Finite Group Databasebeta

← #24998899

Subgroups — #24998899

Order 11008.

744 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583096C211yesmaximal, characteristic, complemented
2C2×#14583091C211yesmaximal, characteristic
3#19139518C211yesmaximal, characteristic, complemented
4C2×#14582631C211yesmaximal, characteristic, complemented
5C2×#14582628C211yesmaximal, characteristic, complemented
6#19132478C211yesmaximal, characteristic, complemented
7C43×#1957C211yesmaximal, characteristic, complemented
8C22×#10621883—21no—
9C22×#10621882—21no—
10C2×#13063305—21no—
11C2×C4×Dic86C2211yescharacteristic
12C2×C4×D172C2211yescharacteristic
13#14583096—22no—
14#14583096—22no—
15#14583091—22no—
16#14583091—22no—
17C2×C4⋊(C43⋊C8)C2211yescharacteristic
18C2×C4⋊(C43⋊C8)C2211yescharacteristic
19C2×#13063246—21no—
20C2×#13063246—21no—
21#14582821—22no—
22#14582800—21no—
23#14582798—21no—
24#14582756—21no—
25#14582631—22no—
26#14582628—22no—
27C2×#127×C43C2211yescharacteristic
28C2×#102×C43—22no—
29C2×C4×C8×C43C2211yescharacteristic
30C43×#384C2211yescharacteristic
31C22×Dic86D411yescharacteristic
32C22×D172D411yescharacteristic
33C22×C4×D43—21no—
34C2×#10621883—24no—
35C2×#10621883—42no—
36C2×#10621883—42no—
37C2×#10621882—24no—
38C2×#10621882—42no—
39C2×#10621882—42no—
40C22×C43⋊C8—21no—
41C22×C43⋊C8—21no—
42#13063305—42no—
43#13063305—42no—
44C4×Dic86—21no—
45C4×Dic86—21no—
46C4×Dic86—21no—
47C4×Dic86—21no—
48C4×D172—21no—
49C4×D172—21no—
50C4×D172—21no—
51C4×D172—21no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43D411yescharacteristic
54C2×C4⋊Dic43D411yescharacteristic
55C2×Dic43⋊C4—21no—
56C2×(C2×D43)⋊C4—22no—
57C2×(C2×D43)⋊C4—21no—
58C2×(C2×D43)⋊C4—22no—
59C2×C4×Dic43—21no—
60C4⋊(C43⋊C8)—21no—
61C4⋊(C43⋊C8)—21no—
62C4⋊(C43⋊C8)D412yes—
63C4⋊(C43⋊C8)D412yes—
64#13063246—24no—
65#13063246—24no—
66C43⋊#95—22no—
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C22×C8×C43—21no—
71#127×C43—21no—
72#127×C43—21no—
73#127×C43—21no—
74#127×C43D412yes—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43D412yes—
78C2×C42×C43C2311yescharacteristic
79#102×C43—44no—
80C4×C8×C43—21no—
81C4×C8×C43—21no—
82C24×C43—41no—
83C23×D43—21no—
84C2×D4×C43—22no—
85C2×D4×C43—22no—
86C2×D4×C43—22no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—42no—
91C2×D4×C43—42no—
92C2×D4×C43—41no—
93C2×D4×C43—41no—
94C2×D4×C43—41no—
95C2×D4×C43—41no—
96C2×D4×C43—41no—
97C2×D4×C43—41no—
98C2×D4×C43—41no—
99C2×D4×C43—41no—
100C22×C4×C43—22no—
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—21no—
107C2×D172—21no—
108C2×D172—21no—
109C2×D172—21no—
110C2×D172—21no—
111C2×D172—21no—
112C2×D172SD1612yescomplemented
113C2×C4×D43—41no—
114C2×C4×D43—41no—
115C2×C4×D43—41no—
116C2×C4×D43—41no—
117C2×C4×D43—41no—
118C2×C4×D43—41no—
119C2×Dic86—21no—
120C2×Dic86—21no—
121C2×Dic86—21no—
122C2×Dic86—21no—
123C2×Dic86—21no—
124C2×Dic86D812yescomplemented
125C2×C8×C43—22no—
126C2×C8×C43—41no—
127C2×C8×C43—41no—
