Finite Group Databasebeta

← #25146682

Subgroups — #25146682

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×#14583258C211yesmaximal, characteristic
2#19139800C211yesmaximal, characteristic, complemented
3#19137670C211yesmaximal, characteristic
4#19136006C211yesmaximal, characteristic, complemented
5#19136001C211yesmaximal, characteristic
6#19135915C211yesmaximal, characteristic, complemented
7#19135908C211yesmaximal, characteristic
8#19135546C211yesmaximal, characteristic, complemented
9#19135316C211yesmaximal, characteristic, complemented
10#19134938C211yesmaximal, characteristic, complemented
11#19134931C211yesmaximal, characteristic
12#19134598C211yesmaximal, characteristic, complemented
13#19134593C211yesmaximal, characteristic
14#19134425C211yesmaximal, characteristic, complemented
15C2×C43×#464C211yesmaximal, characteristic
16C2×#13063325C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19#14583258—24no—
20C2×Dic43⋊C8C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063236C2211yescharacteristic
29#14582819—21no—
30#14582819—21no—
31#14582806C2211yescharacteristic
32#14582806C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582797—21no—
36#14582797—21no—
37#14582792—21no—
38#14582792—21no—
39#14582774—21no—
40#14582768C2211yescharacteristic
41#14582768C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C22⋊C4×Dic43—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×Q16×C43C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×#124×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C43×#464—24no—
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C22×Dic86—21no—
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063325—22no—
66#13063325—22no—
67Q8×Dic43—22no—
68Q8×Dic43—41no—
69D4×Dic43—22no—
70D4×Dic43—41no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43D411yescharacteristic
74C2×C4⋊Dic43D411yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90Dic43⋊C8—41no—
91Dic43⋊C8—41no—
92#13063249—22no—
93#13063249—22no—
94#13063249—22no—
95#13063249—22no—
96#13063246—22no—
97#13063246—22no—
98#13063236—22no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×Q8×C43C2311yescharacteristic
109C22×Q8×C43C2311yescharacteristic
110C22×D4×C43C2311yescharacteristic
111C2×Q16×C43—22no—
112C2×Q16×C43—22no—
113C2×Q16×C43—41no—
114C2×SD16×C43—22no—
115C2×SD16×C43—22no—
116C2×SD16×C43—41no—
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119#124×C43—22no—
120#124×C43D414yes—
121C4×Q8×C43—22no—
122C4×Q8×C43—22no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C42×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—22no—
130#103×C43—22no—
131#102×C43—22no—
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—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43C2×D412yes—
144C2×Q8×C43#4112yes—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×D412yes—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—42no—
162C22×Dic43—42no—
163C22×Dic43—81no—
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C2×Dic86—42no—
169C2×Dic86—81no—
170C2×Dic86—81no—
171Q16×C43—44no—
172SD16×C43—44no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—42no—
182C22⋊C4×C43—24no—
183C22⋊C4×C43—24no—
184C42×C43—42no—
185C42×C43C2×D412yes—
186C42×C43#4112yes—
187C22⋊Dic43—42no—
188C22⋊Dic43—42no—
189C22⋊Dic43—81no—
190C4⋊Dic43—21no—
191C4⋊Dic43—22no—
192C4⋊Dic43—22no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—42no—
200C4⋊Dic43—42no—
201C4⋊Dic43#4112yes—
202Dic43⋊C4—81no—
203Dic43⋊C4—81no—
204Dic43⋊C4—81no—
205Dic43⋊C4—81no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—42no—
211C4×Dic43—81no—
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—22no—
229Q8×C43—22no—
230Q8×C43—41no—
231Q8×C43—41no—
232Q8×C43—41no—
233Q8×C43—41no—
234D4×C43—22no—
235D4×C43—22no—
236D4×C43—41no—
237D4×C43—41no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
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#12112yes—
252C2×C4×C43#12112yes—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×C4×C432−1+411yescharacteristic
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—22no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
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—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—84no—
282C2×Dic43#13712yes—
283C2×Dic43#13712yes—
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—22no—
306C4×C43—42no—
307C4×C43—42no—
308C4×C43—81no—
309C4×C43#52911yescharacteristic
310C4×C43#54211yescharacteristic
311C4×C43#54611yescharacteristic
312C4×C43#54711yescharacteristic
313Dic43—22no—
