Finite Group Databasebeta

← #24994199

Subgroups — #24994199

Order 11008.

400 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 103 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#19144977C211yesmaximal, characteristic
2#19143697C211yesmaximal, characteristic
3#19133281C212yesmaximal
4#19132484C212yesmaximal
5C43×#1561C211yesmaximal, characteristic
6C2×#13063325C2211yescharacteristic
7#14583269C414yes—
8#14583251—22no—
9#14583030—22no—
10Q8×C43⋊C8—22no—
11#14582960—22no—
12#14582952C2212yes—
13#14582907—22no—
14C4×#10621877C2211yescharacteristic
15#14582644—22no—
16#14582644—22no—
17C43×#533C2211yescharacteristic
18C43×#423C2212yes—
19C43×#332—22no—
20C22×Dic86—21no—
21C2×#10621877—21no—
22#13063325—22no—
23#13063325—21no—
24#13063325C2×C412yes—
25C2×C4⋊Dic43—22no—
26C4⋊(C43⋊C8)—24no—
27C4⋊(C43⋊C8)D412yes—
28C4⋊(C43⋊C8)D412yes—
29#13063248—28no—
30C22⋊(C43⋊C8)—22no—
31#13063236—22no—
32#13063236C2×C412yes—
33C4×C43⋊C8—22no—
34C4×C43⋊C8—21no—
35C4×C43⋊C8—22no—
36C2×M16×C43—22no—
37C4⋊Q8×C43D412yes—
38#125×C43C2×C412yes—
39C22⋊Q8×C43—22no—
40C4×Q8×C43—22no—
41#117×C43D412yes—
42C2×C42×C43C2311yescharacteristic
43C4⋊C8×C43—22no—
44C4⋊C8×C43—22no—
45C2×Q8×C43—22no—
46C22×C4×C43C2×D411yescharacteristic
47C22×C4×C43#4112yes—
48C22×Dic43—41no—
49C2×Dic86—22no—
50C2×Dic86—44no—
51C2×Dic86—41no—
52M16×C43—82no—
53C2×C8×C43—42no—
54C4⋊C4×C43—24no—
55C4⋊C4×C43—22no—
56C4⋊C4×C43C22⋊C414yes—
57C22⋊C4×C43—22no—
58C42×C43—22no—
59C42×C43C22×C411yescharacteristic
60C42×C43C2×D412yes—
61C42×C43C2×D411yescharacteristic
62C4⋊Dic43—24no—
63C4⋊Dic43—42no—
64#10621877—42no—
65C2×C43⋊C8—22no—
66C2×C43⋊C8—22no—
67C2×C43⋊C8—22no—
68C23×C43#12311yescharacteristic
69Q8×C43—42no—
70Q8×C43—42no—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—24no—
75C2×C4×C43C2×C22⋊C411yescharacteristic
76C2×C4×C43C4×D412yes—
77C2×C4×C43#12011yescharacteristic
78C2×C4×C43#12112yes—
79C2×Dic43—42no—
80C2×Dic43—82no—
81Dic86—44no—
82Dic86—82no—
83C8×C43—82no—
84C43⋊C8—42no—
85C43⋊C8—42no—
86C43⋊C8—42no—
87#9436—431nomaximal, Sylow
88C22×C43—21no—
89C22×C43—22no—
90C22×C43#38611yescharacteristic
91C4×C43—21no—
92C4×C43—22no—
93C4×C43—44no—
94C4×C43#45412yes—
95C4×C43#47112yes—
96C4×C43#47312yes—
97Dic43—82no—
98#3139—431no—
99#2986—431no—
100#1561D4311yescharacteristic
101#1549—432no—
102#1299—432no—
103C2×C43—41no—
104C2×C43#188811yescharacteristic
105C2×C43#190812yes—
106#533C2×D4311yescharacteristic
107C2×C4⋊Q8—431no—
108#491—434no—
109#487—862no—
110#446—862no—
111C8×Q8—862no—
112#433—862no—
113#431—432no—
114#423C2×D4312yes—
115#419—862no—
116C4×M16—431no—
117#332—22no—
118#332—862no—
119#332—862no—
120C43#943611yescharacteristic, complemented, Sylow
121C22×Q8—861no—
122C2×M16—22no—
123C2×M16—861no—
124C4⋊Q8—432no—
125C4⋊Q8—862no—
126C4⋊Q8—861no—
127C4⋊Q8C22⋊D4312yes—
128#125C4×D4312yes—
129C22⋊Q8—22no—
130C4×Q8—22no—
131#117D17212yes—
132C2×C4⋊C4—862no—
133C2×C42C22×D4311yescharacteristic
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—432no—
137C4⋊C8—432no—
138C4⋊C8—864no—
139#103—868no—
140C22⋊C8—862no—
141#97—432no—
142#97—862no—
143C4×C8—862no—
144C4×C8—862no—
145C4×C8—861no—
146C2×Q8—22no—
147C2×Q8—862no—
148C2×Q8—1724no—
149C2×Q8—1721no—
150C22×C4—1721no—
151C22×C4C2×D17211yescharacteristic
152C22×C4#1062190012yes—
153M16—82no—
154M16—1722no—
155C2×C8—42no—
156C2×C8—862no—
157C2×C8—862no—
158C2×C8—862no—
159C4⋊C4—24no—
160C4⋊C4—22no—
161C4⋊C4—864no—
162C4⋊C4—1722no—
163C4⋊C4(C2×D43)⋊C414yes—
164C22⋊C4—22no—
165C42—22no—
166C42C2×C4×D4311yescharacteristic
167C42D4×D4312yes—
168C42C2×C22⋊D4311yescharacteristic
169C23#1306330911yescharacteristic
170Q8—42no—
171Q8—42no—
172Q8—3442no—
173Q8—1724no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—3442no—
179C2×C4—1722no—
180C2×C4C2×(C2×D43)⋊C411yescharacteristic
181C2×C4(C22⋊D43)⋊C412yes—
182C2×C4#1306329511yescharacteristic
183C2×C4#1306329712yes—
184C8—82no—
185C8—1722no—
186C8—1722no—
187C8—1722no—
188C22—21no—
189C22—22no—
190C22#1458277611yescharacteristic
191C4—21no—
192C4—22no—
193C4—44no—
194C4—3442no—
195C4#1458307412yes—
196C4#1458316012yes—
197C4#1458317212yes—
198C2—41no—
199C2#1913499611yescharacteristic
200C2#1913510812yes—
subgroupG/H
centerC22#14582776
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1561C2
socleC22×C43#386
prime radicalC23×C43#123
cosocleC2×C42×C43C23
hypercenter#1561D43
hypocenterC43#9436
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1561

Complements

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

NH ≅ G/Ntype
120. C43#9436semidirect

Maximal subgroups

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

subgroupindex
#191449772
#191436972
#191332812
#191324842
C43×#15612
#943643