Finite Group Databasebeta

← D3×#4865 #11866964

Subgroups — D3×#4865 #11866964

Order 1152.

1257 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×D24C211yesmaximal, characteristic, complemented
2C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3D3×#895C212yesmaximal, complemented
4#10592564C211yesmaximal, characteristic, complemented
5C3×#4865C211yesmaximal, characteristic, complemented
6C3×D3×#106C211yesmaximal, characteristic, complemented
7#10590846C211yesmaximal, characteristic, complemented
8#10590835C211yesmaximal, characteristic, complemented
9D3×#809C212yesmaximal, complemented
10#10590586C212yesmaximal, complemented
11#10590508C212yesmaximal, complemented
12D3×#469—31nomaximal
13C2×#4865—31nomaximal
14C2×D3×D12—22no—
15C2×D3×D12C2212yes—
16C2×C4×D32C2211yescharacteristic
17C2×#3745C2211yescharacteristic, complemented
18C2×#3743C2211yescharacteristic, complemented
19#64104C2212yescomplemented
20C2×C3×D24C2211yescharacteristic, complemented
21C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
22C2×C3×D3×C8C2211yescharacteristic
23C3×#895C2212yescomplemented
24C3×D3×C4⋊C4C2212yes—
25D3×(C2×D3)⋊C4—22no—
26#63916C2212yescomplemented
27#63910—22no—
28#63909C2212yescomplemented
29#63886—22no—
30C2×#3714C2212yescomplemented
31C2×#3712C2211yescharacteristic, complemented
32C2×#3711C2211yescharacteristic, complemented
33C2×D3×C3⋊C8C2211yescharacteristic
34D3×D24—24no—
35D3×ΓL(1,𝔽25)—24no—
36C32×#106C2211yescharacteristic, complemented
37#63636C2212yescomplemented
38C3×#817C2211yescharacteristic, complemented
39C3×#809C2212yescomplemented
40C3×#808C2212yescomplemented
41#63564C2212yescomplemented
42#63562C2212yescomplemented
43C2×D3×D8—31no—
44C2×D3×M16—31no—
45C22×D24—31no—
46C22×ΓL(1,𝔽25)—31no—
47D3×#121—32no—
48C2×#895—32no—
49C3×#469—31no—
50C2×C3×#106—31no—
51#5159—31no—
52#5135—31no—
53#5039—32no—
54C2×#809—32no—
55#4865—31no—
56#4865—31no—
57#4865—32no—
58#4865—31no—
59#4865—31no—
60#4865—32no—
61#4865—61no—
62#4865D311yescharacteristic, direct product factor
63D3×#106D311yescharacteristic, complemented
64#4782—32no—
65D3×#102—32no—
66C22×D32—22no—
67C22×D32D411yescharacteristic
68C2×C4⋊(C3⋊D3)—22no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×C3×D12—22no—
72C2×C3×D12C2312yes—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3C2311yescharacteristic
75C2×C3×C4×D3C2311yescharacteristic
76C2×#626—22no—
77C2×#626—22no—
78C2×#626—22no—
79C2×#624D411yescharacteristic
80C2×D3×Dic3D411yescharacteristic
81C2×D3×Dic3D411yescharacteristic
82D3×D12—24no—
83D3×D12—24no—
84D3×D12—48no—
85C4×D32—22no—
86C4×D32—22no—
87C2×C32×C8C2311yescharacteristic
88C32×C4⋊C4C2312yes—
89#3752—22no—
90C2×C3⋊(C3⋊C8)C2311yescharacteristic
91#3745—22no—
92#3743—22no—
93C3×(C2×D3)⋊C4—22no—
94C3×C4⋊Dic3C2312yes—
95C3×Dic3⋊C4—22no—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C3×D24—22no—
99C3×ΓL(1,𝔽25)—22no—
100C3×D3×C8D414yescomplemented
101#3722—22no—
102(C2×D3)⋊Dic3—22no—
