Finite Group Databasebeta

← #25156701

Subgroups — #25156701

Order 11008.

904 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583103C211yesmaximal, characteristic
2C2×C4×#10621873C211yesmaximal, characteristic
3#19138372C211yesmaximal, characteristic, complemented
4#19137496C211yesmaximal, characteristic
5#19136136C211yesmaximal, characteristic, complemented
6#19136095C211yesmaximal, characteristic, complemented
7#19136007C211yesmaximal, characteristic, complemented
8#19135840C211yesmaximal, characteristic, complemented
9#19135152C211yesmaximal, characteristic, complemented
10#19134932C211yesmaximal, characteristic
11#19134930C211yesmaximal, characteristic
12#19134926C211yesmaximal, characteristic
13#19134862C211yesmaximal, characteristic, complemented
14#19134857C211yesmaximal, characteristic
15C43×#1933C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063323C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23C2×C4⋊C4×D43—21no—
24#14583103—24no—
25C4×#10621873—24no—
26C2×#13063257C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35#14582840—21no—
36#14582833—21no—
37#14582806C2211yescharacteristic
38#14582804C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582798C2211yescharacteristic
41#14582782—21no—
42#14582781—21no—
43#14582773—21no—
44#14582770—21no—
45#14582768C2211yescharacteristic
46#14582758—21no—
47C4×Dic43⋊C4C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C2×#10621873—22no—
67C2×#10621873—22no—
68C2×#10621873D414yes—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C2×#10621884—22no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063323—22no—
75#13063323—41no—
76C4×Dic86—22no—
77C4×Dic86—41no—
78C4×D172—22no—
79C4×D172—41no—
80#13063287—22no—
81#13063287—22no—
82#13063287—22no—
83#13063287—41no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4D411yescharacteristic
94C2×Dic43⋊C4D411yescharacteristic
95C4⋊C4×D43—44no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102#13063257—22no—
103#13063256—41no—
104Dic43⋊C8—22no—
105#13063250—22no—
106#13063249—41no—
107#13063248—22no—
108#13063248—22no—
109#13063247—22no—
110#13063245—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95D411yescharacteristic
118C43⋊#95D411yescharacteristic
119C22×Q8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127#103×C43—22no—
128#103×C43—22no—
129C4×C8×C43—22no—
130#95×C43—21no—
131#95×C43—21no—
132#95×C43—21no—
133C23×D43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172C2×D412yes—
158C2×D172#4112yes—
159C2×D172#4112yes—
160C2×C4×D43—24no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×C4×D43—81no—
168C2×C4×D43—81no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86C2×D412yes—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43C2×D412yes—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—42no—
187C4⋊C4×C43#4112yes—
188C42×C43—21no—
189C42×C43—21no—
190#10621884—44no—
191(C2×D43)⋊C4—24no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—42no—
199C4⋊Dic43—42no—
200Dic43⋊C4—41no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205Dic43⋊C4—81no—
206Dic43⋊C4SD1614yescomplemented
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—42no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218#10621873—28no—
219C23×C43C22×D411yescharacteristic
220C22×D43—22no—
221C22×D43—22no—
222C22×D43—22no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43—41no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
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×C43—41no—
248C2×C4×C43C2×SD1612yes—
