Finite Group Databasebeta

← #24987589

Subgroups — #24987589

Order 11008.

510 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 121 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#19143285C211yesmaximal, characteristic
2#19134374C212yesmaximal, complemented
3#19133087C212yesmaximal
4#19132480C211yesmaximal, characteristic, complemented
5C43×#1298C211yesmaximal, characteristic, complemented
6C2×#13063333C411yescharacteristic, complemented
7C23×C43⋊C8C2211yescharacteristic
8#14583410C2211yescharacteristic
9#14582967—22no—
10(C22⋊D43)⋊C8—22no—
11#14582927C411yescharacteristic, complemented
12#14582867C411yescharacteristic, complemented
13#14582857C411yescharacteristic, complemented
14C2×#13063235—22no—
15C4×C22⋊Dic43C2212yes—
16#14582653—22no—
17#14582637C414yescomplemented
18#14582634C414yescomplemented
19C43×#407C2211yescharacteristic
20C2×C22⋊C8×C43C2212yes—
21C2×#10621898C2×C411yescharacteristic
22#13063333—42no—
23C2×#10621872—21no—
24C22×C43⋊C8—42no—
25C22×C43⋊C8C2×C411yescharacteristic
26C22×C43⋊C8C2×C411yescharacteristic
27C22×C43⋊C8D412yes—
28C22×C43⋊C8D412yes—
29C2×C8×D43—21no—
30#13063308—21no—
31#13063304C2×C412yes—
32#13063299C2×C412yes—
33#13063294—21no—
34C4×C22⋊D43—22no—
35#13063284C2×C411yescharacteristic
36C2×C22⋊Dic43—22no—
37C2×C4×Dic43—22no—
38Dic43⋊C8—22no—
39(C2×D43)⋊C8—22no—
40#13063235—21no—
41#13063235—44no—
42C8×Dic43—21no—
43C43⋊#95C2×C414yes—
44C23×C4×C43C2311yescharacteristic
45C2×M16×C43C2×C411yescharacteristic
46C2×M16×C43C2×C411yescharacteristic
47C22×C8×C43—22no—
48C22⋊C8×C43—22no—
49C22⋊C8×C43—22no—
50C22⋊C8×C43C2×C414yes—
51C24×C43#4111yescharacteristic
52C22×C4×C43—41no—
53C22×C4×C43—41no—
54C22×C4×C43C22×C411yescharacteristic
55C22×C4×C43C22×C412yes—
56C22×C4×C43C2×D412yes—
57C22×C4×C43#4111yescharacteristic
58C2×C22⋊D43—21no—
59C2×C22⋊D43—22no—
60C22×Dic43—24no—
61#10621898—41no—
62#10621898—41no—
63C2×D172C4211yescharacteristic
64C2×C4×D43—21no—
65C2×Dic86C4211yescharacteristic
66M16×C43—41no—
67M16×C43—41no—
68C2×C8×C43—21no—
69C2×C8×C43—21no—
70C2×C8×C43—24no—
71C2×C8×C43—42no—
72C2×C8×C43—42no—
73C22⋊Dic43—21no—
74C22⋊Dic43—22no—
75C22⋊Dic43—44no—
76(C2×D43)⋊C4—22no—
77C4⋊Dic43C4212yes—
78Dic43⋊C4—22no—
79C4×Dic43—21no—
80C4×Dic43—42no—
81C4×Dic43—42no—
82C2×C43⋊C8—24no—
83C2×C43⋊C8—22no—
84C2×C43⋊C8—41no—
85C2×C43⋊C8—42no—
86C2×C43⋊C8C22⋊C411yescharacteristic
87C2×C43⋊C8C22⋊C412yes—
88C2×C43⋊C8C22⋊C411yescharacteristic
89#10621872—42no—
90C8×D43—42no—
91C23×C43—24no—
92C23×C43—41no—
93C23×C43#11711yescharacteristic
94C23×C43C4×D412yes—
95C22×D43—21no—
96C2×C4×C43—22no—
97C2×C4×C43—21no—
98C2×C4×C43—22no—
99C2×C4×C43—21no—
100C2×C4×C43—42no—
101C2×C4×C43—41no—
102C2×C4×C43C2×C4211yescharacteristic
103C2×C4×C43C2×C22⋊C411yescharacteristic
104C2×C4×C43C4×D412yes—
105C22⋊D43—42no—
106C22⋊D43—44no—
107C2×Dic43—22no—
108C2×Dic43—21no—
109C2×Dic43—44no—
110C2×Dic43—44no—
111C2×Dic43—44no—
112D172—41no—
113C4×D43—41no—
114C4×D43—41no—
115Dic86—41no—
116C8×C43—44no—
117C8×C43—41no—
118C8×C43—41no—
119C43⋊C8—21no—
120C43⋊C8—22no—
121C43⋊C8#9912yes—
122#8239—431nomaximal, Sylow
123C22×C43—22no—
124C22×C43—22no—
125C22×C43—21no—
126C22×C43—22no—
127C22×C43—44no—
128C22×C43C4×C22⋊C411yescharacteristic
129C22×C43#44414yes—
130C2×D43—41no—
131C2×D43—42no—
132C4×C43—22no—
133C4×C43—21no—
134C4×C43C2×#9911yescharacteristic
135C4×C43#41011yescharacteristic
136Dic43—41no—
137Dic43—42no—
138Dic43—84no—
