Finite Group Databasebeta

← #11865856

Subgroups — #11865856

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
1C2×#63795C212yesmaximal, complemented
2C4×D3×D12C211yesmaximal, characteristic, complemented
3#10593897C211yesmaximal, characteristic, complemented
4#10592540C211yesmaximal, characteristic, complemented
5C3×#4843C211yesmaximal, characteristic, complemented
6C3×#4837C211yesmaximal, characteristic, complemented
7#10590860C212yesmaximal, complemented
8#10590755C212yesmaximal, complemented
9#10590670C212yesmaximal, complemented
10#10590365C211yesmaximal, characteristic, complemented
11#10590355C211yesmaximal, characteristic, complemented
12#80332—31nomaximal
13#79055—31nomaximal
14C2×D3×D12C2211yescharacteristic
15C2×C4×D32—21no—
16C2×#3795C2212yes—
17C2×#3744C2212yes—
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19#64078C2211yescharacteristic, complemented
20C2×C3×D24C2212yes—
21C2×C3×ΓL(1,𝔽25)C2212yes—
22C3×#874C2211yescharacteristic, complemented
23C3×C4×D12C2211yescharacteristic
24C3×C42×D3C2211yescharacteristic
25D3×(C2×D3)⋊C4—21no—
26#63908—21no—
27#63908—21no—
28C4×#626—21no—
29#63894C2211yescharacteristic
30Dic3×D12—21no—
31Dic3×D12—21no—
32Dic3×D12C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63880—21no—
35#63860C2212yescomplemented
36C2×#3716C2212yes—
37C2×#3714C2212yes—
38#63795—28no—
39C32×C4⋊C8C2211yescharacteristic, complemented
40#63643C2212yescomplemented
41C3×#821C2212yescomplemented
42C3×Dic3⋊C8C2212yescomplemented
43C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
44#63567C2212yescomplemented
45#63563C2212yescomplemented
46C2×#911—32no—
47C2×#908—32no—
48#5716—31no—
49C4×D3×D4—31no—
50#5477—31no—
51C2×C4×D12—31no—
52C3×#459—31no—
53C3×#423—31no—
54#5153—32no—
55#5133—32no—
56#5072—31no—
57#5019—31no—
58#4844—32no—
59#4844—32no—
60#4843—31no—
61#4843D311yescharacteristic, complemented
62#4841—31no—
63#4841—31no—
64#4841—31no—
65#4841—61no—
66#4837D311yescharacteristic, complemented
67#4787—32no—
68#4771—32no—
69C22×D32—21no—
70C2×C4⋊(C3⋊D3)C2311yescharacteristic
71C2×C4×C3⋊D3—21no—
72C2×#634C2312yes—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12C2312yes—
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3C2311yescharacteristic
81C2×#626—21no—
82C2×#625—22no—
83C2×#624—21no—
84C2×D3×Dic3—21no—
85C2×D3×Dic3—22no—
86C2×D3×Dic3—21no—
87D3×D12—22no—
88D3×D12D414yescomplemented
89C4×D32—44no—
90#3795—24no—
91#3795—24no—
92C2×C32×C8C2312yes—
93C32×C42C2311yescharacteristic
94#3752—21no—
95C4⋊(C3⋊Dic3)—21no—
96C4⋊(C3⋊Dic3)—21no—
97C4⋊(C3⋊Dic3)C2311yescharacteristic
98#3744—24no—
99C3×(C2×D3)⋊C4—21no—
100C3×C4⋊Dic3C2311yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C2×C3×C3⋊C8C2312yes—
105C3×D24—24no—
106C3×ΓL(1,𝔽25)—24no—
107Dic3⋊Dic3—21no—
108#3722—21no—
109(C2×D3)⋊Dic3—22no—
110(C2×D3)⋊Dic3—22no—
111(C2×D3)⋊Dic3—21no—
112#3716—24no—
113#3714—24no—
114#3036—91noSylow
115C2×#237—32no—
116C2×D3×D4—31no—
117C2×#235—32no—
118C22×D12—31no—
119C22×C4×D3—61no—
120C22×C4×D3—61no—
121C2×C3×D8—32no—
122C2×C3×M16—32no—
123C3×#127—31no—
124C3×C4×D4—31no—
125C2×C3×C42—31no—
126#938—61no—
127#938—61no—
128#936—32no—
129D4×Dic3—31no—
130D4×Dic3—61no—