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C432−1+411yescharacteristic
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—22no—
262C2×Dic43—21no—
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×Dic43C2×SD1612yes—
275C2×Dic43C2×SD1612yes—
276D172—22no—
277D172—22no—
278D172—22no—
279D172#12314yes—
280C4×D43—48no—
281C4×D43—84no—
282C4×D43—84no—
283Dic86—22no—
284Dic86—22no—
285Dic86—41no—
286Dic86—41no—
287C8×C43—22no—
288C8×C43—41no—
289C43⋊C8—41no—
290C43⋊C8—41no—
291#26166—431nomaximal, Sylow
292C22×C43#52511yescharacteristic
293C22×C43D4211yescharacteristic
294C22×C43#54811yescharacteristic
295C22×C43C22×SD1611yescharacteristic
296C22×C43#57511yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57811yescharacteristic
299C2×D43—24no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C4×C43—22no—
307C4×C43—42no—
308C4×C43—41no—
309C4×C43—81no—
310C4×C43—81no—
311C4×C43—81no—
312C4×C43C2×#12311yescharacteristic
313C4×C43#53911yescharacteristic
314C4×C43#54711yescharacteristic
315C4×C43#55311yescharacteristic
316Dic43—22no—
317Dic43—22no—
318Dic43—41no—
319Dic43—42no—
320Dic43—41no—
321Dic43—81no—
322Dic43—81no—
323C2×#461—431no—
324C2×C4×SD16—431no—
325#2446—431no—
326D4×C4⋊C4—431no—
327#2096—431no—
328#2088—431no—
329#2072—431no—
330#2043—431no—
331#1933D4311yescharacteristic, complemented
332#1916—431no—
333#1877—431no—
334#1877—431no—
335#1877—431no—
336#1865—431no—
337#1864—431no—
338C2×C43#244311yescharacteristic
339C2×C43#310111yescharacteristic
340C2×C43#312011yescharacteristic
341C2×C43#326911yescharacteristic
342C2×C43D4×SD1611yescharacteristic
343C2×C43#335911yescharacteristic
344C2×C43#337611yescharacteristic
345D43—44no—
346C22×SD16—431no—
347C22×SD16—431no—
348C2×C4⋊Q8—431no—
349C2×C4×Q8—431no—
350C2×C4×D4—431no—
351C2×C4×D4—431no—
352C2×C4×D4—431no—
353C22×C4⋊C4—861no—
354#461—864no—
355C4×SD16—864no—
356C2×#106—431no—
357C2×#106—431no—
358C2×C4⋊C8—431no—
359C2×#103—431no—
360C2×#103—431no—
361C2×#103—431no—
362C2×#103—431no—
363C2×#103C2×D4311yescharacteristic
364C2×#103C2×D4311yescharacteristic
365C2×#102—431no—
366C2×#102—431no—
367C2×C4×C8C2×D4311yescharacteristic
368#400—861no—
369#398—861no—
370#391—431no—
371#391—431no—
372#391C2×D4311yescharacteristic
373#389—431no—
374#389—431no—
375#389C2×D4311yescharacteristic
376#387—861no—
377#387—861no—
378#385—861no—
379#385—861no—
380#384—431no—
381#380—861no—
382C4×C4⋊C4—431no—
383#340—431no—
384#340—431no—
385#340C2×D4311yescharacteristic
386#340C2×D4311yescharacteristic
387#336—431no—
388#336—431no—
389#336—431no—
390#336—431no—
391C43#2616611yescharacteristic, complemented, Sylow
392C22×Q8—431no—
393C22×Q8C22×D4311yescharacteristic
394C22×D4—431no—
395C23×C4—861no—
396C23×C4—861no—
397C23×C4—861no—
398C2×SD16—434no—
399C2×SD16—862no—
400C2×SD16—862no—
401C2×SD16—862no—
402C2×SD16—862no—
403C2×SD16—862no—
404C22×C8—431no—
405C22×C8—431no—
406C22×C8C22×D4311yescharacteristic
407C22×C8C22×D4311yescharacteristic
408C4⋊Q8—862no—
409C4⋊Q8—1721no—
410C4×Q8—862no—
411C4×Q8—1721no—
412C4×D4—862no—
413C4×D4—862no—
414C4×D4—862no—
415C4×D4—862no—
416C4×D4—1721no—
417C4×D4—1721no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—1724no—
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—861no—
440C2×C42C22×D4311yescharacteristic
441#106—862no—
442#106—1721no—
443C4⋊C8—862no—
444#103—22no—
445#103—22no—
446#103—862no—
447#103—862no—
448#103—862no—
449#103—1721no—
450#102—862no—
451#102—862no—
452C4×C8—22no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—431no—
