Finite Group Databasebeta

← #25155562

Subgroups — #25155562

Order 11008.

714 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139835C211yesmaximal, characteristic, complemented
2#19137543C211yesmaximal, characteristic
3#19136114C211yesmaximal, characteristic
4#19135983C211yesmaximal, characteristic
5#19135979C211yesmaximal, characteristic
6#19135364C211yesmaximal, characteristic, complemented
7#19135361C211yesmaximal, characteristic, complemented
8#19135355C211yesmaximal, characteristic, complemented
9#19135312C211yesmaximal, characteristic, complemented
10#19135189C211yesmaximal, characteristic, complemented
11#19135188C211yesmaximal, characteristic, complemented
12#19134753C211yesmaximal, characteristic, complemented
13#19134593C211yesmaximal, characteristic
14#102×Dic43C211yesmaximal, characteristic
15C43×#2092C211yesmaximal, characteristic
16C2×D4×Dic43C2211yescharacteristic
17C2×#13063281—21no—
18C2×#13063259C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×C8×Dic43C2211yescharacteristic
28#14582840—21no—
29#14582839—21no—
30#14582802C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582796—21no—
34#14582793—21no—
35#14582787—21no—
36#14582768C2211yescharacteristic
37#14582768C2211yescharacteristic
38#14582764C2211yescharacteristic
39#14582763—21no—
40#14582757—21no—
41C4⋊C4×Dic43C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×Dic43⋊C4C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#382C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C23×Dic43—21no—
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62D4×Dic43—22no—
63D4×Dic43Q814yes—
64#13063281—44no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4D411yescharacteristic
76C2×Dic43⋊C4D411yescharacteristic
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43C2311yescharacteristic
84C2×C4×Dic43C2311yescharacteristic
85#13063259—22no—
86#13063258—41no—
87#13063258—41no—
88#13063256—41no—
89C4⋊(C43⋊C8)—22no—
90Dic43⋊C8—22no—
91Dic43⋊C8—22no—
92#13063246—22no—
93#13063246—41no—
94C8×Dic43—22no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95D411yescharacteristic
103C43⋊#95D411yescharacteristic
104C22×D4×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C42×C43C2311yescharacteristic
113#107×C43—22no—
114#106×C43—41no—
115#102×C43—22no—
116#102×C43—41no—
117#95×C43—21no—
118#95×C43—21no—
119C24×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43C2×Q812yes—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2411yescharacteristic
132C22×Dic43—24no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—42no—
138C22×Dic43—42no—
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43#4112yes—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C22⋊C4×C43—42no—
156C22⋊C4×C43—81no—
157C42×C43—21no—
158C42×C43—21no—
159C22⋊Dic43—24no—
160C22⋊Dic43—42no—
161C22⋊Dic43—81no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—81no—
170C4⋊Dic43C2×Q812yes—
171Dic43⋊C4—22no—
172Dic43⋊C4—22no—
173Dic43⋊C4—42no—
174Dic43⋊C4—42no—
175Dic43⋊C4—81no—
176Dic43⋊C4—81no—
177Dic43⋊C4—81no—
178C4×Dic43—21no—
179C4×Dic43—21no—
180C4×Dic43—42no—
181C4×Dic43—42no—
182C4×Dic43—42no—
183C4×Dic43C2×Q812yes—
184C4×Dic43#4112yes—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8#4112yes—
191C23×C43—22no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43C22×D411yescharacteristic
199D4×C43—22no—
200D4×C43—22no—
201D4×C43—41no—
202D4×C43—41no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43C22×Q811yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43H(5,𝔽2)11yescharacteristic
223C2×C4×C432−1+411yescharacteristic
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—22no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—48no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43C22⋊Q812yes—
246C2×Dic43C22⋊Q812yes—
247C2×Dic43#13512yes—
248C2×Dic43AGL(1,ℤ/8)12yes—
249C8×C43—22no—
250C8×C43—41no—
251C43⋊C8—22no—
252C43⋊C8—41no—
253#26087—431nomaximal, Sylow
254C22×C43—42no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—81no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43C2×C22⋊Q811yescharacteristic
262C22×C43#54711yescharacteristic
263C22×C43#55011yescharacteristic
264C22×C43C2×#13511yescharacteristic
265C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C43#57611yescharacteristic
267C22×C43#57811yescharacteristic
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—81no—
271C4×C43—81no—
272C4×C43—81no—
273C4×C43#53311yescharacteristic
274C4×C43#54411yescharacteristic
275C4×C43#55211yescharacteristic
276C4×C43#55311yescharacteristic
277Dic43—22no—
278Dic43—42no—
279Dic43—41no—
280Dic43—41no—
281Dic43—81no—
282Dic43—81no—
283Dic43—81no—
284Dic43#47814yes—
285#2571—431no—
286#2354—431no—
287#2092—431no—
288#2092D4311yescharacteristic
289#2067—431no—
290#2067—431no—
291#1949—431no—
292#1949—431no—
293#1948—431no—
294#1939—431no—
295#1921—431no—
296#1921—431no—
297#1845—431no—
298#1802—431no—
299C4×#102—431no—
300C2×C43—82no—
301C2×C43#244111yescharacteristic
302C2×C43C2×#47811yescharacteristic
303C2×C43#308311yescharacteristic
304C2×C43#334111yescharacteristic
305C2×C43#335311yescharacteristic
306C2×C43#339311yescharacteristic
