Finite Group Databasebeta

← #11865854

Subgroups — #11865854

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
1C2×#63794C212yesmaximal, complemented
2C4×D3×D12C211yesmaximal, characteristic, complemented
3#10593970C211yesmaximal, characteristic, complemented
4#10592542C211yesmaximal, characteristic, complemented
5C3×#4841C211yesmaximal, characteristic, complemented
6C3×#4837C211yesmaximal, characteristic, complemented
7#10590770C212yesmaximal, complemented
8#10590754C212yesmaximal, complemented
9#10590671C212yesmaximal, complemented
10#10590379C211yesmaximal, characteristic, complemented
11#10590349C211yesmaximal, characteristic, complemented
12#80428—31nomaximal
13#79055—31nomaximal
14C2×D3×D12C2211yescharacteristic
15C2×C4×D32—21no—
16C2×#3799C2212yes—
17C2×#3745C2212yes—
18#64083C2211yescharacteristic, complemented
19C4×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×#204C2212yes—
21C2×C3×ΓL(1,𝔽25)C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×C42×D3C2211yescharacteristic
24C3×#869C2211yescharacteristic, complemented
25D3×(C2×D3)⋊C4—21no—
26#63909—21no—
27#63909—21no—
28C4×#626—21no—
29#63894—21no—
30#63894—21no—
31#63894C2211yescharacteristic
32Dic3×D12C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63880—21no—
35#63864C2212yescomplemented
36C2×#3717C2212yes—
37C2×#3714C2212yes—
38#63794—28no—
39C32×C4⋊C8C2211yescharacteristic, complemented
40#63648C2212yescomplemented
41C3×#816C2212yescomplemented
42C3×Dic3⋊C8C2212yescomplemented
43C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
44#63566C2212yescomplemented
45#63564C2212yescomplemented
46C2×#914—32no—
47C2×#908—32no—
48#5725—31no—
49C4×D3×D4—31no—
50#5477—31no—
51C2×C4×D12—31no—
52C3×#461—31no—
53C3×#423—31no—
54#5165—32no—
55#5133—32no—
56#5083—31no—
57#5015—31no—
58#4844—32no—
59#4844—32no—
60#4843—31no—
61#4843—31no—
62#4843—31no—
63#4843—61no—
64#4841—31no—
65#4841D311yescharacteristic, complemented
66#4837D311yescharacteristic, complemented
67#4819—32no—
68#4803—32no—
69C22×D32—21no—
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)C2312yes—
73C2×C4⋊(C3⋊D3)C2311yescharacteristic
74C2×C4×C3⋊D3—21no—
75C2×C3×D12C2311yescharacteristic
76C2×C3×C4×D3—21no—
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3C2311yescharacteristic
80C2×C3×Dic6C2312yes—
81C2×#626—21no—
82C2×#626—22no—
83C2×#624—22no—
84C2×#624—21no—
85C2×D3×Dic3—21no—
86C2×D3×Dic3—21no—
87D3×D12—22no—
88D3×D12D414yescomplemented
89C4×D32—44no—
90#3799—24no—
91#3799—24no—
92C2×C32×C8C2312yes—
93C32×C42C2311yescharacteristic
94#3752—21no—
95C4⋊(C3⋊Dic3)C2311yescharacteristic
96#3745—24no—
97C3×(C2×D3)⋊C4—21no—
98C3×C4⋊Dic3—21no—
99C3×C4⋊Dic3—21no—
100C3×C4⋊Dic3C2311yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C2×C3×C3⋊C8C2312yes—
105C3×#204—24no—
106C3×ΓL(1,𝔽25)—24no—
107Dic3⋊Dic3—21no—
108#3722—22no—
109#3722—22no—
110#3722—21no—
111(C2×D3)⋊Dic3—21no—
112#3717—24no—
113#3714—24no—
