Finite Group Databasebeta

← #25067667

Subgroups — #25067667

Order 11008.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144644C211yesmaximal, characteristic
2#19143599C211yesmaximal, characteristic, complemented
3M16×D172C211yesmaximal, characteristic, complemented
4#19133499C211yesmaximal, characteristic, complemented
5#19133481C211yesmaximal, characteristic, complemented
6#19133461C211yesmaximal, characteristic, complemented
7#19133454C211yesmaximal, characteristic, complemented
8#19133440C211yesmaximal, characteristic, complemented
9#19133426C211yesmaximal, characteristic, complemented
10#19133420C211yesmaximal, characteristic, complemented
11C8×#10621873C211yesmaximal, characteristic, complemented
12#19133384C211yesmaximal, characteristic, complemented
13#19133061C211yesmaximal, characteristic, complemented
14#19132987C211yesmaximal, characteristic, complemented
15C43×#1453C211yesmaximal, characteristic, complemented
16C2×M16×D43—21no—
17#14583433C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19#14583235C411yescharacteristic
20#14583218C411yescharacteristic
21#14583200C411yescharacteristic
22#14583200C411yescharacteristic
23#14583115C411yescharacteristic
24#14583115C411yescharacteristic
25#14583052C411yescharacteristic
26#14583035C411yescharacteristic
27#14583029C2211yescharacteristic, complemented
28C8×Dic86C2211yescharacteristic, complemented
29C4×#10621873C2211yescharacteristic
30C4×#10621873C2211yescharacteristic
31C4×D344C2211yescharacteristic
32C4×D344C2211yescharacteristic
33#14582978C2211yescharacteristic
34#14582978C2211yescharacteristic
35#14582978C2211yescharacteristic, complemented
36#14582975—21no—
37#14582972—21no—
38#14582972—21no—
39#14582968—21no—
40C8×D172C2211yescharacteristic
41C8×D172C2211yescharacteristic
42C8×D172C2211yescharacteristic, complemented
43#14582961—21no—
44#14582952C2211yescharacteristic
45#14582923C2211yescharacteristic
46#14582862—21no—
47#14582856—21no—
48#14582652C2211yescharacteristic, complemented
49#14582652C2211yescharacteristic, complemented
50#14582650C2211yescharacteristic, complemented
51#14582650C2211yescharacteristic, complemented
52#14582631C2211yescharacteristic, complemented
53#14582631C2211yescharacteristic, complemented
54#14582628C2211yescharacteristic
55#14582628C2211yescharacteristic
56#14582628C2211yescharacteristic
57#14582628C2211yescharacteristic
58#14582628C2211yescharacteristic, complemented
59#14582628C2211yescharacteristic, complemented
60C43×#431C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C4×M16×C43C2211yescharacteristic
63C43×#322C2211yescharacteristic, complemented
64C43×#322C2211yescharacteristic, complemented
65C43×#322C2211yescharacteristic, complemented
66C82×C43C2211yescharacteristic, complemented
67C22×D172C2×C411yescharacteristic
68C22×C4×D43—21no—
69C2×#10621873C2×C411yescharacteristic
70C2×#10621873C2×C411yescharacteristic
71C2×D344C2×C411yescharacteristic
72C2×D344C2×C411yescharacteristic
73C2×#10621877—21no—
74C2×#10621872—21no—
75C2×#10621872—21no—
76C2×#10621872—21no—
77M16×D43—44no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80C2×C8×D43—21no—
81#13063319—21no—
82#13063317C2×C411yescharacteristic
83#13063313C2×C411yescharacteristic
84#13063308—21no—
85#13063304C2×C411yescharacteristic
86#13063299C2×C411yescharacteristic
87C4×Dic86C2311yescharacteristic
88C4×D172—21no—
89C4×D172—21no—
90C4×D172C2×C411yescharacteristic
91C4×D172C2×C411yescharacteristic
92C4×D172C2311yescharacteristic
93C4×D172C2311yescharacteristic
94C4×D172C2311yescharacteristic
95C4×C22⋊D43—21no—
96#13063282—21no—
97C2×C4⋊Dic43C2×C411yescharacteristic
98C2×(C2×D43)⋊C4—21no—
99#13063259C2×C411yescharacteristic
100#13063259C2×C411yescharacteristic
101#13063257C2×C411yescharacteristic
102#13063257C2×C411yescharacteristic
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110#13063250C2×C411yescharacteristic
111#13063250C2×C411yescharacteristic
112#13063247C2×C411yescharacteristic
113#13063247C2×C411yescharacteristic
114#13063247C2×C411yescharacteristic
115#13063247C2×C411yescharacteristic
116#13063247C2×C411yescharacteristic
117#13063247C2×C411yescharacteristic
118C22⋊(C43⋊C8)—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125#13063235—21no—
126C4×C43⋊C8—21no—
127C8×Dic43—21no—
128C2×M16×C43D411yescharacteristic
129C2×M16×C43D411yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2×C411yescharacteristic
