Finite Group Databasebeta

← #24997226

Subgroups — #24997226

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#19145370C211yesmaximal, characteristic
2#19144543C212yesmaximal
3#19132958C212yesmaximal
4#19132472C211yesmaximal, characteristic
5C43×#1818C211yesmaximal, characteristic
6C2×#13063304C2212yes—
7#14583240—24no—
8#14583235—22no—
9#14583234—22no—
10#14583229—22no—
11#14583140—22no—
12#14583057—22no—
13#14582942—22no—
14#14582907—22no—
15#14582863C2212yes—
16#14582624—24no—
17C2×#117×C43C2211yescharacteristic
18C2×C22⋊C8×C43C2211yescharacteristic
19C2×C22⋊C8×C43C2211yescharacteristic
20C43×#336—22no—
21C22×Dic86D412yes—
22C2×Dic172—22no—
23C2×#10621877—22no—
24#13063304—22no—
25#13063304—22no—
26#13063304—22no—
27#13063304—22no—
28C2×C4⋊Dic43D412yes—
29C2×Dic43⋊C4—22no—
30C2×C22⋊Dic43—22no—
31#13063259—22no—
32#13063258—24no—
33#13063256—24no—
34#13063250—24no—
35#13063248—24no—
36#13063248—24no—
37C22⋊(C43⋊C8)—22no—
38C22⋊(C43⋊C8)D414yes—
39C23×C4×C43C2311yescharacteristic
40C22×C8×C43—21no—
41C22×C8×C43D412yes—
42#117×C43—22no—
43#117×C43—22no—
44C2×C4⋊C4×C43D411yescharacteristic
45C2×C4⋊C4×C43D411yescharacteristic
46C2×C22⋊C4×C43—21no—
47C2×C42×C43—21no—
48C22⋊C8×C43—22no—
49C22⋊C8×C43—22no—
50C24×C43#4111yescharacteristic
51C22×C4×C43—21no—
52C22×C4×C43—21no—
53C22×C4×C43—42no—
54C22×C4×C43C2×D411yescharacteristic
55C22×C4×C43C2×D412yes—
56C22×C4×C43C2×D412yes—
57C22×C4×C43C2×D411yescharacteristic
58C22×Dic43—22no—
59C22×Dic43—22no—
60C2×Dic86—22no—
61C2×Dic86—22no—
62C2×Dic86—44no—
63C2×C8×C43—22no—
64C2×C8×C43—42no—
65C2×C8×C43—42no—
66C2×C8×C43—41no—
67C4⋊C4×C43—22no—
68C4⋊C4×C43—22no—
69C22⋊C4×C43—42no—
70C42×C43—41no—
71C42×C43—41no—
72C22⋊Dic43—42no—
73C22⋊Dic43—42no—
74C4⋊Dic43—22no—
75C4⋊Dic43—22no—
76Dic43⋊C4—42no—
77Dic43⋊C4—42no—
78#10621877—44no—
79C2×C43⋊C8—24no—
80Dic172—82no—
81C23×C43—22no—
82C23×C43—41no—
83C23×C43—41no—
84C23×C43#12112yes—
85C23×C43#12111yescharacteristic
86C2×C4×C43—24no—
87C2×C4×C43—22no—
88C2×C4×C43—41no—
89C2×C4×C43—42no—
90C2×C4×C43—42no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—42no—
94C2×C4×C43#12011yescharacteristic
95C2×C4×C43#12012yes—
96C2×C4×C43#12711yescharacteristic
97C2×Dic43—44no—
98C2×Dic43—42no—
99C2×Dic43—42no—
100C2×Dic43—82no—
101Dic86—44no—
102Dic86—44no—
103C8×C43—42no—
104C8×C43—81no—
105C43⋊C8—44no—
106#9979—431nomaximal, Sylow
107C22×C43—21no—
108C22×C43—21no—
109C22×C43—22no—
110C22×C43—22no—
111C22×C43—22no—
112C22×C43—82no—
113C22×C43#39211yescharacteristic
114C22×C43#47312yes—
115C4×C43—22no—
116C4×C43—21no—
117C4×C43—81no—
118C4×C43—81no—
119C4×C43#45812yes—
120Dic43—82no—
121Dic43—82no—
122#3189—431no—
123#3095—432no—
124#1818D4311yescharacteristic
125#1472—432no—
126#1293—431no—
127C2×C43—22no—
128C2×C43—42no—
