Finite Group Databasebeta

← #25123999

Subgroups — #25123999

Order 11008.

1378 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 1378 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, complemented
2#19136973C213yesmaximal
3#19135763C213yesmaximal, complemented
4#19135761C211yesmaximal, characteristic, complemented
5#19135759C213yesmaximal
6#19134326C213yesmaximal, complemented
7C43×#2029C211yesmaximal, characteristic
8C24×Dic43C2211yescharacteristic
9#14583528—26no—
10#14583525C2213yes—
11#14583451—26no—
12C2×#13063281C2213yes—
13C2×#13063281C2213yes—
14#14582760C2213yes—
15#14582760C2213yes—
16#14582757—26no—
17#14582755C2213yes—
18C22⋊C4×Dic43—26no—
19#14582666C2213yes—
20#14582665C2216yes—
21C43×#543C2211yescharacteristic
22C43×#379C2213yes—
23C43×#342C2213yes—
24C23×Dic43—23no—
25C23×Dic43—23no—
26C23×Dic43—26no—
27C23×Dic43Q814yescomplemented
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⋊Dic43—26no—
43C2×C22⋊Dic43C2313yes—
44C2×C22⋊Dic43C2313yes—
45C2×C4×Dic43—23no—
46C2×C4×Dic43D416yes—
47C43⋊#95—26no—
48C43⋊#95—26no—
49C25×C43C2311yescharacteristic
50C22⋊Q8×C43—26no—
51C2×C22⋊C4×C43—26no—
52C2×C22⋊C4×C43C2313yes—
53C2×C22⋊C4×C43C2313yes—
54C24×C43—23no—
55C24×C43—23no—
56C24×C43—44no—
57C24×C43C2×Q812yes—
58C24×C43C2411yescharacteristic
59C2×Q8×C43—22no—
60C22×C4×C43—23no—
61C22×C4×C43C2×D416yes—
62C22×Dic43—212no—
63C22×Dic43—212no—
64C22×Dic43—23no—
65C22×Dic43—23no—
66C22×Dic43—23no—
67C22×Dic43—41no—
68C22×Dic43—43no—
69C22×Dic43—46no—
70C22×Dic43—46no—
71C22×Dic43C2×D416yes—
72C22×Dic43C2×D413yes—
73C22×Dic43C2×D413yes—
74C22×Dic43C2×Q812yes—
75C22×Dic43C2×Q812yes—
76C22×Dic43#4116yes—
77C2×Dic86—26no—
78C4⋊C4×C43—26no—
79C22⋊C4×C43—26no—
80C22⋊C4×C43—26no—
81C22⋊C4×C43—412no—
82C22⋊Dic43—26no—
83C22⋊Dic43—26no—
84C22⋊Dic43—412no—
85C4⋊Dic43—26no—
86Dic43⋊C4—212no—
87Dic43⋊C4—212no—
88Dic43⋊C4—46no—
89C4×Dic43—26no—
90C4×Dic43—26no—
91C4×Dic43—46no—
92C23×C43—212no—
93C23×C43—26no—
94C23×C43—44no—
95C23×C43—42no—
96C23×C43—46no—
97C23×C43—412no—
98C23×C43—41no—
99C23×C43—43no—
100C23×C43C22×D413yes—
101C23×C43C22×Q811yescharacteristic
102C23×C43C2×#4113yes—
103Q8×C43—82no—
104C2×C4×C43—26no—
105C2×C4×C43—46no—
106C2×C4×C43—46no—
107C2×C4×C43—43no—
108C2×Dic43—26no—
109C2×Dic43—26no—
110C2×Dic43—41no—
111C2×Dic43—43no—
112C2×Dic43—44no—
113C2×Dic43—412no—
114C2×Dic43—46no—
115C2×Dic43—46no—
116C2×Dic43—43no—
117C2×Dic43#12011yescharacteristic
118C2×Dic43#12013yes—
119C2×Dic43C22⋊Q816yes—
120C2×Dic43C22⋊Q816yes—
121C2×Dic43#12416yes—
122C2×Dic43#12416yes—
123Dic86—86no—
124#23467—431nomaximal, Sylow
125C22×C43—26no—
126C22×C43—212no—
127C22×C43—41no—
128C22×C43—43no—
129C22×C43—412no—
130C22×C43—46no—
131C22×C43—42no—
132C22×C43—44no—
133C22×C43C2×#12011yescharacteristic
134C22×C43C2×C22⋊Q813yes—
135C22×C43C2×#12413yes—
136C4×C43—46no—
137C4×C43—83no—
138Dic43—42no—
139Dic43—46no—
140Dic43—83no—
141Dic43#39312yes—
142Dic43#39316yes—
143#3458—431no—
144#2280—433no—
145#2030—433no—
146#2030—431no—
147#2029—433no—
148#2029D4311yescharacteristic
149#1740—433no—
150C2×C43—23no—
151C2×C43—23no—
152C2×C43—44no—
