Finite Group Databasebeta

← #25006027

Subgroups — #25006027

Order 11008.

330 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 75 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#19143226C211yesmaximal, characteristic
2#19136407C211yesmaximal, characteristic, complemented
3#19132545C212yesmaximal, complemented
4#19132530C212yesmaximal
5C43×#2165C211yesmaximal, characteristic, complemented
6C2×C42×D43C411yescharacteristic
7#14582954—21no—
8#14582954—21no—
9#14582950—21no—
10#14582950—21no—
11#14582922C411yescharacteristic
12#14582922C2211yescharacteristic
13#14582862C411yescharacteristic
14#14582862C2211yescharacteristic
15C4×#10621877C411yescharacteristic
16#14582720—21no—
17#14582681C2212yes—
18#14582677—21no—
19C4×M16×C43C2211yescharacteristic
20C43×#364—21no—
21C43×#349C2212yes—
22C43×#347—21no—
23C22×C4×D43—21no—
24C22×C4×D43C2×C411yescharacteristic
25C2×#10621877C2×C411yescharacteristic
26C2×#10621877C2×C411yescharacteristic
27C2×C4×Dic43—21no—
28C2×C4×Dic43C2×C411yescharacteristic
29C42×D43—21no—
30C42×D43—21no—
31C42×D43—21no—
32C42×D43—21no—
33#13063265—22no—
34Dic43⋊C8—21no—
35Dic43⋊C8—21no—
36Dic43⋊C8—21no—
37Dic43⋊C8—21no—
38(C2×D43)⋊C8—21no—
39(C2×D43)⋊C8—21no—
40(C2×D43)⋊C8—21no—
41(C2×D43)⋊C8—21no—
42#13063236—21no—
43C4×C43⋊C8—21no—
44C2×M16×C43C2×C411yescharacteristic
45C2×M16×C43C2311yescharacteristic
46C2×C42×C43C2×C411yescharacteristic
47M32×C43—22no—
48#97×C43D411yescharacteristic
49#97×C43D411yescharacteristic
50C4×C8×C43D411yescharacteristic
51C4×C8×C43D411yescharacteristic
52C23×D43M1611yescharacteristic
53C22×C4×C43—21no—
54C22×C4×C43C22×C411yescharacteristic
55C22×Dic43—21no—
56C22×Dic43M1611yescharacteristic
57C2×C4×D43—21no—
58C2×C4×D43—21no—
59C2×C4×D43—21no—
60C2×C4×D43—21no—
61C2×C4×D43—21no—
62C2×C4×D43—21no—
63C2×C4×D43—44no—
64C2×C4×D43—41no—
65C2×C4×D43—41no—
66M16×C43—41no—
67M16×C43—41no—
68C2×C8×C43C22⋊C411yescharacteristic
69C2×C8×C43C22⋊C411yescharacteristic
70C2×C8×C43C2×D411yescharacteristic
71C2×C8×C43C2×D411yescharacteristic
72C42×C43—21no—
73C42×C43C22⋊C411yescharacteristic
74C42×C43C22⋊C411yescharacteristic
75C4×Dic43—21no—
76C4×Dic43—21no—
77C4×Dic43—21no—
78C4×Dic43—21no—
79C4×Dic43—21no—
80C4×Dic43M1611yescharacteristic
81C4×Dic43M1611yescharacteristic
82#10621877—41no—
83#10621877—41no—
84C2×C43⋊C8—21no—
85C2×C43⋊C8—21no—
86C16×C43—42no—
87C43⋊C16—42no—
88C23×C43C2×M1611yescharacteristic
89C22×D43—21no—
90C22×D43—42no—
91C22×D43—41no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—42no—
97C2×C4×C43C2×C22⋊C411yescharacteristic
98C2×C4×C43C2×M1611yescharacteristic
99C2×Dic43—21no—
100C2×Dic43—21no—
101C2×Dic43—21no—
102C2×Dic43—42no—
103C2×Dic43—41no—
104C4×D43—24no—
105C4×D43—42no—
106C4×D43—42no—
107C4×D43—42no—
108C4×D43—42no—
109C4×D43—41no—
110C4×D43—41no—
111C8×C43—21no—
112C8×C43—21no—
113C8×C43—21no—
114C8×C43—21no—
115C43⋊C8—41no—
116C43⋊C8—41no—
117#11521—431nomaximal, Sylow
118C22×C43—21no—
119C22×C43—41no—
120C22×C43#40711yescharacteristic
121C2×D43—22no—
122C2×D43—41no—
123C2×D43—42no—
124C2×D43—41no—
125C2×D43—42no—
126C4×C43—22no—
127C4×C43—21no—
128C4×C43—41no—
129C4×C43#41011yescharacteristic
130C4×C43#41311yescharacteristic
131Dic43—22no—
132Dic43—41no—
133Dic43—41no—
134#2920—431no—