103#3714—24no—
104#3712—22no—
105#3711—22no—
106D3×C3⋊C8—22no—
107C2×#469—91noSylow
108C2×D3×D4—32no—
109C2×D3×D4—62no—
110C22×D12—32no—
111C22×D12—62no—
112C22×C4×D3—31no—
113C22×C4×D3—31no—
114C2×C3×D8—31no—
115C2×C3×M16—31no—
116C22×C3×C8—31no—
117C3×#121—32no—
118C2×C3×C4⋊C4—32no—
119#939—62no—
120#938—32no—
121C2×#213—32no—
122#930—32no—
123C2×(C2×D3)⋊C4—62no—
124C2×#208—31no—
125C22×C3⋊C8—31no—
126D3×D8—64no—
127D3×M16—64no—
128C2×D24—32no—
129C2×D24—31no—
130C2×D24—31no—
131C2×D24—61no—
132C2×D24—64no—
133C2×D24C2×D311yescharacteristic, complemented
134C2×ΓL(1,𝔽25)—31no—
135C2×ΓL(1,𝔽25)—31no—
136C2×ΓL(1,𝔽25)—31no—
137C2×ΓL(1,𝔽25)—31no—
138C2×ΓL(1,𝔽25)—31no—
139C2×ΓL(1,𝔽25)—61no—
140C2×ΓL(1,𝔽25)—64no—
141C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
142C2×D3×C8—31no—
143C2×D3×C8C2×D311yescharacteristic
144#895—32no—
145#895—32no—
146#895—32no—
147#895—32no—
148#895—62no—
149#895—62no—
150#895—62no—
151#895C2×D312yescomplemented
152D3×C4⋊C4C2×D312yes—
153#884—62no—
154D3×C22⋊C4—62no—
155C3×#106—21no—
156C3×#106—31no—
157C3×#106—32no—
158C3×#106C2×D311yescharacteristic, complemented
159C3×#106C2×D311yescharacteristic, complemented
160C3×#102—32no—
161#832—32no—
162#821—32no—
163#817C2×D311yescharacteristic, complemented
164#809—32no—
165#809—32no—
166#809—32no—
167#809—32no—
168#809—62no—
169#809C2×D312yescomplemented
170#808C2×D312yescomplemented
171C22×C3⋊D3—22no—
172C22×C3⋊D3C2×D411yescharacteristic
173C22×C3×D3—22no—
174C22×C3×D3C2×D411yescharacteristic
175C22×C3×D3C2×D411yescharacteristic
176C2×D32—22no—
177C2×D32—24no—
178C2×D32—44no—
179C2×D32—44no—
180C2×D32—44no—
181C2×C32×C4—22no—
182C2×C32×C4C2411yescharacteristic
183C2×C3⋊Dic3C2×D411yescharacteristic
184C4⋊(C3⋊D3)—22no—
185C4⋊(C3⋊D3)—22no—
186C4⋊(C3⋊D3)—44no—
187C4×C3⋊D3—21no—
188C4×C3⋊D3—21no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3C2×D411yescharacteristic
191C2×C3×Dic3C2×D411yescharacteristic
192C3×D12—22no—
193C3×D12—22no—
194C3×D12—44no—
195C3×C4×D3—21no—
196C3×C4×D3—21no—
197C3×C4×D3—44no—
198C3×C4×D3C2×D412yes—
199C3×C4×D3#4112yes—
200#626—44no—
201#626—44no—
202#626—44no—
203#624—22no—
204D3×Dic3—22no—
205D3×Dic3—22no—
206C32×C8C2×D412yescomplemented
207C3⋊(C3⋊C8)—21no—
208C3×C3⋊C8—21no—
209C3×C3⋊C8C2×D412yescomplemented
210C22×D8—91no—
211C22×M16—91no—
212C2×#121—92no—
213#469—31no—
214#469—92no—
215#469—92no—
216#469—91no—
217#469—91no—
218#469—91no—
219C2×#106—31no—
220C2×#102—92no—
221C23×D3—31no—
222C23×D3—31no—
223C23×D3—62no—
224C23×D3—62no—
225C2×C3×D4—32no—
226C2×C3×D4—62no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—62no—
230C2×#67—62no—
231C2×#67—62no—
232C2×#67—62no—
233C22×Dic3—31no—
234C22×Dic3—31no—
235D3×D4—64no—
236D3×D4—64no—
237D3×D4—128no—
238C2×D12—22no—
239C2×D12—32no—
240C2×D12—32no—
241C2×D12—62no—
242C2×D12—64no—
243C2×D12—64no—
244C2×D12—62no—
245C2×D12—62no—
246C2×D12—62no—
247C2×D12—62no—
248C2×D12—62no—
249C2×D12—122no—
250C2×D12—128no—
