Finite Group Databasebeta

← #25115768

Subgroups — #25115768

Order 11008.

858 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×#14582990C211yesmaximal, characteristic
2#19137556C211yesmaximal, characteristic, complemented
3#19137500C211yesmaximal, characteristic
4#19135285C211yesmaximal, characteristic, complemented
5#19135283C211yesmaximal, characteristic, complemented
6#19135173C211yesmaximal, characteristic, complemented
7#19135171C211yesmaximal, characteristic, complemented
8#19134929C211yesmaximal, characteristic
9#19134927C211yesmaximal, characteristic
10#19134724C211yesmaximal, characteristic, complemented
11#19134609C211yesmaximal, characteristic, complemented
12#19134603C211yesmaximal, characteristic
13#19134463C211yesmaximal, characteristic, complemented
14#19134422C211yesmaximal, characteristic
15C43×#1762C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063290C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20#14582990C418yescomplemented
21C2×#13063256C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582805C2211yescharacteristic
30#14582804C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582783—21no—
34#14582781—21no—
35#14582772—21no—
36#14582771—21no—
37#14582766—21no—
38#14582764C2211yescharacteristic
39#14582764C2211yescharacteristic
40#14582757—21no—
41C4⋊C4×Dic43C2211yescharacteristic
42C4×Dic43⋊C4C2211yescharacteristic
43#14582745—21no—
44C2×C43⋊#95—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C23×Dic43—21no—
62C23×Dic43—21no—
63C2×#10621883—22no—
64C2×#10621883—22no—
65C2×#10621883C2×C414yes—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063290—22no—
69#13063290C2×C414yescomplemented
70D4×Dic43—22no—
71D4×Dic43—22no—
72D4×Dic43—41no—
73D4×Dic43C2×C414yes—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4D411yescharacteristic
81C2×Dic43⋊C4D411yescharacteristic
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43C2311yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88#13063256C2×C414yescomplemented
89Dic43⋊C8—22no—
90#13063250—41no—
91#13063250C2×C414yescomplemented
92#13063248—41no—
93#13063246—22no—
94#13063235—41no—
95C8×Dic43C2×C414yescomplemented
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C4×D4×C43—22no—
114C4×D4×C43—41no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#102×C43—22no—
122#102×C43C2×C414yes—
123#97×C43—41no—
124#95×C43—21no—
125C24×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43C22×C412yes—
130C2×D4×C43#4112yes—
131C2×D4×C43#4112yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—42no—
136C22×C4×C43—42no—
137C22×C4×C43—81no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—24no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—42no—
147C22×Dic43—42no—
148C22×Dic43—81no—
149C22×Dic43—81no—
150C22×Dic43—81no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86C22×C412yes—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43C22×C412yes—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C22×C412yes—
173C22⋊C4×C43—42no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—42no—
177C22⋊Dic43—24no—
178C22⋊Dic43—42no—
179#10621883—28no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43C22×C412yes—
186Dic43⋊C4—24no—
187Dic43⋊C4—41no—
188Dic43⋊C4—41no—
189Dic43⋊C4—81no—
190Dic43⋊C4—81no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—24no—
194C4×Dic43—42no—
195C4×Dic43C22×C412yes—
196C4×Dic43#4112yes—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C22×C412yes—
203C23×C43—22no—
204C23×C43—22no—
205C23×C43—22no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43C22×D411yescharacteristic
211D4×C43—22no—
212D4×C43—22no—
213D4×C43—22no—
214D4×C43#11714yes—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
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—84no—
231C2×C4×C43C23×C411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C2×C4×C432−1+411yescharacteristic
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—41no—
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—84no—
260C2×Dic43—84no—
261C2×Dic43C4×D412yes—
262C2×Dic43C4×D412yes—
263Dic86—22no—
264Dic86—22no—
265Dic86—41no—
266Dic86—41no—
267C8×C43—22no—
268C8×C43—41no—
269C43⋊C8—22no—
270C43⋊C8—41no—
271#22760—431nomaximal, Sylow
272C22×C43—24no—
273C22×C43—42no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—42no—
279C22×C43C2×C4×D411yescharacteristic
280C22×C43#54611yescharacteristic
281C22×C43#54811yescharacteristic
282C22×C43#57511yescharacteristic
283C22×C43#57511yescharacteristic
284C22×C43#57711yescharacteristic
285C22×C43#57711yescharacteristic
286C4×C43—42no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43C2×#11711yescharacteristic
292C4×C43#52011yescharacteristic
293C4×C43#55211yescharacteristic
294C4×C43#55311yescharacteristic
295Dic43—22no—
296Dic43—22no—
297Dic43—42no—
298Dic43—42no—
299Dic43—41no—
300Dic43—41no—
301Dic43—81no—
302Dic43—81no—
303C2×C4×SD16—431no—
304#2356—431no—
305#2349—431no—
306#1935—431no—
307#1935—431no—
308#1919—431no—
309#1919—431no—
310#1877—431no—
311#1877—431no—
312#1835—431no—
313#1805—431no—
314#1804—431no—
315#1770—431no—
316#1762—431no—
317#1762D4311yescharacteristic
318C2×C43—44no—
319C2×C43#235211yescharacteristic
320C2×C43#294311yescharacteristic
321C2×C43#294911yescharacteristic
