Finite Group Databasebeta

← #25007780

Subgroups — #25007780

Order 11008.

284 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 75 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#19145223C211yesmaximal, characteristic
2#19136200C211yesmaximal, characteristic, complemented
3#19132629C212yesmaximal, complemented
4#19132627C212yesmaximal, complemented
5C43×#2166C211yesmaximal, characteristic, complemented
6#14583511C411yescharacteristic
7#14583504C411yescharacteristic
8C2×#13063265—21no—
9#14583301C411yescharacteristic
10#14583272C411yescharacteristic
11#14583268C2211yescharacteristic
12#14583264C2211yescharacteristic
13#14583145—21no—
14#14583128—21no—
15#14583001—21no—
16C4×#10621873—21no—
17#14582677—21no—
18#14582677C2212yes—
19C43×#405C2211yescharacteristic
20C43×#364—21no—
21C43×#349—21no—
22C43×#347C2212yes—
23C2×#10621873—21no—
24C2×#10621873—21no—
25#13063325C2×C411yescharacteristic
26#13063322C2×C411yescharacteristic
27#13063318—41no—
28#13063317C2×C411yescharacteristic
29#13063317C2×C411yescharacteristic
30#13063315—41no—
31#13063310—41no—
32#13063304—21no—
33#13063299—21no—
34#13063298—41no—
35C4×Dic86—21no—
36C4×D172—21no—
37#13063265—22no—
38#13063265—22no—
39C2×C43⋊C16—22no—
40#13063259—21no—
41#13063257—21no—
42#13063250—21no—
43#13063250—21no—
44#13063247—21no—
45#13063247—21no—
46C2×M16×C43D411yescharacteristic
47C22×C8×C43D411yescharacteristic
48#117×C43C2×C411yescharacteristic
49M32×C43—22no—
50#97×C43D411yescharacteristic
51#97×C43C2311yescharacteristic
52C4×C8×C43C2×C411yescharacteristic
53C4×C8×C43D411yescharacteristic
54C22×C4×C43C22⋊C411yescharacteristic
55C2×C22⋊D43—41no—
56C2×D172—21no—
57C2×D172—41no—
58C2×C4×D43—41no—
59C2×Dic86—21no—
60M16×C43—41no—
61C2×C8×C43—21no—
62C2×C8×C43—21no—
63C2×C8×C43C22⋊C411yescharacteristic
64C2×C8×C43C22⋊C411yescharacteristic
65C2×C8×C43C2×D411yescharacteristic
66C2×C8×C43C2×D411yescharacteristic
67C4⋊C4×C43—21no—
68C22⋊C4×C43—21no—
69C42×C43C22⋊C411yescharacteristic
70C42×C43C22×C411yescharacteristic
71C22⋊Dic43—41no—
72(C2×D43)⋊C4—41no—
73(C2×D43)⋊C4—41no—
74C4⋊Dic43—21no—
75C4⋊Dic43—21no—
76C4⋊Dic43—41no—
77Dic43⋊C4—41no—
78Dic43⋊C4—41no—
79Dic43⋊C4—41no—
80Dic43⋊C4—41no—
81C4×Dic43—41no—
82#10621873—42no—
83#10621873—41no—
84#10621873—41no—
85C16×C43—42no—
86C43⋊C16—24no—
87C23×C43#10011yescharacteristic
88C22×D43—41no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43#10011yescharacteristic
94C2×C4×C43C2×C22⋊C411yescharacteristic
95C22⋊D43—161no—
96C2×Dic43—41no—
97C2×Dic43—41no—
98C2×Dic43—41no—
99D172—41no—
100D172—41no—
101D172—161no—
102C4×D43—161no—
103Dic86—41no—
104Dic86—41no—
105C8×C43—21no—
106C8×C43—21no—
107C8×C43—21no—
108C8×C43#10411yescharacteristic
109C8×C43#10411yescharacteristic
110#11912—431nomaximal, Sylow
111C22×C43—21no—
112C22×C43—41no—
113C22×C43C2×#10011yescharacteristic
114C2×D43—81no—
115C2×D43—81no—
116C2×D43—81no—
117C4×C43—21no—
118C4×C43—41no—
119C4×C43—41no—
120C4×C43C2×#10411yescharacteristic
121C4×C43#42111yescharacteristic
122Dic43—81no—
123Dic43—81no—
124Dic43—81no—
125#3174—431no—
126#2166D4311yescharacteristic, complemented