251C2×D12C22×D312yes—
252C2×C4×D3—22no—
253C2×C4×D3—31no—
254C2×C4×D3—31no—
255C2×C4×D3—31no—
256C2×C4×D3—31no—
257C2×C4×D3—31no—
258C2×C4×D3—31no—
259C2×C4×D3—61no—
260C2×C4×D3—62no—
261C2×C4×D3—62no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C2×C4×D3C22×D311yescharacteristic
265C2×C4×D3C22×D311yescharacteristic
266C3×D8—62no—
267C3×M16—62no—
268C2×C3×C8—21no—
269C2×C3×C8—31no—
270C2×C3×C8—34no—
271C2×C3×C8—31no—
272C2×C3×C8C22×D311yescharacteristic
273C2×C3×C8C22×D311yescharacteristic
274C3×C4⋊C4—22no—
275C3×C4⋊C4—32no—
276C3×C4⋊C4—62no—
277C3×C4⋊C4C22×D312yes—
278C3×C4⋊C4C22×D312yes—
279C3×C22⋊C4—62no—
280#217—62no—
281#213—64no—
282(C2×D3)⋊C4—22no—
283(C2×D3)⋊C4—62no—
284(C2×D3)⋊C4—62no—
285(C2×D3)⋊C4—62no—
286(C2×D3)⋊C4—62no—
287(C2×D3)⋊C4—62no—
288(C2×D3)⋊C4—122no—
289C4⋊Dic3C22×D312yes—
290Dic3⋊C4—22no—
291#208—62no—
292C2×C3⋊C8—31no—
293C2×C3⋊C8—31no—
294C2×C3⋊C8—61no—
295C2×C3⋊C8—62no—
296C2×C3⋊C8C22×D311yescharacteristic
297C2×C3⋊C8C22×D311yescharacteristic
298D24—22no—
299D24—64no—
300D24—62no—
301D24—62no—
302D24—122no—
303ΓL(1,𝔽25)—22no—
304ΓL(1,𝔽25)—62no—
305ΓL(1,𝔽25)—62no—
306ΓL(1,𝔽25)—62no—
307ΓL(1,𝔽25)—62no—
308ΓL(1,𝔽25)—62no—
309ΓL(1,𝔽25)—122no—
310D3×C8—62no—
311D3×C8D1214yescomplemented
312C22×C32C22×D411yescharacteristic
313C2×C3⋊D3—21no—
314C2×C3⋊D3—22no—
315C2×C3⋊D3—42no—
316C2×C3⋊D3—42no—
317C2×C3⋊D3—42no—
318C2×C3×D3—21no—
319C2×C3×D3—22no—
320C2×C3×D3—42no—
321C2×C3×D3—42no—
322C2×C3×D3—42no—
323C2×C3×D3#12112yes—
324C2×C3×D3AGL(1,ℤ/8)14yes—
325D32—44no—
326D32—88no—
327C32×C4—42no—
328C32×C4C22×D411yescharacteristic
329C32×C4C2×#4111yescharacteristic
330C3⋊Dic3—21no—
331C3×Dic3—21no—
332C3×Dic3—42no—
333C3×Dic3#12112yes—
334C22×D4—92no—
335C22×D4—182no—
336C23×C4—91no—
337C2×D8—31no—
338C2×D8—92no—
339C2×D8—91no—
340C2×D8—184no—
341C2×M16—31no—
342C2×M16—91no—
343C2×M16—91no—
344C2×M16—91no—
345C2×M16—184no—
346C22×C8—31no—
347C22×C8—91no—
348#121—32no—
349#121—92no—
350#121—92no—
351#121—92no—
352#121—182no—
353#121—182no—
354C2×C4⋊C4—32no—
355C2×C22⋊C4—182no—
356#106—31no—
357#106—32no—
358#106D3211yescharacteristic, complemented
359#102—32no—
360#102—92no—
361#102—92no—
362#102—92no—
363C23×C3—31no—
364C23×C3—31no—
365C23×C3—62no—
366C22×D3—22no—
367C22×D3—31no—
368C22×D3—31no—
369C22×D3—61no—
370C22×D3—62no—
371C22×D3—64no—
372C22×D3—62no—
373C22×D3—64no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—122no—
377C22×D3—124no—
378C22×D3—124no—
379C22×D3—124no—
380C22×D3—124no—
381C22×D3—124no—
382C22×D3—124no—
383C22×D3D3×D411yescharacteristic
384C22×D3D3×D411yescharacteristic
385C3×D4—62no—
386C3×D4—62no—
387C3×D4—124no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—21no—
391C2×C3×C4—31no—
392C2×C3×C4—32no—
393C2×C3×C4—32no—
394C2×C3×C4—31no—
395C2×C3×C4—42no—
396C2×C3×C4—61no—
397C2×C3×C4—61no—
398C2×C3×C4—62no—
399C2×C3×C4—124no—
400C2×C3×C4C23×D311yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402#67—124no—
403#67—124no—
