Finite Group Databasebeta

← #24997292

Subgroups — #24997292

Order 11008.

698 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#14583054C212yesmaximal
2#19134518C211yesmaximal, characteristic
3#19132959C212yesmaximal
4#19132482C211yesmaximal, characteristic
5C43×#3195C211yesmaximal, characteristic
6C23×Dic86C2211yescharacteristic
7C22×#10621885—22no—
8#14583054—24no—
9#14583054—24no—
10C2×#13063248—22no—
11C2×#13063243—22no—
12#14582863C2211yescharacteristic
13C2×C22⋊(C43⋊C8)C2212yes—
14#14582625—24no—
15C2×C22⋊Q8×C43C2212yes—
16C43×#483—22no—
17C43×#470—22no—
18C43×#451—22no—
19C43×#407C2211yescharacteristic
20C22×Dic86—22no—
21C22×Dic86—21no—
22C22×Dic86—22no—
23C22×Dic86—44no—
24C22×Dic86D412yes—
25C23×Dic43—21no—
26C2×#10621885—28no—
27C2×#10621885—48no—
28C2×#10621877—21no—
29C22×C43⋊C8—22no—
30#13063248—28no—
31#13063243—44no—
32C22⋊(C43⋊C8)—22no—
33C22⋊(C43⋊C8)—22no—
34C22⋊(C43⋊C8)D414yes—
35C22×Q8×C43D412yes—
36C23×C4×C43C2311yescharacteristic
37C2×Q16×C43—22no—
38C2×M16×C43D412yes—
39C22⋊Q8×C43—22no—
40C22⋊Q8×C43—22no—
41C22⋊Q8×C43—22no—
42C22⋊Q8×C43—22no—
43C2×C4⋊C4×C43—22no—
44C2×C4⋊C4×C43D412yes—
45C2×C22⋊C4×C43—22no—
46#106×C43—22no—
47#103×C43—24no—
48C22⋊C8×C43—22no—
49C24×C43#4111yescharacteristic
50C2×Q8×C43—22no—
51C2×Q8×C43—22no—
52C2×Q8×C43—44no—
53C22×C4×C43—22no—
54C22×C4×C43—22no—
55C22×C4×C43—42no—
56C22×C4×C43C2×D411yescharacteristic
57C22×C4×C43C2×D412yes—
58C22×C4×C43C2×D412yes—
59C22×C4×C43C2×D411yescharacteristic
60C22×Dic43—22no—
61C22×Dic43—44no—
62C22×Dic43—42no—
63C2×Dic86—28no—
64C2×Dic86—24no—
65C2×Dic86—24no—
66C2×Dic86—44no—
67C2×Dic86—48no—
68C2×Dic86—44no—
69C2×Dic86—42no—
70C2×Dic86—41no—
71C2×Dic86—41no—
72Q16×C43—82no—
73M16×C43—42no—
74C2×C8×C43—22no—
75C4⋊C4×C43—22no—
76C4⋊C4×C43—22no—
77C4⋊C4×C43—42no—
78C4⋊C4×C43—42no—
79C22⋊C4×C43—42no—
80C22⋊C4×C43—42no—
81#10621885—416no—
82#10621877—42no—
83C2×C43⋊C8—24no—
84C2×C43⋊C8—44no—
85C2×C43⋊C8—41no—
86C23×C43—24no—
87C23×C43—41no—
88C23×C43#12111yescharacteristic
89C23×C43#12112yes—
90Q8×C43—44no—
91Q8×C43—44no—
92C2×C4×C43—24no—
93C2×C4×C43—22no—
94C2×C4×C43—41no—
95C2×C4×C43—42no—
96C2×C4×C43—42no—
97C2×C4×C43—42no—
98C2×C4×C43—44no—
99C2×C4×C43—82no—
100C2×C4×C43#12012yes—
101C2×C4×C43#12011yescharacteristic
102C2×C4×C43#12711yescharacteristic
103C2×Dic43—24no—
104C2×Dic43—48no—
105C2×Dic43—42no—
106C2×Dic43—42no—
107Dic86—28no—
108Dic86—44no—
109Dic86—44no—
110Dic86—44no—
111C8×C43—42no—
112C43⋊C8—44no—
113C43⋊C8—81no—
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—82no—
125C4×C43—82no—
126C4×C43B(4,𝔽2)12yes—
127Dic43—44no—
128#3195D4311yescharacteristic
129C2×#451—432no—
130#1784—431no—
