Finite Group Databasebeta

← D43×#1696 #25079227

Subgroups — D43×#1696 #25079227

Order 11008.

618 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#500×D43C211yesmaximal, characteristic
2#477×D43C212yesmaximal
3#446×D43C211yesmaximal, characteristic
4#19134124C211yesmaximal, characteristic, complemented
5#19134123C211yesmaximal, characteristic, complemented
6#19134122C212yesmaximal, complemented
7#19134121C212yesmaximal, complemented
8#19134120C211yesmaximal, characteristic, complemented
9#334×D43C211yesmaximal, characteristic
10#333×D43C212yesmaximal
11C43×#1696C211yesmaximal, characteristic, complemented
12C4⋊Q8×D43C2212yes—
13C4×Q8×D43C2211yescharacteristic
14#14583304C2211yescharacteristic
15#14583303—21no—
16#14583303—21no—
17#14583302C2212yes—
18#14583195C2212yes—
19#14583194C2212yes—
20#14583193—22no—
21#14583192—22no—
22#14583191C2212yes—
23#14583030C2211yescharacteristic
24#14583029C2211yescharacteristic
25#14583028—21no—
26#14583027—21no—
27#14583026C2211yescharacteristic
28#107×D43—21no—
29#107×D43—21no—
30#107×D43—22no—
31C4⋊C8×D43—21no—
32C4⋊C8×D43C2211yescharacteristic
33C4⋊C8×D43C2212yes—
34#103×D43—22no—
35#97×D43—21no—
36C4×C8×D43C2211yescharacteristic
37#14582650C2211yescharacteristic
38#14582649C2212yes—
39#14582648C2212yes—
40#14582647C2212yes—
41#14582647C2212yes—
42C43×#500C2211yescharacteristic
43C43×#477C2212yes—
44C43×#446C2211yescharacteristic
45C43×#334C2211yescharacteristic
46C43×#333C2212yes—
47C2×Q8×D43—22no—
48C2×Q8×D43D411yescharacteristic
49C2×C8×D43—21no—
50C2×C8×D43—22no—
51C2×C8×D43D411yescharacteristic
52C2×C8×D43D411yescharacteristic
53#13063325C2312yes—
54#13063324—22no—
55#13063324—22no—
56#13063323—22no—
57Q8×Dic43D411yescharacteristic
58C4×Dic86—21no—
59C4×Dic86C2311yescharacteristic
60#13063290—21no—
61#13063290D411yescharacteristic
62C4⋊C4×D43—21no—
63C4⋊C4×D43—22no—
64C4⋊C4×D43—22no—
65C4⋊C4×D43D411yescharacteristic
66C42×D43—21no—
67C42×D43C2311yescharacteristic
68#13063259—21no—
69#13063259—21no—
70#13063259—22no—
71#13063258—22no—
72#13063258—22no—
73#13063258—22no—
74#13063258—22no—
75C4⋊(C43⋊C8)—21no—
76C4⋊(C43⋊C8)C2311yescharacteristic
77C4⋊(C43⋊C8)C2312yes—
78Dic43⋊C8—21no—
79Dic43⋊C8—22no—
80Dic43⋊C8—21no—
81Dic43⋊C8—21no—
82#13063250—22no—
83#13063249—22no—
84#13063248—22no—
85#13063236—21no—
86#13063235—21no—
87#13063235—21no—
88C4×C43⋊C8C2311yescharacteristic
89C8×Dic43D411yescharacteristic
90C8×Dic43D411yescharacteristic
91C4⋊Q8×C43C2312yes—
92C4×Q8×C43C2311yescharacteristic
93#107×C43—21no—
94#107×C43—21no—
95#107×C43—22no—
96C4⋊C8×C43—21no—
97C4⋊C8×C43C2311yescharacteristic
98C4⋊C8×C43C2312yes—
99#103×C43—22no—
100#97×C43—21no—
101C4×C8×C43C2311yescharacteristic
102C2×Q8×C43—22no—
103C2×Q8×C43C2×D411yescharacteristic
104Q8×D43—24no—
105Q8×D43—84no—
106C2×C4×D43—21no—
107C2×C4×D43—21no—
108C2×C4×D43—42no—
109C2×C4×D43C2×D411yescharacteristic
110C2×C4×D43C2×D411yescharacteristic
111C2×C4×D43#4111yescharacteristic
112C2×Dic86—21no—
113C2×Dic86—22no—
114C2×Dic86—42no—
115C2×Dic86C2×D411yescharacteristic
116C2×C8×C43—21no—
117C2×C8×C43—22no—
118C2×C8×C43C2×D411yescharacteristic
119C2×C8×C43C2×D411yescharacteristic
