Finite Group Databasebeta

← #24988639

Subgroups — #24988639

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#41×Dic86C211yesmaximal, characteristic
2C4×#13063248C211yesmaximal, characteristic, complemented
3#19133093C211yesmaximal, characteristic, complemented
4#19133049C211yesmaximal, characteristic, complemented
5#19133023C211yesmaximal, characteristic, complemented
6#19132977C211yesmaximal, characteristic
7C43×#1806C211yesmaximal, characteristic
8Q8×Dic86C411yescharacteristic, complemented
9#14583628C411yescharacteristic, complemented
10#14583625—21no—
11#14583608—22no—
12#14583608—21no—
13#14583606—21no—
14#14583606C411yescharacteristic, complemented
15D4×Dic86—21no—
16D4×Dic86C411yescharacteristic, complemented
17#14583456—21no—
18#14583456C2211yescharacteristic
19#14583452—22no—
20#14583452—21no—
21#41×Dic43—21no—
22C2×C4×Dic86—21no—
23C2×C4×Dic86C2211yescharacteristic
24#14582952C2211yescharacteristic
25C2×#13063248—21no—
26C2×C4×C43⋊C8C2211yescharacteristic
27#14582661—21no—
28#14582635—22no—
29Q8⋊(C43⋊C8)—21no—
30#14582629—21no—
31#14582629—21no—
32#14582629—22no—
33D4⋊(C43⋊C8)—21no—
34C4×#41×C43C2211yescharacteristic
35C43×#423C2211yescharacteristic
36C2×#104×C43—21no—
37C4×C4⋊C4×C43C2211yescharacteristic
38C43×#339—21no—
39C22×Dic86—21no—
40C22×Dic86D411yescharacteristic
41C22×C43⋊C8—21no—
42#13063325—21no—
43#13063325—21no—
44#13063325C2×C411yescharacteristic
45#13063325C2×C411yescharacteristic
46#13063324—22no—
47#13063324—22no—
48#13063324—21no—
49#13063324—21no—
50#13063317—22no—
51#13063317—21no—
52#13063316—22no—
53#13063316—21no—
54#13063316—21no—
55#13063316—22no—
56#13063304—22no—
57#13063304—21no—
58#13063304—21no—
59#13063304—21no—
60#13063304D412yes—
61#13063302—22no—
62#13063302—22no—
63#13063302—22no—
64#13063302—22no—
65#13063302—22no—
66#13063302—22no—
67Q8×Dic43—21no—
68Q8×Dic43—21no—
69C4×Dic86—22no—
70C4×Dic86—22no—
71C4×Dic86—22no—
72C4×Dic86—21no—
73C4×Dic86—21no—
74C4×Dic86—21no—
75C4×Dic86—21no—
76C4×Dic86—21no—
77C4×Dic86C2×C411yescharacteristic
78C4×Dic86C2×C411yescharacteristic
79C4×Dic86D411yescharacteristic
80C4×Dic86D411yescharacteristic
81C4×Dic86D412yes—
82D4×Dic43—22no—
83D4×Dic43—22no—
84D4×Dic43—21no—
85D4×Dic43—21no—
86#13063284—22no—
87#13063284—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43D411yescharacteristic
90C2×Dic43⋊C4—22no—
91C2×Dic43⋊C4—21no—
92C2×C4×Dic43—22no—
93C2×C4×Dic43—21no—
94C4⋊(C43⋊C8)—21no—
95#13063248—24no—
96C22⋊(C43⋊C8)—21no—
97C4×C43⋊C8—21no—
98C4×C43⋊C8—21no—
99C4×C43⋊C8—21no—
100C2×#41×C43D411yescharacteristic
101C2×M16×C43—21no—
102C4×Q8×C43C2×C411yescharacteristic
103C4×Q8×C43D411yescharacteristic
104C4×D4×C43—21no—
105C4×D4×C43—21no—
106C4×D4×C43C2×C411yescharacteristic
107C4×D4×C43D411yescharacteristic
108#117×C43—21no—
109#117×C43D411yescharacteristic
110C2×C4⋊C4×C43—21no—
111C2×C42×C43—21no—
112C2×C42×C43—21no—
113C2×C42×C43C2311yescharacteristic
114C4⋊C8×C43—21no—
115C4⋊C8×C43—21no—
116#104×C43—42no—
117#95×C43—21no—
118#41×C43—21no—
119#41×C43—21no—
120#41×C43SD1612yes—
121#41×C43Q1612yes—
122C2×Q8×C43C22⋊C411yescharacteristic
123C2×D4×C43—21no—
124C2×D4×C43C22⋊C411yescharacteristic
