Finite Group Databasebeta

← #25006031

Subgroups — #25006031

Order 11008.

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

normal subgroups only

This group has 284 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#19143231C211yesmaximal, characteristic
2#19136407C211yesmaximal, characteristic, complemented
3#19132545C212yesmaximal, complemented
4#19132530C212yesmaximal
5C43×#2165C211yesmaximal, characteristic, complemented
6C2×#13063282C411yescharacteristic
7#14582961—21no—
8#14582961—21no—
9#14582958—21no—
10#14582958—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×D43C2×C411yescharacteristic
24C2×#10621877C2×C411yescharacteristic
25C2×#10621877C2×C411yescharacteristic
26#13063282—21no—
27#13063282—21no—
28#13063282—22no—
29C2×Dic43⋊C4—21no—
30C2×(C2×D43)⋊C4—21no—
31C2×C4×Dic43C2×C411yescharacteristic
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—
41#13063236—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
51C23×D43M1611yescharacteristic
52C22×C4×C43—21no—
53C22×C4×C43C22×C411yescharacteristic
54C22×Dic43—21no—
55C22×Dic43M1611yescharacteristic
56C2×C4×D43—21no—
57C2×C4×D43—21no—
58C2×C4×D43—41no—
59C2×C4×D43—41no—
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
69(C2×D43)⋊C4—22no—
70(C2×D43)⋊C4—22no—
71Dic43⋊C4—22no—
72Dic43⋊C4—22no—
73C4×Dic43—21no—
74C4×Dic43M1612yes—
75#10621877—41no—
76#10621877—41no—
77C2×C43⋊C8—21no—
78C2×C43⋊C8—21no—
79C16×C43—42no—
80C43⋊C16—42no—
81C23×C43C2×M1611yescharacteristic
82C22×D43—21no—
83C22×D43—41no—
84C22×D43—81no—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—81no—
90C2×C4×C43C2×C22⋊C411yescharacteristic
91C2×C4×C43C2×M1611yescharacteristic
92C2×Dic43—22no—
93C2×Dic43—21no—
94C2×Dic43—41no—
95C2×Dic43—81no—
96C4×D43—42no—
97C4×D43—41no—
98C4×D43—41no—
99C8×C43—21no—
100C8×C43—21no—
101C8×C43—21no—
102C8×C43—21no—
103C43⋊C8—41no—
104C43⋊C8—41no—
105#11522—431nomaximal, Sylow
106C22×C43—21no—
107C22×C43—41no—
108C22×C43#40711yescharacteristic
109C2×D43—42no—
110C2×D43—41no—
111C2×D43—82no—
112C4×C43—21no—
113C4×C43—41no—
114C4×C43—41no—
115C4×C43#41011yescharacteristic
116C4×C43#41311yescharacteristic
117Dic43—42no—
118Dic43—41no—
119#2921—431no—
120#2165—431no—
121#2165D4311yescharacteristic, complemented
122#1327—432no—
123#1320—432no—
124C2×C43—21no—
125C2×C43—41no—
126C2×C43#146411yescharacteristic
127D43—81no—
128C2×#117—431no—
129#433—861no—
130#433—861no—
131#433—861no—
132#433—861no—
133#423—431no—
134#423—431no—
135#407—431no—
136#407—431no—
137C4×M16—431no—
138C4×M16C2×D4311yescharacteristic
139#364—21no—
140#364—861no—
141#349—432no—
142#349C2×D4312yes—
143#347—21no—
144#347—861no—
145C43#1152211yescharacteristic, complemented, Sylow
146C23×C4—431no—
147C2×M16—431no—
148C2×M16—431no—
149C2×M16C4×D4311yescharacteristic
150C2×M16C22×D4311yescharacteristic
151#117—862no—
152#117—861no—
153#117—861no—
154C2×C4⋊C4—861no—
155C2×C22⋊C4—861no—
156C2×C42—431no—
157C2×C42C4×D4311yescharacteristic
158M32—22no—
159M32—862no—
160C4⋊C8—861no—
161C4⋊C8—861no—
162C4⋊C8—861no—
163C4⋊C8—861no—
164C22⋊C8—861no—
165C22⋊C8—861no—
166C22⋊C8—861no—
167C22⋊C8—861no—
168#97—861no—
169#97D17211yescharacteristic
170#97C22⋊D4311yescharacteristic
171C4×C8—861no—
172C4×C8D17211yescharacteristic
173C4×C8C22⋊D4311yescharacteristic
174C24—431no—
175C22×C4—21no—
176C22×C4—431no—
177C22×C4—861no—
178C22×C4—861no—
179C22×C4—861no—
180C22×C4—1721no—
181C22×C4—1721no—
182C22×C4C2×C4×D4311yescharacteristic
183M16—41no—
184M16—41no—
185M16—1721no—
186M16—1721no—
187C2×C8—861no—
188C2×C8—861no—
189C2×C8(C2×D43)⋊C411yescharacteristic
190C2×C8(C2×D43)⋊C411yescharacteristic
191C2×C8C2×D17211yescharacteristic
192C2×C8C2×C22⋊D4311yescharacteristic
193C4⋊C4—862no—
194C4⋊C4—862no—
195C22⋊C4—862no—
196C22⋊C4—862no—
197C42—21no—
198C42—432no—
199C42—861no—
200C42(C2×D43)⋊C411yescharacteristic
201C42(C2×D43)⋊C411yescharacteristic
202C16—42no—
203C16—1722no—
204C23—861no—
205C23—3441no—
206C23—1721no—
207C23M16×D4311yescharacteristic
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—81no—
213C2×C4—862no—
214C2×C4—861no—
215C2×C4—3441no—
216C2×C4—1722no—
217C2×C4—1721no—
218C2×C4—1721no—
219C2×C4—1721no—
220C2×C4C2×(C2×D43)⋊C411yescharacteristic
221C2×C4M16×D4311yescharacteristic
222C8—21no—
223C8—21no—
224C8—21no—
225C8—21no—
226C8—1721no—
227C8—1721no—
228C22—21no—
229C22—41no—
230C22—3442no—
231C22—1722no—
232C22—1721no—
233C22#1458286211yescharacteristic
234C4—21no—
235C4—41no—
236C4—41no—
237C4—1722no—
238C4—1721no—
239C4#1458287211yescharacteristic
240C4#1458288111yescharacteristic
241C2—21no—
242C2—41no—
243C2—3441no—
244C2#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#11522
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
121. #2165D43semidirect
145. C43#11522semidirect

Maximal subgroups

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

subgroupindex
#191432312
#191364072
#191325452
#191325302
C43×#21652
#1152243