Finite Group Databasebeta

← #25007789

Subgroups — #25007789

Order 11008.

326 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 61 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#19144968C211yesmaximal, characteristic
2#19136405C212yesmaximal, complemented
3#19132628C211yesmaximal, characteristic, complemented
4#19132627C212yesmaximal, complemented
5C43×#1355C211yesmaximal, characteristic, complemented
6#14583455C411yescharacteristic
7#127×D43C411yescharacteristic
8#14583265C411yescharacteristic
9#14583264C2211yescharacteristic
10#14583263C411yescharacteristic
11#14583244—22no—
12#14582902—22no—
13#14582851C2211yescharacteristic
14#14582719—22no—
15#14582680—22no—
16#14582677C2212yescomplemented
17C43×#490C2211yescharacteristic
18C43×#347C2212yescomplemented
19C2×D4×D43—21no—
20C2×D4×D43—41no—
21C2×#10621872D412yes—
22#13063324—21no—
23#13063322C2×C411yescharacteristic
24#13063321—21no—
25#13063321—41no—
26#13063317C2×C411yescharacteristic
27#13063303—41no—
28#13063290—41no—
29#13063283—21no—
30C42×D43C2×C411yescharacteristic
31#13063265—22no—
32#13063247—22no—
33#13063246—22no—
34#13063245—22no—
35#13063236C2×C411yescharacteristic
36C8×Dic43D412yes—
37#127×C43C2×C411yescharacteristic
38#125×C43C2×C411yescharacteristic
39M32×C43—22no—
40#102×C43—22no—
41#97×C43C2311yescharacteristic
42C23×D43—41no—
43C2×D4×C43—21no—
44C2×D4×C43—41no—
45C2×C22⋊D43—42no—
46C2×C22⋊D43—41no—
47D4×D43—44no—
48D4×D43—84no—
49C2×D172—21no—
50C2×D172—41no—
51C2×C4×D43—21no—
52C2×C4×D43C22⋊C411yescharacteristic
53C2×Dic86—41no—
54C2×C8×C43C2×D412yes—
55C4⋊C4×C43—21no—
56C4⋊C4×C43—41no—
57C42×C43C22×C411yescharacteristic
58(C2×D43)⋊C4—41no—
59C4⋊Dic43—21no—
60Dic43⋊C4—41no—
61Dic43⋊C4—41no—
62C4×Dic43—21no—
63C4×Dic43—41no—
64C4×Dic43C22⋊C411yescharacteristic
65C2×C43⋊C8C22⋊C412yes—
66#10621872—42no—
67C16×C43—42no—
68C43⋊C16—42no—
69C23×C43—41no—
70C22×D43—41no—
71C22×D43—82no—
72C22×D43—84no—
73C22×D43#10011yescharacteristic
74D4×C43—42no—
75D4×C43—82no—
76C2×C4×C43—21no—
77C2×C4×C43—41no—
78C2×C4×C43C2×C22⋊C411yescharacteristic
79C22⋊D43—82no—
80C22⋊D43—84no—
81C2×Dic43—21no—
82C2×Dic43—41no—
83C2×Dic43#10011yescharacteristic
84D172—42no—
85D172—82no—
86C4×D43—22no—
87C4×D43—42no—
88Dic86—82no—
89C8×C43—22no—
90C43⋊C8—22no—
91#11915—431nomaximal, Sylow
92C22×C43—82no—
93C22×C43—81no—
94C22×C43C2×#10011yescharacteristic
95C2×D43—21no—
96C2×D43—41no—
97C2×D43—82no—
98C2×D43—81no—
99C2×D43—164no—
100C4×C43—41no—
101C4×C43—81no—
102C4×C43#42112yes—
103Dic43—22no—
104Dic43—21no—
105Dic43—81no—
106#3138—431no—
107#2165—432no—
108#1355—431no—
109#1355—432no—
110#1355D4311yescharacteristic, complemented
111C2×C43—21no—
112C2×C43—161no—
113C2×C43#153311yescharacteristic
114D43—41no—
115D43—161no—
116#533—431no—
117C2×#127—431no—
118#490—431no—
119#490—431no—
120#490—431no—
121#490C2×D4311yescharacteristic
122#486—862no—
123#418—862no—
124C4×M16—431no—
125#364—862no—
126#349—862no—
127#347—432no—
128#347C2×D4312yescomplemented
129C43#1191511yescharacteristic, complemented, Sylow
130C22×D4—861no—
131C22×D4—1721no—
132C2×M16—432no—
133C4⋊Q8—861no—
134#127—431no—
135#127—861no—
136#127—1721no—
137#127C4×D4311yescharacteristic
138#125—431no—
139#125C4×D4311yescharacteristic
140C22⋊Q8—1721no—
141C4×Q8—1721no—
142#117—861no—
143C2×C42—431no—
144M32—22no—
145M32—862no—
146#102—22no—
147#102—862no—
148#102—862no—
149#102—862no—
150#97—431no—
151#97C22×D4311yescharacteristic
152C4×C8—432no—
153C24—1721no—
154C2×Q8—1721no—
155C2×D4—21no—
156C2×D4—41no—
157C2×D4—861no—
158C2×D4—3444no—
159C2×D4—1721no—
160C2×D4—1721no—
161C2×D4—1724no—
162C2×D4—1722no—
163C22×C4—431no—
164C22×C4—861no—
165M16—1722no—
166C2×C8—432no—
167C2×C8D4×D4312yes—
168C4⋊C4—21no—
169C4⋊C4—41no—
170C4⋊C4—861no—
171C4⋊C4—1721no—
172C4⋊C4—1721no—
173C22⋊C4—1721no—
174C42—431no—
175C42—861no—
176C42—1721no—
177C42C2×C4×D4311yescharacteristic
178C16—42no—
179C16—1722no—
180C23—41no—
181C23—431no—
182C23—3442no—
183C23—3444no—
184C23—1721no—
185Q8—3442no—
186D4—42no—
187D4—82no—
188D4—3442no—
189D4—3444no—
190D4—3442no—
191D4—1722no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—431no—
195C2×C4—861no—
196C2×C4—862no—
197C2×C4—1722no—
198C2×C4—1721no—
199C2×C4C22⋊C4×D4311yescharacteristic
200C8—22no—
201C8—862no—
202C22—82no—
203C22—81no—
204C22—861no—
205C22—3442no—
206C22—3441no—
207C22—1721no—
208C22—6884no—
209C22#100×D4311yescharacteristic
210C4—41no—
211C4—81no—
212C4—862no—
213C4—861no—
214C4—3441no—
215C4#1458291412yes—
216C2—21no—
217C2—161no—
218C2—1721no—
219C2—6881no—
220C2#1913321711yescharacteristic
subgroupG/H
centerC2#19133217
commutatorC42×C43C22×C4
Frattini#97C22×D43
FittingC43×#1355C2
socleC2×C43#1533
prime radical#127×D43C4
cosocle#97×C43C23
hypercenter#1355D43
hypocenterC43#11915
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1355

Complements

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

NH ≅ G/Ntype
2. #19136405C2semidirect
3. #19132628C2semidirect
4. #19132627C2semidirect
5. C43×#1355C2semidirect
16. #14582677C22semidirect
18. C43×#347C22semidirect
110. #1355D43semidirect
128. #347C2×D43semidirect
129. C43#11915semidirect

Maximal subgroups

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

subgroupindex
#191449682
#191364052
#191326282
#191326272
C43×#13552
#1191543