Finite Group Databasebeta

← #25016949

Subgroups — #25016949

Order 11008.

326 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 59 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#19144994C211yesmaximal, characteristic
2#19136257C212yesmaximal
3#19132766C211yesmaximal, characteristic, complemented
4#19132765C212yesmaximal, complemented
5C43×#1412C211yesmaximal, characteristic, complemented
6#14583447C2211yescharacteristic
7#125×D43C411yescharacteristic, complemented
8#14583269C411yescharacteristic, complemented
9#14583268C411yescharacteristic, complemented
10#14583263C2211yescharacteristic
11#14583252—22no—
12#14582897—22no—
13#14582871—22no—
14#14582851C411yescharacteristic, complemented
15#14582693—22no—
16#14582692C2212yes—
17C43×#490C2211yescharacteristic
18C43×#353C2212yes—
19C2×#10621900D412yes—
20C2×#10621872—21no—
21#13063325C2×C411yescharacteristic
22#13063317C2×C411yescharacteristic
23#13063316—21no—
24#13063315—41no—
25#13063312D412yes—
26#13063296—41no—
27D4×Dic43—41no—
28#13063281—42no—
29C4⋊C4×D43—21no—
30C4⋊C4×D43—41no—
31C42×D43C2×C411yescharacteristic
32#13063250—22no—
33#13063248—22no—
34#13063246—22no—
35#13063240—22no—
36#13063239—42no—
37#13063236C2×C411yescharacteristic
38C8×Dic43—21no—
39#127×C43C2311yescharacteristic
40#125×C43C2×C411yescharacteristic
41#102×C43—22no—
42#99×C43—22no—
43#97×C43C2×C411yescharacteristic
44C2×D4×C43—41no—
45C2×D4×C43C2×D412yes—
46C2×C22⋊D43—22no—
47C22×Dic43—22no—
48#10621900—42no—
49#10621900—42no—
50C2×C4×D43—21no—
51C2×C4×D43—41no—
52C2×C4×D43C22⋊C411yescharacteristic
53C2×Dic86C22⋊C412yes—
54C2×C8×C43—21no—
55C4⋊C4×C43—21no—
56C4⋊C4×C43—41no—
57C22⋊C4×C43—42no—
58C42×C43C22×C411yescharacteristic
59C22⋊Dic43—42no—
60C22⋊Dic43—42no—
61C4⋊Dic43—21no—
62C4⋊Dic43—41no—
63C4⋊Dic43—41no—
64Dic43⋊C4—41no—
65Dic43⋊C4—41no—
66Dic43⋊C4—41no—
67Dic43⋊C4—82no—
68C4×Dic43—21no—
69C4×Dic43—82no—
70C4×Dic43C22⋊C411yescharacteristic
71C2×C43⋊C8—21no—
72#10621872—42no—
73C23×C43—22no—
74C22×D43#9911yescharacteristic
75D4×C43—42no—
76D4×C43—82no—
77C2×C4×C43—21no—
78C2×C4×C43—41no—
79C2×C4×C43—82no—
80C2×C4×C43C2×C22⋊C411yescharacteristic
81C22⋊D43—82no—
82C2×Dic43—21no—
83C2×Dic43—22no—
84C2×Dic43—42no—
85C2×Dic43—42no—
86C2×Dic43—41no—
87C2×Dic43—82no—
88C2×Dic43#9911yescharacteristic
89C4×D43—22no—
90C4×D43—81no—
91C4×D43—82no—
92Dic86—42no—
93C8×C43—41no—
94C43⋊C8—41no—
95#13596—431nomaximal, Sylow
96C22×C43—42no—
97C22×C43—82no—
98C22×C43C2×#9911yescharacteristic
99C2×D43—21no—
100C2×D43—41no—
101C4×C43—21no—
102C4×C43—41no—
103C4×C43—81no—
104C4×C43—162no—
105Dic43—41no—
106Dic43—42no—
107Dic43—81no—
108Dic43—162no—
109Dic43#35412yes—
110#3142—431no—
111#2126—432no—
112#1412—431no—
113#1412—432no—
