Finite Group Databasebeta

← #25080152

Subgroups — #25080152

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145902C211yesmaximal, characteristic
2#19145520C211yesmaximal, characteristic, complemented
3#19143341C211yesmaximal, characteristic, complemented
4#19134153C212yesmaximal, complemented
5#19134139C212yesmaximal, complemented
6#19134029C212yesmaximal, complemented
7#19134015C212yesmaximal, complemented
8#19133347C211yesmaximal, characteristic, complemented
9#19133244C211yesmaximal, characteristic, complemented
10C2×#14582645C211yesmaximal, characteristic, complemented
11C43×#3141C211yesmaximal, characteristic, complemented
12C2×#13063333—21no—
13#14583449C2211yescharacteristic
14#14583273—21no—
15#14583249—21no—
16#14583179—21no—
17#14583176C2212yes—
18#14583133—22no—
19#14583101C2212yes—
20#14583101C2212yes—
21#14583094—21no—
22#14583091C2212yes—
23#14583038—22no—
24#14582978C2212yes—
25#14582972—22no—
26C8×D172C2212yes—
27#14582952C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30#14582867—21no—
31#14582652C2212yes—
32#14582650C2212yes—
33#14582645C2212yes—
34#14582645C2212yes—
35#14582645C2211yescharacteristic
36#14582645C2211yescharacteristic
37#14582643C2211yescharacteristic
38#14582643C2211yescharacteristic
39C43×#532C2211yescharacteristic
40C2×C4⋊Q8×C43C2211yescharacteristic
41C43×#489—22no—
42C43×#487C2212yes—
43C43×#486C2212yes—
44C43×#417—21no—
45C43×#417—21no—
46C4×M16×C43C2211yescharacteristic
47C2×#10621898—21no—
48C2×#10621884—22no—
49C2×#10621884—22no—
50C2×#10621882—22no—
51#13063333—44no—
52C2×#10621872—22no—
53C22×C43⋊C8—21no—
54C22×C43⋊C8—21no—
55C2×C8×D43—22no—
56#13063325D411yescharacteristic
57#13063322D411yescharacteristic
58#13063313—21no—
59#13063299—21no—
60#13063299D412yes—
61C4×D172—21no—
62C4×D172C2312yes—
63#13063258—22no—
64C4⋊(C43⋊C8)—21no—
65C4⋊(C43⋊C8)—21no—
66C4⋊(C43⋊C8)C2312yes—
67C4⋊(C43⋊C8)C2311yescharacteristic
68C4⋊(C43⋊C8)C2311yescharacteristic
69C4⋊(C43⋊C8)C2311yescharacteristic
70C4⋊(C43⋊C8)C2311yescharacteristic
71#13063249—22no—
72#13063249—22no—
73#13063246—22no—
74#13063245—22no—
75C22⋊(C43⋊C8)—21no—
76(C2×D43)⋊C8—22no—
77(C2×D43)⋊C8—22no—
78C4×C43⋊C8—21no—
79C2×#41×C43—21no—
80C22×Q8×C43—21no—
81C2×M16×C43D411yescharacteristic
82C2×M16×C43D411yescharacteristic
83C4⋊Q8×C43—21no—
84C4⋊Q8×C43—21no—
85C4⋊Q8×C43—21no—
86C4⋊Q8×C43C2312yes—
87C4⋊Q8×C43C2311yescharacteristic
88#127×C43C2311yescharacteristic
89#124×C43—21no—
90#121×C43—21no—
91#121×C43—21no—
92C4×D4×C43—21no—
93C4×D4×C43—21no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C42×C43C2311yescharacteristic
97#103×C43—22no—
98#103×C43—22no—
99#102×C43—22no—
100#102×C43—22no—
101#97×C43D412yes—
102C4×C8×C43C2312yes—
103#41×C43—42no—
104#41×C43—42no—
105C2×Q8×C43—21no—
106C2×Q8×C43—22no—
107C2×Q8×C43—41no—
108C2×Q8×C43—81no—
109C2×Q8×C43—81no—
110C2×D4×C43—21no—
111C2×D4×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—41no—
114C22×C4×C43—41no—
115C22×C4×C43—41no—
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C2×C22⋊D43—22no—
120#10621898—42no—
121#10621898—42no—
122C2×D172—21no—
123C2×D172—21no—
124C2×D172C2×D412yes—
125C2×C4×D43—22no—
126C2×Dic86—21no—
127M16×C43—22no—
128M16×C43—22no—
129C2×C8×C43C2×D412yes—
130C2×C8×C43C2×D412yes—
131C4⋊C4×C43—22no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—22no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—41no—
136C4⋊C4×C43—41no—
137C22⋊C4×C43—41no—
138C22⋊C4×C43—41no—
