Finite Group Databasebeta

← C3×#83395 #11865138

Subgroups — C3×#83395 #11865138

Order 1152.

1639 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic, complemented
2C32×#535C211yesmaximal, characteristic, complemented
3C2×C3×#932C212yesmaximal, complemented
4C3×#5237C211yesmaximal, characteristic, complemented
5C3×#5077C214yesmaximal, complemented
6C3×#5062C214yesmaximal, complemented
7C3×#5005C212yesmaximal, complemented
8C3×#3021—31nomaximal
9#83395C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C22×C32×D4C2211yescharacteristic, complemented
12C3×#1010—22no—
13C3×#1009—22no—
14C3×D3×#41—24no—
15C3×#1007C2212yescomplemented
16C3×#1004—22no—
17C3×#1004C2212yescomplemented
18C2×C3×#235—22no—
19C2×C3×#235C2212yes—
20C32×#127C2212yescomplemented
21C32×#124C2212yescomplemented
22C32×#121—22no—
23C32×#120—22no—
24C32×#117C2211yescharacteristic, complemented
25C2×C3×#214—22no—
26C3×#932—24no—
27C3×#932C2218yescomplemented
28C2×C3×#213—22no—
29C2×C3×#208C2212yescomplemented
30C3×#836C2212yescomplemented
31C3×#833C2212yescomplemented
32C3×#805C2218yescomplemented
33C3×#585—31no—
34#5964C2×C311yescharacteristic, complemented
35C2×C3×AGL(1,ℤ/8)—32no—
36C3×#535—21no—
37C3×#535D311yescharacteristic, complemented
38C3×#535C2×C311yescharacteristic, complemented
39C2×#932C2×C312yescomplemented
40C3×#454—34no—
41C3×#453—34no—
42C3×#421—32no—
43C3×#413—31no—
44#5237C2×C311yescharacteristic, complemented
45#5077C2×C314yescomplemented
46#5062C2×C314yescomplemented
47#5005C2×C312yescomplemented
48C24×C32—21no—
49C32×#41—22no—
50C32×#41—22no—
51C2×C32×Q8C2311yescharacteristic
52C2×C32×D4—24no—
53C2×C32×D4—22no—
54C2×C32×D4—22no—
55C2×C32×D4—21no—
56C2×C32×D4D412yes—
57C2×C32×D4C2312yes—
58C2×C32×D4C2311yescharacteristic
59C22×C32×C4D412yes—
60C22×C32×C4C2311yescharacteristic
61C2×C3×#67—24no—
62C2×C3×#67—22no—
63C3×#239—24no—
64C3×D3×Q8—24no—
65C3×#237—28no—
66C3×#237—24no—
67C3×D3×D4—28no—
68C3×D3×D4—24no—
69C3×#235—24no—
70C3×#235—24no—
71C3×#235—22no—
72C3×#235—24no—
73C3×#235—22no—
74C3×#235D414yescomplemented
75C3×#235C2314yes—
76C2×C3×D12—22no—
77C2×C3×D12D412yescomplemented
78C2×C3×C4×D3—24no—
79C2×C3×C4×D3—22no—
80C2×C3×Dic6—22no—
81C2×C3×Dic6D412yescomplemented
82C32×C4⋊C4—21no—
83C32×C22⋊C4—21no—
84C32×C22⋊C4—24no—
85C32×C42C2312yes—
86C3×#214—28no—
87C3×#213—28no—
88C3×#208—22no—
89C3×#208C2314yes—
90C2×C3×C3⋊C8—22no—
91#3021—31noSylow
92C3×2−1+4—32no—
93C3×2−1+4—62no—
94C3×H(5,𝔽2)—32no—
95C3×H(5,𝔽2)—62no—
96C3×H(5,𝔽2)—62no—
97C2×C3×#41—21no—
98C2×C3×#41—32no—
99C2×C3×#41—64no—
100C2×C3×#41—62no—
101C2×C3×#41C2×D311yescharacteristic
102C2×C3×#41C22×C311yescharacteristic
103C22×C3×D4—21no—
104C22×C3×D4C2×D311yescharacteristic, complemented
105C22×C3×D4C22×C311yescharacteristic, complemented
106#1010—22no—
107#1009—22no—
108D3×#41—24no—
