Finite Group Databasebeta

← #25067715

Subgroups — #25067715

Order 11008.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144651C211yesmaximal, characteristic
2#19143611C211yesmaximal, characteristic, complemented
3#19143340C211yesmaximal, characteristic, complemented
4#19133477C211yesmaximal, characteristic, complemented
5#19133471C211yesmaximal, characteristic, complemented
6#19133457C211yesmaximal, characteristic, complemented
7#19133437C211yesmaximal, characteristic, complemented
8#19133425C211yesmaximal, characteristic, complemented
9#19133409C211yesmaximal, characteristic, complemented
10#19133398C211yesmaximal, characteristic, complemented
11#19133377C211yesmaximal, characteristic, complemented
12#19133062C211yesmaximal, characteristic, complemented
13#19132979C211yesmaximal, characteristic, complemented
14#19132891C211yesmaximal, characteristic, complemented
15C43×#1594C211yesmaximal, characteristic, complemented
16C2×#13063333—21no—
17#14583446C2211yescharacteristic
18C4×#10621900C2211yescharacteristic
19#14583226C411yescharacteristic
20#14583222C411yescharacteristic
21#14583193C411yescharacteristic
22#14583187C411yescharacteristic
23#14583098C411yescharacteristic
24#14583092C411yescharacteristic
25#14583045C411yescharacteristic
26#14583041C411yescharacteristic
27C8×Dic86C2211yescharacteristic
28#14583023C2211yescharacteristic
29C4×#10621873C2211yescharacteristic
30C4×#10621883C2211yescharacteristic
31C4×#10621882C2211yescharacteristic
32#14582977C2211yescharacteristic
33#14582976C2211yescharacteristic
34#14582975—21no—
35#14582974—21no—
36#14582968—21no—
37#14582967—21no—
38C8×D172C2211yescharacteristic
39D4×C43⋊C8C2211yescharacteristic
40#14582955C2211yescharacteristic
41#14582953—21no—
42#14582950C2211yescharacteristic
43#14582950C2211yescharacteristic
44C4⋊C8×D43C2211yescharacteristic
45#14582864—21no—
46M16×Dic43—21no—
47C4×#10621872C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582631C2211yescharacteristic
52#14582629C2211yescharacteristic
53#14582628C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582621C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C4×D8×C43C2211yescharacteristic
61C43×#436C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621900C2×C411yescharacteristic
69C2×#10621873C2×C411yescharacteristic
70C2×#10621883C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72#13063333—44no—
73C2×#10621877—21no—
74C2×#10621872—21no—
75C2×#10621872D411yescharacteristic
76C2×#10621872D411yescharacteristic
77C22×C43⋊C8—21no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80#13063324C2×C411yescharacteristic
81#13063321C2×C411yescharacteristic
82#13063311—21no—
83#13063300C2×C411yescharacteristic
84#13063298—21no—
85#13063296C2×C411yescharacteristic
86C4×Dic86C2311yescharacteristic
87#13063290C2×C411yescharacteristic
88C4×D172C2311yescharacteristic
89D4×Dic43C2×C411yescharacteristic
90C4×C22⋊D43—21no—
91C4×C22⋊D43—21no—
92(C22⋊D43)⋊C4—21no—
93#13063283C2×C411yescharacteristic
94#13063281—21no—
95C2×C4×Dic43—21no—
96C42×D43C2311yescharacteristic
97#13063258C2×C411yescharacteristic
98#13063257C2×C411yescharacteristic
99#13063256C2×C411yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8C2×C411yescharacteristic
107Dic43⋊C8C2×C411yescharacteristic
108#13063250C2×C411yescharacteristic
109#13063248C2×C411yescharacteristic
110#13063247C2×C411yescharacteristic
111#13063246C2×C411yescharacteristic
112#13063246C2×C411yescharacteristic
113#13063245C2×C411yescharacteristic
114C22⋊(C43⋊C8)—21no—
115C22⋊(C43⋊C8)—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8C2×C411yescharacteristic
121(C2×D43)⋊C8C2×C411yescharacteristic
122#13063235—21no—
123#13063235D411yescharacteristic
124#13063235D411yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C8×Dic43—21no—
130C2×D8×C43C2×C411yescharacteristic
131C2×M16×C43—21no—
132C2×M16×C43—21no—
133C4×D4×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#107×C43C2×C411yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#102×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C2×D4×C43C22×C411yescharacteristic
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C2×C22⋊D43—21no—
150C2×C22⋊D43—21no—
151C2×C22⋊D43—21no—
152C2×C22⋊D43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155#10621900—22no—
156#10621900—41no—
157#10621898—42no—
158#10621898—42no—
159C2×D172—21no—
160C2×D172C22×C411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43C22×C411yescharacteristic
