Finite Group Databasebeta

← #25006039

Subgroups — #25006039

Order 11008.

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

normal subgroups only

This group has 288 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#19143240C211yesmaximal, characteristic
2#19136407C211yesmaximal, characteristic, complemented
3#19132547C212yesmaximal, complemented
4#19132532C212yesmaximal
5C43×#2165C211yesmaximal, characteristic, complemented
6C4×#10621898C411yescharacteristic
7#14582961—21no—
8#14582961—21no—
9#14582950—21no—
10#14582950—21no—
11#14582927C411yescharacteristic
12#14582927C2211yescharacteristic
13#14582867C411yescharacteristic
14#14582867C2211yescharacteristic
15C2×C4×C43⋊C8C411yescharacteristic
16#14582720—21no—
17#14582681C2212yes—
18#14582677—21no—
19C4×M16×C43C2211yescharacteristic
20C43×#364—21no—
21C43×#349C2212yes—
22C43×#347—21no—
23C2×#10621898C2×C411yescharacteristic
24C22×C43⋊C8C2×C411yescharacteristic
25C22×C43⋊C8C2×C411yescharacteristic
26C4×Dic86—21no—
27C4×D172—21no—
28C4×C22⋊D43—22no—
29#13063284C2×C411yescharacteristic
30#13063282—21no—
31C42×D43—21no—
32#13063265—22no—
33Dic43⋊C8—21no—
34Dic43⋊C8—21no—
35Dic43⋊C8—21no—
36Dic43⋊C8—21no—
37(C2×D43)⋊C8—21no—
38(C2×D43)⋊C8—21no—
39(C2×D43)⋊C8—21no—
40(C2×D43)⋊C8—21no—
41C4×C43⋊C8—21no—
42C4×C43⋊C8—21no—
43C2×M16×C43C2×C411yescharacteristic
44C2×M16×C43C2311yescharacteristic
45C2×C42×C43C2×C411yescharacteristic
46M32×C43—22no—
47#97×C43D411yescharacteristic
48#97×C43D411yescharacteristic
49C4×C8×C43D411yescharacteristic
50C4×C8×C43D411yescharacteristic
51C22×C4×C43—21no—
52C22×C4×C43C22×C411yescharacteristic
53C2×C22⋊D43—21no—
54#10621898—41no—
55#10621898—41no—
56C2×D172M1611yescharacteristic
57C2×C4×D43—22no—
58C2×C4×D43—21no—
59C2×Dic86M1611yescharacteristic
60M16×C43—41no—
61M16×C43—41no—
62C2×C8×C43C22⋊C411yescharacteristic
63C2×C8×C43C22⋊C411yescharacteristic
64C2×C8×C43C2×D411yescharacteristic
65C2×C8×C43C2×D411yescharacteristic
66C42×C43—21no—
67C42×C43C22⋊C411yescharacteristic
68C42×C43C22⋊C411yescharacteristic
69C22⋊Dic43M1612yes—
70(C2×D43)⋊C4—22no—
71C4⋊Dic43—21no—
72Dic43⋊C4—22no—
73C4×Dic43—22no—
74C4×Dic43—21no—
75C2×C43⋊C8—21no—
76C2×C43⋊C8—21no—
77C2×C43⋊C8—41no—
78C2×C43⋊C8—41no—
79C16×C43—42no—
80C43⋊C16—42no—
81C23×C43C2×M1611yescharacteristic
82C22×D43—21no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—42no—
88C2×C4×C43C2×C22⋊C411yescharacteristic
89C2×C4×C43C2×M1611yescharacteristic
90C22⋊D43—42no—
91C2×Dic43—21no—
92C2×Dic43—22no—
93D172—41no—
94C4×D43—44no—
95C4×D43—41no—
96C4×D43—41no—
97Dic86—41no—
98C8×C43—21no—
99C8×C43—21no—
100C8×C43—21no—
101C8×C43—21no—
102C43⋊C8—41no—
103C43⋊C8—41no—
104#11524—431nomaximal, Sylow
105C22×C43—21no—
106C22×C43—41no—
107C22×C43#40711yescharacteristic
108C2×D43—42no—
109C2×D43—41no—
110C4×C43—22no—
111C4×C43—21no—
112C4×C43—41no—
113C4×C43#41011yescharacteristic
114C4×C43#41311yescharacteristic
115Dic43—42no—
116Dic43—41no—
