Finite Group Databasebeta

← #25104807

Subgroups — #25104807

Order 11008.

786 conjugacy classes of subgroups; only the 283 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 283 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
1C4×#13063319C211yesmaximal, characteristic
2#19135199C213yesmaximal
3#19135150C213yesmaximal, complemented
4#19134456C213yesmaximal, complemented
5#19134365C213yesmaximal
6C42×C43⋊C8C211yesmaximal, characteristic, complemented
7C43×#1839C211yesmaximal, characteristic, complemented
8C22×C8×D43C2211yescharacteristic
9C2×#13063319C411yescharacteristic
10C2×Dic43⋊C8C2213yes—
11C2×(C2×D43)⋊C8C2213yes—
12C2×C4×C43⋊C8C2213yes—
13C2×C4×C43⋊C8C2213yes—
14C2×C8×Dic43C2213yes—
15#14582790C413yes—
16#14582783C413yes—
17#14582767C411yescharacteristic
18C4×Dic43⋊C4C2213yes—
19C4×(C2×D43)⋊C4C2213yes—
20#14582653C2213yes—
21#14582653C2213yes—
22C43×C43C2211yescharacteristic
23C43×#336C2213yes—
24C43×#336C2213yes—
25C22×C4×D43C2311yescharacteristic
26C22×C43⋊C8C2313yes—
27C22×C43⋊C8C2311yescharacteristic
28C2×C8×D43—26no—
29#13063319C818yescomplemented
30C2×Dic43⋊C4C2×C413yes—
31C2×Dic43⋊C4C2×C413yes—
32C2×(C2×D43)⋊C4C2×C413yes—
33C2×(C2×D43)⋊C4C2×C413yes—
34C2×C4×Dic43C2313yes—
35Dic43⋊C8—26no—
36(C2×D43)⋊C8—26no—
37C4×C43⋊C8—26no—
38C4×C43⋊C8—26no—
39C8×Dic43—26no—
40C43⋊#95C2×C413yes—
41C43⋊#95C2×C413yes—
42C43⋊#95C2×C413yes—
43C43⋊#95C2×C413yes—
44C22×C8×C43C2313yes—
45C22×C8×C43C2311yescharacteristic
46C2×C42×C43C2×C413yes—
47C2×C42×C43C2×C411yescharacteristic
48C2×C42×C43C2313yes—
49C23×D43C22×C411yescharacteristic
50C22×C4×C43C22×C413yes—
51C22×C4×C43C22×C413yes—
52C22×C4×C43C2411yescharacteristic
53C22×Dic43C22×C411yescharacteristic
54C22×Dic43C22×C413yes—
55C22×Dic43C22×C413yes—
56C2×C4×D43—23no—
57C2×C4×D43—23no—
58C2×C8×C43—23no—
59C2×C8×C43—23no—
60C2×C8×C43—23no—
61C2×C8×C43—23no—
62C42×C43—26no—
63C42×C43—23no—
64C42×C43—23no—
65C42×C43C2×C814yescomplemented
66(C2×D43)⋊C4—26no—
67(C2×D43)⋊C4C2×C8112yes—
68Dic43⋊C4—26no—
69Dic43⋊C4C2×C8112yescomplemented
70C4×Dic43—23no—
71C4×Dic43—23no—
72C2×C43⋊C8—23no—
73C2×C43⋊C8—23no—
74C2×C43⋊C8#4116yes—
75C2×C43⋊C8#4116yes—
76C8×D43—44no—
77C23×C43C23×C411yescharacteristic
78C22×D43—23no—
79C22×D43—23no—
80C22×D43C22×C812yes—
81C2×C4×C43—23no—
82C2×C4×C43—23no—
83C2×C4×C43—23no—
84C2×C4×C43—23no—
85C2×C4×C43C22×C816yes—
86C2×C4×C43#13116yes—
87C2×C4×C43C2×#4113yes—
88C2×C4×C43C2×#4113yes—
89C2×Dic43—23no—
90C2×Dic43—23no—
91C2×Dic43—23no—
92C2×Dic43—23no—
93C2×Dic43—23no—
94C2×Dic43—23no—
95C2×Dic43C22×C816yes—
96C4×D43—41no—
97C4×D43—43no—
98C8×C43—41no—
99C8×C43—43no—
100C43⋊C8—26no—
101C43⋊C8#12614yescomplemented
102C8×#126—431nomaximal, Sylow
103C22×C43C4×#4113yes—
104C22×C43C23×C811yescharacteristic
105C22×C43C2×#13113yes—
106C2×D43—26no—
107C2×D43—41no—
108C2×D43—43no—
109C4×C43—26no—
110C4×C43—26no—
111C4×C43C2×#12611yescharacteristic
112C4×C43#52913yes—
113Dic43—26no—
114Dic43—41no—
115Dic43—43no—
116C4×#126—431no—
117#1923—433no—
118#1916—433no—
119#1839D4311yescharacteristic, complemented