109#1007C22×C312yescomplemented
110#1004—22no—
111#1004C22×C312yescomplemented
112C2×#235—22no—
113C2×#235C22×C312yes—
114C3×AGL(1,ℤ/8)—38no—
115C3×AGL(1,ℤ/8)—64no—
116C2×C3×SD16—62no—
117C2×C3×D8—62no—
118C2×C3×M16—32no—
119C3×#127—22no—
120C3×#127C2×D312yescomplemented
121C3×#127C22×C312yescomplemented
122C3×#124—22no—
123C3×#124C2×D312yescomplemented
124C3×#124C22×C312yescomplemented
125C3×#121—24no—
126C3×#121—22no—
127C3×#121—22no—
128C3×#120—24no—
129C3×#120—22no—
130C3×#120—22no—
131C3×#117—21no—
132C3×#117C2×D311yescharacteristic, complemented
133C3×#117C22×C311yescharacteristic, complemented
134C2×#214—22no—
135#932—24no—
136#932C22×C318yescomplemented
137C2×#213—22no—
138C2×#208C22×C312yescomplemented
139C3×#104—38no—
140C3×#101—32no—
141C3×#100—32no—
142#836C22×C312yescomplemented
143#833C22×C312yescomplemented
144#805C22×C318yescomplemented
145C23×C32—22no—
146C23×C32—42no—
147C23×C32—82no—
148C23×C32C2×D412yes—
149C23×C32C2×D411yescharacteristic
150C22×C3×D3—24no—
151C22×C3×D3—22no—
152C32×Q8—22no—
153C32×D4—24no—
154C32×D4—22no—
155C32×D4—24no—
156C32×D4—41no—
157C32×D4—41no—
158C32×D4—84no—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4—22no—
162C2×C32×C4C2×D412yes—
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C3×#67—28no—
168C3×#67—24no—
169C3×#67—24no—
170C2×C3×Dic3—24no—
171C2×C3×Dic3—22no—
172C3×D12—24no—
173C3×D12—22no—
174C3×D12C2×D414yes—
175C3×C4×D3—28no—
176C3×C4×D3—24no—
177C3×C4×D3—24no—
178C3×Dic6—24no—
179C3×Dic6—22no—
180C3×Dic6C2×D414yes—
181C3×C3⋊C8—24no—
182#585—31no—
183C2×AGL(1,ℤ/8)—32no—
184#535C3×D311yescharacteristic, complemented
185#454—34no—
186#453—34no—
187#421—32no—
188#413—31no—
189C24×C3—22no—
190C24×C3—21no—
191C24×C3—21no—
192C3×#41—22no—
193C3×#41—22no—
194C3×#41—22no—
195C3×#41—22no—
196C3×#41—34no—
197C3×#41—34no—
198C3×#41—42no—
199C3×#41—42no—
200C3×#41—64no—
201C3×#41—64no—
202C3×#41—64no—
203C3×#41—68no—
204C3×#41—64no—
205C3×#41—62no—
206C3×#41—62no—
207C3×#41—64no—
208C2×C3×Q8—21no—
209C2×C3×Q8—32no—
210C2×C3×Q8—62no—
211C2×C3×Q8—64no—
212C2×C3×Q8C22×D311yescharacteristic
213C2×C3×Q8C23×C311yescharacteristic
214C2×C3×D4—22no—
215C2×C3×D4—28no—
216C2×C3×D4—24no—
217C2×C3×D4—24no—
218C2×C3×D4—22no—
219C2×C3×D4—22no—
220C2×C3×D4—21no—
221C2×C3×D4—22no—
222C2×C3×D4—22no—
223C2×C3×D4—21no—
224C2×C3×D4—22no—
225C2×C3×D4—22no—
226C2×C3×D4—21no—
227C2×C3×D4—32no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—62no—
231C2×C3×D4—64no—
232C2×C3×D4—68no—
233C2×C3×D4—62no—
234C2×C3×D4—64no—
235C2×C3×D4#6712yes—
236C2×C3×D4C3×D412yes—
237C2×C3×D4C22×D312yes—
238C2×C3×D4C22×D311yescharacteristic
239C2×C3×D4C23×C312yes—
240C2×C3×D4C23×C311yescharacteristic
241C22×C3×C4—22no—
242C22×C3×C4—21no—
243C22×C3×C4—64no—
244C22×C3×C4—62no—
245C22×C3×C4#6712yes—
246C22×C3×C4C3×D412yes—
