Finite Group Databasebeta

← #25009379

Subgroups — #25009379

Order 11008.

380 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 59 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#19141627C211yesmaximal, characteristic
2#19135756C211yesmaximal, characteristic
3#19133605C212yesmaximal
4#19132602C212yesmaximal
5C43×#1319C211yesmaximal, characteristic
6#14583530C2211yescharacteristic
7C2×#13063323—21no—
8#14583230—22no—
9#14582908—21no—
10#14582829C2212yes—
11#14582820—22no—
12#14582797—21no—
13#14582784—22no—
14#14582668C2211yescharacteristic
15#14582659—21no—
16#14582637—22no—
17C43×#391C2211yescharacteristic
18C43×#324C2212yes—
19C22×Dic86—21no—
20C2×#10621877—21no—
21#13063324—41no—
22#13063323—42no—
23#13063323—42no—
24#13063316—41no—
25#13063304—22no—
26#13063284—21no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43D412yes—
30C2×Dic43⋊C4—22no—
31C2×Dic43⋊C4—22no—
32C2×C4×Dic43—21no—
33#13063257—42no—
34#13063250—42no—
35#13063249—41no—
36#13063249—41no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95D412yes—
40C22×Q8×C43D411yescharacteristic
41C2×C4⋊C4×C43C2311yescharacteristic
42C2×C42×C43D411yescharacteristic
43C22⋊C8×C43—22no—
44#95×C43—22no—
45C2×Q8×C43—21no—
46C2×Q8×C43—41no—
47C2×Q8×C43—41no—
48C2×Q8×C43SD1612yes—
49C22×C4×C43—21no—
50C22×C4×C43—21no—
51C22×C4×C43C2×D411yescharacteristic
52C22×C4×C43C2×D412yes—
53C22×Dic43—22no—
54C22×Dic43—22no—
55C2×Dic86—22no—
56C2×Dic86—42no—
57C2×Dic86—81no—
58C2×Dic86—81no—
59C2×C8×C43—42no—
60C4⋊C4×C43—41no—
61C42×C43—41no—
62C22⋊Dic43—41no—
63C4⋊Dic43—24no—
64C4⋊Dic43—21no—
65C4⋊Dic43—21no—
66C4⋊Dic43—22no—
67C4⋊Dic43—42no—
68C4⋊Dic43—81no—
69Dic43⋊C4—44no—
70Dic43⋊C4—42no—
71Dic43⋊C4—42no—
72Dic43⋊C4—42no—
73C4×Dic43—42no—
74C4×Dic43—41no—
75#10621877—41no—
76#10621877—41no—
77C2×C43⋊C8—41no—
78C23×C43#12011yescharacteristic
79Q8×C43—42no—
80Q8×C43—81no—
81C2×C4×C43—21no—
82C2×C4×C43—21no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—41no—
89C2×C4×C43—41no—
90C2×C4×C43—42no—
91C2×C4×C43C2×SD1611yescharacteristic
92C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
93C2×Dic43—24no—
94C2×Dic43—42no—
95C2×Dic43—42no—
96C2×Dic43—42no—
97C2×Dic43—42no—
98C2×Dic43—41no—
99C2×Dic43—41no—
100C2×Dic43—42no—
101Dic86—84no—
102Dic86—82no—
103C8×C43—82no—
104C43⋊C8—81no—
105#12213—431nomaximal, Sylow
106C22×C43—21no—
107C22×C43—21no—
108C22×C43#45011yescharacteristic
109C22×C43#45511yescharacteristic
110C22×C43B(4,𝔽2)11yescharacteristic
111C4×C43—21no—
112C4×C43—21no—
113C4×C43—42no—
114C4×C43—42no—
115C4×C43—42no—
116Dic43—44no—
117Dic43—82no—
118Dic43—81no—
119Dic43—81no—
120#2734—431no—
121#2028—431no—
122#1611—432no—
123#1346—432no—
124#1319D4311yescharacteristic
125C2×C43—21no—
126C2×C43—21no—
127C2×C43#160111yescharacteristic
128C2×C43#220111yescharacteristic
129C2×C43#220511yescharacteristic
130#544—431no—
131C2×C4⋊Q8—861no—
132#483—862no—
133#419—861no—
134#398—432no—
135#395—862no—
136#391C2×D4311yescharacteristic
137#389—861no—
138#387—862no—
139#343—431no—
140#339—861no—
141#328—862no—
142#324C2×D4312yes—
143C43#1221311yescharacteristic, complemented, Sylow
144C22×Q8—861no—
145C22×Q8D17211yescharacteristic
146C2×M16—861no—
147C4⋊Q8—1721no—
148C4⋊Q8—1722no—
149C4⋊Q8—1722no—
150#125—1721no—
151C22⋊Q8—862no—
152#117—861no—
153C2×C4⋊C4—432no—
154C2×C4⋊C4—861no—
155C2×C4⋊C4—861no—
156C2×C4⋊C4—862no—
157C2×C4⋊C4—862no—
158C2×C4⋊C4C22×D4311yescharacteristic
159C2×C42—861no—
160C2×C42D17211yescharacteristic
161#106—1722no—
162#103—1721no—
163#103—1721no—
164#103—1722no—
165C22⋊C8—22no—
166#95—22no—
167#95—432no—
168#95—862no—
169#95—862no—
170C2×Q8—21no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—862no—
174C2×Q8—3441no—
175C2×Q8—3441no—
176C2×Q8—1722no—
177C2×Q8#1062187312yes—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—862no—
181C22×C4—862no—
182C22×C4C2×D17211yescharacteristic
183C22×C4D4×D4312yes—
184M16—1721no—
185M16—1721no—
186C2×C8—42no—
187C2×C8—1721no—
188C4⋊C4—41no—
189C4⋊C4—864no—
190C4⋊C4—861no—
191C4⋊C4—861no—
192C4⋊C4—862no—
193C4⋊C4—3441no—
194C4⋊C4—1722no—
195C4⋊C4—1724no—
196C4⋊C4—1722no—
197C4⋊C4—1722no—
198C4⋊C4—1722no—
199C22⋊C4—1721no—
200C42—41no—
201C42—1722no—
202C42—1721no—
203C23#1306329511yescharacteristic
204Q8—42no—
205Q8—81no—
206Q8—3442no—
207Q8—3444no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—864no—
219C2×C4—1722no—
220C2×C4—1722no—
221C2×C4—1721no—
222C2×C4—1721no—
223C2×C4—1722no—
224C2×C4—1722no—
225C2×C4—1722no—
226C2×C4C2×#1062187311yescharacteristic
227C2×C4#1306335311yescharacteristic
228C8—82no—
229C8—3441no—
230C22—21no—
231C22—21no—
232C22#1458305211yescharacteristic
233C22#1458307911yescharacteristic
234C22#1458308711yescharacteristic
235C4—21no—
236C4—21no—
237C4—42no—
238C4—42no—
239C4—42no—
240C4—3441no—
241C4—3442no—
242C4—3441no—
243C4—1724no—
244C2—21no—
245C2—21no—
246C2#1913354911yescharacteristic
247C2#1913661011yescharacteristic
248C2#1913662611yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1319C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1319D43
hypocenterC43#12213
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
143. C43#12213semidirect

Maximal subgroups

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

subgroupindex
#191416272
#191357562
#191336052
#191326022
C43×#13192
#1221343