Finite Group Databasebeta

← #11865862

Subgroups — #11865862

Order 1152.

1166 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×D4C211yesmaximal, characteristic, complemented
2C2×#63934C212yesmaximal, complemented
3#10593970C211yesmaximal, characteristic, complemented
4#10592714C211yesmaximal, characteristic, complemented
5C3×#5019C211yesmaximal, characteristic, complemented
6#10591471C212yesmaximal, complemented
7#10590609C212yesmaximal, complemented
8#10590534C212yesmaximal, complemented
9#10590363C211yesmaximal, characteristic, complemented
10#10590349C211yesmaximal, characteristic, complemented
11#10590336C211yesmaximal, characteristic, complemented
12#82307—31nomaximal
13#80428—31nomaximal
14C2×C3×D3×D4C2211yescharacteristic
15C22×C3×C4×D3—21no—
16C2×#3799C2212yes—
17C32×C4×D4C2211yescharacteristic
18C2×#3753C2212yes—
19#64083C2211yescharacteristic, complemented
20C3×D4×Dic3C2211yescharacteristic
21C2×C3×#214C2212yes—
22C3×C4×#67—21no—
23C3×#893C2211yescharacteristic
24C3×D3×C4⋊C4C2211yescharacteristic
25C3×#67⋊C4—21no—
26C3×D3×C22⋊C4—21no—
27C3×C4×D12C2211yescharacteristic
28C3×C42×D3C2211yescharacteristic
29C3×#869C2211yescharacteristic, complemented
30#63934—28no—
31#63909—21no—
32#63909—21no—
33#63894—21no—
34#63894—21no—
35#63864C2212yescomplemented
36C2×#3715C2212yes—
37C2×#3714C2212yes—
38C2×#3711C2212yes—
39#63636C2212yescomplemented
40C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
41C3×#810C2212yescomplemented
42C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
43Dic3⋊(C3⋊C8)C2212yescomplemented
44#63565C2212yescomplemented
45#63564C2212yescomplemented
46C2×C3×C4×D4—31no—
47C2×#932—32no—
48C2×#914—32no—
49#5725—31no—
50C4×D3×D4D311yescharacteristic, complemented
51#5477—31no—
52C3×#461—31no—
53#5165—32no—
54#5083—31no—
55#5019—31no—
56#5019D311yescharacteristic, complemented
57#5016—32no—
58#5016—32no—
59#5015—31no—
60#5015—31no—
61#5015—31no—
62#5015—61no—
63#4966—32no—
64#4924—31no—
65#4843—31no—
66#4837—31no—
67#4819—32no—
68#4803—32no—
69C23×C3×D3—21no—
70C2×C32×D4C2311yescharacteristic
71C22×C32×C4—21no—
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)—21no—
74C2×C4⋊(C3⋊D3)C2312yes—
75C2×C3×#67—21no—
76C22×C3×Dic3—21no—
77C3×D3×D4—22no—
78C3×D3×D4D414yescomplemented
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×C4×D3—21no—
82C2×C3×C4×D3—21no—
83C2×C3×C4×D3—44no—
84C2×C3×C4×D3D411yescharacteristic
85C2×C3×C4×D3D411yescharacteristic
86C2×C3×C4×D3C2311yescharacteristic
87C2×C3×Dic6C2312yes—
88C2×#626—22no—
89C2×#624—22no—
90#3799—24no—
91#3799—24no—
92C32×C4⋊C4C2311yescharacteristic
93C32×C22⋊C4—21no—
94C32×C42C2311yescharacteristic
95#3753—24no—
96C2×C3⋊(C3⋊C8)C2312yes—
97C3×#217—21no—
98C3×#214—24no—
99C3×(C2×D3)⋊C4—21no—
100C3×(C2×D3)⋊C4—21no—
