Finite Group Databasebeta

← #25010144

Subgroups — #25010144

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#19147599C211yesmaximal, characteristic
2#19136642C211yesmaximal, characteristic
3#19133962C211yesmaximal, characteristic
4#19132644C211yesmaximal, characteristic
5#19132575C211yesmaximal, characteristic
6#19132560C211yesmaximal, characteristic
7C43×#2247C211yesmaximal, characteristic
8#14583624—21no—
9C2×#13063271—21no—
10#14583277—21no—
11#14583181—21no—
12#14583107—22no—
13#14583106—21no—
14C8×Dic86C2211yescharacteristic
15C4×Dic172C2211yescharacteristic
16Q16×Dic43—21no—
17C4⋊(C43⋊C16)C2211yescharacteristic
18#14582703—21no—
19#14582652C2211yescharacteristic
20#14582645—21no—
21C2×Q32×C43—22no—
22C43×#494C2211yescharacteristic
23C43×#494C2211yescharacteristic
24C4×C16×C43C2211yescharacteristic
25C2×Dic172D411yescharacteristic
26C2×#10621885—22no—
27#13063323—22no—
28#13063316—41no—
29#13063315—42no—
30Q8×Dic43—22no—
31C4×Dic86—21no—
32C4×Dic86D411yescharacteristic
33#13063290—41no—
34#13063271—42no—
35C2×C43⋊C16—21no—
36#13063259D411yescharacteristic
37#13063256—41no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)D411yescharacteristic
40Dic43⋊C8—21no—
41#13063250—21no—
42#13063249—22no—
43#13063248—41no—
44C8×Dic43—21no—
45C2×Q16×C43—21no—
46C2×Q16×C43—21no—
47C2×Q16×C43—21no—
48C2×Q16×C43D412yes—
49C4⋊Q8×C43—21no—
50C4⋊Q8×C43—21no—
51Q32×C43—44no—
52C2×C16×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×Q8×C43—22no—
55C2×Q8×C43—41no—
56C2×Dic86—21no—
57C2×Dic86D811yescharacteristic
58Q16×C43—42no—
59Q16×C43—42no—
60Q16×C43—41no—
61Q16×C43—41no—
62Q16×C43—41no—
63Q16×C43—41no—
64C2×C8×C43C2×D411yescharacteristic
65C2×C8×C43C2×D411yescharacteristic
66C4⋊C4×C43—41no—
67C4⋊C4×C43—41no—
68C4⋊C4×C43—41no—
69C4⋊C4×C43—41no—
70C42×C43C2×D411yescharacteristic
71#10621885—82no—
72C4⋊Dic43—21no—
73C4⋊Dic43—42no—
74C4⋊Dic43D811yescharacteristic
75Dic43⋊C4—21no—
76Dic43⋊C4—42no—
77Dic43⋊C4—42no—
78Dic43⋊C4—41no—
79C4×Dic43—21no—
80C4×Dic43—42no—
81C4×Dic43—41no—
82C2×C43⋊C8—21no—
83C2×C43⋊C8—41no—
84Dic172—21no—
85Dic172—21no—
86C16×C43—22no—
87C43⋊C16—41no—
88Q8×C43—42no—
89Q8×C43—42no—
90Q8×C43—81no—
91Q8×C43—81no—
92C2×C4×C43—42no—
93C2×C4×C43—81no—
94C2×C4×C43#12011yescharacteristic
95C2×C4×C43C2×D811yescharacteristic
96C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
97C2×Dic43—21no—
98C2×Dic43—21no—
99C2×Dic43—41no—
100C2×Dic43—41no—
101Dic86—21no—
102Dic86—41no—
103Dic86—41no—
104Dic86Q3212yescomplemented
105C8×C43—21no—
106C8×C43#13511yescharacteristic
107C8×C43AGL(1,ℤ/8)11yescharacteristic
108C43⋊C8—41no—
109C43⋊C8—81no—
110#12334—431nomaximal, Sylow
111C22×C43#44711yescharacteristic
112C4×C43—21no—
113C4×C43—82no—
114C4×C43—161no—
115C4×C43#44911yescharacteristic
116C4×C43#45311yescharacteristic
117C4×C43C2×Q3211yescharacteristic
