Finite Group Databasebeta

← #25154684

Subgroups — #25154684

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139627C211yesmaximal, characteristic, complemented
2#19137543C211yesmaximal, characteristic
3#19135969C211yesmaximal, characteristic
4#19135967C211yesmaximal, characteristic
5#19135739C211yesmaximal, characteristic
6#19135553C211yesmaximal, characteristic, complemented
7#19135551C211yesmaximal, characteristic, complemented
8#19135357C211yesmaximal, characteristic, complemented
9#19135312C211yesmaximal, characteristic, complemented
10#19135174C211yesmaximal, characteristic, complemented
11#19135171C211yesmaximal, characteristic, complemented
12#19134721C211yesmaximal, characteristic, complemented
13#19134593C211yesmaximal, characteristic
14#102×Dic43C211yesmaximal, characteristic
15C43×#2025C211yesmaximal, characteristic
16C2×#13063316C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×#13063281—21no—
19C2×#13063257C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×C8×Dic43C2211yescharacteristic
27#14582830—21no—
28#14582829—21no—
29#14582802C2211yescharacteristic
30#14582797C2211yescharacteristic
31#14582795C2211yescharacteristic
32#14582794—21no—
33#14582793—21no—
34#14582787—21no—
35#14582768—21no—
36#14582768C2211yescharacteristic
37#14582768C2211yescharacteristic
38#14582757—21no—
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4×Dic43⋊C4C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#125×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C23×Dic43—21no—
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62#13063316—22no—
63#13063316—41no—
64D4×Dic43—22no—
65D4×Dic43Q814yes—
66#13063281—44no—
67C2×C4⋊Dic43—21no—
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×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4D411yescharacteristic
80C2×Dic43⋊C4D411yescharacteristic
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063257—22no—
90#13063256—22no—
91C4⋊(C43⋊C8)—41no—
92Dic43⋊C8—22no—
93Dic43⋊C8—41no—
94#13063246—22no—
95#13063246—41no—
96C8×Dic43—22no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95D411yescharacteristic
103C43⋊#95D411yescharacteristic
104C22×D4×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107#125×C43—22no—
108#125×C43—41no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#102×C43—22no—
118#102×C43—41no—
119C24×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43C2×Q812yes—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2411yescharacteristic
132C22×Dic43—24no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—42no—
138C22×Dic43—42no—
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—42no—
155C4⋊C4×C43—42no—
156C4⋊C4×C43#4112yes—
157C22⋊C4×C43—42no—
158C22⋊C4×C43—81no—
159C42×C43—21no—
160C42×C43—21no—
161C22⋊Dic43—24no—
162C22⋊Dic43—42no—
163C22⋊Dic43—81no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—42no—
171C4⋊Dic43C2×Q812yes—
172C4⋊Dic43#4112yes—
173Dic43⋊C4—22no—
174Dic43⋊C4—22no—
175Dic43⋊C4—42no—
176Dic43⋊C4—42no—
177Dic43⋊C4—42no—
178Dic43⋊C4—81no—
179Dic43⋊C4—81no—
180Dic43⋊C4—81no—
181Dic43⋊C4—81no—
182C4×Dic43—21no—
183C4×Dic43—21no—
184C4×Dic43—42no—
185C4×Dic43—42no—
186C4×Dic43—42no—
187C4×Dic43C2×Q812yes—
188C4×Dic43#4112yes—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C23×C43—22no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43C22×D411yescharacteristic
203D4×C43—22no—
204D4×C43—22no—
205D4×C43—41no—
206D4×C43—41no—
207C2×C4×C43—22no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
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×C43C22×Q811yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43H(5,𝔽2)11yescharacteristic
227C2×C4×C432−1+411yescharacteristic
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—22no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—22no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—48no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43C22⋊Q812yes—
250C2×Dic43C22⋊Q812yes—
251C2×Dic43#13512yes—
252C2×Dic43AGL(1,ℤ/8)12yes—
253C8×C43—41no—
254C8×C43—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#26021—431nomaximal, Sylow
258C22×C43—42no—
259C22×C43—42no—
260C22×C43—42no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43C2×C22⋊Q811yescharacteristic
266C22×C43#54611yescharacteristic
267C22×C43#54811yescharacteristic
268C22×C43C2×#13511yescharacteristic
269C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C43#57711yescharacteristic
271C22×C43#57711yescharacteristic
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—42no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43#53311yescharacteristic
278C4×C43#54411yescharacteristic
279C4×C43#55511yescharacteristic
280C4×C43#55611yescharacteristic
281Dic43—22no—
282Dic43—42no—
283Dic43—41no—
284Dic43—42no—
285Dic43—41no—
286Dic43—81no—
287Dic43—81no—
288Dic43#47814yes—
289#2552—431no—
290#2354—431no—
291#2065—431no—
292#2065—431no—
293#2025—431no—
294#2025D4311yescharacteristic
295#1989—431no—
296#1989—431no—
297#1948—431no—
298#1939—431no—
299#1919—431no—
300#1919—431no—
