Finite Group Databasebeta

← #25154821

Subgroups — #25154821

Order 11008.

736 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139612C211yesmaximal, characteristic, complemented
2#19137543C211yesmaximal, characteristic
3#19135969C211yesmaximal, characteristic
4#19135967C211yesmaximal, characteristic
5#19135739C211yesmaximal, characteristic
6#19135549C211yesmaximal, characteristic, complemented
7#19135548C211yesmaximal, characteristic, complemented
8#19135357C211yesmaximal, characteristic, complemented
9#19135317C211yesmaximal, characteristic, complemented
10#19135181C211yesmaximal, characteristic, complemented
11#19135171C211yesmaximal, characteristic, complemented
12#19134727C211yesmaximal, characteristic, complemented
13#19134603C211yesmaximal, characteristic
14#19134422C211yesmaximal, characteristic
15C43×#2023C211yesmaximal, 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×#13063235C2211yescharacteristic
27#14582829—21no—
28#14582818—21no—
29#14582806—21no—
30#14582802C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582794—21no—
34#14582793—21no—
35#14582787—21no—
36#14582768C2211yescharacteristic
37#14582764C2211yescharacteristic
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×C4⋊Q8×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×Dic43Q814yescomplemented
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⋊C4D411yescharacteristic
78C2×Dic43⋊C4D411yescharacteristic
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43C2311yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87#13063257—22no—
88#13063256—22no—
89C4⋊(C43⋊C8)—41no—
90Dic43⋊C8—22no—
91Dic43⋊C8—41no—
92#13063246—22no—
93#13063246—41no—
94#13063235—22no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95D411yescharacteristic
103C43⋊#95D411yescharacteristic
104C22×Q8×C43—21no—
105C22×D4×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C4⋊Q8×C43—22no—
109C4⋊Q8×C43—41no—
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×Q8×C43—42no—
121C2×Q8×C43—42no—
122C2×Q8×C43—81no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43C2×Q812yes—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C22×Dic43—24no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—42no—
141C22×Dic43—42no—
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×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—42no—
158C4⋊C4×C43#4112yes—
159C22⋊C4×C43—42no—
160C22⋊C4×C43—81no—
161C42×C43—21no—
162C42×C43—21no—
163C22⋊Dic43—24no—
164C22⋊Dic43—42no—
165C22⋊Dic43—81no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—42no—
173C4⋊Dic43C2×Q812yes—
174C4⋊Dic43#4112yes—
175Dic43⋊C4—22no—
176Dic43⋊C4—41no—
177Dic43⋊C4—42no—
178Dic43⋊C4—42no—
179Dic43⋊C4—42no—
180Dic43⋊C4—81no—
181Dic43⋊C4—81no—
182C4×Dic43—21no—
183C4×Dic43—21no—
184C4×Dic43—42no—
185C4×Dic43—42no—
186C4×Dic43—81no—
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
203Q8×C43—84no—
204D4×C43—22no—
205D4×C43—22no—
206D4×C43—41no—
207D4×C43—41no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—22no—
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×C43AGL(1,ℤ/8)12yes—
223C2×C4×C43C22×Q811yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43H(5,𝔽2)11yescharacteristic
228C2×C4×C432−1+411yescharacteristic
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—22no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—22no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—48no—
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×Dic43C22⋊Q812yes—
253C2×Dic43C22⋊Q812yes—
254C8×C43—41no—
255C8×C43—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258#26032—431nomaximal, Sylow
259C22×C43—42no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43C2×C22⋊Q811yescharacteristic
267C22×C43#54611yescharacteristic
268C22×C43#54811yescharacteristic
269C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C43#57511yescharacteristic
271C22×C43#57711yescharacteristic
272C22×C43#57711yescharacteristic
273C4×C43—22no—
274C4×C43—42no—
275C4×C43—41no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43#53311yescharacteristic
279C4×C43#54411yescharacteristic
280C4×C43#55511yescharacteristic
281C4×C43#55611yescharacteristic
282Dic43—22no—
283Dic43—22no—
284Dic43—42no—
285Dic43—42no—
286Dic43—41no—
287Dic43—41no—
288Dic43—81no—
289Dic43—81no—
290#2550—431no—
291#2354—431no—
292#2065—431no—
293#2065—431no—
294#2025—431no—
295#2023D4311yescharacteristic
296#1989—431no—
297#1988—431no—
298#1948—431no—
299#1940—431no—
300#1920—431no—
301#1919—431no—
302#1836—431no—
303#1804—431no—
304#1762—431no—
305C2×C43—82no—
306C2×C43#243911yescharacteristic
307C2×C43#307711yescharacteristic
308C2×C43#308411yescharacteristic
309C2×C43#330611yescharacteristic
310C2×C43#332111yescharacteristic
311C2×C43#336811yescharacteristic
