Finite Group Databasebeta

← #25097145

Subgroups — #25097145

Order 11008.

886 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×Dic43C211yesmaximal, characteristic
2#19136997C211yesmaximal, characteristic
3#19136990C211yesmaximal, characteristic
4#19134762C211yesmaximal, characteristic, complemented
5#19134760C211yesmaximal, characteristic, complemented
6#19134727C211yesmaximal, characteristic, complemented
7#19134727C211yesmaximal, characteristic, complemented
8#19134628C211yesmaximal, characteristic
9#19134626C211yesmaximal, characteristic
10#19134626C211yesmaximal, characteristic
11#107×Dic43C211yesmaximal, characteristic, complemented
12#19134487C211yesmaximal, characteristic, complemented
13#106×Dic43C211yesmaximal, characteristic, complemented
14#19134483C211yesmaximal, characteristic, complemented
15C43×#1809C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×#13063281—21no—
18C22×C4×Dic43C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25M16×Dic43C418yescomplemented
26C2×#13063235C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582768C2211yescharacteristic
31#14582768C2211yescharacteristic
32#14582766—21no—
33#14582764C2211yescharacteristic
34#14582764C2211yescharacteristic
35#14582763—21no—
36#14582760—21no—
37#14582759C2211yescharacteristic
38#14582759C2211yescharacteristic
39#14582757—21no—
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44#14582750—21no—
45C22⋊C4×Dic43—21no—
46#14582744—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C22×M16×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C23×Dic43D411yescharacteristic
61C23×Dic43D411yescharacteristic
62C2×#10621877—22no—
63C2×#10621877—22no—
64C2×#10621877C2×C414yes—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063281—44no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43C2×C414yes—
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43Q814yes—
86C2×C4×Dic43C2311yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88#13063259—22no—
89#13063258—22no—
90#13063258—22no—
91#13063257—22no—
92#13063256—22no—
93#13063256—22no—
94#13063235C2×C414yes—
95#13063235C2×C414yes—
96C8×Dic43C2×C414yes—
97C8×Dic43C2×C414yes—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C23×C4×C43C2311yescharacteristic
109C2×M16×C43—22no—
110C2×M16×C43—22no—
111C2×M16×C43C2×C414yes—
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120#107×C43—22no—
121#106×C43—22no—
122#95×C43—21no—
123#95×C43—21no—
124C24×C43C2×D411yescharacteristic
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43C22×C412yes—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×Q812yes—
136C22×C4×C43C2411yescharacteristic
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—41no—
144C22×Dic43—41no—
145C22×Dic43C4⋊C414yes—
146C22×Dic43C4⋊C414yes—
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151M16×C43—28no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43C22×C412yes—
155C2×C8×C43C22×C412yes—
156C2×C8×C43#4112yes—
157C2×C8×C43#4112yes—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C22⋊C4×C43—42no—
167C22⋊C4×C43—42no—
168C22⋊Dic43—42no—
169C22⋊Dic43—42no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178Dic43⋊C4—42no—
179Dic43⋊C4—42no—
180Dic43⋊C4—42no—
181Dic43⋊C4—42no—
182C4×Dic43—42no—
183C4×Dic43—42no—
184C4×Dic43—42no—
185C4×Dic43—42no—
186C4×Dic43C4⋊C414yes—
187C4×Dic43C4⋊C414yes—
188C4×Dic43C22×C412yes—
189C4×Dic43C22×C412yes—
190C4×Dic43C2×Q812yes—
191C4×Dic43C2×Q812yes—
192#10621877—28no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8C22×C412yes—
