Finite Group Databasebeta

← #11865864

Subgroups — #11865864

Order 1152.

1156 conjugacy classes of subgroups.

The subgroup lattice has 687 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×D4C211yesmaximal, characteristic, complemented
2C2×#63932C212yesmaximal, complemented
3#10593897C211yesmaximal, characteristic, complemented
4#10592718C211yesmaximal, characteristic, complemented
5C3×#5015C211yesmaximal, characteristic, complemented
6#10591468C212yesmaximal, complemented
7#10590607C212yesmaximal, complemented
8#10590530C212yesmaximal, complemented
9#10590365C211yesmaximal, characteristic, complemented
10#10590347C211yesmaximal, characteristic, complemented
11#10590336C211yesmaximal, characteristic, complemented
12#82307—31nomaximal
13#80332—31nomaximal
14C2×C3×D3×D4C2211yescharacteristic
15C22×C3×C4×D3—21no—
16C2×#3795C2212yes—
17C32×C4×D4C2211yescharacteristic
18C2×#3754C2212yes—
19#64078C2211yescharacteristic, complemented
20C3×D4×Dic3C2211yescharacteristic
21C2×C3×#213C2212yes—
22C3×C4×#67—21no—
23C3×#893C2211yescharacteristic
24C3×D3×C4⋊C4C2211yescharacteristic
25C3×#67⋊C4—21no—
26C3×D3×C22⋊C4—21no—
27C3×#874C2211yescharacteristic, complemented
28C3×C4×D12C2211yescharacteristic
29C3×C42×D3C2211yescharacteristic
30#63932—28no—
31#63908—21no—
32#63908—21no—
33Dic3×D12—21no—
34Dic3×D12—21no—
35#63860C2212yescomplemented
36C2×#3716C2212yes—
37C2×#3713C2212yes—
38C2×#3711C2212yes—
39#63637C2212yescomplemented
40C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
41C3×#809C2212yescomplemented
42C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
43Dic3⋊(C3⋊C8)C2212yescomplemented
44#63567C2212yescomplemented
45#63562C2212yescomplemented
46C2×C3×C4×D4—31no—
47C2×#932—32no—
48C2×#911—32no—
49#5716—31no—
50C4×D3×D4D311yescharacteristic, complemented
51#5477—31no—
52C3×#459—31no—
53#5153—32no—
54#5072—31no—
55#5019—31no—
56#5019—31no—
57#5019—31no—
58#5019—61no—
59#5016—32no—
60#5016—32no—
61#5015—31no—
62#5015D311yescharacteristic, complemented
63#4966—32no—
64#4924—31no—
65#4841—31no—
66#4837—31no—
67#4787—32no—
68#4771—32no—
69C23×C3×D3—21no—
70C2×C32×D4C2311yescharacteristic
71C22×C32×C4—21no—
72C2×#634C2312yes—
73C2×C3×#67—21no—
74C22×C3×Dic3—21no—
75C3×D3×D4—22no—
76C3×D3×D4D414yescomplemented
77C2×C3×D12—21no—
78C2×C3×D12—21no—
79C2×C3×D12C2312yes—
80C2×C3×D12C2311yescharacteristic
81C2×C3×C4×D3—21no—
82C2×C3×C4×D3—21no—
83C2×C3×C4×D3—21no—
84C2×C3×C4×D3—44no—
85C2×C3×C4×D3D411yescharacteristic
86C2×C3×C4×D3D411yescharacteristic
87C2×C3×C4×D3C2311yescharacteristic
88C2×#625—22no—
89C2×D3×Dic3—22no—
90#3795—24no—
91#3795—24no—
92C32×C4⋊C4C2311yescharacteristic
93C32×C22⋊C4—21no—
94C32×C42C2311yescharacteristic
95#3754—24no—
96C4⋊(C3⋊Dic3)—21no—
97C4⋊(C3⋊Dic3)—21no—
98C2×C3⋊(C3⋊C8)C2312yes—
99C3×#217—21no—
100C3×#213—24no—
101C3×(C2×D3)⋊C4—21no—
102C3×(C2×D3)⋊C4—21no—
103C3×C4⋊Dic3C2311yescharacteristic
104C3×Dic3⋊C4—21no—
105C3×C4×Dic3D411yescharacteristic
106C3×C4×Dic3D411yescharacteristic
107C3×C4×Dic3C2311yescharacteristic
