Finite Group Databasebeta

← #25146444

Subgroups — #25146444

Order 11008.

838 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583248C211yesmaximal, characteristic, complemented
2C2×#14583102C211yesmaximal, characteristic
3#19139766C211yesmaximal, characteristic
4#19137652C211yesmaximal, characteristic, complemented
5#19136017C211yesmaximal, characteristic, complemented
6#19136013C211yesmaximal, characteristic, complemented
7#19135911C211yesmaximal, characteristic
8#19135541C211yesmaximal, characteristic, complemented
9#19135310C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic
11#19134952C211yesmaximal, characteristic
12#19134611C211yesmaximal, characteristic, complemented
13#19134608C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic
15C43×#2055C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063323C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22#14583248—24no—
23#14583102—24no—
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582811—21no—
34#14582811—21no—
35#14582804C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582796—21no—
38#14582786—21no—
39#14582781—21no—
40#14582765C2211yescharacteristic
41#14582764C2211yescharacteristic
42#14582757—21no—
43#14582757—21no—
44C4⋊C4×Dic43C2211yescharacteristic
45C4×Dic43⋊C4C2211yescharacteristic
46#14582750—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C2×#10621883—22no—
65C2×#10621883—22no—
66C2×#10621883—41no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063324—22no—
70#13063324—22no—
71#13063323—22no—
72#13063323D414yes—
73Q8×Dic43—22no—
74Q8×Dic43—41no—
75C4×Dic86—22no—
76C4×Dic86—41no—
77D4×Dic43—22no—
78D4×Dic43—22no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4D411yescharacteristic
88C2×Dic43⋊C4D411yescharacteristic
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97Dic43⋊C8—22no—
98Dic43⋊C8—41no—
99#13063250—22no—
100#13063250—22no—
101#13063249—22no—
102#13063249—22no—
103#13063248—22no—
104#13063246—22no—
105C8×Dic43—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95D411yescharacteristic
114C43⋊#95D411yescharacteristic
115C22×Q8×C43C2311yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C2×SD16×C43—22no—
118C2×SD16×C43—22no—
119C2×SD16×C43—41no—
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C42×C43C2311yescharacteristic
127C4⋊C8×C43—41no—
128#103×C43—22no—
129#102×C43—22no—
130#95×C43—21no—
131#95×C43—21no—
132C24×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43C2×D412yes—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43#4112yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—42no—
156C22×Dic43—42no—
157C22×Dic43—42no—
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—42no—
168C2×Dic86—81no—
169C2×Dic86—81no—
170C2×Dic86C2×D412yes—
171SD16×C43—44no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C22⋊C4×C43—81no—
183C22⋊C4×C43—81no—
184C42×C43—21no—
185C42×C43—21no—
186C22⋊Dic43—42no—
187C22⋊Dic43—81no—
188C22⋊Dic43—81no—
189#10621883—44no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—42no—
196C4⋊Dic43#4112yes—
197Dic43⋊C4—24no—
198Dic43⋊C4—24no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—42no—
206C4×Dic43—42no—
207C4×Dic43—42no—
208C4×Dic43C2×D412yes—
209C4×Dic43#4112yes—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C23×C43—22no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43C22×D411yescharacteristic
224Q8×C43—22no—
225Q8×C43—22no—
226Q8×C43—41no—
227Q8×C43—41no—
228D4×C43—22no—
229D4×C43—22no—
230D4×C43—41no—
231D4×C43—41no—
232C2×C4×C43—22no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43H(5,𝔽2)11yescharacteristic
252C2×C4×C432−1+411yescharacteristic
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—22no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—84no—
274C2×Dic43#12112yes—
275C2×Dic43#12112yes—
276C2×Dic43#13512yes—
277C2×Dic43#13712yes—
278Dic86—22no—
279Dic86—22no—
280Dic86—41no—
281Dic86—41no—
282Dic86—84no—
283C8×C43—41no—
284C8×C43—41no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287#25319—431nomaximal, Sylow
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43C2×#12111yescharacteristic
296C22×C43#54611yescharacteristic
297C22×C43#54811yescharacteristic
298C22×C43C2×#13511yescharacteristic
299C22×C43C2×#13711yescharacteristic
300C22×C43#57711yescharacteristic
301C22×C43#57711yescharacteristic
302C4×C43—41no—
303C4×C43—42no—
304C4×C43—41no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43#52911yescharacteristic
308C4×C43#54211yescharacteristic
309C4×C43#54611yescharacteristic
310C4×C43#54711yescharacteristic
311Dic43—22no—
312Dic43—41no—
313Dic43—42no—
314Dic43—41no—
315Dic43—42no—
316Dic43—81no—
317Dic43—81no—
318Dic43#46414yes—
319C2×#487—431no—
320C2×#461—431no—
321#2563—431no—
322#2365—431no—
323#2074—431no—
324#2074—431no—
325#2055—431no—
326#2055D4311yescharacteristic
327#1987—431no—
328#1939—431no—
329#1880—431no—
330#1880—431no—
331#1805—431no—
332#1805—431no—
333C4×#102—431no—
334C2×C43—82no—
335C2×C43#242711yescharacteristic
336C2×C43C2×#46411yescharacteristic
337C2×C43#304311yescharacteristic
338C2×C43#330311yescharacteristic
339C2×C43#332911yescharacteristic
340C2×C43#336011yescharacteristic
