Finite Group Databasebeta

← #11865855

Subgroups — #11865855

Order 1152.

1159 conjugacy classes of subgroups.

The subgroup lattice has 689 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63798C212yesmaximal, complemented
2C4×#3802C211yesmaximal, characteristic, complemented
3#10593907C211yesmaximal, characteristic, complemented
4#10592536C211yesmaximal, characteristic, complemented
5C3×#4843C211yesmaximal, characteristic, complemented
6C3×#4841C211yesmaximal, characteristic, complemented
7#10590957C212yesmaximal, complemented
8#10590751C212yesmaximal, complemented
9#10590750C212yesmaximal, complemented
10#10590363C211yesmaximal, characteristic, complemented
11#10590347C211yesmaximal, characteristic, complemented
12#80428—31nomaximal
13#80332—31nomaximal
14C2×#3802C2211yescharacteristic
15C2×C4×D32—21no—
16C2×#3796C2212yes—
17C2×#3743C2212yes—
18C42×C3⋊D3C2211yescharacteristic
19C2×C3×D24C2212yes—
20C2×C3×#204C2212yes—
21C3×#874C2211yescharacteristic, complemented
22C3×C4×D12C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×#869C2211yescharacteristic, complemented
25#63921—21no—
26#63916—21no—
27#63916—21no—
28#63902—21no—
29C4×#625—21no—
30#63900C2211yescharacteristic
31#63898—21no—
32#63898—21no—
33#63898C2211yescharacteristic
34#63898C2211yescharacteristic
35#63863C2212yescomplemented
36C2×#3715C2212yes—
37C2×#3713C2212yes—
38#63798—28no—
39C32×C4⋊C8C2211yescharacteristic, complemented
40#63641C2212yescomplemented
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
42C3×#821C2212yescomplemented
43C3×#816C2212yescomplemented
44#63565C2212yescomplemented
45#63562C2212yescomplemented
46C2×#914—32no—
47C2×#911—32no—
48#5725—31no—
49#5716—31no—
50C4×D3×D4—31no—
51C4×D3×D4—31no—
52C3×#461—31no—
53C3×#459—31no—
54#5165—32no—
55#5153—32no—
56#5083—31no—
57#5072—31no—
58#5019—31no—
59#5015—31no—
60#4843D311yescharacteristic, complemented
61#4841D311yescharacteristic, complemented
62#4837—31no—
63#4837—31no—
64#4837—61no—
65#4819—32no—
66#4803—32no—
67#4787—32no—
68#4771—32no—
69C22×D32—21no—
70C2×C4×C3⋊D3D411yescharacteristic
71C2×C4×C3⋊D3D411yescharacteristic
72C2×C4×C3⋊D3C2311yescharacteristic
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12C2312yes—
76C2×C3×D12C2311yescharacteristic
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—21no—
80C2×C3×Dic6C2312yes—
81C2×#626—22no—
82C2×#625—21no—
83C2×#624—21no—
84C2×D3×Dic3—22no—
85C2×D3×Dic3—21no—
86C2×D3×Dic3—21no—
87#3802—22no—
88#3802D414yescomplemented
89C4×D32—44no—
90#3796—24no—
91#3796—24no—
92C2×C32×C8C2312yes—
93C32×C42C2311yescharacteristic
94C4×C3⋊Dic3D411yescharacteristic
95C4×C3⋊Dic3D411yescharacteristic
96C4×C3⋊Dic3C2311yescharacteristic
97C2×C3⋊(C3⋊C8)C2312yes—
98#3743—24no—
99C3×(C2×D3)⋊C4—21no—
100C3×(C2×D3)⋊C4—21no—
101C3×C4⋊Dic3—21no—
102C3×C4⋊Dic3—21no—
103C3×C4⋊Dic3C2311yescharacteristic
104C3×C4⋊Dic3C2311yescharacteristic
105C3×D24—24no—
106C3×#204—24no—
107#3724—21no—
