Finite Group Databasebeta

← #25009059

Subgroups — #25009059

Order 11008.

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

normal subgroups only

This group has 354 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#19145940C211yesmaximal, characteristic
2#19136529C212yesmaximal
3#19132606C212yesmaximal
4#19132535C211yesmaximal, characteristic
5C43×#2056C211yesmaximal, characteristic
6#14583456—21no—
7C2×#13063271—22no—
8#14583195—22no—
9#14583140—21no—
10#14583140C2212yes—
11#14583110—22no—
12#14582703—22no—
13C22⋊(C43⋊C16)C2212yes—
14C22×Q16×C43C2211yescharacteristic
15C2×C4⋊C8×C43C2211yescharacteristic
16C2×#103×C43—21no—
17C43×#391—21no—
18C43×#340C2211yescharacteristic
19C2×Dic172—21no—
20C2×Dic172D412yes—
21#13063325—21no—
22#13063325—21no—
23#13063317—41no—
24#13063304—22no—
25#13063304—41no—
26C4×Dic86—22no—
27C4×Dic86—41no—
28#13063284—41no—
29#13063271—44no—
30C2×C43⋊C16—22no—
31#13063259—21no—
32#13063259D412yes—
33#13063250—22no—
34#13063250—22no—
35C22×Q8×C43—21no—
36C2×Q16×C43—22no—
37C2×Q16×C43—42no—
38C22×C8×C43D411yescharacteristic
39C22×C8×C43C2311yescharacteristic
40C2×C4⋊C4×C43—21no—
41C2×C42×C43D411yescharacteristic
42C4⋊C8×C43—22no—
43#103×C43—42no—
44#95×C43—41no—
45#95×C43—41no—
46C2×Q8×C43—22no—
47C2×Q8×C43—41no—
48C2×Q8×C43—41no—
49C2×Q8×C43—41no—
50C2×Q8×C43—41no—
51C2×Q8×C43—41no—
52C22×C4×C43—41no—
53C22×C4×C43—41no—
54C22×C4×C43D811yescharacteristic
55C22×C4×C43D811yescharacteristic
56C22×C4×C43C2×D411yescharacteristic
57C2×Dic86—22no—
58C2×Dic86—41no—
59Q16×C43—24no—
60Q16×C43—42no—
61C2×C8×C43—21no—
62C2×C8×C43—41no—
63C2×C8×C43—41no—
64C2×C8×C43C2×D412yes—
65C4⋊C4×C43—41no—
66C4⋊C4×C43—41no—
67C42×C43—21no—
68C42×C43—21no—
69C22⋊Dic43—42no—
70C4⋊Dic43—22no—
71C4⋊Dic43—41no—
72C4⋊Dic43—41no—
73C4⋊Dic43—41no—
74Dic43⋊C4—42no—
75Dic43⋊C4—42no—
76C4×Dic43—42no—
77Dic172—42no—
78Dic172—81no—
79C43⋊C16—42no—
80C23×C43C2×D811yescharacteristic
81Q8×C43—42no—
82Q8×C43—42no—
83Q8×C43—81no—
84Q8×C43—81no—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—41no—
91C2×C4×C43—42no—
92C2×C4×C43—81no—
93C2×C4×C43—81no—
94C2×C4×C43—81no—
95C2×C4×C43—81no—
96C2×C4×C43—81no—
97C2×C4×C43Q3212yescomplemented
98C2×C4×C43#12011yescharacteristic
99C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
100C2×Dic43—42no—
101C2×Dic43—42no—
102Dic86—42no—
103Dic86—42no—
104Dic86—82no—
105C8×C43—22no—
106C8×C43—41no—
107#12162—431nomaximal, Sylow
108C22×C43—21no—
109C22×C43—21no—
110C22×C43#44711yescharacteristic
111C22×C43C2×Q3211yescharacteristic
112C22×C43#51011yescharacteristic
113C4×C43—21no—
114C4×C43—22no—
115C4×C43—41no—
116C4×C43—82no—
117C4×C43—161no—
118C4×C43#45411yescharacteristic
119C4×C43B(4,𝔽2)11yescharacteristic
120Dic43—82no—
121Dic43—82no—
122#3249—431no—
123#2188—432no—
124#2056D4311yescharacteristic
125#1348—432no—
126#1322—431no—
127C2×C43—21no—
128C2×C43—21no—
129C2×C43#159811yescharacteristic
