Finite Group Databasebeta

← #25155568

Subgroups — #25155568

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#19139836C211yesmaximal, characteristic, complemented
2#19137540C211yesmaximal, characteristic
3#19136115C211yesmaximal, characteristic
4#19136113C211yesmaximal, characteristic
5#19135984C211yesmaximal, characteristic
6#19135980C211yesmaximal, characteristic
7#19135363C211yesmaximal, characteristic, complemented
8#19135362C211yesmaximal, characteristic, complemented
9#19135357C211yesmaximal, characteristic, complemented
10#19135312C211yesmaximal, characteristic, complemented
11#19135186C211yesmaximal, characteristic, complemented
12#19134753C211yesmaximal, characteristic, complemented
13#19134594C211yesmaximal, characteristic
14#19134409C211yesmaximal, characteristic
15C43×#1921C211yesmaximal, characteristic, complemented
16C2×#13063287C2211yescharacteristic
17C2×#13063282—21no—
18C2×#13063259C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582840—21no—
32#14582837—21no—
33#14582801C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582794—21no—
37#14582790—21no—
38#14582788—21no—
39#14582768C2211yescharacteristic
40#14582768C2211yescharacteristic
41#14582765C2211yescharacteristic
42#14582764C2211yescharacteristic
43#14582763—21no—
44#14582758—21no—
45C4⋊C4×Dic43C2211yescharacteristic
46C4⋊C4×Dic43C2211yescharacteristic
47C4×Dic43⋊C4C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C4×D43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063287—22no—
64#13063287Q814yes—
65#13063282—44no—
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4D411yescharacteristic
75C2×Dic43⋊C4D411yescharacteristic
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—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#13063257—41no—
89#13063256—41no—
90C4⋊(C43⋊C8)—22no—
91Dic43⋊C8—22no—
92Dic43⋊C8—22no—
93#13063247—22no—
94#13063247—41no—
95#13063245—22no—
96#13063245—41no—
97C8×Dic43—22no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116#107×C43—22no—
117#95×C43—21no—
118#95×C43—21no—
119C23×D43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43C2×D411yescharacteristic
131C22×Dic43C2×D411yescharacteristic
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172C2×Q812yes—
140C2×C4×D43—24no—
141C2×C4×D43—42no—
142C2×C4×D43—42no—
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—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—81no—
157C4⋊C4×C43C2×Q812yes—
158C42×C43—21no—
159C42×C43—21no—
160C42×C43—42no—
161(C2×D43)⋊C4—24no—
162(C2×D43)⋊C4—42no—
163(C2×D43)⋊C4—42no—
164(C2×D43)⋊C4—81no—
165(C2×D43)⋊C4—81no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172Dic43⋊C4—22no—
173Dic43⋊C4—22no—
174Dic43⋊C4—42no—
175Dic43⋊C4—42no—
176Dic43⋊C4—81no—
177Dic43⋊C4—81no—
178Dic43⋊C4—81no—
179C4×Dic43—21no—
180C4×Dic43—21no—
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×C43C22×D411yescharacteristic
192C22×D43—22no—
193C22×D43—41no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—41no—
199C2×C4×C43—22no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
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×C43C22×Q811yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43H(5,𝔽2)11yescharacteristic
222C2×C4×C432−1+411yescharacteristic
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43C22⋊Q812yes—
241C2×Dic43C22⋊Q812yes—
242C2×Dic43#13512yes—
243C2×Dic43AGL(1,ℤ/8)12yes—
244D172—22no—
245D172—22no—
246D172—41no—
247D172—41no—
248C4×D43—48no—
249C8×C43—22no—
250C8×C43—41no—
251C43⋊C8—22no—
252C43⋊C8—41no—
253#26087—431nomaximal, Sylow
254C22×C43C2×C22⋊Q811yescharacteristic
255C22×C43#54711yescharacteristic
256C22×C43#55011yescharacteristic
257C22×C43C2×#13511yescharacteristic
258C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
259C22×C43#57611yescharacteristic
260C22×C43#57811yescharacteristic
261C2×D43—42no—
262C2×D43—42no—
263C2×D43—42no—
264C2×D43—81no—
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—81no—
268C4×C43—42no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—81no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43#53311yescharacteristic
275C4×C43#54411yescharacteristic
276C4×C43#55211yescharacteristic
277C4×C43#55311yescharacteristic
278Dic43—22no—
279Dic43—41no—
280Dic43—41no—
281Dic43—81no—
282Dic43—81no—
283Dic43—81no—
284Dic43#47814yes—
285#2571—431no—
286#2354—431no—
287#2092—431no—
288#2092—431no—
289#2067—431no—
290#2067—431no—
291#1949—431no—
292#1949—431no—
293#1948—431no—
294#1939—431no—
295#1921—431no—
296#1921D4311yescharacteristic, complemented
297#1845—431no—
298#1802—431no—
299C4×#102—431no—
300C2×C43#244111yescharacteristic
301C2×C43C2×#47811yescharacteristic
302C2×C43#308311yescharacteristic
303C2×C43#334111yescharacteristic
304C2×C43#335311yescharacteristic
