Finite Group Databasebeta

← #25064349

Subgroups — #25064349

Order 11008.

938 conjugacy classes of subgroups; only the 395 normal subgroups are shown.

normal subgroups only

This group has 938 conjugacy classes of subgroups — too many to draw. Only its 395 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#19143676C211yesmaximal, characteristic
2#19137516C211yesmaximal, characteristic
3#19133159C216yesmaximal
4#19133094C216yesmaximal
5C43×#3502C211yesmaximal, characteristic
6C2×Q8×Dic43—21no—
7Q8×C43⋊C8—24no—
8#14582952C2216yes—
9#14582798—23no—
10#14582765C2213yes—
11C4×C4⋊Dic43C2213yes—
12#14582636C2214yes—
13#14582636C22112yes—
14Q82×C43C414yescomplemented
15C43×#557—24no—
16C43×#557C414yescomplemented
17C43×#544—23no—
18C43×#533C2216yes—
19C43×#519—21no—
20C2×C4×Q8×C43C2211yescharacteristic
21Q8×Dic43—44no—
22C2×C4⋊Dic43—23no—
23C2×C4⋊Dic43—23no—
24C2×C4×Dic43—23no—
25C4⋊(C43⋊C8)—26no—
26C22⋊(C43⋊C8)C2314yes—
27C4×C43⋊C8—26no—
28C43⋊#95—23no—
29C43⋊#95C2311yescharacteristic
30C43⋊#95C2313yes—
31C22×Q8×C43D411yescharacteristic
32C4⋊Q8×C43—212no—
33C4⋊Q8×C43C2×C416yes—
34C4⋊Q8×C43C2×C416yes—
35#125×C43—212no—
36#125×C43—26no—
37C22⋊Q8×C43—26no—
38C22⋊Q8×C43C2314yes—
39C4×Q8×C43—24no—
40C4×Q8×C43—24no—
41C4×Q8×C43—26no—
42C4×Q8×C43C2×C4112yes—
43C4×Q8×C43C2×C414yes—
44C4×Q8×C43D414yes—
45#117×C43—26no—
46C2×C4⋊C4×C43D413yes—
47C2×C42×C43C2313yes—
48C2×Q8×C43—26no—
49C2×Q8×C43C22⋊C414yes—
50C2×Q8×C43SD1614yes—
51C2×Q8×C43Q1614yes—
52C2×Q8×C43C22×C414yes—
53C22×C4×C43C2×D413yes—
54C22×C4×C43C2×D413yes—
55C22×C4×C43C2411yescharacteristic
56C22×Dic43—21no—
57C22×Dic43—23no—
58C4⋊C4×C43—26no—
59C4⋊C4×C43—26no—
60C4⋊C4×C43—26no—
61C4⋊C4×C43—212no—
62C4⋊C4×C43—24no—
63C4⋊C4×C43C22⋊C4112yes—
64C4⋊C4×C43C22×C414yes—
65C22⋊C4×C43—24no—
66C42×C43—212no—
67C42×C43C22×C416yes—
68C42×C43C2×D416yes—
69C4⋊Dic43—46no—
70C4⋊Dic43—46no—
71C4×Dic43—46no—
72C2×C43⋊C8—24no—
73C23×C43C22×D411yescharacteristic
74Q8×C43—44no—
75Q8×C43—86no—
76Q8×C43#103116yes—
77C2×C4×C43—24no—
78C2×C4×C43—24no—
79C2×C4×C43—43no—
80C2×C4×C43—41no—
81C2×C4×C43C2×C22⋊C416yes—
82C2×C4×C43C2×C22⋊C416yes—
83C2×C4×C43C2×SD1616yes—
84C2×C4×C43C2×Q1616yes—
85C2×C4×C43C23×C411yescharacteristic
86C2×C4×C43C22×D411yescharacteristic
87C2×Dic43—22no—
88C2×Dic43—41no—
89C2×Dic43—41no—
90C2×Dic43—43no—
91C2×Dic43—43no—
92C2×Dic43—43no—
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—44no—
104C4×C43—44no—
105C4×C43C2×#103112yes—
106Dic43—42no—
107Dic43—83no—
108#3502D4311yescharacteristic
109#2982—431no—
110#2351—431no—
111#1518—436no—
112#1503—436no—
113C2×C43—21no—
114C2×C43—21no—
115C2×C43#288411yescharacteristic
116C2×C43C22×#10311yescharacteristic
117C2×C43#290111yescharacteristic
118Q82Dic4314yescomplemented
