Finite Group Databasebeta

← #24994202

Subgroups — #24994202

Order 11008.

400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 111 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#19143697C211yesmaximal, characteristic
2#19133333C211yesmaximal, characteristic
3#19133280C212yesmaximal
4#19132485C212yesmaximal
5C43×#3139C211yesmaximal, characteristic
6#14583030—22no—
7Q8×C43⋊C8—22no—
8#14582960—22no—
9#14582952C2212yes—
10#14582923C2212yes—
11#14582645—22no—
12#14582645—22no—
13#14582645—22no—
14C43×#533C2211yescharacteristic
15C2×C4⋊Q8×C43C2211yescharacteristic
16C43×#491C414yes—
17C43×#487—22no—
18C43×#419—22no—
19C4×M16×C43C2211yescharacteristic
20C2×#10621877—22no—
21C4⋊(C43⋊C8)—24no—
22C4⋊(C43⋊C8)—22no—
23C4⋊(C43⋊C8)—22no—
24C4⋊(C43⋊C8)D412yes—
25C4⋊(C43⋊C8)D412yes—
26C22⋊(C43⋊C8)—22no—
27#13063236—22no—
28C4×C43⋊C8—22no—
29C4×C43⋊C8—22no—
30C22×Q8×C43—21no—
31C2×M16×C43—21no—
32C4⋊Q8×C43—22no—
33C4⋊Q8×C43—21no—
34C4⋊Q8×C43C2×C412yes—
35C4⋊Q8×C43D412yes—
36#125×C43C2×C412yes—
37C22⋊Q8×C43—22no—
38C4×Q8×C43—22no—
39#117×C43D412yes—
40C2×C4⋊C4×C43—22no—
41C2×C42×C43C2311yescharacteristic
42#103×C43—28no—
43#97×C43C2×C412yes—
44C4×C8×C43—21no—
45C2×Q8×C43—22no—
46C2×Q8×C43—22no—
47C2×Q8×C43—44no—
48C2×Q8×C43—41no—
49C22×C4×C43—41no—
50C22×C4×C43C2×D411yescharacteristic
51C22×C4×C43#4112yes—
52M16×C43—42no—
53C2×C8×C43—22no—
54C4⋊C4×C43—24no—
55C4⋊C4×C43—22no—
56C4⋊C4×C43—24no—
57C4⋊C4×C43—42no—
58C4⋊C4×C43C22⋊C414yes—
59C22⋊C4×C43—22no—
60C42×C43—22no—
61C42×C43C22×C411yescharacteristic
62C42×C43C2×D412yes—
63C42×C43C2×D411yescharacteristic
64#10621877—82no—
65C2×C43⋊C8—22no—
66C2×C43⋊C8—22no—
67C2×C43⋊C8—42no—
68C23×C43#12311yescharacteristic
69Q8×C43—44no—
70Q8×C43—42no—
71Q8×C43—42no—
72Q8×C43—82no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—24no—
77C2×C4×C43—42no—
78C2×C4×C43—82no—
79C2×C4×C43C2×C22⋊C411yescharacteristic
80C2×C4×C43C4×D412yes—
81C2×C4×C43#12011yescharacteristic
82C2×C4×C43#12112yes—
83C8×C43—42no—
84C43⋊C8—42no—
85C43⋊C8—42no—
86C43⋊C8—82no—
87#9436—431nomaximal, Sylow
88C22×C43—21no—
89C22×C43—22no—
90C22×C43#38611yescharacteristic
91C4×C43—21no—
92C4×C43—22no—
93C4×C43—44no—
94C4×C43—82no—
95C4×C43#45412yes—
96C4×C43#47112yes—
97C4×C43#47312yes—
98#3139D4311yescharacteristic
99#2986—431no—
100#1561—431no—
101#1549—432no—
102#1299—432no—
103C2×C43—41no—
104C2×C43#188811yescharacteristic
105C2×C43#190812yes—
106#533C2×D4311yescharacteristic
107C2×C4⋊Q8C2×D4311yescharacteristic
108#491Dic4314yes—
109#487—22no—
110#446—862no—
111C8×Q8—862no—
112#433—862no—
113#431—432no—
114#423—432no—
115#419—22no—
116C4×M16C2×D4311yescharacteristic
117#332—862no—
118#332—862no—
119#332—862no—
120C43#943611yescharacteristic, complemented, Sylow
121C22×Q8—21no—
122C2×M16—21no—
123C2×M16—862no—
124C4⋊Q8—22no—
125C4⋊Q8—21no—
126C4⋊Q8C2×Dic4312yes—
127C4⋊Q8C22⋊D4312yes—
128#125C2×Dic4312yes—
129C22⋊Q8—22no—
130C4×Q8—22no—
131#117C22⋊D4312yes—
132C2×C4⋊C4—22no—
133C2×C42C22×D4311yescharacteristic
134C4⋊C8—432no—
135C4⋊C8—432no—
136C4⋊C8—864no—
137C4⋊C8—862no—
138C4⋊C8—862no—
139#103—28no—
140C22⋊C8—862no—
141#97—862no—
142#97C2×Dic4312yes—
143C4×C8—21no—
144C4×C8—862no—
145C4×C8—862no—
146C2×Q8—22no—
147C2×Q8—22no—
148C2×Q8—44no—
149C2×Q8—41no—
150C22×C4—41no—
151C22×C4#1062190012yes—
152C22×C4C2×C22⋊D4311yescharacteristic
153M16—42no—
154M16—3442no—
155C2×C8—22no—
156C2×C8—862no—
157C2×C8—862no—
158C2×C8—1722no—
159C4⋊C4—24no—
160C4⋊C4—22no—
161C4⋊C4—24no—
162C4⋊C4—42no—
163C4⋊C4C22⋊Dic4314yes—
164C22⋊C4—22no—
165C42—22no—
166C42D4×D4312yes—
167C42C22×Dic4311yescharacteristic
168C42C2×C22⋊D4311yescharacteristic
169C23#1306330611yescharacteristic
170Q8—44no—
171Q8—42no—
172Q8—42no—
173Q8—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—42no—
179C2×C4—82no—
180C2×C4C2×C22⋊Dic4311yescharacteristic
181C2×C4D4×Dic4312yes—
182C2×C4#1306329311yescharacteristic
183C2×C4#1306329712yes—
184C8—42no—
185C8—3442no—
186C8—1722no—
187C8—1722no—
188C22—21no—
189C22—22no—
190C22#1458277911yescharacteristic
191C4—21no—
192C4—22no—
193C4—44no—
194C4—82no—
195C4#1458307112yes—
196C4#1458316412yes—
197C4#1458317212yes—
198C2—41no—
199C2#1913499911yescharacteristic
200C2#1913511212yes—
subgroupG/H
centerC22#14582779
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#3139C2
socleC22×C43#386
prime radicalC23×C43#123
cosocleC2×C42×C43C23
hypercenter#3139D43
hypocenterC43#9436
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

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
#191436972
#191333332
#191332802
#191324852
C43×#31392
#943643