Finite Group Databasebeta

← #24996835

Subgroups — #24996835

Order 11008.

856 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583217C211yesmaximal, characteristic, complemented
2#19140329C211yesmaximal, characteristic
3#19134685C211yesmaximal, characteristic, complemented
4C2×#14582632C211yesmaximal, characteristic, complemented
5C2×#14582623C211yesmaximal, characteristic, complemented
6#19132474C211yesmaximal, characteristic, complemented
7C2×C43×#399C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C2×#13063294—21no—
10#14583217—22no—
11#14583217—22no—
12C2×#13063256—21no—
13C2×#13063245—21no—
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16#14582824—21no—
17#14582815—22no—
18#14582808—21no—
19#14582778—21no—
20#14582759C2211yescharacteristic
21#14582661—22no—
22#14582632—22no—
23#14582623—22no—
24C22×C4⋊C4×C43—21no—
25C22×C4⋊C4×C43C2211yescharacteristic
26C22×C22⋊C4×C43—21no—
27C22×C22⋊C4×C43C2211yescharacteristic
28C43×#399—22no—
29C43×#399—22no—
30C2×#95×C43C2211yescharacteristic
31C22×D172D411yescharacteristic
32C22×C22⋊D43—21no—
33C22×C22⋊D43—22no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36#13063299—21no—
37#13063299—21no—
38#13063299—21no—
39#13063299—21no—
40#13063294—42no—
41#13063294—42no—
42C2×C4⋊Dic43D411yescharacteristic
43C2×C4⋊Dic43D412yes—
44C2×C22⋊Dic43—22no—
45C2×C22⋊Dic43—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—22no—
48#13063256—24no—
49#13063245—24no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)D412yescomplemented
54C43⋊#95—22no—
55C43⋊#95—21no—
56C25×C43D411yescharacteristic
57C23×C4×C43—21no—
58C23×C4×C43—21no—
59C23×C4×C43D411yescharacteristic
60C23×C4×C43C2311yescharacteristic
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—24no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—44no—
68C2×C4⋊C4×C43D412yescomplemented
69C2×C22⋊C4×C43—24no—
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43—21no—
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—44no—
77#95×C43—21no—
78#95×C43D412yescomplemented
79C24×C43—21no—
80C24×C43—21no—
81C24×C43—21no—
82C24×C43—21no—
83C24×C43—21no—
84C24×C43—21no—
85C24×C43—42no—
86C24×C43—42no—
87C24×C43SD1612yes—
88C24×C43C2×D411yescharacteristic
89C23×D43—21no—
90C22×C4×C43—24no—
91C22×C4×C43—22no—
92C22×C4×C43—21no—
93C22×C4×C43—22no—
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—42no—
97C22×C4×C43—42no—
98C22×C4×C43—42no—
99C22×C4×C43—42no—
100C22×C4×C43—42no—
101C22×C4×C43—41no—
102C22×C4×C43—41no—
103C22×C4×C43—41no—
104C22×C4×C43—41no—
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C2×C22⋊D43—44no—
112C2×C22⋊D43—41no—
113C2×C22⋊D43—41no—
114C2×C22⋊D43—41no—
115C2×C22⋊D43—41no—
116C2×C22⋊D43—41no—
117C2×C22⋊D43—41no—
118C2×C22⋊D43—82no—
119C2×C22⋊D43—82no—
120C22×Dic43—21no—
121C22×Dic43—22no—
122C2×D172—21no—
123C2×D172—21no—
124C2×D172—42no—
125C4⋊C4×C43—22no—
126C4⋊C4×C43—22no—
127C4⋊C4×C43—48no—
128C4⋊C4×C43—41no—
129C4⋊C4×C43—41no—
130C22⋊C4×C43—48no—
131C22⋊C4×C43—41no—
132C22⋊C4×C43—41no—
133C22⋊C4×C43—41no—
134C22⋊C4×C43—41no—
135C22⋊Dic43—44no—
136C22⋊Dic43—41no—
137C22⋊Dic43—41no—
138(C2×D43)⋊C4—41no—
139(C2×D43)⋊C4—41no—
140(C2×D43)⋊C4—82no—
141C4⋊Dic43—21no—
142C4⋊Dic43—21no—
143C4⋊Dic43—42no—
144C2×C43⋊C8—22no—
145C2×C43⋊C8—42no—
146C2×C43⋊C8—42no—
147C2×C43⋊C8—41no—
148C23×C43—22no—
149C23×C43—22no—
150C23×C43—22no—
151C23×C43—22no—
152C23×C43—22no—
153C23×C43—44no—
154C23×C43—42no—
155C23×C43—44no—
156C23×C43—42no—
157C23×C43—41no—
158C23×C43—41no—
159C23×C43—41no—
160C23×C43—42no—
161C23×C43—42no—
162C23×C43—41no—
163C23×C43—82no—
164C23×C43—82no—
165C23×C43—81no—
