Finite Group Databasebeta

← #25009167

Subgroups — #25009167

Order 11008.

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

normal subgroups only

This group has 472 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#19139624C211yesmaximal, characteristic, complemented
2#19133564C212yesmaximal
3#19132624C212yesmaximal, complemented
4#19132541C211yesmaximal, characteristic, complemented
5C43×#2039C211yesmaximal, characteristic
6C2×#13063324—22no—
7#14583037—22no—
8#14582819—21no—
9#14582819C2212yes—
10#14582795—22no—
11C4×C4⋊Dic43—21no—
12#14582633—22no—
13#14582625C2212yes—
14C43×#537C2211yescharacteristic
15C2×#104×C43—21no—
16C43×#417—21no—
17C43×#384C2211yescharacteristic
18C43×#343C2211yescharacteristic
19C22×Dic86—21no—
20C22×Dic86D412yes—
21C2×#10621883—42no—
22#13063324—48no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43—21no—
25C2×Dic43⋊C4—22no—
26C2×Dic43⋊C4—22no—
27C2×C4×Dic43—22no—
28#13063248—42no—
29C22⋊(C43⋊C8)—22no—
30C43⋊#95—21no—
31C43⋊#95—22no—
32C43⋊#95D412yes—
33C2×#41×C43—21no—
34C2×M16×C43—21no—
35C22⋊Q8×C43—41no—
36#121×C43—22no—
37#121×C43—41no—
38C2×C4⋊C4×C43—22no—
39C2×C4⋊C4×C43D411yescharacteristic
40C2×C4⋊C4×C43C2311yescharacteristic
41C2×C42×C43D411yescharacteristic
42#104×C43—42no—
43#103×C43—41no—
44#102×C43—41no—
45#41×C43—41no—
46#41×C43—41no—
47#41×C43—41no—
48#41×C43—41no—
49C2×Q8×C43—21no—
50C2×D4×C43—21no—
51C2×D4×C43—22no—
52C2×D4×C43—41no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—41no—
56C22×C4×C43C2×D412yes—
57C22×C4×C43C2×D411yescharacteristic
58C22×Dic43—22no—
59C22×Dic43—22no—
60C2×Dic86—42no—
61C2×Dic86—44no—
62C2×Dic86—44no—
63C2×Dic86—81no—
64M16×C43—41no—
65M16×C43—41no—
66C2×C8×C43—41no—
67C4⋊C4×C43—22no—
68C4⋊C4×C43—41no—
69C4⋊C4×C43—41no—
70C4⋊C4×C43—44no—
71C22⋊C4×C43—42no—
72C42×C43—21no—
73C42×C43SD1612yescomplemented
74#10621883—84no—
75C4⋊Dic43—24no—
76C4⋊Dic43—24no—
77Dic43⋊C4—44no—
78Dic43⋊C4—44no—
79C4×Dic43—44no—
80C2×C43⋊C8—42no—
81C23×C43—41no—
82C23×C43#12011yescharacteristic
83Q8×C43—41no—
84Q8×C43—41no—
85D4×C43—41no—
86D4×C43—41no—
87D4×C43—82no—
88D4×C43—81no—
89D4×C43—81no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43—22no—
96C2×C4×C43—42no—
97C2×C4×C43—42no—
98C2×C4×C43—41no—
99C2×C4×C43—41no—
100C2×C4×C43—81no—
101C2×C4×C43—81no—
102C2×C4×C43C2×SD1611yescharacteristic
103C2×C4×C43#13711yescharacteristic
104C2×Dic43—24no—
105C2×Dic43—24no—
106C2×Dic43—42no—
107C2×Dic43—42no—
108C2×Dic43—42no—
109C2×Dic43—42no—
110Dic86—44no—
111Dic86—82no—
112Dic86—84no—
113C8×C43—81no—
114C43⋊C8—82no—
115#12180—431nomaximal, Sylow
116C22×C43—21no—
117C22×C43—21no—
118C22×C43—81no—
119C22×C43—81no—
120C22×C43—81no—
121C22×C43#44811yescharacteristic
122C22×C43#45411yescharacteristic
123C22×C43B(4,𝔽2)11yescharacteristic
124C4×C43—24no—
125C4×C43—21no—
126C4×C43—21no—
127C4×C43—42no—
128C4×C43—81no—
129C4×C43—81no—
130Dic43—44no—
131Dic43—44no—
132#2551—431no—
133#2039D4311yescharacteristic
134#1604—432no—
135#1354—432no—
136#1325—431no—
137C2×C43—21no—
