Finite Group Databasebeta

← #25008808

Subgroups — #25008808

Order 11008.

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

normal subgroups only

This group has 458 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#19133614C212yesmaximal
3#19132619C212yesmaximal, complemented
4#19132525C211yesmaximal, characteristic, complemented
5C43×#2607C211yesmaximal, characteristic, complemented
6#14583461C2211yescharacteristic
7C2×#13063308—21no—
8#14583217—22no—
9C2×#13063239—21no—
10#14582666C2211yescharacteristic
11#14582632—22no—
12#14582623C2212yes—
13C43×#399C2212yes—
14C43×#393—21no—
15C43×#391—22no—
16C43×#387—22no—
17C43×#381C2211yescharacteristic
18C4×C22⋊C4×C43—21no—
19C22×C22⋊D43—21no—
20#13063309—41no—
21#13063308—42no—
22#13063308—42no—
23#13063299—22no—
24#13063295—41no—
25C2×Dic43⋊C4—41no—
26C2×C22⋊Dic43—21no—
27C2×(C2×D43)⋊C4—41no—
28#13063256—42no—
29#13063245—42no—
30#13063239—42no—
31C22⋊(C43⋊C8)—22no—
32C22×Q8×C43—21no—
33C23×C4×C43D411yescharacteristic
34C2×C4⋊C4×C43—22no—
35C2×C4⋊C4×C43D412yes—
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—81no—
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×C43SD1612yes—
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—42no—
69C4⋊C4×C43—44no—
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(C2×D43)⋊C4—42no—
78(C2×D43)⋊C4—44no—
79C4⋊Dic43—22no—
80Dic43⋊C4—44no—
81C2×C43⋊C8—42no—
82C23×C43—21no—
83C23×C43—21no—
84C23×C43—42no—
85C23×C43#12011yescharacteristic
86C23×C43C2×SD1611yescharacteristic
87C23×C43#13711yescharacteristic
88C22×D43—41no—
89C22×D43—41no—
90C22×D43—41no—
91C22×D43—82no—
92Q8×C43—84no—
93C2×C4×C43—24no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—42no—
97C2×C4×C43—41no—
98C2×C4×C43—42no—
99C2×C4×C43—41no—
100C2×C4×C43—42no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—41no—
106C2×C4×C43—42no—
107C2×C4×C43—81no—
108C22⋊D43—81no—
109C22⋊D43—81no—
110C22⋊D43—81no—
111C22⋊D43—81no—
112C2×Dic43—41no—
113C2×Dic43—42no—
114C2×Dic43—41no—
115C2×Dic43—41no—
116C2×Dic43—82no—
117D172—82no—
118C43⋊C8—82no—
119#12122—431nomaximal, Sylow
120C22×C43—22no—
121C22×C43—21no—
122C22×C43—21no—
123C22×C43—41no—
124C22×C43—41no—
125C22×C43—42no—
126C22×C43—81no—
127C22×C43#44811yescharacteristic
128C22×C43#45311yescharacteristic
129C22×C43B(4,𝔽2)11yescharacteristic
130C2×D43—82no—
131C2×D43—81no—
132C2×D43—82no—
133C2×D43—161no—
134C4×C43—44no—
135C4×C43—42no—
136C4×C43—42no—
137C4×C43—81no—
138C4×C43—82no—
139Dic43—82no—
140Dic43—81no—
141#2607D4311yescharacteristic, complemented
142#2022—431no—
143#1613—432no—
144#1352—432no—
145#1317—431no—
146C2×C43—21no—
147C2×C43—21no—
148C2×C43—41no—
149C2×C43—41no—
150C2×C43#159611yescharacteristic
151C2×C43#219812yes—
152D43—161no—
153#534—431no—
154C2×#123—861no—
155#481—862no—
156C2×#99—861no—
157#399C2×D4312yes—
158#393—21no—
159#391—22no—
160#387—22no—
161#381C2×D4311yescharacteristic
162C4×C22⋊C4—21no—
163#342—431no—
164#327—862no—
165#323—432no—
166C43#1212211yescharacteristic, complemented, Sylow
167C22×Q8—21no—
168C22×D4—861no—
169C23×C4C22⋊D4311yescharacteristic
170#123—1721no—
171#123—1722no—
172#123—1722no—
173#121—862no—
174#120—1721no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—1721no—
177C2×C4⋊C4C22⋊D4312yes—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—861no—
180C2×C22⋊C4—1721no—
181C2×C22⋊C4C22⋊D4311yescharacteristic
182C2×C22⋊C4C22×D4311yescharacteristic
183C2×C42—21no—
184C2×C42—21no—
185#106—1722no—
186#102—1722no—
187#99—1722no—
188C22⋊C8—862no—
189#95—22no—
190#95—21no—
191#95—22no—
192#95—22no—
193#95C22⋊D4312yes—
194C24—861no—
195C24C2×C22⋊D4311yescharacteristic
196C2×Q8—44no—
197C2×Q8—81no—
198C2×D4—862no—
199C2×D4—1721no—
200C2×D4—1721no—
201C2×D4—1721no—
202C2×D4—1721no—
203C2×D4—1721no—
204C2×D4—1721no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—861no—
213C22×C4—1721no—
214C22×C4#1062188412yes—
215C22×C4C2×C22⋊D4312yes—
216C2×C8—1722no—
217C4⋊C4—42no—
218C4⋊C4—44no—
219C4⋊C4—862no—
220C4⋊C4—1724no—
221C22⋊C4—41no—
222C22⋊C4—44no—
223C22⋊C4—41no—
224C22⋊C4—862no—
225C22⋊C4—1722no—
226C22⋊C4—1724no—
227C22⋊C4—1721no—
228C42—81no—
229C42—81no—
230C23—21no—
231C23—21no—
232C23—42no—
233C23—3442no—
234C23—1721no—
235C23—1721no—
236C23—1721no—
237C23#1306329411yescharacteristic
238C23C2×#1062188411yescharacteristic
239C23#1306335611yescharacteristic
240Q8—84no—
241D4—3442no—
242D4—3441no—
243D4—3441no—
244D4—3441no—
245D4—3441no—
246C2×C4—24no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—81no—
261C2×C4—3442no—
262C2×C4—1722no—
263C2×C4—1721no—
264C2×C4—1721no—
265C2×C4—1721no—
266C8—3442no—
267C22—22no—
268C22—21no—
269C22—21no—
270C22—41no—
271C22—41no—
272C22—42no—
273C22—81no—
274C22—3442no—
275C22—3441no—
276C22—3442no—
277C22—6881no—
278C22#1458303811yescharacteristic
279C22#1458306711yescharacteristic
280C22#1458308611yescharacteristic
281C4—44no—
282C4—42no—
283C4—42no—
284C4—81no—
285C4—82no—
286C4—3442no—
287C4—3441no—
288C2—21no—
289C2—21no—
290C2—41no—
291C2—41no—
292C2—6881no—
293C2#1913351811yescharacteristic
294C2#1913659112yes—
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#12122
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. #19132619C2semidirect
4. #19132525C2semidirect
5. C43×#2607C2semidirect
141. #2607D43semidirect
166. C43#12122semidirect

Maximal subgroups

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

subgroupindex
#191357262
#191336142
#191326192
#191325252
C43×#26072
#1212243