Finite Group Databasebeta

← #25070522

Subgroups — #25070522

Order 11008.

940 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583528C211yesmaximal, characteristic
2#19145370C211yesmaximal, characteristic
3#19145367C211yesmaximal, characteristic
4#19140411C211yesmaximal, characteristic
5#19133638C214yesmaximal, complemented
6#19133570C214yesmaximal, complemented
7#19133166C211yesmaximal, characteristic
8C2×#14582624C211yesmaximal, characteristic
9C43×#1520C211yesmaximal, characteristic
10#14583528—22no—
11#14583528—22no—
12#14583528—22no—
13#14583528C2214yes—
14C2×#13063324—21no—
15C2×#13063323—21no—
16C2×#13063315—21no—
17C2×#13063315—21no—
18C2×#13063304C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×#13063302—21no—
21C2×#13063281—21no—
22C22×Dic43⋊C4C2211yescharacteristic
23#14583235—21no—
24#14583235C2212yes—
25#14583234—21no—
26#14583232C2212yes—
27#14583140—22no—
28#14583138—22no—
29#14583057—21no—
30#14583057C2212yes—
31#14583055—21no—
32#14583054C2212yes—
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34#14582839C2212yes—
35#14582829—22no—
36#14582820C2212yes—
37#14582774—21no—
38#14582760—21no—
39#14582635C2214yes—
40#14582624C2214yes—
41C2×C22⋊Q8×C43C2211yescharacteristic
42C2×C22⋊C8×C43C2211yescharacteristic
43C43×#380C2211yescharacteristic
44C43×#328C2214yes—
45C22×Dic86—21no—
46C22×Dic86D411yescharacteristic
47C22×Dic86C2311yescharacteristic
48C23×Dic43D411yescharacteristic
49C23×Dic43D411yescharacteristic
50C2×Dic172—22no—
51C2×#10621885—22no—
52C22×C43⋊C8—21no—
53#13063324—24no—
54#13063324—24no—
55#13063323—24no—
56#13063323—24no—
57#13063315—24no—
58#13063315—24no—
59#13063315—24no—
60#13063315—24no—
61#13063304—21no—
62#13063304—21no—
63#13063304—21no—
64#13063304—21no—
65#13063304—21no—
66#13063304—21no—
67#13063304D412yes—
68#13063304C2312yes—
69#13063302—24no—
70#13063302—24no—
71#13063281—24no—
72#13063281—24no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—22no—
75C2×C4⋊Dic43D411yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4D412yes—
88C2×Dic43⋊C4C2312yes—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93#13063259—22no—
94#13063258—22no—
95#13063250—22no—
96#13063250—22no—
97#13063249—22no—
98#13063248—22no—
99C22⋊(C43⋊C8)—21no—
100C22⋊(C43⋊C8)C2312yes—
101C43⋊#95—22no—
102C43⋊#95—22no—
103C43⋊#95—22no—
104C22×Q8×C43D411yescharacteristic
105C23×C4×C43C2311yescharacteristic
106C22×C8×C43—21no—
107C22⋊Q8×C43—21no—
108C22⋊Q8×C43—21no—
109C22⋊Q8×C43D412yes—
110C22⋊Q8×C43C2312yes—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C22⋊C8×C43—21no—
117C22⋊C8×C43C2312yes—
118#95×C43C2312yes—
119C24×C43C2×D411yescharacteristic
120C2×Q8×C43—21no—
121C2×Q8×C43—81no—
122C2×Q8×C43C2×D412yes—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43—81no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—22no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—81no—
143C22×Dic43Q1614yescomplemented
144C22×Dic43C2×D412yes—
145C22×Dic43C2×D412yes—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—24no—
149C2×Dic86—21no—
150C2×Dic86—81no—
151C2×Dic86—81no—
152C2×Dic86—82no—
153C2×Dic86C2×D412yes—
154C2×C8×C43—22no—
155C2×C8×C43—81no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—81no—
160C4⋊C4×C43C2×D412yes—
161C22⋊C4×C43—22no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—42no—
164C22⋊Dic43—22no—
165C22⋊Dic43—22no—
166C22⋊Dic43—41no—
167C22⋊Dic43—41no—
168#10621885—82no—
169C4⋊Dic43—24no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—82no—
174C4⋊Dic43C2×D412yes—
175Dic43⋊C4—24no—