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—41no—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C2×Dic86—22no—
137C2×Dic86—22no—
138C2×Dic86—21no—
139C2×Dic86—21no—
140C2×Dic86—22no—
141C2×Dic86—41no—
142C2×Dic86—42no—
143C2×Dic86—42no—
144C2×Dic86C22⋊C411yescharacteristic
145C2×Dic86C22⋊C411yescharacteristic
146C2×Dic86C22⋊C412yes—
147M16×C43—41no—
148M16×C43—41no—
149C2×C8×C43—41no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—41no—
154C4⋊C4×C43C22⋊C411yescharacteristic
155C4⋊C4×C43C22⋊C411yescharacteristic
156C22⋊C4×C43—21no—
157C22⋊C4×C43—21no—
158C22⋊C4×C43—21no—
159C42×C43—21no—
160C42×C43—21no—
161C42×C43—21no—
162C42×C43—41no—
163C42×C43—41no—
164C42×C43C22×C411yescharacteristic
165C42×C43C2×D411yescharacteristic
166C42×C43C2×D411yescharacteristic
167C42×C43C2×D411yescharacteristic
168C22⋊Dic43—22no—
169C22⋊Dic43—22no—
170C22⋊Dic43—22no—
171C4⋊Dic43—22no—
172C4⋊Dic43—22no—
173C4⋊Dic43—22no—
174C4⋊Dic43—22no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43C22⋊C411yescharacteristic
180C4⋊Dic43C22⋊C411yescharacteristic
181C4⋊Dic43C22⋊C412yes—
182Dic43⋊C4—22no—
183Dic43⋊C4—22no—
184Dic43⋊C4—22no—
185Dic43⋊C4—22no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—22no—
190Dic43⋊C4—21no—
191Dic43⋊C4—22no—
192C4×Dic43—22no—
193C4×Dic43—22no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—22no—
198C4×Dic43—21no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—41no—
201C2×C43⋊C8—41no—
202C2×C43⋊C8—41no—
203C23×C43—21no—
204C23×C43#12011yescharacteristic
205Q8×C43—21no—
206Q8×C43#10312yescomplemented
207D4×C43—22no—
208D4×C43—22no—
209D4×C43—21no—
210D4×C43#10312yescomplemented
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—42no—
222C2×C4×C43—81no—
223C2×C4×C43—81no—
224C2×C4×C43—81no—
225C2×C4×C43C2×C22⋊C411yescharacteristic
226C2×C4×C43C2×C22⋊C411yescharacteristic
227C2×C4×C43C2×C22⋊C411yescharacteristic
228C2×C4×C43#12011yescharacteristic
229C2×C4×C43#12011yescharacteristic
230C2×C4×C43#12011yescharacteristic
231C2×C4×C43C2×SD1611yescharacteristic
232C2×C4×C43C2×Q1611yescharacteristic
233C2×C4×C43#13711yescharacteristic
234C2×C4×C43#13711yescharacteristic
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—22no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—22no—
241C2×Dic43—42no—
242C2×Dic43—44no—
243C2×Dic43—81no—
244C2×Dic43—82no—
245Dic86—21no—
246Dic86—21no—
247Dic86—21no—
248Dic86—42no—
249Dic86—44no—
250Dic86—41no—
251Dic86—41no—
252Dic86—42no—
253Dic86—82no—
254Dic86#10412yescomplemented
255C8×C43—81no—
256C43⋊C8—42no—
257C43⋊C8—81no—
258#8439—431nomaximal, Sylow
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—22no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43#37911yescharacteristic
265C22×C43#44811yescharacteristic
266C22×C43#45111yescharacteristic
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—22no—
270C4×C43—21no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—82no—
274C4×C43C2×#10311yescharacteristic
275C4×C43#41911yescharacteristic
276C4×C43C2×#10411yescharacteristic
277C4×C43#42111yescharacteristic
278C4×C43#44811yescharacteristic
279C4×C43#45111yescharacteristic
