Finite Group Databasebeta

← C3×#80964 #11868534

Subgroups — C3×#80964 #11868534

Order 1152.

830 conjugacy classes of subgroups.

The subgroup lattice has 581 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic, complemented
2C3×C4×#237C211yesmaximal, characteristic
3C32×#474C211yesmaximal, characteristic, complemented
4C3×#5094C211yesmaximal, characteristic, complemented
5C3×#5008C211yesmaximal, characteristic, complemented
6C3×#4880C212yesmaximal, complemented
7C3×#4877C212yesmaximal, complemented
8C3×#4850C211yesmaximal, characteristic, complemented
9C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
10C3×#4772C212yesmaximal
11C3×#4766C212yesmaximal, complemented
12C3×#3076—31nomaximal
13#80964C311yesmaximal, characteristic, direct product factor
14C2×C3×#237C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C3×#946—21no—
18C3×Q8×Dic3—21no—
19C3×D4×Dic3C2211yescharacteristic
20C3×C4×#67—21no—
21C2×C3×C4×Dic3—21no—
22C2×C3×D3×C8C2212yes—
23C3×#897—21no—
24C3×#892C2211yescharacteristic
25C3×#892C2212yes—
26C3×#890C2212yes—
27C3×#887—21no—
28C3×#887C2211yescharacteristic
29C3×#67⋊C4—21no—
30C3×#877—21no—
31C3×C42×D3C2211yescharacteristic
32C3×#869C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34C32×#107C2212yes—
35C32×C4⋊C8C2211yescharacteristic
36C32×#102C2212yes—
37C3×#832C2212yes—
38C3×#818C2212yes—
39C3×#816C2212yes—
40C3×Dic3⋊C8C2212yes—
41C3×#810C2212yes—
42C3×#808C2212yes—
43C3×#808C2212yes—
44C3×C4⋊(C3⋊C8)C2211yescharacteristic
45C3×#533—31no—
46C3×C4×#41—31no—
47#5728C2×C311yescharacteristic, complemented
48C4×#237C2×C311yescharacteristic
49C3×#479—32no—
50C3×#478—32no—
51C3×#477—31no—
52C3×#476—31no—
53C3×#475—31no—
54C3×#474—21no—
55C3×#474D311yescharacteristic, complemented
56C3×#474C2×C311yescharacteristic, complemented
57C3×#427—32no—
58C2×C3×C4⋊C8—31no—
59C3×#416—32no—
60#5094C2×C311yescharacteristic, complemented
61#5008C2×C311yescharacteristic, complemented
62#4880C2×C312yescomplemented
63#4877C2×C312yescomplemented
64#4850C2×C311yescharacteristic, complemented
65D3×C4⋊C8C2×C311yescharacteristic, complemented
66#4772C2×C312yes—
67#4766C2×C312yescomplemented
68C2×C32×Q8—21no—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4—21no—
71C2×C3×#67—21no—
72C22×C3×Dic3—21no—
73C22×C3×Dic3—21no—
74C3×#237—22no—
75C3×#237Q814yescomplemented
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79C2×C3×Dic6—21no—
80C2×C3×Dic6C2311yescharacteristic
81C2×C32×C8C2312yes—
82C32×C4⋊C4—21no—
83C32×C4⋊C4C2311yescharacteristic
84C32×C4⋊C4C2312yes—
85C32×C22⋊C4—21no—
86C32×C42C2311yescharacteristic
87C3×#217—21no—
88C3×(C2×D3)⋊C4—21no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—22no—
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×Dic3⋊C4—21no—
