Finite Group Databasebeta

← #25099615

Subgroups — #25099615

Order 11008.

966 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583001C211yesmaximal, characteristic
2#19137072C211yesmaximal, characteristic, complemented
3C42×D172C211yesmaximal, characteristic
4#19135237C211yesmaximal, characteristic, complemented
5#19135230C211yesmaximal, characteristic, complemented
6#19135188C211yesmaximal, characteristic, complemented
7#19135167C211yesmaximal, characteristic, complemented
8#19134928C211yesmaximal, characteristic
9#19134928C211yesmaximal, characteristic
10#19134859C211yesmaximal, characteristic
11#19134845C211yesmaximal, characteristic
12#19134492C211yesmaximal, characteristic, complemented
13#19134426C211yesmaximal, characteristic, complemented
14#19134421C211yesmaximal, characteristic
15C43×#1745C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C42×D43—21no—
22#14583001C418yescomplemented
23C2×#13063259C2211yescharacteristic
24C2×#13063259C2211yescharacteristic
25C2×#13063257C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32#14582805C2211yescharacteristic
33#14582805C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582783—21no—
37#14582783—21no—
38C4×Dic43⋊C4—21no—
39C4×C4⋊Dic43C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C4×(C2×D43)⋊C4—21no—
44C4×(C2×D43)⋊C4—21no—
45C4×(C2×D43)⋊C4—21no—
46#14582745—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C2×#97×C43C2211yescharacteristic
54C2×#97×C43C2211yescharacteristic
55C43×C43C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C2×#10621873—22no—
66C2×#10621873—22no—
67C2×#10621873C2×C414yes—
68C4×Dic86—22no—
69C4×Dic86C2×C414yescomplemented
70C4×D172—22no—
71C4×D172—22no—
72C4×D172—22no—
73C4×D172—22no—
74C4×D172—22no—
75C4×D172C2×C414yes—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C42×D43—44no—
94#13063259—22no—
95#13063259C2×C414yescomplemented
96#13063257—22no—
97#13063250—22no—
98#13063250—22no—
99#13063250C2×C414yescomplemented
100#13063247—22no—
101#13063247—22no—
102#13063247C2×C414yes—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C2×C42×C43D411yescharacteristic
118C2×C42×C43D411yescharacteristic
119C2×C42×C43D411yescharacteristic
120C2×C42×C43D411yescharacteristic
121C2×C42×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123C2×C42×C43C2311yescharacteristic
124#97×C43—22no—
125#97×C43C2×C414yescomplemented
126C23×D43—21no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172C22×C412yes—
145C2×D172#4112yes—
146C2×D172#4112yes—
147C2×C4×D43—24no—
148C2×C4×D43—24no—
149C2×C4×D43—24no—
150C2×C4×D43—42no—
151C2×C4×D43—42no—
152C2×C4×D43—42no—
153C2×C4×D43—42no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86C22×C412yes—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43C22×C412yes—
173C2×C8×C43C22×C412yes—
174C42×C43—22no—
175C42×C43—22no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—41no—
181C42×C43—41no—
182C42×C43C22×C412yes—
183C42×C43#4112yes—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—24no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43C22×C412yes—
196C4⋊Dic43C22×C412yes—
197C4⋊Dic43#4112yes—
198C4⋊Dic43#4112yes—
199Dic43⋊C4—24no—
200Dic43⋊C4—42no—
201Dic43⋊C4—42no—
202C4×Dic43—24no—
203C4×Dic43—42no—
204C4×Dic43—42no—
205C4×Dic43—42no—
206C4×Dic43—42no—
207#10621873—28no—
208C23×C43C22×D411yescharacteristic
209C22×D43—22no—
210C22×D43—22no—
211C22×D43—22no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
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—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43C4×D412yes—
231C2×C4×C43C4×D412yes—
232C2×C4×C43AGL(1,ℤ/8)12yes—
233C2×C4×C43#13712yes—
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
