Finite Group Databasebeta

← #24997294

Subgroups — #24997294

Order 11008.

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

normal subgroups only

This group has 698 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
2C2×#14583055C212yesmaximal
3#19132960C212yesmaximal
4#19132482C211yesmaximal, characteristic
5C43×#1784C211yesmaximal, characteristic
6C22×#10621885—22no—
7C2×#13063304C2212yes—
8#14583230—22no—
9#14583157—22no—
10#14583057—22no—
11#14583055—24no—
12#14583055—24no—
13C2×#13063249—22no—
14C2×C22⋊(C43⋊C8)C2212yes—
15#14582624—24no—
16C23×Q8×C43C2211yescharacteristic
17C2×#101×C43—22no—
18C43×#407C2211yescharacteristic
19C43×#407C2211yescharacteristic
20C22×Dic86D412yes—
21C2×Dic172—22no—
22C2×#10621885—28no—
23C2×#10621885—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#13063249—28no—
35C22⋊(C43⋊C8)—22no—
36C22⋊(C43⋊C8)D414yes—
37C22×Q8×C43—21no—
38C22×Q8×C43—22no—
39C22×Q8×C43—22no—
40C22×Q8×C43—44no—
41C22×Q8×C43D412yes—
42C23×C4×C43—21no—
43C23×C4×C43C2311yescharacteristic
44C2×M16×C43—21no—
45C2×M16×C43D412yes—
46#101×C43—44no—
47C22⋊C8×C43—22no—
48C22⋊C8×C43—22no—
49C24×C43#4111yescharacteristic
50C2×Q8×C43—24no—
51C2×Q8×C43—28no—
52C2×Q8×C43—24no—
53C2×Q8×C43—44no—
54C2×Q8×C43—44no—
55C2×Q8×C43—42no—
56C2×Q8×C43—48no—
57C2×Q8×C43—41no—
58C2×Q8×C43—41no—
59C22×C4×C43—22no—
60C22×C4×C43—42no—
61C22×C4×C43—44no—
62C22×C4×C43—42no—
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D412yes—
65C22×C4×C43C2×D412yes—
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—22no—
68C22×Dic43—22no—
69C2×Dic86—22no—
70C2×Dic86—22no—
71C2×Dic86—44no—
72M16×C43—42no—
73M16×C43—42no—
74C2×C8×C43—22no—
75C2×C8×C43—41no—
76C22⋊Dic43—42no—
77C22⋊Dic43—42no—
78#10621885—416no—
79C4⋊Dic43—22no—
80C4⋊Dic43—22no—
81Dic43⋊C4—42no—
82Dic43⋊C4—42no—
83C2×C43⋊C8—24no—
84C2×C43⋊C8—44no—
85Dic172—82no—
86C23×C43—24no—
87C23×C43—41no—
88C23×C43#12112yes—
89C23×C43#12111yescharacteristic
90Q8×C43—28no—
91Q8×C43—44no—
92Q8×C43—44no—
93Q8×C43—44no—
94C2×C4×C43—24no—
95C2×C4×C43—22no—
96C2×C4×C43—24no—
97C2×C4×C43—41no—
98C2×C4×C43—42no—
99C2×C4×C43—42no—
100C2×C4×C43—48no—
101C2×C4×C43—42no—
102C2×C4×C43#12011yescharacteristic
103C2×C4×C43#12012yes—
104C2×C4×C43#12711yescharacteristic
105C2×Dic43—42no—
106C2×Dic43—42no—
107C2×Dic43—44no—
108C2×Dic43—82no—
109Dic86—44no—
110Dic86—44no—
111C8×C43—42no—
112C8×C43—81no—
113C43⋊C8—44no—
114#9991—431nomaximal, Sylow
115C22×C43—22no—
116C22×C43—22no—
117C22×C43—22no—
118C22×C43—21no—
119C22×C43—44no—
120C22×C43#39211yescharacteristic
121C22×C43#47314yes—
122C4×C43—22no—
123C4×C43—21no—
124C4×C43—44no—
125C4×C43B(4,𝔽2)12yes—
126Dic43—82no—
127Dic43—82no—
128#3195—431no—
129C2×#451—432no—
130#1784D4311yescharacteristic
131#1472—432no—
132#1298—431no—
133C2×C43—24no—
134C2×C43—41no—
135C2×C43#202012yes—