176Dic43⋊C4—24no—
177Dic43⋊C4—24no—
178Dic43⋊C4—24no—
179Dic43⋊C4—22no—
180Dic43⋊C4—22no—
181Dic43⋊C4—22no—
182Dic43⋊C4—22no—
183Dic43⋊C4—22no—
184Dic43⋊C4—22no—
185Dic43⋊C4—41no—
186Dic43⋊C4—41no—
187C4×Dic43—24no—
188C4×Dic43—24no—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—81no—
191Dic172—82no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43#12011yescharacteristic
195C23×C43#12011yescharacteristic
196C23×C43C2×Q1612yes—
197C23×C43#13712yes—
198C23×C43C22×D411yescharacteristic
199Q8×C43—42no—
200Q8×C43—81no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43#12011yescharacteristic
215C2×C4×C43#12011yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×Dic43—22no—
219C2×Dic43—22no—
220C2×Dic43—24no—
221C2×Dic43—24no—
222C2×Dic43—22no—
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—42no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43—42no—
229C2×Dic43—42no—
230C2×Dic43—42no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—81no—
234C2×Dic43C2×Q1614yes—
235Dic86—42no—
236Dic86—42no—
237Dic86—42no—
238Dic86—81no—
239Dic86—84no—
240C8×C43—42no—
241C43⋊C8—42no—
242#18295—431nomaximal, Sylow
243C22×C43—21no—
244C22×C43—21no—
245C22×C43—21no—
246C22×C43—21no—
247C22×C43—21no—
248C22×C43—21no—
249C22×C43—42no—
250C22×C43—42no—
251C22×C43#45112yes—
252C22×C43#45112yes—
253C22×C43C2×#12011yescharacteristic
254C22×C43C22×Q1611yescharacteristic
255C22×C43C2×#13711yescharacteristic
256C4×C43—21no—
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—42no—
261C4×C43—42no—
262C4×C43—82no—
263Dic43—24no—
264Dic43—42no—
265Dic43—42no—
266Dic43—42no—
267Dic43—81no—
268Dic43—81no—
269C2×#544—431no—
270#3189—431no—
271#3189—431no—
272#2627—431no—
273#1617—434no—
274#1605—434no—
275#1520—431no—
276#1520D4311yescharacteristic
277C2×#324—431no—
278C2×C43—21no—
279C2×C43—21no—
280C2×C43—22no—
281C2×C43—22no—
282C2×C43C2×#45111yescharacteristic
283C2×C43#302011yescharacteristic
284C2×C43#302611yescharacteristic
285#544—434no—
286#544—862no—
287#544—862no—
288#544—862no—
289C2×C4⋊Q8—861no—
290C2×C4⋊Q8—861no—
291C2×#125—861no—
292C2×#125—861no—
293C2×C22⋊Q8—431no—
294C2×C22⋊Q8—431no—
295C2×C22⋊Q8—861no—
296C2×C22⋊Q8C2×D4311yescharacteristic
297C2×#117—861no—
298C22×C4⋊C4—431no—
299#484—432no—
300#484—432no—
301#484—861no—
302#484—861no—
303#467—862no—
304#467—862no—
305#451—432no—
306#451—432no—
307#451—861no—
308#451—861no—
309C2×C22⋊C8—431no—
310C2×C22⋊C8C2×D4311yescharacteristic
311#400—432no—
312#398—862no—
313#395—432no—
314#385—861no—
315#381—861no—
316#380C2×D4311yescharacteristic
317#328—434no—
318#328C2×D4314yes—
319#324—434no—
320C43#1829511yescharacteristic, complemented, Sylow
321C22×Q8—431no—
322C22×Q8—431no—
323C22×Q8—861no—
324C22×Q8D17211yescharacteristic
325C23×C4—431no—
326C23×C4—431no—
327C23×C4C22×D4311yescharacteristic
328C2×Q16—862no—
329C2×Q16—862no—
330C22×C8—21no—
331C22×C8—861no—
332C4⋊Q8—864no—
333C4⋊Q8—864no—
334C4⋊Q8—864no—
335C4⋊Q8—864no—
336#125—864no—
337#125—864no—
338#125—864no—
339#125—864no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8—432no—
343C22⋊Q8—432no—
344C22⋊Q8—864no—
345C22⋊Q8—864no—
346C22⋊Q8—861no—
347C22⋊Q8—861no—
348C22⋊Q8—861no—
349C22⋊Q8—861no—
350C22⋊Q8—861no—
351C22⋊Q8—861no—
352C22⋊Q8D17212yes—
353C22⋊Q8C22×D4312yes—
354#117—864no—
355#117—864no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—431no—
359C2×C4⋊C4—432no—
360C2×C4⋊C4—432no—
361C2×C4⋊C4—431no—
362C2×C4⋊C4—861no—
363C2×C4⋊C4—861no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—862no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4D17211yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—861no—