128C4⋊C4×C43—42no—
129C4⋊C4×C43—41no—
130C4⋊C4×C43—41no—
131C4⋊C4×C43—41no—
132C4⋊C4×C43—41no—
133C42×C43C2×D411yescharacteristic
134C42×C43C2×D411yescharacteristic
135C42×C43C2×D411yescharacteristic
136C42×C43#4111yescharacteristic
137#10621883—48no—
138#10621882—48no—
139(C2×D43)⋊C4—44no—
140(C2×D43)⋊C4—41no—
141(C2×D43)⋊C4—41no—
142(C2×D43)⋊C4—82no—
143C4⋊Dic43—21no—
144C4⋊Dic43—21no—
145C4⋊Dic43—21no—
146C4⋊Dic43—21no—
147C4⋊Dic43—44no—
148Dic43⋊C4—41no—
149Dic43⋊C4—41no—
150C4×Dic43—41no—
151C4×Dic43—41no—
152C2×C43⋊C8—22no—
153C2×C43⋊C8—22no—
154C2×C43⋊C8—41no—
155C2×C43⋊C8—41no—
156C2×C43⋊C8—41no—
157C2×C43⋊C8—41no—
158C23×C43—42no—
159C23×C43—81no—
160C23×C43—81no—
161C23×C43—81no—
162C23×C43—81no—
163C23×C43—81no—
164C23×C43—81no—
165C23×C43#12011yescharacteristic
166C22×D43—22no—
167C22×D43—41no—
168C22×D43—41no—
169C22×D43—41no—
170C22×D43—41no—
171C22×D43—41no—
172C22×D43—41no—
173D4×C43—44no—
174D4×C43—42no—
175D4×C43—42no—
176D4×C43—42no—
177D4×C43—42no—
178D4×C43—82no—
179D4×C43—81no—
180D4×C43—81no—
181D4×C43—81no—
182D4×C43—81no—
183C2×C4×C43—21no—
184C2×C4×C43—21no—
185C2×C4×C43—42no—
186C2×C4×C43—42no—
187C2×C4×C43—42no—
188C2×C4×C43#12011yescharacteristic
189C2×C4×C43#12011yescharacteristic
190C2×C4×C43#12111yescharacteristic
191C2×C4×C43#12111yescharacteristic
192C2×C4×C43#12111yescharacteristic
193C2×C4×C43#12711yescharacteristic
194C2×C4×C43C2×D811yescharacteristic
195C2×C4×C43C2×SD1611yescharacteristic
196C2×C4×C43#13511yescharacteristic
197C2×C4×C43#13511yescharacteristic
198C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
199C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
200C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
201C2×C4×C43#13711yescharacteristic
202C2×Dic43—22no—
203C2×Dic43—41no—
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211D172—22no—
212D172—22no—
213D172—41no—
214D172—41no—
215C4×D43—81no—
216C4×D43—81no—
217C4×D43—81no—
218C4×D43—81no—
219Dic86—22no—
220Dic86—22no—
221Dic86—41no—
222Dic86—41no—
223C8×C43—42no—
224C43⋊C8—42no—
225C43⋊C8—42no—
226#10229—431nomaximal, Sylow
227C22×C43—82no—
228C22×C43—82no—
229C22×C43—82no—
230C22×C43—161no—
231C22×C43—161no—
232C22×C43—161no—
233C22×C43—161no—
234C22×C43#39211yescharacteristic
235C22×C43#44711yescharacteristic
236C22×C43#44811yescharacteristic
237C22×C43#44911yescharacteristic
238C22×C43#44911yescharacteristic
239C22×C43#45311yescharacteristic
240C22×C43#45411yescharacteristic
241C2×D43—42no—
242C2×D43—42no—
243C2×D43—42no—
244C2×D43—81no—
245C2×D43—81no—
246C2×D43—81no—
247C2×D43—81no—
248C4×C43—21no—
249C4×C43—21no—
250C4×C43—82no—
251C4×C43#44711yescharacteristic
252C4×C43#44911yescharacteristic
253C4×C43#45011yescharacteristic
254C4×C43#45211yescharacteristic
255C4×C43#46511yescharacteristic
256C4×C43#46611yescharacteristic
257C4×C43#46811yescharacteristic
258C4×C43#46911yescharacteristic
259Dic43—42no—
260Dic43—81no—
261Dic43—81no—
262C2×#460—431no—
263C2×#459—431no—
