Finite Group Databasebeta

← #24985727

Subgroups — #24985727

Order 11008.

366 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 83 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#19142583C211yesmaximal, characteristic
2#19136067C212yesmaximal
3#19132421C211yesmaximal, characteristic
4#19132417C212yesmaximal
5C43×#2096C211yesmaximal, characteristic
6C2×#13063258—22no—
7#14582838—21no—
8#14582831—22no—
9#14582806—21no—
10#14582797C2212yes—
11#14582786—22no—
12#14582661—22no—
13#14582654C2212yes—
14C2×#106×C43—21no—
15C2×#103×C43—21no—
16C43×#391C2211yescharacteristic
17C43×#384C2211yescharacteristic
18C43×#336C2211yescharacteristic
19C22×C43⋊C8—22no—
20C2×C4⋊Dic43—21no—
21C2×C4⋊Dic43—21no—
22C2×C4⋊Dic43D412yes—
23C2×C4⋊Dic43D412yes—
24C2×Dic43⋊C4—22no—
25C2×C4×Dic43—21no—
26#13063258—44no—
27C43⋊#95—21no—
28C43⋊#95—22no—
29C43⋊#95—22no—
30C43⋊#95—22no—
31C22×Q8×C43D411yescharacteristic
32C22×C8×C43—21no—
33C2×C4⋊C4×C43—22no—
34C2×C4⋊C4×C43—21no—
35C2×C4⋊C4×C43D411yescharacteristic
36C2×C42×C43C2311yescharacteristic
37#106×C43—42no—
38#103×C43—42no—
39#95×C43—22no—
40C2×Q8×C43—21no—
41C2×Q8×C43—41no—
42C2×Q8×C43—41no—
43C2×Q8×C43Q1612yes—
44C22×C4×C43—21no—
45C22×C4×C43—21no—
46C22×C4×C43—41no—
47C22×C4×C43C2×D412yes—
48C22×C4×C43C2×D411yescharacteristic
49C22×Dic43—22no—
50C22×Dic43—22no—
51C2×C8×C43—22no—
52C2×C8×C43—41no—
53C2×C8×C43—41no—
54C4⋊C4×C43—41no—
55C4⋊C4×C43—41no—
56C4⋊C4×C43—41no—
57C4⋊C4×C43—42no—
58C4⋊C4×C43—42no—
59C42×C43—41no—
60C4⋊Dic43—22no—
61C4⋊Dic43—22no—
62C4⋊Dic43—42no—
63C4⋊Dic43—81no—
64C4⋊Dic43—81no—
65Dic43⋊C4—42no—
66Dic43⋊C4—42no—
67C4×Dic43—81no—
68C2×C43⋊C8—24no—
69C2×C43⋊C8—42no—
70C2×C43⋊C8—42no—
71C23×C43#12011yescharacteristic
72Q8×C43—42no—
73Q8×C43—81no—
74C2×C4×C43—21no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—21no—
78C2×C4×C43—22no—
79C2×C4×C43—41no—
80C2×C4×C43—41no—
81C2×C4×C43—41no—
82C2×C4×C43—42no—
83C2×C4×C43—82no—
84C2×C4×C43—81no—
85C2×C4×C43C2×Q1611yescharacteristic
86C2×C4×C43#13512yes—
87C2×C4×C43AGL(1,ℤ/8)12yes—
88C2×C4×C43#13711yescharacteristic
89C2×Dic43—42no—
90C2×Dic43—42no—
91C2×Dic43—42no—
92C2×Dic43—42no—
93C2×Dic43—42no—
94C2×Dic43—42no—
95C8×C43—42no—
96C43⋊C8—44no—
97#7802—431nomaximal, Sylow
98C22×C43#44912yes—
99C22×C43#45111yescharacteristic
100C22×C43#45311yescharacteristic
101C22×C43#45612yes—
102C22×C43#45811yescharacteristic
103C4×C43—22no—
104C4×C43—22no—
105C4×C43—21no—
106C4×C43—21no—
107C4×C43—42no—
108C4×C43—81no—
109C4×C43—161no—
110Dic43—82no—
111Dic43—82no—
112#2809—431no—
113#2096D4311yescharacteristic
114#2083—432no—
115#1272—431no—
116#1271—432no—
117C2×C43#160912yes—
118C2×C43#161411yescharacteristic
119C2×C43#162411yescharacteristic
120C2×C43#164812yes—
121C2×C43#166011yescharacteristic
122C2×#107—862no—
123C2×#106—21no—
124C2×#103—21no—
125#400—861no—
126#398—862no—
127#391—861no—
128#391C2×D4311yescharacteristic
129#389—432no—
130#387—862no—
131#384C2×D4311yescharacteristic
132#340—862no—
133#336—432no—
134#336C2×D4311yescharacteristic
135C43#780211yescharacteristic, complemented, Sylow
136C22×Q8C22⋊D4311yescharacteristic
137C22×C8—21no—
138C22×C8—862no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—432no—
142C2×C4⋊C4—432no—
143C2×C4⋊C4—861no—
144C2×C4⋊C4—861no—
145C2×C4⋊C4—862no—
146C2×C4⋊C4C22⋊D4311yescharacteristic
147C2×C42—861no—
148C2×C42C22×D4311yescharacteristic
149#107—1724no—
150#106—42no—
151#103—42no—
152#95—22no—
153#95—861no—
154#95—862no—
155#95—862no—
156#95—862no—
157C2×Q8—21no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8#1062188512yes—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—41no—
164C22×C4—862no—
165C22×C4—862no—
166C22×C4D4×D4312yes—
167C22×C4C2×C22⋊D4311yescharacteristic
168C2×C8—22no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—864no—
172C2×C8—1722no—
173C2×C8—1722no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4—862no—
180C4⋊C4—862no—
181C4⋊C4—3441no—
182C4⋊C4—3441no—
183C4⋊C4—1722no—
184C4⋊C4—1722no—
185C4⋊C4—1722no—
186C42—41no—
187C42—3441no—
188C23#1306329311yescharacteristic
189Q8—42no—
190Q8—81no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—82no—
201C2×C4—81no—
202C2×C4—1722no—
203C2×C4—1722no—
204C2×C4—1722no—
205C2×C4—1722no—
206C2×C4—1722no—
207C2×C4—1722no—
208C2×C4C2×#1062188511yescharacteristic
209C2×C4#1306334612yes—
210C2×C4#1306335212yes—
211C2×C4#1306335511yescharacteristic
212C8—42no—
213C8—1724no—
214C22#1458304312yes—
215C22#1458305411yescharacteristic
216C22#1458306611yescharacteristic
217C22#1458308012yes—
218C22#1458308811yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—42no—
224C4—81no—
225C4—161no—
226C4—3442no—
227C4—3442no—
228C2#1913359112yes—
229C2#1913361911yescharacteristic
230C2#1913367611yescharacteristic
231C2#1913383612yes—
232C2#1913390411yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2096C2
socle, prime radicalC23×C43#120
hypercenter#2096D43
hypocenterC43#7802
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2096

Complements

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

NH ≅ G/Ntype
135. C43#7802semidirect

Maximal subgroups

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

subgroupindex
#191425832
#191360672
#191324212
#191324172
C43×#20962
#780243