Finite Group Databasebeta

← C3×#81012 #11868783

Subgroups — C3×#81012 #11868783

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C3×C4×#239C211yesmaximal, characteristic
3C32×#475C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5C3×#5020C211yesmaximal, characteristic, complemented
6C3×#4870C212yesmaximal, complemented
7C3×#4861C212yesmaximal, complemented
8C3×#4846C211yesmaximal, characteristic, complemented
9C3×#4837C211yesmaximal, characteristic, complemented
10C3×#4803C212yesmaximal
11C3×#4793C212yesmaximal, complemented
12C3×#3079—31nomaximal
13#81012C311yesmaximal, characteristic, direct product factor
14C2×C3×#239C2211yescharacteristic
15C2×C3×D3×Q8—21no—
16C32×C4⋊Q8C2211yescharacteristic
17C32×C4×Q8C2211yescharacteristic
18C3×Q8×Dic3C2211yescharacteristic
19C3×#944—21no—
20C2×C3×ΓL(1,𝔽25)C2212yes—
21C3×#893—21no—
22C3×#893C2211yescharacteristic
23C3×#892—21no—
24C3×#892C2211yescharacteristic
25C3×D3×C4⋊C4—21no—
26C3×D3×C4⋊C4C2212yes—
27C3×#888—21no—
28C3×#888C2212yes—
29C3×C4×D12—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C42×D3—21no—
32C3×C42×D3C2211yescharacteristic
33C3×#869C2211yescharacteristic
34C32×#106C2212yes—
35C32×C4⋊C8C2211yescharacteristic
36C32×#103C2212yes—
37C3×#835C2212yes—
38C3×#821C2212yes—
39C3×#818C2212yes—
40C3×Dic3⋊C8C2212yes—
41C3×#809C2212yes—
42C3×#808C2212yes—
43C3×#807C2212yes—
44C3×C4⋊(C3⋊C8)C2211yescharacteristic
45C2×C3×C4⋊Q8—31no—
46C3×C4×#41—31no—
47D3×C4⋊Q8C2×C311yescharacteristic, complemented
48C4×#239C2×C311yescharacteristic
49C3×#477—32no—
50C3×#476—32no—
51C3×#475—21no—
52C3×#475—31no—
53C3×#475D311yescharacteristic, complemented
54C3×#475C2×C311yescharacteristic, complemented
55C3×#474—31no—
56C3×#474—31no—
57C3×#428—32no—
58C3×#423—31no—
59C3×#417—32no—
60#5087C2×C311yescharacteristic, complemented
61#5020C2×C311yescharacteristic, complemented
62#4870C2×C312yescomplemented
63#4861C2×C312yescomplemented
64#4846C2×C311yescharacteristic, complemented
65#4837C2×C311yescharacteristic, complemented
66#4803C2×C312yes—
67#4793C2×C312yescomplemented
68C2×C32×Q8—21no—
69C2×C32×Q8C2311yescharacteristic
70C3×#239—22no—
71C3×#239Q814yescomplemented
72C3×D3×Q8—44no—
73C2×C3×D12—21no—
74C2×C3×D12C2311yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3D411yescharacteristic
81C2×C3×C4×D3C2311yescharacteristic
82C2×C3×Dic6—21no—
83C2×C3×Dic6—22no—
84C2×C32×C8C2312yes—
85C32×C4⋊C4—21no—
86C32×C4⋊C4—21no—
87C32×C4⋊C4C2312yes—
88C32×C4⋊C4C2311yescharacteristic
89C32×C42—21no—
90C32×C42C2311yescharacteristic
91C3×(C2×D3)⋊C4—21no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3C2312yes—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×Dic3⋊C4—22no—
99C3×Dic3⋊C4—22no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3—21no—
