Finite Group Databasebeta

← #25135478

Subgroups — #25135478

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583037C211yesmaximal, characteristic
2C2×#14582957C211yesmaximal, characteristic, complemented
3#19140385C211yesmaximal, characteristic
4#19137179C211yesmaximal, characteristic, complemented
5#19135991C211yesmaximal, characteristic, complemented
6#19135977C211yesmaximal, characteristic, complemented
7#19135911C211yesmaximal, characteristic, complemented
8#19135911C211yesmaximal, characteristic, complemented
9#19135477C211yesmaximal, characteristic, complemented
10#19135450C211yesmaximal, characteristic, complemented
11#19135283C211yesmaximal, characteristic, complemented
12#19135269C211yesmaximal, characteristic, complemented
13#19134794C211yesmaximal, characteristic, complemented
14#19134531C211yesmaximal, characteristic, complemented
15C43×#1875C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20#14583037—24no—
21#14582957—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×#13063235C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35#14582835—21no—
36#14582824—21no—
37#14582813—21no—
38#14582813—21no—
39#14582805—21no—
40#14582805—21no—
41#14582804C2211yescharacteristic
42#14582804C2211yescharacteristic
43#14582804C2211yescharacteristic
44#14582804C2211yescharacteristic
45#14582802C2211yescharacteristic
46#14582802C2211yescharacteristic
47#14582795C2211yescharacteristic
48#14582795C2211yescharacteristic
49#14582760—21no—
50#14582760—21no—
51#14582759C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×#121×C43C2211yescharacteristic
55C2×#117×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86—22no—
63C22×Dic86—22no—
64C22×Dic86—22no—
65C22×Dic86—22no—
66C22×Dic86—41no—
67C22×Dic86—41no—
68C22×Dic86C2311yescharacteristic
69C22×Dic86C2311yescharacteristic
70C23×Dic43—21no—
71C2×#10621883—22no—
72C2×#10621883—22no—
73C2×#10621883—22no—
74C2×#10621883—22no—
75C2×#10621883—41no—
76C2×#10621883—41no—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063284—22no—
80#13063284—22no—
81C2×C4⋊Dic43D411yescharacteristic
82C2×C4⋊Dic43D411yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43D411yescharacteristic
93C2×C22⋊Dic43D411yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96#13063258—41no—
97#13063256—41no—
98Dic43⋊C8—22no—
99Dic43⋊C8—22no—
100#13063250—22no—
101#13063250—22no—
102#13063250—41no—
103#13063250—41no—
104#13063248—22no—
105#13063248—22no—
106C22⋊(C43⋊C8)D414yes—
107#13063235—22no—
108C8×Dic43—22no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C22×D4×C43—21no—
121C22×D4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125#121×C43—22no—
126#121×C43—22no—
127#117×C43—41no—
128#117×C43—41no—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C42×C43—21no—
135#102×C43—41no—
136#102×C43—41no—
137C22⋊C8×C43—22no—
138C24×C43—21no—
139C24×C43C2×D411yescharacteristic
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—42no—
147C2×D4×C43—81no—
148C2×D4×C43—81no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43C2×D412yes—
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43#4112yes—
159C22×C4×C43C2411yescharacteristic