101C3×C4⋊Dic3—21no—
102C3×C4⋊Dic3—21no—
103C3×C4⋊Dic3C2311yescharacteristic
104C3×Dic3⋊C4—21no—
105C3×C4×Dic3D411yescharacteristic
106C3×C4×Dic3D411yescharacteristic
107C3×C4×Dic3C2311yescharacteristic
108C2×C3×C3⋊C8C2312yes—
109#3722—22no—
110#3722—22no—
111#3715—24no—
112#3714—24no—
113#3711—24no—
114#3036—91noSylow
115C22×C3×D4—31no—
116C23×C3×C4—61no—
117C2×#239—32no—
118C2×D3×D4C2×D311yescharacteristic
119C2×#235—32no—
120C22×C4×D3—21no—
121C2×C3×SD16—32no—
122C3×C4⋊Q8—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#947—32no—
135C2×#215—32no—
136D4×Dic3C2×D311yescharacteristic
137C2×#214—32no—
138C2×#214C2×D312yes—
139#932—68no—
140C2×#213—32no—
141C2×#213—32no—
142C2×#213—32no—
143C2×#213—62no—
144#930—61no—
145#930—61no—
146C4×#67—21no—
147C2×#208—32no—
148#914—68no—
149C2×D24—32no—
150C2×ΓL(1,𝔽25)—32no—
151#895—61no—
152#895—61no—
153#893—61no—
154#893—61no—
155#893C2×D311yescharacteristic
156D3×C4⋊C4C2×D311yescharacteristic
157#67⋊C4—21no—
158D3×C22⋊C4—21no—
159#875—32no—
160#874—31no—
161#874—31no—
162#874—61no—
163C4×D12—61no—
164C4×D12—61no—
165C4×D12C2×D311yescharacteristic
166C42×D3C2×D311yescharacteristic
167#869C2×D311yescharacteristic, complemented
168C3×C4⋊C8—31no—
169C3×#103—32no—
170#835—32no—
171#821—32no—
172Dic3⋊C8—32no—
173#810—32no—
174#810C2×D312yescomplemented
175#809—32no—
176#809—32no—
177#809—32no—
178#809—62no—
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—22no—
186C22×C3×D3—21no—
187C22×C3×D3—24no—
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
198C4⋊(C3⋊D3)—22no—
199C4⋊(C3⋊D3)—22no—
200C4⋊(C3⋊D3)—42no—
201C4⋊(C3⋊D3)—42no—
202C3×#67—24no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—42no—
206C2×C3×Dic3C2×D411yescharacteristic
207C2×C3×Dic3C2×D411yescharacteristic
208C2×C3×Dic3C2×D411yescharacteristic
209C3×D12—21no—
210C3×D12C2×D412yes—
211C3×C4×D3—22no—
212C3×C4×D3—41no—
213C3×C4×D3—42no—
214C3×C4×D3—42no—
215C3×C4×D3—42no—
216C3×C4×D3C2×D412yes—
217C3×C4×D3#4112yes—
218C3×Dic6—22no—
219C3×Dic6—22no—
220#626—44no—
221#624—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—31no—
230#461—91no—
231#459—91no—
232#459—91no—
233#423—91no—
234#417—92no—
235C24×C3—61no—
236C23×D3—21no—
237C2×C3×Q8—32no—
238C2×C3×D4—21no—
239C2×C3×D4—34no—
240C2×C3×D4—31no—
241C2×C3×D4—62no—
242C2×C3×D4—61no—
243C2×C3×D4C22×D311yescharacteristic
244C2×C3×D4C22×D311yescharacteristic
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—31no—
248C22×C3×C4—31no—
249C22×C3×C4—31no—
250C22×C3×C4—41no—
251C22×C3×C4—61no—
252C22×C3×C4—61no—
253C22×C3×C4—61no—
254C22×C3×C4—61no—
255C22×C3×C4—124no—
256C2×#67—21no—
257C2×#67—62no—
258C22×Dic3—21no—
259#239—64no—
260#239—64no—
261D3×D4—22no—
262D3×D4D1214yescomplemented
263#235—64no—
264#235—64no—
