Finite Group Databasebeta

← #25005902

Subgroups — #25005902

Order 11008.

368 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 83 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#19143297C211yesmaximal, characteristic
2#19136214C212yesmaximal, complemented
3#19132548C211yesmaximal, characteristic, complemented
4#19132530C212yesmaximal, complemented
5C43×#1328C211yesmaximal, characteristic, complemented
6C2×#13063333C2211yescharacteristic
7C22×#10621872C411yescharacteristic
8#14583411C411yescharacteristic
9M32×D43—22no—
10#14582976—22no—
11#14582969—22no—
12#14582865C411yescharacteristic
13#14582862C2211yescharacteristic
14#14582855C411yescharacteristic
15#14582681C2212yes—
16#14582680—22no—
17C43×#424C2211yescharacteristic
18C43×#349C2212yes—
19C2×#10621898C2×C411yescharacteristic
20C22×C4×D43C2×C411yescharacteristic
21#13063333—42no—
22C2×#10621877C2×C411yescharacteristic
23C2×#10621872—21no—
24C2×#10621872—21no—
25C2×#10621872—42no—
26C2×#10621872D412yes—
27C22×C43⋊C8C2×C411yescharacteristic
28C2×C8×D43D412yes—
29#13063309C812yes—
30#13063305—21no—
31#13063300—21no—
32#13063295C812yes—
33C4×D172—22no—
34#13063265—22no—
35#13063264—42no—
36C16×D43—42no—
37(C2×D43)⋊C8—22no—
38(C2×D43)⋊C8—22no—
39#13063236—21no—
40C4×C43⋊C8—21no—
41C2×M16×C43C2311yescharacteristic
42C22×C8×C43C2×C411yescharacteristic
43#117×C43C2×C411yescharacteristic
44M32×C43—22no—
45C4⋊C8×C43—22no—
46C23×D43C2×C811yescharacteristic
47C22×C4×C43C22×C411yescharacteristic
48C2×C22⋊D43C2×C812yes—
49C22×Dic43C2×C811yescharacteristic
50#10621898—41no—
51#10621898—41no—
52C2×D172—22no—
53C2×D172M1611yescharacteristic
54C2×C4×D43—21no—
55C2×C4×D43—21no—
56C2×C4×D43—41no—
57C2×C4×D43—41no—
58C2×C4×D43C22⋊C412yes—
59C2×Dic86M1611yescharacteristic
60M16×C43—41no—
61C2×C8×C43—21no—
62C2×C8×C43—41no—
63C2×C8×C43C2×D412yes—
64C4⋊C4×C43—21no—
65C22⋊C4×C43C2×C812yes—
66C42×C43—21no—
67(C2×D43)⋊C4—22no—
68(C2×D43)⋊C4—22no—
69C4⋊Dic43—22no—
70#10621877—41no—
71C2×C43⋊C8—22no—
72C2×C43⋊C8—21no—
73C2×C43⋊C8C22⋊C411yescharacteristic
74C2×C43⋊C8C22⋊C411yescharacteristic
75#10621872—42no—
76#10621872—42no—
77#10621872—42no—
78C8×D43—22no—
79C8×D43—22no—
80C16×C43—42no—
81C43⋊C16—42no—
82C23×C43C22×C811yescharacteristic
83C22×D43—21no—
84C22×D43—41no—
85C22×D43—81no—
86C22×D43C22⋊C812yes—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—22no—
90C2×C4×C43C2×C22⋊C411yescharacteristic
91C2×C4×C43C2×M1611yescharacteristic
92C22⋊D43—42no—
93C2×Dic43—21no—
94C2×Dic43—41no—
95C2×Dic43C22⋊C812yes—
96D172—41no—
97D172—82no—
98C4×D43—22no—
99C4×D43—22no—
100C4×D43—42no—
101C4×D43—41no—
102C4×D43—41no—
103Dic86—41no—
104C8×C43—22no—
105C8×C43—41no—
106C43⋊C8—21no—
107C43⋊C8—41no—
108C43⋊C8#9912yes—
109#11484—431nomaximal, Sylow
110C22×C43—21no—
111C22×C43—41no—
112C22×C43C2×C22⋊C811yescharacteristic
113C2×D43—22no—
114C2×D43—42no—
115C2×D43—41no—
116C2×D43—41no—
117C2×D43—41no—
118C2×D43—82no—
119C4×C43—21no—
120C4×C43—42no—
121C4×C43C2×#9911yescharacteristic
122C4×C43#41311yescharacteristic
123Dic43—22no—
124Dic43—41no—
