Finite Group Databasebeta

← #24988641

Subgroups — #24988641

Order 11008.

760 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148173C211yesmaximal, characteristic
2#19134612C211yesmaximal, characteristic
3C4×#13063250C211yesmaximal, characteristic, complemented
4#19133094C211yesmaximal, characteristic, complemented
5#19133023C211yesmaximal, characteristic, complemented
6#19132978C211yesmaximal, characteristic
7C43×#1493C211yesmaximal, characteristic, complemented
8#14583629C411yescharacteristic, complemented
9#14583626—21no—
10#14583624C411yescharacteristic, complemented
11#14583610C411yescharacteristic, complemented
12#14583607—21no—
13#14583605—21no—
14#14583603—22no—
15#14583564C411yescharacteristic, complemented
16#14583562—21no—
17#14583453—21no—
18#14583453—22no—
19#14583452—21no—
20C4×#10621898C2211yescharacteristic
21#14583367—21no—
22C2×C4×Dic86C2211yescharacteristic
23C4×Q8×D43—21no—
24#14582952C2211yescharacteristic
25C2×#13063251—21no—
26C2×#13063250—21no—
27C4×C4⋊Dic43C2211yescharacteristic
28#14582662—21no—
29#14582660—21no—
30#14582636—22no—
31#14582631—21no—
32#14582629—21no—
33#14582629—21no—
34#14582628—21no—
35C43×#533C2211yescharacteristic
36C43×#423C2211yescharacteristic
37C2×C4×C8×C43C2211yescharacteristic
38C43×Q8⋊C8—22no—
39C2×#10621898D411yescharacteristic
40C22×Dic86D411yescharacteristic
41C2×Q8×D43—21no—
42#13063324—22no—
43#13063324—21no—
44#13063324—21no—
45#13063324—21no—
46#13063323—22no—
47#13063323—21no—
48#13063316—21no—
49#13063316—21no—
50#13063315—22no—
51#13063315—22no—
52#13063315—22no—
53#13063305—22no—
54#13063305—21no—
55#13063303—22no—
56#13063303—22no—
57#13063303—22no—
58#13063302—22no—
59#13063302—22no—
60#13063301—22no—
61#13063301—21no—
62Q8×Dic43—21no—
63C4×Dic86—22no—
64C4×Dic86—22no—
65C4×Dic86—21no—
66C4×Dic86—21no—
67C4×Dic86C2×C411yescharacteristic
68C4×Dic86C2×C411yescharacteristic
69C4×Dic86C2×C411yescharacteristic
70C4×Dic86D411yescharacteristic
71C4×Dic86D411yescharacteristic
72C4×Dic86D411yescharacteristic
73#13063290—22no—
74#13063290—21no—
75#13063290—21no—
76#13063290—21no—
77C4×D172C2×C411yescharacteristic
78C4×D172D411yescharacteristic
79#13063287—21no—
80#13063287—21no—
81C4×C22⋊D43—21no—
82C4×C22⋊D43—21no—
83(C22⋊D43)⋊C4—22no—
84(C22⋊D43)⋊C4—22no—
85#13063284D411yescharacteristic
86#13063282—22no—
87#13063282—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43D411yescharacteristic
90C2×Dic43⋊C4—21no—
91C4⋊C4×D43—22no—
92C4⋊C4×D43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C42×D43—22no—
96C42×D43—21no—
97C4⋊(C43⋊C8)—21no—
98#13063251—42no—
99#13063250—24no—
100C22⋊(C43⋊C8)—21no—
101C4×C43⋊C8—21no—
102C43⋊#95—21no—
103C2×M16×C43—21no—
104C22×C8×C43—21no—
105C4⋊Q8×C43C2×C411yescharacteristic
106C4⋊Q8×C43C2×C411yescharacteristic
107#125×C43—21no—
108C22⋊Q8×C43—21no—
109C22⋊Q8×C43D412yes—
110C4×Q8×C43—21no—
111C4×Q8×C43D412yes—
112#117×C43—21no—
113C2×C42×C43C2311yescharacteristic
114C4⋊C8×C43—21no—
115C4⋊C8×C43—21no—
116C4×C8×C43—21no—
117C4×C8×C43—21no—
118C2×Q8×C43—21no—
