Finite Group Databasebeta

← #24990952

Subgroups — #24990952

Order 11008.

500 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 115 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#19135412C211yesmaximal, characteristic
2#19134764C212yesmaximal, complemented
3C2×#14582639C211yesmaximal, characteristic
4#19132476C212yesmaximal, complemented
5C43×#2379C211yesmaximal, characteristic
6C2×#13063258—22no—
7C2×#13063256—22no—
8C2×#13063249—21no—
9C2×#13063246—21no—
10C2×#13063236C2211yescharacteristic
11C2×#13063236C2212yes—
12#14582769C2211yescharacteristic
13#14582639C414yescomplemented
14C2×#124×C43C2211yescharacteristic
15C43×#391—21no—
16C43×#388—22no—
17C43×#386—21no—
18C43×#385—22no—
19C43×#382C2212yes—
20C22×C43⋊C8—22no—
21C22×C43⋊C8—21no—
22C2×C4⋊Dic43—21no—
23C2×C4⋊Dic43—22no—
24#13063258—44no—
25#13063256—44no—
26#13063249—42no—
27#13063246—42no—
28#13063236—22no—
29#13063236—22no—
30#13063236C2×C414yescomplemented
31C22×Q8×C43D411yescharacteristic
32C22×D4×C43D411yescharacteristic
33C23×C4×C43—21no—
34#124×C43—22no—
35#124×C43C2×C412yes—
36#124×C43Q812yes—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43D412yes—
39C2×C4⋊C4×C43D412yes—
40C2×C22⋊C4×C43—22no—
41C2×C22⋊C4×C43—22no—
42C2×C22⋊C4×C43—21no—
43C2×C42×C43—21no—
44C2×C42×C43C2311yescharacteristic
45#95×C43—22no—
46#95×C43—22no—
47#95×C43—22no—
48C24×C43—21no—
49C2×Q8×C43—21no—
50C2×Q8×C43—41no—
51C2×Q8×C43—41no—
52C2×Q8×C43C4⋊C412yes—
53C2×D4×C43—21no—
54C2×D4×C43—41no—
55C2×D4×C43—41no—
56C2×D4×C43C4⋊C412yes—
57C22×C4×C43—21no—
58C22×C4×C43—22no—
59C22×C4×C43—22no—
60C22×C4×C43—82no—
61C22×C4×C43—81no—
62C22×C4×C43C2×D411yescharacteristic
63C22×C4×C43C2×D412yes—
64C22×Dic43—41no—
65C4⋊C4×C43—42no—
66C4⋊C4×C43—42no—
67C4⋊C4×C43—81no—
68C22⋊C4×C43—24no—
69C22⋊C4×C43—24no—
70C22⋊C4×C43—82no—
71C22⋊C4×C43—81no—
72C42×C43—81no—
73C42×C43C22×C411yescharacteristic
74C42×C43C2×Q811yescharacteristic
75C42×C43#4112yes—
76C4⋊Dic43—41no—
77C4⋊Dic43—41no—
78C4⋊Dic43—42no—
79C4⋊Dic43—42no—
80C2×C43⋊C8—24no—
81C2×C43⋊C8—24no—
82C2×C43⋊C8—24no—
83C2×C43⋊C8—22no—
84C2×C43⋊C8—41no—
85C2×C43⋊C8—41no—
86C23×C43—22no—
87C23×C43—42no—
88C23×C43—41no—
89C23×C43—41no—
90C23×C43—42no—
91C23×C43#12011yescharacteristic
92Q8×C43—42no—
93Q8×C43—81no—
94D4×C43—42no—
95D4×C43—81no—
96C2×C4×C43—22no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—41no—
102C2×C4×C43—41no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—42no—
106C2×C4×C43—42no—
107C2×C4×C43—42no—
108C2×C4×C43—42no—
109C2×C4×C43—84no—
110C2×C4×C43C2×C4⋊C411yescharacteristic
111C2×C4×C43C4×D412yes—
112C2×C4×C43C22⋊Q812yes—
113C2×C4×C43#12311yescharacteristic
114C2×Dic43—81no—
115C2×Dic43—82no—
116C43⋊C8—28no—
117C43⋊C8—42no—
118#8910—431nomaximal, Sylow
119C22×C43—42no—
120C22×C43—44no—
121C22×C43—81no—
122C22×C43—81no—
123C22×C43—82no—
124C22×C43#38511yescharacteristic
125C22×C43#45311yescharacteristic
126C22×C43#45312yes—
127C22×C43#45511yescharacteristic
128C22×C43#45612yes—
129C4×C43—21no—
130C4×C43—21no—
131C4×C43—22no—
132C4×C43—22no—
133C4×C43—42no—
134C4×C43—82no—
135C4×C43—82no—
136Dic43—161no—
137#2379D4311yescharacteristic
138#1959—431no—
139#1847—432no—
140C2×#329—431no—
141#1295—432no—
142C2×C43—82no—
