Finite Group Databasebeta

← #24988414

Subgroups — #24988414

Order 11008.

868 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×#14583528C211yesmaximal, characteristic
2#19134902C211yesmaximal, characteristic
3C2×#14582637C211yesmaximal, characteristic
4C2×#14582636C211yesmaximal, characteristic
5C2×#14582624C211yesmaximal, characteristic
6#19132845C211yesmaximal, characteristic
7C43×#1872C211yesmaximal, characteristic
8#14583528—22no—
9#14583528—22no—
10#14583528—22no—
11#14583528C414yescomplemented
12C2×#13063324—21no—
13C2×#13063323—21no—
14C2×#13063315—21no—
15C2×#13063315—21no—
16C2×#13063304C2211yescharacteristic
17C2×#13063302—21no—
18C2×#13063281—21no—
19C22×Dic43⋊C4C2211yescharacteristic
20C2×#13063248—21no—
21C2×C22⋊(C43⋊C8)C2211yescharacteristic
22C2×C43⋊#95—21no—
23C2×C43⋊#95—21no—
24C2×C43⋊#95C2211yescharacteristic
25#14582661—21no—
26#14582637—22no—
27#14582636—22no—
28#14582624—22no—
29C2×C22⋊Q8×C43C2211yescharacteristic
30C22×C4⋊C4×C43C2211yescharacteristic
31C2×#103×C43—21no—
32C2×C22⋊C8×C43C2211yescharacteristic
33C43×#340—21no—
34C22×Dic86—21no—
35C22×Dic86D411yescharacteristic
36C23×Dic43—21no—
37C23×Dic43D411yescharacteristic
38C23×Dic43D411yescharacteristic
39C22×C43⋊C8—21no—
40#13063324—24no—
41#13063324—24no—
42#13063323—24no—
43#13063323—24no—
44#13063315—24no—
45#13063315—24no—
46#13063315—24no—
47#13063315—24no—
48#13063304—21no—
49#13063304—21no—
50#13063304C2×C412yes—
51#13063304D412yes—
52#13063302—24no—
53#13063302—24no—
54#13063281—24no—
55#13063281—24no—
56C2×C4⋊Dic43—21no—
57C2×C4⋊Dic43D411yescharacteristic
58C2×Dic43⋊C4—21no—
59C2×Dic43⋊C4—21no—
60C2×Dic43⋊C4—21no—
61C2×Dic43⋊C4—21no—
62C2×Dic43⋊C4—21no—
63C2×Dic43⋊C4—21no—
64C2×Dic43⋊C4—21no—
65C2×Dic43⋊C4—21no—
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4C2×C412yes—
68C2×Dic43⋊C4D412yes—
69C2×C22⋊Dic43—21no—
70C2×C4×Dic43—21no—
71C2×C4×Dic43—21no—
72#13063248—42no—
73C22⋊(C43⋊C8)—21no—
74C22⋊(C43⋊C8)—21no—
75C43⋊#95—21no—
76C43⋊#95—21no—
77C43⋊#95—42no—
78C43⋊#95—42no—
79C22×Q8×C43D411yescharacteristic
80C23×C4×C43—21no—
81C23×C4×C43C2311yescharacteristic
82C22×C8×C43—21no—
83C22⋊Q8×C43—21no—
84C22⋊Q8×C43—21no—
85C22⋊Q8×C43C2×C412yes—
86C22⋊Q8×C43D412yes—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43—42no—
91C2×C4⋊C4×C43D411yescharacteristic
92C2×C22⋊C4×C43—21no—
93#103×C43—42no—
94C22⋊C8×C43—21no—
95C22⋊C8×C43—21no—
96C24×C43C2×D411yescharacteristic
97C2×Q8×C43—21no—
98C2×Q8×C43—41no—
99C2×Q8×C43—41no—
100C2×Q8×C43C22⋊C412yes—
101C22×C4×C43—22no—
102C22×C4×C43—21no—
103C22×C4×C43—21no—
104C22×C4×C43—41no—
105C22×C4×C43—41no—
106C22×C4×C43—41no—
107C22×C4×C43—41no—
108C22×C4×C43—41no—
109C22×C4×C43—41no—
110C22×C4×C43—41no—
111C22×C4×C43—41no—
112C22×C4×C43C22×C411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×Dic43—22no—
