Finite Group Databasebeta

← C3×#81075 #11887088

Subgroups — C3×#81075 #11887088

Order 1152.

978 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×#5730C211yesmaximal, characteristic, complemented
2C3×D4×D12C211yesmaximal, characteristic
3C32×#476C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic, complemented
5C3×C4×#214C211yesmaximal, characteristic, complemented
6C3×#4864C212yesmaximal, complemented
7C3×#4863C212yesmaximal, complemented
8C3×#4848C211yesmaximal, characteristic, complemented
9C3×#4834C211yesmaximal, characteristic, complemented
10C3×#4776C212yesmaximal, complemented
11C3×D3×#102C212yesmaximal, complemented
12C3×#3295—31nomaximal
13#81075C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×D4C2212yes—
15C22×C3×D12—21no—
16C32×C4⋊Q8C2211yescharacteristic, complemented
17C32×C4×D4C2211yescharacteristic
18C3×#946—22no—
19C2×C3×#214C2211yescharacteristic
20C3×#930—21no—
21C2×C3×#204C2212yescomplemented
22C2×C3×D3×C8C2212yescomplemented
23C3×#897C2212yescomplemented
24C3×#895C2212yes—
25C3×#893—21no—
26C3×D3×C4⋊C4C2212yescomplemented
27C3×#890—21no—
28C3×#882—22no—
29C3×#874C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic, complemented
32C32×#106C2212yescomplemented
33C32×C4⋊C8C2211yescharacteristic, complemented
34C32×#102C2212yes—
35C3×#832C2211yescharacteristic
36C3×#821C2212yescomplemented
37C3×(C2×D3)⋊C8C2212yescomplemented
38C3×#810C2211yescharacteristic, complemented
39C3×#809C2212yescomplemented
40C3×#809C2212yescomplemented
41C3×#808C2211yescharacteristic, complemented
42C3×C4×C3⋊C8C2211yescharacteristic, complemented
43C3×#554—31no—
44C3×D42—31no—
45#5730C2×C311yescharacteristic, complemented
46D4×D12C2×C311yescharacteristic
47C3×#486—31no—
48C3×#481—32no—
49C3×#476—21no—
50C3×#476D311yescharacteristic, complemented
51C3×#476C2×C311yescharacteristic, complemented
52C3×#465—32no—
53C3×#460—31no—
54C3×#450—32no—
55C3×C4×SD16—31no—
56C3×C8×D4—31no—
57C2×C3×#102—32no—
58#5088C2×C311yescharacteristic, complemented
59C4×#214C2×C311yescharacteristic, complemented
60#4864C2×C312yescomplemented
61#4863C2×C312yescomplemented
62#4848C2×C311yescharacteristic, complemented
63#4834C2×C311yescharacteristic, complemented
64#4776C2×C312yescomplemented
65D3×#102C2×C312yescomplemented
66C23×C3×D3—22no—
67C2×C32×Q8—21no—
68C2×C32×D4C2311yescharacteristic
69C22×C32×C4—21no—
70C2×C3×#67—22no—
71C3×D3×D4—24no—
72C3×D3×D4—42no—
73C2×C3×D12—22no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12—44no—
77C2×C3×D12D411yescharacteristic
78C2×C3×D12C2312yes—
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3C2312yes—
81C2×C3×Dic6C2311yescharacteristic
82C2×C32×C8C2312yes—
83C32×C4⋊C4—21no—
84C32×C4⋊C4C2312yes—
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C32×C42C2311yescharacteristic
88C3×#214—22no—
89C3×(C2×D3)⋊C4—22no—
90C3×(C2×D3)⋊C4—22no—
91C3×(C2×D3)⋊C4D412yes—
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3D411yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—22no—