131D4×Dic3—61no—
132C2×#214—32no—
133C2×#213—32no—
134#930—61no—
135#930—61no—
136C4×#67—61no—
137C2×(C2×D3)⋊C4—61no—
138C2×C4⋊Dic3—31no—
139#911—68no—
140#908—68no—
141C2×D24—32no—
142C2×D24C2×D312yes—
143C2×#204—32no—
144C2×#204—32no—
145C2×#204—32no—
146C2×#204—62no—
147C2×ΓL(1,𝔽25)C2×D312yes—
148#893—31no—
149D3×C4⋊C4—31no—
150#67⋊C4—61no—
151D3×C22⋊C4—61no—
152#875—32no—
153#874C2×D311yescharacteristic, complemented
154C4×D12—31no—
155C4×D12—31no—
156C4×D12—31no—
157C4×D12—31no—
158C4×D12—61no—
159C4×D12—61no—
160C4×D12—61no—
161C4×D12—61no—
162C4×D12—61no—
163C4×D12C2×D311yescharacteristic
164C42×D3C2×D311yescharacteristic
165#869—31no—
166#869—31no—
167#869—61no—
168C3×C4⋊C8—21no—
169C3×C4⋊C8—32no—
170C3×C4⋊C8—31no—
171C3×C4⋊C8C2×D311yescharacteristic, complemented
172C3×C4⋊C8C2×D311yescharacteristic, complemented
173C3×#102—32no—
174#832—32no—
175#821—32no—
176#821C2×D312yescomplemented
177#816—32no—
178#816—32no—
179#816—32no—
180#816—62no—
181Dic3⋊C8C2×D312yescomplemented
182#810—32no—
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—
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2411yescharacteristic
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3—21no—
196C4⋊(C3⋊D3)—21no—
197C4⋊(C3⋊D3)C2×D412yes—
198C4×C3⋊D3—42no—
199#634—22no—
200#634—22no—
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—42no—
210C3×D12C2×D412yes—
211C3×C4×D3—22no—
212C3×C4×D3—41no—
213C3×C4×D3—42no—
214C3×C4×D3C2×D412yes—
215C3×C4×D3#4112yes—
216#626—24no—
217#625—44no—
218#624—42no—
219D3×Dic3—42no—
220D3×Dic3—42no—
221D3×Dic3—44no—
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—91no—
230#461—91no—
231#459—31no—
232#459—91no—
233#423—31no—
234#417—92no—
235C23×D3—61no—
236C23×D3—61no—
237C2×C3×D4—31no—
238C2×C3×D4—32no—
239C2×C3×D4—61no—
240C2×C3×D4—61no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—31no—
244C22×C3×C4—61no—
245C2×#67—62no—
246C2×#67—62no—
247C2×#67—61no—
248C22×Dic3—61no—
249C22×Dic3—61no—
250C22×Dic3—62no—
251#237—64no—
252#237—64no—
253D3×D4—34no—
254D3×D4—62no—
255#235—64no—
256#235—64no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—31no—
260C2×D12—31no—
261C2×D12—34no—
262C2×D12—61no—
263C2×D12—62no—
264C2×D12—61no—
265C2×D12C22×D312yes—
266C2×D12C22×D311yescharacteristic
267C2×C4×D3—21no—
268C2×C4×D3—61no—
269C2×C4×D3—61no—
270C2×C4×D3—62no—
271C2×C4×D3—61no—
272C2×C4×D3—61no—
273C2×C4×D3—61no—
274C2×C4×D3—61no—
275C2×C4×D3—121no—
276C2×C4×D3—124no—
277C2×C4×D3—124no—
278C2×C4×D3D1211yescharacteristic
279C2×C4×D3D1211yescharacteristic
280C2×C4×D3C22×D311yescharacteristic
281C2×Dic6—32no—
282C2×Dic6—32no—
283C2×Dic6—62no—
284C3×D8—64no—
285C3×M16—64no—
286C2×C3×C8—22no—
287C2×C3×C8—32no—
288C2×C3×C8C22×D312yes—
289C2×C3×C8C22×D312yes—
290C3×C4⋊C4—31no—
291C3×C22⋊C4—61no—
292C3×C42—21no—
293C3×C42—31no—
294C3×C42—31no—
295C3×C42—31no—
296C3×C42C22×D311yescharacteristic
297C3×C42C22×D311yescharacteristic
298#217—61no—
299#217—62no—
300#217—62no—
301#214—64no—
302#213—64no—
303(C2×D3)⋊C4—21no—
304(C2×D3)⋊C4—61no—
305(C2×D3)⋊C4—61no—
306(C2×D3)⋊C4—62no—
307(C2×D3)⋊C4—62no—
308(C2×D3)⋊C4—61no—
309(C2×D3)⋊C4—61no—
310(C2×D3)⋊C4—61no—
311(C2×D3)⋊C4—121no—