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C23×C311yescharacteristic
249C2×#67—24no—
250C2×#67—22no—
251#239—24no—
252D3×Q8—24no—
253#237—28no—
254#237—24no—
255D3×D4—28no—
256D3×D4—24no—
257#235—24no—
258#235—24no—
259#235—22no—
260#235—24no—
261#235—22no—
262#235C3×D414yescomplemented
263#235C23×C314yes—
264C2×D12—22no—
265C2×D12C3×D412yescomplemented
266C2×C4×D3—24no—
267C2×C4×D3—22no—
268C2×Dic6—22no—
269C2×Dic6C3×D412yescomplemented
270C3×SD16—68no—
271C3×D8—68no—
272C3×M16—34no—
273C3×M16—62no—
274C2×C3×C8—62no—
275C3×C4⋊C4—22no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C22⋊C4—22no—
279C3×C22⋊C4—28no—
280C3×C22⋊C4—21no—
281C3×C22⋊C4—21no—
282C3×C22⋊C4—24no—
283C3×C22⋊C4—24no—
284C3×C42—22no—
285C3×C42C22×D312yes—
286C3×C42C23×C312yes—
287#214—28no—
288#213—28no—
289#208—22no—
290#208C23×C314yes—
291C2×C3⋊C8—22no—
292C22×C32—22no—
293C22×C32—41no—
294C22×C32—42no—
295C22×C32—44no—
296C22×C32—42no—
297C22×C32—84no—
298C22×C32#12012yes—
299C22×C32C22×D411yescharacteristic
300C2×C3×D3—24no—
301C2×C3×D3—82no—
302C2×C3×D3—84no—
303C32×C4—22no—
304C32×C4—42no—
305C32×C4#12011yescharacteristic
306C32×C4#12011yescharacteristic
307C32×C4C22×D412yes—
308C3×Dic3—24no—
3092−1+4—32no—
3102−1+4—62no—
311H(5,𝔽2)—32no—
312H(5,𝔽2)—62no—
313H(5,𝔽2)—62no—
314C2×#41—32no—
315C2×#41—64no—
316C2×#41—62no—
317C2×#41C2×C3×D311yescharacteristic
318C22×D4C2×C3×D311yescharacteristic, complemented
319AGL(1,ℤ/8)—38no—
320AGL(1,ℤ/8)—64no—
321C2×SD16—62no—
322C2×D8—62no—
323C2×M16—32no—
324#127C2×C3×D312yescomplemented
325#124C2×C3×D312yescomplemented
326#121—22no—
327#120—22no—
328#117C2×C3×D311yescharacteristic, complemented
329#104—38no—
330#101—32no—
331#100—32no—
332C23×C3—24no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—21no—
336C23×C3—22no—
337C23×C3—44no—
338C23×C3—42no—
339C23×C3—42no—
340C23×C3—64no—
341C23×C3—62no—
342C23×C3—82no—
343C23×C3—82no—
344C23×C3—84no—
345C23×C3C2×#6712yes—
346C23×C3C2×#6711yescharacteristic
347C23×C3C2×C3×D412yes—
348C23×C3C2×C3×D411yescharacteristic
349C22×D3—24no—
350C22×D3—22no—
351C3×Q8—22no—
352C3×Q8—22no—
353C3×Q8—34no—
354C3×Q8—42no—
355C3×Q8—64no—
356C3×Q8—62no—
357C3×D4—24no—
358C3×D4—24no—
359C3×D4—22no—
360C3×D4—24no—
361C3×D4—22no—
362C3×D4—24no—
363C3×D4—34no—
364C3×D4—44no—
365C3×D4—42no—
366C3×D4—44no—
367C3×D4—42no—
368C3×D4—42no—
369C3×D4—41no—
370C3×D4—41no—
371C3×D4—41no—
372C3×D4—41no—
373C3×D4—64no—
374C3×D4—68no—
375C3×D4—64no—
376C3×D4—64no—
377C3×D4—62no—
378C3×D4—84no—
379C3×D4—84no—
380C3×D4—88no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—24no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—22no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—68no—
396C2×C3×C4—64no—
397C2×C3×C4—62no—
398C2×C3×C4—64no—
399C2×C3×C4—64no—
400C2×C3×C4D3×D412yes—
