Finite Group Databasebeta

← #11865857

Subgroups — #11865857

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×#5725C211yesmaximal, characteristic, complemented
2C2×#63939C212yesmaximal, complemented
3C4×D3×D12C211yesmaximal, characteristic, complemented
4#10592782C211yesmaximal, characteristic, complemented
5C3×#5083C211yesmaximal, characteristic, complemented
6#10591568C212yesmaximal, complemented
7#10591567C212yesmaximal, complemented
8#10591550C212yesmaximal, complemented
9#10590355C211yesmaximal, characteristic, complemented
10#10590347C211yesmaximal, characteristic, complemented
11#10590336C211yesmaximal, characteristic, complemented
12#83297—31nomaximal
13#80428—31nomaximal
14C2×C3×#239C2212yes—
15C2×D3×D12C2211yescharacteristic
16C2×C4×D32—21no—
17C32×C4⋊Q8C2211yescharacteristic, complemented
18C2×#3755C2212yes—
19C4×C4⋊(C3⋊D3)C2211yescharacteristic
20C3×#947C2212yescomplemented
21C2×C3×#215C2212yes—
22C3×#895—21no—
23C3×#895—21no—
24C3×#893—21no—
25C3×#893—21no—
26C3×#874C2211yescharacteristic, complemented
27C3×C4×D12C2211yescharacteristic
28C3×C42×D3C2211yescharacteristic
29#63939—28no—
30D3×(C2×D3)⋊C4—21no—
31C4×#626—21no—
32#63894C2211yescharacteristic
33Dic3×D12C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic
35#63880—21no—
36C2×#3714C2212yes—
37C2×#3713C2212yes—
38C2×#3711C2212yes—
39#63662C2212yescomplemented
40C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
41C3×#835C2212yescomplemented
42C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
43Dic3⋊(C3⋊C8)C2212yescomplemented
44#63563C2212yescomplemented
45#63562C2212yescomplemented
46C3×#532—31no—
47C2×#949—32no—
48C2×#914—32no—
49#5725D311yescharacteristic, complemented
50C4×D3×D4—31no—
51C2×C4×D12—31no—
52C3×#461—31no—
53#5232—32no—
54#5165—32no—
55#5083—31no—
56#5083—31no—
57#5083—61no—
58#5083D311yescharacteristic, complemented
59#5072—31no—
60#5072—31no—
61#5057—32no—
62#5057—32no—
63#5015—31no—
64#4924—31no—
65#4843—31no—
66#4837—31no—
67#4819—32no—
68#4803—32no—
69C22×D32—21no—
70C2×C32×Q8C2312yes—
71C2×C4⋊(C3⋊D3)C2311yescharacteristic
72C2×C4×C3⋊D3—21no—
73C3×#239—24no—
74C3×#239—24no—
75C2×C3×D12—22no—
76C2×C3×D12—21no—
77C2×C3×D12—21no—
78C2×C3×D12C2312yes—
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3D411yescharacteristic
83C2×C3×C4×D3D411yescharacteristic
84C2×C3×C4×D3C2311yescharacteristic
85C2×#626—21no—
86C2×#624—21no—
87C2×D3×Dic3—21no—
88C2×D3×Dic3—21no—
89D3×D12—22no—
90D3×D12D414yescomplemented
91C4×D32—44no—
92C32×C4⋊C4—21no—
93C32×C4⋊C4—21no—
94C32×C42C2311yescharacteristic
95#3755—24no—
96#3752—21no—
97C4⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊C8)C2312yes—
99C3×#215—24no—
100C3×(C2×D3)⋊C4—21no—
101C3×(C2×D3)⋊C4—22no—
102C3×(C2×D3)⋊C4—22no—
103C3×C4⋊Dic3C2311yescharacteristic
104C3×C4×Dic3D411yescharacteristic
105C3×C4×Dic3D411yescharacteristic
106C3×C4×Dic3C2311yescharacteristic
107C2×C3×C3⋊C8C2312yes—
108Dic3⋊Dic3—21no—
109#3722—21no—