404#67—124no—
405C2×Dic3—22no—
406C2×Dic3—31no—
407C2×Dic3—31no—
408C2×Dic3—61no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3D3×D411yescharacteristic
412C2×Dic3D3×D411yescharacteristic
413D12—22no—
414D12—22no—
415D12—44no—
416D12—62no—
417D12—62no—
418D12—62no—
419D12—62no—
420D12—122no—
421D12—122no—
422D12—124no—
423D12—124no—
424D12—124no—
425D12—124no—
426D12—124no—
427D12—244no—
428C4×D3—21no—
429C4×D3—21no—
430C4×D3—44no—
431C4×D3—62no—
432C4×D3—62no—
433C4×D3—62no—
434C4×D3—61no—
435C4×D3—61no—
436C4×D3—61no—
437C4×D3—61no—
438C4×D3—62no—
439C4×D3—121no—
440C4×D3—121no—
441C4×D3C2×D1212yes—
442C4×D3#23912yes—
443C3×C8—22no—
444C3×C8—32no—
445C3×C8—61no—
446C3×C8C2×D1212yescomplemented
447C3×C8D3×D412yescomplemented
448C3⋊C8—21no—
449C3⋊C8—61no—
450C3⋊C8—61no—
451C3⋊C8—121no—
452C3⋊C8C2×D1212yescomplemented
453C2×C32C2×#12111yescharacteristic
454C2×C32C2×AGL(1,ℤ/8)12yes—
455C3⋊D3—41no—
456C3⋊D3—82no—
457C3×D3—41no—
458C3×D3—82no—
459C3×D3#46914yescomplemented
460C24—91no—
461C24—182no—
462C2×D4—32no—
463C2×D4—62no—
464C2×D4—92no—
465C2×D4—182no—
466C2×D4—184no—
467C2×D4—184no—
468C2×D4—182no—
469C2×D4—182no—
470C2×D4—182no—
471C2×D4—368no—
472C22×C4—31no—
473C22×C4—31no—
474C22×C4—62no—
475C22×C4—91no—
476C22×C4—91no—
477C22×C4—91no—
478C22×C4—91no—
479C22×C4—182no—
480C22×C4—182no—
481D8—62no—
482D8—184no—
483D8—182no—
484M16—62no—
485M16—182no—
486M16—182no—
487M16—182no—
488C2×C8—31no—
489C2×C8—34no—
490C2×C8—31no—
491C2×C8—91no—
492C2×C8—182no—
493C2×C8C2×D3211yescharacteristic
494C4⋊C4—32no—
495C4⋊C4—62no—
496C4⋊C4C2×D3212yes—
497C22⋊C4—62no—
498C22⋊C4—182no—
499C22⋊C4—182no—
500C22⋊C4—182no—
501C22×C3—21no—
502C22×C3—34no—
503C22×C3—32no—
504C22×C3—62no—
505C22×C3—61no—
506C22×C3—122no—
507C22×C3—122no—
508C22×C3—122no—
509C22×C3C2×D3×D411yescharacteristic
510C22×C3C2×D3×D411yescharacteristic
511C2×D3—22no—
512C2×D3—21no—
513C2×D3—42no—
514C2×D3—42no—
515C2×D3—42no—
516C2×D3—62no—
517C2×D3—61no—
518C2×D3—62no—
519C2×D3—61no—
520C2×D3—121no—
521C2×D3—122no—
522C2×D3—124no—
523C2×D3—124no—
524C2×D3—122no—
525C2×D3—122no—
526C2×D3—122no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—242no—
531C2×D3—242no—
532C2×D3—242no—
533C2×D3—248no—
534C2×D3—248no—
535C2×D3#89512yes—
536C2×D3#91414yes—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—32no—
540C3×C4—42no—
541C3×C4—42no—
542C3×C4—61no—
543C3×C4—82no—
544C3×C4—122no—
545C3×C4C22×D1211yescharacteristic
546C3×C4C2×D3×D411yescharacteristic
547C3×C4C2×#23911yescharacteristic
548C3×C4D3×#4111yescharacteristic
549Dic3—21no—
550Dic3—42no—
551Dic3—61no—
552Dic3—61no—
553Dic3—121no—
554Dic3#89512yes—
555C32C2×#46911yescharacteristic, complemented, Sylow
556C23—31no—
557C23—31no—
558C23—62no—
559C23—91no—
560C23—182no—
561C23—184no—
562C23—182no—
563C23—364no—
564C23—364no—
565C23—364no—
566D4—62no—
567D4—62no—
568D4—124no—
569D4—182no—
570D4—182no—
571D4—364no—
572D4—364no—
573D4—364no—
574D4—364no—
