Finite Group Databasebeta

← D43×#2091 #25126342

Subgroups — D43×#2091 #25126342

Order 11008.

1102 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 207 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#430×D43C213yesmaximal, complemented
2#407×D43C213yesmaximal
3#19136112C211yesmaximal, characteristic, complemented
4#19136111C213yesmaximal, complemented
5#19136110C213yesmaximal, complemented
6#338×D43C211yesmaximal, characteristic, complemented
7C43×#2091C211yesmaximal, characteristic, complemented
8C23×C4×D43C2211yescharacteristic
9C2×M16×D43C2213yes—
10C2×M16×D43C2213yes—
11#14582948C2213yescomplemented
12#14582947C2216yescomplemented
13#14582946—26no—
14#108×D43—26no—
15#14582863C2213yes—
16#14582862C2213yes—
17#14582862C2213yes—
18#14582861—26no—
19C22⋊C8×D43—26no—
20C43⋊#338C2213yescomplemented
21C43×#430C2213yescomplemented
22C43×#407C2213yes—
23C43×#338C2211yescharacteristic, complemented
24C24×D43Q811yescharacteristic
25C23×Dic43Q811yescharacteristic
26C22×C4×D43—23no—
27C22×C4×D43—23no—
28C22×C4×D43—23no—
29C22×C4×D43—23no—
30C22×C4×D43Q811yescharacteristic
31C22×C4×D43Q811yescharacteristic
32C22×C4×D43C2311yescharacteristic
33C22×C4×D43C2311yescharacteristic
34C2×#10621877C2313yes—
35C2×#10621877C2313yes—
36C2×#10621872—23no—
37C2×#10621872D416yes—
38M16×D43—26no—
39M16×D43—26no—
40M16×D43—26no—
41M16×D43—26no—
42C2×C8×D43—23no—
43C2×C8×D43D416yes—
44#13063261—26no—
45#13063260—212no—
46C22⋊(C43⋊C8)—26no—
47(C2×D43)⋊C8—26no—
48(C2×D43)⋊C8—26no—
49C23×C4×C43C2311yescharacteristic
50C2×M16×C43C2313yes—
51C2×M16×C43C2313yes—
52#108×C43—26no—
53C22⋊C8×C43—26no—
54C24×C43C2×Q811yescharacteristic
55C23×D43—23no—
56C23×D43—23no—
57C23×D43—44no—
58C23×D43C2×Q811yescharacteristic
59C23×D43C2×Q811yescharacteristic
60C22×C4×C43—23no—
61C22×C4×C43—23no—
62C22×C4×C43C2×Q811yescharacteristic
63C22×C4×C43C2411yescharacteristic
64C22×Dic43—23no—
65C22×Dic43—23no—
66C22×Dic43C2×Q811yescharacteristic
67C22×Dic43C2×Q811yescharacteristic
68C2×C4×D43—23no—
69C2×C4×D43—23no—
70C2×C4×D43—23no—
71C2×C4×D43—23no—
72C2×C4×D43—23no—
73C2×C4×D43—23no—
74C2×C4×D43—43no—
75C2×C4×D43—43no—
76C2×C4×D43—46no—
77C2×C4×D43—41no—
78C2×C4×D43—43no—
79C2×C4×D43C2×D413yes—
80C2×C4×D43C2×D413yes—
81C2×C4×D43#4113yes—
82C2×C4×D43#4113yes—
83M16×C43—26no—
84M16×C43—26no—
85C2×C8×C43—23no—
86C2×C8×C43C2×D416yes—
87#10621877—26no—
88#10621877—26no—
89C2×C43⋊C8—23no—
90C2×C43⋊C8C2×D416yes—
91#10621872—212no—
92#10621872—46no—
93C8×D43—26no—
94C8×D43—26no—
95C8×D43—43no—
96C8×D43—43no—
97C23×C43—23no—
98C23×C43—42no—
99C23×C43C22×Q811yescharacteristic
100C22×D43—212no—
101C22×D43—23no—
102C22×D43—42no—
103C22×D43—42no—
104C22×D43—46no—
105C22×D43—46no—
106C22×D43—46no—
107C22×D43—43no—
108C22×D43—41no—
109C22×D43C22⋊Q813yes—
110C22×D43C22⋊Q813yes—
111C2×C4×C43—23no—
112C2×C4×C43—43no—
113C2×C4×C43—41no—
114C2×C4×C43C22×D413yes—
115C2×C4×C43C2×#4113yes—
116C2×Dic43—23no—
117C2×Dic43—41no—
118C2×Dic43—43no—
119C2×Dic43C22⋊Q813yes—
120C2×Dic43C22⋊Q813yes—
121C4×D43—43no—
122C4×D43—41no—
123C4×D43—43no—
124C4×D43—41no—
125C4×D43—41no—
126C4×D43—43no—
127C4×D43#12313yes—
128C4×D43#12313yes—
129C4×D43#12316yes—
130C4×D43#12711yescharacteristic
131C4×D43#12713yes—
132C8×C43—26no—
133C8×C43—43no—
134C43⋊C8—26no—
135C43⋊C8—43no—
136C2×#2091—431nomaximal, Sylow
137C22×C43—26no—
138C22×C43—41no—
139C22×C43—43no—
140C22×C43—41no—
141C22×C43C2×C22⋊Q813yes—
142C2×D43—26no—
143C2×D43—26no—
144C2×D43—43no—
145C2×D43—412no—
146C2×D43—43no—
147C2×D43—41no—
148C2×D43—44no—
149C2×D43#39913yes—
150C2×D43#39911yescharacteristic
151C4×C43—41no—
152C4×C43C2×#12313yes—
153C4×C43C2×#12711yescharacteristic
154Dic43—41no—
155Dic43#39911yescharacteristic
156Dic43#39913yes—
157C2×#430—433no—
158C2×#407—433no—
159#2091—433no—
160#2091—433no—
161#2091—431no—
