Finite Group Databasebeta

← #25010150

Subgroups — #25010150

Order 11008.

306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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#19147600C211yesmaximal, characteristic
2#19136848C211yesmaximal, characteristic
3#19136645C211yesmaximal, characteristic
4#19133966C211yesmaximal, characteristic
5#19132643C211yesmaximal, characteristic
6#19132575C211yesmaximal, characteristic
7C43×#1332C211yesmaximal, characteristic
8#14583627—21no—
9C2×Dic344—22no—
10C2×#13063271—21no—
11#14583279C2211yescharacteristic
12#14583279C2211yescharacteristic
13#14583277—21no—
14#14583185—21no—
15#14583109—21no—
16#14583108—22no—
17C8×Dic86C2211yescharacteristic
18#14582993—21no—
19C4⋊(C43⋊C16)C2211yescharacteristic
20#14582702—21no—
21#14582644—21no—
22C4×Q16×C43C2211yescharacteristic
23C4×C16×C43C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×Dic172—21no—
26C2×Dic172—21no—
27C2×Dic172—21no—
28C2×Dic172D412yes—
29C2×#10621885—22no—
30#13063325—21no—
31#13063325—21no—
32#13063323—22no—
33#13063317—41no—
34#13063315—42no—
35C4×Dic86—41no—
36C4×Dic86D411yescharacteristic
37#13063290—22no—
38Dic344—44no—
39#13063271—42no—
40C2×C43⋊C16—21no—
41#13063257—41no—
42C4⋊(C43⋊C8)D411yescharacteristic
43Dic43⋊C8—21no—
44#13063250—41no—
45#13063248—22no—
46C8×Dic43—21no—
47C2×Q16×C43D411yescharacteristic
48C4×Q8×C43—21no—
49C2×C16×C43—21no—
50#107×C43D411yescharacteristic
51C4⋊C8×C43—21no—
52#103×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×Q8×C43—21no—
55C2×Dic86—22no—
56C2×Dic86—41no—
57C2×Dic86D811yescharacteristic
58Q16×C43—21no—
59Q16×C43—21no—
60C2×C8×C43—41no—
61C2×C8×C43C2×D411yescharacteristic
62C2×C8×C43C2×D411yescharacteristic
63C4⋊C4×C43—21no—
64C4⋊C4×C43—41no—
65C42×C43—41no—
66C42×C43C2×D411yescharacteristic
67#10621885—82no—
68C4⋊Dic43—41no—
69C4⋊Dic43—41no—
70C4⋊Dic43—41no—
71C4⋊Dic43—41no—
72C4⋊Dic43D811yescharacteristic
73Dic43⋊C4—21no—
74Dic43⋊C4—42no—
75Dic43⋊C4—42no—
76Dic43⋊C4—42no—
77C4×Dic43—21no—
78C4×Dic43—42no—
79C2×C43⋊C8—21no—
80Dic172—42no—
81Dic172—42no—
82Dic172—41no—
83Dic172—41no—
84Dic172—41no—
85Dic172—41no—
86C16×C43—22no—
87C43⋊C16—41no—
88Q8×C43—41no—
89Q8×C43—41no—
90C2×C4×C43—41no—
91C2×C4×C43—41no—
92C2×C4×C43#12011yescharacteristic
93C2×C4×C43C2×D811yescharacteristic
94C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
95C2×Dic43—21no—
96C2×Dic43—21no—
97C2×Dic43—42no—
98C2×Dic43—81no—
99Dic86—21no—
100Dic86—42no—
101Dic86—42no—
102Dic86—81no—
103Dic86—81no—
104Dic86Q3212yescomplemented
105C8×C43—21no—
106C8×C43—81no—
107C8×C43#13511yescharacteristic
108C8×C43AGL(1,ℤ/8)11yescharacteristic
109C43⋊C8—41no—
110#12334—431nomaximal, Sylow
111C22×C43#44711yescharacteristic
112C4×C43—21no—
113C4×C43—81no—
114C4×C43—81no—
115C4×C43#44911yescharacteristic
116C4×C43#45311yescharacteristic
117C4×C43C2×Q3211yescharacteristic
118C4×C43#51011yescharacteristic
119Dic43—22no—
120Dic43—41no—
121Dic43—82no—
122Dic43—161no—
123#3395—431no—
