Finite Group Databasebeta

← #24984124

Subgroups — #24984124

Order 11008.

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

normal subgroups only

This group has 268 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#19135641C211yesmaximal, characteristic
2#19132421C211yesmaximal, characteristic, complemented
3C43×#1394C211yesmaximal, characteristic, complemented
4C2×#13063356—21no—
5#14583480C411yescharacteristic
6C2×#13063253—21no—
7#14582668C411yescharacteristic
8#14582654—21no—
9C2×#101×C43—21no—
10C43×#391C2211yescharacteristic
11C2×#10621898—21no—
12#13063356—42no—
13#13063356—41no—
14#13063356—41no—
15C2×#10621885—41no—
16C2×#10621884—41no—
17C2×#10621877—21no—
18C22×C43⋊C8—41no—
19#13063305—41no—
20#13063300—41no—
21#13063299—41no—
22#13063253—42no—
23C22×Q8×C43D411yescharacteristic
24C2×M16×C43—41no—
25C2×C4⋊C4×C43C2×C411yescharacteristic
26C2×C42×C43D411yescharacteristic
27#101×C43—22no—
28#101×C43—41no—
29#95×C43—41no—
30C2×Q8×C43—21no—
31C2×Q8×C43—41no—
32C2×Q8×C43—41no—
33C2×Q8×C43D811yescharacteristic
34C2×Q8×C43SD1611yescharacteristic
35C22×C4×C43—21no—
36C22×C4×C43—21no—
37C22×C4×C43—21no—
38C22×C4×C43C22⋊C411yescharacteristic
39C2×C22⋊D43—41no—
40#10621898—41no—
41#10621898—41no—
42#10621898—41no—
43#10621898—41no—
44C2×D172—21no—
45C2×D172—41no—
46C2×C4×D43—41no—
47C2×Dic86—21no—
48M16×C43—42no—
49M16×C43—81no—
50C2×C8×C43—81no—
51C4⋊C4×C43—41no—
52C42×C43—41no—
53#10621885—42no—
54#10621885—42no—
55#10621884—42no—
56#10621884—42no—
57(C2×D43)⋊C4—42no—
58C4⋊Dic43—41no—
59#10621877—22no—
60#10621877—41no—
61C2×C43⋊C8—41no—
62C2×C43⋊C8—42no—
63C2×C43⋊C8—81no—
64C2×C43⋊C8—81no—
65C23×C43#9911yescharacteristic
66C22×D43—41no—
67Q8×C43—41no—
68Q8×C43—41no—
69Q8×C43—81no—
70C2×C4×C43—21no—
71C2×C4×C43—21no—
72C2×C4×C43—21no—
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
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#10211yescharacteristic
83C2×C4×C43#10411yescharacteristic
84C22⋊D43—81no—
85C22⋊D43—81no—
86C2×Dic43—41no—
87D172—41no—
88D172—41no—
89D172—161no—
90C4×D43—81no—
91C4×D43—81no—
92Dic86—41no—
93Dic86—41no—
94C8×C43—82no—
95C43⋊C8—42no—
96C43⋊C8—82no—
97#7409—431nomaximal, Sylow
98C22×C43—21no—
99C22×C43—21no—
100C22×C43#32711yescharacteristic
101C22×C43AΣL(1,𝔽16)11yescharacteristic
102C22×C43#35311yescharacteristic
103C2×D43—81no—
104C2×D43—81no—
105C2×D43—81no—
106C4×C43—21no—
107C4×C43—21no—
108C4×C43—41no—
109C4×C43—41no—
110C4×C43—41no—
111C4×C43—41no—
112C4×C43—81no—
113Dic43—81no—
114#2007—431no—
115#1394D4311yescharacteristic, complemented
116#1272—431no—
117C2×C43—21no—
118C2×C43—21no—
119C2×C43#134311yescharacteristic
120C2×C43#140311yescharacteristic
121C2×C43#140511yescharacteristic
122D43—161no—
123C2×#137—861no—
124#537—431no—
125C2×#104—861no—
126C2×#101—21no—
127#391C2×D4311yescharacteristic
128#343—431no—
129#336—861no—
130C43#740911yescharacteristic, complemented, Sylow
131C2×#41—861no—
132C22×Q8C22⋊D4311yescharacteristic
133#137—1722no—
134#137—1721no—
135#137—1721no—
136C2×Q16—1721no—
137C2×SD16—1721no—
138C2×M16—41no—
139C2×M16—861no—
140C22×C8—1721no—
141C22⋊Q8—1721no—
142#121—1721no—
143#121—1721no—
144C2×C4⋊C4C4×D4311yescharacteristic
145C2×C42D17211yescharacteristic
146#104—1722no—
147#101—22no—
148#101—41no—
149#95—41no—
150#41—1721no—
151#41—1721no—
152#41—1721no—
153#41—1721no—
154C2×Q8—21no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—861no—
158C2×Q8#1062188211yescharacteristic
159C2×Q8#1062188411yescharacteristic
160C2×D4—861no—
161C2×D4—1721no—
162C2×D4—1721no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—1721no—
167C22×C4(C2×D43)⋊C411yescharacteristic
168Q16—1722no—
169Q16—1722no—
170SD16—1722no—
171SD16—1722no—
172M16—42no—
173M16—81no—
174M16—862no—
175M16—1721no—
176C2×C8—81no—
177C2×C8—3441no—
178C2×C8—3441no—
179C2×C8—1722no—
180C2×C8—1721no—
181C4⋊C4—41no—
182C4⋊C4—1721no—
183C22⋊C4—1722no—
184C42—41no—
185C23—1721no—
186C23#1306323911yescharacteristic
187Q8—41no—
188Q8—41no—
189Q8—81no—
190Q8—1721no—
191Q8—1721no—
192D4—3441no—
193D4—3441no—
194D4—1721no—
195D4—1721no—
196D4—6881no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—81no—
209C2×C4—3441no—
210C2×C4—3441no—
211C2×C4—1721no—
212C2×C4#1306324511yescharacteristic
213C2×C4#1306325311yescharacteristic
214C8—82no—
215C8—3442no—
216C8—1722no—
217C22—21no—
218C22—21no—
219C22—3441no—
220C22—3441no—
221C22—3441no—
222C22#1458263211yescharacteristic
223C22#1458268511yescharacteristic
224C22#1458269111yescharacteristic
225C4—21no—
226C4—21no—
227C4—41no—
228C4—41no—
229C4—41no—
230C4—41no—
231C4—81no—
232C4—3441no—
233C2—21no—
234C2—21no—
235C2—6881no—
236C2#1913259111yescharacteristic
237C2#1913274211yescharacteristic
238C2#1913274811yescharacteristic
subgroupG/H
centerC22#14582685
commutatorC2×C4⋊C4×C43C2×C4
Frattini#391C2×D43
FittingC43×#1394C2
socleC22×C43AΣL(1,𝔽16)
prime radical#14583480C4
cosocleC43×#391C22
hypercenter#1394D43
hypocenterC43#7409
LCSG ▷ C2×C4⋊C4×C43 ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #1394

Complements

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

NH ≅ G/Ntype
2. #19132421C2semidirect
3. C43×#1394C2semidirect
115. #1394D43semidirect
130. C43#7409semidirect

Maximal subgroups

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

subgroupindex
#191356412
#191324212
C43×#13942
#740943