Finite Group Databasebeta

← C3×#82035 #11899622

Subgroups — C3×#82035 #11899622

Order 1152.

773 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#135C211yesmaximal, characteristic, complemented
2C2×C3×#912C211yesmaximal, characteristic, complemented
3C32×#509C211yesmaximal, characteristic, complemented
4C3×#5195C211yesmaximal, characteristic, complemented
5C3×#5147C211yesmaximal, characteristic, complemented
6C3×#4916C212yesmaximal, complemented
7C3×#4915C212yesmaximal, complemented
8C3×#4912C212yesmaximal, complemented
9C3×#4911C212yesmaximal, complemented
10C3×#4909C211yesmaximal, characteristic, complemented
11C3×D3×M32C211yesmaximal, characteristic, complemented
12C3×#3414—31nomaximal
13#82035C311yesmaximal, characteristic, direct product factor
14C3×D3×#41—21no—
15C2×C3×#237—21no—
16C32×#135C2211yescharacteristic
17C2×C32×D8C2211yescharacteristic, complemented
18C3×#950—21no—
19C2×C3×#214—21no—
20C3×#919C2211yescharacteristic, complemented
21C3×D3×Q16C2211yescharacteristic, complemented
22C3×#916—21no—
23C3×D3×SD16—21no—
24C3×#912—21no—
25C3×#912—21no—
26C3×#912C2212yes—
27C3×#912C2211yescharacteristic, complemented
28C3×#912C2212yescomplemented
29C3×D3×D8C2211yescharacteristic, complemented
30C2×C3×Dic12C2211yescharacteristic, complemented
31C3×#904C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33C32×SD32C2212yescomplemented
34C32×D16C2212yescomplemented
35C32×M32C2211yescharacteristic, complemented
36C3×#829C2212yescomplemented
37C3×#827C2212yescomplemented
38C3×#827C2212yescomplemented
39C3×#826C2212yescomplemented
40C3×#812C2211yescharacteristic, complemented
41C3×Dic24C2212yescomplemented
42C3×#800C2212yescomplemented
43C3×#798C2212yescomplemented
44C3×D3×C16C2212yescomplemented
45C2×C3×#135—31no—
46C2×C3×#135—31no—
47D3×#135C2×C311yescharacteristic, complemented
48C2×#912C2×C311yescharacteristic, complemented
49C3×#510—31no—
50C3×#510—32no—
51C3×#510—31no—
52C3×#509—21no—
53C3×#509—31no—
54C3×#509—32no—
55C3×#509D311yescharacteristic, complemented
56C3×#509C2×C311yescharacteristic, complemented
57C3×#508—32no—
58C3×#508—32no—
59C2×C3×M32—31no—
60#5195C2×C311yescharacteristic, complemented
61#5147C2×C311yescharacteristic, complemented
62#4916C2×C312yescomplemented
63#4915C2×C312yescomplemented
64#4912C2×C312yescomplemented
65#4911C2×C312yescomplemented
66#4909C2×C311yescharacteristic, complemented
67D3×M32C2×C311yescharacteristic, complemented
68C32×#41—21no—
69C2×C32×D4—21no—
70C2×C3×#67—41no—
71C22×C3×Dic3—41no—
72C3×#239—21no—
73C3×D3×Q8—21no—
74C3×#237—22no—
75C3×#237—22no—
76C3×#237—21no—
77C3×#237—41no—
78C3×#237—41no—
79C3×#237—41no—
80C3×D3×D4—21no—
81C3×D3×D4—41no—
82C3×#235—21no—
