Finite Group Databasebeta

← #24990121

Subgroups — #24990121

Order 11008.

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

normal subgroups only

This group has 566 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#19137180C211yesmaximal, characteristic
2#19134518C212yesmaximal
3#19132504C212yesmaximal
4#19132503C211yesmaximal, characteristic
5C43×#1306C211yesmaximal, characteristic
6C23×Dic86C2211yescharacteristic
7C2×#13063281C412yes—
8C2×#13063243—24no—
9#14582863C2212yes—
10#14582803—24no—
11#14582762C2211yescharacteristic
12#14582760C412yes—
13C43×#407C2212yes—
14C43×#381C2211yescharacteristic
15C22×Dic86—22no—
16C22×Dic86—21no—
17C22×Dic86—21no—
18C22×Dic86—44no—
19C22×Dic86D414yes—
20C23×Dic43C2×C411yescharacteristic
21C23×Dic43C2×C411yescharacteristic
22C2×#10621877—22no—
23#13063281—44no—
24C2×Dic43⋊C4—22no—
25C2×C22⋊Dic43C2×C412yes—
26C2×C4×Dic43—22no—
27#13063243—48no—
28C22⋊(C43⋊C8)—22no—
29C22⋊(C43⋊C8)—22no—
30C43⋊#95—22no—
31C43⋊#95—24no—
32C23×C4×C43C2311yescharacteristic
33C2×M16×C43—22no—
34C2×C22⋊C4×C43C2×C412yes—
35C22⋊C8×C43—22no—
36C22⋊C8×C43—22no—
37#95×C43—22no—
38C24×C43C22×C411yescharacteristic
39C22×C4×C43—22no—
40C22×C4×C43—42no—
41C22×C4×C43C2×D412yes—
42C22×C4×C43#4112yes—
43C22×C4×C43#4111yescharacteristic
44C22×C4×C43#4111yescharacteristic
45C22×Dic43—24no—
46C22×Dic43—22no—
47C22×Dic43—21no—
48C22×Dic43—21no—
49C22×Dic43—21no—
50C22×Dic43—21no—
51C22×Dic43—42no—
52C22×Dic43C22⋊C412yes—
53C22×Dic43C22⋊C412yes—
54C2×Dic86—24no—
55C2×Dic86—24no—
56C2×Dic86—28no—
57C2×Dic86—44no—
58C2×Dic86—48no—
59C2×Dic86—44no—
60C2×Dic86—44no—
61M16×C43—44no—
62C2×C8×C43—42no—
63C22⋊C4×C43—42no—
64C22⋊Dic43—42no—
65Dic43⋊C4—44no—
66C4×Dic43—44no—
67#10621877—44no—
68C2×C43⋊C8—42no—
69C23×C43—22no—
70C23×C43—42no—
71C23×C43C2×C22⋊C411yescharacteristic
72C23×C43#11711yescharacteristic
73C23×C43#11711yescharacteristic
74C2×C4×C43—24no—
75C2×C4×C43—42no—
76C2×C4×C43—41no—
77C2×C4×C43—41no—
78C2×C4×C43—44no—
79C2×C4×C43—42no—
80C2×C4×C43#12312yes—
81C2×C4×C43#12312yes—
82C2×Dic43—24no—
83C2×Dic43—24no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43—24no—
88C2×Dic43—42no—
89C2×Dic43—42no—
90C2×Dic43—44no—
91C2×Dic43—42no—
92C2×Dic43#9914yes—
93Dic86—48no—
94Dic86—48no—
95C8×C43—82no—
96C43⋊C8—82no—
97#8754—431nomaximal, Sylow
98C22×C43—22no—
99C22×C43—21no—
100C22×C43—21no—
101C22×C43—22no—
102C22×C43—22no—
103C22×C43—44no—
104C22×C43#38111yescharacteristic
105C22×C43C2×#9912yes—
106C4×C43—22no—
107C4×C43—22no—
108C4×C43—82no—
109Dic43—24no—
110Dic43—42no—
111Dic43—82no—
112#2310—431no—
113#1784—432no—
114#1306—432no—