166C23×C43—81no—
167C23×C43#12011yescharacteristic
168C23×C43#12011yescharacteristic
169C23×C43#12111yescharacteristic
170C23×C43C2×SD1611yescharacteristic
171C23×C43#13511yescharacteristic
172C23×C43AGL(1,ℤ/8)11yescharacteristic
173C23×C43#13711yescharacteristic
174C22×D43—41no—
175C22×D43—41no—
176C22×D43—41no—
177C22×D43—42no—
178C22×D43—42no—
179C2×C4×C43—22no—
180C2×C4×C43—22no—
181C2×C4×C43—24no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—44no—
187C2×C4×C43—44no—
188C2×C4×C43—42no—
189C2×C4×C43—42no—
190C2×C4×C43—42no—
191C2×C4×C43—42no—
192C2×C4×C43—42no—
193C2×C4×C43—41no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—82no—
197C2×C4×C43—82no—
198C2×C4×C43—81no—
199C2×C4×C43#12011yescharacteristic
200C2×C4×C43#12111yescharacteristic
201C2×C4×C43#12111yescharacteristic
202C2×C4×C43#12711yescharacteristic
203C22⋊D43—88no—
204C22⋊D43—81no—
205C22⋊D43—81no—
206C22⋊D43—81no—
207C22⋊D43—81no—
208C2×Dic43—41no—
209C2×Dic43—42no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—42no—
213C2×Dic43—42no—
214D172—42no—
215D172—81no—
216C43⋊C8—42no—
217C43⋊C8—81no—
218#9920—431nomaximal, Sylow
219C22×C43—22no—
220C22×C43—22no—
221C22×C43—22no—
222C22×C43—22no—
223C22×C43—21no—
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—21no—
227C22×C43—44no—
228C22×C43—44no—
229C22×C43—42no—
230C22×C43—82no—
231C22×C43—82no—
232C22×C43—82no—
233C22×C43—82no—
234C22×C43—81no—
235C22×C43—81no—
236C22×C43#39211yescharacteristic
237C22×C43#44811yescharacteristic
238C22×C43#44911yescharacteristic
239C22×C43#45011yescharacteristic
240C22×C43#45211yescharacteristic
241C22×C43#45312yes—
242C22×C43#45812yes—
243C22×C43#46511yescharacteristic
244C22×C43#46811yescharacteristic
245C2×D43—82no—
246C2×D43—82no—
247C2×D43—81no—
248C2×D43—81no—
249C2×D43—81no—
250C4×C43—21no—
251C4×C43—21no—
252C4×C43—21no—
253C4×C43—21no—
254C4×C43—44no—
255C4×C43—81no—
256C4×C43—82no—
257Dic43—82no—
258Dic43—81no—
259C2×#481—431no—
260#2617—431no—
261C2×#399D4311yescharacteristic, complemented
262#1824—431no—
263C2×#327—431no—
264C2×#323—431no—
265#1294—431no—
266C2×C43—21no—
267C2×C43—21no—
268C2×C43—21no—
269C2×C43—21no—
270C2×C43—82no—
271C2×C43#161312yes—
272C2×C43#161812yes—
273C2×C43#200011yescharacteristic
274C2×C43#200211yescharacteristic
275C2×C43#202211yescharacteristic
276D43—161no—
277C2×#121—431no—
278C2×#120—861no—
279C22×C4⋊C4—21no—
280C22×C4⋊C4C2×D4311yescharacteristic
281C22×C22⋊C4—21no—
282C22×C22⋊C4C2×D4311yescharacteristic
283#481—862no—
284#481—862no—
285C2×#106—861no—
286C2×#102—861no—
287C2×C22⋊C8—431no—
288C2×C22⋊C8—431no—
289#399—22no—
290#399—22no—
291#397—861no—
292#394—862no—
293#392—861no—
294#386—861no—
295#380—431no—
296C2×#95C2×D4311yescharacteristic
297#340—862no—
298#327—862no—
299#323—862no—
300C43#992011yescharacteristic, complemented, Sylow
301C25C22⋊D4311yescharacteristic
302C22×D4—431no—
303C22×D4—862no—
304C22×D4—861no—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4C22⋊D4311yescharacteristic
308C23×C4C22×D4311yescharacteristic
309C22×C8—861no—
310C22×C8—861no—
311#121—861no—
312#121—861no—
313#121—861no—
314#121—861no—
315#120—1722no—
316#120—1722no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—431no—
325C2×C4⋊C4—432no—
326C2×C4⋊C4C22⋊D4312yescomplemented
327C2×C22⋊C4—24no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—862no—
336C2×C22⋊C4—862no—
337C2×C22⋊C4—861no—
338C2×C22⋊C4—861no—
339#106—864no—
340#102—864no—
341C22⋊C8—432no—
342C22⋊C8—861no—
343C22⋊C8—861no—
344C22⋊C8—861no—
345#95—21no—
346#95—862no—
347#95—861no—
348#95C22⋊D4312yescomplemented
