Finite Group Databasebeta

← #24992186

Subgroups — #24992186

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582953C211yesmaximal, characteristic, complemented
2#19142927C211yesmaximal, characteristic
3C2×#14582634C211yesmaximal, characteristic
4C2×#14582632C211yesmaximal, characteristic
5#19132819C211yesmaximal, characteristic, complemented
6#19132473C211yesmaximal, characteristic, complemented
7C43×#1294C211yesmaximal, characteristic, complemented
8C2×#13063309—21no—
9C2×#13063299C2211yescharacteristic
10C22×C4×Dic43C2211yescharacteristic
11#14582953—22no—
12#14582953—22no—
13C2×Dic43⋊C8—21no—
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15C2×#13063235—21no—
16#14582800C411yescharacteristic, complemented
17#14582800C411yescharacteristic, complemented
18#14582798C411yescharacteristic, complemented
19#14582798C411yescharacteristic, complemented
20#14582791—21no—
21#14582791—21no—
22#14582776—21no—
23C2×C43⋊#95—21no—
24C2×C43⋊#95—21no—
25C2×C43⋊#95C2211yescharacteristic
26#14582634—22no—
27#14582632—22no—
28C2×C22⋊C8×C43C2211yescharacteristic
29C43×#380C2211yescharacteristic
30C2×#95×C43C2211yescharacteristic
31C22×D172C2×C411yescharacteristic
32C22×C22⋊D43—21no—
33C23×Dic43—21no—
34C23×Dic43D411yescharacteristic
35C23×Dic43D411yescharacteristic
36C22×C43⋊C8—21no—
37#13063309—42no—
38#13063309—42no—
39#13063299—21no—
40#13063299—21no—
41#13063299—21no—
42#13063299—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43C2×C411yescharacteristic
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×C4×Dic43—21no—
52C2×C4×Dic43—21no—
53C2×C4×Dic43—21no—
54C2×C4×Dic43—21no—
55C2×C4×Dic43C2×C411yescharacteristic
56C2×C4×Dic43C2×C411yescharacteristic
57C2×C4×Dic43D411yescharacteristic
58C2×C4×Dic43D411yescharacteristic
59Dic43⋊C8—24no—
60C22⋊(C43⋊C8)—21no—
61C22⋊(C43⋊C8)D412yes—
62#13063235—24no—
63C43⋊#95—24no—
64C43⋊#95—21no—
65C43⋊#95—21no—
66C43⋊#95—21no—
67C43⋊#95—21no—
68C43⋊#95—42no—
69C23×C4×C43—21no—
70C23×C4×C43C2311yescharacteristic
71C22×C8×C43—21no—
72C2×C4⋊C4×C43C2×C411yescharacteristic
73C2×C4⋊C4×C43C2×C411yescharacteristic
74C2×C22⋊C4×C43—21no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43D412yes—
77#95×C43—21no—
78#95×C43—21no—
79#95×C43—21no—
80C24×C43C2×D411yescharacteristic
81C23×D43—21no—
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—41no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43C22×C411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43#4111yescharacteristic
98C22×C4×C43#4111yescharacteristic
99C2×C22⋊D43—41no—
100C2×C22⋊D43—41no—
101C2×C22⋊D43—41no—
102C2×C22⋊D43—41no—
103C2×C22⋊D43—41no—
104C2×C22⋊D43—41no—
105C22×Dic43—22no—
106C22×Dic43—22no—
107C22×Dic43—21no—
108C22×Dic43—21no—
109C22×Dic43—21no—
110C22×Dic43—21no—
111C22×Dic43—21no—
112C22×Dic43—21no—
113C22×Dic43—21no—
114C22×Dic43—21no—
115C22×Dic43—21no—
116C22×Dic43—41no—
117C22×Dic43—41no—
118C22×Dic43—41no—
119C22×Dic43—41no—
120C22×Dic43—41no—
121C22×Dic43—41no—
122C22×Dic43—41no—
123C22×Dic43C22⋊C411yescharacteristic
