Finite Group Databasebeta

← #24991765

Subgroups — #24991765

Order 11008.

678 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×#14583217C211yesmaximal, characteristic
2#19137298C211yesmaximal, characteristic
3#19134685C211yesmaximal, characteristic, complemented
4C2×#14582632C211yesmaximal, characteristic
5#19132474C211yesmaximal, characteristic, complemented
6#19132438C211yesmaximal, characteristic, complemented
7C43×#1445C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C2×C4×C22⋊D43—21no—
10#14583217—22no—
11#14583217C414yescomplemented
12C2×#13063256—21no—
13C2×#13063245—21no—
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16#14582791—21no—
17#14582784—21no—
18#14582778—21no—
19#14582777—21no—
20#14582773—21no—
21#14582759C2211yescharacteristic
22#14582661—21no—
23#14582661—21no—
24#14582632—22no—
25C22×C4⋊C4×C43C2211yescharacteristic
26C2×#95×C43—21no—
27C2×#95×C43—21no—
28C2×#95×C43C2211yescharacteristic
29C2×#95×C43C2211yescharacteristic
30C22×D172D411yescharacteristic
31C22×C22⋊D43—21no—
32C22×C4×D43—21no—
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35#13063299—21no—
36#13063299—21no—
37#13063299C2×C412yes—
38#13063299D412yes—
39C4×C22⋊D43—42no—
40C4×C22⋊D43—42no—
41C2×C4⋊Dic43D411yescharacteristic
42C2×C4⋊Dic43D411yescharacteristic
43C2×C4⋊Dic43D411yescharacteristic
44C2×Dic43⋊C4—21no—
45C2×C22⋊Dic43—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×C4×Dic43—21no—
51#13063256—24no—
52#13063245—24no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)C2×C412yescomplemented
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C23×C4×C43—21no—
61C23×C4×C43—21no—
62C23×C4×C43D411yescharacteristic
63C23×C4×C43D411yescharacteristic
64C23×C4×C43C2311yescharacteristic
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43C2×C412yescomplemented
71#95×C43—21no—
72#95×C43—21no—
73#95×C43—21no—
74#95×C43—21no—
75#95×C43—42no—
76#95×C43—42no—
77C24×C43C2×D411yescharacteristic
78C23×D43—21no—
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43—41no—
99C22×C4×C43—41no—
100C22×C4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43—41no—
103C22×C4×C43—41no—
104C22×C4×C43SD1612yes—
105C22×C4×C43C22×C411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C2×C22⋊D43—22no—
112C2×C22⋊D43—22no—
113C2×C22⋊D43—41no—
114C2×C22⋊D43—41no—
115C2×C22⋊D43—41no—
116C2×C22⋊D43—41no—
117C22×Dic43—21no—
118C22×Dic43—21no—
119C22×Dic43—21no—
120C2×D172—21no—
121C2×D172—41no—
122C2×D172—41no—
123C2×D172C22⋊C412yes—
124C2×C4×D43—42no—
125C2×C4×D43—81no—
126C2×C4×D43—81no—
127C4⋊C4×C43—22no—
128C4⋊C4×C43—22no—
129C4⋊C4×C43—41no—
130C4⋊C4×C43—41no—
131C22⋊Dic43—41no—
132C22⋊Dic43—41no—
133(C2×D43)⋊C4—22no—
134(C2×D43)⋊C4—22no—
135(C2×D43)⋊C4—42no—
136(C2×D43)⋊C4—81no—
137(C2×D43)⋊C4—81no—
138C4⋊Dic43—21no—
139C4⋊Dic43—41no—
140C4⋊Dic43—41no—
141C4⋊Dic43C22⋊C412yes—
142Dic43⋊C4—42no—
143C4×Dic43—42no—
144C2×C43⋊C8—22no—
145C2×C43⋊C8—41no—
146C2×C43⋊C8—41no—
147C2×C43⋊C8—41no—
148C2×C43⋊C8—41no—
149C2×C43⋊C8—41no—
150C23×C43—21no—
151C23×C43—21no—
152C23×C43—21no—
153C23×C43—21no—
154C23×C43C4×D411yescharacteristic
155C23×C43#12011yescharacteristic
156C23×C43#12111yescharacteristic
157C23×C43C2×SD1611yescharacteristic
158C23×C43#13511yescharacteristic
159C23×C43AGL(1,ℤ/8)11yescharacteristic
160C23×C43#13711yescharacteristic
161C22×D43—22no—
162C22×D43—41no—
163C22×D43—41no—
164C22×D43—41no—
165C22×D43—41no—
166C22×D43—41no—