265C2×D12—32no—
266C2×D12—32no—
267C2×D12—62no—
268C2×D12—62no—
269C2×D12—61no—
270C2×D12—61no—
271C2×D12—61no—
272C2×D12—61no—
273C2×D12—121no—
274C2×D12—121no—
275C2×D12C22×D311yescharacteristic
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—44no—
280C2×C4×D3—62no—
281C2×C4×D3—62no—
282C2×C4×D3#6711yescharacteristic
283C2×C4×D3#6711yescharacteristic
284C2×C4×D3C22×D311yescharacteristic
285C2×Dic6C22×D312yes—
286C3×SD16—64no—
287C2×C3×C8—32no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—31no—
290C3×C4⋊C4—61no—
291C3×C4⋊C4—61no—
292C3×C4⋊C4—61no—
293C3×C4⋊C4C22×D311yescharacteristic
294C3×C4⋊C4C22×D311yescharacteristic
295C3×C22⋊C4—21no—
296C3×C22⋊C4—21no—
297C3×C22⋊C4—41no—
298C3×C22⋊C4—61no—
299C3×C22⋊C4—61no—
300C3×C22⋊C4—61no—
301C3×C42—21no—
302C3×C42—31no—
303C3×C42—31no—
304C3×C42—31no—
305C3×C42C22×D311yescharacteristic
306C3×C42C22×D311yescharacteristic
307#217—21no—
308#215—64no—
309#214—24no—
310#214—64no—
311#213—64no—
312#213—64no—
313#213—64no—
314#213—124no—
315(C2×D3)⋊C4—21no—
316(C2×D3)⋊C4—21no—
317(C2×D3)⋊C4—62no—
318(C2×D3)⋊C4—62no—
319(C2×D3)⋊C4—62no—
320(C2×D3)⋊C4—62no—
321C4⋊Dic3—21no—
322C4⋊Dic3—21no—
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—
333D24—64no—
334ΓL(1,𝔽25)—64no—
335C22×C32—22no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32C22×D411yescharacteristic
339C2×C3⋊D3—42no—
340C2×C3⋊D3—42no—
341C2×C3⋊D3—42no—
342C2×C3×D3—21no—
343C2×C3×D3—21no—
344C2×C3×D3—22no—
345C2×C3×D3—48no—
346C2×C3×D3—41no—
347C2×C3×D3—41no—
348C2×C3×D3#12112yes—
349C32×C4—21no—
350C32×C4—41no—
351C32×C4AGL(1,ℤ/8)12yescomplemented
352C32×C4C22×D411yescharacteristic
353C32×C4C2×#4111yescharacteristic
354C3×Dic3—21no—
355C3×Dic3—21no—
356C3×Dic3—42no—
357C3×Dic3—41no—
358C3×Dic3#12112yes—
359C2×#41—92no—
360C22×D4—31no—
361C23×C4—61no—
362AGL(1,ℤ/8)—188no—
363C2×SD16—32no—
364C2×SD16—92no—
365C2×D8—92no—
366C2×D8—92no—
367C2×M16—92no—
368C4⋊Q8—31no—
369#127—91no—
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—32no—
388#103—92no—
389#102—92no—
390#102—92no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—31no—
394C23×C3—41no—
395C23×C3—64no—
396C23×C3—61no—
397C23×C3—122no—
398C23×C3—122no—
399C22×D3—21no—
400C22×D3—24no—
401C22×D3—42no—
402C22×D3—42no—
403C22×D3—62no—
404C22×D3—62no—
405C22×D3—122no—
406C22×D3C2×#6711yescharacteristic
407C3×Q8—62no—
408C3×Q8—62no—
409C3×D4—21no—
410C3×D4—21no—
411C3×D4—22no—
412C3×D4—32no—
413C3×D4—41no—
414C3×D4—64no—
415C3×D4—61no—
416C3×D4C2×D1212yes—
417C3×D4D3×D412yes—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—31no—
424C2×C3×C4—32no—
425C2×C3×C4—32no—
426C2×C3×C4—31no—
427C2×C3×C4—31no—
428C2×C3×C4—41no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—62no—
432C2×C3×C4—61no—
433C2×C3×C4—62no—
