Finite Group Databasebeta

← #25155646

Subgroups — #25155646

Order 11008.

678 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139823C211yesmaximal, characteristic, complemented
2#19137568C211yesmaximal, characteristic
3#19136121C211yesmaximal, characteristic
4#19136114C211yesmaximal, characteristic
5#19135967C211yesmaximal, characteristic
6#19135967C211yesmaximal, characteristic
7#19135363C211yesmaximal, characteristic, complemented
8#19135362C211yesmaximal, characteristic, complemented
9#19135357C211yesmaximal, characteristic, complemented
10#19135313C211yesmaximal, characteristic, complemented
11#19135186C211yesmaximal, characteristic, complemented
12#19135165C211yesmaximal, characteristic, complemented
13#19134759C211yesmaximal, characteristic, complemented
14#19134605C211yesmaximal, characteristic
15C4×#102×C43C211yesmaximal, characteristic
16C2×#13063259C2211yescharacteristic
17C2×#13063259C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27#14582841—21no—
28#14582833—21no—
29#14582802C2211yescharacteristic
30#14582802C2211yescharacteristic
31#14582795C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582792—21no—
34#14582792—21no—
35#14582783—21no—
36#14582783—21no—
37#14582768C2211yescharacteristic
38#14582765C2211yescharacteristic
39#14582765C2211yescharacteristic
40#14582764C2211yescharacteristic
41#14582762—21no—
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45C4×C22⋊Dic43—21no—
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×C43⋊C8C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C2×C4⋊Dic43D411yescharacteristic
62C2×C4⋊Dic43D411yescharacteristic
63C2×C4⋊Dic43C2311yescharacteristic
64C2×C4⋊Dic43C2311yescharacteristic
65C2×C4⋊Dic43C2311yescharacteristic
66C2×C4⋊Dic43C2311yescharacteristic
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×C22⋊Dic43—21no—
72C2×C22⋊Dic43—21no—
73C2×C22⋊Dic43—21no—
74C2×C22⋊Dic43—21no—
75C2×C4×Dic43—21no—
76C2×C4×Dic43—21no—
77C2×C4×Dic43C2311yescharacteristic
78C2×C4×Dic43C2311yescharacteristic
79#13063259—22no—
80#13063259—22no—
81#13063258—41no—
82#13063257—41no—
83#13063257—41no—
84#13063256—41no—
85C4⋊(C43⋊C8)—22no—
86Dic43⋊C8—22no—
87Dic43⋊C8—22no—
88#13063246—41no—
89#13063246—41no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95D411yescharacteristic
101C43⋊#95D411yescharacteristic
102C22×D4×C43C2311yescharacteristic
103C23×C4×C43—21no—
104C22×C8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C4×D4×C43—22no—
107C4×D4×C43Q814yes—
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C22⋊C4×C43—21no—
112C2×C42×C43—21no—
113C2×C42×C43C2311yescharacteristic
114#102×C43—22no—
115#102×C43—22no—
116C4×C8×C43—22no—
117#95×C43—21no—
118C24×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43C2×Q812yes—
125C22×C4×C43—24no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—81no—
130C22×C4×C43—81no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43#4112yes—
147C2×C8×C43#4112yes—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43C2×Q812yes—
154C22⋊C4×C43—24no—
155C42×C43—81no—
156C42×C43C2×Q812yes—
157C42×C43#4112yes—
158C22⋊Dic43—42no—
159C22⋊Dic43—42no—
160C22⋊Dic43—81no—
161C22⋊Dic43—81no—
162C4⋊Dic43—22no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—41no—
172Dic43⋊C4—42no—
173Dic43⋊C4—42no—
174Dic43⋊C4—81no—
175Dic43⋊C4—81no—
176C4×Dic43—21no—
177C4×Dic43—21no—
178C4×Dic43—21no—
179C4×Dic43—21no—
180C4×Dic43—81no—
181C4×Dic43—81no—
182C2×C43⋊C8—21no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C23×C43—22no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43—41no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43C22×D411yescharacteristic
