Finite Group Databasebeta

← #25146949

Subgroups — #25146949

Order 11008.

840 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583183C211yesmaximal, characteristic, complemented
2C2×#14582967C211yesmaximal, characteristic
3#19139765C211yesmaximal, characteristic
4#19139506C211yesmaximal, characteristic
5#19136034C211yesmaximal, characteristic, complemented
6#19135799C211yesmaximal, characteristic, complemented
7#19135794C211yesmaximal, characteristic, complemented
8#19135566C211yesmaximal, characteristic, complemented
9#19135366C211yesmaximal, characteristic, complemented
10#19135027C211yesmaximal, characteristic, complemented
11#19135016C211yesmaximal, characteristic, complemented
12#19134625C211yesmaximal, characteristic, complemented
13#19134618C211yesmaximal, characteristic, complemented
14#19134424C211yesmaximal, characteristic, complemented
15C43×#2077C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18C2×#13063324C2211yescharacteristic
19C2×#13063305C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×C4×C22⋊D43C2211yescharacteristic
23#14583183—24no—
24#14582967—24no—
25C2×#13063259C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×#13063235C2211yescharacteristic
35#14582833—21no—
36#14582814—21no—
37#14582812—21no—
38#14582811—21no—
39#14582799—21no—
40#14582792—21no—
41#14582788—21no—
42#14582764C2211yescharacteristic
43#14582763—21no—
44#14582759C2211yescharacteristic
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47#14582756C2211yescharacteristic
48C4⋊C4×Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×C22⋊C8×C43C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C22×C22⋊D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C2×#10621872—22no—
66C2×#10621872—22no—
67C2×#10621872—41no—
68C22×C43⋊C8—22no—
69C22×C43⋊C8—22no—
70C22×C43⋊C8—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063324—22no—
74#13063324—22no—
75#13063305—22no—
76#13063305—41no—
77#13063304—22no—
78#13063304—41no—
79#13063290—22no—
80#13063290—22no—
81C4×C22⋊D43—22no—
82C4×C22⋊D43—22no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4D411yescharacteristic
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43D411yescharacteristic
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4D411yescharacteristic
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43C2311yescharacteristic
102#13063259—41no—
103#13063256—22no—
104#13063256—41no—
105Dic43⋊C8D414yes—
106#13063250—22no—
107#13063250—22no—
108#13063248—22no—
109#13063248—22no—
110(C2×D43)⋊C8—22no—
111#13063235—22no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C23×C4×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128#106×C43—22no—
129C22⋊C8×C43—22no—
130#95×C43—21no—
131#95×C43—21no—
132C24×C43C2×D411yescharacteristic
133C23×D43C2×D411yescharacteristic
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C2×C22⋊D43—22no—
147C2×C22⋊D43—22no—
148C2×C22⋊D43—41no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
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×Dic86#4112yes—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43C2×D412yes—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C22⋊C4×C43—42no—
186C22⋊C4×C43—81no—
187C22⋊Dic43—22no—
188C22⋊Dic43—42no—
189C22⋊Dic43—81no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—81no—
194(C2×D43)⋊C4—81no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—42no—
202Dic43⋊C4—22no—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205Dic43⋊C4—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—44no—
215C2×C43⋊C8C2×D412yes—
216C2×C43⋊C8#4112yes—
217#10621872—44no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43#13712yes—
225C23×C43C22×D411yescharacteristic