139C42×C43C2×D411yescharacteristic
140C42×C43C2×D411yescharacteristic
141C42×C43#4111yescharacteristic
142C42×C43C2411yescharacteristic
143#10621884—82no—
144#10621884—82no—
145#10621882—82no—
146(C2×D43)⋊C4—22no—
147(C2×D43)⋊C4—22no—
148C4⋊Dic43—21no—
149C4⋊Dic43C2×D412yes—
150C2×C43⋊C8—21no—
151C2×C43⋊C8—21no—
152C2×C43⋊C8—21no—
153C2×C43⋊C8—21no—
154C2×C43⋊C8—22no—
155C2×C43⋊C8—42no—
156C2×C43⋊C8—81no—
157#10621872—44no—
158C8×D43—44no—
159C23×C43—41no—
160C23×C43#12111yescharacteristic
161C22×D43—22no—
162Q8×C43—41no—
163Q8×C43—41no—
164Q8×C43—42no—
165Q8×C43—42no—
166Q8×C43—82no—
167D4×C43—41no—
168D4×C43—41no—
169D4×C43—41no—
170D4×C43—41no—
171D4×C43—81no—
172D4×C43—82no—
173C2×C4×C43—21no—
174C2×C4×C43—21no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—42no—
178C2×C4×C43—82no—
179C2×C4×C43—82no—
180C2×C4×C43#12111yescharacteristic
181C2×C4×C43#12111yescharacteristic
182C2×C4×C43#12111yescharacteristic
183C2×C4×C43#13512yes—
184C2×C4×C43AGL(1,ℤ/8)12yes—
185C2×C4×C43C22×D411yescharacteristic
186C2×C4×C43C22×D411yescharacteristic
187C2×C4×C43C2×#4111yescharacteristic
188C22⋊D43—44no—
189C2×Dic43—22no—
190D172—22no—
191D172—22no—
192D172—42no—
193D172—81no—
194C4×D43—42no—
195C4×D43—42no—
196Dic86—42no—
197C8×C43—22no—
198C8×C43—22no—
199C43⋊C8—41no—
200C43⋊C8—41no—
201C43⋊C8—42no—
202C43⋊C8—41no—
203C43⋊C8—41no—
204#19237—431nomaximal, Sylow
205C22×C43—21no—
206C22×C43—21no—
207C22×C43—81no—
208C22×C43—81no—
209C22×C43—81no—
210C22×C43#46312yes—
211C22×C43C2×#12111yescharacteristic
212C2×D43—42no—
213C2×D43—42no—
214C2×D43—42no—
215C4×C43—21no—
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—81no—
219C4×C43—82no—
220C4×C43#46312yes—
221C4×C43C2×#13511yescharacteristic
222C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
223C4×C43#57611yescharacteristic
224C4×C43#57711yescharacteristic
225Dic43—42no—
226#3245—431no—
227#3206—431no—
228#3141D4311yescharacteristic, complemented
229#2935—431no—
230#1701—432no—
231#1699—432no—
232#1681—432no—
233#1679—432no—
234#1565—431no—
235#1540—431no—
236C2×#332—431no—
237C2×C43—22no—
238C2×C43—161no—
239C2×C43C2×#46311yescharacteristic
240C2×C43#306211yescharacteristic
241C2×C43#306911yescharacteristic
242D43—82no—
243C2×#131—861no—
244#532—431no—
245#532C2×D4311yescharacteristic
246C2×C4⋊Q8C2×D4311yescharacteristic
247#492—861no—
248#489—22no—
249#487—861no—
250#487C2×D4312yes—
251#486C2×D4312yes—
252#474—432no—
253#474—861no—
254#466—862no—
255#461—432no—
256#461—432no—
257#459—432no—
258#459—861no—
259#448—862no—
260#436—432no—
261#435—862no—
262C8×D4—432no—
263#431—431no—
264C2×C4⋊C8—431no—
265C2×C4⋊C8—431no—
266#417—21no—
267#417—21no—
268#408—861no—
269C4×M16C2×D4311yescharacteristic
270#335—432no—
271#334—432no—
272#332—432no—
273#332—432no—
274#332—431no—
275#332—431no—
276#331—431no—
277#331—431no—
278C43#1923711yescharacteristic, complemented, Sylow
279C2×#41—21no—
280C2×#41—861no—
281C22×Q8—21no—
282C2×SD16—862no—
283C2×SD16—862no—
284C2×D8—862no—
285#131—1724no—
286C2×M16—862no—
287C2×M16C22⋊D4311yescharacteristic
288C2×M16C22⋊D4311yescharacteristic
289C22×C8—861no—
290C22×C8—861no—
291C22×C8—862no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8—431no—
296C4⋊Q8C22×D4312yes—
297C4⋊Q8C22×D4311yescharacteristic
298#127—431no—
299#127C22×D4311yescharacteristic
300#124—21no—
301#124—861no—
302#121—21no—
303#121—21no—
304#121—432no—
305#121—861no—
306C4×D4—21no—
307C4×D4—21no—
308C4×D4—432no—