401C2×C3×C4D3×D412yes—
402C2×C3×C4C2×#6712yes—
403C2×C3×C4C2×#6711yescharacteristic
404C2×C3×C4C2×C3×D412yes—
405C2×C3×C4C2×C3×D412yes—
406C2×C3×C4C2×C3×D412yes—
407C2×C3×C4C2×C3×D411yescharacteristic
408C2×C3×C4C23×D311yescharacteristic
409C2×C3×C4C24×C311yescharacteristic
410#67—28no—
411#67—24no—
412#67—24no—
413C2×Dic3—24no—
414C2×Dic3—22no—
415D12—24no—
416D12—22no—
417D12C2×C3×D414yes—
418C4×D3—28no—
419C4×D3—24no—
420C4×D3—24no—
421Dic6—24no—
422Dic6—22no—
423Dic6C2×C3×D414yes—
424C3×C8—64no—
425C3⋊C8—24no—
426C2×C32—21no—
427C2×C32—22no—
428C2×C32—42no—
429C2×C32—82no—
430C2×C32C2×#12011yescharacteristic
431C3×D3—44no—
432C24—21no—
433#41—22no—
434#41—22no—
435#41—34no—
436#41—34no—
437#41—64no—
438#41—64no—
439#41—64no—
440#41—68no—
441#41—64no—
442#41—62no—
443#41—62no—
444#41—64no—
445C2×Q8—32no—
446C2×Q8—62no—
447C2×Q8—64no—
448C2×Q8C22×C3×D311yescharacteristic
449C2×D4—24no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—32no—
454C2×D4—62no—
455C2×D4—64no—
456C2×D4—68no—
457C2×D4—62no—
458C2×D4—64no—
459C2×D4C3×#6712yes—
460C2×D4C22×C3×D312yes—
461C2×D4C22×C3×D311yescharacteristic
462C22×C4—64no—
463C22×C4—62no—
464C22×C4C3×#6712yes—
465C22×C4C22×C3×D311yescharacteristic
466SD16—68no—
467D8—68no—
468M16—34no—
469M16—62no—
470C2×C8—62no—
471C4⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—24no—
474C42C22×C3×D312yes—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—21no—
479C22×C3—42no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—42no—
485C22×C3—44no—
486C22×C3—44no—
487C22×C3—48no—
488C22×C3—44no—
489C22×C3—44no—
490C22×C3—42no—
491C22×C3—42no—
492C22×C3—64no—
493C22×C3—84no—
494C22×C3—84no—
495C22×C3—88no—
496C22×C3—242no—
497C22×C3—244no—
498C22×C3#93712yes—
499C22×C3C3×#12012yes—
500C22×C3C22×#6711yescharacteristic
501C22×C3C22×C3×D411yescharacteristic
502C2×D3—24no—
503C2×D3—82no—
504C2×D3—84no—
505C3×C4—22no—
506C3×C4—22no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—22no—
510C3×C4—42no—
511C3×C4—44no—
512C3×C4—42no—
513C3×C4—42no—
514C3×C4—64no—
515C3×C4#93711yescharacteristic
516C3×C4#93711yescharacteristic
517C3×C4C3×#12011yescharacteristic
518C3×C4C3×#12011yescharacteristic
519C3×C4C2×D3×D412yes—
520C3×C4C22×C3×D412yes—
521Dic3—24no—
522C32#302111yescharacteristic, complemented, Sylow
523C23—22no—
524C23—42no—
525C23—64no—
526C23—62no—
527C23—82no—
528C23C2×C3×#6712yes—
529C23C2×C3×#6711yescharacteristic
530Q8—22no—
531Q8—34no—
532Q8—64no—
533Q8—62no—
534D4—24no—
535D4—22no—
536D4—24no—
537D4—34no—
538D4—41no—
539D4—41no—
540D4—64no—
541D4—68no—
542D4—64no—
543D4—64no—
544D4—62no—
545D4—84no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—68no—
550C2×C4—64no—
551C2×C4—62no—
552C2×C4—64no—
553C2×C4—64no—
554C2×C4C3×D3×D412yes—
555C2×C4C3×D3×D412yes—
556C2×C4C2×C3×#6712yes—
