Finite Group Databasebeta

← #24991546

Subgroups — #24991546

Order 11008.

416 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 99 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#19144940C211yesmaximal, characteristic
2#19133257C211yesmaximal, characteristic
3#19133067C212yesmaximal, complemented
4#19132493C212yesmaximal, complemented
5C43×#2980C211yesmaximal, characteristic
6#14583456C2211yescharacteristic
7#14583267—21no—
8#14583263—21no—
9#14583258C414yes—
10#14582952C2212yes—
11#14582895—22no—
12C2×#13063236C2211yescharacteristic
13#14582648—21no—
14#14582643—21no—
15#14582629—24no—
16C43×#532C2211yescharacteristic
17C43×#435—24no—
18C43×#432C2212yes—
19C43×#408—22no—
20C22×C43⋊C8—21no—
21#13063325C2×C412yes—
22#13063317—21no—
23#13063304—22no—
24C4×Dic86—22no—
25#13063284—21no—
26C4⋊(C43⋊C8)—22no—
27#13063249—24no—
28#13063246—24no—
29C22⋊(C43⋊C8)—22no—
30#13063236—21no—
31#13063236C2×C412yes—
32C4×C43⋊C8—22no—
33C2×#41×C43D412yes—
34C2×M16×C43—22no—
35C22×C8×C43—22no—
36C4⋊Q8×C43D411yescharacteristic
37#127×C43D411yescharacteristic
38#124×C43C2×C412yes—
39#121×C43—22no—
40C4×D4×C43—22no—
41C2×C42×C43C2311yescharacteristic
42C4⋊C8×C43D414yes—
43C22⋊C8×C43—24no—
44C22⋊C8×C43—22no—
45#97×C43—22no—
46#41×C43—42no—
47#41×C43—42no—
48C2×Q8×C43C22⋊C412yes—
49C2×D4×C43—22no—
50C2×D4×C43—22no—
51C2×D4×C43C22⋊C412yes—
52C22×C4×C43—22no—
53C22×C4×C43C2×D411yescharacteristic
54C22×C4×C43#4112yes—
55C2×Dic86—22no—
56M16×C43—82no—
57C2×C8×C43—24no—
58C2×C8×C43—82no—
59C4⋊C4×C43—22no—
60C22⋊C4×C43—24no—
61C42×C43C22×C411yescharacteristic
62C42×C43C2×D411yescharacteristic
63C42×C43C2×D412yes—
64C22⋊Dic43—41no—
65C4⋊Dic43—22no—
66C4⋊Dic43—22no—
67Dic43⋊C4—42no—
68C4×Dic43—41no—
69C2×C43⋊C8—22no—
70C2×C43⋊C8—42no—
71C2×C43⋊C8—42no—
72C23×C43—22no—
73C23×C43#12311yescharacteristic
74Q8×C43—42no—
75D4×C43—42no—
76D4×C43—82no—
77D4×C43—82no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—42no—
81C2×C4×C43—42no—
82C2×C4×C43—42no—
83C2×C4×C43C2×C22⋊C411yescharacteristic
84C2×C4×C43C4×D412yes—
85C2×C4×C43#12011yescharacteristic
86C2×C4×C43#12112yes—
87C2×Dic43—42no—
88Dic86—44no—
89C8×C43—44no—
90C43⋊C8—42no—
91C43⋊C8—82no—
92#9005—431nomaximal, Sylow
93C22×C43—22no—
94C22×C43—21no—
95C22×C43—44no—
96C22×C43—42no—
97C22×C43#38611yescharacteristic
98C4×C43—22no—
99C4×C43—22no—
100C4×C43—21no—
101C4×C43—42no—
102C4×C43#45512yes—
103Dic43—82no—
104#3135—431no—
105#2980D4311yescharacteristic
106#1543—431no—
107#1497—432no—
108#1302—432no—
109C2×C43—41no—
110C2×C43—82no—
111C2×C43#188112yes—
112C2×C43#188511yescharacteristic
113#533—431no—
114#532C2×D4311yescharacteristic
115#491—861no—
116#490—861no—
117#489—434no—
118#435—24no—
119#432C2×D4312yes—
120#431—432no—
121#416—862no—
122#408—22no—
123C2×#97—431no—
124#333—861no—
125#331—861no—
126Q8⋊C8—864no—
127C43#900511yescharacteristic, complemented, Sylow
128C2×#41C22⋊D4312yes—
129C2×M16—22no—
130C22×C8—22no—
131C22×C8—861no—
132C4⋊Q8—432no—
133C4⋊Q8D17211yescharacteristic
134#127D17211yescharacteristic
135#125—861no—
136#124C4×D4312yes—
137C22⋊Q8—862no—
138#121—22no—
139C4×Q8—862no—
140C4×D4—22no—
141#117—861no—
142C2×C42C22×D4311yescharacteristic
143C4⋊C8—862no—
144C4⋊C8C22⋊D4314yes—
145#103—864no—
146#102—864no—
147C22⋊C8—24no—
148C22⋊C8—22no—
149C22⋊C8—862no—
150#97—22no—
151#97—432no—
152#97—861no—
153C4×C8—862no—
154#41—42no—
155#41—42no—
156C2×Q8—862no—
157C2×Q8(C2×D43)⋊C412yes—
158C2×D4—22no—
159C2×D4—22no—
160C2×D4(C2×D43)⋊C412yes—
161C22×C4—22no—
162C22×C4#1062189812yes—
163C22×C4C2×C22⋊D4311yescharacteristic
164M16—82no—
165C2×C8—24no—
166C2×C8—82no—
167C2×C8—862no—
168C2×C8—1722no—
169C2×C8—1722no—
170C4⋊C4—22no—
171C4⋊C4—862no—
172C4⋊C4—862no—
173C4⋊C4—1722no—
174C22⋊C4—24no—
175C22⋊C4—1721no—
176C42—1721no—
177C42C2×C4×D4311yescharacteristic
178C42C2×D17211yescharacteristic
179C42C2×C22⋊D4312yes—
180C23—22no—
181C23#1306330811yescharacteristic
182Q8—42no—
183Q8—1724no—
184D4—42no—
185D4—82no—
186D4—82no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—1722no—
193C2×C4C2×(C2×D43)⋊C411yescharacteristic
194C2×C4C4×C22⋊D4312yes—
195C2×C4#1306329411yescharacteristic
196C2×C4#1306329912yes—
197C8—44no—
198C8—3442no—
199C8—1722no—
200C22—21no—
201C22—22no—
202C22—42no—
203C22—44no—
204C22#1458277811yescharacteristic
205C4—21no—
206C4—22no—
207C4—22no—
208C4—42no—
209C4—3442no—
210C4#1458307712yes—
211C2—41no—
212C2—82no—
213C2#1913495712yes—
214C2#1913498311yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2980C2
socleC22×C43#386
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#2980D43
hypocenterC43#9005
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2980

Complements

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

NH ≅ G/Ntype
3. #19133067C2semidirect
4. #19132493C2semidirect
127. C43#9005semidirect

Maximal subgroups

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

subgroupindex
#191449402
#191332572
#191330672
#191324932
C43×#29802
#900543