Finite Group Databasebeta

← #24997289

Subgroups — #24997289

Order 11008.

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

normal subgroups only

This group has 826 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#19145419C211yesmaximal, characteristic, complemented
2C2×#14583050C212yesmaximal
3#19132960C212yesmaximal, complemented
4#19132482C211yesmaximal, characteristic, complemented
5C43×#1783C211yesmaximal, characteristic
6C22×#10621883—22no—
7C2×#13063304C2212yes—
8#14583230—22no—
9#14583157—22no—
10#14583057—22no—
11#14583050—24no—
12#14583050—24no—
13C2×#13063246—22no—
14C2×C22⋊(C43⋊C8)C2212yes—
15#14582624—24no—
16C23×D4×C43C2211yescharacteristic
17C2×#100×C43—22no—
18C43×#407C2211yescharacteristic
19C43×#407C2211yescharacteristic
20C22×Dic86D412yes—
21C2×Dic172—22no—
22C2×#10621883—28no—
23C2×#10621883—48no—
24C22×C43⋊C8—22no—
25#13063304—22no—
26#13063304—22no—
27#13063304—22no—
28#13063304—22no—
29C2×C4⋊Dic43D412yes—
30C2×Dic43⋊C4—22no—
31C2×C22⋊Dic43—22no—
32#13063257—22no—
33#13063250—24no—
34#13063246—28no—
35C22⋊(C43⋊C8)—22no—
36C22⋊(C43⋊C8)D414yes—
37C25×C43—21no—
38C22×D4×C43—22no—
39C22×D4×C43—21no—
40C22×D4×C43—22no—
41C22×D4×C43—44no—
42C22×D4×C43D412yes—
43C23×C4×C43C2311yescharacteristic
44C2×M16×C43—21no—
45C2×M16×C43D412yes—
46#100×C43—44no—
47C22⋊C8×C43—22no—
48C22⋊C8×C43—22no—
49C24×C43—22no—
50C24×C43—44no—
51C24×C43—42no—
52C24×C43—84no—
53C24×C43#4111yescharacteristic
54C2×D4×C43—24no—
55C2×D4×C43—28no—
56C2×D4×C43—24no—
57C2×D4×C43—44no—
58C2×D4×C43—44no—
59C2×D4×C43—42no—
60C2×D4×C43—48no—
61C2×D4×C43—41no—
62C2×D4×C43—41no—
63C22×C4×C43—42no—
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D412yes—
66C22×C4×C43C2×D412yes—
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—22no—
69C22×Dic43—22no—
70C2×Dic86—22no—
71C2×Dic86—22no—
72C2×Dic86—44no—
73M16×C43—42no—
74M16×C43—42no—
75C2×C8×C43—22no—
76C2×C8×C43—41no—
77C22⋊Dic43—42no—
78C22⋊Dic43—42no—
79#10621883—416no—
80C4⋊Dic43—22no—
81C4⋊Dic43—22no—
82Dic43⋊C4—42no—
83Dic43⋊C4—42no—
84C2×C43⋊C8—24no—
85C2×C43⋊C8—44no—
86Dic172—82no—
87C23×C43—24no—
88C23×C43—24no—
89C23×C43—41no—
90C23×C43—48no—
91C23×C43—42no—
92C23×C43—42no—
93C23×C43—84no—
94C23×C43—84no—
95C23×C43—816no—
96C23×C43—84no—
97C23×C43#12112yes—
98C23×C43#12111yescharacteristic
99D4×C43—28no—
100D4×C43—44no—
101D4×C43—44no—
102D4×C43—44no—
103C2×C4×C43—24no—
104C2×C4×C43—22no—
105C2×C4×C43—41no—
106C2×C4×C43—42no—
107C2×C4×C43#12011yescharacteristic
108C2×C4×C43#12012yes—
109C2×C4×C43#12711yescharacteristic
110C2×Dic43—42no—
111C2×Dic43—42no—
112C2×Dic43—44no—
113C2×Dic43—82no—
114Dic86—44no—
115Dic86—44no—
116C8×C43—42no—
117C8×C43—81no—
118C43⋊C8—44no—
119#9990—431nomaximal, Sylow
120C22×C43—22no—
121C22×C43—22no—
122C22×C43—22no—
123C22×C43—21no—
124C22×C43—44no—
125C22×C43—44no—
126C22×C43—816no—
127C22×C43—84no—
128C22×C43—84no—
129C22×C43—84no—
130C22×C43#39211yescharacteristic
131C22×C43#47114yes—
132C4×C43—22no—
133C4×C43—21no—
134C4×C43B(4,𝔽2)12yes—
135Dic43—82no—
136Dic43—82no—
137#3195—431no—
138C2×#450—432no—