127#2110—431no—
128#1356—432no—
129#1355—432no—
130C2×C43—21no—
131C2×C43—41no—
132C2×C43#153011yescharacteristic
133D43—161no—
134#541—431no—
135#540—431no—
136C2×M32—861no—
137#499—431no—
138#492—431no—
139#491—431no—
140#490—431no—
141#468—861no—
142#465—861no—
143#440—861no—
144C4×SD16—861no—
145#405C2×D4311yescharacteristic
146#364—21no—
147#349—21no—
148#347—432no—
149#347—861no—
150#347C2×D4312yes—
151C43#1191211yescharacteristic, complemented, Sylow
152C2×SD16—861no—
153C2×SD16—861no—
154C2×M16C22⋊D4311yescharacteristic
155C22×C8D17211yescharacteristic
156C4⋊Q8—431no—
157#127—431no—
158#126—1721no—
159#125—431no—
160#125—431no—
161#125—1721no—
162#123—1721no—
163C22⋊Q8—861no—
164#121—861no—
165#121—1721no—
166C4×Q8—861no—
167C4×D4—861no—
168#117C4×D4311yescharacteristic
169M32—22no—
170M32—862no—
171M32—862no—
172C2×C16—862no—
173#107—861no—
174#106—861no—
175#103—861no—
176#103—861no—
177#102—861no—
178#102—861no—
179#97D17211yescharacteristic
180#97C22×D4311yescharacteristic
181C4×C8C4×D4311yescharacteristic
182C4×C8C22⋊D4311yescharacteristic
183C2×Q8—861no—
184C2×D4—861no—
185C2×D4—1721no—
186C2×D4—1721no—
187C22×C4—1721no—
188C22×C4(C2×D43)⋊C411yescharacteristic
189SD16—1722no—
190SD16—1721no—
191SD16—1721no—
192M16—41no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8(C2×D43)⋊C411yescharacteristic
196C2×C8(C2×D43)⋊C411yescharacteristic
197C2×C8C2×D17211yescharacteristic
198C2×C8C2×C22⋊D4311yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—861no—
201C4⋊C4—861no—
202C4⋊C4—1721no—
203C4⋊C4—1721no—
204C4⋊C4—1721no—
205C4⋊C4—1721no—
206C4⋊C4—1721no—
207C22⋊C4—21no—
208C22⋊C4—1721no—
209C22⋊C4—1721no—
210C22⋊C4—1721no—
211C42—1721no—
212C42(C2×D43)⋊C411yescharacteristic
213C42C2×C4×D4311yescharacteristic
214C16—42no—
215C16—864no—
216C23—1721no—
217C23#1306324111yescharacteristic
218Q8—1721no—
219Q8—1721no—
220D4—1721no—
221D4—1721no—
222D4—6881no—
223D4—6881no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—1721no—
229C2×C4—1721no—
230C2×C4—1721no—
231C2×C4—6881no—
232C2×C4#1306324111yescharacteristic
233C2×C4C2×(C2×D43)⋊C411yescharacteristic
234C8—21no—
235C8—21no—
236C8—21no—
237C8#1306325111yescharacteristic
238C8#1306325111yescharacteristic
239C22—21no—
240C22—41no—
241C22—3441no—
242C22—3441no—
243C22—3441no—
244C22C2×#1306324111yescharacteristic
245C4—21no—
246C4—41no—
247C4—41no—
248C4—3441no—
249C4—3441no—
250C4—3441no—
251C4C2×#1306325111yescharacteristic
252C4#1458291711yescharacteristic
253C2—21no—
254C2—41no—
255C2—6881no—
256C2#1913320711yescharacteristic
subgroupG/H
centerC2#19133207
commutatorC42×C43C22×C4
Frattini#97C22×D43
FittingC43×#2166C2
socleC2×C43#1530
prime radical#14583504C4
cosocle#97×C43C23
hypercenter#2166D43
hypocenterC43#11912
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
2. #19136200C2semidirect
3. #19132629C2semidirect
4. #19132627C2semidirect
5. C43×#2166C2semidirect
126. #2166D43semidirect
151. C43#11912semidirect

Maximal subgroups

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

subgroupindex
#191452232
#191362002
#191326292
#191326272
C43×#21662
#1191243