Finite Group Databasebeta

← #24999957

Subgroups — #24999957

Order 11008.

708 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139537C211yesmaximal, characteristic
2#19135400C211yesmaximal, characteristic, complemented
3#19134592C211yesmaximal, characteristic, complemented
4C2×#14582642C211yesmaximal, characteristic, complemented
5C2×#14582626C211yesmaximal, characteristic, complemented
6#19132436C211yesmaximal, characteristic, complemented
7C43×#1947C211yesmaximal, characteristic, complemented
8C2×#13063322—21no—
9C2×#13063322C2211yescharacteristic
10C2×#13063300—21no—
11C2×#13063300—21no—
12C2×C4×D172C2211yescharacteristic
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×#13063245—21no—
15C2×#13063245—22no—
16C2×C4×C43⋊C8C2211yescharacteristic
17#14582809—22no—
18#14582801—21no—
19#14582661—21no—
20#14582642—22no—
21#14582626—22no—
22C2×#107×C43—21no—
23C2×C4⋊C8×C43C2211yescharacteristic
24C43×#384C2211yescharacteristic
25C4×C4⋊C4×C43C2211yescharacteristic
26C43×#340—21no—
27C22×D172—21no—
28C22×D172—21no—
29C22×D172—22no—
30C22×D172—22no—
31C22×D172D411yescharacteristic
32C22×D172D412yes—
33C22×C4×D43—21no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36#13063322—21no—
37#13063322—21no—
38#13063322—21no—
39#13063322—21no—
40#13063322—42no—
41#13063322—42no—
42#13063300—42no—
43#13063300—42no—
44#13063300—42no—
45#13063300—42no—
46C4×D172—21no—
47C4×D172—21no—
48C4×D172—21no—
49C4×D172—21no—
50C2×C4⋊Dic43D411yescharacteristic
51C2×(C2×D43)⋊C4—22no—
52C2×(C2×D43)⋊C4—22no—
53C2×(C2×D43)⋊C4—21no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)—21no—
56#13063245—44no—
57#13063245—42no—
58C4×C43⋊C8—21no—
59C4×C43⋊C8—21no—
60C22×C8×C43—21no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43D411yescharacteristic
65C2×C4⋊C4×C43D411yescharacteristic
66C2×C42×C43—21no—
67C2×C42×C43C2311yescharacteristic
68#107×C43—42no—
69C4⋊C8×C43—21no—
70C4⋊C8×C43D412yescomplemented
71#95×C43—21no—
72C23×D43—21no—
73C23×D43—22no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—41no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×Dic43—21no—
81C2×D172—21no—
82C2×D172—21no—
83C2×D172—21no—
84C2×D172—21no—
85C2×D172—21no—
86C2×D172—22no—
87C2×D172—22no—
88C2×D172—44no—
89C2×D172—44no—
90C2×D172—44no—
91C2×D172—44no—
92C2×D172—41no—
93C2×D172—41no—
94C2×D172—41no—
95C2×D172—41no—
96C2×D172—41no—
97C2×D172—41no—
98C2×D172—41no—
99C2×D172—41no—
100C2×D172—41no—
101C2×D172—41no—
102C2×D172—41no—
103C2×D172—41no—
104C2×D172—42no—
105C2×D172—42no—
106C2×D172—82no—
107C2×D172—82no—
108C2×D172D812yes—
109C2×C4×D43—41no—
110C2×C4×D43—41no—
111C2×C4×D43—41no—
112C2×C4×D43—41no—
113C2×C4×D43—41no—
114C2×C4×D43—41no—
115C2×C8×C43—22no—
116C2×C8×C43—41no—
117C2×C8×C43—41no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—21no—
120C4⋊C4×C43—42no—
121C4⋊C4×C43—41no—
122C4⋊C4×C43—41no—
123C4⋊C4×C43—41no—
124C4⋊C4×C43—41no—
125C4⋊C4×C43D812yes—
126C4⋊C4×C43SD1612yes—
127C42×C43—41no—
128C42×C43—41no—
129C42×C43C2×D411yescharacteristic
130C42×C43#4111yescharacteristic
131C42×C43#4111yescharacteristic
132C42×C43#4111yescharacteristic
133(C2×D43)⋊C4—44no—
134(C2×D43)⋊C4—44no—
135(C2×D43)⋊C4—41no—
136(C2×D43)⋊C4—41no—
137C4⋊Dic43—21no—
138C4⋊Dic43—21no—
139C2×C43⋊C8—22no—
140C2×C43⋊C8—41no—
141C2×C43⋊C8—41no—
142C2×C43⋊C8—41no—
143C2×C43⋊C8—41no—
144C2×C43⋊C8—41no—
145C23×C43#12011yescharacteristic
146C22×D43—22no—
147C22×D43—41no—
148C22×D43—41no—
149C22×D43—41no—
150C22×D43—41no—
151C22×D43—41no—
152C22×D43—41no—
153C22×D43—42no—
154C22×D43—42no—
155C22×D43—42no—
156C22×D43—42no—
157C22×D43—42no—
158C22×D43—42no—
159C22×D43—42no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—22no—
163C2×C4×C43—22no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—81no—
169C2×C4×C43—81no—
170C2×C4×C43—81no—