119C22×Dic43—21no—
120C22×Dic43—21no—
121C22×Dic43—21no—
122C22×Dic43—21no—
123C22×Dic43—21no—
124C22×Dic43—21no—
125C22×Dic43—21no—
126C22×Dic43—21no—
127C22×Dic43—41no—
128C22×Dic43—41no—
129C22×Dic43—41no—
130C22×Dic43—41no—
131C22×Dic43—41no—
132C22×Dic43—41no—
133C22×Dic43—41no—
134C22×Dic43—41no—
135C22×Dic43C22⋊C412yes—
136C22×Dic43C22⋊C412yes—
137C22×Dic43SD1612yes—
138C22×Dic43Q1612yes—
139C2×Dic86—24no—
140C2×Dic86—21no—
141C2×Dic86—41no—
142C2×Dic86—41no—
143C2×Dic86—81no—
144C2×Dic86—81no—
145C2×Dic86C22⋊C412yes—
146C2×C8×C43—41no—
147C2×C8×C43—41no—
148C2×C8×C43—41no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—41no—
155C4⋊C4×C43—41no—
156C4⋊C4×C43C22⋊C412yes—
157C22⋊C4×C43—22no—
158C22⋊C4×C43—22no—
159C22⋊Dic43—22no—
160C22⋊Dic43—22no—
161C4⋊Dic43—24no—
162C4⋊Dic43—21no—
163C4⋊Dic43C22⋊C412yes—
164Dic43⋊C4—24no—
165Dic43⋊C4—24no—
166Dic43⋊C4—24no—
167Dic43⋊C4—24no—
168Dic43⋊C4—22no—
169Dic43⋊C4—22no—
170Dic43⋊C4—22no—
171Dic43⋊C4—22no—
172Dic43⋊C4—22no—
173Dic43⋊C4—22no—
174C4×Dic43—24no—
175C4×Dic43—24no—
176C2×C43⋊C8—41no—
177C2×C43⋊C8—41no—
178C2×C43⋊C8—41no—
179C23×C43—21no—
180C23×C43—21no—
181C23×C43—21no—
182C23×C43—21no—
183C23×C43C2×C22⋊C411yescharacteristic
184C23×C43#12011yescharacteristic
185C23×C43#12011yescharacteristic
186C23×C43C2×SD1611yescharacteristic
187C23×C43C2×Q1611yescharacteristic
188C23×C43#13711yescharacteristic
189C23×C43#13711yescharacteristic
190Q8×C43—42no—
191Q8×C43—81no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—81no—
210C2×C4×C43—81no—
211C2×C4×C43—81no—
212C2×C4×C43—81no—
213C2×C4×C43C2×C22⋊C411yescharacteristic
214C2×C4×C43C2×C22⋊C411yescharacteristic
215C2×C4×C43#12011yescharacteristic
216C2×C4×C43#12011yescharacteristic
217C2×Dic43—22no—
218C2×Dic43—22no—
219C2×Dic43—22no—
220C2×Dic43—22no—
221C2×Dic43—22no—
222C2×Dic43—22no—
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—81no—
237C2×Dic43—81no—
238C2×Dic43—81no—
239C2×Dic43—81no—
240C2×Dic43—81no—
241C2×Dic43#10314yescomplemented
242Dic86—42no—
243Dic86—81no—
244Dic86—84no—
245C8×C43—81no—
246C43⋊C8—81no—
247#8406—431nomaximal, Sylow
248C22×C43—21no—
249C22×C43—21no—
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43#37911yescharacteristic
261C22×C43C2×#10311yescharacteristic
262C22×C43#41911yescharacteristic
263C22×C43#44811yescharacteristic
264C22×C43#44811yescharacteristic
265C22×C43#45111yescharacteristic
266C22×C43#45111yescharacteristic
267C22×C43#45411yescharacteristic
268C22×C43#45611yescharacteristic
269C22×C43B(4,𝔽2)11yescharacteristic
270C22×C43#45811yescharacteristic
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—42no—
276C4×C43—42no—
277C4×C43—82no—
278Dic43—24no—
279Dic43—42no—
280Dic43—42no—
281Dic43—42no—
282Dic43—82no—
283C2×#544—431no—
284#1872—431no—
