Finite Group Databasebeta

← #24985335

Subgroups — #24985335

Order 11008.

536 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 87 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#19141627C211yesmaximal, characteristic, complemented
2#19135826C212yesmaximal
3#19132421C211yesmaximal, characteristic, complemented
4#19132419C212yesmaximal, complemented
5C43×#2014C211yesmaximal, characteristic
6C2×#13063323—21no—
7C2×#13063246—22no—
8C2×#13063246—22no—
9#14582829—21no—
10#14582820—22no—
11#14582797C2212yes—
12#14582784—22no—
13#14582654C2212yes—
14C22×SD16×C43—21no—
15C2×#127×C43C2211yescharacteristic
16C2×#102×C43—21no—
17C43×#391C2211yescharacteristic
18C43×#336C2211yescharacteristic
19C22×Dic86—21no—
20C22×C43⋊C8—22no—
21#13063323—42no—
22#13063323—42no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43D412yes—
25C2×C4⋊Dic43D412yes—
26C2×Dic43⋊C4—22no—
27C2×Dic43⋊C4—22no—
28C2×C4×Dic43—21no—
29#13063246—44no—
30#13063246—44no—
31C43⋊#95—21no—
32C43⋊#95—22no—
33C43⋊#95—22no—
34C22×Q8×C43D411yescharacteristic
35C22×D4×C43—21no—
36C22×D4×C43—22no—
37C2×SD16×C43—42no—
38C2×SD16×C43—42no—
39C2×SD16×C43—42no—
40C22×C8×C43—21no—
41#127×C43—42no—
42C2×C4⋊C4×C43D411yescharacteristic
43C2×C42×C43C2311yescharacteristic
44#102×C43—42no—
45#95×C43—22no—
46C24×C43—41no—
47C2×Q8×C43—21no—
48C2×Q8×C43—41no—
49C2×Q8×C43—41no—
50C2×Q8×C43D812yes—
51C2×D4×C43—22no—
52C2×D4×C43—24no—
53C2×D4×C43—42no—
54C2×D4×C43—41no—
55C2×D4×C43—41no—
56C2×D4×C43—41no—
57C2×D4×C43—42no—
58C2×D4×C43—42no—
59C2×D4×C43—41no—
60C2×D4×C43—42no—
61C2×D4×C43—41no—
62C2×D4×C43—42no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43C2×D412yes—
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—22no—
68C22×Dic43—22no—
69C2×Dic86—42no—
70C2×Dic86—81no—
71C2×Dic86—81no—
72SD16×C43—48no—
73C2×C8×C43—22no—
74C2×C8×C43—41no—
75C2×C8×C43—41no—
76C4⋊C4×C43—41no—
77C42×C43—41no—
78C4⋊Dic43—22no—
79C4⋊Dic43—42no—
80C4⋊Dic43—81no—
81C4⋊Dic43SD1614yescomplemented
82Dic43⋊C4—44no—
83Dic43⋊C4—42no—
84Dic43⋊C4—42no—
85C4×Dic43—42no—
86C2×C43⋊C8—42no—
87C2×C43⋊C8—42no—
88C2×C43⋊C8—42no—
89C23×C43—42no—
90C23×C43—81no—
91C23×C43—82no—
92C23×C43—81no—
93C23×C43—82no—
94C23×C43#12011yescharacteristic
95Q8×C43—42no—
96Q8×C43—81no—
97D4×C43—42no—
98D4×C43—42no—
99D4×C43—44no—
100D4×C43—44no—
101D4×C43—81no—
102D4×C43—81no—
103D4×C43—82no—
104D4×C43—82no—
105C2×C4×C43—21no—
106C2×C4×C43—22no—
107C2×C4×C43—22no—
108C2×C4×C43—21no—
109C2×C4×C43—22no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—42no—
114C2×C4×C43C2×D811yescharacteristic
115C2×C4×C43C2×SD1612yes—
116C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C43#13712yes—
118C2×Dic43—24no—
119C2×Dic43—42no—
120C2×Dic43—42no—
121C2×Dic43—42no—
122C2×Dic43—42no—
123C2×Dic43—42no—
124Dic86—84no—
125C8×C43—42no—
126C43⋊C8—82no—
127#7741—431nomaximal, Sylow
128C22×C43—82no—
129C22×C43—84no—
130C22×C43—161no—
131C22×C43—162no—
132C22×C43—161no—
133C22×C43#44711yescharacteristic
134C22×C43#44812yes—
135C22×C43#45311yescharacteristic
136C22×C43#45412yes—
137C22×C43B(4,𝔽2)11yescharacteristic
138C4×C43—21no—
139C4×C43—21no—
140C4×C43—22no—
141C4×C43—22no—
142C4×C43—42no—
143C4×C43—81no—
144Dic43—44no—
145Dic43—82no—
146#2734—431no—
147#2041—432no—
148#2014D4311yescharacteristic
149#1272—431no—
150#1271—432no—