119C2×Q8×C43C22⋊C412yes—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C2×C22⋊D43—21no—
124C22×Dic43—21no—
125C22×Dic43—21no—
126C22×Dic43—41no—
127Q8×D43—42no—
128Q8×D43—42no—
129#10621898—21no—
130#10621898—21no—
131#10621898SD1612yes—
132#10621898Q1612yes—
133C2×D172C22⋊C411yescharacteristic
134C2×C4×D43—21no—
135C2×C4×D43—22no—
136C2×C4×D43—21no—
137C2×C4×D43—22no—
138C2×C4×D43—21no—
139C2×Dic86—22no—
140C2×Dic86—22no—
141C2×Dic86—21no—
142C2×Dic86—22no—
143C2×Dic86—41no—
144C2×Dic86C22⋊C411yescharacteristic
145C2×Dic86C22⋊C411yescharacteristic
146C2×Dic86C22⋊C411yescharacteristic
147M16×C43—41no—
148M16×C43—41no—
149C2×C8×C43—22no—
150C2×C8×C43—41no—
151C2×C8×C43—41no—
152C2×C8×C43—41no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43C22⋊C412yes—
159C22⋊C4×C43—22no—
160C42×C43—22no—
161C42×C43C22×C411yescharacteristic
162C42×C43C2×D411yescharacteristic
163C42×C43C2×D411yescharacteristic
164C42×C43C2×D411yescharacteristic
165C22⋊Dic43—21no—
166(C2×D43)⋊C4—22no—
167(C2×D43)⋊C4—22no—
168(C2×D43)⋊C4—21no—
169(C2×D43)⋊C4—21no—
170C4⋊Dic43—22no—
171C4⋊Dic43—22no—
172C4⋊Dic43—21no—
173C4⋊Dic43—22no—
174C4⋊Dic43—41no—
175C4⋊Dic43C22⋊C411yescharacteristic
176C4⋊Dic43C22⋊C411yescharacteristic
177C4⋊Dic43C22⋊C411yescharacteristic
178C4⋊Dic43C22⋊C411yescharacteristic
179Dic43⋊C4—22no—
180Dic43⋊C4—22no—
181Dic43⋊C4—22no—
182Dic43⋊C4—22no—
183Dic43⋊C4—22no—
184Dic43⋊C4—22no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191C4×Dic43—22no—
192C4×Dic43—22no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—41no—
201C4×Dic43—41no—
202C2×C43⋊C8—41no—
203C23×C43#12011yescharacteristic
204C22×D43—21no—
205Q8×C43—42no—
206Q8×C43—41no—
207Q8×C43—41no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—41no—
213C2×C4×C43C2×C22⋊C411yescharacteristic
214C2×C4×C43C2×C22⋊C411yescharacteristic
215C2×C4×C43C2×C22⋊C411yescharacteristic
216C2×C4×C43#12011yescharacteristic
217C2×C4×C43#12011yescharacteristic
218C2×C4×C43#12011yescharacteristic
219C2×C4×C43C2×SD1611yescharacteristic
220C2×C4×C43C2×Q1611yescharacteristic
221C2×C4×C43#13711yescharacteristic
222C2×C4×C43#13711yescharacteristic
223C22⋊D43—22no—
224C22⋊D43—22no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—81no—
235C2×Dic43—81no—
236C2×Dic43—81no—
237D172—21no—
238D172#10312yescomplemented
239C4×D43—22no—
240C4×D43—22no—
241C4×D43—44no—
242C4×D43—41no—
243C4×D43—41no—
244C4×D43—81no—
245C4×D43—82no—
246Dic86—21no—
247Dic86—21no—
248Dic86—21no—
249Dic86—21no—
250Dic86—42no—
251Dic86—44no—
252Dic86—82no—
253Dic86#10312yescomplemented
254Dic86#10412yescomplemented
255C8×C43—42no—
256C8×C43—81no—
257C43⋊C8—81no—
258#8439—431nomaximal, Sylow
259C22×C43—21no—
260C22×C43—21no—
261C22×C43#37911yescharacteristic
262C22×C43#44811yescharacteristic
263C22×C43#45111yescharacteristic
264C2×D43—22no—
265C2×D43—41no—
266C2×D43—41no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—42no—
271C4×C43—42no—
272C4×C43C2×#10311yescharacteristic
273C4×C43#41911yescharacteristic
274C4×C43C2×#10411yescharacteristic
275C4×C43#42111yescharacteristic
276C4×C43#44811yescharacteristic
277C4×C43#45111yescharacteristic
