Finite Group Databasebeta

← C3×#83811 #11861138

Subgroups — C3×#83811 #11861138

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#568C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic
3C3×#5745C211yesmaximal, characteristic, complemented
4C2×C3×#837C211yesmaximal, characteristic, complemented
5C3×#5145C214yesmaximal, complemented
6C3×#5144C214yesmaximal, complemented
7C2×C3×#825C211yesmaximal, characteristic, complemented
8C3×#5124C211yesmaximal, characteristic, complemented
9C3×Dic3×M16C211yesmaximal, characteristic, complemented
10C3×#2956—31nomaximal
11#83811C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C32×#131—22no—
15C32×#131C2214yescomplemented
16C2×C32×M16—22no—
17C2×C32×M16C2211yescharacteristic
18C2×C32×M16C2211yescharacteristic
19C3×#951C412yescomplemented
20C3×#950C2214yes—
21C3×#949C412yescomplemented
22C3×#942C412yescomplemented
23C3×#932C412yescomplemented
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C3×#907—22no—
28C3×D3×M16—22no—
29C3×#901C2214yescomplemented
30C3×#837C2212yescomplemented
31C3×#837C2212yescomplemented
32C3×#825C2212yescomplemented
33C3×#825C2212yescomplemented
34C3×#822C2214yescomplemented
35C3×#815C2212yescomplemented
36C3×C8×Dic3C2212yescomplemented
37C3×#575—31no—
38C3×#568—21no—
39C3×#568—31no—
40C3×#568D311yescharacteristic, complemented
41C3×#568C2×C311yescharacteristic, complemented
42#5822C2×C311yescharacteristic
43#5745C2×C311yescharacteristic, complemented
44C3×#444—34no—
45C3×#443—34no—
46C3×#430—31no—
47C2×C3×#104—31no—
48C2×C3×#104—31no—
49C3×C4×M16—31no—
50C2×#837C2×C311yescharacteristic, complemented
51#5145C2×C314yescomplemented
52#5144C2×C314yescomplemented
53C2×#825C2×C311yescharacteristic, complemented
54#5124C2×C311yescharacteristic, complemented
55Dic3×M16C2×C311yescharacteristic, complemented
56C32×#41—21no—
57C32×#41—21no—
58C32×#41C2×C412yes—
59C32×#41C2312yes—
60C2×C32×Q8C2×C411yescharacteristic
61C2×C32×D4—21no—
62C2×C32×D4C2×C411yescharacteristic
63C22×C32×C4—21no—
64C22×C32×C4C2311yescharacteristic
65C2×C3×#67—21no—
66C22×C3×Dic3—21no—
67C3×#235—21no—
68C3×#235—21no—
69C3×#235C2×C412yes—
70C3×#235C2312yes—
71C2×C3×D12C2×C411yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×Dic6C2×C411yescharacteristic
74C32×M16—21no—
75C32×M16—24no—
76C32×M16D412yes—
77C32×M16D412yes—
78C32×M16C2312yes—
79C2×C32×C8—21no—
80C2×C32×C8—24no—
81C2×C32×C8C2312yes—
82C3×#216C2×C414yescomplemented
83C3×#215C2×C414yescomplemented
84C3×#214C2×C414yescomplemented
85C3×#213C2×C414yescomplemented
86C3×C4×Dic3—21no—
87C3×C4×Dic3C2311yescharacteristic
88C3×C4×Dic3C2311yescharacteristic
89C3×#208—21no—
90C3×#208C2×C412yes—
91C3×#208C2×C412yes—
92C3×#208C2312yes—
93C2×C3×C3⋊C8—21no—
94C2×C3×C3⋊C8C2312yes—
95C3×ΓL(1,𝔽25)—24no—
96C3×D3×C8—24no—
97#2956—31noSylow
98C2×C3×#41—21no—
99C2×C3×#41—31no—
100C2×C3×#41C2×D311yescharacteristic
101C2×C3×#41C22×C311yescharacteristic
102C2×#235C22×C311yescharacteristic
103C3×#137—32no—
104C3×#137—32no—
105C3×AGL(1,ℤ/8)—32no—
106C3×AGL(1,ℤ/8)—32no—
107C3×#135—34no—
108C3×#131—24no—
109C3×#131—22no—
110C3×#131—22no—
111C3×#131—24no—
112C3×#131—34no—
113C3×#131—62no—
114C3×#131C2×D314yescomplemented
115C3×#131C22×C314yescomplemented
116C2×C3×M16—24no—
117C2×C3×M16—22no—
