Finite Group Databasebeta

← #24983271

Subgroups — #24983271

Order 11008.

338 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 49 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#19135593C211yesmaximal, characteristic
2#19132463C211yesmaximal, characteristic, complemented
3C43×#1314C211yesmaximal, characteristic, complemented
4C22×D344C411yescharacteristic, complemented
5C2×#13063299—21no—
6C2×#13063247—21no—
7#14582759—21no—
8#14582662C411yescharacteristic, complemented
9C2×C22⋊C8×C43C2211yescharacteristic
10C43×C22⋊C16—21no—
11C22×D172—21no—
12C22×C22⋊D43—41no—
13C2×D344—41no—
14C2×D344—42no—
15#13063299—42no—
16#13063299—42no—
17C2×C4⋊Dic43—21no—
18C2×C4⋊Dic43—41no—
19C2×C22⋊Dic43—41no—
20C2×(C2×D43)⋊C4—41no—
21#13063247—42no—
22C43⋊#95—22no—
23C23×C4×C43D411yescharacteristic
24C22×C8×C43C2×C411yescharacteristic
25C22×C8×C43D411yescharacteristic
26C2×C16×C43—41no—
27C22⋊C8×C43—41no—
28C24×C43D811yescharacteristic
29C23×D43—41no—
30C22×C4×C43—21no—
31C22×C4×C43—21no—
32C22×C4×C43—41no—
33C22×C4×C43—41no—
34C22×C4×C43C22⋊C411yescharacteristic
35C22×C4×C43SD1611yescharacteristic
36C2×C22⋊D43—44no—
37C2×C22⋊D43—82no—
38C2×C22⋊D43—81no—
39C2×C22⋊D43—81no—
40C22×Dic43—42no—
41C22×Dic43—41no—
42C2×D172—22no—
43C2×D172—41no—
44C2×D172—41no—
45C2×D172—41no—
46C2×D172—41no—
47C2×D172—41no—
48C2×C8×C43—21no—
49C2×C8×C43—21no—
50C2×C8×C43—41no—
51C2×C8×C43—41no—
52C22⋊Dic43—81no—
53C22⋊Dic43—81no—
54(C2×D43)⋊C4—44no—
55C4⋊Dic43—22no—
56C4⋊Dic43—41no—
57C4⋊Dic43—81no—
58C4⋊Dic43—81no—
59D344—42no—
60D344—42no—
61C16×C43—81no—
62C23×C43—21no—
63C23×C43—21no—
64C23×C43—41no—
65C23×C43—41no—
66C23×C43#10211yescharacteristic
67C23×C43D1611yescharacteristic
68C23×C43SD3211yescharacteristic
69C22×D43—42no—
70C22×D43—81no—
71C22×D43—81no—
72C22×D43—81no—
73C22×D43—81no—
74C22×D43—81no—
75C22×D43—81no—
76C2×C4×C43—21no—
77C2×C4×C43—21no—
78C2×C4×C43—21no—
79C2×C4×C43—41no—
80C2×C4×C43—41no—
81C2×C4×C43—41no—
82C2×C4×C43—81no—
83C2×C4×C43#9911yescharacteristic
84C2×C4×C43#10411yescharacteristic
85C22⋊D43—84no—
86C22⋊D43—84no—
87C2×Dic43—42no—
88C2×Dic43—81no—
89C2×Dic43—81no—
90C2×Dic43—82no—
91C2×Dic43—82no—
92C2×Dic43—82no—
93D172—42no—
94D172—42no—
95D172—81no—
96D172—81no—
97C8×C43—41no—
98C8×C43—41no—
99#7076—431nomaximal, Sylow
100C22×C43—21no—
101C22×C43—21no—
102C22×C43—21no—
103C22×C43—21no—
104C22×C43—41no—
105C22×C43—41no—
106C22×C43—41no—
107C22×C43—41no—
108C22×C43—81no—
109C22×C43#32711yescharacteristic
110C22×C43#35711yescharacteristic
111C22×C43#36011yescharacteristic
112C2×D43—82no—
113C2×D43—82no—
114C2×D43—82no—
115C2×D43—161no—
116C2×D43—161no—
117C2×D43—161no—
118C2×D43—161no—
119C4×C43—21no—
120C4×C43—41no—
121C4×C43AΣL(1,𝔽16)11yescharacteristic
122C4×C43#35311yescharacteristic
123Dic43—82no—
124Dic43—162no—
125#1999—431no—
126#1314D4311yescharacteristic, complemented
127#1289—431no—
128C2×C43—21no—
129C2×C43—21no—
130C2×C43—41no—
131C2×C43—41no—
132C2×C43#133911yescharacteristic
