Finite Group Databasebeta

← #25006096

Subgroups — #25006096

Order 11008.

348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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#19143292C211yesmaximal, characteristic
2#19136408C212yesmaximal, complemented
3#19132533C211yesmaximal, characteristic, complemented
4#19132530C212yesmaximal, complemented
5C43×#1321C211yesmaximal, characteristic, complemented
6C2×#13063332C411yescharacteristic
7C22×C8×D43C411yescharacteristic
8#14583406C411yescharacteristic
9#14582973—22no—
10(C22⋊D43)⋊C8—22no—
11#14582925C411yescharacteristic
12#14582862C2211yescharacteristic
13#14582857C2211yescharacteristic
14#14582719—22no—
15#14582681C2212yes—
16#14582676—22no—
17C43×#408C2211yescharacteristic
18C43×#349C2212yes—
19C22×C4×D43C2×C411yescharacteristic
20#13063332—42no—
21C2×#10621877—21no—
22C2×#10621877C2×C411yescharacteristic
23C22×C43⋊C8—21no—
24C22×C43⋊C8C2×C411yescharacteristic
25C2×C8×D43—21no—
26C2×C8×D43—21no—
27C2×C8×D43—42no—
28#13063306—21no—
29#13063301—21no—
30#13063296—21no—
31#13063293—21no—
32C4×C22⋊D43—22no—
33#13063284C2×C411yescharacteristic
34#13063265—22no—
35Dic43⋊C8—22no—
36(C2×D43)⋊C8—22no—
37#13063235D412yes—
38C8×Dic43D412yes—
39C2×#41×C43C2×C411yescharacteristic
40C2×M16×C43C2311yescharacteristic
41C22×C8×C43C2×C411yescharacteristic
42M32×C43—22no—
43C22⋊C8×C43—22no—
44C23×D43M1611yescharacteristic
45#41×C43—41no—
46#41×C43—41no—
47C2×Q8×C43M1611yescharacteristic
48C2×D4×C43—21no—
49C2×D4×C43M1611yescharacteristic
50C22×C4×C43—21no—
51C22×C4×C43C22×C411yescharacteristic
52C2×C22⋊D43—22no—
53C22×Dic43M1611yescharacteristic
54C2×C4×D43—21no—
55C2×C4×D43—21no—
56C2×C4×D43—41no—
57C2×C4×D43—41no—
58M16×C43—41no—
59C2×C8×C43—21no—
60C2×C8×C43—41no—
61C2×C8×C43C2×D412yes—
62C22⋊Dic43—22no—
63C22⋊Dic43—21no—
64(C2×D43)⋊C4—22no—
65C4⋊Dic43—21no—
66Dic43⋊C4—22no—
67C4×Dic43C22⋊C412yes—
68#10621877—42no—
69#10621877—41no—
70C2×C43⋊C8—22no—
71C2×C43⋊C8—21no—
72C2×C43⋊C8—42no—
73C2×C43⋊C8C22⋊C411yescharacteristic
74C2×C43⋊C8C22⋊C411yescharacteristic
75C8×D43—42no—
76C8×D43—42no—
77C16×C43—42no—
78C43⋊C16—42no—
79C23×C43—21no—
80C23×C43C2×M1611yescharacteristic
81C22×D43—21no—
82C22×D43—42no—
83C22×D43—41no—
84Q8×C43—41no—
85D4×C43—41no—
86D4×C43—42no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—41no—
91C2×C4×C43—41no—
92C2×C4×C43C2×C22⋊C411yescharacteristic
93C2×C4×C43C2×M1611yescharacteristic
94C22⋊D43—44no—
95C2×Dic43—22no—
96C2×Dic43—21no—
97C2×Dic43—41no—
98C4×D43—42no—
99C4×D43—41no—
100C4×D43—41no—
101C8×C43—22no—
102C8×C43—41no—
103C43⋊C8—21no—
104C43⋊C8—41no—
105C43⋊C8#10012yes—
106#11537—431nomaximal, Sylow
107C22×C43—21no—
108C22×C43—41no—
109C22×C43—42no—
110C22×C43—41no—
111C22×C43#40711yescharacteristic
112C2×D43—22no—
113C2×D43—41no—
114C2×D43—42no—
115C2×D43—41no—
116C2×D43—42no—
117C4×C43—21no—
118C4×C43—41no—
119C4×C43#41011yescharacteristic
120C4×C43C2×#10011yescharacteristic
121Dic43—42no—
122Dic43—41no—
123#2929—431no—
124#2166—432no—
