Finite Group Databasebeta

← #24988045

Subgroups — #24988045

Order 11008.

908 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583433C211yesmaximal, characteristic
2#19134663C211yesmaximal, characteristic, complemented
3C2×#14582635C212yesmaximal, complemented
4C2×#14582632C212yesmaximal
5C43×#1434C211yesmaximal, characteristic, complemented
6#14583433—24no—
7#14583433—24no—
8C2×#13063319—21no—
9C2×#13063317C411yescharacteristic, complemented
10C2×#13063313C411yescharacteristic, complemented
11C2×#13063308—21no—
12C2×#13063304C2211yescharacteristic
13C2×#13063299C2211yescharacteristic
14C2×C4×Dic86C411yescharacteristic, complemented
15C2×C4×D172C411yescharacteristic, complemented
16C2×C4×C22⋊D43—21no—
17C2×#13063282—21no—
18C2×C22⋊(C43⋊C8)C2212yes—
19#14582654—21no—
20#14582654—21no—
21#14582635—24no—
22#14582632—24no—
23C22×C42×C43C2211yescharacteristic
24C2×#95×C43—21no—
25C2×#95×C43—21no—
26C2×#95×C43C2212yes—
27C22×Dic86C2×C411yescharacteristic
28C22×D172C2×C411yescharacteristic
29C22×C22⋊D43—21no—
30C22×C4×D43—21no—
31C22×C43⋊C8—22no—
32#13063319—28no—
33#13063317—22no—
34#13063317—22no—
35#13063313—22no—
36#13063313—22no—
37#13063308—28no—
38#13063304—22no—
39#13063304D414yes—
40#13063299—22no—
41#13063299D414yes—
42C4×Dic86—22no—
43C4×Dic86—22no—
44C4×D172—22no—
45C4×D172—22no—
46C4×C22⋊D43—28no—
47#13063282—28no—
48C2×C4⋊Dic43C2×C411yescharacteristic
49C2×C4⋊Dic43C2×C411yescharacteristic
50C2×Dic43⋊C4—21no—
51C2×Dic43⋊C4—21no—
52C2×Dic43⋊C4—21no—
53C2×Dic43⋊C4—21no—
54C2×C22⋊Dic43—21no—
55C2×(C2×D43)⋊C4—21no—
56C2×(C2×D43)⋊C4—21no—
57C2×(C2×D43)⋊C4—21no—
58C2×(C2×D43)⋊C4—21no—
59C2×C4×Dic43—21no—
60C22⋊(C43⋊C8)—22no—
61C22⋊(C43⋊C8)—22no—
62C23×C4×C43—22no—
63C23×C4×C43D411yescharacteristic
64C23×C4×C43D411yescharacteristic
65C23×C4×C43C2311yescharacteristic
66C2×C42×C43—22no—
67C2×C42×C43—22no—
68C2×C42×C43C2×C411yescharacteristic
69C2×C42×C43C2×C411yescharacteristic
70C2×C42×C43D411yescharacteristic
71C2×C42×C43D411yescharacteristic
72#95×C43—24no—
73#95×C43—22no—
74#95×C43—22no—
75#95×C43—42no—
76C24×C43C2×D411yescharacteristic
77C23×D43—21no—
78C22×C4×C43—22no—
79C22×C4×C43—24no—
80C22×C4×C43—22no—
81C22×C4×C43—22no—
82C22×C4×C43—22no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—42no—
89C22×C4×C43—42no—
90C22×C4×C43—42no—
91C22×C4×C43—42no—
92C22×C4×C43—42no—
93C22×C4×C43—42no—
94C22×C4×C43C22⋊C411yescharacteristic
95C22×C4×C43C22⋊C411yescharacteristic
96C22×C4×C43C22⋊C411yescharacteristic
97C22×C4×C43C22⋊C411yescharacteristic
98C22×C4×C43C22×C411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D412yes—
101C22×C4×C43C2×D412yes—
102C2×C22⋊D43—24no—
103C2×C22⋊D43—42no—
104C2×C22⋊D43—41no—
105C2×C22⋊D43—41no—
106C22×Dic43—21no—
107C22×Dic43—21no—
108C22×Dic43—21no—
109C2×D172—21no—
110C2×D172—41no—
111C2×D172—41no—
112C2×D172C22⋊C412yes—
113C2×C4×D43—24no—
114C2×C4×D43—42no—
115C2×C4×D43—42no—
116C2×Dic86—21no—
117C2×Dic86—41no—
118C2×Dic86—41no—
119C2×Dic86C22⋊C412yes—
120C42×C43—21no—
121C42×C43—21no—
122C42×C43—21no—
123C42×C43—21no—
124C42×C43—22no—
125C42×C43—22no—
126C22⋊Dic43—24no—
127(C2×D43)⋊C4—24no—
128(C2×D43)⋊C4—24no—
129(C2×D43)⋊C4—24no—
130(C2×D43)⋊C4—24no—
131C4⋊Dic43—21no—
132C4⋊Dic43—21no—
133C4⋊Dic43C22⋊C412yes—
134C4⋊Dic43C22⋊C412yes—
135Dic43⋊C4—24no—
136Dic43⋊C4—24no—
137Dic43⋊C4—24no—
138Dic43⋊C4—24no—
139C4×Dic43—24no—
140C2×C43⋊C8—42no—
141C2×C43⋊C8—42no—
142C2×C43⋊C8—42no—
143C23×C43—21no—
144C23×C43—21no—
145C23×C43—21no—
146C23×C43—21no—