119#557—24no—
120#557Dic4314yescomplemented
121#544—23no—
122#533C2×D4316yes—
123#519—21no—
124C2×C4×Q8—861no—
125C2×C4×Q8C2×D4311yescharacteristic
126C8×Q8—864no—
127#431—436no—
128#389—863no—
129#382—433no—
130C4×C4⋊C4—433no—
131#328—434no—
132#328—4312no—
133C43#1761911yescharacteristic, complemented, Sylow
134C22×Q8C22⋊D4311yescharacteristic
135C4⋊Q8—212no—
136C4⋊Q8C2×Dic4316yes—
137C4⋊Q8C2×Dic4316yes—
138#125—212no—
139#125—26no—
140C22⋊Q8—26no—
141C22⋊Q8C22×D4314yes—
142C4×Q8—24no—
143C4×Q8—24no—
144C4×Q8—26no—
145C4×Q8—1724no—
146C4×Q8C2×Dic43112yes—
147C4×Q8C2×Dic4314yes—
148C4×Q8C22⋊D4314yes—
149#117—26no—
150C2×C4⋊C4—863no—
151C2×C4⋊C4—863no—
152C2×C4⋊C4C22⋊D4313yes—
153C2×C42—863no—
154C2×C42C22×D4313yes—
155C4⋊C8—866no—
156C22⋊C8—434no—
157C4×C8—866no—
158#95—431no—
159#95—433no—
160#95—863no—
161C2×Q8—26no—
162C2×Q8#1062188414yes—
163C2×Q8#1062188514yes—
164C2×Q8C22⋊Dic4314yes—
165C2×Q8C22×Dic4314yes—
166C22×C4—861no—
167C22×C4—863no—
168C22×C4C2×C22⋊D4313yes—
169C22×C4C2×C22⋊D4313yes—
170C22×C4C23×D4311yescharacteristic
171C2×C8—864no—
172C4⋊C4—26no—
173C4⋊C4—26no—
174C4⋊C4—26no—
175C4⋊C4—212no—
176C4⋊C4—24no—
177C4⋊C4—1726no—
178C4⋊C4—1726no—
179C4⋊C4C22⋊Dic43112yes—
180C4⋊C4C22×Dic4314yes—
181C22⋊C4—24no—
182C42—212no—
183C42—1726no—
184C42C22×Dic4316yes—
185C42C2×C22⋊D4316yes—
186C23C22×C22⋊D4311yescharacteristic
187Q8—44no—
188Q8—86no—
189Q8#13063249116yes—
190C2×C4—24no—
191C2×C4—24no—
192C2×C4—43no—
193C2×C4—41no—
194C2×C4—862no—
195C2×C4—1723no—
196C2×C4—1723no—
197C2×C4—1723no—
198C2×C4—1721no—
199C2×C4—1721no—
200C2×C4C2×C22⋊Dic4316yes—
201C2×C4C2×C22⋊Dic4316yes—
202C2×C4C2×#1062188416yes—
203C2×C4C2×#1062188516yes—
204C2×C4C23×Dic4311yescharacteristic
205C2×C4C22×C22⋊D4311yescharacteristic
206C8—1724no—
207C22—21no—
208C22—21no—
209C22C22×C22⋊Dic4311yescharacteristic
210C22C22×#1062188411yescharacteristic
211C22C22×#1062188511yescharacteristic
212C4—21no—
213C4—21no—
214C4—26no—
215C4—44no—
216C4—44no—
217C4—3443no—
218C4—1722no—
219C4C2×#13063249112yes—
220C2—21no—
221C2—21no—
222C2#1914305911yescharacteristic
223C2C22×#1306324911yescharacteristic
224C2#1914314211yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#3502C2
socleC22×C43C22×C22⋊C4
prime radicalC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenter#3502D43
hypocenterC43#17619
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #3502

Complements

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

NH ≅ G/Ntype
14. Q82×C43C4semidirect
16. C43×#557C4semidirect
118. Q82Dic43semidirect
120. #557Dic43semidirect
133. C43#17619semidirect

Maximal subgroups

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

subgroupindex
#191436762
#191375162
#191331592
#191330942
C43×#35022
#1761943