118C2×C3×M16—22no—
119C2×C3×M16—21no—
120C2×C3×M16—21no—
121C2×C3×M16—31no—
122C2×C3×M16—31no—
123C2×C3×M16—62no—
124C2×C3×M16C2×D311yescharacteristic
125C2×C3×M16C2×D311yescharacteristic
126C2×C3×M16C22×C311yescharacteristic
127C2×C3×M16C22×C311yescharacteristic
128C2×C3×C42—31no—
129#951C3×C412yescomplemented
130#950C22×C314yes—
131#949C3×C412yescomplemented
132#942C3×C412yescomplemented
133#932C3×C412yescomplemented
134C2×C4×Dic3C22×C311yescharacteristic
135C2×#208C22×C311yescharacteristic
136C2×#208C22×C311yescharacteristic
137#907—22no—
138D3×M16—22no—
139#901C22×C314yescomplemented
140C3×#108—34no—
141C3×#104—32no—
142C3×#104—32no—
143C3×#104—32no—
144C3×#104—32no—
145C3×#97—32no—
146C3×C4×C8—32no—
147#837C22×C312yescomplemented
148#837C22×C312yescomplemented
149#825C22×C312yescomplemented
150#825C22×C312yescomplemented
151#822C22×C314yescomplemented
152#815C22×C312yescomplemented
153C8×Dic3C22×C312yescomplemented
154C23×C32—21no—
155C23×C32#4111yescharacteristic
156C22×C3×D3—21no—
157C32×Q8—21no—
158C32×Q8C22×C412yes—
159C32×D4—22no—
160C32×D4—22no—
161C32×D4—21no—
162C32×D4C22×C412yes—
163C2×C32×C4—21no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4C22×C411yescharacteristic
167C2×C32×C4C22×C411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4#4111yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C3×#67—22no—
173C3×#67—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—42no—
178C3×D12—21no—
179C3×D12C22×C412yes—
180C3×C4×D3—22no—
181C3×C4×D3—22no—
182C3×Dic6—21no—
183C3×Dic6C22×C412yes—
184C32×C8—22no—
185C32×C8C2×D414yes—
186C3×C3⋊C8—22no—
187C3×C3⋊C8C22×C414yes—
188#575—31no—
189#568—31no—
190#568C3×D311yescharacteristic, complemented
191#444—34no—
192#443—34no—
193#430—31no—
194C2×#104—31no—
195C2×#104—31no—
196C4×M16—31no—
197C3×#41—22no—
198C3×#41—22no—
199C3×#41—21no—
200C3×#41—21no—
201C3×#41—21no—
202C3×#41—21no—
203C3×#41—22no—
204C3×#41—22no—
205C3×#41—32no—
206C3×#41—32no—
207C3×#41—61no—
208C3×#41—61no—
209C3×#41C4×D312yes—
210C3×#41C2×C3×C412yes—
211C3×#41C22×D312yes—
212C3×#41C23×C312yes—
213C2×C3×Q8—21no—
214C2×C3×Q8—31no—
215C2×C3×Q8C4×D311yescharacteristic
216C2×C3×Q8C2×C3×C411yescharacteristic
217C2×C3×D4—22no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—31no—
222C2×C3×D4—61no—
223C2×C3×D4C4×D311yescharacteristic
224C2×C3×D4C2×C3×C411yescharacteristic
225C22×C3×C4—22no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—61no—
230C22×C3×C4—61no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C23×C311yescharacteristic
233C2×#67—21no—
234C22×Dic3—21no—
235#235—21no—
236#235—21no—
237#235C2×C3×C412yes—
238#235C23×C312yes—
239C2×D12C2×C3×C411yescharacteristic
240C2×C4×D3—21no—
241C2×Dic6C2×C3×C411yescharacteristic
242C3×Q16—34no—
243C3×SD16—34no—
244C3×SD16—34no—
245C3×D8—34no—
246C3×M16—22no—
247C3×M16—28no—
248C3×M16—21no—
249C3×M16—21no—
250C3×M16—24no—
251C3×M16—24no—
252C3×M16—22no—
253C3×M16—22no—
254C3×M16—22no—
255C3×M16—32no—
256C3×M16—32no—
257C3×M16—32no—
258C3×M16—61no—
259C3×M16—64no—
260C3×M16#6712yes—
261C3×M16#6712yes—
262C3×M16C3×D412yes—
263C3×M16C3×D412yes—
264C3×M16C22×D312yes—
265C3×M16C23×C312yes—
266C2×C3×C8—22no—
267C2×C3×C8—28no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—24no—
271C2×C3×C8—24no—