278Dic43—22no—
279Dic43—22no—
280Dic43—41no—
281Dic43—41no—
282Dic43—41no—
283Dic43—41no—
284Dic43—41no—
285Dic43—82no—
286Q8×#41—431no—
287#1806—431no—
288C4×#103—431no—
289#1503—431no—
290#1493D4311yescharacteristic, complemented
291#1487—431no—
292#1476—431no—
293C2×C43—21no—
294C2×C43—21no—
295C2×C43#178711yescharacteristic
296C2×C43#178911yescharacteristic
297C2×C43#179411yescharacteristic
298D43—42no—
299Q82—431no—
300#557—431no—
301#557—861no—
302#554—431no—
303#554—861no—
304#554—861no—
305#554—862no—
306D4×Q8—431no—
307D4×Q8—861no—
308#533—861no—
309#533—861no—
310#533—862no—
311#533C2×D4311yescharacteristic
312C4×#41—431no—
313C4×#41—861no—
314C2×C4×Q8—431no—
315C2×C4×Q8—861no—
316#431—431no—
317#423C2×D4311yescharacteristic
318C2×#104—861no—
319C2×#103—861no—
320C2×C4×C8C2×D4311yescharacteristic
321C4×C4⋊C4—431no—
322#340—861no—
323#339—861no—
324#328—862no—
325Q8⋊C8—22no—
326Q8⋊C8—861no—
327Q8⋊C8—861no—
328Q8⋊C8—861no—
329D4⋊C8—861no—
330C43#843911yescharacteristic, complemented, Sylow
331C2×#41—431no—
332C22×Q8—431no—
333C22×Q8—861no—
334C2×M16—21no—
335C22×C8—21no—
336C4⋊Q8—861no—
337C4⋊Q8—861no—
338C4⋊Q8—861no—
339C4⋊Q8—862no—
340C4⋊Q8—861no—
341C4⋊Q8—862no—
342C4⋊Q8C4×D4311yescharacteristic
343C4⋊Q8C4×D4311yescharacteristic
344#125—21no—
345#125—861no—
346#125—861no—
347#125—862no—
348#125—862no—
349#125—862no—
350C22⋊Q8—21no—
351C22⋊Q8—862no—
352C22⋊Q8—862no—
353C22⋊Q8—861no—
354C22⋊Q8—862no—
355C22⋊Q8—862no—
356C22⋊Q8—862no—
357C22⋊Q8—861no—
358C22⋊Q8—862no—
359C22⋊Q8—862no—
360C22⋊Q8D17212yes—
361C4×Q8—21no—
362C4×Q8—431no—
363C4×Q8—431no—
364C4×Q8—431no—
365C4×Q8—431no—
366C4×Q8—431no—
367C4×Q8—431no—
368C4×Q8—862no—
369C4×Q8—862no—
370C4×Q8—861no—
371C4×Q8—861no—
372C4×Q8—861no—
373C4×Q8—862no—
374C4×Q8—861no—
375C4×Q8—861no—
376C4×Q8—861no—
377C4×Q8C22⋊D4312yes—
378C4×D4—431no—
379C4×D4—431no—
380C4×D4—862no—
381C4×D4—862no—
382C4×D4—861no—
383C4×D4—861no—
384C4×D4—861no—
385C4×D4—861no—
386#117—21no—
387#117—431no—
388#117—862no—
389#117—861no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—862no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C42—862no—
396C2×C42—861no—
397C2×C42—861no—
398C2×C42—861no—
399C2×C42C22×D4311yescharacteristic
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8—861no—
403#104—1722no—
404#103—864no—
405C22⋊C8—861no—
406C4×C8—21no—
407C4×C8—21no—
408C4×C8—861no—
409#95—861no—
410#41—432no—
411#41—432no—
412#41—861no—
413#41—861no—
414C2×Q8—21no—
415C2×Q8—431no—
416C2×Q8—431no—
417C2×Q8—431no—
418C2×Q8—862no—
419C2×Q8—862no—
420C2×Q8—862no—
421C2×Q8—861no—
422C2×Q8—1721no—
423C2×Q8—1722no—
424C2×Q8—1722no—
425C2×Q8(C2×D43)⋊C412yes—
426C2×D4—431no—
427C2×D4—861no—
428C22×C4—862no—
429C22×C4—862no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—1721no—
436C22×C4C2×D17211yescharacteristic
437C22×C4D4×D4311yescharacteristic
438C22×C4D4×D4311yescharacteristic
439M16—41no—
440M16—41no—
441C2×C8—22no—
442C2×C8—41no—
443C2×C8—41no—
444C2×C8—41no—
445C2×C8—1721no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—431no—
452C4⋊C4—431no—
