Finite Group Databasebeta

← #25072679

Subgroups — #25072679

Order 11008.

1068 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 179 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
1#19145045C211yesmaximal, characteristic
2#19144717C212yesmaximal, complemented
3#19133716C214yesmaximal, complemented
4#19133654C214yesmaximal, complemented
5#19133309C211yesmaximal, characteristic, complemented
6#19133042C212yesmaximal, complemented
7C2×C43×#559C211yesmaximal, characteristic, complemented
8C2×#13063351—22no—
9#14583449C2211yescharacteristic
10#14583286—22no—
11#14583275C2212yes—
12#14583271C2212yes—
13#14583212—22no—
14#14583194C2214yescomplemented
15#14583099C2214yescomplemented
16#14583038—22no—
17#14582997—24no—
18#14582956C2212yes—
19C4×#10621877C2211yescharacteristic
20#14582643C2214yes—
21Q8⋊(C43⋊C8)C2218yescomplemented
22C43×#559—22no—
23C43×#559—24no—
24C43×#559C2214yes—
25C2×#127×C43C2211yescharacteristic
26C2×#124×C43—22no—
27C2×#123×C43—22no—
28C2×C4×Q8×C43C2212yes—
29C2×C4×D4×C43—22no—
30C2×#10621898—21no—
31#13063351—48no—
32C2×#10621883—24no—
33C2×#10621884—24no—
34C2×#10621882—24no—
35C2×#10621877—21no—
36#13063325C2311yescharacteristic
37#13063322C2311yescharacteristic
38#13063313—21no—
39#13063299—22no—
40C4×D172—22no—
41#13063258—24no—
42C4⋊(C43⋊C8)C2314yes—
43#13063249—24no—
44#13063245—24no—
45C22⋊(C43⋊C8)—22no—
46#13063236—21no—
47#13063236—22no—
48C4×C43⋊C8C2312yes—
49C22×Q8×C43D412yes—
50C22×D4×C43—22no—
51C22×D4×C43D412yes—
52C23×C4×C43—22no—
53#127×C43—22no—
54#127×C43D412yes—
55#127×C43C2312yes—
56#124×C43—28no—
57#124×C43—28no—
58#123×C43—28no—
59#123×C43—28no—
60C4×Q8×C43—22no—
61C4×Q8×C43—22no—
62C4×Q8×C43D414yes—
63C4×Q8×C43C2314yes—
64C4×D4×C43—28no—
65C4×D4×C43—28no—
66C2×C4⋊C4×C43—22no—
67C2×C4⋊C4×C43D412yes—
68C2×C22⋊C4×C43—24no—
69C2×C22⋊C4×C43—22no—
70C2×C42×C43—22no—
71C2×C42×C43C2311yescharacteristic
72C24×C43—22no—
73C2×Q8×C43—22no—
74C2×Q8×C43—44no—
75C2×Q8×C43C2×D414yes—
76C2×D4×C43—24no—
77C2×D4×C43—22no—
78C2×D4×C43—24no—
79C2×D4×C43—48no—
80C2×D4×C43—44no—
81C2×D4×C43C2×D414yes—
82C22×C4×C43—28no—
83C22×C4×C43—22no—
84C22×C4×C43—22no—
85C22×C4×C43—84no—
86C22×C4×C43C2×D412yes—
87C22×C4×C43C2×D411yescharacteristic
88C2×C22⋊D43—41no—
89#10621898—44no—
90C2×D172—22no—
91C2×D172—21no—
92C2×C4×D43—41no—
93C2×Dic86—21no—
94C4⋊C4×C43—24no—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—24no—
97C4⋊C4×C43C2×D414yes—
98C22⋊C4×C43—216no—
99C22⋊C4×C43—28no—
100C42×C43—24no—
101C42×C43—24no—
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D412yes—
104C42×C43C2411yescharacteristic
105#10621884—48no—
106#10621883—48no—
107#10621882—48no—
108(C2×D43)⋊C4—42no—
109C4⋊Dic43—22no—
110#10621877—24no—
111C2×C43⋊C8—22no—
112C2×C43⋊C8—24no—
113C23×C43—24no—
114C23×C43—48no—
115C23×C43—44no—
116C23×C43#12011yescharacteristic
117C22×D43—41no—
118Q8×C43—24no—
119Q8×C43—24no—
120Q8×C43—44no—
121D4×C43—44no—
122D4×C43—48no—
123D4×C43—48no—
124D4×C43—82no—
125C2×C4×C43—22no—
126C2×C4×C43—24no—
127C2×C4×C43—24no—
128C2×C4×C43—24no—
129C2×C4×C43—44no—
130C2×C4×C43—44no—
131C2×C4×C43—88no—
132C2×C4×C43#12012yes—
133C2×C4×C43#12011yescharacteristic
134C2×C4×C43C22×D411yescharacteristic
135C2×C4×C43C22×D412yes—
136C22⋊D43—82no—
137C2×Dic43—41no—
138D172—42no—
139D172—44no—
140C4×D43—82no—
141Dic86—42no—
142C43⋊C8—24no—
143C43⋊C8—44no—
144#18526—431nomaximal, Sylow
145C22×C43—22no—
146C22×C43—48no—
147C22×C43—44no—
148C22×C43—88no—
149C22×C43#45312yes—
150C22×C43C2×#12011yescharacteristic
151C2×D43—82no—
152C2×D43—81no—
153C4×C43—22no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—44no—
157C4×C43—44no—
158C4×C43#57514yes—
159Dic43—81no—