378C2×C22⋊C4—861no—
379C2×C42—861no—
380C2×C42—861no—
381#107—862no—
382#107—862no—
383#103—862no—
384#103—862no—
385#103—862no—
386#103—862no—
387C22⋊C8—21no—
388C22⋊C8—432no—
389C22⋊C8—861no—
390C22⋊C8C22×D4312yes—
391#95—862no—
392#95—862no—
393#95—862no—
394#95C22×D4312yes—
395C24D4×D4311yescharacteristic
396C2×Q8—21no—
397C2×Q8—81no—
398C2×Q8—432no—
399C2×Q8—864no—
400C2×Q8—861no—
401C2×Q8—861no—
402C2×Q8—861no—
403C2×Q8—3442no—
404C2×Q8—3441no—
405C2×Q8—3441no—
406C2×Q8C2×D17212yes—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—81no—
411C22×C4—434no—
412C22×C4—432no—
413C22×C4—432no—
414C22×C4—861no—
415C22×C4—861no—
416C22×C4—862no—
417C22×C4—861no—
418C22×C4—861no—
419C22×C4—861no—
420C22×C4—861no—
421C22×C4—861no—
422C22×C4—861no—
423C22×C4—3441no—
424C22×C4C2×D17211yescharacteristic
425C22×C4C2×D17211yescharacteristic
426C22×C4D4×D4311yescharacteristic
427C22×C4D4×D4311yescharacteristic
428C22×C4D4×D4311yescharacteristic
429C22×C4C23×D4311yescharacteristic
430Q16—3442no—
431Q16—3442no—
432C2×C8—22no—
433C2×C8—81no—
434C2×C8—862no—
435C2×C8—3441no—
436C4⋊C4—22no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—81no—
440C4⋊C4—432no—
441C4⋊C4—864no—
442C4⋊C4—864no—
443C4⋊C4—864no—
444C4⋊C4—864no—
445C4⋊C4—864no—
446C4⋊C4—862no—
447C4⋊C4—862no—
448C4⋊C4—861no—
449C4⋊C4—862no—
450C4⋊C4—862no—
451C4⋊C4—862no—
452C4⋊C4—862no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—3442no—
456C4⋊C4—1721no—
457C4⋊C4—1721no—
458C4⋊C4C2×D17212yes—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—42no—
462C22⋊C4—862no—
463C22⋊C4—862no—
464C22⋊C4—1721no—
465C22⋊C4—1721no—
466C42—864no—
467C42—864no—
468C23—41no—
469C23—41no—
470C23#1306329511yescharacteristic
471C23#1306329511yescharacteristic
472C23Q16×D4312yes—
473C23#1306335412yes—
474C23C2×D4×D4311yescharacteristic
475Q8—42no—
476Q8—81no—
477Q8—3441no—
478Q8—3444no—
479Q8—1722no—
480Q8—1722no—
481Q8—1722no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—434no—
496C2×C4—864no—
497C2×C4—864no—
498C2×C4—862no—
499C2×C4—862no—
500C2×C4—862no—
501C2×C4—862no—
502C2×C4—862no—
503C2×C4—3441no—
504C2×C4—1722no—
505C2×C4—1722no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—1722no—
509C2×C4—1722no—
510C2×C4—1722no—
511C2×C4—1722no—
512C2×C4#1306329511yescharacteristic
513C2×C4#1306329511yescharacteristic
514C2×C4C2×D4×D4311yescharacteristic
515C2×C4C22×D17211yescharacteristic
516C8—42no—
517C8—1722no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—42no—
525C22—42no—
526C22#1458305612yes—
527C22#1458305612yes—
528C22C2×#1306329511yescharacteristic
529C22C2×Q16×D4311yescharacteristic
530C22C2×#1306335411yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—21no—
535C4—42no—
536C4—42no—
537C4—82no—
538C4—864no—
539C4—3441no—
540C4—3441no—
541C4—1722no—
542C4—1722no—
543C4—1722no—
544C2—21no—
545C2—22no—
546C2—22no—
547C2—21no—
548C2C2×#1458305611yescharacteristic
549C2#1914396111yescharacteristic
550C2#1914399411yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1520C2
socleC22×C43C2×#120
prime radicalC24×C43C2×D4
hypercenter#1520D43
hypocenterC43#18295
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
5. #19133638C2semidirect
6. #19133570C2semidirect
143. C22×Dic43Q16semidirect
320. C43#18295semidirect

Maximal subgroups

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

subgroupindex
C2×#145835282
#191453702
#191453672
#191404112
#191336382
#191335702
#191331662
C2×#145826242
C43×#15202
#1829543