83C3×#235—41no—
84C2×C3×C4×D3—41no—
85C2×C3×C4×D3D411yescharacteristic
86C2×C3×Dic6—21no—
87C32×Q16C2311yescharacteristic
88C32×SD16—21no—
89C32×D8—21no—
90C32×D8C2311yescharacteristic
91C32×D8C2312yes—
92C2×C32×C8C2311yescharacteristic
93C3×#216—21no—
94C3×#215—21no—
95C3×#214—22no—
96C3×#214—22no—
97C3×#214—21no—
98C3×#213—21no—
99C2×C3×C3⋊C8D411yescharacteristic
100C3×Dic12—21no—
101C3×Dic12C2311yescharacteristic
102C3×Dic12C2312yes—
103C3×D24C2311yescharacteristic
104C3×#204—21no—
105C3×D3×C8D411yescharacteristic
106C3×D3×C8D411yescharacteristic
107C3×D3×C8C2311yescharacteristic
108C3×D3×C8C2311yescharacteristic
109C32×C16C2312yes—
110C3×C3⋊C16C2312yes—
111#3414—31noSylow
112C2×C3×#41—61no—
113C2×C3×#41—61no—
114D3×#41—21no—
115C2×#237—21no—
116C3×#135—21no—
117C3×#135—31no—
118C3×#135—32no—
119C3×#135—31no—
120C3×#135—32no—
121C3×#135—31no—
122C3×#135—61no—
123C3×#135—61no—
124C3×#135—61no—
125C3×#135—61no—
126C3×#135C2×D311yescharacteristic
127C3×#135C22×C311yescharacteristic
128C2×C3×Q16—31no—
129C2×C3×Q16—31no—
130C2×C3×SD16—61no—
131C2×C3×SD16—61no—
132C2×C3×D8—21no—
133C2×C3×D8—31no—
134C2×C3×D8C2×D311yescharacteristic, complemented
135C2×C3×D8C22×C311yescharacteristic, complemented
136C22×C3×C8—31no—
137#950—21no—
138C2×#214—21no—
139#919C22×C311yescharacteristic, complemented
140D3×Q16C22×C311yescharacteristic, complemented
141#916—21no—
142D3×SD16—21no—
143#912—21no—
144#912—21no—
145#912C22×C312yes—
146#912C22×C311yescharacteristic, complemented
147#912C22×C312yescomplemented
148D3×D8C22×C311yescharacteristic, complemented
149C2×Dic12C22×C311yescharacteristic, complemented
150#904C22×C311yescharacteristic
151C2×D3×C8C22×C311yescharacteristic
152C3×Q32—32no—
153C3×Q32—32no—
154C3×SD32—22no—
155C3×SD32—32no—
156C3×SD32—32no—
157C3×SD32—32no—
158C3×SD32C2×D312yescomplemented
159C3×SD32C22×C312yescomplemented
160C3×D16—22no—
161C3×D16—32no—
162C3×D16C2×D312yescomplemented
163C3×D16C22×C312yescomplemented
164C3×M32—21no—
165C3×M32—31no—
166C3×M32—32no—
167C3×M32C2×D311yescharacteristic, complemented
168C3×M32C22×C311yescharacteristic, complemented
169C2×C3×C16—32no—
170#829C22×C312yescomplemented
171#827C22×C312yescomplemented
172#827C22×C312yescomplemented
173#826C22×C312yescomplemented
174#812C22×C311yescharacteristic, complemented
175Dic24C22×C312yescomplemented
176#800C22×C312yescomplemented
177#798C22×C312yescomplemented
178D3×C16C22×C312yescomplemented
179C23×C32—41no—
180C22×C3×D3—41no—
181C22×C3×D3D811yescharacteristic
182C32×Q8—21no—
183C32×D4—21no—
184C32×D4—22no—
185C32×D4—41no—
186C32×D4—41no—
187C2×C32×C4—41no—
188C2×C32×C4C2×D411yescharacteristic
189C3×#67—41no—
190C3×#67—41no—
191C3×#67—42no—
192C3×#67—42no—
