Finite Group Databasebeta

← #25146683

Subgroups — #25146683

Order 11008.

840 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583257C211yesmaximal, characteristic
2C2×#14583119C211yesmaximal, characteristic
3#19139805C211yesmaximal, characteristic, complemented
4#19137668C211yesmaximal, characteristic
5#19136005C211yesmaximal, characteristic, complemented
6#19136001C211yesmaximal, characteristic
7#19135917C211yesmaximal, characteristic, complemented
8#19135908C211yesmaximal, characteristic
9#19135545C211yesmaximal, characteristic, complemented
10#19135317C211yesmaximal, characteristic, complemented
11#19134933C211yesmaximal, characteristic, complemented
12#19134599C211yesmaximal, characteristic, complemented
13#19134595C211yesmaximal, characteristic
14#19134427C211yesmaximal, characteristic, complemented
15C43×#1877C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063312C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21#14583257—24no—
22#14583119—24no—
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33#14582820—21no—
34#14582820—21no—
35#14582806C2211yescharacteristic
36#14582805C2211yescharacteristic
37#14582802C2211yescharacteristic
38#14582796—21no—
39#14582796—21no—
40#14582793—21no—
41#14582787—21no—
42#14582772—21no—
43#14582769C2211yescharacteristic
44#14582768C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4×Dic43⋊C4C2211yescharacteristic
47C4×C22⋊Dic43—21no—
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C2×#10621885—22no—
64C2×#10621885—22no—
65C2×#10621885—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063324—22no—
69#13063324—22no—
70#13063312—22no—
71#13063312D414yes—
72Q8×Dic43—22no—
73Q8×Dic43—22no—
74#13063290—22no—
75#13063290—41no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4D411yescharacteristic
87C2×Dic43⋊C4D411yescharacteristic
88C2×C22⋊Dic43—21no—
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
97C4⋊(C43⋊C8)—41no—
98Dic43⋊C8—22no—
99Dic43⋊C8—41no—
100#13063250—22no—
101#13063250—22no—
102#13063249—22no—
103#13063248—22no—
104#13063246—22no—
105#13063246—22no—
106#13063235—22no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95D411yescharacteristic
113C43⋊#95D411yescharacteristic
114C22×Q8×C43C2311yescharacteristic
115C22×D4×C43C2311yescharacteristic
116C23×C4×C43—21no—
117C2×SD16×C43—22no—
118C2×SD16×C43—22no—
119C2×SD16×C43—41no—
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C4×D4×C43—22no—
123C4×D4×C43—41no—
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C42×C43C2311yescharacteristic
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×C43#4112yes—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43C2×D412yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—42no—
149C22×C4×C43—42no—
150C22×C4×C43—81no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
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#4112yes—
182C22⋊C4×C43—42no—
183C42×C43—21no—
184C42×C43—21no—
185C22⋊Dic43—24no—
186C22⋊Dic43—24no—
187C22⋊Dic43—42no—
188C22⋊Dic43—81no—
189#10621885—44no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—42no—
197C4⋊Dic43—81no—
198C4⋊Dic43—81no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—81no—
204Dic43⋊C4—81no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—42no—
208C4×Dic43—42no—
209C4×Dic43—81no—
210C4×Dic43C2×D412yes—
211C4×Dic43#4112yes—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C23×C43—22no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43C22×D411yescharacteristic
226Q8×C43—22no—
227Q8×C43—22no—
228Q8×C43—41no—
229Q8×C43—41no—
230D4×C43—22no—
231D4×C43—22no—
232D4×C43—41no—
233D4×C43—41no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
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×C43—41no—
248C2×C4×C43—84no—
249C2×C4×C43#13712yes—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C432−1+411yescharacteristic
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43#12112yes—
278C2×Dic43#12112yes—
279C2×Dic43#13712yes—
280Dic86—22no—
281Dic86—22no—
282Dic86—41no—
283Dic86—41no—
284Dic86—84no—
285C8×C43—41no—
286C8×C43—41no—
287C43⋊C8—41no—
288C43⋊C8—41no—
289#25336—431nomaximal, Sylow
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43C2×#12111yescharacteristic
298C22×C43#54611yescharacteristic
299C22×C43#54811yescharacteristic
300C22×C43C2×#13711yescharacteristic
301C22×C43C2×#13711yescharacteristic
302C22×C43#57611yescharacteristic
303C22×C43#57711yescharacteristic
304C4×C43—22no—
305C4×C43—42no—
306C4×C43—42no—
307C4×C43—41no—
308C4×C43—81no—
309C4×C43#52911yescharacteristic
310C4×C43#54211yescharacteristic
311C4×C43#54611yescharacteristic
312C4×C43#54711yescharacteristic
313Dic43—22no—
314Dic43—22no—
315Dic43—22no—
316Dic43—42no—
317Dic43—41no—
318Dic43—81no—
319Dic43—81no—
320Dic43—81no—
321C2×#489—431no—
322C2×#464—431no—
323#2567—431no—
324#2367—431no—
325#2072—431no—
326#2071—431no—
327#2056—431no—
328#2055—431no—
329#1988—431no—
330#1940—431no—
331#1878—431no—
332#1877D4311yescharacteristic
333#1803—431no—
334#1802—431no—
335#1763—431no—
336C2×C43—82no—
337C2×C43#242711yescharacteristic
338C2×C43#303911yescharacteristic
339C2×C43#304511yescharacteristic
340C2×C43#331411yescharacteristic
