Finite Group Databasebeta

← #25008803

Subgroups — #25008803

Order 11008.

470 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135726C211yesmaximal, characteristic
2#19133546C212yesmaximal
3#19132616C212yesmaximal, complemented
4#19132525C211yesmaximal, characteristic, complemented
5C43×#2607C211yesmaximal, characteristic, complemented
6#14583461C2211yescharacteristic
7C2×#13063308—21no—
8#14583038—22no—
9C2×#13063239—21no—
10#14582666C2211yescharacteristic
11#14582632—22no—
12#14582623C2212yes—
13C43×#399—21no—
14C43×#393C2212yes—
15C43×#391—22no—
16C43×#387—22no—
17C43×#381C2211yescharacteristic
18C4×C22⋊C4×C43—21no—
19C22×C22⋊D43—21no—
20C2×#10621884—42no—
21#13063309—41no—
22#13063308—42no—
23#13063308—42no—
24#13063299—22no—
25#13063295—41no—
26C2×Dic43⋊C4—41no—
27C2×C22⋊Dic43—21no—
28C2×(C2×D43)⋊C4—41no—
29#13063249—42no—
30#13063239—42no—
31C22⋊(C43⋊C8)—22no—
32C22×Q8×C43D412yes—
33C23×C4×C43D411yescharacteristic
34C2×C4⋊C4×C43—22no—
35C2×C4⋊C4×C43—21no—
36C2×C22⋊C4×C43—22no—
37C2×C22⋊C4×C43D411yescharacteristic
38C2×C22⋊C4×C43C2311yescharacteristic
39C2×C42×C43—21no—
40C2×C42×C43—21no—
41#95×C43—22no—
42#95×C43—21no—
43#95×C43—22no—
44#95×C43—22no—
45#95×C43D412yes—
46C24×C43C2×D411yescharacteristic
47C23×D43—21no—
48C2×Q8×C43—44no—
49C2×Q8×C43—42no—
50C22×C4×C43—21no—
51C22×C4×C43—22no—
52C22×C4×C43—21no—
53C22×C4×C43—22no—
54C22×C4×C43—21no—
55C22×C4×C43—41no—
56C22×C4×C43—41no—
57C22×C4×C43SD1612yescomplemented
58C22×C4×C43C2×D412yes—
59C2×C22⋊D43—41no—
60C2×C22⋊D43—41no—
61C2×C22⋊D43—41no—
62C2×C22⋊D43—41no—
63C2×C22⋊D43—41no—
64C2×C22⋊D43—41no—
65C22×Dic43—21no—
66C22×Dic43—41no—
67C2×D172—22no—
68C4⋊C4×C43—44no—
69C4⋊C4×C43—81no—
70C22⋊C4×C43—41no—
71C22⋊C4×C43—41no—
72C22⋊C4×C43—44no—
73C42×C43—81no—
74C42×C43—81no—
75C22⋊Dic43—22no—
76C22⋊Dic43—41no—
77#10621884—84no—
78(C2×D43)⋊C4—42no—
79(C2×D43)⋊C4—44no—
80C4⋊Dic43—22no—
81Dic43⋊C4—44no—
82C2×C43⋊C8—42no—
83C23×C43—21no—
84C23×C43—21no—
85C23×C43—42no—
86C23×C43#12011yescharacteristic
87C23×C43C2×SD1611yescharacteristic
88C23×C43#13711yescharacteristic
89C22×D43—41no—
90C22×D43—41no—
91C22×D43—41no—
92C22×D43—82no—
93Q8×C43—44no—
94Q8×C43—82no—
95C2×C4×C43—24no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—42no—
99C2×C4×C43—41no—
100C2×C4×C43—41no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—42no—
106C2×C4×C43—42no—
107C2×C4×C43—42no—
108C2×C4×C43—41no—
109C2×C4×C43—81no—
110C22⋊D43—81no—
111C22⋊D43—81no—
112C22⋊D43—81no—
113C22⋊D43—81no—
114C2×Dic43—41no—
115C2×Dic43—42no—
116C2×Dic43—41no—
117C2×Dic43—41no—
118C2×Dic43—82no—
119D172—82no—
120C43⋊C8—82no—
121#12121—431nomaximal, Sylow
122C22×C43—22no—
123C22×C43—21no—
124C22×C43—21no—
125C22×C43—41no—
126C22×C43—41no—
127C22×C43—42no—
128C22×C43—81no—
129C22×C43#44811yescharacteristic
130C22×C43#45311yescharacteristic
131C22×C43B(4,𝔽2)11yescharacteristic
132C2×D43—82no—
133C2×D43—81no—
134C2×D43—82no—
135C2×D43—161no—
136C4×C43—42no—
137C4×C43—42no—
138C4×C43—44no—
139C4×C43—82no—
140C4×C43—81no—
141Dic43—82no—
142Dic43—81no—
143#2607D4311yescharacteristic, complemented
144#2022—431no—
145#1601—432no—