305C2×C43#339311yescharacteristic
306C2×C43#339911yescharacteristic
307D43—82no—
308C2×C4×D4—431no—
309C2×#117—861no—
310C2×#107—431no—
311C2×#107—431no—
312C2×#107—431no—
313C2×#107C2×D4311yescharacteristic
314C2×#106—431no—
315C2×#106—431no—
316C2×C4⋊C8—431no—
317C2×C4⋊C8—431no—
318C2×C4⋊C8—431no—
319C2×#102—431no—
320C2×#102—431no—
321C2×#102—431no—
322C2×#102—431no—
323C2×C4×C8—431no—
324#400—861no—
325#400—861no—
326#390—431no—
327#390—431no—
328#389—431no—
329#389—861no—
330#389C2×D4311yescharacteristic
331#388—861no—
332#388—861no—
333#384—431no—
334#384—431no—
335#382—431no—
336#382—431no—
337#382—861no—
338#380—861no—
339C4×C4⋊C4—431no—
340C4×C4⋊C4—431no—
341C4×C4⋊C4—431no—
342C4×C4⋊C4C2×D4311yescharacteristic
343#340—431no—
344#340—431no—
345#340—431no—
346#340C2×D4311yescharacteristic
347#340C2×D4311yescharacteristic
348#340C2×D4311yescharacteristic
349#336—431no—
350#336C2×D4311yescharacteristic
351C43#2608711yescharacteristic, complemented, Sylow
352C22×D4—431no—
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—21no—
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⋊C4C22×D4311yescharacteristic
373C2×C4⋊C4C22×D4311yescharacteristic
374C2×C4⋊C4C22×D4311yescharacteristic
375C2×C4⋊C4C22×D4311yescharacteristic
376C2×C22⋊C4—861no—
377C2×C22⋊C4—861no—
378C2×C22⋊C4—861no—
379C2×C22⋊C4—861no—
380C2×C22⋊C4—861no—
381C2×C42—21no—
382C2×C42—431no—
383C2×C42—431no—
384C2×C42—861no—
385C2×C42—861no—
386C2×C42C22×D4311yescharacteristic
387#107—22no—
388#107—862no—
389#107—1721no—
390#107—1721no—
391#106—1721no—
392#106—1721no—
393C4⋊C8—862no—
394C4⋊C8—862no—
395C4⋊C8—862no—
396#102—862no—
397#102—862no—
398#102—1721no—
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—861no—
413C2×D4—432no—
414C2×D4—861no—
415C2×D4—861no—
416C2×D4—861no—
417C2×D4—861no—
418C2×D4—861no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—431no—
424C22×C4—431no—
425C22×C4—431no—
426C22×C4—431no—
427C22×C4—864no—
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#1062189812yes—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—81no—
456C4⋊C4—862no—
457C4⋊C4—862no—
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—1722no—
468C4⋊C4—1722no—
469C4⋊C4Q8×D4312yes—
470C22⋊C4—864no—
471C22⋊C4—3441no—
472C22⋊C4—3441no—
473C22⋊C4—1722no—
474C22⋊C4—1722no—
475C42—21no—
476C42—21no—
477C42—42no—
478C42—432no—
479C42—432no—
480C42—861no—
481C42—861no—
482C42—1722no—
483C42—1722no—
484C23—862no—
485C23—1721no—
486C23—1721no—
487C23—1721no—
488C23—1721no—
489C23—1721no—
490C23—1721no—
491C23C2×D4×D4311yescharacteristic
492D4—862no—
493D4—862no—
494D4—1721no—
495D4—1721no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
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—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—432no—
515C2×C4—432no—
516C2×C4—432no—
517C2×C4—432no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—1728no—
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×#1062189811yescharacteristic
540C2×C4#1306337111yescharacteristic
541C2×C4#1306337211yescharacteristic
542C8—22no—
543C8—41no—
544C8—862no—
545C8—1721no—
546C22—3441no—
547C22—3441no—
548C22—3441no—
549C22—3441no—
550C22—1722no—
551C22—1722no—
552C22—1722no—
553C22C22⋊Q8×D4311yescharacteristic
554C22#1458354711yescharacteristic
555C22#1458357011yescharacteristic
556C22#135×D4311yescharacteristic
557C22AGL(1,ℤ/8)×D4311yescharacteristic
558C22#1458370311yescharacteristic
559C22#1458371211yescharacteristic
560C4—41no—
561C4—42no—
562C4—41no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—434no—
567C4—862no—
568C4—3441no—
569C4—3441no—
570C4—3441no—
571C4—1721no—
572C4—1721no—
573C4#1458345311yescharacteristic
574C4#1458352911yescharacteristic
575C4#1458358211yescharacteristic
576C4#1458360011yescharacteristic
577C2—3442no—
578C2#1913830711yescharacteristic
579C2#478×D4311yescharacteristic
580C2#1914444311yescharacteristic
581C2#1914701211yescharacteristic
582C2#1914717211yescharacteristic
583C2#1914758311yescharacteristic
584C2#1914763811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1921C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1921D43
hypocenterC43#26087
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
1. #19139836C2semidirect
7. #19135363C2semidirect
8. #19135362C2semidirect
9. #19135357C2semidirect
10. #19135312C2semidirect
11. #19135186C2semidirect
12. #19134753C2semidirect
15. C43×#1921C2semidirect
296. #1921D43semidirect
351. C43#26087semidirect

Maximal subgroups

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

subgroupindex
#191398362
#191375402
#191361152
#191361132
#191359842
#191359802
#191353632
#191353622
#191353572
#191353122
#191351862
#191347532
#191345942
#191344092
C43×#19212
#2608743