Finite Group Databasebeta

← #24997920

Subgroups — #24997920

Order 11008.

600 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 95 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×#14583261C212yesmaximal, complemented
2#19142641C211yesmaximal, characteristic
3C2×#14582638C212yesmaximal, complemented
4#19132476C211yesmaximal, characteristic, complemented
5C43×#1960C211yesmaximal, characteristic, complemented
6C2×#13063313C2212yes—
7#14583261—24no—
8#14583261—24no—
9C2×#13063248—22no—
10C2×#13063245—22no—
11C2×#13063236C2212yes—
12#14582816—22no—
13#14582812—22no—
14#14582809—22no—
15#14582638—24no—
16C2×C4⋊Q8×C43C2211yescharacteristic
17C2×#103×C43—22no—
18C2×#97×C43C2211yescharacteristic
19C43×#382C2211yescharacteristic
20C22×Dic86D412yes—
21C22×D172—22no—
22C22×D172D412yes—
23C22×C43⋊C8—22no—
24#13063313—22no—
25#13063313—22no—
26#13063313—22no—
27#13063313—22no—
28C2×(C2×D43)⋊C4—22no—
29C2×(C2×D43)⋊C4—22no—
30C2×(C2×D43)⋊C4—24no—
31#13063248—28no—
32#13063245—28no—
33#13063236—22no—
34#13063236D414yescomplemented
35C43⋊#95—22no—
36C22×Q8×C43—21no—
37C22×C8×C43—21no—
38C4⋊Q8×C43—22no—
39C4⋊Q8×C43—21no—
40C4⋊Q8×C43D412yescomplemented
41C2×C4⋊C4×C43—22no—
42C2×C4⋊C4×C43D412yes—
43C2×C42×C43C2311yescharacteristic
44#103×C43—44no—
45#97×C43—22no—
46#95×C43—22no—
47C23×D43—22no—
48C2×Q8×C43—22no—
49C2×Q8×C43—42no—
50C2×Q8×C43—42no—
51C2×Q8×C43—41no—
52C22×C4×C43—22no—
53C22×C4×C43—41no—
54C22×C4×C43C2×D412yes—
55C22×C4×C43C2×D411yescharacteristic
56C22×Dic43—22no—
57C2×D172—22no—
58C2×D172—22no—
59C2×D172—44no—
60C2×D172—82no—
61C2×D172—84no—
62C2×Dic86—22no—
63C2×Dic86—22no—
64C2×Dic86—44no—
65C2×C8×C43—22no—
66C2×C8×C43—41no—
67C2×C8×C43—41no—
68C4⋊C4×C43—24no—
69C4⋊C4×C43—42no—
70C4⋊C4×C43—42no—
71C42×C43C2×D411yescharacteristic
72C42×C43C2×D412yes—
73C42×C43#4111yescharacteristic
74(C2×D43)⋊C4—42no—
75(C2×D43)⋊C4—42no—
76(C2×D43)⋊C4—42no—
77(C2×D43)⋊C4—42no—
78(C2×D43)⋊C4—84no—
79C2×C43⋊C8—24no—
80C2×C43⋊C8—44no—
81C23×C43#12011yescharacteristic
82C22×D43—42no—
83C22×D43—42no—
84C22×D43—42no—
85C22×D43—44no—
86C22×D43—44no—
87Q8×C43—44no—
88Q8×C43—82no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—24no—
92C2×C4×C43—42no—
93C2×C4×C43—42no—
94C2×C4×C43—44no—
95C2×C4×C43—81no—
96C2×C4×C43—81no—
97C2×C4×C43#12012yes—
98C2×C4×C43#12112yes—
99C2×C4×C43#12111yescharacteristic
100C2×C4×C43#12711yescharacteristic
101C2×Dic43—42no—
102C2×Dic43—44no—
103D172—44no—
104D172—82no—
105D172—88no—
106Dic86—44no—
107Dic86—82no—
108C8×C43—42no—
109C43⋊C8—44no—
110#10085—431nomaximal, Sylow
111C22×C43#39211yescharacteristic
112C22×C43#45311yescharacteristic
113C22×C43#45411yescharacteristic
114C22×C43#45514yes—
115C2×D43—84no—
116C2×D43—84no—
117C2×D43—82no—
118C2×D43—82no—
119C2×D43—82no—
120C4×C43—22no—
121C4×C43—22no—
122C4×C43—21no—
123C4×C43—21no—
124C4×C43—82no—
125C4×C43—82no—
126Dic43—82no—
127C2×#489—432no—
128#2819—431no—
129#1960D4311yescharacteristic, complemented
130C2×#329—432no—
131#1295—431no—
132C2×C43#165912yes—
133C2×C43#166212yes—