264#2538—431no—
265#1957D4311yescharacteristic, complemented
266C2×Q8⋊C8—431no—
267C2×D4⋊C8—431no—
268#1296—431no—
269C2×C43—162no—
270C2×C43#162111yescharacteristic
271C2×C43#162211yescharacteristic
272C2×C43#162711yescharacteristic
273C2×C43#162811yescharacteristic
274C2×C43#199911yescharacteristic
275C2×C43#200011yescharacteristic
276C2×C43#200611yescharacteristic
277D43—82no—
278C22×SD16—861no—
279C22×D8—861no—
280C2×#127C2×D4311yescharacteristic
281C2×C22⋊Q8—861no—
282C2×C4×Q8—431no—
283C2×C4×D4—431no—
284#460—862no—
285#460—862no—
286#459—862no—
287#459—862no—
288C2×C4⋊C8—431no—
289C2×C4⋊C8—431no—
290C2×#102—22no—
291C2×#102—861no—
292C2×#102—861no—
293C2×C4×C8C2×D4311yescharacteristic
294#396—862no—
295#390—861no—
296#389—861no—
297#384C2×D4311yescharacteristic
298#380—861no—
299Q8⋊C8—862no—
300D4⋊C8—862no—
301C43#1022911yescharacteristic, complemented, Sylow
302C22×Q8—431no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4—431no—
307C23×C4—861no—
308C2×SD16—864no—
309C2×SD16—1722no—
310C2×SD16—1722no—
311C2×D8—864no—
312C2×D8—1722no—
313C2×D8—1722no—
314C22×C8—21no—
315C22×C8—861no—
316C22×C8—861no—
317#127—21no—
318#127—21no—
319#127—21no—
320#127D17212yes—
321C22⋊Q8—1722no—
322C22⋊Q8—1722no—
323C4×Q8—861no—
324C4×Q8—861no—
325C4×Q8—861no—
326C4×Q8—861no—
327C4×D4—861no—
328C4×D4—861no—
329C4×D4—861no—
330C4×D4—861no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—431no—
334C2×C4⋊C4—431no—
335C2×C4⋊C4—862no—
336C2×C4⋊C4—861no—
337C2×C4⋊C4C22⋊D4312yes—
338C2×C22⋊C4—862no—
339C2×C22⋊C4—862no—
340C2×C22⋊C4—861no—
341C2×C42—861no—
342C2×C42C22×D4311yescharacteristic
343C4⋊C8—432no—
344C4⋊C8—432no—
345C4⋊C8—861no—
346C4⋊C8—861no—
347#102—44no—
348#102—864no—
349#102—864no—
350C4×C8—21no—
351C4×C8—21no—
352#95—862no—
353C24—41no—
354C24—861no—
355C2×Q8—432no—
356C2×Q8—861no—
357C2×Q8—861no—
358C2×Q8—861no—
359C2×Q8—861no—
360C2×Q8—861no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—432no—
378C2×D4—861no—
379C2×D4—861no—
380C2×D4—861no—
381C2×D4—861no—
382C2×D4—861no—
383C22×C4—22no—
384C22×C4—861no—
385C22×C4—861no—
386C22×C4—861no—
387C22×C4—1721no—
388C22×C4—1721no—
389C22×C4—1721no—
390C22×C4—1721no—
391C22×C4—1721no—
392C22×C4—1721no—
393C22×C4D4×D4311yescharacteristic
394C22×C4D4×D4311yescharacteristic
395C22×C4C2×C22⋊D4311yescharacteristic
396SD16—1728no—
397D8—1728no—
398C2×C8—22no—
399C2×C8—41no—
400C2×C8—41no—
401C2×C8—862no—
402C2×C8—862no—
403C2×C8—1721no—
404C2×C8—1721no—
405C2×C8—1721no—
406C2×C8—1721no—
407C4⋊C4—42no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—861no—
413C4⋊C4—861no—
414C4⋊C4—861no—
415C4⋊C4—861no—
416C4⋊C4—1724no—
417C4⋊C4—1721no—
418C4⋊C4—1721no—
419C22⋊C4—3442no—
420C22⋊C4—1724no—
421C22⋊C4—1721no—
422C22⋊C4—1721no—
423C42—1721no—
424C42—1721no—
425C42C2×D17211yescharacteristic
426C42#1062189811yescharacteristic
427C42D4×D4311yescharacteristic
428C42D4×D4311yescharacteristic
429C23—42no—
430C23—81no—
431C23—81no—
