Finite Group Databasebeta

← #25007138

Subgroups — #25007138

Order 11008.

316 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 75 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#19145245C211yesmaximal, characteristic
2#19136411C211yesmaximal, characteristic, complemented
3#19132585C212yesmaximal, complemented
4#19132579C212yesmaximal, complemented
5C43×#1747C211yesmaximal, characteristic, complemented
6#14583504—21no—
7#14583301C411yescharacteristic, complemented
8#14583276C411yescharacteristic, complemented
9#14583264—21no—
10#14583152C2212yes—
11#14583135—21no—
12#14583012C412yescomplemented
13C4×D344—21no—
14#14582720—21no—
15#14582681C2212yes—
16#14582677—21no—
17C43×#405—21no—
18C43×#405C2211yescharacteristic
19C43×#338C2211yescharacteristic
20C43×H(3,ℤ/4)—21no—
21C43×H(3,ℤ/4)C2211yescharacteristic
22C2×D344—21no—
23C2×D344C2×C412yes—
24#13063322—21no—
25#13063317—21no—
26#13063310—42no—
27#13063299—22no—
28#13063298—42no—
29C4×D172—22no—
30#13063265—22no—
31#13063259—21no—
32#13063257C2×C412yes—
33#13063247—22no—
34#13063247—22no—
35C2×M16×C43—21no—
36C2×M16×C43C2311yescharacteristic
37C22×C8×C43D411yescharacteristic
38#117×C43—21no—
39#117×C43D411yescharacteristic
40#97×C43—22no—
41#97×C43C2×C411yescharacteristic
42#97×C43D411yescharacteristic
43C4×C8×C43—22no—
44C4×C8×C43C2×C411yescharacteristic
45C4×C8×C43D411yescharacteristic
46C22×C4×C43C2×D411yescharacteristic
47C2×C22⋊D43—42no—
48C2×D172—22no—
49C2×D172—42no—
50C2×C4×D43—42no—
51M16×C43—41no—
52M16×C43—41no—
53M16×C43—41no—
54C2×C8×C43—21no—
55C2×C8×C43—21no—
56C2×C8×C43—22no—
57C2×C8×C43C22⋊C411yescharacteristic
58C2×C8×C43C22⋊C411yescharacteristic
59C2×C8×C43C22×C411yescharacteristic
60C2×C8×C43C2×D411yescharacteristic
61C4⋊C4×C43—21no—
62C4⋊C4×C43—41no—
63C22⋊C4×C43—21no—
64C22⋊C4×C43—41no—
65C42×C43—22no—
66C42×C43C22⋊C411yescharacteristic
67C42×C43C22⋊C411yescharacteristic
68(C2×D43)⋊C4—42no—
69(C2×D43)⋊C4—42no—
70C4⋊Dic43—22no—
71Dic43⋊C4—42no—
72D344—42no—
73D344—41no—
74D344—41no—
75C43⋊C16—42no—
76C23×C43AGL(1,ℤ/8)11yescharacteristic
77C22×D43—42no—
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—42no—
83C2×C4×C43C2×C22⋊C411yescharacteristic
84C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
85C22⋊D43—162no—
86C2×Dic43—42no—
87D172—42no—
88D172—42no—
89D172—162no—
90C4×D43—162no—
91C8×C43—21no—
92C8×C43—21no—
93C8×C43—21no—
94C8×C43—42no—
95C8×C43#10411yescharacteristic
96C8×C43#10411yescharacteristic
97#11770—431nomaximal, Sylow
98C22×C43—21no—
99C22×C43—41no—
100C22×C43#41811yescharacteristic
101C2×D43—82no—
102C2×D43—82no—
103C2×D43—82no—
104C4×C43—21no—
105C4×C43—41no—
106C4×C43—41no—
107C4×C43—82no—
108C4×C43#41011yescharacteristic
109C4×C43C2×#10411yescharacteristic
110Dic43—82no—
111#3176—431no—
112#2166—431no—
113#1747D4311yescharacteristic, complemented
114#1341—432no—
115#1339—432no—
116C2×C43—21no—
117C2×C43—41no—
118C2×C43#150511yescharacteristic
