Finite Group Databasebeta

← #25097171

Subgroups — #25097171

Order 11008.

810 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582857C211yesmaximal, characteristic
2#19137202C211yesmaximal, characteristic
3#19137202C211yesmaximal, characteristic
4#19134762C211yesmaximal, characteristic, complemented
5#19134760C211yesmaximal, characteristic, complemented
6#19134724C211yesmaximal, characteristic, complemented
7#19134721C211yesmaximal, characteristic, complemented
8#19134628C211yesmaximal, characteristic
9#19134622C211yesmaximal, characteristic
10#19134618C211yesmaximal, characteristic
11#19134491C211yesmaximal, characteristic, complemented
12#19134491C211yesmaximal, characteristic, complemented
13#107×Dic43C211yesmaximal, characteristic, complemented
14#106×Dic43C211yesmaximal, characteristic, complemented
15C43×#1809C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C2×#13063259C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24#14582857C418yescomplemented
25C2×#13063235C2211yescharacteristic
26C2×#13063235C2211yescharacteristic
27C2×C8×Dic43C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582793—21no—
30#14582793—21no—
31#14582787—21no—
32#14582787—21no—
33#14582784—21no—
34#14582784—21no—
35#14582782—21no—
36#14582782—21no—
37#14582768C2211yescharacteristic
38#14582768C2211yescharacteristic
39#14582764C2211yescharacteristic
40#14582764C2211yescharacteristic
41#14582759C2211yescharacteristic
42#14582759C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4⋊C4×Dic43C2211yescharacteristic
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
60C22×C43⋊C8—22no—
61C22×C43⋊C8—22no—
62C22×C43⋊C8C2×C414yes—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063284C2×C414yes—
66#13063284Q814yes—
67C2×C4⋊Dic43D411yescharacteristic
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43D411yescharacteristic
80C2×C22⋊Dic43D411yescharacteristic
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43C2311yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87#13063259—22no—
88#13063258—22no—
89#13063258—22no—
90#13063257—22no—
91#13063256—22no—
92#13063256—22no—
93#13063235C2×C414yes—
94#13063235C2×C414yes—
95C8×Dic43C2×C414yes—
96C8×Dic43C2×C414yes—
97C43⋊#95—21no—
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—
107C23×C4×C43C2311yescharacteristic
108C2×M16×C43—22no—
109C2×M16×C43—22no—
110C2×M16×C43C2×C414yes—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119#107×C43—22no—
120#106×C43—22no—
121#95×C43—21no—
122#95×C43—21no—
123C24×C43C2×D411yescharacteristic
124C22×C4×C43—21no—
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×C43C22×C412yes—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×Q812yes—
135C22×C4×C43C2411yescharacteristic
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144M16×C43—28no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43C22×C412yes—
148C2×C8×C43C22×C412yes—
149C2×C8×C43#4112yes—
150C2×C8×C43#4112yes—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C22⋊C4×C43—81no—
160C22⋊C4×C43—81no—
161C22⋊Dic43—81no—
162C22⋊Dic43—81no—
163C22⋊Dic43C4⋊C414yes—
164C22⋊Dic43C4⋊C414yes—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43C4⋊C414yes—
174C4⋊Dic43C4⋊C414yes—
175Dic43⋊C4—81no—
176Dic43⋊C4—81no—
177Dic43⋊C4—81no—
178Dic43⋊C4—81no—
179C4×Dic43—81no—
180C4×Dic43—81no—
181C4×Dic43—81no—
182C4×Dic43—81no—
183C4×Dic43C22×C412yes—
184C4×Dic43C22×C412yes—
185C4×Dic43C2×Q812yes—
186C4×Dic43C2×Q812yes—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—28no—
190C2×C43⋊C8C22×C412yes—
191C2×C43⋊C8C22×C412yes—
192C2×C43⋊C8#4112yes—
193C2×C43⋊C8#4112yes—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43C2×C4⋊C412yes—
201C23×C43C22×D411yescharacteristic
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
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×C43C2×C4⋊C412yes—
221C2×C4×C43C23×C411yescharacteristic
222C2×C4×C43C22×Q811yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43C2×C4⋊C412yes—
248C2×Dic43C2×C4⋊C412yes—
249C2×Dic43C2×C4⋊C412yes—
250C2×Dic43C2×C4⋊C412yes—
251C8×C43—22no—
252C8×C43#11714yes—
253C43⋊C8—22no—
254C43⋊C8#11714yes—
255#20822—431nomaximal, Sylow
256C22×C43—22no—
257C22×C43—22no—
258C22×C43—22no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43C22×C4⋊C411yescharacteristic
264C22×C43#53211yescharacteristic
265C22×C43#53211yescharacteristic
266C22×C43#57611yescharacteristic
267C22×C43#57711yescharacteristic
268C22×C43#57711yescharacteristic
269C22×C43#57811yescharacteristic
270C4×C43—22no—
271C4×C43—81no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43C2×#11711yescharacteristic
276C4×C43C2×#11711yescharacteristic
277C4×C43#53311yescharacteristic
278C4×C43#53311yescharacteristic
279Dic43—22no—
280Dic43—22no—
281Dic43—22no—
282Dic43—22no—
283Dic43—81no—
284Dic43—81no—
285Dic43—81no—
286Dic43—81no—
287C2×#405—431no—
288#2314—431no—
289#2314—431no—
290#1847—431no—
291#1847—431no—
292#1835—431no—
293#1834—431no—
294#1809—431no—
295#1809D4311yescharacteristic
296#1808—431no—
297#1807—431no—
298#1776—431no—
