Finite Group Databasebeta

← #25064348

Subgroups — #25064348

Order 11008.

938 conjugacy classes of subgroups; only the 355 normal subgroups are shown.

normal subgroups only

This group has 938 conjugacy classes of subgroups — too many to draw. Only its 355 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#19148405C211yesmaximal, characteristic
2#19143676C211yesmaximal, characteristic
3#19133158C216yesmaximal
4#19133093C216yesmaximal
5C43×#2351C211yesmaximal, characteristic
6Q8×Dic86C414yescomplemented
7#14583628C414yescomplemented
8#14583625—24no—
9#14583530—23no—
10#14583456C2216yes—
11#14583377—21no—
12Q8×C43⋊C8—24no—
13#14582952C2216yes—
14#14582635C2214yes—
15#14582635C22112yes—
16C2×C4×Q8×C43—21no—
17C2×C4×Q8×C43C2211yescharacteristic
18C43×#389—23no—
19C43×#382C2213yes—
20C4×C4⋊C4×C43C2213yes—
21#13063325C2×C416yes—
22#13063325C2×C416yes—
23#13063324—212no—
24#13063317—26no—
25#13063316—212no—
26#13063304—26no—
27#13063304C2314yes—
28Q8×Dic43—24no—
29Q8×Dic43—24no—
30C4×Dic86—26no—
31C4×Dic86C2×C4112yes—
32#13063284—26no—
33C4⋊(C43⋊C8)—26no—
34C22⋊(C43⋊C8)C2314yes—
35C4×C43⋊C8—26no—
36C22×Q8×C43D411yescharacteristic
37C4×Q8×C43—44no—
38C4×Q8×C43C2×C414yes—
39C4×Q8×C43D414yes—
40C2×C4⋊C4×C43—23no—
41C2×C4⋊C4×C43—23no—
42C2×C4⋊C4×C43D413yes—
43C2×C42×C43—23no—
44C2×C42×C43C2313yes—
45#95×C43—23no—
46#95×C43C2311yescharacteristic
47#95×C43C2313yes—
48C2×Q8×C43C22⋊C414yes—
49C2×Q8×C43SD1614yes—
50C2×Q8×C43Q1614yes—
51C22×C4×C43—21no—
52C22×C4×C43—23no—
53C22×C4×C43C2×D413yes—
54C22×C4×C43C2×D413yes—
55C22×C4×C43C2411yescharacteristic
56C2×Dic86—26no—
57C2×Dic86C22×C414yes—
58C4⋊C4×C43—46no—
59C4⋊C4×C43—46no—
60C4⋊C4×C43C22⋊C4112yes—
61C42×C43—46no—
62C42×C43C22×C416yes—
63C42×C43C2×D416yes—
64C22⋊Dic43—24no—
65C4⋊Dic43—26no—
66C4⋊Dic43—26no—
67C4⋊Dic43—26no—
68C4⋊Dic43C22×C414yes—
69Dic43⋊C4—212no—
70Dic43⋊C4—24no—
71C4×Dic43—212no—
72C2×C43⋊C8—24no—
73C23×C43C22×D411yescharacteristic
74Q8×C43#103116yes—
75C2×C4×C43—22no—
76C2×C4×C43—43no—
77C2×C4×C43—41no—
78C2×C4×C43—41no—
79C2×C4×C43—41no—
80C2×C4×C43—43no—
81C2×C4×C43—43no—
82C2×C4×C43—43no—
83C2×C4×C43C2×C22⋊C416yes—
84C2×C4×C43C2×C22⋊C416yes—
85C2×C4×C43C2×SD1616yes—
86C2×C4×C43C2×Q1616yes—
87C2×C4×C43C23×C411yescharacteristic
88C2×C4×C43C22×D411yescharacteristic
89C2×Dic43—24no—
90C2×Dic43—24no—
91Dic86—44no—
92Dic86—86no—
93C43⋊C8—44no—
94#17619—431nomaximal, Sylow
95C22×C43—21no—
96C22×C43—21no—
97C22×C43C22×C22⋊C411yescharacteristic
98C22×C43C22×SD1611yescharacteristic
99C22×C43C22×Q1611yescharacteristic
100C4×C43—21no—
101C4×C43—21no—
102C4×C43—26no—
103C4×C43—42no—
104C4×C43—83no—
105C4×C43C2×#103112yes—
106Dic43—44no—
107Dic43—44no—
108#3502—431no—
109#2982—431no—
110#2351D4311yescharacteristic
111#1518—436no—
112#1503—436no—
113C2×C43—21no—