108(C2×D3)⋊Dic3—22no—
109(C2×D3)⋊Dic3—22no—
110(C2×D3)⋊Dic3—21no—
111(C2×D3)⋊Dic3—21no—
112#3715—24no—
113#3713—24no—
114#3036—91noSylow
115C2×#239—32no—
116C2×#237—32no—
117C2×D3×D4—31no—
118C2×D3×D4—31no—
119C22×C4×D3—61no—
120C22×C4×D3—61no—
121C2×C3×SD16—32no—
122C2×C3×D8—32no—
123C3×C4⋊Q8—31no—
124C3×#127—31no—
125C3×C4×D4—31no—
126C3×C4×D4—31no—
127#947—32no—
128C2×#215—32no—
129#938—61no—
130#938—61no—
131#936—32no—
132D4×Dic3—31no—
133D4×Dic3—31no—
134D4×Dic3—61no—
135D4×Dic3—61no—
136C2×#214—32no—
137C2×#213—32no—
138C2×#213—32no—
139C4×#67—61no—
140C4×#67—61no—
141#914—68no—
142#911—68no—
143C2×D24C2×D312yes—
144C2×#204C2×D312yes—
145C2×ΓL(1,𝔽25)—32no—
146C2×ΓL(1,𝔽25)—32no—
147C2×ΓL(1,𝔽25)—62no—
148#895—61no—
149#895—61no—
150#893—31no—
151#893—31no—
152#893—61no—
153#893—61no—
154D3×C4⋊C4—31no—
155D3×C4⋊C4—31no—
156#67⋊C4—61no—
157#67⋊C4—61no—
158D3×C22⋊C4—61no—
159D3×C22⋊C4—61no—
160#874C2×D311yescharacteristic, complemented
161C4×D12C2×D311yescharacteristic
162C4×D12C2×D311yescharacteristic
163C42×D3—31no—
164C42×D3—31no—
165C42×D3—61no—
166#869C2×D311yescharacteristic, complemented
167C3×C4⋊C8—21no—
168C3×C4⋊C8C2×D311yescharacteristic, complemented
169C3×C4⋊C8C2×D311yescharacteristic, complemented
170C3×#103—32no—
171C3×#102—32no—
172#835—32no—
173#832—32no—
174#821C2×D312yescomplemented
175#816C2×D312yescomplemented
176Dic3⋊C8—32no—
177Dic3⋊C8—32no—
178Dic3⋊C8—62no—
179#810—32no—
180#809—32no—
181C4⋊(C3⋊C8)—31no—
182C4⋊(C3⋊C8)—31no—
183C4⋊(C3⋊C8)—61no—
184C22×C3⋊D3C2×D411yescharacteristic
185C22×C3×D3—21no—
186C22×C3×D3—21no—
187C22×C3×D3—22no—
188C2×D32—24no—
189C2×D32—42no—
190C2×D32—42no—
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2411yescharacteristic
194C2×C3⋊Dic3C2×D411yescharacteristic
195C2×C3⋊Dic3C2×D411yescharacteristic
196C2×C3⋊Dic3C2×D411yescharacteristic
197C4×C3⋊D3—22no—
198C4×C3⋊D3—41no—
199C4×C3⋊D3C2×D412yes—
200C4×C3⋊D3#4112yes—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C3×D12—22no—
205C3×D12—21no—
206C3×D12—21no—
207C3×D12—22no—
208C3×D12—42no—
209C3×D12—42no—
210C3×D12C2×D412yes—
211C3×D12C2×D412yes—
212C3×C4×D3—42no—
213C3×C4×D3—42no—
214C3×Dic6—22no—
215C3×Dic6—22no—
216#626—44no—
217#625—24no—
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—31no—
230#461—91no—
231#459—31no—
232#459—91no—
233#423—91no—
234#417—92no—
235C23×D3—61no—
236C23×D3—61no—
237C2×C3×Q8—32no—
238C2×C3×D4—31no—
239C2×C3×D4—31no—
240C2×C3×D4—32no—
241C2×C3×D4—61no—
242C2×C3×D4—61no—
243C22×C3×C4—61no—
244C22×C3×C4—61no—
245C2×#67—62no—
246C2×#67—61no—
247C2×#67—61no—
248C22×Dic3—61no—
249C22×Dic3—61no—
250C22×Dic3—62no—
251#239—64no—
252#239—64no—
253#237—64no—
254#237—64no—
255D3×D4—34no—
256D3×D4—34no—
257D3×D4—62no—
258D3×D4—62no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—62no—
262C2×D12C22×D312yes—
263C2×D12C22×D311yescharacteristic
264C2×D12C22×D311yescharacteristic
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—31no—
