Finite Group Databasebeta

← #24999732

Subgroups — #24999732

Order 11008.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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#19135427C211yesmaximal, characteristic
2#19133089C212yesmaximal
3#19132498C212yesmaximal, complemented
4#19132424C211yesmaximal, characteristic, complemented
5C43×#2402C211yesmaximal, characteristic, complemented
6#14583449C2211yescharacteristic
7#14582952C2212yes—
8#14582923C2211yescharacteristic
9C2×#13063253—22no—
10#14582632—22no—
11#14582632—22no—
12C43×#400—22no—
13C43×#398—22no—
14C4×C4⋊C4×C43—22no—
15C4×C4⋊C4×C43C2212yes—
16C43×#376C2211yescharacteristic
17C2×#10621898—21no—
18C2×#10621877—21no—
19#13063325Q811yescharacteristic
20#13063322Q811yescharacteristic
21#13063313—21no—
22#13063299—22no—
23C4×D172—22no—
24C4⋊(C43⋊C8)—22no—
25C4⋊(C43⋊C8)—22no—
26#13063253—44no—
27C22⋊(C43⋊C8)—22no—
28C4×C43⋊C8—22no—
29C2×C4⋊C4×C43—22no—
30C2×C4⋊C4×C43—22no—
31C2×C4⋊C4×C43—22no—
32C2×C42×C43—22no—
33C2×C42×C43D412yes—
34C2×C42×C43C2311yescharacteristic
35#95×C43—22no—
36#95×C43—22no—
37#95×C43—22no—
38#95×C43D412yes—
39#95×C43D412yes—
40C22×C4×C43—22no—
41C22×C4×C43—22no—
42C22×C4×C43—22no—
43C22×C4×C43C2×D412yes—
44C22×C4×C43C2×D411yescharacteristic
45C2×C22⋊D43—41no—
46#10621898—42no—
47#10621898—42no—
48C2×D172—21no—
49C2×D172—22no—
50C2×C4×D43—41no—
51C2×Dic86—21no—
52C4⋊C4×C43—44no—
53C4⋊C4×C43—44no—
54C4⋊C4×C43—44no—
55C42×C43—22no—
56C42×C43—22no—
57C42×C43—42no—
58C42×C43—42no—
59C42×C43C2×Q811yescharacteristic
60C42×C43#4112yes—
61C42×C43#4111yescharacteristic
62(C2×D43)⋊C4—42no—
63C4⋊Dic43—22no—
64#10621877—42no—
65C2×C43⋊C8—42no—
66C2×C43⋊C8—41no—
67C23×C43#12011yescharacteristic
68C22×D43—41no—
69C2×C4×C43—24no—
70C2×C4×C43—42no—
71C2×C4×C43—42no—
72C2×C4×C43—42no—
73C2×C4×C43—42no—
74C2×C4×C43—42no—
75C2×C4×C43—42no—
76C2×C4×C43—42no—
77C2×C4×C43—42no—
78C2×C4×C43—42no—
79C2×C4×C43C22⋊Q812yes—
80C2×C4×C43C22⋊Q811yescharacteristic
81C2×C4×C43#12412yes—
82C2×C4×C43#12411yescharacteristic
83C2×C4×C43#13512yes—
84C2×C4×C43AGL(1,ℤ/8)12yes—
85C22⋊D43—82no—
86C2×Dic43—41no—
87D172—42no—
88D172—82no—
89C4×D43—81no—
90C4×D43—81no—
91Dic86—42no—
92C43⋊C8—82no—
93C43⋊C8—81no—
94#10372—431nomaximal, Sylow
95C22×C43—22no—
96C22×C43#39311yescharacteristic
97C22×C43#44912yes—
98C2×D43—81no—
99C2×D43—82no—
100C4×C43—22no—
101C4×C43—22no—
102C4×C43—44no—
103C4×C43—82no—
104C4×C43—82no—
105C4×C43#47812yes—
106C4×C43#48811yescharacteristic
107C4×C43#49011yescharacteristic
108Dic43—81no—
109#2402D4311yescharacteristic, complemented
110#1963—431no—
111#1502—432no—
112#1303—432no—
113#1274—431no—
114C2×C43—22no—
115C2×C43#202511yescharacteristic
116C2×C43#203112yes—
117D43—161no—
118#532—431no—
119#431—432no—
120#423—431no—
121C2×#104—862no—
122#400—22no—
123#398—22no—
124C4×C4⋊C4—22no—
125C4×C4⋊C4C2×D4312yes—
126#376C2×D4311yescharacteristic
127#327—862no—
128#327—862no—
129C43#1037211yescharacteristic, complemented, Sylow
130C2×#41—861no—
131C2×M16—861no—
132C4⋊Q8—431no—
133#127—431no—
134#124—861no—
135#121—862no—
136C4×D4—862no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C42—22no—
141C2×C42C22⋊D4312yes—
142C2×C42C22×D4311yescharacteristic
143C4⋊C8—862no—
144C4⋊C8—862no—
145#104—1724no—
146C22⋊C8—862no—
147C4×C8—862no—
148#95—22no—
149#95—22no—
150#95—22no—
151#95C22⋊D4312yes—
152#95C22⋊D4312yes—
153#41—1722no—
154#41—1722no—
155C2×Q8—861no—
156C2×D4—862no—
157C2×D4—861no—
158C2×D4—1721no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—1721no—
163C22×C4C2×C22⋊D4312yes—
164C22×C4C2×C22⋊D4311yescharacteristic
165M16—1722no—
166C2×C8—1722no—
167C2×C8—1721no—
168C4⋊C4—44no—
169C4⋊C4—44no—
170C4⋊C4—44no—
171C4⋊C4—862no—
172C22⋊C4—1722no—
173C42—22no—
174C42—22no—
175C42—42no—
176C42—42no—
177C42Q8×D4311yescharacteristic
178C42#1062190211yescharacteristic
179C42#1062190212yes—
180C23—1721no—
181C23#1306329411yescharacteristic
182Q8—1722no—
183D4—3442no—
184D4—3442no—
185D4—1722no—
186C2×C4—24no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—3441no—
197C2×C4—3441no—
198C2×C4—1721no—
199C2×C4#1306330112yes—
200C2×C4#1306330111yescharacteristic
201C2×C4#1306331412yes—
202C2×C4#1306331411yescharacteristic
203C2×C4#1306334512yes—
204C2×C4#1306335012yes—
205C8—3442no—
206C8—3441no—
207C22—22no—
208C22—3442no—
209C22—3441no—
210C22#1458281011yescharacteristic
211C22#1458304412yes—
212C4—22no—
213C4—22no—
214C4—44no—
215C4—82no—
216C4—82no—
217C4—3441no—
218C4#1458319612yes—
219C4#1458325611yescharacteristic
220C4#1458326511yescharacteristic
221C2—22no—
222C2—6881no—
223C2#1913573811yescharacteristic
224C2#1913576412yes—
subgroupG/H
centerC2×C4#13063314
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2402C2
socleC22×C43#393
prime radical#14583449C22
hypercenter#2402D43
hypocenterC43#10372
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2402

Complements

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

NH ≅ G/Ntype
3. #19132498C2semidirect
4. #19132424C2semidirect
5. C43×#2402C2semidirect
109. #2402D43semidirect
129. C43#10372semidirect

Maximal subgroups

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

subgroupindex
#191354272
#191330892
#191324982
#191324242
C43×#24022
#1037243