97C3×C4×Dic3—21no—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2311yescharacteristic
100C3×#204—42no—
101C3×D3×C8—42no—
102#3295—31noSylow
103C22×C3×D4—32no—
104C22×C3×D4—61no—
105C2×D3×D4C22×C312yes—
106C22×D12—21no—
107C2×C3×SD16—31no—
108C2×C3×SD16—32no—
109C22×C3×C8—32no—
110C3×C4⋊Q8—21no—
111C3×C4⋊Q8C2×D311yescharacteristic, complemented
112C3×C4⋊Q8C22×C311yescharacteristic, complemented
113C3×#127—31no—
114C3×#125—61no—
115C3×C22⋊Q8—32no—
116C3×C22⋊Q8—62no—
117C3×#121—32no—
118C3×#121—61no—
119C3×#120—62no—
120C3×C4×Q8—31no—
121C3×C4×D4—21no—
122C3×C4×D4—31no—
123C3×C4×D4—61no—
124C3×C4×D4C2×D311yescharacteristic
125C3×C4×D4C22×C311yescharacteristic
126C2×C3×C4⋊C4—32no—
127#946—22no—
128C2×#214C22×C311yescharacteristic
129#930—21no—
130C2×#204C22×C312yescomplemented
131C2×D3×C8C22×C312yescomplemented
132#897C22×C312yescomplemented
133#895C22×C312yes—
134#893—21no—
135D3×C4⋊C4C22×C312yescomplemented
136#890—21no—
137#882—22no—
138#874C22×C311yescharacteristic
139C4×D12C22×C311yescharacteristic
140C4×Dic6C22×C311yescharacteristic, complemented
141C3×#106—22no—
142C3×#106—31no—
143C3×#106C2×D312yescomplemented
144C3×#106C22×C312yescomplemented
145C3×C4⋊C8—21no—
146C3×C4⋊C8C2×D311yescharacteristic, complemented
147C3×C4⋊C8C22×C311yescharacteristic, complemented
148C3×#103—31no—
149C3×#102—22no—
150C3×#102—31no—
151C3×#102—32no—
152C3×#102—32no—
153C3×#102—32no—
154C3×#102C2×D312yes—
155C3×#102C22×C312yes—
156C3×C22⋊C8—32no—
157C3×C4×C8—31no—
158#832C22×C311yescharacteristic
159#821C22×C312yescomplemented
160(C2×D3)⋊C8C22×C312yescomplemented
161#810C22×C311yescharacteristic, complemented
162#809C22×C312yescomplemented
163#809C22×C312yescomplemented
164#808C22×C311yescharacteristic, complemented
165C4×C3⋊C8C22×C311yescharacteristic, complemented
166C23×C32—21no—
167C22×C3×D3—22no—
168C22×C3×D3—44no—
169C22×C3×D3—44no—
170C22×C3×D3—82no—
171C22×C3×D3C2×D412yes—
172C32×Q8—81no—
173C32×D4—21no—
174C32×D4#4112yes—
175C2×C32×C4—22no—
176C2×C32×C4—21no—
177C2×C32×C4—42no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C3×#67—44no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3C2×D412yes—
185C3×D12—22no—
186C3×D12—22no—
187C3×D12—44no—
188C3×D12—42no—
189C3×D12—81no—
190C3×D12SD1614yescomplemented
191C3×C4×D3—22no—
192C3×C4×D3—22no—
193C3×C4×D3—82no—
194C3×Dic6—21no—
195C3×Dic6—21no—
196C32×C8—22no—
197C3×C3⋊C8—21no—
198C3×C3⋊C8—21no—
199#554—31no—
200D42—31no—
201#486—31no—
202#481—32no—
203#476C3×D311yescharacteristic, complemented
204#465—32no—
205#460—31no—
206#450—32no—
207C4×SD16—31no—
208C8×D4—31no—
209C2×#102—32no—
210C24×C3—62no—
211C23×D3—22no—
212C2×C3×Q8—21no—
213C2×C3×Q8—21no—
214C2×C3×Q8—31no—
215C2×C3×Q8—41no—
216C2×C3×D4—21no—
217C2×C3×D4—31no—
218C2×C3×D4—32no—
219C2×C3×D4—62no—
220C2×C3×D4—62no—
221C2×C3×D4—64no—
222C2×C3×D4—61no—
223C2×C3×D4—61no—
224C2×C3×D4—124no—
225C2×C3×D4—122no—
226C2×C3×D4C22×D311yescharacteristic
227C2×C3×D4C23×C311yescharacteristic