167C22×D43—41no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—22no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—42no—
180C2×C4×C43—42no—
181C2×C4×C43—42no—
182C2×C4×C43—42no—
183C2×C4×C43—42no—
184C2×C4×C43—42no—
185C2×C4×C43—42no—
186C2×C4×C43—42no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—81no—
191C2×C4×C43—81no—
192C2×C4×C43—81no—
193C2×C4×C43—81no—
194C2×C4×C43—81no—
195C2×C4×C43—81no—
196C2×C4×C43—81no—
197C2×C4×C43—81no—
198C2×C4×C43—81no—
199C2×C4×C43—81no—
200C2×C4×C43C2×C22⋊C411yescharacteristic
201C2×C4×C43C4×D411yescharacteristic
202C2×C4×C43#12111yescharacteristic
203C2×C4×C43#12311yescharacteristic
204C22⋊D43—42no—
205C22⋊D43—42no—
206C22⋊D43—42no—
207C22⋊D43—42no—
208C2×Dic43—22no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—41no—
214C2×Dic43—41no—
215C2×Dic43—41no—
216C2×Dic43—41no—
217D172—42no—
218D172—81no—
219C4×D43—84no—
220C43⋊C8—42no—
221C43⋊C8—81no—
222#9045—431nomaximal, Sylow
223C22×C43—21no—
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—21no—
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43#38611yescharacteristic
236C22×C43C4×SD1611yescharacteristic
237C22×C43#44011yescharacteristic
238C22×C43#45011yescharacteristic
239C22×C43#45211yescharacteristic
240C22×C43#45311yescharacteristic
241C22×C43#45411yescharacteristic
242C22×C43#45811yescharacteristic
243C22×C43#45811yescharacteristic
244C22×C43#46111yescharacteristic
245C22×C43#46311yescharacteristic
246C2×D43—42no—
247C2×D43—42no—
248C2×D43—42no—
249C2×D43—81no—
250C2×D43—81no—
251C2×D43—81no—
252C2×D43—81no—
253C4×C43—21no—
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—42no—
258C4×C43—82no—
259C4×C43—81no—
260C4×C43—82no—
261Dic43—42no—
262Dic43—81no—
263Dic43—81no—
264C2×#481—431no—
265#2325—431no—
266#1824—431no—
267C2×#327—431no—
268#1445D4311yescharacteristic, complemented
269#1294—431no—
270#1280—431no—
271C2×C43—21no—
272C2×C43—21no—
273C2×C43—21no—
274C2×C43—21no—
275C2×C43#161311yescharacteristic
276C2×C43#161511yescharacteristic
277C2×C43#161611yescharacteristic
278C2×C43#161811yescharacteristic
279C2×C43#187711yescharacteristic
280C2×C43#188311yescharacteristic
281C2×C43#189011yescharacteristic
282D43—82no—
283C2×#121—431no—
284C2×C4×D4—861no—
285C22×C4⋊C4C2×D4311yescharacteristic
286#481—434no—
287#481—862no—
288C2×#106—861no—
289C2×#102—861no—
290C2×C22⋊C8—431no—
291C2×C22⋊C8—431no—
292#388—861no—
293#387—861no—
294#386—861no—
295#386—861no—
296#385—861no—
297#380—431no—
298C2×#95—21no—
299C2×#95—21no—
300C2×#95C2×D4311yescharacteristic
301C2×#95C2×D4311yescharacteristic
302#340—861no—
303#340—861no—
304#327—862no—
305C43#904511yescharacteristic, complemented, Sylow
306C22×D4—431no—
307C22×D4—861no—
308C23×C4—21no—
309C23×C4—21no—
310C23×C4—861no—
311C23×C4C22⋊D4311yescharacteristic
312C23×C4C22⋊D4311yescharacteristic
313C23×C4C22×D4311yescharacteristic
314C22×C8—861no—
315C22×C8—861no—
316#121—432no—
317#121—432no—
318#121—861no—
319#121—861no—
320C4×D4—1722no—
321C4×D4—1722no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—431no—
328C2×C4⋊C4—431no—
329C2×C4⋊C4—431no—
330C2×C4⋊C4—861no—
331C2×C4⋊C4C4×D4312yescomplemented
332C2×C22⋊C4—861no—
333C2×C22⋊C4—861no—
334C2×C22⋊C4—861no—
335C2×C22⋊C4—861no—
336C2×C22⋊C4—861no—
337C2×C42—861no—
338#106—864no—
339#102—864no—
340C22⋊C8—432no—
341C22⋊C8—861no—
342C22⋊C8—861no—
343C22⋊C8—861no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—42no—
349#95—42no—
350#95—861no—
351#95—861no—
352#95—861no—
353C24—861no—
