Finite Group Databasebeta

← #24994462

Subgroups — #24994462

Order 11008.

454 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 119 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#19143680C211yesmaximal, characteristic
2#19134591C211yesmaximal, characteristic
3#19133024C212yesmaximal
4#19132453C212yesmaximal
5C43×#2581C211yesmaximal, characteristic
6#14583030—24no—
7#14582956—22no—
8#14582952C2212yes—
9#14582923C2212yes—
10C2×#13063244—21no—
11#14582668—21no—
12Q8⋊(C43⋊C8)—24no—
13C2×C4×Q8×C43C2211yescharacteristic
14C2×C4×Q8×C43C2211yescharacteristic
15C43×#400C412yes—
16C43×#395C412yes—
17C43×#391—21no—
18C43×#389—21no—
19C43×#387—22no—
20C43×#382C2211yescharacteristic
21C2×#10621877—22no—
22C4⋊(C43⋊C8)—24no—
23C4⋊(C43⋊C8)—22no—
24C4⋊(C43⋊C8)—22no—
25C4⋊(C43⋊C8)—22no—
26#13063244—42no—
27C22⋊(C43⋊C8)—22no—
28#13063236—24no—
29C4×C43⋊C8D414yes—
30C22×Q8×C43C2×C411yescharacteristic
31C22×Q8×C43D411yescharacteristic
32C4×Q8×C43—22no—
33C4×Q8×C43—22no—
34C4×Q8×C43—22no—
35C4×Q8×C43—22no—
36C2×C4⋊C4×C43—22no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43C2×C411yescharacteristic
40C2×C4⋊C4×C43C2×C412yes—
41C2×C4⋊C4×C43D411yescharacteristic
42C2×C42×C43—21no—
43C2×C42×C43D412yes—
44C2×C42×C43C2311yescharacteristic
45#95×C43—22no—
46#95×C43—22no—
47#95×C43—22no—
48#95×C43—21no—
49#95×C43C2×C412yes—
50C2×Q8×C43—22no—
51C2×Q8×C43—21no—
52C2×Q8×C43—21no—
53C2×Q8×C43—22no—
54C2×Q8×C43—22no—
55C2×Q8×C43—42no—
56C22×C4×C43—21no—
57C22×C4×C43—22no—
58C22×C4×C43—21no—
59C22×C4×C43C22⋊C412yes—
60C22×C4×C43C22⋊C412yes—
61C22×C4×C43C22×C411yescharacteristic
62C22×C4×C43C2×D411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C4⋊C4×C43—24no—
65C4⋊C4×C43—22no—
66C4⋊C4×C43—22no—
67C4⋊C4×C43—44no—
68C4⋊C4×C43—41no—
69C4⋊C4×C43—41no—
70C4⋊C4×C43—41no—
71C4⋊C4×C43—41no—
72C42×C43—22no—
73C42×C43—22no—
74C42×C43—42no—
75C42×C43C2×D412yes—
76C42×C43#4112yes—
77#10621877—42no—
78#10621877—42no—
79C2×C43⋊C8—24no—
80C2×C43⋊C8—42no—
81C23×C43C2×C22⋊C411yescharacteristic
82Q8×C43—24no—
83Q8×C43—42no—
84Q8×C43—42no—
85Q8×C43—42no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43—42no—
96C2×C4×C43—42no—
97C2×C4×C43—42no—
98C2×C4×C43—42no—
99C2×C4×C43—41no—
100C2×C4×C43—42no—
101C2×C4×C43C4×D412yes—
102C2×C4×C43#12011yescharacteristic
103C2×C4×C43#12112yes—
104C2×C4×C43#12311yescharacteristic
105C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
106C2×C4×C43#13711yescharacteristic
107C2×C4×C43#13712yes—
108C43⋊C8—44no—
109C43⋊C8—82no—
110#9488—431nomaximal, Sylow
111C22×C43—21no—
112C22×C43—21no—
113C22×C43#38611yescharacteristic
114C22×C43#41711yescharacteristic
115C22×C43#41911yescharacteristic
116C4×C43—22no—
117C4×C43—21no—
118C4×C43—21no—
119C4×C43—42no—
120C4×C43—42no—
121C4×C43—42no—
122C4×C43—82no—
123C4×C43—81no—
124C4×C43#46812yes—
125C4×C43#47012yes—
126#2983—431no—
127#2581D4311yescharacteristic
128#1801—431no—
129#1487—432no—
130#1286—432no—