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—22no—
97C3×C4×Dic3—21no—
98C3×C4×Dic3—21no—
99C3×C4×Dic3—21no—
100C3×C4×Dic3—22no—
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C2×C3×C3⋊C8C2312yes—
105C3×D3×C8—24no—
106#3076—31noSylow
107C2×C3×#41—31no—
108C2×#237C22×C311yescharacteristic
109C22×C3×C8—32no—
110C3×C4⋊Q8—21no—
111C3×C4⋊Q8—31no—
112C3×C4⋊Q8C2×D311yescharacteristic
113C3×C4⋊Q8C22×C311yescharacteristic
114C3×#125—32no—
115C3×C22⋊Q8—61no—
116C3×C22⋊Q8—61no—
117C3×C4×Q8—31no—
118C3×C4×Q8—31no—
119C3×C4×Q8—61no—
120C3×C4×Q8—61no—
121C3×C4×D4—21no—
122C3×C4×D4—31no—
123C3×C4×D4—61no—
124C3×C4×D4—61no—
125C3×C4×D4C2×D311yescharacteristic
126C3×C4×D4C22×C311yescharacteristic
127C3×#117—32no—
128C3×#117—31no—
129C3×#117—61no—
130C2×C3×C42—31no—
131C2×C3×C42—61no—
132#946—21no—
133Q8×Dic3—21no—
134D4×Dic3C22×C311yescharacteristic
135C4×#67—21no—
136C2×C4×Dic3—21no—
137C2×D3×C8C22×C312yes—
138#897—21no—
139#892C22×C311yescharacteristic
140#892C22×C312yes—
141#890C22×C312yes—
142#887—21no—
143#887C22×C311yescharacteristic
144#67⋊C4—21no—
145#877—21no—
146C42×D3C22×C311yescharacteristic
147#869C22×C311yescharacteristic
148C4×Dic6C22×C311yescharacteristic
149C3×#107—22no—
150C3×#107—32no—
151C3×#107C2×D312yes—
152C3×#107C22×C312yes—
153C3×#106—32no—
154C3×#106—32no—
155C3×C4⋊C8—21no—
156C3×C4⋊C8—32no—
157C3×C4⋊C8—31no—
158C3×C4⋊C8C2×D311yescharacteristic
159C3×C4⋊C8C22×C311yescharacteristic
160C3×#103—32no—
161C3×#103—32no—
162C3×#102—22no—
163C3×#102—32no—
164C3×#102C2×D312yes—
165C3×#102C22×C312yes—
166#832C22×C312yes—
167#818C22×C312yes—
168#816C22×C312yes—
169Dic3⋊C8C22×C312yes—
170#810C22×C312yes—
171#808C22×C312yes—
172#808C22×C312yes—
173C4⋊(C3⋊C8)C22×C311yescharacteristic
174C23×C32—21no—
175C22×C3×D3C2×D411yescharacteristic
176C32×Q8—42no—
177C32×D4—21no—
178C32×D4C2×Q812yes—
179C2×C32×C4—21no—
180C2×C32×C4—22no—
181C2×C32×C4—42no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185C3×#67—24no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—42no—
191C2×C3×Dic3C2×D411yescharacteristic
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C3×C4×D3—22no—
195C3×C4×D3—41no—
196C3×C4×D3C2×Q812yes—
197C3×C4×D3#4112yes—
198C3×Dic6—21no—
199C3×Dic6—42no—
200C3×Dic6C2×Q812yes—
201C32×C8—22no—
202C3×C3⋊C8—22no—
203#533—31no—
204C4×#41—31no—
205#479—32no—
206#478—32no—
207#477—31no—
208#476—31no—
209#475—31no—
210#474C3×D311yescharacteristic, complemented
211#427—32no—
212C2×C4⋊C8—31no—
213#416—32no—
214C3×#41—34no—
215C3×#41—62no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—31no—
219C2×C3×Q8—41no—
220C2×C3×Q8—61no—
221C2×C3×D4—21no—
222C2×C3×D4—61no—
223C2×C3×D4C22×D311yescharacteristic