163C2×C4×D43C2×D411yescharacteristic
164C2×C4×D43#4111yescharacteristic
165C2×Dic86—21no—
166C2×Dic86C22×C411yescharacteristic
167D8×C43—41no—
168M16×C43—42no—
169M16×C43—42no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43C22×C411yescharacteristic
174C2×C8×C43C22×C411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C4⋊C4×C43C22×C411yescharacteristic
178C4⋊C4×C43C22×C411yescharacteristic
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C42×C43C2411yescharacteristic
182C22⋊Dic43—21no—
183C22⋊Dic43—21no—
184#10621883—22no—
185#10621882—41no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189C4⋊Dic43C22×C411yescharacteristic
190C4⋊Dic43C22×C411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43C22×C411yescharacteristic
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43#4111yescharacteristic
200#10621877—42no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—42no—
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C22×C411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209#10621873—22no—
210#10621872—22no—
211#10621872—41no—
212#10621872—42no—
213C8×D43—42no—
214C8×D43—42no—
215C23×C43—21no—
216C23×C43—21no—
217C22×D43—21no—
218C22×D43C4×D411yescharacteristic
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43C23×C411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C22⋊D43—42no—
233C22⋊D43—42no—
234C22⋊D43—42no—
235C22⋊D43—81no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—42no—
240C2×Dic43—81no—
241C2×Dic43C4×D411yescharacteristic
242C2×Dic43C4×D411yescharacteristic
243C2×Dic43C4×D411yescharacteristic
244D172—21no—
245D172—21no—
246D172—42no—
247C4×D43—21no—
248C4×D43—21no—
249C4×D43—21no—
250C4×D43—21no—
251C4×D43—41no—
252C4×D43—41no—
253C4×D43—41no—
254Dic86—21no—
255Dic86—42no—
256Dic86#13112yescomplemented
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—41no—
262C8×C43—41no—
263C8×C43—41no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—21no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8AGL(1,ℤ/8)12yes—
271#18011—431nomaximal, Sylow
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43C2×C4×D411yescharacteristic
279C2×D43—21no—
280C2×D43—21no—
281C2×D43—21no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—41no—
285C4×C43—21no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43C2×#13111yescharacteristic
289C4×C43#56811yescharacteristic
290C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
291C4×C43#57511yescharacteristic
292Dic43—22no—
293Dic43—21no—
294Dic43—21no—
295Dic43—21no—
296Dic43—41no—
297Dic43—41no—
298#3106—431no—
299#2971—431no—
300#2935—431no—
301#1594D4311yescharacteristic, complemented
302#1589—431no—
303#1588—431no—
304#1586—431no—
305#1583—431no—
306#1581—431no—
307SD16⋊C8—431no—
308C8×SD16—431no—
309#1573—431no—
310#1496—431no—
311#1477—431no—
312#1453—431no—
313C2×C43—81no—
314C2×C43—81no—
315C2×C43#293311yescharacteristic
316C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
317C2×C43#295711yescharacteristic
318D43—41no—
319D43—81no—
320C2×#131—861no—
321#532—431no—
322C4×#41—431no—
323#482—431no—
324#482—431no—
325#477—431no—
326#476—431no—
327#460—431no—
328#459—431no—
329#449—431no—
330#449—431no—
331C8×Q8—431no—
332C8×Q8—431no—
333C4×SD16—431no—
334C4×SD16—431no—
335C4×D8—431no—
336C4×D8C2×D4311yescharacteristic
337#436—431no—
338#436—431no—
339#436—861no—
340#436—861no—
341#436C2×D4311yescharacteristic
342#436C2×D4311yescharacteristic
343#435—861no—
344#435—861no—
345C8×D4—431no—
346C8×D4—431no—
347#432—431no—
348#432—861no—
349#431—431no—
350#431—431no—
351C2×C4⋊C8—431no—
352#408—861no—
353C4×M16—431no—
354C4×M16—861no—
355#335—431no—
356#335—431no—
357#334—431no—
358#334C2×D4311yescharacteristic
359Q8⋊C8—431no—
360Q8⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364D4⋊C8—431no—
365D4⋊C8C2×D4311yescharacteristic
366D4⋊C8C2×D4311yescharacteristic
367#322—431no—
368#322—431no—
369#322C2×D4311yescharacteristic
370C82—431no—
371C43#1801111yescharacteristic, complemented, Sylow
372C2×#41—431no—
373C2×#41—861no—
374C2×SD16—431no—
375C2×SD16—431no—
376C2×D8—431no—
377C2×D8C4×D4311yescharacteristic
378#131—1724no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—431no—
382C2×M16—431no—
383C2×M16—861no—
384C2×M16—861no—
385C22×C8—861no—
386C22×C8—861no—
387C22×C8—861no—
388C4⋊Q8—431no—
389#127—431no—
390#124—861no—
391#121—431no—
392#121—431no—
393#121—861no—