160C22×Dic43—24no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—42no—
166C22×Dic43—42no—
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—24no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—44no—
183C2×Dic86—44no—
184C2×Dic86—44no—
185C2×Dic86—44no—
186C2×Dic86—42no—
187C2×Dic86—42no—
188C2×Dic86#4112yes—
189C2×Dic86#4112yes—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C22⋊C4×C43—42no—
203C22⋊C4×C43—42no—
204C42×C43—42no—
205C22⋊Dic43—22no—
206C22⋊Dic43—22no—
207C22⋊Dic43—81no—
208C22⋊Dic43—81no—
209C22⋊Dic43—81no—
210C22⋊Dic43—81no—
211C22⋊Dic43—81no—
212#10621883—44no—
213#10621883—44no—
214C4⋊Dic43—22no—
215C4⋊Dic43—22no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220Dic43⋊C4—81no—
221Dic43⋊C4—81no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8C2×D412yes—
231C2×C43⋊C8C2×D412yes—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43#12112yes—
246C23×C43C22×D411yescharacteristic
247D4×C43—41no—
248D4×C43—41no—
249D4×C43—41no—
250D4×C43—41no—
251D4×C43—84no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—22no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—22no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43#12112yes—
268C2×C4×C43C22×D411yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C43H(5,𝔽2)11yescharacteristic
273C2×C4×C43H(5,𝔽2)11yescharacteristic
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—22no—
279C2×Dic43—22no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—48no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299Dic86—22no—
300Dic86—22no—
301Dic86—22no—
302Dic86—22no—
303Dic86—48no—
304Dic86—41no—
305Dic86—41no—
306Dic86—41no—
307Dic86—41no—
308C8×C43—41no—
309C8×C43—41no—
310C43⋊C8—22no—
311C43⋊C8—22no—
312#24518—431nomaximal, Sylow
313C22×C43—22no—
314C22×C43—22no—
315C22×C43—22no—
316C22×C43—41no—
317C22×C43—41no—
318C22×C43—41no—
319C22×C43—41no—
320C22×C43—81no—
321C22×C43—81no—
322C22×C43—81no—
323C22×C43—81no—
324C22×C43—81no—
325C22×C43—81no—
326C22×C43—81no—
327C22×C43C2×#12111yescharacteristic
328C22×C43#52511yescharacteristic
329C22×C43#53511yescharacteristic
330C22×C43#57711yescharacteristic
331C22×C43#57711yescharacteristic
332C22×C43#57711yescharacteristic
333C22×C43#57811yescharacteristic
334C4×C43—22no—
335C4×C43—81no—
336C4×C43—81no—
337C4×C43—81no—
338C4×C43#54611yescharacteristic
339C4×C43#54611yescharacteristic
340C4×C43#55111yescharacteristic
341C4×C43#55111yescharacteristic
342Dic43—42no—
343Dic43—42no—
344Dic43—41no—
345Dic43—41no—
346Dic43—41no—
347Dic43—41no—
348Dic43—81no—
349Dic43—81no—
350C2×#448—431no—
351C2×#433—431no—
352#2624—431no—
353#2310—431no—
354#2068—431no—
355#2066—431no—
356#2055—431no—
357#2055—431no—
358#1973—431no—
359#1968—431no—
360#1935—431no—
361#1933—431no—
362#1875D4311yescharacteristic
363#1854—431no—
364#1787—431no—
365C2×C43—42no—
366C2×C43—161no—
367C2×C43#241111yescharacteristic
368C2×C43#305711yescharacteristic
369C2×C43#306311yescharacteristic
370C2×C43#312111yescharacteristic
371C2×C43#312611yescharacteristic
372C2×C43#322111yescharacteristic
373C2×C43#322511yescharacteristic
374C23×Q8—431no—
375C22×SD16—431no—
376C22×SD16—431no—
377C2×#121C2×D4311yescharacteristic
