Finite Group Databasebeta

← D43×#1831 #25096737

Subgroups — D43×#1831 #25096737

Order 11008.

1246 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C8×D43C212yesmaximal
2C43×D43C211yesmaximal, characteristic
3#19134712C211yesmaximal, characteristic, complemented
4#19134711C212yesmaximal, complemented
5#19134710C214yesmaximal, complemented
6#336×D43C214yesmaximal
7C43×#1831C211yesmaximal, characteristic, complemented
8C22×C8×D43C2214yes—
9C2×C42×D43C412yes—
10C2×C42×D43C411yescharacteristic
11C2×C42×D43C411yescharacteristic
12C2×C42×D43C2212yes—
13C2×C42×D43C2211yescharacteristic
14C2×C4⋊(C43⋊C8)C2212yes—
15C2×Dic43⋊C8C2214yes—
16C4⋊C8×D43—28no—
17C42×Dic43C412yes—
18C42×Dic43C411yescharacteristic
19C42×Dic43C411yescharacteristic
20C42×Dic43C2212yes—
21C42×Dic43C2211yescharacteristic
22#14582654C2214yes—
23#14582653C2218yes—
24C2×C4⋊C8×C43C2212yes—
25C43×C43C2211yescharacteristic
26C43×#336C2214yes—
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43C2×C412yes—
29C22×C4×D43C2×C412yes—
30C22×C4×D43C2×C411yescharacteristic
31C22×C4×D43C2311yescharacteristic
32C22×C43⋊C8C2314yes—
33C2×C8×D43—28no—
34C2×C8×D43—216no—
35C2×C4×Dic43C2×C412yes—
36C2×C4×Dic43C2×C411yescharacteristic
37C2×C4×Dic43C2×C412yes—
38C2×C4×Dic43C2×C412yes—
39C2×C4×Dic43C2×C412yes—
40C2×C4×Dic43C2×C412yes—
41C2×C4×Dic43C2×C412yes—
42C2×C4×Dic43C2×C411yescharacteristic
43C2×C4×Dic43C2×C411yescharacteristic
44C2×C4×Dic43C2×C411yescharacteristic
45C2×C4×Dic43C2×C412yes—
46C2×C4×Dic43C2312yes—
47C2×C4×Dic43C2311yescharacteristic
48C42×D43—28no—
49C42×D43—24no—
50C42×D43—28no—
51C42×D43C818yescomplemented
52C42×D43D414yes—
53C42×D43Q814yes—
54C4⋊(C43⋊C8)—24no—
55Dic43⋊C8—28no—
56C22×C8×C43C2314yes—
57C2×C42×C43C2×C412yes—
58C2×C42×C43C2×C411yescharacteristic
59C2×C42×C43C2×C411yescharacteristic
60C2×C42×C43C2312yes—
61C2×C42×C43C2311yescharacteristic
62C4⋊C8×C43—24no—
63C23×D43C22×C411yescharacteristic
64C22×C4×C43C22×C411yescharacteristic
65C22×C4×C43C22×C412yes—
66C22×C4×C43C22×C412yes—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2411yescharacteristic
69C22×Dic43C22×C411yescharacteristic
70C22×Dic43C22×C412yes—
71C22×Dic43C22×C412yes—
72C22×Dic43C22×C411yescharacteristic
73C22×Dic43C22×C411yescharacteristic
74C2×C4×D43—24no—
75C2×C4×D43—24no—
76C2×C4×D43—24no—
77C2×C4×D43—24no—
78C2×C4×D43—24no—
79C2×C4×D43C4⋊C414yes—
80C2×C4×D43C4⋊C414yes—
81C2×C4×D43C2×C818yes—
82C2×C4×D43C2×C814yes—
83C2×C4×D43M1618yes—
84C2×C4×D43M1614yes—
85C2×C4×D43C2×D412yes—
86C2×C4×D43C2×Q812yes—
87C2×C4×D43#4118yes—
88C2×C8×C43—24no—
89C2×C8×C43—28no—
90C42×C43—24no—
91C42×C43—22no—
92C42×C43—24no—
93C42×C43C2×C814yescomplemented
94C42×C43C2×D412yes—
95C42×C43C2×Q812yes—
96C4×Dic43—24no—
97C4×Dic43—22no—
98C4×Dic43—24no—
99C4×Dic43—24no—
100C4×Dic43—24no—
101C4×Dic43—24no—
102C4×Dic43—24no—
103C4×Dic43—24no—
104C4×Dic43C4⋊C414yes—
105C4×Dic43C4⋊C414yes—
106C4×Dic43C2×C814yescomplemented
107C4×Dic43C2×C818yescomplemented