114#1412D4311yescharacteristic, complemented
115C2×C43—21no—
116C2×C43—82no—
117C2×C43C2×#35411yescharacteristic
118D43—41no—
119#532—431no—
120C2×#125—431no—
121#491—431no—
122#491—431no—
123#490—431no—
124#490C2×D4311yescharacteristic
125#488—862no—
126#417—862no—
127#410—862no—
128C4×M16—431no—
129#354—862no—
130#353—432no—
131#353C2×D4312yes—
132C43#1359611yescharacteristic, complemented, Sylow
133C2×#41—432no—
134C2×M16—861no—
135C4⋊Q8—431no—
136#127C22×D4311yescharacteristic
137#125—431no—
138#125—861no—
139#125—1721no—
140#125C4×D4311yescharacteristic
141#124—432no—
142#121—1721no—
143C4×D4—1721no—
144#117—1722no—
145C2×C4⋊C4—861no—
146C2×C4⋊C4—1721no—
147C2×C42—431no—
148#103—862no—
149#103—862no—
150#102—22no—
151#102—862no—
152#99—22no—
153#99—862no—
154#99—1722no—
155#97—431no—
156#97C4×D4311yescharacteristic
157C4×C8—861no—
158#41—1722no—
159#41—1722no—
160C2×Q8—432no—
161C2×D4—41no—
162C2×D4—862no—
163C2×D4D4×D4312yes—
164C22×C4—431no—
165C22×C4—861no—
166C22×C4—862no—
167C22×C4—1721no—
168M16—1722no—
169C2×C8—21no—
170C2×C8—861no—
171C4⋊C4—21no—
172C4⋊C4—41no—
173C4⋊C4—861no—
174C4⋊C4—3442no—
175C4⋊C4—1721no—
176C4⋊C4—1721no—
177C4⋊C4—1721no—
178C4⋊C4—1721no—
179C4⋊C4—1721no—
180C22⋊C4—42no—
181C22⋊C4—1722no—
182C22⋊C4—1722no—
183C42—431no—
184C42—861no—
185C42—3442no—
186C42C2×C4×D4311yescharacteristic
187C23—22no—
188C23—431no—
189Q8—1722no—
190D4—42no—
191D4—82no—
192D4—3442no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—82no—
196C2×C4—431no—
197C2×C4—862no—
198C2×C4—861no—
199C2×C4—862no—
200C2×C4—3441no—
201C2×C4—3442no—
202C2×C4—3442no—
203C2×C4—1722no—
204C2×C4—1722no—
205C2×C4—1721no—
206C2×C4C22⋊C4×D4311yescharacteristic
207C8—41no—
208C8—1721no—
209C22—42no—
210C22—82no—
211C22—861no—
212C22—1721no—
213C22#99×D4311yescharacteristic
214C4—21no—
215C4—41no—
216C4—81no—
217C4—162no—
218C4—432no—
219C4—3441no—
220C4—1721no—
221C4—1722no—
222C4—6882no—
223C2—21no—
224C2—82no—
225C2—1721no—
226C2#354×D4311yescharacteristic
subgroupG/H
centerC2#354×D43
commutatorC42×C43C22×C4
Frattini#127C22×D43
FittingC43×#1412C2
socleC2×C43C2×#354
prime radical#14583447C22
cosocle#127×C43C23
hypercenter#1412D43
hypocenterC43#13596
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #1412

Complements

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

NH ≅ G/Ntype
3. #19132766C2semidirect
4. #19132765C2semidirect
5. C43×#1412C2semidirect
7. #125×D43C4semidirect
8. #14583269C4semidirect
9. #14583268C4semidirect
14. #14582851C4semidirect
114. #1412D43semidirect
132. C43#13596semidirect

Maximal subgroups

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

subgroupindex
#191449942
#191362572
#191327662
#191327652
C43×#14122
#1359643