Finite Group Databasebeta

← #25169335

Subgroups — #25169335

Order 11008.

700 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139007C211yesmaximal, characteristic
2#19137599C211yesmaximal, characteristic
3#19136017C211yesmaximal, characteristic, complemented
4#19135985C211yesmaximal, characteristic, complemented
5#19135800C211yesmaximal, characteristic
6#19135794C211yesmaximal, characteristic
7#19135360C211yesmaximal, characteristic, complemented
8#19135201C211yesmaximal, characteristic
9#19135177C211yesmaximal, characteristic, complemented
10#19135169C211yesmaximal, characteristic, complemented
11#19134848C211yesmaximal, characteristic, complemented
12#19134781C211yesmaximal, characteristic
13#19134680C211yesmaximal, characteristic
14C4×#13063250C211yesmaximal, characteristic, complemented
15C43×#1942C211yesmaximal, characteristic, complemented
16C2×#13063305C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×C4⋊C4×D43C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28#14582838—21no—
29#14582825—21no—
30#14582804C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582795—21no—
33#14582791—21no—
34#14582782—21no—
35#14582770—21no—
36#14582766—21no—
37#14582764C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42C4×(C2×D43)⋊C4C2211yescharacteristic
43#14582746—21no—
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×C4×C8×C43C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C4×D43—21no—
61C22×C4×D43C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063305—22no—
65#13063305—22no—
66C4×Dic86—22no—
67C4×Dic86—41no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C4⋊C4×D43—22no—
76C4⋊C4×D43—41no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4D411yescharacteristic
81C2×(C2×D43)⋊C4D411yescharacteristic
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43C2311yescharacteristic
86#13063258—22no—
87#13063256—22no—
88Dic43⋊C8—22no—
89#13063250—22no—
90#13063250—22no—
91#13063248—22no—
92#13063248—41no—
93(C2×D43)⋊C8—22no—
94(C2×D43)⋊C8—41no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115#107×C43—22no—
116#107×C43—41no—
117C4×C8×C43—41no—
118#95×C43—21no—
119#95×C43—21no—
120C23×D43C2×D411yescharacteristic
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—21no—
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—42no—
142C2×C4×D43—42no—
143C2×C4×D43—81no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86#4112yes—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43#4112yes—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—81no—
164C4⋊C4×C43—81no—
165C4⋊C4×C43#4112yes—
166C42×C43—21no—
167C42×C43—21no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—22no—
170(C2×D43)⋊C4—22no—
171(C2×D43)⋊C4—42no—
172(C2×D43)⋊C4—81no—
173C4⋊Dic43—24no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—81no—
180C4⋊Dic43#4112yes—
181Dic43⋊C4—42no—
182Dic43⋊C4—42no—
183C4×Dic43—21no—
184C4×Dic43—21no—
185C4×Dic43—42no—
186C4×Dic43—42no—
187C4×Dic43—81no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C23×C43C22×D411yescharacteristic
195C22×D43—21no—
196C22×D43—21no—
197C22×D43—21no—
198C22×D43—21no—
199C22×D43—21no—
200C22×D43—21no—
201C22×D43#13512yes—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—22no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
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#13712yes—
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43H(5,𝔽2)11yescharacteristic
225C2×C4×C432−1+411yescharacteristic
226C2×Dic43—21no—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
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—
247C4×D43—41no—
248C4×D43—41no—
249C4×D43—41no—
250C4×D43—41no—
251C4×D43—84no—
252Dic86—22no—
253Dic86—22no—
254Dic86—41no—
255Dic86—41no—
256C8×C43—22no—
257C8×C43—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260#27035—431nomaximal, Sylow
261C22×C43#52511yescharacteristic
262C22×C43#54611yescharacteristic
263C22×C43#54711yescharacteristic
264C22×C43C2×#13511yescharacteristic
265C22×C43C2×#13711yescharacteristic
266C22×C43#57611yescharacteristic
267C22×C43#57811yescharacteristic
268C2×D43—22no—
269C2×D43—22no—
270C2×D43—22no—
271C2×D43—41no—
272C2×D43—41no—
273C2×D43—41no—
274C2×D43—41no—
275C4×C43—22no—
276C4×C43—42no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43#52911yescharacteristic
282C4×C43#53911yescharacteristic
283C4×C43#55311yescharacteristic
284C4×C43#55611yescharacteristic
285Dic43—41no—
286Dic43—41no—
287Dic43—42no—
288Dic43—41no—
289Dic43—42no—
290Dic43—81no—
291Dic43—81no—
292#2495—431no—
293#2360—431no—
294#2074—431no—
295#2068—431no—
296#2036—431no—
297#2035—431no—
298#1949—431no—
299#1942D4311yescharacteristic, complemented
300#1923—431no—
301#1920—431no—
302#1918—431no—
303#1863—431no—
304#1852—431no—
305#1823—431no—
306C4×#103—431no—
307C2×C43#246611yescharacteristic
308C2×C43#310811yescharacteristic
309C2×C43#312411yescharacteristic
310C2×C43#329711yescharacteristic
311C2×C43#331211yescharacteristic
312C2×C43#333611yescharacteristic
313C2×C43#335711yescharacteristic
314D43—42no—
315C2×C22⋊Q8—431no—
316C2×C4×Q8—431no—
317C22×C4⋊C4—431no—