196C2×C43⋊C8C22×C412yes—
197C2×C43⋊C8#4112yes—
198C2×C43⋊C8#4112yes—
199C23×C43—21no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43C2×C4⋊C412yes—
206C23×C43C22×D411yescharacteristic
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43C2×C4⋊C412yes—
226C2×C4×C43C23×C411yescharacteristic
227C2×C4×C43C22×Q811yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—28no—
239C2×Dic43—44no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43C2×C4⋊C412yes—
253C2×Dic43C2×C4⋊C412yes—
254C2×Dic43C2×C4⋊C412yes—
255C2×Dic43C2×C4⋊C412yes—
256C2×Dic43AGL(1,ℤ/8)12yes—
257C2×Dic43#13712yes—
258C8×C43—22no—
259C8×C43#11714yescomplemented
260C43⋊C8—22no—
261C43⋊C8#11714yescomplemented
262#20819—431nomaximal, Sylow
263C22×C43—22no—
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43C22×C4⋊C411yescharacteristic
271C22×C43#53211yescharacteristic
272C22×C43#53211yescharacteristic
273C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
274C22×C43C2×#13711yescharacteristic
275C22×C43#57511yescharacteristic
276C22×C43#57511yescharacteristic
277C4×C43—22no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43C2×#11711yescharacteristic
283C4×C43C2×#11711yescharacteristic
284C4×C43#53311yescharacteristic
285C4×C43#53311yescharacteristic
286Dic43—22no—
287Dic43—22no—
288Dic43—22no—
289Dic43—81no—
290Dic43—81no—
291Dic43—81no—
292Dic43—81no—
293Dic43#42814yes—
294C2×C4×M16—431no—
295#2285—431no—
296#2283—431no—
297#1847—431no—
298#1847—431no—
299#1836—431no—
300#1836—431no—
301#1809—431no—
302#1809—431no—
303#1809—431no—
304#1809D4311yescharacteristic
305C4×#107—431no—
306C4×#107—431no—
307C4×#106—431no—
308C4×#106—431no—
309C2×C43—42no—
310C2×C43#228511yescharacteristic
311C2×C43C2×#42811yescharacteristic
312C2×C43#291111yescharacteristic
313C2×C43#317111yescharacteristic
314C2×C43#317111yescharacteristic
315C2×C43#317211yescharacteristic
316C2×C43#317211yescharacteristic
317C22×M16—431no—
318C22×M16C2×D4311yescharacteristic
319C2×#117—861no—
320C22×C42—431no—
321C2×#107—431no—
322C2×#107—431no—
323C2×#107—431no—
324C2×#107C2×D4311yescharacteristic
325C2×#106—431no—
326C2×#106—431no—
327C2×#106—431no—
328C2×#106C2×D4311yescharacteristic
329C4×M16—438no—
330C2×#97—431no—
331C2×#97—431no—
332C2×C4×C8—431no—
333C2×C4×C8—431no—
334#384—431no—
335#384—431no—
336#383—861no—
337#382—431no—
338#382—431no—
339#382—861no—
340#381—861no—
341#380—431no—
342#380—431no—
343#380—861no—
344#380C2×D4311yescharacteristic
345#380C2×D4311yescharacteristic
346C4×C4⋊C4—431no—
347C4×C4⋊C4—431no—
348C4×C4⋊C4—431no—
349C4×C4⋊C4—431no—
350C4×C4⋊C4—861no—
351C4×C22⋊C4—861no—
352#376—861no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340C2×D4311yescharacteristic
360#340C2×D4311yescharacteristic
361C43#2081911yescharacteristic, complemented, Sylow
362C23×C4—431no—
363C23×C4—431no—
364C23×C4C22×D4311yescharacteristic
365C2×M16—22no—
366C2×M16—22no—
367C2×M16—434no—
368C2×M16—862no—
369C2×M16—862no—
370C2×M16C4×D4314yes—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8C22×D4311yescharacteristic
374C22×C8C22×D4311yescharacteristic
375#117—1724no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C42—434no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—434no—
396C2×C42—431no—
397C2×C42—431no—
398C2×C42—861no—
399C2×C42—861no—
400C2×C42—861no—
401C2×C42—861no—
402#107—22no—
403#107—862no—
404#107—862no—
405#107—862no—
406#106—22no—
407#106—862no—
408#106—862no—
409#106—862no—
410#97—434no—
411#97—434no—
412C4×C8—434no—
