Finite Group Databasebeta

← D43×#1355 #25007766

Subgroups — D43×#1355 #25007766

Order 11008.

366 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 71 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#490×D43C211yesmaximal, characteristic
2#347×D43C212yesmaximal, complemented
3#19132628C211yesmaximal, characteristic, complemented
4#19132627C212yesmaximal, complemented
5C43×#1355C211yesmaximal, characteristic, complemented
6#127×D43C411yescharacteristic
7#125×D43C411yescharacteristic
8M32×D43—22no—
9#14583265C411yescharacteristic
10#14583264C2211yescharacteristic
11#14583263C411yescharacteristic
12#14583262—22no—
13#102×D43—22no—
14#97×D43C2211yescharacteristic
15#14582677C2212yescomplemented
16#14582676—22no—
17C43×#490C2211yescharacteristic
18C43×#347C2212yescomplemented
19C2×D4×D43—21no—
20C2×D4×D43—41no—
21C2×C8×D43D412yes—
22#13063322C2×C411yescharacteristic
23#13063321—21no—
24#13063321—41no—
25#13063317C2×C411yescharacteristic
26#13063316—21no—
27#13063315—41no—
28C4⋊C4×D43—21no—
29C4⋊C4×D43—41no—
30C42×D43C2×C411yescharacteristic
31#13063265—22no—
32#13063264—24no—
33C16×D43—24no—
34#13063247—22no—
35#13063246—22no—
36#13063245—22no—
37#13063236C2×C411yescharacteristic
38#13063235D412yes—
39#127×C43C2×C411yescharacteristic
40#125×C43C2×C411yescharacteristic
41M32×C43—22no—
42#102×C43—22no—
43#97×C43C2311yescharacteristic
44C23×D43—41no—
45C2×D4×C43—21no—
46C2×D4×C43—41no—
47C2×C22⋊D43—42no—
48C2×C22⋊D43—41no—
49D4×D43—42no—
50D4×D43—42no—
51D4×D43—84no—
52C2×D172—21no—
53C2×D172—41no—
54C2×C4×D43—21no—
55C2×C4×D43—41no—
56C2×C4×D43C22⋊C411yescharacteristic
57C2×C8×C43C2×D412yes—
58C4⋊C4×C43—21no—
59C4⋊C4×C43—41no—
60C42×C43C22×C411yescharacteristic
61C4⋊Dic43—21no—
62C4⋊Dic43—41no—
63Dic43⋊C4—41no—
64Dic43⋊C4—41no—
65Dic43⋊C4—41no—
66C4×Dic43—21no—
67C4×Dic43C22⋊C411yescharacteristic
68C2×C43⋊C8C22⋊C412yes—
69C8×D43—22no—
70C8×D43—22no—
71C16×C43—24no—
72C43⋊C16—24no—
73C23×C43—41no—
74C22×D43—41no—
75C22×D43—84no—
76C22×D43—81no—
77C22×D43—81no—
78C22×D43#10011yescharacteristic
79D4×C43—42no—
80D4×C43—82no—
81C2×C4×C43—21no—
82C2×C4×C43—41no—
83C2×C4×C43C2×C22⋊C411yescharacteristic
84C22⋊D43—84no—
85C22⋊D43—82no—
86C2×Dic43—21no—
87C2×Dic43—41no—
88C2×Dic43#10011yescharacteristic
89D172—42no—
90D172—82no—
91C4×D43—42no—
92C4×D43—82no—
93C4×D43#10412yes—
94C4×D43#10412yes—
95C8×C43—22no—
96C43⋊C8—22no—
97C2×#1355—431nomaximal, Sylow
98C22×C43—82no—
99C22×C43—81no—
100C22×C43C2×#10011yescharacteristic
101C2×D43—22no—
102C2×D43—82no—
103C2×D43—81no—
104C2×D43—162no—
105C2×D43—162no—
106C2×D43#32911yescharacteristic
107C2×D43#32911yescharacteristic
108C4×C43—41no—
109C4×C43—81no—
110C4×C43C2×#10412yes—
111Dic43—41no—
112Dic43—81no—
113Dic43#32912yes—
114C2×#490—431no—
115C2×#347—432no—
116#1355—431no—
117#1355—432no—
118#1355D4311yescharacteristic, direct product factor