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—32no—
231C22×C3×C4—41no—
232C22×C3×C4—62no—
233C2×#67—22no—
234D3×D4—24no—
235D3×D4—42no—
236C2×D12—22no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—44no—
240C2×D12C3×D411yescharacteristic
241C2×D12C23×C312yes—
242C2×C4×D3—22no—
243C2×C4×D3C23×C312yes—
244C2×Dic6C23×C311yescharacteristic
245C3×SD16—62no—
246C3×SD16—122no—
247C2×C3×C8—22no—
248C2×C3×C8—31no—
249C2×C3×C8—31no—
250C2×C3×C8—122no—
251C2×C3×C8C22×D312yes—
252C2×C3×C8C23×C312yes—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—31no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—41no—
260C3×C4⋊C4—62no—
261C3×C4⋊C4—62no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4C22×D312yes—
264C3×C4⋊C4C22×D311yescharacteristic
265C3×C4⋊C4C23×C311yescharacteristic
266C3×C4⋊C4C23×C312yes—
267C3×C22⋊C4—21no—
268C3×C22⋊C4—21no—
269C3×C22⋊C4—32no—
270C3×C22⋊C4—41no—
271C3×C22⋊C4—62no—
272C3×C22⋊C4—62no—
273C3×C42—21no—
274C3×C42—61no—
275C3×C42C22×D311yescharacteristic
276C3×C42C23×C311yescharacteristic
277#214—22no—
278(C2×D3)⋊C4—22no—
279(C2×D3)⋊C4—22no—
280(C2×D3)⋊C4C3×D412yes—
281C4⋊Dic3—22no—
282C4⋊Dic3C3×D411yescharacteristic
283C4⋊Dic3C23×C311yescharacteristic
284Dic3⋊C4—21no—
285Dic3⋊C4—22no—
286C4×Dic3—21no—
287C2×C3⋊C8C23×C311yescharacteristic
288C2×C3⋊C8C23×C311yescharacteristic
289#204—42no—
290D3×C8—42no—
291C22×C32—22no—
292C22×C32—41no—
293C22×C32—41no—
294C22×C32C22×D411yescharacteristic
295C2×C3×D3—22no—
296C2×C3×D3—22no—
297C2×C3×D3—42no—
298C2×C3×D3—42no—
299C2×C3×D3—42no—
300C2×C3×D3—88no—
301C2×C3×D3C2×SD1614yes—
302C32×C4—21no—
303C32×C4—41no—
304C32×C4—42no—
305C32×C4C2×SD1612yes—
306C32×C4C2×#4111yescharacteristic
307C32×C4H(5,𝔽2)11yescharacteristic
308C3×Dic3—22no—
309C3×Dic3—41no—
310C3×Dic3—41no—
311C22×D4—32no—
312C22×D4—61no—
313C2×SD16—31no—
314C2×SD16—32no—
315C22×C8—32no—
316C4⋊Q8C2×C3×D311yescharacteristic, complemented
317#127—31no—
318#125—61no—
319C22⋊Q8—32no—
320C22⋊Q8—62no—
321#121—32no—
322#121—61no—
323#120—62no—
324C4×Q8—31no—
325C4×D4—31no—
326C4×D4—61no—
327C4×D4C2×C3×D311yescharacteristic
328C2×C4⋊C4—32no—
329#106—31no—
330#106C2×C3×D312yescomplemented
331C4⋊C8C2×C3×D311yescharacteristic, complemented
332#103—31no—
333#102—31no—
334#102—32no—
335#102—32no—
336#102—32no—
337#102C2×C3×D312yes—
338C22⋊C8—32no—
339C4×C8—31no—
340C23×C3—21no—
341C23×C3—21no—
342C23×C3—32no—
343C23×C3—41no—
344C23×C3—62no—
345C23×C3—124no—
346C23×C3—124no—
347C23×C3—242no—
348C22×D3—22no—
349C22×D3—44no—
350C22×D3—44no—
351C22×D3—82no—
352C22×D3C2×C3×D412yes—
353C3×Q8—61no—
354C3×Q8—61no—
355C3×Q8—81no—
356C3×Q8—81no—
357C3×Q8—82no—
358C3×D4—21no—
359C3×D4—21no—
360C3×D4—22no—
361C3×D4—34no—
362C3×D4—41no—
363C3×D4—62no—
364C3×D4—62no—
365C3×D4—124no—
366C3×D4—124no—
367C3×D4—122no—
368C3×D4—241no—
369C3×D4#23912yes—
370C3×D4C3×#4112yes—
371C2×C3×C4—21no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—32no—
379C2×C3×C4—41no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4—82no—
