Finite Group Databasebeta

← #24992311

Subgroups — #24992311

Order 11008.

1270 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142883C211yesmaximal, characteristic
2C2×#95×D43C211yesmaximal, characteristic
3#19134504C211yesmaximal, characteristic
4C2×#14582637C211yesmaximal, characteristic, complemented
5C2×#14582635C211yesmaximal, characteristic, complemented
6#19132473C211yesmaximal, characteristic, complemented
7C43×#1294C211yesmaximal, characteristic, complemented
8C23×C4×D43—21no—
9C23×C4×D43C2211yescharacteristic
10C2×#13063305C412yescomplemented
11C2×#13063304C2211yescharacteristic
12C2×C22⋊(C43⋊C8)C2211yescharacteristic
13C2×(C2×D43)⋊C8—22no—
14#14582774—21no—
15#14582773—22no—
16#14582756C412yescomplemented
17#14582754—21no—
18C2×C43⋊#95—21no—
19C2×C43⋊#95C2211yescharacteristic
20#95×D43—22no—
21#95×D43—22no—
22#14582637—22no—
23#14582635—22no—
24C2×C22⋊C8×C43C2211yescharacteristic
25C43×#380C2211yescharacteristic
26C2×#95×C43C2211yescharacteristic
27C24×D43D411yescharacteristic
28C22×Dic86C2×C411yescharacteristic, complemented
29C23×Dic43—21no—
30C23×Dic43D411yescharacteristic
31C22×C4×D43—28no—
32C22×C4×D43—24no—
33C22×C4×D43—21no—
34C22×C4×D43—21no—
35C22×C4×D43—21no—
36C22×C4×D43—21no—
37C22×C4×D43—44no—
38C22×C4×D43—44no—
39C22×C4×D43—42no—
40C22×C4×D43—42no—
41C22×C4×D43C2×C412yes—
42C22×C4×D43D412yes—
43C22×C43⋊C8—21no—
44#13063305—44no—
45#13063304—21no—
46#13063304—21no—
47#13063304—21no—
48#13063304—21no—
49C2×C4⋊Dic43—22no—
50C2×C4⋊Dic43C2×C411yescharacteristic, complemented
51C2×Dic43⋊C4—21no—
52C2×C22⋊Dic43—21no—
53C2×(C2×D43)⋊C4—22no—
54C2×(C2×D43)⋊C4—22no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57(C2×D43)⋊C8—44no—
58C43⋊#95—24no—
59C43⋊#95—21no—
60C43⋊#95—22no—
61C43⋊#95D412yes—
62C23×C4×C43—21no—
63C23×C4×C43C2311yescharacteristic
64C22×C8×C43—21no—
65C2×C4⋊C4×C43C2×C412yescomplemented
66C2×C22⋊C4×C43—21no—
67C22⋊C8×C43—21no—
68C22⋊C8×C43—21no—
69#95×C43—21no—
70#95×C43—21no—
71#95×C43D412yes—
72C24×C43C2×D411yescharacteristic
73C23×D43—21no—
74C23×D43—21no—
75C23×D43—21no—
76C23×D43—21no—
77C23×D43—24no—
78C23×D43—24no—
79C23×D43C22⋊C412yes—
80C23×D43SD1612yes—
81C23×D43Q1612yes—
82C22×C4×C43—24no—
83C22×C4×C43—22no—
84C22×C4×C43—22no—
85C22×C4×C43—42no—
86C22×C4×C43—42no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43C22×C411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C22×C4×C43#4111yescharacteristic
95C22×Dic43—24no—
96C22×Dic43—21no—
97C22×Dic43—21no—
98C22×Dic43—21no—
99C22×Dic43—22no—
100C22×Dic43—21no—
101C22×Dic43—42no—
102C22×Dic43—42no—
103C22×Dic43—41no—
104C22×Dic43—41no—
105C22×Dic43C22⋊C412yes—
106C2×C4×D43—216no—
107C2×C4×D43—22no—
108C2×C4×D43—22no—
109C2×C4×D43—22no—
110C2×C4×D43—22no—
111C2×C4×D43—24no—
112C2×C4×D43—24no—