114#3036—91noSylow
115C2×#239—32no—
116C2×D3×D4—31no—
117C2×#235—32no—
118C22×D12—31no—
119C22×C4×D3—61no—
120C22×C4×D3—61no—
121C2×C3×SD16—32no—
122C2×C3×M16—32no—
123C3×C4⋊Q8—31no—
124C3×C4×D4—31no—
125C2×C3×C42—31no—
126#947—32no—
127C2×#215—32no—
128D4×Dic3—31no—
129C2×#213—32no—
130#930—61no—
131#930—61no—
132C4×#67—61no—
133C2×(C2×D3)⋊C4—61no—
134C2×C4⋊Dic3—31no—
135#914—68no—
136#908—68no—
137C2×D24—32no—
138C2×D24—32no—
139C2×D24—32no—
140C2×D24—62no—
141C2×#204—32no—
142C2×#204C2×D312yes—
143C2×ΓL(1,𝔽25)C2×D312yes—
144#895—61no—
145#895—61no—
146#893—31no—
147#893—61no—
148#893—61no—
149D3×C4⋊C4—31no—
150#67⋊C4—61no—
151D3×C22⋊C4—61no—
152#875—32no—
153#874—31no—
154#874—31no—
155#874—61no—
156C4×D12—31no—
157C4×D12—31no—
158C4×D12—31no—
159C4×D12—31no—
160C4×D12—61no—
161C4×D12—61no—
162C4×D12—61no—
163C4×D12—61no—
164C4×D12—61no—
165C4×D12C2×D311yescharacteristic
166C42×D3C2×D311yescharacteristic
167#869C2×D311yescharacteristic, complemented
168C3×C4⋊C8—21no—
169C3×C4⋊C8—32no—
170C3×C4⋊C8—31no—
171C3×C4⋊C8C2×D311yescharacteristic, complemented
172C3×C4⋊C8C2×D311yescharacteristic, complemented
173C3×#103—32no—
174#835—32no—
175#821—32no—
176#821—32no—
177#821—32no—
178#821—62no—
179#816—32no—
180#816C2×D312yescomplemented
181Dic3⋊C8C2×D312yescomplemented
182#809—32no—
183C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
184C22×C3⋊D3—21no—
185C22×C3⋊D3—22no—
186C22×C3×D3—21no—
187C22×C3×D3C2×D411yescharacteristic
188C2×D32—24no—
189C2×D32—42no—
190C2×D32—42no—
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2411yescharacteristic
194C2×C3⋊Dic3—21no—
195C4⋊(C3⋊D3)—22no—
196C4⋊(C3⋊D3)—21no—
197C4⋊(C3⋊D3)—22no—
198C4⋊(C3⋊D3)—42no—
199C4⋊(C3⋊D3)—42no—
200C4⋊(C3⋊D3)C2×D412yes—
201C4×C3⋊D3—42no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3C2×D411yescharacteristic
205C2×C3×Dic3C2×D411yescharacteristic
206C2×C3×Dic3C2×D411yescharacteristic
207C3×D12—21no—
208C3×D12C2×D412yes—
209C3×C4×D3—22no—
210C3×C4×D3—41no—
211C3×C4×D3—42no—
212C3×C4×D3C2×D412yes—
213C3×C4×D3#4112yes—
214C3×Dic6—22no—
215C3×Dic6—22no—
216#626—24no—
217#626—44no—
218#624—42no—
219#624—44no—
220D3×Dic3—42no—
221D3×Dic3—42no—
222C32×C8—22no—
223C3×C3⋊C8—22no—
224C2×AGL(1,ℤ/8)—92no—
225#532—91no—
226C2×C4×D4—91no—
227#463—92no—
228#463—92no—
229#461—31no—
230#461—91no—
231#459—91no—
232#459—91no—
233#423—31no—
234#417—92no—
235C23×D3—61no—
236C23×D3—61no—
237C2×C3×Q8—32no—
238C2×C3×D4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—61no—
243C2×#67—62no—
244C2×#67—61no—
245C22×Dic3—61no—
246C22×Dic3—61no—
247#239—64no—
248#239—64no—
249D3×D4—34no—
250D3×D4—62no—
251#235—64no—
252#235—64no—
253C2×D12—31no—
254C2×D12—31no—
255C2×D12—34no—
256C2×D12—32no—
257C2×D12—32no—
258C2×D12—61no—
259C2×D12—62no—
260C2×D12—62no—
261C2×D12—61no—
262C2×D12—62no—
263C2×D12—61no—
264C2×D12—61no—
265C2×D12—61no—
266C2×D12—61no—
267C2×D12—121no—
268C2×D12—121no—