118C4×C43#51011yescharacteristic
119Dic43—22no—
120Dic43—41no—
121Dic43—81no—
122Dic43—81no—
123#3395—431no—
124#2247D4311yescharacteristic
125#2209—431no—
126#1670—431no—
127#1362—431no—
128Q8⋊C16—431no—
129#1332—431no—
130C2×C43#162111yescharacteristic
131C2×C43#218811yescharacteristic
132C2×C43#219511yescharacteristic
133#557—861no—
134C2×Q32—22no—
135C2×Q32—861no—
136#494—861no—
137#494C2×D4311yescharacteristic
138#494C2×D4311yescharacteristic
139#475—861no—
140#462—861no—
141#462—862no—
142C8×Q8—431no—
143C4×Q16—431no—
144C4×Q16—861no—
145C4⋊C16—431no—
146#358—861no—
147C4×C16C2×D4311yescharacteristic
148#335—431no—
149#332—861no—
150C43#1233411yescharacteristic, complemented, Sylow
151C2×Q16—21no—
152C2×Q16—21no—
153C2×Q16—21no—
154C2×Q16—431no—
155C2×Q16—862no—
156C2×Q16C22⋊D4312yes—
157C4⋊Q8—21no—
158C4⋊Q8—21no—
159C4⋊Q8—862no—
160#125—1721no—
161#125—1722no—
162C4×Q8—431no—
163C4×Q8—862no—
164C4×Q8—861no—
165C4×Q8—1721no—
166Q32—44no—
167Q32—1722no—
168C2×C16—21no—
169C2×C16—861no—
170#107—431no—
171#106—1721no—
172C4⋊C8—431no—
173C4⋊C8—861no—
174C4⋊C8—861no—
175#103—862no—
176#103—861no—
177#103—1721no—
178C4×C8—861no—
179C4×C8C22×D4311yescharacteristic
180C2×Q8—22no—
181C2×Q8—41no—
182C2×Q8—431no—
183C2×Q8—861no—
184Q16—42no—
185Q16—42no—
186Q16—41no—
187Q16—41no—
188Q16—41no—
189Q16—41no—
190Q16—861no—
191Q16—861no—
192Q16—3442no—
193C2×C8—861no—
194C2×C8—1721no—
195C2×C8D4×D4311yescharacteristic
196C2×C8C2×C22⋊D4311yescharacteristic
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—431no—
202C4⋊C4—861no—
203C4⋊C4—861no—
204C4⋊C4—1722no—
205C4⋊C4—1722no—
206C4⋊C4—1722no—
207C4⋊C4—1721no—
208C42—861no—
209C42—1722no—
210C42—1721no—
211C42D4×D4311yescharacteristic
212C16—22no—
213C16—1721no—
214Q8—42no—
215Q8—42no—
216Q8—81no—
217Q8—81no—
218Q8—432no—
219Q8—861no—
220Q8—1721no—
221Q8—1721no—
222C2×C4—42no—
223C2×C4—81no—
224C2×C4—861no—
225C2×C4—861no—
226C2×C4—1721no—
227C2×C4—1721no—
228C2×C4#1306329311yescharacteristic
229C2×C4D8×D4311yescharacteristic
230C2×C4#1306334911yescharacteristic
231C8—21no—
232C8—3441no—
233C8—1721no—
234C8#1306334411yescharacteristic
235C8#1306334911yescharacteristic
236C22#1458303111yescharacteristic
237C4—21no—
238C4—82no—
239C4—161no—
240C4—862no—
241C4—3441no—
242C4—3441no—
243C4—1721no—
244C4#1458304111yescharacteristic
245C4#1458306611yescharacteristic
246C4Q32×D4311yescharacteristic
247C4#1458334111yescharacteristic
248C2#1913365711yescharacteristic
249C2#1913652711yescharacteristic
250C2#1913657211yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2247C2
socle, prime radicalC22×C43#447
hypercenter#2247D43
hypocenterC43#12334
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2247

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
#191475992
#191366422
#191339622
#191326442
#191325752
#191325602
C43×#22472
#1233443