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—41no—
260C2×Dic43—41no—
261D172—22no—
262D172—22no—
263D172—22no—
264D172#11714yes—
265C4×D43—48no—
266C4×D43—48no—
267C4×D43—48no—
268Dic86—22no—
269Dic86—22no—
270Dic86—41no—
271Dic86—41no—
272C8×C43—22no—
273C8×C43—22no—
274C8×C43—41no—
275C8×C43—41no—
276#21121—431nomaximal, Sylow
277C22×C43C2×C4×D411yescharacteristic
278C22×C43#52511yescharacteristic
279C22×C43#52511yescharacteristic
280C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C43C2×#13711yescharacteristic
282C22×C43#57511yescharacteristic
283C22×C43#57511yescharacteristic
284C2×D43—24no—
285C2×D43—42no—
286C2×D43—42no—
287C2×D43—42no—
288C2×D43—42no—
289C2×D43—42no—
290C2×D43—42no—
291C4×C43—22no—
292C4×C43—22no—
293C4×C43—22no—
294C4×C43—22no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43C2×#11711yescharacteristic
298C4×C43C4×#4111yescharacteristic
299C4×C43#52911yescharacteristic
300C4×C43#52911yescharacteristic
301Dic43—42no—
302Dic43—42no—
303Dic43—42no—
304Dic43—42no—
305Dic43—42no—
306Dic43—81no—
307Dic43—81no—
308C2×#440—431no—
309#2295—431no—
310C42×D4—431no—
311#1928—431no—
312#1927—431no—
313#1921—431no—
314#1918—431no—
315#1877—431no—
316#1877—431no—
317#1864—431no—
318#1862—431no—
319#1776—431no—
320#1763—431no—
321#1762—431no—
322#1745D4311yescharacteristic, complemented
323C2×C43#229011yescharacteristic
324C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
325C2×C43C4×#13711yescharacteristic
326C2×C43#311011yescharacteristic
327C2×C43#311111yescharacteristic
328C2×C43#311411yescharacteristic
329C2×C43#311611yescharacteristic
330D43—44no—
331C22×SD16—431no—
332C2×C4×Q8—431no—
333C2×C4×D4—431no—
334C2×C4×D4—431no—
335C2×C4×D4—431no—
336C22×C42—861no—
337#440—438no—
338C2×#107—431no—
339C2×#107—431no—
340C2×#106—431no—
341C2×#103—431no—
342C2×#103—431no—
343C2×#103—431no—
344C2×#102—431no—
345C2×#102—431no—
346C2×#102—431no—
347C2×#97C2×D4311yescharacteristic
348C2×#97C2×D4311yescharacteristic
349#391—431no—
350#391—431no—
351#389—431no—
352#389—431no—
353#387—861no—
354#387—861no—
355C4×C4⋊C4—431no—
356C4×C4⋊C4—431no—
357C4×C4⋊C4—431no—
358C4×C4⋊C4—431no—
359C4×C4⋊C4—861no—
360C4×C22⋊C4—861no—
361C4×C22⋊C4—861no—
362C4×C22⋊C4—861no—
363#376—861no—
364C43C2×D4311yescharacteristic
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#336C2×D4311yescharacteristic
372#336C2×D4311yescharacteristic
373#336C2×D4311yescharacteristic
374#336C2×D4311yescharacteristic
375C43#2112111yescharacteristic, complemented, Sylow
376C22×Q8—431no—
377C22×D4—431no—
378C23×C4—861no—
379C23×C4—861no—
380C23×C4—861no—
381C2×SD16—434no—
382C2×SD16—862no—
383C2×SD16—862no—
384C22×C8C22×D4311yescharacteristic
385C22×C8C22×D4311yescharacteristic
386C22×C8C22×D4311yescharacteristic
387C22×C8C22×D4311yescharacteristic
388C4×Q8—434no—
389C4×Q8—862no—
390C4×D4—434no—
391C4×D4—862no—
392C4×D4—862no—
393C4×D4—862no—
394C4×D4—862no—
395C4×D4—862no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C42—861no—
409C2×C42—861no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42—861no—
413C2×C42—1724no—
414C2×C42D17211yescharacteristic
415C2×C42D17211yescharacteristic
416C2×C42D17211yescharacteristic
417C2×C42D17211yescharacteristic
418C2×C42C22×D4311yescharacteristic
419C2×C42C22×D4311yescharacteristic
420C2×C42C22×D4311yescharacteristic
421#107—434no—
422#107—862no—
423#106—862no—
424#103—434no—
425#103—862no—
426#103—862no—
427#102—434no—
428#102—862no—
429#102—862no—
430#97—22no—
431#97C4×D4314yescomplemented
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442C24—861no—
443C2×Q8—432no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×D4—432no—
450C2×D4—432no—