120C4⋊C4×C43—21no—
121C4⋊C4×C43—22no—
122C4⋊C4×C43—22no—
123C4⋊C4×C43C2×D411yescharacteristic
124C42×C43—21no—
125C42×C43C2411yescharacteristic
126C4⋊Dic43—21no—
127C4⋊Dic43—22no—
128C4⋊Dic43—22no—
129C4⋊Dic43C2×D411yescharacteristic
130Dic43⋊C4—21no—
131Dic43⋊C4—21no—
132Dic43⋊C4—21no—
133Dic43⋊C4—42no—
134Dic43⋊C4—42no—
135C4×Dic43—21no—
136C4×Dic43—21no—
137C4×Dic43—21no—
138C4×Dic43C2×D411yescharacteristic
139C4×Dic43C2×D411yescharacteristic
140C4×Dic43#4111yescharacteristic
141C2×C43⋊C8—21no—
142C2×C43⋊C8—22no—
143C2×C43⋊C8C2×D411yescharacteristic
144C2×C43⋊C8C2×D411yescharacteristic
145C8×D43—22no—
146C8×D43—42no—
147C8×D43—44no—
148C8×D43Q1614yes—
149C22×D43#12111yescharacteristic
150Q8×C43—22no—
151Q8×C43—82no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—42no—
155C2×C4×C43C22×D411yescharacteristic
156C2×C4×C43C22×D411yescharacteristic
157C2×C4×C43C2×#4111yescharacteristic
158C2×Dic43—21no—
159C2×Dic43—21no—
160C2×Dic43—42no—
161C2×Dic43#12111yescharacteristic
162C2×Dic43#12111yescharacteristic
163C2×Dic43#12111yescharacteristic
164C4×D43—22no—
165C4×D43—42no—
166C4×D43—42no—
167C4×D43—84no—
168C4×D43C2×Q1612yes—
169C4×D43#13712yes—
170C4×D43#13714yes—
171Dic86—22no—
172Dic86—42no—
173Dic86—84no—
174Dic86—82no—
175C8×C43—21no—
176C8×C43—41no—
177C8×C43—42no—
178C8×C43C2×Q1612yes—
179C43⋊C8—21no—
180C43⋊C8—41no—
181C43⋊C8—42no—
182C43⋊C8C2×Q1612yes—
183C2×#1696—431nomaximal, Sylow
184C22×C43C2×#12111yescharacteristic
185C2×D43#46212yes—
186C2×D43#47012yes—
187C2×D43#47212yes—
188C4×C43—21no—
189C4×C43—41no—
190C4×C43—41no—
191C4×C43—82no—
192C4×C43C22×Q1611yescharacteristic
193C4×C43C2×#13711yescharacteristic
194C4×C43C2×#13712yes—
195Dic43—21no—
196Dic43—41no—
197Dic43—41no—
198Dic43—82no—
199Dic43#46212yes—
200Dic43#47012yes—
201C2×#500—431no—
202C2×#477—432no—
203C2×#446—431no—
204#1696—431no—
205#1696—432no—
206#1696—431no—
207#1696—431no—
208#1696—432no—
209#1696D4311yescharacteristic, direct product factor
210C2×#334—431no—
211C2×#333—432no—
212C2×C43C2×#46211yescharacteristic
213C2×C43C2×#47011yescharacteristic
214C2×C43C2×#47211yescharacteristic
215D43#169614yesdirect product factor
216C2×C4⋊Q8—432no—
217C2×C4×Q8—431no—
218#500—432no—
219#500—431no—
220#500—861no—
221#500—861no—
222#500C2×D4311yescharacteristic
223#477—432no—
224#477—432no—
225#477—432no—
226#477—862no—
227#477—862no—
228#477C2×D4312yes—
229#446—431no—
230#446—431no—
231#446—431no—
232#446—861no—
233#446—861no—
234#446C2×D4311yescharacteristic
235C2×#107—862no—
236C2×#107—861no—
237C2×#107—861no—
238C2×C4⋊C8—432no—
239C2×C4⋊C8—431no—
240C2×C4⋊C8—861no—
241C2×#103—862no—
242C2×#97—861no—
243C2×C4×C8—431no—
244#334—432no—
245#334—431no—
246#334C2×D4311yescharacteristic
247#333—432no—
248#333—432no—
249#333—432no—
250#333C2×D4312yes—
251C43C2×#169611yescharacteristic, complemented, Sylow
252C22×Q8—431no—
253C22×Q8—862no—
254C22×C8—431no—
255C22×C8—431no—
256C22×C8—861no—
257C22×C8—862no—
258C4⋊Q8—432no—
259C4⋊Q8—862no—
260C4⋊Q8—862no—
261C4⋊Q8—862no—
262C4⋊Q8C22×D4312yes—
263C4×Q8—431no—
264C4×Q8—431no—
265C4×Q8—431no—
266C4×Q8—861no—
267C4×Q8—861no—
268C4×Q8C22×D4311yescharacteristic
269C2×C4⋊C4—431no—
