Finite Group Databasebeta

← #25072857

Subgroups — #25072857

Order 11008.

1004 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 171 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×#14583629C211yesmaximal, characteristic, complemented
2#19144713C212yesmaximal
3#19133733C214yesmaximal, complemented
4#19133671C214yesmaximal, complemented
5#19133321C211yesmaximal, characteristic, complemented
6#19133043C212yesmaximal, complemented
7C43×#3152C211yesmaximal, characteristic
8#14583629—24no—
9#14583629—22no—
10#14583629C2214yes—
11C2×#13063324—22no—
12C2×#13063323—22no—
13C2×C4×Dic86C2212yes—
14C2×#13063290—22no—
15#14583210—22no—
16#14583191C2214yes—
17#14583096C2214yes—
18#14583037—22no—
19#14582999—24no—
20#14582956C2212yes—
21#14582648C2214yes—
22#14582631C2218yes—
23C2×#137×C43—22no—
24C43×#532C2211yescharacteristic
25C2×C4⋊Q8×C43C2211yescharacteristic
26C43×#497—22no—
27C43×#494C2212yes—
28C43×#492C2212yes—
29C4×M16×C43C2211yescharacteristic
30C22×Dic86—22no—
31C22×Dic86D412yes—
32C2×#10621883—24no—
33#13063324—28no—
34#13063324—28no—
35#13063323—28no—
36#13063323—28no—
37C4×Dic86—22no—
38C4×Dic86—22no—
39C4×Dic86D414yes—
40C4×Dic86C2314yes—
41#13063290—28no—
42#13063290—28no—
43C2×C4⋊Dic43D412yes—
44C2×Dic43⋊C4—24no—
45C2×Dic43⋊C4—22no—
46C2×C4×Dic43—22no—
47C2×C4×Dic43—22no—
48#13063258—24no—
49C4⋊(C43⋊C8)C2314yes—
50#13063248—24no—
51#13063246—24no—
52C22⋊(C43⋊C8)—22no—
53#13063236—22no—
54C2×#41×C43—21no—
55C22×Q8×C43D412yes—
56#137×C43—48no—
57C2×Q16×C43—24no—
58C2×SD16×C43—24no—
59C2×M16×C43—21no—
60C4⋊Q8×C43—22no—
61C4⋊Q8×C43D412yes—
62C4⋊Q8×C43C2311yescharacteristic
63C4⋊Q8×C43C2312yes—
64#127×C43C2311yescharacteristic
65#124×C43—21no—
66#121×C43—22no—
67C4×D4×C43—22no—
68C2×C4⋊C4×C43—22no—
69C2×C42×C43C2311yescharacteristic
70#97×C43—21no—
71C4×C8×C43C2312yes—
72#41×C43—44no—
73C2×Q8×C43—22no—
74C2×Q8×C43—21no—
75C2×Q8×C43—44no—
76C2×Q8×C43C2×D414yes—
77C2×D4×C43—22no—
78C2×D4×C43—21no—
79C2×D4×C43—41no—
80C22×C4×C43—22no—
81C22×C4×C43—41no—
82C22×C4×C43C2×D412yes—
83C22×C4×C43C2×D411yescharacteristic
84C22×Dic43—22no—
85C22×Dic43—22no—
86C2×Dic86—22no—
87C2×Dic86—28no—
88C2×Dic86—28no—
89C2×Dic86—84no—
90C2×Dic86C2×D414yes—
91Q16×C43—48no—
92SD16×C43—48no—
93M16×C43—24no—
94C2×C8×C43—22no—
95C4⋊C4×C43—24no—
96C4⋊C4×C43—24no—
97C4⋊C4×C43—22no—
98C22⋊C4×C43—42no—
99C42×C43C2×D412yes—
100C42×C43C2×D411yescharacteristic
101C42×C43C2411yescharacteristic
102#10621883—48no—
103C4⋊Dic43—22no—
104C4⋊Dic43C2×D414yes—
105Dic43⋊C4—216no—
106Dic43⋊C4—24no—
107Dic43⋊C4—24no—
108C4×Dic43—28no—
109C4×Dic43—24no—
110C4×Dic43—24no—
111C2×C43⋊C8—24no—
112C23×C43—41no—
113C23×C43#12011yescharacteristic
114Q8×C43—44no—
115Q8×C43—42no—
116Q8×C43—82no—
117D4×C43—42no—
118D4×C43—44no—
119D4×C43—82no—
120C2×C4×C43—22no—
121C2×C4×C43—24no—
122C2×C4×C43—24no—
123C2×C4×C43—44no—
124C2×C4×C43—41no—
125C2×C4×C43—82no—
126C2×C4×C43#12012yes—
127C2×C4×C43#12011yescharacteristic
128C2×C4×C43C22×D412yes—
129C2×C4×C43C22×D411yescharacteristic
130C2×Dic43—28no—
131C2×Dic43—24no—
132C2×Dic43—24no—
133C2×Dic43—44no—
134Dic86—28no—
135Dic86—24no—
136Dic86—88no—
137Dic86#13718yescomplemented
138C8×C43—24no—
139C43⋊C8—44no—
140#18546—431nomaximal, Sylow
141C22×C43—22no—
142C22×C43—82no—
143C22×C43—81no—
144C22×C43#45312yes—
145C22×C43C2×#12011yescharacteristic
146C4×C43—22no—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—44no—
150C4×C43—81no—
151C4×C43C2×#13714yes—
152Dic43—28no—
153Dic43—44no—
154C2×Q82—431no—
155#3152D4311yescharacteristic