129C2×C43#201711yescharacteristic
130C2×C43#202011yescharacteristic
131C2×C43#202211yescharacteristic
132C2×C22⋊Q8—432no—
133C2×#117C2×D4311yescharacteristic
134#485—864no—
135#484—862no—
136#484—862no—
137#483—862no—
138#467—862no—
139#451—862no—
140#428—862no—
141#419—862no—
142#407—432no—
143C2×C22⋊C8C2×D4311yescharacteristic
144C2×C22⋊C8C2×D4311yescharacteristic
145#336—22no—
146#324—864no—
147C43#997911yescharacteristic, complemented, Sylow
148C22×Q8—432no—
149C23×C4C22×D4311yescharacteristic
150C2×Q16—862no—
151C2×M16—862no—
152C22×C8—21no—
153C22×C8C22⋊D4312yes—
154C22⋊Q8—862no—
155C22⋊Q8—862no—
156C22⋊Q8—862no—
157C22⋊Q8—862no—
158#117—22no—
159#117—22no—
160C2×C4⋊C4—432no—
161C2×C4⋊C4—862no—
162C2×C4⋊C4D17211yescharacteristic
163C2×C4⋊C4D17211yescharacteristic
164C2×C22⋊C4—21no—
165C2×C22⋊C4—862no—
166C2×C42—21no—
167#107—864no—
168#107—862no—
169#106—864no—
170#103—864no—
171#103—864no—
172#103—864no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175C22⋊C8—434no—
176C22⋊C8—862no—
177C24#1062189811yescharacteristic
178C2×Q8—862no—
179C2×Q8—862no—
180C2×Q8—1724no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—42no—
184C22×C4—862no—
185C22×C4—862no—
186C22×C4C2×D17211yescharacteristic
187C22×C4D4×D4312yes—
188C22×C4D4×D4312yes—
189C22×C4C2×C22⋊D4311yescharacteristic
190Q16—3442no—
191M16—1724no—
192C2×C8—22no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—41no—
196C2×C8—864no—
197C4⋊C4—22no—
198C4⋊C4—22no—
199C4⋊C4—862no—
200C4⋊C4—862no—
201C4⋊C4—1722no—
202C4⋊C4—1722no—
203C22⋊C4—42no—
204C22⋊C4—1722no—
205C22⋊C4—1722no—
206C42—41no—
207C42—41no—
208C23—22no—
209C23—41no—
210C23—41no—
211C23#1306329812yes—
212C23#1306329911yescharacteristic
213Q8—1724no—
214Q8—1724no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—3442no—
224C2×C4—1724no—
225C2×C4—1722no—
226C2×C4—1722no—
227C2×C4#1306329311yescharacteristic
228C2×C4#1306329512yes—
229C2×C4#1306332111yescharacteristic
230C8—42no—
231C8—81no—
232C8—1724no—
233C22—21no—
234C22—21no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—82no—
239C22#1458280811yescharacteristic
240C22#1458317412yes—
241C4—21no—
242C4—22no—
243C4—81no—
244C4—81no—
245C4—3442no—
246C4—3442no—
247C4#1458308812yes—
248C2—22no—
249C2—42no—
250C2#1913569911yescharacteristic
251C2#1913571611yescharacteristic
252C2#1913572611yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1818C2
socleC22×C43#392
prime radicalC24×C43#41
hypercenter#1818D43
hypocenterC43#9979
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1818

Complements

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

NH ≅ G/Ntype
147. C43#9979semidirect

Maximal subgroups

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

subgroupindex
#191453702
#191445432
#191329582
#191324722
C43×#18182
#997943