196D4×C43—22no—
197D4×C43—22no—
198D4×C43—41no—
199D4×C43—41no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—22no—
205C2×C4×C43—41no—
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—84no—
214C2×C4×C43C22⋊Q812yes—
215C2×C4×C43C22⋊Q812yes—
216C2×C4×C43C22×Q811yescharacteristic
217C2×C4×C43C2×#4111yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×C4×C43H(5,𝔽2)11yescharacteristic
221C2×C4×C432−1+411yescharacteristic
222C2×Dic43—21no—
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—21no—
232C2×Dic43—21no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
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×Dic43#13512yes—
246C8×C43—22no—
247C8×C43—22no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250#26094—431nomaximal, Sylow
251C22×C43—42no—
252C22×C43—42no—
253C22×C43—42no—
254C22×C43—81no—
255C22×C43—81no—
256C22×C43—81no—
257C22×C43—81no—
258C22×C43C2×C22⋊Q811yescharacteristic
259C22×C43#54711yescharacteristic
260C22×C43#55011yescharacteristic
261C22×C43C2×#13511yescharacteristic
262C22×C43#57511yescharacteristic
263C22×C43#57611yescharacteristic
264C22×C43#57711yescharacteristic
265C4×C43—22no—
266C4×C43—22no—
267C4×C43—42no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43#53311yescharacteristic
271C4×C43#54411yescharacteristic
272C4×C43#55211yescharacteristic
273C4×C43#55311yescharacteristic
274Dic43—22no—
275Dic43—41no—
276Dic43—41no—
277Dic43—41no—
278Dic43—81no—
279Dic43—81no—
280Dic43—81no—
281Dic43—81no—
282#2570—431no—
283#2357—431no—
284#2093—431no—
285#2092—431no—
286#2065—431no—
287#2065—431no—
288#1949—431no—
289#1949—431no—
290#1948—431no—
291#1939—431no—
292#1921—431no—
293#1918—431no—
294#1846—431no—
295#1804—431no—
296C4×#102D4311yescharacteristic
297C2×C43—82no—
298C2×C43#244111yescharacteristic
299C2×C43#307611yescharacteristic
300C2×C43#308111yescharacteristic
301C2×C43#333711yescharacteristic
302C2×C43#335511yescharacteristic
303C2×C43#339611yescharacteristic
304C2×C43#340111yescharacteristic
305C2×C4×D4C2×D4311yescharacteristic
306C2×#107—431no—
307C2×#107—431no—
308C2×#107—431no—
309C2×#106—431no—
310C2×#106—431no—
311C2×#106—431no—
312C2×C4⋊C8—431no—
313C2×C4⋊C8—431no—
314C2×C4⋊C8—431no—
315C2×#102—431no—
316C2×#102—431no—
317C2×#102C2×D4311yescharacteristic
318C2×#102C2×D4311yescharacteristic
319C2×C4×C8C2×D4311yescharacteristic
320#400—861no—
321#398—861no—
322#390—431no—
323#390—431no—
324#389—431no—
325#389—431no—
326#388—861no—
327#388—861no—
328#387—861no—
329#387—861no—
330#384—431no—
331#382—431no—
332#382—431no—
333#382—431no—
334#381—861no—
335C4×C4⋊C4—431no—
336C4×C4⋊C4—431no—
337C4×C4⋊C4—431no—
338C4×C4⋊C4C2×D4311yescharacteristic
339C4×C22⋊C4—861no—
340#340—431no—
341#340—431no—
342#340—431no—
343#340—431no—
344#340C2×D4311yescharacteristic
345#340C2×D4311yescharacteristic
346#336—431no—
347#336—431no—
348C43#2609411yescharacteristic, complemented, Sylow
349C22×D4C22×D4311yescharacteristic
350C23×C4—21no—
351C22×C8—431no—
352C22×C8—431no—
353C22×C8C22×D4311yescharacteristic
354C22×C8C22×D4311yescharacteristic
355C4×D4—22no—
356C4×D4Dic8614yes—
357C2×C4⋊C4—431no—
358C2×C4⋊C4—431no—
359C2×C4⋊C4—431no—
360C2×C4⋊C4—431no—
361C2×C4⋊C4—431no—
362C2×C4⋊C4—431no—
363C2×C4⋊C4—861no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4C22×D4311yescharacteristic
368C2×C4⋊C4C22×D4311yescharacteristic
369C2×C4⋊C4C22×D4311yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—861no—
372C2×C22⋊C4—861no—
373C2×C22⋊C4—861no—
374C2×C22⋊C4—861no—
375C2×C42—21no—
376C2×C42—431no—
377C2×C42—431no—
378C2×C42—861no—
