Finite Group Databasebeta

← #25009197

Subgroups — #25009197

Order 11008.

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

normal subgroups only

This group has 360 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#19135824C211yesmaximal, characteristic
2#19133631C212yesmaximal
3#19132622C212yesmaximal, complemented
4#19132539C211yesmaximal, characteristic, complemented
5C43×#2844C211yesmaximal, characteristic, complemented
6#14583480C2211yescharacteristic
7#14583217—22no—
8C2×#13063253—21no—
9#14582898—21no—
10#14582668C2211yescharacteristic
11#14582632—22no—
12#14582625C2212yes—
13C43×#400—22no—
14C43×#400C2212yes—
15C43×#395—22no—
16C43×#395—21no—
17C43×#382—21no—
18C43×#382C2211yescharacteristic
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—
30C22×Q8×C43—21no—
31C2×C4⋊C4×C43—21no—
32C2×C4⋊C4×C43—21no—
33C2×C4⋊C4×C43—22no—
34C2×C4⋊C4×C43D411yescharacteristic
35C2×C4⋊C4×C43D412yes—
36C2×C4⋊C4×C43C2311yescharacteristic
37C2×C42×C43D411yescharacteristic
38#95×C43—22no—
39#95×C43—21no—
40#95×C43—22no—
41#95×C43—22no—
42#95×C43—22no—
43#95×C43D412yes—
44C2×Q8×C43—82no—
45C2×Q8×C43—81no—
46C22×C4×C43—21no—
47C22×C4×C43—22no—
48C22×C4×C43—22no—
49C22×C4×C43—21no—
50C22×C4×C43C2×D411yescharacteristic
51C22×C4×C43C2×D412yes—
52C2×C22⋊D43—41no—
53#10621898—41no—
54#10621898—41no—
55#10621898—41no—
56#10621898—41no—
57C2×D172—21no—
58C2×D172—22no—
59C2×C4×D43—41no—
60C2×Dic86—21no—
61C4⋊C4×C43—41no—
62C4⋊C4×C43—41no—
63C4⋊C4×C43—42no—
64C4⋊C4×C43—81no—
65C4⋊C4×C43—81no—
66C4⋊C4×C43—82no—
67C42×C43—21no—
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—
77Q8×C43—84no—
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—41no—
83C2×C4×C43—41no—
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—42no—
91C2×C4×C43—41no—
92C2×C4×C43—42no—
93C2×C4×C43C2×SD1611yescharacteristic
94C2×C4×C43#13711yescharacteristic
95C22⋊D43—81no—
96C22⋊D43—81no—
97C2×Dic43—41no—
98D172—41no—
99D172—41no—
100D172—82no—
101C4×D43—81no—
102C4×D43—81no—
103Dic86—41no—
104Dic86—41no—
105C43⋊C8—81no—
106C43⋊C8—82no—
107#12185—431nomaximal, Sylow
108C22×C43—21no—
109C22×C43—21no—
110C22×C43#44811yescharacteristic
111C22×C43#45411yescharacteristic
112C22×C43B(4,𝔽2)11yescharacteristic
113C2×D43—81no—
114C2×D43—81no—
115C2×D43—81no—
116C4×C43—21no—
117C4×C43—21no—
118C4×C43—42no—
119C4×C43—42no—
120C4×C43—82no—
121C4×C43—81no—
122C4×C43—82no—
123Dic43—81no—
124#2844D4311yescharacteristic, complemented
125#2040—431no—
126#1616—432no—
127#1353—432no—
128#1324—431no—
129C2×C43—21no—
130C2×C43—21no—
131C2×C43#159911yescharacteristic
132C2×C43#220111yescharacteristic
133C2×C43#220211yescharacteristic
134D43—161no—
135#537—431no—
136#481—862no—
137C2×#104—861no—
138#417—861no—
139#400—22no—
140#400C2×D4312yes—
141#395—22no—
142#395—21no—
143#382—21no—
144#382C2×D4311yescharacteristic
145#343—431no—
146#327—862no—
147#324—432no—
148C43#1218511yescharacteristic, complemented, Sylow
149C2×#41—861no—
150C22×Q8—21no—
151C2×M16—861no—
152C22⋊Q8—1721no—
153#121—862no—
154#121—1721no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4C22⋊D4311yescharacteristic
159C2×C4⋊C4C22⋊D4312yes—
160C2×C4⋊C4C22×D4311yescharacteristic
161C2×C42C22⋊D4311yescharacteristic
162#106—1722no—
163#104—1722no—
164#103—1721no—
165#102—1721no—
166#102—1722no—
167C22⋊C8—862no—
168#95—22no—
169#95—21no—
170#95—22no—
171#95—22no—
172#95—22no—
173#95C22⋊D4312yes—
174#41—1721no—
175#41—1721no—
176#41—1721no—
177#41—1721no—
178C2×Q8—82no—
179C2×Q8—81no—
180C2×Q8—861no—
181C2×D4—862no—
182C2×D4—861no—
183C2×D4—1721no—
184C22×C4—21no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—21no—
188C22×C4—1721no—
189C22×C4C2×C22⋊D4311yescharacteristic
190C22×C4C2×C22⋊D4312yes—
191M16—1721no—
192M16—1721no—
193C2×C8—1722no—
194C2×C8—1721no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C4⋊C4—82no—
201C4⋊C4—862no—
202C22⋊C4—1722no—
203C42—21no—
204C42#1062188412yes—
205C23—1721no—
206C23#1306329411yescharacteristic
207Q8—84no—
208Q8—1721no—
209Q8—1721no—
210D4—3442no—
211D4—3441no—
212D4—3441no—
213D4—1721no—
214D4—1721no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—3441no—
231C2×C4—3441no—
232C2×C4—1721no—
233C2×C4C2×#1062188411yescharacteristic
234C2×C4#1306335611yescharacteristic
235C8—3441no—
236C8—3442no—
237C22—21no—
238C22—21no—
239C22—3441no—
240C22—3441no—
241C22—3441no—
242C22#1458303811yescharacteristic
243C22#1458307211yescharacteristic
244C22#1458308611yescharacteristic
245C4—21no—
246C4—21no—
247C4—42no—
248C4—42no—
249C4—82no—
250C4—81no—
251C4—82no—
252C4—3441no—
253C2—21no—
254C2—21no—
255C2—6881no—
256C2#1913353511yescharacteristic
257C2#1913660811yescharacteristic
258C2#1913661211yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2844C2
socleC22×C43B(4,𝔽2)
prime radical#14583480C22
hypercenter#2844D43
hypocenterC43#12185
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2844

Complements

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

NH ≅ G/Ntype
3. #19132622C2semidirect
4. #19132539C2semidirect
5. C43×#2844C2semidirect
124. #2844D43semidirect
148. C43#12185semidirect

Maximal subgroups

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

subgroupindex
#191358242
#191336312
#191326222
#191325392
C43×#28442
#1218543