Finite Group Databasebeta

← #24997554

Subgroups — #24997554

Order 11008.

520 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 85 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#19145940C211yesmaximal, characteristic, complemented
2#19144695C212yesmaximal
3#19135392C211yesmaximal, characteristic
4#19133211C212yesmaximal, complemented
5C43×#1290C211yesmaximal, characteristic, complemented
6#14583456C2212yes—
7C2×C4×D172C2211yescharacteristic
8#14583235—22no—
9#14583195—22no—
10#14583180—22no—
11#14583140—22no—
12#14583110—22no—
13#14583105—22no—
14#14583052—22no—
15#14583001—24no—
16C2×(C2×D43)⋊C8—22no—
17C2×#13063236C2211yescharacteristic
18#14582640—24no—
19C43×#432C2212yes—
20C2×C4⋊C8×C43C2211yescharacteristic
21C22×D172D411yescharacteristic
22C22×C4×D43—21no—
23C2×Dic172—22no—
24C2×#10621873—24no—
25C22×C43⋊C8—21no—
26#13063325D412yes—
27#13063325D412yes—
28#13063317—22no—
29#13063304—22no—
30#13063304—22no—
31C4×Dic86—22no—
32C4×Dic86—22no—
33C4×D172—22no—
34C4×D172—22no—
35#13063284—22no—
36C2×C4⋊Dic43D411yescharacteristic
37C2×(C2×D43)⋊C4—21no—
38#13063259—22no—
39#13063259—24no—
40#13063250—24no—
41#13063250—24no—
42#13063247—24no—
43(C2×D43)⋊C8—44no—
44#13063236—22no—
45C22×C8×C43D412yes—
46C2×C42×C43C2311yescharacteristic
47C4⋊C8×C43—22no—
48C4⋊C8×C43—22no—
49C22⋊C8×C43—22no—
50#97×C43D414yes—
51C23×D43—21no—
52C22×C4×C43C2×D411yescharacteristic
53C22×C4×C43C2×D411yescharacteristic
54C22×C4×C43#4111yescharacteristic
55C22×Dic43—21no—
56C2×D172—22no—
57C2×D172—42no—
58C2×C4×D43—42no—
59C2×C4×D43—42no—
60C2×C4×D43—41no—
61C2×C4×D43—41no—
62C2×Dic86—22no—
63C2×Dic86—22no—
64C2×C8×C43—24no—
65C2×C8×C43—22no—
66C2×C8×C43—42no—
67C42×C43C2×D412yes—
68C42×C43C2×D412yes—
69C22⋊Dic43—42no—
70(C2×D43)⋊C4—42no—
71C4⋊Dic43—22no—
72C4⋊Dic43—22no—
73C4⋊Dic43—22no—
74C4⋊Dic43—22no—
75C4⋊Dic43—22no—
76Dic43⋊C4—42no—
77Dic43⋊C4—42no—
78C4×Dic43—42no—
79C2×C43⋊C8—22no—
80C2×C43⋊C8—41no—
81C2×C43⋊C8—41no—
82Dic172—82no—
83#10621873—48no—
84C23×C43#12111yescharacteristic
85C22×D43—22no—
86C22×D43—42no—
87C22×D43—41no—
88C22×D43—41no—
89C22×D43—42no—
90C2×C4×C43—22no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—41no—
94C2×C4×C43#12012yes—
95C2×C4×C43#12011yescharacteristic
96C2×C4×C43#12112yes—
97C2×C4×C43#12711yescharacteristic
98C2×Dic43—42no—
99C2×Dic43—42no—
100C2×Dic43—42no—
101C2×Dic43—41no—
102D172—24no—
103D172—42no—
104C4×D43—82no—
105C4×D43—81no—
106C4×D43—81no—
107Dic86—44no—
108Dic86—42no—
109Dic86—42no—
110C8×C43—44no—
111C8×C43—42no—
112C43⋊C8—42no—
113#10030—431nomaximal, Sylow
114C22×C43—21no—
115C22×C43—21no—
116C22×C43#39211yescharacteristic
117C22×C43#47312yes—
118C2×D43—44no—
119C2×D43—42no—
120C2×D43—82no—
121C2×D43—81no—
122C2×D43—81no—
123C4×C43—21no—
124C4×C43—22no—
125C4×C43—22no—
126C4×C43#45311yescharacteristic
127C4×C43#45411yescharacteristic
128Dic43—82no—
129Dic43—81no—
130Dic43—82no—
131#3249—431no—
132#3110—432no—
133#1955—431no—
134#1531—432no—
135#1290D4311yescharacteristic, complemented
136C2×C43—22no—
