Finite Group Databasebeta

← #25010139

Subgroups — #25010139

Order 11008.

324 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 65 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#19147605C211yesmaximal, characteristic
2#19136852C211yesmaximal, characteristic
3#19133962C211yesmaximal, characteristic, complemented
4#19132642C211yesmaximal, characteristic
5#19132573C211yesmaximal, characteristic, complemented
6#19132559C211yesmaximal, characteristic, complemented
7C43×#2209C211yesmaximal, characteristic, complemented
8#14583634—21no—
9C2×#13063268—22no—
10#14583284—21no—
11#14583276C2211yescharacteristic
12#14583181—21no—
13#14583117—22no—
14#14583099—21no—
15C8×Dic86C2211yescharacteristic
16#14582981—21no—
17C4×C43⋊C16C2211yescharacteristic
18#14582652C2211yescharacteristic
19#14582645—21no—
20C2×Q32×C43—21no—
21C43×#494C2211yescharacteristic
22C4×Q16×C43C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#358—21no—
25C2×#10621884—22no—
26C2×D344—21no—
27C2×D344D412yes—
28#13063322—21no—
29#13063314—22no—
30#13063313—41no—
31#13063310—42no—
32C4×Dic86D411yescharacteristic
33C4×D172—41no—
34#13063287—22no—
35#13063268—44no—
36C2×C43⋊C16—21no—
37#13063256—41no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)D411yescharacteristic
40Dic43⋊C8—21no—
41#13063248—41no—
42#13063245—22no—
43C8×Dic43—21no—
44C2×Q16×C43—21no—
45C2×Q16×C43—21no—
46C2×Q16×C43D411yescharacteristic
47C4⋊Q8×C43—21no—
48C4×Q8×C43—21no—
49Q32×C43—42no—
50C2×C16×C43—21no—
51#107×C43D411yescharacteristic
52#103×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×Q8×C43—21no—
55C2×Q8×C43—41no—
56C2×D172—22no—
57C2×D172—41no—
58C2×D172—41no—
59C2×C4×D43—42no—
60C2×Dic86D811yescharacteristic
61Q16×C43—21no—
62Q16×C43—21no—
63Q16×C43—42no—
64Q16×C43—41no—
65Q16×C43—41no—
66C2×C8×C43C2×D411yescharacteristic
67C2×C8×C43C2×D411yescharacteristic
68C4⋊C4×C43—21no—
69C4⋊C4×C43—41no—
70C4⋊C4×C43—41no—
71C4⋊C4×C43—41no—
72C42×C43—41no—
73C42×C43C2×D411yescharacteristic
74#10621884—82no—
75(C2×D43)⋊C4—42no—
76(C2×D43)⋊C4—42no—
77(C2×D43)⋊C4—42no—
78C4⋊Dic43D811yescharacteristic
79Dic43⋊C4—21no—
80C4×Dic43—21no—
81C2×C43⋊C8—21no—
82C2×C43⋊C8—41no—
83D344—42no—
84D344—41no—
85D344—41no—
86C16×C43—41no—
87C43⋊C16—22no—
88C22×D43—42no—
89Q8×C43—41no—
90Q8×C43—41no—
91Q8×C43—81no—
92Q8×C43—81no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43—81no—
96C2×C4×C43#12011yescharacteristic
97C2×C4×C43C2×D811yescharacteristic
98C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
99C2×Dic43—21no—
100C2×Dic43—21no—
101D172—42no—
102D172—42no—
103D172—81no—
104D172—81no—
105D172—161no—
106C4×D43—162no—
107Dic86—21no—
108Dic86—21no—
109C8×C43—21no—
110C8×C43#13511yescharacteristic
111C8×C43AGL(1,ℤ/8)11yescharacteristic
112C43⋊C8—41no—
113C43⋊C8—81no—
114#12333—431nomaximal, Sylow
115C22×C43#44711yescharacteristic
116C2×D43—82no—
117C2×D43—82no—
118C2×D43—82no—
119C4×C43—21no—
120C4×C43—81no—
121C4×C43—81no—
122C4×C43—161no—
123C4×C43#44911yescharacteristic
124C4×C43#45311yescharacteristic
125C4×C43#50811yescharacteristic
126C4×C43#51011yescharacteristic
127Dic43—41no—
