Finite Group Databasebeta

← #25009621

Subgroups — #25009621

Order 11008.

342 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 59 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#19142663C211yesmaximal, characteristic
2#19135945C211yesmaximal, characteristic
3#19133605C212yesmaximal
4#19132602C212yesmaximal
5C43×#1324C211yesmaximal, characteristic
6#14583530C2211yescharacteristic
7C2×#13063317—21no—
8#14583230—22no—
9#14582939—21no—
10#14582839—22no—
11#14582831—22no—
12#14582829—21no—
13#14582829C2212yes—
14#14582668C2211yescharacteristic
15#14582659—21no—
16#14582637—22no—
17C43×#382C2211yescharacteristic
18C43×#324C2212yes—
19C2×#10621877—21no—
20#13063324—41no—
21#13063317—42no—
22#13063317—42no—
23#13063316—41no—
24#13063304—22no—
25#13063284—21no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43D412yes—
30C2×Dic43⋊C4—22no—
31C2×Dic43⋊C4—22no—
32#13063258—41no—
33#13063257—42no—
34#13063256—41no—
35#13063250—42no—
36C43⋊#95—22no—
37C43⋊#95—21no—
38C43⋊#95—22no—
39C43⋊#95D412yes—
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C4⋊C4×C43C2311yescharacteristic
42C2×C42×C43D411yescharacteristic
43C22⋊C8×C43—22no—
44#95×C43—22no—
45C22×C4×C43—21no—
46C22×C4×C43—21no—
47C22×C4×C43C2×D411yescharacteristic
48C22×C4×C43C2×D412yes—
49C22×Dic43—22no—
50C22×Dic43—22no—
51C2×Dic86—22no—
52C2×C8×C43—42no—
53C4⋊C4×C43—41no—
54C4⋊C4×C43—41no—
55C42×C43—21no—
56C42×C43SD1612yes—
57C22⋊Dic43—41no—
58C4⋊Dic43—21no—
59C4⋊Dic43—22no—
60C4⋊Dic43—21no—
61C4⋊Dic43—42no—
62C4⋊Dic43—42no—
63C4⋊Dic43—42no—
64C4⋊Dic43—81no—
65Dic43⋊C4—44no—
66Dic43⋊C4—42no—
67Dic43⋊C4—42no—
68Dic43⋊C4—42no—
69C4×Dic43—41no—
70#10621877—22no—
71#10621877—41no—
72C2×C43⋊C8—41no—
73C23×C43#12011yescharacteristic
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—41no—
79C2×C4×C43—41no—
80C2×C4×C43—42no—
81C2×C4×C43—42no—
82C2×C4×C43—41no—
83C2×C4×C43C2×SD1611yescharacteristic
84C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
85C2×Dic43—42no—
86C2×Dic43—42no—
87C2×Dic43—42no—
88C2×Dic43—42no—
89C2×Dic43—42no—
90C2×Dic43—41no—
91C2×Dic43—41no—
92C2×Dic43—42no—
93Dic86—82no—
94C8×C43—82no—
95C43⋊C8—42no—
96#12251—431nomaximal, Sylow
97C22×C43—21no—
98C22×C43—21no—
99C22×C43#45011yescharacteristic
100C22×C43#45611yescharacteristic
101C22×C43B(4,𝔽2)11yescharacteristic
102C4×C43—21no—
103C4×C43—21no—
104C4×C43—42no—
105C4×C43—42no—
106C4×C43—81no—
107Dic43—82no—
108Dic43—82no—
109Dic43—81no—
110Dic43—81no—
111#2822—431no—
112#2061—431no—
113#1611—432no—
114#1346—432no—
115#1324D4311yescharacteristic
116C2×C43—21no—
117C2×C43—21no—
118C2×C43#160411yescharacteristic
119C2×C43#220111yescharacteristic
120C2×C43#220311yescharacteristic
121#544—431no—
122C2×#125—861no—
123#483—862no—
124#428—861no—
125#400—862no—
126#398—432no—
127#398—862no—
128#398—861no—
129#382C2×D4311yescharacteristic
130#343—431no—
131#339—861no—
132#328—862no—
133#324C2×D4312yes—
134C43#1225111yescharacteristic, complemented, Sylow
135C2×M16—861no—
136C4⋊Q8—1721no—
137#125—1722no—
138#125—1721no—
139#125—1722no—
140C22⋊Q8—862no—
141#117—861no—
142C2×C4⋊C4—432no—
143C2×C4⋊C4—861no—
144C2×C4⋊C4—862no—
145C2×C4⋊C4—861no—
146C2×C4⋊C4—861no—
147C2×C4⋊C4—862no—
148C2×C4⋊C4D17211yescharacteristic
149C2×C4⋊C4C22×D4311yescharacteristic
150C2×C42D17211yescharacteristic
151#107—1721no—
152#106—1721no—
153#106—1722no—
154#103—1722no—
155C22⋊C8—22no—
156#95—22no—
157#95—432no—
158#95—862no—
159#95—861no—
160#95—862no—
161C2×Q8—862no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—862no—
165C22×C4—862no—
166C22×C4C2×D17211yescharacteristic
167C22×C4D4×D4312yes—
168M16—862no—
169M16—1721no—
170C2×C8—42no—
171C2×C8—1721no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—861no—
175C4⋊C4—862no—
176C4⋊C4—861no—
177C4⋊C4—3441no—
178C4⋊C4—1722no—
179C4⋊C4—1724no—
180C4⋊C4—1722no—
181C4⋊C4—1722no—
182C4⋊C4—1722no—
183C4⋊C4—1722no—
184C4⋊C4—1722no—
185C22⋊C4—1721no—
186C42—21no—
187C42—1721no—
188C42#1062187312yes—
189C23#1306329511yescharacteristic
190Q8—3442no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—41no—
200C2×C4—1722no—
201C2×C4—1722no—
202C2×C4—1722no—
203C2×C4—1722no—
204C2×C4—1722no—
205C2×C4—1721no—
206C2×C4—1721no—
207C2×C4—1722no—
208C2×C4C2×#1062187311yescharacteristic
209C2×C4#1306335311yescharacteristic
210C8—82no—
211C8—1722no—
212C22—21no—
213C22—21no—
214C22#1458305211yescharacteristic
215C22#1458308411yescharacteristic
216C22#1458308711yescharacteristic
217C4—21no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—81no—
222C4—3442no—
223C4—3441no—
224C4—3441no—
225C4—3442no—
226C2—21no—
227C2—21no—
228C2#1913356611yescharacteristic
229C2#1913661011yescharacteristic
230C2#1913661811yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1324C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1324D43
hypocenterC43#12251
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
134. C43#12251semidirect

Maximal subgroups

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

subgroupindex
#191426632
#191359452
#191336052
#191326022
C43×#13242
#1225143