388C2×C3×C4—242no—
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4C2×C3×D411yescharacteristic
392C2×C3×C4C2×C3×D411yescharacteristic
393C2×C3×C4C23×D311yescharacteristic
394C2×C3×C4C24×C311yescharacteristic
395#67—44no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3C2×C3×D412yes—
399D12—22no—
400D12—22no—
401D12—44no—
402D12—42no—
403D12—81no—
404D12C3×SD1614yescomplemented
405C4×D3—22no—
406C4×D3—22no—
407C4×D3—82no—
408Dic6—21no—
409Dic6—21no—
410C3×C8—22no—
411C3×C8—22no—
412C3×C8—42no—
413C3×C8—61no—
414C3×C8—61no—
415C3⋊C8—21no—
416C3⋊C8—21no—
417C2×C32—42no—
418C2×C32#54611yescharacteristic
419C2×C32C22×SD1611yescharacteristic
420C2×C32#57611yescharacteristic
421C3×D3—24no—
422C3×D3—82no—
423C24—62no—
424C2×Q8—21no—
425C2×Q8—31no—
426C2×D4—32no—
427C2×D4—31no—
428C2×D4—62no—
429C2×D4—62no—
430C2×D4—64no—
431C2×D4—61no—
432C2×D4—61no—
433C2×D4—124no—
434C2×D4—122no—
435C2×D4C22×C3×D311yescharacteristic
436C22×C4—21no—
437C22×C4—32no—
438C22×C4—62no—
439SD16—62no—
440SD16—122no—
441C2×C8—31no—
442C2×C8—31no—
443C2×C8—122no—
444C2×C8C22×C3×D312yes—
445C4⋊C4—21no—
446C4⋊C4—31no—
447C4⋊C4—31no—
448C4⋊C4—62no—
449C4⋊C4—62no—
450C4⋊C4—61no—
451C4⋊C4C22×C3×D312yes—
452C4⋊C4C22×C3×D311yescharacteristic
453C22⋊C4—21no—
454C22⋊C4—32no—
455C22⋊C4—62no—
456C22⋊C4—62no—
457C42—61no—
458C42C22×C3×D311yescharacteristic
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—21no—
462C22×C3—34no—
463C22×C3—42no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—62no—
469C22×C3—62no—
470C22×C3—81no—
471C22×C3—81no—
472C22×C3—122no—
473C22×C3—122no—
474C22×C3—122no—
475C22×C3—248no—
476C22×C3C2×D3×D411yescharacteristic
477C22×C3C22×C3×D411yescharacteristic
478C2×D3—22no—
479C2×D3—22no—
480C2×D3—42no—
481C2×D3—42no—
482C2×D3—42no—
483C2×D3—88no—
484C2×D3C2×C3×SD1614yes—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—41no—
491C3×C4—41no—
492C3×C4—42no—
493C3×C4—41no—
494C3×C4—42no—
495C3×C4—62no—
496C3×C4—81no—
497C3×C4—82no—
498C3×C4—121no—
499C3×C4—121no—
500C3×C4D3×SD1612yes—
501C3×C4C2×C3×SD1612yes—
502C3×C4C2×#23911yescharacteristic
503C3×C4#100911yescharacteristic
504C3×C4C2×C3×#4111yescharacteristic
505C3×C4C3×H(5,𝔽2)11yescharacteristic
506Dic3—22no—
507Dic3—41no—
508Dic3—41no—
509C32#329511yescharacteristic, complemented, Sylow
510C23—21no—
511C23—32no—
512C23—62no—
513C23—124no—
514C23—124no—
515C23—242no—
516Q8—61no—
517Q8—61no—
518Q8—81no—
519D4—21no—
520D4—34no—
521D4—62no—
522D4—62no—
523D4—124no—
524D4—124no—
525D4—122no—
526D4—241no—
527D4C3×#23912yes—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—32no—
531C2×C4—42no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—61no—
535C2×C4—61no—
536C2×C4—242no—
537C2×C4C3×D3×D411yescharacteristic
538C2×C4C3×D3×D411yescharacteristic
539C2×C4C23×C3×D311yescharacteristic
540C8—22no—
541C8—61no—
542C8—61no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—42no—
547C2×C3—42no—
548C2×C3—64no—
549C2×C3—82no—
550C2×C3—242no—