138C2×C43—21no—
139C2×C43—161no—
140C2×C43#159911yescharacteristic
141C2×C43#219611yescharacteristic
142C2×C43#220511yescharacteristic
143#537C2×D4311yescharacteristic
144C2×C4⋊Q8—862no—
145#448—862no—
146C2×#104—21no—
147#417—21no—
148#395—432no—
149#395—861no—
150#389—862no—
151#384C2×D4311yescharacteristic
152C4×C4⋊C4—861no—
153#343C2×D4311yescharacteristic
154#327—862no—
155#324—432no—
156C43#1218011yescharacteristic, complemented, Sylow
157C2×#41—21no—
158C22×Q8—432no—
159C22×Q8—861no—
160C2×SD16—1722no—
161C2×M16—21no—
162C4⋊Q8—1728no—
163C22⋊Q8—41no—
164#121—22no—
165#121—41no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—861no—
168C2×C4⋊C4—861no—
169C2×C4⋊C4—862no—
170C2×C4⋊C4—862no—
171C2×C4⋊C4C22⋊D4311yescharacteristic
172C2×C4⋊C4C22×D4311yescharacteristic
173C2×C42—862no—
174C2×C42C22⋊D4311yescharacteristic
175#104—42no—
176#103—41no—
177#103—1722no—
178#102—41no—
179C22⋊C8—862no—
180#95—432no—
181#95—861no—
182#95—862no—
183#41—41no—
184#41—41no—
185#41—41no—
186#41—41no—
187C2×Q8—21no—
188C2×Q8—3441no—
189C2×Q8—1722no—
190C2×Q8—1724no—
191C2×Q8—1724no—
192C2×D4—21no—
193C2×D4—22no—
194C2×D4—41no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—41no—
198C22×C4—862no—
199C22×C4—862no—
200C22×C4D4×D4312yes—
201C22×C4C2×C22⋊D4311yescharacteristic
202SD16—3444no—
203M16—41no—
204M16—41no—
205C2×C8—41no—
206C2×C8—1722no—
207C4⋊C4—22no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—44no—
211C4⋊C4—864no—
212C4⋊C4—864no—
213C4⋊C4—1724no—
214C4⋊C4—1724no—
215C22⋊C4—42no—
216C42—21no—
217C42—1724no—
218C42#1062188312yescomplemented
219C23—41no—
220C23#1306329311yescharacteristic
221Q8—41no—
222Q8—41no—
223Q8—3442no—
224Q8—3444no—
225Q8—1724no—
226D4—41no—
227D4—41no—
228D4—82no—
229D4—81no—
230D4—81no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—864no—
244C2×C4—864no—
245C2×C4—1722no—
246C2×C4—1722no—
247C2×C4—1722no—
248C2×C4—1722no—
249C2×C4C2×#1062188311yescharacteristic
250C2×C4#1306335511yescharacteristic
251C8—81no—
252C8—3442no—
253C22—21no—
254C22—21no—
255C22—81no—
256C22—81no—
257C22—81no—
258C22#1458303711yescharacteristic
259C22#1458307111yescharacteristic
260C22#1458308511yescharacteristic
261C4—24no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—81no—
266C4—81no—
267C4—1724no—
268C4—1724no—
269C2—21no—
270C2—21no—
271C2—161no—
272C2#1913353411yescharacteristic
273C2#1913657811yescharacteristic
274C2#1913662411yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2039C2
socleC22×C43B(4,𝔽2)
prime radicalC43×#537C22
hypercenter#2039D43
hypocenterC43#12180
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2039

Complements

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

NH ≅ G/Ntype
1. #19139624C2semidirect
3. #19132624C2semidirect
4. #19132541C2semidirect
73. C42×C43SD16semidirect
156. C43#12180semidirect
218. C42#10621883semidirect

Maximal subgroups

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

subgroupindex
#191396242
#191335642
#191326242
#191325412
C43×#20392
#1218043