Finite Group Databasebeta

← #24996078

Subgroups — #24996078

Order 11008.

406 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 127 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#19134767C211yesmaximal, characteristic
2#19133280C211yesmaximal, characteristic
3#19133276C211yesmaximal, characteristic
4#19133267C211yesmaximal, characteristic
5#19133267C211yesmaximal, characteristic
6#19132887C211yesmaximal, characteristic
7C2×C43×#487C211yesmaximal, characteristic
8#14582952C2211yescharacteristic
9#14582952C2211yescharacteristic
10C2×#13063261—22no—
11#14582923C2211yescharacteristic
12#14582923C2211yescharacteristic
13#14582648—22no—
14#14582645—22no—
15#14582645—22no—
16#14582645—22no—
17#14582621—22no—
18C2×C4⋊Q8×C43C2211yescharacteristic
19C2×C4⋊Q8×C43C2211yescharacteristic
20C43×#487—22no—
21C43×#487C414yes—
22C2×#103×C43—22no—
23C2×C4×C8×C43C2211yescharacteristic
24C2×#10621877—21no—
25C2×#10621877—21no—
26#13063261—44no—
27C4⋊(C43⋊C8)—21no—
28C4⋊(C43⋊C8)—21no—
29C4⋊(C43⋊C8)—21no—
30C4⋊(C43⋊C8)—21no—
31C4⋊(C43⋊C8)D412yes—
32C4⋊(C43⋊C8)D412yes—
33C22⋊(C43⋊C8)—21no—
34C22⋊(C43⋊C8)—21no—
35C4×C43⋊C8—21no—
36C4×C43⋊C8—21no—
37C22×Q8×C43—21no—
38C22×Q8×C43—21no—
39C22×C8×C43D412yes—
40C4⋊Q8×C43—21no—
41C4⋊Q8×C43—21no—
42C4⋊Q8×C43—21no—
43C4⋊Q8×C43—21no—
44C4⋊Q8×C43—21no—
45C4⋊Q8×C43—21no—
46C4⋊Q8×C43C2×C412yes—
47C4⋊Q8×C43C2×C412yes—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43—21no—
52C2×C42×C43C2311yescharacteristic
53#103×C43—28no—
54C4×C8×C43C2×C412yes—
55C4×C8×C43D412yes—
56C2×Q8×C43—22no—
57C2×Q8×C43—22no—
58C2×Q8×C43—41no—
59C2×Q8×C43—41no—
60C2×Q8×C43—42no—
61C2×Q8×C43—42no—
62C2×Q8×C43—82no—
63C22×C4×C43—41no—
64C22×C4×C43—41no—
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43#4111yescharacteristic
67C22×C4×C43#4111yescharacteristic
68C2×C8×C43—22no—
69C2×C8×C43—22no—
70C2×C8×C43C22⋊C414yes—
71C4⋊C4×C43—22no—
72C4⋊C4×C43—22no—
73C4⋊C4×C43—22no—
74C4⋊C4×C43—22no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C42×C43C22×C411yescharacteristic
80C42×C43C2×D411yescharacteristic
81C42×C43C2×D411yescharacteristic
82C42×C43C2×D411yescharacteristic
83#10621877—42no—
84#10621877—42no—
85C2×C43⋊C8—22no—
86C2×C43⋊C8—22no—
87C2×C43⋊C8—41no—
88C2×C43⋊C8—41no—
89C23×C43#12411yescharacteristic
90Q8×C43—44no—
91Q8×C43—82no—
92Q8×C43—82no—
93Q8×C43—81no—
94Q8×C43—81no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—42no—
98C2×C4×C43—42no—
99C2×C4×C43—82no—
100C2×C4×C43—82no—
101C2×C4×C43C2×C22⋊C411yescharacteristic
102C2×C4×C43C4×D411yescharacteristic
103C2×C4×C43C4×D411yescharacteristic
104C2×C4×C43#12111yescharacteristic
105C2×C4×C43#12111yescharacteristic
106C2×C4×C43#12711yescharacteristic
107C2×C4×C43AGL(1,ℤ/8)12yes—
108C2×C4×C43#13712yes—
109C8×C43—24no—
110C43⋊C8—42no—
111C43⋊C8—42no—
112C43⋊C8—81no—
113C43⋊C8—81no—
114#9775—431nomaximal, Sylow
115C22×C43—21no—
116C22×C43—21no—
117C22×C43#39011yescharacteristic
118C22×C43#48912yes—
119C4×C43—21no—
120C4×C43—21no—
121C4×C43—82no—
122C4×C43—82no—
123C4×C43#41712yes—
124C4×C43#47112yes—
125C4×C43#47312yes—
126C4×C43#49611yescharacteristic
