Finite Group Databasebeta

← #24985390

Subgroups — #24985390

Order 11008.

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

normal subgroups only

This group has 492 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#19141525C211yesmaximal, characteristic
2#19135924C212yesmaximal, complemented
3#19135677C211yesmaximal, characteristic
4#19132417C212yesmaximal, complemented
5C43×#1270C211yesmaximal, characteristic
6C22×#10621883—21no—
7C2×#13063325C2211yescharacteristic
8C2×#13063306—21no—
9C2×#13063259—22no—
10C2×#13063248—21no—
11#14582829—21no—
12#14582824—22no—
13#14582797C2212yes—
14#14582774—22no—
15#14582662—22no—
16#14582654C2211yescharacteristic
17C43×#390C2211yescharacteristic
18C43×#336C2212yes—
19C22×Dic86—21no—
20C23×Dic43—21no—
21C2×#10621883—42no—
22C2×#10621883—42no—
23C2×#10621883—42no—
24C22×C43⋊C8—21no—
25#13063325—42no—
26#13063306—42no—
27#13063306—42no—
28C2×C4⋊Dic43—22no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43D412yes—
31C2×C4⋊Dic43D412yes—
32C2×Dic43⋊C4—22no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—22no—
35#13063259—44no—
36#13063248—42no—
37C43⋊#95—21no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C22×D4×C43D411yescharacteristic
41C22×C8×C43—22no—
42C2×C4⋊C4×C43D411yescharacteristic
43C2×C22⋊C4×C43—22no—
44C2×C42×C43C2311yescharacteristic
45C24×C43—21no—
46C2×D4×C43—21no—
47C2×D4×C43—41no—
48C2×D4×C43—41no—
49C2×D4×C43D812yes—
50C22×C4×C43—21no—
51C22×C4×C43C2×D411yescharacteristic
52C22×C4×C43C2×D412yes—
53C22×Dic43—22no—
54C22×Dic43—22no—
55C22×Dic43—42no—
56C22×Dic43—41no—
57C22×Dic43—81no—
58C22×Dic43—81no—
59C2×Dic86—22no—
60C2×Dic86—41no—
61C2×Dic86—41no—
62C2×Dic86—41no—
63C2×Dic86—41no—
64C2×Dic86—41no—
65C2×C8×C43—24no—
66C2×C8×C43—42no—
67C2×C8×C43—42no—
68C4⋊C4×C43—41no—
69C22⋊C4×C43—42no—
70C22⋊C4×C43—42no—
71C42×C43—41no—
72C22⋊Dic43—42no—
73C22⋊Dic43—44no—
74#10621883—48no—
75C4⋊Dic43—24no—
76C4⋊Dic43—22no—
77C4⋊Dic43—22no—
78C4⋊Dic43—42no—
79C4⋊Dic43—42no—
80C4⋊Dic43—81no—
81Dic43⋊C4—42no—
82Dic43⋊C4—42no—
83C2×C43⋊C8—22no—
84C2×C43⋊C8—41no—
85C2×C43⋊C8—41no—
86C23×C43—22no—
87C23×C43—42no—
88C23×C43—41no—
89C23×C43—42no—
90C23×C43—41no—
91C23×C43#12011yescharacteristic
92D4×C43—42no—
93D4×C43—81no—
94C2×C4×C43—21no—
95C2×C4×C43—22no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43—42no—
99C2×C4×C43—41no—
100C2×C4×C43C2×D811yescharacteristic
101C2×C4×C43#13512yes—
102C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
103C2×C4×C43#13712yes—
104C2×Dic43—42no—
105C2×Dic43—42no—
106C2×Dic43—42no—
107C2×Dic43—42no—
108C2×Dic43—42no—
109C2×Dic43—42no—
110C2×Dic43—42no—
111C2×Dic43—84no—
112C2×Dic43—81no—
113C2×Dic43—81no—
114Dic86—42no—
115Dic86—42no—
116Dic86—81no—
117Dic86—81no—
118C8×C43—44no—
119C43⋊C8—42no—
120#7751—431nomaximal, Sylow
121C22×C43—42no—
122C22×C43—44no—
123C22×C43—82no—
124C22×C43—81no—
125C22×C43—81no—
126C22×C43#44711yescharacteristic
127C22×C43#45212yes—
128C22×C43#45311yescharacteristic
129C22×C43#45612yes—
130C22×C43B(4,𝔽2)11yescharacteristic
131C4×C43—21no—
132C4×C43—21no—
133C4×C43—22no—
134C4×C43—22no—
135C4×C43—81no—
136Dic43—82no—
137Dic43—82no—
138Dic43—82no—
139#2724—431no—
140#2057—432no—