413C4×C8—434no—
414#95—21no—
415#95—21no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426C24D4×D4311yescharacteristic
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—431no—
436C22×C4—434no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—434no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—1721no—
448C22×C4—1721no—
449C22×C4C2×C4×D4312yes—
450C22×C4D4×D4311yescharacteristic
451C22×C4Q8×D4312yes—
452C22×C4C23×D4311yescharacteristic
453M16—28no—
454M16—868no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—432no—
458C2×C8—432no—
459C2×C8—432no—
460C2×C8—432no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8C2×C4×D4312yes—
464C2×C8C2×C4×D4312yes—
465C2×C8#1062190012yes—
466C2×C8#1062190012yes—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—1722no—
484C4⋊C4—1722no—
485C4⋊C4—1722no—
486C4⋊C4—1722no—
487C22⋊C4—42no—
488C22⋊C4—42no—
489C22⋊C4—1722no—
490C22⋊C4—1722no—
491C42—434no—
492C42—434no—
493C42—432no—
494C42—432no—
495C42—432no—
496C42—432no—
497C42—1722no—
498C42—1722no—
499C42—1722no—
500C42—1722no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—21no—
507C23C4⋊C4×D4312yes—
508C23C2×D4×D4311yescharacteristic
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
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—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—432no—
528C2×C4—432no—
529C2×C4—432no—
530C2×C4—432no—
531C2×C4—432no—
532C2×C4—432no—
533C2×C4—868no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—1724no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4C4⋊C4×D4312yes—
554C2×C4C22×C4×D4311yescharacteristic
555C2×C4C2×Q8×D4311yescharacteristic
556C2×C4#41×D4311yescharacteristic
557C2×C4#41×D4311yescharacteristic
558C2×C4C2×#1062190011yescharacteristic
559C2×C4C2×#1062190011yescharacteristic
560C8—22no—
561C8—434no—
562C8—862no—
563C8#1306328114yescomplemented
564C22—22no—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22C2×C4⋊C4×D4311yescharacteristic
572C22#1458344411yescharacteristic
573C22#1458344411yescharacteristic
574C22AGL(1,ℤ/8)×D4311yescharacteristic
575C22#137×D4311yescharacteristic
576C22#1458369511yescharacteristic
577C22#1458369811yescharacteristic
578C4—22no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—434no—
584C4—862no—
585C4—862no—
586C4—862no—
587C4—3441no—
588C4—3441no—
589C4—3441no—
590C4—3441no—
591C4#117×D4311yescharacteristic
592C4C2×#1306328111yescharacteristic
593C4#1458345111yescharacteristic
594C4#1458345111yescharacteristic
595C2—42no—
596C2#1913699711yescharacteristic
597C2#428×D4311yescharacteristic
598C2#1914318211yescharacteristic
599C2#1914518311yescharacteristic
600C2#1914518511yescharacteristic
601C2#1914519411yescharacteristic
602C2#1914519611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1809C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1809D43
hypocenterC43#20819
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
4. #19134762C2semidirect
5. #19134760C2semidirect
6. #19134727C2semidirect
7. #19134727C2semidirect
11. #107×Dic43C2semidirect
12. #19134487C2semidirect
13. #106×Dic43C2semidirect
14. #19134483C2semidirect
25. M16×Dic43C4semidirect
259. C8×C43#117semidirect
261. C43⋊C8#117semidirect
361. C43#20819semidirect
563. C8#13063281semidirect

Maximal subgroups

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

subgroupindex
C2×M16×Dic432
#191369972
#191369902
#191347622
#191347602
#191347272
#191346282
#191346262
#107×Dic432
#191344872
#106×Dic432
#191344832
C43×#18092
#2081943