134C2×C43#200412yes—
135C2×C43#200611yescharacteristic
136D43—162no—
137C2×C4⋊Q8C2×D4311yescharacteristic
138C2×#124—432no—
139#489—864no—
140#489—864no—
141C2×#103—22no—
142C2×#103—862no—
143C2×#102—862no—
144C2×#97—432no—
145C2×#97C2×D4311yescharacteristic
146#394—862no—
147#393—862no—
148#392—862no—
149#382C2×D4311yescharacteristic
150#329—864no—
151C43#1008511yescharacteristic, complemented, Sylow
152C22×Q8—21no—
153C22×Q8—432no—
154C22×D4—432no—
155C22×D4—862no—
156C22×C8—21no—
157C22×C8—862no—
158C4⋊Q8—21no—
159C4⋊Q8—22no—
160C4⋊Q8D17212yescomplemented
161#124—862no—
162#124—862no—
163#124—862no—
164#124—862no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4C22⋊D4312yes—
167C2×C22⋊C4—864no—
168C2×C22⋊C4—862no—
169C2×C22⋊C4—862no—
170C2×C42C22×D4311yescharacteristic
171#103—44no—
172#103—868no—
173#102—868no—
174#97—22no—
175#97—434no—
176#97—862no—
177#95—22no—
178#95—862no—
179C24—862no—
180C2×Q8—22no—
181C2×Q8—42no—
182C2×Q8—42no—
183C2×Q8—41no—
184C2×Q8—862no—
185C2×Q8—862no—
186C2×Q8—1724no—
187C2×D4—862no—
188C2×D4—862no—
189C2×D4—3442no—
190C2×D4—3444no—
191C2×D4—1724no—
192C22×C4—22no—
193C22×C4—41no—
194C22×C4—862no—
195C22×C4D4×D4312yes—
196C22×C4C2×C22⋊D4311yescharacteristic
197C2×C8—22no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—864no—
201C2×C8—1724no—
202C4⋊C4—24no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C22⋊C4—3444no—
206C22⋊C4—1722no—
207C22⋊C4—1722no—
208C22⋊C4—1722no—
209C22⋊C4—1722no—
210C42C2×D17211yescharacteristic
211C42#1062189811yescharacteristic
212C42D4×D4312yes—
213C23—1722no—
214C23—1722no—
215C23—1722no—
216C23—1724no—
217C23—1724no—
218C23#1306329311yescharacteristic
219Q8—44no—
220Q8—82no—
221Q8—3442no—
222Q8—1724no—
223D4—3442no—
224D4—3448no—
225D4—1724no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—24no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—44no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—1722no—
235C2×C4—1724no—
236C2×C4#1306329512yes—
237C2×C4#1306329812yes—
238C2×C4#1306329911yescharacteristic
239C2×C4#1306332111yescharacteristic
240C8—42no—
241C8—1724no—
242C22—3442no—
243C22—3442no—
244C22—3442no—
245C22—3444no—
246C22—3444no—
247C22#1458280811yescharacteristic
248C22#1458306611yescharacteristic
249C22#1458307111yescharacteristic
250C22#1458307514yes—
251C4—22no—
252C4—22no—
253C4—21no—
254C4—21no—
255C4—82no—
256C4—82no—
257C4—3442no—
258C2—6882no—
259C2#1913389912yes—
260C2#1913391612yes—
261C2#1913562512yes—
262C2#1913563611yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1960C2
socleC23×C43#120
prime radical#19142641C2
hypercenter#1960D43
hypocenterC43#10085
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
1. C2×#14583261C2semidirect
3. C2×#14582638C2semidirect
4. #19132476C2semidirect
5. C43×#1960C2semidirect
34. #13063236D4semidirect
40. C4⋊Q8×C43D4semidirect
129. #1960D43semidirect
151. C43#10085semidirect
160. C4⋊Q8D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145832612
#191426412
C2×#145826382
#191324762
C43×#19602
#1008543