Finite Group Databasebeta

← #25009173

Subgroups — #25009173

Order 11008.

372 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135819C211yesmaximal, characteristic
2#19133631C212yesmaximal
3#19132622C212yesmaximal, complemented
4#19132541C211yesmaximal, characteristic, complemented
5C43×#2571C211yesmaximal, characteristic, complemented
6#14583480C2211yescharacteristic
7#14583217—22no—
8C2×#13063253—21no—
9#14582898—21no—
10#14582668C2211yescharacteristic
11#14582632—22no—
12#14582625C2212yes—
13C43×#400—21no—
14C43×#400C2212yes—
15C43×#389—22no—
16C43×#384C2211yescharacteristic
17C43×#382—22no—
18C4×C4⋊C4×C43—21no—
19C2×#10621898—21no—
20C2×#10621877—21no—
21#13063305—41no—
22#13063300—41no—
23#13063299—22no—
24#13063256—42no—
25#13063253—42no—
26#13063248—41no—
27#13063245—41no—
28#13063245—42no—
29C22⋊(C43⋊C8)—22no—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43—21no—
32C2×C4⋊C4×C43—22no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43D411yescharacteristic
35C2×C4⋊C4×C43D412yes—
36C2×C4⋊C4×C43C2311yescharacteristic
37C2×C42×C43—22no—
38C2×C42×C43D411yescharacteristic
39#95×C43—21no—
40#95×C43—22no—
41#95×C43—22no—
42#95×C43—22no—
43#95×C43D412yes—
44C22×C4×C43—21no—
45C22×C4×C43—22no—
46C22×C4×C43—22no—
47C22×C4×C43—21no—
48C22×C4×C43C2×D411yescharacteristic
49C22×C4×C43C2×D412yes—
50C2×C22⋊D43—41no—
51#10621898—41no—
52#10621898—41no—
53#10621898—41no—
54#10621898—41no—
55C2×D172—21no—
56C2×D172—22no—
57C2×C4×D43—41no—
58C2×Dic86—21no—
59C4⋊C4×C43—41no—
60C4⋊C4×C43—41no—
61C4⋊C4×C43—42no—
62C4⋊C4×C43—42no—
63C4⋊C4×C43—44no—
64C4⋊C4×C43—42no—
65C4⋊C4×C43—81no—
66C42×C43—21no—
67C42×C43—44no—
68C42×C43SD1612yes—
69(C2×D43)⋊C4—42no—
70C4⋊Dic43—22no—
71#10621877—41no—
72#10621877—41no—
73C2×C43⋊C8—42no—
74C2×C43⋊C8—41no—
75C23×C43#12011yescharacteristic
76C22×D43—41no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—22no—
83C2×C4×C43—42no—
84C2×C4×C43—42no—
85C2×C4×C43—42no—
86C2×C4×C43—42no—
87C2×C4×C43—42no—
88C2×C4×C43—42no—
89C2×C4×C43—42no—
90C2×C4×C43—41no—
91C2×C4×C43—42no—
92C2×C4×C43C2×SD1611yescharacteristic
93C2×C4×C43#13711yescharacteristic
94C22⋊D43—81no—
95C22⋊D43—81no—
96C2×Dic43—41no—
97D172—41no—
98D172—41no—
99D172—82no—
100C4×D43—81no—
101C4×D43—81no—
102Dic86—41no—
103Dic86—41no—
104C43⋊C8—81no—
105C43⋊C8—82no—
106#12181—431nomaximal, Sylow
107C22×C43—21no—
108C22×C43—21no—
109C22×C43#44811yescharacteristic
110C22×C43#45411yescharacteristic
111C22×C43B(4,𝔽2)11yescharacteristic
112C2×D43—81no—
113C2×D43—81no—
114C2×D43—81no—
115C4×C43—24no—
116C4×C43—21no—
117C4×C43—21no—
118C4×C43—42no—
119C4×C43—82no—
120C4×C43—81no—
121C4×C43—82no—
122Dic43—81no—
123#2571D4311yescharacteristic, complemented
124#2039—431no—
125#1616—432no—
126#1353—432no—
127#1325—431no—
128C2×C43—21no—
129C2×C43—21no—
130C2×C43#159911yescharacteristic
131C2×C43#219811yescharacteristic
132C2×C43#220411yescharacteristic
133D43—161no—
134#537—431no—
135#481—862no—
136C2×#104—861no—
137#417—861no—
138#400—21no—
139#400C2×D4312yes—
140#389—22no—
141#384C2×D4311yescharacteristic
142#382—22no—
143C4×C4⋊C4—21no—
144#343—431no—
145#327—862no—
146#324—432no—
147C43#1218111yescharacteristic, complemented, Sylow
148C2×#41—861no—
149C2×M16—861no—
150C22⋊Q8—1721no—
151#121—862no—
152#121—1721no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C22⋊D4311yescharacteristic
158C2×C4⋊C4C22⋊D4312yes—
159C2×C4⋊C4C22×D4311yescharacteristic
160C2×C42—22no—
161C2×C42C22⋊D4311yescharacteristic
162#106—1722no—
163#104—1722no—
164#103—1721no—
165#102—1721no—
166#102—1722no—
167C22⋊C8—862no—
168#95—21no—
169#95—22no—
170#95—22no—
171#95—22no—
172#95C22⋊D4312yes—
173#41—1721no—
174#41—1721no—
175#41—1721no—
176#41—1721no—
177C2×Q8—861no—
178C2×D4—862no—
179C2×D4—861no—
180C2×D4—1721no—
181C22×C4—21no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—21no—
185C22×C4—1721no—
186C22×C4C2×C22⋊D4311yescharacteristic
187C22×C4C2×C22⋊D4312yes—
188M16—1721no—
189M16—1721no—
190C2×C8—1722no—
191C2×C8—1721no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—44no—
197C4⋊C4—42no—
198C4⋊C4—81no—
199C4⋊C4—862no—
200C22⋊C4—1722no—
201C42—21no—
202C42—44no—
203C42#1062188412yes—
204C23—1721no—
205C23#1306329411yescharacteristic
206Q8—1721no—
207Q8—1721no—
208D4—3442no—
209D4—3441no—
210D4—3441no—
211D4—1721no—
212D4—1721no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—3441no—
229C2×C4—3441no—
230C2×C4—1721no—
231C2×C4C2×#1062188411yescharacteristic
232C2×C4#1306335611yescharacteristic
233C8—3441no—
234C8—3442no—
235C22—21no—
236C22—21no—
237C22—3441no—
238C22—3441no—
239C22—3441no—
240C22#1458303811yescharacteristic
241C22#1458307211yescharacteristic
242C22#1458308611yescharacteristic
243C4—24no—
244C4—21no—
245C4—21no—
246C4—42no—
247C4—82no—
248C4—81no—
249C4—82no—
250C4—3441no—
251C2—21no—
252C2—21no—
253C2—6881no—
254C2#1913353511yescharacteristic
255C2#1913659111yescharacteristic
256C2#1913662111yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2571C2
socleC22×C43B(4,𝔽2)
prime radical#14583480C22
hypercenter#2571D43
hypocenterC43#12181
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2571

Complements

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

NH ≅ G/Ntype
3. #19132622C2semidirect
4. #19132541C2semidirect
5. C43×#2571C2semidirect
123. #2571D43semidirect
147. C43#12181semidirect

Maximal subgroups

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

subgroupindex
#191358192
#191336312
#191326222
#191325412
C43×#25712
#1218143