378C2×#117—431no—
379C2×#117C2×D4311yescharacteristic
380#448—864no—
381#433—864no—
382C2×#107—431no—
383C2×#106—431no—
384C2×C4⋊C8—431no—
385C2×C4⋊C8—431no—
386C2×#103—431no—
387C2×#103—431no—
388C2×#103—431no—
389C2×#103—431no—
390C2×#103—431no—
391C2×#103—431no—
392C2×#102C2×D4311yescharacteristic
393C2×#102C2×D4311yescharacteristic
394C2×C22⋊C8—431no—
395C2×C22⋊C8C2×D4311yescharacteristic
396C2×#97—431no—
397C2×C4×C8—431no—
398#399—861no—
399#397—861no—
400#394—861no—
401#394—861no—
402#391—431no—
403#391—431no—
404#391—431no—
405#391—431no—
406#391—861no—
407#391—861no—
408#390—431no—
409#390—431no—
410#389—431no—
411#389—431no—
412#381—861no—
413#381—861no—
414#380—431no—
415#340—431no—
416#340—431no—
417#340C2×D4311yescharacteristic
418#340C2×D4311yescharacteristic
419C43#2451811yescharacteristic, complemented, Sylow
420C22×Q8—431no—
421C22×Q8—431no—
422C22×Q8—862no—
423C22×Q8—862no—
424C22×Q8—861no—
425C22×Q8—862no—
426C22×Q8—862no—
427C22×Q8—1721no—
428C22×Q8—1721no—
429C22×D4—21no—
430C22×D4C22×D4311yescharacteristic
431C23×C4—861no—
432C23×C4C22×D4311yescharacteristic
433C2×SD16—862no—
434C2×SD16—862no—
435C2×SD16—862no—
436C2×SD16—862no—
437C2×SD16—1721no—
438C2×SD16—1721no—
439C22×C8—431no—
440C22×C8—431no—
441C22×C8C22×D4311yescharacteristic
442C22×C8C22×D4311yescharacteristic
443#121—22no—
444#121—22no—
445#117—41no—
446#117—41no—
447#117—862no—
448#117—862no—
449C2×C4⋊C4—431no—
450C2×C4⋊C4—431no—
451C2×C4⋊C4—431no—
452C2×C4⋊C4—431no—
453C2×C4⋊C4—861no—
454C2×C4⋊C4—861no—
455C2×C4⋊C4C22×D4311yescharacteristic
456C2×C4⋊C4C22×D4311yescharacteristic
457C2×C4⋊C4C22×D4311yescharacteristic
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—431no—
461C2×C22⋊C4—431no—
462C2×C22⋊C4—861no—
463C2×C22⋊C4—861no—
464C2×C22⋊C4—861no—
465C2×C22⋊C4—861no—
466C2×C22⋊C4—861no—
467C2×C42—21no—
468C2×C42—431no—
469C2×C42—431no—
470#107—1721no—
471#106—1721no—
472C4⋊C8—862no—
473C4⋊C8—862no—
474#103—862no—
475#103—862no—
476#103—862no—
477#103—862no—
478#103—1721no—
479#103—1721no—
480#102—41no—
481#102—41no—
482C22⋊C8—22no—
483C22⋊C8—434no—
484#97—862no—
485C4×C8—862no—
486#95—861no—
487#95—861no—
488#95—861no—
489#95—861no—
490#95—861no—
491#95—861no—
492#95—861no—
493#95—861no—
494#95—861no—
495#95—861no—
496#95—861no—
497C24—21no—
498C24D4×D4311yescharacteristic
499C2×Q8—432no—
500C2×Q8—432no—
501C2×Q8—864no—
502C2×Q8—861no—
503C2×Q8—861no—
504C2×Q8—861no—
505C2×Q8—861no—
506C2×Q8—861no—
507C2×Q8—861no—
508C2×Q8—861no—
509C2×Q8—861no—
510C2×Q8—861no—
511C2×Q8—861no—
512C2×Q8—1724no—
513C2×Q8—1724no—
514C2×Q8—1724no—
515C2×Q8—1724no—
516C2×Q8—1722no—
517C2×Q8—1722no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—42no—
525C2×D4—81no—
526C2×D4—81no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—431no—
535C22×C4—431no—
536C22×C4—431no—
537C22×C4—431no—
538C22×C4—864no—
539C22×C4—861no—
540C22×C4—861no—
541C22×C4—861no—
542C22×C4—861no—
543C22×C4—1722no—
544C22×C4—1722no—
545C22×C4#1062189812yes—
546C22×C4D4×D4311yescharacteristic
547C22×C4D4×D4312yes—
548C22×C4C23×D4311yescharacteristic
549SD16—1724no—
550SD16—1724no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—432no—