551C2×C3#563011yescharacteristic
552C2×C3C2×D3×SD1611yescharacteristic
553C2×C3#577411yescharacteristic
554C2×C3C3×#54611yescharacteristic
555C2×C3C22×C3×SD1611yescharacteristic
556C2×C3C3×#57611yescharacteristic
557D3—24no—
558D3—82no—
559C22—22no—
560C22—34no—
561C22—41no—
562C22—41no—
563C22—62no—
564C22—62no—
565C22—122no—
566C22—122no—
567C22—122no—
568C22—248no—
569C22C2×C3×D3×D411yescharacteristic
570C4—21no—
571C4—41no—
572C4—42no—
573C4—62no—
574C4—121no—
575C4—121no—
576C4C3×D3×SD1612yes—
577C4C2×C3×#23911yescharacteristic
578C4C3×#100911yescharacteristic
579C3—21no—
580C3#8107511yescharacteristic, direct product factor
581C3C3×#329511yescharacteristic, complemented
582C2—42no—
583C2—64no—
584C2—242no—
585C2C3×#563011yescharacteristic
586C2C2×C3×D3×SD1611yescharacteristic
587C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#476C2
socleC22×C32C22×D4
prime radicalC3×D4×D12C2
hypercenterC3×#476D3
hypocenterC3C3×#3295
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#476

Complements

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

NH ≅ G/Ntype
1. C3×#5730C2semidirect
3. C32×#476C2semidirect
4. C3×#5088C2semidirect
5. C3×C4×#214C2semidirect
6. C3×#4864C2semidirect
7. C3×#4863C2semidirect
8. C3×#4848C2semidirect
9. C3×#4834C2semidirect
10. C3×#4776C2semidirect
11. C3×D3×#102C2semidirect
13. #81075C3direct (N × H)
16. C32×C4⋊Q8C22semidirect
21. C2×C3×#204C22semidirect
22. C2×C3×D3×C8C22semidirect
23. C3×#897C22semidirect
26. C3×D3×C4⋊C4C22semidirect
31. C3×C4×Dic6C22semidirect
32. C32×#106C22semidirect
33. C32×C4⋊C8C22semidirect
36. C3×#821C22semidirect
37. C3×(C2×D3)⋊C8C22semidirect
38. C3×#810C22semidirect
39. C3×#809C22semidirect
40. C3×#809C22semidirect
41. C3×#808C22semidirect
42. C3×C4×C3⋊C8C22semidirect
45. #5730C2×C3semidirect
50. C3×#476D3semidirect
51. C3×#476C2×C3semidirect
58. #5088C2×C3semidirect
59. C4×#214C2×C3semidirect
60. #4864C2×C3semidirect
61. #4863C2×C3semidirect
62. #4848C2×C3semidirect
63. #4834C2×C3semidirect
64. #4776C2×C3semidirect
65. D3×#102C2×C3semidirect
111. C3×C4⋊Q8C2×D3semidirect
112. C3×C4⋊Q8C22×C3semidirect
130. C2×#204C22×C3semidirect
131. C2×D3×C8C22×C3semidirect
132. #897C22×C3semidirect
135. D3×C4⋊C4C22×C3semidirect
140. C4×Dic6C22×C3semidirect
143. C3×#106C2×D3semidirect
144. C3×#106C22×C3semidirect
146. C3×C4⋊C8C2×D3semidirect
147. C3×C4⋊C8C22×C3semidirect
159. #821C22×C3semidirect
160. (C2×D3)⋊C8C22×C3semidirect
161. #810C22×C3semidirect
162. #809C22×C3semidirect
163. #809C22×C3semidirect
164. #808C22×C3semidirect
165. C4×C3⋊C8C22×C3semidirect
190. C3×D12SD16semidirect
203. #476C3×D3semidirect
316. C4⋊Q8C2×C3×D3semidirect
330. #106C2×C3×D3semidirect
331. C4⋊C8C2×C3×D3semidirect
404. D12C3×SD16semidirect
509. C32#3295semidirect
580. C3#81075direct (N × H)
581. C3C3×#3295semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
C3×D4×D122
C32×#4762
C3×#50882
C3×C4×#2142
C3×#48642
C3×#48632
C3×#48482
C3×#48342
C3×#47762
C3×D3×#1022
C3×#32953
#810753