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24—42no—
356C24—42no—
357C24—861no—
358C24#1062188412yes—
359C24C2×C22⋊D4311yescharacteristic
360C2×D4—861no—
361C2×D4—861no—
362C2×D4—3442no—
363C2×D4—3442no—
364C2×D4—1722no—
365C2×D4—1724no—
366C2×D4—1721no—
367C2×D4—1721no—
368C2×D4—1721no—
369C2×D4—1721no—
370C2×D4—1721no—
371C2×D4—1721no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—861no—
388C22×C4—862no—
389C22×C4D4×D4311yescharacteristic
390C22×C4D4×D4311yescharacteristic
391C22×C4D4×D4311yescharacteristic
392C22×C4#1062190011yescharacteristic
393C22×C4C2×C22⋊D4311yescharacteristic
394C22×C4C2×C22⋊D4311yescharacteristic
395C2×C8—862no—
396C2×C8—1722no—
397C2×C8—1721no—
398C2×C8—1722no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—48no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—861no—
405C4⋊C4—861no—
406C4⋊C4—1722no—
407C22⋊C4—48no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—3442no—
413C22⋊C4—1724no—
414C22⋊C4—1721no—
415C22⋊C4—1721no—
416C22⋊C4—1721no—
417C22⋊C4—1721no—
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—44no—
424C23—42no—
425C23—44no—
426C23—42no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—42no—
431C23—42no—
432C23—41no—
433C23—82no—
434C23—81no—
435C23—82no—
436C23—81no—
437C23—1721no—
438C23—1721no—
439C23—1721no—
440C23—1722no—
441C23—1722no—
442C23#1306329311yescharacteristic
443C23#1306329411yescharacteristic
444C23#1306329711yescharacteristic
445C23C2×#1062188411yescharacteristic
446C23#1306334511yescharacteristic
447C23#1306335011yescharacteristic
448C23#1306335611yescharacteristic
449D4—3441no—
450D4—3448no—
451D4—3441no—
452D4—3441no—
453D4—3441no—
454D4—3441no—
455D4—1722no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—82no—
474C2×C4—82no—
475C2×C4—81no—
476C2×C4—1721no—
477C2×C4—1722no—
478C2×C4—1721no—
479C2×C4—1721no—
480C2×C4—1722no—
481C2×C4—1722no—
482C2×C4#1306329311yescharacteristic
483C2×C4#1306329611yescharacteristic
484C2×C4#1306329711yescharacteristic
485C2×C4#1306332111yescharacteristic
486C8—3441no—
487C8—1722no—
488C22—21no—
489C22—21no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—21no—
495C22—21no—
496C22—44no—
497C22—42no—
498C22—44no—
499C22—82no—
500C22—82no—
501C22—82no—
502C22—81no—
503C22—82no—
504C22—81no—
505C22—3441no—
506C22—3441no—
507C22—3442no—
508C22—3442no—
509C22—3441no—
510C22#1458280711yescharacteristic
511C22#1458303811yescharacteristic
512C22#1458304411yescharacteristic
513C22#1458304911yescharacteristic
514C22#1458305911yescharacteristic
515C22#1458306612yes—
516C22#1458308812yes—
517C22#1458313011yescharacteristic
518C22#1458314711yescharacteristic
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—44no—
524C4—81no—
525C4—82no—
526C4—3441no—
527C4—3442no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—82no—
533C2—6881no—
534C2#1913361412yes—
535C2#1913364112yes—
536C2#1913559611yescharacteristic
537C2#1913561011yescharacteristic
538C2#1913572311yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC2×C43×#399C2
socleC23×C43#120
prime radical#19140329C2
hypercenterC2×#399D43
hypocenterC43#9920
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C2×#14583217C2semidirect
3. #19134685C2semidirect
4. C2×#14582632C2semidirect
5. C2×#14582623C2semidirect
6. #19132474C2semidirect
7. C2×C43×#399C2semidirect
53. C22⋊(C43⋊C8)D4semidirect
68. C2×C4⋊C4×C43D4semidirect
78. #95×C43D4semidirect
261. C2×#399D43semidirect
300. C43#9920semidirect
326. C2×C4⋊C4C22⋊D43semidirect
348. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832172
#191403292
#191346852
C2×#145826322
C2×#145826232
#191324742
C2×C43×#3992
#992043