171C2×C4×C43#12111yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×C4×C43#12111yescharacteristic
174C2×C4×C43#12311yescharacteristic
175C2×C4×C43#12311yescharacteristic
176C2×C4×C43#12411yescharacteristic
177C2×C4×C43C2×D811yescharacteristic
178C2×C4×C43C2×D811yescharacteristic
179C2×C4×C43C2×SD1611yescharacteristic
180C2×C4×C43#13511yescharacteristic
181C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C43#13711yescharacteristic
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188D172—22no—
189D172—22no—
190D172—44no—
191D172—41no—
192D172—41no—
193D172—82no—
194D172—88no—
195D172—88no—
196D172—81no—
197D172—81no—
198D172—81no—
199D172—81no—
200D172—81no—
201D172—81no—
202D172—81no—
203D172—81no—
204C4×D43—81no—
205C4×D43—81no—
206C4×D43—81no—
207C4×D43—81no—
208C8×C43—42no—
209C43⋊C8—42no—
210C43⋊C8—81no—
211#10408—431nomaximal, Sylow
212C22×C43#39411yescharacteristic
213C22×C43#44711yescharacteristic
214C22×C43#44711yescharacteristic
215C22×C43#45011yescharacteristic
216C22×C43#45211yescharacteristic
217C22×C43#45311yescharacteristic
218C22×C43#45511yescharacteristic
219C2×D43—42no—
220C2×D43—42no—
221C2×D43—42no—
222C2×D43—81no—
223C2×D43—81no—
224C2×D43—81no—
225C2×D43—81no—
226C2×D43—82no—
227C2×D43—82no—
228C2×D43—82no—
229C2×D43—82no—
230C2×D43—82no—
231C2×D43—82no—
232C2×D43—82no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—42no—
236C4×C43—42no—
237C4×C43—161no—
238C4×C43#45911yescharacteristic
239C4×C43#46011yescharacteristic
240C4×C43#46611yescharacteristic
241C4×C43#46811yescharacteristic
242C4×C43#48011yescharacteristic
243C4×C43#48211yescharacteristic
244C4×C43#48611yescharacteristic
245C4×C43#49011yescharacteristic
246Dic43—81no—
247#2541—431no—
248#1957—431no—
249#1947D4311yescharacteristic, complemented
250#1802—431no—
251C2×#331—431no—
252C2×D4⋊C8—431no—
253#1279—431no—
254C2×C43#161911yescharacteristic
255C2×C43#163111yescharacteristic
256C2×C43#163911yescharacteristic
257C2×C43#164111yescharacteristic
258C2×C43#203311yescharacteristic
259C2×C43#203711yescharacteristic
260C2×C43#204111yescharacteristic
261D43—82no—
262D43—162no—
263C2×#127—431no—
264C2×#127—861no—
265C2×#121—861no—
266C2×#121—861no—
267C2×C4×D4—431no—
268C2×#107—21no—
269C2×C4⋊C8—431no—
270C2×C4⋊C8C2×D4311yescharacteristic
271C2×#102—861no—
272C2×#102—862no—
273C2×C4×C8—431no—
274#392—862no—
275#390—861no—
276#384C2×D4311yescharacteristic
277C4×C4⋊C4C2×D4311yescharacteristic
278#340—21no—
279#340—861no—
280#331—862no—
281D4⋊C8—862no—
282C43#1040811yescharacteristic, complemented, Sylow
283C22×D4—431no—
284C22×D4—432no—
285C22×D4—862no—
286C22×D4—862no—
287C22×D4—861no—
288C22×D4—861no—
289C23×C4—861no—
290C22×C8—21no—
291C22×C8—861no—
292C22×C8—861no—
293#127—861no—
294#127—861no—
295#127—861no—
296#127—861no—
297#127—1722no—
298#127—1722no—
299#121—1722no—
300#121—1722no—
301#121—1722no—
302#121—1722no—
303C4×D4—861no—
304C4×D4—861no—
305C4×D4—861no—
306C4×D4—861no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—431no—
311C2×C4⋊C4C22⋊D4311yescharacteristic
312C2×C4⋊C4C22⋊D4311yescharacteristic
313C2×C22⋊C4—862no—
314C2×C22⋊C4—862no—
315C2×C22⋊C4—861no—
316C2×C42—21no—
317C2×C42C22×D4311yescharacteristic
318#107—42no—
319C4⋊C8—21no—
320C4⋊C8—861no—
321C4⋊C8—861no—
322C4⋊C8D17212yescomplemented
323#102—1724no—
324#102—1722no—
325C4×C8—861no—
326C4×C8—861no—
327#95—21no—
328C24—861no—
329C24—862no—
330C2×D4—432no—
331C2×D4—861no—
332C2×D4—862no—
333C2×D4—861no—
334C2×D4—862no—
335C2×D4—861no—
336C2×D4—861no—
337C2×D4—861no—
338C2×D4—3442no—
339C2×D4—3442no—
340C2×D4—1724no—
341C2×D4—1724no—
342C2×D4—1722no—
343C2×D4—1722no—
344C2×D4—1724no—
345C2×D4—1724no—
346C2×D4—1721no—
347C2×D4—1721no—
348C2×D4—1721no—
349C2×D4—1721no—
350C2×D4—1721no—
351C2×D4—1721no—
352C2×D4—1721no—
353C2×D4—1721no—
354C2×D4—1721no—
