Finite Group Databasebeta

← #24999835

Subgroups — #24999835

Order 11008.

414 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 73 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#19140260C211yesmaximal, characteristic
2#19134692C212yesmaximal
3#19134670C211yesmaximal, characteristic
4#19132449C212yesmaximal
5C43×#1306C211yesmaximal, characteristic
6C2×#13063284C2211yescharacteristic
7#14582835—21no—
8#14582811—21no—
9#14582803—22no—
10#14582786—22no—
11#14582762C2211yescharacteristic
12C4×C22⋊Dic43C2212yes—
13#14582665—21no—
14#14582665—21no—
15#14582660—22no—
16#14582660—22no—
17C43×#407C2212yes—
18C43×#381C2211yescharacteristic
19C22×Dic86—21no—
20#13063284—22no—
21#13063284—22no—
22C2×C4⋊Dic43—21no—
23C2×C4⋊Dic43Q812yescomplemented
24C2×Dic43⋊C4—22no—
25C2×C22⋊Dic43—22no—
26C2×C22⋊Dic43—21no—
27C2×C22⋊Dic43—21no—
28C2×C4×Dic43—21no—
29C2×C4×Dic43D412yes—
30C2×C4×Dic43D412yes—
31C43⋊#95—21no—
32C43⋊#95—22no—
33C43⋊#95—21no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C23×C4×C43C2311yescharacteristic
37C2×M16×C43—22no—
38C2×C22⋊C4×C43D411yescharacteristic
39C2×C22⋊C4×C43D411yescharacteristic
40C22⋊C8×C43—22no—
41C22⋊C8×C43—22no—
42#95×C43—22no—
43C24×C43C2×D411yescharacteristic
44C22×C4×C43—21no—
45C22×C4×C43—21no—
46C22×C4×C43—41no—
47C22×C4×C43—41no—
48C22×C4×C43C2×D412yes—
49C22×C4×C43C2×Q811yescharacteristic
50C22×C4×C43#4111yescharacteristic
51C22×C4×C43#4112yes—
52C22×Dic43—22no—
53C22×Dic43—22no—
54C22×Dic43—22no—
55C22×Dic43—41no—
56C2×Dic86—44no—
57C2×Dic86—81no—
58M16×C43—42no—
59M16×C43—42no—
60C2×C8×C43—42no—
61C22⋊C4×C43—41no—
62C22⋊C4×C43—41no—
63C22⋊Dic43—41no—
64C22⋊Dic43—41no—
65C22⋊Dic43—44no—
66C22⋊Dic43—41no—
67C22⋊Dic43—41no—
68C4⋊Dic43—24no—
69C4⋊Dic43—81no—
70Dic43⋊C4—44no—
71C4×Dic43—42no—
72C4×Dic43—42no—
73C4×Dic43—42no—
74C23×C43—21no—
75C23×C43—21no—
76C23×C43—42no—
77C23×C43#12011yescharacteristic
78C23×C43C22⋊Q811yescharacteristic
79C23×C43#12411yescharacteristic
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—41no—
83C2×C4×C43—42no—
84C2×C4×C43—41no—
85C2×C4×C43—42no—
86C2×C4×C43—42no—
87C2×C4×C43—41no—
88C2×C4×C43—41no—
89C2×C4×C43C22⋊Q812yes—
90C2×C4×C43#12412yes—
91C2×Dic43—24no—
92C2×Dic43—42no—
93C2×Dic43—42no—
94C2×Dic43—42no—
95C2×Dic43—42no—
96C2×Dic43—42no—
97C2×Dic43—42no—
98C2×Dic43—82no—
99C2×Dic43—81no—
100C2×Dic43—82no—
101Dic86—84no—
102C8×C43—82no—
103#10387—431nomaximal, Sylow
104C22×C43—22no—
105C22×C43—21no—
106C22×C43—21no—
107C22×C43—22no—
108C22×C43—22no—
109C22×C43—81no—
110C22×C43—81no—
111C22×C43#39311yescharacteristic
112C22×C43#45811yescharacteristic
113C22×C43#45811yescharacteristic
114C4×C43—22no—
115C4×C43—22no—
116C4×C43—81no—
117C4×C43—81no—
118Dic43—44no—
119Dic43—82no—
120Dic43—82no—
121Dic43—161no—
122#2607—431no—