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—
448C2×Dic3—22no—
449C2×Dic3—21no—
450C2×Dic3—42no—
451C2×Dic3C2×#6711yescharacteristic
452C2×Dic3C2×#6711yescharacteristic
453C2×Dic3C2×#6711yescharacteristic
454D12—21no—
455D12—62no—
456D12—62no—
457D12—62no—
458D12—62no—
459D12—122no—
460D12—122no—
461D12—122no—
462D12—122no—
463D12—124no—
464D12—122no—
465D12—122no—
466D12—242no—
467D12—242no—
468D12C2×D1212yes—
469C4×D3—22no—
470C4×D3—41no—
471C4×D3—42no—
472C4×D3—42no—
473C4×D3—42no—
474C4×D3—124no—
475C4×D3—124no—
476C4×D3C2×D1212yes—
477C4×D3#23512yes—
478Dic6—22no—
479Dic6—22no—
480C3×C8—62no—
481C3⋊C8—22no—
482C3⋊C8—62no—
483C3⋊C8—62no—
484C3⋊C8—122no—
485C2×C32—42no—
486C2×C32C2×#12111yescharacteristic
487C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
488C2×C32#57511yescharacteristic
489C3⋊D3—82no—
490C3×D3—22no—
491C3×D3—42no—
492C24—61no—
493#41—184no—
494#41—184no—
495C2×Q8—32no—
496C2×D4—34no—
497C2×D4—31no—
498C2×D4—62no—
499C2×D4—61no—
500C2×D4—92no—
501C2×D4—182no—
502C2×D4—181no—
503C2×D4—181no—
504C2×D4C2×D3211yescharacteristic
505C22×C4—21no—
506C22×C4—31no—
507C22×C4—31no—
508C22×C4—31no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—124no—
514C22×C4—182no—
515SD16—64no—
516SD16—184no—
517D8—184no—
518D8—184no—
519M16—184no—
520C2×C8—32no—
521C2×C8—92no—
522C4⋊C4—31no—
523C4⋊C4—61no—
524C4⋊C4—61no—
525C4⋊C4—61no—
526C4⋊C4C2×D3211yescharacteristic
527C22⋊C4—21no—
528C22⋊C4—61no—
529C22⋊C4—61no—
530C22⋊C4—61no—
531C22⋊C4—182no—
532C22⋊C4—182no—
533C42—31no—
534C42—31no—
535C42—31no—
536C42C2×D3211yescharacteristic
537C22×C3—22no—
538C22×C3—22no—
539C22×C3—21no—
540C22×C3—32no—
541C22×C3—42no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—41no—
545C22×C3—41no—
546C22×C3—61no—
547C22×C3—61no—
548C22×C3—62no—
549C22×C3—81no—
550C22×C3—81no—
551C22×C3—128no—
552C22×C3—121no—
553C22×C3—121no—
554C22×C3C2×D3×D411yescharacteristic
555C22×C3C22×#6711yescharacteristic
556C2×D3—21no—
557C2×D3—21no—
558C2×D3—22no—
559C2×D3—48no—
560C2×D3—41no—
561C2×D3—41no—
562C2×D3—122no—
563C2×D3—122no—
564C2×D3—122no—
565C2×D3—122no—
566C2×D3—122no—
567C2×D3—122no—
568C2×D3—242no—
569C2×D3—242no—
570C2×D3—242no—
571C2×D3#93012yes—
572C3×C4—21no—
573C3×C4—21no—
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—22no—
577C3×C4—32no—
578C3×C4—41no—
579C3×C4—41no—
580C3×C4—41no—
581C3×C4—61no—
582C3×C4—61no—
583C3×C4—81no—
584C3×C4—121no—
585C3×C4—122no—
586C3×C4#91412yescomplemented
587C3×C4#93212yescomplemented
588C3×C4C22×D1211yescharacteristic
589C3×C4C2×#23511yescharacteristic
590C3×C4C2×D3×D411yescharacteristic
591C3×C4D3×#4111yescharacteristic
592Dic3—21no—
593Dic3—21no—
594Dic3—41no—
595Dic3—42no—
596Dic3#93012yes—
597C32#303611yescharacteristic, complemented, Sylow
