Finite Group Databasebeta

← #25068300

Subgroups — #25068300

Order 11008.

668 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143683C211yesmaximal, characteristic, complemented
2#19143627C211yesmaximal, characteristic
3C4×SD16×D43C211yesmaximal, characteristic
4#19133497C211yesmaximal, characteristic, complemented
5#19133494C211yesmaximal, characteristic, complemented
6#19133439C211yesmaximal, characteristic, complemented
7#19133433C211yesmaximal, characteristic, complemented
8#19133430C211yesmaximal, characteristic, complemented
9#19133410C211yesmaximal, characteristic, complemented
10#19133405C211yesmaximal, characteristic, complemented
11#19133355C211yesmaximal, characteristic, complemented
12#19133040C211yesmaximal, characteristic, complemented
13#19133036C211yesmaximal, characteristic
14#19132883C211yesmaximal, characteristic, complemented
15C43×#1583C211yesmaximal, characteristic, complemented
16C2×SD16×D43C411yescharacteristic
17C4×Q8×D43C2211yescharacteristic
18C4×D4×D43C2211yescharacteristic
19#14583029—21no—
20#14583029C2211yescharacteristic, complemented
21#14583026—21no—
22#14583026C2211yescharacteristic, complemented
23Q8×C43⋊C8C2211yescharacteristic, complemented
24#14582990C411yescharacteristic
25C4×#10621873C2211yescharacteristic
26SD16×Dic43C411yescharacteristic
27C4×#10621884C2211yescharacteristic
28#14582986C411yescharacteristic
29C4×#10621883C2211yescharacteristic
30#14582984C411yescharacteristic
31#14582977C2211yescharacteristic
32#14582973—21no—
33#14582968—21no—
34C8×D172C2211yescharacteristic
35#14582964C2211yescharacteristic
36#14582955—21no—
37#14582955C2211yescharacteristic
38#14582955C2211yescharacteristic
39#14582950—21no—
40#14582950C2211yescharacteristic
41#106×D43C411yescharacteristic
42#103×D43C411yescharacteristic
43#102×D43C411yescharacteristic
44#14582862—21no—
45C22⋊C8×D43—21no—
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582651C2211yescharacteristic, complemented
49#14582651C2211yescharacteristic, complemented
50#14582650C2211yescharacteristic, complemented
51#14582631C2211yescharacteristic, complemented
52Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
53#14582629C2211yescharacteristic, complemented
54#14582628C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic, complemented
58#14582621C2211yescharacteristic, complemented
59#14582621C2211yescharacteristic, complemented
60C8×Q8×C43C2211yescharacteristic, complemented
61C4×SD16×C43C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#334C2211yescharacteristic, complemented
64C43×Q8⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic, complemented
67C2×Q8×D43C2×C411yescharacteristic
68C2×D4×D43C2×C411yescharacteristic
69C22×C4×D43—21no—
70C2×#10621873C2×C411yescharacteristic
71C2×#10621883C2×C411yescharacteristic
72C2×#10621884C2×C411yescharacteristic
73SD16×D43—24no—
74C2×#10621877—21no—
75C2×#10621872—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43C2×C411yescharacteristic
79C2×C8×D43C2×C411yescharacteristic
80Q8×Dic43C2×C411yescharacteristic
81C4×Dic86—21no—
82C4×Dic86C2311yescharacteristic
83#13063290—21no—
84#13063290C2×C411yescharacteristic
85C4×D172C2311yescharacteristic
86D4×Dic43C2×C411yescharacteristic
87#13063287C2×C411yescharacteristic
88C4×C22⋊D43—21no—
89(C22⋊D43)⋊C4—21no—
90C4⋊C4×D43—21no—
91C4⋊C4×D43C2×C411yescharacteristic
92C4⋊C4×D43C2×C411yescharacteristic
93C22⋊C4×D43—21no—
94C42×D43—21no—
95C42×D43C2311yescharacteristic