193C3×#67—41no—
194C2×C3×Dic3—41no—
195C2×C3×Dic3—41no—
196C2×C3×Dic3—42no—
197C2×C3×Dic3—42no—
198C2×C3×Dic3D811yescharacteristic
199C3×D12—21no—
200C3×D12—41no—
201C3×C4×D3—41no—
202C3×C4×D3—41no—
203C3×C4×D3—41no—
204C3×C4×D3D811yescharacteristic
205C3×C4×D3D811yescharacteristic
206C3×C4×D3C2×D411yescharacteristic
207C3×C4×D3C2×D411yescharacteristic
208C3×Dic6—21no—
209C3×Dic6—22no—
210C3×Dic6—41no—
211C3×Dic6—41no—
212C32×C8C2×D411yescharacteristic
213C32×C8C2411yescharacteristic
214C3×C3⋊C8C2×D411yescharacteristic
215C3×C3⋊C8C2×D411yescharacteristic
216C2×#135—31no—
217C2×#135—31no—
218#510—31no—
219#510—32no—
220#510—31no—
221#509—31no—
222#509—32no—
223#509C3×D311yescharacteristic, complemented
224#508—32no—
225#508—32no—
226C2×M32—31no—
227C3×#41—21no—
228C3×#41—21no—
229C3×#41—41no—
230C3×#41—62no—
231C3×#41—62no—
232C3×#41—61no—
233C3×#41—61no—
234C3×#41—61no—
235C3×#41—121no—
236C3×#41—121no—
237C3×#41—121no—
238C3×#41—121no—
239C2×C3×Q8—61no—
240C2×C3×Q8—61no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—41no—
244C2×C3×D4—61no—
245C2×C3×D4—121no—
246C2×C3×D4—121no—
247C22×C3×C4—31no—
248C22×C3×C4—121no—
249C22×C3×C4—121no—
250C2×#67—41no—
251C22×Dic3—41no—
252#239—21no—
253D3×Q8—21no—
254#237—22no—
255#237—22no—
256#237—21no—
257#237—41no—
258#237—41no—
259#237—41no—
260D3×D4—21no—
261D3×D4—41no—
262#235—21no—
263#235—41no—
264C2×C4×D3—41no—
265C2×C4×D3C3×D411yescharacteristic
266C2×Dic6—21no—
267C3×Q16—21no—
268C3×Q16—31no—
269C3×Q16—32no—
270C3×Q16—61no—
271C3×Q16—61no—
272C3×Q16C22×D311yescharacteristic
273C3×Q16C23×C311yescharacteristic
274C3×SD16—21no—
275C3×SD16—21no—
276C3×SD16—41no—
277C3×SD16—62no—
278C3×SD16—62no—
279C3×SD16—61no—
280C3×SD16—61no—
281C3×SD16—61no—
282C3×D8—21no—
283C3×D8—21no—
284C3×D8—21no—
285C3×D8—22no—
286C3×D8—31no—
287C3×D8—41no—
288C3×D8—61no—
289C3×D8C22×D312yes—
290C3×D8C22×D311yescharacteristic
291C3×D8C23×C312yes—
292C3×D8C23×C311yescharacteristic
293C2×C3×C8—21no—
294C2×C3×C8—31no—
295C2×C3×C8—31no—
296C2×C3×C8—31no—
297C2×C3×C8—31no—
298C2×C3×C8—31no—
299C2×C3×C8C22×D311yescharacteristic
300C2×C3×C8C23×C311yescharacteristic
301#216—21no—
302#215—21no—
303#214—22no—
304#214—22no—
305#214—21no—
306#213—21no—
307C2×C3⋊C8C3×D411yescharacteristic
308Dic12—21no—
309Dic12C23×C312yes—
310Dic12C23×C311yescharacteristic
311D24C23×C311yescharacteristic
312#204—21no—
313D3×C8C3×D411yescharacteristic
314D3×C8C3×D411yescharacteristic
315D3×C8C23×C311yescharacteristic
316D3×C8C23×C311yescharacteristic
317C3×C16—22no—
318C3×C16—32no—
319C3×C16C22×D312yes—
320C3×C16C23×C312yes—
321C3⋊C16C23×C312yes—
322C22×C32—42no—
323C22×C32—41no—
324C22×C32—82no—
325C22×C32C2×D811yescharacteristic