285#1872D4311yescharacteristic
286C2×#328—431no—
287C2×#328—431no—
288C2×#324—431no—
289#1441—431no—
290C2×C43—21no—
291C2×C43—21no—
292C2×C43—21no—
293C2×C43—21no—
294C2×C43#159911yescharacteristic
295C2×C43#160511yescharacteristic
296C2×C43#161111yescharacteristic
297C2×C43#161711yescharacteristic
298C2×C43#178711yescharacteristic
299C2×C43#179011yescharacteristic
300C2×C43#179311yescharacteristic
301#544—434no—
302#544—862no—
303#544—862no—
304#544—862no—
305C2×C4⋊Q8—861no—
306C2×C4⋊Q8—861no—
307C2×#125—861no—
308C2×#125—861no—
309C2×C22⋊Q8—431no—
310C2×C22⋊Q8—861no—
311C2×C22⋊Q8C2×D4311yescharacteristic
312C2×#117—861no—
313C22×C4⋊C4—431no—
314C22×C4⋊C4C2×D4311yescharacteristic
315C2×#103—21no—
316C2×#103—861no—
317C2×C22⋊C8—431no—
318C2×C22⋊C8C2×D4311yescharacteristic
319C2×#95—431no—
320C2×#95—861no—
321C2×#95—861no—
322#340—21no—
323#340—861no—
324#328—862no—
325#328—862no—
326#324—862no—
327C43#840611yescharacteristic, complemented, Sylow
328C22×Q8—431no—
329C22×Q8—861no—
330C22×Q8C22⋊D4311yescharacteristic
331C23×C4—21no—
332C23×C4—431no—
333C23×C4—431no—
334C23×C4—861no—
335C23×C4C22×D4311yescharacteristic
336C22×C8—21no—
337C22×C8—861no—
338C4⋊Q8—864no—
339C4⋊Q8—864no—
340C4⋊Q8—864no—
341C4⋊Q8—864no—
342#125—864no—
343#125—864no—
344#125—864no—
345#125—864no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C22⋊Q8—432no—
349C22⋊Q8—432no—
350C22⋊Q8—864no—
351C22⋊Q8—864no—
352C22⋊Q8—861no—
353C22⋊Q8—861no—
354C22⋊Q8C4×D4312yes—
355C22⋊Q8D17212yes—
356#117—864no—
357#117—864no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—431no—
363C2×C4⋊C4—432no—
364C2×C4⋊C4—432no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4C22⋊D4311yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—861no—
378C2×C42—861no—
379C2×C42—861no—
380#103—42no—
381#103—1722no—
382C22⋊C8—21no—
383C22⋊C8—21no—
384C22⋊C8—861no—
385C22⋊C8—861no—
386#95—861no—
387#95—861no—
388#95—1722no—
389#95—1722no—
390C24D4×D4311yescharacteristic
391C2×Q8—21no—
392C2×Q8—41no—
393C2×Q8—41no—
394C2×Q8—432no—
395C2×Q8—864no—
396C2×Q8—861no—
397C2×Q8—3441no—
398C2×Q8—3441no—
399C2×Q8—1721no—
400C2×Q8—1721no—
401C2×Q8(C2×D43)⋊C412yes—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—432no—
414C22×C4—432no—
415C22×C4—432no—
416C22×C4—432no—
417C22×C4—861no—
418C22×C4—861no—
419C22×C4—861no—
420C22×C4—861no—
421C22×C4—861no—
422C22×C4—861no—
423C22×C4—861no—
424C22×C4—861no—
425C22×C4—862no—
426C22×C4—1721no—
427C22×C4—1721no—
428C22×C4—1721no—
429C22×C4—1721no—
430C22×C4—1721no—
431C22×C4—1721no—
432C22×C4—1721no—
433C22×C4—1721no—
434C22×C4C2×C4×D4311yescharacteristic
435C22×C4C2×D17211yescharacteristic
436C22×C4D4×D4311yescharacteristic
437C22×C4D4×D4311yescharacteristic
438C22×C4D4×D4311yescharacteristic
439C22×C4C2×C22⋊D4311yescharacteristic
440C2×C8—41no—
441C2×C8—41no—