108C2×C3×C3⋊C8C2312yes—
109(C2×D3)⋊Dic3—22no—
110(C2×D3)⋊Dic3—22no—
111#3716—24no—
112#3713—24no—
113#3711—24no—
114#3036—91noSylow
115C22×C3×D4—31no—
116C23×C3×C4—61no—
117C2×#237—32no—
118C2×D3×D4C2×D311yescharacteristic
119C2×#235—32no—
120C22×C4×D3—21no—
121C2×C3×D8—32no—
122C3×#127—31no—
123C3×C4×D4—21no—
124C3×C4×D4—31no—
125C3×C4×D4—31no—
126C3×C4×D4—31no—
127C3×C4×D4—61no—
128C3×C4×D4—61no—
129C3×C4×D4C2×D311yescharacteristic
130C3×C4×D4C2×D311yescharacteristic
131C2×C3×C4⋊C4—31no—
132C2×C3×C22⋊C4—61no—
133C2×C3×C42—31no—
134#938—61no—
135#938—61no—
136#936—32no—
137D4×Dic3—61no—
138D4×Dic3—61no—
139D4×Dic3C2×D311yescharacteristic
140C2×#214—32no—
141C2×#214—32no—
142C2×#214—32no—
143C2×#214—62no—
144#932—68no—
145C2×#213—32no—
146C2×#213—32no—
147C2×#213C2×D312yes—
148#930—61no—
149#930—61no—
150C4×#67—21no—
151C2×#208—32no—
152#911—68no—
153C2×#204—32no—
154C2×ΓL(1,𝔽25)—32no—
155#893C2×D311yescharacteristic
156D3×C4⋊C4C2×D311yescharacteristic
157#67⋊C4—21no—
158D3×C22⋊C4—21no—
159#875—32no—
160#874C2×D311yescharacteristic, complemented
161C4×D12—61no—
162C4×D12—61no—
163C4×D12C2×D311yescharacteristic
164C42×D3C2×D311yescharacteristic
165#869—31no—
166#869—31no—
167#869—61no—
168C3×C4⋊C8—31no—
169C3×#102—32no—
170#832—32no—
171#816—32no—
172Dic3⋊C8—32no—
173#810—32no—
174#810—32no—
175#810—32no—
176#810—62no—
177#809—32no—
178#809C2×D312yescomplemented
179C4⋊(C3⋊C8)—31no—
180C4⋊(C3⋊C8)—31no—
181C4⋊(C3⋊C8)—32no—
182C4⋊(C3⋊C8)—61no—
183C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
184C23×C32—21no—
185C22×C3×D3—21no—
186C22×C3×D3—24no—
187C22×C3×D3—22no—
188C22×C3×D3—42no—
189C22×C3×D3—42no—
190C22×C3×D3C2×D411yescharacteristic
191C32×D4—21no—
192C32×D4C2×D412yes—
193C2×C32×C4—21no—
194C2×C32×C4—42no—
195C2×C32×C4C2×D411yescharacteristic
196C2×C32×C4C2×D411yescharacteristic
197C2×C32×C4C2411yescharacteristic
198C2×C3⋊Dic3—22no—
199#634—22no—
200#634—22no—
201C3×#67—24no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—42no—
204C2×C3×Dic3C2×D411yescharacteristic
205C2×C3×Dic3C2×D411yescharacteristic
206C2×C3×Dic3C2×D411yescharacteristic
207C3×D12—22no—
208C3×D12—21no—
209C3×D12—22no—
210C3×D12—42no—
211C3×D12—42no—
212C3×D12C2×D412yes—
213C3×C4×D3—22no—
214C3×C4×D3—41no—
215C3×C4×D3—42no—
216C3×C4×D3—42no—
217C3×C4×D3—42no—
218C3×C4×D3C2×D412yes—
219C3×C4×D3#4112yes—
220#625—44no—
221D3×Dic3—44no—
222C3⋊(C3⋊C8)—22no—
223C3×C3⋊C8—22no—
224C2×AGL(1,ℤ/8)—92no—
225#532—91no—
226C2×C4×D4—31no—
227#463—92no—
228#463—92no—
229#461—91no—
230#461—91no—
231#459—31no—
232#459—91no—
233#423—91no—
234#417—92no—
235C24×C3—61no—
236C23×D3—21no—
237C2×C3×D4—21no—
238C2×C3×D4—34no—
239C2×C3×D4—31no—
240C2×C3×D4—32no—
241C2×C3×D4—62no—
242C2×C3×D4—61no—
243C2×C3×D4—61no—
244C2×C3×D4—61no—
245C2×C3×D4C22×D311yescharacteristic
246C2×C3×D4C22×D311yescharacteristic
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—31no—
250C22×C3×C4—31no—
251C22×C3×C4—31no—
252C22×C3×C4—41no—
253C22×C3×C4—61no—
254C22×C3×C4—61no—
255C22×C3×C4—61no—
256C22×C3×C4—61no—