133C4⋊C8×C43C2×C411yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43C2×C411yescharacteristic
136C22⋊C8×C43C2×C411yescharacteristic
137#97×C43D411yescharacteristic
138#97×C43D411yescharacteristic
139C4×C8×C43C2311yescharacteristic
140C4×C8×C43C2311yescharacteristic
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43#4111yescharacteristic
149C2×C22⋊D43—21no—
150C22×Dic43—21no—
151C2×D172—21no—
152C2×D172—22no—
153C2×D172—41no—
154C2×D172C22×C411yescharacteristic
155C2×D172C22×C411yescharacteristic
156C2×D172C22×C411yescharacteristic
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×Dic86C22×C411yescharacteristic
165M16×C43—22no—
166M16×C43—41no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C22×C411yescharacteristic
170C2×C8×C43C22×C411yescharacteristic
171C2×C8×C43C22×C411yescharacteristic
172C2×C8×C43C22×C411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C42×C43C22×C411yescharacteristic
178C42×C43C2×D411yescharacteristic
179C42×C43#4111yescharacteristic
180C42×C43C2411yescharacteristic
181C22⋊Dic43—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43C22×C411yescharacteristic
192C4⋊Dic43C22×C411yescharacteristic
193C4⋊Dic43C22×C411yescharacteristic
194C4⋊Dic43C22×C411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198Dic43⋊C4—21no—
199C4×Dic43—21no—
200#10621877—42no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205D344—22no—
206D344—41no—
207#10621873—22no—
208#10621873—41no—
209#10621872—42no—
210#10621872—42no—
211#10621872—42no—
212C8×D43—42no—
213C8×D43—42no—
214C8×D43—42no—
215C23×C43C4×D411yescharacteristic
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—42no—
220C22×D43—42no—
221C22×D43—81no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43C4×D411yescharacteristic
228C2×C4×C43C4×D411yescharacteristic
229C2×C4×C43C4×D411yescharacteristic
230C2×C4×C43C23×C411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C22⋊D43—81no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—42no—
240D172—21no—
241D172—21no—
242D172—21no—
243D172—21no—
244D172—21no—
245D172—42no—
246D172#13112yes—
247C4×D43—42no—
248C4×D43—42no—
249C4×D43—41no—
250C4×D43—41no—
251C4×D43—41no—
252C4×D43—41no—
253C4×D43—41no—
254C4×D43—41no—
255Dic86—21no—
256Dic86—21no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—41no—
265C8×C43—41no—
266C8×C43AGL(1,ℤ/8)12yes—
267C43⋊C8—41no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271#18008—431nomaximal, Sylow
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—21no—
275C22×C43C2×C4×D411yescharacteristic
276C2×D43—22no—
277C2×D43—41no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—84no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43C2×#13111yescharacteristic
291C4×C43#56811yescharacteristic
292C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
293C4×C43#57511yescharacteristic
294Dic43—41no—
295Dic43—41no—
296Dic43—41no—
297Dic43—41no—
298Dic43—41no—
299#3105—431no—
300#2969—431no—
301D4×M16—431no—
302#1592—431no—
303#1589—431no—
304#1586—431no—
305#1585—431no—
306#1583—431no—
307#1581—431no—
308#1580—431no—
309C8×SD16—431no—
310#1574—431no—
311#1495—431no—
312#1478—431no—
313#1453D4311yescharacteristic, complemented
314C2×C43—41no—
315C2×C43#293311yescharacteristic
316C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
317C2×C43#295711yescharacteristic
318D43—42no—
319D43—81no—
320D43—81no—
321C22×M16—861no—
322#529—431no—
323C2×C4×D4—431no—
324#484—431no—
325#481—431no—
326#478—431no—
327#478—431no—
328#463—431no—
329#463—431no—
330#450—431no—
331#447—431no—
332#446—431no—
333C8×Q8—431no—
334C4×SD16—431no—
335C4×SD16—431no—
336C4×D8—431no—
337C4×D8—431no—
338#436—431no—
339#436—431no—
340#436—431no—
341#436—861no—
342#435—861no—
343#435—861no—
344#435—861no—
345C8×D4—431no—
346C8×D4—431no—
347C8×D4—431no—
348#433—861no—
349#431—431no—
350#431C2×D4311yescharacteristic
351#431C2×D4311yescharacteristic
352#423—431no—
353#407—861no—
354#405—861no—
355C4×M16C2×D4311yescharacteristic
356#335—431no—
357#335—431no—
358#334—431no—
359#334—431no—
360Q8⋊C8—431no—
361Q8⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364D4⋊C8—431no—
365D4⋊C8—431no—
366D4⋊C8—431no—
367D4⋊C8—431no—
368#322C2×D4311yescharacteristic, complemented
369#322C2×D4311yescharacteristic, complemented
370#322C2×D4311yescharacteristic, complemented
371C82C2×D4311yescharacteristic, complemented