96#13063257C2×C411yescharacteristic
97#13063256C2×C411yescharacteristic
98#13063256C2×C411yescharacteristic
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8D411yescharacteristic
105Dic43⋊C8D411yescharacteristic
106#13063250C2×C411yescharacteristic
107#13063249C2×C411yescharacteristic
108#13063248C2×C411yescharacteristic
109#13063247C2×C411yescharacteristic
110#13063246C2×C411yescharacteristic
111#13063245C2×C411yescharacteristic
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8D411yescharacteristic
118(C2×D43)⋊C8D411yescharacteristic
119#13063235—21no—
120#13063235—21no—
121#13063235—21no—
122#13063235—21no—
123#13063235—21no—
124C4×C43⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43C2×C411yescharacteristic
129C8×Dic43C2×C411yescharacteristic
130C2×SD16×C43C2×C411yescharacteristic
131C2×M16×C43—21no—
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#106×C43C2×C411yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140C22⋊C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C2×Q8×C43C22×C411yescharacteristic
147C2×D4×C43C22×C411yescharacteristic
148C22×C4×C43—21no—
149C2×C22⋊D43—21no—
150C22×Dic43—21no—
151Q8×D43—22no—
152Q8×D43—41no—
153D4×D43—22no—
154D4×D43—41no—
155C2×D172C22×C411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×C4×D43C22×C411yescharacteristic
164C2×C4×D43C2×D411yescharacteristic
165C2×C4×D43#4111yescharacteristic
166C2×Dic86—21no—
167C2×Dic86C22×C411yescharacteristic
168SD16×C43—22no—
169M16×C43—81no—
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×C43—21no—
178C4⋊C4×C43C22×C411yescharacteristic
179C4⋊C4×C43C22×C411yescharacteristic
180C22⋊C4×C43—21no—
181C42×C43—21no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—21no—
184#10621884M1614yescomplemented
185#10621883—22no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43C22×C411yescharacteristic
190C4⋊Dic43C22×C411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43C22×C411yescharacteristic
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43#4111yescharacteristic
201#10621877—81no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C22×C411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209#10621873—22no—
210#10621872—42no—
211C8×D43—22no—
212C8×D43—41no—
213C8×D43—81no—
214C8×D43—81no—
215C23×C43—21no—
216C22×D43—21no—
217C22×D43—42no—
218C22×D43—42no—
219C22×D43—81no—
220C22×D43C4×D411yescharacteristic
221Q8×C43—21no—
222Q8×C43C2×M1612yes—
223D4×C43—21no—
224D4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C23×C411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C22⋊D43—42no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—81no—
238C2×Dic43C4×D411yescharacteristic
239C2×Dic43C4×D411yescharacteristic
240C2×Dic43C4×D411yescharacteristic
241D172—21no—
242D172C2×M1612yes—
243C4×D43—22no—
244C4×D43—21no—
245C4×D43—21no—
246C4×D43—21no—
247C4×D43—21no—
248C4×D43—42no—
249C4×D43—42no—
250C4×D43—41no—
251C4×D43—41no—
252C4×D43—81no—
253C4×D43—81no—
254Dic86—21no—
255Dic86—21no—
256Dic86—42no—
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⋊C8C2×M1612yes—
271#18060—431nomaximal, Sylow
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43C2×C4×D411yescharacteristic
276C2×D43—21no—
277C2×D43—21no—
278C2×D43—22no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—84no—
282C2×D43#44412yes—
283C4×C43—22no—
284C4×C43—21no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43C22×M1611yescharacteristic
288C4×C43#56811yescharacteristic
289C4×C43#57711yescharacteristic