117#2922—431no—
118#2165—431no—
119#2165D4311yescharacteristic, complemented
120#1328—432no—
121#1321—432no—
122C2×C43—21no—
123C2×C43—41no—
124C2×C43#146411yescharacteristic
125D43—81no—
126C4×#41—431no—
127#433—861no—
128#433—861no—
129#431—861no—
130#431—861no—
131#424—431no—
132#424—431no—
133#408—431no—
134#408—431no—
135C4×M16C2×D4311yescharacteristic
136C2×C4×C8—431no—
137#364—21no—
138#364—861no—
139#349—432no—
140#349C2×D4312yes—
141#347—21no—
142#347—861no—
143C43#1152411yescharacteristic, complemented, Sylow
144C2×#41—431no—
145C2×M16C4×D4311yescharacteristic
146C2×M16C22×D4311yescharacteristic
147C22×C8—431no—
148C22×C8—431no—
149C4×Q8—861no—
150C4×D4—861no—
151C4×D4—862no—
152#117—431no—
153#117—861no—
154C2×C42—861no—
155C2×C42C4×D4311yescharacteristic
156M32—22no—
157M32—862no—
158C4⋊C8—861no—
159C4⋊C8—861no—
160C4⋊C8—861no—
161C4⋊C8—861no—
162C22⋊C8—861no—
163C22⋊C8—861no—
164C22⋊C8—861no—
165C22⋊C8—861no—
166#97D17211yescharacteristic
167#97C22⋊D4311yescharacteristic
168C4×C8—861no—
169C4×C8—861no—
170C4×C8D17211yescharacteristic
171C4×C8C22⋊D4311yescharacteristic
172#41—1721no—
173#41—1721no—
174C2×Q8—431no—
175C2×D4—431no—
176C2×D4—861no—
177C22×C4—21no—
178C22×C4—862no—
179C22×C4—861no—
180C22×C4C2×C4×D4311yescharacteristic
181M16—41no—
182M16—41no—
183C2×C8—861no—
184C2×C8—861no—
185C2×C8—1721no—
186C2×C8—1721no—
187C2×C8(C2×D43)⋊C411yescharacteristic
188C2×C8(C2×D43)⋊C411yescharacteristic
189C2×C8C2×D17211yescharacteristic
190C2×C8C2×C22⋊D4311yescharacteristic
191C4⋊C4—862no—
192C4⋊C4—861no—
193C22⋊C4—432no—
194C22⋊C4—862no—
195C42—21no—
196C42—862no—
197C42—861no—
198C42(C2×D43)⋊C411yescharacteristic
199C42(C2×D43)⋊C411yescharacteristic
200C16—42no—
201C16—1722no—
202C23—861no—
203C23M16×D4311yescharacteristic
204Q8—1721no—
205D4—1721no—
206D4—1722no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—42no—
212C2×C4—862no—
213C2×C4—861no—
214C2×C4—1724no—
215C2×C4—1721no—
216C2×C4—1721no—
217C2×C4C2×(C2×D43)⋊C411yescharacteristic
218C2×C4M16×D4311yescharacteristic
219C8—21no—
220C8—21no—
221C8—21no—
222C8—21no—
223C8—1721no—
224C8—1721no—
225C22—21no—
226C22—41no—
227C22—1722no—
228C22—1721no—
229C22#1458286211yescharacteristic
230C4—22no—
231C4—21no—
232C4—41no—
233C4—1722no—
234C4—1721no—
235C4#1458287211yescharacteristic
236C4#1458288111yescharacteristic
237C2—21no—
238C2—41no—
239C2—3441no—
240C2#1913292711yescharacteristic
subgroupG/H
centerC4#14582872
commutatorC22×C4×C43C22×C4
FrattiniC2×M16C22×D43
FittingC43×#2165C2
socleC2×C43#1464
prime radicalC2×#10621898C2×C4
cosocleC2×M16×C43C23
hypercenter#2165D43
hypocenterC43#11524
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. #19132547C2semidirect
5. C43×#2165C2semidirect
119. #2165D43semidirect
143. C43#11524semidirect

Maximal subgroups

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

subgroupindex
#191432402
#191364072
#191325472
#191325322
C43×#21652
#1152443