341C2×C43#337211yescharacteristic
342C22×SD16—431no—
343C22×SD16C2×D4311yescharacteristic
344C2×C4⋊Q8—431no—
345C2×C4⋊Q8—431no—
346C2×C4×Q8—431no—
347C2×C4×Q8—431no—
348C2×C4×D4—431no—
349#487—864no—
350#461—864no—
351C2×C4⋊C8—431no—
352C2×C4⋊C8—431no—
353C2×C4⋊C8C2×D4311yescharacteristic
354C2×#103—431no—
355C2×#103—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#103—431no—
359C2×#103C2×D4311yescharacteristic
360C2×#102—431no—
361C2×#102C2×D4311yescharacteristic
362C2×C4×C8—431no—
363#393—861no—
364#393—861no—
365#391—431no—
366#391C2×D4311yescharacteristic
367#390—431no—
368#390C2×D4311yescharacteristic
369#389—861no—
370#387—861no—
371#387—861no—
372#382—431no—
373#382—431no—
374#380—861no—
375#380—861no—
376C4×C4⋊C4—431no—
377C4×C4⋊C4—431no—
378C4×C4⋊C4—861no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340C2×D4311yescharacteristic
385#336—431no—
386#336—431no—
387C43#2531911yescharacteristic, complemented, Sylow
388C22×Q8—431no—
389C22×Q8—861no—
390C22×Q8C22×D4311yescharacteristic
391C22×D4C22×D4311yescharacteristic
392C23×C4—861no—
393C2×SD16—22no—
394C2×SD16—22no—
395C2×SD16—41no—
396C2×SD16—862no—
397C2×SD16—862no—
398C2×SD16—1721no—
399C22×C8—431no—
400C22×C8—431no—
401C22×C8C22×D4311yescharacteristic
402C22×C8C22×D4311yescharacteristic
403C4⋊Q8—434no—
404C4⋊Q8—862no—
405C4⋊Q8—862no—
406C4⋊Q8—862no—
407C4×Q8—862no—
408C4×Q8—862no—
409C4×Q8—1721no—
410C4×Q8—1721no—
411C4×D4—862no—
412C4×D4—862no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C42—431no—
431C2×C42—431no—
432C2×C42—861no—
433C2×C42—861no—
434C2×C42—861no—
435C2×C42C22×D4311yescharacteristic
436C4⋊C8—41no—
437C4⋊C8—862no—
438C4⋊C8—1721no—
439#103—22no—
440#103—862no—
441#103—862no—
442#103—862no—
443#103—862no—
444#103—862no—
445#102—22no—
446#102—862no—
447C4×C8—862no—
448#95—21no—
449#95—21no—
450#95—431no—
451#95—431no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459C24—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—432no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—3441no—
472C2×Q8—3441no—
473C2×Q8—1722no—
474C2×Q8D4×D4312yes—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4#1062190012yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4—1722no—
495C22×C4D4×D4311yescharacteristic
496C22×C4D4×D4311yescharacteristic
497C22×C4C23×D4311yescharacteristic
498SD16—44no—
499SD16—1724no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—432no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—864no—
520C4⋊C4—864no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—1722no—
527C4⋊C4—1722no—
528C4⋊C4—1722no—
529C22⋊C4—81no—
530C22⋊C4—81no—
531C22⋊C4—3441no—
532C22⋊C4—3441no—
533C22⋊C4—1722no—
534C42—21no—
535C42—21no—
536C42—432no—
537C42—432no—
538C42—861no—
539C42—861no—
540C42—1722no—
541C42—1722no—
542C42—1722no—
543C23—22no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23C2×D4×D4311yescharacteristic
551Q8—22no—
552Q8—22no—
553Q8—41no—
554Q8—41no—
555Q8—862no—
556Q8—862no—
557Q8—3444no—
558Q8—1721no—
559Q8—1721no—
560D4—22no—
561D4—22no—
562D4—41no—
563D4—41no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—432no—
580C2×C4—432no—
581C2×C4—432no—
582C2×C4—432no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—862no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—862no—
593C2×C4—3444no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4C2×D4×D4311yescharacteristic
605C2×C4#41×D4311yescharacteristic
606C2×C4#41×D4311yescharacteristic
607C2×C4C2×#1062190011yescharacteristic
608C2×C4#1306337011yescharacteristic
609C2×C4#1306337211yescharacteristic
610C8—41no—
611C8—41no—
612C8—1721no—
613C8—1721no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22#121×D4311yescharacteristic
622C22#1458353811yescharacteristic
623C22#1458355511yescharacteristic
624C22#135×D4311yescharacteristic
625C22#137×D4311yescharacteristic
626C22#1458370511yescharacteristic
627C22#1458370911yescharacteristic
628C4—41no—
629C4—42no—
630C4—41no—
631C4—81no—
632C4—81no—
633C4—434no—
634C4—862no—
635C4—3441no—
636C4—3441no—
637C4—1721no—
638C4—1722no—
639C4—1722no—
640C4—1721no—
641C4#1458342611yescharacteristic
642C4#1458351311yescharacteristic
643C4#1458353611yescharacteristic
644C4#1458354711yescharacteristic
645C2—82no—
646C2#1913816511yescharacteristic
647C2#464×D4311yescharacteristic
648C2#1914411111yescharacteristic
649C2#1914651811yescharacteristic
650C2#1914688411yescharacteristic
651C2#1914723911yescharacteristic
652C2#1914737111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2055C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2055D43
hypocenterC43#25319
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
1. C2×#14583248C2semidirect
4. #19137652C2semidirect
5. #19136017C2semidirect
6. #19136013C2semidirect
8. #19135541C2semidirect
9. #19135310C2semidirect
12. #19134611C2semidirect
13. #19134608C2semidirect
387. C43#25319semidirect

Maximal subgroups

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

subgroupindex
C2×#145832482
C2×#145831022
#191397662
#191376522
#191360172
#191360132
#191359112
#191355412
#191353102
#191349532
#191349522
#191346112
#191346082
#102×Dic432
C43×#20552
#2531943