322C2×C43#332311yescharacteristic
323C2×C43#332311yescharacteristic
324C2×C43#337611yescharacteristic
325C2×C43#337611yescharacteristic
326C22×SD16—431no—
327C2×C4×Q8—431no—
328C2×C4×D4—431no—
329C2×C4×D4—431no—
330C2×C4×D4C2×D4311yescharacteristic
331C4×SD16—438no—
332C2×#106—431no—
333C2×C4⋊C8—431no—
334C2×#103—431no—
335C2×#103—431no—
336C2×#103—431no—
337C2×#102—431no—
338C2×#102C2×D4311yescharacteristic
339C2×#102C2×D4311yescharacteristic
340C2×#97—431no—
341C2×#97C2×D4311yescharacteristic
342C2×C4×C8—431no—
343#391—431no—
344#391—431no—
345#389—431no—
346#389—431no—
347#387—861no—
348#387—861no—
349#385—861no—
350#385—861no—
351#383—861no—
352#382—431no—
353#382—431no—
354#380—861no—
355C4×C4⋊C4—431no—
356C4×C4⋊C4—431no—
357C4×C4⋊C4C2×D4311yescharacteristic
358#376—861no—
359C2×#95—861no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340C2×D4311yescharacteristic
367#340C2×D4311yescharacteristic
368#336—431no—
369#336—431no—
370C43#2276011yescharacteristic, complemented, Sylow
371C22×Q8—431no—
372C22×D4C22×D4311yescharacteristic
373C23×C4—21no—
374C23×C4—861no—
375C23×C4—861no—
376C2×SD16—434no—
377C2×SD16—862no—
378C2×SD16—862no—
379C22×C8—431no—
380C22×C8—431no—
381C22×C8C22×D4311yescharacteristic
382C22×C8C22×D4311yescharacteristic
383C4×Q8—434no—
384C4×Q8—862no—
385C4×D4—22no—
386C4×D4—41no—
387C4×D4—434no—
388C4×D4—862no—
389C4×D4—862no—
390C4×D4—1721no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C42—21no—
406C2×C42—431no—
407C2×C42—431no—
408C2×C42—861no—
409C2×C42—861no—
410C2×C42C22×D4311yescharacteristic
411#106—434no—
412C4⋊C8—862no—
413#103—434no—
414#103—1721no—
415#103—1721no—
416#102—22no—
417#102—862no—
418#102C4×D4314yes—
419#97—41no—
420#97—1721no—
421C4×C8—434no—
422#95—21no—
423#95—431no—
424#95—431no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436C24—21no—
437C2×Q8—432no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4C2×C4×D4312yes—
447C2×D4#1062189812yes—
448C2×D4#1062189812yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—81no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—864no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—3441no—
465C22×C4—3441no—
466C22×C4—3441no—
467C22×C4—1722no—
468C22×C4—1722no—
469C22×C4D4×D4311yescharacteristic
470C22×C4D4×D4311yescharacteristic
471C22×C4C23×D4311yescharacteristic
472SD16—868no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—432no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8C2×C4×D4312yes—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—432no—
491C4⋊C4—864no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—3441no—
498C4⋊C4—3441no—
499C4⋊C4—1721no—
500C4⋊C4—1721no—
501C4⋊C4C2×C4×D4312yes—
502C22⋊C4—42no—
503C22⋊C4—864no—
504C22⋊C4—1722no—
505C42—21no—
506C42—21no—
507C42—42no—
508C42—432no—
509C42—432no—
510C42—864no—
511C42—861no—
512C42—861no—
513C42—1722no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C2×D4×D4311yescharacteristic
522Q8—862no—
523Q8—862no—
524Q8—1721no—
525Q8—1721no—
526D4—22no—
527D4—22no—
528D4—22no—
529D4#1306328214yes—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—84no—
546C2×C4—432no—
547C2×C4—432no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—3444no—
561C2×C4—3444no—
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—1721no—
571C2×C4—1721no—
572C2×C4C22×C4×D4311yescharacteristic
573C2×C4#41×D4311yescharacteristic
574C2×C4C2×#1062189811yescharacteristic
575C2×C4C2×#1062189811yescharacteristic
576C2×C4#1306337011yescharacteristic
577C2×C4#1306337211yescharacteristic
578C8—22no—
579C8—41no—
580C8—862no—
581C8—1721no—
582C22—24no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22C4×D4×D4311yescharacteristic
590C22#1458353911yescharacteristic
591C22#1458355811yescharacteristic
592C22#1458369511yescharacteristic
593C22#1458369511yescharacteristic
594C22#1458370811yescharacteristic
595C22#1458370911yescharacteristic
596C4—41no—
597C4—41no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—862no—
602C4—862no—
603C4—3441no—
604C4—3441no—
605C4—1722no—
606C4—1721no—
607C4—1721no—
608C4—1722no—
609C4C2×#1306328211yescharacteristic
610C4#1458337811yescharacteristic
611C4#1458358211yescharacteristic
612C4#1458359811yescharacteristic
613C2—44no—
614C2#1913751811yescharacteristic
615C2#1914339211yescharacteristic
616C2#1914345111yescharacteristic
617C2#1914680711yescharacteristic
618C2#1914681211yescharacteristic
619C2#1914742311yescharacteristic
620C2#1914742711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1762C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1762D43
hypocenterC43#22760
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. #19137556C2semidirect
4. #19135285C2semidirect
5. #19135283C2semidirect
6. #19135173C2semidirect
7. #19135171C2semidirect
10. #19134724C2semidirect
11. #19134609C2semidirect
13. #19134463C2semidirect
20. #14582990C4semidirect
69. #13063290C2×C4semidirect
88. #13063256C2×C4semidirect
91. #13063250C2×C4semidirect
95. C8×Dic43C2×C4semidirect
370. C43#22760semidirect

Maximal subgroups

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

subgroupindex
C2×#145829902
#191375562
#191375002
#191352852
#191352832
#191351732
#191351712
#191349292
#191349272
#191347242
#191346092
#191346032
#191344632
#191344222
C43×#17622
#2276043