Finite Group Databasebeta

← #25105920

Subgroups — #25105920

Order 11008.

1450 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#124×D43C211yesmaximal, characteristic
2C2×#14582951C211yesmaximal, characteristic, complemented
3#19136991C211yesmaximal, characteristic, complemented
4#19135528C211yesmaximal, characteristic, complemented
5#19135527C211yesmaximal, characteristic, complemented
6#19135525C211yesmaximal, characteristic, complemented
7#19135405C212yesmaximal, complemented
8#19135403C212yesmaximal, complemented
9#19134528C212yesmaximal, complemented
10#19134524C212yesmaximal
11C43×#1983C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2211yescharacteristic
13C22×D4×D43C2211yescharacteristic
14C2×#13063314C2211yescharacteristic
15C2×#13063313C2211yescharacteristic
16C2×#13063312C2211yescharacteristic
17C2×#13063311—21no—
18C2×#13063311—21no—
19#124×D43—24no—
20#124×D43C418yescomplemented
21C2×C22⋊C4×D43—21no—
22C2×C22⋊C4×D43—21no—
23C2×C42×D43C2211yescharacteristic
24#14582951—24no—
25C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
26C2×#13063250C2212yescomplemented
27C2×#13063249C2212yescomplemented
28C2×#13063248C2212yescomplemented
29C2×#13063247C2212yes—
30C2×#13063246C2212yes—
31C2×#13063245C2212yes—
32C2×(C2×D43)⋊C8C2212yes—
33C2×C8×Dic43C2212yescomplemented
34#14582766—21no—
35#14582764C2212yescomplemented
36#14582761—21no—
37#14582756C2212yes—
38C4×C4⋊Dic43C2211yescharacteristic, complemented
39C4×(C2×D43)⋊C4—21no—
40#14582745—21no—
41C2×#124×C43C2211yescharacteristic
42C2×C4⋊C8×C43C2211yescharacteristic, complemented
43C2×#103×C43C2212yescomplemented
44C2×#102×C43C2212yes—
45C4×C4⋊C4×C43C2211yescharacteristic, complemented
46C24×D43—21no—
47C22×Dic86—21no—
48C22×Dic86C2311yescharacteristic
49C2×Q8×D43—22no—
50C2×Q8×D43—42no—
51C2×Q8×D43—42no—
52C2×Q8×D43C2×C414yes—
53C22×D172C2311yescharacteristic
54C22×C22⋊D43—21no—
55C2×D4×D43—22no—
56C2×D4×D43—42no—
57C2×D4×D43—42no—
58C2×D4×D43C2×C414yes—
59C22×C4×D43—21no—
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2312yes—
64#13063314—22no—
65#13063314C2×C414yes—
66#13063313—22no—
67#13063313C2×C414yes—
68#13063312—22no—
69#13063312C2×C414yes—
70#13063311—28no—
71#13063311—28no—
72C2×C4⋊Dic43C2312yes—
73C2×C22⋊Dic43—21no—
74C2×C22⋊Dic43—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—22no—
80C22⋊C4×D43—28no—
81C22⋊C4×D43—28no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86C42×D43C2×C414yes—
87C42×D43D414yes—
88C4⋊(C43⋊C8)—22no—
89#13063250—42no—
90#13063249—42no—
91#13063248—42no—
92#13063247—42no—
93#13063246—42no—
94#13063245—42no—
95(C2×D43)⋊C8—24no—
96C8×Dic43—24no—
97C43⋊#95—21no—
98C43⋊#95—22no—
99C43⋊#95—22no—
100C43⋊#95—22no—
101C22×Q8×C43C2311yescharacteristic
102C22×D4×C43C2311yescharacteristic
103C22×C8×C43C2312yes—
104#124×C43—22no—
105#124×C43C2×C414yes—
106C2×C4⋊C4×C43C2312yes—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C42×C43—21no—
110C2×C42×C43C2311yescharacteristic
111C4⋊C8×C43—22no—
112#103×C43—42no—
113#102×C43—42no—
114#95×C43—21no—
115C24×C43—21no—
116C23×D43—21no—
117C23×D43—24no—
118C23×D43—44no—
119C23×D43—42no—
120C23×D43—42no—
121C23×D43—44no—
122C23×D43C2×D411yescharacteristic
123C2×Q8×C43—21no—
124C2×Q8×C43—22no—
125C2×Q8×C43—22no—
126C2×Q8×C43C22×C412yes—
127C2×D4×C43—21no—
