Finite Group Databasebeta

← C43×#20302 #24940319

Subgroups — C43×#20302 #24940319

Order 11008.

690 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 198 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
1C43×#3325C214yesmaximal, complemented
2C43×#1709C211yesmaximal, characteristic, complemented
3C43×#1697C214yesmaximal, complemented
4C43×#1634C212yesmaximal, complemented
5C43×#1619C212yesmaximal, complemented
6C43×#1589C212yesmaximal, complemented
7C43×#555C2212yes—
8D42×C43C2212yescomplemented
9C43×#494C2211yescharacteristic, complemented
10C43×#493C2211yescharacteristic
11C43×#486C2214yescomplemented
12C43×#482—24no—
13C43×#476C2214yescomplemented
14C43×#469—24no—
15C43×#459C2214yes—
16C43×#447—24no—
17C4×D8×C43C2212yes—
18C43×#436C2214yescomplemented
19C43×#418—24no—
20C43×#335C2212yescomplemented
21C43×#333C2212yescomplemented
22C43×#331C2212yescomplemented
23C43×D4⋊C8C2214yescomplemented
24C82×C43C2211yescharacteristic, complemented
25C22×D4×C43—24no—
26C2×Q16×C43—41no—
27C2×D8×C43—24no—
28C2×D8×C43—41no—
29C2×D8×C43D412yes—
30C2×M16×C43—24no—
31C4⋊Q8×C43C2312yes—
32#127×C43C2312yes—
33#124×C43—42no—
34#121×C43—24no—
35#121×C43—24no—
36#120×C43—42no—
37C4×D4×C43C2314yes—
38#117×C43—24no—
39#107×C43D412yes—
40#106×C43—24no—
41C4⋊C8×C43C2314yes—
42#102×C43—24no—
43#102×C43—24no—
44#102×C43—24no—
45#102×C43—24no—
46#102×C43D414yes—
47C22⋊C8×C43—24no—
48C4×C8×C43C2311yescharacteristic
49C4×C8×C43C2312yes—
50C24×C43—42no—
51C2×Q8×C43—22no—
52C2×D4×C43—24no—
53C2×D4×C43—22no—
54C2×D4×C43—42no—
55C2×D4×C43—44no—
56C2×D4×C43—48no—
57C2×D4×C43—84no—
58C2×D4×C43C2×D414yes—
59C22×C4×C43—24no—
60Q16×C43—82no—
61D8×C43—42no—
62D8×C43—82no—
63D8×C43—84no—
64M16×C43—84no—
65C2×C8×C43—21no—
66C2×C8×C43—24no—
67C2×C8×C43C2×D412yes—
68C2×C8×C43C2×D412yes—
69C4⋊C4×C43—24no—
70C4⋊C4×C43C2×D414yes—
71C22⋊C4×C43—24no—
72C22⋊C4×C43—44no—
73C22⋊C4×C43—42no—
74C42×C43—42no—
75C42×C43C2411yescharacteristic
76C23×C43—24no—
77C23×C43—42no—
78C23×C43—88no—
79C23×C43—162no—
80Q8×C43—82no—
81D4×C43—24no—
82D4×C43—24no—
83D4×C43—44no—
84D4×C43—44no—
85D4×C43—82no—
86D4×C43—88no—
87D4×C43—162no—
88C2×C4×C43—24no—
89C2×C4×C43—44no—
90C2×C4×C43—44no—
91C2×C4×C43—42no—
92C2×C4×C43C22×D412yes—
93C2×C4×C43H(5,𝔽2)11yescharacteristic
94C8×C43—22no—
95C8×C43—22no—
96C8×C43—22no—
97C8×C43—44no—
98#20302C4311yesmaximal, characteristic, direct product factor, Sylow
99C22×C43—44no—
100C22×C43—44no—
101C22×C43—44no—
102C22×C43—84no—
103C22×C43—82no—
104C22×C43—168no—
105C22×C43D4211yescharacteristic
106C4×C43—21no—
107C4×C43—44no—
108C4×C43—82no—
109C4×C43#57512yes—
110C4×C43#57612yes—
111#3325C2×C4314yescomplemented
112#1709C2×C4311yescharacteristic, complemented
113#1697C2×C4314yescomplemented
114#1634C2×C4312yescomplemented
115#1619C2×C4312yescomplemented
116#1589C2×C4312yescomplemented
117C2×C43—84no—
118C2×C43—162no—
119C2×C43#327312yes—
120C2×C43#329211yescharacteristic
121#555C22×C4312yes—
122D42C22×C4312yescomplemented
123#494C22×C4311yescharacteristic, complemented