124C22×Dic43C22⋊C411yescharacteristic
125C22×Dic43C22⋊C411yescharacteristic
126C22×Dic43C22⋊C411yescharacteristic
127C2×D172—21no—
128C2×D172—21no—
129C2×D172—41no—
130C2×D172—41no—
131C2×C8×C43—22no—
132C2×C8×C43—41no—
133C2×C8×C43—41no—
134C4⋊C4×C43—41no—
135C4⋊C4×C43—41no—
136C22⋊C4×C43—41no—
137C22⋊C4×C43—41no—
138(C2×D43)⋊C4—42no—
139(C2×D43)⋊C4—42no—
140(C2×D43)⋊C4—42no—
141(C2×D43)⋊C4—41no—
142(C2×D43)⋊C4—41no—
143(C2×D43)⋊C4—42no—
144C4⋊Dic43—21no—
145C4⋊Dic43—21no—
146C4⋊Dic43—42no—
147C4⋊Dic43—42no—
148C4×Dic43—21no—
149C4×Dic43—21no—
150C4×Dic43—21no—
151C4×Dic43—21no—
152C4×Dic43—21no—
153C4×Dic43—21no—
154C4×Dic43—21no—
155C4×Dic43—21no—
156C2×C43⋊C8—22no—
157C2×C43⋊C8—41no—
158C2×C43⋊C8—41no—
159C23×C43—21no—
160C23×C43—21no—
161C23×C43—21no—
162C23×C43—21no—
163C23×C43C2×C22⋊C411yescharacteristic
164C23×C43#12111yescharacteristic
165C23×C43#12111yescharacteristic
166C23×C43AGL(1,ℤ/8)11yescharacteristic
167C23×C43AGL(1,ℤ/8)11yescharacteristic
168C23×C43AGL(1,ℤ/8)11yescharacteristic
169C23×C43#13711yescharacteristic
170C22×D43—41no—
171C22×D43—41no—
172C22×D43—41no—
173C22×D43—41no—
174C22×D43—41no—
175C22×D43—41no—
176C22×D43—41no—
177C2×C4×C43—21no—
178C2×C4×C43—21no—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—42no—
186C2×C4×C43—42no—
187C2×C4×C43—42no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—81no—
195C2×C4×C43—81no—
196C2×C4×C43—81no—
197C2×C4×C43—81no—
198C2×C4×C43C4×D411yescharacteristic
199C2×C4×C43C4×D411yescharacteristic
200C2×C4×C43#12011yescharacteristic
201C2×C4×C43#12311yescharacteristic
202C22⋊D43—81no—
203C22⋊D43—81no—
204C22⋊D43—81no—
205C22⋊D43—81no—
206C2×Dic43—21no—
207C2×Dic43—21no—
208C2×Dic43—21no—
209C2×Dic43—21no—
210C2×Dic43—21no—
211C2×Dic43—21no—
212C2×Dic43—21no—
213C2×Dic43—21no—
214C2×Dic43—21no—
215C2×Dic43—21no—
216C2×Dic43—21no—
217C2×Dic43—42no—
218C2×Dic43—42no—
219C2×Dic43—41no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—42no—
224C2×Dic43—42no—
225C2×Dic43—42no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—81no—
230C2×Dic43—81no—
231C2×Dic43—81no—
232C2×Dic43—81no—
233C2×Dic43#10412yes—
234D172—81no—
235D172—81no—
236C8×C43—42no—
237C43⋊C8—42no—
238#9118—431nomaximal, Sylow
239C22×C43—21no—
240C22×C43—21no—
241C22×C43—21no—
242C22×C43—21no—
243C22×C43—21no—
244C22×C43—21no—
245C22×C43—21no—
246C22×C43—21no—
247C22×C43—21no—
248C22×C43—21no—
249C22×C43—21no—
250C22×C43—21no—
251C22×C43#38611yescharacteristic
252C22×C43#41011yescharacteristic
253C22×C43#41011yescharacteristic
254C22×C43#41711yescharacteristic
255C22×C43#41811yescharacteristic
256C22×C43C2×#10411yescharacteristic
257C22×C43#42111yescharacteristic
258C22×C43#46811yescharacteristic
259C22×C43#46811yescharacteristic
260C22×C43#46911yescharacteristic
261C22×C43#46911yescharacteristic
262C2×D43—81no—
263C2×D43—81no—
264C2×D43—81no—
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—81no—
268C2×D43—81no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—82no—
