Finite Group Databasebeta

← D43×#3162 #25966209

Subgroups — D43×#3162 #25966209

Order 11008.

1902 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C212yesmaximal
2#19145119C211yesmaximal, characteristic, complemented
3#19145118C214yesmaximal, complemented
4#19145117C212yesmaximal, complemented
5#19145116C218yesmaximal, complemented
6#501×D43C218yesmaximal, complemented
7#427×D43C214yesmaximal
8C2×#97×D43C211yesmaximal, characteristic
9C43×#3162C211yesmaximal, characteristic, complemented
10C22×C8×D43C2212yes—
11#14583456C2212yes—
12#14583455C2214yes—
13#14583454C2214yes—
14#14583453—24no—
15#14583452C2214yes—
16#14583451—24no—
17C4⋊Q8×D43C2214yes—
18#125×D43C2214yes—
19C22⋊Q8×D43—24no—
20C4×Q8×D43—24no—
21#117×D43C2214yes—
22C2×C42×D43C2211yescharacteristic
23#14583309C2218yescomplemented
24#14583308C2218yescomplemented
25#14583307C22116yescomplemented
26#14583306C22116yescomplemented
27#14583305C2218yescomplemented
28#14582937C2214yes—
29#14582936C2218yes—
30#14582935C2218yes—
31#14582934C2218yes—
32#107×D43C2218yes—
33#106×D43C2218yes—
34C2×#13063236C2211yescharacteristic
35C2×#13063235C2212yes—
36#97×D43C2214yes—
37#97×D43C2214yes—
38C43×#533C2212yes—
39C43×#501C2218yescomplemented
40C43×#427C2214yes—
41C2×#97×C43C2211yescharacteristic
42C2×Q8×D43—24no—
43C22×C4×D43D412yes—
44C22×C4×D43C2311yescharacteristic
45C22×C43⋊C8C2312yes—
46C2×C8×D43Q8116yescomplemented
47C2×C8×D43C2314yes—
48C2×C8×D43C2314yes—
49#13063325C2314yes—
50#13063324—24no—
51#13063324C2318yes—
52#13063323—24no—
53#13063317C2314yes—
54#13063316C2318yes—
55#13063315—28no—
56#13063305—24no—
57#13063304—24no—
58#13063303—28no—
59#13063302—28no—
60#13063301—24no—
61Q8×Dic43—24no—
62C4×Dic86—24no—
63C4×Dic86—28no—
64#13063290—24no—
65#13063290—28no—
66#13063284C2314yes—
67#13063283C2318yes—
68#13063282—24no—
69#13063281—24no—
70C4⋊C4×D43—28no—
71C4⋊C4×D43—24no—
72C4⋊C4×D43C2318yes—
73C22⋊C4×D43—24no—
74C2×C4×Dic43D412yes—
75C2×C4×Dic43C2311yescharacteristic
76C42×D43—24no—
77C42×D43D412yes—
78C42×D43D412yes—
79C42×D43C2312yes—
80C42×D43C2312yes—
81#13063259C2318yes—
82#13063258C23116yes—
83#13063257C2318yes—
84#13063256C23116yes—
85#13063236C2314yes—
86#13063235C2318yes—
87C22×C8×C43C2312yes—
88C4⋊Q8×C43C2314yes—
89#125×C43C2314yes—
90C22⋊Q8×C43—24no—
91C4×Q8×C43—24no—
92#117×C43C2314yes—
93C2×C42×C43C2311yescharacteristic
94#107×C43C2318yes—
95#106×C43C2318yes—
96#97×C43C2314yes—
97C23×D43C2×D411yescharacteristic
98C2×Q8×C43—24no—
99C22×C4×C43C2×D412yes—
100C22×C4×C43C2411yescharacteristic
101C22×Dic43C2×D412yes—
102C22×Dic43C2×D411yescharacteristic
103Q8×D43—416no—
104C2×C4×D43—28no—
105C2×C4×D43—44no—
106C2×C4×D43C2×D414yes—
107C2×C4×D43C2×D414yes—
108C2×C4×D43C2×D411yescharacteristic
109C2×C4×D43C2×D411yescharacteristic
110C2×C4×D43C2×Q818yes—
111C2×C4×D43C2411yescharacteristic
112C2×C4×D43C2411yescharacteristic
113C2×Dic86—24no—
114C2×Dic86—28no—
115C2×C8×C43C2×Q818yescomplemented
116C2×C8×C43C2414yes—
117C4⋊C4×C43—28no—
118C4⋊C4×C43—24no—
119C4⋊C4×C43C2418yes—
120C22⋊C4×C43—24no—
121C42×C43—24no—