139#1783D4311yescharacteristic
140#1472—432no—
141#1298—431no—
142C2×C43—24no—
143C2×C43—41no—
144C2×C43—84no—
145C2×C43#201912yes—
146C2×C43#202111yescharacteristic
147C23×D4C2×D4311yescharacteristic
148C22×SD16—862no—
149C2×C22⋊Q8—432no—
150#483—862no—
151#470—862no—
152#451—862no—
153#450—864no—
154#450—864no—
155C2×#102—862no—
156C2×#100—22no—
157#407C2×D4311yescharacteristic
158#407C2×D4311yescharacteristic
159C2×C22⋊C8—432no—
160#324—864no—
161C43#999011yescharacteristic, complemented, Sylow
162C25—21no—
163C22×Q8—432no—
164C22×D4—22no—
165C22×D4—22no—
166C22×D4—21no—
167C22×D4—44no—
168C22×D4D17212yes—
169C23×C4C22×D4311yescharacteristic
170C2×Q16—862no—
171C2×SD16—868no—
172C2×SD16—1728no—
173C2×M16—21no—
174C2×M16C22⋊D4312yes—
175C22×C8—862no—
176C22⋊Q8—862no—
177C22⋊Q8—862no—
178C22⋊Q8—862no—
179C22⋊Q8—862no—
180C2×C4⋊C4—432no—
181C2×C4⋊C4—862no—
182C2×C22⋊C4—862no—
183#106—862no—
184#103—864no—
185#102—868no—
186#100—44no—
187C22⋊C8—22no—
188C22⋊C8—22no—
189C22⋊C8—434no—
190C22⋊C8—862no—
191C24—22no—
192C24—44no—
193C24—42no—
194C24—84no—
195C24#1062189811yescharacteristic
196C2×Q8—862no—
197C2×Q8—862no—
198C2×Q8—1724no—
199C2×D4—28no—
200C2×D4—24no—
201C2×D4—24no—
202C2×D4—44no—
203C2×D4—42no—
204C2×D4—44no—
205C2×D4—48no—
206C2×D4—41no—
207C2×D4—41no—
208C22×C4—42no—
209C22×C4—862no—
210C22×C4—862no—
211C22×C4C2×D17211yescharacteristic
212C22×C4D4×D4312yes—
213C22×C4D4×D4312yes—
214C22×C4C2×C22⋊D4311yescharacteristic
215Q16—3442no—
216SD16—17216no—
217M16—42no—
218M16—42no—
219C2×C8—22no—
220C2×C8—41no—
221C2×C8—864no—
222C2×C8—1724no—
223C4⋊C4—862no—
224C4⋊C4—862no—
225C4⋊C4—1722no—
226C4⋊C4—1722no—
227C22⋊C4—1722no—
228C22⋊C4—1722no—
229C23—24no—
230C23—24no—
231C23—41no—
232C23—48no—
233C23—42no—
234C23—42no—
235C23—84no—
236C23—84no—
237C23—816no—
238C23—84no—
239C23#1306329812yes—
240C23#1306329911yescharacteristic
241Q8—1724no—
242Q8—1724no—
243D4—28no—
244D4—44no—
245D4—44no—
246D4—44no—
247C2×C4—24no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—3442no—
252C2×C4—1722no—
253C2×C4—1722no—
254C2×C4—1724no—
255C2×C4#1306329311yescharacteristic
256C2×C4#1306329512yes—
257C2×C4#1306332111yescharacteristic
258C8—42no—
259C8—81no—
260C8—1724no—
261C22—22no—
262C22—22no—
263C22—22no—
264C22—21no—
265C22—44no—
266C22—44no—
267C22—816no—
268C22—84no—
269C22—84no—
270C22—84no—
271C22#1458280811yescharacteristic
272C22#1458316114yes—
273C4—21no—
274C4—22no—
275C4—3442no—
276C4—3442no—
277C4#1458308512yes—
278C2—24no—
279C2—41no—
280C2—84no—
281C2#1913571112yes—
282C2#1913572111yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1783C2
socleC22×C43#392
prime radicalC23×D4×C43C22
hypercenter#1783D43
hypocenterC43#9990
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1783

Complements

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

NH ≅ G/Ntype
1. #19145419C2semidirect
3. #19132960C2semidirect
4. #19132482C2semidirect
161. C43#9990semidirect

Maximal subgroups

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

subgroupindex
#191454192
C2×#145830502
#191329602
#191324822
C43×#17832
#999043