153C2×C43C2×#39311yescharacteristic
154C2×C43#302512yes—
155C24×C4—431no—
156#544—866no—
157#543—433no—
158#543C2×D4311yescharacteristic
159#533—866no—
160C2×#117—433no—
161C2×#117—433no—
162#381—433no—
163#381—433no—
164#380—866no—
165#379—433no—
166#379C2×D4313yes—
167C4×C22⋊C4—866no—
168#342—436no—
169#342—433no—
170#342C2×D4313yes—
171C43#2346711yescharacteristic, complemented, Sylow
172C25C22×D4311yescharacteristic
173C23×C4—431no—
174C23×C4—434no—
175C23×C4—431no—
176C23×C4—863no—
177C23×C4—863no—
178C23×C4—866no—
179C4⋊Q8—866no—
180C4⋊Q8—866no—
181#125—8612no—
182C22⋊Q8—26no—
183C22⋊Q8—8612no—
184C22⋊Q8—866no—
185C4×Q8—866no—
186C4×Q8—862no—
187#117—866no—
188#117—866no—
189#117—8612no—
190C2×C4⋊C4—436no—
191C2×C4⋊C4—863no—
192C2×C22⋊C4—26no—
193C2×C22⋊C4—433no—
194C2×C22⋊C4—433no—
195C2×C22⋊C4—866no—
196C2×C22⋊C4C22×D4313yes—
197C2×C22⋊C4C22×D4313yes—
198C2×C42—436no—
199C2×C42—863no—
200#95—866no—
201#95—866no—
202C24—23no—
203C24—23no—
204C24—44no—
205C24Q8×D4312yes—
206C24C23×D4311yescharacteristic
207C2×Q8—22no—
208C2×Q8—866no—
209C22×C4—23no—
210C22×C4—433no—
211C22×C4—433no—
212C22×C4—432no—
213C22×C4—436no—
214C22×C4—432no—
215C22×C4—436no—
216C22×C4—8612no—
217C22×C4—8612no—
218C22×C4—863no—
219C22×C4—863no—
220C22×C4—863no—
221C22×C4—1721no—
222C22×C4—1723no—
223C22×C4—1726no—
224C22×C4—1726no—
225C22×C4D4×D4316yes—
226C4⋊C4—26no—
227C4⋊C4—8612no—
228C4⋊C4—8612no—
229C4⋊C4—866no—
230C4⋊C4—1726no—
231C22⋊C4—26no—
232C22⋊C4—26no—
233C22⋊C4—412no—
234C22⋊C4—866no—
235C22⋊C4—866no—
236C22⋊C4—17212no—
237C42—866no—
238C42—866no—
239C42—1726no—
240C23—212no—
241C23—26no—
242C23—44no—
243C23—42no—
244C23—46no—
245C23—412no—
246C23—41no—
247C23—43no—
248C23C2×D4×D4313yes—
249C23C2×Q8×D4311yescharacteristic
250C23#41×D4313yes—
251Q8—82no—
252Q8—3446no—
253C2×C4—26no—
254C2×C4—46no—
255C2×C4—46no—
256C2×C4—43no—
257C2×C4—431no—
258C2×C4—433no—
259C2×C4—436no—
260C2×C4—436no—
261C2×C4—436no—
262C2×C4—436no—
263C2×C4—866no—
264C2×C4—866no—
265C2×C4—1724no—
266C2×C4—17212no—
267C2×C4—1726no—
268C2×C4—1723no—
269C2×C4—1721no—
270C2×C4—1723no—
271C2×C4—1726no—
272C22—26no—
273C22—212no—
274C22—41no—
275C22—43no—
276C22—412no—
277C22—46no—
278C22—42no—
279C22—44no—
280C22#120×D4311yescharacteristic
281C22C22⋊Q8×D4313yes—
282C22#124×D4313yes—
283C4—46no—
284C4—83no—
285C4—432no—
286C4—436no—
287C4—3443no—
288C4—1722no—
289C4—1726no—
290C2—23no—
291C2—23no—
292C2—44no—
293C2#393×D4311yescharacteristic
294C2#1914398512yes—
subgroupG/H
centerC22#120×D43
commutator, cosocleC24×C43C24
FrattiniC24C23×D43
FittingC43×#2029C2
socleC22×C43C2×#120
prime radicalC25×C43C23
hypercenter#2029D43
hypocenterC43#23467
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ #2029

Complements

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

NH ≅ G/Ntype
1. #19147997C2semidirect
3. #19135763C2semidirect
4. #19135761C2semidirect
6. #19134326C2semidirect
27. C23×Dic43Q8semidirect
171. C43#23467semidirect

Maximal subgroups

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

subgroupindex
#191479972
#191369732
#191357632
#191357612
#191357592
#191343262
C43×#20292
#2346743