Finite Group Databasebeta

← #24997469

Subgroups — #24997469

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#19144635C212yesmaximal
2#19137888C211yesmaximal, characteristic
3#19135576C211yesmaximal, characteristic
4#19133025C212yesmaximal
5C43×#1274C211yesmaximal, characteristic
6#14583456C2211yescharacteristic
7C2×C4×Dic86C2212yes—
8#14583235—22no—
9#14583195—22no—
10#14583110—22no—
11#14583057—22no—
12C4×Dic172—24no—
13#14582923C2211yescharacteristic
14#14582831—22no—
15#14582820—22no—
16C4×C4⋊Dic43—22no—
17#14582659—22no—
18#14582631—24no—
19C43×#431C2212yes—
20C43×#376C2211yescharacteristic
21C22×Dic86D412yes—
22C2×Dic172—24no—
23C2×#10621877—21no—
24#13063325D412yes—
25#13063317—21no—
26#13063304—22no—
27C4×Dic86—22no—
28C4×Dic86—22no—
29C4×Dic86—22no—
30C4×Dic86—22no—
31C4×Dic86—22no—
32#13063284—21no—
33C2×C4⋊Dic43—24no—
34C2×C4⋊Dic43D412yes—
35C2×Dic43⋊C4—22no—
36C2×C4×Dic43—22no—
37#13063259—24no—
38C4⋊(C43⋊C8)—22no—
39#13063250—24no—
40#13063250—24no—
41C43⋊#95—22no—
42C43⋊#95—22no—
43C2×C42×C43D412yes—
44C2×C42×C43C2311yescharacteristic
45C4⋊C8×C43—22no—
46C22⋊C8×C43—22no—
47C4×C8×C43D414yes—
48#95×C43—22no—
49C22×C4×C43—22no—
50C22×C4×C43C2×D411yescharacteristic
51C22×C4×C43C2×D412yes—
52C22×Dic43—22no—
53C22×Dic43—22no—
54C2×Dic86—22no—
55C2×Dic86—22no—
56C2×Dic86—22no—
57C2×Dic86—44no—
58C2×C8×C43—24no—
59C42×C43—22no—
60C42×C43Q1614yescomplemented
61C42×C43C2×D412yes—
62C42×C43C2×D411yescharacteristic
63C42×C43#4111yescharacteristic
64C22⋊Dic43—41no—
65C4⋊Dic43—22no—
66C4⋊Dic43—22no—
67C4⋊Dic43—22no—
68C4⋊Dic43—22no—
69C4⋊Dic43—48no—
70Dic43⋊C4—42no—
71Dic43⋊C4—42no—
72Dic43⋊C4—42no—
73C4×Dic43—42no—
74C4×Dic43—42no—
75C4×Dic43—41no—
76#10621877—42no—
77C2×C43⋊C8—41no—
78Dic172—48no—
79C23×C43#12011yescharacteristic
80C2×C4×C43—24no—
81C2×C4×C43—42no—
82C2×C4×C43—44no—
83C2×C4×C43#12012yes—
84C2×C4×C43#12112yes—
85C2×C4×C43#12111yescharacteristic
86C2×C4×C43#12711yescharacteristic
87C2×C4×C43C2×Q1612yes—
88C2×C4×C43#13712yes—
89C2×Dic43—24no—
90C2×Dic43—42no—
91C2×Dic43—42no—
92C2×Dic43—44no—
93C2×Dic43—42no—
94C2×Dic43—42no—
95Dic86—24no—
96Dic86—24no—
97Dic86—42no—
98Dic86—42no—
99Dic86—44no—
100C8×C43—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#46212yes—
110C4×C43#49411yescharacteristic
111C4×C43#49711yescharacteristic
112Dic43—44no—
113Dic43—82no—
114Dic43—82no—
115#3104—432no—
116#2399—431no—
117#1995—431no—
118#1487—432no—
119#1274D4311yescharacteristic
120C2×C43—22no—
121C2×C43#201012yes—
122C2×C43#201611yescharacteristic
123#533—431no—