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
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×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C2×C4×C432−1+411yescharacteristic
258C22⋊D43—44no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—22no—
265C2×Dic43—21no—
266C2×Dic43—21no—
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—41no—
278C2×Dic43#12112yes—
279C2×Dic43#12112yes—
280C4×D43—41no—
281C4×D43—41no—
282C4×D43—41no—
283C4×D43—41no—
284Dic86—22no—
285Dic86—22no—
286Dic86—41no—
287Dic86—41no—
288Dic86—84no—
289C8×C43—22no—
290C8×C43—41no—
291C43⋊C8—22no—
292C43⋊C8—22no—
293#25356—431nomaximal, Sylow
294C22×C43—22no—
295C22×C43—22no—
296C22×C43—22no—
297C22×C43—41no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43C2×#12111yescharacteristic
302C22×C43#54611yescharacteristic
303C22×C43#54711yescharacteristic
304C22×C43C2×#13711yescharacteristic
305C22×C43#57511yescharacteristic
306C22×C43#57711yescharacteristic
307C22×C43#57711yescharacteristic
308C2×D43—41no—
309C2×D43—41no—
310C2×D43—41no—
311C2×D43—41no—
312C2×D43—41no—
313C2×D43—41no—
314C2×D43—41no—
315C4×C43—41no—
316C4×C43—81no—
317C4×C43—81no—
318C4×C43—81no—
319C4×C43—81no—
320C4×C43#52911yescharacteristic
321C4×C43#54211yescharacteristic
322C4×C43#54611yescharacteristic
323C4×C43#54811yescharacteristic
324Dic43—22no—
325Dic43—22no—
326Dic43—42no—
327Dic43—41no—
328Dic43—81no—
329Dic43—81no—
330Dic43—81no—
331C2×#475—431no—
332C2×#435—431no—
333#2563—431no—
334#2536—431no—
335#2077—431no—
336#2077D4311yescharacteristic, complemented
337#2036—431no—
338#2035—431no—
339#1993—431no—
340#1949—431no—
341#1894—431no—
342#1892—431no—
343#1809—431no—
344#1807—431no—
345#1763—431no—
346C2×C43—42no—
347C2×C43#242711yescharacteristic
348C2×C43#305611yescharacteristic
349C2×C43#305711yescharacteristic
350C2×C43#331611yescharacteristic
351C2×C43#332111yescharacteristic
352C2×C43#334411yescharacteristic
353C2×C43#334811yescharacteristic
354D43—81no—
355C22×M16—431no—
356C23×C8—431no—
357C2×C4⋊Q8—431no—
358C2×C22⋊Q8—431no—
359C2×C22⋊Q8—431no—
360C2×C4×Q8—431no—
361C2×C4×D4—431no—
362#475—864no—
363#435—864no—
364C2×#107—431no—
365C2×#106—431no—
366C2×#106—431no—
367C2×#106C2×D4311yescharacteristic
368C2×C4⋊C8—431no—
369C2×#103—431no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×C22⋊C8—431no—
374C2×C22⋊C8C2×D4311yescharacteristic
375C2×#97—431no—
376#398—861no—
377#394—861no—
378#393—861no—
379#393—861no—
380#390—861no—
381#388—861no—
382#388—861no—
383#382—431no—
384#382—861no—
385#380—431no—
386#380—431no—
387#380—431no—
388#380—431no—
389#380C2×D4311yescharacteristic
390#380C2×D4311yescharacteristic
391C4×C4⋊C4—431no—
392#340—431no—
393#340—431no—
394#340—431no—
395#340—431no—
396#340—431no—
397#340C2×D4311yescharacteristic
398#340C2×D4311yescharacteristic
399#340C2×D4311yescharacteristic
400C43#2535611yescharacteristic, complemented, Sylow
401C22×Q8—431no—
402C22×Q8—861no—
403C22×D4—431no—
404C23×C4—431no—
405C23×C4C22×D4311yescharacteristic
406C2×M16—862no—
407C2×M16—862no—
408C2×M16—1721no—
409C22×C8—431no—
410C22×C8—431no—
411C22×C8—862no—
412C22×C8—862no—
413C22×C8—1721no—
414C22×C8C22×D4311yescharacteristic
415C22×C8C22×D4311yescharacteristic
416C4⋊Q8—862no—
417C4⋊Q8—862no—
418C22⋊Q8—862no—
419C22⋊Q8—862no—
420C22⋊Q8—1721no—
421C22⋊Q8—1721no—
422C4×Q8—862no—
423C4×Q8—862no—
424C4×D4—862no—
425C4×D4—862no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4C22×D4311yescharacteristic
435C2×C4⋊C4C22×D4311yescharacteristic
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—431no—
441C2×C22⋊C4—431no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C42—431no—
449C2×C42—861no—
450C2×C42—861no—
451#107—1721no—
452#106—22no—