131#1472—432no—
132#1298—431no—
133C2×C43—24no—
134C2×C43—41no—
135C2×C43#202012yes—
136C2×C43#202111yescharacteristic
137C23×Q8—431no—
138C22×Q16—862no—
139C2×C22⋊Q8C2×D4312yes—
140#483—22no—
141#470—22no—
142#451—22no—
143#451—864no—
144#451—864no—
145C2×#103—862no—
146C2×#101—862no—
147#407—431no—
148#407C2×D4311yescharacteristic
149C2×C22⋊C8—432no—
150#324—864no—
151C43#999111yescharacteristic, complemented, Sylow
152C22×Q8—432no—
153C22×Q8—861no—
154C22×Q8—862no—
155C22×Q8—862no—
156C22×Q8—1724no—
157C22×Q8C22⋊D4312yes—
158C23×C4—861no—
159C23×C4C22×D4311yescharacteristic
160C2×Q16—22no—
161C2×Q16—868no—
162C2×Q16—1728no—
163C2×M16—861no—
164C2×M16C22⋊D4312yes—
165C22×C8—862no—
166C22⋊Q8—22no—
167C22⋊Q8—22no—
168C22⋊Q8—22no—
169C22⋊Q8—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4C22⋊D4312yes—
172C2×C22⋊C4—22no—
173#106—22no—
174#103—24no—
175#103—868no—
176#101—1724no—
177C22⋊C8—22no—
178C22⋊C8—434no—
179C22⋊C8—862no—
180C22⋊C8—862no—
181C24#1062190011yescharacteristic
182C2×Q8—22no—
183C2×Q8—22no—
184C2×Q8—44no—
185C2×Q8—864no—
186C2×Q8—868no—
187C2×Q8—864no—
188C2×Q8—1724no—
189C2×Q8—1722no—
190C2×Q8—1724no—
191C2×Q8—1728no—
192C2×Q8—1721no—
193C2×Q8—1721no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—42no—
197C22×C4—862no—
198C22×C4—1724no—
199C22×C4—1722no—
200C22×C4D4×D4311yescharacteristic
201C22×C4D4×D4312yes—
202C22×C4C2×C22⋊D4312yes—
203C22×C4C2×C22⋊D4311yescharacteristic
204Q16—82no—
205Q16—17216no—
206M16—42no—
207M16—1722no—
208C2×C8—22no—
209C2×C8—864no—
210C2×C8—1721no—
211C2×C8—1724no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C22⋊C4—42no—
217C22⋊C4—42no—
218C23—24no—
219C23—41no—
220C23#1306329611yescharacteristic
221C23#1306329712yes—
222Q8—44no—
223Q8—44no—
224Q8—868no—
225Q8—1724no—
226Q8—1724no—
227Q8—1724no—
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—44no—
235C2×C4—82no—
236C2×C4—864no—
237C2×C4—1722no—
238C2×C4—1728no—
239C2×C4—1722no—
240C2×C4#1306329312yes—
241C2×C4#1306329411yescharacteristic
242C2×C4#1306332111yescharacteristic
243C8—42no—
244C8—3441no—
245C8—1724no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—21no—
250C22—44no—
251C22#1458280711yescharacteristic
252C22#1458317214yes—
253C4—21no—
254C4—22no—
255C4—82no—
256C4—82no—
257C4—1724no—
258C4#1458308612yes—
259C2—24no—
260C2—41no—
261C2#1913571312yes—
262C2#1913571911yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#3195C2
socleC22×C43#392
prime radicalC24×C43#41
hypercenter#3195D43
hypocenterC43#9991
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

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
C2×#145830542
#191345182
#191329592
#191324822
C43×#31952
#999143