113C2×C4×D43—42no—
114C2×C4×D43—42no—
115C2×C4×D43—44no—
116C2×C4×D43—44no—
117C2×C4×D43—48no—
118C2×C4×D43—44no—
119C2×C4×D43—44no—
120C2×C4×D43—416no—
121C2×C4×D43—48no—
122C2×C4×D43—416no—
123C2×Dic86—21no—
124C2×Dic86—21no—
125C2×Dic86—42no—
126C2×C8×C43—42no—
127C2×C8×C43—41no—
128C4⋊C4×C43—42no—
129C22⋊C4×C43—41no—
130C22⋊C4×C43—41no—
131C22⋊Dic43—41no—
132C22⋊Dic43—41no—
133(C2×D43)⋊C4—44no—
134(C2×D43)⋊C4—44no—
135C4⋊Dic43—21no—
136C4⋊Dic43—21no—
137C4⋊Dic43—44no—
138Dic43⋊C4—41no—
139Dic43⋊C4—41no—
140C2×C43⋊C8—42no—
141C2×C43⋊C8—41no—
142C23×C43—22no—
143C23×C43—22no—
144C23×C43C2×C22⋊C411yescharacteristic
145C23×C43#12011yescharacteristic
146C23×C43#12311yescharacteristic
147C23×C43C2×SD1611yescharacteristic
148C23×C43C2×Q1611yescharacteristic
149C23×C43AGL(1,ℤ/8)11yescharacteristic
150C23×C43#13711yescharacteristic
151C22×D43—24no—
152C22×D43—24no—
153C22×D43—24no—
154C22×D43—28no—
155C22×D43—24no—
156C22×D43—28no—
157C22×D43—22no—
158C22×D43—22no—
159C22×D43—22no—
160C22×D43—22no—
161C22×D43—22no—
162C22×D43—22no—
163C22×D43—22no—
164C22×D43—22no—
165C22×D43—28no—
166C22×D43—28no—
167C22×D43#9914yes—
168C22×D43#10314yes—
169C22×D43#10414yes—
170C2×C4×C43—22no—
171C2×C4×C43—22no—
172C2×C4×C43—24no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—42no—
178C2×C4×C43—44no—
179C2×C4×C43—44no—
180C2×C4×C43—42no—
181C2×C4×C43—42no—
182C2×C4×C43—42no—
183C2×C4×C43—42no—
184C2×C4×C43C4×D411yescharacteristic
185C2×C4×C43C4×D411yescharacteristic
186C2×C4×C43#12111yescharacteristic
187C2×C4×C43#12111yescharacteristic
188C2×Dic43—24no—
189C2×Dic43—22no—
190C2×Dic43—22no—
191C2×Dic43—22no—
192C2×Dic43—42no—
193C2×Dic43—44no—
194C2×Dic43—44no—
195C2×Dic43—42no—
196C2×Dic43—42no—
197C2×Dic43—42no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—42no—
201C2×Dic43—42no—
202C4×D43—44no—
203C4×D43—44no—
204C4×D43—44no—
205C4×D43—44no—
206C4×D43—432no—
207Dic86—81no—
208Dic86—81no—
209C8×C43—81no—
210C43⋊C8—81no—
211#9143—431nomaximal, Sylow
212C22×C43—21no—
213C22×C43—21no—
214C22×C43—21no—
215C22×C43—21no—
216C22×C43—22no—
217C22×C43—22no—
218C22×C43—22no—
219C22×C43—22no—
220C22×C43#38611yescharacteristic
221C22×C43C2×#9912yes—
222C22×C43C2×#10311yescharacteristic
223C22×C43#41711yescharacteristic
224C22×C43C2×#10412yes—
225C22×C43#45011yescharacteristic
226C22×C43#45111yescharacteristic
227C22×C43#48311yescharacteristic
228C22×C43#48411yescharacteristic
229C2×D43—28no—
230C2×D43—28no—
231C2×D43—28no—
232C2×D43—28no—
233C2×D43—24no—
234C2×D43—24no—
235C2×D43—24no—
236C2×D43—24no—
237C2×D43—24no—
238C2×D43—24no—
239C2×D43#32818yescomplemented
240C4×C43—21no—
241C4×C43—21no—
242C4×C43—21no—
243C4×C43—21no—
244C4×C43—44no—
245C4×C43—82no—
246Dic43—44no—
247Dic43—42no—
248Dic43—81no—
249Dic43—81no—
