Finite Group Databasebeta

← #25010153

Subgroups — #25010153

Order 11008.

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

normal subgroups only

This group has 312 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#19147581C211yesmaximal, characteristic
2#19136847C211yesmaximal, characteristic, complemented
3#19133962C211yesmaximal, characteristic, complemented
4#19132645C211yesmaximal, characteristic, complemented
5#19132573C211yesmaximal, characteristic, complemented
6#19132556C211yesmaximal, characteristic
7C43×#2208C211yesmaximal, characteristic
8#14583619—21no—
9C2×#13063271—22no—
10#14583282—21no—
11#14583279C2211yescharacteristic
12#14583181—21no—
13#14583120—22no—
14#14583104—21no—
15C8×Dic86C2211yescharacteristic
16#14582993—21no—
17C4×C43⋊C16C2211yescharacteristic
18#14582652C2211yescharacteristic
19#14582645—21no—
20C2×SD32×C43—21no—
21C43×#494C2211yescharacteristic
22C4×D8×C43C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#358—21no—
25C2×Dic172—21no—
26C2×Dic172D412yes—
27C2×#10621883—22no—
28#13063325—21no—
29#13063318—42no—
30#13063312—22no—
31#13063304—41no—
32C4×Dic86D411yescharacteristic
33#13063290—22no—
34#13063284—41no—
35#13063271—44no—
36C2×C43⋊C16—21no—
37#13063256—41no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)D411yescharacteristic
40Dic43⋊C8—21no—
41#13063248—22no—
42#13063248—41no—
43C8×Dic43—21no—
44C2×Q16×C43—21no—
45C2×Q16×C43—21no—
46C2×D8×C43D411yescharacteristic
47C4⋊Q8×C43—21no—
48C4×D4×C43—21no—
49SD32×C43—42no—
50C2×C16×C43—21no—
51#107×C43D411yescharacteristic
52#102×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×Q8×C43—41no—
55C2×D4×C43—21no—
56C22×C4×C43—41no—
57C2×Dic86—22no—
58C2×Dic86D811yescharacteristic
59Q16×C43—42no—
60Q16×C43—41no—
61Q16×C43—41no—
62D8×C43—21no—
63D8×C43—21no—
64C2×C8×C43C2×D411yescharacteristic
65C2×C8×C43C2×D411yescharacteristic
66C4⋊C4×C43—21no—
67C4⋊C4×C43—41no—
68C4⋊C4×C43—41no—
69C22⋊C4×C43—41no—
70C42×C43C2×D411yescharacteristic
71C22⋊Dic43—42no—
72C22⋊Dic43—42no—
73#10621883—82no—
74C4⋊Dic43—41no—
75C4⋊Dic43—41no—
76C4⋊Dic43D811yescharacteristic
77Dic43⋊C4—21no—
78Dic43⋊C4—42no—
79C4×Dic43—21no—
80C4×Dic43—42no—
81C2×C43⋊C8—21no—
82C2×C43⋊C8—41no—
83Dic172—42no—
84Dic172—41no—
85Dic172—41no—
86C16×C43—41no—
87C43⋊C16—22no—
88C23×C43—41no—
89Q8×C43—81no—
90Q8×C43—81no—
91D4×C43—41no—
92D4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—81no—
95C2×C4×C43—81no—
96C2×C4×C43—81no—
97C2×C4×C43#12011yescharacteristic
98C2×C4×C43C2×D811yescharacteristic
99C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
100C2×Dic43—21no—
101C2×Dic43—21no—
102C2×Dic43—42no—
103Dic86—21no—
104Dic86—21no—
105Dic86—42no—
106Dic86—42no—
107C8×C43—21no—
108C8×C43#13511yescharacteristic
109C8×C43AGL(1,ℤ/8)11yescharacteristic
110C43⋊C8—41no—
111C43⋊C8—81no—
112#12335—431nomaximal, Sylow
113C22×C43—81no—
114C22×C43—81no—
115C22×C43—81no—
116C22×C43#44711yescharacteristic
117C4×C43—21no—
118C4×C43—81no—
119C4×C43—161no—
120C4×C43#44911yescharacteristic
121C4×C43#45311yescharacteristic
122C4×C43#50811yescharacteristic
123C4×C43#51011yescharacteristic