379C2×C42—861no—
380C2×C42C22×D4311yescharacteristic
381#107—862no—
382#107—862no—
383#107—1721no—
384#106—1721no—
385#106—1721no—
386#106—1721no—
387C4⋊C8—862no—
388C4⋊C8—862no—
389C4⋊C8—862no—
390#102—22no—
391#102—22no—
392#102—1721no—
393#102—1721no—
394C4×C8—22no—
395#95—21no—
396#95—431no—
397#95—431no—
398#95—861no—
399#95—861no—
400#95—861no—
401#95—861no—
402#95—861no—
403#95—861no—
404#95—861no—
405#95—861no—
406#95—861no—
407#95—861no—
408C24—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4C2×Dic8612yes—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—81no—
420C22×C4—81no—
421C22×C4—431no—
422C22×C4—431no—
423C22×C4—431no—
424C22×C4—431no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4D4×D4311yescharacteristic
430C22×C4D4×D4311yescharacteristic
431C22×C4C23×D4311yescharacteristic
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—861no—
437C2×C8—861no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—861no—
442C2×C8#1062189812yes—
443C2×C8#1062189812yes—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—862no—
450C4⋊C4—861no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—3441no—
459C4⋊C4—3441no—
460C4⋊C4—1721no—
461C4⋊C4—1722no—
462C4⋊C4—1722no—
463C4⋊C4C2×Dic8612yes—
464C22⋊C4—24no—
465C22⋊C4—3441no—
466C22⋊C4—3441no—
467C22⋊C4—1722no—
468C22⋊C4—1722no—
469C42—81no—
470C42—861no—
471C42—861no—
472C42—861no—
473C42—861no—
474C42—3441no—
475C42—3441no—
476C42C2×Dic8612yes—
477C42#1062190012yes—
478C23—22no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23C2×D4×D4311yescharacteristic
486D4—22no—
487D4—22no—
488D4—41no—
489D4—41no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
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—84no—
504C2×C4—432no—
505C2×C4—861no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4#1306330212yes—
529C2×C4#1306330212yes—
530C2×C4C22×Dic8611yescharacteristic
531C2×C4C2×#1062190011yescharacteristic
532C2×C4C2×#1062189811yescharacteristic
533C2×C4C2×#1062189811yescharacteristic
534C2×C4#1306337111yescharacteristic
535C2×C4#1306337211yescharacteristic
536C8—22no—
537C8—22no—
538C8—1721no—
539C8—1721no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22C2×#1306330211yescharacteristic
548C22#1458355411yescharacteristic
549C22#1458357011yescharacteristic
550C22#135×D4311yescharacteristic
551C22#1458369611yescharacteristic
552C22#1458370011yescharacteristic
553C22#1458370511yescharacteristic
554C4—22no—
555C4—22no—
556C4—42no—
557C4—81no—
558C4—81no—
559C4—862no—
560C4—3441no—
561C4—3441no—
562C4—3441no—
563C4—3441no—
564C4—1721no—
565C4—1721no—
566C4—1721no—
567C4#1458345611yescharacteristic
568C4#1458352711yescharacteristic
569C4#1458358911yescharacteristic
570C4#1458359511yescharacteristic
571C2—82no—
572C2#1913830811yescharacteristic
573C2#1914437911yescharacteristic
574C2#1914442211yescharacteristic
575C2#1914697911yescharacteristic
576C2#1914720211yescharacteristic
577C2#1914760711yescharacteristic
578C2#1914765711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenterC4×#102D43
hypocenterC43#26094
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. #19139823C2semidirect
7. #19135363C2semidirect
8. #19135362C2semidirect
9. #19135357C2semidirect
10. #19135313C2semidirect
11. #19135186C2semidirect
12. #19135165C2semidirect
13. #19134759C2semidirect
348. C43#26094semidirect

Maximal subgroups

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

subgroupindex
#191398232
#191375682
#191361212
#191361142
#191359672
#191353632
#191353622
#191353572
#191353132
#191351862
#191351652
#191347592
#191346052
C4×#102×C432
#2609443