115#1306—431no—
116#1306D4311yescharacteristic
117C2×C43—22no—
118C2×C43—41no—
119C2×C43—41no—
120C2×C43#181911yescharacteristic
121C2×C43#183012yes—
122C23×Q8—431no—
123C2×#117—432no—
124C2×#101—864no—
125#407—432no—
126#407C2×D4312yes—
127#391—864no—
128#381—431no—
129#381—432no—
130#381C2×D4311yescharacteristic
131C43#875411yescharacteristic, complemented, Sylow
132C22×Q8—434no—
133C22×Q8—862no—
134C22×Q8—861no—
135C22×Q8—861no—
136C22×Q8—1724no—
137C23×C4—431no—
138C23×C4—431no—
139C23×C4C22×D4311yescharacteristic
140C2×M16—22no—
141C2×M16—862no—
142#117—1724no—
143C2×C4⋊C4—862no—
144C2×C22⋊C4—432no—
145C2×C22⋊C4C4×D4312yes—
146C2×C42—862no—
147#101—1728no—
148C22⋊C8—22no—
149C22⋊C8—22no—
150C22⋊C8—862no—
151C22⋊C8—862no—
152#95—22no—
153#95—864no—
154#95—862no—
155C24C2×C4×D4311yescharacteristic
156C2×Q8—868no—
157C2×Q8—864no—
158C2×Q8—864no—
159C2×Q8—1724no—
160C2×Q8—1728no—
161C2×Q8—1724no—
162C2×Q8—1724no—
163C22×C4—22no—
164C22×C4—42no—
165C22×C4—432no—
166C22×C4—432no—
167C22×C4—864no—
168C22×C4—861no—
169C22×C4—861no—
170C22×C4—861no—
171C22×C4—861no—
172C22×C4—862no—
173C22×C4—1722no—
174C22×C4#1062189812yes—
175C22×C4D4×D4312yes—
176C22×C4#1062190011yescharacteristic
177C22×C4#1062190211yescharacteristic
178M16—44no—
179M16—1724no—
180C2×C8—42no—
181C2×C8—1722no—
182C4⋊C4—1724no—
183C22⋊C4—42no—
184C22⋊C4—1722no—
185C42—1724no—
186C23—22no—
187C23—42no—
188C23C22⋊C4×D4311yescharacteristic
189C23#1306328211yescharacteristic
190C23#1306328311yescharacteristic
191Q8—1728no—
192Q8—1728no—
193C2×C4—24no—
194C2×C4—42no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—44no—
198C2×C4—42no—
199C2×C4—434no—
200C2×C4—864no—
201C2×C4—864no—
202C2×C4—862no—
203C2×C4—862no—
204C2×C4—864no—
205C2×C4—862no—
206C2×C4—1724no—
207C2×C4—1722no—
208C2×C4—1722no—
209C2×C4—1722no—
210C2×C4#1306330712yes—
211C2×C4#1306331012yes—
212C8—82no—
213C8—3442no—
214C22—22no—
215C22—21no—
216C22—21no—
217C22—22no—
218C22—22no—
219C22—44no—
220C22#1458276111yescharacteristic
221C22#99×D4312yes—
222C4—22no—
223C4—22no—
224C4—82no—
225C4—864no—
226C4—3442no—
227C4—1722no—
228C2—22no—
229C2—41no—
230C2—41no—
231C2#1913466811yescharacteristic
232C2#1913470812yes—
subgroupG/H
centerC22#14582761
commutator, prime radicalC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1306C2
socleC22×C43#381
cosocleC23×C4×C43C23
hypercenter#1306D43
hypocenterC43#8754
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
131. C43#8754semidirect

Maximal subgroups

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

subgroupindex
#191371802
#191345182
#191325042
#191325032
C43×#13062
#875443