Finite Group Databasebeta

← #24998891

Subgroups — #24998891

Order 11008.

466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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#19145741C212yesmaximal
2#19145119C211yesmaximal, characteristic
3#19135415C211yesmaximal, characteristic
4#19133160C212yesmaximal
5C43×#1281C211yesmaximal, characteristic
6#14583456C2212yes—
7C2×#13063325C2211yescharacteristic
8#14583308—22no—
9#14583308—22no—
10#14583297—22no—
11#14583250—22no—
12#14583230—24no—
13#14583185—24no—
14#14582937—22no—
15C2×#13063250—22no—
16#14582765C2211yescharacteristic
17#14582637—24no—
18C43×#431C2212yes—
19C2×#97×C43C2211yescharacteristic
20C22×Dic86—21no—
21#13063325—22no—
22#13063325—21no—
23#13063325D412yes—
24#13063325D412yes—
25#13063325D412yes—
26#13063317—22no—
27#13063304—22no—
28#13063304—22no—
29C4×Dic86—22no—
30C4×Dic86—22no—
31#13063284—22no—
32C2×C4⋊Dic43—22no—
33C2×C4⋊Dic43—21no—
34#13063259—24no—
35#13063257—28no—
36#13063257—22no—
37#13063257—22no—
38#13063250—28no—
39#13063250—44no—
40C43⋊#95—22no—
41C22×C8×C43D412yes—
42C2×C42×C43C2311yescharacteristic
43C4⋊C8×C43—22no—
44C22⋊C8×C43D414yes—
45#97×C43—22no—
46C4×C8×C43—22no—
47C22×C4×C43C2×D412yes—
48C22×C4×C43C2×D411yescharacteristic
49C22×Dic43—41no—
50C22×Dic43—41no—
51C2×Dic86—22no—
52C2×Dic86—22no—
53C2×Dic86—22no—
54C2×Dic86—42no—
55C2×Dic86—42no—
56C2×Dic86—41no—
57C2×C8×C43—22no—
58C2×C8×C43—22no—
59C2×C8×C43—24no—
60C2×C8×C43SD1614yes—
61C42×C43C2×D412yes—
62C42×C43C2×D411yescharacteristic
63C42×C43#4111yescharacteristic
64C22⋊Dic43—42no—
65C4⋊Dic43—24no—
66C4⋊Dic43—22no—
67C4⋊Dic43—22no—
68C4⋊Dic43—22no—
69C4⋊Dic43—22no—
70C4⋊Dic43—42no—
71C4⋊Dic43—42no—
72Dic43⋊C4—42no—
73Dic43⋊C4—42no—
74C4×Dic43—42no—
75C23×C43#12711yescharacteristic
76C2×C4×C43—42no—
77C2×C4×C43#12012yes—
78C2×C4×C43#12011yescharacteristic
79C2×C4×C43#12112yes—
80C2×C4×C43#12111yescharacteristic
81C2×C4×C43C2×SD1612yes—
82C2×C4×C43#13712yes—
83C2×Dic43—42no—
84C2×Dic43—42no—
85C2×Dic43—42no—
86C2×Dic43—81no—
87C2×Dic43—81no—
88C2×Dic43—82no—
89C2×Dic43—81no—
90Dic86—44no—
91Dic86—44no—
92Dic86—82no—
93Dic86—82no—
94C8×C43—24no—
95C8×C43—44no—
96#10227—431nomaximal, Sylow
97C22×C43—22no—
98C22×C43#39211yescharacteristic
99C22×C43#49211yescharacteristic
100C22×C43#49711yescharacteristic
101C4×C43—22no—
102C4×C43—22no—
103C4×C43#44812yes—
104C4×C43#46112yes—
105Dic43—82no—
106Dic43—82no—
107Dic43—82no—
108Dic43—161no—
109#3229—432no—
110#3162—431no—
111#1960—431no—
112#1518—432no—
113#1281D4311yescharacteristic
114C2×C43—21no—
115C2×C43—21no—
116C2×C43#200912yes—
117C2×C43#201311yescharacteristic
118#533—432no—
119C2×C4⋊Q8—431no—
120#501—862no—
121#501—862no—
122#498—862no—
123#487—862no—
124#483—864no—
125#475—864no—
126#431C2×D4312yes—
127#427—862no—
128C2×#103—862no—
129C2×#97C2×D4311yescharacteristic
130#382—431no—
131#328—864no—
132C43#1022711yescharacteristic, complemented, Sylow
133C22×Q8—861no—
134C22×C8D17212yes—
135C4⋊Q8—432no—
136C4⋊Q8—432no—
137C4⋊Q8—432no—
138C4⋊Q8—862no—
139C4⋊Q8—861no—
140#125—862no—
141C22⋊Q8—862no—
142C22⋊Q8—862no—
143C4×Q8—862no—
144C4×Q8—862no—
145#117—862no—
146C2×C4⋊C4—862no—
147C2×C4⋊C4—861no—
148C2×C42C22×D4311yescharacteristic
149#107—864no—
150#106—862no—
151#106—862no—
152#106—868no—
153C4⋊C8—22no—
154#103—868no—
155#103—1724no—
156C22⋊C8D17214yes—
157#97—22no—
158C4×C8—22no—
159#95—862no—
160C2×Q8—862no—
161C2×Q8—862no—
162C2×Q8—862no—
163C2×Q8—1722no—
164C2×Q8—1722no—
165C2×Q8—1721no—
166C22×C4—1721no—
167C22×C4—1721no—
168C22×C4C2×D17212yes—
169C22×C4C2×D17211yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—24no—
173C2×C8#1062187314yes—
174C4⋊C4—864no—
175C4⋊C4—862no—
176C4⋊C4—862no—
177C4⋊C4—862no—
178C4⋊C4—862no—
179C4⋊C4—1722no—
180C4⋊C4—1722no—
181C4⋊C4—1722no—
182C4⋊C4—1722no—
183C22⋊C4—1722no—
184C42—1722no—
185C42D4×D4312yes—
186C42D4×D4311yescharacteristic
187C42#1062190211yescharacteristic
188C23#1306332211yescharacteristic
189Q8—3442no—
190Q8—3442no—
191Q8—1724no—
192Q8—1724no—
193C2×C4—42no—
194C2×C4—3441no—
195C2×C4—3441no—
196C2×C4—3442no—
197C2×C4—3441no—
198C2×C4—1722no—
199C2×C4—1722no—
200C2×C4—1722no—
201C2×C4#1306329512yes—
202C2×C4#1306329511yescharacteristic
203C2×C4#1306330012yes—
204C2×C4#1306330011yescharacteristic
205C2×C4C2×#1062187312yes—
206C2×C4#1306335812yes—
207C8—24no—
208C8—44no—
209C22—22no—
210C22#1458280911yescharacteristic
211C22#1458327211yescharacteristic
212C22#1458329311yescharacteristic
213C4—22no—
214C4—22no—
215C4—3442no—
216C4—3442no—
217C4—3442no—
218C4—6881no—
219C4#1458304012yes—
220C4#1458310512yes—
221C2—21no—
222C2—21no—
223C2#1913565812yes—
224C2#1913568011yescharacteristic
subgroupG/H
centerC22#14582809
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1281C2
socleC22×C43#392
prime radicalC23×C43#127
hypercenter#1281D43
hypocenterC43#10227
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1281

Complements

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

NH ≅ G/Ntype
132. C43#10227semidirect

Maximal subgroups

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

subgroupindex
#191457412
#191451192
#191354152
#191331602
C43×#12812
#1022743