Finite Group Databasebeta

← #25137879

Subgroups — #25137879

Order 11008.

784 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583206C211yesmaximal, characteristic, complemented
2C2×#14582955C211yesmaximal, characteristic
3#19142906C211yesmaximal, characteristic
4C4×#13063301C211yesmaximal, characteristic
5#19136034C211yesmaximal, characteristic
6#19136027C211yesmaximal, characteristic
7#19135796C211yesmaximal, characteristic
8#19135789C211yesmaximal, characteristic
9#19135550C211yesmaximal, characteristic, complemented
10#19135361C211yesmaximal, characteristic, complemented
11#19135337C211yesmaximal, characteristic, complemented
12#19135332C211yesmaximal, characteristic, complemented
13#19135287C211yesmaximal, characteristic, complemented
14#19135287C211yesmaximal, characteristic, complemented
15C43×#1805C211yesmaximal, characteristic, complemented
16C2×#13063317C2211yescharacteristic
17C2×#13063301C2211yescharacteristic
18C2×C42×D43C2211yescharacteristic
19#14583206—24no—
20#14582955—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32#14582806C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582784—21no—
37#14582784—21no—
38#14582780—21no—
39#14582773—21no—
40#14582773—21no—
41#14582770—21no—
42#14582756C2211yescharacteristic
43#14582756C2211yescharacteristic
44#14582756C2211yescharacteristic
45C4×Dic43⋊C4—21no—
46C4×C4⋊Dic43C2211yescharacteristic
47C4×(C2×D43)⋊C4—21no—
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C43×#382C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063317—22no—
67#13063317—22no—
68#13063301—22no—
69#13063301—22no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88C42×D43—22no—
89C42×D43—22no—
90#13063258—22no—
91#13063258—22no—
92#13063256—22no—
93#13063256—22no—
94C4⋊(C43⋊C8)D414yes—
95#13063249—22no—
96#13063249—22no—
97(C2×D43)⋊C8—22no—
98(C2×D43)⋊C8—22no—
99#13063235—22no—
100#13063235—22no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C22×Q8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C4×Q8×C43—22no—
114C4×Q8×C43—22no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121C4⋊C8×C43—22no—
122#103×C43—22no—
123#103×C43—22no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43C2×D411yescharacteristic
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43#4112yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—22no—
156C2×C4×D43—41no—
157C2×C4×D43—41no—
158C2×C4×D43—41no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—42no—
172C42×C43—42no—
173C42×C43C2×D412yes—
174C42×C43#4112yes—
175(C2×D43)⋊C4—24no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—42no—
178(C2×D43)⋊C4—42no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—42no—
187C4⋊Dic43—42no—
188C4⋊Dic43#4112yes—
189Dic43⋊C4—24no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193C4×Dic43—22no—
194C4×Dic43—22no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—42no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C2×D412yes—
203C2×C43⋊C8C2×D412yes—
204C23×C43C22×D411yescharacteristic
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43#13712yes—
212Q8×C43—22no—
213Q8×C43—22no—
214Q8×C43—41no—
215Q8×C43—41no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—22no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43#12112yes—
233C2×C4×C43#12112yes—
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C432−1+411yescharacteristic
239C2×C4×C432−1+411yescharacteristic
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—22no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C4×D43—44no—
262C4×D43—44no—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—41no—
267C8×C43—41no—
268C8×C43—41no—
269C43⋊C8—22no—
270C43⋊C8—22no—
271#24707—431nomaximal, Sylow
272C22×C43C2×#12111yescharacteristic
273C22×C43#52511yescharacteristic
274C22×C43#53611yescharacteristic
275C22×C43C2×#13711yescharacteristic
276C22×C43#57511yescharacteristic
277C22×C43#57511yescharacteristic
278C22×C43#57511yescharacteristic
279C2×D43—22no—
280C2×D43—22no—
281C2×D43—22no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C4×C43—22no—
287C4×C43—22no—
288C4×C43—42no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43#54711yescharacteristic
293C4×C43#54811yescharacteristic
294C4×C43#55211yescharacteristic
295C4×C43#55611yescharacteristic
296Dic43—42no—
297Dic43—41no—
298Dic43—41no—
299Dic43—41no—
300Dic43—81no—
301Dic43—81no—
302Dic43—81no—
303C2×#479—431no—
304C2×#432—431no—
305#2851—431no—
306C4×C22⋊Q8—431no—
307#2077—431no—
308#2076—431no—
309#2036—431no—
310#2035—431no—
311#1989—431no—
312#1949—431no—
313#1944—431no—
314#1943—431no—
315#1935—431no—
316#1935—431no—
317#1805D4311yescharacteristic, complemented
318C2×C43#241511yescharacteristic
319C2×C43#305411yescharacteristic
320C2×C43#305611yescharacteristic
321C2×C43#311111yescharacteristic
322C2×C43#311711yescharacteristic
323C2×C43#323611yescharacteristic