372C43#1800811yescharacteristic, complemented, Sylow
373C22×D4—431no—
374C23×C4—861no—
375C2×SD16—431no—
376C2×SD16—431no—
377C2×D8—431no—
378C2×D8—431no—
379C2×M16—861no—
380C2×M16—861no—
381C2×M16—861no—
382C2×M16—861no—
383C2×M16—1724no—
384C2×M16D17211yescharacteristic
385C2×M16D17211yescharacteristic
386C22×C8—861no—
387C22×C8—861no—
388C22×C8—861no—
389#126—861no—
390#125—431no—
391#124—431no—
392#123—861no—
393C22⋊Q8—431no—
394#121—431no—
395C4×Q8—431no—
396C4×D4—431no—
397C4×D4—431no—
398C4×D4—431no—
399C4×D4—431no—
400C4×D4—431no—
401C4×D4—861no—
402C4×D4—861no—
403C4×D4—861no—
404#117—861no—
405C2×C4⋊C4—431no—
406C2×C22⋊C4—861no—
407C2×C42C22×D4311yescharacteristic
408#107—431no—
409#107—431no—
410#106—431no—
411#106—431no—
412C4⋊C8—21no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—431no—
417C4⋊C8—861no—
418C4⋊C8—861no—
419C4⋊C8—861no—
420C4⋊C8C4×D4311yescharacteristic
421C4⋊C8C4×D4311yescharacteristic
422#103—431no—
423#103—431no—
424#102—431no—
425#102—431no—
426#102—431no—
427#102—431no—
428#102—431no—
429#102—431no—
430C22⋊C8—21no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8C4×D4311yescharacteristic
439C22⋊C8C4×D4311yescharacteristic
440#97—861no—
441#97D17211yescharacteristic
442#97D17211yescharacteristic
443C4×C8—861no—
444C4×C8—861no—
445C4×C8C22×D4311yescharacteristic
446C4×C8C22×D4311yescharacteristic
447C4×C8C22×D4311yescharacteristic
448C4×C8C22×D4311yescharacteristic
449C4×C8C22×D4311yescharacteristic
450C4×C8C22×D4311yescharacteristic
451C24—861no—
452C2×Q8—431no—
453C2×D4—431no—
454C2×D4—431no—
455C2×D4—431no—
456C2×D4—862no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—1721no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—1722no—
467C22×C4—1722no—
468C22×C4C2×C4×D4311yescharacteristic
469C22×C4C2×D17211yescharacteristic
470C22×C4#1062189811yescharacteristic
471SD16—862no—
472SD16—1721no—
473D8—862no—
474D8—1721no—
475M16—22no—
476M16—41no—
477M16—1722no—
478M16—1722no—
479M16—1722no—
480M16—1722no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—1722no—
488C2×C8—1722no—
489C2×C8—1722no—
490C2×C8C2×C4×D4311yescharacteristic
491C2×C8C2×C4×D4311yescharacteristic
492C2×C8C2×C4×D4311yescharacteristic
493C2×C8C2×C4×D4311yescharacteristic
494C2×C8C2×D17211yescharacteristic
495C2×C8C2×D17211yescharacteristic
496C2×C8C2×D17211yescharacteristic
497C2×C8C2×D17211yescharacteristic
498C4⋊C4—431no—
499C4⋊C4—431no—
500C4⋊C4—431no—
501C4⋊C4—431no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C22⋊C4—861no—
508C22⋊C4—861no—
509C22⋊C4—861no—
510C22⋊C4—861no—
511C22⋊C4—861no—
512C22⋊C4—861no—
513C22⋊C4—861no—
514C22⋊C4—861no—
515C22⋊C4—861no—
516C42—861no—
517C42C2×C4×D4311yescharacteristic
518C42C2×D17211yescharacteristic
519C42#1062189811yescharacteristic
520C42C23×D4311yescharacteristic
521C23—861no—
522C23—861no—
523C23—861no—
524C23—3441no—
525C23—1722no—
526C23—1722no—
527C23C4×D17211yescharacteristic
528Q8—861no—
529Q8—861no—
530D4—432no—
531D4—861no—
532D4—861no—
533D4—861no—
534D4—861no—
535D4—861no—
536D4—3441no—
537D4—1722no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—1722no—
549C2×C4—1722no—
550C2×C4—1722no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4C4×D17211yescharacteristic
558C2×C4C4×D17211yescharacteristic
559C2×C4C4×D17211yescharacteristic
560C2×C4C22×C4×D4311yescharacteristic
561C2×C4C22×D17211yescharacteristic
562C2×C4C2×#1062189811yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—1721no—
573C8—1721no—
574C8—1721no—
575C8—1721no—
576C8#1306335312yes—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—862no—
581C22—3444no—
582C22—1721no—
583C22—1721no—
584C22—1721no—
585C22—1721no—
586C22—1721no—
587C22—1721no—
588C22—1721no—
589C22—1721no—
590C22C2×C4×D17211yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—1721no—
596C4—1721no—
597C4—1721no—
598C4—1721no—
599C4—1721no—
600C4#131×D4311yescharacteristic
601C4#1458366411yescharacteristic
602C4C2×#1306335311yescharacteristic
603C4#1458369911yescharacteristic
604C2—41no—
605C2—3441no—
606C2—3441no—
607C2—1722no—
608C2#1914332311yescharacteristic
609C2C4×#1306335311yescharacteristic
610C2#1914351311yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1453C2
socleC22×C43C2×C4×D4
prime radical#14583035C4
cosocleC42×C43C24
hypercenter#1453D43
hypocenterC43#18008
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1453

