Finite Group Databasebeta

← #25007444

Subgroups — #25007444

Order 11008.

324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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#19136407C211yesmaximal, characteristic, complemented
2#19134744C211yesmaximal, characteristic, complemented
3#19132586C212yesmaximal, complemented
4#19132580C212yesmaximal, complemented
5C43×#3184C211yesmaximal, characteristic
6#14582720—21no—
7#14582681C2212yes—
8#14582677—21no—
9#14582670—21no—
10#14582659—21no—
11C43⋊#338C2211yescharacteristic
12#14582656C2211yescharacteristic
13C43×#532—21no—
14C43×#498C411yescharacteristic, complemented
15C43×#493C411yescharacteristic, complemented
16C43×#486—21no—
17C43×#469—21no—
18C43×#469C2212yes—
19C43×#442—21no—
20C43×#442C412yescomplemented
21C4×M16×C43C2211yescharacteristic
22C2×#10621877—21no—
23#13063284—21no—
24#13063265—22no—
25C2×#41×C43—41no—
26C2×D8×C43—21no—
27C2×D8×C43C2×C412yes—
28C2×M16×C43D411yescharacteristic
29C2×M16×C43C2311yescharacteristic
30C4⋊Q8×C43—21no—
31#127×C43—21no—
32#124×C43—41no—
33#121×C43—22no—
34#121×C43—41no—
35C4×D4×C43—22no—
36C4×D4×C43—41no—
37C2×C42×C43D411yescharacteristic
38#106×C43—21no—
39#106×C43C2×C412yes—
40#102×C43—22no—
41#102×C43—22no—
42#97×C43C2×C411yescharacteristic
43#97×C43D411yescharacteristic
44C4×C8×C43C2×C411yescharacteristic
45C4×C8×C43D411yescharacteristic
46#41×C43—84no—
47C2×Q8×C43—41no—
48C2×D4×C43—22no—
49C2×D4×C43—41no—
50C2×D4×C43—41no—
51C2×D4×C43—42no—
52C22×C4×C43—21no—
53C22×C4×C43—42no—
54C22×C4×C43C2×D411yescharacteristic
55D8×C43—42no—
56D8×C43—42no—
57M16×C43—41no—
58M16×C43—41no—
59C2×C8×C43C22⋊C411yescharacteristic
60C2×C8×C43C22⋊C411yescharacteristic
61C2×C8×C43C22×C411yescharacteristic
62C2×C8×C43C2×D411yescharacteristic
63C4⋊C4×C43—22no—
64C4⋊C4×C43—41no—
65C22⋊C4×C43—42no—
66C22⋊C4×C43—42no—
67C42×C43—21no—
68C42×C43C22⋊C411yescharacteristic
69C42×C43C22⋊C411yescharacteristic
70C22⋊Dic43—41no—
71C4⋊Dic43—41no—
72C4×Dic43—41no—
73#10621877—41no—
74#10621877—41no—
75C2×C43⋊C8—41no—
76C43⋊C16—42no—
77C23×C43—42no—
78C23×C43AGL(1,ℤ/8)11yescharacteristic
79Q8×C43—82no—
80D4×C43—42no—
81D4×C43—42no—
82D4×C43—82no—
83D4×C43—82no—
84D4×C43—84no—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—42no—
90C2×C4×C43—42no—
91C2×C4×C43—84no—
92C2×C4×C43C2×C22⋊C411yescharacteristic
93C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
94C2×Dic43—81no—
95C8×C43—21no—
96C8×C43—21no—
97C8×C43—21no—
98C8×C43—21no—
99C43⋊C8—81no—
100#11837—431nomaximal, Sylow
101C22×C43—21no—
102C22×C43—41no—
103C22×C43—82no—
104C22×C43—82no—
105C22×C43—82no—
106C22×C43#41811yescharacteristic
107C4×C43—22no—
108C4×C43—21no—
109C4×C43—41no—
110C4×C43—82no—
111C4×C43#41011yescharacteristic
112C4×C43#42111yescharacteristic
113Dic43—161no—
114#3184D4311yescharacteristic
115#2165—431no—
116#1841—431no—
117#1341—432no—
118#1339—432no—
119C2×C43—21no—
120C2×C43—41no—
121C2×C43—162no—
122C2×C43#151411yescharacteristic
