Finite Group Databasebeta

← #24994441

Subgroups — #24994441

Order 11008.

474 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 131 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#19139957C211yesmaximal, characteristic
2#19134591C211yesmaximal, characteristic
3#19133025C212yesmaximal
4#19132454C212yesmaximal
5C43×#2982C211yesmaximal, characteristic
6C2×C4×Dic86C2211yescharacteristic
7#14582923C2212yes—
8C2×#13063244—21no—
9#14582838C412yes—
10#14582819C412yes—
11#14582806—21no—
12#14582795—21no—
13#14582783—22no—
14#14582765C2211yescharacteristic
15#14582668—21no—
16#14582631—24no—
17C2×C4×Q8×C43C2211yescharacteristic
18C8×Q8×C43—24no—
19C43×#431—22no—
20C43×#431C2212yes—
21C22×Dic86C2×C411yescharacteristic
22C2×#10621877—22no—
23C4×Dic86—22no—
24C4×Dic86—22no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×Dic43⋊C4—22no—
28C2×Dic43⋊C4—21no—
29C2×C4×Dic43—21no—
30C4⋊(C43⋊C8)—22no—
31C4⋊(C43⋊C8)—22no—
32#13063244—42no—
33C43⋊#95—22no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C43⋊#95—21no—
37C43⋊#95C2×C412yes—
38C22×Q8×C43D411yescharacteristic
39C4×Q8×C43—22no—
40C4×Q8×C43—22no—
41C2×C4⋊C4×C43C2×C412yes—
42C2×C4⋊C4×C43D411yescharacteristic
43C2×C42×C43D412yes—
44C2×C42×C43C2311yescharacteristic
45C4⋊C8×C43—24no—
46C4⋊C8×C43—22no—
47C22⋊C8×C43—22no—
48C4×C8×C43—24no—
49C4×C8×C43D414yes—
50C2×Q8×C43—22no—
51C2×Q8×C43—22no—
52C2×Q8×C43SD1612yes—
53C2×Q8×C43Q1612yes—
54C22×C4×C43C22⋊C412yes—
55C22×C4×C43C22⋊C412yes—
56C22×C4×C43C22×C411yescharacteristic
57C22×C4×C43C2×D411yescharacteristic
58C22×C4×C43C2×D411yescharacteristic
59C22×Dic43—21no—
60C22×Dic43—22no—
61C22×Dic43—21no—
62C2×Dic86—22no—
63C2×Dic86—42no—
64C2×C8×C43—24no—
65C4⋊C4×C43—24no—
66C4⋊C4×C43—22no—
67C42×C43—22no—
68C42×C43—22no—
69C42×C43C2×D412yes—
70C42×C43#4112yes—
71C4⋊Dic43—22no—
72C4⋊Dic43—42no—
73Dic43⋊C4—44no—
74Dic43⋊C4—41no—
75Dic43⋊C4—41no—
76C4×Dic43—42no—
77#10621877—42no—
78#10621877—42no—
79C2×C43⋊C8—42no—
80C23×C43C2×C22⋊C411yescharacteristic
81Q8×C43—24no—
82Q8×C43—24no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—42no—
89C2×C4×C43#10314yes—
90C2×C4×C43C4×D412yes—
91C2×C4×C43#12011yescharacteristic
92C2×C4×C43#12112yes—
93C2×C4×C43#12311yescharacteristic
94C2×C4×C43C2×SD1611yescharacteristic
95C2×C4×C43C2×Q1611yescharacteristic
96C2×C4×C43#13512yes—
97C2×Dic43—22no—
98C2×Dic43—41no—
99C2×Dic43—41no—
100C2×Dic43—42no—
101C2×Dic43—42no—
102C2×Dic43—42no—
103C2×Dic43—41no—
104C2×Dic43—42no—
105Dic86—24no—
106Dic86—42no—
107C8×C43—44no—
108C43⋊C8—82no—
109#9484—431nomaximal, Sylow
110C22×C43—21no—
111C22×C43—21no—
112C22×C43#38611yescharacteristic
113C22×C43C2×#10311yescharacteristic
114C22×C43#41611yescharacteristic
115C4×C43—22no—
116C4×C43—24no—
117C4×C43—21no—
118C4×C43—21no—
119C4×C43—42no—
120C4×C43#46512yes—
121C4×C43#46712yes—
122Dic43—42no—
123Dic43—82no—
124Dic43—81no—
125#2982D4311yescharacteristic
126#2581—431no—
127#1801—431no—
128#1487—432no—
129#1286—432no—