146#1351—432no—
147#1317—431no—
148C2×C43—21no—
149C2×C43—21no—
150C2×C43—41no—
151C2×C43—41no—
152C2×C43#159611yescharacteristic
153C2×C43#219712yes—
154D43—161no—
155#534—431no—
156C2×#123—861no—
157#448—862no—
158C2×#99—861no—
159#399—21no—
160#393C2×D4312yes—
161#391—22no—
162#387—22no—
163#381C2×D4311yescharacteristic
164C4×C22⋊C4—21no—
165#342—431no—
166#327—862no—
167#323—432no—
168C43#1212111yescharacteristic, complemented, Sylow
169C22×Q8C22⋊D4312yes—
170C22×D4—861no—
171C23×C4C22⋊D4311yescharacteristic
172C2×SD16—1722no—
173#123—1721no—
174#123—1722no—
175#123—1722no—
176#121—862no—
177#120—1721no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—1721no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—861no—
183C2×C22⋊C4—1721no—
184C2×C22⋊C4C22⋊D4311yescharacteristic
185C2×C22⋊C4C22×D4311yescharacteristic
186C2×C42—21no—
187C2×C42—21no—
188#103—1722no—
189#99—1722no—
190C22⋊C8—862no—
191#95—22no—
192#95—21no—
193#95—22no—
194#95—22no—
195#95C22⋊D4312yes—
196C24—861no—
197C24C2×C22⋊D4311yescharacteristic
198C2×Q8—44no—
199C2×Q8—42no—
200C2×D4—862no—
201C2×D4—1721no—
202C2×D4—1721no—
203C2×D4—1721no—
204C2×D4—1721no—
205C2×D4—1721no—
206C2×D4—1721no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—861no—
215C22×C4—1721no—
216C22×C4#1062188412yescomplemented
217C22×C4C2×C22⋊D4312yes—
218SD16—3444no—
219C2×C8—1722no—
220C4⋊C4—44no—
221C4⋊C4—81no—
222C4⋊C4—862no—
223C4⋊C4—1724no—
224C22⋊C4—41no—
225C22⋊C4—44no—
226C22⋊C4—41no—
227C22⋊C4—862no—
228C22⋊C4—1722no—
229C22⋊C4—1724no—
230C22⋊C4—1721no—
231C42—81no—
232C42—81no—
233C23—21no—
234C23—21no—
235C23—42no—
236C23—3442no—
237C23—1721no—
238C23—1721no—
239C23—1721no—
240C23#1306329411yescharacteristic
241C23C2×#1062188411yescharacteristic
242C23#1306335611yescharacteristic
243Q8—44no—
244Q8—82no—
245D4—3442no—
246D4—3441no—
247D4—3441no—
248D4—3441no—
249D4—3441no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—81no—
265C2×C4—3442no—
266C2×C4—1722no—
267C2×C4—1721no—
268C2×C4—1721no—
269C2×C4—1721no—
270C8—3442no—
271C22—22no—
272C22—21no—
273C22—21no—
274C22—41no—
275C22—41no—
276C22—42no—
277C22—81no—
278C22—3442no—
279C22—3442no—
280C22—3441no—
281C22—6881no—
282C22#1458303811yescharacteristic
283C22#1458306711yescharacteristic
284C22#1458308611yescharacteristic
285C4—42no—
286C4—44no—
287C4—42no—
288C4—82no—
289C4—81no—
290C4—3442no—
291C4—3441no—
292C2—21no—
293C2—21no—
294C2—41no—
295C2—41no—
296C2—6881no—
297C2#1913351811yescharacteristic
298C2#1913658512yes—
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2607C2
socleC22×C43B(4,𝔽2)
prime radical#14583461C22
hypercenter#2607D43
hypocenterC43#12121
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2607

Complements

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

NH ≅ G/Ntype
3. #19132616C2semidirect
4. #19132525C2semidirect
5. C43×#2607C2semidirect
57. C22×C4×C43SD16semidirect
143. #2607D43semidirect
168. C43#12121semidirect
216. C22×C4#10621884semidirect

Maximal subgroups

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

subgroupindex
#191357262
#191335462
#191326162
#191325252
C43×#26072
#1212143