257C22×C3×C4—124no—
258C2×#67—21no—
259C2×#67—62no—
260C2×#67—62no—
261C22×Dic3—21no—
262C22×Dic3—62no—
263#237—64no—
264#237—64no—
265D3×D4—22no—
266D3×D4D1214yescomplemented
267#235—64no—
268#235—64no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12C22×D312yes—
272C2×D12C22×D311yescharacteristic
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—44no—
277C2×C4×D3—62no—
278C2×C4×D3#6711yescharacteristic
279C2×C4×D3#6711yescharacteristic
280C2×C4×D3C22×D311yescharacteristic
281C2×Dic6—32no—
282C2×Dic6—32no—
283C2×Dic6—62no—
284C3×D8—64no—
285C2×C3×C8—32no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—31no—
288C3×C4⋊C4—61no—
289C3×C4⋊C4C22×D311yescharacteristic
290C3×C4⋊C4C22×D311yescharacteristic
291C3×C22⋊C4—21no—
292C3×C22⋊C4—21no—
293C3×C22⋊C4—41no—
294C3×C22⋊C4—61no—
295C3×C22⋊C4—61no—
296C3×C22⋊C4—61no—
297C3×C42—21no—
298C3×C42—31no—
299C3×C42—31no—
300C3×C42—31no—
301C3×C42C22×D311yescharacteristic
302C3×C42C22×D311yescharacteristic
303#217—21no—
304#217—62no—
305#217—62no—
306#214—64no—
307#214—64no—
308#214—64no—
309#214—124no—
310#213—24no—
311#213—64no—
312#213—64no—
313(C2×D3)⋊C4—21no—
314(C2×D3)⋊C4—21no—
315(C2×D3)⋊C4—62no—
316(C2×D3)⋊C4—62no—
317C4⋊Dic3—61no—
318C4⋊Dic3—61no—
319C4⋊Dic3—61no—
320C4⋊Dic3—61no—
321C4⋊Dic3—121no—
322C4⋊Dic3—121no—
323C4⋊Dic3C22×D311yescharacteristic
324Dic3⋊C4—21no—
325C4×Dic3#6711yescharacteristic
326C4×Dic3#6711yescharacteristic
327C4×Dic3C22×D311yescharacteristic
328#208—64no—
329C2×C3⋊C8—32no—
330C2×C3⋊C8—32no—
331C2×C3⋊C8—62no—
332C2×C3⋊C8C22×D312yes—
333#204—64no—
334ΓL(1,𝔽25)—64no—
335C22×C32—22no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32C22×D411yescharacteristic
339C2×C3×D3—21no—
340C2×C3×D3—21no—
341C2×C3×D3—22no—
342C2×C3×D3—48no—
343C2×C3×D3—41no—
344C2×C3×D3—41no—
345C2×C3×D3—42no—
346C2×C3×D3—42no—
347C2×C3×D3—42no—
348C2×C3×D3#12112yes—
349C32×C4—21no—
350C32×C4—41no—
351C32×C4AGL(1,ℤ/8)12yescomplemented
352C32×C4C22×D411yescharacteristic
353C32×C4C2×#4111yescharacteristic
354C3⋊Dic3—42no—
355C3×Dic3—21no—
356C3×Dic3—21no—
357C3×Dic3—41no—
358C3×Dic3#12112yes—
359C2×#41—92no—
360C22×D4—31no—
361C23×C4—61no—
362AGL(1,ℤ/8)—188no—
363C2×SD16—92no—
364C2×SD16—92no—
365C2×D8—32no—
366C2×D8—92no—
367C2×M16—92no—
368C4⋊Q8—91no—
369#127—31no—
370#124—92no—
371#121—181no—
372#121—181no—
373C4×D4—31no—
374C4×D4—31no—
375C4×D4—31no—
376C4×D4—61no—
377C4×D4—61no—
378C4×D4—181no—
379C4×D4—181no—
380C4×D4D3211yescharacteristic
381C2×C4⋊C4—31no—
382C2×C22⋊C4—61no—
383C2×C42—31no—
384C4⋊C8—31no—
385C4⋊C8—92no—
386C4⋊C8—91no—
387#103—92no—
388#103—92no—
389#102—32no—
390#102—92no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—31no—
394C23×C3—41no—
395C23×C3—64no—
396C23×C3—61no—
397C23×C3—62no—
398C23×C3—122no—
399C23×C3—122no—
400C22×D3—21no—
401C22×D3—24no—
402C22×D3—22no—
403C22×D3—42no—
404C22×D3—42no—
405C22×D3C2×#6711yescharacteristic
406C3×D4—21no—
407C3×D4—21no—
408C3×D4—22no—
409C3×D4—32no—
410C3×D4—41no—
411C3×D4—64no—
412C3×D4—62no—
413C3×D4—62no—
414C3×D4—61no—
415C3×D4—122no—