120C8×C4⋊C4—433no—
121C8×C22⋊C4—433no—
122C42×C8—431no—
123C2×C43C4×#12611yescharacteristic
124C2×C43C8×#4113yes—
125C2×C43#296613yes—
126D43—42no—
127C23×C8—431no—
128C2×#126—431no—
129C2×C4⋊C8—433no—
130C2×C22⋊C8—433no—
131C2×C4×C8—433no—
132C2×C4×C8—433no—
133C2×C4×C8—433no—
134#388—433no—
135#387—433no—
136#383—431no—
137C4×C4⋊C4—433no—
138C4×C22⋊C4—433no—
139C43C2×D4311yescharacteristic
140#336—433no—
141#336—433no—
142#336C2×D4313yes—
143#336C2×D4313yes—
144C43C8×#12611yescharacteristic, complemented, Sylow
145C23×C4—431no—
146C22×C8—431no—
147C22×C8—433no—
148C22×C8—866no—
149C22×C8C22×D4311yescharacteristic
150C22×C8C22×D4313yes—
151#126—438no—
152C2×C4⋊C4—433no—
153C2×C4⋊C4—433no—
154C2×C22⋊C4—433no—
155C2×C22⋊C4—433no—
156C2×C42—433no—
157C2×C42C4×D4313yes—
158C2×C42C4×D4311yescharacteristic
159C2×C42C22×D4313yes—
160C4⋊C8—866no—
161C22⋊C8—866no—
162C4×C8—866no—
163C4×C8—866no—
164C4×C8—866no—
165#95—433no—
166#95—433no—
167#95—433no—
168#95—433no—
169C24—431no—
170C22×C4—433no—
171C22×C4—431no—
172C22×C4—433no—
173C22×C4—863no—
174C22×C4—863no—
175C22×C4C2×C4×D4313yes—
176C22×C4C2×C4×D4313yes—
177C22×C4C23×D4311yescharacteristic
178C2×C8—23no—
179C2×C8—23no—
180C2×C8—23no—
181C2×C8—23no—
182C2×C8—436no—
183C2×C8—436no—
184C2×C8—863no—
185C2×C8—863no—
186C2×C8—1724no—
187C4⋊C4—4312no—
188C4⋊C4—866no—
189C22⋊C4—4312no—
190C22⋊C4—866no—
191C42—26no—
192C42—23no—
193C42—23no—
194C42—863no—
195C42—863no—
196C42C8×D4314yescomplemented
197C23—432no—
198C23—863no—
199C23—863no—
200C23C22×C4×D4311yescharacteristic
201C2×C4—23no—
202C2×C4—23no—
203C2×C4—23no—
204C2×C4—23no—
205C2×C4—436no—
206C2×C4—863no—
207C2×C4—863no—
208C2×C4—863no—
209C2×C4—863no—
210C2×C4—863no—
211C2×C4—863no—
212C2×C4—1721no—
213C2×C4—1723no—
214C2×C4C2×C8×D4316yes—
215C2×C4#1306333316yes—
216C2×C4#41×D4313yes—
217C2×C4#41×D4313yes—
218C8—41no—
219C8—43no—
220C8—434no—
221C8—866no—
222C22—866no—
223C22—1721no—
224C22—1723no—
225C22#1458336713yes—
226C22C22×C8×D4311yescharacteristic
227C22C2×#1306333313yes—
228C4—26no—
229C4—26no—
230C4—866no—
231C4—1721no—
232C4—1723no—
233C4#126×D4311yescharacteristic
234C4#1458343213yes—
235C2—1722no—
236C2#1913714311yescharacteristic
237C2#1914355113yes—
238C2#1914356413yes—
subgroupG/H
center, FrattiniC22×C4C23×D43
commutatorC22×C43C23×C8
FittingC43×#1839C2
socleC23×C43C23×C4
prime radicalC23×D43C22×C4
cosocleC22×C4×C43C24
hypercenter#1839D43
hypocenterC43C8×#126
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1839

Complements

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

NH ≅ G/Ntype
3. #19135150C2semidirect
4. #19134456C2semidirect
6. C42×C43⋊C8C2semidirect
7. C43×#1839C2semidirect
29. #13063319C8semidirect
65. C42×C43C2×C8semidirect
69. Dic43⋊C4C2×C8semidirect
101. C43⋊C8#126semidirect
119. #1839D43semidirect
144. C43C8×#126semidirect
196. C42C8×D43semidirect

Maximal subgroups

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

subgroupindex
C4×#130633192
#191351992
#191351502
#191344562
#191343652
C42×C43⋊C82
C43×#18392
C8×#12643