Finite Group Databasebeta

← #25010307

Subgroups — #25010307

Order 11008.

282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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#19147484C211yesmaximal, characteristic
2#19136822C211yesmaximal, characteristic
3#19133962C211yesmaximal, characteristic
4#19132649C211yesmaximal, characteristic
5#19132573C211yesmaximal, characteristic
6#19132559C211yesmaximal, characteristic
7C43×#2209C211yesmaximal, characteristic
8#14583628—21no—
9#14583304C2211yescharacteristic
10#14583300—21no—
11#14583208—22no—
12#14583184—21no—
13#14583181—21no—
14C8×Dic86C2211yescharacteristic
15Q16×Dic43—21no—
16#14582703—22no—
17C4×C43⋊C16C2211yescharacteristic
18#14582652C2211yescharacteristic
19#14582645—21no—
20C2×Q32×C43—21no—
21C43×#494C2211yescharacteristic
22C4×Q16×C43C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#358—21no—
25#13063325—21no—
26#13063325—41no—
27#13063316—22no—
28#13063316—42no—
29Q8×Dic43—22no—
30C4×Dic86—41no—
31C4×Dic86D411yescharacteristic
32C2×C43⋊C16—21no—
33#13063259—21no—
34#13063259D412yes—
35#13063256—22no—
36#13063256—41no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)D411yescharacteristic
39Dic43⋊C8—21no—
40#13063249—22no—
41#13063248—41no—
42C8×Dic43—21no—
43C2×Q16×C43—21no—
44C2×Q16×C43—21no—
45C2×Q16×C43D411yescharacteristic
46C4⋊Q8×C43—21no—
47C4×Q8×C43—21no—
48Q32×C43—42no—
49C2×C16×C43—21no—
50#107×C43D411yescharacteristic
51#103×C43—21no—
52C4×C8×C43C2311yescharacteristic
53C2×Q8×C43—21no—
54C2×Q8×C43—41no—
55C2×Dic86—41no—
56C2×Dic86D811yescharacteristic
57Q16×C43—21no—
58Q16×C43—42no—
59Q16×C43—41no—
60Q16×C43—41no—
61Q16×C43SD1612yes—
62C2×C8×C43C2×D411yescharacteristic
63C2×C8×C43C2×D411yescharacteristic
64C4⋊C4×C43—21no—
65C4⋊C4×C43—41no—
66C4⋊C4×C43—41no—
67C4⋊C4×C43—41no—
68C42×C43—41no—
69C42×C43C2×D411yescharacteristic
70C4⋊Dic43—22no—
71C4⋊Dic43—42no—
72C4⋊Dic43—42no—
73C4⋊Dic43—41no—
74C4⋊Dic43D811yescharacteristic
75Dic43⋊C4—21no—
76Dic43⋊C4—42no—
77C4×Dic43—21no—
78C4×Dic43—42no—
79C2×C43⋊C8—21no—
80C2×C43⋊C8—41no—
81C16×C43—41no—
82C43⋊C16—41no—
83Q8×C43—22no—
84Q8×C43—41no—
85Q8×C43—81no—
86Q8×C43—81no—
87C2×C4×C43—41no—
88C2×C4×C43—41no—
89C2×C4×C43—81no—
90C2×C4×C43#12011yescharacteristic
91C2×C4×C43C2×D811yescharacteristic
92C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
93C2×Dic43—21no—
94C2×Dic43—21no—
95C2×Dic43—42no—
96Dic86—21no—
97Dic86—21no—
98Dic86—81no—
99Dic86—81no—
100C8×C43—21no—
101C8×C43C2×SD1611yescharacteristic
102C8×C43#13711yescharacteristic
103C43⋊C8—41no—
104C43⋊C8—81no—
105#12357—431nomaximal, Sylow
106C22×C43#44711yescharacteristic
107C4×C43—21no—
108C4×C43—42no—
109C4×C43—81no—
110C4×C43—161no—
111C4×C43#44811yescharacteristic
112C4×C43#45411yescharacteristic
113C4×C43#50811yescharacteristic
114C4×C43#51011yescharacteristic
115Dic43—41no—
116Dic43—41no—
117Dic43—82no—