127C4×C43#49711yescharacteristic
128C2×#487D4311yescharacteristic
129#1848—431no—
130#1549—431no—
131#1548—431no—
132#1546—431no—
133#1546—431no—
134#1452—431no—
135C2×C43—22no—
136C2×C43#195911yescharacteristic
137C2×C43#197711yescharacteristic
138C2×C43#197911yescharacteristic
139C2×C4⋊Q8C2×D4311yescharacteristic
140C2×C4⋊Q8C2×D4311yescharacteristic
141#487—22no—
142#487Dic4314yes—
143#431—431no—
144#431—431no—
145C2×#108—862no—
146#423—431no—
147#423—431no—
148C2×#103—22no—
149C2×C4×C8C2×D4311yescharacteristic
150#333—862no—
151#332—862no—
152#332—862no—
153#332—862no—
154#322—862no—
155C43#977511yescharacteristic, complemented, Sylow
156C22×Q8—21no—
157C22×Q8—21no—
158C2×M16—861no—
159C2×M16—861no—
160C22×C8C22⋊D4312yes—
161C4⋊Q8—21no—
162C4⋊Q8—21no—
163C4⋊Q8—21no—
164C4⋊Q8—21no—
165C4⋊Q8—21no—
166C4⋊Q8—21no—
167C4⋊Q8C2×Dic4312yes—
168C4⋊Q8C2×Dic4312yes—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C42C22×D4311yescharacteristic
174#108—1724no—
175C4⋊C8—432no—
176C4⋊C8—432no—
177C4⋊C8—861no—
178C4⋊C8—861no—
179C4⋊C8—861no—
180C4⋊C8—861no—
181#103—28no—
182C22⋊C8—861no—
183C22⋊C8—861no—
184C4×C8—861no—
185C4×C8—861no—
186C4×C8C2×Dic4312yes—
187C4×C8C22⋊D4312yes—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—42no—
193C2×Q8—42no—
194C2×Q8—82no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4#1062190011yescharacteristic
198C22×C4#1062190011yescharacteristic
199C22×C4C2×C22⋊D4311yescharacteristic
200M16—1722no—
201M16—1722no—
202C2×C8—22no—
203C2×C8—22no—
204C2×C8—862no—
205C2×C8—862no—
206C2×C8—1721no—
207C2×C8—1721no—
208C2×C8C22⋊Dic4314yes—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C42D4×D4311yescharacteristic
218C42D4×D4311yescharacteristic
219C42C22×Dic4311yescharacteristic
220C42C2×C22⋊D4311yescharacteristic
221C23#1306331211yescharacteristic
222Q8—44no—
223Q8—82no—
224Q8—82no—
225Q8—81no—
226Q8—81no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—82no—
232C2×C4—82no—
233C2×C4C2×C22⋊Dic4311yescharacteristic
234C2×C4D4×Dic4311yescharacteristic
235C2×C4D4×Dic4311yescharacteristic
236C2×C4#1306329611yescharacteristic
237C2×C4#1306329611yescharacteristic
238C2×C4#1306332111yescharacteristic
239C2×C4#1306335012yes—
240C2×C4#1306335512yes—
241C8—24no—
242C8—3441no—
243C8—3441no—
244C8—1722no—
245C8—1722no—
246C22—21no—
247C22—21no—
248C22#1458280211yescharacteristic
249C22#1458325812yes—
250C4—21no—
251C4—21no—
252C4—82no—
253C4—82no—
254C4#1458290012yes—
255C4#1458315912yes—
256C4#1458317112yes—
257C4#1458328911yescharacteristic
258C4#1458329411yescharacteristic
259C2—22no—
260C2#1913541211yescharacteristic
261C2#1913550011yescharacteristic
262C2#1913551111yescharacteristic
subgroupG/H
centerC22#14582802
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#487C2
socleC22×C43#390
prime radicalC23×C43#124
cosocleC2×C42×C43C23
hypercenterC2×#487D43
hypocenterC43#9775
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
155. C43#9775semidirect

Maximal subgroups

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

subgroupindex
#191347672
#191332802
#191332762
#191332672
#191328872
C2×C43×#4872
#977543