139#2929—431no—
140#1752—432no—
141#1501—432no—
142#1298D4311yescharacteristic, complemented
143#1297—431no—
144C2×C43—24no—
145C2×C43—41no—
146C2×C43C4×#9911yescharacteristic
147C2×C43#176512yes—
148D43—81no—
149C2×#131—431no—
150C23×C8—431no—
151#525—431no—
152#435—862no—
153C8×D4—862no—
154#424—431no—
155#408—431no—
156#407C2×D4311yescharacteristic
157C2×C22⋊C8C2×D4312yes—
158#405—431no—
159C2×#97—862no—
160C4×C22⋊C4—432no—
161#336—862no—
162#328—434no—
163#327—434no—
164C43#823911yescharacteristic, complemented, Sylow
165C2×#41—431no—
166C23×C4C22×D4311yescharacteristic
167#131—1722no—
168C2×M16—861no—
169C2×M16C4×D4311yescharacteristic
170C2×M16C4×D4311yescharacteristic
171C22×C8—22no—
172C22×C8—431no—
173C22×C8—432no—
174C22×C8—431no—
175C22×C8—432no—
176C22×C8—861no—
177C22×C8—1722no—
178#123—861no—
179C22⋊Q8—432no—
180#121—432no—
181#120—861no—
182C4×D4—862no—
183#117—431no—
184C2×C22⋊C4—862no—
185C2×C42—862no—
186C4⋊C8—862no—
187C22⋊C8—22no—
188C22⋊C8—22no—
189C22⋊C8—862no—
190C22⋊C8C4×D4314yes—
191#97—861no—
192#97—1724no—
193C4×C8—861no—
194#95—434no—
195C24#1062190211yescharacteristic
196#41—1721no—
197#41—1721no—
198C2×Q8—431no—
199C2×D4—431no—
200C2×D4—861no—
201C2×D4—862no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—861no—
205C22×C4—864no—
206C22×C4C2×C4×D4311yescharacteristic
207C22×C4C2×C4×D4312yes—
208C22×C4D4×D4312yes—
209C22×C4#1062190011yescharacteristic
210M16—41no—
211M16—41no—
212M16—1722no—
213C2×C8—21no—
214C2×C8—21no—
215C2×C8—24no—
216C2×C8—42no—
217C2×C8—42no—
218C2×C8—431no—
219C2×C8—431no—
220C2×C8—432no—
221C2×C8—864no—
222C2×C8—862no—
223C2×C8—1722no—
224C2×C8—1722no—
225C2×C8—1721no—
226C4⋊C4—432no—
227C4⋊C4—862no—
228C22⋊C4—861no—
229C22⋊C4—862no—
230C22⋊C4—862no—
231C22⋊C4—1724no—
232C42—861no—
233C42—1722no—
234C42—1722no—
235C23—24no—
236C23—41no—
237C23—861no—
238C23#1306328311yescharacteristic
239C23#1306328712yes—
240Q8—1721no—
241D4—1721no—
242D4—1722no—
243D4—1724no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—862no—
251C2×C4—861no—
252C2×C4—1724no—
253C2×C4—1724no—
254C2×C4—1724no—
255C2×C4—1721no—
256C2×C4—1721no—
257C2×C4C42×D4311yescharacteristic
258C2×C4C22⋊C4×D4311yescharacteristic
259C2×C4(C22⋊D43)⋊C412yes—
260C8—44no—
261C8—41no—
262C8—41no—
263C8—432no—
264C8—861no—
265C8—862no—
266C22—22no—
267C22—22no—
268C22—21no—
269C22—22no—
270C22—44no—
271C22—1721no—
272C22—1722no—
273C22#1458274611yescharacteristic
274C22#1458302014yes—
275C4—22no—
276C4—21no—
277C4—3444no—
278C4—1721no—
279C4—1722no—
280C4#99×D4311yescharacteristic
281C4#1458287111yescharacteristic
282C2—24no—
283C2—41no—
284C2—3441no—
285C2#1913438211yescharacteristic
286C2#1913443812yes—
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC43×#1298C2
socleC22×C43C4×C22⋊C4
prime radical#14583410C22
cosocleC23×C4×C43C23
hypercenter#1298D43
hypocenterC43#8239
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1298

Complements

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

NH ≅ G/Ntype
2. #19134374C2semidirect
4. #19132480C2semidirect
5. C43×#1298C2semidirect
6. C2×#13063333C4semidirect
11. #14582927C4semidirect
12. #14582867C4semidirect
13. #14582857C4semidirect
17. #14582637C4semidirect
18. #14582634C4semidirect
142. #1298D43semidirect
164. C43#8239semidirect

Maximal subgroups

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

subgroupindex
#191432852
#191343742
#191330872
#191324802
C43×#12982
#823943