280Dic43—22no—
281Dic43—42no—
282Dic43—41no—
283Dic43—41no—
284Dic43—41no—
285Dic43—42no—
286Q8×#41—431no—
287#1806D4311yescharacteristic
288C4×#103—431no—
289#1503—431no—
290#1493—431no—
291#1487—431no—
292#1476—431no—
293C2×C43—21no—
294C2×C43—21no—
295C2×C43—42no—
296C2×C43#178711yescharacteristic
297C2×C43#178911yescharacteristic
298C2×C43#179411yescharacteristic
299Q82—431no—
300#557—431no—
301#557—861no—
302#554—431no—
303#554—861no—
304#554—862no—
305#554—861no—
306D4×Q8—431no—
307D4×Q8—861no—
308#533—431no—
309#533—861no—
310#533—862no—
311#533—861no—
312C4×#41—861no—
313C4×#41C2×D4311yescharacteristic
314C2×C4×Q8—431no—
315C2×C4×Q8—861no—
316#431—431no—
317#423C2×D4311yescharacteristic
318C2×#104—21no—
319C2×#103—861no—
320C2×C4×C8—431no—
321C4×C4⋊C4C2×D4311yescharacteristic
322#340—861no—
323#339—21no—
324#328—862no—
325Q8⋊C8—861no—
326Q8⋊C8—861no—
327Q8⋊C8—862no—
328Q8⋊C8—861no—
329D4⋊C8—861no—
330C43#843911yescharacteristic, complemented, Sylow
331C2×#41C22⋊D4311yescharacteristic
332C22×Q8—431no—
333C22×Q8—861no—
334C2×M16—21no—
335C22×C8—861no—
336C4⋊Q8—431no—
337C4⋊Q8—431no—
338C4⋊Q8—861no—
339C4⋊Q8—861no—
340C4⋊Q8—862no—
341C4⋊Q8—862no—
342C4⋊Q8—861no—
343C4⋊Q8—861no—
344#125—862no—
345#125—862no—
346#125—862no—
347#125—861no—
348#125—861no—
349#125—861no—
350C22⋊Q8—432no—
351C22⋊Q8—862no—
352C22⋊Q8—862no—
353C22⋊Q8—862no—
354C22⋊Q8—862no—
355C22⋊Q8—862no—
356C22⋊Q8—862no—
357C22⋊Q8—861no—
358C22⋊Q8—861no—
359C22⋊Q8—862no—
360C22⋊Q8—861no—
361C4×Q8—431no—
362C4×Q8—431no—
363C4×Q8—431no—
364C4×Q8—431no—
365C4×Q8—432no—
366C4×Q8—861no—
367C4×Q8—861no—
368C4×Q8—862no—
369C4×Q8—862no—
370C4×Q8—862no—
371C4×Q8—861no—
372C4×Q8—861no—
373C4×Q8—861no—
374C4×Q8—861no—
375C4×Q8—861no—
376C4×Q8C4×D4311yescharacteristic
377C4×Q8D17211yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—862no—
381C4×D4—862no—
382C4×D4—861no—
383C4×D4—861no—
384C4×D4C4×D4311yescharacteristic
385C4×D4D17211yescharacteristic
386#117—21no—
387#117—862no—
388#117—861no—
389#117C22⋊D4311yescharacteristic
390C2×C4⋊C4—21no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—862no—
394C2×C4⋊C4—861no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—862no—
398C2×C42—861no—
399C2×C42C22×D4311yescharacteristic
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8—861no—
403#104—42no—
404#103—864no—
405C22⋊C8—861no—
406C4×C8—861no—
407C4×C8—861no—
408C4×C8—861no—
409#95—21no—
410#41—21no—
411#41—21no—
412#41#1062188312yes—
413#41#1062188512yes—
414C2×Q8—431no—
415C2×Q8—431no—
416C2×Q8—432no—
417C2×Q8—862no—
418C2×Q8—862no—
419C2×Q8—862no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—1721no—
423C2×Q8—1722no—
424C2×Q8—1722no—
425C2×Q8(C2×D43)⋊C411yescharacteristic
426C2×D4—21no—
427C2×D4(C2×D43)⋊C411yescharacteristic
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—41no—
432C22×C4—862no—
433C22×C4—861no—
434C22×C4—862no—
435C22×C4—861no—
436C22×C4D4×D4311yescharacteristic
437C22×C4D4×D4311yescharacteristic
438C22×C4C2×C22⋊D4311yescharacteristic
439M16—41no—
440M16—41no—
441C2×C8—41no—
442C2×C8—862no—
443C2×C8—1721no—
444C2×C8—1721no—
445C2×C8—1721no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—41no—