119C2×C43—21no—
120C2×C43—161no—
121C2×C43C2×#32911yescharacteristic
122D43—21no—
123D43—161no—
124D43#135512yesdirect product factor
125C2×#127—431no—
126C2×#125—431no—
127C2×M32—862no—
128#490—431no—
129#490—431no—
130#490—431no—
131#490—862no—
132#490C2×D4311yescharacteristic
133C2×#102—862no—
134C2×#97—431no—
135#347—432no—
136#347—862no—
137#347C2×D4312yescomplemented
138C43C2×#135511yescharacteristic, complemented, Sylow
139C22×D4—861no—
140C22×D4—1721no—
141C22×C8—432no—
142#127—431no—
143#127—861no—
144#127—1721no—
145#127C4×D4311yescharacteristic
146#125—431no—
147#125—861no—
148#125—1721no—
149#125C4×D4311yescharacteristic
150C2×C4⋊C4—861no—
151C2×C4⋊C4—1721no—
152C2×C42—431no—
153M32—22no—
154M32—864no—
155M32—862no—
156C2×C16—864no—
157#102—22no—
158#102—862no—
159#102—862no—
160#102—862no—
161#97—432no—
162#97—431no—
163#97C22×D4311yescharacteristic
164C24—1721no—
165C2×D4—21no—
166C2×D4—41no—
167C2×D4—861no—
168C2×D4—3444no—
169C2×D4—1721no—
170C2×D4—1722no—
171C2×D4—1722no—
172C2×D4—1721no—
173C2×D4—1722no—
174C22×C4—431no—
175C22×C4—861no—
176C22×C4—1721no—
177C2×C8—432no—
178C2×C8—862no—
179C2×C8—862no—
180C2×C8D4×D4312yes—
181C4⋊C4—21no—
182C4⋊C4—41no—
183C4⋊C4—861no—
184C4⋊C4—1721no—
185C4⋊C4—1721no—
186C4⋊C4—1721no—
187C4⋊C4—1721no—
188C42—431no—
189C42—861no—
190C42C2×C4×D4311yescharacteristic
191C16—24no—
192C16—864no—
193C23—41no—
194C23—431no—
195C23—3441no—
196C23—3441no—
197C23—3444no—
198C23—1721no—
199D4—42no—
200D4—82no—
201D4—3442no—
202D4—3442no—
203D4—3444no—
204D4—1722no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—431no—
208C2×C4—432no—
209C2×C4—432no—
210C2×C4—861no—
211C2×C4—3442no—
212C2×C4—1722no—
213C2×C4—1721no—
214C2×C4C22⋊C4×D4311yescharacteristic
215C8—22no—
216C8—862no—
217C22—82no—
218C22—81no—
219C22—431no—
220C22—431no—
221C22—862no—
222C22—3442no—
223C22—3441no—
224C22—6882no—
225C22—6882no—
226C22#100×D4311yescharacteristic
227C4—41no—
228C4—81no—
229C4—432no—
230C4—3441no—
231C4—1721no—
232C4#104×D4312yes—
233C2—21no—
234C2—161no—
235C2—432no—
236C2—861no—
237C2—6881no—
238C2#329×D4311yescharacteristic
subgroupG/H
centerC2#329×D43
commutatorC42×C43C22×C4
Frattini#97C22×D43
FittingC43×#1355C2
socleC2×C43C2×#329
prime radical#127×D43C4
cosocle#97×C43C23
hypercenter#1355D43
hypocenterC43C2×#1355
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1355

Complements

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

NH ≅ G/Ntype
2. #347×D43C2semidirect
3. #19132628C2semidirect
4. #19132627C2semidirect
5. C43×#1355C2semidirect
15. #14582677C22semidirect
18. C43×#347C22semidirect
118. #1355D43direct (N × H)
124. D43#1355direct (N × H)
137. #347C2×D43semidirect
138. C43C2×#1355semidirect

Maximal subgroups

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

subgroupindex
#490×D432
#347×D432
#191326282
#191326272
C43×#13552
C2×#135543