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C2×C3×D3—82no—
329C2×C3×D3C2×D811yescharacteristic
330C2×C3×D3C2×D811yescharacteristic
331C32×C4—41no—
332C32×C4C2×D811yescharacteristic
333C32×C4C22×D411yescharacteristic
334C3×Dic3—41no—
335C3×Dic3—42no—
336C3×Dic3C2×D811yescharacteristic
337C3×Dic3C2×D811yescharacteristic
338C2×#41—61no—
339C2×#41—61no—
340#135—31no—
341#135—32no—
342#135—32no—
343#135—31no—
344#135—31no—
345#135—61no—
346#135—61no—
347#135—61no—
348#135—61no—
349#135C2×C3×D311yescharacteristic
350C2×Q16—31no—
351C2×Q16—31no—
352C2×SD16—61no—
353C2×SD16—61no—
354C2×D8—31no—
355C2×D8C2×C3×D311yescharacteristic, complemented
356C22×C8—31no—
357Q32—32no—
358Q32—32no—
359SD32—32no—
360SD32—32no—
361SD32—32no—
362SD32C2×C3×D312yescomplemented
363D16—32no—
364D16C2×C3×D312yescomplemented
365M32—31no—
366M32—32no—
367M32C2×C3×D311yescharacteristic, complemented
368C2×C16—32no—
369C23×C3—31no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3—81no—
373C23×C3—121no—
374C22×D3—41no—
375C22×D3C3×D811yescharacteristic
376C3×Q8—21no—
377C3×Q8—21no—
378C3×Q8—41no—
379C3×Q8—61no—
380C3×Q8—62no—
381C3×Q8—121no—
382C3×Q8—121no—
383C3×D4—22no—
384C3×D4—21no—
385C3×D4—21no—
386C3×D4—22no—
387C3×D4—42no—
388C3×D4—41no—
389C3×D4—41no—
390C3×D4—41no—
391C3×D4—41no—
392C3×D4—41no—
393C3×D4—61no—
394C3×D4—81no—
395C3×D4—81no—
396C3×D4—121no—
397C3×D4—121no—
398C3×D4—122no—
399C3×D4—121no—
400C3×D4—122no—
401C3×D4—121no—
402C2×C3×C4—21no—
403C2×C3×C4—31no—
404C2×C3×C4—31no—
405C2×C3×C4—31no—
406C2×C3×C4—31no—
407C2×C3×C4—31no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—81no—
411C2×C3×C4—121no—
412C2×C3×C4—121no—
413C2×C3×C4—122no—
414C2×C3×C4—122no—
415C2×C3×C4—121no—
416C2×C3×C4—121no—
417C2×C3×C4—121no—
418C2×C3×C4D3×D411yescharacteristic
419C2×C3×C4C2×C3×D411yescharacteristic
420#67—41no—
421#67—41no—
422#67—42no—
423#67—42no—
424#67—41no—
425C2×Dic3—41no—
426C2×Dic3—41no—
427C2×Dic3—42no—
428C2×Dic3—42no—
429C2×Dic3C3×D811yescharacteristic
430D12—21no—
431D12—41no—
432C4×D3—41no—
433C4×D3—41no—
434C4×D3—41no—
435C4×D3C3×D811yescharacteristic
436C4×D3C3×D811yescharacteristic
437C4×D3C2×C3×D411yescharacteristic
438C4×D3C2×C3×D411yescharacteristic
439Dic6—21no—
440Dic6—22no—
441Dic6—41no—
442Dic6—41no—
443C3×C8—21no—
444C3×C8—21no—
445C3×C8—31no—
446C3×C8—31no—
447C3×C8D3×D411yescharacteristic
448C3×C8C2×C3×D411yescharacteristic
449C3×C8C23×D311yescharacteristic
450C3×C8C24×C311yescharacteristic
451C3⋊C8C2×C3×D411yescharacteristic
452C3⋊C8C2×C3×D411yescharacteristic
453C2×C32—21no—
454C2×C32—81no—
455C2×C32—82no—
456C2×C32C22×D811yescharacteristic
457C3×D3—21no—
458C3×D3—21no—
459C3×D3—81no—
460#41—21no—