416C3×D4—122no—
417C3×D4C2×D1212yes—
418C3×D4D3×D412yes—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—31no—
425C2×C3×C4—32no—
426C2×C3×C4—32no—
427C2×C3×C4—31no—
428C2×C3×C4—31no—
429C2×C3×C4—41no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—62no—
433C2×C3×C4—61no—
434C2×C3×C4—82no—
435C2×C3×C4—121no—
436C2×C3×C4—122no—
437C2×C3×C4—122no—
438C2×C3×C4—122no—
439C2×C3×C4—122no—
440C2×C3×C4D3×D411yescharacteristic
441C2×C3×C4D3×D411yescharacteristic
442C2×C3×C4C2×#6711yescharacteristic
443C2×C3×C4C2×#6711yescharacteristic
444C2×C3×C4C23×D311yescharacteristic
445C2×C3×C4C23×D311yescharacteristic
446#67—24no—
447#67—124no—
448#67—124no—
449C2×Dic3—21no—
450C2×Dic3—42no—
451C2×Dic3—62no—
452C2×Dic3—62no—
453C2×Dic3—122no—
454C2×Dic3—124no—
455C2×Dic3C2×#6711yescharacteristic
456C2×Dic3C2×#6711yescharacteristic
457C2×Dic3C2×#6711yescharacteristic
458D12—21no—
459D12—22no—
460D12—22no—
461D12—42no—
462D12—42no—
463D12C2×D1212yes—
464C4×D3—22no—
465C4×D3—41no—
466C4×D3—42no—
467C4×D3—42no—
468C4×D3—42no—
469C4×D3—124no—
470C4×D3C2×D1212yes—
471C4×D3#23512yes—
472Dic6—62no—
473Dic6—62no—
474Dic6—62no—
475Dic6—62no—
476Dic6—122no—
477Dic6—122no—
478C3×C8—62no—
479C3⋊C8—22no—
480C3⋊C8—62no—
481C3⋊C8—62no—
482C3⋊C8—122no—
483C2×C32—42no—
484C2×C32C2×#12111yescharacteristic
485C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
486C2×C32#57511yescharacteristic
487C3×D3—22no—
488C3×D3—42no—
489C3×D3—82no—
490C24—61no—
491#41—184no—
492#41—184no—
493C2×Q8—92no—
494C2×D4—34no—
495C2×D4—31no—
496C2×D4—32no—
497C2×D4—62no—
498C2×D4—61no—
499C2×D4—61no—
500C2×D4—61no—
501C2×D4—182no—
502C2×D4C2×D3211yescharacteristic
503C22×C4—21no—
504C22×C4—31no—
505C22×C4—31no—
506C22×C4—31no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—124no—
512C22×C4—182no—
513SD16—184no—
514SD16—184no—
515D8—64no—
516D8—184no—
517M16—184no—
518C2×C8—32no—
519C2×C8—92no—
520C4⋊C4—31no—
521C4⋊C4—61no—
522C4⋊C4—181no—
523C4⋊C4—181no—
524C4⋊C4C2×D3211yescharacteristic
525C22⋊C4—21no—
526C22⋊C4—61no—
527C22⋊C4—61no—
528C22⋊C4—61no—
529C22⋊C4—182no—
530C22⋊C4—182no—
531C42—31no—
532C42—31no—
533C42—31no—
534C42C2×D3211yescharacteristic
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—21no—
538C22×C3—32no—
539C22×C3—42no—
540C22×C3—41no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—61no—
545C22×C3—61no—
546C22×C3—62no—
547C22×C3—81no—
548C22×C3—81no—
549C22×C3—128no—
550C22×C3—121no—
551C22×C3—121no—
552C22×C3—122no—
553C22×C3—122no—
554C22×C3—122no—
555C22×C3C2×D3×D411yescharacteristic
556C22×C3C22×#6711yescharacteristic
557C2×D3—21no—
558C2×D3—21no—
559C2×D3—22no—
560C2×D3—48no—
561C2×D3—41no—
562C2×D3—41no—
563C2×D3—42no—
564C2×D3—42no—
565C2×D3—42no—
566C2×D3#93012yes—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—21no—
571C3×C4—22no—
572C3×C4—32no—
573C3×C4—41no—
574C3×C4—41no—
575C3×C4—41no—
576C3×C4—61no—
577C3×C4—61no—
578C3×C4—81no—
579C3×C4—121no—
580C3×C4#91112yescomplemented
581C3×C4#93212yescomplemented
582C3×C4C22×D1211yescharacteristic
