Finite Group Databasebeta

← #24984189

Subgroups — #24984189

Order 11008.

236 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 41 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#19135751C211yesmaximal, characteristic
2#19132720C211yesmaximal, characteristic
3C43×#1270C211yesmaximal, characteristic
4#14583530C411yescharacteristic, complemented
5#14582904—21no—
6C2×#13063240—21no—
7#14582668C411yescharacteristic, complemented
8#14582659—21no—
9C43×#390C2211yescharacteristic
10C43×#336—21no—
11C2×#10621877—21no—
12#13063324—41no—
13#13063316—41no—
14#13063304—41no—
15#13063284—21no—
16C2×C22⋊Dic43—41no—
17#13063246—41no—
18#13063246—41no—
19#13063240—22no—
20#13063240—41no—
21C22×D4×C43D411yescharacteristic
22C22×C8×C43—41no—
23C2×C4⋊C4×C43C2×C411yescharacteristic
24C2×C22⋊C4×C43—41no—
25C2×C42×C43D411yescharacteristic
26C24×C43—21no—
27C2×D4×C43—21no—
28C2×D4×C43—41no—
29C2×D4×C43—41no—
30C2×D4×C43SD1611yescharacteristic
31C2×D4×C43Q1611yescharacteristic
32C22×C4×C43—21no—
33C22×C4×C43—21no—
34C22×C4×C43C22⋊C411yescharacteristic
35C22×Dic43—81no—
36C2×Dic86—41no—
37C2×C8×C43—42no—
38C2×C8×C43—81no—
39C2×C8×C43—81no—
40C4⋊C4×C43—41no—
41C22⋊C4×C43—81no—
42C22⋊C4×C43—81no—
43C42×C43—41no—
44C22⋊Dic43—42no—
45C22⋊Dic43—41no—
46C22⋊Dic43—81no—
47C4⋊Dic43—21no—
48C4⋊Dic43—21no—
49C4⋊Dic43—41no—
50Dic43⋊C4—42no—
51C4×Dic43—41no—
52#10621877—41no—
53#10621877—41no—
54C2×C43⋊C8—41no—
55C23×C43—21no—
56C23×C43—21no—
57C23×C43—41no—
58C23×C43—41no—
59C23×C43—81no—
60C23×C43—81no—
61C23×C43#9911yescharacteristic
62D4×C43—41no—
63D4×C43—41no—
64D4×C43—81no—
65C2×C4×C43—21no—
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43—21no—
69C2×C4×C43—41no—
70C2×C4×C43—41no—
71C2×C4×C43—41no—
72C2×C4×C43—81no—
73C2×C4×C43#10311yescharacteristic
74C2×C4×C43#10411yescharacteristic
75C2×Dic43—41no—
76C2×Dic43—41no—
77C2×Dic43—82no—
78C2×Dic43—161no—
79C2×Dic43—161no—
80Dic86—161no—
81C8×C43—82no—
82C43⋊C8—81no—
83#7430—431nomaximal, Sylow
84C22×C43—21no—
85C22×C43—21no—
86C22×C43—41no—
87C22×C43—41no—
88C22×C43—81no—
89C22×C43—81no—
90C22×C43—81no—
91C22×C43—81no—
92C22×C43—161no—
93C22×C43#32811yescharacteristic
94C22×C43AΣL(1,𝔽16)11yescharacteristic
95C22×C43#35411yescharacteristic
96C4×C43—21no—
97C4×C43—21no—
98C4×C43—41no—
99C4×C43—41no—
100C4×C43—81no—
101Dic43—81no—
102Dic43—81no—
103Dic43—162no—
104#2027—431no—
105#1393—431no—
106#1270D4311yescharacteristic
107C2×C43—21no—
108C2×C43—21no—
109C2×C43—81no—
110C2×C43—81no—
111C2×C43#135111yescharacteristic
112C2×C43#140211yescharacteristic
113C2×C43#140411yescharacteristic
114#544—431no—
115#418—861no—
116C2×#99—861no—
117#390C2×D4311yescharacteristic
118#343—431no—
119#339—861no—
120#336—21no—
121C43#743011yescharacteristic, complemented, Sylow
122C22×D4D17211yescharacteristic
123C2×M16—861no—
124C22×C8—41no—
125C4⋊Q8—1721no—
126#125—1721no—
127C22⋊Q8—1721no—
128#117—861no—
129C2×C4⋊C4C4×D4311yescharacteristic
130C2×C22⋊C4—41no—
131C2×C22⋊C4—1721no—
132C2×C42C22⋊D4311yescharacteristic
133#102—1721no—
134#102—1721no—
135#99—862no—
136#99—1721no—
137C24—21no—
138C2×Q8—1721no—
139C2×D4—21no—
140C2×D4—41no—
141C2×D4—41no—
142C2×D4#1062187311yescharacteristic
143C2×D4Dic17211yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—3441no—
147C22×C4(C2×D43)⋊C411yescharacteristic
148M16—1721no—
149M16—1721no—
150C2×C8—42no—
151C2×C8—81no—
152C2×C8—81no—
153C2×C8—1721no—
154C4⋊C4—41no—
155C4⋊C4—861no—
156C4⋊C4—861no—
157C4⋊C4—1721no—
158C4⋊C4—1722no—
159C22⋊C4—81no—
160C22⋊C4—81no—
161C22⋊C4—3441no—
162C22⋊C4—1722no—
163C22⋊C4—1721no—
164C42—41no—
165C42—1721no—
166C23—21no—
167C23—21no—
168C23—41no—
169C23—41no—
170C23—81no—
171C23—81no—
172C23#1306323911yescharacteristic
173Q8—6881no—
174D4—41no—
175D4—41no—
176D4—81no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—3442no—
186C2×C4—1721no—
187C2×C4—1721no—
188C2×C4—6881no—
189C2×C4—6881no—
190C2×C4#1306325011yescharacteristic
191C2×C4#1306325111yescharacteristic
192C8—82no—
193C8—3441no—
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—81no—
199C22—81no—
200C22—81no—
201C22—81no—
202C22—161no—
203C22#1458263711yescharacteristic
204C22#1458268711yescharacteristic
205C22#1458269311yescharacteristic
206C4—21no—
207C4—21no—
208C4—41no—
209C4—41no—
210C4—81no—
211C4—3441no—
212C4—3441no—
213C4—6882no—
214C2—21no—
215C2—21no—
216C2—81no—
217C2—81no—
218C2#1913261711yescharacteristic
219C2#1913274111yescharacteristic
220C2#1913274711yescharacteristic
subgroupG/H
centerC22#14582687
commutatorC2×C4⋊C4×C43C2×C4
Frattini#390C2×D43
FittingC43×#1270C2
socleC22×C43AΣL(1,𝔽16)
prime radicalC22×D4×C43D4
cosocleC43×#390C22
hypercenter#1270D43
hypocenterC43#7430
LCSG ▷ C2×C4⋊C4×C43 ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1270

Complements

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

NH ≅ G/Ntype
4. #14583530C4semidirect
7. #14582668C4semidirect
121. C43#7430semidirect

Maximal subgroups

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

subgroupindex
#191357512
#191327202
C43×#12702
#743043