Finite Group Databasebeta

← #24994459

Subgroups — #24994459

Order 11008.

454 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 111 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#19139957C211yesmaximal, characteristic
3#19133023C212yesmaximal
4#19132455C212yesmaximal
5C43×#1801C211yesmaximal, characteristic
6C2×C4×Dic86C2211yescharacteristic
7#14583030—24no—
8#14582956—22no—
9#14582952C2212yes—
10#14582838C412yes—
11#14582819C412yes—
12#14582806—21no—
13#14582795—21no—
14#14582783—22no—
15#14582765C2211yescharacteristic
16#14582629—24no—
17C2×C4×Q8×C43C2211yescharacteristic
18C43×#423C2212yes—
19C2×#101×C43—21no—
20C43×#343—21no—
21C22×Dic86C2×C411yescharacteristic
22C4×Dic86—22no—
23C4×Dic86—22no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43C2×C411yescharacteristic
26C2×Dic43⋊C4—22no—
27C2×Dic43⋊C4—21no—
28C2×C4×Dic43—21no—
29C4⋊(C43⋊C8)—24no—
30C4⋊(C43⋊C8)—22no—
31C22⋊(C43⋊C8)—22no—
32#13063236—24no—
33C4×C43⋊C8D414yes—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C43⋊#95—22no—
37C43⋊#95—21no—
38C43⋊#95C2×C412yes—
39C22×Q8×C43D411yescharacteristic
40C2×M16×C43—22no—
41C4×Q8×C43—22no—
42C4×Q8×C43—22no—
43C2×C4⋊C4×C43C2×C412yes—
44C2×C4⋊C4×C43D411yescharacteristic
45C2×C42×C43D412yes—
46C2×C42×C43C2311yescharacteristic
47C4⋊C8×C43—22no—
48C4⋊C8×C43—22no—
49#101×C43—42no—
50C2×Q8×C43—22no—
51C2×Q8×C43—21no—
52C2×Q8×C43—22no—
53C2×Q8×C43—21no—
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—
64M16×C43—42no—
65M16×C43—42no—
66C2×C8×C43—42no—
67C4⋊C4×C43—24no—
68C4⋊C4×C43—22no—
69C42×C43—22no—
70C42×C43—22no—
71C42×C43C2×D412yes—
72C42×C43#4112yes—
73C4⋊Dic43—22no—
74C4⋊Dic43—41no—
75C4⋊Dic43—41no—
76Dic43⋊C4—44no—
77Dic43⋊C4—41no—
78Dic43⋊C4—41no—
79C4×Dic43—42no—
80C2×C43⋊C8—24no—
81C23×C43C2×C22⋊C411yescharacteristic
82Q8×C43—42no—
83Q8×C43—42no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—41no—
89C2×C4×C43—41no—
90C2×C4×C43—42no—
91C2×C4×C43C4×D412yes—
92C2×C4×C43#12011yescharacteristic
93C2×C4×C43#12112yes—
94C2×C4×C43#12311yescharacteristic
95C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
96C2×C4×C43#13712yes—
97C2×C4×C43#13711yescharacteristic
98C2×Dic43—22no—
99C2×Dic43—41no—
100C2×Dic43—41no—
101C2×Dic43—42no—
102C2×Dic43—42no—
103C2×Dic43—42no—
104C2×Dic43—41no—
105C2×Dic43—42no—
106Dic86—24no—
107Dic86—42no—
108C8×C43—82no—
109C43⋊C8—44no—
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#46812yes—
122C4×C43#47012yes—
123Dic43—42no—
124Dic43—82no—
125Dic43—81no—
126#2983—431no—
127#2581—431no—
128#1801D4311yescharacteristic
129#1487—432no—
130#1286—432no—
131C2×C43—21no—
132C2×C43—21no—
133C2×C43#189111yescharacteristic
134C2×C43#189411yescharacteristic
