, characteristic, complemented
5C43×#1820C211yesmaximal, characteristic, complemented
6C2×#13063299C2212yes—
7#14583223—24no—
8#14583217—22no—
9#14583212—22no—
10#14582942—22no—
11#14582903—22no—
12#14582863C2212yes—
13#14582826—22no—
14#14582809—22no—
15#14582808—22no—
16#14582632—24no—
17C2×#117×C43C2211yescharacteristic
18C43×#381C2211yescharacteristic
19C43×#381C2211yescharacteristic
20C43×#342—22no—
21C22×D172—22no—
22C22×D172D412yes—
23C22×C22⋊D43—22no—
24C2×#10621877—22no—
25#13063299—22no—
26#13063299—22no—
27#13063299—22no—
28#13063299—22no—
29C2×C4⋊Dic43D412yes—
30C2×(C2×D43)⋊C4—22no—
31C2×(C2×D43)⋊C4—24no—
32#13063258—24no—
33#13063256—24no—
34#13063245—24no—
35#13063245—24no—
36C22⋊(C43⋊C8)—22no—
37C22⋊(C43⋊C8)D414yescomplemented
38C43⋊#95—22no—
39C23×C4×C43C2311yescharacteristic
40#117×C43—22no—
41#117×C43—22no—
42C2×C4⋊C4×C43D412yescomplemented
43C2×C22⋊C4×C43—21no—
44C2×C22⋊C4×C43—21no—
45C2×C22⋊C4×C43D412yes—
46C2×C42×C43—21no—
47#95×C43—22no—
48#95×C43—22no—
49C24×C43C2×D411yescharacteristic
50C23×D43—22no—
51C22×C4×C43—22no—
52C22×C4×C43—22no—
53C22×C4×C43—42no—
54C22×C4×C43—41no—
55C22×C4×C43C2×D412yes—
56C22×C4×C43C2×D411yescharacteristic
57C22×C4×C43C2×D412yes—
58C22×C4×C43#4111yescharacteristic
59C2×C22⋊D43—42no—
60C2×C22⋊D43—42no—
61C2×C22⋊D43—84no—
62C22×Dic43—22no—
63C2×D172—22no—
64C2×D172—22no—
65C2×D172—44no—
66C2×D172—84no—
67C2×D172—82no—
68C4⋊C4×C43—22no—
69C4⋊C4×C43—22no—
70C22⋊C4×C43—42no—
71C22⋊C4×C43—42no—
72C22⋊C4×C43—41no—
73C22⋊C4×C43—41no—
74C42×C43—42no—
75(C2×D43)⋊C4—42no—
76(C2×D43)⋊C4—42no—
77(C2×D43)⋊C4—84no—
78C4⋊Dic43—22no—
79C4⋊Dic43—22no—
80#10621877—44no—
81C2×C43⋊C8—24no—
82C23×C43—22no—
83C23×C43—42no—
84C23×C43#12011yescharacteristic
85C23×C43#12111yescharacteristic
86C23×C43#12711yescharacteristic
87C22×D43—42no—
88C22×D43—42no—
89C22×D43—44no—
90C22×D43—42no—
91C22×D43—44no—
92C2×C4×C43—24no—
93C2×C4×C43—41no—
94C2×C4×C43—42no—
95C2×C4×C43—41no—
96C2×C4×C43—44no—
97C2×C4×C43—42no—
98C2×C4×C43—42no—
99C2×C4×C43—82no—
100C2×C4×C43—81no—
101C2×C4×C43—82no—
102C2×C4×C43#12012yes—
103C2×C4×C43#12112yes—
104C22⋊D43—84no—
105C22⋊D43—84no—
106C2×Dic43—44no—
107C2×Dic43—42no—
108D172—44no—
109D172—82no—
110D172—88no—
111C43⋊C8—44no—
112#9983—431nomaximal, Sylow
113C22×C43—22no—
114C22×C43—22no—
115C22×C43—22no—
116C22×C43—21no—
117C22×C43—21no—
118C22×C43—82no—
119C22×C43#39211yescharacteristic
120C22×C43#45812yes—
121C2×D43—84no—
122C2×D43—84no—
123C2×D43—82no—
124C2×D43—82no—
125C2×D43—82no—
126C4×C43—22no—
127C4×C43—22no—
128C4×C43—82no—
129C4×C43—82no—
130C4×C43—161no—
131Dic43—82no—
132#3094—432no—
133#2815—431no—
134#1820D4311yescharacteristic, complemented
135#1510—432no—
136#1306—431no—
137C2×C43—22no—
138C2×C43—41no—
139C2×C43—41no—
140C2×C43#200812yes—
141C2×C43#202211yescharacteristic
142D43—162no—
143C2×#121—432no—
144C2×#117C2×D4311yescharacteristic
145#482—864no—
146#481—862no—