269C2×D12C22×D311yescharacteristic
270C2×C4×D3—21no—
271C2×C4×D3—61no—
272C2×C4×D3—62no—
273C2×C4×D3—61no—
274C2×C4×D3—61no—
275C2×C4×D3—61no—
276C2×C4×D3—61no—
277C2×C4×D3—61no—
278C2×C4×D3—62no—
279C2×C4×D3—121no—
280C2×C4×D3—124no—
281C2×C4×D3—124no—
282C2×C4×D3D1211yescharacteristic
283C2×C4×D3D1211yescharacteristic
284C2×C4×D3C22×D311yescharacteristic
285C2×Dic6C22×D312yes—
286C3×SD16—64no—
287C3×M16—64no—
288C2×C3×C8—22no—
289C2×C3×C8—32no—
290C2×C3×C8C22×D312yes—
291C2×C3×C8C22×D312yes—
292C3×C4⋊C4—31no—
293C3×C4⋊C4—61no—
294C3×C4⋊C4—61no—
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—64no—
304#213—64no—
305(C2×D3)⋊C4—21no—
306(C2×D3)⋊C4—61no—
307(C2×D3)⋊C4—62no—
308(C2×D3)⋊C4—62no—
309(C2×D3)⋊C4—61no—
310(C2×D3)⋊C4—61no—
311(C2×D3)⋊C4—61no—
312(C2×D3)⋊C4—61no—
313(C2×D3)⋊C4—62no—
314(C2×D3)⋊C4—62no—
315(C2×D3)⋊C4—121no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—31no—
319C4⋊Dic3—31no—
320C4⋊Dic3—61no—
321C4⋊Dic3—61no—
322C4⋊Dic3C22×D311yescharacteristic
323Dic3⋊C4—61no—
324C4×Dic3D1211yescharacteristic
325C4×Dic3D1211yescharacteristic
326C4×Dic3C22×D311yescharacteristic
327C2×C3⋊C8C22×D312yes—
328D24—64no—
329D24—64no—
330D24—64no—
331D24—124no—
332#204—24no—
333#204—64no—
334ΓL(1,𝔽25)—24no—
335C22×C32C22×D411yescharacteristic
336C2×C3⋊D3—22no—
337C2×C3⋊D3—41no—
338C2×C3⋊D3—41no—
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—41no—
346C2×C3×D3—41no—
347C2×C3×D3#12112yes—
348D32—48no—
349C32×C4—21no—
350C32×C4AGL(1,ℤ/8)12yescomplemented
351C32×C4C22×D411yescharacteristic
352C32×C4C2×#4111yescharacteristic
353C3⋊Dic3—41no—
354C3×Dic3—21no—
355C3×Dic3—21no—
356C3×Dic3—42no—
357C3×Dic3—41no—
358C3×Dic3#12112yes—
359C2×#41—92no—
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—32no—
368C4⋊Q8—31no—
369#127—91no—
370#124—92no—
371#121—181no—
372#121—181no—
373C4×D4—31no—
374C4×D4—91no—
375C4×D4—91no—
376C4×D4—91no—
377C4×D4—181no—
378C4×D4—181no—
379C4×D4—181no—
380C4×D4—181no—
381C2×C4⋊C4—91no—
382C2×C22⋊C4—181no—
383C2×C42—31no—
384C4⋊C8—32no—
385C4⋊C8—31no—
386C4⋊C8D3211yescharacteristic, complemented
387#103—32no—
388#103—92no—
389#102—92no—
390#102—92no—
391C23×C3—31no—
392C23×C3—61no—
393C22×D3—21no—
394C22×D3—64no—
395C22×D3—61no—
396C22×D3—61no—
397C22×D3—64no—
398C22×D3—62no—
399C22×D3—62no—
400C22×D3—121no—
401C22×D3—122no—
402C22×D3—122no—
403C22×D3—122no—
404C22×D3—122no—
405C22×D3—122no—
406C22×D3C2×D1211yescharacteristic
407C3×Q8—62no—
408C3×Q8—62no—
409C3×D4—32no—
410C3×D4—61no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—31no—
415C2×C3×C4—32no—
416C2×C3×C4—32no—
417C2×C3×C4—31no—
418C2×C3×C4—31no—
419C2×C3×C4—62no—
420C2×C3×C4—61no—
421C2×C3×C4—62no—
422C2×C3×C4—121no—
423C2×C3×C4—122no—
424C2×C3×C4C2×D1211yescharacteristic
425C2×C3×C4C2×D1211yescharacteristic
426C2×C3×C4D3×D411yescharacteristic
427C2×C3×C4D3×D411yescharacteristic
428C2×C3×C4C23×D311yescharacteristic
429C2×C3×C4C23×D311yescharacteristic