557C2×C4C2×C3×#6711yescharacteristic
558C2×C4C23×C3×D311yescharacteristic
559C8—64no—
560C2×C3—22no—
561C2×C3—21no—
562C2×C3—22no—
563C2×C3—21no—
564C2×C3—22no—
565C2×C3—21no—
566C2×C3—42no—
567C2×C3—42no—
568C2×C3—42no—
569C2×C3—82no—
570C2×C3—84no—
571C2×C3—82no—
572C2×C3—82no—
573C2×C3—124no—
574C2×C3C2×#93711yescharacteristic
575C2×C3C2×C3×#12011yescharacteristic
576D3—44no—
577C22—22no—
578C22—41no—
579C22—42no—
580C22—44no—
581C22—42no—
582C22—64no—
583C22—84no—
584C22—242no—
585C22—244no—
586C22C3×#93712yes—
587C22C22×C3×#6711yescharacteristic
588C4—22no—
589C4—42no—
590C4—64no—
591C4C3×#93711yescharacteristic
592C4C3×#93711yescharacteristic
593C4C2×C3×D3×D412yes—
594C3—21no—
595C3#8339511yescharacteristic, direct product factor
596C3C3×#302111yescharacteristic, complemented
597C2—21no—
598C2—22no—
599C2—42no—
600C2—82no—
601C2—124no—
602C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC2×C3C2×#937
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#535C2
socleC2×C32C2×#120
hypercenterC3×#535D3
hypocenterC3C3×#3021
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#535

Complements

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

NH ≅ G/Ntype
1. C3×#5964C2semidirect
2. C32×#535C2semidirect
3. C2×C3×#932C2semidirect
4. C3×#5237C2semidirect
5. C3×#5077C2semidirect
6. C3×#5062C2semidirect
7. C3×#5005C2semidirect
9. #83395C3direct (N × H)
11. C22×C32×D4C22semidirect
15. C3×#1007C22semidirect
17. C3×#1004C22semidirect
20. C32×#127C22semidirect
21. C32×#124C22semidirect
24. C32×#117C22semidirect
27. C3×#932C22semidirect
29. C2×C3×#208C22semidirect
30. C3×#836C22semidirect
31. C3×#833C22semidirect
32. C3×#805C22semidirect
34. #5964C2×C3semidirect
37. C3×#535D3semidirect
38. C3×#535C2×C3semidirect
39. C2×#932C2×C3semidirect
44. #5237C2×C3semidirect
45. #5077C2×C3semidirect
46. #5062C2×C3semidirect
47. #5005C2×C3semidirect
74. C3×#235D4semidirect
77. C2×C3×D12D4semidirect
81. C2×C3×Dic6D4semidirect
104. C22×C3×D4C2×D3semidirect
105. C22×C3×D4C22×C3semidirect
109. #1007C22×C3semidirect
111. #1004C22×C3semidirect
120. C3×#127C2×D3semidirect
121. C3×#127C22×C3semidirect
123. C3×#124C2×D3semidirect
124. C3×#124C22×C3semidirect
132. C3×#117C2×D3semidirect
133. C3×#117C22×C3semidirect
136. #932C22×C3semidirect
138. C2×#208C22×C3semidirect
142. #836C22×C3semidirect
143. #833C22×C3semidirect
144. #805C22×C3semidirect
184. #535C3×D3semidirect
262. #235C3×D4semidirect
265. C2×D12C3×D4semidirect
269. C2×Dic6C3×D4semidirect
318. C22×D4C2×C3×D3semidirect
324. #127C2×C3×D3semidirect
325. #124C2×C3×D3semidirect
328. #117C2×C3×D3semidirect
522. C32#3021semidirect
595. C3#83395direct (N × H)
596. C3C3×#3021semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
C32×#5352
C2×C3×#9322
C3×#52372
C3×#50772
C3×#50622
C3×#50052
C3×#30213
#833953