Finite Group Databasebeta

← #24997449

Subgroups — #24997449

Order 11008.

566 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 103 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#19144622C212yesmaximal
2#19137888C211yesmaximal, characteristic, complemented
3#19133023C212yesmaximal, complemented
4#19132424C211yesmaximal, characteristic, complemented
5C43×#1963C211yesmaximal, characteristic
6C2×C4×Dic86C2212yes—
7#14583215—22no—
8#14583181—22no—
9#14583096—22no—
10#14583037—22no—
11C4×#10621883—24no—
12#14582952C2212yes—
13#14582831—22no—
14#14582820—22no—
15C4×C4⋊Dic43—22no—
16#14582629—24no—
17C43×#532C2211yescharacteristic
18C43×#423C2211yescharacteristic
19C2×#104×C43—22no—
20C43×#376C2211yescharacteristic
21C22×Dic86D412yes—
22C2×#10621883—24no—
23C4×Dic86—22no—
24C4×Dic86—22no—
25C4×Dic86—22no—
26C4×Dic86—22no—
27C2×C4⋊Dic43—24no—
28C2×C4⋊Dic43D412yes—
29C2×Dic43⋊C4—22no—
30C2×C4×Dic43—22no—
31#13063256—24no—
32C4⋊(C43⋊C8)—22no—
33#13063248—24no—
34#13063246—24no—
35C22⋊(C43⋊C8)—22no—
36C4×C43⋊C8D414yes—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C2×#41×C43—21no—
40C2×M16×C43—21no—
41C4⋊Q8×C43D411yescharacteristic
42#127×C43D411yescharacteristic
43#124×C43—21no—
44#121×C43—22no—
45C4×D4×C43—22no—
46C2×C42×C43D412yes—
47C2×C42×C43C2311yescharacteristic
48C4⋊C8×C43—22no—
49#104×C43—44no—
50#95×C43—22no—
51#41×C43—42no—
52#41×C43—42no—
53C2×Q8×C43—21no—
54C2×D4×C43—22no—
55C2×D4×C43—21no—
56C2×D4×C43—41no—
57C22×C4×C43—22no—
58C22×C4×C43—41no—
59C22×C4×C43C2×D412yes—
60C22×C4×C43C2×D411yescharacteristic
61C22×Dic43—22no—
62C22×Dic43—22no—
63C2×Dic86—22no—
64C2×Dic86—22no—
65C2×Dic86—44no—
66M16×C43—42no—
67C2×C8×C43—41no—
68C4⋊C4×C43—22no—
69C22⋊C4×C43—42no—
70C42×C43—22no—
71C42×C43SD1614yescomplemented
72C42×C43C2×D411yescharacteristic
73C42×C43C2×D412yes—
74C42×C43#4111yescharacteristic
75#10621883—48no—
76C4⋊Dic43—22no—
77C4⋊Dic43—22no—
78C4⋊Dic43—48no—
79Dic43⋊C4—42no—
80Dic43⋊C4—42no—
81C4×Dic43—42no—
82C4×Dic43—42no—
83C2×C43⋊C8—24no—
84C23×C43—41no—
85C23×C43#12011yescharacteristic
86Q8×C43—42no—
87D4×C43—44no—
88D4×C43—42no—
89D4×C43—82no—
90C2×C4×C43—24no—
91C2×C4×C43—42no—
92C2×C4×C43—44no—
93C2×C4×C43—41no—
94C2×C4×C43—81no—
95C2×C4×C43—81no—
96C2×C4×C43#12012yes—
97C2×C4×C43#12112yes—
98C2×C4×C43#12111yescharacteristic
99C2×C4×C43#12711yescharacteristic
100C2×C4×C43C2×SD1612yes—
101C2×C4×C43#13712yes—
102C2×Dic43—24no—
103C2×Dic43—42no—
104C2×Dic43—42no—
105C2×Dic43—44no—
106C2×Dic43—42no—
107Dic86—24no—
108Dic86—24no—
109Dic86—42no—
110Dic86—42no—
111C8×C43—81no—
112C43⋊C8—44no—
113#10014—431nomaximal, Sylow
114C22×C43—22no—
115C22×C43—82no—
116C22×C43—81no—
117C22×C43#39211yescharacteristic
118C22×C43#44812yes—
119C4×C43—22no—
120C4×C43—22no—
121C4×C43—44no—
122C4×C43—81no—
123C4×C43#46112yes—
124C4×C43#49211yescharacteristic
125C4×C43#49711yescharacteristic
126Dic43—44no—
127Dic43—82no—
128#3103—432no—
129#2399—431no—
130#1963D4311yescharacteristic
131#1487—432no—