124Dic43—41no—
125Dic43—41no—
126Dic43—82no—
127#3393—431no—
128#2247—431no—
129#2208D4311yescharacteristic
130#1670—431no—
131#1362—431no—
132Q8⋊C16—431no—
133#1331—431no—
134C2×C43—161no—
135C2×C43#162111yescharacteristic
136C2×C43#218911yescharacteristic
137C2×C43#219511yescharacteristic
138#556—861no—
139C2×Q32—862no—
140C2×SD32—21no—
141#495—861no—
142#494—431no—
143#494C2×D4311yescharacteristic
144#475—861no—
145#464—862no—
146#461—861no—
147C8×Q8—431no—
148C4×Q16—861no—
149C4×D8C2×D4311yescharacteristic
150C4⋊C16C2×D4311yescharacteristic
151#358—21no—
152C4×C16—431no—
153#335—431no—
154#332—861no—
155C43#1233511yescharacteristic, complemented, Sylow
156C2×Q16—21no—
157C2×Q16—21no—
158C2×Q16—432no—
159C2×Q16—861no—
160C2×SD16—862no—
161C2×D8C22⋊D4311yescharacteristic
162C4⋊Q8—21no—
163C4⋊Q8—861no—
164#126—1722no—
165#124—862no—
166C22⋊Q8—1721no—
167C4×Q8—431no—
168C4×Q8—862no—
169C4×D4—21no—
170#117—1721no—
171Q32—1724no—
172SD32—42no—
173C2×C16—21no—
174C2×C16—861no—
175#107C22⋊D4311yescharacteristic
176#106—1721no—
177C4⋊C8—431no—
178C4⋊C8—861no—
179C4⋊C8—861no—
180#103—862no—
181#103—1721no—
182#102—21no—
183C4×C8—861no—
184C4×C8C22×D4311yescharacteristic
185C2×Q8—41no—
186C2×Q8—431no—
187C2×Q8—862no—
188C2×D4—21no—
189C22×C4—41no—
190Q16—42no—
191Q16—41no—
192Q16—41no—
193Q16—1722no—
194Q16—1721no—
195Q16—1721no—
196SD16—3442no—
197D8—21no—
198D8—21no—
199C2×C8—861no—
200C2×C8—1721no—
201C2×C8D4×D4311yescharacteristic
202C2×C8C2×C22⋊D4311yescharacteristic
203C4⋊C4—21no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—431no—
207C4⋊C4—861no—
208C4⋊C4—1722no—
209C4⋊C4—1721no—
210C4⋊C4—1721no—
211C22⋊C4—41no—
212C22⋊C4—1722no—
213C22⋊C4—1722no—
214C42—861no—
215C42—1722no—
216C42D4×D4311yescharacteristic
217C16—41no—
218C16—862no—
219C23—41no—
220Q8—81no—
221Q8—81no—
222Q8—861no—
223Q8—861no—
224Q8—1722no—
225Q8—1722no—
226D4—41no—
227D4—41no—
228C2×C4—41no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—861no—
233C2×C4—861no—
234C2×C4—1722no—
235C2×C4#1306329311yescharacteristic
236C2×C4D8×D4311yescharacteristic
237C2×C4#1306334911yescharacteristic
238C8—21no—
239C8—3441no—
240C8—1721no—
241C8#1306334511yescharacteristic
242C8#1306335111yescharacteristic
243C22—81no—
244C22—81no—
245C22—81no—
246C22#1458303111yescharacteristic
247C4—21no—
248C4—81no—
249C4—161no—
250C4—3442no—
251C4—1721no—
252C4—1721no—
253C4#1458304211yescharacteristic
254C4#1458306511yescharacteristic
255C4#1458333011yescharacteristic
256C4#1458333811yescharacteristic
257C2—161no—
258C2#1913365911yescharacteristic
259C2#1913653211yescharacteristic
260C2#1913657011yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2208C2
socleC22×C43#447
prime radicalC2×D8×C43D4
hypercenter#2208D43
hypocenterC43#12335
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
2. #19136847C2semidirect
3. #19133962C2semidirect
4. #19132645C2semidirect
5. #19132573C2semidirect
155. C43#12335semidirect

Maximal subgroups

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

subgroupindex
#191475812
#191368472
#191339622
#191326452
#191325732
#191325562
C43×#22082
#1233543