312C4⋊Dic3—31no—
313C4⋊Dic3—31no—
314C4⋊Dic3—61no—
315C4⋊Dic3—61no—
316C4⋊Dic3—61no—
317C4⋊Dic3—61no—
318C4⋊Dic3—61no—
319C4⋊Dic3—61no—
320C4⋊Dic3—121no—
321C4⋊Dic3—121no—
322C4⋊Dic3C22×D311yescharacteristic
323Dic3⋊C4—61no—
324C4×Dic3D1211yescharacteristic
325C4×Dic3D1211yescharacteristic
326C4×Dic3C22×D311yescharacteristic
327C2×C3⋊C8C22×D312yes—
328D24—24no—
329D24—64no—
330#204—64no—
331#204—64no—
332#204—64no—
333#204—124no—
334ΓL(1,𝔽25)—24no—
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×C4AGL(1,ℤ/8)12yescomplemented
351C32×C4C22×D411yescharacteristic
352C32×C4C2×#4111yescharacteristic
353C3⋊Dic3—42no—
354C3⋊Dic3—41no—
355C3×Dic3—21no—
356C3×Dic3—21no—
357C3×Dic3—41no—
358C3×Dic3#12112yes—
359C2×#41—92no—
360C22×D4—91no—
361C23×C4—181no—
362AGL(1,ℤ/8)—188no—
363C2×SD16—92no—
364C2×SD16—92no—
365C2×D8—32no—
366C2×D8—92no—
367C2×M16—32no—
368C4⋊Q8—91no—
369#127—31no—
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—92no—
388#103—92no—
389#102—32no—
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×D1211yescharacteristic
406C3×D4—32no—
407C3×D4—62no—
408C3×D4—61no—
409C3×D4—62no—
410C3×D4—122no—
411C3×D4—122no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—31no—
416C2×C3×C4—32no—
417C2×C3×C4—32no—
418C2×C3×C4—31no—
419C2×C3×C4—31no—
420C2×C3×C4—62no—
421C2×C3×C4—61no—
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—
432#67—124no—
433C2×Dic3—21no—
434C2×Dic3—61no—
435C2×Dic3—62no—
436C2×Dic3—61no—
437C2×Dic3—62no—
438C2×Dic3—121no—
439C2×Dic3—122no—
440C2×Dic3—122no—
441C2×Dic3—122no—
442C2×Dic3—124no—
443C2×Dic3C2×D1211yescharacteristic
444C2×Dic3C2×D1211yescharacteristic
445C2×Dic3C2×D1211yescharacteristic
446D12—22no—
447D12—21no—
448D12—22no—
449D12—32no—
450D12—32no—
451D12—42no—
452D12—42no—
453D12—62no—
454D12—64no—
455D12—61no—
456D12—61no—
457D12—121no—
458D12D3×D412yes—
459C4×D3—22no—
460C4×D3—41no—
461C4×D3—42no—
462C4×D3—122no—
463C4×D3—122no—
464C4×D3—124no—
465C4×D3—122no—
466C4×D3—122no—
467C4×D3—122no—
468C4×D3—122no—
469C4×D3—242no—
470C4×D3D3×D412yes—
471C4×D3#23912yes—
472Dic6—62no—
473Dic6—62no—
474Dic6—62no—
475Dic6—62no—
476Dic6—122no—
477Dic6—122no—
478C3×C8—22no—
479C3×C8—22no—
480C3×C8—42no—
481C3×C8—62no—
482C3⋊C8—22no—
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—184no—
492#41—184no—
493C2×Q8—92no—
494C2×D4—31no—
495C2×D4—32no—
496C2×D4—61no—
497C2×D4—61no—
498C2×D4—94no—
499C2×D4—91no—
500C2×D4—182no—
501C2×D4—181no—
502C2×D4—182no—
503C22×C4—31no—
504C22×C4—31no—
505C22×C4—31no—
506C22×C4—61no—
507C22×C4—181no—
508C22×C4—181no—
509C22×C4—182no—
510C22×C4—181no—
511C22×C4—181no—
512C22×C4—364no—
513SD16—184no—
514SD16—184no—
515D8—64no—
516D8—184no—
517M16—64no—
518C2×C8—32no—
519C2×C8C2×D3212yes—
520C4⋊C4—31no—
521C4⋊C4—91no—
522C4⋊C4—181no—
523C4⋊C4—181no—
524C4⋊C4—181no—
525C22⋊C4—61no—
526C22⋊C4—181no—
527C22⋊C4—181no—
528C22⋊C4—182no—
529C22⋊C4—182no—
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×C3C22×D1211yescharacteristic
546C22×C3C2×D3×D411yescharacteristic
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#89512yes—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—22no—
570C3×C4—21no—
571C3×C4—21no—