160C2×#559D4311yescharacteristic, complemented
161#3151—431no—
162#3112—432no—
163#1630—434no—
164#1620—434no—
165#1555—431no—
166#1491—432no—
167C2×C43—22no—
168C2×C43—84no—
169C2×C43#300512yes—
170C2×C43C2×#45311yescharacteristic
171D43—161no—
172C2×AGL(1,ℤ/8)—862no—
173#559—22no—
174#559—24no—
175#559C2×D4314yes—
176#532—431no—
177C2×#127C2×D4311yescharacteristic
178C2×#124—22no—
179C2×#123—22no—
180C2×C4×Q8C2×D4312yes—
181C2×C4×D4—22no—
182#496—862no—
183#493—432no—
184#492—432no—
185#480—862no—
186#477—434no—
187#460—434no—
188#448—862no—
189#440—864no—
190#432—432no—
191C4×M16—431no—
192#331—434no—
193Q8⋊C8—438no—
194C43#1852611yescharacteristic, complemented, Sylow
195C2×#41—861no—
196C22×Q8C22⋊D4312yes—
197C22×D4—22no—
198C22×D4C22⋊D4312yes—
199C23×C4—22no—
200AGL(1,ℤ/8)—1728no—
201C2×SD16—864no—
202C2×SD16—864no—
203C2×D8—864no—
204C2×M16—861no—
205C4⋊Q8—431no—
206#127—22no—
207#127—431no—
208#127C22⋊D4312yes—
209#127C22×D4312yes—
210#124—28no—
211#124—28no—
212#124—861no—
213#123—28no—
214#123—28no—
215#121—862no—
216C4×Q8—22no—
217C4×Q8—22no—
218C4×Q8C22⋊D4314yes—
219C4×Q8C22×D4314yes—
220C4×D4—28no—
221C4×D4—28no—
222C4×D4—862no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4C22⋊D4312yes—
225C2×C22⋊C4—24no—
226C2×C22⋊C4—22no—
227C2×C42—22no—
228C2×C42C22×D4311yescharacteristic
229#107—864no—
230C4⋊C8—434no—
231#103—864no—
232#102—864no—
233C22⋊C8—862no—
234#97—861no—
235#97—862no—
236C4×C8—432no—
237C24—22no—
238#41—1724no—
239C2×Q8—22no—
240C2×Q8—44no—
241C2×Q8—861no—
242C2×Q8C2×C22⋊D4314yes—
243C2×D4—24no—
244C2×D4—22no—
245C2×D4—24no—
246C2×D4—48no—
247C2×D4—44no—
248C2×D4—862no—
249C2×D4—861no—
250C2×D4—1721no—
251C2×D4C2×C22⋊D4314yes—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—28no—
255C22×C4—84no—
256C22×C4—1721no—
257C22×C4C2×C22⋊D4312yes—
258C22×C4C2×C22⋊D4311yescharacteristic
259SD16—1728no—
260SD16—1728no—
261D8—1728no—
262M16—864no—
263C2×C8—862no—
264C2×C8—864no—
265C4⋊C4—24no—
266C4⋊C4—22no—
267C4⋊C4—24no—
268C4⋊C4—862no—
269C4⋊C4C2×C22⋊D4314yes—
270C22⋊C4—216no—
271C22⋊C4—28no—
272C22⋊C4—1722no—
273C42—24no—
274C42—24no—
275C42C2×C22⋊D4312yes—
276C42C2×C22⋊D4311yescharacteristic
277C42C23×D4311yescharacteristic
278C23—24no—
279C23—48no—
280C23—44no—
281C23—1721no—
282C23#1306329411yescharacteristic
283Q8—24no—
284Q8—24no—
285Q8—44no—
286Q8—1722no—
287D4—44no—
288D4—48no—
289D4—48no—
290D4—82no—
291D4—3442no—
292D4—1722no—
293D4—1724no—
294C2×C4—22no—
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—88no—
301C2×C4—3442no—
302C2×C4—1721no—
303C2×C4#1306329412yes—
304C2×C4#1306329411yescharacteristic
305C2×C4C22×C22⋊D4311yescharacteristic
306C2×C4C22×C22⋊D4312yes—
307C8—864no—
308C8—1724no—
309C22—22no—
310C22—48no—
311C22—44no—
312C22—88no—
313C22—3442no—
314C22—3441no—
315C22#1458306712yes—
316C22C2×#1306329411yescharacteristic
317C4—22no—
318C4—21no—
319C4—21no—
320C4—44no—
321C4—44no—
322C4—3441no—
323C4#1458369714yes—
324C2—22no—
325C2—84no—
326C2—6881no—
327C2#1914383712yes—
328C2C2×#1458306711yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#559C2
socleC22×C43C2×#120
prime radical#19145045C2
hypercenterC2×#559D43
hypocenterC43#18526
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
2. #19144717C2semidirect
3. #19133716C2semidirect
4. #19133654C2semidirect
5. #19133309C2semidirect
6. #19133042C2semidirect
7. C2×C43×#559C2semidirect
14. #14583194C22semidirect
15. #14583099C22semidirect
21. Q8⋊(C43⋊C8)C22semidirect
160. C2×#559D43semidirect
194. C43#18526semidirect

Maximal subgroups

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

subgroupindex
#191450452
#191447172
#191337162
#191336542
#191333092
#191330422
C2×C43×#5592
#1852643