Finite Group Databasebeta

← #25133282

Subgroups — #25133282

Order 11008.

1198 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148398C211yesmaximal, characteristic, complemented
2#19140400C212yesmaximal, complemented
3#19135948C212yesmaximal, complemented
4#19135759C212yesmaximal, complemented
5#19135580C212yesmaximal, complemented
6#19135004C212yesmaximal
7#19134875C212yesmaximal, complemented
8#19134583C211yesmaximal, characteristic, complemented
9C43×#2321C211yesmaximal, characteristic
10#14583608—24no—
11#14583606—22no—
12D4×Dic86—22no—
13#14583530—21no—
14#14583525—21no—
15#14583525C2212yes—
16#14583456—21no—
17C2×#13063304—21no—
18C2×#13063304C2212yes—
19#14583374C2212yes—
20C2×#13063240C2212yes—
21#14582835—22no—
22#14582822—24no—
23#14582811—22no—
24#14582772C2214yes—
25#14582759C2212yes—
26#14582755C2214yes—
27#14582666C2212yes—
28#14582665C2214yes—
29#14582665C2214yes—
30C2×#120×C43C2211yescharacteristic
31C2×C4×D4×C43C2211yescharacteristic
32C22×C22⋊C4×C43C2211yescharacteristic
33C43×#390—21no—
34C43×#388—21no—
35C43×#388—21no—
36C43×#386—21no—
37C43×#386C2211yescharacteristic
38C43×#385C2211yescharacteristic
39C43×#379C2211yescharacteristic
40C4×C22⋊C4×C43C2211yescharacteristic
41C22×Dic86—21no—
42C22×Dic86D412yescomplemented
43#13063325—21no—
44#13063325—21no—
45#13063324—24no—
46#13063317—22no—
47#13063316—24no—
48#13063304—22no—
49#13063304—22no—
50#13063304—22no—
51#13063304—22no—
52#13063304—22no—
53#13063304—22no—
54#13063304—22no—
55#13063304—22no—
56#13063302—24no—
57#13063302—24no—
58#13063302—24no—
59#13063302—24no—
60C4×Dic86—22no—
61C4×Dic86—22no—
62D4×Dic43—24no—
63D4×Dic43—24no—
64#13063284—22no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—22no—
67C2×C4⋊Dic43D412yescomplemented
68C2×Dic43⋊C4—22no—
69C2×Dic43⋊C4—24no—
70C2×Dic43⋊C4D414yescomplemented
71C2×C22⋊Dic43—22no—
72C2×C22⋊Dic43—24no—
73C2×C22⋊Dic43—24no—
74C2×C22⋊Dic43C2314yes—
75C2×C22⋊Dic43C2314yes—
76#13063240—24no—
77C43⋊#95—22no—
78C43⋊#95—24no—
79C25×C43C2311yescharacteristic
80C22×D4×C43—21no—
81C22×D4×C43C2311yescharacteristic
82C23×C4×C43D411yescharacteristic
83C23×C4×C43C2311yescharacteristic
84C23×C4×C43C2311yescharacteristic
85#120×C43—22no—
86#120×C43Q814yescomplemented
87C4×D4×C43—22no—
88C4×D4×C43—22no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43D411yescharacteristic
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—22no—
93C2×C22⋊C4×C43—22no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43D411yescharacteristic
100C2×C22⋊C4×C43C2311yescharacteristic
101C2×C22⋊C4×C43C2311yescharacteristic
102C2×C22⋊C4×C43C2311yescharacteristic
103C2×C42×C43—21no—
104C2×C42×C43D411yescharacteristic
105#95×C43—21no—
106#95×C43—21no—
107#95×C43—21no—
108C24×C43—21no—
109C24×C43—22no—
110C24×C43—21no—
111C24×C43—22no—
112C24×C43—81no—
113C24×C43—81no—
114C24×C43C2×D411yescharacteristic
115C24×C43C2×Q812yescomplemented
116C24×C43C2411yescharacteristic
117C2×D4×C43—24no—
118C2×D4×C43—22no—
119C2×D4×C43—22no—
120C2×D4×C43—81no—
121C2×D4×C43—81no—
122C2×D4×C43C2×Q812yes—
123C2×D4×C43#4112yes—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—22no—