272C2×C3×C8—22no—
273C2×C3×C8—32no—
274C2×C3×C8—61no—
275C2×C3×C8—64no—
276C2×C3×C8C22×D312yes—
277C2×C3×C8C23×C312yes—
278C3×C42—31no—
279C3×C42—31no—
280C3×C42—61no—
281#216C2×C3×C414yescomplemented
282#215C2×C3×C414yescomplemented
283#214C2×C3×C414yescomplemented
284#213C2×C3×C414yescomplemented
285C4×Dic3—21no—
286C4×Dic3C23×C311yescharacteristic
287C4×Dic3C23×C311yescharacteristic
288#208—21no—
289#208C2×C3×C412yes—
290#208C2×C3×C412yes—
291#208C23×C312yes—
292C2×C3⋊C8—21no—
293C2×C3⋊C8C23×C312yes—
294ΓL(1,𝔽25)—24no—
295D3×C8—24no—
296C22×C32—22no—
297C22×C32—41no—
298C22×C32—81no—
299C22×C32C4×D411yescharacteristic
300C22×C32C4×D411yescharacteristic
301C22×C32C2×#4111yescharacteristic
302C2×C3×D3—22no—
303C2×C3×D3—81no—
304C32×C4—22no—
305C32×C4C4×D411yescharacteristic
306C32×C4C4×D411yescharacteristic
307C32×C4C23×C411yescharacteristic
308C32×C4C22×D411yescharacteristic
309C3×Dic3—22no—
310C3×Dic3—22no—
311C3×Dic3—41no—
312C2×#41—31no—
313C2×#41C2×C3×D311yescharacteristic
314#137—32no—
315#137—32no—
316AGL(1,ℤ/8)—32no—
317AGL(1,ℤ/8)—32no—
318#135—34no—
319#131—22no—
320#131—34no—
321#131—62no—
322#131C2×C3×D314yescomplemented
323C2×M16—22no—
324C2×M16—31no—
325C2×M16—31no—
326C2×M16—62no—
327C2×M16C2×C3×D311yescharacteristic
328C2×M16C2×C3×D311yescharacteristic
329C2×C42—31no—
330#108—34no—
331#104—32no—
332#104—32no—
333#104—32no—
334#104—32no—
335#97—32no—
336C4×C8—32no—
337C23×C3—22no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—21no—
341C23×C3—61no—
342C23×C3#23511yescharacteristic
343C23×C3C3×#4111yescharacteristic
344C22×D3—21no—
345C3×Q8—22no—
346C3×Q8—21no—
347C3×Q8—21no—
348C3×Q8—22no—
349C3×Q8—32no—
350C3×Q8—61no—
351C3×Q8C2×C4×D312yes—
352C3×Q8C22×C3×C412yes—
353C3×D4—24no—
354C3×D4—24no—
355C3×D4—22no—
356C3×D4—22no—
357C3×D4—22no—
358C3×D4—22no—
359C3×D4—22no—
360C3×D4—21no—
361C3×D4—21no—
362C3×D4—22no—
363C3×D4—32no—
364C3×D4—62no—
365C3×D4—62no—
366C3×D4—61no—
367C3×D4C2×C4×D312yes—
368C3×D4C22×C3×C412yes—
369C2×C3×C4—24no—
370C2×C3×C4—22no—
371C2×C3×C4—24no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—61no—
385C2×C3×C4—61no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—61no—
389C2×C3×C4—122no—
390C2×C3×C4C2×C4×D311yescharacteristic
391C2×C3×C4C2×C4×D311yescharacteristic
392C2×C3×C4#23511yescharacteristic
393C2×C3×C4C2×#6711yescharacteristic
394C2×C3×C4C2×#6711yescharacteristic
395C2×C3×C4C22×C3×C411yescharacteristic
396C2×C3×C4C22×C3×C411yescharacteristic
397C2×C3×C4C2×C3×D411yescharacteristic
398C2×C3×C4C2×C3×D411yescharacteristic
399C2×C3×C4C3×#4111yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401C2×C3×C4C24×C311yescharacteristic
402#67—22no—
403#67—22no—
404C2×Dic3—21no—
405C2×Dic3—21no—
406C2×Dic3—21no—
407C2×Dic3—42no—
408D12—21no—
409D12C22×C3×C412yes—
410C4×D3—22no—
411C4×D3—22no—
412Dic6—21no—
413Dic6C22×C3×C412yes—
414C3×C8—24no—
415C3×C8—22no—
416C3×C8—22no—
417C3×C8—24no—
418C3×C8—34no—
419C3×C8—62no—
420C3×C8C2×#6714yes—
421C3×C8C2×C3×D414yes—
422C3⋊C8—22no—
423C3⋊C8C22×C3×C414yes—
424C2×C32—21no—
425C2×C32—21no—
426C2×C32—21no—
427C2×C32—42no—
428C2×C32C2×C4×D411yescharacteristic
429C3×D3—42no—
430#41—21no—
431#41—21no—
432#41—32no—
433#41—32no—
434#41—61no—
435#41—61no—
436#41C3×C4×D312yes—