430#67—64no—
431#67—124no—
432C2×Dic3—22no—
433C2×Dic3—21no—
434C2×Dic3—61no—
435C2×Dic3—61no—
436C2×Dic3—121no—
437C2×Dic3—122no—
438C2×Dic3—122no—
439C2×Dic3C2×D1211yescharacteristic
440C2×Dic3C2×D1211yescharacteristic
441C2×Dic3C2×D1211yescharacteristic
442D12—21no—
443D12—32no—
444D12—32no—
445D12—62no—
446D12—64no—
447D12—62no—
448D12—62no—
449D12—61no—
450D12—62no—
451D12—61no—
452D12—62no—
453D12—121no—
454D12—122no—
455D12—122no—
456D12—122no—
457D12—122no—
458D12—124no—
459D12—122no—
460D12—122no—
461D12—242no—
462D12—242no—
463D12D3×D412yes—
464C4×D3—22no—
465C4×D3—41no—
466C4×D3—42no—
467C4×D3—122no—
468C4×D3—124no—
469C4×D3—122no—
470C4×D3—122no—
471C4×D3—122no—
472C4×D3—122no—
473C4×D3—122no—
474C4×D3—124no—
475C4×D3—242no—
476C4×D3D3×D412yes—
477C4×D3#23912yes—
478Dic6—22no—
479Dic6—22no—
480C3×C8—22no—
481C3×C8—22no—
482C3×C8—42no—
483C3×C8—62no—
484C3⋊C8—22no—
485C2×C32C2×#12111yescharacteristic
486C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
487C2×C32#57511yescharacteristic
488C3⋊D3—42no—
489C3⋊D3—82no—
490C3×D3—22no—
491C3×D3—42no—
492C24—181no—
493#41—184no—
494#41—184no—
495C2×Q8—32no—
496C2×D4—31no—
497C2×D4—94no—
498C2×D4—91no—
499C2×D4—92no—
500C2×D4—182no—
501C2×D4—181no—
502C2×D4—182no—
503C2×D4—181no—
504C2×D4—181no—
505C22×C4—31no—
506C22×C4—31no—
507C22×C4—31no—
508C22×C4—61no—
509C22×C4—181no—
510C22×C4—182no—
511C22×C4—181no—
512C22×C4—181no—
513C22×C4—181no—
514C22×C4—364no—
515SD16—64no—
516SD16—184no—
517D8—184no—
518D8—184no—
519M16—64no—
520C2×C8—32no—
521C2×C8C2×D3212yes—
522C4⋊C4—31no—
523C4⋊C4—61no—
524C4⋊C4—61no—
525C4⋊C4—91no—
526C4⋊C4—181no—
527C22⋊C4—61no—
528C22⋊C4—181no—
529C22⋊C4—182no—
530C22⋊C4—182no—
531C22⋊C4—181no—
532C22⋊C4—181no—
533C42—31no—
534C42—31no—
535C42—31no—
536C42C2×D3211yescharacteristic
537C22×C3—21no—
538C22×C3—32no—
539C22×C3—61no—
540C22×C3—61no—
541C22×C3—62no—
542C22×C3—121no—
543C22×C3—121no—
544C22×C3C22×D1211yescharacteristic
545C22×C3C2×D3×D411yescharacteristic
546C2×D3—21no—
547C2×D3—21no—
548C2×D3—22no—
549C2×D3—41no—
550C2×D3—41no—
551C2×D3—62no—
552C2×D3—62no—
553C2×D3—122no—
554C2×D3—128no—
555C2×D3—128no—
556C2×D3—121no—
557C2×D3—121no—
558C2×D3—121no—
559C2×D3—121no—
560C2×D3—122no—
561C2×D3—122no—
562C2×D3—122no—
563C2×D3—122no—
564C2×D3—122no—
565C2×D3—122no—
566C2×D3—241no—
567C2×D3—241no—
568C2×D3—242no—
569C2×D3—242no—
570C2×D3—242no—
571C2×D3#89512yes—
572C3×C4—21no—
573C3×C4—21no—
574C3×C4—22no—
575C3×C4—21no—
576C3×C4—21no—
577C3×C4—32no—
578C3×C4—41no—
579C3×C4—61no—
580C3×C4—61no—
581C3×C4—121no—
582C3×C4—122no—
583C3×C4#90812yescomplemented
584C3×C4#91412yescomplemented
585C3×C4C2×D3×D411yescharacteristic
586C3×C4C2×D3×D411yescharacteristic
587C3×C4C2×#23911yescharacteristic
588C3×C4D3×#4111yescharacteristic
589Dic3—21no—
590Dic3—21no—
591Dic3—41no—
592Dic3—42no—
593Dic3—121no—
594Dic3—121no—
595Dic3—241no—
596Dic3#89512yes—