461#41—62no—
462#41—62no—
463#41—61no—
464#41—61no—
465#41—61no—
466#41—121no—
467#41—121no—
468#41—121no—
469#41—121no—
470C2×Q8—61no—
471C2×Q8—61no—
472C2×D4—21no—
473C2×D4—61no—
474C2×D4—121no—
475C2×D4—121no—
476C22×C4—31no—
477C22×C4—121no—
478C22×C4—121no—
479Q16—31no—
480Q16—32no—
481Q16—61no—
482Q16—61no—
483Q16C22×C3×D311yescharacteristic
484SD16—21no—
485SD16—62no—
486SD16—62no—
487SD16—61no—
488SD16—61no—
489SD16—61no—
490D8—21no—
491D8—31no—
492D8—61no—
493D8C22×C3×D312yes—
494D8C22×C3×D311yescharacteristic
495C2×C8—31no—
496C2×C8—31no—
497C2×C8—31no—
498C2×C8—31no—
499C2×C8—31no—
500C2×C8C22×C3×D311yescharacteristic
501C16—32no—
502C16C22×C3×D312yes—
503C22×C3—21no—
504C22×C3—31no—
505C22×C3—31no—
506C22×C3—42no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3—42no—
510C22×C3—81no—
511C22×C3—82no—
512C22×C3—82no—
513C22×C3—82no—
514C22×C3—121no—
515C22×C3—121no—
516C22×C3—162no—
517C22×C3—242no—
518C22×C3D3×D811yescharacteristic
519C22×C3C2×C3×D811yescharacteristic
520C2×D3—41no—
521C2×D3—41no—
522C2×D3—82no—
523C2×D3C2×C3×D811yescharacteristic
524C2×D3C2×C3×D811yescharacteristic
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—31no—
528C3×C4—31no—
529C3×C4—41no—
530C3×C4—41no—
531C3×C4—81no—
532C3×C4—122no—
533C3×C4—121no—
534C3×C4D3×D811yescharacteristic
535C3×C4C2×C3×D811yescharacteristic
536C3×C4C2×D3×D411yescharacteristic
537C3×C4C22×C3×D411yescharacteristic
538Dic3—41no—
539Dic3—42no—
540Dic3C2×C3×D811yescharacteristic
541Dic3C2×C3×D811yescharacteristic
542C32#341411yescharacteristic, complemented, Sylow
543C23—31no—
544C23—41no—
545C23—121no—
546Q8—21no—
547Q8—62no—
548Q8—61no—
549Q8—121no—
550Q8—121no—
551D4—22no—
552D4—21no—
553D4—41no—
554D4—41no—
555D4—61no—
556D4—121no—
557D4—121no—
558D4—122no—
559D4—121no—
560D4—122no—
561D4—121no—
562C2×C4—31no—
563C2×C4—31no—
564C2×C4—31no—
565C2×C4—31no—
566C2×C4—31no—
567C2×C4—41no—
568C2×C4—121no—
569C2×C4—121no—
570C2×C4—122no—
571C2×C4—122no—
572C2×C4—121no—
573C2×C4—121no—
574C2×C4—121no—
575C2×C4C3×D3×D411yescharacteristic
576C8—31no—
577C8—31no—
578C8C3×D3×D411yescharacteristic
579C8C23×C3×D311yescharacteristic
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—41no—
584C2×C3—61no—
585C2×C3—61no—
586C2×C3—81no—
587C2×C3—82no—
588C2×C3—82no—
589C2×C3—81no—
590C2×C3—162no—
591C2×C3—161no—
592C2×C3—241no—
593C2×C3C2×D3×D811yescharacteristic
594C2×C3C22×C3×D811yescharacteristic
595D3—21no—
596D3—21no—
597D3—81no—
598C22—31no—
599C22—31no—
600C22—41no—
601C22—42no—
602C22—82no—
603C22—121no—
604C22—121no—
605C22—242no—
606C22C3×D3×D811yescharacteristic
607C4—31no—
608C4—31no—
609C4—41no—
610C4—122no—
611C4—121no—
612C4C3×D3×D811yescharacteristic