147C23×C43C2×C22⋊C411yescharacteristic
148C23×C43#12012yes—
149C23×C43#13512yes—
150C23×C43AGL(1,ℤ/8)11yescharacteristic
151C23×C43#13711yescharacteristic
152C22×D43—22no—
153C22×D43—41no—
154C22×D43—41no—
155C22×D43—41no—
156C22×D43—41no—
157C22×D43—41no—
158C22×D43—41no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
166C2×C4×C43—21no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—21no—
173C2×C4×C43—21no—
174C2×C4×C43—42no—
175C2×C4×C43—42no—
176C2×C4×C43—44no—
177C2×C4×C43—42no—
178C2×C4×C43—42no—
179C2×C4×C43—44no—
180C2×C4×C43—44no—
181C2×C4×C43—44no—
182C2×C4×C43—82no—
183C2×C4×C43—82no—
184C2×C4×C43—82no—
185C2×C4×C43—82no—
186C2×C4×C43#10412yes—
187C2×C4×C43C2×C22⋊C411yescharacteristic
188C2×C4×C43C2×C22⋊C411yescharacteristic
189C2×C4×C43#12012yes—
190C22⋊D43—44no—
191C22⋊D43—44no—
192C2×Dic43—22no—
193C2×Dic43—22no—
194C2×Dic43—22no—
195C2×Dic43—41no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—41no—
201D172—42no—
202D172—42no—
203C4×D43—48no—
204Dic86—42no—
205Dic86—42no—
206C43⋊C8—82no—
207#8330—431nomaximal, Sylow
208C22×C43—22no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—22no—
214C22×C43—22no—
215C22×C43—22no—
216C22×C43#37911yescharacteristic
217C22×C43#41011yescharacteristic
218C22×C43#41011yescharacteristic
219C22×C43#41611yescharacteristic
220C22×C43#41711yescharacteristic
221C22×C43C2×#10411yescharacteristic
222C22×C43#42111yescharacteristic
223C22×C43#44912yes—
224C22×C43#45212yes—
225C2×D43—42no—
226C2×D43—42no—
227C2×D43—42no—
228C2×D43—81no—
229C2×D43—81no—
230C2×D43—81no—
231C2×D43—81no—
232C4×C43—22no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—22no—
236C4×C43—41no—
237C4×C43—41no—
238C4×C43—41no—
239C4×C43—84no—
240Dic43—42no—
241Dic43—42no—
242Dic43—42no—
243C2×#529—431no—
244#1817—431no—
245C2×#328—432no—
246C2×#327—432no—
247#1434D4311yescharacteristic, complemented
248C2×C43—22no—
249C2×C43—22no—
250C2×C43#150011yescharacteristic
251C2×C43#150911yescharacteristic
252C2×C43#151211yescharacteristic
253C2×C43#152111yescharacteristic
254C2×C43#178211yescharacteristic
255C2×C43#178811yescharacteristic
256C2×C43#178911yescharacteristic
257D43—82no—
258#529—864no—
259#529—864no—
260C2×#126—861no—
261C2×#125—431no—
262C2×#124—431no—
263C2×#123—861no—
264C2×C22⋊Q8—431no—
265C2×#121—431no—
266C2×C4×Q8—431no—
267C2×C4×D4—431no—
268C2×C4×D4—861no—
269C2×#117—861no—
270C22×C42C2×D4311yescharacteristic
271C2×C22⋊C8—432no—
272C2×#95—21no—
273C2×#95—21no—
274C2×#95C2×D4312yes—
275#336—861no—
276#336—861no—
277#328—864no—
278#327—864no—
279C43#833011yescharacteristic, complemented, Sylow
280C22×Q8—431no—
281C22×D4—431no—
282C22×D4—861no—
283C23×C4—22no—
284C23×C4—861no—
285C23×C4C22⋊D4311yescharacteristic
286C23×C4C22⋊D4311yescharacteristic
287C23×C4C22×D4311yescharacteristic
288C22×C8—862no—
289#126—868no—
290#125—862no—
291#125—862no—
292#124—862no—
293#124—862no—
294#123—868no—
295C22⋊Q8—434no—
296C22⋊Q8—862no—
297#121—434no—
298#121—862no—
299C4×Q8—862no—
300C4×Q8—862no—
301C4×D4—862no—
302C4×D4—862no—
303C4×D4—868no—
304#117—868no—
305C2×C4⋊C4—431no—
306C2×C4⋊C4—431no—
307C2×C4⋊C4—861no—
308C2×C4⋊C4—861no—
309C2×C4⋊C4—861no—
310C2×C4⋊C4—861no—
311C2×C22⋊C4—861no—
312C2×C22⋊C4—861no—
313C2×C22⋊C4—861no—
314C2×C22⋊C4—861no—
315C2×C22⋊C4—861no—
316C2×C42—22no—
317C2×C42—22no—
318C2×C42—861no—
319C2×C42C4×D4311yescharacteristic
320C2×C42C4×D4311yescharacteristic
321C2×C42D17211yescharacteristic
322C2×C42D17211yescharacteristic
323C22⋊C8—862no—