301#1834—431no—
302#1802—431no—
303C4×#102—431no—
304C2×C43—82no—
305C2×C43#243911yescharacteristic
306C2×C43C2×#47811yescharacteristic
307C2×C43#308411yescharacteristic
308C2×C43#330311yescharacteristic
309C2×C43#333211yescharacteristic
310C2×C43#336011yescharacteristic
311C2×C43#336811yescharacteristic
312C2×#125—431no—
313C2×#125C2×D4311yescharacteristic
314C2×C4×D4—431no—
315C2×#117—861no—
316C2×#106—431no—
317C2×#106—431no—
318C2×C4⋊C8—431no—
319C2×C4⋊C8—431no—
320C2×C4⋊C8—431no—
321C2×#102—431no—
322C2×#102—431no—
323C2×#102C2×D4311yescharacteristic
324C2×#102C2×D4311yescharacteristic
325C2×C4×C8—431no—
326#398—861no—
327#398—861no—
328#390—431no—
329#390C2×D4311yescharacteristic
330#389—431no—
331#389—431no—
332#389—861no—
333#388—861no—
334#388—861no—
335#384—431no—
336#384—431no—
337#384—861no—
338#380—861no—
339C4×C4⋊C4—431no—
340C4×C4⋊C4—431no—
341C4×C4⋊C4—431no—
342C4×C4⋊C4—431no—
343#340—431no—
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340C2×D4311yescharacteristic
352#340C2×D4311yescharacteristic
353#336—431no—
354#336C2×D4311yescharacteristic
355C43#2602111yescharacteristic, complemented, Sylow
356C22×D4C22×D4311yescharacteristic
357C23×C4—861no—
358C22×C8—431no—
359C22×C8—431no—
360C22×C8C22×D4311yescharacteristic
361C22×C8C22×D4311yescharacteristic
362#125—22no—
363#125—41no—
364#125—862no—
365#125—1721no—
366C4×D4—434no—
367C4×D4—862no—
368#117—1724no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
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×C22⋊C4—861no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—861no—
396C2×C42—861no—
397C2×C42—861no—
398C2×C42C22×D4311yescharacteristic
399#106—862no—
400#106—862no—
401C4⋊C8—862no—
402C4⋊C8—1721no—
403C4⋊C8—1721no—
404#102—22no—
405#102—41no—
406#102—862no—
407#102—1721no—
408C4×C8—862no—
409#95—431no—
410#95—431no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416C24—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4Q8×D4312yes—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—431no—
427C22×C4—431no—
428C22×C4—431no—
429C22×C4—431no—
430C22×C4—864no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—1722no—
436C22×C4—1722no—
437C22×C4D4×D4311yescharacteristic
438C22×C4D4×D4311yescharacteristic
439C22×C4C23×D4311yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—432no—
460C4⋊C4—432no—
461C4⋊C4—862no—
462C4⋊C4—862no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—3441no—
470C4⋊C4—3441no—
471C4⋊C4—3441no—
472C4⋊C4—3441no—
473C4⋊C4—1722no—
474C4⋊C4—1722no—
475C4⋊C4—1722no—
476C4⋊C4—1722no—
477C4⋊C4#1062190012yes—
478C22⋊C4—42no—
479C22⋊C4—81no—
480C22⋊C4—864no—
481C22⋊C4—3441no—
482C22⋊C4—1722no—
483C42—21no—
484C42—21no—
485C42—432no—
486C42—432no—
487C42—861no—
488C42—861no—
489C42—1722no—
490C42—1722no—
491C42—1722no—
492C23—22no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23C2×D4×D4311yescharacteristic
500D4—22no—
501D4—22no—
502D4—41no—
503D4—41no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—432no—
520C2×C4—432no—
521C2×C4—432no—
522C2×C4—432no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—1728no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4C2×Q8×D4311yescharacteristic
545C2×C4#41×D4311yescharacteristic
546C2×C4#41×D4311yescharacteristic
547C2×C4C2×#1062190011yescharacteristic
548C2×C4#1306337011yescharacteristic
549C2×C4#1306337211yescharacteristic
550C8—41no—
551C8—41no—
552C8—1721no—
553C8—1721no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22C22⋊Q8×D4311yescharacteristic
562C22#1458353611yescharacteristic
563C22#1458355711yescharacteristic
564C22#135×D4311yescharacteristic
565C22AGL(1,ℤ/8)×D4311yescharacteristic
566C22#1458370611yescharacteristic
567C22#1458370911yescharacteristic
568C4—41no—
569C4—42no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—434no—
574C4—862no—
575C4—3441no—
576C4—3441no—
577C4—1721no—
578C4—1722no—
579C4—1721no—
580C4—1722no—
581C4#1458345111yescharacteristic
582C4#1458352811yescharacteristic
583C4#1458361111yescharacteristic
584C4#1458361811yescharacteristic
585C2—82no—
586C2#1913827911yescharacteristic
587C2#478×D4311yescharacteristic
588C2#1914445811yescharacteristic
589C2#1914651611yescharacteristic
590C2#1914691511yescharacteristic
591C2#1914724111yescharacteristic
592C2#1914732111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2025C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2025D43
hypocenterC43#26021
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2025

Complements

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

NH ≅ G/Ntype
1. #19139627C2semidirect
6. #19135553C2semidirect
7. #19135551C2semidirect
8. #19135357C2semidirect
9. #19135312C2semidirect
10. #19135174C2semidirect
11. #19135171C2semidirect
12. #19134721C2semidirect
355. C43#26021semidirect

Maximal subgroups

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

subgroupindex
#191396272
#191375432
#191359692
#191359672
#191357392
#191355532
#191355512
#191353572
#191353122
#191351742
#191351712
#191347212
#191345932
#102×Dic432
C43×#20252
#2602143