290C4×C43#57711yescharacteristic
291Dic43—21no—
292Dic43—21no—
293Dic43—21no—
294Dic43—41no—
295Dic43—41no—
296Dic43—41no—
297#2984—431no—
298#2974—431no—
299C2×C4×SD16—431no—
300#1592—431no—
301#1592—431no—
302#1583—431no—
303#1583D4311yescharacteristic, complemented
304#1582—431no—
305#1582—431no—
306SD16⋊C8—431no—
307SD16⋊C8—431no—
308#1568—431no—
309#1491—431no—
310#1490—431no—
311#1451—431no—
312C2×C43—81no—
313C2×C43D4×M1611yescharacteristic
314C2×C43#294911yescharacteristic
315C2×C43C2×#44411yescharacteristic
316D43—22no—
317D43—42no—
318C22×SD16—431no—
319C2×C4×Q8—431no—
320C2×C4×D4—431no—
321#446—431no—
322#446—431no—
323#446—861no—
324#446—861no—
325C8×Q8—431no—
326C8×Q8C2×D4311yescharacteristic, complemented
327C4×SD16—431no—
328C4×SD16—431no—
329C4×SD16—431no—
330C4×SD16—431no—
331C4×SD16—431no—
332C4×SD16—431no—
333C4×SD16—431no—
334C4×SD16C2×D4311yescharacteristic
335#436—431no—
336#436C2×D4311yescharacteristic
337#435—861no—
338#435—861no—
339C8×D4—431no—
340C8×D4—431no—
341#432—431no—
342#432—431no—
343#432—861no—
344#431—431no—
345#431—861no—
346C2×#106—431no—
347C2×#103—431no—
348C2×#102—431no—
349#407—861no—
350C2×C22⋊C8—861no—
351C4×M16—431no—
352C2×C4×C8—431no—
353#335—431no—
354#335—431no—
355#334—431no—
356#334C2×D4311yescharacteristic, complemented
357Q8⋊C8—431no—
358Q8⋊C8—431no—
359Q8⋊C8—431no—
360Q8⋊C8C2×D4311yescharacteristic, complemented
361D4⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364D4⋊C8C2×D4311yescharacteristic
365#322—431no—
366#322—431no—
367#322—431no—
368#322C2×D4311yescharacteristic, complemented
369C43#1806011yescharacteristic, complemented, Sylow
370C22×Q8—431no—
371C22×D4—431no—
372C23×C4—861no—
373C2×SD16—431no—
374C2×SD16—431no—
375C2×SD16—431no—
376C2×SD16—864no—
377C2×SD16C4×D4311yescharacteristic
378C2×M16—21no—
379C2×M16—861no—
380C2×M16—861no—
381C22×C8—431no—
382C22×C8—431no—
383C22×C8—861no—
384C22×C8—861no—
385C4×Q8—431no—
386C4×Q8—431no—
387C4×Q8—431no—
388C4×Q8—861no—
389C4×Q8—861no—
390C4×Q8C22×D4311yescharacteristic
391C4×D4—431no—
392C4×D4—431no—
393C4×D4—431no—
394C4×D4—861no—
395C4×D4—861no—
396C4×D4C22×D4311yescharacteristic
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C42—431no—
402C2×C42—861no—
403#106—431no—
404#106—431no—
405#106—431no—
406#106C4×D4311yescharacteristic
407C4⋊C8—21no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8—861no—
415C4⋊C8C22×D4311yescharacteristic
416C4⋊C8C22×D4311yescharacteristic
417#103—431no—
418#103—431no—
419#103—431no—
420#103C4×D4311yescharacteristic
421#102—431no—
422#102—431no—
423#102—431no—
424#102C4×D4311yescharacteristic
425C22⋊C8—21no—
426C22⋊C8—431no—
427C22⋊C8—431no—
428C22⋊C8—861no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433#97—861no—
434#97—861no—
435#97—861no—
436#97—861no—
437#97—861no—
438C4×C8—21no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—431no—
442C4×C8—431no—
443C4×C8—431no—
444C4×C8—861no—
445C4×C8C22×D4311yescharacteristic
446C4×C8C22×D4311yescharacteristic
447C4×C8C22×D4311yescharacteristic
448C24—861no—
449C2×Q8—431no—
450C2×Q8—861no—
451C2×Q8—862no—
452C2×Q8—1721no—
453C2×Q8C2×C4×D4311yescharacteristic
454C2×D4—431no—
455C2×D4—861no—
456C2×D4—862no—
457C2×D4—1721no—
458C2×D4C2×C4×D4311yescharacteristic
459C22×C4—21no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—3441no—
470C22×C4—3441no—
471SD16—22no—
472SD16—434no—
473SD16—862no—
474SD16—862no—
475M16—81no—
476M16—3441no—