270C2×C4⋊C4—861no—
271C2×C4⋊C4—862no—
272C2×C4⋊C4—862no—
273C2×C42—431no—
274C2×C42—861no—
275#107—21no—
276#107—21no—
277#107—22no—
278#107—862no—
279#107—862no—
280#107—862no—
281#107—862no—
282#107—861no—
283#107—861no—
284#107—862no—
285C4⋊C8—21no—
286C4⋊C8—431no—
287C4⋊C8—432no—
288C4⋊C8—861no—
289C4⋊C8—861no—
290C4⋊C8—862no—
291C4⋊C8—861no—
292C4⋊C8—861no—
293C4⋊C8C22×D4311yescharacteristic
294C4⋊C8C22×D4312yes—
295#103—22no—
296#103—862no—
297#103—862no—
298#103—862no—
299#97—21no—
300#97—861no—
301#97—861no—
302#97—861no—
303C4×C8—431no—
304C4×C8—431no—
305C4×C8—431no—
306C4×C8C22×D4311yescharacteristic
307C2×Q8—22no—
308C2×Q8—431no—
309C2×Q8—861no—
310C2×Q8—864no—
311C2×Q8—862no—
312C2×Q8—3444no—
313C2×Q8—1722no—
314C2×Q8D4×D4311yescharacteristic
315C22×C4—431no—
316C22×C4—431no—
317C22×C4—431no—
318C22×C4—861no—
319C22×C4—861no—
320C22×C4—1722no—
321C2×C8—21no—
322C2×C8—22no—
323C2×C8—431no—
324C2×C8—434no—
325C2×C8—431no—
326C2×C8—862no—
327C2×C8—861no—
328C2×C8—862no—
329C2×C8—1722no—
330C2×C8—1724no—
331C2×C8D4×D4311yescharacteristic
332C2×C8D4×D4311yescharacteristic
333C4⋊C4—21no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—431no—
337C4⋊C4—861no—
338C4⋊C4—861no—
339C4⋊C4—861no—
340C4⋊C4—861no—
341C4⋊C4—862no—
342C4⋊C4—862no—
343C4⋊C4—1722no—
344C4⋊C4—1722no—
345C4⋊C4D4×D4311yescharacteristic
346C42—21no—
347C42—431no—
348C42—431no—
349C42—431no—
350C42—861no—
351C42—861no—
352C42—861no—
353C42C23×D4311yescharacteristic
354C23—431no—
355Q8—22no—
356Q8—82no—
357Q8—862no—
358Q8—3442no—
359Q8—3444no—
360Q8—1722no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—431no—
365C2×C4—431no—
366C2×C4—432no—
367C2×C4—432no—
368C2×C4—434no—
369C2×C4—431no—
370C2×C4—862no—
371C2×C4—861no—
372C2×C4—861no—
373C2×C4—3444no—
374C2×C4—1722no—
375C2×C4—1722no—
376C2×C4—1722no—
377C2×C4C2×D4×D4311yescharacteristic
378C2×C4C2×D4×D4311yescharacteristic
379C2×C4#41×D4311yescharacteristic
380C8—21no—
381C8—42no—
382C8—41no—
383C8—432no—
384C8—861no—
385C8—1722no—
386C8—1721no—
387C8Q16×D4312yes—
388C22—432no—
389C22—432no—
390C22—432no—
391C22#121×D4311yescharacteristic
392C4—21no—
393C4—41no—
394C4—41no—
395C4—82no—
396C4—432no—
397C4—432no—
398C4—861no—
399C4—3442no—
400C4—1721no—
401C4—1721no—
402C4C2×Q16×D4311yescharacteristic
403C4#137×D4312yes—
404C4#137×D4311yescharacteristic
405C2—434no—
406C2#462×D4311yescharacteristic
407C2#470×D4311yescharacteristic
408C2#472×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1696C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1696D43
hypocenterC43C2×#1696
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1696

Complements

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

NH ≅ G/Ntype
4. #19134124C2semidirect
5. #19134123C2semidirect
6. #19134122C2semidirect
7. #19134121C2semidirect
8. #19134120C2semidirect
11. C43×#1696C2semidirect
209. #1696D43direct (N × H)
215. D43#1696direct (N × H)
251. C43C2×#1696semidirect

Maximal subgroups

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

subgroupindex
#500×D432
#477×D432
#446×D432
#191341242
#191341232
#191341222
#191341212
#191341202
#334×D432
#333×D432
C43×#16962
C2×#169643