114C2×C43—21no—
115C2×C43#288411yescharacteristic
116C2×C43C22×#10311yescharacteristic
117C2×C43#290111yescharacteristic
118Q82—434no—
119#557—434no—
120#557—864no—
121#544—863no—
122#533—436no—
123#519—861no—
124C2×C4×Q8—21no—
125C2×C4×Q8C2×D4311yescharacteristic
126C8×Q8—864no—
127#431—436no—
128#389—23no—
129#382C2×D4313yes—
130C4×C4⋊C4C2×D4313yes—
131#328—434no—
132#328—4312no—
133C43#1761911yescharacteristic, complemented, Sylow
134C22×Q8C22⋊D4311yescharacteristic
135C4⋊Q8—436no—
136C4⋊Q8—436no—
137C4⋊Q8—8612no—
138#125—8612no—
139#125—866no—
140C22⋊Q8—434no—
141C22⋊Q8—866no—
142C4×Q8—44no—
143C4×Q8—4312no—
144C4×Q8—864no—
145C4×Q8—864no—
146C4×Q8—866no—
147C4×Q8C4×D4314yes—
148C4×Q8D17214yes—
149#117—866no—
150C2×C4⋊C4—23no—
151C2×C4⋊C4—23no—
152C2×C4⋊C4C22⋊D4313yes—
153C2×C42—23no—
154C2×C42C22×D4313yes—
155C4⋊C8—866no—
156C22⋊C8—434no—
157C4×C8—866no—
158#95—23no—
159#95C22×D4311yescharacteristic
160#95C22×D4313yes—
161C2×Q8—434no—
162C2×Q8—866no—
163C2×Q8(C2×D43)⋊C414yes—
164C2×Q8#1062188314yes—
165C2×Q8#1062188514yes—
166C22×C4—21no—
167C22×C4—23no—
168C22×C4C2×C22⋊D4313yes—
169C22×C4C2×C22⋊D4313yes—
170C22×C4C23×D4311yescharacteristic
171C2×C8—864no—
172C4⋊C4—46no—
173C4⋊C4—46no—
174C4⋊C4—434no—
175C4⋊C4—866no—
176C4⋊C4—866no—
177C4⋊C4—8612no—
178C4⋊C4—866no—
179C4⋊C4—864no—
180C4⋊C4(C2×D43)⋊C4112yes—
181C22⋊C4—864no—
182C42—46no—
183C42—8612no—
184C42C2×C4×D4316yes—
185C42C2×D17216yes—
186C23C22×C22⋊D4311yescharacteristic
187Q8—3446no—
188Q8—1724no—
189Q8#13063248116yes—
190C2×C4—22no—
191C2×C4—43no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—43no—
196C2×C4—43no—
197C2×C4—43no—
198C2×C4—864no—
199C2×C4—864no—
200C2×C4C2×(C2×D43)⋊C416yes—
201C2×C4C2×(C2×D43)⋊C416yes—
202C2×C4C2×#1062188316yes—
203C2×C4C2×#1062188516yes—
204C2×C4C22×C4×D4311yescharacteristic
205C2×C4C22×D17211yescharacteristic
206C8—1724no—
207C22—21no—
208C22—21no—
209C22C22×(C2×D43)⋊C411yescharacteristic
210C22C22×#1062188311yescharacteristic
211C22C22×#1062188511yescharacteristic
212C4—21no—
213C4—21no—
214C4—26no—
215C4—42no—
216C4—83no—
217C4—1724no—
218C4—1724no—
219C4C2×#13063248112yes—
220C2—21no—
221C2—21no—
222C2#1914305811yescharacteristic
223C2C22×#1306324811yescharacteristic
224C2#1914314311yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2351C2
socleC22×C43C22×C22⋊C4
prime radicalC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenter#2351D43
hypocenterC43#17619
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #2351

Complements

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

NH ≅ G/Ntype
6. Q8×Dic86C4semidirect
7. #14583628C4semidirect
133. C43#17619semidirect

Maximal subgroups

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

subgroupindex
#191484052
#191436762
#191331582
#191330932
C43×#23512
#1761943