Complements

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

NH ≅ G/Ntype
2. #19143599C2semidirect
3. M16×D172C2semidirect
4. #19133499C2semidirect
5. #19133481C2semidirect
6. #19133461C2semidirect
7. #19133454C2semidirect
8. #19133440C2semidirect
9. #19133426C2semidirect
10. #19133420C2semidirect
11. C8×#10621873C2semidirect
12. #19133384C2semidirect
13. #19133061C2semidirect
14. #19132987C2semidirect
15. C43×#1453C2semidirect
27. #14583029C22semidirect
28. C8×Dic86C22semidirect
35. #14582978C22semidirect
42. C8×D172C22semidirect
48. #14582652C22semidirect
49. #14582652C22semidirect
50. #14582650C22semidirect
51. #14582650C22semidirect
52. #14582631C22semidirect
53. #14582631C22semidirect
58. #14582628C22semidirect
59. #14582628C22semidirect
63. C43×#322C22semidirect
64. C43×#322C22semidirect
65. C43×#322C22semidirect
66. C82×C43C22semidirect
313. #1453D43semidirect
368. #322C2×D43semidirect
369. #322C2×D43semidirect
370. #322C2×D43semidirect
371. C82C2×D43semidirect
372. C43#18008semidirect

Maximal subgroups

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

subgroupindex
#191446442
#191435992
M16×D1722
#191334992
#191334812
#191334612
#191334542
#191334402
#191334262
#191334202
C8×#106218732
#191333842
#191330612
#191329872
C43×#14532
#1800843