Finite Group Databasebeta

← #24991536

Subgroups — #24991536

Order 11008.

578 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C2×#14583294C211yesmaximal, characteristic
2#19135567C212yesmaximal, complemented
3C2×#14582639C211yesmaximal, characteristic
4#19132476C212yesmaximal, complemented
5C43×#2379C211yesmaximal, characteristic
6C22×#10621885—21no—
7C22×#10621883—21no—
8C2×#13063325C2211yescharacteristic
9#14583294—22no—
10#14583294C414yescomplemented
11C2×#13063236C2212yes—
12C2×#13063236C2211yescharacteristic
13#14582661—22no—
14#14582661—22no—
15#14582639—22no—
16C2×#124×C43C2211yescharacteristic
17C43×#391—21no—
18C43×#388—22no—
19C43×#386—21no—
20C43×#385—22no—
21C43×#382C2212yes—
22C22×Dic86—21no—
23C2×#10621885—24no—
24C2×#10621885—42no—
25C2×#10621885—42no—
26C2×#10621883—24no—
27C2×#10621883—42no—
28C2×#10621883—42no—
29C22×C43⋊C8—21no—
30C22×C43⋊C8—22no—
31#13063325—22no—
32#13063325—21no—
33#13063325C2×C412yescomplemented
34C2×C4⋊Dic43—22no—
35#13063236—21no—
36#13063236—22no—
37#13063236—22no—
38#13063236C2×C412yescomplemented
39C22×Q8×C43D411yescharacteristic
40C22×D4×C43D411yescharacteristic
41C23×C4×C43—21no—
42#124×C43—22no—
43#124×C43C2×C412yes—
44#124×C43D412yes—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43D412yes—
47C2×C4⋊C4×C43D412yes—
48C2×C22⋊C4×C43—22no—
49C2×C22⋊C4×C43—22no—
50C2×C22⋊C4×C43—21no—
51C2×C42×C43—21no—
52C2×C42×C43C2311yescharacteristic
53#95×C43—22no—
54#95×C43—22no—
55#95×C43—22no—
56C24×C43—21no—
57C2×Q8×C43—21no—
58C2×Q8×C43—41no—
59C2×Q8×C43—41no—
60C2×Q8×C43C22⋊C412yes—
61C2×D4×C43—21no—
62C2×D4×C43—41no—
63C2×D4×C43—41no—
64C2×D4×C43C22⋊C412yes—
65C22×C4×C43—21no—
66C22×C4×C43—22no—
67C22×C4×C43—22no—
68C22×C4×C43—81no—
69C22×C4×C43—82no—
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D412yes—
72C22×Dic43—41no—
73C2×Dic86—22no—
74C2×Dic86—41no—
75C2×Dic86—41no—
76C2×Dic86—41no—
77C2×Dic86—41no—
78C2×Dic86—41no—
79C4⋊C4×C43—42no—
80C4⋊C4×C43—42no—
81C4⋊C4×C43—81no—
82C22⋊C4×C43—24no—
83C22⋊C4×C43—24no—
84C22⋊C4×C43—81no—
85C22⋊C4×C43—82no—
86C42×C43—81no—
87C42×C43C22×C411yescharacteristic
88C42×C43C2×D411yescharacteristic
89C42×C43#4112yes—
90#10621885—48no—
91#10621883—48no—
92C4⋊Dic43—24no—
93C4⋊Dic43—42no—
94C2×C43⋊C8—22no—
95C2×C43⋊C8—22no—
96C2×C43⋊C8—22no—
97C2×C43⋊C8—24no—
98C2×C43⋊C8—42no—
99C2×C43⋊C8—42no—
100C23×C43—22no—
101C23×C43—41no—
102C23×C43—41no—
103C23×C43—42no—
104C23×C43—42no—
105C23×C43#12011yescharacteristic
106Q8×C43—42no—
107Q8×C43—81no—
108D4×C43—42no—
109D4×C43—81no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—22no—
113C2×C4×C43—22no—
114C2×C4×C43—22no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—42no—
118C2×C4×C43—42no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43—84no—
124C2×C4×C43C2×C22⋊C411yescharacteristic
125C2×C4×C43C4×D412yes—
126C2×C4×C43#12112yes—
127C2×C4×C43#12311yescharacteristic
128C2×Dic43—42no—
129C2×Dic43—81no—
130C2×Dic43—81no—
131Dic86—42no—
132Dic86—42no—
133Dic86—81no—
134Dic86—81no—
135C43⋊C8—24no—
136C43⋊C8—44no—
137#9003—431nomaximal, Sylow
138C22×C43—44no—
139C22×C43—42no—
140C22×C43—81no—
141C22×C43—81no—
142C22×C43—82no—
143C22×C43#38611yescharacteristic
144C22×C43#45311yescharacteristic
145C22×C43#45311yescharacteristic
146C22×C43#45512yes—
147C22×C43#45612yes—
148C4×C43—22no—
149C4×C43—22no—
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—42no—
153C4×C43—82no—
154C4×C43—82no—
155Dic43—82no—
156C2×#497—431no—
157#2379D4311yescharacteristic
158#1993—432no—
159C2×#329—431no—
160#1295—432no—
161C2×C43—82no—
162C2×C43#165911yescharacteristic