123#1826—432no—
124#1820—431no—
125#1306D4311yescharacteristic
126#1284—432no—
127C2×C43—21no—
128C2×C43—21no—
129C2×C43—41no—
130C2×C43—41no—
131C2×C43#203011yescharacteristic
132C2×C43#203112yes—
133C2×#117—431no—
134#407C2×D4312yes—
135#399—861no—
136#393—861no—
137#391—862no—
138#387—862no—
139#381—431no—
140#381C2×D4311yescharacteristic
141C4×C22⋊C4—432no—
142#342—861no—
143#342—861no—
144#339—862no—
145#339—862no—
146C43#1038711yescharacteristic, complemented, Sylow
147C22×Q8—861no—
148C23×C4C22×D4311yescharacteristic
149C2×M16—22no—
150#117—862no—
151#117—862no—
152C2×C4⋊C4—432no—
153C2×C4⋊C4—861no—
154C2×C4⋊C4—862no—
155C2×C22⋊C4—861no—
156C2×C22⋊C4—862no—
157C2×C22⋊C4—861no—
158C2×C22⋊C4D17211yescharacteristic
159C2×C22⋊C4D17211yescharacteristic
160C2×C42—432no—
161C2×C42—432no—
162C2×C42—861no—
163C22⋊C8—22no—
164C22⋊C8—22no—
165#95—22no—
166#95—861no—
167#95—862no—
168#95—861no—
169#95—862no—
170#95—862no—
171C24C2×D17211yescharacteristic
172C2×Q8—3441no—
173C2×Q8—1724no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—862no—
179C22×C4—862no—
180C22×C4—862no—
181C22×C4—1721no—
182C22×C4#1062189812yes—
183C22×C4D4×D4312yes—
184C22×C4#1062190011yescharacteristic
185C22×C4Q8×D4311yescharacteristic
186M16—42no—
187M16—42no—
188C2×C8—42no—
189C4⋊C4—864no—
190C4⋊C4—3441no—
191C4⋊C4—1724no—
192C22⋊C4—41no—
193C22⋊C4—41no—
194C22⋊C4—1724no—
195C22⋊C4—1721no—
196C22⋊C4—1721no—
197C22⋊C4—1721no—
198C22⋊C4—1721no—
199C42—1722no—
200C42—1722no—
201C42—1722no—
202C23—21no—
203C23—21no—
204C23—42no—
205C23#1306329511yescharacteristic
206C23#1306330511yescharacteristic
207C23#1306331311yescharacteristic
208Q8—3444no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—864no—
219C2×C4—3442no—
220C2×C4—3441no—
221C2×C4—3442no—
222C2×C4—1722no—
223C2×C4—1722no—
224C2×C4—1722no—
225C2×C4—1722no—
226C2×C4—1722no—
227C2×C4—1722no—
228C2×C4#1306330312yes—
229C2×C4#1306331112yes—
230C8—82no—
231C22—22no—
232C22—21no—
233C22—21no—
234C22—22no—
235C22—22no—
236C22—81no—
237C22—81no—
238C22#1458281211yescharacteristic
239C22#1458309011yescharacteristic
240C22#1458309011yescharacteristic
241C4—22no—
242C4—22no—
243C4—81no—
244C4—81no—
245C4—3442no—
246C4—3442no—
247C4—1724no—
248C4—6881no—
249C2—21no—
250C2—21no—
251C2—41no—
252C2—41no—
253C2#1913576311yescharacteristic
254C2#1913577012yes—
subgroupG/H
centerC22#14582812
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1306C2
socleC22×C43#393
prime radicalC24×C43C2×D4
hypercenter#1306D43
hypocenterC43#10387
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
23. C2×C4⋊Dic43Q8semidirect
146. C43#10387semidirect

Maximal subgroups

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

subgroupindex
#191402602
#191346922
#191346702
#191324492
C43×#13062
#1038743