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C2×C3×C3⋊C8C2312yes—
106C3×ΓL(1,𝔽25)—24no—
107#3079—31noSylow
108C2×C3×#41—31no—
109C22×C3×Q8—61no—
110C2×#239C22×C311yescharacteristic
111C2×D3×Q8—21no—
112C2×C3×M16—32no—
113C3×C4⋊Q8—21no—
114C3×C4⋊Q8—32no—
115C3×C4⋊Q8—31no—
116C3×C4⋊Q8—61no—
117C3×C4⋊Q8—61no—
118C3×C4⋊Q8C2×D311yescharacteristic
119C3×C4⋊Q8C22×C311yescharacteristic
120C3×C4×Q8—21no—
121C3×C4×Q8—31no—
122C3×C4×Q8C2×D311yescharacteristic
123C3×C4×Q8C22×C311yescharacteristic
124C3×C4×D4—31no—
125C3×C4×D4—31no—
126C3×C4×D4—61no—
127C3×C4×D4—61no—
128C3×#117—31no—
129C3×#117—61no—
130C2×C3×C4⋊C4—32no—
131C2×C3×C4⋊C4—61no—
132C2×C3×C42—31no—
133C2×C3×C42—61no—
134Q8×Dic3C22×C311yescharacteristic
135#944—21no—
136C2×ΓL(1,𝔽25)C22×C312yes—
137#893—21no—
138#893C22×C311yescharacteristic
139#892—21no—
140#892C22×C311yescharacteristic
141D3×C4⋊C4—21no—
142D3×C4⋊C4C22×C312yes—
143#888—21no—
144#888C22×C312yes—
145C4×D12—21no—
146C4×D12C22×C311yescharacteristic
147C42×D3—21no—
148C42×D3C22×C311yescharacteristic
149#869C22×C311yescharacteristic
150C3×#107—32no—
151C3×#107—32no—
152C3×#106—22no—
153C3×#106—32no—
154C3×#106C2×D312yes—
155C3×#106C22×C312yes—
156C3×C4⋊C8—21no—
157C3×C4⋊C8—32no—
158C3×C4⋊C8—31no—
159C3×C4⋊C8C2×D311yescharacteristic
160C3×C4⋊C8C22×C311yescharacteristic
161C3×#103—22no—
162C3×#103—32no—
163C3×#103C2×D312yes—
164C3×#103C22×C312yes—
165C3×#102—32no—
166C3×#102—32no—
167#835C22×C312yes—
168#821C22×C312yes—
169#818C22×C312yes—
170Dic3⋊C8C22×C312yes—
171#809C22×C312yes—
172#808C22×C312yes—
173#807C22×C312yes—
174C4⋊(C3⋊C8)C22×C311yescharacteristic
175C22×C3×D3—21no—
176C22×C3×D3C2×D411yescharacteristic
177C32×Q8—21no—
178C32×Q8—42no—
179C32×Q8C2×Q812yescomplemented
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—22no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C3×D12—24no—
192C3×D12—21no—
193C3×D12C2×Q812yescomplemented
194C3×C4×D3—22no—
195C3×C4×D3—24no—
196C3×C4×D3—22no—
197C3×C4×D3—44no—
198C3×C4×D3—42no—
199C3×C4×D3—42no—
200C3×C4×D3C2×Q812yes—
201C3×C4×D3#4112yes—
202C3×Dic6—44no—
203C3×Dic6—42no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206C2×C4⋊Q8—31no—
207C4×#41—31no—
208#477—32no—
209#476—32no—
210#475—31no—
211#475C3×D311yescharacteristic, complemented
212#474—31no—
213#474—31no—
214#428—32no—
215#423—31no—
216#417—32no—
217C3×#41—34no—
218C3×#41—62no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—41no—
223C2×C3×Q8—62no—
224C2×C3×Q8—61no—
225C2×C3×Q8—124no—
226C2×C3×Q8C22×D311yescharacteristic
227C2×C3×Q8C23×C311yescharacteristic
228C2×C3×D4—31no—
229C2×C3×D4—61no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—61no—
234C22×C3×C4—61no—
235C22×C3×C4—62no—
236C22×C3×C4—61no—
237#239—22no—
238#239C3×Q814yescomplemented