163C2×C43#166011yescharacteristic
164C2×C43#166112yes—
165C2×C43#188212yes—
166C2×C43#188711yescharacteristic
167C22×Q16—861no—
168C22×SD16—861no—
169C2×C4⋊Q8—431no—
170C2×#124C2×D4311yescharacteristic
171#497—434no—
172#497—862no—
173C2×#97—431no—
174C2×#97—432no—
175#391—21no—
176#388—22no—
177#386—21no—
178#385—22no—
179#382C2×D4312yes—
180#340—862no—
181#340—862no—
182#329—862no—
183C43#900311yescharacteristic, complemented, Sylow
184C22×Q8—861no—
185C22×Q8C22⋊D4311yescharacteristic
186C22×D4C22⋊D4311yescharacteristic
187C23×C4—21no—
188C2×Q16—864no—
189C2×Q16—1722no—
190C2×Q16—1722no—
191C2×SD16—864no—
192C2×SD16—1722no—
193C2×SD16—1722no—
194C22×C8—861no—
195C22×C8—862no—
196C4⋊Q8—432no—
197C4⋊Q8—861no—
198C4⋊Q8—862no—
199#124—22no—
200#124C4×D4312yes—
201#124D17212yes—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—862no—
204C2×C4⋊C4C22⋊D4312yes—
205C2×C4⋊C4C22⋊D4312yes—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—22no—
208C2×C22⋊C4—21no—
209C2×C42—21no—
210C2×C42C22×D4311yescharacteristic
211#97—432no—
212#97—861no—
213#97—862no—
214#97—862no—
215#95—22no—
216#95—22no—
217#95—22no—
218C24—21no—
219C2×Q8—21no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—862no—
223C2×Q8—1721no—
224C2×Q8—1721no—
225C2×Q8—1721no—
226C2×Q8—1721no—
227C2×Q8—1721no—
228C2×Q8(C2×D43)⋊C412yes—
229C2×D4—21no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4(C2×D43)⋊C412yes—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—81no—
237C22×C4—82no—
238C22×C4—1721no—
239C22×C4C2×C22⋊D4311yescharacteristic
240C22×C4C2×C22⋊D4312yes—
241Q16—1728no—
242SD16—1728no—
243C2×C8—862no—
244C2×C8—862no—
245C2×C8—862no—
246C2×C8—864no—
247C2×C8—1722no—
248C2×C8—1722no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—81no—
252C4⋊C4—864no—
253C4⋊C4—1722no—
254C22⋊C4—24no—
255C22⋊C4—24no—
256C22⋊C4—81no—
257C22⋊C4—82no—
258C42—81no—
259C42C2×C4×D4311yescharacteristic
260C42C2×D17211yescharacteristic
261C42#1062189812yes—
262C23—22no—
263C23—41no—
264C23—41no—
265C23—42no—
266C23—42no—
267C23#1306329411yescharacteristic
268Q8—42no—
269Q8—81no—
270Q8—3441no—
271Q8—3441no—
272Q8—1722no—
273Q8—1722no—
274D4—42no—
275D4—81no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—84no—
290C2×C4—3441no—
291C2×C4—3441no—
292C2×C4—1722no—
293C2×C4C2×(C2×D43)⋊C411yescharacteristic
294C2×C4C4×C22⋊D4312yes—
295C2×C4#1306329912yes—
296C2×C4#1306330811yescharacteristic
297C8—864no—
298C8—1724no—
299C22—42no—
300C22—44no—
301C22—81no—
302C22—81no—
303C22—82no—
304C22#1458277811yescharacteristic
305C22#1458306711yescharacteristic
306C22#1458306711yescharacteristic
307C22#1458307712yes—
308C22#1458308212yes—
309C4—21no—
310C4—21no—
311C4—22no—
312C4—22no—
313C4—42no—
314C4—82no—
315C4—82no—
316C4—3442no—
317C2—82no—
318C2#1913390111yescharacteristic
319C2#1913390611yescharacteristic
320C2#1913391212yes—
321C2#1913496412yes—
322C2#1913499311yescharacteristic
subgroupG/H
centerC23#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2379C2
socleC23×C43#120
prime radicalC22×D4×C43D4
cosocleC2×C42×C43C23
hypercenter#2379D43
hypocenterC43#9003
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2379

Complements

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

NH ≅ G/Ntype
2. #19135567C2semidirect
4. #19132476C2semidirect
10. #14583294C4semidirect
33. #13063325C2×C4semidirect
38. #13063236C2×C4semidirect
183. C43#9003semidirect

Maximal subgroups

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

subgroupindex
C2×#145832942
#191355672
C2×#145826392
#191324762
C43×#23792
#900343