125#1321—431no—
126#1321D4311yescharacteristic, complemented
127#1320—432no—
128C2×C43—21no—
129C2×C43—41no—
130C2×C43—81no—
131C2×C43#146611yescharacteristic
132D43—42no—
133C2×#131—431no—
134C23×C8—431no—
135#525—431no—
136#435—862no—
137C8×D4—862no—
138#424—431no—
139#408C2×D4311yescharacteristic
140#407—431no—
141#405—431no—
142#364—862no—
143#349—432no—
144#349C2×D4312yes—
145#347—862no—
146C43#1153711yescharacteristic, complemented, Sylow
147C2×#41C4×D4311yescharacteristic
148C23×C4—431no—
149#131—1722no—
150C2×M16—431no—
151C2×M16—861no—
152C2×M16C22×D4311yescharacteristic
153C22×C8—431no—
154C22×C8—861no—
155C22×C8—861no—
156C22×C8—861no—
157C22×C8—1722no—
158C22×C8C4×D4311yescharacteristic
159#123—861no—
160C22⋊Q8—861no—
161#121—861no—
162#120—861no—
163C4×D4—862no—
164#117—431no—
165M32—22no—
166M32—862no—
167C4⋊C8—862no—
168C22⋊C8—22no—
169C22⋊C8—862no—
170#97—432no—
171C4×C8—432no—
172C24—431no—
173#41—41no—
174#41—41no—
175C2×Q8#1062187211yescharacteristic
176C2×D4—21no—
177C2×D4—862no—
178C2×D4#1062187211yescharacteristic
179C22×C4—21no—
180C22×C4—431no—
181C22×C4—861no—
182C22×C4—861no—
183C22×C4—1721no—
184C22×C4—1721no—
185C22×C4C2×C4×D4311yescharacteristic
186M16—41no—
187M16—1722no—
188M16—1721no—
189C2×C8—21no—
190C2×C8—41no—
191C2×C8—431no—
192C2×C8—431no—
193C2×C8—862no—
194C2×C8—861no—
195C2×C8—1722no—
196C2×C8—1722no—
197C2×C8—1722no—
198C2×C8D4×D4312yes—
199C4⋊C4—862no—
200C4⋊C4—861no—
201C22⋊C4—862no—
202C22⋊C4—862no—
203C22⋊C4—861no—
204C42—432no—
205C16—42no—
206C16—1722no—
207C23—21no—
208C23—861no—
209C23—1721no—
210C23—1722no—
211C23M16×D4311yescharacteristic
212Q8—41no—
213D4—41no—
214D4—42no—
215D4—1724no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—862no—
222C2×C4—861no—
223C2×C4—1722no—
224C2×C4—1721no—
225C2×C4—1721no—
226C2×C4—1721no—
227C2×C4C22⋊C4×D4311yescharacteristic
228C2×C4C2×#1062187211yescharacteristic
229C8—22no—
230C8—41no—
231C8—432no—
232C8—861no—
233C8—1721no—
234C22—21no—
235C22—41no—
236C22—42no—
237C22—41no—
238C22—862no—
239C22—1721no—
240C22—1722no—
241C22—1722no—
242C22—1721no—
243C22#1458286111yescharacteristic
244C4—21no—
245C4—41no—
246C4—1722no—
247C4—1721no—
248C4#1458287111yescharacteristic
249C4#100×D4311yescharacteristic
250C2—21no—
251C2—41no—
252C2—81no—
253C2—1722no—
254C2#1913293411yescharacteristic
subgroupG/H
centerC4#14582871
commutatorC22×C4×C43C22×C4
FrattiniC2×M16C22×D43
FittingC43×#1321C2
socleC2×C43#1466
prime radical#14583406C4
cosocleC2×M16×C43C23
hypercenter#1321D43
hypocenterC43#11537
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1321

Complements

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

NH ≅ G/Ntype
2. #19136408C2semidirect
3. #19132533C2semidirect
4. #19132530C2semidirect
5. C43×#1321C2semidirect
126. #1321D43semidirect
146. C43#11537semidirect

Maximal subgroups

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

subgroupindex
#191432922
#191364082
#191325332
#191325302
C43×#13212
#1153743