324C2×C43#324011yescharacteristic
325D43—42no—
326C2×#125—431no—
327C2×C22⋊Q8—431no—
328C2×C4×Q8C2×D4311yescharacteristic
329C22×C42—431no—
330#479—864no—
331#432—864no—
332C2×#107—431no—
333C2×#107—431no—
334C2×#106—431no—
335C2×#106—431no—
336C2×C4⋊C8—431no—
337C2×C4⋊C8C2×D4311yescharacteristic
338C2×#103—431no—
339C2×#103—431no—
340C2×#103C2×D4311yescharacteristic
341C2×#103C2×D4311yescharacteristic
342C2×C22⋊C8—431no—
343C2×C22⋊C8—431no—
344C2×#97—431no—
345C2×#97—431no—
346#391—431no—
347#389—431no—
348#389—431no—
349#389—431no—
350#387—861no—
351#387—861no—
352#387—861no—
353#385—861no—
354#385—861no—
355#385—861no—
356#382C2×D4311yescharacteristic
357#380—431no—
358#380—431no—
359#380—431no—
360C4×C4⋊C4—431no—
361C4×C4⋊C4—861no—
362C4×C22⋊C4—861no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340C2×D4311yescharacteristic
370#340C2×D4311yescharacteristic
371C43#2470711yescharacteristic, complemented, Sylow
372C22×Q8C22×D4311yescharacteristic
373C23×C4—431no—
374C23×C4—431no—
375C23×C4—431no—
376C22×C8—431no—
377C22×C8—431no—
378C22×C8C22×D4311yescharacteristic
379C22×C8C22×D4311yescharacteristic
380#125—862no—
381#125—862no—
382C22⋊Q8—862no—
383C22⋊Q8—862no—
384C4×Q8—22no—
385C4×Q8—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C22⋊C4—861no—
401C2×C22⋊C4—861no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C42—21no—
405C2×C42—431no—
406C2×C42—431no—
407C2×C42—431no—
408C2×C42—862no—
409C2×C42—862no—
410C2×C42—861no—
411C2×C42C22×D4311yescharacteristic
412#107—862no—
413#107—862no—
414#106—862no—
415#106—862no—
416C4⋊C8—22no—
417C4⋊C8—434no—
418#103—22no—
419#103—22no—
420#103—862no—
421#103—862no—
422C22⋊C8—862no—
423C22⋊C8—862no—
424#97—862no—
425#97—862no—
426#95—21no—
427#95—21no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437C24—431no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8#1062190012yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—862no—
452C22×C4—861no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—1721no—
465C22×C4—1721no—
466C22×C4—1721no—
467C22×C4D4×D4311yescharacteristic
468C22×C4D4×D4311yescharacteristic
469C22×C4C23×D4311yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—432no—
477C2×C8—432no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—42no—
489C4⋊C4—432no—
490C4⋊C4—864no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C4⋊C4—1722no—
502C4⋊C4—1722no—
503C22⋊C4—864no—
504C22⋊C4—1722no—
505C22⋊C4—1722no—
506C22⋊C4—1722no—
507C42—42no—
508C42—862no—
509C42—862no—
510C42—861no—
511C42—861no—
512C42—1722no—
513C42#1062189812yes—
514C42D4×D4312yes—
515C23—432no—
516C23—861no—
517C23—861no—
518C23—861no—
519C23—861no—
520C23—861no—
521C23—861no—
522C23C2×D4×D4311yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—862no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—1724no—
554C2×C4—1724no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4#1306329812yes—
571C2×C4#1306329812yes—
572C2×C4C2×D4×D4311yescharacteristic
573C2×C4#41×D4311yescharacteristic
574C2×C4C2×#1062190011yescharacteristic
575C2×C4C2×#1062189811yescharacteristic
576C2×C4#1306337211yescharacteristic
577C2×C4#1306337311yescharacteristic
578C8—41no—
579C8—41no—
580C8—862no—
581C8—862no—
582C22—862no—
583C22—862no—
584C22—862no—
585C22—1721no—
586C22—1721no—
587C22—1721no—
588C22—1721no—
589C22C2×#1306329811yescharacteristic
590C22#1458340911yescharacteristic
591C22#1458347211yescharacteristic
592C22#137×D4311yescharacteristic
593C22#1458369611yescharacteristic
594C22#1458369611yescharacteristic
595C22#1458369811yescharacteristic
596C4—22no—
597C4—22no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—3441no—
603C4—3441no—
604C4—3441no—
605C4—1721no—
606C4—1721no—
607C4—1721no—
608C4—1722no—
609C4#1458355111yescharacteristic
610C4#1458355511yescharacteristic
611C4#1458358411yescharacteristic
612C4#1458361711yescharacteristic
613C2—1722no—
614C2#1913802611yescharacteristic
615C2#1914420311yescharacteristic
616C2#1914422311yescharacteristic
617C2#1914470311yescharacteristic
618C2#1914476511yescharacteristic
619C2#1914579911yescharacteristic
620C2#1914584011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1805C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1805D43
hypocenterC43#24707
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
1. C2×#14583206C2semidirect
9. #19135550C2semidirect
10. #19135361C2semidirect
11. #19135337C2semidirect
12. #19135332C2semidirect
13. #19135287C2semidirect
14. #19135287C2semidirect
15. C43×#1805C2semidirect
317. #1805D43semidirect
371. C43#24707semidirect

Maximal subgroups

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

subgroupindex
C2×#145832062
C2×#145829552
#191429062
C4×#130633012
#191360342
#191360272
#191357962
#191357892
#191355502
#191353612
#191353372
#191353322
#191352872
C43×#18052
#2470743