224C2×C3×D4C23×C311yescharacteristic
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—31no—
230C22×C3×C4—41no—
231C22×C3×C4—61no—
232C22×C3×C4—61no—
233C2×#67—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236#237—22no—
237#237C3×Q814yescomplemented
238C2×C4×D3C3×D411yescharacteristic
239C2×C4×D3C3×D411yescharacteristic
240C2×C4×D3C23×C311yescharacteristic
241C2×Dic6—21no—
242C2×Dic6C23×C311yescharacteristic
243C2×C3×C8—22no—
244C2×C3×C8—32no—
245C2×C3×C8—64no—
246C2×C3×C8C22×D312yes—
247C2×C3×C8C23×C312yes—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—22no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—32no—
253C3×C4⋊C4—31no—
254C3×C4⋊C4—41no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4—62no—
257C3×C4⋊C4—62no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4C22×D312yes—
261C3×C4⋊C4C22×D311yescharacteristic
262C3×C4⋊C4C23×C311yescharacteristic
263C3×C4⋊C4C23×C312yes—
264C3×C22⋊C4—21no—
265C3×C22⋊C4—21no—
266C3×C22⋊C4—41no—
267C3×C22⋊C4—61no—
268C3×C22⋊C4—62no—
269C3×C22⋊C4—61no—
270C3×C42—21no—
271C3×C42—31no—
272C3×C42—31no—
273C3×C42—31no—
274C3×C42—61no—
275C3×C42—61no—
276C3×C42—62no—
277C3×C42—61no—
278C3×C42C22×D311yescharacteristic
279C3×C42C23×C311yescharacteristic
280#217—21no—
281(C2×D3)⋊C4—21no—
282(C2×D3)⋊C4—22no—
283C4⋊Dic3—21no—
284C4⋊Dic3—22no—
285C4⋊Dic3C23×C311yescharacteristic
286C4⋊Dic3C23×C312yes—
287Dic3⋊C4—21no—
288Dic3⋊C4—21no—
289Dic3⋊C4—22no—
290C4×Dic3—21no—
291C4×Dic3—21no—
292C4×Dic3—21no—
293C4×Dic3—22no—
294C4×Dic3C3×D411yescharacteristic
295C4×Dic3C3×D411yescharacteristic
296C4×Dic3C23×C311yescharacteristic
297C2×C3⋊C8C23×C312yes—
298D3×C8—24no—
299C22×C32—22no—
300C22×C32—41no—
301C22×C32—41no—
302C22×C32C22×D411yescharacteristic
303C2×C3×D3—21no—
304C2×C3×D3—21no—
305C2×C3×D3C22⋊Q812yes—
306C32×C4—21no—
307C32×C4—41no—
308C32×C4—42no—
309C32×C4#13512yes—
310C32×C4C22×Q811yescharacteristic
311C32×C4C2×#4111yescharacteristic
312C3×Dic3—22no—
313C3×Dic3—21no—
314C3×Dic3—21no—
315C3×Dic3—42no—
316C3×Dic3—41no—
317C3×Dic3C22⋊Q812yes—
318C2×#41—31no—
319C22×C8—32no—
320C4⋊Q8—31no—
321C4⋊Q8C2×C3×D311yescharacteristic
322#125—32no—
323C22⋊Q8—61no—
324C22⋊Q8—61no—
325C4×Q8—31no—
326C4×Q8—31no—
327C4×Q8—61no—
328C4×Q8—61no—
329C4×D4—31no—
330C4×D4—61no—
331C4×D4—61no—
332C4×D4C2×C3×D311yescharacteristic
333#117—31no—
334#117—32no—
335#117—61no—
336C2×C42—31no—
337C2×C42—61no—
338#107—32no—
339#107C2×C3×D312yes—
340#106—32no—
341#106—32no—
342C4⋊C8—32no—
343C4⋊C8—31no—
344C4⋊C8C2×C3×D311yescharacteristic
345#103—32no—
346#103—32no—
347#102—32no—
348#102C2×C3×D312yes—
349C23×C3—21no—
350C23×C3—21no—
351C23×C3—31no—
352C23×C3—41no—
353C22×D3C2×C3×D411yescharacteristic
354C3×Q8—32no—
355C3×Q8—42no—
356C3×Q8—42no—
