Finite Group Databasebeta

← #25072905

Subgroups — #25072905

Order 11008.

982 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 163 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×#14583615C211yesmaximal, characteristic
2#19144975C211yesmaximal, characteristic, complemented
3#19144695C212yesmaximal, complemented
4#19133824C218yesmaximal, complemented
5#19133037C212yesmaximal, complemented
6C43×#1558C211yesmaximal, characteristic, complemented
7#14583615—24no—
8#14583615—22no—
9#14583615C2214yes—
10#14583456C2211yescharacteristic
11C2×#13063314—22no—
12C2×#13063300—22no—
13C2×C4×D172C2212yes—
14C2×#13063283—22no—
15#14583267—22no—
16#14583249C2214yescomplemented
17#14583235—22no—
18#14583180C2214yescomplemented
19#14583105C2214yescomplemented
20#14583052—22no—
21#14583001—24no—
22#14582908—22no—
23C4×#10621877C2211yescharacteristic
24#14582626C2218yescomplemented
25C2×C4⋊Q8×C43C2211yescharacteristic
26C43×#432C2212yes—
27C43×#333C2214yescomplemented
28C22×D172—22no—
29C22×D172D412yes—
30C22×C4×D43—22no—
31C2×#10621873—24no—
32C2×#10621877—21no—
33#13063325C2312yes—
34#13063317—21no—
35#13063314—28no—
36#13063314—28no—
37#13063304—22no—
38#13063300—28no—
39#13063300—28no—
40C4×Dic86—22no—
41C4×D172—22no—
42C4×D172—22no—
43C4×D172D414yes—
44C4×D172C2314yes—
45#13063284—21no—
46#13063283—28no—
47#13063283—28no—
48C2×C4⋊Dic43D412yes—
49C2×(C2×D43)⋊C4—24no—
50C2×(C2×D43)⋊C4—22no—
51C2×C4×Dic43—22no—
52#13063259—24no—
53#13063250—24no—
54#13063249—28no—
55#13063247—24no—
56#13063236—21no—
57C4×C43⋊C8C2312yes—
58C22×Q8×C43D412yes—
59C4⋊Q8×C43—22no—
60C4⋊Q8×C43D412yes—
61C4⋊Q8×C43C2312yes—
62C2×C4⋊C4×C43—22no—
63C2×C42×C43C2311yescharacteristic
64C4⋊C8×C43C2314yes—
65C22⋊C8×C43—22no—
66#97×C43—22no—
67C23×D43—22no—
68C2×Q8×C43—22no—
69C2×Q8×C43—44no—
70C2×Q8×C43C2×D414yes—
71C22×C4×C43—22no—
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D412yes—
74C22×Dic43—22no—
75C2×D172—22no—
76C2×D172—28no—
77C2×D172—44no—
78C2×D172—84no—
79C2×D172C2×D414yes—
80C2×C4×D43—24no—
81C2×C4×D43—24no—
82C2×C4×D43—48no—
83C2×Dic86—22no—
84C2×C8×C43—24no—
85C4⋊C4×C43—24no—
86C4⋊C4×C43—24no—
87C42×C43C2×D411yescharacteristic
88C42×C43C2×D412yes—
89C42×C43C2411yescharacteristic
90C22⋊Dic43—41no—
91(C2×D43)⋊C4—216no—
92(C2×D43)⋊C4—24no—
93(C2×D43)⋊C4—24no—
94C4⋊Dic43—22no—
95C4⋊Dic43—22no—
96C4⋊Dic43—22no—
97C4⋊Dic43C2×D414yes—
98Dic43⋊C4—42no—
99C4×Dic43—28no—
100C4×Dic43—41no—
101#10621877—42no—
102C2×C43⋊C8—22no—
103#10621873—48no—
104C23×C43#12011yescharacteristic
105C22×D43—24no—
106C22×D43—44no—
107C22×D43—44no—
108C22×D43—44no—
109Q8×C43—44no—
110Q8×C43—82no—
111C2×C4×C43—22no—
112C2×C4×C43—24no—
113C2×C4×C43—24no—
114C2×C4×C43—44no—
115C2×C4×C43#12011yescharacteristic
116C2×C4×C43#12012yes—
117C2×C4×C43C22×D412yes—
118C2×C4×C43C22×D411yescharacteristic
119C2×Dic43—24no—
120C2×Dic43—44no—
121C2×Dic43—42no—
122D172—24no—
123D172—24no—
124D172—44no—
125D172—88no—
126C4×D43—48no—
127C4×D43—48no—
128Dic86—44no—
129C8×C43—44no—
130C43⋊C8—42no—
131#18552—431nomaximal, Sylow
132C22×C43—22no—
133C22×C43#45512yes—
134C22×C43C2×#12011yescharacteristic
135C2×D43—44no—
136C2×D43—44no—
137C2×D43—44no—
138C2×D43—88no—
139C4×C43—22no—
140C4×C43—21no—
141C4×C43—21no—
142C4×C43—44no—
143C4×C43#57514yes—
144Dic43—44no—
145Dic43—82no—
146C2×#555—431no—
147#3139—431no—
148#3110—432no—
149#1646—438no—
150#1558D4311yescharacteristic, complemented
151#1490—432no—
152C2×C43—22no—