110(C2×D3)⋊Dic3—21no—
111#3714—24no—
112#3713—24no—
113#3711—24no—
114#3036—91noSylow
115C2×C3×#41—32no—
116C2×#239C2×D312yes—
117C2×D3×D4—31no—
118C22×D12—31no—
119C22×C4×D3—61no—
120C22×C4×D3—61no—
121C2×C3×SD16—32no—
122C3×C4⋊Q8—21no—
123C3×C4⋊Q8C2×D311yescharacteristic, complemented
124C3×C4⋊Q8C2×D311yescharacteristic, complemented
125C3×#127—31no—
126C3×#124—32no—
127C3×#121—61no—
128C3×#121—61no—
129C3×C4×D4—31no—
130C3×C4×D4—61no—
131C3×C4×D4—61no—
132C2×C3×C42—31no—
133#949—68no—
134#947C2×D312yescomplemented
135C2×#215—32no—
136C2×#215—32no—
137C2×#215—62no—
138C2×#215C2×D312yes—
139D4×Dic3—31no—
140C2×#213—32no—
141C2×#213—32no—
142C2×#213—32no—
143C4×#67—61no—
144C2×(C2×D3)⋊C4—61no—
145C2×C4⋊Dic3—31no—
146C2×#208—32no—
147#914—68no—
148C2×D24—32no—
149C2×ΓL(1,𝔽25)—32no—
150#895—21no—
151#895—21no—
152#893—21no—
153#893—21no—
154#893—31no—
155D3×C4⋊C4—31no—
156#67⋊C4—61no—
157D3×C22⋊C4—61no—
158#874C2×D311yescharacteristic, complemented
159C4×D12—31no—
160C4×D12—31no—
161C4×D12—31no—
162C4×D12—31no—
163C4×D12—61no—
164C4×D12—61no—
165C4×D12—61no—
166C4×D12C2×D311yescharacteristic
167C42×D3C2×D311yescharacteristic
168C3×C4⋊C8—31no—
169C3×#103—32no—
170#835—32no—
171#835—32no—
172#835—62no—
173#835C2×D312yescomplemented
174#832—32no—
175#832—32no—
176#821—32no—
177Dic3⋊C8—32no—
178#809—32no—
179C4⋊(C3⋊C8)—31no—
180C4⋊(C3⋊C8)—31no—
181C4⋊(C3⋊C8)—32no—
182C4⋊(C3⋊C8)—61no—
183C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
184C22×C3⋊D3—21no—
185C22×C3×D3—21no—
186C22×C3×D3—22no—
187C22×C3×D3C2×D411yescharacteristic
188C2×D32—24no—
189C2×D32—42no—
190C2×D32—42no—
191C32×Q8—22no—
192C32×Q8—22no—
193C2×C32×C4—22no—
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4C2×D411yescharacteristic
196C2×C32×C4C2411yescharacteristic
197C2×C3⋊Dic3—21no—
198C4⋊(C3⋊D3)—21no—
199C4⋊(C3⋊D3)C2×D412yes—
200C4×C3⋊D3—42no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3C2×D411yescharacteristic
203C2×C3×Dic3C2×D411yescharacteristic
204C2×C3×Dic3C2×D411yescharacteristic
205C3×D12—22no—
206C3×D12—21no—
207C3×D12—22no—
208C3×D12—42no—
209C3×D12—44no—
210C3×D12—42no—
211C3×D12C2×D412yes—
212C3×C4×D3—22no—
213C3×C4×D3—41no—
214C3×C4×D3—42no—
215C3×C4×D3—44no—
216C3×C4×D3C2×D412yes—
217C3×C4×D3#4112yes—
218#626—24no—
219#624—42no—
220D3×Dic3—42no—
221D3×Dic3—42no—
222C3⋊(C3⋊C8)—22no—
223C3×C3⋊C8—22no—
224C2×AGL(1,ℤ/8)—92no—
225#532—31no—
226C2×C4×D4—91no—
227#463—92no—
228#463—92no—
229#461—31no—
230#461—91no—
231#459—91no—
232#459—91no—
233#423—91no—
234#417—92no—
235C23×D3—61no—
236C23×D3—61no—
237C3×#41—64no—
238C3×#41—64no—
239C2×C3×Q8—22no—
240C2×C3×Q8C22×D312yes—
241C2×C3×Q8C22×D312yes—
242C2×C3×D4—31no—
243C2×C3×D4—32no—
244C2×C3×D4—62no—
245C2×C3×D4—61no—
246C2×C3×D4—61no—
247C22×C3×C4—31no—
248C22×C3×C4—31no—
249C22×C3×C4—31no—
250C22×C3×C4—62no—
251C22×C3×C4—61no—
252C2×#67—61no—
253C22×Dic3—61no—
254C22×Dic3—61no—
255#239—24no—
256#239—24no—
257D3×D4—34no—