357C3×Q8—61no—
358C3×Q8—82no—
359C3×Q8—122no—
360C3×D4—21no—
361C3×D4—21no—
362C3×D4—22no—
363C3×D4—41no—
364C3×D4—64no—
365C3×D4D3×Q812yes—
366C3×D4C2×C3×Q812yes—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—21no—
370C2×C3×C4—22no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—31no—
375C2×C3×C4—32no—
376C2×C3×C4—32no—
377C2×C3×C4—31no—
378C2×C3×C4—31no—
379C2×C3×C4—41no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—64no—
384C2×C3×C4—61no—
385C2×C3×C4—62no—
386C2×C3×C4—61no—
387C2×C3×C4—62no—
388C2×C3×C4—82no—
389C2×C3×C4—121no—
390C2×C3×C4—122no—
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4C2×C3×D411yescharacteristic
394C2×C3×C4C2×C3×D411yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396C2×C3×C4C24×C311yescharacteristic
397#67—24no—
398C2×Dic3—21no—
399C2×Dic3—24no—
400C2×Dic3—21no—
401C2×Dic3—22no—
402C2×Dic3—42no—
403C2×Dic3C2×C3×D411yescharacteristic
404C2×Dic3C2×C3×D411yescharacteristic
405C2×Dic3C2×C3×D411yescharacteristic
406C4×D3—22no—
407C4×D3—41no—
408C4×D3C2×C3×Q812yes—
409C4×D3C3×#4112yes—
410Dic6—21no—
411Dic6—42no—
412Dic6C2×C3×Q812yes—
413C3×C8—22no—
414C3×C8—22no—
415C3×C8—42no—
416C3×C8—62no—
417C3⋊C8—22no—
418C2×C32—42no—
419C2×C32C2×C22⋊Q811yescharacteristic
420C2×C32C2×#13511yescharacteristic
421C2×C32#57511yescharacteristic
422C3×D3—22no—
423#41—34no—
424#41—62no—
425C2×Q8—21no—
426C2×Q8—31no—
427C2×Q8—61no—
428C2×D4—61no—
429C2×D4C22×C3×D311yescharacteristic
430C22×C4—21no—
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—31no—
434C22×C4—61no—
435C22×C4—61no—
436C2×C8—32no—
437C2×C8—64no—
438C2×C8C22×C3×D312yes—
439C4⋊C4—21no—
440C4⋊C4—32no—
441C4⋊C4—31no—
442C4⋊C4—61no—
443C4⋊C4—62no—
444C4⋊C4—62no—
445C4⋊C4—61no—
446C4⋊C4—61no—
447C4⋊C4C22×C3×D312yes—
448C4⋊C4C22×C3×D311yescharacteristic
449C22⋊C4—21no—
450C22⋊C4—61no—
451C22⋊C4—62no—
452C22⋊C4—61no—
453C42—31no—
454C42—31no—
455C42—31no—
456C42—61no—
457C42—61no—
458C42—62no—
459C42—61no—
460C42C22×C3×D311yescharacteristic
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—21no—
464C22×C3—32no—
465C22×C3—42no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—41no—
470C22×C3—61no—
471C22×C3—61no—
472C22×C3—81no—
473C22×C3—81no—
474C22×C3C2×D3×D411yescharacteristic
475C22×C3C22×C3×D411yescharacteristic
476C2×D3—21no—
477C2×D3—21no—
478C2×D3C3×C22⋊Q812yes—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—22no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—32no—
485C3×C4—41no—
486C3×C4—41no—
487C3×C4—42no—
488C3×C4—41no—
489C3×C4—42no—
490C3×C4—61no—
491C3×C4—61no—
492C3×C4—62no—
493C3×C4—81no—
494C3×C4—82no—
495C3×C4—121no—
496C3×C4—122no—
497C3×C4#91212yes—
498C3×C4C3×#13512yes—
499C3×C4C2×D3×Q811yescharacteristic