239D3×Q8—44no—
240C2×D12—21no—
241C2×D12C23×C311yescharacteristic
242C2×C4×D3—21no—
243C2×C4×D3—22no—
244C2×C4×D3—21no—
245C2×C4×D3—21no—
246C2×C4×D3C3×D411yescharacteristic
247C2×C4×D3C3×D411yescharacteristic
248C2×C4×D3C23×C311yescharacteristic
249C2×Dic6—21no—
250C2×Dic6—22no—
251C3×M16—64no—
252C2×C3×C8—22no—
253C2×C3×C8—32no—
254C2×C3×C8C22×D312yes—
255C2×C3×C8C23×C312yes—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—22no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—32no—
263C3×C4⋊C4—31no—
264C3×C4⋊C4—41no—
265C3×C4⋊C4—41no—
266C3×C4⋊C4—62no—
267C3×C4⋊C4—62no—
268C3×C4⋊C4—61no—
269C3×C4⋊C4—61no—
270C3×C4⋊C4C22×D312yes—
271C3×C4⋊C4C22×D311yescharacteristic
272C3×C4⋊C4C23×C312yes—
273C3×C4⋊C4C23×C311yescharacteristic
274C3×C22⋊C4—61no—
275C3×C22⋊C4—61no—
276C3×C22⋊C4—61no—
277C3×C42—21no—
278C3×C42—21no—
279C3×C42—21no—
280C3×C42—31no—
281C3×C42—31no—
282C3×C42—31no—
283C3×C42—41no—
284C3×C42—61no—
285C3×C42—61no—
286C3×C42C22×D311yescharacteristic
287C3×C42C23×C311yescharacteristic
288(C2×D3)⋊C4—21no—
289(C2×D3)⋊C4—21no—
290(C2×D3)⋊C4—21no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293C4⋊Dic3C23×C311yescharacteristic
294C4⋊Dic3C23×C312yes—
295Dic3⋊C4—22no—
296Dic3⋊C4—22no—
297C4×Dic3—21no—
298C4×Dic3—21no—
299C4×Dic3C3×D411yescharacteristic
300C4×Dic3C3×D411yescharacteristic
301C4×Dic3C23×C311yescharacteristic
302C2×C3⋊C8C23×C312yes—
303ΓL(1,𝔽25)—24no—
304C22×C32C22×D411yescharacteristic
305C2×C3×D3—21no—
306C2×C3×D3—21no—
307C2×C3×D3—22no—
308C2×C3×D3—41no—
309C2×C3×D3—41no—
310C2×C3×D3C22⋊Q812yes—
311C32×C4—22no—
312C32×C4—21no—
313C32×C4—42no—
314C32×C4—41no—
315C32×C4AGL(1,ℤ/8)12yes—
316C32×C4C22×Q811yescharacteristic
317C32×C4C2×#4111yescharacteristic
318C3×Dic3—21no—
319C3×Dic3—42no—
320C3×Dic3—41no—
321C3×Dic3C22⋊Q812yes—
322C3×Dic3#13712yes—
323C2×#41—31no—
324C22×Q8—61no—
325C2×M16—32no—
326C4⋊Q8—32no—
327C4⋊Q8—31no—
328C4⋊Q8—61no—
329C4⋊Q8—61no—
330C4⋊Q8C2×C3×D311yescharacteristic
331C4×Q8—31no—
332C4×Q8C2×C3×D311yescharacteristic
333C4×D4—31no—
334C4×D4—31no—
335C4×D4—61no—
336C4×D4—61no—
337#117—31no—
338#117—61no—
339C2×C4⋊C4—32no—
340C2×C4⋊C4—61no—
341C2×C42—31no—
342C2×C42—61no—
343#107—32no—
344#107—32no—
345#106—32no—
346#106C2×C3×D312yes—
347C4⋊C8—32no—
348C4⋊C8—31no—
349C4⋊C8C2×C3×D311yescharacteristic
350#103—32no—
351#103C2×C3×D312yes—
352#102—32no—
353#102—32no—
354C23×C3—31no—
355C23×C3—61no—
356C22×D3—21no—
357C22×D3C2×C3×D411yescharacteristic
358C3×Q8—21no—
359C3×Q8—21no—
360C3×Q8—22no—
361C3×Q8—41no—
362C3×Q8—42no—
363C3×Q8—42no—
364C3×Q8—82no—
365C3×Q8—124no—
366C3×Q8—122no—
367C3×Q8D3×Q812yescomplemented
368C3×Q8C2×C3×Q812yescomplemented
369C3×D4—32no—
370C3×D4—64no—
371C3×D4—61no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—22no—