299#1776—431no—
300C4×#107—431no—
301C4×#106—431no—
302C2×C43—42no—
303C2×C43#228511yescharacteristic
304C2×C43#291211yescharacteristic
305C2×C43#291311yescharacteristic
306C2×C43#317811yescharacteristic
307C2×C43#317811yescharacteristic
308C2×C43#317911yescharacteristic
309C2×C43#317911yescharacteristic
310C22×M16C2×D4311yescharacteristic
311C23×C8—431no—
312C2×#117—431no—
313C2×#107—431no—
314C2×#107—431no—
315C2×#107—431no—
316C2×#107C2×D4311yescharacteristic
317C2×#106—431no—
318C2×#106—431no—
319C2×#106—431no—
320C2×#106C2×D4311yescharacteristic
321#405—438no—
322C2×#97—431no—
323C2×#97—431no—
324C2×C4×C8—431no—
325C2×C4×C8—431no—
326#388—861no—
327#388—861no—
328#388—861no—
329#388—861no—
330#387—861no—
331#387—861no—
332#387—861no—
333#387—861no—
334#384—431no—
335#384—431no—
336#382—431no—
337#382—431no—
338#380—431no—
339#380—431no—
340#380C2×D4311yescharacteristic
341#380C2×D4311yescharacteristic
342C4×C4⋊C4—431no—
343C4×C4⋊C4—431no—
344C4×C4⋊C4—431no—
345C4×C4⋊C4—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340C2×D4311yescharacteristic
353#340C2×D4311yescharacteristic
354C43#2082211yescharacteristic, complemented, Sylow
355C23×C4C22×D4311yescharacteristic
356C2×M16—22no—
357C2×M16—22no—
358C2×M16C4×D4314yes—
359C22×C8—431no—
360C22×C8—434no—
361C22×C8—431no—
362C22×C8—862no—
363C22×C8—862no—
364C22×C8C22×D4311yescharacteristic
365C22×C8C22×D4311yescharacteristic
366#117—434no—
367#117—434no—
368C2×C4⋊C4—431no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C4⋊C4C22×D4311yescharacteristic
381C2×C4⋊C4C22×D4311yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—431no—
385C2×C22⋊C4—431no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C42—431no—
389C2×C42—431no—
390C2×C42—861no—
391C2×C42—861no—
392C2×C42—861no—
393C2×C42—861no—
394#107—22no—
395#107—862no—
396#107—862no—
397#107—862no—
398#106—22no—
399#106—862no—
400#106—862no—
401#106—862no—
402#97—434no—
403#97—434no—
404C4×C8—434no—
405C4×C8—434no—
406#95—21no—
407#95—21no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418C24D4×D4311yescharacteristic
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—431no—
428C22×C4—431no—
429C22×C4—431no—
430C22×C4—431no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4C2×C4×D4312yes—
436C22×C4D4×D4311yescharacteristic
437C22×C4Q8×D4312yes—
438C22×C4C23×D4311yescharacteristic
439M16—28no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—432no—
443C2×C8—432no—
444C2×C8—432no—
445C2×C8—432no—
446C2×C8—868no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8C2×C4×D4312yes—
450C2×C8C2×C4×D4312yes—
451C2×C8#1062190012yes—
452C2×C8#1062190012yes—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—434no—
462C4⋊C4—434no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—3441no—
472C4⋊C4—3441no—
473C4⋊C4—3441no—
474C4⋊C4—3441no—
475C22⋊C4—81no—
476C22⋊C4—81no—
477C22⋊C4—434no—
478C22⋊C4—434no—
479C22⋊C4—3441no—
480C22⋊C4—3441no—
481C42—432no—
482C42—432no—
483C42—432no—
484C42—432no—
485C42—3441no—
486C42—3441no—
487C42—3441no—
488C42—3441no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23C4⋊C4×D4312yes—
496C23C2×D4×D4311yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—432no—
516C2×C4—432no—
517C2×C4—432no—
518C2×C4—432no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4C4⋊C4×D4312yes—
540C2×C4C22×C4×D4311yescharacteristic
541C2×C4C2×Q8×D4311yescharacteristic
542C2×C4#41×D4311yescharacteristic
543C2×C4#41×D4311yescharacteristic
544C2×C4C2×#1062190011yescharacteristic
545C2×C4C2×#1062190011yescharacteristic
546C8—22no—
547C8—434no—
548C8—862no—
549C8#1306328114yes—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C2×C4⋊C4×D4311yescharacteristic
558C22#1458344411yescharacteristic
559C22#1458344411yescharacteristic
560C22#1458370311yescharacteristic
561C22#1458370811yescharacteristic
562C22#1458370911yescharacteristic
563C22#1458371511yescharacteristic
564C4—22no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—862no—
570C4—862no—
571C4—862no—
572C4—862no—
573C4—3441no—
574C4—3441no—
575C4—3441no—
576C4—3441no—
577C4#117×D4311yescharacteristic
578C4C2×#1306328111yescharacteristic
579C4#1458345111yescharacteristic
580C4#1458345111yescharacteristic
581C2—42no—
582C2#1913699711yescharacteristic
583C2#1914318911yescharacteristic
584C2#1914319411yescharacteristic
585C2#1914525611yescharacteristic
586C2#1914526411yescharacteristic
587C2#1914527111yescharacteristic
588C2#1914527911yescharacteristic
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#20822
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. #19134724C2semidirect
7. #19134721C2semidirect
11. #19134491C2semidirect
12. #19134491C2semidirect
13. #107×Dic43C2semidirect
14. #106×Dic43C2semidirect
24. #14582857C4semidirect
354. C43#20822semidirect

Maximal subgroups

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

subgroupindex
C2×#145828572
#191372022
#191347622
#191347602
#191347242
#191347212
#191346282
#191346222
#191346182
#191344912
#107×Dic432
#106×Dic432
C43×#18092
#2082243