355C2×D4—1721no—
356C2×D4—1721no—
357C2×D4—1721no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—41no—
361C22×C4—861no—
362C22×C4—1721no—
363C22×C4—1721no—
364C22×C4—1721no—
365C22×C4—1721no—
366C22×C4—1721no—
367C22×C4—1721no—
368C22×C4D4×D4311yescharacteristic
369C22×C4D4×D4311yescharacteristic
370C22×C4C2×C22⋊D4311yescharacteristic
371C2×C8—22no—
372C2×C8—41no—
373C2×C8—41no—
374C2×C8—862no—
375C2×C8—1721no—
376C2×C8—1721no—
377C2×C8—1721no—
378C2×C8—1721no—
379C2×C8—1721no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—42no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—861no—
388C4⋊C4—861no—
389C4⋊C4#1062188212yes—
390C4⋊C4#1062188412yes—
391C22⋊C4—1724no—
392C22⋊C4—1724no—
393C22⋊C4—1721no—
394C22⋊C4—1721no—
395C42—41no—
396C42—41no—
397C42C2×D17211yescharacteristic
398C42#1062189811yescharacteristic
399C42#1062190211yescharacteristic
400C42#1062190211yescharacteristic
401C23—862no—
402C23—1722no—
403C23—1722no—
404C23—1722no—
405C23—1722no—
406C23—1722no—
407C23—1722no—
408C23—1722no—
409C23—1721no—
410C23—1721no—
411C23—1721no—
412C23—1721no—
413C23—1721no—
414C23—1721no—
415C23#1306329311yescharacteristic
416D4—862no—
417D4—862no—
418D4—3442no—
419D4—3448no—
420D4—3448no—
421D4—3441no—
422D4—3441no—
423D4—3441no—
424D4—3441no—
425D4—3441no—
426D4—3441no—
427D4—3441no—
428D4—3441no—
429D4—1724no—
430D4—1721no—
431D4—1721no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—3441no—
444C2×C4—3441no—
445C2×C4—3441no—
446C2×C4—3441no—
447C2×C4—1721no—
448C2×C4—1721no—
449C2×C4—1721no—
450C2×C4#1306329911yescharacteristic
451C2×C4#1306330011yescharacteristic
452C2×C4#1306330011yescharacteristic
453C2×C4#1306331011yescharacteristic
454C2×C4#1306331011yescharacteristic
455C2×C4#1306331411yescharacteristic
456C2×C4D8×D4311yescharacteristic
457C2×C4C2×#1062188211yescharacteristic
458C2×C4C2×#1062188411yescharacteristic
459C2×C4#1306334811yescharacteristic
460C2×C4#1306334911yescharacteristic
461C2×C4#1306335011yescharacteristic
462C2×C4#1306335011yescharacteristic
463C2×C4#1306335711yescharacteristic
464C8—42no—
465C8—3441no—
466C8—1722no—
467C22—3441no—
468C22—3441no—
469C22—3441no—
470C22—3441no—
471C22—3442no—
472C22—3442no—
473C22—3442no—
474C22—3442no—
475C22—3442no—
476C22—3442no—
477C22—3442no—
478C22—1722no—
479C22—1722no—
480C22—1722no—
481C22#1458281611yescharacteristic
482C22#1458303111yescharacteristic
483C22#1458303211yescharacteristic
484C22#1458304911yescharacteristic
485C22#1458306011yescharacteristic
486C22#1458306511yescharacteristic
487C22#1458307511yescharacteristic
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—161no—
493C4—3441no—
494C4#1458309411yescharacteristic
495C4#1458309911yescharacteristic
496C4#1458313611yescharacteristic
497C4#1458314611yescharacteristic
498C4#1458321411yescharacteristic
499C4#1458322611yescharacteristic
500C4#1458324711yescharacteristic
501C4#1458326511yescharacteristic
502C2—3442no—
503C2—6882no—
504C2#1913364811yescharacteristic
505C2#1913372011yescharacteristic
506C2#1913377311yescharacteristic
507C2#1913378611yescharacteristic
508C2#1913577911yescharacteristic
509C2#1913580711yescharacteristic
510C2#1913582911yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1947C2
socleC23×C43#120
prime radical#19139537C2
hypercenter#1947D43
hypocenterC43#10408
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
2. #19135400C2semidirect
3. #19134592C2semidirect
4. C2×#14582642C2semidirect
5. C2×#14582626C2semidirect
6. #19132436C2semidirect
7. C43×#1947C2semidirect
70. C4⋊C8×C43D4semidirect
249. #1947D43semidirect
282. C43#10408semidirect
322. C4⋊C8D172semidirect

Maximal subgroups

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

subgroupindex
#191395372
#191354002
#191345922
C2×#145826422
C2×#145826262
#191324362
C43×#19472
#1040843