151C2×C43—162no—
152C2×C43#159511yescharacteristic
153C2×C43#159912yes—
154C2×C43#162311yescharacteristic
155C2×C43#162712yes—
156C2×C43#165711yescharacteristic
157C22×SD16—21no—
158C2×C4⋊Q8—861no—
159C2×#127C2×D4311yescharacteristic
160C2×#102—21no—
161C2×#102—862no—
162C2×#102—862no—
163#398—861no—
164#395—862no—
165#391C2×D4311yescharacteristic
166#389—432no—
167#387—862no—
168#336—432no—
169#336C2×D4311yescharacteristic
170C43#774111yescharacteristic, complemented, Sylow
171C22×Q8—861no—
172C22×Q8C22⋊D4311yescharacteristic
173C22×D4—22no—
174C22×D4—21no—
175C2×SD16—42no—
176C2×SD16—42no—
177C2×SD16—42no—
178C22×C8—21no—
179C22×C8—862no—
180C4⋊Q8—1722no—
181C4⋊Q8—1722no—
182#127—42no—
183C2×C4⋊C4—432no—
184C2×C4⋊C4—432no—
185C2×C4⋊C4—861no—
186C2×C4⋊C4—862no—
187C2×C4⋊C4—862no—
188C2×C4⋊C4C22⋊D4311yescharacteristic
189C2×C42—861no—
190C2×C42C22×D4311yescharacteristic
191#102—42no—
192#102—1724no—
193#102—1724no—
194#95—22no—
195#95—861no—
196#95—862no—
197#95—862no—
198C24—41no—
199C2×Q8—21no—
200C2×Q8—41no—
201C2×Q8—41no—
202C2×Q8—3441no—
203C2×Q8—3441no—
204C2×Q8—1722no—
205C2×Q8#1062188212yes—
206C2×D4—24no—
207C2×D4—22no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—42no—
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—41no—
214C2×D4—41no—
215C2×D4—42no—
216C2×D4—41no—
217C2×D4—42no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—862no—
221C22×C4—862no—
222C22×C4D4×D4312yes—
223C22×C4C2×C22⋊D4311yescharacteristic
224SD16—48no—
225C2×C8—22no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—1722no—
229C2×C8—1722no—
230C2×C8—1722no—
231C4⋊C4—41no—
232C4⋊C4—434no—
233C4⋊C4—862no—
234C4⋊C4—3441no—
235C4⋊C4—1722no—
236C4⋊C4—1724no—
237C4⋊C4—1722no—
238C4⋊C4—1722no—
239C42—41no—
240C42—1722no—
241C23—42no—
242C23—81no—
243C23—82no—
244C23—81no—
245C23—82no—
246C23#1306329311yescharacteristic
247Q8—42no—
248Q8—81no—
249Q8—3444no—
250D4—42no—
251D4—42no—
252D4—44no—
253D4—44no—
254D4—81no—
255D4—81no—
256D4—82no—
257D4—82no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—864no—
268C2×C4—1722no—
269C2×C4—1722no—
270C2×C4—1722no—
271C2×C4—1722no—
272C2×C4—1722no—
273C2×C4C2×#1062188211yescharacteristic
274C2×C4SD16×D4312yes—
275C2×C4#1306335011yescharacteristic
276C2×C4#1306335412yes—
277C8—42no—
278C8—3442no—
279C22—82no—
280C22—84no—
281C22—162no—
282C22—161no—
283C22—161no—
284C22#1458303211yescharacteristic
285C22#1458303612yes—
286C22#1458306611yescharacteristic
287C22#1458307012yes—
288C22#1458308511yescharacteristic
289C4—21no—
290C4—21no—
291C4—22no—
292C4—22no—
293C4—42no—
294C4—81no—
295C4—3442no—
296C4—1724no—
297C2—162no—
298C2#1913351211yescharacteristic
299C2#1913353312yes—
300C2#1913367111yescharacteristic
301C2#1913369612yes—
302C2#1913389111yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2014C2
socleC23×C43#120
prime radicalC2×#127×C43C22
hypercenter#2014D43
hypocenterC43#7741
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2014

Complements

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

NH ≅ G/Ntype
1. #19141627C2semidirect
3. #19132421C2semidirect
4. #19132419C2semidirect
81. C4⋊Dic43SD16semidirect
170. C43#7741semidirect

Maximal subgroups

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

subgroupindex
#191416272
#191358262
#191324212
#191324192
C43×#20142
#774143