128Dic43—41no—
129#3396—431no—
130#2248—431no—
131#2209D4311yescharacteristic, complemented
132#1670—431no—
133#1361—431no—
134Q8⋊C16—431no—
135#1332—431no—
136C2×C43#162111yescharacteristic
137C2×C43#218911yescharacteristic
138C2×C43#219411yescharacteristic
139D43—162no—
140#559—861no—
141C2×Q32—21no—
142C2×SD32—862no—
143#495—861no—
144#494C2×D4311yescharacteristic
145#493—431no—
146#475—861no—
147#463—862no—
148#460—861no—
149C8×Q8—431no—
150C4×Q16C2×D4311yescharacteristic
151C4×D8—861no—
152C4⋊C16C2×D4311yescharacteristic
153#358—21no—
154C4×C16—431no—
155#335—431no—
156#332—861no—
157C43#1233311yescharacteristic, complemented, Sylow
158C2×Q16—21no—
159C2×Q16—21no—
160C2×Q16C22⋊D4311yescharacteristic
161C2×SD16—862no—
162C2×D8—432no—
163C2×D8—861no—
164C4⋊Q8—21no—
165#127—861no—
166#124—862no—
167#124—1721no—
168#123—1722no—
169C4×Q8—21no—
170C4×Q8—431no—
171C4×D4—862no—
172C4×D4—1721no—
173Q32—42no—
174SD32—1724no—
175C2×C16—21no—
176C2×C16—861no—
177#107C22⋊D4311yescharacteristic
178#106—1721no—
179C4⋊C8—431no—
180C4⋊C8—861no—
181C4⋊C8—861no—
182#103—21no—
183#103—1721no—
184#102—862no—
185C4×C8—861no—
186C4×C8C22×D4311yescharacteristic
187C2×Q8—21no—
188C2×Q8—41no—
189C2×Q8—431no—
190C2×D4—862no—
191C2×D4—1721no—
192C2×D4—1721no—
193C22×C4—1722no—
194Q16—21no—
195Q16—21no—
196Q16—42no—
197Q16—41no—
198Q16—41no—
199SD16—3442no—
200D8—1722no—
201D8—1721no—
202D8—1721no—
203C2×C8—861no—
204C2×C8—1721no—
205C2×C8D4×D4311yescharacteristic
206C2×C8C2×C22⋊D4311yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—431no—
212C4⋊C4—861no—
213C22⋊C4—1722no—
214C22⋊C4—1722no—
215C22⋊C4—1722no—
216C42—41no—
217C42—861no—
218C42D4×D4311yescharacteristic
219C16—41no—
220C16—862no—
221C23—1722no—
222Q8—41no—
223Q8—41no—
224Q8—81no—
225Q8—81no—
226Q8—861no—
227Q8—861no—
228D4—3441no—
229D4—3441no—
230D4—1722no—
231D4—1722no—
232D4—6881no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—81no—
236C2×C4—861no—
237C2×C4—861no—
238C2×C4—6882no—
239C2×C4#1306329311yescharacteristic
240C2×C4D8×D4311yescharacteristic
241C2×C4#1306334911yescharacteristic
242C8—21no—
243C8—3441no—
244C8—1721no—
245C8#1306334511yescharacteristic
246C8#1306335111yescharacteristic
247C22—3442no—
248C22—3442no—
249C22—3442no—
250C22#1458303111yescharacteristic
251C4—21no—
252C4—81no—
253C4—81no—
254C4—161no—
255C4—1721no—
256C4—1721no—
257C4#1458304211yescharacteristic
258C4#1458306511yescharacteristic
259C4#1458333211yescharacteristic
260C4#1458334111yescharacteristic
261C2—6882no—
262C2#1913365911yescharacteristic
263C2#1913653411yescharacteristic
264C2#1913656311yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2209C2
socleC22×C43#447
prime radical#14583276C22
hypercenter#2209D43
hypocenterC43#12333
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
3. #19133962C2semidirect
5. #19132573C2semidirect
6. #19132559C2semidirect
7. C43×#2209C2semidirect
131. #2209D43semidirect
157. C43#12333semidirect

Maximal subgroups

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

subgroupindex
#191476052
#191368522
#191339622
#191326422
#191325732
#191325592
C43×#22092
#1233343