Finite Group Databasebeta

← #25077868

Subgroups — #25077868

Order 11008.

850 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 850 conjugacy classes of subgroups — too many to draw. Only its 155 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×#14583649C211yesmaximal, characteristic
2#19145803C212yesmaximal, complemented
3#19144981C211yesmaximal, characteristic
4#19133932C218yesmaximal, complemented
5#19133198C212yesmaximal, complemented
6C43×#1533C211yesmaximal, characteristic
7#14583649—24no—
8#14583649—22no—
9#14583649C2214yes—
10#14583456C2211yescharacteristic
11C2×#13063323—21no—
12C2×#13063318—22no—
13C2×#13063317C2212yes—
14C2×#13063306—21no—
15C2×#13063302—22no—
16#14583308C2214yescomplemented
17#14583268C2214yescomplemented
18#14583258C2214yes—
19#14583253—22no—
20#14583235—22no—
21#14583230—22no—
22#14583207—24no—
23#14582908—21no—
24#14582904—21no—
25C4×#10621877C2211yescharacteristic
26#14582640C2218yescomplemented
27C2×#124×C43C2211yescharacteristic
28C43×#432C2212yes—
29C43×#329C2214yes—
30C22×Dic86—21no—
31C23×Dic43—21no—
32C2×#10621877—21no—
33#13063325C2312yes—
34#13063323—24no—
35#13063323—24no—
36#13063318—28no—
37#13063318—28no—
38#13063317—22no—
39#13063317—22no—
40#13063317—21no—
41#13063317D414yes—
42#13063317C2314yes—
43#13063306—24no—
44#13063306—24no—
45#13063304—22no—
46#13063302—28no—
47#13063302—28no—
48C4×Dic86—22no—
49#13063284—21no—
50C2×C4⋊Dic43D412yes—
51C2×C4⋊Dic43D412yes—
52C2×Dic43⋊C4—22no—
53C2×Dic43⋊C4—22no—
54C2×Dic43⋊C4—22no—
55C2×C22⋊Dic43—22no—
56C2×C22⋊Dic43—21no—
57C2×C4×Dic43—21no—
58#13063259—24no—
59#13063257—24no—
60#13063250—24no—
61#13063250—24no—
62#13063249—24no—
63#13063246—24no—
64#13063236C2312yes—
65C4×C43⋊C8—21no—
66C22×Q8×C43D411yescharacteristic
67C22×D4×C43D411yescharacteristic
68#124×C43—22no—
69#124×C43D412yes—
70#124×C43C2312yes—
71C2×C22⋊C4×C43—22no—
72C2×C42×C43C2311yescharacteristic
73C4⋊C8×C43—22no—
74C22⋊C8×C43—22no—
75#97×C43C2314yes—
76C24×C43—21no—
77C2×Q8×C43—21no—
78C2×Q8×C43—42no—
79C2×Q8×C43C2×D412yes—
80C2×D4×C43—21no—
81C2×D4×C43—42no—
82C2×D4×C43C2×D412yes—
83C22×C4×C43—21no—
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D412yes—
86C22×Dic43—24no—
87C22×Dic43—22no—
88C22×Dic43—22no—
89C22×Dic43—82no—
90C2×Dic86—22no—
91C2×Dic86—24no—
92C2×Dic86—82no—
93C2×C8×C43—24no—
94C22⋊C4×C43—24no—
95C22⋊C4×C43—24no—
96C42×C43C2×D411yescharacteristic
97C42×C43C2×D412yes—
98C42×C43C2411yescharacteristic
99C22⋊Dic43—28no—
100C22⋊Dic43—24no—
101C22⋊Dic43—41no—
102C4⋊Dic43—22no—
103C4⋊Dic43—22no—
104C4⋊Dic43—22no—
105C4⋊Dic43—22no—
106C4⋊Dic43C2×D414yes—
107C4⋊Dic43C2×D414yes—
108Dic43⋊C4—28no—
109Dic43⋊C4—24no—
110Dic43⋊C4—24no—
111Dic43⋊C4—24no—
112Dic43⋊C4—24no—
113Dic43⋊C4—42no—
114C4×Dic43—24no—
115C4×Dic43—41no—
116#10621877—42no—
117C2×C43⋊C8—22no—
118C23×C43—22no—
119C23×C43—44no—
120C23×C43—42no—
121C23×C43#12011yescharacteristic
122Q8×C43—42no—
123Q8×C43—81no—
124D4×C43—42no—
125D4×C43—81no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43#12011yescharacteristic
131C2×C4×C43#12012yes—
132C2×C4×C43C22×D412yes—
133C2×C4×C43C22×D411yescharacteristic
134C2×Dic43—24no—
135C2×Dic43—24no—
136C2×Dic43—44no—
137C2×Dic43—44no—
138C2×Dic43—42no—
139C2×Dic43—84no—
140Dic86—44no—
141Dic86—84no—
142C8×C43—44no—
143C43⋊C8—42no—
144#18999—431nomaximal, Sylow
145C22×C43—22no—
146C22×C43—42no—
147C22×C43—44no—
148C22×C43—84no—
149C22×C43#45512yes—
150C22×C43C2×#12011yescharacteristic
151C4×C43—21no—
152C4×C43—21no—
153C4×C43—22no—
154C4×C43—22no—
155C4×C43—42no—
156Dic43—44no—
157Dic43—44no—
158Dic43—82no—
159C2×#563—431no—