354C24C2×C22⋊D4311yescharacteristic
355C2×D4—432no—
356C2×D4—862no—
357C2×D4—862no—
358C2×D4—861no—
359C2×D4—1721no—
360C2×D4—1721no—
361C2×D4—1721no—
362C2×D4—1721no—
363C2×D4—1721no—
364C2×D4—1721no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—861no—
391C22×C4—861no—
392C22×C4—861no—
393C22×C4—3441no—
394C22×C4—3441no—
395C22×C4—1722no—
396C22×C4#1062188412yes—
397C22×C4C2×C4×D4311yescharacteristic
398C22×C4#1062189811yescharacteristic
399C22×C4D4×D4311yescharacteristic
400C22×C4D4×D4311yescharacteristic
401C22×C4D4×D4311yescharacteristic
402C22×C4#1062190011yescharacteristic
403C2×C8—862no—
404C2×C8—1721no—
405C2×C8—1721no—
406C2×C8—1721no—
407C2×C8—1721no—
408C2×C8—1721no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—432no—
414C4⋊C4—861no—
415C4⋊C4—1721no—
416C4⋊C4—1721no—
417C4⋊C4—1722no—
418C22⋊C4—862no—
419C22⋊C4—862no—
420C22⋊C4—3441no—
421C22⋊C4—3441no—
422C22⋊C4—1722no—
423C22⋊C4—1721no—
424C22⋊C4—1721no—
425C42—1722no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—862no—
431C23—1721no—
432C23—1721no—
433C23—1721no—
434C23—1721no—
435C23—1721no—
436C23—1721no—
437C23C4×C22⋊D4311yescharacteristic
438C23#1306329311yescharacteristic
439C23#1306329611yescharacteristic
440C23C2×#1062188411yescharacteristic
441C23#1306334511yescharacteristic
442C23#1306335011yescharacteristic
443C23#1306335611yescharacteristic
444D4—3441no—
445D4—1722no—
446D4—1722no—
447D4—1722no—
448D4—1722no—
449D4—1722no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4—862no—
483C2×C4—3444no—
484C2×C4—1721no—
485C2×C4—1721no—
486C2×C4—1721no—
487C2×C4—1721no—
488C2×C4—1721no—
489C2×C4—1721no—
490C2×C4—1721no—
491C2×C4—1721no—
492C2×C4C22⋊C4×D4311yescharacteristic
493C2×C4(C22⋊D43)⋊C411yescharacteristic
494C2×C4#1306329811yescharacteristic
495C2×C4#1306330711yescharacteristic
496C8—3441no—
497C8—1722no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—3441no—
511C22—3441no—
512C22—3441no—
513C22—3441no—
514C22—1722no—
515C22—1722no—
516C22—1722no—
517C22#1458277511yescharacteristic
518C22C4×#1062188411yescharacteristic
519C22#1458299711yescharacteristic
520C22#1458304911yescharacteristic
521C22#1458305911yescharacteristic
522C22#1458306611yescharacteristic
523C22#1458307111yescharacteristic
524C22#1458308811yescharacteristic
525C22#1458308811yescharacteristic
526C22#1458310111yescharacteristic
527C22#1458311111yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—42no—
533C4—82no—
534C4—81no—
535C4—82no—
536C4—3441no—
537C4—3441no—
538C4—1722no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—3442no—
544C2#1913361411yescharacteristic
545C2#1913362411yescharacteristic
546C2#1913363111yescharacteristic
547C2#1913364111yescharacteristic
548C2#1913493211yescharacteristic
549C2#1913497411yescharacteristic
550C2#1913500511yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1445C2
socleC23×C43#120
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1445D43
hypocenterC43#9045
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1445

Complements

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

NH ≅ G/Ntype
3. #19134685C2semidirect
5. #19132474C2semidirect
6. #19132438C2semidirect
7. C43×#1445C2semidirect
11. #14583217C4semidirect
56. C22⋊(C43⋊C8)C2×C4semidirect
70. C2×C4⋊C4×C43C2×C4semidirect
268. #1445D43semidirect
305. C43#9045semidirect
331. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832172
#191372982
#191346852
C2×#145826322
#191324742
#191324382
C43×#14452
#904543