147#480—862no—
148#428—862no—
149#418—862no—
150#407—432no—
151#397—862no—
152#392—862no—
153#392—862no—
154#381C2×D4311yescharacteristic
155#381C2×D4311yescharacteristic
156#342—22no—
157#327—864no—
158C43#998311yescharacteristic, complemented, Sylow
159C22×D4—432no—
160C22×D4—862no—
161C22×D4—862no—
162C23×C4C22×D4311yescharacteristic
163C2×M16—862no—
164#121—862no—
165#121—862no—
166#121—862no—
167#121—862no—
168#117—22no—
169#117—22no—
170C2×C4⋊C4—432no—
171C2×C4⋊C4D17212yescomplemented
172C2×C22⋊C4—21no—
173C2×C22⋊C4—21no—
174C2×C22⋊C4—864no—
175C2×C22⋊C4—862no—
176C2×C22⋊C4C22⋊D4312yes—
177C2×C42—21no—
178#107—864no—
179#106—864no—
180#102—864no—
181#102—864no—
182C22⋊C8—434no—
183C22⋊C8—862no—
184#95—22no—
185#95—22no—
186#95—862no—
187C24—862no—
188C24C2×C22⋊D4311yescharacteristic
189C2×D4—862no—
190C2×D4—862no—
191C2×D4—3444no—
192C2×D4—3442no—
193C2×D4—3444no—
194C2×D4—1724no—
195C2×D4—1722no—
196C2×D4—1722no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—42no—
200C22×C4—41no—
201C22×C4—862no—
202C22×C4C2×D17211yescharacteristic
203C22×C4#1062189811yescharacteristic
204C22×C4D4×D4312yes—
205C22×C4D4×D4312yes—
206M16—1724no—
207C2×C8—864no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—862no—
211C4⋊C4—862no—
212C22⋊C4—41no—
213C22⋊C4—41no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—3444no—
217C22⋊C4—1722no—
218C22⋊C4—1722no—
219C42—42no—
220C23—22no—
221C23—42no—
222C23—1722no—
223C23—1722no—
224C23—1724no—
225C23—1722no—
226C23—1724no—
227C23#1306329311yescharacteristic
228C23#1306329911yescharacteristic
229C23#1306332111yescharacteristic
230D4—3442no—
231D4—3448no—
232D4—3444no—
233D4—3444no—
234D4—1724no—
235C2×C4—24no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—44no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—82no—
243C2×C4—81no—
244C2×C4—82no—
245C2×C4—1724no—
246C2×C4—1722no—
247C2×C4#1306329512yes—
248C2×C4#1306329812yes—
249C8—1724no—
250C22—22no—
251C22—22no—
252C22—22no—
253C22—21no—
254C22—21no—
255C22—82no—
256C22—3444no—
257C22—3444no—
258C22—3442no—
259C22—3442no—
260C22—3442no—
261C22#1458280811yescharacteristic
262C22#1458308812yes—
263C4—22no—
264C4—22no—
265C4—82no—
266C4—82no—
267C4—161no—
268C4—3442no—
269C2—22no—
270C2—41no—
271C2—41no—
272C2—6882no—
273C2#1913564712yes—
274C2#1913572611yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1820C2
socleC22×C43#392
prime radical#19142619C2
hypercenter#1820D43
hypocenterC43#9983
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
1. #19144535C2semidirect
3. #19133123C2semidirect
4. #19132503C2semidirect
5. C43×#1820C2semidirect
37. C22⋊(C43⋊C8)D4semidirect
42. C2×C4⋊C4×C43D4semidirect
134. #1820D43semidirect
158. C43#9983semidirect
171. C2×C4⋊C4D172semidirect

Maximal subgroups

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

subgroupindex
#191445352
#191426192
#191331232
#191325032
C43×#18202
#998343