572C3×C4—32no—
573C3×C4—41no—
574C3×C4—61no—
575C3×C4—61no—
576C3×C4—121no—
577C3×C4#90812yescomplemented
578C3×C4#91112yescomplemented
579C3×C4C2×D3×D411yescharacteristic
580C3×C4C2×D3×D411yescharacteristic
581C3×C4C2×#23911yescharacteristic
582C3×C4D3×#4111yescharacteristic
583Dic3—21no—
584Dic3—21no—
585Dic3—41no—
586Dic3—121no—
587Dic3—121no—
588Dic3—122no—
589Dic3—122no—
590Dic3—242no—
591Dic3—241no—
592Dic3#89512yes—
593C32#303611yescharacteristic, complemented, Sylow
594C23—31no—
595C23—61no—
596C23—62no—
597C23—184no—
598C23—181no—
599C23—362no—
600C23—362no—
601Q8—182no—
602Q8—182no—
603D4—32no—
604D4—62no—
605D4—61no—
606D4—62no—
607D4—92no—
608D4—122no—
609D4—122no—
610D4—184no—
611D4—181no—
612D4—364no—
613C2×C4—31no—
614C2×C4—32no—
615C2×C4—32no—
616C2×C4—31no—
617C2×C4—31no—
618C2×C4—62no—
619C2×C4—61no—
620C2×C4—121no—
621C2×C4—122no—
622C2×C4—181no—
623C2×C4—182no—
624C2×C4—364no—
625C2×C4—362no—
626C2×C4—362no—
627C2×C4—362no—
628C2×C4—362no—
629C2×C4D3×D1211yescharacteristic
630C2×C4D3×D1211yescharacteristic
631C2×C4C22×D3211yescharacteristic
632C8—22no—
633C8—62no—
634C2×C3—21no—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—62no—
638C2×C3—122no—
639C2×C3—242no—
640C2×C3C2×#89511yescharacteristic
641C2×C3D3×#12111yescharacteristic
642C2×C3C2×#90811yescharacteristic
643C2×C3#574811yescharacteristic
644C2×C3C2×#91111yescharacteristic
645C2×C3#577311yescharacteristic
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×D1211yescharacteristic
666C4—21no—
667C4—32no—
668C4—61no—
669C4—61no—
670C4—121no—
671C4—362no—
672C4—361no—
673C4#6379512yescomplemented
674C4D32×D411yescharacteristic
675C4D3×#23911yescharacteristic
676C3—21no—
677C3#7905511yescharacteristic, complemented
678C3#8033211yescharacteristic, complemented
679C2—62no—
680C2—122no—
681C2—242no—
682C2—362no—
683C2D3×#89511yescharacteristic
684C2C2×#6379511yescharacteristic
685C2#1059471211yescharacteristic
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×#63795C2semidirect
2. C4×D3×D12C2semidirect
3. #10593897C2semidirect
4. #10592540C2semidirect
5. C3×#4843C2semidirect
6. C3×#4837C2semidirect
7. #10590860C2semidirect
8. #10590755C2semidirect
9. #10590670C2semidirect
10. #10590365C2semidirect
11. #10590355C2semidirect
19. #64078C22semidirect
22. C3×#874C22semidirect
35. #63860C22semidirect
39. C32×C4⋊C8C22semidirect
40. #63643C22semidirect
41. C3×#821C22semidirect
42. C3×Dic3⋊C8C22semidirect
43. C3×C4⋊(C3⋊C8)C22semidirect
44. #63567C22semidirect
45. #63563C22semidirect
61. #4843D3semidirect
66. #4837D3semidirect
88. D3×D12D4semidirect
153. #874C2×D3semidirect
171. C3×C4⋊C8C2×D3semidirect
172. C3×C4⋊C8C2×D3semidirect
176. #821C2×D3semidirect
181. Dic3⋊C8C2×D3semidirect
183. C4⋊(C3⋊C8)C2×D3semidirect
350. C32×C4AGL(1,ℤ/8)semidirect
386. C4⋊C8D32semidirect
577. C3×C4#908semidirect
578. C3×C4#911semidirect
593. C32#3036semidirect
673. C4#63795semidirect
677. C3#79055semidirect
678. C3#80332semidirect

Maximal subgroups

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

subgroupindex
C2×#637952
C4×D3×D122
#105938972
#105925402
C3×#48432
C3×#48372
#105908602
#105907552
#105906702
#105903652
#105903552
#803323
#790553