Finite Group Databasebeta

← #24997467

Subgroups — #24997467

Order 11008.

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

normal subgroups only

This group has 528 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#19144634C212yesmaximal
2#19135576C211yesmaximal, characteristic
3#19133024C212yesmaximal
4#19132424C211yesmaximal, characteristic
5C43×#2399C211yesmaximal, characteristic
6#14583456C2211yescharacteristic
7#14583234—22no—
8#14583194—22no—
9#14583109—22no—
10#14583055—22no—
11C4×#10621885—24no—
12#14582952C2212yes—
13#14582923C2211yescharacteristic
14#14582659—22no—
15Q8⋊(C43⋊C8)—24no—
16C2×C4×Q8×C43C2212yes—
17C43×#398—22no—
18C43×#395—22no—
19C4×C4⋊C4×C43—22no—
20C43×#376C2211yescharacteristic
21C2×#10621885—24no—
22C2×#10621877—21no—
23#13063325D412yes—
24#13063317—21no—
25#13063304—22no—
26C4×Dic86—22no—
27#13063284—21no—
28#13063258—24no—
29C4⋊(C43⋊C8)—22no—
30C4⋊(C43⋊C8)—22no—
31#13063249—24no—
32#13063248—24no—
33C22⋊(C43⋊C8)—22no—
34C4×C43⋊C8D414yes—
35C22×Q8×C43D412yes—
36C4×Q8×C43—22no—
37C4×Q8×C43—22no—
38C4×Q8×C43—22no—
39C4×Q8×C43—22no—
40C2×C4⋊C4×C43—24no—
41C2×C4⋊C4×C43—22no—
42C2×C4⋊C4×C43D412yes—
43C2×C42×C43—22no—
44C2×C42×C43D412yes—
45C2×C42×C43C2311yescharacteristic
46#95×C43—22no—
47#95×C43—22no—
48#95×C43—22no—
49C2×Q8×C43—22no—
50C2×Q8×C43—22no—
51C2×Q8×C43—44no—
52C22×C4×C43—22no—
53C22×C4×C43—22no—
54C22×C4×C43—22no—
55C22×C4×C43C2×D412yes—
56C22×C4×C43C2×D411yescharacteristic
57C2×Dic86—22no—
58C4⋊C4×C43—22no—
59C4⋊C4×C43—22no—
60C4⋊C4×C43—48no—
61C4⋊C4×C43—42no—
62C4⋊C4×C43—42no—
63C42×C43—22no—
64C42×C43—42no—
65C42×C43—42no—
66C42×C43Q1614yescomplemented
67C42×C43C2×D411yescharacteristic
68C42×C43C2×D412yes—
69C42×C43#4111yescharacteristic
70C22⋊Dic43—41no—
71#10621885—48no—
72C4⋊Dic43—22no—
73C4⋊Dic43—22no—
74Dic43⋊C4—42no—
75C4×Dic43—41no—
76#10621877—42no—
77C2×C43⋊C8—24no—
78C2×C43⋊C8—41no—
79C23×C43#12011yescharacteristic
80Q8×C43—24no—
81Q8×C43—24no—
82Q8×C43—42no—
83Q8×C43—42no—
84C2×C4×C43—24no—
85C2×C4×C43—24no—
86C2×C4×C43—42no—
87C2×C4×C43—44no—
88C2×C4×C43—42no—
89C2×C4×C43—42no—
90C2×C4×C43—44no—
91C2×C4×C43—42no—
92C2×C4×C43#12012yes—
93C2×C4×C43#12111yescharacteristic
94C2×C4×C43#12112yes—
95C2×C4×C43#12711yescharacteristic
96C2×C4×C43C2×Q1612yes—
97C2×C4×C43#13712yes—
98C2×Dic43—42no—
99Dic86—44no—
100C43⋊C8—44no—
101C43⋊C8—81no—
102#10017—431nomaximal, Sylow
103C22×C43—22no—
104C22×C43#39211yescharacteristic
105C22×C43#45112yes—
106C4×C43—22no—
107C4×C43—22no—
108C4×C43—44no—
109C4×C43—44no—
110C4×C43—82no—
111C4×C43#46212yes—
112C4×C43#49411yescharacteristic
113C4×C43#49711yescharacteristic
114Dic43—82no—
115#3104—432no—
116#2399D4311yescharacteristic
117#1995—431no—
118#1487—432no—
119#1274—431no—
120C2×C43—22no—
121C2×C43#201012yes—
122C2×C43#201611yescharacteristic
123#533—431no—
124C2×C4×Q8C2×D4312yes—
125#484—862no—
126#477—862no—
127#462—862no—
128#451—862no—
129C4×Q16—864no—
130#431—432no—
131#423—431no—
132#398—22no—
133#395—22no—
134C4×C4⋊C4—22no—
135#376C2×D4311yescharacteristic
136#339—862no—
137Q8⋊C8—864no—
138C43#1001711yescharacteristic, complemented, Sylow
139C22×Q8C22⋊D4312yes—
140C2×Q16—864no—
141C2×M16—861no—
142C4⋊Q8—432no—
143#125—861no—
144C22⋊Q8—862no—
145C4×Q8—22no—
146C4×Q8—22no—
147C4×Q8—22no—
148C4×Q8—22no—
149C4×Q8—862no—
150#117—861no—
151C2×C4⋊C4—24no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4C22⋊D4312yes—
154C2×C42—22no—
155C2×C42C22⋊D4312yes—
156C2×C42C22×D4311yescharacteristic
157#107—864no—
158C4⋊C8—862no—
159C4⋊C8—862no—
160#103—864no—
161#103—864no—
162C22⋊C8—862no—
163C4×C8—434no—
164#95—22no—
165#95—22no—
166#95—22no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—44no—
170C2×Q8—862no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4C2×C22⋊D4312yes—
175C22×C4C2×C22⋊D4311yescharacteristic
176Q16—1728no—
177M16—1722no—
178C2×C8—864no—
179C2×C8—1721no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—48no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—862no—
186C4⋊C4—862no—
187C4⋊C4—1722no—
188C22⋊C4—1721no—
189C42—22no—
190C42—42no—
191C42—42no—
192C42—1721no—
193C42#1062188514yescomplemented
194C42D4×D4311yescharacteristic
195C42D4×D4312yes—
196C42#1062190011yescharacteristic
197C23#1306329411yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—42no—
201Q8—42no—
202Q8—1724no—
203C2×C4—24no—
204C2×C4—24no—
205C2×C4—42no—
206C2×C4—44no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—44no—
210C2×C4—42no—
211C2×C4—1722no—
212C2×C4#1306329312yes—
213C2×C4#1306329611yescharacteristic
214C2×C4#1306329712yes—
215C2×C4#1306332111yescharacteristic
216C2×C4C2×#1062188512yes—
217C2×C4#1306335612yes—
218C8—3441no—
219C8—1724no—
220C22—22no—
221C22#1458280711yescharacteristic
222C22#1458305512yes—
223C4—22no—
224C4—22no—
225C4—44no—
226C4—44no—
227C4—82no—
228C4—3442no—
229C4#1458310612yes—
230C4#1458327811yescharacteristic
231C4#1458329111yescharacteristic
232C2—22no—
233C2#1913566012yes—
234C2#1913569511yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2399C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#2399D43
hypocenterC43#10017
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2399

Complements

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

NH ≅ G/Ntype
66. C42×C43Q16semidirect
138. C43#10017semidirect
193. C42#10621885semidirect

Maximal subgroups

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

subgroupindex
#191446342
#191355762
#191330242
#191324242
C43×#23992
#1001743