376C2×C3×C4—21no—
377C2×C3×C4—22no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—31no—
382C2×C3×C4—31no—
383C2×C3×C4—32no—
384C2×C3×C4—32no—
385C2×C3×C4—31no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—42no—
389C2×C3×C4—62no—
390C2×C3×C4—64no—
391C2×C3×C4—62no—
392C2×C3×C4—61no—
393C2×C3×C4—62no—
394C2×C3×C4—122no—
395C2×C3×C4—124no—
396C2×C3×C4—122no—
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4C2×C3×D411yescharacteristic
400C2×C3×C4C2×C3×D411yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402C2×C3×C4C24×C311yescharacteristic
403C2×Dic3—21no—
404C2×Dic3—22no—
405C2×Dic3C2×C3×D411yescharacteristic
406C2×Dic3C2×C3×D411yescharacteristic
407C2×Dic3C2×C3×D411yescharacteristic
408D12—24no—
409D12—21no—
410D12C2×C3×Q812yescomplemented
411C4×D3—22no—
412C4×D3—24no—
413C4×D3—22no—
414C4×D3—44no—
415C4×D3—42no—
416C4×D3—42no—
417C4×D3C2×C3×Q812yes—
418C4×D3C3×#4112yes—
419Dic6—44no—
420Dic6—42no—
421C3×C8—22no—
422C3×C8—22no—
423C3×C8—42no—
424C3×C8—62no—
425C3⋊C8—22no—
426C2×C32C2×C22⋊Q811yescharacteristic
427C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
428C2×C32C2×#13711yescharacteristic
429C3×D3—22no—
430C3×D3—42no—
431#41—34no—
432#41—62no—
433C2×Q8—21no—
434C2×Q8—62no—
435C2×Q8—61no—
436C2×Q8—124no—
437C2×Q8C22×C3×D311yescharacteristic
438C2×D4—31no—
439C2×D4—61no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—61no—
444C22×C4—61no—
445C22×C4—62no—
446C22×C4—61no—
447M16—64no—
448C2×C8—32no—
449C2×C8C22×C3×D312yes—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—32no—
453C4⋊C4—31no—
454C4⋊C4—62no—
455C4⋊C4—62no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4C22×C3×D312yes—
459C4⋊C4C22×C3×D311yescharacteristic
460C22⋊C4—61no—
461C22⋊C4—61no—
462C22⋊C4—61no—
463C42—21no—
464C42—31no—
465C42—31no—
466C42—31no—
467C42—61no—
468C42—61no—
469C42C22×C3×D311yescharacteristic
470C22×C3—21no—
471C22×C3—32no—
472C22×C3—61no—
473C22×C3—61no—
474C22×C3—62no—
475C22×C3—121no—
476C22×C3—121no—
477C22×C3C2×D3×D411yescharacteristic
478C22×C3C22×C3×D411yescharacteristic
479C2×D3—21no—
480C2×D3—21no—
481C2×D3—22no—
482C2×D3—41no—
483C2×D3—41no—
484C2×D3C3×C22⋊Q812yes—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—22no—
489C3×C4—22no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—32no—
493C3×C4—32no—
494C3×C4—41no—
495C3×C4—42no—
496C3×C4—42no—
497C3×C4—41no—
498C3×C4—42no—
499C3×C4—41no—
500C3×C4—61no—
501C3×C4—82no—
502C3×C4—81no—
503C3×C4—122no—
504C3×C4—121no—
505C3×C4#91412yes—
506C3×C4C3×AGL(1,ℤ/8)12yes—
507C3×C4C2×D3×Q811yescharacteristic
508C3×C4D3×#4111yescharacteristic
509C3×C4C22×C3×Q811yescharacteristic
510C3×C4C2×C3×#4111yescharacteristic
511Dic3—21no—
512Dic3—42no—
513Dic3—41no—
514Dic3C3×C22⋊Q812yes—