125#2930—431no—
126#2115—432no—
127#1328—431no—
128#1328D4311yescharacteristic, complemented
129#1320—432no—
130C2×C43—21no—
131C2×C43—41no—
132C2×C43#145911yescharacteristic
133D43—42no—
134D43—81no—
135C2×#131—431no—
136C22×M16—431no—
137#525—431no—
138C2×M32—862no—
139#436—862no—
140#435—862no—
141#424C2×D4311yescharacteristic
142#408—431no—
143#407—431no—
144#405—431no—
145#349—432no—
146#349—862no—
147#349C2×D4312yes—
148C43#1148411yescharacteristic, complemented, Sylow
149C2×#41—431no—
150C23×C4—431no—
151#131—1722no—
152C2×M16—432no—
153C2×M16—431no—
154C2×M16—861no—
155C2×M16—861no—
156C2×M16—1722no—
157C2×M16C22×D4311yescharacteristic
158C22×C8—431no—
159C22×C8—432no—
160C22×C8C4×D4311yescharacteristic
161#123—432no—
162C22⋊Q8—861no—
163#121—861no—
164#120—432no—
165C4×D4—862no—
166#117C4×D4311yescharacteristic
167M32—22no—
168M32—862no—
169M32—1722no—
170C2×C16—1722no—
171C4⋊C8—22no—
172C22⋊C8—862no—
173C22⋊C8—862no—
174#97—861no—
175C4×C8—861no—
176C24—431no—
177#41—1721no—
178#41—1721no—
179C2×Q8—431no—
180C2×D4—432no—
181C2×D4—431no—
182C2×D4—862no—
183C22×C4—432no—
184C22×C4—431no—
185C22×C4—861no—
186C22×C4—861no—
187C22×C4—1721no—
188C22×C4—1721no—
189C22×C4C2×C4×D4311yescharacteristic
190M16—41no—
191M16—1722no—
192M16—1722no—
193M16—1722no—
194M16—1721no—
195C2×C8—21no—
196C2×C8—41no—
197C2×C8—431no—
198C2×C8—431no—
199C2×C8—862no—
200C2×C8—862no—
201C2×C8—862no—
202C2×C8—861no—
203C2×C8D4×D4312yes—
204C4⋊C4—21no—
205C4⋊C4—862no—
206C22⋊C4—862no—
207C22⋊C4—862no—
208C22⋊C4C8×D4312yes—
209C42—21no—
210C16—42no—
211C16—1722no—
212C23—432no—
213C23—861no—
214C23—3441no—
215C23—1721no—
216C23C2×C8×D4311yescharacteristic
217Q8—1721no—
218D4—3442no—
219D4—1721no—
220D4—1722no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—432no—
225C2×C4—862no—
226C2×C4—862no—
227C2×C4—861no—
228C2×C4—1722no—
229C2×C4—1721no—
230C2×C4—1721no—
231C2×C4—1721no—
232C2×C4C22⋊C4×D4311yescharacteristic
233C2×C4M16×D4311yescharacteristic
234C8—22no—
235C8—41no—
236C8—432no—
237C8—861no—
238C8—1721no—
239C22—21no—
240C22—41no—
241C22—862no—
242C22—3442no—
243C22—1721no—
244C22—1721no—
245C22—1722no—
246C22—1721no—
247C22C22⋊C8×D4311yescharacteristic
248C4—21no—
249C4—42no—
250C4—862no—
251C4—1721no—
252C4#99×D4311yescharacteristic
253C4#1458288211yescharacteristic
254C2—21no—
255C2—41no—
256C2—3441no—
257C2—1722no—
258C2#1913291211yescharacteristic
subgroupG/H
centerC4#99×D43
commutatorC23×C43C22×C8
FrattiniC2×M16C22×D43
FittingC43×#1328C2
socleC2×C43#1459
prime radical#14583411C4
cosocleC2×M16×C43C23
hypercenter#1328D43
hypocenterC43#11484
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1328

Complements

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

NH ≅ G/Ntype
2. #19136214C2semidirect
3. #19132548C2semidirect
4. #19132530C2semidirect
5. C43×#1328C2semidirect
128. #1328D43semidirect
148. C43#11484semidirect

Maximal subgroups

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

subgroupindex
#191432972
#191362142
#191325482
#191325302
C43×#13282
#1148443