450C4⋊C4—431no—
451C4⋊C4—431no—
452C4⋊C4—432no—
453C4⋊C4—862no—
454C4⋊C4—862no—
455C4⋊C4—862no—
456C4⋊C4—862no—
457C4⋊C4—862no—
458C4⋊C4—862no—
459C4⋊C4—862no—
460C4⋊C4—862no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—862no—
470C4⋊C4—862no—
471C4⋊C4(C2×D43)⋊C411yescharacteristic
472C4⋊C4(C2×D43)⋊C411yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—862no—
477C22⋊C4—862no—
478C22⋊C4—862no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42—41no—
484C42—862no—
485C42—862no—
486C42—861no—
487C42—861no—
488C42—861no—
489C42—862no—
490C42—861no—
491C42C2×C4×D4311yescharacteristic
492C42C2×D17211yescharacteristic
493C42D4×D4311yescharacteristic
494C42D4×D4311yescharacteristic
495C23—21no—
496C23#1306329311yescharacteristic
497Q8—21no—
498Q8—432no—
499Q8—861no—
500Q8—861no—
501Q8—861no—
502Q8—3442no—
503Q8—1722no—
504Q8—1722no—
505Q8—1724no—
506Q8—1721no—
507Q8—1721no—
508Q8#1306324812yescomplemented
509D4—22no—
510D4—22no—
511D4—21no—
512D4#1306324812yescomplemented
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—81no—
525C2×C4—81no—
526C2×C4—81no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—862no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—862no—
533C2×C4—3441no—
534C2×C4—3442no—
535C2×C4—1722no—
536C2×C4—1724no—
537C2×C4C22⋊C4×D4311yescharacteristic
538C2×C4C22⋊C4×D4311yescharacteristic
539C2×C4C2×(C2×D43)⋊C411yescharacteristic
540C2×C4#1306329311yescharacteristic
541C2×C4#1306329511yescharacteristic
542C2×C4#1306329511yescharacteristic
543C2×C4C2×#1062188311yescharacteristic
544C2×C4C2×#1062188511yescharacteristic
545C2×C4#1306335511yescharacteristic
546C2×C4#1306335511yescharacteristic
547C8—81no—
548C8—3441no—
549C8—1722no—
550C22—21no—
551C22—21no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22#1458275411yescharacteristic
556C22#1458303711yescharacteristic
557C22#1458305411yescharacteristic
558C4—22no—
559C4—21no—
560C4—21no—
561C4—21no—
562C4—41no—
563C4—41no—
564C4—82no—
565C4—862no—
566C4—1721no—
567C4—1722no—
568C4—1721no—
569C4—1721no—
570C4—1722no—
571C4C2×#1306324811yescharacteristic
572C4#1458290711yescharacteristic
573C4#104×D4311yescharacteristic
574C4#1458291411yescharacteristic
575C4#1458303711yescharacteristic
576C4#1458305411yescharacteristic
577C2—21no—
578C2—21no—
579C2—42no—
580C2#1913452911yescharacteristic
581C2#1913453711yescharacteristic
582C2#1913455711yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1806C2
socleC22×C43#379
prime radicalC2×#41×C43D4
cosocleC2×C42×C43C23
hypercenter#1806D43
hypocenterC43#8439
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. C4×#13063248C2semidirect
3. #19133093C2semidirect
4. #19133049C2semidirect
5. #19133023C2semidirect
8. Q8×Dic86C4semidirect
9. #14583628C4semidirect
14. #14583606C4semidirect
16. D4×Dic86C4semidirect
206. Q8×C43#103semidirect
210. D4×C43#103semidirect
254. Dic86#104semidirect
330. C43#8439semidirect
508. Q8#13063248semidirect
512. D4#13063248semidirect

Maximal subgroups

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

subgroupindex
#41×Dic862
C4×#130632482
#191330932
#191330492
#191330232
#191329772
C43×#18062
#843943