274C4×C43—81no—
275C4×C43—81no—
276Dic43—22no—
277Dic43—41no—
278Dic43—41no—
279Dic43—41no—
280Dic43—82no—
281Dic43—81no—
282C2×#432—431no—
283#2854—431no—
284C2×#327—431no—
285C2×#327—431no—
286#1434—431no—
287#1294—431no—
288#1294D4311yescharacteristic, complemented
289C2×C43—21no—
290C2×C43—21no—
291C2×C43—21no—
292C2×C43—21no—
293C2×C43#150511yescharacteristic
294C2×C43#150911yescharacteristic
295C2×C43#151211yescharacteristic
296C2×C43#151411yescharacteristic
297C2×C43#187111yescharacteristic
298C2×C43#189511yescharacteristic
299C2×C43#189911yescharacteristic
300D43—161no—
301C2×#123—861no—
302C2×#121—431no—
303C22×C42—431no—
304#432—862no—
305#432—862no—
306C2×C4⋊C8—861no—
307C2×C22⋊C8—431no—
308C2×C22⋊C8C2×D4311yescharacteristic
309C2×#97—861no—
310#390—431no—
311#390—431no—
312#389—431no—
313#389—431no—
314#388—861no—
315#388—861no—
316#386—861no—
317#380C2×D4311yescharacteristic
318C2×#95—431no—
319C2×#95—861no—
320C2×#95—861no—
321C2×#95C2×D4311yescharacteristic
322#327—862no—
323#327—862no—
324C43#911811yescharacteristic, complemented, Sylow
325C22×D4—431no—
326C22×D4—861no—
327C23×C4—21no—
328C23×C4—431no—
329C23×C4—431no—
330C23×C4—861no—
331C23×C4C22×D4311yescharacteristic
332C22×C8—21no—
333C22×C8—861no—
334#123—1722no—
335#123—1722no—
336#121—861no—
337#121—861no—
338#121—861no—
339#121—861no—
340C2×C4⋊C4—431no—
341C2×C4⋊C4—861no—
342C2×C4⋊C4—861no—
343C2×C4⋊C4C4×D4311yescharacteristic
344C2×C4⋊C4C4×D4311yescharacteristic
345C2×C22⋊C4—21no—
346C2×C22⋊C4—861no—
347C2×C22⋊C4—861no—
348C2×C22⋊C4—861no—
349C2×C22⋊C4—861no—
350C2×C22⋊C4—861no—
351C2×C42—431no—
352C2×C42—431no—
353C2×C42—431no—
354C2×C42—431no—
355C2×C42—861no—
356C2×C42—861no—
357C2×C42—861no—
358C2×C42—861no—
359C4⋊C8—864no—
360C22⋊C8—21no—
361C22⋊C8—432no—
362C22⋊C8—861no—
363C22⋊C8D17212yes—
364#97—864no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—861no—
369#95—861no—
370#95—864no—
371#95—861no—
372#95—861no—
373#95—1722no—
374C24—861no—
375C24D4×D4311yescharacteristic
376C2×D4—861no—
377C2×D4—861no—
378C2×D4—1721no—
379C2×D4—1721no—
380C2×D4—1721no—
381C2×D4—1721no—
382C2×D4—1721no—
383C2×D4—1721no—
384C2×D4—1721no—
385C2×D4—1721no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—431no—
398C22×C4—431no—
399C22×C4—431no—
400C22×C4—431no—
401C22×C4—862no—
402C22×C4—861no—
403C22×C4—861no—
404C22×C4—861no—
405C22×C4—861no—
406C22×C4—861no—
407C22×C4—861no—
408C22×C4—861no—
409C22×C4—861no—
410C22×C4—862no—
411C22×C4—861no—
412C22×C4—1721no—
413C22×C4—1721no—
414C22×C4—1721no—
415C22×C4—1721no—
416C22×C4—1721no—
417C22×C4—1721no—
418C22×C4—1721no—
419C22×C4C2×C4×D4311yescharacteristic
420C22×C4C2×D17211yescharacteristic
421C22×C4#1062189811yescharacteristic
422C22×C4D4×D4311yescharacteristic
423C22×C4D4×D4311yescharacteristic
424C22×C4#1062190211yescharacteristic
425C2×C8—22no—
426C2×C8—41no—
427C2×C8—41no—
428C2×C8—862no—
429C2×C8—1721no—
430C2×C8—1721no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—861no—
434C4⋊C4—861no—
435C4⋊C4—1722no—