130C22×C4×C43—81no—
131C22×C4×C43—81no—
132C22×C4×C43—81no—
133C22×C4×C43C2×D412yes—
134C22×C4×C43C2×D412yes—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—24no—
143C22×Dic43C2×D414yes—
144C22×Dic43C2×D414yes—
145C2×Dic86—22no—
146C2×Dic86—22no—
147C2×Dic86—22no—
148C2×Dic86—22no—
149C2×Dic86—82no—
150C2×Dic86—82no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—81no—
153C22⋊C4×C43—22no—
154C22⋊C4×C43—24no—
155C22⋊C4×C43—22no—
156C22⋊C4×C43—21no—
157C22⋊C4×C43—22no—
158C22⋊C4×C43—41no—
159C22⋊C4×C43—42no—
160C22⋊C4×C43—41no—
161C22⋊C4×C43—81no—
162C22⋊C4×C43—81no—
163C22⋊C4×C43—81no—
164C22⋊C4×C43C2×Q812yescomplemented
165C42×C43—21no—
166C42×C43—21no—
167C42×C43—81no—
168C22⋊Dic43—24no—
169C22⋊Dic43—24no—
170C22⋊Dic43—24no—
171C22⋊Dic43—24no—
172C22⋊Dic43—24no—
173C22⋊Dic43—84no—
174C22⋊Dic43—84no—
175C4⋊Dic43—22no—
176C4⋊Dic43—22no—
177C4⋊Dic43—22no—
178C4⋊Dic43—22no—
179C4⋊Dic43—22no—
180C4⋊Dic43—22no—
181C4⋊Dic43—82no—
182Dic43⋊C4—24no—
183Dic43⋊C4—24no—
184Dic43⋊C4—24no—
185Dic43⋊C4—24no—
186Dic43⋊C4—84no—
187C4×Dic43—24no—
188C23×C43—21no—
189C23×C43—21no—
190C23×C43—22no—
191C23×C43—24no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—44no—
197C23×C43—44no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—42no—
205C23×C43—82no—
206C23×C43—82no—
207C23×C43—84no—
208C23×C43C22⋊Q812yes—
209C23×C43C22×D412yes—
210C23×C43C22×D411yescharacteristic
211C23×C43C22×Q811yescharacteristic
212C23×C43C2×#4111yescharacteristic
213C23×C432−1+412yes—
214D4×C43—24no—
215D4×C43—24no—
216D4×C43—84no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—22no—
222C2×C4×C43—42no—
223C2×C4×C43—41no—
224C2×C4×C43—42no—
225C2×C4×C43—41no—
226C2×C4×C43—42no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—44no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—81no—
239C2×C4×C43#12011yescharacteristic
240C2×C4×C43#12012yes—
241C2×C4×C43#12011yescharacteristic
242C2×C4×C43C22⋊Q812yes—
243C2×Dic43—24no—
244C2×Dic43—24no—
245C2×Dic43—44no—
246C2×Dic43—44no—
247C2×Dic43—44no—
248C2×Dic43—44no—
249C2×Dic43—44no—
250C2×Dic43—82no—
251C2×Dic43—82no—
252Dic86—44no—
253Dic86—82no—
254Dic86—82no—
255Dic86—82no—
256#24352—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—22no—
259C22×C43—21no—
260C22×C43—22no—
261C22×C43—22no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—42no—
265C22×C43—42no—
266C22×C43—42no—
267C22×C43—48no—
268C22×C43—42no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—42no—
272C22×C43—81no—
273C22×C43—84no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43C2×#12011yescharacteristic
279C22×C43C2×C22⋊Q811yescharacteristic
280C22×C43#53611yescharacteristic
281C22×C43#54812yes—
282C22×C43D4×Q812yes—
283C4×C43—22no—
284C4×C43—21no—
285C4×C43—22no—
286C4×C43—21no—
287C4×C43—42no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—81no—
291C4×C43—81no—
292Dic43—44no—
293Dic43—44no—
294Dic43—84no—
295#3501—431no—
296#2626—432no—
297#2321D4311yescharacteristic
298#2062—432no—
299#2029—432no—
300#1996—432no—
301#1889—432no—
302#1867—432no—
303#1799—431no—
304C2×C43—22no—