160#3236—432no—
161#3140—431no—
162#1664—438no—
163#1533D4311yescharacteristic
164#1528—432no—
165C2×C43—22no—
166C2×C43—82no—
167C2×C43C2×#45511yescharacteristic
168C2×C43#302012yes—
169#563—434no—
170#563—864no—
171#563—862no—
172#533—431no—
173C2×C4⋊Q8—861no—
174C2×#126—862no—
175C2×#125—432no—
176C2×#124C2×D4311yescharacteristic
177C2×#123—861no—
178C2×C22⋊Q8—862no—
179#501—434no—
180#491—434no—
181#489—434no—
182#488—862no—
183#484—862no—
184#483—862no—
185#479—864no—
186#432C2×D4312yes—
187#419—861no—
188#418—861no—
189C4×M16—431no—
190#330—438no—
191#329C2×D4314yes—
192C43#1899911yescharacteristic, complemented, Sylow
193C22×Q8—861no—
194C22×Q8D17211yescharacteristic
195C22×D4D17211yescharacteristic
196C23×C4—861no—
197C2×M16—861no—
198C4⋊Q8—432no—
199C4⋊Q8—864no—
200C4⋊Q8—864no—
201#126—868no—
202#126—868no—
203#125—434no—
204#125—434no—
205#125—862no—
206#125—861no—
207#125—862no—
208#124—22no—
209#124D17212yes—
210#124C22×D4312yes—
211#123—864no—
212#123—864no—
213C22⋊Q8—868no—
214C22⋊Q8—868no—
215C22⋊Q8—862no—
216C4×Q8—862no—
217#117—861no—
218C2×C4⋊C4—432no—
219C2×C4⋊C4—432no—
220C2×C4⋊C4—862no—
221C2×C4⋊C4—862no—
222C2×C4⋊C4—862no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—862no—
225C2×C22⋊C4—861no—
226C2×C42—861no—
227C2×C42C22×D4311yescharacteristic
228#107—864no—
229#106—864no—
230C4⋊C8—22no—
231#103—864no—
232#103—864no—
233#103—864no—
234#102—864no—
235C22⋊C8—22no—
236#97—432no—
237#97C22×D4314yes—
238C4×C8—861no—
239C24—21no—
240C2×Q8—21no—
241C2×Q8—42no—
242C2×Q8—864no—
243C2×Q8—862no—
244C2×Q8—3442no—
245C2×Q8C2×D17212yes—
246C2×D4—21no—
247C2×D4—42no—
248C2×D4C2×D17212yes—
249C22×C4—21no—
250C22×C4—864no—
251C22×C4—862no—
252C22×C4—862no—
253C22×C4—3442no—
254C22×C4C2×D17211yescharacteristic
255C22×C4D4×D4312yes—
256M16—1722no—
257C2×C8—24no—
258C2×C8—862no—
259C4⋊C4—434no—
260C4⋊C4—434no—
261C4⋊C4—868no—
262C4⋊C4—862no—
263C4⋊C4—862no—
264C4⋊C4—864no—
265C4⋊C4—864no—
266C4⋊C4—864no—
267C4⋊C4—864no—
268C4⋊C4—862no—
269C4⋊C4—862no—
270C4⋊C4—1722no—
271C22⋊C4—24no—
272C22⋊C4—24no—
273C22⋊C4—868no—
274C22⋊C4—864no—
275C22⋊C4—1721no—
276C42—864no—
277C42—1721no—
278C42C2×D17211yescharacteristic
279C42D4×D4312yes—
280C42C23×D4311yescharacteristic
281C23—22no—
282C23—44no—
283C23—42no—
284C23#1306329511yescharacteristic
285Q8—42no—
286Q8—81no—
287Q8—3444no—
288Q8—1724no—
289D4—42no—
290D4—81no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—864no—
296C2×C4—864no—
297C2×C4—3444no—
298C2×C4—1722no—
299C2×C4—1724no—
300C2×C4—1724no—
301C2×C4#1306329511yescharacteristic
302C2×C4#1306329512yes—
303C2×C4C2×D4×D4312yes—
304C2×C4C22×D17211yescharacteristic
305C8—44no—
306C8—1722no—
307C22—22no—
308C22—44no—
309C22—42no—
310C22—84no—
311C22#1458307912yes—
312C22C2×#1306329511yescharacteristic
313C4—22no—
314C4—22no—
315C4—21no—
316C4—21no—
317C4—42no—
318C4—3442no—
319C4—1724no—
320C4—1724no—
321C2—22no—
322C2—82no—
323C2C2×#1458307911yescharacteristic
324C2#1914396112yes—
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1533C2
socleC22×C43C2×#120
prime radicalC22×D4×C43D4
hypercenter#1533D43
hypocenterC43#18999
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1533

Complements

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

NH ≅ G/Ntype
2. #19145803C2semidirect
4. #19133932C2semidirect
5. #19133198C2semidirect
16. #14583308C22semidirect
17. #14583268C22semidirect
26. #14582640C22semidirect
192. C43#18999semidirect

Maximal subgroups

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

subgroupindex
C2×#145836492
#191458032
#191449812
#191339322
#191331982
C43×#15332
#1899943