307C2×C43#339911yescharacteristic
308C2×C4×D4—431no—
309C2×#117—861no—
310C2×#107—431no—
311C2×#107—431no—
312C2×#107—431no—
313C2×#107C2×D4311yescharacteristic
314C2×#106—431no—
315C2×#106C2×D4311yescharacteristic
316C2×C4⋊C8—431no—
317C2×C4⋊C8—431no—
318C2×C4⋊C8—431no—
319C2×#102—431no—
320C2×#102—431no—
321C2×#102C2×D4311yescharacteristic
322C2×#102C2×D4311yescharacteristic
323C2×C4×C8—431no—
324#400—861no—
325#400—861no—
326#390—431no—
327#390C2×D4311yescharacteristic
328#389—431no—
329#389—431no—
330#389—861no—
331#388—861no—
332#388—861no—
333#384—431no—
334#384—431no—
335#382—431no—
336#382—861no—
337#382C2×D4311yescharacteristic
338#380—861no—
339C4×C4⋊C4—431no—
340C4×C4⋊C4—431no—
341C4×C4⋊C4—431no—
342C4×C4⋊C4—431no—
343#340—431no—
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#336—431no—
350#336C2×D4311yescharacteristic
351C43#2608711yescharacteristic, complemented, Sylow
352C22×D4C22×D4311yescharacteristic
353C23×C4—861no—
354C22×C8—431no—
355C22×C8—431no—
356C22×C8C22×D4311yescharacteristic
357C22×C8C22×D4311yescharacteristic
358C4×D4—434no—
359C4×D4—862no—
360#117—1724no—
361C2×C4⋊C4—431no—
362C2×C4⋊C4—431no—
363C2×C4⋊C4—431no—
364C2×C4⋊C4—431no—
365C2×C4⋊C4—431no—
366C2×C4⋊C4—431no—
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⋊C4C22×D4311yescharacteristic
374C2×C4⋊C4C22×D4311yescharacteristic
375C2×C4⋊C4C22×D4311yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—861no—
379C2×C22⋊C4—861no—
380C2×C22⋊C4—861no—
381C2×C42—431no—
382C2×C42—431no—
383C2×C42—861no—
384C2×C42—861no—
385C2×C42—861no—
386C2×C42C22×D4311yescharacteristic
387#107—22no—
388#107—862no—
389#107—1721no—
390#107—1721no—
391#106—41no—
392#106—1721no—
393C4⋊C8—862no—
394C4⋊C8—862no—
395C4⋊C8—862no—
396#102—22no—
397#102—41no—
398#102—862no—
399#102—1721no—
400C4×C8—862no—
401#95—21no—
402#95—21no—
403#95—431no—
404#95—431no—
405#95—861no—
406#95—861no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412C24—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4Q8×D4312yes—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—431no—
423C22×C4—431no—
424C22×C4—431no—
425C22×C4—431no—
426C22×C4—864no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—1722no—
432C22×C4—1722no—
433C22×C4D4×D4311yescharacteristic
434C22×C4D4×D4311yescharacteristic
435C22×C4C23×D4311yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—432no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8#1062190012yes—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—432no—
455C4⋊C4—862no—
456C4⋊C4—862no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—3441no—
465C4⋊C4—3441no—
466C4⋊C4—3441no—
467C4⋊C4—3441no—
468C4⋊C4—1722no—
469C4⋊C4—1722no—
470C22⋊C4—42no—
471C22⋊C4—81no—
472C22⋊C4—864no—
473C22⋊C4—3441no—
474C22⋊C4—1722no—
475C42—21no—
476C42—21no—
477C42—432no—
478C42—432no—
479C42—861no—
480C42—861no—
481C42—1722no—
482C42—1722no—
483C42—1722no—
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23C2×D4×D4311yescharacteristic
492D4—22no—
493D4—22no—
494D4—41no—
495D4—41no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—432no—
512C2×C4—432no—
513C2×C4—432no—
514C2×C4—432no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—862no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—1728no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4C2×Q8×D4311yescharacteristic
537C2×C4#41×D4311yescharacteristic
538C2×C4#41×D4311yescharacteristic
539C2×C4C2×#1062190011yescharacteristic
540C2×C4#1306337011yescharacteristic
541C2×C4#1306337211yescharacteristic
542C8—22no—
543C8—41no—
544C8—862no—
545C8—1721no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C22⋊Q8×D4311yescharacteristic
554C22#1458354711yescharacteristic
555C22#1458356911yescharacteristic
556C22#135×D4311yescharacteristic
557C22AGL(1,ℤ/8)×D4311yescharacteristic
558C22#1458370311yescharacteristic
559C22#1458371311yescharacteristic
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4—434no—
566C4—862no—
567C4—3441no—
568C4—3441no—
569C4—3441no—
570C4—1721no—
571C4—1722no—
572C4—1721no—
573C4#1458345111yescharacteristic
574C4#1458352811yescharacteristic
575C4#1458358611yescharacteristic
576C4#1458359411yescharacteristic
577C2—82no—
578C2#1913830111yescharacteristic
579C2#478×D4311yescharacteristic
580C2#1914444711yescharacteristic
581C2#1914701211yescharacteristic
582C2#1914717711yescharacteristic
583C2#1914758011yescharacteristic
584C2#1914763411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2092C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2092D43
hypocenterC43#26087
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2092

Complements

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

NH ≅ G/Ntype
1. #19139835C2semidirect
6. #19135364C2semidirect
7. #19135361C2semidirect
8. #19135355C2semidirect
9. #19135312C2semidirect
10. #19135189C2semidirect
11. #19135188C2semidirect
12. #19134753C2semidirect
351. C43#26087semidirect

Maximal subgroups

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

subgroupindex
#191398352
#191375432
#191361142
#191359832
#191359792
#191353642
#191353612
#191353552
#191353122
#191351892
#191351882
#191347532
#191345932
#102×Dic432
C43×#20922
#2608743