Finite Group Databasebeta

← #25009062

Subgroups — #25009062

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#19136531C212yesmaximal
3#19135918C211yesmaximal, characteristic
4#19132608C212yesmaximal
5C43×#1322C211yesmaximal, characteristic
6C22×Dic172C2211yescharacteristic
7#14583456—21no—
8C2×Dic344—22no—
9#14583195—22no—
10#14583140—21no—
11#14583140C2212yes—
12#14583110—22no—
13C2×#13063250—21no—
14#14582805—21no—
15#14582704—22no—
16#14582662C2211yescharacteristic
17C2×C4⋊C8×C43C2211yescharacteristic
18C43×C22⋊C16C2212yes—
19C22×Dic86—21no—
20C2×Dic172—22no—
21C2×Dic172—21no—
22C2×Dic172—42no—
23C2×Dic172D412yes—
24#13063325—21no—
25#13063325—21no—
26#13063317—41no—
27#13063304—22no—
28#13063304—41no—
29C4×Dic86—22no—
30C4×Dic86—41no—
31#13063284—41no—
32C2×C4⋊Dic43—21no—
33Dic344—44no—
34#13063259—21no—
35#13063259D412yes—
36#13063250—22no—
37#13063250—22no—
38#13063250—42no—
39C43⋊#95—41no—
40C43⋊#95—41no—
41C22×C8×C43D411yescharacteristic
42C22×C8×C43C2311yescharacteristic
43C2×C42×C43D411yescharacteristic
44C2×C16×C43—22no—
45C4⋊C8×C43—22no—
46C22×C4×C43D811yescharacteristic
47C22×C4×C43D811yescharacteristic
48C22×C4×C43C2×D411yescharacteristic
49C22×Dic43—41no—
50C22×Dic43—41no—
51C2×Dic86—22no—
52C2×Dic86—22no—
53C2×Dic86—41no—
54C2×Dic86—41no—
55C2×Dic86—41no—
56C2×Dic86—41no—
57C2×Dic86—41no—
58C2×Dic86—41no—
59C2×C8×C43—21no—
60C2×C8×C43—41no—
61C2×C8×C43—41no—
62C2×C8×C43C2×D412yes—
63C42×C43—21no—
64C42×C43—21no—
65C22⋊Dic43—42no—
66C4⋊Dic43—22no—
67C4⋊Dic43—41no—
68C4⋊Dic43—41no—
69C4⋊Dic43—41no—
70C4⋊Dic43—41no—
71C4⋊Dic43—41no—
72Dic43⋊C4—42no—
73Dic43⋊C4—42no—
74C4×Dic43—42no—
75Dic172—24no—
76Dic172—42no—
77Dic172—42no—
78Dic172—81no—
79C16×C43—42no—
80C23×C43C2×D811yescharacteristic
81C2×C4×C43—21no—
82C2×C4×C43—21no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43—41no—
87C2×C4×C43Q3212yescomplemented
88C2×C4×C43#12011yescharacteristic
89C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
90C2×Dic43—42no—
91C2×Dic43—42no—
92C2×Dic43—42no—
93C2×Dic43—81no—
94C2×Dic43—81no—
95C2×Dic43—81no—
96C2×Dic43—81no—
97C2×Dic43—81no—
98Dic86—42no—
99Dic86—42no—
100Dic86—42no—
101Dic86—42no—
102Dic86—81no—
103Dic86—82no—
104Dic86—81no—
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#45411yescharacteristic
117C4×C43B(4,𝔽2)11yescharacteristic
118Dic43—82no—
119Dic43—82no—
120Dic43—82no—
121Dic43—161no—
122#3249—431no—
123#2188—432no—
124#2056—431no—
125#1348—432no—
126#1322D4311yescharacteristic
127C2×C43—21no—
128C2×C43—21no—
129C2×C43#159811yescharacteristic
130C2×C43#218811yescharacteristic
131C2×C43#219111yescharacteristic
132C22×Q16—431no—
133#533—861no—
134C2×Q32—862no—
135#477—862no—
136#467—432no—
137#467—861no—
138#462—862no—
139C2×C4⋊C8C2×D4311yescharacteristic
140C2×#103—861no—
141#391—861no—
142#358—862no—
143C22⋊C16C2×D4312yes—
144#340—431no—
145C43#1216211yescharacteristic, complemented, Sylow
146C22×Q8—861no—
147C2×Q16—432no—
148C2×Q16—861no—
149C2×Q16—862no—
150C2×Q16—1722no—
151C22×C8D17211yescharacteristic
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—861no—
162C2×C42D17211yescharacteristic
163Q32—1724no—
164C2×C16—22no—
165#107—432no—
166#107—861no—
167C4⋊C8—22no—
168#103—862no—
169#103—862no—
170#103—1722no—
171#95—1721no—
172#95—1721no—
173C2×Q8—862no—
174C2×Q8—862no—
175C2×Q8—1721no—
176C2×Q8—1721no—
177C2×Q8—1721no—
178C2×Q8—1721no—
179C2×Q8—1721no—
180C2×Q8—1721no—
181C22×C4—1721no—
182C22×C4—1721no—
183C22×C4D34411yescharacteristic
184C22×C4D34411yescharacteristic
185C22×C4C2×D17211yescharacteristic
186Q16—864no—
187Q16—3441no—
188Q16—1722no—
189Q16—1722no—
190C2×C8—21no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8D4×D4312yes—
194C4⋊C4—862no—
195C4⋊C4—1721no—
196C4⋊C4—1721no—
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—42no—
207C23C2×D34411yescharacteristic
208Q8—3441no—
209Q8—3442no—
210Q8—3441no—
211Q8—1722no—
212Q8—1722no—
213Q8—1722no—
214Q8—1722no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—3441no—
222C2×C4—3441no—
223C2×C4—3441no—
224C2×C4—3441no—
225C2×C4—3441no—
226C2×C4—1722no—
227C2×C4—1722no—
228C2×C4—1722no—
229C2×C4Dic34412yescomplemented
230C2×C4#1306329511yescharacteristic
231C2×C4#1306335311yescharacteristic
232C8—22no—
233C8—41no—
234C22—21no—
235C22—21no—
236C22#1458303511yescharacteristic
237C22C2×Dic34411yescharacteristic
238C22#1458334211yescharacteristic
239C4—22no—
240C4—21no—
241C4—41no—
242C4—3442no—
243C4—3442no—
244C4—3442no—
245C4—6881no—
246C4#1458307411yescharacteristic
247C4#1458308711yescharacteristic
248C2—21no—
249C2—21no—
250C2#1913353211yescharacteristic
251C2#1913653111yescharacteristic
252C2#1913654811yescharacteristic
subgroupG/H
centerC22#14583035
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#1322C2
socleC22×C43#447
prime radicalC23×C43C2×D8
hypercenter#1322D43
hypocenterC43#12162
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
87. C2×C4×C43Q32semidirect
145. C43#12162semidirect
229. C2×C4Dic344semidirect

Maximal subgroups

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

subgroupindex
#191459402
#191365312
#191359182
#191326082
C43×#13222
#1216243