268C2×C4×D3—31no—
269C2×C4×D3—31no—
270C2×C4×D3—31no—
271C2×C4×D3—31no—
272C2×C4×D3—31no—
273C2×C4×D3—61no—
274C2×C4×D3—61no—
275C2×C4×D3—61no—
276C2×C4×D3—61no—
277C2×C4×D3—61no—
278C2×C4×D3—61no—
279C2×C4×D3—61no—
280C2×C4×D3—62no—
281C2×C4×D3—124no—
282C2×C4×D3—124no—
283C2×Dic6C22×D312yes—
284C3×SD16—64no—
285C3×D8—64no—
286C2×C3×C8—22no—
287C2×C3×C8C22×D312yes—
288C2×C3×C8C22×D312yes—
289C3×C4⋊C4—31no—
290C3×C4⋊C4—31no—
291C3×C4⋊C4—61no—
292C3×C4⋊C4—61no—
293C3×C22⋊C4—61no—
294C3×C22⋊C4—61no—
295C3×C42—21no—
296C3×C42C22×D311yescharacteristic
297C3×C42C22×D311yescharacteristic
298#217—61no—
299#217—61no—
300#217—62no—
301#217—62no—
302#215—64no—
303#214—64no—
304#213—64no—
305#213—64no—
306(C2×D3)⋊C4—21no—
307(C2×D3)⋊C4—21no—
308(C2×D3)⋊C4—61no—
309(C2×D3)⋊C4—61no—
310(C2×D3)⋊C4—62no—
311(C2×D3)⋊C4—62no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3C22×D311yescharacteristic
315C4⋊Dic3C22×D311yescharacteristic
316Dic3⋊C4—61no—
317Dic3⋊C4—61no—
318C4×Dic3—31no—
319C4×Dic3—31no—
320C4×Dic3—31no—
321C4×Dic3—31no—
322C4×Dic3—31no—
323C4×Dic3—31no—
324C4×Dic3—61no—
325C4×Dic3—61no—
326C4×Dic3—61no—
327C2×C3⋊C8—32no—
328C2×C3⋊C8—32no—
329C2×C3⋊C8—62no—
330D24—24no—
331#204—24no—
332ΓL(1,𝔽25)—64no—
333ΓL(1,𝔽25)—64no—
334ΓL(1,𝔽25)—124no—
335C22×C32C22×D411yescharacteristic
336C2×C3⋊D3—21no—
337C2×C3⋊D3—21no—
338C2×C3⋊D3#12112yes—
339C2×C3×D3—22no—
340C2×C3×D3—22no—
341C2×C3×D3—41no—
342C2×C3×D3—41no—
343C2×C3×D3—41no—
344C2×C3×D3—41no—
345C2×C3×D3—42no—
346C2×C3×D3—42no—
347C2×C3×D3—42no—
348D32—48no—
349C32×C4—21no—
350C32×C4AGL(1,ℤ/8)12yescomplemented
351C32×C4C22×D411yescharacteristic
352C32×C4C2×#4111yescharacteristic
353C3⋊Dic3—21no—
354C3⋊Dic3—21no—
355C3⋊Dic3#12112yes—
356C3×Dic3—42no—
357C3×Dic3—41no—
358C3×Dic3—41no—
359C2×#41—92no—
360C22×D4—91no—
361C23×C4—181no—
362AGL(1,ℤ/8)—188no—
363C2×SD16—32no—
364C2×SD16—92no—
365C2×D8—32no—
366C2×D8—92no—
367C2×M16—92no—
368C4⋊Q8—31no—
369#127—31no—
370#124—92no—
371#121—181no—
372#121—181no—
373C4×D4—31no—
374C4×D4—31no—
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—91no—
384C4⋊C8—92no—
385C4⋊C8—91no—
386C4⋊C8D3211yescharacteristic, complemented
387#103—32no—
388#103—92no—
389#102—32no—
390#102—92no—
391C23×C3—61no—
392C23×C3—61no—
393C23×C3—62no—
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—22no—
397C22×D3—31no—
398C22×D3—31no—
399C22×D3—61no—
400C22×D3—64no—
401C22×D3—64no—
402C22×D3—122no—
403C22×D3—122no—
404C22×D3—122no—
405C22×D3—122no—
406C3×Q8—62no—
407C3×Q8—62no—
408C3×D4—32no—
409C3×D4—32no—
410C3×D4—62no—
411C3×D4—61no—
412C3×D4—61no—
413C3×D4—62no—
414C3×D4—122no—
415C3×D4—122no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—61no—
420C2×C3×C4—61no—
421C2×C3×C4—62no—
422C2×C3×C4—122no—
423C2×C3×C4—122no—
424C2×C3×C4D3×D411yescharacteristic
425C2×C3×C4D3×D411yescharacteristic
426C2×C3×C4D3×D411yescharacteristic
427C2×C3×C4D3×D411yescharacteristic