137C2×C43#200611yescharacteristic
138C2×C43#201011yescharacteristic
139C2×C43#202011yescharacteristic
140D43—82no—
141#533—432no—
142C2×C4×D4—431no—
143#484—862no—
144#477—862no—
145#474—862no—
146#467—862no—
147#462—862no—
148#461—862no—
149#450—862no—
150#440—864no—
151#432C2×D4312yes—
152C2×C4⋊C8C2×D4311yescharacteristic
153C2×C22⋊C8—862no—
154C2×#97—431no—
155#330—864no—
156C43#1003011yescharacteristic, complemented, Sylow
157C22×D4—431no—
158C23×C4—861no—
159C2×Q16—862no—
160C2×SD16—864no—
161C22×C8—861no—
162C22×C8D17212yes—
163C4⋊Q8—432no—
164C4⋊Q8—432no—
165#125—862no—
166C22⋊Q8—862no—
167C22⋊Q8—862no—
168C4×Q8—862no—
169C4×Q8—862no—
170C4×D4—862no—
171C4×D4—862no—
172#117—862no—
173C2×C4⋊C4—431no—
174C2×C22⋊C4—861no—
175C2×C42C22×D4311yescharacteristic
176#107—864no—
177#107—862no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180#103—864no—
181#103—864no—
182#102—864no—
183C22⋊C8—22no—
184C22⋊C8—1724no—
185#97—862no—
186#97D17214yes—
187C24—861no—
188C2×Q8—862no—
189C2×Q8—862no—
190C2×D4—862no—
191C2×D4—1722no—
192C22×C4—861no—
193C22×C4—1722no—
194C22×C4—1722no—
195C22×C4—1721no—
196C22×C4—1721no—
197C22×C4C2×D17211yescharacteristic
198C22×C4D4×D4311yescharacteristic
199C22×C4#1062190211yescharacteristic
200Q16—3442no—
201SD16—1728no—
202C2×C8—24no—
203C2×C8—22no—
204C2×C8—42no—
205C2×C8—862no—
206C2×C8—1721no—
207C2×C8—1721no—
208C4⋊C4—862no—
209C4⋊C4—862no—
210C4⋊C4—862no—
211C4⋊C4—862no—
212C4⋊C4—862no—
213C4⋊C4—1722no—
214C4⋊C4—1722no—
215C22⋊C4—1722no—
216C22⋊C4—1722no—
217C42—1722no—
218C42C2×D17212yes—
219C42D4×D4312yes—
220C23—862no—
221C23—1722no—
222C23—1721no—
223C23—1721no—
224C23—1722no—
225C23#1306330011yescharacteristic
226Q8—1724no—
227Q8—1722no—
228Q8—1722no—
229D4—864no—
230D4—1722no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—3442no—
236C2×C4—3441no—
237C2×C4—3441no—
238C2×C4—1722no—
239C2×C4—1722no—
240C2×C4—1722no—
241C2×C4—1721no—
242C2×C4#1306329512yes—
243C2×C4#1306329511yescharacteristic
244C2×C4#1306330012yes—
245C2×C4#1306332211yescharacteristic
246C8—44no—
247C8—42no—
248C8—1722no—
249C22—21no—
250C22—21no—
251C22—3442no—
252C22—3441no—
253C22—3441no—
254C22—1724no—
255C22—1722no—
256C22#1458280911yescharacteristic
257C22#1458317512yes—
258C4—21no—
259C4—22no—
260C4—22no—
261C4—3441no—
262C4—3442no—
263C4—3442no—
264C4#1458306911yescharacteristic
265C4#1458307411yescharacteristic
266C2—22no—
267C2—3442no—
268C2#1913563911yescharacteristic
269C2#1913566311yescharacteristic
270C2#1913571711yescharacteristic
subgroupG/H
centerC22#14582809
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1290C2
socleC22×C43#392
prime radicalC22×D172D4
hypercenter#1290D43
hypocenterC43#10030
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
1. #19145940C2semidirect
4. #19133211C2semidirect
5. C43×#1290C2semidirect
135. #1290D43semidirect
156. C43#10030semidirect

Maximal subgroups

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

subgroupindex
#191459402
#191446952
#191353922
#191332112
C43×#12902
#1003043