453C4⋊C4—431no—
454C4⋊C4—431no—
455C4⋊C4—862no—
456C4⋊C4—862no—
457C4⋊C4—862no—
458C4⋊C4—862no—
459C4⋊C4—862no—
460C4⋊C4—862no—
461C4⋊C4—862no—
462C4⋊C4—862no—
463C4⋊C4—862no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—1721no—
472C4⋊C4(C2×D43)⋊C412yes—
473C22⋊C4—22no—
474C22⋊C4—862no—
475C22⋊C4—862no—
476C22⋊C4—861no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C42—22no—
480C42—862no—
481C42—862no—
482C42—861no—
483C42—861no—
484C42—861no—
485C42—861no—
486C42—861no—
487C42—861no—
488C42—861no—
489C42—1721no—
490C42—1721no—
491C42C2×C4×D4311yescharacteristic
492C42D4×D4311yescharacteristic
493C42D4×D4311yescharacteristic
494C42C2×C22⋊D4311yescharacteristic
495C23—861no—
496C23#1306329511yescharacteristic
497Q8—42no—
498Q8—41no—
499Q8—41no—
500Q8—432no—
501Q8—432no—
502Q8—861no—
503Q8—861no—
504Q8—861no—
505Q8—861no—
506Q8—3442no—
507Q8—1722no—
508Q8—1724no—
509D4—432no—
510D4—862no—
511D4—862no—
512D4—861no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—41no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—862no—
521C2×C4—862no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—3441no—
528C2×C4—3442no—
529C2×C4—3441no—
530C2×C4—3441no—
531C2×C4—3441no—
532C2×C4—1724no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4C22⋊C4×D4311yescharacteristic
538C2×C4C22⋊C4×D4311yescharacteristic
539C2×C4C2×(C2×D43)⋊C411yescharacteristic
540C2×C4#1306329311yescharacteristic
541C2×C4#1306329311yescharacteristic
542C2×C4#1306329511yescharacteristic
543C2×C4SD16×D4311yescharacteristic
544C2×C4Q16×D4311yescharacteristic
545C2×C4#1306335411yescharacteristic
546C2×C4#1306335711yescharacteristic
547C8—42no—
548C8—81no—
549C8—3441no—
550C22—21no—
551C22—21no—
552C22—862no—
553C22—1721no—
554C22—1721no—
555C22#1458275411yescharacteristic
556C22#1458303911yescharacteristic
557C22#1458305611yescharacteristic
558C4—21no—
559C4—21no—
560C4—21no—
561C4—42no—
562C4—42no—
563C4—862no—
564C4—862no—
565C4—3442no—
566C4—1721no—
567C4—1721no—
568C4—1721no—
569C4—1721no—
570C4—1721no—
571C4#103×D4311yescharacteristic
572C4#1458290611yescharacteristic
573C4#104×D4311yescharacteristic
574C4#1458291411yescharacteristic
575C4#1458303611yescharacteristic
576C4#1458305311yescharacteristic
577C2—21no—
578C2—21no—
579C2—1722no—
580C2#1913452811yescharacteristic
581C2#1913453711yescharacteristic
582C2#1913455811yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1493C2
socleC22×C43#379
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1493D43
hypocenterC43#8439
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
3. C4×#13063250C2semidirect
4. #19133094C2semidirect
5. #19133023C2semidirect
7. C43×#1493C2semidirect
8. #14583629C4semidirect
10. #14583624C4semidirect
11. #14583610C4semidirect
15. #14583564C4semidirect
238. D172#103semidirect
253. Dic86#103semidirect
254. Dic86#104semidirect
290. #1493D43semidirect
330. C43#8439semidirect

Maximal subgroups

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

subgroupindex
#191481732
#191346122
C4×#130632502
#191330942
#191330232
#191329782
C43×#14932
#843943