437#41C22×C3×D312yes—
438C2×Q8—31no—
439C2×Q8C3×C4×D311yescharacteristic
440C2×D4—21no—
441C2×D4—31no—
442C2×D4—61no—
443C2×D4C3×C4×D311yescharacteristic
444C22×C4—21no—
445C22×C4—61no—
446C22×C4—61no—
447C22×C4C22×C3×D311yescharacteristic
448Q16—34no—
449SD16—34no—
450SD16—34no—
451D8—34no—
452M16—21no—
453M16—24no—
454M16—32no—
455M16—32no—
456M16—32no—
457M16—61no—
458M16—64no—
459M16C3×#6712yes—
460M16C3×#6712yes—
461M16C22×C3×D312yes—
462C2×C8—21no—
463C2×C8—24no—
464C2×C8—32no—
465C2×C8—61no—
466C2×C8—64no—
467C2×C8C22×C3×D312yes—
468C42—31no—
469C42—31no—
470C42—61no—
471C22×C3—24no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3—62no—
480C22×C3—81no—
481C22×C3—81no—
482C22×C3—81no—
483C22×C3—82no—
484C22×C3—241no—
485C22×C3C4×#6711yescharacteristic
486C22×C3C4×#6711yescharacteristic
487C22×C3C3×C4×D411yescharacteristic
488C22×C3C3×C4×D411yescharacteristic
489C22×C3C2×#23511yescharacteristic
490C22×C3C2×C3×#4111yescharacteristic
491C2×D3—22no—
492C2×D3—81no—
493C3×C4—24no—
494C3×C4—22no—
495C3×C4—22no—
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—62no—
501C3×C4—62no—
502C3×C4—121no—
503C3×C4C4×#6711yescharacteristic
504C3×C4C4×#6711yescharacteristic
505C3×C4C3×C4×D411yescharacteristic
506C3×C4C3×C4×D411yescharacteristic
507C3×C4C22×C4×D311yescharacteristic
508C3×C4C22×#6711yescharacteristic
509C3×C4C23×C3×C411yescharacteristic
510C3×C4C22×C3×D411yescharacteristic
511Dic3—22no—
512Dic3—22no—
513Dic3—41no—
514C32#295611yescharacteristic, complemented, Sylow
515C23—21no—
516C23—61no—
517C23C3×#23511yescharacteristic
518Q8—21no—
519Q8—32no—
520Q8—61no—
521Q8C2×C3×C4×D312yes—
522D4—22no—
523D4—22no—
524D4—21no—
525D4—32no—
526D4—62no—
527D4—62no—
528D4—61no—
529D4C2×C3×C4×D312yes—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—61no—
534C2×C4—61no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—61no—
538C2×C4—122no—
539C2×C4C2×C3×C4×D311yescharacteristic
540C2×C4C2×C3×C4×D311yescharacteristic
541C2×C4C3×#23511yescharacteristic
542C2×C4C2×C3×#6711yescharacteristic
543C2×C4C2×C3×#6711yescharacteristic
544C2×C4C23×C3×D311yescharacteristic
545C8—22no—
546C8—34no—
547C8—62no—
548C8C2×C3×#6714yes—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—41no—
557C2×C3—41no—
558C2×C3—41no—
559C2×C3—44no—
560C2×C3—42no—
561C2×C3—42no—
562C2×C3—122no—
563C2×C3C2×C4×#6711yescharacteristic
564C2×C3C2×C3×C4×D411yescharacteristic
565D3—42no—
566C22—22no—
567C22—41no—
568C22—62no—
569C22—81no—
570C22—241no—
571C22C3×C4×#6711yescharacteristic
572C22C3×C4×#6711yescharacteristic
573C22C2×C3×#23511yescharacteristic
574C4—22no—
575C4—62no—
576C4—62no—
577C4—121no—
578C4C3×C4×#6711yescharacteristic
579C4C3×C4×#6711yescharacteristic
580C4C22×C3×C4×D311yescharacteristic
581C4C22×C3×#6711yescharacteristic
582C3—21no—
583C3#8381111yescharacteristic, direct product factor
584C3C3×#295611yescharacteristic, complemented
585C2—21no—
586C2—21no—
587C2—21no—
588C2—42no—
589C2—122no—
590C2C2×C3×C4×#6711yescharacteristic
subgroupG/H
centerC3×C4C22×#67
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#568C2
socleC2×C32C2×C4×D4
prime radicalC3×#5822C2
cosocleC2×C3×C4C24×C3
hypercenterC3×#568D3
hypocenterC3C3×#2956
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C2×C3×M16 ◁ C3×#568