130C2×C43—21no—
131C2×C43—21no—
132C2×C43#189111yescharacteristic
133C2×C43#189211yescharacteristic
134C2×C43#191211yescharacteristic
135C2×C4×Q8—431no—
136C2×C4×Q8C2×D4311yescharacteristic
137C8×Q8—24no—
138#431—22no—
139#431C2×D4312yes—
140#423—432no—
141C2×#101—861no—
142#400—432no—
143#395—432no—
144#391—861no—
145#389—861no—
146#387—862no—
147#382—431no—
148#343—861no—
149Q8⋊C8—864no—
150C43#948411yescharacteristic, complemented, Sylow
151C22×Q8—431no—
152C22×Q8D17211yescharacteristic
153C2×M16—862no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—862no—
157C4×Q8—862no—
158C2×C4⋊C4—431no—
159C2×C4⋊C4—862no—
160C2×C4⋊C4—861no—
161C2×C4⋊C4—861no—
162C2×C4⋊C4C4×D4312yes—
163C2×C4⋊C4D17211yescharacteristic
164C2×C42—861no—
165C2×C42C22⋊D4312yes—
166C2×C42C22×D4311yescharacteristic
167C4⋊C8—24no—
168C4⋊C8—22no—
169C4⋊C8—862no—
170C4⋊C8—862no—
171#101—1722no—
172C22⋊C8—22no—
173C4×C8—24no—
174C4×C8C22⋊D4314yes—
175#95—432no—
176#95—862no—
177#95—862no—
178#95—862no—
179#95—861no—
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—862no—
183C2×Q8—1722no—
184C2×Q8#1062187312yes—
185C2×Q8Dic17212yes—
186C22×C4—861no—
187C22×C4—862no—
188C22×C4—861no—
189C22×C4(C2×D43)⋊C412yes—
190C22×C4(C2×D43)⋊C412yes—
191C22×C4C2×C4×D4311yescharacteristic
192C22×C4C2×D17211yescharacteristic
193C22×C4C2×C22⋊D4311yescharacteristic
194M16—1722no—
195M16—1722no—
196C2×C8—24no—
197C2×C8—1722no—
198C4⋊C4—24no—
199C4⋊C4—22no—
200C4⋊C4—862no—
201C4⋊C4—1724no—
202C4⋊C4—1721no—
203C4⋊C4—1721no—
204C4⋊C4—1722no—
205C42—22no—
206C42—22no—
207C42—1722no—
208C42#1062189812yes—
209C42C2×C22⋊D4312yes—
210C23C2×(C2×D43)⋊C411yescharacteristic
211Q8—24no—
212Q8—24no—
213Q8—864no—
214Q8—1722no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—862no—
222C2×C4—1722no—
223C2×C4—1722no—
224C2×C4—1722no—
225C2×C4—1722no—
226C2×C4—1721no—
227C2×C4—1721no—
228C2×C4—1721no—
229C2×C4#1306325014yes—
230C2×C4C4×C22⋊D4312yes—
231C2×C4#1306329411yescharacteristic
232C2×C4#1306329912yes—
233C2×C4#1306330811yescharacteristic
234C2×C4C2×#1062187311yescharacteristic
235C2×C4C2×Dic17211yescharacteristic
236C2×C4#1306334712yes—
237C8—44no—
238C8—3442no—
239C22—21no—
240C22—21no—
241C22#1458277811yescharacteristic
242C22C2×#1306325011yescharacteristic
243C22#1458289611yescharacteristic
244C4—22no—
245C4—24no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—3442no—
250C4—3441no—
251C4—1722no—
252C4#1458312812yes—
253C4#1458314012yes—
254C2—21no—
255C2—21no—
256C2#1913501311yescharacteristic
257C2#1913501811yescharacteristic
258C2#1913513211yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2982C2
socleC22×C43#386
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#2982D43
hypocenterC43#9484
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
150. C43#9484semidirect

Maximal subgroups

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

subgroupindex
#191399572
#191345912
#191330252
#191324542
C43×#29822
#948443