124C2×C4×Q8—432no—
125#484—862no—
126#477—862no—
127#462—862no—
128#451—862no—
129C4×Q16—864no—
130#431C2×D4312yes—
131#423—431no—
132#398—862no—
133#395—862no—
134C4×C4⋊C4—862no—
135#376C2×D4311yescharacteristic
136#339—862no—
137Q8⋊C8—864no—
138C43#1001711yescharacteristic, complemented, Sylow
139C22×Q8—432no—
140C2×Q16—864no—
141C2×M16—861no—
142C4⋊Q8—432no—
143#125—861no—
144C22⋊Q8—862no—
145C4×Q8—862no—
146C4×Q8—862no—
147C4×Q8—862no—
148C4×Q8—862no—
149C4×Q8—862no—
150#117—861no—
151C2×C4⋊C4—432no—
152C2×C4⋊C4—864no—
153C2×C4⋊C4—862no—
154C2×C42—862no—
155C2×C42D17212yes—
156C2×C42C22×D4311yescharacteristic
157#107—864no—
158C4⋊C8—22no—
159C4⋊C8—862no—
160#103—864no—
161#103—864no—
162C22⋊C8—22no—
163C4×C8D17214yes—
164#95—22no—
165#95—862no—
166#95—862no—
167C2×Q8—862no—
168C2×Q8—862no—
169C2×Q8—862no—
170C2×Q8—1724no—
171C22×C4—22no—
172C22×C4—862no—
173C22×C4—862no—
174C22×C4C2×D17211yescharacteristic
175C22×C4D4×D4312yes—
176Q16—1728no—
177M16—1722no—
178C2×C8—24no—
179C2×C8—1721no—
180C4⋊C4—862no—
181C4⋊C4—862no—
182C4⋊C4—862no—
183C4⋊C4—862no—
184C4⋊C4—1728no—
185C4⋊C4—1722no—
186C4⋊C4—1722no—
187C4⋊C4—1722no—
188C22⋊C4—1721no—
189C42—22no—
190C42—1722no—
191C42—1722no—
192C42—1721no—
193C42Dic17214yescomplemented
194C42C2×D17212yes—
195C42D4×D4311yescharacteristic
196C42#1062190211yescharacteristic
197C23#1306329511yescharacteristic
198Q8—864no—
199Q8—864no—
200Q8—1724no—
201Q8—1722no—
202Q8—1722no—
203C2×C4—24no—
204C2×C4—42no—
205C2×C4—44no—
206C2×C4—864no—
207C2×C4—1724no—
208C2×C4—1722no—
209C2×C4—1722no—
210C2×C4—1722no—
211C2×C4—1722no—
212C2×C4#1306329512yes—
213C2×C4#1306330012yes—
214C2×C4#1306330011yescharacteristic
215C2×C4#1306332211yescharacteristic
216C2×C4C2×Dic17212yes—
217C2×C4#1306335812yes—
218C8—44no—
219C8—3441no—
220C22—22no—
221C22#1458280911yescharacteristic
222C22#1458305712yes—
223C4—22no—
224C4—22no—
225C4—44no—
226C4—3442no—
227C4—3442no—
228C4—1724no—
229C4#1458311012yes—
230C4#1458327911yescharacteristic
231C4#1458329311yescharacteristic
232C2—22no—
233C2#1913566312yes—
234C2#1913569711yescharacteristic
subgroupG/H
centerC2×C4#13063322
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1274C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#1274D43
hypocenterC43#10017
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
60. C42×C43Q16semidirect
138. C43#10017semidirect
193. C42Dic172semidirect

Maximal subgroups

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

subgroupindex
#191446352
#191378882
#191355762
#191330252
C43×#12742
#1001743