Finite Group Databasebeta

← #24985900

Subgroups — #24985900

Order 11008.

494 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 83 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#19141621C211yesmaximal, characteristic
2#19136129C212yesmaximal, complemented
3#19132421C211yesmaximal, characteristic, complemented
4#19132415C212yesmaximal, complemented
5C43×#2095C211yesmaximal, characteristic, complemented
6C2×#13063314—21no—
7C2×#13063256—22no—
8C2×#13063245—22no—
9#14582816—21no—
10#14582809—22no—
11#14582801C2212yes—
12#14582791—22no—
13#14582654C2212yes—
14C2×#107×C43—21no—
15C2×#103×C43—21no—
16C43×#391C2211yescharacteristic
17C43×#384C2211yescharacteristic
18C43×#336C2211yescharacteristic
19C22×D172—21no—
20C22×D172—21no—
21C22×D172D412yes—
22C22×C43⋊C8—22no—
23#13063314—42no—
24#13063314—42no—
25C2×C4⋊Dic43D412yes—
26C2×(C2×D43)⋊C4—22no—
27C2×(C2×D43)⋊C4—22no—
28C2×(C2×D43)⋊C4—22no—
29C2×(C2×D43)⋊C4—22no—
30C2×C4×Dic43—21no—
31#13063256—44no—
32#13063245—44no—
33C43⋊#95—21no—
34C22×Q8×C43D411yescharacteristic
35C22×C8×C43—21no—
36C2×C4⋊C4×C43—22no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43D411yescharacteristic
39C2×C42×C43C2311yescharacteristic
40#107×C43—42no—
41#103×C43—42no—
42#95×C43—22no—
43C23×D43—22no—
44C2×Q8×C43—21no—
45C2×Q8×C43—41no—
46C2×Q8×C43—41no—
47C2×Q8×C43SD1612yes—
48C22×C4×C43—21no—
49C22×C4×C43—21no—
50C22×C4×C43—41no—
51C22×C4×C43C2×D412yes—
52C22×C4×C43C2×D411yescharacteristic
53C22×Dic43—22no—
54C2×D172—22no—
55C2×D172—22no—
56C2×D172—42no—
57C2×D172—42no—
58C2×D172—42no—
59C2×D172—82no—
60C2×D172—81no—
61C2×D172—81no—
62C2×D172—81no—
63C2×C8×C43—22no—
64C2×C8×C43—41no—
65C2×C8×C43—41no—
66C4⋊C4×C43—41no—
67C4⋊C4×C43—41no—
68C4⋊C4×C43—41no—
69C4⋊C4×C43—42no—
70C4⋊C4×C43—42no—
71C42×C43—41no—
72(C2×D43)⋊C4—44no—
73(C2×D43)⋊C4—42no—
74(C2×D43)⋊C4—42no—
75(C2×D43)⋊C4—42no—
76(C2×D43)⋊C4—42no—
77(C2×D43)⋊C4—82no—
78C4⋊Dic43—42no—
79C4×Dic43—42no—
80C2×C43⋊C8—24no—
81C2×C43⋊C8—42no—
82C2×C43⋊C8—42no—
83C23×C43#12011yescharacteristic
84C22×D43—42no—
85C22×D43—42no—
86C22×D43—42no—
87C22×D43—42no—
88C22×D43—42no—
89C22×D43—42no—
90C22×D43—42no—
91Q8×C43—42no—
92Q8×C43—81no—
93C2×C4×C43—22no—
94C2×C4×C43—21no—
95C2×C4×C43—22no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43—41no—
99C2×C4×C43—41no—
100C2×C4×C43—42no—
101C2×C4×C43—41no—
102C2×C4×C43—82no—
103C2×C4×C43—81no—
104C2×C4×C43C2×SD1611yescharacteristic
105C2×C4×C43#13512yes—
106C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
107C2×C4×C43#13712yes—
108C2×Dic43—42no—
109C2×Dic43—42no—
110C2×Dic43—42no—
111D172—44no—
112D172—82no—
113D172—84no—
114D172—84no—
115C8×C43—42no—
116C43⋊C8—44no—
117#7830—431nomaximal, Sylow
118C22×C43#45011yescharacteristic
119C22×C43#45212yes—
120C22×C43#45312yes—
121C22×C43#45311yescharacteristic
122C22×C43#45811yescharacteristic
123C2×D43—82no—
124C2×D43—82no—
125C2×D43—82no—
126C2×D43—82no—
127C2×D43—82no—
128C2×D43—82no—
129C2×D43—82no—
130C4×C43—21no—
131C4×C43—21no—
132C4×C43—22no—
133C4×C43—22no—
134C4×C43—42no—
135C4×C43—81no—
136C4×C43—161no—
137Dic43—82no—
138#2733—431no—
139#2095D4311yescharacteristic, complemented
140#2094—432no—
141#1272—431no—
142#1270—432no—
143C2×C43#161311yescharacteristic