143C2×C43#165511yescharacteristic
144C2×C43#166011yescharacteristic
145C2×C43#166112yes—
146C2×C43#185611yescharacteristic
147C2×C43#185912yes—
148C2×#124C2×D4311yescharacteristic
149C2×#107—862no—
150C2×#106—862no—
151C2×#103—861no—
152C2×#102—861no—
153C2×#97—432no—
154C2×#97—431no—
155#391—21no—
156#388—22no—
157#386—21no—
158#385—22no—
159#384—431no—
160#382C2×D4312yes—
161#329—434no—
162C43#891011yescharacteristic, complemented, Sylow
163C22×Q8C22⋊D4311yescharacteristic
164C22×D4C22⋊D4311yescharacteristic
165C23×C4—21no—
166C22×C8—862no—
167C22×C8—861no—
168#124—22no—
169#124Dic8612yes—
170#124C4×D4312yes—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—861no—
173C2×C4⋊C4—862no—
174C2×C4⋊C4C22⋊D4312yes—
175C2×C4⋊C4C22⋊D4312yes—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—21no—
179C2×C42—21no—
180C2×C42C22×D4311yescharacteristic
181#107—1724no—
182#106—1724no—
183#103—1722no—
184#102—1722no—
185#97—434no—
186#97—862no—
187#97—862no—
188#95—22no—
189#95—22no—
190#95—22no—
191C24—21no—
192C2×Q8—21no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8Dic43⋊C412yes—
196C2×D4—21no—
197C2×D4—41no—
198C2×D4—41no—
199C2×D4Dic43⋊C412yes—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—82no—
204C22×C4—81no—
205C22×C4—1721no—
206C22×C4C2×C22⋊D4311yescharacteristic
207C22×C4C2×C22⋊D4312yes—
208C2×C8—864no—
209C2×C8—864no—
210C2×C8—864no—
211C2×C8—862no—
212C2×C8—1721no—
213C2×C8—1721no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C4⋊C4—81no—
217C4⋊C4—1721no—
218C4⋊C4—1721no—
219C4⋊C4—1722no—
220C4⋊C4—1722no—
221C22⋊C4—24no—
222C22⋊C4—24no—
223C22⋊C4—82no—
224C22⋊C4—81no—
225C42—81no—
226C42C2×Dic8611yescharacteristic
227C42C2×C4×D4311yescharacteristic
228C42#1062189812yes—
229C23—22no—
230C23—42no—
231C23—41no—
232C23—41no—
233C23—42no—
234C23#1306329411yescharacteristic
235Q8—42no—
236Q8—81no—
237D4—42no—
238D4—81no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—84no—
253C2×C4—3441no—
254C2×C4—3442no—
255C2×C4C2×Dic43⋊C411yescharacteristic
256C2×C4C4×C22⋊D4312yes—
257C2×C4#1306330412yes—
258C2×C4#1306330811yescharacteristic
259C8—868no—
260C8—1722no—
261C22—42no—
262C22—44no—
263C22—81no—
264C22—81no—
265C22—82no—
266C22#1458277211yescharacteristic
267C22#1458306711yescharacteristic
268C22#1458306712yes—
269C22#1458307711yescharacteristic
270C22#1458308212yes—
271C4—21no—
272C4—21no—
273C4—22no—
274C4—22no—
275C4—42no—
276C4—82no—
277C4—82no—
278C4—6881no—
279C2—82no—
280C2#1913388411yescharacteristic
281C2#1913390611yescharacteristic
282C2#1913391212yes—
283C2#1913480511yescharacteristic
284C2#1913482112yes—
subgroupG/H
centerC23#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2379C2
socleC23×C43#120
prime radicalC22×D4×C43D4
cosocleC2×C42×C43C23
hypercenter#2379D43
hypocenterC43#8910
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2379

Complements

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

NH ≅ G/Ntype
2. #19134764C2semidirect
4. #19132476C2semidirect
13. #14582639C4semidirect
30. #13063236C2×C4semidirect
162. C43#8910semidirect

Maximal subgroups

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

subgroupindex
#191354122
#191347642
C2×#145826392
#191324762
C43×#23792
#891043