428C2×C3×C4C23×D311yescharacteristic
429C2×C3×C4C23×D311yescharacteristic
430#67—64no—
431#67—64no—
432#67—124no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—22no—
436C2×Dic3—31no—
437C2×Dic3—31no—
438C2×Dic3—31no—
439C2×Dic3—31no—
440C2×Dic3—31no—
441C2×Dic3—31no—
442C2×Dic3—61no—
443C2×Dic3—61no—
444C2×Dic3—61no—
445C2×Dic3—124no—
446C2×Dic3—122no—
447C2×Dic3—122no—
448D12—22no—
449D12—21no—
450D12—21no—
451D12—22no—
452D12—42no—
453D12—42no—
454D12—124no—
455D12D3×D412yes—
456D12D3×D412yes—
457C4×D3—32no—
458C4×D3—32no—
459C4×D3—32no—
460C4×D3—32no—
461C4×D3—42no—
462C4×D3—42no—
463C4×D3—62no—
464C4×D3—62no—
465C4×D3—62no—
466C4×D3—62no—
467C4×D3—122no—
468C4×D3—124no—
469C4×D3—122no—
470C4×D3—122no—
471C4×D3—121no—
472C4×D3—121no—
473C4×D3—122no—
474C4×D3—122no—
475C4×D3—122no—
476Dic6—22no—
477Dic6—22no—
478C3×C8—22no—
479C3×C8—22no—
480C3×C8—42no—
481C3⋊C8—62no—
482C3⋊C8—62no—
483C3⋊C8—122no—
484C2×C32C2×#12111yescharacteristic
485C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
486C2×C32#57511yescharacteristic
487C3⋊D3—22no—
488C3×D3—42no—
489C3×D3—42no—
490C3×D3—82no—
491C24—181no—
492#41—184no—
493#41—184no—
494C2×Q8—32no—
495C2×D4—31no—
496C2×D4—31no—
497C2×D4—32no—
498C2×D4—61no—
499C2×D4—61no—
500C2×D4—94no—
501C2×D4—182no—
502C2×D4—182no—
503C2×D4—181no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—91no—
507C22×C4—91no—
508C22×C4—91no—
509C22×C4—181no—
510C22×C4—181no—
511C22×C4—181no—
512C22×C4—182no—
513C22×C4—364no—
514SD16—64no—
515SD16—184no—
516D8—64no—
517D8—184no—
518M16—184no—
519C2×C8—92no—
520C2×C8C2×D3212yes—
521C4⋊C4—31no—
522C4⋊C4—31no—
523C4⋊C4—61no—
524C4⋊C4—61no—
525C4⋊C4—181no—
526C22⋊C4—61no—
527C22⋊C4—61no—
528C22⋊C4—181no—
529C22⋊C4—181no—
530C22⋊C4—182no—
531C22⋊C4—182no—
532C42—91no—
533C42—91no—
534C42—91no—
535C42C2×D3211yescharacteristic
536C22×C3—21no—
537C22×C3—62no—
538C22×C3—62no—
539C22×C3—121no—
540C22×C3—121no—
541C22×C3—121no—
542C22×C3—121no—
543C22×C3—122no—
544C22×C3—122no—
545C22×C3—122no—
546C22×C3C2×D3×D411yescharacteristic
547C22×C3C2×D3×D411yescharacteristic
548C2×D3—22no—
549C2×D3—22no—
550C2×D3—32no—
551C2×D3—32no—
552C2×D3—41no—
553C2×D3—41no—
554C2×D3—41no—
555C2×D3—41no—
556C2×D3—42no—
557C2×D3—42no—
558C2×D3—42no—
559C2×D3—62no—
560C2×D3—61no—
561C2×D3—61no—
562C2×D3—61no—
563C2×D3—61no—
564C2×D3—121no—
565C2×D3—121no—
566C2×D3—128no—
567C2×D3—128no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—22no—
571C3×C4—21no—
572C3×C4—21no—
573C3×C4—41no—
574C3×C4—121no—
575C3×C4—121no—
576C3×C4—122no—
577C3×C4#91112yescomplemented
578C3×C4#91412yescomplemented
579C3×C4C2×D3×D411yescharacteristic
580C3×C4C2×D3×D411yescharacteristic
581C3×C4D3×#4111yescharacteristic
582C3×C4D3×#4111yescharacteristic
583Dic3—32no—
584Dic3—32no—
585Dic3—41no—
586Dic3—41no—
587Dic3—42no—
588Dic3—62no—
589Dic3—62no—
590Dic3—61no—
591Dic3—61no—
592Dic3—61no—
593Dic3—61no—
594Dic3—121no—
595C32#303611yescharacteristic, complemented, Sylow