258D3×D4—62no—
259C2×D12—22no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—31no—
263C2×D12—31no—
264C2×D12—34no—
265C2×D12—61no—
266C2×D12—62no—
267C2×D12—61no—
268C2×D12C22×D312yes—
269C2×D12C22×D311yescharacteristic
270C2×C4×D3—21no—
271C2×C4×D3—22no—
272C2×C4×D3—61no—
273C2×C4×D3—61no—
274C2×C4×D3—61no—
275C2×C4×D3—61no—
276C2×C4×D3—61no—
277C2×C4×D3—61no—
278C2×C4×D3—121no—
279C2×C4×D3—124no—
280C2×C4×D3—124no—
281C2×C4×D3#6711yescharacteristic
282C2×C4×D3#6711yescharacteristic
283C2×C4×D3C22×D311yescharacteristic
284C3×SD16—64no—
285C2×C3×C8—32no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—31no—
291C3×C4⋊C4—41no—
292C3×C4⋊C4—41no—
293C3×C22⋊C4—62no—
294C3×C22⋊C4—62no—
295C3×C22⋊C4—61no—
296C3×C42—21no—
297C3×C42—31no—
298C3×C42—31no—
299C3×C42—31no—
300C3×C42C22×D311yescharacteristic
301C3×C42C22×D311yescharacteristic
302#217—61no—
303#215—24no—
304#215—64no—
305#215—64no—
306#215—124no—
307#213—64no—
308#213—64no—
309#213—64no—
310(C2×D3)⋊C4—21no—
311(C2×D3)⋊C4—22no—
312(C2×D3)⋊C4—22no—
313(C2×D3)⋊C4—61no—
314(C2×D3)⋊C4—61no—
315(C2×D3)⋊C4—61no—
316(C2×D3)⋊C4—61no—
317(C2×D3)⋊C4—61no—
318(C2×D3)⋊C4—121no—
319C4⋊Dic3—31no—
320C4⋊Dic3—31no—
321C4⋊Dic3—61no—
322C4⋊Dic3—61no—
323C4⋊Dic3C22×D311yescharacteristic
324Dic3⋊C4—61no—
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×C32C22×D411yescharacteristic
336C2×C3⋊D3—22no—
337C2×C3⋊D3—41no—
338C2×C3⋊D3—41no—
339C2×C3×D3—21no—
340C2×C3×D3—21no—
341C2×C3×D3—22no—
342C2×C3×D3—41no—
343C2×C3×D3—41no—
344C2×C3×D3—42no—
345C2×C3×D3—42no—
346C2×C3×D3—42no—
347C2×C3×D3#12112yes—
348D32—48no—
349C32×C4—21no—
350C32×C4—42no—
351C32×C4AGL(1,ℤ/8)12yescomplemented
352C32×C4C22×D411yescharacteristic
353C32×C4C2×#4111yescharacteristic
354C3⋊Dic3—41no—
355C3×Dic3—21no—
356C3×Dic3—21no—
357C3×Dic3—41no—
358C3×Dic3#12112yes—
359C2×#41—32no—
360C22×D4—91no—
361C23×C4—181no—
362AGL(1,ℤ/8)—188no—
363C2×SD16—32no—
364C2×SD16—92no—
365C2×D8—92no—
366C2×D8—92no—
367C2×M16—92no—
368C4⋊Q8D3211yescharacteristic, complemented
369#127—31no—
370#124—32no—
371#121—61no—
372#121—61no—
373C4×D4—31no—
374C4×D4—61no—
375C4×D4—61no—
376C4×D4—91no—
377C4×D4—91no—
378C4×D4—91no—
379C4×D4—181no—
380C4×D4—181no—
381C2×C4⋊C4—91no—
382C2×C22⋊C4—181no—
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—31no—
392C23×C3—61no—
393C23×C3—62no—
394C22×D3—21no—
395C22×D3—22no—
396C22×D3—64no—
397C22×D3—61no—
398C22×D3—61no—
399C22×D3—64no—
400C22×D3—121no—
401C22×D3—122no—
402C22×D3—122no—
403C22×D3—122no—
404C22×D3—122no—
405C22×D3C2×#6711yescharacteristic
406C3×Q8—22no—
407C3×Q8—22no—
408C3×Q8—22no—
409C3×Q8—22no—
410C3×Q8—42no—
411C3×Q8—42no—
412C3×D4—32no—
413C3×D4—62no—
414C3×D4—61no—
415C3×D4—62no—
416C3×D4—122no—
417C3×D4—124no—
418C3×D4—122no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
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—42no—
430C2×C3×C4—62no—
431C2×C3×C4—61no—
432C2×C3×C4—121no—
433C2×C3×C4—124no—
