Finite Group Databasebeta

← #25007792

Subgroups — #25007792

Order 11008.

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

normal subgroups only

This group has 274 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#19144974C211yesmaximal, characteristic
2#19136405C212yesmaximal
3#19132630C211yesmaximal, characteristic, complemented
4#19132629C212yesmaximal, complemented
5C43×#1356C211yesmaximal, characteristic, complemented
6#14583455C411yescharacteristic
7C4⋊Q8×D43C411yescharacteristic
8#14583269C411yescharacteristic
9#14583268C2211yescharacteristic
10#14583267C411yescharacteristic
11#14583248—22no—
12#14582906—22no—
13#14582851C2211yescharacteristic
14#14582719—22no—
15#14582680—22no—
16#14582677C2212yes—
17C43×#491C2211yescharacteristic
18C43×#347C2212yes—
19C2×Q8×D43—21no—
20C2×#10621872D412yes—
21#13063325C2×C411yescharacteristic
22#13063324—21no—
23#13063324—41no—
24#13063323—21no—
25#13063317C2×C411yescharacteristic
26#13063303—41no—
27#13063290—41no—
28#13063283—21no—
29C4⋊C4×D43—41no—
30C42×D43C2×C411yescharacteristic
31#13063265—22no—
32#13063250—22no—
33#13063249—22no—
34#13063248—22no—
35#13063236C2×C411yescharacteristic
36C8×Dic43D412yes—
37C4⋊Q8×C43C2×C411yescharacteristic
38#125×C43C2×C411yescharacteristic
39M32×C43—22no—
40#103×C43—22no—
41#97×C43C2311yescharacteristic
42C2×Q8×C43—21no—
43Q8×D43—44no—
44C2×C4×D43—21no—
45C2×C4×D43—41no—
46C2×C4×D43C22⋊C411yescharacteristic
47C2×Dic86—21no—
48C2×Dic86—41no—
49C2×Dic86—41no—
50C2×C8×C43C2×D412yes—
51C4⋊C4×C43—21no—
52C4⋊C4×C43—41no—
53C4⋊C4×C43—41no—
54C42×C43C22×C411yescharacteristic
55(C2×D43)⋊C4—41no—
56C4⋊Dic43—21no—
57C4⋊Dic43—41no—
58Dic43⋊C4—42no—
59Dic43⋊C4—41no—
60Dic43⋊C4—41no—
61C4×Dic43—21no—
62C4×Dic43—41no—
63C4×Dic43C22⋊C411yescharacteristic
64C2×C43⋊C8C22⋊C412yes—
65#10621872—42no—
66C16×C43—42no—
67C43⋊C16—42no—
68C22×D43#10011yescharacteristic
69Q8×C43—42no—
70C2×C4×C43—21no—
71C2×C4×C43—41no—
72C2×C4×C43—41no—
73C2×C4×C43C2×C22⋊C411yescharacteristic
74C2×Dic43—21no—
75C2×Dic43—41no—
76C2×Dic43—41no—
77C2×Dic43#10011yescharacteristic
78C4×D43—22no—
79C4×D43—42no—
80C4×D43—82no—
81Dic86—42no—
82Dic86—82no—
83Dic86—82no—
84C8×C43—22no—
85C43⋊C8—22no—
86#11916—431nomaximal, Sylow
87C22×C43C2×#10011yescharacteristic
88C2×D43—21no—
89C2×D43—41no—
90C4×C43—41no—
91C4×C43—81no—
92C4×C43—81no—
93C4×C43#42112yes—
94Dic43—22no—
95Dic43—21no—
96Dic43—81no—
97Dic43—81no—
98#3139—431no—
99#2165—432no—
100#1356—431no—
101#1356—432no—
102#1356D4311yescharacteristic, complemented
103C2×C43—21no—
104C2×C43#153311yescharacteristic
105D43—41no—
106#533—431no—
107C2×C4⋊Q8—431no—
108#491—431no—
109#491—431no—
110#491—431no—
111#491C2×D4311yescharacteristic
112#487—862no—
113#419—862no—
114C4×M16—431no—
115#364—862no—
116#349—862no—
117#347—432no—
118#347C2×D4312yes—
119C43#1191611yescharacteristic, complemented, Sylow
120C22×Q8—861no—
121C2×M16—432no—
122C4⋊Q8—431no—
123C4⋊Q8—861no—
124C4⋊Q8—861no—
125C4⋊Q8—1721no—
126C4⋊Q8C4×D4311yescharacteristic
127#125—431no—
128#125C4×D4311yescharacteristic
129C22⋊Q8—1721no—
130C4×Q8—1721no—
131#117—861no—
132C2×C4⋊C4—1721no—
133C2×C42—431no—
134M32—22no—
135M32—862no—
136#103—22no—
137#103—862no—
138#103—862no—
139#103—862no—
140#97—431no—
141#97C22×D4311yescharacteristic
142C4×C8—432no—
143C2×Q8—21no—
144C2×Q8—861no—
145C2×Q8—1721no—
146C2×Q8—1721no—
147C2×Q8—1724no—
148C22×C4—431no—
149C22×C4—861no—
150C22×C4—1721no—
151M16—1722no—
152C2×C8—432no—
153C2×C8D4×D4312yes—
154C4⋊C4—21no—
155C4⋊C4—41no—
156C4⋊C4—41no—
157C4⋊C4—861no—
158C4⋊C4—1721no—
159C4⋊C4—1721no—
160C4⋊C4—1722no—
161C4⋊C4—1721no—
162C22⋊C4—1721no—
163C42—431no—
164C42—861no—
165C42—1721no—
166C42C2×C4×D4311yescharacteristic
167C16—42no—
168C16—1722no—
169C23—431no—
170Q8—42no—
171Q8—3442no—
172Q8—3442no—
173Q8—1722no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—431no—
178C2×C4—861no—
179C2×C4—862no—
180C2×C4—3442no—
181C2×C4—1722no—
182C2×C4—1721no—
183C2×C4—1721no—
184C2×C4C22⋊C4×D4311yescharacteristic
185C8—22no—
186C8—862no—
187C22—861no—
188C22—1721no—
189C22#100×D4311yescharacteristic
190C4—41no—
191C4—81no—
192C4—81no—
193C4—862no—
194C4—861no—
195C4—3441no—
196C4—3441no—
197C4#1458291412yes—
198C2—21no—
199C2—1721no—
200C2#1913321711yescharacteristic
subgroupG/H
centerC2#19133217
commutatorC42×C43C22×C4
Frattini#97C22×D43
FittingC43×#1356C2
socleC2×C43#1533
prime radicalC22×D43#100
cosocle#97×C43C23
hypercenter#1356D43
hypocenterC43#11916
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1356

Complements

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

NH ≅ G/Ntype
3. #19132630C2semidirect
4. #19132629C2semidirect
5. C43×#1356C2semidirect
102. #1356D43semidirect
119. C43#11916semidirect

Maximal subgroups

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

subgroupindex
#191449742
#191364052
#191326302
#191326292
C43×#13562
#1191643