130C2×C43#218811yescharacteristic
131C2×C43#219111yescharacteristic
132C22×Q16C2×D4311yescharacteristic
133#533—861no—
134C2×Q32—862no—
135#477—862no—
136#467—432no—
137#467—861no—
138#462—862no—
139C2×C4⋊C8C2×D4311yescharacteristic
140C2×#103—21no—
141#391—21no—
142#358—862no—
143C22⋊C16—432no—
144#340C2×D4311yescharacteristic
145C43#1216211yescharacteristic, complemented, Sylow
146C22×Q8—21no—
147C2×Q16—22no—
148C2×Q16—42no—
149C2×Q16—432no—
150C2×Q16—861no—
151C22×C8C22⋊D4311yescharacteristic
152C22×C8C22×D4311yescharacteristic
153C4⋊Q8—861no—
154C4⋊Q8—861no—
155#125—1721no—
156C22⋊Q8—862no—
157C22⋊Q8—1721no—
158C4×Q8—862no—
159C4×Q8—1721no—
160#117—1721no—
161C2×C4⋊C4—21no—
162C2×C42C22⋊D4311yescharacteristic
163Q32—1724no—
164C2×C16—862no—
165#107—432no—
166#107—861no—
167C4⋊C8—22no—
168#103—42no—
169#103—862no—
170#103—862no—
171#95—41no—
172#95—41no—
173C2×Q8—22no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—862no—
180C2×Q8—1721no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4#1062188211yescharacteristic
184C22×C4#1062188211yescharacteristic
185C22×C4C2×C22⋊D4311yescharacteristic
186Q16—24no—
187Q16—42no—
188Q16—3441no—
189Q16—1722no—
190C2×C8—21no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8D4×D4312yes—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—862no—
197C4⋊C4—1721no—
198C4⋊C4—1721no—
199C4⋊C4—1722no—
200C4⋊C4—1721no—
201C4⋊C4—1722no—
202C22⋊C4—1722no—
203C42—21no—
204C42—21no—
205C42—1722no—
206C16—1722no—
207C23C2×#1062188211yescharacteristic
208Q8—42no—
209Q8—42no—
210Q8—81no—
211Q8—81no—
212Q8—3442no—
213Q8—1722no—
214Q8—1722no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—81no—
223C2×C4—81no—
224C2×C4—81no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4—1722no—
228C2×C4—1722no—
229C2×C4#1306327112yescomplemented
230C2×C4#1306329311yescharacteristic
231C2×C4#1306335011yescharacteristic
232C8—22no—
233C8—41no—
234C22—21no—
235C22—21no—
236C22#1458303211yescharacteristic
237C22C2×#1306327111yescharacteristic
238C22#1458333911yescharacteristic
239C4—22no—
240C4—21no—
241C4—41no—
242C4—82no—
243C4—161no—
244C4—3442no—
245C4—3442no—
246C4#1458307111yescharacteristic
247C4#1458308511yescharacteristic
248C2—21no—
249C2—21no—
250C2#1913352911yescharacteristic
251C2#1913652811yescharacteristic
252C2#1913654511yescharacteristic
subgroupG/H
centerC22#14583032
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#2056C2
socleC22×C43#447
prime radicalC23×C43C2×D8
hypercenter#2056D43
hypocenterC43#12162
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2056

Complements

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

NH ≅ G/Ntype
97. C2×C4×C43Q32semidirect
145. C43#12162semidirect
229. C2×C4#13063271semidirect

Maximal subgroups

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

subgroupindex
#191459402
#191365292
#191326062
#191325352
C43×#20562
#1216243