Finite Group Databasebeta

← #25137969

Subgroups — #25137969

Order 11008.

746 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583192C211yesmaximal, characteristic, complemented
2C2×#14582961C211yesmaximal, characteristic
3#19140422C211yesmaximal, characteristic
4#19137280C211yesmaximal, characteristic
5#19136027C211yesmaximal, characteristic
6#19136020C211yesmaximal, characteristic
7#19135796C211yesmaximal, characteristic
8#19135790C211yesmaximal, characteristic
9#19135545C211yesmaximal, characteristic, complemented
10#19135362C211yesmaximal, characteristic, complemented
11#19135338C211yesmaximal, characteristic, complemented
12#19135325C211yesmaximal, characteristic, complemented
13#19135274C211yesmaximal, characteristic, complemented
14#19134608C211yesmaximal, characteristic, complemented
15C43×#1935C211yesmaximal, characteristic, complemented
16C2×#13063324C2211yescharacteristic
17C2×#13063301C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×#13063282C2211yescharacteristic
20#14583192—24no—
21#14582961—24no—
22C2×#13063259C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063257C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33#14582840—21no—
34#14582834—21no—
35#14582819—21no—
36#14582812—21no—
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582796—21no—
40#14582791—21no—
41#14582788—21no—
42#14582781—21no—
43#14582764C2211yescharacteristic
44#14582756C2211yescharacteristic
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063324—22no—
66#13063324—22no—
67#13063301—22no—
68#13063301—22no—
69Q8×Dic43—22no—
70Q8×Dic43—22no—
71#13063282—22no—
72#13063282—22no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4D411yescharacteristic
83C2×Dic43⋊C4D411yescharacteristic
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4D411yescharacteristic
89C2×(C2×D43)⋊C4D411yescharacteristic
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93#13063259—22no—
94#13063258—22no—
95#13063258—22no—
96#13063257—22no—
97Dic43⋊C8—22no—
98Dic43⋊C8D414yes—
99#13063249—22no—
100#13063249—22no—
101(C2×D43)⋊C8—22no—
102(C2×D43)⋊C8—22no—
103C4×C43⋊C8—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C22×Q8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#103×C43—22no—
121#103×C43—22no—
122#97×C43—22no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43C2×D411yescharacteristic
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43#4112yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×Dic86—42no—
154C2×Dic86—81no—
155C2×Dic86—81no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43C2×D412yes—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—81no—
169C42×C43—21no—
170C42×C43—21no—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—22no—
173(C2×D43)⋊C4—22no—
174(C2×D43)⋊C4—81no—
175(C2×D43)⋊C4—81no—
176(C2×D43)⋊C4—81no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—42no—
185C4⋊Dic43#4112yes—
186Dic43⋊C4—24no—
187Dic43⋊C4—22no—
188Dic43⋊C4—22no—
189Dic43⋊C4—42no—
190Dic43⋊C4—81no—
191Dic43⋊C4—81no—
192C4×Dic43—42no—
193C4×Dic43—81no—
194C4×Dic43C2×D412yes—
195C4×Dic43#4112yes—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8C2×D412yes—
202C23×C43C22×D411yescharacteristic
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210Q8×C43—22no—
211Q8×C43—22no—
212Q8×C43—41no—
213Q8×C43—41no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—22no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C432−1+411yescharacteristic
237C2×C4×C432−1+411yescharacteristic
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—22no—
245C2×Dic43—21no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43#12112yes—
258C2×Dic43#12112yes—
259C4×D43—41no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—41no—
263Dic86—84no—
264C8×C43—22no—
265C8×C43—41no—
266C43⋊C8—22no—
267C43⋊C8—41no—
268#24714—431nomaximal, Sylow
269C22×C43C2×#12111yescharacteristic
270C22×C43#52511yescharacteristic
271C22×C43#53611yescharacteristic
272C22×C43#57611yescharacteristic
273C22×C43#57711yescharacteristic
274C22×C43#57811yescharacteristic
275C22×C43#57811yescharacteristic
276C2×D43—41no—
277C2×D43—41no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C4×C43—42no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43#54711yescharacteristic
290C4×C43#54811yescharacteristic
291C4×C43#55211yescharacteristic
292C4×C43#55611yescharacteristic
293Dic43—22no—
294Dic43—22no—
295Dic43—42no—
296Dic43—41no—
297Dic43—81no—
298Dic43—81no—
299Dic43—81no—
300C2×#477—431no—
301C2×#433—431no—
302#2628—431no—
303#2323—431no—
304#2076—431no—
305#2075—431no—
306#2036—431no—
307#2035—431no—
308#1988—431no—
309#1949—431no—
310#1944—431no—
311#1942—431no—
312#1935D4311yescharacteristic, complemented
313#1933—431no—
314#1805—431no—
315C2×C43#241511yescharacteristic
316C2×C43#305911yescharacteristic
317C2×C43#306211yescharacteristic
318C2×C43#312111yescharacteristic
319C2×C43#312411yescharacteristic
320C2×C43#324211yescharacteristic