613C4C2×C3×D3×D411yescharacteristic
614C3—21no—
615C3#8203511yescharacteristic, direct product factor
616C3C3×#341411yescharacteristic, complemented
617C2—21no—
618C2—61no—
619C2—61no—
620C2—82no—
621C2—81no—
622C2—241no—
623C2C2×C3×D3×D811yescharacteristic
subgroupG/H
centerC2×C3C2×D3×D8
commutator, cosocleC3×C8C24×C3
FrattiniC8C23×C3×D3
FittingC32×#509C2
socleC2×C32C22×D8
hypercenterC3×#509D3
hypocenterC3C3×#3414
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#509

Complements

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

NH ≅ G/Ntype
1. C3×D3×#135C2semidirect
2. C2×C3×#912C2semidirect
3. C32×#509C2semidirect
4. C3×#5195C2semidirect
5. C3×#5147C2semidirect
6. C3×#4916C2semidirect
7. C3×#4915C2semidirect
8. C3×#4912C2semidirect
9. C3×#4911C2semidirect
10. C3×#4909C2semidirect
11. C3×D3×M32C2semidirect
13. #82035C3direct (N × H)
17. C2×C32×D8C22semidirect
20. C3×#919C22semidirect
21. C3×D3×Q16C22semidirect
27. C3×#912C22semidirect
28. C3×#912C22semidirect
29. C3×D3×D8C22semidirect
30. C2×C3×Dic12C22semidirect
33. C32×SD32C22semidirect
34. C32×D16C22semidirect
35. C32×M32C22semidirect
36. C3×#829C22semidirect
37. C3×#827C22semidirect
38. C3×#827C22semidirect
39. C3×#826C22semidirect
40. C3×#812C22semidirect
41. C3×Dic24C22semidirect
42. C3×#800C22semidirect
43. C3×#798C22semidirect
44. C3×D3×C16C22semidirect
47. D3×#135C2×C3semidirect
48. C2×#912C2×C3semidirect
55. C3×#509D3semidirect
56. C3×#509C2×C3semidirect
60. #5195C2×C3semidirect
61. #5147C2×C3semidirect
62. #4916C2×C3semidirect
63. #4915C2×C3semidirect
64. #4912C2×C3semidirect
65. #4911C2×C3semidirect
66. #4909C2×C3semidirect
67. D3×M32C2×C3semidirect
134. C2×C3×D8C2×D3semidirect
135. C2×C3×D8C22×C3semidirect
139. #919C22×C3semidirect
140. D3×Q16C22×C3semidirect
146. #912C22×C3semidirect
147. #912C22×C3semidirect
148. D3×D8C22×C3semidirect
149. C2×Dic12C22×C3semidirect
158. C3×SD32C2×D3semidirect
159. C3×SD32C22×C3semidirect
162. C3×D16C2×D3semidirect
163. C3×D16C22×C3semidirect
167. C3×M32C2×D3semidirect
168. C3×M32C22×C3semidirect
170. #829C22×C3semidirect
171. #827C22×C3semidirect
172. #827C22×C3semidirect
173. #826C22×C3semidirect
174. #812C22×C3semidirect
175. Dic24C22×C3semidirect
176. #800C22×C3semidirect
177. #798C22×C3semidirect
178. D3×C16C22×C3semidirect
223. #509C3×D3semidirect
355. C2×D8C2×C3×D3semidirect
362. SD32C2×C3×D3semidirect
364. D16C2×C3×D3semidirect
367. M32C2×C3×D3semidirect
542. C32#3414semidirect
615. C3#82035direct (N × H)
616. C3C3×#3414semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1352
C2×C3×#9122
C32×#5092
C3×#51952
C3×#51472
C3×#49162
C3×#49152
C3×#49122
C3×#49112
C3×#49092
C3×D3×M322
C3×#34143
#820353