122C42×C43C2×D412yes—
123C42×C43C2412yes—
124C22⋊Dic43—24no—
125(C2×D43)⋊C4—28no—
126C4⋊Dic43—24no—
127C4⋊Dic43—28no—
128C4⋊Dic43C2418yes—
129Dic43⋊C4—28no—
130Dic43⋊C4—28no—
131Dic43⋊C4—28no—
132Dic43⋊C4—28no—
133C4×Dic43—24no—
134C4×Dic43—28no—
135C4×Dic43C2×D412yes—
136C4×Dic43C2×D414yes—
137C4×Dic43C2×D414yes—
138C4×Dic43C2412yes—
139C2×C43⋊C8C2×Q818yescomplemented
140C2×C43⋊C8C2414yes—
141C8×D43C2×Q8116yes—
142C8×D43C2×Q8116yescomplemented
143C23×C43C22×D411yescharacteristic
144C22×D43—24no—
145C22×D43C4⋊Q814yes—
146C22×D43C22×D411yescharacteristic
147C22×D43C22×D411yescharacteristic
148Q8×C43—48no—
149C2×C4×C43—28no—
150C2×C4×C43—42no—
151C2×C4×C43C22×D414yes—
152C2×C4×C43C22×D411yescharacteristic
153C2×C4×C43C22×Q814yes—
154C2×C4×C43C2511yescharacteristic
155C2×Dic43—28no—
156C2×Dic43—42no—
157C2×Dic43C4⋊Q814yes—
158C2×Dic43C22×D414yes—
159C2×Dic43C22×D411yescharacteristic
160C2×Dic43C22×D411yescharacteristic
161C4×D43—28no—
162C4×D43—44no—
163C4×D43—416no—
164C4×D43C4⋊Q814yes—
165C4×D43C4⋊Q814yes—
166C4×D43C22×Q814yes—
167C4×D43C22×Q814yes—
168Dic86—416no—
169Dic86—48no—
170C8×C43C22×Q818yes—
171C43⋊C8C22×Q818yes—
172C2×#3162—431nomaximal, Sylow
173C22×C43—22no—
174C22×C43C2×C4⋊Q812yes—
175C22×C43C23×D411yescharacteristic
176C2×D43—22no—
177C2×D43—28no—
178C2×D43C2×C4⋊Q812yes—
179C2×D43C2×C4⋊Q812yes—
180C2×D43#57514yes—
181C4×C43—24no—
182C4×C43—48no—
183C4×C43C2×C4⋊Q812yes—
184C4×C43C23×Q812yes—
185Dic43—24no—
186Dic43—48no—
187Dic43C2×C4⋊Q812yes—
188Dic43C2×C4⋊Q812yes—
189C2×#533—432no—
190#3162—438no—
191#3162—434no—
192#3162—431no—
193#3162—432no—
194#3162D4311yescharacteristic, direct product factor
195C2×#501—438no—
196C2×#427—434no—
197C22×#97—431no—
198C2×C43—22no—
199C2×C43C22×C4⋊Q811yescharacteristic
200C2×C43C2×#57512yes—
201D43—22no—
202D43#316214yesdirect product factor
203C23×C8—432no—
204#533—434no—
205#533—434no—
206#533—434no—
207#533—432no—
208#533—864no—
209#533—864no—
210#533C2×D4312yes—
211C2×C4⋊Q8—434no—
212C2×#125—434no—
213C2×C22⋊Q8—864no—
214C2×C4×Q8—864no—
215C2×#117—434no—
216C22×C42—431no—
217#501—438no—
218#501—438no—
219#501—4316no—
220#501—4316no—
221#501—438no—
222#501C2×D4318yescomplemented
223#427—434no—
224#427—438no—
225#427—438no—
226#427—438no—
227#427C2×D4314yes—
228C2×#107—438no—
229C2×#106—438no—
230C2×#97—432no—
231C2×#97—431no—
232C2×#97—434no—
233C2×#97—434no—
234C2×#97C2×D4311yescharacteristic
235C43C2×#316211yescharacteristic, complemented, Sylow
236C22×Q8—864no—
237C23×C4—431no—
238C23×C4—432no—
239C22×C8—432no—
240C22×C8—4316no—
241C22×C8—434no—
242C22×C8—434no—
243C22×C8C22×D4312yes—
244C4⋊Q8—438no—
245C4⋊Q8—434no—
246C4⋊Q8—864no—
247C4⋊Q8—864no—
248C4⋊Q8C22×D4314yes—
249#125—438no—
250#125—434no—
251#125—868no—
252#125C22×D4314yes—
253C22⋊Q8—24no—
254C22⋊Q8—868no—
255C22⋊Q8—868no—
256C22⋊Q8—864no—
257C22⋊Q8—864no—
258C22⋊Q8—864no—
259C4×Q8—24no—
260C4×Q8—868no—
261C4×Q8—868no—
262C4×Q8—864no—
263C4×Q8—864no—
264C4×Q8—864no—
265#117—434no—
266#117—438no—
267#117—864no—
268#117—864no—
269#117C22×D4314yes—
270C2×C4⋊C4—438no—
271C2×C4⋊C4—868no—
