Finite Group Databasebeta

← #24983276

Subgroups — #24983276

Order 11008.

286 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 51 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#19132519C211yesmaximal, characteristic
2#19132463C211yesmaximal, characteristic
3C43×#2001C211yesmaximal, characteristic
4#14582759—21no—
5C22⋊(C43⋊C16)—21no—
6C22×Q16×C43C411yescharacteristic, complemented
7C2×C22⋊Q8×C43—21no—
8C2×#103×C43—21no—
9C2×C22⋊C8×C43C2211yescharacteristic
10C43×#340C411yescharacteristic, complemented
11C2×C4⋊Dic43—41no—
12C2×C22⋊Dic43—41no—
13C2×C43⋊C16—41no—
14C43⋊#95—22no—
15C22×Q8×C43—21no—
16C23×C4×C43D411yescharacteristic
17C2×Q16×C43—41no—
18C2×Q16×C43—42no—
19C22×C8×C43C2×C411yescharacteristic
20C22×C8×C43D411yescharacteristic
21C22⋊Q8×C43—42no—
22C22⋊Q8×C43—42no—
23C2×C4⋊C4×C43—21no—
24C2×C4⋊C4×C43—41no—
25C2×C22⋊C4×C43—41no—
26#103×C43—42no—
27C22⋊C8×C43—41no—
28C24×C43D811yescharacteristic
29C2×Q8×C43—22no—
30C2×Q8×C43—41no—
31C2×Q8×C43—41no—
32C2×Q8×C43—41no—
33C2×Q8×C43—41no—
34C2×Q8×C43—41no—
35C22×C4×C43—21no—
36C22×C4×C43—21no—
37C22×C4×C43—41no—
38C22×C4×C43—41no—
39C22×C4×C43—41no—
40C22×C4×C43—41no—
41C22×C4×C43C22⋊C411yescharacteristic
42C22×C4×C43SD1611yescharacteristic
43C22×Dic43—42no—
44Q16×C43—42no—
45Q16×C43—42no—
46C2×C8×C43—21no—
47C2×C8×C43—21no—
48C2×C8×C43—41no—
49C2×C8×C43—41no—
50C4⋊C4×C43—22no—
51C4⋊C4×C43—41no—
52C4⋊C4×C43—44no—
53C22⋊C4×C43—44no—
54C22⋊Dic43—81no—
55C22⋊Dic43—81no—
56C4⋊Dic43—81no—
57C4⋊Dic43—81no—
58C43⋊C16—81no—
59C23×C43—21no—
60C23×C43—21no—
61C23×C43—41no—
62C23×C43—41no—
63C23×C43#10211yescharacteristic
64C23×C43SD3211yescharacteristic
65C23×C43Q3211yescharacteristic
66Q8×C43—42no—
67Q8×C43—42no—
68Q8×C43—81no—
69Q8×C43—81no—
70C2×C4×C43—21no—
71C2×C4×C43—21no—
72C2×C4×C43—21no—
73C2×C4×C43—41no—
74C2×C4×C43—41no—
75C2×C4×C43—41no—
76C2×C4×C43—42no—
77C2×C4×C43—42no—
78C2×C4×C43—81no—
79C2×C4×C43—81no—
80C2×C4×C43—81no—
81C2×C4×C43—81no—
82C2×C4×C43—81no—
83C2×C4×C43#9911yescharacteristic
84C2×C4×C43#10411yescharacteristic
85C2×Dic43—82no—
86C2×Dic43—82no—
87C2×Dic43—82no—
88C8×C43—41no—
89C8×C43—41no—
90#7078—431nomaximal, Sylow
91C22×C43—21no—
92C22×C43—21no—
93C22×C43—21no—
94C22×C43—21no—
95C22×C43—41no—
96C22×C43—41no—
97C22×C43—41no—
98C22×C43—41no—
99C22×C43—81no—
100C22×C43#32711yescharacteristic
101C22×C43#35811yescharacteristic
102C22×C43#36011yescharacteristic
103C4×C43—21no—
104C4×C43—41no—
105C4×C43—82no—
106C4×C43—82no—
107C4×C43AΣL(1,𝔽16)11yescharacteristic
108C4×C43#35311yescharacteristic
109Dic43—162no—
110#2001D4311yescharacteristic
111#1314—431no—
112#1289—431no—
113C2×C43—21no—
114C2×C43—21no—
115C2×C43—41no—
116C2×C43—41no—