598C23—21no—
599C23—31no—
600C23—64no—
601C23—61no—
602C23—122no—
603C23—122no—
604C23—182no—
605Q8—62no—
606Q8—62no—
607D4—21no—
608D4—32no—
609D4—64no—
610D4—61no—
611D4—182no—
612D4—182no—
613D4—362no—
614D4—364no—
615D4—362no—
616D4D3×D1212yes—
617C2×C4—21no—
618C2×C4—31no—
619C2×C4—32no—
620C2×C4—32no—
621C2×C4—31no—
622C2×C4—31no—
623C2×C4—42no—
624C2×C4—62no—
625C2×C4—61no—
626C2×C4—62no—
627C2×C4—121no—
628C2×C4—122no—
629C2×C4—122no—
630C2×C4—122no—
631C2×C4—122no—
632C2×C4—364no—
633C2×C4D3×#6711yescharacteristic
634C2×C4D3×#6711yescharacteristic
635C2×C4C22×D3211yescharacteristic
636C8—62no—
637C8—182no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—42no—
642C2×C3—42no—
643C2×C3—62no—
644C2×C3—82no—
645C2×C3—122no—
646C2×C3D3×#12111yescharacteristic
647C2×C3C2×#91411yescharacteristic
648C2×C3#577711yescharacteristic
649C2×C3C2×#93011yescharacteristic
650C2×C3C2×#93211yescharacteristic
651C2×C3#582211yescharacteristic
652D3—22no—
653D3—42no—
654D3—242no—
655D3—242no—
656D3—482no—
657C22—22no—
658C22—32no—
659C22—41no—
660C22—41no—
661C22—61no—
662C22—61no—
663C22—62no—
664C22—128no—
665C22—121no—
666C22—121no—
667C22—362no—
668C22—362no—
669C22—362no—
670C22C2×D3×#6711yescharacteristic
671C4—21no—
672C4—32no—
673C4—41no—
674C4—61no—
675C4—61no—
676C4—121no—
677C4—122no—
678C4#6393412yescomplemented
679C4C2×D3×D1211yescharacteristic
680C4D3×#23511yescharacteristic
681C3—21no—
682C3#8042811yescharacteristic, complemented
683C3#8230711yescharacteristic, complemented
684C2—42no—
685C2—62no—
686C2—122no—
687C2—722no—
688C2D3×#93011yescharacteristic
689C2C2×#6393411yescharacteristic
690C2#1059547011yescharacteristic
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×#63934C2semidirect
3. #10593970C2semidirect
4. #10592714C2semidirect
5. C3×#5019C2semidirect
6. #10591471C2semidirect
7. #10590609C2semidirect
8. #10590534C2semidirect
9. #10590363C2semidirect
10. #10590349C2semidirect
11. #10590336C2semidirect
19. #64083C22semidirect
29. C3×#869C22semidirect
35. #63864C22semidirect
39. #63636C22semidirect
40. C4⋊(C3⋊(C3⋊C8))C22semidirect
41. C3×#810C22semidirect
42. C3×C4⋊(C3⋊C8)C22semidirect
43. Dic3⋊(C3⋊C8)C22semidirect
44. #63565C22semidirect
45. #63564C22semidirect
50. C4×D3×D4D3semidirect
56. #5019D3semidirect
78. C3×D3×D4D4semidirect
167. #869C2×D3semidirect
174. #810C2×D3semidirect
183. C4⋊(C3⋊C8)C2×D3semidirect
262. D3×D4D12semidirect
351. C32×C4AGL(1,ℤ/8)semidirect
586. C3×C4#914semidirect
587. C3×C4#932semidirect
597. C32#3036semidirect
678. C4#63934semidirect
682. C3#80428semidirect
683. 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×#639342
#105939702
#105927142
C3×#50192
#105914712
#105906092
#105905342
#105903632
#105903492
#105903362
#823073
#804283