144C2×C43#161812yes—
145C2×C43#163112yes—
146C2×C43#163411yescharacteristic
147C2×C43#165511yescharacteristic
148D43—162no—
149C2×#124—861no—
150C2×#107—21no—
151C2×#106—862no—
152C2×#103—21no—
153C2×#102—862no—
154#394—861no—
155#392—862no—
156#391C2×D4311yescharacteristic
157#390—432no—
158#388—862no—
159#384C2×D4311yescharacteristic
160#336—432no—
161#336C2×D4311yescharacteristic
162C43#783011yescharacteristic, complemented, Sylow
163C22×Q8C22⋊D4311yescharacteristic
164C22×D4—432no—
165C22×D4—861no—
166C22×D4—861no—
167C22×C8—21no—
168C22×C8—862no—
169#124—1722no—
170#124—1722no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—432no—
174C2×C4⋊C4C22⋊D4311yescharacteristic
175C2×C22⋊C4—862no—
176C2×C22⋊C4—862no—
177C2×C22⋊C4—862no—
178C2×C22⋊C4—862no—
179C2×C42—861no—
180C2×C42C22×D4311yescharacteristic
181#107—42no—
182#106—1724no—
183#103—42no—
184#102—1724no—
185#95—22no—
186#95—861no—
187C24—862no—
188C2×Q8—21no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8#1062188412yes—
192C2×D4—862no—
193C2×D4—862no—
194C2×D4—3441no—
195C2×D4—3441no—
196C2×D4—3442no—
197C2×D4—3441no—
198C2×D4—1722no—
199C2×D4—1722no—
200C2×D4—1722no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—41no—
204C22×C4—862no—
205C22×C4D4×D4312yes—
206C22×C4C2×C22⋊D4311yescharacteristic
207C2×C8—22no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—864no—
211C2×C8—1722no—
212C2×C8—1722no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—41no—
216C4⋊C4—42no—
217C4⋊C4—41no—
218C4⋊C4—1722no—
219C22⋊C4—3442no—
220C22⋊C4—1724no—
221C22⋊C4—1722no—
222C22⋊C4—1722no—
223C22⋊C4—1722no—
224C22⋊C4—1722no—
225C42—41no—
226C42—1722no—
227C23—1722no—
228C23—1722no—
229C23—1722no—
230C23—1722no—
231C23—1722no—
232C23—1722no—
233C23—1722no—
234C23#1306329311yescharacteristic
235Q8—42no—
236Q8—81no—
237D4—3442no—
238D4—3444no—
239D4—3444no—
240D4—1724no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—82no—
251C2×C4—81no—
252C2×C4—1722no—
253C2×C4—1722no—
254C2×C4—1722no—
255C2×C4C2×#1062188411yescharacteristic
256C2×C4#1306334812yes—
257C2×C4#1306335011yescharacteristic
258C2×C4#1306335712yes—
259C8—42no—
260C8—1724no—
261C22—3442no—
262C22—3442no—
263C22—3442no—
264C22—3442no—
265C22—3442no—
266C22—3442no—
267C22—3442no—
268C22#1458304911yescharacteristic
269C22#1458306012yes—
270C22#1458306512yes—
271C22#1458306611yescharacteristic
272C22#1458308811yescharacteristic
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—42no—
278C4—81no—
279C4—161no—
280C4—3442no—
281C2—6882no—
282C2#1913361411yescharacteristic
283C2#1913364212yes—
284C2#1913372012yes—
285C2#1913373811yescharacteristic
286C2#1913388311yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2095C2
socleC23×C43#120
prime radical#19141621C2
hypercenter#2095D43
hypocenterC43#7830
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2095

Complements

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

NH ≅ G/Ntype
2. #19136129C2semidirect
3. #19132421C2semidirect
4. #19132415C2semidirect
5. C43×#2095C2semidirect
139. #2095D43semidirect
162. C43#7830semidirect

Maximal subgroups

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

subgroupindex
#191416212
#191361292
#191324212
#191324152
C43×#20952
#783043