Finite Group Databasebeta

← #25077865

Subgroups — #25077865

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#19145797C212yesmaximal, complemented
3#19133928C218yesmaximal, complemented
4#19133219C211yesmaximal, characteristic
5#19133196C212yesmaximal, complemented
6C43×#3140C211yesmaximal, characteristic
7#14583649—24no—
8#14583649—22no—
9#14583649C2214yes—
10C2×#13063323—21no—
11C2×#13063318—22no—
12C2×#13063317C2212yes—
13C2×#13063306—21no—
14C2×#13063302—22no—
15#14583305C2214yescomplemented
16#14583267C2214yescomplemented
17#14583232—22no—
18#14583227—22no—
19#14583206—24no—
20#14582956C2212yes—
21#14582640C2218yescomplemented
22#14582639C2214yes—
23C43×#533C2211yescharacteristic
24C2×#124×C43C2211yescharacteristic
25C43×#489C2214yes—
26C43×#488—22no—
27C43×#419—21no—
28C43×#418—21no—
29C4×M16×C43C2211yescharacteristic
30C22×Dic86—21no—
31C23×Dic43—21no—
32#13063323—24no—
33#13063323—24no—
34#13063318—28no—
35#13063318—28no—
36#13063317—22no—
37#13063317—22no—
38#13063317D414yes—
39#13063317C2314yes—
40#13063306—24no—
41#13063306—24no—
42#13063302—28no—
43#13063302—28no—
44C2×C4⋊Dic43D412yes—
45C2×C4⋊Dic43D412yes—
46C2×Dic43⋊C4—22no—
47C2×Dic43⋊C4—22no—
48C2×Dic43⋊C4—22no—
49C2×C22⋊Dic43—22no—
50C2×C22⋊Dic43—21no—
51C2×C4×Dic43—21no—
52#13063258—24no—
53#13063256—24no—
54C4⋊(C43⋊C8)—22no—
55#13063249—24no—
56#13063249—24no—
57C22⋊(C43⋊C8)—22no—
58#13063236C2314yes—
59C22×Q8×C43D411yescharacteristic
60C22×D4×C43D411yescharacteristic
61C2×M16×C43—21no—
62C4⋊Q8×C43C2312yes—
63#125×C43—21no—
64#124×C43—22no—
65#124×C43D412yes—
66#124×C43C2312yes—
67C22⋊Q8×C43—22no—
68C4×Q8×C43—22no—
69#117×C43—21no—
70C2×C22⋊C4×C43—22no—
71C2×C42×C43C2311yescharacteristic
72#103×C43—24no—
73#102×C43—24no—
74#97×C43C2312yes—
75C4×C8×C43—21no—
76C24×C43—21no—
77C2×Q8×C43—21no—
78C2×Q8×C43—22no—
79C2×Q8×C43—42no—
80C2×Q8×C43C2×D412yes—
81C2×D4×C43—21no—
82C2×D4×C43—42no—
83C2×D4×C43C2×D412yes—
84C22×C4×C43—21no—
85C22×C4×C43C2×D412yes—
86C22×C4×C43C2×D411yescharacteristic
87C22×Dic43—24no—
88C22×Dic43—22no—
89C22×Dic43—22no—
90C22×Dic43—82no—
91C2×Dic86—24no—
92C2×Dic86—82no—
93M16×C43—42no—
94C2×C8×C43—22no—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—42no—
98C22⋊C4×C43—24no—
99C22⋊C4×C43—24no—
100C22⋊C4×C43—41no—
101C42×C43—41no—
102C42×C43C2×D412yes—
103C42×C43C2×D411yescharacteristic
104C42×C43C2411yescharacteristic
105C22⋊Dic43—28no—
106C22⋊Dic43—24no—
107C4⋊Dic43—22no—
108C4⋊Dic43—22no—
109C4⋊Dic43C2×D414yes—
110C4⋊Dic43C2×D414yes—
111Dic43⋊C4—28no—
112Dic43⋊C4—24no—
113Dic43⋊C4—24no—
114Dic43⋊C4—24no—
115Dic43⋊C4—24no—
116C4×Dic43—24no—
117C2×C43⋊C8—24no—
118C23×C43—22no—
119C23×C43—44no—
120C23×C43—42no—
121C23×C43#12011yescharacteristic
122Q8×C43—42no—
123Q8×C43—44no—
124Q8×C43—81no—
125D4×C43—42no—
126D4×C43—81no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43#12011yescharacteristic
133C2×C4×C43#12012yes—
134C2×C4×C43C22×D412yes—
135C2×C4×C43C22×D411yescharacteristic
136C2×Dic43—24no—
137C2×Dic43—24no—
138C2×Dic43—44no—
139C2×Dic43—44no—
140C2×Dic43—84no—
141Dic86—84no—
142C8×C43—42no—
143C43⋊C8—44no—
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—
156C4×C43—82no—
157Dic43—44no—