321C2×C43#324311yescharacteristic
322D43—81no—
323C2×C4⋊Q8—431no—
324C2×C22⋊Q8—431no—
325C2×C4×Q8—431no—
326C2×#117—431no—
327#477—864no—
328#433—864no—
329C2×#107—431no—
330C2×#107—431no—
331C2×#107—431no—
332C2×#106—431no—
333C2×C4⋊C8—431no—
334C2×C4⋊C8—431no—
335C2×#103—431no—
336C2×#103—431no—
337C2×#103C2×D4311yescharacteristic
338C2×#103C2×D4311yescharacteristic
339C2×C22⋊C8—431no—
340C2×C22⋊C8—431no—
341C2×#97C2×D4311yescharacteristic
342C2×C4×C8—431no—
343#400—861no—
344#399—861no—
345#395—861no—
346#393—861no—
347#391C2×D4311yescharacteristic
348#389—431no—
349#389—431no—
350#389—861no—
351#389C2×D4311yescharacteristic
352#388—861no—
353#388—861no—
354#387—861no—
355#382—431no—
356#380—431no—
357#380—431no—
358#380—431no—
359C4×C4⋊C4—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340C2×D4311yescharacteristic
367#340C2×D4311yescharacteristic
368C43#2471411yescharacteristic, complemented, Sylow
369C22×Q8—861no—
370C22×Q8C22×D4311yescharacteristic
371C23×C4—431no—
372C22×C8—431no—
373C22×C8—431no—
374C22×C8C22×D4311yescharacteristic
375C22×C8C22×D4311yescharacteristic
376C4⋊Q8—862no—
377C4⋊Q8—862no—
378C22⋊Q8—862no—
379C22⋊Q8—862no—
380C4×Q8—862no—
381C4×Q8—862no—
382#117—862no—
383#117—862no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C22⋊C4—431no—
400C2×C22⋊C4—431no—
401C2×C22⋊C4—861no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C42—431no—
406C2×C42—861no—
407C2×C42—861no—
408C2×C42C22×D4311yescharacteristic
409#107—862no—
410#107—862no—
411#107—862no—
412#106—862no—
413C4⋊C8—434no—
414C4⋊C8—862no—
415#103—22no—
416#103—22no—
417#103—862no—
418#103—862no—
419C22⋊C8—862no—
420C22⋊C8—862no—
421#97—22no—
422C4×C8—862no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434C24—431no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—3441no—
441C2×Q8—3441no—
442C2×Q8—1722no—
443C2×Q8#1062189812yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4D4×D4311yescharacteristic
462C22×C4D4×D4311yescharacteristic
463C22×C4C23×D4311yescharacteristic
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—432no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8D4×D4312yes—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—81no—
483C4⋊C4—432no—
484C4⋊C4—862no—
485C4⋊C4—862no—
486C4⋊C4—864no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—3441no—
495C4⋊C4—3441no—
496C4⋊C4—1722no—
497C4⋊C4—1722no—
498C22⋊C4—862no—
499C22⋊C4—862no—
500C22⋊C4—864no—
501C22⋊C4—3441no—
502C22⋊C4—3441no—
503C22⋊C4—3441no—
504C42—21no—
505C42—21no—
506C42—432no—
507C42—432no—
508C42—3441no—
509C42—1722no—
510C23—861no—
511C23—861no—
512C23—861no—
513C23—861no—
514C23—861no—
515C23—861no—
516C23—861no—
517C23C2×D4×D4311yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522Q8—3444no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—432no—
542C2×C4—432no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—862no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4C2×D4×D4311yescharacteristic
567C2×C4#41×D4311yescharacteristic
568C2×C4#41×D4311yescharacteristic
569C2×C4C2×#1062189811yescharacteristic
570C2×C4#1306337211yescharacteristic
571C2×C4#1306337211yescharacteristic
572C8—22no—
573C8—41no—
574C8—862no—
575C8—1721no—
576C22—1721no—
577C22—1721no—
578C22—1721no—
579C22—1721no—
580C22—1721no—
581C22—1721no—
582C22—1721no—
583C22#121×D4311yescharacteristic
584C22#1458340811yescharacteristic
585C22#1458346911yescharacteristic
586C22#1458370311yescharacteristic
587C22#1458370811yescharacteristic
588C22#1458371511yescharacteristic
589C22#1458371511yescharacteristic
590C4—41no—
591C4—41no—
592C4—42no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4—862no—
597C4—862no—
598C4—3441no—
599C4—3441no—
600C4—3441no—
601C4—1722no—
602C4—1721no—
603C4#1458354711yescharacteristic
604C4#1458355811yescharacteristic
605C4#1458358211yescharacteristic
606C4#1458361611yescharacteristic
607C2—3441no—
608C2#1913802111yescharacteristic
609C2#1914424811yescharacteristic
610C2#1914427011yescharacteristic
611C2#1914482811yescharacteristic
612C2#1914485511yescharacteristic
613C2#1914585811yescharacteristic
614C2#1914587311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1935C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1935D43
hypocenterC43#24714
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1935

Complements

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

NH ≅ G/Ntype
1. C2×#14583192C2semidirect
9. #19135545C2semidirect
10. #19135362C2semidirect
11. #19135338C2semidirect
12. #19135325C2semidirect
13. #19135274C2semidirect
14. #19134608C2semidirect
15. C43×#1935C2semidirect
312. #1935D43semidirect
368. C43#24714semidirect

Maximal subgroups

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

subgroupindex
C2×#145831922
C2×#145829612
#191404222
#191372802
#191360272
#191360202
#191357962
#191357902
#191355452
#191353622
#191353382
#191353252
#191352742
#191346082
C43×#19352
#2471443