123#532—21no—
124#498Dic4311yescharacteristic, complemented
125#493Dic4311yescharacteristic, complemented
126#486—21no—
127#469—21no—
128#469C2×D4312yes—
129#442—21no—
130#442Dic4312yescomplemented
131C4×M16C2×D4311yescharacteristic
132#364—861no—
133#349—432no—
134#347—861no—
135#344—861no—
136#339—861no—
137#338—431no—
138H(3,ℤ/4)—431no—
139C43#1183711yescharacteristic, complemented, Sylow
140C2×#41—41no—
141C2×D8—21no—
142C2×D8C2×Dic4312yes—
143C2×M16—861no—
144C2×M16C22⋊D4311yescharacteristic
145C2×M16C22×D4311yescharacteristic
146C4⋊Q8—21no—
147#127—21no—
148#124—41no—
149#121—22no—
150#121—41no—
151C4×D4—22no—
152C4×D4—41no—
153#117—861no—
154C2×C42C22⋊D4311yescharacteristic
155M32—862no—
156#106—21no—
157#106C2×Dic4312yes—
158#102—22no—
159#102—22no—
160#97C2×Dic4311yescharacteristic
161#97C22⋊D4311yescharacteristic
162C4×C8C2×Dic4311yescharacteristic
163C4×C8C22⋊D4311yescharacteristic
164#41—84no—
165C2×Q8—41no—
166C2×D4—22no—
167C2×D4—41no—
168C2×D4—41no—
169C2×D4—42no—
170C22×C4—21no—
171C22×C4—42no—
172C22×C4C2×C22⋊D4311yescharacteristic
173D8—42no—
174D8—42no—
175M16—41no—
176M16—41no—
177M16—1721no—
178M16—1721no—
179C2×C8—1721no—
180C2×C8C22⋊Dic4311yescharacteristic
181C2×C8C22⋊Dic4311yescharacteristic
182C2×C8C22×Dic4311yescharacteristic
183C2×C8C2×C22⋊D4311yescharacteristic
184C4⋊C4—22no—
185C4⋊C4—41no—
186C4⋊C4—1721no—
187C22⋊C4—42no—
188C22⋊C4—42no—
189C22⋊C4—1721no—
190C42—21no—
191C42—1721no—
192C42C22⋊Dic4311yescharacteristic
193C42C22⋊Dic4311yescharacteristic
194C16—1722no—
195C23—42no—
196C23#1306335111yescharacteristic
197Q8—82no—
198D4—42no—
199D4—42no—
200D4—82no—
201D4—82no—
202D4—84no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—84no—
210C2×C4—3441no—
211C2×C4C2×C22⋊Dic4311yescharacteristic
212C2×C4#1306335111yescharacteristic
213C8—21no—
214C8—21no—
215C8—21no—
216C8—21no—
217C8—3441no—
218C22—21no—
219C22—41no—
220C22—82no—
221C22—82no—
222C22—82no—
223C22#1458290411yescharacteristic
224C4—22no—
225C4—21no—
226C4—41no—
227C4—82no—
228C4—6881no—
229C4#1458287311yescharacteristic
230C4#1458291611yescharacteristic
231C2—21no—
232C2—41no—
233C2—162no—
234C2#1913314211yescharacteristic
subgroupG/H
centerC2#19133142
commutatorC2×C8×C43C22×C4
FrattiniC2×M16C22×D43
Fitting, prime radicalC43×#3184C2
socleC2×C43#1514
cosocleC2×M16×C43C23
hypercenter#3184D43
hypocenterC43#11837
LCSG ▷ C2×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #3184

Complements

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

NH ≅ G/Ntype
1. #19136407C2semidirect
2. #19134744C2semidirect
3. #19132586C2semidirect
4. #19132580C2semidirect
14. C43×#498C4semidirect
15. C43×#493C4semidirect
20. C43×#442C4semidirect
124. #498Dic43semidirect
125. #493Dic43semidirect
130. #442Dic43semidirect
139. C43#11837semidirect

Maximal subgroups

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

subgroupindex
#191364072
#191347442
#191325862
#191325802
C43×#31842
#1183743