Finite Group Databasebeta

← #25199824

Subgroups — #25199824

Order 11008.

660 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140558C211yesmaximal, characteristic
2#19137241C211yesmaximal, characteristic, complemented
3#19136094C211yesmaximal, characteristic, complemented
4#19135977C211yesmaximal, characteristic, complemented
5#19135970C211yesmaximal, characteristic
6#19135914C211yesmaximal, characteristic
7#19135447C211yesmaximal, characteristic
8#19135322C211yesmaximal, characteristic, complemented
9#19135290C211yesmaximal, characteristic
10#19135286C211yesmaximal, characteristic, complemented
11#19135222C211yesmaximal, characteristic
12#19134949C211yesmaximal, characteristic
13#19134862C211yesmaximal, characteristic, complemented
14#19134451C211yesmaximal, characteristic, complemented
15C43×#1920C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×#13063256C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×Dic43⋊C8C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582828—21no—
31#14582826—21no—
32#14582825—21no—
33#14582821—21no—
34#14582804C2211yescharacteristic
35#14582804C2211yescharacteristic
36#14582801C2211yescharacteristic
37#14582800C2211yescharacteristic
38#14582800C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582795C2211yescharacteristic
41#14582795C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582783—21no—
44#14582783—21no—
45#14582766—21no—
46#14582763—21no—
47#14582745C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C2×#10621873—22no—
62C2×#10621873—22no—
63C2×#10621873—41no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C4×Dic86—22no—
67C4×Dic86—22no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
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×Dic43C2311yescharacteristic
83C2×C4×Dic43C2311yescharacteristic
84#13063256—22no—
85#13063256—41no—
86Dic43⋊C8—22no—
87Dic43⋊C8—22no—
88#13063250—41no—
89#13063248—22no—
90#13063248—22no—
91#13063247—22no—
92#13063245—22no—
93#13063245—41no—
94#13063235—41no—
95C8×Dic43—41no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#106×C43—22no—
118#95×C43—21no—
119#95×C43—21no—
120C23×D43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43C2×D411yescharacteristic
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×Dic86—21no—
142C2×Dic86—21no—
143C2×Dic86—21no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86#4112yes—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43#4112yes—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—81no—
162C42×C43—21no—
163C42×C43—21no—
164C42×C43—81no—
165(C2×D43)⋊C4—81no—
166(C2×D43)⋊C4—81no—
167(C2×D43)⋊C4—81no—
168(C2×D43)⋊C4—81no—
169(C2×D43)⋊C4—81no—
170(C2×D43)⋊C4—81no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—81no—
175C4⋊Dic43#4112yes—
176Dic43⋊C4—24no—
177Dic43⋊C4—81no—
178Dic43⋊C4—81no—
179Dic43⋊C4—81no—
180C4×Dic43—24no—
181C4×Dic43—21no—
182C4×Dic43—21no—
183C4×Dic43—21no—
184C4×Dic43—21no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8#4112yes—
191#10621873—44no—
192C23×C43C22×D411yescharacteristic
193C22×D43—41no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—41no—
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×C43—41no—
218C2×C4×C43C2×#4111yescharacteristic
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—22no—
225C2×Dic43—22no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245D172—41no—
246D172—41no—
247D172—41no—
248D172—41no—
249Dic86—22no—
250Dic86—22no—
251Dic86—41no—
252Dic86—41no—
253C8×C43—22no—
254C8×C43—41no—
255C43⋊C8—22no—
256C43⋊C8—41no—
257#29442—431nomaximal, Sylow
258C22×C43#52511yescharacteristic
259C22×C43#53211yescharacteristic
260C22×C43#53711yescharacteristic
261C22×C43#57711yescharacteristic
262C22×C43#57711yescharacteristic
263C22×C43#57711yescharacteristic
264C22×C43#57711yescharacteristic
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—81no—
268C2×D43—81no—
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—81no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43#55111yescharacteristic
279C4×C43#55211yescharacteristic
280C4×C43#55311yescharacteristic
281C4×C43#55611yescharacteristic
282Dic43—42no—
283Dic43—42no—
284Dic43—41no—
285Dic43—41no—
286Dic43—41no—
287Dic43—41no—
288Dic43—81no—
289#2644—431no—
290#2320—431no—
291#2088—431no—
292#2066—431no—
293#2065—431no—
294#2055—431no—
295#1968—431no—
296#1941—431no—
297#1936—431no—
298#1935—431no—
299#1926—431no—
300#1920D4311yescharacteristic, complemented
301#1880—431no—
302#1865—431no—
303#1768—431no—
304C2×C43#260111yescharacteristic
305C2×C43#312511yescharacteristic
306C2×C43#312611yescharacteristic
307C2×C43#317311yescharacteristic
308C2×C43#317411yescharacteristic
309C2×C43#326011yescharacteristic
310C2×C43#326311yescharacteristic
311D43—161no—
312C22×SD16—431no—
313C2×C4×Q8—431no—
314C2×#106—431no—
315C2×#106—431no—
316C2×#106C2×D4311yescharacteristic
317C2×C4⋊C8—431no—