575C2×C4—22no—
576C2×C4—31no—
577C2×C4—32no—
578C2×C4—32no—
579C2×C4—31no—
580C2×C4—61no—
581C2×C4—61no—
582C2×C4—62no—
583C2×C4—91no—
584C2×C4—124no—
585C2×C4—182no—
586C2×C4—182no—
587C2×C4—182no—
588C2×C4—181no—
589C2×C4—181no—
590C2×C4C22×D3211yescharacteristic
591C8—32no—
592C8—61no—
593C8—181no—
594C8D3×D1212yescomplemented
595C2×C3—21no—
596C2×C3—22no—
597C2×C3—34no—
598C2×C3—121no—
599C2×C3—242no—
600C2×C3C2×#89511yescharacteristic
601C2×C3D3×#12111yescharacteristic
602C2×C3C2×#91412yes—
603C2×C3D3×AGL(1,ℤ/8)12yes—
604D3—41no—
605D3—82no—
606D3—121no—
607D3—121no—
608D3—241no—
609D3—242no—
610D3—242no—
611D3—482no—
612D3#486514yesdirect product factor
613C22—32no—
614C22—34no—
615C22—61no—
616C22—62no—
617C22—122no—
618C22—122no—
619C22—122no—
620C22—181no—
621C22—182no—
622C22—364no—
623C22—362no—
624C22—362no—
625C22—362no—
626C22—728no—
627C22D32×D411yescharacteristic
628C4—32no—
629C4—42no—
630C4—61no—
631C4—122no—
632C4—181no—
633C4C2×D3×D1211yescharacteristic
634C4D3×#23911yescharacteristic
635C3—21no—
636C3C2×#486511yescharacteristic, complemented
637C3D3×#46911yescharacteristic, complemented
638C2—34no—
639C2—121no—
640C2—242no—
641C2—361no—
642C2—722no—
643C2D3×#89511yescharacteristic
644C2D3×#91412yes—
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
hypercenter#106D32
hypocenterC32C2×#469
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. C2×D3×D24C2semidirect
2. C2×D3×ΓL(1,𝔽25)C2semidirect
3. D3×#895C2semidirect
4. #10592564C2semidirect
5. C3×#4865C2semidirect
6. C3×D3×#106C2semidirect
7. #10590846C2semidirect
8. #10590835C2semidirect
9. D3×#809C2semidirect
10. #10590586C2semidirect
11. #10590508C2semidirect
17. C2×#3745C22semidirect
18. C2×#3743C22semidirect
19. #64104C22semidirect
20. C2×C3×D24C22semidirect
21. C2×C3×ΓL(1,𝔽25)C22semidirect
23. C3×#895C22semidirect
26. #63916C22semidirect
28. #63909C22semidirect
30. C2×#3714C22semidirect
31. C2×#3712C22semidirect
32. C2×#3711C22semidirect
36. C32×#106C22semidirect
37. #63636C22semidirect
38. C3×#817C22semidirect
39. C3×#809C22semidirect
40. C3×#808C22semidirect
41. #63564C22semidirect
42. #63562C22semidirect
62. #4865D3direct (N × H)
63. D3×#106D3semidirect
100. C3×D3×C8D4semidirect
133. C2×D24C2×D3semidirect
141. C2×ΓL(1,𝔽25)C2×D3semidirect
151. #895C2×D3semidirect
158. C3×#106C2×D3semidirect
159. C3×#106C2×D3semidirect
163. #817C2×D3semidirect
169. #809C2×D3semidirect
170. #808C2×D3semidirect
206. C32×C8C2×D4semidirect
209. C3×C3⋊C8C2×D4semidirect
311. D3×C8D12semidirect
358. #106D32semidirect
446. C3×C8C2×D12semidirect
447. C3×C8D3×D4semidirect
452. C3⋊C8C2×D12semidirect
459. C3×D3#469semidirect
555. C32C2×#469semidirect
594. C8D3×D12semidirect
612. D3#4865direct (N × H)
636. C3C2×#4865semidirect
637. C3D3×#469semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D242
C2×D3×ΓL(1,𝔽25)2
D3×#8952
#105925642
C3×#48652
C3×D3×#1062
#105908462
#105908352
D3×#8092
#105905862
#105905082
D3×#4693
C2×#48653