Finite Group Databasebeta

← #24984084

Subgroups — #24984084

Order 11008.

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

normal subgroups only

This group has 284 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#19135726C211yesmaximal, characteristic
2#19132503C211yesmaximal, characteristic, complemented
3C43×#1317C211yesmaximal, characteristic, complemented
4#14583461C411yescharacteristic
5C2×#13063308—21no—
6C2×#13063239—21no—
7#14582863—21no—
8#14582666C411yescharacteristic
9C43×#381C2211yescharacteristic
10C43×#323—21no—
11C22×C22⋊D43—21no—
12C2×#10621877—41no—
13#13063309—41no—
14#13063308—42no—
15#13063308—41no—
16#13063308—41no—
17#13063299—41no—
18#13063295—41no—
19C2×Dic43⋊C4—41no—
20C2×C22⋊Dic43—21no—
21C2×(C2×D43)⋊C4—41no—
22#13063239—42no—
23C22⋊(C43⋊C8)—22no—
24C22⋊(C43⋊C8)—41no—
25C23×C4×C43D411yescharacteristic
26C2×C22⋊C4×C43C2×C411yescharacteristic
27C2×C22⋊C4×C43D411yescharacteristic
28C22⋊C8×C43—41no—
29#95×C43—41no—
30C24×C43C22⋊C411yescharacteristic
31C23×D43—21no—
32C22×C4×C43—21no—
33C22×C4×C43—21no—
34C22×C4×C43—21no—
35C22×C4×C43—21no—
36C22×C4×C43—41no—
37C22×C4×C43—41no—
38C22×C4×C43D811yescharacteristic
39C22×C4×C43SD1611yescharacteristic
40C2×C22⋊D43—41no—
41C2×C22⋊D43—41no—
42C2×C22⋊D43—41no—
43C2×C22⋊D43—41no—
44C2×C22⋊D43—41no—
45C2×C22⋊D43—41no—
46C22×Dic43—21no—
47C22×Dic43—41no—
48C2×D172—41no—
49C2×C8×C43—81no—
50C22⋊C4×C43—41no—
51C22⋊C4×C43—41no—
52C22⋊Dic43—22no—
53C22⋊Dic43—41no—
54(C2×D43)⋊C4—42no—
55(C2×D43)⋊C4—42no—
56(C2×D43)⋊C4—42no—
57C4⋊Dic43—41no—
58Dic43⋊C4—42no—
59Dic43⋊C4—42no—
60#10621877—81no—
61#10621877—81no—
62C2×C43⋊C8—42no—
63C23×C43—21no—
64C23×C43—21no—
65C23×C43—81no—
66C23×C43#9911yescharacteristic
67C23×C43#10211yescharacteristic
68C23×C43#10411yescharacteristic
69C22×D43—41no—
70C22×D43—41no—
71C22×D43—41no—
72C22×D43—82no—
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—41no—
76C2×C4×C43—41no—
77C2×C4×C43—41no—
78C2×C4×C43—41no—
79C2×C4×C43—41no—
80C2×C4×C43—41no—
81C2×C4×C43—81no—
82C2×C4×C43—81no—
83C2×C4×C43—81no—
84C22⋊D43—81no—
85C22⋊D43—81no—
86C22⋊D43—81no—
87C22⋊D43—81no—
88C2×Dic43—41no—
89C2×Dic43—42no—
90C2×Dic43—41no—
91C2×Dic43—41no—
92C2×Dic43—82no—
93D172—161no—
94C8×C43—161no—
95C43⋊C8—82no—
96#7395—431nomaximal, Sylow
97C22×C43—21no—
98C22×C43—21no—
99C22×C43—41no—
100C22×C43—41no—
101C22×C43—41no—
102C22×C43—42no—
103C22×C43—81no—
104C22×C43#32711yescharacteristic
105C22×C43AΣL(1,𝔽16)11yescharacteristic
106C22×C43#35311yescharacteristic
107C2×D43—82no—
108C2×D43—82no—
109C2×D43—81no—
110C2×D43—161no—
111C4×C43—41no—
112C4×C43—41no—
113C4×C43—81no—
114C4×C43—81no—
115Dic43—82no—
116Dic43—81no—
117#2022—431no—
118#1317D4311yescharacteristic, complemented
119#1306—431no—