132#1274—431no—
133C2×C43—22no—
134C2×C43—161no—
135C2×C43#201012yes—
136C2×C43#201311yescharacteristic
137#532C2×D4311yescharacteristic
138C2×C4×Q8—432no—
139#481—862no—
140#475—862no—
141#460—862no—
142#448—862no—
143C4×SD16—864no—
144#431—432no—
145#423C2×D4311yescharacteristic
146C2×#104—22no—
147#398—862no—
148#395—862no—
149C4×C4⋊C4—862no—
150#376C2×D4311yescharacteristic
151Q8⋊C8—864no—
152C43#1001411yescharacteristic, complemented, Sylow
153C2×#41—21no—
154C22×Q8—432no—
155C2×SD16—864no—
156C2×M16—21no—
157C4⋊Q8D17211yescharacteristic
158#127D17211yescharacteristic
159#124—21no—
160#121—22no—
161C4×Q8—862no—
162C4×Q8—862no—
163C4×Q8—862no—
164C4×Q8—862no—
165C4×D4—22no—
166C2×C4⋊C4—432no—
167C2×C4⋊C4—864no—
168C2×C4⋊C4—862no—
169C2×C42—862no—
170C2×C42C22⋊D4312yes—
171C2×C42C22×D4311yescharacteristic
172#106—864no—
173C4⋊C8—22no—
174C4⋊C8—862no—
175#104—44no—
176#103—864no—
177#102—864no—
178C22⋊C8—862no—
179C4×C8—434no—
180#95—22no—
181#95—862no—
182#95—862no—
183#41—42no—
184#41—42no—
185C2×Q8—21no—
186C2×Q8—862no—
187C2×Q8—862no—
188C2×Q8—1724no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—41no—
192C22×C4—22no—
193C22×C4—41no—
194C22×C4—862no—
195C22×C4—862no—
196C22×C4D4×D4312yes—
197C22×C4C2×C22⋊D4311yescharacteristic
198SD16—1728no—
199M16—42no—
200C2×C8—41no—
201C2×C8—864no—
202C4⋊C4—22no—
203C4⋊C4—862no—
204C4⋊C4—862no—
205C4⋊C4—1728no—
206C4⋊C4—1722no—
207C4⋊C4—1722no—
208C22⋊C4—42no—
209C42—22no—
210C42—1722no—
211C42—1722no—
212C42#1062188314yescomplemented
213C42C2×D17211yescharacteristic
214C42#1062189811yescharacteristic
215C42D4×D4312yes—
216C23—41no—
217C23#1306329311yescharacteristic
218Q8—42no—
219Q8—864no—
220Q8—864no—
221Q8—1722no—
222Q8—1722no—
223D4—44no—
224D4—42no—
225D4—82no—
226C2×C4—24no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—41no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—864no—
233C2×C4—1724no—
234C2×C4—1722no—
235C2×C4—1722no—
236C2×C4—1722no—
237C2×C4#1306329512yes—
238C2×C4#1306329812yes—
239C2×C4#1306329911yescharacteristic
240C2×C4#1306332111yescharacteristic
241C2×C4C2×#1062188312yes—
242C2×C4#1306335512yes—
243C8—81no—
244C8—1724no—
245C22—22no—
246C22—82no—
247C22—81no—
248C22#1458280811yescharacteristic
249C22#1458303712yes—
250C4—22no—
251C4—22no—
252C4—44no—
253C4—81no—
254C4—3442no—
255C4—1724no—
256C4#1458310412yes—
257C4#1458327111yescharacteristic
258C4#1458329411yescharacteristic
259C2—22no—
260C2—161no—
261C2#1913566112yes—
262C2#1913567711yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1963C2
socleC22×C43#392
prime radicalC43×#532C22
hypercenter#1963D43
hypocenterC43#10014
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
2. #19137888C2semidirect
3. #19133023C2semidirect
4. #19132424C2semidirect
71. C42×C43SD16semidirect
152. C43#10014semidirect
212. C42#10621883semidirect

Maximal subgroups

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

subgroupindex
#191446222
#191378882
#191330232
#191324242
C43×#19632
#1001443