119D43—162no—
120#540—861no—
121#499—431no—
122#493—431no—
123#490—861no—
124#469—432no—
125#466—861no—
126#442—432no—
127C4×D8—861no—
128#405—21no—
129#405C2×D4311yescharacteristic
130#364—861no—
131#349—432no—
132#347—861no—
133#338C2×D4311yescharacteristic
134H(3,ℤ/4)—21no—
135H(3,ℤ/4)C2×D4311yescharacteristic
136C43#1177011yescharacteristic, complemented, Sylow
137C2×D8—432no—
138C2×D8—861no—
139C2×M16—21no—
140C2×M16C22×D4311yescharacteristic
141C22×C8C22⋊D4311yescharacteristic
142#127—861no—
143#125—861no—
144#123—1722no—
145#121—862no—
146#121—1722no—
147C4×D4—862no—
148#117—21no—
149#117C22⋊D4311yescharacteristic
150M32—862no—
151#107—861no—
152#106—432no—
153#102—862no—
154#102—862no—
155#97—22no—
156#97C4×D4311yescharacteristic
157#97D17211yescharacteristic
158C4×C8—22no—
159C4×C8C4×D4311yescharacteristic
160C4×C8D17211yescharacteristic
161C2×D4—862no—
162C2×D4—1722no—
163C2×D4—1722no—
164C22×C4—1722no—
165C22×C4C2×C22⋊D4311yescharacteristic
166D8—1722no—
167D8—1721no—
168D8—1721no—
169M16—41no—
170M16—41no—
171M16—41no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—22no—
175C2×C8(C2×D43)⋊C411yescharacteristic
176C2×C8(C2×D43)⋊C411yescharacteristic
177C2×C8C2×C4×D4311yescharacteristic
178C2×C8C2×D17211yescharacteristic
179C4⋊C4—21no—
180C4⋊C4—41no—
181C4⋊C4—862no—
182C4⋊C4—1722no—
183C22⋊C4—21no—
184C22⋊C4—41no—
185C22⋊C4—1722no—
186C22⋊C4—1722no—
187C42—22no—
188C42(C2×D43)⋊C411yescharacteristic
189C42(C2×D43)⋊C411yescharacteristic
190C16—1722no—
191C23—1722no—
192C23#1306335011yescharacteristic
193D4—1722no—
194D4—1722no—
195D4—6882no—
196D4—6882no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—1722no—
203C2×C4—6882no—
204C2×C4C2×(C2×D43)⋊C411yescharacteristic
205C2×C4#1306335011yescharacteristic
206C8—21no—
207C8—21no—
208C8—21no—
209C8—42no—
210C8#1306325311yescharacteristic
211C8#1306325311yescharacteristic
212C22—21no—
213C22—41no—
214C22—3442no—
215C22—3442no—
216C22—3442no—
217C22#1458290311yescharacteristic
218C4—21no—
219C4—41no—
220C4—41no—
221C4—82no—
222C4—3442no—
223C4#1458287211yescharacteristic
224C4C2×#1306325311yescharacteristic
225C2—21no—
226C2—41no—
227C2—6882no—
228C2#1913310211yescharacteristic
subgroupG/H
centerC2#19133102
commutatorC2×C8×C43C22×C4
FrattiniC2×M16C22×D43
FittingC43×#1747C2
socleC2×C43#1505
prime radical#19145245C2
cosocleC2×M16×C43C23
hypercenter#1747D43
hypocenterC43#11770
LCSG ▷ C2×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #1747

Complements

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

NH ≅ G/Ntype
2. #19136411C2semidirect
3. #19132585C2semidirect
4. #19132579C2semidirect
5. C43×#1747C2semidirect
7. #14583301C4semidirect
8. #14583276C4semidirect
12. #14583012C4semidirect
113. #1747D43semidirect
136. C43#11770semidirect

Maximal subgroups

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

subgroupindex
#191452452
#191364112
#191325852
#191325792
C43×#17472
#1177043