108C4×Dic43C2×D412yes—
109C4×Dic43C2×Q812yes—
110C2×C43⋊C8—24no—
111C2×C43⋊C8—28no—
112C8×D43—416no—
113C23×C43C23×C411yescharacteristic
114C22×D43C2×C4⋊C412yes—
115C22×D43#11714yes—
116C22×D43C22×C812yes—
117C22×D43C2×M1612yes—
118C22×D43C2×M1614yes—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43C2×C4⋊C412yes—
125C2×C4×C43C2×C4⋊C412yes—
126C2×C4×C43C22×C814yes—
127C2×C4×C43C22×C812yes—
128C2×C4×C43C2×M1614yes—
129C2×C4×C43C2×M1612yes—
130C2×C4×C43C22×D411yescharacteristic
131C2×C4×C43C22×Q811yescharacteristic
132C2×C4×C43C2×#4114yes—
133C2×Dic43—22no—
134C2×Dic43—22no—
135C2×Dic43—22no—
136C2×Dic43—22no—
137C2×Dic43—22no—
138C2×Dic43C2×C4⋊C412yes—
139C2×Dic43C2×C4⋊C412yes—
140C2×Dic43C2×C4⋊C412yes—
141C2×Dic43#11714yes—
142C2×Dic43C22×C814yes—
143C2×Dic43C22×C812yes—
144C2×Dic43C2×M1614yes—
145C2×Dic43C2×M1612yes—
146C4×D43—28no—
147C4×D43—216no—
148C4×D43—216no—
149C4×D43C4⋊C8116yes—
150C4×D43#12418yes—
151C4×D43#12518yes—
152C8×C43—44no—
153C43⋊C8—44no—
154C2×#1831—431nomaximal, Sylow
155C22×C43C22×C4⋊C411yescharacteristic
156C22×C43C2×#11712yes—
157C22×C43C23×C811yescharacteristic
158C22×C43C22×M1611yescharacteristic
159C22×C43C22×M1612yes—
160C2×D43#38214yes—
161C2×D43C2×C4⋊C814yes—
162C2×D43#42314yes—
163C2×D43#43118yes—
164C2×D43#43218yes—
165C4×C43—22no—
166C4×C43—24no—
167C4×C43—24no—
168C4×C43C2×C4⋊C814yes—
169C4×C43C2×#12412yes—
170C4×C43C2×#12512yes—
171Dic43—22no—
172Dic43—24no—
173Dic43—24no—
174Dic43#38214yes—
175Dic43C2×C4⋊C814yes—
176C22×C4⋊C8—432no—
177C2×C43—431no—
178#1831—432no—
179#1831—431no—
180#1831—434no—
181#1831D4311yescharacteristic, direct product factor
182C2×#336—434no—
183C2×C43C2×#38211yescharacteristic
184C2×C43C22×C4⋊C811yescharacteristic
185C2×C43C2×#42311yescharacteristic
186C2×C43C2×#43112yes—
187C2×C43C2×#43212yes—
188D43#183118yesdirect product factor
189C23×C8—434no—
190C22×C42—431no—
191C22×C42—431no—
192C22×C42—432no—
193C22×C42—431no—
194C22×C42—432no—
195C2×C4⋊C8—434no—
196C2×C4⋊C8—432no—
197C2×C4⋊C8—868no—
198C2×C4⋊C8C2×D4312yes—
199C43—432no—
200C43—431no—
201C43—432no—
202C43—431no—
203C43—431no—
204C43C2×D4311yescharacteristic
205#336—438no—
206#336—434no—
207#336C2×D4314yes—
208C43C2×#183111yescharacteristic, complemented, Sylow
209C23×C4—431no—
210C23×C4—431no—
211C23×C4—431no—
212C23×C4—432no—
213C23×C4—432no—
214C22×C8—434no—
215C22×C8—8616no—
216C22×C8—868no—
217C22×C8C22×D4314yes—
218C2×C42—431no—
219C2×C42—431no—
220C2×C42—432no—
221C2×C42—431no—
222C2×C42—431no—
223C2×C42—438no—
224C2×C42—434no—
225C2×C42—434no—
226C2×C42—432no—
227C2×C42—432no—
228C2×C42—432no—
229C2×C42—432no—
230C2×C42—432no—
231C2×C42—432no—
232C2×C42—431no—
233C2×C42—432no—
234C2×C42—864no—
235C2×C42—868no—
236C2×C42—868no—
237C2×C42C4×D4312yes—
238C2×C42C4×D4311yescharacteristic
239C2×C42C4×D4311yescharacteristic
240C2×C42C22×D4312yes—
241C2×C42C22×D4311yescharacteristic
242C4⋊C8—24no—
243C4⋊C8—868no—
244C4⋊C8—864no—