124#493C22×C4311yescharacteristic
125#486C22×C4314yescomplemented
126#482—24no—
127#476C22×C4314yescomplemented
128#469—24no—
129#459C22×C4314yes—
130#447—24no—
131C4×D8C22×C4312yes—
132#436C22×C4314yescomplemented
133#418—24no—
134#335C22×C4312yescomplemented
135#333C22×C4312yescomplemented
136#331C22×C4312yescomplemented
137D4⋊C8C22×C4314yescomplemented
138C82C22×C4311yescharacteristic, complemented
139C43#2030211yescharacteristic, direct product factor, Sylow
140C22×D4—24no—
141C2×Q16—41no—
142C2×D8—24no—
143C2×D8—41no—
144C2×D8D4×C4312yes—
145C2×M16—24no—
146C4⋊Q8C23×C4312yes—
147#127C23×C4312yes—
148#124—42no—
149#121—24no—
150#121—24no—
151#120—42no—
152C4×D4C23×C4314yes—
153#117—24no—
154#107D4×C4312yes—
155#106—24no—
156C4⋊C8C23×C4314yes—
157#102—24no—
158#102—24no—
159#102—24no—
160#102—24no—
161#102D4×C4314yes—
162C22⋊C8—24no—
163C4×C8C23×C4311yescharacteristic
164C4×C8C23×C4312yes—
165C24—42no—
166C2×Q8—22no—
167C2×D4—24no—
168C2×D4—22no—
169C2×D4—44no—
170C2×D4—48no—
171C2×D4—42no—
172C2×D4—84no—
173C2×D4C2×D4×C4314yes—
174C22×C4—24no—
175Q16—82no—
176D8—42no—
177D8—82no—
178D8—84no—
179M16—84no—
180C2×C8—21no—
181C2×C8—24no—
182C2×C8C2×D4×C4312yes—
183C2×C8C2×D4×C4312yes—
184C4⋊C4—24no—
185C4⋊C4C2×D4×C4314yes—
186C22⋊C4—24no—
187C22⋊C4—42no—
188C22⋊C4—44no—
189C42—42no—
190C42C24×C4311yescharacteristic
191C23—24no—
192C23—42no—
193C23—88no—
194C23—162no—
195Q8—82no—
196D4—24no—
197D4—24no—
198D4—44no—
199D4—44no—
200D4—82no—
201D4—88no—
202D4—162no—
203C2×C4—24no—
204C2×C4—44no—
205C2×C4—44no—
206C2×C4—42no—
207C2×C4C22×D4×C4312yes—
208C2×C4H(5,𝔽2)×C4311yescharacteristic
209C8—22no—
210C8—22no—
211C8—22no—
212C8—44no—
213C22—44no—
214C22—44no—
215C22—44no—
216C22—84no—
217C22—82no—
218C22—168no—
219C22D42×C4311yescharacteristic
220C4—21no—
221C4—44no—
222C4—82no—
223C4C43×#57512yes—
224C4C43×#57612yes—
225C2—84no—
226C2—162no—
227C2C43×#327312yes—
228C2C43×#329211yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3325C2semidirect
2. C43×#1709C2semidirect
3. C43×#1697C2semidirect
4. C43×#1634C2semidirect
5. C43×#1619C2semidirect
6. C43×#1589C2semidirect
8. D42×C43C22semidirect
9. C43×#494C22semidirect
11. C43×#486C22semidirect
13. C43×#476C22semidirect
18. C43×#436C22semidirect
20. C43×#335C22semidirect
21. C43×#333C22semidirect
22. C43×#331C22semidirect
23. C43×D4⋊C8C22semidirect
24. C82×C43C22semidirect
98. #20302C43direct (N × H)
111. #3325C2×C43semidirect
112. #1709C2×C43semidirect
113. #1697C2×C43semidirect
114. #1634C2×C43semidirect
115. #1619C2×C43semidirect
116. #1589C2×C43semidirect
122. D42C22×C43semidirect
123. #494C22×C43semidirect
125. #486C22×C43semidirect
127. #476C22×C43semidirect
132. #436C22×C43semidirect
134. #335C22×C43semidirect
135. #333C22×C43semidirect
136. #331C22×C43semidirect
137. D4⋊C8C22×C43semidirect
138. C82C22×C43semidirect
139. C43#20302direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33252
C43×#17092
C43×#16972
C43×#16342
C43×#16192
C43×#15892
#2030243