434C2×C3×C4—122no—
435C2×C3×C4D3×D411yescharacteristic
436C2×C3×C4D3×D411yescharacteristic
437C2×C3×C4C2×#6711yescharacteristic
438C2×C3×C4C2×#6711yescharacteristic
439C2×C3×C4C23×D311yescharacteristic
440C2×C3×C4C23×D311yescharacteristic
441#67—64no—
442C2×Dic3—21no—
443C2×Dic3—61no—
444C2×Dic3—61no—
445C2×Dic3—121no—
446C2×Dic3—122no—
447C2×Dic3—122no—
448C2×Dic3C2×#6711yescharacteristic
449C2×Dic3C2×#6711yescharacteristic
450C2×Dic3C2×#6711yescharacteristic
451D12—22no—
452D12—22no—
453D12—21no—
454D12—32no—
455D12—32no—
456D12—42no—
457D12—44no—
458D12—42no—
459D12—62no—
460D12—64no—
461D12—61no—
462D12—61no—
463D12—121no—
464D12D3×D412yes—
465C4×D3—22no—
466C4×D3—41no—
467C4×D3—42no—
468C4×D3—44no—
469C4×D3—122no—
470C4×D3—122no—
471C4×D3—122no—
472C4×D3—122no—
473C4×D3—122no—
474C4×D3—122no—
475C4×D3—242no—
476C4×D3D3×D412yes—
477C4×D3#23712yes—
478C3×C8—62no—
479C3⋊C8—22no—
480C3⋊C8—62no—
481C3⋊C8—62no—
482C3⋊C8—122no—
483C2×C32C2×#12111yescharacteristic
484C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
485C2×C32#57511yescharacteristic
486C3⋊D3—42no—
487C3×D3—22no—
488C3×D3—42no—
489C3×D3—82no—
490C24—181no—
491#41—64no—
492#41—64no—
493C2×Q8C2×D3212yes—
494C2×D4—31no—
495C2×D4—32no—
496C2×D4—62no—
497C2×D4—61no—
498C2×D4—61no—
499C2×D4—94no—
500C2×D4—91no—
501C2×D4—182no—
502C2×D4—181no—
503C22×C4—31no—
504C22×C4—31no—
505C22×C4—31no—
506C22×C4—62no—
507C22×C4—61no—
508C22×C4—181no—
509C22×C4—181no—
510C22×C4—181no—
511C22×C4—181no—
512C22×C4—364no—
513SD16—64no—
514SD16—184no—
515D8—184no—
516D8—184no—
517M16—184no—
518C2×C8—32no—
519C2×C8—92no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—31no—
523C4⋊C4—91no—
524C4⋊C4—181no—
525C22⋊C4—62no—
526C22⋊C4—62no—
527C22⋊C4—61no—
528C22⋊C4—181no—
529C22⋊C4—181no—
530C22⋊C4—181no—
531C42—31no—
532C42—31no—
533C42—31no—
534C42C2×D3211yescharacteristic
535C22×C3—21no—
536C22×C3—32no—
537C22×C3—61no—
538C22×C3—61no—
539C22×C3—62no—
540C22×C3—121no—
541C22×C3—121no—
542C22×C3—122no—
543C22×C3—122no—
544C22×C3—122no—
545C22×C3C2×D3×D411yescharacteristic
546C22×C3C22×#6711yescharacteristic
547C2×D3—21no—
548C2×D3—21no—
549C2×D3—22no—
550C2×D3—41no—
551C2×D3—41no—
552C2×D3—42no—
553C2×D3—42no—
554C2×D3—42no—
555C2×D3—62no—
556C2×D3—62no—
557C2×D3—122no—
558C2×D3—128no—
559C2×D3—128no—
560C2×D3—121no—
561C2×D3—121no—
562C2×D3—121no—
563C2×D3—121no—
564C2×D3—241no—
565C2×D3—241no—
566C2×D3#93812yes—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—21no—
571C3×C4—22no—
572C3×C4—32no—
573C3×C4—41no—
574C3×C4—42no—
575C3×C4—42no—
576C3×C4—61no—
577C3×C4—61no—
578C3×C4—82no—
579C3×C4—121no—
580C3×C4#91412yescomplemented
581C3×C4#94912yescomplemented
582C3×C4C2×D3×D411yescharacteristic
583C3×C4C2×D3×D411yescharacteristic
584C3×C4C2×#23711yescharacteristic
585C3×C4D3×#4111yescharacteristic
586Dic3—21no—
587Dic3—21no—
588Dic3—41no—
589Dic3—121no—
590Dic3—121no—
591Dic3—241no—
592Dic3#93812yes—