318C2×#107—431no—
319C2×#107C2×D4311yescharacteristic
320C2×#107C2×D4311yescharacteristic
321C2×#106—431no—
322C2×C4⋊C8—431no—
323C2×#103—431no—
324C2×#103—431no—
325C2×#103—431no—
326C2×#103—431no—
327C2×C22⋊C8—431no—
328C2×C22⋊C8—431no—
329C2×C4×C8C2×D4311yescharacteristic
330#400—861no—
331#397—861no—
332#391—431no—
333#389—431no—
334#389—861no—
335#389C2×D4311yescharacteristic
336#389C2×D4311yescharacteristic
337#388—861no—
338#387—861no—
339#385—861no—
340#383—861no—
341#382—431no—
342#380—431no—
343#380—431no—
344C4×C4⋊C4—431no—
345C4×C4⋊C4—431no—
346C4×C22⋊C4—431no—
347C4×C22⋊C4—861no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340C2×D4311yescharacteristic
355#340C2×D4311yescharacteristic
356#336—431no—
357#336—431no—
358C43#2703511yescharacteristic, complemented, Sylow
359C22×Q8—431no—
360C23×C4—431no—
361C23×C4—861no—
362C22×C8—431no—
363C22×C8—431no—
364C22×C8C22×D4311yescharacteristic
365C22×C8C22×D4311yescharacteristic
366C22⋊Q8—862no—
367C22⋊Q8—862no—
368C4×Q8—862no—
369C4×Q8—1721no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—862no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—1721no—
381C2×C4⋊C4C22×D4311yescharacteristic
382C2×C4⋊C4C22×D4311yescharacteristic
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C22⋊C4—431no—
386C2×C22⋊C4—431no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C42—431no—
391C2×C42—861no—
392C2×C42—861no—
393C2×C42—861no—
394C2×C42C22×D4311yescharacteristic
395#107—22no—
396#107—41no—
397#107—862no—
398#106—862no—
399C4⋊C8—862no—
400#103—862no—
401#103—862no—
402#103—862no—
403#103—1721no—
404C22⋊C8—862no—
405C22⋊C8—1721no—
406C4×C8—41no—
407#95—21no—
408#95—21no—
409#95—431no—
410#95—431no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420C24—431no—
421C2×Q8—432no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—861no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—431no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—3441no—
445C22×C4—1722no—
446C22×C4—1722no—
447C22×C4D4×D4311yescharacteristic
448C22×C4D4×D4311yescharacteristic
449C22×C4C23×D4311yescharacteristic
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8#1062190212yes—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4—432no—
472C4⋊C4—864no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—3441no—
479C4⋊C4—1722no—
480C4⋊C4—1722no—
481C4⋊C4#1062189812yes—
482C22⋊C4—862no—
483C22⋊C4—864no—
484C22⋊C4—862no—
485C22⋊C4—3441no—
486C22⋊C4—1722no—
487C42—21no—
488C42—21no—
489C42—861no—
490C42—861no—
491C42—3441no—
492C42—1722no—
493C42—1722no—
494C23—432no—
495C23—861no—
496C23—861no—
497C23—861no—
498C23—861no—
499C23—861no—
500C23—861no—
501C23C2×D4×D4311yescharacteristic
502Q8—862no—
503Q8—862no—
504Q8—1721no—
505Q8—1721no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
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—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—862no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—862no—
533C2×C4—861no—
534C2×C4—3444no—
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—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4#1306335712yes—
550C2×C4#41×D4311yescharacteristic
551C2×C4#41×D4311yescharacteristic
552C2×C4C2×#1062189811yescharacteristic
553C2×C4C2×#1062190211yescharacteristic
554C2×C4#1306337011yescharacteristic
555C2×C4#1306337311yescharacteristic
556C8—22no—
557C8—41no—
558C8—1721no—
559C8—1721no—
560C22—862no—
561C22—862no—
562C22—862no—
563C22—1721no—
564C22—1721no—
565C22—1721no—
566C22—1721no—
567C22#1458340811yescharacteristic
568C22#1458353811yescharacteristic
569C22#1458355211yescharacteristic
570C22#135×D4311yescharacteristic
571C22C2×#1306335711yescharacteristic
572C22#1458370011yescharacteristic
573C22#1458371311yescharacteristic
574C4—22no—
575C4—42no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—3441no—
581C4—3441no—
582C4—1721no—
583C4—1722no—
584C4—1722no—
585C4—1721no—
586C4—1721no—
587C4#1458343411yescharacteristic
588C4#1458349511yescharacteristic
589C4#1458359711yescharacteristic
590C4#1458362111yescharacteristic
591C2—1722no—
592C2#1913863711yescharacteristic
593C2#1914467911yescharacteristic
594C2#1914485311yescharacteristic
595C2#1914644011yescharacteristic
596C2#1914665211yescharacteristic
597C2#1914696211yescharacteristic
598C2#1914722011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1942C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1942D43
hypocenterC43#27035
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1942

Complements

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

NH ≅ G/Ntype
3. #19136017C2semidirect
4. #19135985C2semidirect
7. #19135360C2semidirect
9. #19135177C2semidirect
10. #19135169C2semidirect
11. #19134848C2semidirect
14. C4×#13063250C2semidirect
15. C43×#1942C2semidirect
299. #1942D43semidirect
358. C43#27035semidirect

Maximal subgroups

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

subgroupindex
#191390072
#191375992
#191360172
#191359852
#191358002
#191357942
#191353602
#191352012
#191351772
#191351692
#191348482
#191347812
#191346802
C4×#130632502
C43×#19422
#2703543