272C2×C4⋊C4—864no—
273C2×C22⋊C4—864no—
274C2×C42—432no—
275C2×C42—431no—
276C2×C42—432no—
277C2×C42—432no—
278C2×C42—432no—
279C2×C42—432no—
280C2×C42—864no—
281C2×C42C22×D4311yescharacteristic
282#107—438no—
283#107—4316no—
284#107C22×D4318yes—
285#106—438no—
286#106—4316no—
287#106C22×D4318yes—
288#97—438no—
289#97—434no—
290#97C22×D4314yes—
291C24—431no—
292C2×Q8—24no—
293C2×Q8—868no—
294C2×Q8—864no—
295C2×Q8—17216no—
296C22×C4—431no—
297C22×C4—431no—
298C22×C4—431no—
299C22×C4—438no—
300C22×C4—431no—
301C22×C4—431no—
302C22×C4—432no—
303C22×C4—434no—
304C22×C4—434no—
305C22×C4—868no—
306C22×C4—1724no—
307C22×C4D4×D4312yes—
308C22×C4C23×D4311yescharacteristic
309C2×C8—438no—
310C2×C8—434no—
311C2×C8—4316no—
312C2×C8—4316no—
313C2×C8Q8×D4318yescomplemented
314C2×C8C23×D4314yes—
315C4⋊C4—28no—
316C4⋊C4—24no—
317C4⋊C4—438no—
318C4⋊C4—868no—
319C4⋊C4—868no—
320C4⋊C4—868no—
321C4⋊C4—868no—
322C4⋊C4—868no—
323C4⋊C4—864no—
324C4⋊C4C23×D4318yes—
325C22⋊C4—24no—
326C22⋊C4—868no—
327C22⋊C4—864no—
328C42—24no—
329C42—434no—
330C42—434no—
331C42—432no—
332C42—432no—
333C42—868no—
334C42—864no—
335C42D4×D4312yes—
336C42C23×D4312yes—
337C23—431no—
338C23—434no—
339C23—431no—
340C23—864no—
341C23C2×D4×D4311yescharacteristic
342Q8—48no—
343Q8—1728no—
344Q8—17216no—
345C2×C4—28no—
346C2×C4—42no—
347C2×C4—434no—
348C2×C4—431no—
349C2×C4—431no—
350C2×C4—434no—
351C2×C4—434no—
352C2×C4—434no—
353C2×C4—434no—
354C2×C4—434no—
355C2×C4—868no—
356C2×C4—868no—
357C2×C4—1724no—
358C2×C4—17216no—
359C2×C4—1722no—
360C2×C4C2×D4×D4314yes—
361C2×C4C2×D4×D4311yescharacteristic
362C2×C4C2×Q8×D4314yes—
363C2×C4C24×D4311yescharacteristic
364C8—438no—
365C8C2×Q8×D4318yes—
366C22—22no—
367C22—434no—
368C22—432no—
369C22—432no—
370C22—868no—
371C22—862no—
372C22C4⋊Q8×D4312yes—
373C22C22×D4×D4311yescharacteristic
374C4—24no—
375C4—48no—
376C4—432no—
377C4—432no—
378C4—864no—
379C4—1728no—
380C4C4⋊Q8×D4312yes—
381C4C22×Q8×D4312yes—
382C2—22no—
383C2—434no—
384C2—862no—
385C2C2×C4⋊Q8×D4311yescharacteristic
386C2#575×D4312yes—
subgroupG/H
centerC2×C4C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3162C2
socleC22×C43C23×D4
prime radicalC23×D43C2×D4
hypercenter#3162D43
hypocenterC43C2×#3162
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3162

Complements

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

NH ≅ G/Ntype
2. #19145119C2semidirect
3. #19145118C2semidirect
4. #19145117C2semidirect
5. #19145116C2semidirect
6. #501×D43C2semidirect
9. C43×#3162C2semidirect
23. #14583309C22semidirect
24. #14583308C22semidirect
25. #14583307C22semidirect
26. #14583306C22semidirect
27. #14583305C22semidirect
39. C43×#501C22semidirect
46. C2×C8×D43Q8semidirect
115. C2×C8×C43C2×Q8semidirect
139. C2×C43⋊C8C2×Q8semidirect
142. C8×D43C2×Q8semidirect
194. #3162D43direct (N × H)
202. D43#3162direct (N × H)
222. #501C2×D43semidirect
235. C43C2×#3162semidirect
313. C2×C8Q8×D43semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#191451192
#191451182
#191451172
#191451162
#501×D432
#427×D432
C2×#97×D432
C43×#31622
C2×#316243