Finite Group Databasebeta

← #25011755

Subgroups — #25011755

Order 11008.

456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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#19143301C211yesmaximal, characteristic
2#19136237C212yesmaximal
3#19134398C212yesmaximal, complemented
4#19132716C211yesmaximal, characteristic, complemented
5C43×#1392C211yesmaximal, characteristic, complemented
6C2×#13063332C2211yescharacteristic
7C22×#10621872C411yescharacteristic, complemented
8#14583406C2211yescharacteristic
9#14582974—22no—
10#14582967—22no—
11#14582925C411yescharacteristic, complemented
12#14582873C2212yes—
13#14582862C411yescharacteristic, complemented
14#14582857—22no—
15#14582857C411yescharacteristic, complemented
16#14582690C414yescomplemented
17#14582687C414yescomplemented
18#14582671—22no—
19C43×#413C2212yes—
20C43×#408C2211yescharacteristic
21C22×C4×D43C2×C411yescharacteristic
22#13063332—42no—
23C2×#10621877C2×C411yescharacteristic
24C2×#10621877D412yes—
25C2×#10621872—21no—
26C2×#10621872—21no—
27C2×#10621872—42no—
28C22×C43⋊C8C2×C411yescharacteristic
29C22×C43⋊C8D412yes—
30#13063306C2×C412yes—
31#13063301—21no—
32#13063296—21no—
33#13063293C2×C412yes—
34C4×C22⋊D43—22no—
35#13063284—22no—
36#13063284C2×C411yescharacteristic
37Dic43⋊C8—22no—
38#13063240—22no—
39#13063240C2×C414yes—
40(C2×D43)⋊C8—22no—
41#13063235—21no—
42#13063235—42no—
43C8×Dic43—21no—
44C8×Dic43—42no—
45C2×#41×C43C2311yescharacteristic
46C2×M16×C43—22no—
47C2×M16×C43C2×C411yescharacteristic
48C22×C8×C43C2×C411yescharacteristic
49#101×C43—22no—
50#100×C43C2×C414yes—
51C22⋊C8×C43—22no—
52C23×D43C4211yescharacteristic
53#41×C43—41no—
54#41×C43—41no—
55C2×Q8×C43#4111yescharacteristic
56C2×D4×C43C22×C412yes—
57C2×D4×C43#4111yescharacteristic
58C22×C4×C43C22×C411yescharacteristic
59C22×C4×C43C2×D412yes—
60C2×C22⋊D43—22no—
61C22×Dic43C4211yescharacteristic
62C2×C4×D43—21no—
63C2×C4×D43—21no—
64C2×C4×D43—41no—
65C2×C4×D43—41no—
66M16×C43—24no—
67M16×C43—42no—
68M16×C43—41no—
69C2×C8×C43—21no—
70C2×C8×C43—21no—
71C2×C8×C43—42no—
72C2×C8×C43—41no—
73C22⋊Dic43—22no—
74C22⋊Dic43—24no—
75C22⋊Dic43C4212yes—
76(C2×D43)⋊C4—22no—
77C4⋊Dic43—21no—
78C4⋊Dic43—42no—
79Dic43⋊C4—22no—
80C4×Dic43—21no—
81C4×Dic43—42no—
82#10621877—41no—
83#10621877—42no—
84C2×C43⋊C8—22no—
85C2×C43⋊C8—22no—
86C2×C43⋊C8—22no—
87C2×C43⋊C8C22⋊C411yescharacteristic
88C2×C43⋊C8C22⋊C412yes—
89C2×C43⋊C8C22⋊C411yescharacteristic
90#10621872—42no—
91#10621872—42no—
92C23×C43C2×C4211yescharacteristic
93C23×C43C4×D412yes—
94C22×D43—21no—
95C22×D43—41no—
96C22×D43—81no—
97Q8×C43—41no—
98D4×C43—42no—
99D4×C43—41no—
100C2×C4×C43—22no—
101C2×C4×C43—21no—
102C2×C4×C43—22no—
103C2×C4×C43—21no—
104C2×C4×C43C2×C22⋊C411yescharacteristic
105C2×C4×C43#11711yescharacteristic
106C2×C4×C43C4×D412yes—
107C22⋊D43—82no—
108C2×Dic43—22no—
109C2×Dic43—21no—
110C2×Dic43—41no—
111C2×Dic43—44no—
112C4×D43—42no—
113C4×D43—41no—
114C4×D43—41no—
115C8×C43—44no—
116C8×C43—41no—
117C8×C43—41no—
118C43⋊C8—21no—
119C43⋊C8—22no—
120C43⋊C8#9912yes—
121#12624—431nomaximal, Sylow
122C22×C43—21no—
123C22×C43—22no—
124C22×C43—41no—
125C22×C43—42no—
126C22×C43C4×C22⋊C411yescharacteristic
127C2×D43—41no—
128C2×D43—41no—
129C2×D43—41no—
130C2×D43—82no—
131C4×C43—22no—
132C4×C43—21no—
133C4×C43C2×#9911yescharacteristic
134C4×C43#41011yescharacteristic
135Dic43—42no—
136Dic43—41no—
137Dic43—84no—
138#2930—431no—
139#2120—432no—