593C32#303611yescharacteristic, complemented, Sylow
594C23—31no—
595C23—61no—
596C23—62no—
597C23—184no—
598C23—181no—
599C23—362no—
600C23—362no—
601Q8—22no—
602Q8—22no—
603D4—32no—
604D4—62no—
605D4—61no—
606D4—62no—
607D4—92no—
608D4—122no—
609D4—124no—
610D4—122no—
611D4—184no—
612D4—181no—
613C2×C4—22no—
614C2×C4—31no—
615C2×C4—32no—
616C2×C4—32no—
617C2×C4—31no—
618C2×C4—31no—
619C2×C4—62no—
620C2×C4—61no—
621C2×C4—121no—
622C2×C4—124no—
623C2×C4—122no—
624C2×C4—181no—
625C2×C4—362no—
626C2×C4—362no—
627C2×C4—362no—
628C2×C4—362no—
629C2×C4D3×#6711yescharacteristic
630C2×C4D3×#6711yescharacteristic
631C2×C4C22×D3211yescharacteristic
632C8—62no—
633C8—182no—
634C2×C3—21no—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—62no—
638C2×C3—122no—
639C2×C3—242no—
640C2×C3D3×#12111yescharacteristic
641C2×C3C2×#91411yescharacteristic
642C2×C3#577711yescharacteristic
643C2×C3C2×#93811yescharacteristic
644C2×C3C2×#94911yescharacteristic
645C2×C3#582211yescharacteristic
646D3—22no—
647D3—42no—
648D3—82no—
649D3—122no—
650D3—122no—
651D3—242no—
652C22—32no—
653C22—61no—
654C22—61no—
655C22—62no—
656C22—121no—
657C22—121no—
658C22—122no—
659C22—122no—
660C22—122no—
661C22—182no—
662C22—368no—
663C22—361no—
664C22—361no—
665C22C2×D3×#6711yescharacteristic
666C4—21no—
667C4—32no—
668C4—42no—
669C4—61no—
670C4—61no—
671C4—121no—
672C4—361no—
673C4#6393912yescomplemented
674C4D32×D411yescharacteristic
675C4D3×#23711yescharacteristic
676C3—21no—
677C3#8042811yescharacteristic, complemented
678C3#8329711yescharacteristic, complemented
679C2—62no—
680C2—122no—
681C2—242no—
682C2—362no—
683C2D3×#93811yescharacteristic
684C2C2×#6393911yescharacteristic
685C2#1059531711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5725C2semidirect
2. C2×#63939C2semidirect
3. C4×D3×D12C2semidirect
4. #10592782C2semidirect
5. C3×#5083C2semidirect
6. #10591568C2semidirect
7. #10591567C2semidirect
8. #10591550C2semidirect
9. #10590355C2semidirect
10. #10590347C2semidirect
11. #10590336C2semidirect
17. C32×C4⋊Q8C22semidirect
20. C3×#947C22semidirect
26. C3×#874C22semidirect
39. #63662C22semidirect
40. C4⋊(C3⋊(C3⋊C8))C22semidirect
41. C3×#835C22semidirect
42. C3×C4⋊(C3⋊C8)C22semidirect
43. Dic3⋊(C3⋊C8)C22semidirect
44. #63563C22semidirect
45. #63562C22semidirect
49. #5725D3semidirect
58. #5083D3semidirect
90. D3×D12D4semidirect
123. C3×C4⋊Q8C2×D3semidirect
124. C3×C4⋊Q8C2×D3semidirect
134. #947C2×D3semidirect
158. #874C2×D3semidirect
173. #835C2×D3semidirect
183. C4⋊(C3⋊C8)C2×D3semidirect
351. C32×C4AGL(1,ℤ/8)semidirect
368. C4⋊Q8D32semidirect
580. C3×C4#914semidirect
581. C3×C4#949semidirect
593. C32#3036semidirect
673. C4#63939semidirect
677. C3#80428semidirect
678. C3#83297semidirect

Maximal subgroups

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

subgroupindex
C3×#57252
C2×#639392
C4×D3×D122
#105927822
C3×#50832
#105915682
#105915672
#105915502
#105903552
#105903472
#105903362
#832973
#804283