477M16—1722no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—862no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—3441no—
490C2×C8—3441no—
491C2×C8—1721no—
492C2×C8C2×C4×D4311yescharacteristic
493C2×C8C2×C4×D4311yescharacteristic
494C2×C8D4×D4311yescharacteristic
495C2×C8D4×D4311yescharacteristic
496C4⋊C4—21no—
497C4⋊C4—431no—
498C4⋊C4—431no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4C2×C4×D4311yescharacteristic
505C4⋊C4C2×C4×D4311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—861no—
508C22⋊C4—861no—
509C22⋊C4—861no—
510C42—21no—
511C42—431no—
512C42—431no—
513C42—431no—
514C42—861no—
515C42—861no—
516C42—861no—
517C42C23×D4311yescharacteristic
518C23—21no—
519C23—431no—
520C23—861no—
521C23—3441no—
522C23—1722no—
523C23—1722no—
524Q8—21no—
525Q8—861no—
526Q8—861no—
527Q8—1722no—
528Q8M16×D4312yes—
529D4—21no—
530D4—21no—
531D4—432no—
532D4—861no—
533D4—1722no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—431no—
540C2×C4—431no—
541C2×C4—431no—
542C2×C4—862no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—3441no—
551C2×C4—3441no—
552C2×C4—3441no—
553C2×C4—1722no—
554C2×C4—1722no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4C22×C4×D4311yescharacteristic
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4#41×D4311yescharacteristic
560C8—21no—
561C8—21no—
562C8—21no—
563C8—21no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—432no—
568C8—861no—
569C8—861no—
570C8—861no—
571C8—1721no—
572C8—1721no—
573C8—1721no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—432no—
578C22—861no—
579C22—861no—
580C22—862no—
581C22—3444no—
582C22—1721no—
583C22—1721no—
584C22C4×D4×D4311yescharacteristic
585C4—21no—
586C4—22no—
587C4—41no—
588C4—41no—
589C4—861no—
590C4—861no—
591C4—861no—
592C4—1721no—
593C4—1721no—
594C4—1721no—
595C4C2×M16×D4311yescharacteristic
596C4#1458366411yescharacteristic
597C4#1458370511yescharacteristic
598C4#1458370611yescharacteristic
599C2—81no—
600C2—862no—
601C2—1722no—
602C2#1914332811yescharacteristic
603C2#1914344911yescharacteristic
604C2#444×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1583C2
socleC22×C43C2×C4×D4
prime radicalC2×D4×D43C2×C4
cosocleC42×C43C24
hypercenter#1583D43
hypocenterC43#18060
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
1. #19143683C2semidirect
4. #19133497C2semidirect
5. #19133494C2semidirect
6. #19133439C2semidirect
7. #19133433C2semidirect
8. #19133430C2semidirect
9. #19133410C2semidirect
10. #19133405C2semidirect
11. #19133355C2semidirect
12. #19133040C2semidirect
14. #19132883C2semidirect
15. C43×#1583C2semidirect
20. #14583029C22semidirect
22. #14583026C22semidirect
23. Q8×C43⋊C8C22semidirect
48. #14582651C22semidirect
49. #14582651C22semidirect
50. #14582650C22semidirect
51. #14582631C22semidirect
52. Q8⋊(C43⋊C8)C22semidirect
53. #14582629C22semidirect
57. #14582621C22semidirect
58. #14582621C22semidirect
59. #14582621C22semidirect
60. C8×Q8×C43C22semidirect
63. C43×#334C22semidirect
64. C43×Q8⋊C8C22semidirect
66. C43×#322C22semidirect
184. #10621884M16semidirect
303. #1583D43semidirect
326. C8×Q8C2×D43semidirect
356. #334C2×D43semidirect
360. Q8⋊C8C2×D43semidirect
368. #322C2×D43semidirect
369. C43#18060semidirect

Maximal subgroups

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

subgroupindex
#191436832
#191436272
C4×SD16×D432
#191334972
#191334942
#191334392
#191334332
#191334302
#191334102
#191334052
#191333552
#191330402
#191330362
#191328832
C43×#15832
#1806043