124#2247—431no—
125#2209—431no—
126#1670—431no—
127#1362—431no—
128Q8⋊C16—431no—
129#1332D4311yescharacteristic
130C2×C43#162111yescharacteristic
131C2×C43#218811yescharacteristic
132C2×C43#219511yescharacteristic
133#557—861no—
134C2×Q32—862no—
135C2×Q32—861no—
136#494—431no—
137#494—431no—
138#494—861no—
139#475—861no—
140#462—862no—
141#462—861no—
142C8×Q8—431no—
143C4×Q16—861no—
144C4×Q16C2×D4311yescharacteristic
145C4⋊C16—431no—
146#358—861no—
147C4×C16C2×D4311yescharacteristic
148#335C2×D4311yescharacteristic
149#332—861no—
150C43#1233411yescharacteristic, complemented, Sylow
151C2×Q16—432no—
152C2×Q16—862no—
153C2×Q16—861no—
154C2×Q16—861no—
155C2×Q16—861no—
156C2×Q16D17211yescharacteristic
157C4⋊Q8—862no—
158C4⋊Q8—861no—
159C4⋊Q8—861no—
160#125—1721no—
161#125—1722no—
162C4×Q8—21no—
163C4×Q8—431no—
164C4×Q8—862no—
165C4×Q8—1721no—
166Q32—1724no—
167Q32—1722no—
168C2×C16—21no—
169C2×C16—861no—
170#107D17211yescharacteristic
171#106—1721no—
172C4⋊C8—21no—
173C4⋊C8—431no—
174C4⋊C8—861no—
175#103—21no—
176#103—862no—
177#103—1721no—
178C4×C8—861no—
179C4×C8C22×D4311yescharacteristic
180C2×Q8—21no—
181C2×Q8—431no—
182C2×Q8—862no—
183C2×Q8—1721no—
184Q16—21no—
185Q16—21no—
186Q16—3442no—
187Q16—1722no—
188Q16—1722no—
189Q16—1721no—
190Q16—1721no—
191Q16—1721no—
192Q16—1721no—
193C2×C8—41no—
194C2×C8—861no—
195C2×C8C2×D17211yescharacteristic
196C2×C8D4×D4311yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—41no—
199C4⋊C4—431no—
200C4⋊C4—861no—
201C4⋊C4—1722no—
202C4⋊C4—1722no—
203C4⋊C4—1722no—
204C4⋊C4—1721no—
205C4⋊C4—1721no—
206C4⋊C4—1721no—
207C4⋊C4—1721no—
208C42—41no—
209C42—861no—
210C42—1722no—
211C42D4×D4311yescharacteristic
212C16—22no—
213C16—1721no—
214Q8—41no—
215Q8—41no—
216Q8—432no—
217Q8—861no—
218Q8—3441no—
219Q8—3441no—
220Q8—1722no—
221Q8—1722no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—861no—
225C2×C4—861no—
226C2×C4—3441no—
227C2×C4—1722no—
228C2×C4#1306329511yescharacteristic
229C2×C4D8×D4311yescharacteristic
230C2×C4#1306335211yescharacteristic
231C8—21no—
232C8—81no—
233C8—1721no—
234C8#1306334711yescharacteristic
235C8#1306335311yescharacteristic
236C22#1458303411yescharacteristic
237C4—21no—
238C4—81no—
239C4—81no—
240C4—862no—
241C4—3442no—
242C4—1721no—
243C4—6881no—
244C4#1458304611yescharacteristic
245C4#1458306811yescharacteristic
246C4Q32×D4311yescharacteristic
247C4#1458333811yescharacteristic
248C2#1913366311yescharacteristic
249C2#1913653011yescharacteristic
250C2#1913657411yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1332C2
socle, prime radicalC22×C43#447
hypercenter#1332D43
hypocenterC43#12334
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1332

Complements

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

NH ≅ G/Ntype
104. Dic86Q32semidirect
150. C43#12334semidirect

Maximal subgroups

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

subgroupindex
#191476002
#191368482
#191366452
#191339662
#191326432
#191325752
C43×#13322
#1233443