558C2×C8—432no—
559C2×C8—861no—
560C2×C8—861no—
561C2×C8—861no—
562C2×C8—861no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—862no—
570C4⋊C4—862no—
571C4⋊C4—861no—
572C4⋊C4—861no—
573C4⋊C4—861no—
574C4⋊C4—861no—
575C4⋊C4—3441no—
576C4⋊C4—3441no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—862no—
580C22⋊C4—862no—
581C22⋊C4—3441no—
582C22⋊C4—3441no—
583C22⋊C4—3441no—
584C22⋊C4—3441no—
585C22⋊C4—3441no—
586C42—42no—
587C42—861no—
588C42—861no—
589C42—861no—
590C42—861no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23#1306329812yes—
605C23C2×D4×D4311yescharacteristic
606Q8—862no—
607Q8—862no—
608Q8—862no—
609Q8—862no—
610Q8—1728no—
611Q8—1721no—
612Q8—1721no—
613Q8—1721no—
614Q8—1721no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—84no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—861no—
636C2×C4—861no—
637C2×C4—861no—
638C2×C4—861no—
639C2×C4—862no—
640C2×C4—862no—
641C2×C4—861no—
642C2×C4—861no—
643C2×C4—861no—
644C2×C4—861no—
645C2×C4—861no—
646C2×C4—861no—
647C2×C4—861no—
648C2×C4—861no—
649C2×C4—1721no—
650C2×C4—1721no—
651C2×C4—1721no—
652C2×C4—1721no—
653C2×C4—1721no—
654C2×C4—1721no—
655C2×C4—1728no—
656C2×C4—1721no—
657C2×C4—1721no—
658C2×C4—1721no—
659C2×C4—1721no—
660C2×C4#1306329812yes—
661C2×C4C2×D4×D4311yescharacteristic
662C2×C4#41×D4311yescharacteristic
663C2×C4#41×D4311yescharacteristic
664C2×C4C2×#1062189811yescharacteristic
665C2×C4#1306337011yescharacteristic
666C2×C4#1306337011yescharacteristic
667C8—41no—
668C8—41no—
669C8—862no—
670C8—862no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22C2×#1306329811yescharacteristic
686C22#1458340711yescharacteristic
687C22#1458346411yescharacteristic
688C22#1458370611yescharacteristic
689C22#1458370911yescharacteristic
690C22#1458370911yescharacteristic
691C22#1458371311yescharacteristic
692C4—22no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4—3441no—
697C4—3441no—
698C4—1721no—
699C4—1721no—
700C4—1721no—
701C4—1721no—
702C4—1722no—
703C4—1722no—
704C4#1458353811yescharacteristic
705C4#1458353811yescharacteristic
706C4#1458357811yescharacteristic
707C4#1458357811yescharacteristic
708C2—42no—
709C2—161no—
710C2#1913798311yescharacteristic
711C2#1914423311yescharacteristic
712C2#1914428911yescharacteristic
713C2#1914481911yescharacteristic
714C2#1914488211yescharacteristic
715C2#1914565411yescharacteristic
716C2#1914570011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1875C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#1875D43
hypocenterC43#24518
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
2. C2×#14582957C2semidirect
4. #19137179C2semidirect
5. #19135991C2semidirect
6. #19135977C2semidirect
7. #19135911C2semidirect
8. #19135911C2semidirect
9. #19135477C2semidirect
10. #19135450C2semidirect
11. #19135283C2semidirect
12. #19135269C2semidirect
13. #19134794C2semidirect
14. #19134531C2semidirect
419. C43#24518semidirect

Maximal subgroups

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

subgroupindex
C2×#145830372
C2×#145829572
#191403852
#191371792
#191359912
#191359772
#191359112
#191354772
#191354502
#191352832
#191352692
#191347942
#191345312
C43×#18752
#2451843