318C2×C4⋊C8—431no—
319C2×#103—431no—
320C2×#103—431no—
321C2×#103—431no—
322C2×#102—431no—
323C2×#102—431no—
324C2×#102—431no—
325C2×#97—431no—
326C2×C4×C8—431no—
327#397—861no—
328#397—861no—
329#397—861no—
330#396—861no—
331#391—431no—
332#391—431no—
333#390—431no—
334#390—431no—
335#390—431no—
336#389—431no—
337#389—431no—
338#389—431no—
339#389—431no—
340#389C2×D4311yescharacteristic
341#387—861no—
342#387—861no—
343#383—861no—
344#382—861no—
345C4×C4⋊C4C2×D4311yescharacteristic
346#376—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340C2×D4311yescharacteristic
351#340C2×D4311yescharacteristic
352#340C2×D4311yescharacteristic
353#336—431no—
354#336C2×D4311yescharacteristic
355C43#2944211yescharacteristic, complemented, Sylow
356C22×Q8—431no—
357C22×D4—431no—
358C2×SD16—862no—
359C2×SD16—862no—
360C2×SD16—1721no—
361C22×C8—431no—
362C22×C8—431no—
363C22×C8C22×D4311yescharacteristic
364C22×C8C22×D4311yescharacteristic
365C4×Q8—862no—
366C4×Q8—862no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—431no—
369C2×C4⋊C4—431no—
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×C4⋊C4C22×D4311yescharacteristic
377C2×C4⋊C4C22×D4311yescharacteristic
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C22⋊C4—861no—
380C2×C22⋊C4—861no—
381C2×C22⋊C4—861no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C42—21no—
386C2×C42—431no—
387C2×C42—431no—
388C2×C42—861no—
389C2×C42C22×D4311yescharacteristic
390#106—22no—
391#106—862no—
392#106—1721no—
393C4⋊C8—862no—
394C4⋊C8—862no—
395#103—862no—
396#103—862no—
397#103—1721no—
398#102—862no—
399#102—862no—
400#102—1721no—
401#97—1721no—
402C4×C8—1721no—
403#95—21no—
404#95—21no—
405#95—431no—
406#95—431no—
407#95—431no—
408#95—431no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417C24—861no—
418C2×Q8—432no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×D4—861no—
425C2×D4—861no—
426C2×D4—861no—
427C2×D4—861no—
428C2×D4—861no—
429C2×D4—861no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4D4×D4311yescharacteristic
442C22×C4D4×D4311yescharacteristic
443C22×C4C23×D4311yescharacteristic
444SD16—1724no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—432no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8#1062189812yes—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—81no—
466C4⋊C4—432no—
467C4⋊C4—864no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—3441no—
472C4⋊C4—3441no—
473C4⋊C4—3441no—
474C4⋊C4—3441no—
475C22⋊C4—3441no—
476C22⋊C4—3441no—
477C22⋊C4—3441no—
478C22⋊C4—3441no—
479C22⋊C4—3441no—
480C22⋊C4—3441no—
481C42—21no—
482C42—21no—
483C42—81no—
484C42—864no—
485C42—861no—
486C42—861no—
487C42—861no—
488C42—861no—
489C23—1721no—
490C23—1721no—
491C23—1721no—
492C23—1721no—
493C23—1721no—
494C23—1721no—
495C23—1721no—
496C23C2×D4×D4311yescharacteristic
497Q8—862no—
498Q8—862no—
499Q8—1721no—
500Q8—1721no—
501D4—1721no—
502D4—1721no—
503D4—1721no—
504D4—1721no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—862no—
524C2×C4—862no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4#41×D4311yescharacteristic
545C2×C4#41×D4311yescharacteristic
546C2×C4#41×D4311yescharacteristic
547C2×C4C2×#1062189811yescharacteristic
548C2×C4#1306337111yescharacteristic
549C2×C4#1306337311yescharacteristic
550C8—22no—
551C8—41no—
552C8—862no—
553C8—1721no—
554C22—3441no—
555C22—3441no—
556C22—3441no—
557C22—3441no—
558C22—3441no—
559C22—3441no—
560C22—3441no—
561C22#1458340711yescharacteristic
562C22#1458344611yescharacteristic
563C22#1458347911yescharacteristic
564C22#1458370511yescharacteristic
565C22#1458370611yescharacteristic
566C22#1458370811yescharacteristic
567C22#1458370911yescharacteristic
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—3441no—
575C4—1721no—
576C4—1721no—
577C4—1721no—
578C4—1722no—
579C4—1722no—
580C4—1721no—
581C4#1458357311yescharacteristic
582C4#1458358111yescharacteristic
583C4#1458360011yescharacteristic
584C4#1458362111yescharacteristic
585C2—6881no—
586C2#1914019011yescharacteristic
587C2#1914486711yescharacteristic
588C2#1914488211yescharacteristic
589C2#1914520811yescharacteristic
590C2#1914522111yescharacteristic
591C2#1914604011yescharacteristic
592C2#1914606711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1920C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1920D43
hypocenterC43#29442
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
2. #19137241C2semidirect
3. #19136094C2semidirect
4. #19135977C2semidirect
8. #19135322C2semidirect
10. #19135286C2semidirect
13. #19134862C2semidirect
14. #19134451C2semidirect
15. C43×#1920C2semidirect
300. #1920D43semidirect
355. C43#29442semidirect

Maximal subgroups

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

subgroupindex
#191405582
#191372412
#191360942
#191359772
#191359702
#191359142
#191354472
#191353222
#191352902
#191352862
#191352222
#191349492
#191348622
#191344512
C43×#19202
#2944243