309C4×D4—861no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C42C22×D4311yescharacteristic
313#107—862no—
314C4⋊C8—431no—
315C4⋊C8—431no—
316C4⋊C8—431no—
317C4⋊C8—431no—
318C4⋊C8—432no—
319C4⋊C8—861no—
320C4⋊C8—861no—
321#103—22no—
322#103—22no—
323#103—862no—
324#103—862no—
325#102—22no—
326#102—22no—
327#102—862no—
328#102—862no—
329C22⋊C8—861no—
330C22⋊C8—862no—
331C22⋊C8—862no—
332#97C22⋊D4312yes—
333C4×C8—861no—
334C4×C8C22×D4312yes—
335#41—42no—
336#41—42no—
337#41—1722no—
338#41—1722no—
339C2×Q8—22no—
340C2×Q8—21no—
341C2×Q8—41no—
342C2×Q8—81no—
343C2×Q8—81no—
344C2×Q8—861no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—41no—
349C2×D4—432no—
350C2×D4—862no—
351C2×D4—861no—
352C2×D4—861no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—862no—
356C22×C4D4×D4311yescharacteristic
357C22×C4#1062190011yescharacteristic
358C22×C4C2×C22⋊D4311yescharacteristic
359SD16—3442no—
360SD16—3442no—
361D8—3442no—
362M16—22no—
363M16—22no—
364M16—1724no—
365C2×C8—861no—
366C2×C8—861no—
367C2×C8—862no—
368C2×C8—861no—
369C2×C8—861no—
370C2×C8—3441no—
371C2×C8—1724no—
372C2×C8—1722no—
373C2×C8C2×C22⋊D4312yes—
374C2×C8C2×C22⋊D4312yes—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—432no—
382C4⋊C4—861no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—862no—
386C22⋊C4—862no—
387C42D4×D4311yescharacteristic
388C42#1062190011yescharacteristic
389C42C2×C22⋊D4311yescharacteristic
390C42C23×D4311yescharacteristic
391C23—41no—
392C23—862no—
393C23#1306329611yescharacteristic
394Q8—41no—
395Q8—41no—
396Q8—42no—
397Q8—42no—
398Q8—82no—
399Q8—1722no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—41no—
404D4—81no—
405D4—82no—
406D4—862no—
407D4—862no—
408D4—3441no—
409D4—1724no—
410D4—1722no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4—862no—
419C2×C4—1722no—
420C2×C4—1722no—
421C2×C4#1306329611yescharacteristic
422C2×C4#1306329611yescharacteristic
423C2×C4#1306329611yescharacteristic
424C2×C4#1306334512yes—
425C2×C4#1306335012yes—
426C2×C4C2×D4×D4311yescharacteristic
427C2×C4C22×C22⋊D4311yescharacteristic
428C2×C4C2×#1062190011yescharacteristic
429C8—22no—
430C8—22no—
431C8—1721no—
432C8—1721no—
433C8—1722no—
434C8—1721no—
435C8—1721no—
436C22—21no—
437C22—21no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—1722no—
442C22—1722no—
443C22—1722no—
444C22#1458311112yes—
445C22C2×#1306329611yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—82no—
450C4—81no—
451C4—1722no—
452C4#1458311112yes—
453C4C2×#1306334511yescharacteristic
454C4C2×#1306335011yescharacteristic
455C4#1458370311yescharacteristic
456C4#1458370911yescharacteristic
457C2—22no—
458C2—161no—
459C2—3442no—
460C2C2×#1458311111yescharacteristic
461C2#1914426911yescharacteristic
462C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3141C2
socleC22×C43C2×#121
prime radical#19145902C2
hypercenter#3141D43
hypocenterC43#19237
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. #19145520C2semidirect
3. #19143341C2semidirect
4. #19134153C2semidirect
5. #19134139C2semidirect
6. #19134029C2semidirect
7. #19134015C2semidirect
8. #19133347C2semidirect
9. #19133244C2semidirect
10. C2×#14582645C2semidirect
11. C43×#3141C2semidirect
228. #3141D43semidirect
278. C43#19237semidirect

Maximal subgroups

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

subgroupindex
#191459022
#191455202
#191433412
#191341532
#191341392
#191340292
#191340152
#191333472
#191332442
C2×#145826452
C43×#31412
#1923743