Finite Group Databasebeta

← #25124013

Subgroups — #25124013

Order 11008.

1178 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 209 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#19147997C211yesmaximal, characteristic
2#19137180C213yesmaximal
3#19135763C213yesmaximal
4#19135762C213yesmaximal
5#19135761C211yesmaximal, characteristic
6#19134326C213yesmaximal
7C43×#2030C211yesmaximal, characteristic
8C23×Dic86C2211yescharacteristic
9#14583528—26no—
10#14583525C2213yes—
11#14583451—26no—
12C2×#13063281C2213yes—
13C2×#13063281C2213yes—
14#14582803—26no—
15#14582803—26no—
16#14582762C2213yes—
17#14582760C2213yes—
18#14582760C2213yes—
19#14582666C2213yes—
20#14582665C2216yes—
21C43×#543C2211yescharacteristic
22C43×#381C2213yes—
23C43×#342C2213yes—
24C22×Dic86—23no—
25C22×Dic86—23no—
26C22×Dic86—26no—
27C22×Dic86Q814yescomplemented
28C23×Dic43C2311yescharacteristic
29C23×Dic43C2311yescharacteristic
30#13063324—26no—
31#13063323—26no—
32#13063315—212no—
33#13063304—26no—
34#13063302—212no—
35Q8×Dic43—22no—
36#13063290—26no—
37#13063281—26no—
38#13063281—26no—
39#13063281—212no—
40C2×Dic43⋊C4—23no—
41C2×Dic43⋊C4D416yes—
42C2×C22⋊Dic43C2313yes—
43C2×C22⋊Dic43C2313yes—
44C2×C4×Dic43—23no—
45C2×C4×Dic43D416yes—
46C43⋊#95—26no—
47C43⋊#95—26no—
48C43⋊#95—26no—
49C23×C4×C43C2311yescharacteristic
50C22⋊Q8×C43—26no—
51C2×C22⋊C4×C43C2313yes—
52C2×C22⋊C4×C43C2313yes—
53#95×C43—26no—
54C24×C43C2411yescharacteristic
55C2×Q8×C43—22no—
56C22×C4×C43—23no—
57C22×C4×C43—23no—
58C22×C4×C43—23no—
59C22×C4×C43C2×D416yes—
60C22×C4×C43C2×Q812yes—
61C22×Dic43—23no—
62C22×Dic43—23no—
63C22×Dic43—23no—
64C22×Dic43C2×D416yes—
65C22×Dic43C2×D413yes—
66C22×Dic43C2×D413yes—
67C22×Dic43C2×Q812yes—
68C22×Dic43C2×Q812yes—
69C22×Dic43#4116yes—
70C2×Dic86—212no—
71C2×Dic86—212no—
72C2×Dic86—26no—
73C2×Dic86—41no—
74C2×Dic86—43no—
75C2×Dic86—46no—
76C2×Dic86—46no—
77C4⋊C4×C43—26no—
78C22⋊C4×C43—26no—
79C22⋊C4×C43—26no—
80C22⋊Dic43—26no—
81C22⋊Dic43—26no—
82C4⋊Dic43—26no—
83Dic43⋊C4—212no—
84Dic43⋊C4—212no—
85Dic43⋊C4—46no—
86C4×Dic43—26no—
87C4×Dic43—26no—
88C4×Dic43—46no—
89C23×C43—42no—
90C23×C43C22×D413yes—
91C23×C43C22×Q811yescharacteristic
92C23×C43C2×#4113yes—
93Q8×C43—82no—
94C2×C4×C43—26no—
95C2×C4×C43—26no—
96C2×C4×C43—41no—
97C2×C4×C43—43no—
98C2×C4×C43—46no—
99C2×C4×C43—46no—
100C2×C4×C43—43no—
101C2×Dic43—26no—
102C2×Dic43—26no—
103C2×Dic43—41no—
104C2×Dic43—43no—
105C2×Dic43—46no—
106C2×Dic43—46no—
107C2×Dic43—43no—
108C2×Dic43#12011yescharacteristic
109C2×Dic43#12013yes—
110C2×Dic43C22⋊Q816yes—
111C2×Dic43C22⋊Q816yes—
112C2×Dic43#12416yes—
113C2×Dic43#12416yes—
114Dic86—44no—
115Dic86—412no—
116Dic86—86no—
117#23470—431nomaximal, Sylow
118C22×C43—26no—
119C22×C43—41no—
120C22×C43—43no—
121C22×C43C2×#12011yescharacteristic
122C22×C43C2×C22⋊Q813yes—
123C22×C43C2×#12413yes—
124C4×C43—42no—
125C4×C43—46no—
126C4×C43—83no—
127Dic43—42no—
128Dic43—46no—
129Dic43—83no—
130Dic43#39312yes—
131Dic43#39316yes—
132#3458—431no—