Complements

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

NH ≅ G/Ntype
1. C32×#568C2semidirect
3. C3×#5745C2semidirect
4. C2×C3×#837C2semidirect
5. C3×#5145C2semidirect
6. C3×#5144C2semidirect
7. C2×C3×#825C2semidirect
8. C3×#5124C2semidirect
9. C3×Dic3×M16C2semidirect
11. #83811C3direct (N × H)
15. C32×#131C22semidirect
19. C3×#951C4semidirect
21. C3×#949C4semidirect
22. C3×#942C4semidirect
23. C3×#932C4semidirect
29. C3×#901C22semidirect
30. C3×#837C22semidirect
31. C3×#837C22semidirect
32. C3×#825C22semidirect
33. C3×#825C22semidirect
34. C3×#822C22semidirect
35. C3×#815C22semidirect
36. C3×C8×Dic3C22semidirect
40. C3×#568D3semidirect
41. C3×#568C2×C3semidirect
43. #5745C2×C3semidirect
50. C2×#837C2×C3semidirect
51. #5145C2×C3semidirect
52. #5144C2×C3semidirect
53. C2×#825C2×C3semidirect
54. #5124C2×C3semidirect
55. Dic3×M16C2×C3semidirect
82. C3×#216C2×C4semidirect
83. C3×#215C2×C4semidirect
84. C3×#214C2×C4semidirect
85. C3×#213C2×C4semidirect
114. C3×#131C2×D3semidirect
115. C3×#131C22×C3semidirect
129. #951C3×C4semidirect
131. #949C3×C4semidirect
132. #942C3×C4semidirect
133. #932C3×C4semidirect
139. #901C22×C3semidirect
147. #837C22×C3semidirect
148. #837C22×C3semidirect
149. #825C22×C3semidirect
150. #825C22×C3semidirect
151. #822C22×C3semidirect
152. #815C22×C3semidirect
153. C8×Dic3C22×C3semidirect
190. #568C3×D3semidirect
281. #216C2×C3×C4semidirect
282. #215C2×C3×C4semidirect
283. #214C2×C3×C4semidirect
284. #213C2×C3×C4semidirect
322. #131C2×C3×D3semidirect
514. C32#2956semidirect
583. C3#83811direct (N × H)
584. C3C3×#2956semidirect

Maximal subgroups

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

subgroupindex
C32×#5682
C3×#58222
C3×#57452
C2×C3×#8372
C3×#51452
C3×#51442
C2×C3×#8252
C3×#51242
C3×Dic3×M162
C3×#29563
#838113