Finite Group Databasebeta

← D43×#2842 #25303006

Subgroups — D43×#2842 #25303006

Order 11008.

3294 conjugacy classes of subgroups; only the 579 normal subgroups are shown.

normal subgroups only

This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 579 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#19142860C214yesmaximal, complemented
2#19142859C213yesmaximal, complemented
3#19142858C218yesmaximal, complemented
4#399×D43C214yesmaximal, complemented
5#396×D43C218yesmaximal, complemented
6#379×D43C213yesmaximal
7C43×#2842C211yesmaximal, characteristic, complemented
8C25×D43C2211yescharacteristic
9C2×C4⋊C4×D43C22112yescomplemented
10C2×C22⋊C4×D43C22112yes—
11C2×C22⋊C4×D43C2216yes—
12#14582836C2214yescomplemented
13#14582835C22112yescomplemented
14#14582834C22112yescomplemented
15#14582823C2218yescomplemented
16#14582822C22124yescomplemented
17#14582821C22124yescomplemented
18#14582755C2213yes—
19#14582754C22112yes—
20#14582754C2216yes—
21#95×D43C2214yescomplemented
22C43×#399C2214yescomplemented
23C43×#396C2218yescomplemented
24C43×#379C2213yes—
25C24×D43—412no—
26C24×D43Q818yes—
27C24×D43C2312yes—
28C24×D43C2311yescharacteristic
29C24×D43C2312yes—
30C24×D43C2311yescharacteristic
31C22×C4×D43C23112yes—
32C2×C4⋊Dic43C23112yescomplemented
33C2×Dic43⋊C4C23124yescomplemented
34C4⋊C4×D43—424no—
35C2×C22⋊Dic43C23112yes—
36C2×C22⋊Dic43C2316yes—
37C2×(C2×D43)⋊C4C23124yes—
38C2×(C2×D43)⋊C4C23112yes—
39C22⋊C4×D43—424no—
40C22⋊C4×D43—412no—
41C43⋊#95C23112yescomplemented
42C25×C43C2311yescharacteristic
43C2×C4⋊C4×C43C23112yescomplemented
44C2×C22⋊C4×C43C23112yes—
45C2×C22⋊C4×C43C2316yes—
46#95×C43C2314yescomplemented
47C24×C43—46no—
48C24×C43C2×Q814yes—
49C24×C43C2412yes—
50C24×C43C2411yescharacteristic
51C23×D43—224no—
52C23×D43—212no—
53C23×D43—448no—
54C23×D43—412no—
55C23×D43—46no—
56C23×D43—464no—
57C23×D43C2×Q818yes—
58C23×D43C2×Q814yes—
59C23×D43C2×Q818yes—
60C23×D43C2×Q814yes—
61C23×D43C2412yes—
62C23×D43C2411yescharacteristic
63C23×D43C2411yescharacteristic
64C22×C4×C43C24112yes—
65C22×Dic43C24112yes—
66C2×C4×D43—224no—
67C2×C4×D43—248no—
68C4⋊C4×C43—412no—
69C22⋊C4×C43—412no—
70C22⋊C4×C43—46no—
71C22⋊Dic43—46no—
72C22⋊Dic43—412no—
73(C2×D43)⋊C4—412no—
74(C2×D43)⋊C4—424no—
75C4⋊Dic43—412no—
76Dic43⋊C4—424no—
77C23×C43—26no—
78C23×C43—212no—
79C23×C43—412no—
80C23×C43—416no—
81C23×C43C22×Q814yes—
82C23×C43C22×Q812yes—
83C23×C43C2511yescharacteristic
84C22×D43—26no—
85C22×D43—212no—
86C22×D43—248no—
87C22×D43—224no—
88C22×D43—424no—
89C22×D43—412no—
90C22×D43—432no—
91C22×D43—416no—
92C22×D43—4128no—
93C22×D43—432no—
94C22×D43—416no—
95C22×D43C22×Q814yes—
96C22×D43C22×Q812yes—
97C22×D43C22×Q812yes—
98C22×D43H(5,𝔽2)112yes—
99C2×C4×C43—224no—
100C2×C4×C43—212no—
101C2×Dic43—212no—
102C2×Dic43—224no—
103C4×D43—448no—
104C2×#2842—431nomaximal, Sylow
105C22×C43—26no—
106C22×C43—212no—
107C22×C43—416no—
108C22×C43—44no—
109C22×C43—48no—
110C22×C43C23×Q811yescharacteristic
111C22×C43C2×H(5,𝔽2)16yes—
112C2×D43—26no—
113C2×D43—212no—
114C2×D43—432no—
115C2×D43—416no—
116C2×D43—44no—
117C2×D43—48no—
118C2×D43—432no—
119C2×D43—416no—
120C2×D43#543112yes—
121C2×D43#560116yes—
122C4×C43—412no—
123Dic43—412no—
124#2842—434no—
125#2842—438no—
126#2842—433no—
127#2842D4311yescharacteristic, direct product factor
128C2×#399—434no—
129C2×#396—438no—
130C2×#379—433no—
131C2×C43—42no—
132C2×C43—44no—
133C2×C43C2×#54313yes—
134C2×C43C2×#56014yes—
135D43—42no—
136D43—44no—