128C2×D4×C43—22no—
129C2×D4×C43—22no—
130C2×D4×C43C22×C412yes—
131C22×C4×C43—21no—
132C22×C4×C43—22no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C2×C22⋊D43—24no—
137C2×C22⋊D43—44no—
138C22×Dic43—21no—
139C22×Dic43—22no—
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143Q8×D43—48no—
144Q8×D43—44no—
145Q8×D43—44no—
146D4×D43—48no—
147D4×D43—44no—
148D4×D43—44no—
149C2×D172—21no—
150C2×D172—22no—
151C2×D172—22no—
152C2×D172C22×C412yes—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—24no—
156C2×C4×D43—24no—
157C2×C4×D43—41no—
158C2×C4×D43—41no—
159C2×C4×D43—44no—
160C2×C4×D43C22⋊C414yes—
161C2×C4×D43C22⋊C414yes—
162C2×C4×D43C22×C412yes—
163C2×C4×D43C2×D412yes—
164C2×Dic86—22no—
165C2×Dic86—22no—
166C2×Dic86—21no—
167C2×Dic86—24no—
168C2×Dic86—44no—
169C2×Dic86C22×C412yes—
170C2×C8×C43—22no—
171C2×C8×C43—22no—
172C2×C8×C43—22no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—22no—
175C22⋊C4×C43—24no—
176C22⋊C4×C43—24no—
177C42×C43—42no—
178C42×C43C22×C412yes—
179C42×C43C2×D412yes—
180C22⋊Dic43—24no—
181C22⋊Dic43—24no—
182(C2×D43)⋊C4—24no—
183(C2×D43)⋊C4—24no—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—44no—
187C4⋊Dic43—22no—
188C4⋊Dic43—22no—
189C4×Dic43—42no—
190C4×Dic43C22⋊C414yes—
191C4×Dic43C22⋊C414yes—
192C4×Dic43C22×C412yes—
193C4×Dic43C2×D412yes—
194C2×C43⋊C8—22no—
195C2×C43⋊C8—22no—
196C2×C43⋊C8—22no—
197C23×C43—22no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43C22×D411yescharacteristic
203C22×D43—22no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—22no—
207C22×D43—48no—
208C22×D43—48no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—48no—
214C22×D43—88no—
215C22×D43—88no—
216C22×D43C2×C22⋊C412yes—
217C22×D43#13514yes—
218Q8×C43—24no—
219Q8×C43—41no—
220Q8×C43—41no—
221D4×C43—24no—
222D4×C43—41no—
223D4×C43—41no—
224C2×C4×C43—22no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—22no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43C2×C22⋊C412yes—
233C2×C4×C43C2×C22⋊C412yes—
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43H(5,𝔽2)12yes—
237C2×C4×C43H(5,𝔽2)12yes—
238C22⋊D43—48no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—22no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43C2×C22⋊C412yes—
249C2×Dic43C2×C22⋊C412yes—
250C2×Dic43C2×C22⋊C412yes—
251D172—24no—
252D172—41no—
253D172—41no—
254C4×D43—28no—
255C4×D43—24no—
256C4×D43—22no—
257C4×D43—22no—
258C4×D43—44no—
259C4×D43—48no—
260Dic86—24no—
261Dic86—48no—
262Dic86—41no—
263Dic86—41no—
264C8×C43—42no—
265C43⋊C8—42no—
266#21806—431nomaximal, Sylow
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—82no—
271C22×C43—82no—
272C22×C43C22×C22⋊C411yescharacteristic
273C22×C43#53512yes—
274C22×C43C2×#13512yes—
275C22×C43#57511yescharacteristic
276C22×C43#57511yescharacteristic
277C2×D43—22no—
278C2×D43—22no—
279C2×D43—24no—
280C2×D43—24no—
281C2×D43—42no—
282C2×D43—42no—
283C2×D43—42no—
284C2×D43—816no—
285C2×D43—82no—
286C2×D43—82no—
287C2×D43#41614yes—
288C4×C43—22no—
289C4×C43—22no—
290C4×C43—42no—
291C4×C43—82no—
292C4×C43#51812yes—
293C4×C43#53511yescharacteristic
294C4×C43#53511yescharacteristic
295Dic43—22no—
296Dic43—22no—
297Dic43—22no—
298Dic43—42no—
299Dic43—82no—
300C22×#124—431no—
301C2×#431—431no—
302#2283—431no—
303#1983—431no—
304#1983—431no—
305#1983—431no—