135#2165—431no—
136#2165D4311yescharacteristic, complemented
137#1327—432no—
138#1320—432no—
139C2×C43—21no—
140C2×C43—41no—
141C2×C43#146411yescharacteristic
142D43—42no—
143C22×C42—431no—
144#432—861no—
145#432—861no—
146#431—861no—
147#431—861no—
148#423—431no—
149#423—431no—
150#407—431no—
151#407—431no—
152C4×M16—431no—
153C4×M16C2×D4311yescharacteristic
154#364—21no—
155#364—861no—
156#349—432no—
157#349C2×D4312yes—
158#347—21no—
159#347—861no—
160C43#1152111yescharacteristic, complemented, Sylow
161C23×C4—431no—
162C23×C4—861no—
163C2×M16—431no—
164C2×M16—431no—
165C2×M16C4×D4311yescharacteristic
166C2×M16C22×D4311yescharacteristic
167C2×C42—431no—
168C2×C42—861no—
169C2×C42—861no—
170C2×C42—861no—
171C2×C42—861no—
172C2×C42—861no—
173C2×C42C4×D4311yescharacteristic
174M32—22no—
175M32—862no—
176C4⋊C8—861no—
177C4⋊C8—861no—
178C4⋊C8—861no—
179C4⋊C8—861no—
180C22⋊C8—861no—
181C22⋊C8—861no—
182C22⋊C8—861no—
183C22⋊C8—861no—
184#97—861no—
185#97D17211yescharacteristic
186#97C22⋊D4311yescharacteristic
187C4×C8—861no—
188C4×C8D17211yescharacteristic
189C4×C8C22⋊D4311yescharacteristic
190C24—431no—
191C22×C4—21no—
192C22×C4—431no—
193C22×C4—861no—
194C22×C4—861no—
195C22×C4—861no—
196C22×C4—861no—
197C22×C4—861no—
198C22×C4—861no—
199C22×C4—861no—
200C22×C4—1721no—
201C22×C4—1721no—
202C22×C4—1724no—
203C22×C4C2×C4×D4311yescharacteristic
204M16—41no—
205M16—41no—
206M16—1721no—
207M16—1721no—
208C2×C8—861no—
209C2×C8—861no—
210C2×C8(C2×D43)⋊C411yescharacteristic
211C2×C8(C2×D43)⋊C411yescharacteristic
212C2×C8C2×D17211yescharacteristic
213C2×C8C2×C22⋊D4311yescharacteristic
214C42—21no—
215C42—431no—
216C42—431no—
217C42—861no—
218C42—861no—
219C42—861no—
220C42—861no—
221C42—861no—
222C42(C2×D43)⋊C411yescharacteristic
223C42(C2×D43)⋊C411yescharacteristic
224C16—42no—
225C16—1722no—
226C23—861no—
227C23—1721no—
228C23—1722no—
229C23M16×D4311yescharacteristic
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—864no—
236C2×C4—861no—
237C2×C4—861no—
238C2×C4—861no—
239C2×C4—1722no—
240C2×C4—1722no—
241C2×C4—1722no—
242C2×C4—1722no—
243C2×C4—1722no—
244C2×C4—1721no—
245C2×C4—1721no—
246C2×C4—1721no—
247C2×C4C2×(C2×D43)⋊C411yescharacteristic
248C2×C4M16×D4311yescharacteristic
249C8—21no—
250C8—21no—
251C8—21no—
252C8—21no—
253C8—1721no—
254C8—1721no—
255C22—21no—
256C22—41no—
257C22—862no—
258C22—1721no—
259C22—1722no—
260C22—1722no—
261C22—1721no—
262C22#1458286211yescharacteristic
263C4—22no—
264C4—21no—
265C4—41no—
266C4—862no—
267C4—1721no—
268C4—1721no—
269C4#1458287211yescharacteristic
270C4#1458288111yescharacteristic
271C2—21no—
272C2—41no—
273C2—1722no—
274C2#1913292711yescharacteristic
subgroupG/H
centerC4#14582872
commutatorC22×C4×C43C22×C4
FrattiniC2×M16C22×D43
FittingC43×#2165C2
socleC2×C43#1464
prime radicalC23×D43M16
cosocleC2×M16×C43C23
hypercenter#2165D43
hypocenterC43#11521
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C42 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
2. #19136407C2semidirect
3. #19132545C2semidirect
5. C43×#2165C2semidirect
136. #2165D43semidirect
160. C43#11521semidirect

Maximal subgroups

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

subgroupindex
#191432262
#191364072
#191325452
#191325302
C43×#21652
#1152143