131C2×C43—21no—
132C2×C43—21no—
133C2×C43#189111yescharacteristic
134C2×C43#189411yescharacteristic
135C2×C43#191211yescharacteristic
136C2×C4×Q8C2×D4311yescharacteristic
137C2×C4×Q8C2×D4311yescharacteristic
138#446—864no—
139#432—862no—
140#431—432no—
141#423—432no—
142C2×#101—861no—
143#400Dic4312yes—
144#395Dic4312yes—
145#391—21no—
146#389—21no—
147#387—22no—
148#382C2×D4311yescharacteristic
149#343—861no—
150Q8⋊C8—864no—
151C43#948811yescharacteristic, complemented, Sylow
152C22×Q8C2×Dic4311yescharacteristic
153C22×Q8C22⋊D4311yescharacteristic
154C2×M16—862no—
155C4×Q8—22no—
156C4×Q8—22no—
157C4×Q8—22no—
158C4×Q8—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4C2×Dic4311yescharacteristic
163C2×C4⋊C4C2×Dic4312yes—
164C2×C4⋊C4C22⋊D4311yescharacteristic
165C2×C42—21no—
166C2×C42C22⋊D4312yes—
167C2×C42C22×D4311yescharacteristic
168C4⋊C8—864no—
169C4⋊C8—862no—
170C4⋊C8—862no—
171C4⋊C8—862no—
172#101—1722no—
173C22⋊C8—862no—
174#97—864no—
175C4×C8—434no—
176#95—22no—
177#95—22no—
178#95—22no—
179#95—21no—
180#95C2×Dic4312yes—
181C2×Q8—22no—
182C2×Q8—21no—
183C2×Q8—21no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—42no—
187C22×C4—21no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4C22⋊Dic4312yes—
191C22×C4C22⋊Dic4312yes—
192C22×C4C22×Dic4311yescharacteristic
193C22×C4C2×C22⋊D4311yescharacteristic
194C22×C4C2×C22⋊D4311yescharacteristic
195M16—1722no—
196M16—1722no—
197C2×C8—864no—
198C2×C8—1722no—
199C4⋊C4—24no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—44no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C42—22no—
208C42—22no—
209C42—42no—
210C42D4×D4312yes—
211C42#1062190012yes—
212C23C2×C22⋊Dic4311yescharacteristic
213Q8—24no—
214Q8—42no—
215Q8—42no—
216Q8—42no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4D4×Dic4312yes—
233C2×C4#1306329311yescharacteristic
234C2×C4#1306329712yes—
235C2×C4#1306330611yescharacteristic
236C2×C4#1306335011yescharacteristic
237C2×C4#1306335511yescharacteristic
238C2×C4#1306335612yes—
239C8—3442no—
240C8—1724no—
241C22—21no—
242C22—21no—
243C22#1458277911yescharacteristic
244C22#1458290011yescharacteristic
245C22#1458290811yescharacteristic
246C4—22no—
247C4—21no—
248C4—21no—
249C4—42no—
250C4—42no—
251C4—42no—
252C4—82no—
253C4—81no—
254C4#1458314712yes—
255C4#1458315512yes—
256C2—21no—
257C2—21no—
258C2#1913501411yescharacteristic
259C2#1913502911yescharacteristic
260C2#1913513311yescharacteristic
subgroupG/H
centerC22#14582779
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2581C2
socleC22×C43#386
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#2581D43
hypocenterC43#9488
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2581

Complements

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

NH ≅ G/Ntype
151. C43#9488semidirect

Maximal subgroups

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

subgroupindex
#191436802
#191345912
#191330242
#191324532
C43×#25812
#948843