118#3383—431no—
119#2241—431no—
120#2209D4311yescharacteristic
121#1670—431no—
122#1364—431no—
123Q8⋊C16—431no—
124#1332—431no—
125C2×C43#162711yescharacteristic
126C2×C43#218911yescharacteristic
127C2×C43#219511yescharacteristic
128#557—861no—
129C2×Q32—21no—
130#500—431no—
131#499—861no—
132#494C2×D4311yescharacteristic
133#479—862no—
134#475—861no—
135#475—861no—
136C8×Q8—431no—
137C4×Q16—861no—
138C4×Q16C2×D4311yescharacteristic
139C4⋊C16C2×D4311yescharacteristic
140#358—21no—
141#358—862no—
142C4×C16—431no—
143#335—431no—
144#332—861no—
145C43#1235711yescharacteristic, complemented, Sylow
146C2×Q16—21no—
147C2×Q16—21no—
148C2×Q16C22⋊D4311yescharacteristic
149C4⋊Q8—21no—
150C4⋊Q8—861no—
151C4⋊Q8—1721no—
152#125—862no—
153#125—1722no—
154C4×Q8—21no—
155C4×Q8—431no—
156C4×Q8—862no—
157C4×Q8—1721no—
158Q32—42no—
159C2×C16—21no—
160C2×C16—861no—
161#107—432no—
162#107—861no—
163#107C22⋊D4311yescharacteristic
164#106—862no—
165#106—1721no—
166C4⋊C8—431no—
167C4⋊C8—861no—
168C4⋊C8—861no—
169#103—21no—
170#103—862no—
171#103—1721no—
172C4×C8—861no—
173C4×C8C22×D4311yescharacteristic
174C2×Q8—21no—
175C2×Q8—41no—
176C2×Q8—431no—
177C2×Q8—1721no—
178Q16—21no—
179Q16—42no—
180Q16—41no—
181Q16—41no—
182Q16#1062188312yes—
183C2×C8—861no—
184C2×C8—1721no—
185C2×C8D4×D4311yescharacteristic
186C2×C8C2×C22⋊D4311yescharacteristic
187C4⋊C4—21no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—431no—
192C4⋊C4—861no—
193C4⋊C4—862no—
194C4⋊C4—1722no—
195C4⋊C4—1722no—
196C4⋊C4—1722no—
197C4⋊C4—1721no—
198C42—41no—
199C42—861no—
200C42—1722no—
201C42D4×D4311yescharacteristic
202C16—41no—
203C16—1721no—
204Q8—22no—
205Q8—41no—
206Q8—81no—
207Q8—81no—
208Q8—861no—
209Q8—861no—
210Q8—3441no—
211Q8—3441no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—81no—
215C2×C4—861no—
216C2×C4—861no—
217C2×C4—1722no—
218C2×C4#1306329311yescharacteristic
219C2×C4D8×D4311yescharacteristic
220C2×C4#1306334911yescharacteristic
221C8—21no—
222C8—3441no—
223C8—1721no—
224C8C2×#1062188311yescharacteristic
225C8#1306335511yescharacteristic
226C22#1458303111yescharacteristic
227C4—21no—
228C4—42no—
229C4—81no—
230C4—161no—
231C4—3442no—
232C4—1721no—
233C4—1721no—
234C4#1458303711yescharacteristic
235C4#1458307011yescharacteristic
236C4#1458333211yescharacteristic
237C4#1458334111yescharacteristic
238C2#1913369711yescharacteristic
239C2#1913653411yescharacteristic
240C2#1913657011yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2209C2
socle, prime radicalC22×C43#447
hypercenter#2209D43
hypocenterC43#12357
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2209

Complements

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

NH ≅ G/Ntype
145. C43#12357semidirect

Maximal subgroups

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

subgroupindex
#191474842
#191368222
#191339622
#191326492
#191325732
#191325592
C43×#22092
#1235743