250#2848—431no—
251C22×#95—431no—
252#1779—431no—
253C2×#328—431no—
254C2×#328—431no—
255#1294—431no—
256#1294D4311yescharacteristic, complemented
257C2×C43—21no—
258C2×C43—21no—
259C2×C43—21no—
260C2×C43—21no—
261C2×C43C2×#32812yes—
262C2×C43#150412yes—
263C2×C43#187211yescharacteristic
264C2×C43#189611yescharacteristic
265C2×C43#189811yescharacteristic
266D43—28no—
267C24×C4—431no—
268C24×C4—861no—
269C2×C22⋊Q8—431no—
270C2×C22⋊Q8—432no—
271C2×C22⋊C8—431no—
272C2×C22⋊C8—862no—
273C2×C22⋊C8C2×D4311yescharacteristic
274#385—862no—
275#385—861no—
276#380—432no—
277#380C2×D4311yescharacteristic
278#379—861no—
279C2×#95—431no—
280C2×#95—862no—
281C2×#95—861no—
282C2×#95—862no—
283C2×#95C2×D4311yescharacteristic
284#328—862no—
285#328—862no—
286C43#914311yescharacteristic, complemented, Sylow
287C25—431no—
288C22×Q8—431no—
289C23×C4—21no—
290C23×C4—431no—
291C23×C4—432no—
292C23×C4—432no—
293C23×C4—864no—
294C23×C4—868no—
295C23×C4—861no—
296C23×C4—861no—
297C23×C4—861no—
298C23×C4—861no—
299C23×C4—861no—
300C23×C4—1724no—
301C23×C4—1722no—
302C23×C4—1724no—
303C23×C4—1722no—
304C23×C4C22×D4311yescharacteristic
305C22×C8—21no—
306C22×C8—861no—
307C22⋊Q8—861no—
308C22⋊Q8—861no—
309C22⋊Q8—861no—
310C22⋊Q8—861no—
311C22⋊Q8—1724no—
312C2×C4⋊C4—431no—
313C2×C4⋊C4—862no—
314C2×C4⋊C4—861no—
315C2×C4⋊C4C4×D4312yescomplemented
316C2×C22⋊C4—21no—
317C2×C22⋊C4—862no—
318C2×C22⋊C4—862no—
319C2×C22⋊C4—861no—
320C22⋊C8—21no—
321C22⋊C8—21no—
322C22⋊C8—861no—
323C22⋊C8—861no—
324C22⋊C8—1724no—
325#95—21no—
326#95—21no—
327#95—432no—
328#95—862no—
329#95—864no—
330#95—861no—
331#95D17212yes—
332C24—432no—
333C24—432no—
334C24—432no—
335C24—864no—
336C24—864no—
337C24—861no—
338C24—861no—
339C24—861no—
340C24—861no—
341C24D4×D4311yescharacteristic
342C2×Q8—861no—
343C2×Q8—861no—
344C2×Q8—1722no—
345C22×C4—24no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—432no—
353C22×C4—864no—
354C22×C4—864no—
355C22×C4—8616no—
356C22×C4—864no—
357C22×C4—862no—
358C22×C4—861no—
359C22×C4—861no—
360C22×C4—862no—
361C22×C4—862no—
362C22×C4—862no—
363C22×C4—862no—
364C22×C4—861no—
365C22×C4—861no—
366C22×C4—1722no—
367C22×C4—1722no—
368C22×C4—1724no—
369C22×C4—1724no—
370C22×C4—1724no—
371C22×C4—1724no—
372C22×C4—17216no—
373C22×C4—1728no—
374C22×C4—17216no—
375C22×C4—1728no—
376C22×C4—1722no—
377C22×C4—1722no—
378C22×C4—1721no—
379C22×C4—1721no—
380C22×C4C2×C4×D4311yescharacteristic
381C22×C4C2×D17211yescharacteristic
382C22×C4#1062189811yescharacteristic
383C22×C4D4×D4311yescharacteristic
384C22×C4D4×D4311yescharacteristic
385C22×C4#1062190211yescharacteristic
386C2×C8—42no—
387C2×C8—41no—
388C2×C8—1722no—
389C2×C8—1721no—
390C4⋊C4—42no—
391C4⋊C4—861no—
392C4⋊C4—861no—
393C4⋊C4—1724no—
394C4⋊C4—1721no—
