Finite Group Databasebeta

← #25007797

Subgroups — #25007797

Order 11008.

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

normal subgroups only

This group has 280 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#19144997C211yesmaximal, characteristic
2#19136405C212yesmaximal, complemented
3#19132630C211yesmaximal, characteristic, complemented
4#19132627C212yesmaximal, complemented
5C43×#1356C211yesmaximal, characteristic, complemented
6#14583450C411yescharacteristic
7#125×D43C411yescharacteristic
8#14583267C411yescharacteristic
9#14583265C411yescharacteristic
10#14583264C2211yescharacteristic
11#14583255—22no—
12#14582899—22no—
13#14582851C2211yescharacteristic
14#14582719—22no—
15#14582680—22no—
16#14582677C2212yes—
17C43×#491C2211yescharacteristic
18C43×#347C2212yes—
19C2×#10621902—21no—
20C2×#10621872D412yes—
21#13063322C2×C411yescharacteristic
22#13063317C2×C411yescharacteristic
23#13063316—21no—
24#13063315—41no—
25#13063314—21no—
26#13063300—41no—
27#13063287—41no—
28C4⋊C4×D43—21no—
29C4⋊C4×D43—41no—
30C42×D43C2×C411yescharacteristic
31#13063265—22no—
32#13063249—22no—
33#13063247—22no—
34#13063245—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—
43#10621902—44no—
44C2×D172—21no—
45C2×D172—41no—
46C2×D172—41no—
47C2×C4×D43—21no—
48C2×C4×D43—41no—
49C2×C4×D43—41no—
50C2×C4×D43C22⋊C411yescharacteristic
51C2×C8×C43C2×D412yes—
52C4⋊C4×C43—21no—
53C4⋊C4×C43—41no—
54C4⋊C4×C43—41no—
55C42×C43C22×C411yescharacteristic
56(C2×D43)⋊C4—42no—
57C4⋊Dic43—21no—
58C4⋊Dic43—41no—
59Dic43⋊C4—41no—
60Dic43⋊C4—41no—
61Dic43⋊C4—41no—
62C4×Dic43—21no—
63C4×Dic43C22⋊C411yescharacteristic
64C2×C43⋊C8C22⋊C412yes—
65#10621872—42no—
66C16×C43—42no—
67C43⋊C16—42no—
68C22×D43—41no—
69C22×D43#10011yescharacteristic
70Q8×C43—42no—
71C2×C4×C43—21no—
72C2×C4×C43—41no—
73C2×C4×C43—41no—
74C2×C4×C43C2×C22⋊C411yescharacteristic
75C2×Dic43—21no—
76C2×Dic43—41no—
77C2×Dic43#10011yescharacteristic
78D172—42no—
79D172—82no—
80D172—82no—
81C4×D43—22no—
82C4×D43—82no—
83C4×D43—81no—
84C4×D43—82no—
85C8×C43—22no—
86C43⋊C8—22no—
87#11917—431nomaximal, Sylow
88C22×C43C2×#10011yescharacteristic
89C2×D43—21no—
90C2×D43—41no—
91C2×D43—82no—
92C2×D43—81no—
93C4×C43—41no—
94C4×C43—81no—
95C4×C43—81no—
96C4×C43#42112yes—
97Dic43—21no—
98Dic43—41no—
99Dic43—81no—
100#3142—431no—
101#2165—432no—
102#1356—431no—
103#1356D4311yescharacteristic, complemented
104#1355—432no—
105C2×C43—21no—
106C2×C43#153311yescharacteristic
107D43—41no—
108D43—161no—
109#532—431no—
110C2×#125—431no—
111#491—431no—
112#491C2×D4311yescharacteristic
113#490—431no—
114#490—431no—
115#488—862no—
116#417—862no—
117C4×M16—431no—
118#364—862no—
119#349—862no—
120#347—432no—
121#347C2×D4312yes—
122C43#1191711yescharacteristic, complemented, Sylow
123C2×#41—861no—
124C2×M16—432no—
125C4⋊Q8C4×D4311yescharacteristic
126#127—431no—
127#125—431no—
128#125—861no—
129#125—1721no—
130#125C4×D4311yescharacteristic
131#124—861no—
132#121—1721no—
133C4×D4—1721no—
134C2×C4⋊C4—861no—
135C2×C4⋊C4—1721no—
136C2×C42—431no—
137M32—22no—
138M32—862no—
139#103—22no—
140#103—862no—
141#102—862no—
142#102—862no—
143#97—431no—
144#97C22×D4311yescharacteristic
145C4×C8—432no—
146#41—1724no—
147C2×Q8—21no—
148C2×D4—861no—
149C2×D4—1721no—
150C2×D4—1721no—
151C22×C4—431no—
152C22×C4—861no—
153C22×C4—1721no—
154C22×C4—1721no—
155M16—1722no—
156C2×C8—432no—
157C2×C8D4×D4312yes—
158C4⋊C4—21no—
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—861no—
162C4⋊C4—1721no—
163C4⋊C4—1721no—
164C4⋊C4—1721no—
165C4⋊C4—1721no—
166C22⋊C4—1722no—
167C42—431no—
168C42—861no—
169C42C2×C4×D4311yescharacteristic
170C16—42no—
171C16—1722no—
172C23—431no—
173C23—1721no—
174Q8—42no—
175D4—3442no—
176D4—3442no—
177D4—1722no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—431no—
182C2×C4—862no—
183C2×C4—861no—
184C2×C4—3441no—
185C2×C4—3442no—
186C2×C4—3442no—
187C2×C4—1721no—
188C2×C4C22⋊C4×D4311yescharacteristic
189C8—22no—
190C8—862no—
191C22—861no—
192C22—3442no—
193C22—3441no—
194C22—1721no—
195C22#100×D4311yescharacteristic
196C4—41no—
197C4—81no—
198C4—81no—
199C4—861no—
200C4—3441no—
201C4—1721no—
202C4#1458291412yes—
203C2—21no—
204C2—1721no—
205C2—6881no—
206C2#1913321711yescharacteristic
subgroupG/H
centerC2#19133217
commutatorC42×C43C22×C4
Frattini#97C22×D43
FittingC43×#1356C2
socleC2×C43#1533
prime radical#14583450C4
cosocle#97×C43C23
hypercenter#1356D43
hypocenterC43#11917
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
2. #19136405C2semidirect
3. #19132630C2semidirect
4. #19132627C2semidirect
5. C43×#1356C2semidirect
103. #1356D43semidirect
122. C43#11917semidirect

Maximal subgroups

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

subgroupindex
#191449972
#191364052
#191326302
#191326272
C43×#13562
#1191743