432C23—81no—
433C23—81no—
434C23—81no—
435C23—81no—
436C23—862no—
437C23—1721no—
438C23—1721no—
439C23—1721no—
440C23—1721no—
441C23—1721no—
442C23—1721no—
443C23#1306329311yescharacteristic
444Q8—862no—
445Q8—862no—
446Q8—1721no—
447Q8—1721no—
448D4—44no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—42no—
453D4—82no—
454D4—81no—
455D4—81no—
456D4—81no—
457D4—81no—
458D4—862no—
459D4—862no—
460D4—1721no—
461D4—1721no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—862no—
468C2×C4—3441no—
469C2×C4—3441no—
470C2×C4—3441no—
471C2×C4—3441no—
472C2×C4—1721no—
473C2×C4—1721no—
474C2×C4—1721no—
475C2×C4—1721no—
476C2×C4—1721no—
477C2×C4—1721no—
478C2×C4—1721no—
479C2×C4—1721no—
480C2×C4#1306329511yescharacteristic
481C2×C4#1306329511yescharacteristic
482C2×C4#1306329811yescharacteristic
483C2×C4#1306329811yescharacteristic
484C2×C4#1306329911yescharacteristic
485C2×C4#1306332111yescharacteristic
486C2×C4D8×D4311yescharacteristic
487C2×C4SD16×D4311yescharacteristic
488C2×C4#1306334411yescharacteristic
489C2×C4#1306334611yescharacteristic
490C2×C4#1306334911yescharacteristic
491C2×C4#1306334911yescharacteristic
492C2×C4#1306335211yescharacteristic
493C2×C4#1306335411yescharacteristic
494C8—42no—
495C8—1722no—
496C8—1722no—
497C22—82no—
498C22—82no—
499C22—82no—
500C22—161no—
501C22—161no—
502C22—161no—
503C22—161no—
504C22—3441no—
505C22—3441no—
506C22—3441no—
507C22—3441no—
508C22—1722no—
509C22—1722no—
510C22—1722no—
511C22#1458280811yescharacteristic
512C22#1458303111yescharacteristic
513C22#1458303611yescharacteristic
514C22#1458304111yescharacteristic
515C22#1458304311yescharacteristic
516C22#1458306611yescharacteristic
517C22#1458307111yescharacteristic
518C4—21no—
519C4—21no—
520C4—82no—
521C4—3441no—
522C4—3441no—
523C4—1722no—
524C4#1458303411yescharacteristic
525C4#1458304511yescharacteristic
526C4#1458305111yescharacteristic
527C4#1458306211yescharacteristic
528C4#1458312711yescharacteristic
529C4#1458313411yescharacteristic
530C4#1458314411yescharacteristic
531C4#1458315111yescharacteristic
532C2—162no—
533C2—3442no—
534C2#1913365711yescharacteristic
535C2#1913366411yescharacteristic
536C2#1913369511yescharacteristic
537C2#1913370211yescharacteristic
538C2#1913559211yescharacteristic
539C2#1913559911yescharacteristic
540C2#1913563611yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1957C2
socleC23×C43#120
prime radicalC2×#14583091C2
hypercenter#1957D43
hypocenterC43#10229
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
1. C2×#14583096C2semidirect
3. #19139518C2semidirect
4. C2×#14582631C2semidirect
5. C2×#14582628C2semidirect
6. #19132478C2semidirect
7. C43×#1957C2semidirect
112. C2×D172SD16semidirect
124. C2×Dic86D8semidirect
265. #1957D43semidirect
301. C43#10229semidirect

Maximal subgroups

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

subgroupindex
C2×#145830962
C2×#145830912
#191395182
C2×#145826312
C2×#145826282
#191324782
C43×#19572
#1022943