158Dic43—44no—
159C2×#563—431no—
160#3236—432no—
161#3140D4311yescharacteristic
162#1664—438no—
163#1533—431no—
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#533C2×D4311yescharacteristic
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#489C2×D4314yes—
182#488—22no—
183#484—862no—
184#483—862no—
185#479—864no—
186#432—432no—
187#419—21no—
188#418—21no—
189C4×M16C2×D4311yescharacteristic
190#330—438no—
191#329—434no—
192C43#1899911yescharacteristic, complemented, Sylow
193C22×Q8—861no—
194C22×Q8C22⋊D4311yescharacteristic
195C22×D4C22⋊D4311yescharacteristic
196C23×C4—861no—
197C2×M16—21no—
198C4⋊Q8—864no—
199C4⋊Q8—864no—
200C4⋊Q8C22×D4312yes—
201#126—868no—
202#126—868no—
203#125—21no—
204#125—434no—
205#125—434no—
206#125—862no—
207#125—862no—
208#124—22no—
209#124C22⋊D4312yes—
210#124C22×D4312yes—
211#123—864no—
212#123—864no—
213C22⋊Q8—22no—
214C22⋊Q8—868no—
215C22⋊Q8—868no—
216C4×Q8—22no—
217#117—21no—
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—862no—
231#103—24no—
232#103—864no—
233#103—864no—
234#102—24no—
235C22⋊C8—862no—
236#97—434no—
237#97C22×D4312yes—
238C4×C8—21no—
239C24—21no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—42no—
243C2×Q8—864no—
244C2×Q8—3442no—
245C2×Q8C2×C22⋊D4312yes—
246C2×D4—21no—
247C2×D4—42no—
248C2×D4C2×C22⋊D4312yes—
249C22×C4—21no—
250C22×C4—864no—
251C22×C4—862no—
252C22×C4—862no—
253C22×C4—3442no—
254C22×C4D4×D4312yes—
255C22×C4C2×C22⋊D4311yescharacteristic
256M16—42no—
257C2×C8—22no—
258C2×C8—864no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—42no—
262C4⋊C4—434no—
263C4⋊C4—434no—
264C4⋊C4—868no—
265C4⋊C4—862no—
266C4⋊C4—862no—
267C4⋊C4—864no—
268C4⋊C4—864no—
269C4⋊C4—864no—
270C4⋊C4—864no—
271C22⋊C4—24no—
272C22⋊C4—24no—
273C22⋊C4—41no—
274C22⋊C4—868no—
275C22⋊C4—864no—
276C42—41no—
277C42—864no—
278C42D4×D4312yes—
279C42C2×C22⋊D4311yescharacteristic
280C42C23×D4311yescharacteristic
281C23—22no—
282C23—44no—
283C23—42no—
284C23#1306329311yescharacteristic
285Q8—42no—
286Q8—44no—
287Q8—81no—
288Q8—3444no—
289D4—42no—
290D4—81no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—864no—
297C2×C4—864no—
298C2×C4—3444no—
299C2×C4—1724no—
300C2×C4—1724no—
301C2×C4#1306329311yescharacteristic
302C2×C4#1306329312yes—
303C2×C4C2×D4×D4312yes—
304C2×C4C22×C22⋊D4311yescharacteristic
305C8—42no—
306C8—1724no—
307C22—22no—
308C22—44no—
309C22—42no—
310C22—84no—
311C22#1458307612yes—
312C22C2×#1306329311yescharacteristic
313C4—22no—
314C4—22no—
315C4—21no—
316C4—21no—
317C4—42no—
318C4—82no—
319C4—1724no—
320C4—1724no—
321C2—22no—
322C2—82no—
323C2C2×#1458307611yescharacteristic
324C2#1914395712yes—
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3140C2
socleC22×C43C2×#120
prime radicalC22×D4×C43D4
hypercenter#3140D43
hypocenterC43#18999
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3140

Complements

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

NH ≅ G/Ntype
2. #19145797C2semidirect
3. #19133928C2semidirect
5. #19133196C2semidirect
15. #14583305C22semidirect
16. #14583267C22semidirect
21. #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
#191457972
#191339282
#191332192
#191331962
C43×#31402
#1899943