394C4×Q8—431no—
395C4×Q8—431no—
396C4×D4—431no—
397C4×D4—431no—
398C4×D4—861no—
399C4×D4—861no—
400C4×D4—861no—
401C4×D4C22×D4311yescharacteristic
402C4×D4C22×D4311yescharacteristic
403#117—431no—
404#117—861no—
405C2×C42—431no—
406C2×C42—861no—
407#107—431no—
408#107C4×D4311yescharacteristic
409#106—431no—
410#106—431no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—861no—
416C4⋊C8—861no—
417C4⋊C8—861no—
418C4⋊C8—861no—
419C4⋊C8C22×D4311yescharacteristic
420C4⋊C8C22×D4311yescharacteristic
421#103—431no—
422#103—431no—
423#102—431no—
424#102—431no—
425#102—431no—
426#102—431no—
427#102C4×D4311yescharacteristic
428#102C4×D4311yescharacteristic
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—431no—
432C22⋊C8—431no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439#97—431no—
440#97—431no—
441#97—861no—
442C4×C8—431no—
443C4×C8—431no—
444C4×C8—431no—
445C4×C8—861no—
446C4×C8—861no—
447C4×C8C22×D4311yescharacteristic
448C4×C8C22×D4311yescharacteristic
449C4×C8C22×D4311yescharacteristic
450#41—862no—
451#41—1722no—
452#41—1722no—
453#41—1721no—
454C2×Q8—431no—
455C2×Q8—861no—
456C2×D4—431no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4C2×C4×D4311yescharacteristic
463C2×D4C2×C4×D4311yescharacteristic
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472SD16—862no—
473SD16—862no—
474D8—41no—
475D8—1721no—
476M16—42no—
477M16—42no—
478M16—862no—
479M16—1721no—
480M16—1722no—
481M16—1722no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—431no—
486C2×C8—431no—
487C2×C8—431no—
488C2×C8—431no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—1722no—
493C2×C8—1722no—
494C2×C8—1722no—
495C2×C8C2×C4×D4311yescharacteristic
496C2×C8C2×C4×D4311yescharacteristic
497C2×C8D4×D4311yescharacteristic
498C2×C8D4×D4311yescharacteristic
499C4⋊C4—431no—
500C4⋊C4—431no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4C2×C4×D4311yescharacteristic
505C4⋊C4C2×C4×D4311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—861no—
509C22⋊C4—861no—
510C22⋊C4—861no—
511C22⋊C4—861no—
512C22⋊C4—861no—
513C42—431no—
514C42—431no—
515C42—431no—
516C42—861no—
517C42—861no—
518C42—861no—
519C42C23×D4311yescharacteristic
520C23—21no—
521C23—21no—
522C23—431no—
523C23—861no—
524Q8—432no—
525Q8—861no—
526Q8—1722no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—861no—
532D4—861no—
533D4—3441no—
534D4—1722no—
535D4—1722no—
536D4—1722no—
537D4—1722no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—431no—
545C2×C4—431no—
546C2×C4—431no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—3441no—
555C2×C4—1721no—
556C2×C4—1722no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4C22×C4×D4311yescharacteristic
560C2×C4C2×D4×D4311yescharacteristic
561C2×C4#41×D4311yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—432no—
570C8—861no—
571C8—861no—
572C8—861no—
573C8—1721no—
574C8—1721no—
575C8—1721no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—861no—
583C22—861no—
584C22—861no—
585C22—1721no—
586C22—1721no—
587C22—1721no—
588C22C4×D4×D4311yescharacteristic
589C4—21no—
590C4—41no—
591C4—41no—
592C4—861no—
593C4—861no—
594C4—862no—
595C4—861no—
596C4—1721no—
597C4—1721no—
598C4#131×D4311yescharacteristic
599C4#1458366511yescharacteristic
600C4AGL(1,ℤ/8)×D4311yescharacteristic
601C4#1458369511yescharacteristic
602C2—81no—
603C2—81no—
604C2—3441no—
605C2—1721no—
606C2#1914332411yescharacteristic
607C2#1914340611yescharacteristic
608C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1594C2
socleC22×C43C2×C4×D4
prime radical#19144651C2
cosocleC42×C43C24
hypercenter#1594D43
hypocenterC43#18011
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1594

Complements

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

NH ≅ G/Ntype
2. #19143611C2semidirect
3. #19143340C2semidirect
4. #19133477C2semidirect
5. #19133471C2semidirect
6. #19133457C2semidirect
7. #19133437C2semidirect
8. #19133425C2semidirect
9. #19133409C2semidirect
10. #19133398C2semidirect
11. #19133377C2semidirect
12. #19133062C2semidirect
13. #19132979C2semidirect
14. #19132891C2semidirect
15. C43×#1594C2semidirect
256. Dic86#131semidirect
301. #1594D43semidirect
371. C43#18011semidirect

Maximal subgroups

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

subgroupindex
#191446512
#191436112
#191433402
#191334772
#191334712
#191334572
#191334372
#191334252
#191334092
#191333982
#191333772
#191330622
#191329792
#191328912
C43×#15942
#1801143