Finite Group Databasebeta

← #24997258

Subgroups — #24997258

Order 11008.

502 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 81 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#19144539C212yesmaximal
2#19134670C211yesmaximal, characteristic
3#19133128C212yesmaximal
4#19132503C211yesmaximal, characteristic
5C43×#2817C211yesmaximal, characteristic
6C2×#13063284C2211yescharacteristic
7#14583237—24no—
8#14583232—22no—
9#14583227—22no—
10#14582939—22no—
11#14582908—22no—
12#14582863C2212yes—
13#14582762C2211yescharacteristic
14#14582665—22no—
15#14582636—24no—
16C2×C22⋊Q8×C43C2212yes—
17C43×#400—22no—
18C43×#397—22no—
19C43×#395—22no—
20C43×#381C2211yescharacteristic
21C2×#10621877—22no—
22#13063284—22no—
23#13063284—22no—
24C2×C4⋊Dic43D412yes—
25C2×C22⋊Dic43—21no—
26C2×C22⋊Dic43—21no—
27C2×C4×Dic43—21no—
28#13063258—24no—
29#13063256—24no—
30#13063249—24no—
31#13063249—24no—
32C22⋊(C43⋊C8)—22no—
33C22⋊(C43⋊C8)D414yes—
34C43⋊#95—22no—
35C22×Q8×C43D412yes—
36C23×C4×C43C2311yescharacteristic
37C22⋊Q8×C43—22no—
38C22⋊Q8×C43—22no—
39C22⋊Q8×C43—22no—
40C22⋊Q8×C43—22no—
41C2×C4⋊C4×C43—22no—
42C2×C4⋊C4×C43—22no—
43C2×C4⋊C4×C43D412yes—
44C2×C22⋊C4×C43—22no—
45C2×C22⋊C4×C43D412yes—
46#95×C43—24no—
47#95×C43—22no—
48#95×C43—22no—
49C24×C43C2×D411yescharacteristic
50C2×Q8×C43—22no—
51C2×Q8×C43—22no—
52C2×Q8×C43—44no—
53C22×C4×C43—22no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—42no—
57C22×C4×C43C2×D412yes—
58C22×C4×C43C2×D411yescharacteristic
59C22×C4×C43C2×D412yes—
60C22×C4×C43#4111yescharacteristic
61C22×Dic43—22no—
62C22×Dic43—41no—
63C4⋊C4×C43—22no—
64C4⋊C4×C43—22no—
65C4⋊C4×C43—42no—
66C4⋊C4×C43—42no—
67C4⋊C4×C43—82no—
68C22⋊C4×C43—42no—
69C22⋊C4×C43—42no—
70C22⋊C4×C43—42no—
71C22⋊Dic43—42no—
72C22⋊Dic43—41no—
73C22⋊Dic43—41no—
74C4⋊Dic43—22no—
75C4⋊Dic43—22no—
76C4×Dic43—42no—
77#10621877—44no—
78C2×C43⋊C8—24no—
79C23×C43—22no—
80C23×C43—42no—
81C23×C43#12011yescharacteristic
82C23×C43#12111yescharacteristic
83C23×C43#12711yescharacteristic
84Q8×C43—44no—
85Q8×C43—82no—
86C2×C4×C43—24no—
87C2×C4×C43—41no—
88C2×C4×C43—42no—
89C2×C4×C43—41no—
90C2×C4×C43—44no—
91C2×C4×C43—44no—
92C2×C4×C43—42no—
93C2×C4×C43—42no—
94C2×C4×C43—42no—
95C2×C4×C43—44no—
96C2×C4×C43#12012yes—
97C2×C4×C43#12112yes—
98C2×Dic43—42no—
99C2×Dic43—82no—
100C2×Dic43—81no—
101C2×Dic43—82no—
102C43⋊C8—44no—
103#9985—431nomaximal, Sylow
104C22×C43—22no—
105C22×C43—22no—
106C22×C43—22no—
107C22×C43—21no—
108C22×C43—21no—
109C22×C43—82no—
110C22×C43#39211yescharacteristic
111C22×C43#45812yes—
112C4×C43—22no—
113C4×C43—22no—
114C4×C43—82no—
115C4×C43—82no—
116C4×C43—82no—
117Dic43—82no—
118Dic43—161no—
119#3095—432no—
120#2817D4311yescharacteristic
121#1820—431no—
122#1511—432no—
123#1306—431no—
124C2×C43—22no—
125C2×C43—41no—
126C2×C43—41no—
127C2×C43#200912yes—
128C2×C43#202211yescharacteristic
129C2×C22⋊Q8C2×D4312yes—
130C2×#117—431no—
131#485—864no—
132#484—862no—
133#483—862no—
134#428—862no—
135#419—862no—
136#407—432no—
137#400—22no—
138#397—22no—
139#395—22no—
140#381—431no—
141#381C2×D4311yescharacteristic
142#342—862no—
143#328—864no—
144C43#998511yescharacteristic, complemented, Sylow
145C22×Q8C22⋊D4312yes—
146C23×C4C22×D4311yescharacteristic
147C2×M16—862no—
148C22⋊Q8—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C22⋊Q8—22no—
152#117—862no—
153#117—862no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—432no—
157C2×C4⋊C4C22⋊D4312yes—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—861no—
160C2×C22⋊C4—861no—
161C2×C22⋊C4C22⋊D4312yes—
162C2×C42—861no—
163#107—864no—
164#106—864no—
165#103—864no—
166#103—864no—
167C22⋊C8—434no—
168C22⋊C8—862no—
169#95—24no—
170#95—22no—
171#95—22no—
172#95—862no—
173C24C2×C22⋊D4311yescharacteristic
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—44no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—42no—
181C22×C4—862no—
182C22×C4—1721no—
183C22×C4D4×D4311yescharacteristic
184C22×C4D4×D4312yes—
185C22×C4#1062190011yescharacteristic
186C22×C4C2×C22⋊D4312yes—
187M16—1724no—
188C2×C8—864no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—82no—
194C4⋊C4—862no—
195C4⋊C4—862no—
196C22⋊C4—42no—
197C22⋊C4—42no—
198C22⋊C4—42no—
199C22⋊C4—1722no—
200C22⋊C4—1721no—
201C22⋊C4—1721no—
202C42—1722no—
203C23—22no—
204C23—42no—
205C23#1306329411yescharacteristic
206C23#1306329611yescharacteristic
207C23#1306332111yescharacteristic
208Q8—44no—
209Q8—82no—
210C2×C4—24no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—44no—
215C2×C4—44no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—44no—
220C2×C4—3442no—
221C2×C4—3441no—
222C2×C4—3442no—
223C2×C4—1722no—
224C2×C4#1306329312yes—
225C2×C4#1306329712yes—
226C8—1724no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—21no—
232C22—82no—
233C22#1458280711yescharacteristic
234C22#1458308912yes—
235C4—22no—
236C4—22no—
237C4—82no—
238C4—82no—
239C4—82no—
240C4—3442no—
241C4—6881no—
242C2—22no—
243C2—41no—
244C2—41no—
245C2#1913565512yes—
246C2#1913572411yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#2817C2
socleC22×C43#392
prime radicalC24×C43C2×D4
hypercenter#2817D43
hypocenterC43#9985
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2817

Complements

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

NH ≅ G/Ntype
144. C43#9985semidirect

Maximal subgroups

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

subgroupindex
#191445392
#191346702
#191331282
#191325032
C43×#28172
#998543