306#1983D4311yescharacteristic, complemented
307#1958—432no—
308#1958—432no—
309#1787—432no—
310#1786—432no—
311C2×C43—82no—
312C2×C43#230911yescharacteristic
313C2×C43C2×#41611yescharacteristic
314C2×C43#289611yescharacteristic
315C2×C43#321112yes—
316C2×C43#321112yes—
317D43—24no—
318D43—82no—
319C23×Q8—431no—
320C23×D4—431no—
321C2×#124—431no—
322C2×#124—431no—
323C2×#124—438no—
324C2×#124—431no—
325C2×#124—861no—
326C2×#124—861no—
327C2×#124—864no—
328C2×#124C2×D4311yescharacteristic
329C22×C22⋊C4—861no—
330C22×C22⋊C4—861no—
331C22×C42—431no—
332#431—864no—
333C2×C4⋊C8—431no—
334C2×C4⋊C8C2×D4311yescharacteristic, complemented
335C2×#103—432no—
336C2×#103—432no—
337C2×#103—432no—
338C2×#103C2×D4312yescomplemented
339C2×#102—432no—
340C2×#102—432no—
341C2×#102—432no—
342C2×#102C2×D4312yes—
343C2×C22⋊C8—432no—
344C2×C4×C8—432no—
345#383—861no—
346#382—432no—
347#381—861no—
348#380—432no—
349C4×C4⋊C4—431no—
350C4×C4⋊C4C2×D4311yescharacteristic, complemented
351C4×C22⋊C4—861no—
352#376—861no—
353C43#2180611yescharacteristic, complemented, Sylow
354C25—861no—
355C22×Q8—434no—
356C22×Q8—431no—
357C22×Q8—861no—
358C22×Q8—862no—
359C22×Q8—1722no—
360C22×Q8—1722no—
361C22×Q8C22×D4311yescharacteristic
362C22×D4—434no—
363C22×D4—431no—
364C22×D4—862no—
365C22×D4—861no—
366C22×D4—1722no—
367C22×D4—1722no—
368C22×D4C22×D4311yescharacteristic
369C23×C4—431no—
370C23×C4—431no—
371C23×C4—431no—
372C23×C4—861no—
373C22×C8—432no—
374C22×C8C22×D4312yes—
375#124—22no—
376#124—434no—
377#124—434no—
378#124—434no—
379#124—868no—
380#124—868no—
381#124—862no—
382#124—862no—
383#124—862no—
384#124C4×D4314yes—
385C2×C4⋊C4—432no—
386C2×C4⋊C4C22×D4312yes—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—868no—
390C2×C22⋊C4—868no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—862no—
398C2×C42—21no—
399C2×C42—431no—
400C2×C42—431no—
401C2×C42—431no—
402C2×C42—434no—
403C2×C42—434no—
404C2×C42—861no—
405C2×C42C22×D4311yescharacteristic
406C4⋊C8—22no—
407C4⋊C8—862no—
408#103—42no—
409#103—1722no—
410#103—1722no—
411#103—1722no—
412#102—42no—
413#102—1722no—
414#102—1722no—
415#102—1722no—
416C22⋊C8—864no—
417C4×C8—864no—
418#95—21no—
419#95—862no—
420#95—862no—
421#95—862no—
422#95—861no—
423C24—21no—
424C24—431no—
425C24—864no—
426C24—861no—
427C24—1724no—
428C24—1724no—
429C24—1722no—
430C24—1722no—
431C2×Q8—21no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—432no—
435C2×Q8—864no—
436C2×Q8—861no—
437C2×Q8—862no—
438C2×Q8—862no—
439C2×Q8—1724no—
440C2×Q8—1728no—
441C2×Q8—1724no—
442C2×Q8—1724no—
443C2×Q8C2×C4×D4312yes—
444C2×D4—21no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—432no—
448C2×D4—864no—
449C2×D4—861no—
450C2×D4—862no—
451C2×D4—862no—
452C2×D4—1728no—
453C2×D4—1724no—
454C2×D4—1724no—
455C2×D4—1724no—
456C2×D4C2×C4×D4312yes—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—434no—
463C22×C4—432no—
464C22×C4—432no—
465C22×C4—434no—
466C22×C4—864no—
467C22×C4—864no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—861no—
471C22×C4—862no—
472C22×C4—1721no—
473C22×C4—1721no—
474C22×C4—1724no—
475C22×C4D4×D4311yescharacteristic
476C22×C4D4×D4311yescharacteristic
477C22×C4C23×D4311yescharacteristic
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—862no—
482C2×C8—862no—