156#3112—432no—
157#1633—434no—
158#1623—434no—
159#1558—431no—
160#1491—432no—
161C2×C43—22no—
162C2×C43—161no—
163C2×C43#300412yes—
164C2×C43C2×#45311yescharacteristic
165C2×#137—22no—
166Q82—434no—
167Q82—864no—
168Q82—862no—
169#532C2×D4311yescharacteristic
170C2×C4⋊Q8—862no—
171C2×C4⋊Q8—862no—
172C2×C4⋊Q8C2×D4311yescharacteristic
173C2×C4×Q8—432no—
174C2×C4×Q8—862no—
175#497—22no—
176#494C2×D4312yes—
177#492C2×D4312yes—
178#480—862no—
179#477—434no—
180#460—434no—
181#448—862no—
182#440—864no—
183#432—432no—
184C4×M16C2×D4311yescharacteristic
185#333—434no—
186Q8⋊C8—438no—
187C43#1854611yescharacteristic, complemented, Sylow
188C2×#41—21no—
189C22×Q8—432no—
190C22×Q8—862no—
191C22×Q8C22⋊D4312yes—
192#137—48no—
193C2×Q16—24no—
194C2×SD16—24no—
195C2×SD16—864no—
196C2×M16—21no—
197C4⋊Q8—22no—
198C4⋊Q8—868no—
199C4⋊Q8—868no—
200C4⋊Q8—868no—
201C4⋊Q8—868no—
202C4⋊Q8C22⋊D4312yes—
203C4⋊Q8C22×D4311yescharacteristic
204C4⋊Q8C22×D4312yes—
205#127C22×D4311yescharacteristic
206#124—21no—
207#121—22no—
208C4×Q8—434no—
209C4×Q8—434no—
210C4×Q8—868no—
211C4×Q8—868no—
212C4×Q8—862no—
213C4×Q8—862no—
214C4×D4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—432no—
217C2×C4⋊C4—864no—
218C2×C4⋊C4—862no—
219C2×C42—862no—
220C2×C42—862no—
221C2×C42C22×D4311yescharacteristic
222#107—864no—
223C4⋊C8—434no—
224#103—864no—
225#102—864no—
226C22⋊C8—862no—
227#97—21no—
228#97—862no—
229C4×C8C22×D4312yes—
230#41—44no—
231C2×Q8—22no—
232C2×Q8—21no—
233C2×Q8—44no—
234C2×Q8—434no—
235C2×Q8—868no—
236C2×Q8—868no—
237C2×Q8—862no—
238C2×Q8—3444no—
239C2×Q8C2×C22⋊D4314yes—
240C2×D4—22no—
241C2×D4—21no—
242C2×D4—41no—
243C22×C4—22no—
244C22×C4—41no—
245C22×C4—862no—
246C22×C4—862no—
247C22×C4D4×D4312yes—
248C22×C4C2×C22⋊D4311yescharacteristic
249Q16—48no—
250SD16—48no—
251SD16—1728no—
252M16—24no—
253C2×C8—22no—
254C2×C8—864no—
255C4⋊C4—24no—
256C4⋊C4—24no—
257C4⋊C4—22no—
258C4⋊C4—434no—
259C4⋊C4—8616no—
260C4⋊C4—862no—
261C4⋊C4—864no—
262C4⋊C4—864no—
263C22⋊C4—42no—
264C42—868no—
265C42—864no—
266C42—864no—
267C42D4×D4312yes—
268C42C2×C22⋊D4311yescharacteristic
269C42C23×D4311yescharacteristic
270C23—41no—
271C23#1306329311yescharacteristic
272Q8—44no—
273Q8—42no—
274Q8—82no—
275Q8—438no—
276Q8—868no—
277Q8—864no—
278Q8—3448no—
279D4—42no—
280D4—44no—
281D4—82no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—44no—
286C2×C4—41no—
287C2×C4—82no—
288C2×C4—868no—
289C2×C4—864no—
290C2×C4—864no—
291C2×C4—1724no—
292C2×C4#1306329312yes—
293C2×C4#1306329311yescharacteristic
294C2×C4C2×D4×D4312yes—
295C2×C4C22×C22⋊D4311yescharacteristic
296C8—24no—
297C8—1724no—
298C22—22no—
299C22—82no—
300C22—81no—
301C22#1458306612yes—
302C22C2×#1306329311yescharacteristic
303C4—22no—
304C4—21no—
305C4—21no—
306C4—44no—
307C4—81no—
308C4—868no—
309C4—1724no—
310C4#137×D4314yes—
311C2—22no—
312C2—161no—
313C2#1914382712yes—
314C2C2×#1458306611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3152C2
socleC22×C43C2×#120
prime radicalC43×#532C22
hypercenter#3152D43
hypocenterC43#18546
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3152

Complements

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

NH ≅ G/Ntype
1. C2×#14583629C2semidirect
3. #19133733C2semidirect
4. #19133671C2semidirect
5. #19133321C2semidirect
6. #19133043C2semidirect
137. Dic86#137semidirect
187. C43#18546semidirect

Maximal subgroups

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

subgroupindex
C2×#145836292
#191447132
#191337332
#191336712
#191333212
#191330432
C43×#31522
#1854643