596C23—61no—
597C23—61no—
598C23—62no—
599C23—91no—
600C23—184no—
601C23—362no—
602C23—362no—
603Q8—62no—
604Q8—62no—
605D4—32no—
606D4—32no—
607D4—62no—
608D4—61no—
609D4—61no—
610D4—62no—
611D4—122no—
612D4—122no—
613D4—184no—
614D4—364no—
615C2×C4—61no—
616C2×C4—61no—
617C2×C4—62no—
618C2×C4—91no—
619C2×C4—92no—
620C2×C4—92no—
621C2×C4—91no—
622C2×C4—91no—
623C2×C4—122no—
624C2×C4—122no—
625C2×C4—182no—
626C2×C4—361no—
627C2×C4—364no—
628C2×C4—362no—
629C2×C4—362no—
630C2×C4—362no—
631C2×C4#380211yescharacteristic
632C2×C4#380211yescharacteristic
633C2×C4C22×D3211yescharacteristic
634C8—22no—
635C8—182no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—122no—
640C2×C3—122no—
641C2×C3—242no—
642C2×C3D3×#12111yescharacteristic
643C2×C3D3×#12111yescharacteristic
644C2×C3C2×#91111yescharacteristic
645C2×C3C2×#91411yescharacteristic
646C2×C3#577311yescharacteristic
647C2×C3#577711yescharacteristic
648D3—42no—
649D3—42no—
650D3—62no—
651D3—62no—
652D3—82no—
653D3—122no—
654C22—62no—
655C22—62no—
656C22—92no—
657C22—121no—
658C22—121no—
659C22—121no—
660C22—121no—
661C22—122no—
662C22—122no—
663C22—122no—
664C22—181no—
665C22—181no—
666C22—368no—
667C22C2×#380211yescharacteristic
668C4—21no—
669C4—92no—
670C4—122no—
671C4—121no—
672C4—121no—
673C4—181no—
674C4—181no—
675C4#6379812yescomplemented
676C4D32×D411yescharacteristic
677C4#6431911yescharacteristic
678C3—21no—
679C3#8033211yescharacteristic, complemented
680C3#8042811yescharacteristic, complemented
681C2—122no—
682C2—122no—
683C2—182no—
684C2—242no—
685C2#1059461211yescharacteristic
686C2C2×#6379811yescharacteristic
687C2#1059471811yescharacteristic
subgroupG/H
centerC22C2×#3802
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×#63798C2semidirect
2. C4×#3802C2semidirect
3. #10593907C2semidirect
4. #10592536C2semidirect
5. C3×#4843C2semidirect
6. C3×#4841C2semidirect
7. #10590957C2semidirect
8. #10590751C2semidirect
9. #10590750C2semidirect
10. #10590363C2semidirect
11. #10590347C2semidirect
21. C3×#874C22semidirect
24. C3×#869C22semidirect
35. #63863C22semidirect
39. C32×C4⋊C8C22semidirect
40. #63641C22semidirect
41. C4⋊(C3⋊(C3⋊C8))C22semidirect
42. C3×#821C22semidirect
43. C3×#816C22semidirect
44. #63565C22semidirect
45. #63562C22semidirect
60. #4843D3semidirect
61. #4841D3semidirect
88. #3802D4semidirect
160. #874C2×D3semidirect
166. #869C2×D3semidirect
168. C3×C4⋊C8C2×D3semidirect
169. C3×C4⋊C8C2×D3semidirect
174. #821C2×D3semidirect
175. #816C2×D3semidirect
350. C32×C4AGL(1,ℤ/8)semidirect
386. C4⋊C8D32semidirect
577. C3×C4#911semidirect
578. C3×C4#914semidirect
595. C32#3036semidirect
675. C4#63798semidirect
679. C3#80332semidirect
680. C3#80428semidirect

Maximal subgroups

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

subgroupindex
C2×#637982
C4×#38022
#105939072
#105925362
C3×#48432
C3×#48412
#105909572
#105907512
#105907502
#105903632
#105903472
#804283
#803323