341C2×C43#331611yescharacteristic
342C2×C43#336911yescharacteristic
343C2×C43#337511yescharacteristic
344C22×Q16—431no—
345C22×SD16C2×D4311yescharacteristic
346C2×C4⋊Q8—431no—
347C2×#124—431no—
348C2×C4×Q8—431no—
349C2×C4×Q8—431no—
350C2×C4×D4C2×D4311yescharacteristic
351#489—864no—
352#464—864no—
353C2×C4⋊C8—431no—
354C2×C4⋊C8—431no—
355C2×C4⋊C8—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#103C2×D4311yescharacteristic
361C2×#102—431no—
362C2×#102—431no—
363C2×#102C2×D4311yescharacteristic
364C2×#97—431no—
365#395—861no—
366#395—861no—
367#391—431no—
368#391—431no—
369#391C2×D4311yescharacteristic
370#390—431no—
371#389—861no—
372#389—861no—
373#388—861no—
374#388—861no—
375#385—861no—
376#384—431no—
377#384—431no—
378C4×C4⋊C4—431no—
379C4×C4⋊C4—431no—
380C4×C22⋊C4—861no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340C2×D4311yescharacteristic
387#336—431no—
388#336C2×D4311yescharacteristic
389C43#2533611yescharacteristic, complemented, Sylow
390C22×Q8—431no—
391C22×Q8—861no—
392C22×Q8C22×D4311yescharacteristic
393C22×D4C22×D4311yescharacteristic
394C23×C4—21no—
395C2×Q16—862no—
396C2×Q16—862no—
397C2×Q16—1721no—
398C2×SD16—22no—
399C2×SD16—22no—
400C2×SD16—41no—
401C22×C8—431no—
402C22×C8—431no—
403C22×C8C22×D4311yescharacteristic
404C22×C8C22×D4311yescharacteristic
405C4⋊Q8—862no—
406C4⋊Q8—862no—
407#124—434no—
408#124—862no—
409C4×Q8—862no—
410C4×Q8—862no—
411C4×Q8—862no—
412C4×Q8—1721no—
413C4×D4—22no—
414C4×D4—41no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—861no—
437C2×C42—861no—
438C2×C42—861no—
439C2×C42C22×D4311yescharacteristic
440C4⋊C8—862no—
441C4⋊C8—1721no—
442C4⋊C8—1721no—
443#103—22no—
444#103—862no—
445#103—862no—
446#103—862no—
447#103—862no—
448#102—22no—
449#102—862no—
450#102—862no—
451#97—862no—
452#95—21no—
453#95—21no—
454#95—431no—
455#95—431no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461C24—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—432no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—3441no—
474C2×Q8—3441no—
475C2×Q8—1722no—
476C2×Q8#1062189812yes—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4D4×D4312yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—81no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4D4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499C22×C4C23×D4311yescharacteristic
500Q16—1724no—
501SD16—44no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—3441no—
526C4⋊C4—3441no—
527C4⋊C4—3441no—
528C4⋊C4—3441no—
529C4⋊C4—1722no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4#1062190012yes—
533C22⋊C4—42no—
534C22⋊C4—864no—
535C22⋊C4—864no—
536C22⋊C4—3441no—
537C22⋊C4—1722no—
538C42—21no—
539C42—21no—
540C42—432no—
541C42—432no—
542C42—861no—
543C42—861no—
544C42—3441no—
545C42—1722no—
546C42—1722no—
547C23—22no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23C2×D4×D4311yescharacteristic
555Q8—22no—
556Q8—22no—
557Q8—41no—
558Q8—41no—
559Q8—862no—
560Q8—862no—
561Q8—3444no—
562Q8—1721no—
563Q8—1721no—
564D4—22no—
565D4—22no—
566D4—41no—
567D4—41no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—84no—
583C2×C4—432no—
584C2×C4—432no—
585C2×C4—432no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—862no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
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×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4#1306335412yes—
608C2×C4C2×D4×D4311yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4C2×#1062190011yescharacteristic
611C2×C4C2×#1062189811yescharacteristic
612C2×C4#1306337011yescharacteristic
613C2×C4#1306337211yescharacteristic
614C8—41no—
615C8—41no—
616C8—1721no—
617C8—1721no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22#121×D4311yescharacteristic
626C22#1458353611yescharacteristic
627C22#1458355811yescharacteristic
628C22#137×D4311yescharacteristic
629C22C2×#1306335411yescharacteristic
630C22#1458370311yescharacteristic
631C22#1458370611yescharacteristic
632C4—22no—
633C4—42no—
634C4—42no—
635C4—41no—
636C4—81no—
637C4—862no—
638C4—862no—
639C4—862no—
640C4—3441no—
641C4—3441no—
642C4—3441no—
643C4—1722no—
644C4—1721no—
645C4#1458342911yescharacteristic
646C4#1458351711yescharacteristic
647C4#1458353911yescharacteristic
648C4#1458354911yescharacteristic
649C2—82no—
650C2#1913816911yescharacteristic
651C2#1914407711yescharacteristic
652C2#1914413511yescharacteristic
653C2#1914668011yescharacteristic
654C2#1914669911yescharacteristic
655C2#1914733311yescharacteristic
656C2#1914741011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1877C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1877D43
hypocenterC43#25336
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
3. #19139805C2semidirect
5. #19136005C2semidirect
7. #19135917C2semidirect
9. #19135545C2semidirect
10. #19135317C2semidirect
11. #19134933C2semidirect
12. #19134599C2semidirect
14. #19134427C2semidirect
389. C43#25336semidirect

Maximal subgroups

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

subgroupindex
C2×#145832572
C2×#145831192
#191398052
#191376682
#191360052
#191360012
#191359172
#191359082
#191355452
#191353172
#191349332
#191345992
#191345952
#191344272
C43×#18772
#2533643