133#2310—433no—
134#2030—433no—
135#2030—433no—
136#2030—431no—
137#2030D4311yescharacteristic
138#1740—433no—
139C2×C43—23no—
140C2×C43—23no—
141C2×C43C2×#39311yescharacteristic
142C2×C43#302812yes—
143C23×Q8—431no—
144#544—866no—
145#543—433no—
146#543C2×D4311yescharacteristic
147#533—866no—
148C2×#117—433no—
149C2×#117—433no—
150#391—866no—
151#391—866no—
152#381—433no—
153#381—433no—
154#381—433no—
155#381C2×D4313yes—
156#342—436no—
157#342—433no—
158#342C2×D4313yes—
159C43#2347011yescharacteristic, complemented, Sylow
160C22×Q8—434no—
161C22×Q8—863no—
162C22×Q8—863no—
163C22×Q8—866no—
164C23×C4—431no—
165C23×C4—431no—
166C23×C4C22×D4311yescharacteristic
167C4⋊Q8—866no—
168C4⋊Q8—866no—
169#125—8612no—
170C22⋊Q8—26no—
171C22⋊Q8—8612no—
172C22⋊Q8—866no—
173C4×Q8—866no—
174C4×Q8—862no—
175#117—866no—
176#117—866no—
177#117—8612no—
178C2×C4⋊C4—436no—
179C2×C4⋊C4—863no—
180C2×C22⋊C4—433no—
181C2×C22⋊C4—433no—
182C2×C22⋊C4C22×D4313yes—
183C2×C22⋊C4C22×D4313yes—
184C2×C42—436no—
185C2×C42—863no—
186#95—26no—
187#95—866no—
188#95—866no—
189#95—866no—
190C24C23×D4311yescharacteristic
191C2×Q8—22no—
192C2×Q8—8612no—
193C2×Q8—8612no—
194C2×Q8—866no—
195C2×Q8—1721no—
196C2×Q8—1723no—
197C2×Q8—1726no—
198C2×Q8—1726no—
199C22×C4—23no—
200C22×C4—23no—
201C22×C4—23no—
202C22×C4—433no—
203C22×C4—433no—
204C22×C4—432no—
205C22×C4—436no—
206C22×C4—432no—
207C22×C4—436no—
208C22×C4—863no—
209C22×C4—863no—
210C22×C4—863no—
211C22×C4D4×D4316yes—
212C22×C4Q8×D4312yes—
213C4⋊C4—26no—
214C4⋊C4—8612no—
215C4⋊C4—8612no—
216C4⋊C4—866no—
217C4⋊C4—1726no—
218C22⋊C4—26no—
219C22⋊C4—26no—
220C22⋊C4—866no—
221C22⋊C4—866no—
222C42—866no—
223C42—866no—
224C42—1726no—
225C23—42no—
226C23C2×D4×D4313yes—
227C23C2×Q8×D4311yescharacteristic
228C23#41×D4313yes—
229Q8—82no—
230Q8—3446no—
231Q8—1724no—
232Q8—17212no—
233C2×C4—26no—
234C2×C4—26no—
235C2×C4—41no—
236C2×C4—43no—
237C2×C4—46no—
238C2×C4—46no—
239C2×C4—43no—
240C2×C4—431no—
241C2×C4—433no—
242C2×C4—436no—
243C2×C4—436no—
244C2×C4—436no—
245C2×C4—436no—
246C2×C4—866no—
247C2×C4—866no—
248C2×C4—1726no—
249C2×C4—1723no—
250C2×C4—1721no—
251C2×C4—1723no—
252C2×C4—1726no—
253C22—26no—
254C22—41no—
255C22—43no—
256C22#120×D4311yescharacteristic
257C22C22⋊Q8×D4313yes—
258C22#124×D4313yes—
259C4—42no—
260C4—46no—
261C4—83no—
262C4—432no—
263C4—436no—
264C4—3443no—
265C4—1722no—
266C4—1726no—
267C2—23no—
268C2—23no—
269C2#393×D4311yescharacteristic
270C2#1914399912yes—
subgroupG/H
centerC22#120×D43
commutator, prime radical, cosocleC24×C43C24
FrattiniC24C23×D43
FittingC43×#2030C2
socleC22×C43C2×#120
hypercenter#2030D43
hypocenterC43#23470
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ #2030

Complements

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

NH ≅ G/Ntype
27. C22×Dic86Q8semidirect
159. C43#23470semidirect

Maximal subgroups

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

subgroupindex
#191479972
#191371802
#191357632
#191357622
#191357612
#191343262
C43×#20302
#2347043