597C32#303611yescharacteristic, complemented, Sylow
598C23—31no—
599C23—61no—
600C23—184no—
601C23—181no—
602C23—182no—
603C23—362no—
604C23—362no—
605Q8—62no—
606Q8—62no—
607D4—32no—
608D4—61no—
609D4—92no—
610D4—184no—
611D4—182no—
612D4—181no—
613D4—182no—
614D4—362no—
615D4—364no—
616D4—362no—
617C2×C4—31no—
618C2×C4—32no—
619C2×C4—32no—
620C2×C4—31no—
621C2×C4—31no—
622C2×C4—62no—
623C2×C4—61no—
624C2×C4—62no—
625C2×C4—121no—
626C2×C4—122no—
627C2×C4—181no—
628C2×C4—364no—
629C2×C4—362no—
630C2×C4—362no—
631C2×C4—362no—
632C2×C4—362no—
633C2×C4D3×D1211yescharacteristic
634C2×C4D3×D1211yescharacteristic
635C2×C4C22×D3211yescharacteristic
636C8—22no—
637C8—62no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—62no—
642C2×C3—122no—
643C2×C3C2×#89511yescharacteristic
644C2×C3D3×#12111yescharacteristic
645C2×C3C2×#90811yescharacteristic
646C2×C3#574811yescharacteristic
647C2×C3C2×#91411yescharacteristic
648C2×C3#577711yescharacteristic
649D3—22no—
650D3—42no—
651D3—122no—
652D3—122no—
653D3—242no—
654D3—242no—
655D3—242no—
656D3—482no—
657C22—32no—
658C22—61no—
659C22—61no—
660C22—62no—
661C22—121no—
662C22—121no—
663C22—182no—
664C22—368no—
665C22—361no—
666C22—361no—
667C22—362no—
668C22—362no—
669C22—362no—
670C22C2×D3×D1211yescharacteristic
671C4—21no—
672C4—32no—
673C4—61no—
674C4—61no—
675C4—122no—
676C4—121no—
677C4—361no—
678C4#6379412yescomplemented
679C4D32×D411yescharacteristic
680C4D3×#23911yescharacteristic
681C3—21no—
682C3#7905511yescharacteristic, complemented
683C3#8042811yescharacteristic, complemented
684C2—62no—
685C2—122no—
686C2—362no—
687C2—722no—
688C2D3×#89511yescharacteristic
689C2C2×#6379411yescharacteristic
690C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63794C2semidirect
2. C4×D3×D12C2semidirect
3. #10593970C2semidirect
4. #10592542C2semidirect
5. C3×#4841C2semidirect
6. C3×#4837C2semidirect
7. #10590770C2semidirect
8. #10590754C2semidirect
9. #10590671C2semidirect
10. #10590379C2semidirect
11. #10590349C2semidirect
18. #64083C22semidirect
24. C3×#869C22semidirect
35. #63864C22semidirect
39. C32×C4⋊C8C22semidirect
40. #63648C22semidirect
41. C3×#816C22semidirect
42. C3×Dic3⋊C8C22semidirect
43. C3×C4⋊(C3⋊C8)C22semidirect
44. #63566C22semidirect
45. #63564C22semidirect
65. #4841D3semidirect
66. #4837D3semidirect
88. D3×D12D4semidirect
167. #869C2×D3semidirect
171. C3×C4⋊C8C2×D3semidirect
172. C3×C4⋊C8C2×D3semidirect
180. #816C2×D3semidirect
181. Dic3⋊C8C2×D3semidirect
183. C4⋊(C3⋊C8)C2×D3semidirect
350. C32×C4AGL(1,ℤ/8)semidirect
386. C4⋊C8D32semidirect
583. C3×C4#908semidirect
584. C3×C4#914semidirect
597. C32#3036semidirect
678. C4#63794semidirect
682. C3#79055semidirect
683. C3#80428semidirect

Maximal subgroups

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

subgroupindex
C2×#637942
C4×D3×D122
#105939702
#105925422
C3×#48412
C3×#48372
#105907702
#105907542
#105906712
#105903792
#105903492
#804283
#790553