136C2×C43#202111yescharacteristic
137C23×Q8C2×D4311yescharacteristic
138C22×Q16—862no—
139C2×C22⋊Q8—432no—
140#483—862no—
141#470—862no—
142#451—862no—
143#451—864no—
144#451—864no—
145C2×#103—862no—
146C2×#101—22no—
147#407C2×D4311yescharacteristic
148#407C2×D4311yescharacteristic
149C2×C22⋊C8—432no—
150#324—864no—
151C43#999111yescharacteristic, complemented, Sylow
152C22×Q8—21no—
153C22×Q8—22no—
154C22×Q8—22no—
155C22×Q8—44no—
156C22×Q8—432no—
157C22×Q8D17212yes—
158C23×C4—21no—
159C23×C4C22×D4311yescharacteristic
160C2×Q16—862no—
161C2×Q16—868no—
162C2×Q16—1728no—
163C2×M16—21no—
164C2×M16C22⋊D4312yes—
165C22×C8—862no—
166C22⋊Q8—862no—
167C22⋊Q8—862no—
168C22⋊Q8—862no—
169C22⋊Q8—862no—
170C2×C4⋊C4—432no—
171C2×C4⋊C4—862no—
172C2×C22⋊C4—862no—
173#106—862no—
174#103—864no—
175#103—868no—
176#101—44no—
177C22⋊C8—22no—
178C22⋊C8—22no—
179C22⋊C8—434no—
180C22⋊C8—862no—
181C24#1062189811yescharacteristic
182C2×Q8—24no—
183C2×Q8—28no—
184C2×Q8—24no—
185C2×Q8—44no—
186C2×Q8—44no—
187C2×Q8—42no—
188C2×Q8—48no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—862no—
192C2×Q8—862no—
193C2×Q8—1724no—
194C22×C4—22no—
195C22×C4—42no—
196C22×C4—44no—
197C22×C4—42no—
198C22×C4—862no—
199C22×C4—862no—
200C22×C4C2×D17211yescharacteristic
201C22×C4D4×D4312yes—
202C22×C4D4×D4312yes—
203C22×C4C2×C22⋊D4311yescharacteristic
204Q16—3442no—
205Q16—17216no—
206M16—42no—
207M16—42no—
208C2×C8—22no—
209C2×C8—41no—
210C2×C8—864no—
211C2×C8—1724no—
212C4⋊C4—862no—
213C4⋊C4—862no—
214C4⋊C4—1722no—
215C4⋊C4—1722no—
216C22⋊C4—1722no—
217C22⋊C4—1722no—
218C23—24no—
219C23—41no—
220C23#1306329812yes—
221C23#1306329911yescharacteristic
222Q8—28no—
223Q8—44no—
224Q8—44no—
225Q8—44no—
226Q8—1724no—
227Q8—1724no—
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—24no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—48no—
235C2×C4—42no—
236C2×C4—3442no—
237C2×C4—1722no—
238C2×C4—1722no—
239C2×C4—1724no—
240C2×C4#1306329311yescharacteristic
241C2×C4#1306329512yes—
242C2×C4#1306332111yescharacteristic
243C8—42no—
244C8—81no—
245C8—1724no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—21no—
250C22—44no—
251C22#1458280811yescharacteristic
252C22#1458317314yes—
253C4—21no—
254C4—22no—
255C4—44no—
256C4—3442no—
257C4—3442no—
258C4#1458308512yes—
259C2—24no—
260C2—41no—
261C2#1913571512yes—
262C2#1913572111yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1784C2
socleC22×C43#392
prime radicalC24×C43#41
hypercenter#1784D43
hypocenterC43#9991
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1784

Complements

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

NH ≅ G/Ntype
151. C43#9991semidirect

Maximal subgroups

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

subgroupindex
#191454192
C2×#145830552
#191329602
#191324822
C43×#17842
#999143