245C24—431no—
246C22×C4—431no—
247C22×C4—431no—
248C22×C4—434no—
249C22×C4—434no—
250C22×C4—434no—
251C22×C4—432no—
252C22×C4—432no—
253C22×C4—438no—
254C22×C4—431no—
255C22×C4—432no—
256C22×C4—432no—
257C22×C4—434no—
258C22×C4—438no—
259C22×C4—438no—
260C22×C4—864no—
261C22×C4—864no—
262C22×C4—864no—
263C22×C4—864no—
264C22×C4—864no—
265C22×C4C2×C4×D4311yescharacteristic
266C22×C4C2×C4×D4312yes—
267C22×C4C2×C4×D4312yes—
268C22×C4C2×C4×D4311yescharacteristic
269C22×C4C23×D4311yescharacteristic
270C2×C8—24no—
271C2×C8—28no—
272C2×C8—864no—
273C2×C8—868no—
274C2×C8—17216no—
275C42—24no—
276C42—22no—
277C42—24no—
278C42—434no—
279C42—434no—
280C42—438no—
281C42—434no—
282C42—432no—
283C42—432no—
284C42—864no—
285C42—864no—
286C42—864no—
287C42—864no—
288C42—864no—
289C42—864no—
290C42—862no—
291C42—864no—
292C42C8×D4314yescomplemented
293C42D4×D4312yes—
294C42Q8×D4312yes—
295C23—432no—
296C23—434no—
297C23—432no—
298C23—434no—
299C23—432no—
300C23C22×C4×D4311yescharacteristic
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—432no—
307C2×C4—432no—
308C2×C4—434no—
309C2×C4—432no—
310C2×C4—432no—
311C2×C4—438no—
312C2×C4—438no—
313C2×C4—4316no—
314C2×C4—432no—
315C2×C4—434no—
316C2×C4—434no—
317C2×C4—8616no—
318C2×C4—8616no—
319C2×C4—868no—
320C2×C4—862no—
321C2×C4—862no—
322C2×C4—862no—
323C2×C4—862no—
324C2×C4—862no—
325C2×C4C4⋊C4×D4312yes—
326C2×C4C4⋊C4×D4312yes—
327C2×C4C2×C8×D4314yes—
328C2×C4C2×C8×D4312yes—
329C2×C4M16×D4314yes—
330C2×C4M16×D4312yes—
331C2×C4C2×D4×D4311yescharacteristic
332C2×C4C2×Q8×D4311yescharacteristic
333C2×C4#41×D4314yes—
334C8—44no—
335C8—1724no—
336C22—438no—
337C22—438no—
338C22—434no—
339C22—434no—
340C22—434no—
341C22C2×C4⋊C4×D4311yescharacteristic
342C22#117×D4312yes—
343C22C22×C8×D4311yescharacteristic
344C22C2×M16×D4312yes—
345C22C2×M16×D4311yescharacteristic
346C4—24no—
347C4—24no—
348C4—22no—
349C4—434no—
350C4—434no—
351C4—864no—
352C4—864no—
353C4—862no—
354C4C4⋊C8×D4314yes—
355C4#124×D4312yes—
356C4#125×D4312yes—
357C2—438no—
358C2#382×D4311yescharacteristic
359C2C2×C4⋊C8×D4311yescharacteristic
360C2#423×D4311yescharacteristic
361C2#431×D4312yes—
362C2#432×D4312yes—
subgroupG/H
center, FrattiniC22×C4C23×D43
commutatorC22×C43C23×C8
FittingC43×#1831C2
socleC23×C43C23×C4
prime radicalC23×D43C22×C4
cosocleC22×C4×C43C24
hypercenter#1831D43
hypocenterC43C2×#1831
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1831

Complements

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

NH ≅ G/Ntype
3. #19134712C2semidirect
4. #19134711C2semidirect
5. #19134710C2semidirect
7. C43×#1831C2semidirect
51. C42×D43C8semidirect
93. C42×C43C2×C8semidirect
106. C4×Dic43C2×C8semidirect
107. C4×Dic43C2×C8semidirect
181. #1831D43direct (N × H)
188. D43#1831direct (N × H)
208. C43C2×#1831semidirect
292. C42C8×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C8×D432
C43×D432
#191347122
#191347112
#191347102
#336×D432
C43×#18312
C2×#183143