314Dic43—22no—
315Dic43—41no—
316Dic43—42no—
317Dic43—41no—
318Dic43—81no—
319Dic43—81no—
320Dic43—81no—
321C2×#489—431no—
322C2×#464D4311yescharacteristic
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#1877—431no—
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×Q16C2×D4311yescharacteristic
345C22×SD16C2×D4311yescharacteristic
346C2×C4⋊Q8—431no—
347C2×#124C2×D4311yescharacteristic
348C2×C4×Q8—431no—
349C2×C4×Q8C2×D4311yescharacteristic
350C2×C4×D4—431no—
351#489—864no—
352#464—24no—
353C2×C4⋊C8—431no—
354C2×C4⋊C8—431no—
355C2×C4⋊C8C2×D4311yescharacteristic
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#391—431no—
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#340—431no—
387#336—431no—
388#336—431no—
389C43#2533611yescharacteristic, complemented, Sylow
390C22×Q8—861no—
391C22×Q8C22×D4311yescharacteristic
392C22×Q8C22×D4311yescharacteristic
393C22×D4C22×D4311yescharacteristic
394C23×C4—861no—
395C2×Q16—22no—
396C2×Q16—22no—
397C2×Q16—41no—
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—22no—
408#124C22⋊D4314yes—
409C4×Q8—22no—
410C4×Q8—22no—
411C4×Q8—862no—
412C4×Q8—1721no—
413C4×D4—862no—
414C4×D4—1721no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C42—21no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—861no—
438C2×C42—861no—
439C2×C42C22×D4311yescharacteristic
440C4⋊C8—22no—
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—431no—
453#95—431no—
454#95—861no—
455#95—861no—
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—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—3441no—
473C2×Q8—3441no—
474C2×Q8—1722no—
475C2×Q8#1062190012yes—
476C2×Q8C2×C22⋊D4312yes—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4C2×C22⋊D4312yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—3441no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4D4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499C22×C4C23×D4311yescharacteristic
500Q16—44no—
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—42no—
517C4⋊C4—432no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—3441no—
528C4⋊C4—3441no—
529C4⋊C4—3441no—
530C4⋊C4—3441no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C22⋊C4—24no—
534C22⋊C4—24no—
535C22⋊C4—3441no—
536C22⋊C4—1722no—
537C22⋊C4—1722no—
538C42—42no—
539C42—861no—
540C42—861no—
541C42—861no—
542C42—861no—
543C42—3441no—
544C42—1722no—
545C42#1062190012yes—
546C42C2×C22⋊D4312yes—
547C23—22no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23C2×D4×D4311yescharacteristic
555Q8—22no—
556Q8—22no—
557Q8—22no—
558Q8—22no—
559Q8—41no—
560Q8—41no—
561Q8—41no—
562Q8—41no—
563Q8—3444no—
564D4—22no—
565D4—22no—
566D4—41no—
567D4—41no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—432no—
582C2×C4—432no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—862no—
594C2×C4—3444no—
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×C4—1721no—
605C2×C4—1721no—
606C2×C4#1306329712yes—
607C2×C4#1306329712yes—
608C2×C4C22×C22⋊D4311yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4C2×#1062190011yescharacteristic
611C2×C4C2×#1062190011yescharacteristic
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—
625C22C2×#1306329711yescharacteristic
626C22#1458354611yescharacteristic
627C22#1458355511yescharacteristic
628C22#137×D4311yescharacteristic
629C22#137×D4311yescharacteristic
630C22#1458370111yescharacteristic
631C22#1458370611yescharacteristic
632C4—22no—
633C4—22no—
634C4—42no—
635C4—42no—
636C4—81no—
637C4—862no—
638C4—862no—
639C4—3441no—
640C4—3441no—
641C4—3441no—
642C4—1721no—
643C4—1722no—
644C4—1721no—
645C4#1458343011yescharacteristic
646C4#1458351611yescharacteristic
647C4#1458354311yescharacteristic
648C4#1458354811yescharacteristic
649C2—82no—
650C2#1913817411yescharacteristic
651C2#1914408011yescharacteristic
652C2#1914413211yescharacteristic
653C2#1914668311yescharacteristic
654C2#1914671311yescharacteristic
655C2#1914733011yescharacteristic
656C2#1914740411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenterC2×#464D43
hypocenterC43#25336
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. #19139800C2semidirect
4. #19136006C2semidirect
6. #19135915C2semidirect
8. #19135546C2semidirect
9. #19135316C2semidirect
10. #19134938C2semidirect
12. #19134598C2semidirect
14. #19134425C2semidirect
389. C43#25336semidirect

Maximal subgroups

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

subgroupindex
C2×#145832582
#191398002
#191376702
#191360062
#191360012
#191359152
#191359082
#191355462
#191353162
#191349382
#191349312
#191345982
#191345932
#191344252
C2×C43×#4642
#2533643