453#106—862no—
454#106—1721no—
455C4⋊C8—434no—
456#103—862no—
457#103—862no—
458#103—862no—
459#103—862no—
460C22⋊C8—22no—
461C22⋊C8—862no—
462#97—862no—
463#95—21no—
464#95—21no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472C24—431no—
473C24D4×D4311yescharacteristic
474C2×Q8—432no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—3441no—
481C2×Q8—3441no—
482C2×Q8—1722no—
483C2×D4—862no—
484C2×D4—862no—
485C2×D4—1721no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4D4×D4311yescharacteristic
510C22×C4C23×D4311yescharacteristic
511M16—1724no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—432no—
518C2×C8—432no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—1724no—
524C2×C8D4×D4312yes—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—862no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—1722no—
541C4⋊C4—1722no—
542C4⋊C4—1722no—
543C4⋊C4—1722no—
544C22⋊C4—42no—
545C22⋊C4—81no—
546C22⋊C4—862no—
547C22⋊C4—862no—
548C22⋊C4—3441no—
549C22⋊C4—3441no—
550C22⋊C4—3441no—
551C22⋊C4—1722no—
552C22⋊C4—1722no—
553C22⋊C4—1722no—
554C42—432no—
555C42—432no—
556C42—1722no—
557C42—1722no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—861no—
565C23—861no—
566C23—861no—
567C23—861no—
568C23—861no—
569C23—861no—
570C23—861no—
571C23#1306335412yes—
572C23C2×D4×D4311yescharacteristic
573Q8—862no—
574Q8—862no—
575Q8—3444no—
576Q8—1721no—
577Q8—1721no—
578D4—1724no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—432no—
599C2×C4—432no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—862no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4C2×D4×D4311yescharacteristic
624C2×C4#41×D4311yescharacteristic
625C2×C4#41×D4311yescharacteristic
626C2×C4#41×D4311yescharacteristic
627C2×C4#1306337111yescharacteristic
628C2×C4#1306337211yescharacteristic
629C8—22no—
630C8—41no—
631C8—862no—
632C8—862no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—1721no—
641C22—1721no—
642C22—1721no—
643C22—1721no—
644C22—1721no—
645C22—1721no—
646C22—1721no—
647C22#121×D4311yescharacteristic
648C22#1458354111yescharacteristic
649C22#1458354711yescharacteristic
650C22C2×#1306335411yescharacteristic
651C22#1458369611yescharacteristic
652C22#1458370811yescharacteristic
653C22#1458370911yescharacteristic
654C4—41no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4—862no—
660C4—862no—
661C4—3441no—
662C4—3441no—
663C4—3441no—
664C4—1721no—
665C4—1722no—
666C4#1458343211yescharacteristic
667C4#1458351511yescharacteristic
668C4#1458354111yescharacteristic
669C4#1458355711yescharacteristic
670C2—42no—
671C2—3441no—
672C2#1913816711yescharacteristic
673C2#1914421811yescharacteristic
674C2#1914423211yescharacteristic
675C2#1914670411yescharacteristic
676C2#1914677911yescharacteristic
677C2#1914705411yescharacteristic
678C2#1914710811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2077C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#2077D43
hypocenterC43#25356
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2077

Complements

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

NH ≅ G/Ntype
1. C2×#14583183C2semidirect
5. #19136034C2semidirect
6. #19135799C2semidirect
7. #19135794C2semidirect
8. #19135566C2semidirect
9. #19135366C2semidirect
10. #19135027C2semidirect
11. #19135016C2semidirect
12. #19134625C2semidirect
13. #19134618C2semidirect
14. #19134424C2semidirect
15. C43×#2077C2semidirect
336. #2077D43semidirect
400. C43#25356semidirect

Maximal subgroups

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

subgroupindex
C2×#145831832
C2×#145829672
#191397652
#191395062
#191360342
#191357992
#191357942
#191355662
#191353662
#191350272
#191350162
#191346252
#191346182
#191344242
C43×#20772
#2535643