324C22⋊C8—862no—
325#95—24no—
326#95—22no—
327#95—22no—
328#95—42no—
329C24—861no—
330C24C2×C22⋊D4311yescharacteristic
331C2×Q8—432no—
332C2×Q8—861no—
333C2×Q8—1721no—
334C2×Q8—1721no—
335C2×D4—432no—
336C2×D4—864no—
337C2×D4—861no—
338C2×D4—1721no—
339C2×D4—1721no—
340C2×D4—1722no—
341C2×D4—1721no—
342C2×D4—1721no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—24no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—864no—
360C22×C4—861no—
361C22×C4—861no—
362C22×C4—861no—
363C22×C4—1722no—
364C22×C4—1722no—
365C22×C4(C2×D43)⋊C411yescharacteristic
366C22×C4(C2×D43)⋊C411yescharacteristic
367C22×C4(C2×D43)⋊C411yescharacteristic
368C22×C4(C2×D43)⋊C411yescharacteristic
369C22×C4C2×C4×D4311yescharacteristic
370C22×C4C2×D17211yescharacteristic
371C22×C4D4×D4312yes—
372C22×C4D4×D4312yes—
373C2×C8—1722no—
374C2×C8—1722no—
375C2×C8—1722no—
376C4⋊C4—432no—
377C4⋊C4—432no—
378C4⋊C4—864no—
379C4⋊C4—864no—
380C4⋊C4—864no—
381C4⋊C4—861no—
382C4⋊C4—861no—
383C4⋊C4—864no—
384C22⋊C4—864no—
385C22⋊C4—864no—
386C22⋊C4—864no—
387C22⋊C4—864no—
388C22⋊C4—864no—
389C42—21no—
390C42—21no—
391C42—21no—
392C42—21no—
393C42—22no—
394C42—22no—
395C42—864no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—862no—
401C23—1721no—
402C23—1721no—
403C23—1721no—
404C23—1721no—
405C23—1721no—
406C23—1721no—
407C23C2×(C2×D43)⋊C411yescharacteristic
408C23#1306329312yes—
409C23#1306334512yes—
410C23#1306335111yescharacteristic
411C23#1306335611yescharacteristic
412Q8—1722no—
413Q8—1722no—
414D4—1722no—
415D4—1722no—
416D4—1724no—
417D4—1724no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—44no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—44no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4—862no—
446C2×C4—862no—
447C2×C4—862no—
448C2×C4—1728no—
449C2×C4—1721no—
450C2×C4—1721no—
451C2×C4—1721no—
452C2×C4—1721no—
453C2×C4—1721no—
454C2×C4—1721no—
455C2×C4#1306325312yes—
456C2×C4C22⋊C4×D4311yescharacteristic
457C2×C4C22⋊C4×D4311yescharacteristic
458C2×C4#1306329512yes—
459C8—3442no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—22no—
468C22—3441no—
469C22—3441no—
470C22—3441no—
471C22—3441no—
472C22—1722no—
473C22—1722no—
474C22—1722no—
475C22#1458275411yescharacteristic
476C22#1458287211yescharacteristic
477C22#1458287211yescharacteristic
478C22#1458289311yescharacteristic
479C22#1458289811yescharacteristic
480C22C2×#1306325311yescharacteristic
481C22#1458291711yescharacteristic
482C22#1458304212yes—
483C22#1458305912yes—
484C4—22no—
485C4—21no—
486C4—21no—
487C4—22no—
488C4—41no—
489C4—41no—
490C4—41no—
491C4—84no—
492C4—1722no—
493C4—1722no—
494C4—1722no—
495C2—22no—
496C2—22no—
497C2—3442no—
498C2#1913307911yescharacteristic
499C2#1913311811yescharacteristic
500C2#1913313111yescharacteristic
501C2#1913317011yescharacteristic
502C2#1913451211yescharacteristic
503C2#1913453311yescharacteristic
504C2#1913454011yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1434C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1434D43
hypocenterC43#8330
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. #19134663C2semidirect
3. C2×#14582635C2semidirect
5. C43×#1434C2semidirect
9. C2×#13063317C4semidirect
10. C2×#13063313C4semidirect
14. C2×C4×Dic86C4semidirect
15. C2×C4×D172C4semidirect
247. #1434D43semidirect
279. C43#8330semidirect

Maximal subgroups

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

subgroupindex
C2×#145834332
#191346632
C2×#145826352
C2×#145826322
C43×#14342
#833043