Finite Group Databasebeta

← #24984088

Subgroups — #24984088

Order 11008.

268 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 37 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#19135662C211yesmaximal, characteristic
2#19132531C211yesmaximal, characteristic, complemented
3C43×#1298C211yesmaximal, characteristic, complemented
4#14583699C411yescharacteristic
5#14583410—21no—
6#14582915—21no—
7#14582681—21no—
8#14582656C411yescharacteristic
9C43×#407C2211yescharacteristic
10C2×C22⋊C8×C43—21no—
11C2×#10621898—21no—
12#13063358—41no—
13#13063353—41no—
14#13063347—41no—
15#13063308—41no—
16#13063304—41no—
17#13063299—41no—
18#13063294—41no—
19C4×C22⋊D43—42no—
20#13063284—21no—
21#13063265—41no—
22#13063251—42no—
23C23×C4×C43D411yescharacteristic
24C2×M16×C43C2×C411yescharacteristic
25C2×M16×C43D411yescharacteristic
26C22×C8×C43—41no—
27C22⋊C8×C43—22no—
28C22⋊C8×C43—41no—
29C22⋊C8×C43—41no—
30C24×C43SD1611yescharacteristic
31C22×C4×C43—21no—
32C22×C4×C43—21no—
33C22×C4×C43—41no—
34C22×C4×C43—41no—
35C22×C4×C43C22⋊C411yescharacteristic
36C22×C4×C43D811yescharacteristic
37C2×C22⋊D43—42no—
38C2×C22⋊D43—41no—
39#10621898—41no—
40#10621898—41no—
41#10621898—41no—
42#10621898—41no—
43C2×D172—21no—
44C2×C4×D43—41no—
45C2×Dic86—21no—
46M16×C43—41no—
47M16×C43—41no—
48C2×C8×C43—21no—
49C2×C8×C43—21no—
50C2×C8×C43—42no—
51C2×C8×C43—81no—
52C2×C8×C43—81no—
53C22⋊Dic43—42no—
54C22⋊Dic43—41no—
55(C2×D43)⋊C4—42no—
56C4⋊Dic43—41no—
57Dic43⋊C4—42no—
58C4×Dic43—22no—
59Dic172—41no—
60D344—41no—
61#10621873—42no—
62C43⋊C16—81no—
63C23×C43—21no—
64C23×C43—41no—
65C23×C43—42no—
66C23×C43#10211yescharacteristic
67C22×D43—41no—
68C2×C4×C43—21no—
69C2×C4×C43—21no—
70C2×C4×C43—21no—
71C2×C4×C43—41no—
72C2×C4×C43—41no—
73C2×C4×C43—41no—
74C2×C4×C43—81no—
75C2×C4×C43#9911yescharacteristic
76C2×C4×C43#10411yescharacteristic
77C22⋊D43—81no—
78C22⋊D43—84no—
79C22⋊D43—81no—
80C2×Dic43—42no—
81C2×Dic43—41no—
82D172—41no—
83D172—41no—
84C4×D43—81no—
85C4×D43—81no—
86Dic86—41no—
87Dic86—41no—
88C8×C43—41no—
89C8×C43—41no—
90C8×C43—82no—
91#7397—431nomaximal, Sylow
92C22×C43—22no—
93C22×C43—21no—
94C22×C43—41no—
95C22×C43—41no—
96C22×C43—42no—
97C22×C43—41no—
98C22×C43—81no—
99C22×C43#32711yescharacteristic
100C2×D43—82no—
101C2×D43—81no—
102C4×C43—21no—
103C4×C43—41no—
104C4×C43AΣL(1,𝔽16)11yescharacteristic
105C4×C43#35311yescharacteristic
106Dic43—82no—
107Dic43—81no—
108#2010—431no—
109#1320—431no—
110#1298D4311yescharacteristic, complemented
111C2×C43—21no—
112C2×C43—41no—
113C2×C43—42no—
114C2×C43#134311yescharacteristic
115D43—161no—
116#575—431no—
117#525—861no—
118#421—861no—
119#407C2×D4311yescharacteristic
120C2×C22⋊C8—21no—
121#349—861no—
122H(3,ℤ/4)—431no—
123C43#739711yescharacteristic, complemented, Sylow
124C2×#41—861no—
125C23×C4C22⋊D4311yescharacteristic
126#137—1721no—
127AGL(1,ℤ/8)—1721no—
128#135—1721no—
129C2×M16C4×D4311yescharacteristic
130C2×M16D17211yescharacteristic
131C22×C8—41no—
132#123—1721no—
133C22⋊Q8—1721no—
134#121—1721no—
135#120—1721no—
136C4×D4—1722no—
137#117—861no—
138M32—1721no—
139#104—1722no—
140C22⋊C8—22no—
141C22⋊C8—41no—
142C22⋊C8—41no—
143C24#1062188411yescharacteristic
144#41—1721no—
145#41—1721no—
146#41—1721no—
147#41—1721no—
148C2×Q8—861no—
149C2×D4—861no—
150C2×D4—1722no—
151C2×D4—1721no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—1721no—
157C22×C4(C2×D43)⋊C411yescharacteristic
158C22×C4#1062188211yescharacteristic
159Q16—1721no—
160SD16—1722no—
161D8—1721no—
162M16—41no—
163M16—41no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—42no—
167C2×C8—81no—
168C2×C8—81no—
169C4⋊C4—1721no—
170C4⋊C4—1722no—
171C22⋊C4—1722no—
172C22⋊C4—1722no—
173C22⋊C4—1721no—
174C42—862no—
175C16—3441no—
176C23—21no—
177C23—41no—
178C23—42no—
179C23—1721no—
180C23#1306324511yescharacteristic
181Q8—1721no—
182Q8—1721no—
183D4—3441no—
184D4—3444no—
185D4—3441no—
186D4—1721no—
187D4—1721no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4—3441no—
196C2×C4—3441no—
197C2×C4—1722no—
198C2×C4—1721no—
199C2×C4#1306323911yescharacteristic
200C2×C4#1306325311yescharacteristic
201C8—41no—
202C8—41no—
203C8—82no—
204C22—22no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—42no—
209C22—41no—
210C22—81no—
211C22—3442no—
212C22—3441no—
213C22#1458263211yescharacteristic
214C4—21no—
215C4—41no—
216C4—3442no—
217C4—3441no—
218C4#1458268511yescharacteristic
219C4#1458269111yescharacteristic
220C2—21no—
221C2—41no—
222C2—42no—
223C2—6881no—
224C2#1913259111yescharacteristic
subgroupG/H
centerC4#14582691
commutatorC2×M16×C43C2×C4
Frattini#407C2×D43
FittingC43×#1298C2
socleC2×C43#1343
prime radical#19135662C2
cosocleC43×#407C22
hypercenter#1298D43
hypocenterC43#7397
LCSG ▷ C2×M16×C43 ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #407 ◁ #1298

Complements

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

NH ≅ G/Ntype
2. #19132531C2semidirect
3. C43×#1298C2semidirect
110. #1298D43semidirect
123. C43#7397semidirect

Maximal subgroups

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

subgroupindex
#191356622
#191325312
C43×#12982
#739743