153C2×C43#300512yes—
154C2×C43C2×#45511yescharacteristic
155D43—84no—
156#555—434no—
157#555—864no—
158#555—862no—
159#533—431no—
160C2×C4⋊Q8C2×D4311yescharacteristic
161C2×#124—862no—
162C2×#121—862no—
163C2×C4×D4—432no—
164C2×#117—862no—
165#491—862no—
166#487—434no—
167#484—862no—
168#474—434no—
169#461—434no—
170#450—862no—
171#440—864no—
172#432C2×D4312yes—
173#419—862no—
174C4×M16—431no—
175#333C2×D4314yescomplemented
176D4⋊C8—438no—
177C43#1855211yescharacteristic, complemented, Sylow
178C22×Q8D17212yes—
179C22×D4—432no—
180C22×D4—862no—
181C23×C4—862no—
182C2×SD16—864no—
183C2×M16—861no—
184C4⋊Q8—22no—
185C4⋊Q8—432no—
186C4⋊Q8D17212yes—
187C4⋊Q8C22×D4312yes—
188#125—861no—
189#124—868no—
190#124—868no—
191C22⋊Q8—862no—
192#121—868no—
193#121—868no—
194C4×Q8—862no—
195C4×D4—434no—
196C4×D4—434no—
197C4×D4—862no—
198C4×D4—862no—
199#117—868no—
200#117—868no—
201#117—861no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—432no—
204C2×C22⋊C4—864no—
205C2×C22⋊C4—862no—
206C2×C42—862no—
207C2×C42C22×D4311yescharacteristic
208#107—864no—
209C4⋊C8C22×D4314yes—
210#103—864no—
211#103—868no—
212#102—864no—
213C22⋊C8—22no—
214#97—22no—
215#97—861no—
216C4×C8—432no—
217C24—862no—
218C2×Q8—22no—
219C2×Q8—44no—
220C2×Q8—862no—
221C2×Q8C2×D17214yes—
222C2×D4—434no—
223C2×D4—868no—
224C2×D4—862no—
225C2×D4—3444no—
226C2×D4—1724no—
227C22×C4—22no—
228C22×C4—862no—
229C22×C4—864no—
230C22×C4—864no—
231C22×C4—1728no—
232C22×C4C2×D17211yescharacteristic
233C22×C4D4×D4312yes—
234SD16—1728no—
235M16—1722no—
236C2×C8—24no—
237C2×C8—862no—
238C4⋊C4—24no—
239C4⋊C4—24no—
240C4⋊C4—434no—
241C4⋊C4—862no—
242C4⋊C4—862no—
243C4⋊C4—862no—
244C4⋊C4—1722no—
245C22⋊C4—8616no—
246C22⋊C4—864no—
247C22⋊C4—864no—
248C22⋊C4—1721no—
249C42—868no—
250C42—1721no—
251C42C2×D17211yescharacteristic
252C42D4×D4312yes—
253C42C23×D4311yescharacteristic
254C23—864no—
255C23—1724no—
256C23—1724no—
257C23—1724no—
258C23#1306329511yescharacteristic
259Q8—44no—
260Q8—82no—
261Q8—1724no—
262D4—864no—
263D4—864no—
264D4—3448no—
265D4—1724no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—44no—
270C2×C4—864no—
271C2×C4—1728no—
272C2×C4—1722no—
273C2×C4—1724no—
274C2×C4—1728no—
275C2×C4#1306329511yescharacteristic
276C2×C4#1306329512yes—
277C2×C4C2×D4×D4312yes—
278C2×C4C22×D17211yescharacteristic
279C8—44no—
280C8—1722no—
281C22—22no—
282C22—3448no—
283C22—1724no—
284C22—1724no—
285C22—1724no—
286C22#1458307912yes—
287C22C2×#1306329511yescharacteristic
288C4—22no—
289C4—21no—
290C4—21no—
291C4—44no—
292C4—3442no—
293C4—1724no—
294C4#1458369814yes—
295C2—22no—
296C2—3444no—
297C2#1914384112yes—
298C2C2×#1458307911yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1558C2
socleC22×C43C2×#120
prime radicalC2×#14583615C2
hypercenter#1558D43
hypocenterC43#18552
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1558

Complements

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

NH ≅ G/Ntype
2. #19144975C2semidirect
3. #19144695C2semidirect
4. #19133824C2semidirect
5. #19133037C2semidirect
6. C43×#1558C2semidirect
16. #14583249C22semidirect
18. #14583180C22semidirect
19. #14583105C22semidirect
24. #14582626C22semidirect
27. C43×#333C22semidirect
150. #1558D43semidirect
175. #333C2×D43semidirect
177. C43#18552semidirect

Maximal subgroups

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

subgroupindex
C2×#145836152
#191449752
#191446952
#191338242
#191330372
C43×#15582
#1855243