451C2×D4—432no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C22×C4—864no—
456C22×C4—864no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—864no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—1722no—
466C22×C4—1722no—
467C22×C4—1722no—
468C22×C4—1722no—
469C22×C4—1722no—
470C22×C4—1722no—
471C22×C4C2×D17211yescharacteristic
472C22×C4C2×D17211yescharacteristic
473C22×C4C2×D17211yescharacteristic
474C22×C4C2×D17211yescharacteristic
475C22×C4C2×D17211yescharacteristic
476C22×C4C2×D17211yescharacteristic
477C22×C4C23×D4311yescharacteristic
478SD16—868no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8C2×C4×D4312yes—
490C2×C8C2×C4×D4312yes—
491C4⋊C4—432no—
492C4⋊C4—432no—
493C4⋊C4—432no—
494C4⋊C4—432no—
495C4⋊C4—864no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—1722no—
505C4⋊C4—1722no—
506C22⋊C4—864no—
507C22⋊C4—864no—
508C22⋊C4—864no—
509C42—22no—
510C42—22no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—41no—
516C42—41no—
517C42—864no—
518C42—1722no—
519C42—1722no—
520C42—1722no—
521C42—1722no—
522C42C2×C4×D4312yes—
523C42#1062189812yes—
524C23—862no—
525C23—862no—
526C23—862no—
527C23—1721no—
528C23—1721no—
529C23—1721no—
530C23—1721no—
531C23C22×D17211yescharacteristic
532Q8—862no—
533Q8—862no—
534Q8—1721no—
535Q8—1721no—
536D4—434no—
537D4—862no—
538D4—862no—
539D4—862no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—1728no—
560C2×C4—1728no—
561C2×C4—1728no—
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×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4C4×D17212yes—
579C2×C4C4×D17212yes—
580C2×C4#1306335312yes—
581C2×C4#1306335812yes—
582C2×C4C22×C4×D4311yescharacteristic
583C2×C4#41×D4311yescharacteristic
584C2×C4#41×D4311yescharacteristic
585C2×C4#41×D4311yescharacteristic
586C2×C4#41×D4311yescharacteristic
587C2×C4C2×#1062189811yescharacteristic
588C8—22no—
589C8—22no—
590C8—41no—
591C8—41no—
592C22—864no—
593C22—1722no—
594C22—1722no—
595C22—1722no—
596C22—1722no—
597C22—1722no—
598C22—1722no—
599C22C2×C4×D17211yescharacteristic
600C22#1458341111yescharacteristic
601C22#1458341111yescharacteristic
602C22C2×#1306335311yescharacteristic
603C22C2×#1306335811yescharacteristic
604C22#1458369911yescharacteristic
605C22#1458369911yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—22no—
610C4—41no—
611C4—41no—
612C4—3441no—
613C4—3441no—
614C4—1722no—
615C4—1722no—
616C4—1722no—
617C4—1722no—
618C4—1722no—
619C4#117×D4311yescharacteristic
620C4#1458336711yescharacteristic
621C4#1458342711yescharacteristic
622C4#1458342711yescharacteristic
623C2—1724no—
624C2#1913703911yescharacteristic
625C2C4×#1306335311yescharacteristic
626C2C4×#1306335811yescharacteristic
627C2#1914469511yescharacteristic
628C2#1914470611yescharacteristic
629C2#1914473511yescharacteristic
630C2#1914475811yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1745C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1745D43
hypocenterC43#21121
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C43 ◁ #1745

Complements

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

NH ≅ G/Ntype
2. #19137072C2semidirect
4. #19135237C2semidirect
5. #19135230C2semidirect
6. #19135188C2semidirect
7. #19135167C2semidirect
12. #19134492C2semidirect
13. #19134426C2semidirect
15. C43×#1745C2semidirect
22. #14583001C4semidirect
69. C4×Dic86C2×C4semidirect
95. #13063259C2×C4semidirect
99. #13063250C2×C4semidirect
125. #97×C43C2×C4semidirect
322. #1745D43semidirect
375. C43#21121semidirect
431. #97C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830012
#191370722
C42×D1722
#191352372
#191352302
#191351882
#191351672
#191349282
#191348592
#191348452
#191344922
#191344262
#191344212
C43×#17452
#2112143