117C2×C43#134011yescharacteristic
118C2×C43#134311yescharacteristic
119C2×C43#134811yescharacteristic
120C22×Q16Dic4311yescharacteristic, complemented
121C2×C22⋊Q8—21no—
122C2×#103—21no—
123C2×C22⋊C8C2×D4311yescharacteristic
124#380—861no—
125C22⋊C16—861no—
126#340Dic4311yescharacteristic, complemented
127C43#707811yescharacteristic, complemented, Sylow
128C22×Q8—21no—
129C23×C4C22⋊D4311yescharacteristic
130C2×Q16—41no—
131C2×Q16—42no—
132C22×C8C2×Dic4311yescharacteristic
133C22×C8C22⋊D4311yescharacteristic
134C22⋊Q8—42no—
135C22⋊Q8—42no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—1721no—
139C2×C22⋊C4—41no—
140C2×C22⋊C4—1721no—
141C2×C16—1721no—
142#103—42no—
143C22⋊C8—41no—
144#95—862no—
145C24#1062188211yescharacteristic
146C2×Q8—22no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—41no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—1722no—
159C22×C4#1062188311yescharacteristic
160C22×C4C22⋊Dic4311yescharacteristic
161Q16—42no—
162Q16—42no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—41no—
166C2×C8—41no—
167C4⋊C4—22no—
168C4⋊C4—41no—
169C4⋊C4—44no—
170C4⋊C4—3441no—
171C4⋊C4—3441no—
172C22⋊C4—44no—
173C22⋊C4—3441no—
174C22⋊C4—3441no—
175C16—3441no—
176C23—21no—
177C23—21no—
178C23—41no—
179C23—41no—
180C23#1306324611yescharacteristic
181C23#1306326811yescharacteristic
182C23#1306327111yescharacteristic
183Q8—42no—
184Q8—42no—
185Q8—81no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—3442no—
201C2×C4—3442no—
202C2×C4—3442no—
203C2×C4#1306324011yescharacteristic
204C2×C4#1306325211yescharacteristic
205C8—41no—
206C8—41no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22—41no—
215C22—81no—
216C22#1458263311yescharacteristic
217C22#1458270311yescharacteristic
218C22#1458270911yescharacteristic
219C4—21no—
220C4—41no—
221C4—82no—
222C4—82no—
223C4—6882no—
224C4#1458268611yescharacteristic
225C4#1458269211yescharacteristic
226C2—21no—
227C2—21no—
228C2—41no—
229C2—41no—
230C2#1913258311yescharacteristic
231C2#1913259211yescharacteristic
232C2#1913260711yescharacteristic
subgroupG/H
centerC22#14582633
commutatorC22×C8×C43C2×C4
FrattiniC2×C22⋊C8C2×D43
FittingC43×#2001C2
socleC22×C43#327
prime radicalC24×C43D8
cosocleC2×C22⋊C8×C43C22
hypercenter#2001D43
hypocenterC43#7078
LCSG ▷ C22×C8×C43 ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #2001

Complements

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

NH ≅ G/Ntype
6. C22×Q16×C43C4semidirect
10. C43×#340C4semidirect
120. C22×Q16Dic43semidirect
126. #340Dic43semidirect
127. C43#7078semidirect

Maximal subgroups

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

subgroupindex
#191325192
#191324632
C43×#20012
#707843