135C2×C43#191211yescharacteristic
136C2×C4×Q8—431no—
137C2×C4×Q8C2×D4311yescharacteristic
138#446—864no—
139#432—862no—
140#431—432no—
141#423C2×D4312yes—
142C2×#101—21no—
143#400—432no—
144#395—432no—
145#391—861no—
146#389—861no—
147#387—862no—
148#382—431no—
149#343—21no—
150Q8⋊C8—864no—
151C43#948811yescharacteristic, complemented, Sylow
152C22×Q8—431no—
153C22×Q8C22⋊D4311yescharacteristic
154C2×M16—22no—
155C4×Q8—22no—
156C4×Q8—22no—
157C4×Q8—862no—
158C4×Q8—862no—
159C2×C4⋊C4—431no—
160C2×C4⋊C4—862no—
161C2×C4⋊C4—861no—
162C2×C4⋊C4—861no—
163C2×C4⋊C4C4×D4312yes—
164C2×C4⋊C4C22⋊D4311yescharacteristic
165C2×C42—861no—
166C2×C42D17212yes—
167C2×C42C22×D4311yescharacteristic
168C4⋊C8—22no—
169C4⋊C8—22no—
170C4⋊C8—864no—
171C4⋊C8—862no—
172#101—42no—
173C22⋊C8—862no—
174#97—864no—
175C4×C8—434no—
176#95—432no—
177#95—862no—
178#95—862no—
179#95—862no—
180#95—861no—
181C2×Q8—22no—
182C2×Q8—21no—
183C2×Q8—22no—
184C2×Q8—21no—
185C2×Q8—862no—
186C2×Q8—1722no—
187C22×C4—861no—
188C22×C4—862no—
189C22×C4—861no—
190C22×C4(C2×D43)⋊C412yes—
191C22×C4(C2×D43)⋊C412yes—
192C22×C4C2×C4×D4311yescharacteristic
193C22×C4C2×D17211yescharacteristic
194C22×C4C2×C22⋊D4311yescharacteristic
195M16—42no—
196M16—42no—
197C2×C8—42no—
198C2×C8—864no—
199C4⋊C4—24no—
200C4⋊C4—22no—
201C4⋊C4—862no—
202C4⋊C4—1724no—
203C4⋊C4—1721no—
204C4⋊C4—1721no—
205C4⋊C4—1721no—
206C4⋊C4—1721no—
207C42—22no—
208C42—22no—
209C42—1722no—
210C42D4×D4312yes—
211C42#1062190012yes—
212C23C2×(C2×D43)⋊C411yescharacteristic
213Q8—42no—
214Q8—42no—
215Q8—864no—
216Q8—1722no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—862no—
225C2×C4—1722no—
226C2×C4—1722no—
227C2×C4—1722no—
228C2×C4—1722no—
229C2×C4—1721no—
230C2×C4—1721no—
231C2×C4—1721no—
232C2×C4(C22⋊D43)⋊C412yes—
233C2×C4#1306329511yescharacteristic
234C2×C4#1306329712yes—
235C2×C4#1306330911yescharacteristic
236C2×C4#1306335111yescharacteristic
237C2×C4#1306335512yes—
238C2×C4#1306335611yescharacteristic
239C8—82no—
240C8—1724no—
241C22—21no—
242C22—21no—
243C22#1458277611yescharacteristic
244C22#1458289811yescharacteristic
245C22#1458290711yescharacteristic
246C4—22no—
247C4—21no—
248C4—21no—
249C4—42no—
250C4—42no—
251C4—3442no—
252C4—3441no—
253C4—1722no—
254C4#1458314312yes—
255C4#1458315512yes—
256C2—21no—
257C2—21no—
258C2#1913501111yescharacteristic
259C2#1913502611yescharacteristic
260C2#1913513011yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1801C2
socleC22×C43#386
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1801D43
hypocenterC43#9488
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

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
#191399572
#191330232
#191324552
C43×#18012
#948843