162#2091D4311yescharacteristic, direct product factor
163C2×#338—431no—
164C2×C43—23no—
165C2×C43—42no—
166C2×C43C2×#39911yescharacteristic
167D43—23no—
168D43—42no—
169D43#209112yesdirect product factor
170C24×C4—431no—
171C22×M16—433no—
172C22×M16—433no—
173#430—436no—
174#430—433no—
175#430—866no—
176#430C2×D4313yescomplemented
177C2×#108—866no—
178#407—433no—
179#407—433no—
180#407—433no—
181#407—866no—
182#407C2×D4313yes—
183C2×C22⋊C8—866no—
184#338—433no—
185#338C2×D4311yescharacteristic, complemented
186C43C2×#209111yescharacteristic, complemented, Sylow
187C25—431no—
188C23×C4—431no—
189C23×C4—431no—
190C23×C4—431no—
191C23×C4—431no—
192C23×C4—431no—
193C23×C4—863no—
194C23×C4—863no—
195C23×C4—863no—
196C23×C4—863no—
197C23×C4C22×D4311yescharacteristic
198C2×M16—433no—
199C2×M16—436no—
200C2×M16—433no—
201C2×M16—863no—
202C2×M16—866no—
203C2×M16—866no—
204C2×M16—866no—
205C2×M16—866no—
206C2×M16C22×D4313yes—
207C2×M16C22×D4313yes—
208C22×C8—436no—
209C22×C8—863no—
210#108—26no—
211#108—8612no—
212#108—866no—
213C22⋊C8—26no—
214C22⋊C8—866no—
215C22⋊C8—866no—
216C22⋊C8—866no—
217C24—431no—
218C24—431no—
219C24—863no—
220C24—863no—
221C24—1724no—
222C24Q8×D4311yescharacteristic
223C22×C4—23no—
224C22×C4—23no—
225C22×C4—431no—
226C22×C4—433no—
227C22×C4—433no—
228C22×C4—433no—
229C22×C4—433no—
230C22×C4—431no—
231C22×C4—863no—
232C22×C4—863no—
233C22×C4—863no—
234C22×C4—863no—
235C22×C4—863no—
236C22×C4—863no—
237C22×C4—863no—
238C22×C4—863no—
239C22×C4—1723no—
240C22×C4—1723no—
241C22×C4—1726no—
242C22×C4—1721no—
243C22×C4—1723no—
244C22×C4Q8×D4311yescharacteristic
245C22×C4C23×D4311yescharacteristic
246M16—26no—
247M16—26no—
248M16—8612no—
249M16—866no—
250M16—866no—
251M16—1726no—
252C2×C8—23no—
253C2×C8—436no—
254C2×C8—866no—
255C2×C8—866no—
256C2×C8—863no—
257C2×C8—1723no—
258C2×C8—1723no—
259C2×C8D4×D4316yes—
260C23—23no—
261C23—42no—
262C23—433no—
263C23—433no—
264C23—8612no—
265C23—863no—
266C23—1726no—
267C23—1721no—
268C23—1723no—
269C23—1722no—
270C23—1722no—
271C23—1726no—
272C23—1726no—
273C23C2×Q8×D4311yescharacteristic
274C2×C4—23no—
275C2×C4—43no—
276C2×C4—41no—
277C2×C4—433no—
278C2×C4—433no—
279C2×C4—433no—
280C2×C4—433no—
281C2×C4—436no—
282C2×C4—431no—
283C2×C4—433no—
284C2×C4—863no—
285C2×C4—1721no—
286C2×C4—1723no—
287C2×C4—1721no—
288C2×C4—1723no—
289C2×C4—1721no—
290C2×C4—1723no—
291C2×C4—1723no—
292C2×C4—1721no—
293C2×C4C2×D4×D4313yes—
294C2×C4#41×D4313yes—
295C8—26no—
296C8—43no—
297C8—866no—
298C8—1723no—
299C22—26no—
300C22—41no—
301C22—43no—
302C22—41no—
303C22—431no—
304C22—433no—
305C22—866no—
306C22—866no—
307C22—1723no—
308C22—1723no—
309C22—1724no—
310C22—17212no—
311C22—1721no—
312C22C22⋊Q8×D4313yes—
313C4—41no—
314C4—431no—
315C4—433no—
316C4—1721no—
317C4#123×D4313yes—
318C4#127×D4311yescharacteristic
319C2—23no—
320C2—42no—
321C2—432no—
322C2—863no—
323C2—1722no—
324C2#399×D4311yescharacteristic
subgroupG/H
centerC4#127×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2091C2
socleC2×C43C2×#399
prime radicalC24×D43Q8
hypercenter#2091D43
hypocenterC43C2×#2091
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #2091

Complements

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

NH ≅ G/Ntype
1. #430×D43C2semidirect
3. #19136112C2semidirect
4. #19136111C2semidirect
5. #19136110C2semidirect
6. #338×D43C2semidirect
7. C43×#2091C2semidirect
11. #14582948C22semidirect
12. #14582947C22semidirect
20. C43⋊#338C22semidirect
21. C43×#430C22semidirect
23. C43×#338C22semidirect
162. #2091D43direct (N × H)
169. D43#2091direct (N × H)
176. #430C2×D43semidirect
185. #338C2×D43semidirect
186. C43C2×#2091semidirect

Maximal subgroups

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

subgroupindex
#430×D432
#407×D432
#191361122
#191361112
#191361102
#338×D432
C43×#20912
C2×#209143