442C2×C8—41no—
443C2×C8—1721no—
444C2×C8—1721no—
445C2×C8—1721no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—432no—
454C4⋊C4—864no—
455C4⋊C4—864no—
456C4⋊C4—864no—
457C4⋊C4—864no—
458C4⋊C4—864no—
459C4⋊C4—862no—
460C4⋊C4—862no—
461C4⋊C4—862no—
462C4⋊C4—862no—
463C4⋊C4—862no—
464C4⋊C4—862no—
465C4⋊C4—861no—
466C4⋊C4(C2×D43)⋊C412yes—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—862no—
470C22⋊C4—862no—
471C42—864no—
472C42—864no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23C22⋊C4×D4311yescharacteristic
478C23#1306329311yescharacteristic
479C23#1306329511yescharacteristic
480C23SD16×D4311yescharacteristic
481C23Q16×D4311yescharacteristic
482C23#1306335411yescharacteristic
483C23#1306335711yescharacteristic
484Q8—42no—
485Q8—81no—
486Q8—3441no—
487Q8—3444no—
488Q8—1722no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—81no—
507C2×C4—81no—
508C2×C4—81no—
509C2×C4—81no—
510C2×C4—434no—
511C2×C4—862no—
512C2×C4—862no—
513C2×C4—862no—
514C2×C4—862no—
515C2×C4—862no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—862no—
519C2×C4—862no—
520C2×C4—3441no—
521C2×C4—3441no—
522C2×C4—3441no—
523C2×C4—3441no—
524C2×C4—3441no—
525C2×C4—1722no—
526C2×C4—1722no—
527C2×C4—1722no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1722no—
535C2×C4C22⋊C4×D4311yescharacteristic
536C2×C4C2×(C2×D43)⋊C411yescharacteristic
537C2×C4#1306329311yescharacteristic
538C2×C4#1306329511yescharacteristic
539C8—81no—
540C8—3441no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22#1458275411yescharacteristic
554C22#103×D4311yescharacteristic
555C22#1458290611yescharacteristic
556C22#1458303611yescharacteristic
557C22#1458303911yescharacteristic
558C22#1458305311yescharacteristic
559C22#1458305611yescharacteristic
560C22#1458307011yescharacteristic
561C22#1458308011yescharacteristic
562C22#1458308511yescharacteristic
563C22#1458308811yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—42no—
569C4—42no—
570C4—82no—
571C4—864no—
572C4—3442no—
573C4—1722no—
574C4—1722no—
575C4—1722no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—21no—
580C2#1913353311yescharacteristic
581C2#1913356711yescharacteristic
582C2#1913360111yescharacteristic
583C2#1913363511yescharacteristic
584C2#1913452811yescharacteristic
585C2#1913454211yescharacteristic
586C2#1913455211yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1872C2
socleC23×C43#120
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1872D43
hypocenterC43#8406
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
11. #14583528C4semidirect
241. C2×Dic43#103semidirect
327. C43#8406semidirect

Maximal subgroups

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

subgroupindex
C2×#145835282
#191349022
C2×#145826372
C2×#145826362
C2×#145826242
#191328452
C43×#18722
#840643