500C3×C4D3×#4111yescharacteristic
501C3×C4C22×C3×Q811yescharacteristic
502C3×C4C2×C3×#4111yescharacteristic
503Dic3—21no—
504Dic3—21no—
505Dic3—22no—
506Dic3—42no—
507Dic3—41no—
508Dic3C3×C22⋊Q812yes—
509C32#307611yescharacteristic, complemented, Sylow
510C23—21no—
511C23—31no—
512Q8—32no—
513Q8—42no—
514Q8—61no—
515Q8—122no—
516D4—21no—
517D4—64no—
518D4C3×D3×Q812yes—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—31no—
522C2×C4—32no—
523C2×C4—32no—
524C2×C4—31no—
525C2×C4—31no—
526C2×C4—42no—
527C2×C4—64no—
528C2×C4—61no—
529C2×C4—62no—
530C2×C4—61no—
531C2×C4—62no—
532C2×C4—121no—
533C2×C4—122no—
534C2×C4C3×D3×D411yescharacteristic
535C2×C4C3×D3×D411yescharacteristic
536C2×C4C23×C3×D311yescharacteristic
537C8—22no—
538C8—62no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—42no—
543C2×C3—42no—
544C2×C3—62no—
545C2×C3—82no—
546C2×C3D3×C22⋊Q811yescharacteristic
547C2×C3C2×#91211yescharacteristic
548C2×C3#577711yescharacteristic
549C2×C3C2×C3×C22⋊Q811yescharacteristic
550C2×C3C2×C3×#13511yescharacteristic
551C2×C3C3×#57511yescharacteristic
552D3—22no—
553C22—22no—
554C22—32no—
555C22—41no—
556C22—41no—
557C22—61no—
558C22—61no—
559C22C2×C3×D3×D411yescharacteristic
560C4—21no—
561C4—32no—
562C4—41no—
563C4—42no—
564C4—61no—
565C4—61no—
566C4—62no—
567C4—121no—
568C4—122no—
569C4C3×#91212yes—
570C4C2×C3×D3×Q811yescharacteristic
571C4C3×D3×#4111yescharacteristic
572C3—21no—
573C3#8096411yescharacteristic, direct product factor
574C3C3×#307611yescharacteristic, complemented
575C2—42no—
576C2—62no—
577C2C3×D3×C22⋊Q811yescharacteristic
578C2C2×C3×#91211yescharacteristic
579C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#474C2
socleC22×C32C22×D4
prime radicalC2×C3×#237C22
hypercenterC3×#474D3
hypocenterC3C3×#3076
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#474

Complements

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

NH ≅ G/Ntype
1. C3×#5728C2semidirect
3. C32×#474C2semidirect
4. C3×#5094C2semidirect
5. C3×#5008C2semidirect
6. C3×#4880C2semidirect
7. C3×#4877C2semidirect
8. C3×#4850C2semidirect
9. C3×D3×C4⋊C8C2semidirect
11. C3×#4766C2semidirect
13. #80964C3direct (N × H)
47. #5728C2×C3semidirect
55. C3×#474D3semidirect
56. C3×#474C2×C3semidirect
60. #5094C2×C3semidirect
61. #5008C2×C3semidirect
62. #4880C2×C3semidirect
63. #4877C2×C3semidirect
64. #4850C2×C3semidirect
65. D3×C4⋊C8C2×C3semidirect
67. #4766C2×C3semidirect
75. C3×#237Q8semidirect
210. #474C3×D3semidirect
237. #237C3×Q8semidirect
509. C32#3076semidirect
573. C3#80964direct (N × H)
574. C3C3×#3076semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
C3×C4×#2372
C32×#4742
C3×#50942
C3×#50082
C3×#48802
C3×#48772
C3×#48502
C3×D3×C4⋊C82
C3×#47722
C3×#47662
C3×#30763
#809643