457#95—431no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464C24—861no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—432no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×D4—432no—
478C2×D4—432no—
479C2×D4—432no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—864no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—3441no—
496C22×C4—3441no—
497C22×C4—1722no—
498C22×C4—1722no—
499C22×C4—1722no—
500C22×C4—1722no—
501C22×C4—1722no—
502C22×C4—1722no—
503C22×C4D4×D4311yescharacteristic
504C22×C4D4×D4311yescharacteristic
505C22×C4C23×D4311yescharacteristic
506SD16—868no—
507SD16—1724no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8D4×D4312yes—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—434no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—3441no—
532C4⋊C4—1721no—
533C4⋊C4—1722no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4—1722no—
539C4⋊C4#1062189812yes—
540C22⋊C4—864no—
541C22⋊C4—1722no—
542C22⋊C4—1722no—
543C42—21no—
544C42—21no—
545C42—861no—
546C42—861no—
547C42—861no—
548C42—861no—
549C42—1722no—
550C23—862no—
551C23—862no—
552C23—862no—
553C23—1721no—
554C23—1721no—
555C23—1721no—
556C23—1721no—
557C23C2×D4×D4311yescharacteristic
558Q8—41no—
559Q8—41no—
560Q8—41no—
561Q8—41no—
562Q8—862no—
563Q8—862no—
564Q8—1721no—
565Q8—1721no—
566D4—434no—
567D4—862no—
568D4—862no—
569D4—862no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—432no—
588C2×C4—432no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—862no—
600C2×C4—3444no—
601C2×C4—3444no—
602C2×C4—1728no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4SD16×D4312yes—
612C2×C4C2×D4×D4311yescharacteristic
613C2×C4#41×D4311yescharacteristic
614C2×C4#41×D4311yescharacteristic
615C2×C4C2×#1062189811yescharacteristic
616C2×C4#1306337111yescharacteristic
617C2×C4#1306337211yescharacteristic
618C8—22no—
619C8—41no—
620C8—1721no—
621C8—1721no—
622C22—864no—
623C22—1722no—
624C22—1722no—
625C22—1722no—
626C22—1722no—
627C22—1722no—
628C22—1722no—
629C22#1458340811yescharacteristic
630C22#1458353311yescharacteristic
631C22#1458355711yescharacteristic
632C22C2×SD16×D4311yescharacteristic
633C22#1458369611yescharacteristic
634C22#1458370611yescharacteristic
635C22#1458371211yescharacteristic
636C4—22no—
637C4—42no—
638C4—41no—
639C4—81no—
640C4—81no—
641C4—81no—
642C4—862no—
643C4—862no—
644C4—3441no—
645C4—3441no—
646C4—1722no—
647C4—1721no—
648C4—1721no—
649C4#123×D4311yescharacteristic
650C4#1458349011yescharacteristic
651C4#1458355411yescharacteristic
652C4#1458359311yescharacteristic
653C2—1724no—
654C2#1913833711yescharacteristic
655C2#1914460111yescharacteristic
656C2#1914481511yescharacteristic
657C2#1914614711yescharacteristic
658C2#1914628811yescharacteristic
659C2#1914723411yescharacteristic
660C2#1914742811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1933C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1933D43
hypocenterC43#26166
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1933

Complements

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

NH ≅ G/Ntype
3. #19138372C2semidirect
5. #19136136C2semidirect
6. #19136095C2semidirect
7. #19136007C2semidirect
8. #19135840C2semidirect
9. #19135152C2semidirect
13. #19134862C2semidirect
15. C43×#1933C2semidirect
206. Dic43⋊C4SD16semidirect
331. #1933D43semidirect
391. C43#26166semidirect

Maximal subgroups

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

subgroupindex
C2×#145831032
C2×C4×#106218732
#191383722
#191374962
#191361362
#191360952
#191360072
#191358402
#191351522
#191349322
#191349302
#191349262
#191348622
#191348572
C43×#19332
#2616643