583C3×C4C2×#23511yescharacteristic
584C3×C4C2×D3×D411yescharacteristic
585C3×C4D3×#4111yescharacteristic
586Dic3—21no—
587Dic3—21no—
588Dic3—41no—
589Dic3—122no—
590Dic3—122no—
591Dic3—242no—
592Dic3#93012yes—
593C32#303611yescharacteristic, complemented, Sylow
594C23—21no—
595C23—31no—
596C23—64no—
597C23—61no—
598C23—62no—
599C23—122no—
600C23—122no—
601Q8—182no—
602Q8—182no—
603D4—21no—
604D4—32no—
605D4—64no—
606D4—62no—
607D4—61no—
608D4—62no—
609D4—122no—
610D4—122no—
611D4—364no—
612D4D3×D1212yes—
613C2×C4—21no—
614C2×C4—31no—
615C2×C4—32no—
616C2×C4—32no—
617C2×C4—31no—
618C2×C4—31no—
619C2×C4—42no—
620C2×C4—62no—
621C2×C4—61no—
622C2×C4—121no—
623C2×C4—122no—
624C2×C4—122no—
625C2×C4—122no—
626C2×C4—122no—
627C2×C4—182no—
628C2×C4—364no—
629C2×C4D3×#6711yescharacteristic
630C2×C4D3×#6711yescharacteristic
631C2×C4C22×D3211yescharacteristic
632C8—62no—
633C8—182no—
634C2×C3—21no—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—42no—
638C2×C3—42no—
639C2×C3—62no—
640C2×C3—82no—
641C2×C3—122no—
642C2×C3—242no—
643C2×C3D3×#12111yescharacteristic
644C2×C3C2×#91111yescharacteristic
645C2×C3#577311yescharacteristic
646C2×C3C2×#93011yescharacteristic
647C2×C3C2×#93211yescharacteristic
648C2×C3#582211yescharacteristic
649D3—22no—
650D3—42no—
651D3—82no—
652C22—22no—
653C22—32no—
654C22—41no—
655C22—41no—
656C22—61no—
657C22—61no—
658C22—62no—
659C22—128no—
660C22—121no—
661C22—121no—
662C22—122no—
663C22—122no—
664C22—122no—
665C22C2×D3×#6711yescharacteristic
666C4—21no—
667C4—32no—
668C4—41no—
669C4—61no—
670C4—61no—
671C4—121no—
672C4—362no—
673C4#6393212yescomplemented
674C4C2×D3×D1211yescharacteristic
675C4D3×#23511yescharacteristic
676C3—21no—
677C3#8033211yescharacteristic, complemented
678C3#8230711yescharacteristic, complemented
679C2—42no—
680C2—62no—
681C2—122no—
682C2—242no—
683C2D3×#93011yescharacteristic
684C2C2×#6393211yescharacteristic
685C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×C4×D3×D4C2semidirect
2. C2×#63932C2semidirect
3. #10593897C2semidirect
4. #10592718C2semidirect
5. C3×#5015C2semidirect
6. #10591468C2semidirect
7. #10590607C2semidirect
8. #10590530C2semidirect
9. #10590365C2semidirect
10. #10590347C2semidirect
11. #10590336C2semidirect
19. #64078C22semidirect
27. C3×#874C22semidirect
35. #63860C22semidirect
39. #63637C22semidirect
40. C4⋊(C3⋊(C3⋊C8))C22semidirect
41. C3×#809C22semidirect
42. C3×C4⋊(C3⋊C8)C22semidirect
43. Dic3⋊(C3⋊C8)C22semidirect
44. #63567C22semidirect
45. #63562C22semidirect
50. C4×D3×D4D3semidirect
62. #5015D3semidirect
76. C3×D3×D4D4semidirect
160. #874C2×D3semidirect
178. #809C2×D3semidirect
183. C4⋊(C3⋊C8)C2×D3semidirect
266. D3×D4D12semidirect
351. C32×C4AGL(1,ℤ/8)semidirect
580. C3×C4#911semidirect
581. C3×C4#932semidirect
593. C32#3036semidirect
673. C4#63932semidirect
677. C3#80332semidirect
678. C3#82307semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×D42
C2×#639322
#105938972
#105927182
C3×#50152
#105914682
#105906072
#105905302
#105903652
#105903472
#105903362
#823073
#803323