140#1757—432no—
141#1392D4311yescharacteristic, complemented
142#1391—431no—
143C2×C43—21no—
144C2×C43—42no—
145C2×C43—41no—
146C2×C43C4×#9911yescharacteristic
147D43—81no—
148C2×#131—431no—
149C22×M16—431no—
150#525—431no—
151#436—862no—
152#435—862no—
153#424—431no—
154#413C2×D4312yes—
155#410—432no—
156#408C2×D4311yescharacteristic
157#407—431no—
158#405—431no—
159#405—862no—
160#352—434no—
161AΣL(1,𝔽16)—434no—
162#344—862no—
163C43#1262411yescharacteristic, complemented, Sylow
164C2×#41C22×D4311yescharacteristic
165C23×C4—431no—
166#131—1722no—
167C2×M16—22no—
168C2×M16—431no—
169C2×M16—432no—
170C2×M16—861no—
171C2×M16—861no—
172C2×M16—1722no—
173C2×M16C4×D4311yescharacteristic
174C22×C8—431no—
175C22×C8—432no—
176C22×C8C4×D4311yescharacteristic
177#123—432no—
178C22⋊Q8—861no—
179#121—861no—
180#120—432no—
181C4×D4—862no—
182#117—431no—
183#117—862no—
184C4⋊C8—862no—
185#101—22no—
186#100C4×D4314yes—
187#99—434no—
188#99—862no—
189C22⋊C8—22no—
190C22⋊C8—862no—
191#97—861no—
192#97—1722no—
193C4×C8—861no—
194C4×C8—1722no—
195C24—431no—
196#41—41no—
197#41—41no—
198C2×Q8#1062190011yescharacteristic
199C2×D4—862no—
200C2×D4C2×C4×D4312yes—
201C2×D4#1062190211yescharacteristic
202C22×C4—431no—
203C22×C4—861no—
204C22×C4—861no—
205C22×C4—1721no—
206C22×C4—1721no—
207C22×C4C2×C4×D4311yescharacteristic
208C22×C4D4×D4312yes—
209M16—24no—
210M16—42no—
211M16—41no—
212M16—1722no—
213M16—1722no—
214M16—1722no—
215M16—1721no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—42no—
219C2×C8—41no—
220C2×C8—431no—
221C2×C8—431no—
222C2×C8—432no—
223C2×C8—862no—
224C2×C8—862no—
225C2×C8—862no—
226C4⋊C4—861no—
227C4⋊C4—862no—
228C4⋊C4—1722no—
229C22⋊C4—432no—
230C22⋊C4—862no—
231C22⋊C4—862no—
232C22⋊C4—864no—
233C42—861no—
234C42—1722no—
235C23—861no—
236C23—3441no—
237C23—1721no—
238C23C42×D4311yescharacteristic
239C23#1306328712yes—
240Q8—41no—
241D4—42no—
242D4—41no—
243D4—3442no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—862no—
249C2×C4—861no—
250C2×C4—1722no—
251C2×C4—1724no—
252C2×C4—1721no—
253C2×C4—1721no—
254C2×C4—1721no—
255C2×C4C22⋊C4×D4311yescharacteristic
256C2×C4#1306328311yescharacteristic
257C2×C4(C22⋊D43)⋊C412yes—
258C8—44no—
259C8—41no—
260C8—41no—
261C8—432no—
262C8—861no—
263C8—862no—
264C22—22no—
265C22—21no—
266C22—42no—
267C22—41no—
268C22—3442no—
269C22—1721no—
270C22—1721no—
271C22—1721no—
272C22#1458274611yescharacteristic
273C4—22no—
274C4—21no—
275C4—3444no—
276C4—1722no—
277C4—1721no—
278C4#99×D4311yescharacteristic
279C4#1458287111yescharacteristic
280C2—21no—
281C2—42no—
282C2—41no—
283C2—3441no—
284C2#1913438211yescharacteristic
subgroupG/H
centerC4#99×D43
commutatorC23×C43C2×C42
FrattiniC2×#41C22×D43
FittingC43×#1392C2
socleC2×C43C4×#99
prime radical#14583406C22
cosocleC2×#41×C43C23
hypercenter#1392D43
hypocenterC43#12624
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1392

Complements

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

NH ≅ G/Ntype
3. #19134398C2semidirect
4. #19132716C2semidirect
5. C43×#1392C2semidirect
7. C22×#10621872C4semidirect
11. #14582925C4semidirect
13. #14582862C4semidirect
15. #14582857C4semidirect
16. #14582690C4semidirect
17. #14582687C4semidirect
141. #1392D43semidirect
163. C43#12624semidirect

Maximal subgroups

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

subgroupindex
#191433012
#191362372
#191343982
#191327162
C43×#13922
#1262443