436C4⋊C4—1722no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—1722no—
440C22⋊C4—1722no—
441C22⋊C4—1722no—
442C22⋊C4—1722no—
443C22⋊C4—1721no—
444C22⋊C4—1721no—
445C42—861no—
446C42—861no—
447C42—861no—
448C42—861no—
449C42—861no—
450C42—861no—
451C42—861no—
452C42—861no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—1721no—
458C23—1721no—
459C23—1721no—
460C23—1721no—
461C23—1721no—
462C23—1721no—
463C23—1721no—
464C23C22⋊C4×D4311yescharacteristic
465C23#1306329811yescharacteristic
466C23#1306330011yescharacteristic
467C23#1306334911yescharacteristic
468C23#1306335211yescharacteristic
469C23#1306335211yescharacteristic
470C23#1306335711yescharacteristic
471D4—3441no—
472D4—3441no—
473D4—3441no—
474D4—3441no—
475D4—3441no—
476D4—3441no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4—81no—
498C2×C4—432no—
499C2×C4—861no—
500C2×C4—861no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4—861no—
504C2×C4—861no—
505C2×C4—861no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—3441no—
511C2×C4—3441no—
512C2×C4—3441no—
513C2×C4—3441no—
514C2×C4—1722no—
515C2×C4—1722no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4—1722no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4#1306328711yescharacteristic
527C2×C4C4×D17211yescharacteristic
528C2×C4#1306329511yescharacteristic
529C2×C4#1306331011yescharacteristic
530C8—42no—
531C8—1722no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—3441no—
545C22—3441no—
546C22—3441no—
547C22—3441no—
548C22—3441no—
549C22—3441no—
550C22—3441no—
551C22#1458277711yescharacteristic
552C22#1458287111yescharacteristic
553C22#1458287111yescharacteristic
554C22#1458289911yescharacteristic
555C22#1458290211yescharacteristic
556C22#104×D4311yescharacteristic
557C22#1458291411yescharacteristic
558C22#1458314611yescharacteristic
559C22#1458314811yescharacteristic
560C22#1458315111yescharacteristic
561C22#1458315311yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—82no—
567C4—81no—
568C4—81no—
569C4—862no—
570C4—3442no—
571C4—3441no—
572C4—1721no—
573C4—1721no—
574C4—1721no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—6881no—
580C2#1913310111yescharacteristic
581C2#1913311911yescharacteristic
582C2#1913313211yescharacteristic
583C2#1913314011yescharacteristic
584C2#1913489611yescharacteristic
585C2#1913503211yescharacteristic
586C2#1913505211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1294C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1294D43
hypocenterC43#9118
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
1. C2×#14582953C2semidirect
5. #19132819C2semidirect
6. #19132473C2semidirect
7. C43×#1294C2semidirect
16. #14582800C4semidirect
17. #14582800C4semidirect
18. #14582798C4semidirect
19. #14582798C4semidirect
288. #1294D43semidirect
324. C43#9118semidirect

Maximal subgroups

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

subgroupindex
C2×#145829532
#191429272
C2×#145826342
C2×#145826322
#191328192
#191324732
C43×#12942
#911843