141#2013—431no—
142#1271—432no—
143#1270D4311yescharacteristic
144C2×C43—82no—
145C2×C43#159511yescharacteristic
146C2×C43#160312yes—
147C2×C43#163011yescharacteristic
148C2×C43#164712yes—
149C2×C43#166011yescharacteristic
150C22×SD16—861no—
151C2×C4⋊Q8—431no—
152C2×#123—861no—
153C2×#107—862no—
154C2×#103—861no—
155#398—861no—
156#397—862no—
157#390C2×D4311yescharacteristic
158#389—432no—
159#385—862no—
160#340—862no—
161#336—431no—
162#336C2×D4312yes—
163C43#775111yescharacteristic, complemented, Sylow
164C22×Q8—861no—
165C22×D4D17211yescharacteristic
166C23×C4—861no—
167C2×SD16—1722no—
168C2×SD16—1722no—
169C2×SD16—1722no—
170C22×C8—22no—
171C22×C8—861no—
172C4⋊Q8—1722no—
173#123—1722no—
174#123—1722no—
175C2×C4⋊C4—432no—
176C2×C4⋊C4—432no—
177C2×C4⋊C4—862no—
178C2×C4⋊C4—861no—
179C2×C4⋊C4—862no—
180C2×C4⋊C4D17211yescharacteristic
181C2×C22⋊C4—22no—
182C2×C22⋊C4—862no—
183C2×C22⋊C4—861no—
184C2×C42C22×D4311yescharacteristic
185#107—1724no—
186#103—1722no—
187#95—862no—
188#95—861no—
189#95—862no—
190C24—21no—
191C2×Q8—862no—
192C2×Q8—1721no—
193C2×Q8—1721no—
194C2×Q8—1721no—
195C2×Q8—1721no—
196C2×Q8—1721no—
197C2×D4—21no—
198C2×D4—41no—
199C2×D4—41no—
200C2×D4D34412yes—
201C22×C4—21no—
202C22×C4—862no—
203C22×C4—862no—
204C22×C4—3441no—
205C22×C4—3441no—
206C22×C4—1722no—
207C22×C4—1721no—
208C22×C4C2×D17211yescharacteristic
209C22×C4D4×D4312yes—
210SD16—1728no—
211C2×C8—24no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—862no—
215C2×C8—1721no—
216C2×C8—1721no—
217C4⋊C4—41no—
218C4⋊C4—864no—
219C4⋊C4—862no—
220C4⋊C4—862no—
221C4⋊C4—3441no—
222C4⋊C4—1722no—
223C4⋊C4—1722no—
224C4⋊C4—1722no—
225C4⋊C4—1722no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C22⋊C4—1722no—
229C22⋊C4—1724no—
230C42—41no—
231C23—22no—
232C23—42no—
233C23—41no—
234C23—42no—
235C23—41no—
236C23#1306329511yescharacteristic
237Q8—3441no—
238Q8—3441no—
239Q8—1722no—
240Q8—1722no—
241D4—42no—
242D4—81no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—3444no—
250C2×C4—3441no—
251C2×C4—3441no—
252C2×C4—1722no—
253C2×C4—1722no—
254C2×C4—1722no—
255C2×C4—1722no—
256C2×C4—1722no—
257C2×C4—1722no—
258C2×C4—1722no—
259C2×C4C2×D34411yescharacteristic
260C2×C4#1306334412yes—
261C2×C4#1306335311yescharacteristic
262C2×C4#1306335412yes—
263C8—44no—
264C8—1722no—
265C22—42no—
266C22—44no—
267C22—81no—
268C22—82no—
269C22—81no—
270C22#1458303511yescharacteristic
271C22#1458306212yes—
272C22#1458306911yescharacteristic
273C22#1458308312yes—
274C22#1458308711yescharacteristic
275C4—21no—
276C4—21no—
277C4—22no—
278C4—22no—
279C4—81no—
280C4—3442no—
281C4—3442no—
282C4—3442no—
283C2—82no—
284C2#1913351511yescharacteristic
285C2#1913355912yes—
286C2#1913371711yescharacteristic
287C2#1913383212yes—
288C2#1913390711yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1270C2
socleC23×C43#120
prime radicalC22×D4×C43D4
hypercenter#1270D43
hypocenterC43#7751
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #19135924C2semidirect
4. #19132417C2semidirect
163. C43#7751semidirect

Maximal subgroups

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

subgroupindex
#191415252
#191359242
#191356772
#191324172
C43×#12702
#775143