305C2×C43—21no—
306C2×C43—21no—
307C2×C43—22no—
308C2×C43—42no—
309C2×C43—82no—
310C2×C43#240911yescharacteristic
311C2×C43#302611yescharacteristic
312C2×C43#302711yescharacteristic
313#554—862no—
314#554—864no—
315D4×Q8—862no—
316#544—861no—
317#543—432no—
318#543—861no—
319#533—861no—
320C2×C22⋊Q8—432no—
321C2×C22⋊Q8—861no—
322C2×#120C2×D4311yescharacteristic
323#518—432no—
324C2×C4×D4C2×D4311yescharacteristic
325C22×C22⋊C4C2×D4311yescharacteristic
326C2×#99—432no—
327#399—862no—
328#396—864no—
329#393—862no—
330#390—21no—
331#388—21no—
332#388—21no—
333#386—21no—
334#386C2×D4311yescharacteristic
335#385—434no—
336#385C2×D4311yescharacteristic
337#380—432no—
338#379—434no—
339#379C2×D4311yescharacteristic
340C4×C22⋊C4C2×D4311yescharacteristic
341#342—432no—
342#342—434no—
343#342—434no—
344C43#2435211yescharacteristic, complemented, Sylow
345C25C22×D4311yescharacteristic
346C22×Q8—432no—
347C22×Q8—861no—
348C22×D4—21no—
349C22×D4C22×D4311yescharacteristic
350C23×C4C22⋊D4311yescharacteristic
351C23×C4C22×D4311yescharacteristic
352C23×C4C22×D4311yescharacteristic
353C4⋊Q8—861no—
354C4⋊Q8—861no—
355C4⋊Q8—864no—
356#125—862no—
357#125—864no—
358C22⋊Q8—864no—
359C22⋊Q8—864no—
360C22⋊Q8—864no—
361C22⋊Q8—864no—
362C22⋊Q8—862no—
363C22⋊Q8—862no—
364C22⋊Q8—862no—
365C22⋊Q8—862no—
366C22⋊Q8—862no—
367C22⋊Q8—862no—
368C22⋊Q8—862no—
369C22⋊Q8—862no—
370#120—22no—
371#120Dic8614yescomplemented
372C4×Q8—862no—
373C4×Q8—862no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—864no—
377C4×D4—864no—
378#117—862no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—434no—
381C2×C4⋊C4—432no—
382C2×C4⋊C4—862no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—864no—
385C2×C4⋊C4—862no—
386C2×C4⋊C4C22⋊D4311yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—434no—
396C2×C22⋊C4—434no—
397C2×C22⋊C4—862no—
398C2×C22⋊C4—864no—
399C2×C22⋊C4—864no—
400C2×C22⋊C4C22⋊D4311yescharacteristic
401C2×C22⋊C4C22×D4311yescharacteristic
402C2×C22⋊C4C22×D4311yescharacteristic
403C2×C22⋊C4C22×D4311yescharacteristic
404C2×C42—21no—
405C2×C42C22⋊D4311yescharacteristic
406#99—864no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—864no—
411#95—862no—
412C24—22no—
413C24—21no—
414C24—21no—
415C24—22no—
416C24—81no—
417C24—81no—
418C24C2×Dic8612yescomplemented
419C24C2×C22⋊D4311yescharacteristic
420C24C23×D4311yescharacteristic
421C2×Q8—862no—
422C2×Q8—862no—
423C2×Q8—862no—
424C2×Q8—862no—
425C2×Q8—3442no—
426C2×Q8—3442no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—24no—
430C2×D4—81no—
431C2×D4—81no—
432C2×D4C2×Dic8612yes—
433C2×D4#1062189812yes—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—81no—
441C22×C4—81no—
442C22×C4—81no—
443C22×C4—434no—
444C22×C4—434no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—864no—
448C22×C4D4×D4312yes—
449C22×C4D4×D4312yes—
450C22×C4C2×C22⋊D4311yescharacteristic
451C22×C4C2×C22⋊D4311yescharacteristic
452C22×C4C2×C22⋊D4311yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454C22×C4C2×C22⋊D4311yescharacteristic
455C4⋊C4—22no—
456C4⋊C4—81no—
457C4⋊C4—862no—
458C4⋊C4—864no—
459C4⋊C4—862no—
460C4⋊C4—862no—