133C2×C43#134311yescharacteristic
134C2×C43#134711yescharacteristic
135D43—162no—
136C22×D8—431no—
137C2×#121—861no—
138C2×#102—861no—
139C2×C22⋊C8C2×D4311yescharacteristic
140#380—861no—
141C22⋊C16—21no—
142#340—431no—
143C43#707611yescharacteristic, complemented, Sylow
144C22×D4—861no—
145C22×D4—1721no—
146C23×C4D17211yescharacteristic
147C2×D8—1721no—
148C2×D8—1722no—
149C22×C8C4×D4311yescharacteristic
150C22×C8C22⋊D4311yescharacteristic
151#121—1722no—
152#121—1722no—
153C2×C4⋊C4—861no—
154C2×C4⋊C4—1721no—
155C2×C22⋊C4—1721no—
156C2×C22⋊C4—1721no—
157C2×C16—41no—
158#102—1722no—
159C22⋊C8—41no—
160#95—862no—
161C24—1721no—
162C24D34411yescharacteristic
163C2×D4—862no—
164C2×D4—3442no—
165C2×D4—3441no—
166C2×D4—3441no—
167C2×D4—1721no—
168C2×D4—1721no—
169C2×D4—1721no—
170C2×D4—1724no—
171C2×D4—1721no—
172C2×D4—1721no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—1722no—
178C22×C4—1721no—
179C22×C4#1062187311yescharacteristic
180C22×C4(C2×D43)⋊C411yescharacteristic
181D8—1722no—
182D8—1722no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—41no—
186C2×C8—41no—
187C4⋊C4—862no—
188C4⋊C4—3441no—
189C4⋊C4—3441no—
190C4⋊C4—1721no—
191C22⋊C4—3441no—
192C22⋊C4—3441no—
193C22⋊C4—1724no—
194C16—81no—
195C23—21no—
196C23—21no—
197C23—41no—
198C23—41no—
199C23—3441no—
200C23—3441no—
201C23—3441no—
202C23—3441no—
203C23—3441no—
204C23—3441no—
205C23—1722no—
206C23#1306324711yescharacteristic
207C23D68811yescharacteristic
208C23#1306327011yescharacteristic
209D4—3441no—
210D4—3444no—
211D4—3444no—
212D4—3441no—
213D4—1722no—
214D4—1722no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—81no—
222C2×C4—3441no—
223C2×C4—3441no—
224C2×C4—3442no—
225C2×C4—3442no—
226C2×C4—3442no—
227C2×C4—1722no—
228C2×C4#1306323911yescharacteristic
229C2×C4#1306325111yescharacteristic
230C8—41no—
231C8—41no—
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—41no—
240C22—81no—
241C22—3442no—
242C22—3442no—
243C22—3442no—
244C22—6881no—
245C22—6881no—
246C22—6881no—
247C22—6881no—
248C22#1458263411yescharacteristic
249C22#1458270111yescharacteristic
250C22#1458271011yescharacteristic
251C4—21no—
252C4—41no—
253C4—3442no—
254C4—6882no—
255C4#1458268711yescharacteristic
256C4#1458269111yescharacteristic
257C2—21no—
258C2—21no—
259C2—41no—
260C2—41no—
261C2—6882no—
262C2#1913258111yescharacteristic
263C2#1913259311yescharacteristic
264C2#1913260511yescharacteristic
subgroupG/H
centerC22#14582634
commutatorC22×C8×C43C2×C4
FrattiniC2×C22⋊C8C2×D43
FittingC43×#1314C2
socleC22×C43#327
prime radical#19135593C2
cosocleC2×C22⋊C8×C43C22
hypercenter#1314D43
hypocenterC43#7076
LCSG ▷ C22×C8×C43 ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. #19132463C2semidirect
3. C43×#1314C2semidirect
4. C22×D344C4semidirect
8. #14582662C4semidirect
126. #1314D43semidirect
143. C43#7076semidirect

Maximal subgroups

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

subgroupindex
#191355932
#191324632
C43×#13142
#707643