515Dic3C3×#13712yes—
516C32#307911yescharacteristic, complemented, Sylow
517C23—31no—
518C23—61no—
519Q8—21no—
520Q8—42no—
521Q8—124no—
522Q8—122no—
523Q8C3×D3×Q812yescomplemented
524D4—32no—
525D4—64no—
526D4—61no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—31no—
531C2×C4—31no—
532C2×C4—32no—
533C2×C4—32no—
534C2×C4—31no—
535C2×C4—62no—
536C2×C4—64no—
537C2×C4—62no—
538C2×C4—61no—
539C2×C4—62no—
540C2×C4—122no—
541C2×C4—124no—
542C2×C4—122no—
543C2×C4C3×D3×D411yescharacteristic
544C2×C4C3×D3×D411yescharacteristic
545C2×C4C23×C3×D311yescharacteristic
546C8—22no—
547C8—62no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—62no—
552C2×C3—122no—
553C2×C3D3×C22⋊Q811yescharacteristic
554C2×C3C2×#91411yescharacteristic
555C2×C3D3×#13711yescharacteristic
556C2×C3C2×C3×C22⋊Q811yescharacteristic
557C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
558C2×C3C2×C3×#13711yescharacteristic
559D3—22no—
560D3—42no—
561C22—32no—
562C22—61no—
563C22—61no—
564C22—62no—
565C22—121no—
566C22—121no—
567C22C2×C3×D3×D411yescharacteristic
568C4—21no—
569C4—22no—
570C4—32no—
571C4—32no—
572C4—42no—
573C4—41no—
574C4—61no—
575C4—122no—
576C4—121no—
577C4C3×#91412yes—
578C4C2×C3×D3×Q811yescharacteristic
579C4C3×D3×#4111yescharacteristic
580C3—21no—
581C3#8101211yescharacteristic, direct product factor
582C3C3×#307911yescharacteristic, complemented
583C2—62no—
584C2—122no—
585C2C3×D3×C22⋊Q811yescharacteristic
586C2C2×C3×#91411yescharacteristic
587C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#475C2
socleC22×C32C22×D4
prime radicalC2×C3×#239C22
hypercenterC3×#475D3
hypocenterC3C3×#3079
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#475

Complements

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

NH ≅ G/Ntype
1. C3×D3×C4⋊Q8C2semidirect
3. C32×#475C2semidirect
4. C3×#5087C2semidirect
5. C3×#5020C2semidirect
6. C3×#4870C2semidirect
7. C3×#4861C2semidirect
8. C3×#4846C2semidirect
9. C3×#4837C2semidirect
11. C3×#4793C2semidirect
13. #81012C3direct (N × H)
47. D3×C4⋊Q8C2×C3semidirect
53. C3×#475D3semidirect
54. C3×#475C2×C3semidirect
60. #5087C2×C3semidirect
61. #5020C2×C3semidirect
62. #4870C2×C3semidirect
63. #4861C2×C3semidirect
64. #4846C2×C3semidirect
65. #4837C2×C3semidirect
67. #4793C2×C3semidirect
71. C3×#239Q8semidirect
179. C32×Q8C2×Q8semidirect
193. C3×D12C2×Q8semidirect
211. #475C3×D3semidirect
238. #239C3×Q8semidirect
367. C3×Q8D3×Q8semidirect
368. C3×Q8C2×C3×Q8semidirect
410. D12C2×C3×Q8semidirect
516. C32#3079semidirect
523. Q8C3×D3×Q8semidirect
581. C3#81012direct (N × H)
582. C3C3×#3079semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
C3×C4×#2392
C32×#4752
C3×#50872
C3×#50202
C3×#48702
C3×#48612
C3×#48462
C3×#48372
C3×#48032
C3×#47932
C3×#30793
#810123