461C4⋊C4—864no—
462C4⋊C4—862no—
463C4⋊C4—864no—
464C4⋊C4—862no—
465C4⋊C4—862no—
466C4⋊C4—864no—
467C4⋊C4—3444no—
468C4⋊C4—3442no—
469C22⋊C4—22no—
470C22⋊C4—21no—
471C22⋊C4—22no—
472C22⋊C4—24no—
473C22⋊C4—22no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—42no—
477C22⋊C4—81no—
478C22⋊C4—81no—
479C22⋊C4—81no—
480C22⋊C4—864no—
481C22⋊C4—864no—
482C22⋊C4—864no—
483C22⋊C4—864no—
484C22⋊C4—864no—
485C22⋊C4—3444no—
486C22⋊C4—3444no—
487C22⋊C4C2×Dic8612yescomplemented
488C42—21no—
489C42—21no—
490C42—81no—
491C42—864no—
492C23—21no—
493C23—21no—
494C23—24no—
495C23—22no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—44no—
503C23—44no—
504C23—41no—
505C23—41no—
506C23—42no—
507C23—41no—
508C23—41no—
509C23—82no—
510C23—82no—
511C23—84no—
512C23#1306330412yes—
513C23C2×D4×D4312yes—
514C23C22×C22⋊D4311yescharacteristic
515C23C22×Dic8611yescharacteristic
516C23C2×#1062189811yescharacteristic
517C23#1306337212yes—
518Q8—3442no—
519Q8—3442no—
520Q8—3442no—
521Q8—1724no—
522D4—24no—
523D4—24no—
524D4—84no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—44no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—81no—
547C2×C4—864no—
548C2×C4—864no—
549C2×C4—3442no—
550C2×C4—3442no—
551C2×C4—1724no—
552C2×C4—1724no—
553C2×C4—1724no—
554C2×C4—1724no—
555C2×C4—1724no—
556C2×C4#1306329311yescharacteristic
557C2×C4#1306329311yescharacteristic
558C2×C4#1306329312yes—
559C2×C4#1306330412yes—
560C22—21no—
561C22—22no—
562C22—21no—
563C22—22no—
564C22—22no—
565C22—41no—
566C22—41no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—48no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—84no—
579C22—81no—
580C22—81no—
581C22C2×#1306329311yescharacteristic
582C22C2×#1306330411yescharacteristic
583C22#1458347011yescharacteristic
584C22#1458355812yes—
585C22D4×Dic8612yes—
586C4—21no—
587C4—21no—
588C4—22no—
589C4—22no—
590C4—42no—
591C4—41no—
592C4—41no—
593C4—81no—
594C4—81no—
595C4—3444no—
596C4—1724no—
597C4—1724no—
598C2—21no—
599C2—21no—
600C2—22no—
601C2—22no—
602C2—42no—
603C2—82no—
604C2#1913796011yescharacteristic
605C2#1914399111yescharacteristic
606C2#1914399611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC24×C43C24
FrattiniC24C23×D43
FittingC43×#2321C2
socleC22×C43C2×#120
prime radicalC2×#120×C43C22
hypercenter#2321D43
hypocenterC43#24352
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2321

Complements

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

NH ≅ G/Ntype
1. #19148398C2semidirect
2. #19140400C2semidirect
3. #19135948C2semidirect
4. #19135759C2semidirect
5. #19135580C2semidirect
7. #19134875C2semidirect
8. #19134583C2semidirect
42. C22×Dic86D4semidirect
67. C2×C4⋊Dic43D4semidirect
70. C2×Dic43⋊C4D4semidirect
86. #120×C43Q8semidirect
115. C24×C43C2×Q8semidirect
164. C22⋊C4×C43C2×Q8semidirect
344. C43#24352semidirect
371. #120Dic86semidirect
418. C24C2×Dic86semidirect
487. C22⋊C4C2×Dic86semidirect

Maximal subgroups

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

subgroupindex
#191483982
#191404002
#191359482
#191357592
#191355802
#191350042
#191348752
#191345832
C43×#23212
#2435243