395C4⋊C4—1721no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—1724no—
399C22⋊C4—1724no—
400C22⋊C4—1721no—
401C22⋊C4—1721no—
402C23—22no—
403C23—22no—
404C23—434no—
405C23—434no—
406C23—434no—
407C23—868no—
408C23—868no—
409C23—864no—
410C23—864no—
411C23—864no—
412C23—868no—
413C23—864no—
414C23—868no—
415C23—862no—
416C23—862no—
417C23—862no—
418C23—862no—
419C23—862no—
420C23—862no—
421C23—862no—
422C23—862no—
423C23C22⋊C4×D4311yescharacteristic
424C23#1306329511yescharacteristic
425C23#1306331011yescharacteristic
426C23SD16×D4311yescharacteristic
427C23Q16×D4311yescharacteristic
428C23#1306334911yescharacteristic
429C23#1306335411yescharacteristic
430Q8—3441no—
431Q8—3441no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—44no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—864no—
447C2×C4—862no—
448C2×C4—862no—
449C2×C4—862no—
450C2×C4—1724no—
451C2×C4—1724no—
452C2×C4—1724no—
453C2×C4—1724no—
454C2×C4—17232no—
455C2×C4—1722no—
456C2×C4—1722no—
457C2×C4—1721no—
458C2×C4—1721no—
459C2×C4—1722no—
460C2×C4—1724no—
461C2×C4—1724no—
462C2×C4—1722no—
463C2×C4—1722no—
464C2×C4—1722no—
465C2×C4#1306328711yescharacteristic
466C2×C4C4×D17211yescharacteristic
467C2×C4#1306329811yescharacteristic
468C2×C4#1306330011yescharacteristic
469C8—81no—
470C8—3441no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—438no—
480C22—868no—
481C22—868no—
482C22—868no—
483C22—868no—
484C22—864no—
485C22—864no—
486C22—864no—
487C22—864no—
488C22—864no—
489C22—864no—
490C22#1458277711yescharacteristic
491C22#99×D4312yes—
492C22#103×D4311yescharacteristic
493C22#1458289711yescharacteristic
494C22#104×D4312yes—
495C22#1458305111yescharacteristic
496C22#1458305611yescharacteristic
497C22#1458323111yescharacteristic
498C22#1458323611yescharacteristic
499C4—21no—
500C4—21no—
501C4—21no—
502C4—21no—
503C4—44no—
504C4—82no—
505C4—3441no—
506C4—3441no—
507C4—1724no—
508C4—1722no—
509C2—21no—
510C2—21no—
511C2—21no—
512C2—21no—
513C2—868no—
514C2#328×D4312yes—
515C2#1913309612yes—
516C2#1913490111yescharacteristic
517C2#1913503711yescharacteristic
518C2#1913504711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1294C2
socleC23×C43C2×C22⋊C4
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenter#1294D43
hypocenterC43#9143
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
4. C2×#14582637C2semidirect
5. C2×#14582635C2semidirect
6. #19132473C2semidirect
7. C43×#1294C2semidirect
10. C2×#13063305C4semidirect
16. #14582756C4semidirect
28. C22×Dic86C2×C4semidirect
50. C2×C4⋊Dic43C2×C4semidirect
65. C2×C4⋊C4×C43C2×C4semidirect
239. C2×D43#328semidirect
256. #1294D43semidirect
286. C43#9143semidirect
315. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191428832
C2×#95×D432
#191345042
C2×#145826372
C2×#145826352
#191324732
C43×#12942
#914343