483C2×C8—862no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—862no—
487C4⋊C4—862no—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—864no—
491C22⋊C4—864no—
492C22⋊C4—864no—
493C22⋊C4—864no—
494C22⋊C4—864no—
495C22⋊C4—864no—
496C22⋊C4—1724no—
497C42—42no—
498C42—434no—
499C42—434no—
500C42—432no—
501C42—432no—
502C42—1722no—
503C42C2×C4×D4312yes—
504C42D4×D4312yes—
505C23—22no—
506C23—42no—
507C23—41no—
508C23—41no—
509C23—42no—
510C23—432no—
511C23—434no—
512C23—861no—
513C23—861no—
514C23—862no—
515C23—862no—
516C23—3448no—
517C23—3448no—
518C23—1728no—
519C23—1728no—
520C23—1728no—
521C23—1722no—
522C23—1721no—
523C23—1721no—
524C23—1722no—
525C23C2×D4×D4311yescharacteristic
526Q8—24no—
527Q8—41no—
528Q8—41no—
529Q8—864no—
530Q8—1728no—
531Q8—1721no—
532Q8—1721no—
533D4—24no—
534D4—41no—
535D4—41no—
536D4—864no—
537D4—1728no—
538D4—1721no—
539D4—1721no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—432no—
549C2×C4—432no—
550C2×C4—432no—
551C2×C4—868no—
552C2×C4—862no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—862no—
556C2×C4—864no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—1724no—
561C2×C4—1728no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1722no—
566C2×C4C22⋊C4×D4312yes—
567C2×C4C22⋊C4×D4312yes—
568C2×C4C22×C4×D4311yescharacteristic
569C2×C4C2×D4×D4311yescharacteristic
570C2×C4#1306337012yes—
571C2×C4#1306337112yes—
572C8—42no—
573C8—1722no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—82no—
578C22—82no—
579C22—434no—
580C22—864no—
581C22—864no—
582C22—862no—
583C22—862no—
584C22—34416no—
585C22—3442no—
586C22—3442no—
587C22—1722no—
588C22—1722no—
589C22—1722no—
590C22C2×C22⋊C4×D4311yescharacteristic
591C22#1458346512yes—
592C22#135×D4312yes—
593C22#1458369511yescharacteristic
594C22#1458369811yescharacteristic
595C4—22no—
596C4—22no—
597C4—42no—
598C4—82no—
599C4—862no—
600C4—862no—
601C4—862no—
602C4—3442no—
603C4—1722no—
604C4#1458337112yes—
605C4#1458346211yescharacteristic
606C4#1458346711yescharacteristic
607C2—82no—
608C2—864no—
609C2—3442no—
610C2#1913717411yescharacteristic
611C2#416×D4311yescharacteristic
612C2#1914311111yescharacteristic
613C2#1914555812yes—
614C2#1914556412yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1983C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1983D43
hypocenterC43#21806
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×#14582951C2semidirect
3. #19136991C2semidirect
4. #19135528C2semidirect
5. #19135527C2semidirect
6. #19135525C2semidirect
7. #19135405C2semidirect
8. #19135403C2semidirect
9. #19134528C2semidirect
11. C43×#1983C2semidirect
20. #124×D43C4semidirect
25. C2×C4⋊(C43⋊C8)C22semidirect
26. C2×#13063250C22semidirect
27. C2×#13063249C22semidirect
28. C2×#13063248C22semidirect
33. C2×C8×Dic43C22semidirect
35. #14582764C22semidirect
38. C4×C4⋊Dic43C22semidirect
42. C2×C4⋊C8×C43C22semidirect
43. C2×#103×C43C22semidirect
45. C4×C4⋊C4×C43C22semidirect
306. #1983D43semidirect
334. C2×C4⋊C8C2×D43semidirect
338. C2×#103C2×D43semidirect
350. C4×C4⋊C4C2×D43semidirect
353. C43#21806semidirect

Maximal subgroups

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

subgroupindex
C2×#124×D432
C2×#145829512
#191369912
#191355282
#191355272
#191355252
#191354052
#191354032
#191345282
#191345242
C43×#19832
#2180643