Finite Group Databasebeta

← #25009864

Subgroups — #25009864

Order 11008.

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

normal subgroups only

This group has 310 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#19136792C212yesmaximal
3#19132606C212yesmaximal
4#19132535C211yesmaximal, characteristic
5C43×#2086C211yesmaximal, characteristic
6#14583456—21no—
7#14583195—22no—
8#14583140—21no—
9#14583140C2212yes—
10#14583110—22no—
11#14582726—22no—
12#14582702—22no—
13C22⋊(C43⋊C16)C2212yes—
14C2×#107×C43C2211yescharacteristic
15C2×C4⋊C8×C43C2211yescharacteristic
16C43×#389—21no—
17C43×#340—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—
29C2×C43⋊C16—22no—
30#13063259—21no—
31#13063259D412yes—
32#13063250—22no—
33#13063250—22no—
34C22×C8×C43D411yescharacteristic
35C22×C8×C43C2311yescharacteristic
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43—41no—
39C2×C42×C43D411yescharacteristic
40#107×C43—22no—
41C4⋊C8×C43—22no—
42#95×C43—41no—
43C22×C4×C43—41no—
44C22×C4×C43—41no—
45C22×C4×C43D811yescharacteristic
46C22×C4×C43D811yescharacteristic
47C22×C4×C43C2×D411yescharacteristic
48C2×Dic86—22no—
49C2×Dic86—41no—
50C2×C8×C43—21no—
51C2×C8×C43—41no—
52C2×C8×C43—41no—
53C2×C8×C43C2×D412yes—
54C4⋊C4×C43—22no—
55C4⋊C4×C43—41no—
56C4⋊C4×C43—41no—
57C4⋊C4×C43—41no—
58C4⋊C4×C43—82no—
59C42×C43—21no—
60C42×C43—21no—
61C22⋊Dic43—42no—
62C4⋊Dic43—22no—
63C4⋊Dic43—41no—
64C4⋊Dic43—41no—
65C4⋊Dic43—41no—
66Dic43⋊C4—42no—
67Dic43⋊C4—42no—
68C4×Dic43—42no—
69Dic172—42no—
70Dic172—81no—
71C43⋊C16—42no—
72C23×C43C2×D811yescharacteristic
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—21no—
77C2×C4×C43—21no—
78C2×C4×C43—41no—
79C2×C4×C43—42no—
80C2×C4×C43—81no—
81C2×C4×C43—81no—
82C2×C4×C43—81no—
83C2×C4×C43—81no—
84C2×C4×C43—81no—
85C2×C4×C43SD3212yes—
86C2×C4×C43#12011yescharacteristic
87C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
88C2×Dic43—42no—
89C2×Dic43—42no—
90Dic86—42no—
91Dic86—42no—
92Dic86—82no—
93C8×C43—22no—
94C8×C43—41no—
95#12289—431nomaximal, Sylow
96C22×C43—21no—
97C22×C43—21no—
98C22×C43#44711yescharacteristic
99C22×C43C2×SD3211yescharacteristic
100C22×C43#51011yescharacteristic
101C4×C43—21no—
102C4×C43—22no—
103C4×C43—41no—
104C4×C43—82no—
105C4×C43—161no—
106C4×C43#45611yescharacteristic
107C4×C43#45811yescharacteristic
108Dic43—82no—
109Dic43—82no—
110#3249—431no—
111#2235—432no—
112#2086D4311yescharacteristic
113#1348—432no—
114#1322—431no—
115C2×C43—21no—
116C2×C43—21no—
117C2×C43#161011yescharacteristic
118C2×C43#218511yescharacteristic
119C2×C43#219111yescharacteristic
120#533—861no—
121#477—862no—
122#467—432no—
123#467—861no—
124#462—862no—
125C2×#107C2×D4311yescharacteristic
126C2×C4⋊C8C2×D4311yescharacteristic
127#389—21no—
128#367—862no—
129#358—862no—
130C22⋊C16—432no—
131#340—21no—
132#340C2×D4311yescharacteristic
133C43#1228911yescharacteristic, complemented, Sylow
134C2×Q16—432no—
135C2×Q16—861no—
136C22×C8C22⋊D4311yescharacteristic
137C22×C8C22×D4311yescharacteristic
138C4⋊Q8—861no—
139C4⋊Q8—861no—
140#125—1721no—
141C22⋊Q8—862no—
142C22⋊Q8—1721no—
143C4×Q8—862no—
144C4×Q8—1721no—
145#117—1721no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—41no—
149C2×C42C22⋊D4311yescharacteristic
150C2×C16—862no—
151#107—22no—
152#107—432no—
153#107—861no—
154C4⋊C8—22no—
155#103—862no—
156#103—862no—
157#95—41no—
158C2×Q8—862no—
159C2×Q8—1721no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4#1062188211yescharacteristic
163C22×C4#1062188211yescharacteristic
164C22×C4C2×C22⋊D4311yescharacteristic
165Q16—3441no—
166Q16—1722no—
167C2×C8—21no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8D4×D4312yes—
171C4⋊C4—22no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—82no—
176C4⋊C4—862no—
177C4⋊C4—1721no—
178C4⋊C4—1721no—
179C4⋊C4—1722no—
180C4⋊C4—1721no—
181C4⋊C4—1722no—
182C22⋊C4—1722no—
183C42—21no—
184C42—21no—
185C42—1722no—
186C16—1722no—
187C23C2×#1062188211yescharacteristic
188Q8—3442no—
189Q8—1722no—
190Q8—1722no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—81no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—1722no—
204C2×C4—1722no—
205C2×C4#1306326912yes—
206C2×C4#1306329311yescharacteristic
207C2×C4#1306335011yescharacteristic
208C8—22no—
209C8—41no—
210C22—21no—
211C22—21no—
212C22#1458303211yescharacteristic
213C22C2×#1306326911yescharacteristic
214C22#1458333911yescharacteristic
215C4—21no—
216C4—22no—
217C4—41no—
218C4—82no—
219C4—161no—
220C4—3442no—
221C4—3442no—
222C4#1458308111yescharacteristic
223C4#1458308811yescharacteristic
224C2—21no—
225C2—21no—
226C2#1913359711yescharacteristic
227C2#1913651111yescharacteristic
228C2#1913654511yescharacteristic
subgroupG/H
centerC22#14583032
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#2086C2
socleC22×C43#447
prime radicalC23×C43C2×D8
hypercenter#2086D43
hypocenterC43#12289
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2086

Complements

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

NH ≅ G/Ntype
133. C43#12289semidirect

Maximal subgroups

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

subgroupindex
#191459402
#191367922
#191326062
#191325352
C43×#20862
#1228943