120C2×C43—21no—
121C2×C43—21no—
122C2×C43—21no—
123C2×C43—41no—
124C2×C43—41no—
125C2×C43#134311yescharacteristic
126D43—161no—
127#534—431no—
128C2×#123—861no—
129C2×#99—861no—
130#407—861no—
131#381C2×D4311yescharacteristic
132#342—431no—
133#323—21no—
134C43#739511yescharacteristic, complemented, Sylow
135C22×D4—861no—
136C23×C4D17211yescharacteristic
137C2×M16—1721no—
138#123—1721no—
139#123—1722no—
140#123—1721no—
141#123—1721no—
142#121—1721no—
143#120—1721no—
144C2×C4⋊C4—1721no—
145C2×C22⋊C4—861no—
146C2×C22⋊C4—1721no—
147C2×C22⋊C4C4×D4311yescharacteristic
148C2×C22⋊C4C22⋊D4311yescharacteristic
149#99—1722no—
150C22⋊C8—41no—
151C22⋊C8—862no—
152C22⋊C8—1721no—
153#95—41no—
154C24—861no—
155C24(C2×D43)⋊C411yescharacteristic
156C2×D4—1721no—
157C2×D4—1721no—
158C2×D4—1721no—
159C2×D4—1721no—
160C2×D4—1721no—
161C2×D4—1721no—
162C2×D4—1721no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—861no—
170C22×C4—1721no—
171C22×C4#1062187311yescharacteristic
172C22×C4D34411yescharacteristic
173M16—3441no—
174M16—3441no—
175C2×C8—81no—
176C2×C8—1722no—
177C4⋊C4—1721no—
178C4⋊C4—1722no—
179C4⋊C4—1722no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C22⋊C4—862no—
183C22⋊C4—1722no—
184C22⋊C4—1722no—
185C22⋊C4—1722no—
186C22⋊C4—1721no—
187C23—21no—
188C23—21no—
189C23—81no—
190C23—3442no—
191C23—1721no—
192C23—1721no—
193C23—1721no—
194C23#1306323911yescharacteristic
195C23#1306324711yescharacteristic
196C23#1306325111yescharacteristic
197D4—3441no—
198D4—3441no—
199D4—3441no—
200D4—3441no—
201D4—6881no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—81no—
211C2×C4—81no—
212C2×C4—81no—
213C2×C4—3442no—
214C2×C4—1722no—
215C2×C4—1721no—
216C2×C4—1721no—
217C2×C4—1721no—
218C8—161no—
219C8—3442no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—81no—
227C22—3442no—
228C22—3442no—
229C22—3441no—
230C22—6881no—
231C22#1458263411yescharacteristic
232C22#1458268711yescharacteristic
233C22#1458269111yescharacteristic
234C4—41no—
235C4—41no—
236C4—81no—
237C4—81no—
238C4—3442no—
239C4—3441no—
240C2—21no—
241C2—21no—
242C2—21no—
243C2—41no—
244C2—41no—
245C2—6881no—
246C2#1913259311yescharacteristic
subgroupG/H
centerC2#19132593
commutatorC2×C22⋊C4×C43C2×C4
Frattini#381C2×D43
FittingC43×#1317C2
socleC2×C43#1343
prime radical#14583461C4
cosocleC43×#381C22
hypercenter#1317D43
hypocenterC43#7395
LCSG ▷ C2×C22⋊C4×C43 ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #1317

Complements

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

NH ≅ G/Ntype
2. #19132503C2semidirect
3. C43×#1317C2semidirect
118. #1317D43semidirect
134. C43#7395semidirect

Maximal subgroups

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

subgroupindex
#191357262
#191325032
C43×#13172
#739543