312C2×C43#337611yescharacteristic
313C2×C4⋊Q8C2×D4311yescharacteristic
314C2×#125—431no—
315C2×C4×D4—431no—
316C2×#117—861no—
317C2×#106—431no—
318C2×#106—431no—
319C2×C4⋊C8—431no—
320C2×C4⋊C8—431no—
321C2×C4⋊C8—431no—
322C2×#102—431no—
323C2×#102—431no—
324C2×#102C2×D4311yescharacteristic
325C2×#102C2×D4311yescharacteristic
326C2×#97—431no—
327#398—861no—
328#395—861no—
329#391—861no—
330#390—431no—
331#390C2×D4311yescharacteristic
332#389—431no—
333#389—431no—
334#389—861no—
335#388—861no—
336#388—861no—
337#384—431no—
338#382—431no—
339#380—861no—
340C4×C4⋊C4—431no—
341C4×C4⋊C4—431no—
342C4×C4⋊C4—431no—
343C4×C4⋊C4—431no—
344#340—431no—
345#340—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
354#336—431no—
355#336C2×D4311yescharacteristic
356C43#2603211yescharacteristic, complemented, Sylow
357C22×Q8—21no—
358C22×D4C22×D4311yescharacteristic
359C23×C4—861no—
360C22×C8—431no—
361C22×C8—431no—
362C22×C8C22×D4311yescharacteristic
363C22×C8C22×D4311yescharacteristic
364C4⋊Q8—22no—
365C4⋊Q8—41no—
366#125—862no—
367#125—1721no—
368C4×D4—434no—
369C4×D4—862no—
370#117—1724no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
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⋊C4C22×D4311yescharacteristic
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C42—431no—
393C2×C42—431no—
394C2×C42—861no—
395C2×C42—861no—
396C2×C42—861no—
397C2×C42C22×D4311yescharacteristic
398#106—862no—
399#106—862no—
400C4⋊C8—862no—
401C4⋊C8—1721no—
402C4⋊C8—1721no—
403#102—22no—
404#102—41no—
405#102—862no—
406#102—1721no—
407#97—862no—
408#95—431no—
409#95—431no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417C24—21no—
418C2×Q8—42no—
419C2×Q8—42no—
420C2×Q8—81no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4Q8×D4312yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—431no—
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—431no—
434C22×C4—864no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—1722no—
440C22×C4—1722no—
441C22×C4D4×D4311yescharacteristic
442C22×C4D4×D4311yescharacteristic
443C22×C4C23×D4311yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—42no—
462C4⋊C4—432no—
463C4⋊C4—432no—
464C4⋊C4—862no—
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—1721no—
474C4⋊C4—1722no—
475C4⋊C4—1722no—
476C4⋊C4—1722no—
477C4⋊C4—1722no—
478C4⋊C4#1062190012yes—
479C22⋊C4—42no—
480C22⋊C4—81no—
481C22⋊C4—864no—
482C22⋊C4—3441no—
483C22⋊C4—1722no—
484C42—21no—
485C42—21no—
486C42—432no—
487C42—432no—
488C42—861no—
489C42—861no—
490C42—3441no—
491C42—1722no—
492C42—1722no—
493C23—22no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23C2×D4×D4311yescharacteristic
501Q8—84no—
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—432no—
521C2×C4—432no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—862no—
527C2×C4—862no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—1728no—
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×C4—1721no—
545C2×C4#1306334912yes—
546C2×C4C2×Q8×D4311yescharacteristic
547C2×C4#41×D4311yescharacteristic
548C2×C4#41×D4311yescharacteristic
549C2×C4C2×#1062190011yescharacteristic
550C2×C4#1306337011yescharacteristic
551C2×C4#1306337211yescharacteristic
552C8—41no—
553C8—41no—
554C8—1721no—
555C8—1721no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22C22⋊Q8×D4311yescharacteristic
564C22#1458353611yescharacteristic
565C22#1458355711yescharacteristic
566C22C2×#1306334911yescharacteristic
567C22#1458369811yescharacteristic
568C22#1458370511yescharacteristic
569C22#1458370911yescharacteristic
570C4—22no—
571C4—41no—
572C4—42no—
573C4—81no—
574C4—81no—
575C4—862no—
576C4—862no—
577C4—3441no—
578C4—3441no—
579C4—1721no—
580C4—1721no—
581C4—1722no—
582C4—1722no—
583C4#1458345111yescharacteristic
584C4#1458352811yescharacteristic
585C4#1458361111yescharacteristic
586C4#1458361811yescharacteristic
587C2—82no—
588C2#1913827911yescharacteristic
589C2#1914438711yescharacteristic
590C2#1914445211yescharacteristic
591C2#1914656011yescharacteristic
592C2#1914677411yescharacteristic
593C2#1914732911yescharacteristic
594C2#1914742111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2023C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2023D43
hypocenterC43#26032
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. #19139612C2semidirect
6. #19135549C2semidirect
7. #19135548C2semidirect
8. #19135357C2semidirect
9. #19135317C2semidirect
10. #19135181C2semidirect
11. #19135171C2semidirect
12. #19134727C2semidirect
65. D4×Dic43Q8semidirect
356. C43#26032semidirect

Maximal subgroups

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

subgroupindex
#191396122
#191375432
#191359692
#191359672
#191357392
#191355492
#191355482
#191353572
#191353172
#191351812
#191351712
#191347272
#191346032
#191344222
C43×#20232
#2603243