137D43#284218yesdirect product factor
138C26—431no—
139C22×C4⋊C4—4312no—
140C22×C22⋊C4—4312no—
141C22×C22⋊C4—436no—
142#399—4312no—
143#399—4312no—
144#399—434no—
145#399C2×D4314yescomplemented
146#396—4324no—
147#396—4324no—
148#396—438no—
149#396C2×D4318yescomplemented
150#379—433no—
151#379—4312no—
152#379—436no—
153#379C2×D4313yes—
154C2×#95—434no—
155C43C2×#284211yescharacteristic, complemented, Sylow
156C25—432no—
157C25—431no—
158C25—438no—
159C25—431no—
160C25—432no—
161C25—17212no—
162C25C22×D4311yescharacteristic
163C23×C4—4312no—
164C2×C4⋊C4—4324no—
165C2×C4⋊C4—4312no—
166C2×C4⋊C4—17224no—
167C2×C4⋊C4C22×D43112yescomplemented
168C2×C22⋊C4—4312no—
169C2×C22⋊C4—436no—
170C2×C22⋊C4—4324no—
171C2×C22⋊C4—4312no—
172C2×C22⋊C4—17224no—
173C2×C22⋊C4—17212no—
174C2×C22⋊C4C22×D43112yes—
175C2×C22⋊C4C22×D4316yes—
176#95—4312no—
177#95C22×D4314yescomplemented
178C24—46no—
179C24—431no—
180C24—438no—
181C24—434no—
182C24—432no—
183C24—431no—
184C24—434no—
185C24—438no—
186C24—8624no—
187C24—8612no—
188C24—17212no—
189C24—1726no—
190C24—17248no—
191C24—17264no—
192C24Q8×D4314yes—
193C24C23×D4312yes—
194C24C23×D4311yescharacteristic
195C22×C4—4312no—
196C22×C4—8648no—
197C22×C4—8624no—
198C22×C4C23×D43112yes—
199C4⋊C4—412no—
200C4⋊C4—17224no—
201C4⋊C4—17212no—
202C22⋊C4—412no—
203C22⋊C4—46no—
204C22⋊C4—17224no—
205C22⋊C4—17212no—
206C22⋊C4—17212no—
207C22⋊C4—1726no—
208C23—212no—
209C23—26no—
210C23—412no—
211C23—416no—
212C23—432no—
213C23—4312no—
214C23—434no—
215C23—432no—
216C23—8648no—
217C23—8624no—
218C23—8612no—
219C23—866no—
220C23—17224no—
221C23—17212no—
222C23—17232no—
223C23—17216no—
224C23—172128no—
225C23—17232no—
226C23—17216no—
227C23C2×Q8×D4314yes—
228C23C2×Q8×D4312yes—
229C23C24×D4311yescharacteristic
230C2×C4—224no—
231C2×C4—212no—
232C2×C4—8612no—
233C2×C4—8624no—
234C2×C4—17248no—
235C22—212no—
236C22—26no—
237C22—416no—
238C22—48no—
239C22—44no—
240C22—4316no—
241C22—4312no—
242C22—8612no—
243C22—866no—
244C22—17232no—
245C22—17216no—
246C22—17232no—
247C22—17216no—
248C22—1728no—
249C22—1724no—
250C22C22×Q8×D4311yescharacteristic
251C22H(5,𝔽2)×D4316yes—
252C4—412no—
253C4—17212no—
254C2—44no—
255C2—42no—
256C2—438no—
257C2—1724no—
258C2—1722no—
259C2#543×D4313yes—
260C2#560×D4314yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2842C2
prime radicalC25×D43C22
hypercenter#2842D43
hypocenterC43C2×#2842
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2842

Complements

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

NH ≅ G/Ntype
1. #19142860C2semidirect
2. #19142859C2semidirect
3. #19142858C2semidirect
4. #399×D43C2semidirect
5. #396×D43C2semidirect
7. C43×#2842C2semidirect
9. C2×C4⋊C4×D43C22semidirect
12. #14582836C22semidirect
13. #14582835C22semidirect
14. #14582834C22semidirect
15. #14582823C22semidirect
16. #14582822C22semidirect
17. #14582821C22semidirect
21. #95×D43C22semidirect
22. C43×#399C22semidirect
23. C43×#396C22semidirect
32. C2×C4⋊Dic43C23semidirect
33. C2×Dic43⋊C4C23semidirect
41. C43⋊#95C23semidirect
43. C2×C4⋊C4×C43C23semidirect
46. #95×C43C23semidirect
127. #2842D43direct (N × H)
137. D43#2842direct (N × H)
145. #399C2×D43semidirect
149. #396C2×D43semidirect
155. C43C2×#2842semidirect
167. C2×C4⋊C4C22×D43semidirect
177. #95C22×D43semidirect

Maximal subgroups

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

subgroupindex
#191428602
#191428592
#191428582
#399×D432
#396×D432
#379×D432
C43×#28422
C2×#284243